LMFDB - Embedded newform 18.10.c.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,10,Mod(7,18)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.27064505095$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 656x^{6} - 4002x^{5} + 415806x^{4} - 1312656x^{3} + 13535681x^{2} + 29074530x + 211120900 $ x^8 + 656x^6 - 4002x^5 + 415806x^4 - 1312656x^3 + 13535681x^2 + 29074530x + 211120900
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.4
Root			$-13.3287 - 23.0860i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.10.c.a.7.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(140.277 - 2.30842i) q^{3} +(-128.000 + 221.703i) q^{4} +(-559.872 + 969.728i) q^{5} +(1154.20 + 1925.27i) q^{6} +(2150.43 + 3724.66i) q^{7} -4096.00 q^{8} +(19672.3 - 647.638i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(140.277 - 2.30842i) q^{3} +(-128.000 + 221.703i) q^{4} +(-559.872 + 969.728i) q^{5} +(1154.20 + 1925.27i) q^{6} +(2150.43 + 3724.66i) q^{7} -4096.00 q^{8} +(19672.3 - 647.638i) q^{9} -17915.9 q^{10} +(7223.04 + 12510.7i) q^{11} +(-17443.7 + 31395.3i) q^{12} +(-60415.7 + 104643. i) q^{13} +(-34406.9 + 59594.5i) q^{14} +(-76298.8 + 137323. i) q^{15} +(-32768.0 - 56755.8i) q^{16} -9991.26 q^{17} +(166353. + 267407. i) q^{18} +99454.6 q^{19} +(-143327. - 248250. i) q^{20} +(310254. + 517520. i) q^{21} +(-115569. + 200171. i) q^{22} +(1.06326e6 - 1.84162e6i) q^{23} +(-574575. + 9455.30i) q^{24} +(349648. + 605608. i) q^{25} -1.93330e6 q^{26} +(2.75808e6 - 136261. i) q^{27} -1.10102e6 q^{28} +(-2.12490e6 - 3.68043e6i) q^{29} +(-2.51319e6 + 41357.5i) q^{30} +(4.86411e6 - 8.42488e6i) q^{31} +(524288. - 908093. i) q^{32} +(1.04211e6 + 1.73829e6i) q^{33} +(-79930.1 - 138443. i) q^{34} -4.81587e6 q^{35} +(-2.37448e6 + 4.44431e6i) q^{36} +1.35717e7 q^{37} +(795637. + 1.37808e6i) q^{38} +(-8.23338e6 + 1.48185e7i) q^{39} +(2.29324e6 - 3.97200e6i) q^{40} +(-1.05064e7 + 1.81977e7i) q^{41} +(-4.68893e6 + 8.43917e6i) q^{42} +(1.46663e7 + 2.54028e7i) q^{43} -3.69820e6 q^{44} +(-1.03860e7 + 1.94394e7i) q^{45} +3.40244e7 q^{46} +(-3.30115e7 - 5.71775e7i) q^{47} +(-4.72762e6 - 7.88590e6i) q^{48} +(1.09281e7 - 1.89280e7i) q^{49} +(-5.59437e6 + 9.68973e6i) q^{50} +(-1.40154e6 + 23064.0i) q^{51} +(-1.54664e7 - 2.67886e7i) q^{52} -1.79115e7 q^{53} +(2.39528e7 + 3.71271e7i) q^{54} -1.61759e7 q^{55} +(-8.80817e6 - 1.52562e7i) q^{56} +(1.39512e7 - 229583. i) q^{57} +(3.39984e7 - 5.88869e7i) q^{58} +(8.09962e6 - 1.40290e7i) q^{59} +(-2.06786e7 - 3.44930e7i) q^{60} +(-7.78845e6 - 1.34900e7i) q^{61} +1.55651e8 q^{62} +(4.47163e7 + 7.18800e7i) q^{63} +1.67772e7 q^{64} +(-6.76502e7 - 1.17174e8i) q^{65} +(-1.57496e7 + 2.83462e7i) q^{66} +(-9.55019e7 + 1.65414e8i) q^{67} +(1.27888e6 - 2.21509e6i) q^{68} +(1.44900e8 - 2.60792e8i) q^{69} +(-3.85270e7 - 6.67307e7i) q^{70} -5.22010e7 q^{71} +(-8.05779e7 + 2.65272e6i) q^{72} -2.93443e8 q^{73} +(1.08573e8 + 1.88054e8i) q^{74} +(5.04456e7 + 8.41458e7i) q^{75} +(-1.27302e7 + 2.20493e7i) q^{76} +(-3.10653e7 + 5.38067e7i) q^{77} +(-2.71198e8 + 4.46288e6i) q^{78} +(2.65586e8 + 4.60009e8i) q^{79} +7.33836e7 q^{80} +(3.86582e8 - 2.54811e7i) q^{81} -3.36206e8 q^{82} +(2.44448e8 + 4.23397e8i) q^{83} +(-1.54448e8 + 2.54162e6i) q^{84} +(5.59383e6 - 9.68880e6i) q^{85} +(-2.34661e8 + 4.06444e8i) q^{86} +(-3.06571e8 - 5.11375e8i) q^{87} +(-2.95856e7 - 5.12437e7i) q^{88} +6.14804e8 q^{89} +(-3.52448e8 + 1.16030e7i) q^{90} -5.19679e8 q^{91} +(2.72195e8 + 4.71455e8i) q^{92} +(6.62875e8 - 1.19305e9i) q^{93} +(5.28183e8 - 9.14841e8i) q^{94} +(-5.56819e7 + 9.64439e7i) q^{95} +(7.14493e7 - 1.28595e8i) q^{96} +(1.13074e8 + 1.95850e8i) q^{97} +3.49699e8 q^{98} +(1.50196e8 + 2.41436e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{2} - 81 q^{3} - 1024 q^{4} + 171 q^{5} + 1440 q^{6} + 7135 q^{7} - 32768 q^{8} + 8937 q^{9}+O(q^{10}) $ 8 * q + 64 * q^2 - 81 * q^3 - 1024 * q^4 + 171 * q^5 + 1440 * q^6 + 7135 * q^7 - 32768 * q^8 + 8937 * q^9	\( 8 q + 64 q^{2} - 81 q^{3} - 1024 q^{4} + 171 q^{5} + 1440 q^{6} + 7135 q^{7} - 32768 q^{8} + 8937 q^{9} + 5472 q^{10} - 26130 q^{11} + 43776 q^{12} - 4163 q^{13} - 114160 q^{14} - 665739 q^{15} - 262144 q^{16} + 1098510 q^{17} + 310608 q^{18} - 436382 q^{19} + 43776 q^{20} - 1515717 q^{21} + 418080 q^{22} - 289383 q^{23} + 331776 q^{24} + 2947937 q^{25} - 133216 q^{26} + 6980904 q^{27} - 3653120 q^{28} - 601707 q^{29} - 10990080 q^{30} + 5671315 q^{31} + 4194304 q^{32} - 551556 q^{33} + 8788080 q^{34} + 29787930 q^{35} + 2681856 q^{36} - 38737148 q^{37} - 3491056 q^{38} - 44596503 q^{39} - 700416 q^{40} - 18418410 q^{41} + 5424336 q^{42} + 35096140 q^{43} + 13378560 q^{44} + 69046263 q^{45} - 9260256 q^{46} - 79830825 q^{47} - 5898240 q^{48} - 40540299 q^{49} - 47166992 q^{50} - 107332533 q^{51} - 1065728 q^{52} + 330697236 q^{53} + 60357312 q^{54} + 56528442 q^{55} - 29224960 q^{56} - 118521549 q^{57} + 9627312 q^{58} - 90704166 q^{59} - 5412096 q^{60} - 122811677 q^{61} + 181482080 q^{62} + 26641197 q^{63} + 134217728 q^{64} - 116600103 q^{65} - 32628528 q^{66} + 221601736 q^{67} - 140609280 q^{68} + 162496665 q^{69} + 238303440 q^{70} + 276408240 q^{71} - 36605952 q^{72} - 988917014 q^{73} - 309897184 q^{74} + 203871807 q^{75} + 55856896 q^{76} - 548139525 q^{77} - 355557600 q^{78} + 592840885 q^{79} - 22413312 q^{80} + 1009312893 q^{81} - 589389120 q^{82} - 478410747 q^{83} + 474812928 q^{84} + 1468792818 q^{85} - 561538240 q^{86} - 2118569607 q^{87} + 107028480 q^{88} + 875519952 q^{89} + 200286432 q^{90} - 3695513062 q^{91} - 74082048 q^{92} + 2631169593 q^{93} + 1277293200 q^{94} + 813906756 q^{95} - 179306496 q^{96} + 2679512242 q^{97} - 1297289568 q^{98} - 46472697 q^{99}+O(q^{100}) \) 8 * q + 64 * q^2 - 81 * q^3 - 1024 * q^4 + 171 * q^5 + 1440 * q^6 + 7135 * q^7 - 32768 * q^8 + 8937 * q^9 + 5472 * q^10 - 26130 * q^11 + 43776 * q^12 - 4163 * q^13 - 114160 * q^14 - 665739 * q^15 - 262144 * q^16 + 1098510 * q^17 + 310608 * q^18 - 436382 * q^19 + 43776 * q^20 - 1515717 * q^21 + 418080 * q^22 - 289383 * q^23 + 331776 * q^24 + 2947937 * q^25 - 133216 * q^26 + 6980904 * q^27 - 3653120 * q^28 - 601707 * q^29 - 10990080 * q^30 + 5671315 * q^31 + 4194304 * q^32 - 551556 * q^33 + 8788080 * q^34 + 29787930 * q^35 + 2681856 * q^36 - 38737148 * q^37 - 3491056 * q^38 - 44596503 * q^39 - 700416 * q^40 - 18418410 * q^41 + 5424336 * q^42 + 35096140 * q^43 + 13378560 * q^44 + 69046263 * q^45 - 9260256 * q^46 - 79830825 * q^47 - 5898240 * q^48 - 40540299 * q^49 - 47166992 * q^50 - 107332533 * q^51 - 1065728 * q^52 + 330697236 * q^53 + 60357312 * q^54 + 56528442 * q^55 - 29224960 * q^56 - 118521549 * q^57 + 9627312 * q^58 - 90704166 * q^59 - 5412096 * q^60 - 122811677 * q^61 + 181482080 * q^62 + 26641197 * q^63 + 134217728 * q^64 - 116600103 * q^65 - 32628528 * q^66 + 221601736 * q^67 - 140609280 * q^68 + 162496665 * q^69 + 238303440 * q^70 + 276408240 * q^71 - 36605952 * q^72 - 988917014 * q^73 - 309897184 * q^74 + 203871807 * q^75 + 55856896 * q^76 - 548139525 * q^77 - 355557600 * q^78 + 592840885 * q^79 - 22413312 * q^80 + 1009312893 * q^81 - 589389120 * q^82 - 478410747 * q^83 + 474812928 * q^84 + 1468792818 * q^85 - 561538240 * q^86 - 2118569607 * q^87 + 107028480 * q^88 + 875519952 * q^89 + 200286432 * q^90 - 3695513062 * q^91 - 74082048 * q^92 + 2631169593 * q^93 + 1277293200 * q^94 + 813906756 * q^95 - 179306496 * q^96 + 2679512242 * q^97 - 1297289568 * q^98 - 46472697 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$3$	140.277	−	2.30842i	0.999865	−	0.0164539i
$3$	140.277	−	2.30842i	0.999865	−	0.0164539i
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−559.872	+	969.728i	−0.400612	+	0.693881i	−0.993800	−	0.111184i	$-0.964536\pi$
$5$	−559.872	+	969.728i	−0.400612	+	0.693881i	0.593188	+	0.805064i	$0.297869\pi$
$6$	1154.20	+	1925.27i	0.363581	+	0.606472i
$7$	2150.43	+	3724.66i	0.338520	+	0.586334i	0.984155	−	0.177313i	$-0.0567403\pi$
$7$	2150.43	+	3724.66i	0.338520	+	0.586334i	−0.645634	+	0.763647i	$0.723407\pi$
$8$	−4096.00			−0.353553
$9$	19672.3	−	647.638i	0.999459	−	0.0329034i
$10$	−17915.9			−0.566551
$11$	7223.04	+	12510.7i	0.148749	+	0.257640i	0.930765	−	0.365617i	$-0.119142\pi$
$11$	7223.04	+	12510.7i	0.148749	+	0.257640i	−0.782017	+	0.623258i	$0.785809\pi$
$12$	−17443.7	+	31395.3i	−0.242841	+	0.437068i
$13$	−60415.7	+	104643.i	−0.586684	+	1.01617i	0.407979	+	0.912991i	$0.366234\pi$
$13$	−60415.7	+	104643.i	−0.586684	+	1.01617i	−0.994663	+	0.103176i	$0.967100\pi$
$14$	−34406.9	+	59594.5i	−0.239370	+	0.414601i
$15$	−76298.8	+	137323.i	−0.389141	+	0.700378i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−9991.26			−0.0290135			−0.0145067	−	0.999895i	$-0.504618\pi$
$17$	−9991.26			−0.0290135			−0.0145067	+	0.999895i	$0.504618\pi$
$18$	166353.	+	267407.i	0.373511	+	0.600408i
$19$	99454.6			0.175079			0.0875395	−	0.996161i	$-0.472100\pi$
$19$	99454.6			0.175079			0.0875395	+	0.996161i	$0.472100\pi$
$20$	−143327.	−	248250.i	−0.200306	−	0.346940i
$21$	310254.	+	517520.i	0.348122	+	0.580685i
$22$	−115569.	+	200171.i	−0.105181	+	0.182179i
$23$	1.06326e6	−	1.84162e6i	0.792254	−	1.37222i	−0.132314	−	0.991208i	$-0.542241\pi$
$23$	1.06326e6	−	1.84162e6i	0.792254	−	1.37222i	0.924568	−	0.381017i	$-0.124426\pi$
$24$	−574575.	+	9455.30i	−0.353506	+	0.00581734i
$25$	349648.	+	605608.i	0.179020	+	0.310071i
$26$	−1.93330e6			−0.829697
$27$	2.75808e6	−	136261.i	0.998782	−	0.0493440i
$28$	−1.10102e6			−0.338520
$29$	−2.12490e6	−	3.68043e6i	−0.557888	−	0.966291i	−0.997673	−	0.0681874i	$-0.978278\pi$
$29$	−2.12490e6	−	3.68043e6i	−0.557888	−	0.966291i	0.439784	−	0.898103i	$-0.355055\pi$
$30$	−2.51319e6	+	41357.5i	−0.566474	+	0.00932199i
$31$	4.86411e6	−	8.42488e6i	0.945966	−	1.63846i	0.192162	−	0.981363i	$-0.438450\pi$
$31$	4.86411e6	−	8.42488e6i	0.945966	−	1.63846i	0.753805	−	0.657099i	$-0.228216\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	1.04211e6	+	1.73829e6i	0.152968	+	0.255158i
$34$	−79930.1	−	138443.i	−0.0102578	−	0.0177671i
$35$	−4.81587e6			−0.542461
$36$	−2.37448e6	+	4.44431e6i	−0.235617	+	0.441004i
$37$	1.35717e7			1.19049			0.595244	−	0.803545i	$-0.297055\pi$
$37$	1.35717e7			1.19049			0.595244	+	0.803545i	$0.297055\pi$
$38$	795637.	+	1.37808e6i	0.0618997	+	0.107214i
$39$	−8.23338e6	+	1.48185e7i	−0.569885	+	1.02568i
$40$	2.29324e6	−	3.97200e6i	0.141638	−	0.245324i
$41$	−1.05064e7	+	1.81977e7i	−0.580669	+	1.00575i	0.414731	+	0.909944i	$0.363876\pi$
$41$	−1.05064e7	+	1.81977e7i	−0.580669	+	1.00575i	−0.995400	+	0.0958040i	$0.969458\pi$
$42$	−4.68893e6	+	8.43917e6i	−0.232516	+	0.418483i
$43$	1.46663e7	+	2.54028e7i	0.654202	+	1.13311i	0.982093	+	0.188396i	$0.0603289\pi$
$43$	1.46663e7	+	2.54028e7i	0.654202	+	1.13311i	−0.327891	+	0.944716i	$0.606338\pi$
$44$	−3.69820e6			−0.148749
$45$	−1.03860e7	+	1.94394e7i	−0.377564	+	0.706686i
$46$	3.40244e7			1.12042
$47$	−3.30115e7	−	5.71775e7i	−0.986789	−	1.70917i	−0.633698	−	0.773580i	$-0.718464\pi$
$47$	−3.30115e7	−	5.71775e7i	−0.986789	−	1.70917i	−0.353091	−	0.935589i	$-0.614869\pi$
$48$	−4.72762e6	−	7.88590e6i	−0.128545	−	0.214420i
$49$	1.09281e7	−	1.89280e7i	0.270808	−	0.469054i
$50$	−5.59437e6	+	9.68973e6i	−0.126586	+	0.219254i
$51$	−1.40154e6	+	23064.0i	−0.0290096	+	0.000477386i
$52$	−1.54664e7	−	2.67886e7i	−0.293342	−	0.508084i
$53$	−1.79115e7			−0.311811			−0.155905	−	0.987772i	$-0.549829\pi$
$53$	−1.79115e7			−0.311811			−0.155905	+	0.987772i	$0.549829\pi$
$54$	2.39528e7	+	3.71271e7i	0.383340	+	0.594181i
$55$	−1.61759e7			−0.238362
$56$	−8.80817e6	−	1.52562e7i	−0.119685	−	0.207300i
$57$	1.39512e7	−	229583.i	0.175055	−	0.00288074i
$58$	3.39984e7	−	5.88869e7i	0.394487	−	0.683271i
$59$	8.09962e6	−	1.40290e7i	0.0870223	−	0.150727i	−0.819229	−	0.573467i	$-0.805598\pi$
$59$	8.09962e6	−	1.40290e7i	0.0870223	−	0.150727i	0.906251	+	0.422740i	$0.138932\pi$
$60$	−2.06786e7	−	3.44930e7i	−0.205987	−	0.343598i
$61$	−7.78845e6	−	1.34900e7i	−0.0720222	−	0.124746i	0.827765	−	0.561075i	$-0.189612\pi$
$61$	−7.78845e6	−	1.34900e7i	−0.0720222	−	0.124746i	−0.899787	+	0.436328i	$0.856279\pi$
$62$	1.55651e8			1.33780
$63$	4.47163e7	+	7.18800e7i	0.357629	+	0.574878i
$64$	1.67772e7			0.125000
$65$	−6.76502e7	−	1.17174e8i	−0.470066	−	0.814178i
$66$	−1.57496e7	+	2.83462e7i	−0.102169	+	0.183885i
$67$	−9.55019e7	+	1.65414e8i	−0.578996	+	1.00285i	0.416599	+	0.909090i	$0.363222\pi$
$67$	−9.55019e7	+	1.65414e8i	−0.578996	+	1.00285i	−0.995595	+	0.0937597i	$0.970111\pi$
$68$	1.27888e6	−	2.21509e6i	0.00725337	−	0.0125632i
$69$	1.44900e8	−	2.60792e8i	0.769569	−	1.38507i
$70$	−3.85270e7	−	6.67307e7i	−0.191789	−	0.332188i
$71$	−5.22010e7			−0.243790			−0.121895	−	0.992543i	$-0.538897\pi$
$71$	−5.22010e7			−0.243790			−0.121895	+	0.992543i	$0.538897\pi$
$72$	−8.05779e7	+	2.65272e6i	−0.353362	+	0.0116331i
$73$	−2.93443e8			−1.20940			−0.604701	−	0.796453i	$-0.706707\pi$
$73$	−2.93443e8			−1.20940			−0.604701	+	0.796453i	$0.706707\pi$
$74$	1.08573e8	+	1.88054e8i	0.420901	+	0.729022i
$75$	5.04456e7	+	8.41458e7i	0.184097	+	0.307084i
$76$	−1.27302e7	+	2.20493e7i	−0.0437697	+	0.0758114i
$77$	−3.10653e7	+	5.38067e7i	−0.100709	+	0.174433i
$78$	−2.71198e8	+	4.46288e6i	−0.829585	+	0.0136518i
$79$	2.65586e8	+	4.60009e8i	0.767157	+	1.32875i	0.939099	+	0.343647i	$0.111662\pi$
$79$	2.65586e8	+	4.60009e8i	0.767157	+	1.32875i	−0.171942	+	0.985107i	$0.555004\pi$
$80$	7.33836e7			0.200306
$81$	3.86582e8	−	2.54811e7i	0.997835	−	0.0657712i
$82$	−3.36206e8			−0.821190
$83$	2.44448e8	+	4.23397e8i	0.565374	+	0.979256i	0.997015	+	0.0772104i	$0.0246013\pi$
$83$	2.44448e8	+	4.23397e8i	0.565374	+	0.979256i	−0.431641	+	0.902045i	$0.642065\pi$
$84$	−1.54448e8	+	2.54162e6i	−0.338474	+	0.00556999i
$85$	5.59383e6	−	9.68880e6i	0.0116232	−	0.0201319i
$86$	−2.34661e8	+	4.06444e8i	−0.462591	+	0.801231i
$87$	−3.06571e8	−	5.11375e8i	−0.573712	−	0.956981i
$88$	−2.95856e7	−	5.12437e7i	−0.0525906	−	0.0910895i
$89$	6.14804e8			1.03868			0.519340	−	0.854568i	$-0.326178\pi$
$89$	6.14804e8			1.03868			0.519340	+	0.854568i	$0.326178\pi$
$90$	−3.52448e8	+	1.16030e7i	−0.566244	+	0.0186415i
$91$	−5.19679e8			−0.794418
$92$	2.72195e8	+	4.71455e8i	0.396127	+	0.686112i
$93$	6.62875e8	−	1.19305e9i	0.918879	−	1.65380i
$94$	5.28183e8	−	9.14841e8i	0.697765	−	1.20857i
$95$	−5.56819e7	+	9.64439e7i	−0.0701387	+	0.121484i
$96$	7.14493e7	−	1.28595e8i	0.0858574	−	0.154527i
$97$	1.13074e8	+	1.95850e8i	0.129685	+	0.224622i	0.923555	−	0.383467i	$-0.125270\pi$
$97$	1.13074e8	+	1.95850e8i	0.129685	+	0.224622i	−0.793869	+	0.608088i	$0.791937\pi$
$98$	3.49699e8			0.382981
$99$	1.50196e8	+	2.41436e8i	0.157145	+	0.252606i
$100$	−1.79020e8			−0.179020
$101$	−6.02716e8	−	1.04394e9i	−0.576324	−	0.998222i	−0.995896	−	0.0905006i	$-0.971153\pi$
$101$	−6.02716e8	−	1.04394e9i	−0.576324	−	0.998222i	0.419572	−	0.907722i	$-0.362180\pi$
$102$	−1.15319e7	−	1.92359e7i	−0.0105488	−	0.0175959i
$103$	−8.13660e7	+	1.40930e8i	−0.0712320	+	0.123378i	−0.899442	−	0.437041i	$-0.856026\pi$
$103$	−8.13660e7	+	1.40930e8i	−0.0712320	+	0.123378i	0.828209	+	0.560419i	$0.189360\pi$
$104$	2.47463e8	−	4.28618e8i	0.207424	−	0.359269i
$105$	−6.75556e8	+	1.11171e7i	−0.542388	+	0.00892561i
$106$	−1.43292e8	−	2.48189e8i	−0.110242	−	0.190944i
$107$	−1.69071e9			−1.24693			−0.623466	−	0.781851i	$-0.714276\pi$
$107$	−1.69071e9			−1.24693			−0.623466	+	0.781851i	$0.714276\pi$
$108$	−3.22825e8	+	6.28916e8i	−0.228329	+	0.444821i
$109$	−5.48663e8			−0.372294			−0.186147	−	0.982522i	$-0.559600\pi$
$109$	−5.48663e8			−0.372294			−0.186147	+	0.982522i	$0.559600\pi$
$110$	−1.29407e8	−	2.24140e8i	−0.0842737	−	0.145966i
$111$	1.90379e9	−	3.13291e7i	1.19033	−	0.0195882i
$112$	1.40931e8	−	2.44099e8i	0.0846300	−	0.146584i
$113$	7.05033e8	−	1.22115e9i	0.406777	−	0.704559i	−0.587749	−	0.809043i	$-0.699986\pi$
$113$	7.05033e8	−	1.22115e9i	0.406777	−	0.704559i	0.994527	+	0.104484i	$0.0333192\pi$
$114$	1.14791e8	+	1.91477e8i	0.0636554	+	0.106180i
$115$	1.19058e9	+	2.06215e9i	0.634773	+	1.09946i
$116$	1.08795e9			0.557888
$117$	−1.12075e9	+	2.09770e9i	−0.552931	+	1.03492i
$118$	2.59188e8			0.123068
$119$	−2.14855e7	−	3.72140e7i	−0.00982165	−	0.0170116i
$120$	3.12520e8	−	5.62475e8i	0.137582	−	0.247621i
$121$	1.07463e9	−	1.86131e9i	0.455748	−	0.789378i
$122$	1.24615e8	−	2.15840e8i	0.0509274	−	0.0882089i
$123$	−1.43181e9	+	2.57697e9i	−0.564042	+	1.01517i
$124$	1.24521e9	+	2.15677e9i	0.472983	+	0.819231i
$125$	−2.97004e9			−1.08809
$126$	−6.38269e8	+	1.19465e9i	−0.225598	+	0.422252i
$127$	−2.39408e9			−0.816625			−0.408312	−	0.912842i	$-0.633883\pi$
$127$	−2.39408e9			−0.816625			−0.408312	+	0.912842i	$0.633883\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	2.11598e9	+	3.52957e9i	0.672758	+	1.12219i
$130$	1.08240e9	−	1.87478e9i	0.332387	−	0.575711i
$131$	−3.50814e8	+	6.07628e8i	−0.104077	+	0.180267i	−0.913361	−	0.407151i	$-0.866522\pi$
$131$	−3.50814e8	+	6.07628e8i	−0.104077	+	0.180267i	0.809283	+	0.587418i	$0.199856\pi$
$132$	−5.18772e8	+	8.53700e6i	−0.148728	+	0.00244750i
$133$	2.13870e8	+	3.70434e8i	0.0592677	+	0.102655i
$134$	−3.05606e9			−0.818824
$135$	−1.41204e9	+	2.75088e9i	−0.365885	+	0.712803i
$136$	4.09242e7			0.0102578
$137$	−1.82945e8	−	3.16870e8i	−0.0443688	−	0.0768490i	0.842988	−	0.537932i	$-0.180794\pi$
$137$	−1.82945e8	−	3.16870e8i	−0.0443688	−	0.0768490i	−0.887357	+	0.461083i	$0.847461\pi$
$138$	4.77284e9	−	7.85426e7i	1.12027	−	0.0184353i
$139$	2.98664e9	−	5.17301e9i	0.678604	−	1.17538i	−0.296798	−	0.954940i	$-0.595919\pi$
$139$	2.98664e9	−	5.17301e9i	0.678604	−	1.17538i	0.975401	−	0.220436i	$-0.0707480\pi$
$140$	6.16431e8	−	1.06769e9i	0.135615	−	0.234893i
$141$	−4.76274e9	−	7.94450e9i	−1.01478	−	1.69270i
$142$	−4.17608e8	−	7.23318e8i	−0.0861929	−	0.149290i
$143$	−1.74554e9			−0.349074
$144$	−6.81381e8	−	1.09530e9i	−0.132056	−	0.212276i
$145$	4.75869e9			0.893987
$146$	−2.34754e9	−	4.06606e9i	−0.427588	−	0.740605i
$147$	1.48927e9	−	2.68039e9i	0.263054	−	0.473446i
$148$	−1.73717e9	+	3.00887e9i	−0.297622	+	0.515496i
$149$	3.62070e9	−	6.27124e9i	0.601803	−	1.04235i	−0.390744	−	0.920499i	$-0.627782\pi$
$149$	3.62070e9	−	6.27124e9i	0.601803	−	1.04235i	0.992548	−	0.121855i	$-0.0388843\pi$
$150$	−7.62394e8	+	1.37216e9i	−0.122961	+	0.221307i
$151$	2.27015e9	+	3.93201e9i	0.355351	+	0.615487i	0.987178	−	0.159623i	$-0.0510279\pi$
$151$	2.27015e9	+	3.93201e9i	0.355351	+	0.615487i	−0.631827	+	0.775110i	$0.717695\pi$
$152$	−4.07366e8			−0.0618997
$153$	−1.96551e8	+	6.47071e6i	−0.0289978	+	0.000954642i
$154$	−9.94090e8			−0.142424
$155$	5.44656e9	+	9.43372e9i	0.757931	+	1.31278i
$156$	−2.23142e9	−	3.72213e9i	−0.301662	−	0.503188i
$157$	5.09608e9	−	8.82667e9i	0.669403	−	1.15944i	−0.308668	−	0.951170i	$-0.599883\pi$
$157$	5.09608e9	−	8.82667e9i	0.669403	−	1.15944i	0.978071	−	0.208271i	$-0.0667836\pi$
$158$	−4.24938e9	+	7.36015e9i	−0.542462	+	0.939571i
$159$	−2.51258e9	+	4.13473e7i	−0.311768	+	0.00513051i
$160$	5.87069e8	+	1.01683e9i	0.0708189	+	0.122662i
$161$	9.14588e9			1.07278
$162$	3.44573e9	+	5.15278e9i	0.393064	+	0.587793i
$163$	−7.29928e9			−0.809908			−0.404954	−	0.914337i	$-0.632713\pi$
$163$	−7.29928e9			−0.809908			−0.404954	+	0.914337i	$0.632713\pi$
$164$	−2.68965e9	−	4.65861e9i	−0.290334	−	0.502874i
$165$	−2.26911e9	+	3.73408e7i	−0.238330	+	0.00392199i
$166$	−3.91117e9	+	6.77435e9i	−0.399779	+	0.692438i
$167$	−1.75859e9	+	3.04597e9i	−0.174961	+	0.303041i	−0.940148	−	0.340767i	$-0.889313\pi$
$167$	−1.75859e9	+	3.04597e9i	−0.174961	+	0.303041i	0.765187	+	0.643808i	$0.222647\pi$
$168$	−1.27080e9	−	2.11976e9i	−0.123080	−	0.205303i
$169$	−1.99786e9	−	3.46039e9i	−0.188397	−	0.326314i
$170$	1.79003e8			0.0164376
$171$	1.95651e9	−	6.44106e7i	0.174984	−	0.00576069i
$172$	−7.50914e9			−0.654202
$173$	7.11932e9	+	1.23310e10i	0.604270	+	1.04663i	0.992166	+	0.124924i	$0.0398686\pi$
$173$	7.11932e9	+	1.23310e10i	0.604270	+	1.04663i	−0.387896	+	0.921703i	$0.626798\pi$
$174$	4.63326e9	−	8.33897e9i	0.383191	−	0.689669i
$175$	−1.50379e9	+	2.60464e9i	−0.121204	+	0.209931i
$176$	4.73369e8	−	8.19899e8i	0.0371871	−	0.0644100i
$177$	1.10381e9	−	1.98664e9i	0.0845305	−	0.152138i
$178$	4.91843e9	+	8.51897e9i	0.367229	+	0.636059i
$179$	5.94472e9			0.432806			0.216403	−	0.976304i	$-0.430568\pi$
$179$	5.94472e9			0.432806			0.216403	+	0.976304i	$0.430568\pi$
$180$	−2.98036e9	−	4.79084e9i	−0.211613	−	0.340162i
$181$	−2.86649e10			−1.98517			−0.992583	−	0.121571i	$-0.961207\pi$
$181$	−2.86649e10			−1.98517			−0.992583	+	0.121571i	$0.961207\pi$
$182$	−4.15743e9	−	7.20089e9i	−0.280869	−	0.486480i
$183$	−1.12368e9	−	1.87436e9i	−0.0740650	−	0.123544i
$184$	−4.35512e9	+	7.54328e9i	−0.280104	+	0.485155i
$185$	−7.59840e9	+	1.31608e10i	−0.476924	+	0.826057i
$186$	2.18343e10	−	3.59309e8i	1.33762	−	0.0220120i
$187$	−7.21672e7	−	1.24997e8i	−0.00431572	−	0.00747504i
$188$	1.69019e10			0.986789
$189$	6.43860e9	+	9.97990e9i	0.367040	+	0.568916i
$190$	−1.78182e9			−0.0991912
$191$	−4.76457e9	−	8.25248e9i	−0.259044	−	0.448677i	0.706942	−	0.707271i	$-0.250074\pi$
$191$	−4.76457e9	−	8.25248e9i	−0.259044	−	0.448677i	−0.965986	+	0.258594i	$0.916741\pi$
$192$	2.35346e9	−	3.87289e7i	0.124983	−	0.00205674i
$193$	−1.04268e10	+	1.80597e10i	−0.540931	+	0.936920i	0.457920	+	0.888993i	$0.348595\pi$
$193$	−1.04268e10	+	1.80597e10i	−0.540931	+	0.936920i	−0.998851	+	0.0479264i	$0.984739\pi$
$194$	−1.80919e9	+	3.13360e9i	−0.0917014	+	0.158831i
$195$	−9.76025e9	−	1.62806e10i	−0.483399	−	0.806333i
$196$	2.79759e9	+	4.84557e9i	0.135404	+	0.234527i
$197$	1.41661e10			0.670120			0.335060	−	0.942197i	$-0.391243\pi$
$197$	1.41661e10			0.670120			0.335060	+	0.942197i	$0.391243\pi$
$198$	−2.14387e9	+	4.01267e9i	−0.0991299	+	0.185541i
$199$	1.68935e10			0.763624			0.381812	−	0.924240i	$-0.375300\pi$
$199$	1.68935e10			0.763624			0.381812	+	0.924240i	$0.375300\pi$
$200$	−1.43216e9	−	2.48057e9i	−0.0632931	−	0.109627i
$201$	−1.30149e10	+	2.34243e10i	−0.562417	+	1.01224i
$202$	9.64346e9	−	1.67030e10i	0.407523	−	0.705850i
$203$	9.13890e9	−	1.58290e10i	0.377713	−	0.654218i
$204$	1.74284e8	−	3.13678e8i	0.00704568	−	0.0126809i
$205$	−1.17645e10	−	2.03768e10i	−0.465246	−	0.805830i
$206$	−2.60371e9			−0.100737
$207$	1.97241e10	−	3.69176e10i	0.746675	−	1.39755i
$208$	7.91880e9			0.293342
$209$	7.18365e8	+	1.24424e9i	0.0260427	+	0.0451073i
$210$	−5.55849e9	−	9.27185e9i	−0.197229	−	0.328988i
$211$	1.11910e10	−	1.93833e10i	0.388684	−	0.673220i	−0.603589	−	0.797296i	$-0.706263\pi$
$211$	1.11910e10	−	1.93833e10i	0.388684	−	0.673220i	0.992273	+	0.124075i	$0.0395965\pi$
$212$	2.29267e9	−	3.97103e9i	0.0779526	−	0.135018i
$213$	−7.32261e9	+	1.20502e8i	−0.243757	+	0.00401131i
$214$	−1.35257e10	−	2.34272e10i	−0.440857	−	0.763586i
$215$	−3.28450e10			−1.04833
$216$	−1.12971e10	+	5.58124e8i	−0.353123	+	0.0174457i
$217$	4.18397e10			1.28091
$218$	−4.38930e9	−	7.60249e9i	−0.131626	−	0.227983i
$219$	−4.11633e10	+	6.77390e8i	−1.20924	+	0.0198994i
$220$	2.07052e9	−	3.58624e9i	0.0595905	−	0.103214i
$221$	6.03629e8	−	1.04552e9i	0.0170218	−	0.0294826i
$222$	1.56645e10	+	2.61291e10i	0.432839	+	0.721998i
$223$	1.49984e9	+	2.59781e9i	0.0406139	+	0.0703453i	0.885618	−	0.464415i	$-0.153735\pi$
$223$	1.49984e9	+	2.59781e9i	0.0406139	+	0.0703453i	−0.845004	+	0.534760i	$0.820402\pi$
$224$	4.50978e9			0.119685
$225$	7.27061e9	+	1.16873e10i	0.189125	+	0.304013i
$226$	2.25611e10			0.575270
$227$	−2.39045e9	−	4.14039e9i	−0.0597536	−	0.103496i	0.834601	−	0.550855i	$-0.185698\pi$
$227$	−2.39045e9	−	4.14039e9i	−0.0597536	−	0.103496i	−0.894355	+	0.447358i	$0.852365\pi$
$228$	−1.73486e9	+	3.12240e9i	−0.0425164	+	0.0765213i
$229$	−2.99041e10	+	5.17954e10i	−0.718573	+	1.24460i	0.242992	+	0.970028i	$0.421871\pi$
$229$	−2.99041e10	+	5.17954e10i	−0.718573	+	1.24460i	−0.961565	+	0.274577i	$0.911462\pi$
$230$	−1.90493e10	+	3.29944e10i	−0.448853	+	0.777436i
$231$	−4.23354e9	+	7.61956e9i	−0.0978250	+	0.176066i
$232$	8.70358e9	+	1.50751e10i	0.197243	+	0.341635i
$233$	−6.06934e10			−1.34909			−0.674543	−	0.738236i	$-0.735659\pi$
$233$	−6.06934e10			−1.34909			−0.674543	+	0.738236i	$0.735659\pi$
$234$	−3.80326e10	+	1.25208e9i	−0.829248	+	0.0272999i
$235$	7.39288e10			1.58128
$236$	2.07350e9	+	3.59141e9i	0.0435111	+	0.0753635i
$237$	3.83176e10	+	6.39157e10i	0.788916	+	1.31595i
$238$	3.43768e8	−	5.95424e8i	0.00694496	−	0.0120290i
$239$	1.45691e10	−	2.52345e10i	0.288831	−	0.500269i	−0.684700	−	0.728825i	$-0.740067\pi$
$239$	1.45691e10	−	2.52345e10i	0.288831	−	0.500269i	0.973531	+	0.228555i	$0.0734002\pi$
$240$	1.02940e10	−	1.69400e8i	0.200279	−	0.00329582i
$241$	−1.73919e10	−	3.01236e10i	−0.332101	−	0.575216i	0.650823	−	0.759230i	$-0.274424\pi$
$241$	−1.73919e10	−	3.01236e10i	−0.332101	−	0.575216i	−0.982924	+	0.184014i	$0.941091\pi$
$242$	3.43881e10			0.644525
$243$	5.41697e10	−	4.46681e9i	0.996617	−	0.0821806i
$244$	3.98768e9			0.0720222
$245$	1.22367e10	+	2.11945e10i	0.216978	+	0.375817i
$246$	−4.71620e10	+	7.76106e8i	−0.821078	+	0.0135118i
$247$	−6.00862e9	+	1.04072e10i	−0.102716	+	0.177909i
$248$	−1.99234e10	+	3.45083e10i	−0.334450	+	0.579284i
$249$	3.52679e10	+	5.88286e10i	0.581410	+	0.969821i
$250$	−2.37603e10	−	4.11540e10i	−0.384699	−	0.666319i
$251$	−9.78083e10			−1.55541			−0.777703	−	0.628632i	$-0.783615\pi$
$251$	−9.78083e10			−1.55541			−0.777703	+	0.628632i	$0.783615\pi$
$252$	−2.16597e10	+	7.13063e8i	−0.338337	+	0.0111385i
$253$	3.07199e10			0.471387
$254$	−1.91527e10	−	3.31734e10i	−0.288720	−	0.500078i
$255$	7.62320e8	−	1.37203e9i	0.0112903	−	0.0203204i
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	5.96425e10	−	1.03304e11i	0.852818	−	1.47712i	−0.0258362	−	0.999666i	$-0.508225\pi$
$257$	5.96425e10	−	1.03304e11i	0.852818	−	1.47712i	0.878654	−	0.477458i	$-0.158442\pi$
$258$	−3.19793e10	+	5.75565e10i	−0.449345	+	0.808734i
$259$	2.91849e10	+	5.05498e10i	0.403004	+	0.698024i
$260$	3.46369e10			0.470066
$261$	−4.41853e10	−	7.10266e10i	−0.589380	−	0.947411i
$262$	−1.12261e10			−0.147188
$263$	−2.69975e10	−	4.67610e10i	−0.347954	−	0.602674i	0.637932	−	0.770093i	$-0.279790\pi$
$263$	−2.69975e10	−	4.67610e10i	−0.347954	−	0.602674i	−0.985886	+	0.167419i	$0.946457\pi$
$264$	−4.26847e9	−	7.12002e9i	−0.0540822	−	0.0902119i
$265$	1.00282e10	−	1.73693e10i	0.124915	−	0.216359i
$266$	−3.42193e9	+	5.92695e9i	−0.0419086	+	0.0725879i
$267$	8.62429e10	−	1.41923e9i	1.03854	−	0.0170904i
$268$	−2.44485e10	−	4.23460e10i	−0.289498	−	0.501425i
$269$	6.90563e10			0.804115			0.402058	−	0.915614i	$-0.368295\pi$
$269$	6.90563e10			0.804115			0.402058	+	0.915614i	$0.368295\pi$
$270$	−4.94136e10	+	2.44124e9i	−0.565861	+	0.0279559i
$271$	−6.75742e10			−0.761060			−0.380530	−	0.924769i	$-0.624258\pi$
$271$	−6.75742e10			−0.761060			−0.380530	+	0.924769i	$0.624258\pi$
$272$	3.27393e8	+	5.67062e8i	0.00362669	+	0.00628160i
$273$	−7.28991e10	+	1.19964e9i	−0.794310	+	0.0130713i
$274$	2.92712e9	−	5.06992e9i	0.0313735	−	0.0543405i
$275$	−5.05104e9	+	8.74866e9i	−0.0532579	+	0.0922454i
$276$	3.92710e10	+	6.55060e10i	0.407363	+	0.679502i
$277$	−2.55097e10	−	4.41840e10i	−0.260343	−	0.450927i	0.705990	−	0.708222i	$-0.250502\pi$
$277$	−2.55097e10	−	4.41840e10i	−0.260343	−	0.450927i	−0.966333	+	0.257294i	$0.917169\pi$
$278$	9.55725e10			0.959691
$279$	9.02322e10	−	1.68887e11i	0.891543	−	1.66870i
$280$	1.97258e10			0.191789
$281$	4.04317e9	+	7.00297e9i	0.0386851	+	0.0670045i	0.884720	−	0.466123i	$-0.154350\pi$
$281$	4.04317e9	+	7.00297e9i	0.0386851	+	0.0670045i	−0.846035	+	0.533128i	$0.821016\pi$
$282$	7.19802e10	−	1.29550e11i	0.677785	−	1.21988i
$283$	−7.71101e10	+	1.33559e11i	−0.714615	+	1.23775i	0.248492	+	0.968634i	$0.420065\pi$
$283$	−7.71101e10	+	1.33559e11i	−0.714615	+	1.23775i	−0.963108	+	0.269116i	$0.913268\pi$
$284$	6.68173e9	−	1.15731e10i	0.0609476	−	0.105564i
$285$	−7.58827e9	+	1.36574e10i	−0.0681304	+	0.122621i
$286$	−1.39643e10	−	2.41869e10i	−0.123416	−	0.213763i
$287$	−9.03736e10			−0.786272
$288$	9.72586e9	−	1.82039e10i	0.0833032	−	0.155918i
$289$	−1.18488e11			−0.999158
$290$	3.80695e10	+	6.59383e10i	0.316072	+	0.547453i
$291$	1.63138e10	+	2.72123e10i	0.133364	+	0.222457i
$292$	3.75607e10	−	6.50570e10i	0.302351	−	0.523686i
$293$	3.10563e10	−	5.37911e10i	0.246176	−	0.426389i	−0.716286	−	0.697807i	$-0.754159\pi$
$293$	3.10563e10	−	5.37911e10i	0.246176	−	0.426389i	0.962462	+	0.271418i	$0.0874926\pi$
$294$	4.90547e10	−	8.07252e8i	0.382929	−	0.00630154i
$295$	9.06951e9	+	1.57088e10i	0.0697244	+	0.120766i
$296$	−5.55895e10			−0.420901
$297$	2.16265e10	+	3.35213e10i	0.161280	+	0.249986i
$298$	1.15862e11			0.851079
$299$	1.28475e11	+	2.22526e11i	0.929607	+	1.61013i
$300$	−2.51124e10	+	4.13253e8i	−0.178996	+	0.00294558i
$301$	−6.30777e10	+	1.09254e11i	−0.442921	+	0.767162i
$302$	−3.63224e10	+	6.29122e10i	−0.251271	+	0.435215i
$303$	−8.69571e10	−	1.45049e11i	−0.592671	−	0.988605i
$304$	−3.25893e9	−	5.64463e9i	−0.0218849	−	0.0379057i
$305$	1.74421e10			0.115412
$306$	−1.66207e9	−	2.67173e9i	−0.0108369	−	0.0174199i
$307$	5.81497e10			0.373616			0.186808	−	0.982396i	$-0.440186\pi$
$307$	5.81497e10			0.373616			0.186808	+	0.982396i	$0.440186\pi$
$308$	−7.95272e9	−	1.37745e10i	−0.0503544	−	0.0872164i
$309$	−1.10885e10	+	1.99571e10i	−0.0691924	+	0.124533i
$310$	−8.71450e10	+	1.50940e11i	−0.535938	+	0.928272i
$311$	−1.27182e11	+	2.20285e11i	−0.770909	+	1.33525i	0.166156	+	0.986099i	$0.446864\pi$
$311$	−1.27182e11	+	2.20285e11i	−0.770909	+	1.33525i	−0.937065	+	0.349154i	$0.886469\pi$
$312$	3.37239e10	−	6.06965e10i	0.201485	−	0.362634i
$313$	−6.97489e10	−	1.20809e11i	−0.410760	−	0.711457i	0.584213	−	0.811600i	$-0.301403\pi$
$313$	−6.97489e10	−	1.20809e11i	−0.410760	−	0.711457i	−0.994973	+	0.100143i	$0.968070\pi$
$314$	1.63075e11			0.946679
$315$	−9.47395e10	+	3.11894e9i	−0.542167	+	0.0178488i
$316$	−1.35980e11			−0.767157
$317$	1.22061e11	+	2.11415e11i	0.678904	+	1.17590i	0.975311	+	0.220835i	$0.0708783\pi$
$317$	1.22061e11	+	2.11415e11i	0.678904	+	1.17590i	−0.296407	+	0.955062i	$0.595788\pi$
$318$	−2.06735e10	−	3.44845e10i	−0.113369	−	0.189104i
$319$	3.06964e10	−	5.31678e10i	0.165970	−	0.287469i
$320$	−9.39310e9	+	1.62693e10i	−0.0500765	+	0.0867351i
$321$	−2.37168e11	+	3.90288e9i	−1.24676	+	0.0205169i
$322$	7.31671e10	+	1.26729e11i	0.379284	+	0.656939i
$323$	−9.93677e8			−0.00507965
$324$	−4.38332e10	+	8.89677e10i	−0.220979	+	0.448518i
$325$	−8.44969e10			−0.420113
$326$	−5.83942e10	−	1.01142e11i	−0.286346	−	0.495966i
$327$	−7.69648e10	+	1.26654e9i	−0.372244	+	0.00612570i
$328$	4.30344e10	−	7.45378e10i	0.205297	−	0.355586i
$329$	1.41978e11	−	2.45913e11i	0.668096	−	1.15718i
$330$	−1.86703e10	−	3.11430e10i	−0.0866640	−	0.144560i
$331$	9.80240e10	+	1.69783e11i	0.448855	+	0.777440i	0.998312	−	0.0580820i	$-0.0184985\pi$
$331$	9.80240e10	+	1.69783e11i	0.448855	+	0.777440i	−0.549456	+	0.835522i	$0.685165\pi$
$332$	−1.25157e11			−0.565374
$333$	2.66986e11	−	8.78951e9i	1.18984	−	0.0391711i
$334$	−5.62750e10			−0.247432
$335$	−1.06938e11	−	1.85222e11i	−0.463905	−	0.803508i
$336$	1.92059e10	−	3.45669e10i	0.0822067	−	0.147956i
$337$	2.00934e11	−	3.48028e11i	0.848631	−	1.46987i	−0.0337995	−	0.999429i	$-0.510761\pi$
$337$	2.00934e11	−	3.48028e11i	0.848631	−	1.46987i	0.882430	−	0.470443i	$-0.155906\pi$
$338$	3.19657e10	−	5.53663e10i	0.133217	−	0.230739i
$339$	9.60811e10	−	1.72927e11i	0.395129	−	0.711157i
$340$	1.43202e9	+	2.48033e9i	0.00581158	+	0.0100659i
$341$	1.40535e11			0.562845
$342$	1.65445e10	+	2.65949e10i	0.0653939	+	0.105119i
$343$	2.67556e11			1.04374
$344$	−6.00731e10	−	1.04050e11i	−0.231295	−	0.400616i
$345$	1.71772e11	+	2.86524e11i	0.652778	+	1.08887i
$346$	−1.13909e11	+	1.97296e11i	−0.427284	+	0.740077i
$347$	−9.67465e10	+	1.67570e11i	−0.358222	+	0.620460i	−0.987664	−	0.156588i	$-0.949950\pi$
$347$	−9.67465e10	+	1.67570e11i	−0.358222	+	0.620460i	0.629441	+	0.777048i	$0.283284\pi$
$348$	1.52614e11	−	2.51144e9i	0.557813	−	0.00917945i
$349$	−9.74193e10	−	1.68735e11i	−0.351504	−	0.608823i	0.635009	−	0.772505i	$-0.280996\pi$
$349$	−9.74193e10	−	1.68735e11i	−0.351504	−	0.608823i	−0.986513	+	0.163682i	$0.947663\pi$
$350$	−4.81212e10			−0.171408
$351$	−1.52373e11	+	2.96847e11i	−0.535828	+	1.04388i
$352$	1.51478e10			0.0525906
$353$	−1.29274e11	−	2.23910e11i	−0.443125	−	0.767515i	0.554795	−	0.831987i	$-0.312797\pi$
$353$	−1.29274e11	−	2.23910e11i	−0.443125	−	0.767515i	−0.997919	+	0.0644725i	$0.979464\pi$
$354$	3.63581e10	−	5.98315e8i	0.123051	−	0.00202495i
$355$	2.92259e10	−	5.06208e10i	0.0976653	−	0.169161i
$356$	−7.86949e10	+	1.36304e11i	−0.259670	+	0.449761i
$357$	−3.09983e9	−	5.17068e9i	−0.0101002	−	0.0168477i
$358$	4.75578e10	+	8.23725e10i	0.153020	+	0.265038i
$359$	−3.16949e10			−0.100708			−0.0503540	−	0.998731i	$-0.516035\pi$
$359$	−3.16949e10			−0.100708			−0.0503540	+	0.998731i	$0.516035\pi$
$360$	4.25409e10	−	7.96238e10i	0.133489	−	0.249851i
$361$	−3.12796e11			−0.969347
$362$	−2.29319e11	−	3.97192e11i	−0.701862	−	1.21566i
$363$	1.46449e11	−	2.63580e11i	0.442698	−	0.796770i
$364$	6.65189e10	−	1.15214e11i	0.198604	−	0.343993i
$365$	1.64291e11	−	2.84560e11i	0.484501	−	0.839181i
$366$	1.69824e10	−	3.05650e10i	0.0494691	−	0.0890349i
$367$	6.45285e10	+	1.11767e11i	0.185675	+	0.321599i	0.943804	−	0.330506i	$-0.107219\pi$
$367$	6.45285e10	+	1.11767e11i	0.185675	+	0.321599i	−0.758129	+	0.652105i	$0.773886\pi$
$368$	−1.39364e11			−0.396127
$369$	−1.94901e11	+	3.64796e11i	−0.547262	+	1.02431i
$370$	−2.43149e11			−0.674472
$371$	−3.85175e10	−	6.67142e10i	−0.105554	−	0.182825i
$372$	1.79653e11	+	2.99671e11i	0.486399	+	0.811338i
$373$	2.84285e11	−	4.92396e11i	0.760439	−	1.31712i	−0.182185	−	0.983264i	$-0.558317\pi$
$373$	2.84285e11	−	4.92396e11i	0.760439	−	1.31712i	0.942624	−	0.333855i	$-0.108350\pi$
$374$	1.15468e9	−	1.99996e9i	0.00305167	−	0.00528565i
$375$	−4.16628e11	+	6.85609e9i	−1.08795	+	0.0179034i
$376$	1.35215e11	+	2.34199e11i	0.348883	+	0.604283i
$377$	5.13509e11			1.30922
$378$	−8.67768e10	+	1.69055e11i	−0.218620	+	0.425907i
$379$	4.13481e11			1.02939			0.514694	−	0.857374i	$-0.327906\pi$
$379$	4.13481e11			1.02939			0.514694	+	0.857374i	$0.327906\pi$
$380$	−1.42546e10	−	2.46896e10i	−0.0350694	−	0.0607419i
$381$	−3.35835e11	+	5.52655e9i	−0.816514	+	0.0134367i
$382$	7.62331e10	−	1.32040e11i	0.183172	−	0.317263i
$383$	−8.49563e10	+	1.47149e11i	−0.201744	+	0.349431i	−0.949091	−	0.315004i	$-0.897994\pi$
$383$	−8.49563e10	+	1.47149e11i	−0.201744	+	0.349431i	0.747346	+	0.664435i	$0.231328\pi$
$384$	1.93643e10	+	3.23007e10i	0.0454477	+	0.0758090i
$385$	−3.47852e10	−	6.02498e10i	−0.0806903	−	0.139760i
$386$	−3.33657e11			−0.764992
$387$	3.04972e11	+	4.90233e11i	0.691131	+	1.11097i
$388$	−5.78940e10			−0.129685
$389$	8.75615e9	+	1.51661e10i	0.0193883	+	0.0335815i	0.875557	−	0.483115i	$-0.160495\pi$
$389$	8.75615e9	+	1.51661e10i	0.0193883	+	0.0335815i	−0.856168	+	0.516697i	$0.827161\pi$
$390$	1.47509e11	−	2.65487e11i	0.322869	−	0.581102i
$391$	−1.06233e10	+	1.84001e10i	−0.0229861	+	0.0398130i
$392$	−4.47615e10	+	7.75291e10i	−0.0957452	+	0.165835i
$393$	−4.78086e10	+	8.60462e10i	−0.101097	+	0.181955i
$394$	1.13329e11	+	1.96291e11i	0.236923	+	0.410363i
$395$	−5.94778e11			−1.22933
$396$	−7.27522e10	+	2.39509e9i	−0.148668	+	0.00489433i
$397$	−3.13291e11			−0.632981			−0.316491	−	0.948596i	$-0.602505\pi$
$397$	−3.13291e11			−0.632981			−0.316491	+	0.948596i	$0.602505\pi$
$398$	1.35148e11	+	2.34083e11i	0.269982	+	0.467622i
$399$	3.08562e10	+	5.14698e10i	0.0609488	+	0.101666i
$400$	2.29145e10	−	3.96891e10i	0.0447550	−	0.0775179i
$401$	−3.66552e11	+	6.34887e11i	−0.707923	+	1.22616i	0.257703	+	0.966224i	$0.417034\pi$
$401$	−3.66552e11	+	6.34887e11i	−0.707923	+	1.22616i	−0.965626	+	0.259935i	$0.916299\pi$
$402$	−4.28695e11	+	7.05468e9i	−0.818713	+	0.0134729i
$403$	5.87737e11	+	1.01799e12i	1.10997	+	1.92252i
$404$	3.08591e11			0.576324
$405$	−1.91727e11	+	3.89145e11i	−0.354107	+	0.718727i
$406$	2.92445e11			0.534167
$407$	9.80286e10	+	1.69790e11i	0.177083	+	0.306717i
$408$	5.74073e9	−	9.44703e7i	0.0102564	−	0.000168781i
$409$	1.35741e11	−	2.35111e11i	0.239860	−	0.415450i	−0.720814	−	0.693129i	$-0.756232\pi$
$409$	1.35741e11	−	2.35111e11i	0.239860	−	0.415450i	0.960674	+	0.277679i	$0.0895652\pi$
$410$	1.88233e11	−	3.26029e11i	0.328979	−	0.569808i
$411$	−2.63945e10	−	4.40273e10i	−0.0456273	−	0.0761086i
$412$	−2.08297e10	−	3.60781e10i	−0.0356160	−	0.0616888i
$413$	6.96707e10			0.117835
$414$	6.69339e11	−	2.20354e10i	1.11981	−	0.0368655i
$415$	−5.47439e11			−0.905982
$416$	6.33504e10	+	1.09726e11i	0.103712	+	0.179635i
$417$	4.07016e11	−	7.32550e11i	0.659172	−	1.18638i
$418$	−1.14938e10	+	1.99079e10i	−0.0184150	+	0.0318957i
$419$	1.44871e11	−	2.50923e11i	0.229624	−	0.397720i	−0.728073	−	0.685500i	$-0.759584\pi$
$419$	1.44871e11	−	2.50923e11i	0.229624	−	0.397720i	0.957697	+	0.287779i	$0.0929170\pi$
$420$	8.40065e10	−	1.51196e11i	0.131732	−	0.237092i
$421$	−1.60715e11	−	2.78366e11i	−0.249337	−	0.431864i	0.714005	−	0.700140i	$-0.246879\pi$
$421$	−1.60715e11	−	2.78366e11i	−0.249337	−	0.431864i	−0.963342	+	0.268277i	$0.913546\pi$
$422$	3.58111e11			0.549682
$423$	−6.86443e11	−	1.10344e12i	−1.04249	−	1.67578i
$424$	7.33656e10			0.110242
$425$	−3.49342e9	−	6.05079e9i	−0.00519399	−	0.00899625i
$426$	−6.02506e10	−	1.00501e11i	−0.0886376	−	0.147852i
$427$	3.34970e10	−	5.80186e10i	0.0487619	−	0.0844582i
$428$	2.16411e11	−	3.74835e11i	0.311733	−	0.539937i
$429$	−2.44859e11	+	4.02944e9i	−0.349027	+	0.00574364i
$430$	−2.62760e11	−	4.55114e11i	−0.370639	−	0.641966i
$431$	−7.55639e11			−1.05479			−0.527396	−	0.849620i	$-0.676831\pi$
$431$	−7.55639e11			−1.05479			−0.527396	+	0.849620i	$0.676831\pi$
$432$	−9.81105e10	−	1.52072e11i	−0.135531	−	0.210075i
$433$	−5.19996e11			−0.710893			−0.355447	−	0.934697i	$-0.615671\pi$
$433$	−5.19996e11			−0.710893			−0.355447	+	0.934697i	$0.615671\pi$
$434$	3.34718e11	+	5.79748e11i	0.452872	+	0.784397i
$435$	6.67535e11	−	1.09851e10i	0.893866	−	0.0147096i
$436$	7.02288e10	−	1.21640e11i	0.0930735	−	0.161208i
$437$	1.05746e11	−	1.83158e11i	0.138707	−	0.240248i
$438$	−3.38693e11	−	5.64957e11i	−0.439716	−	0.733469i
$439$	−5.99942e11	−	1.03913e12i	−0.770937	−	1.33530i	−0.937050	−	0.349195i	$-0.886455\pi$
$439$	−5.99942e11	−	1.03913e12i	−0.770937	−	1.33530i	0.166113	−	0.986107i	$-0.446878\pi$
$440$	6.62566e10			0.0842737
$441$	2.02723e11	−	3.79436e11i	0.255228	−	0.477710i
$442$	1.93161e10			0.0240724
$443$	3.91092e11	+	6.77391e11i	0.482461	+	0.835647i	0.999797	−	0.0201352i	$-0.00640967\pi$
$443$	3.91092e11	+	6.77391e11i	0.482461	+	0.835647i	−0.517336	+	0.855782i	$0.673076\pi$
$444$	−2.36740e11	+	4.26086e11i	−0.289100	+	0.520324i
$445$	−3.44212e11	+	5.96192e11i	−0.416108	+	0.720719i
$446$	−2.39975e10	+	4.15649e10i	−0.0287183	+	0.0497416i
$447$	4.93425e11	−	8.88070e11i	0.584571	−	1.05212i
$448$	3.60783e10	+	6.24894e10i	0.0423150	+	0.0732918i
$449$	9.74123e11			1.13111			0.565555	−	0.824710i	$-0.308662\pi$
$449$	9.74123e11			1.13111			0.565555	+	0.824710i	$0.308662\pi$
$450$	−1.03779e11	+	1.94243e11i	−0.119303	+	0.223300i
$451$	−3.03554e11			−0.345495
$452$	1.80489e11	+	3.12615e11i	0.203389	+	0.352279i
$453$	3.27527e11	+	5.46331e11i	0.365430	+	0.609556i
$454$	3.82473e10	−	6.62462e10i	0.0422522	−	0.0731829i
$455$	2.90954e11	−	5.03947e11i	0.318253	−	0.551231i
$456$	−5.71442e10	+	9.40373e8i	−0.0618914	+	0.00101849i
$457$	8.38442e11	+	1.45222e12i	0.899187	+	1.55744i	0.828536	+	0.559936i	$0.189174\pi$
$457$	8.38442e11	+	1.45222e12i	0.899187	+	1.55744i	0.0706514	+	0.997501i	$0.477492\pi$
$458$	−9.56931e11			−1.01622
$459$	−2.75567e10	+	1.36142e9i	−0.0289781	+	0.00143164i
$460$	−6.09578e11			−0.634773
$461$	−1.59134e11	−	2.75628e11i	−0.164100	−	0.284230i	0.772235	−	0.635337i	$-0.219139\pi$
$461$	−1.59134e11	−	2.75628e11i	−0.164100	−	0.284230i	−0.936335	+	0.351107i	$0.885805\pi$
$462$	−1.39448e11	+	2.29478e9i	−0.142404	+	0.00234343i
$463$	−3.19943e11	+	5.54157e11i	−0.323562	+	0.560426i	−0.981220	−	0.192890i	$-0.938214\pi$
$463$	−3.19943e11	+	5.54157e11i	−0.323562	+	0.560426i	0.657658	+	0.753317i	$0.271547\pi$
$464$	−1.39257e11	+	2.41201e11i	−0.139472	+	0.241573i
$465$	7.85805e11	+	1.31076e12i	0.779429	+	1.30013i
$466$	−4.85547e11	−	8.40992e11i	−0.476974	−	0.826143i
$467$	1.20873e12			1.17599			0.587997	−	0.808863i	$-0.299917\pi$
$467$	1.20873e12			1.17599			0.587997	+	0.808863i	$0.299917\pi$
$468$	−3.21610e11	−	5.16978e11i	−0.309901	−	0.498157i
$469$	−8.21481e11			−0.784007
$470$	5.91431e11	+	1.02439e12i	0.559067	+	0.968332i
$471$	6.94488e11	−	1.24994e12i	0.650235	−	1.17030i
$472$	−3.31760e10	+	5.74626e10i	−0.0307670	+	0.0532901i
$473$	−2.11870e11	+	3.66970e11i	−0.194623	+	0.337098i
$474$	−5.79101e11	+	1.04227e12i	−0.526929	+	0.948370i
$475$	3.47741e10	+	6.02305e10i	0.0313426	+	0.0542870i
$476$	1.10006e10			0.00982165
$477$	−3.52361e11	+	1.16002e10i	−0.311642	+	0.0102596i
$478$	4.66212e11			0.408468
$479$	−9.82917e11	−	1.70246e12i	−0.853114	−	1.47764i	−0.878384	−	0.477956i	$-0.841378\pi$
$479$	−9.82917e11	−	1.70246e12i	−0.853114	−	1.47764i	0.0252702	−	0.999681i	$-0.491955\pi$
$480$	8.46996e10	+	1.41283e11i	0.0728276	+	0.121480i
$481$	−8.19941e11	+	1.42018e12i	−0.698441	+	1.20974i
$482$	2.78270e11	−	4.81978e11i	0.234831	−	0.406739i
$483$	1.28296e12	−	2.11126e10i	1.07263	−	0.0176514i
$484$	2.75105e11	+	4.76496e11i	0.227874	+	0.394689i
$485$	−2.53229e11			−0.207814
$486$	4.95252e11	+	7.14863e11i	0.402683	+	0.581246i
$487$	1.41131e12			1.13695			0.568474	−	0.822701i	$-0.307534\pi$
$487$	1.41131e12			1.13695			0.568474	+	0.822701i	$0.307534\pi$
$488$	3.19015e10	+	5.52550e10i	0.0254637	+	0.0441044i
$489$	−1.02392e12	+	1.68498e10i	−0.809799	+	0.0133262i
$490$	−1.95787e11	+	3.39113e11i	−0.153427	+	0.265743i
$491$	−2.85104e11	+	4.93814e11i	−0.221379	+	0.383440i	−0.955227	−	0.295874i	$-0.904389\pi$
$491$	−2.85104e11	+	4.93814e11i	−0.221379	+	0.383440i	0.733848	+	0.679314i	$0.237722\pi$
$492$	−3.88050e11	−	6.47288e11i	−0.298569	−	0.498029i
$493$	2.12304e10	+	3.67721e10i	0.0161863	+	0.0280355i
$494$	−1.92276e11			−0.145262
$495$	−3.18218e11	+	1.04761e10i	−0.238233	+	0.00784292i
$496$	−6.37549e11			−0.472983
$497$	−1.12255e11	−	1.94431e11i	−0.0825279	−	0.142943i
$498$	−5.33010e11	+	9.59315e11i	−0.388332	+	0.698923i
$499$	−1.22841e11	+	2.12766e11i	−0.0886932	+	0.153621i	−0.906959	−	0.421219i	$-0.861602\pi$
$499$	−1.22841e11	+	2.12766e11i	−0.0886932	+	0.153621i	0.818266	+	0.574840i	$0.194936\pi$
$500$	3.80165e11	−	6.58464e11i	0.272024	−	0.471159i
$501$	−2.39659e11	+	4.31340e11i	−0.169951	+	0.305879i
$502$	−7.82466e11	−	1.35527e12i	−0.549919	−	0.952488i
$503$	−1.01869e12			−0.709557			−0.354778	−	0.934950i	$-0.615444\pi$
$503$	−1.01869e12			−0.709557			−0.354778	+	0.934950i	$0.615444\pi$
$504$	−1.83158e11	−	2.94421e11i	−0.126441	−	0.203250i
$505$	1.34978e12			0.923530
$506$	2.45759e11	+	4.25667e11i	0.166660	+	0.288664i
$507$	−2.88242e11	−	4.80802e11i	−0.193741	−	0.323170i
$508$	3.06443e11	−	5.30774e11i	0.204156	−	0.353609i
$509$	−5.93895e11	+	1.02866e12i	−0.392175	+	0.679267i	−0.992736	−	0.120312i	$-0.961610\pi$
$509$	−5.93895e11	+	1.02866e12i	−0.392175	+	0.679267i	0.600561	+	0.799579i	$0.294944\pi$
$510$	2.51100e10	−	4.13213e8i	0.0164354	−	0.000270463i
$511$	−6.31029e11	−	1.09297e12i	−0.409407	−	0.709114i
$512$	−6.87195e10			−0.0441942
$513$	2.74304e11	−	1.35518e10i	0.174866	−	0.00863909i
$514$	1.90856e12			1.20607
$515$	−9.11092e10	−	1.57806e11i	−0.0570728	−	0.0988531i
$516$	−1.05336e12	+	1.73343e10i	−0.654114	+	0.0107642i
$517$	4.76886e11	−	8.25991e11i	0.293567	−	0.508473i
$518$	−4.66959e11	+	8.08796e11i	−0.284967	+	0.493577i
$519$	1.02714e12	+	1.71333e12i	0.621409	+	1.03654i
$520$	2.77095e11	+	4.79943e11i	0.166193	+	0.287855i
$521$	−8.72094e10			−0.0518554			−0.0259277	−	0.999664i	$-0.508254\pi$
$521$	−8.72094e10			−0.0518554			−0.0259277	+	0.999664i	$0.508254\pi$
$522$	6.30690e11	−	1.18046e12i	0.371791	−	0.695881i
$523$	1.85637e12			1.08494			0.542471	−	0.840075i	$-0.317489\pi$
$523$	1.85637e12			1.08494			0.542471	+	0.840075i	$0.317489\pi$
$524$	−8.98085e10	−	1.55553e11i	−0.0520387	−	0.0901337i
$525$	−2.04935e11	+	3.68843e11i	−0.117733	+	0.211897i
$526$	4.31959e11	−	7.48175e11i	0.246041	−	0.426155i
$527$	−4.85986e10	+	8.41752e10i	−0.0274458	+	0.0475375i
$528$	6.45102e10	−	1.16106e11i	0.0361223	−	0.0650132i
$529$	−1.36047e12	−	2.35641e12i	−0.755334	−	1.30828i
$530$	3.20901e11			0.176657
$531$	1.50253e11	−	2.81228e11i	0.0820157	−	0.153509i
$532$	−1.09502e11			−0.0592677
$533$	−1.26951e12	−	2.19885e12i	−0.681339	−	1.18011i
$534$	7.09609e11	+	1.18366e12i	0.377645	+	0.629930i
$535$	9.46583e11	−	1.63953e12i	0.499536	−	0.865221i
$536$	3.91176e11	−	6.77536e11i	0.204706	−	0.354561i
$537$	8.33909e11	−	1.37229e10i	0.432747	−	0.00712135i
$538$	5.52451e11	+	9.56873e11i	0.284298	+	0.492418i
$539$	3.15736e11			0.161129
$540$	−4.29136e11	−	6.65165e11i	−0.217181	−	0.336634i
$541$	3.88349e12			1.94910			0.974551	−	0.224164i	$-0.0719653\pi$
$541$	3.88349e12			1.94910			0.974551	+	0.224164i	$0.0719653\pi$
$542$	−5.40593e11	−	9.36335e11i	−0.269075	−	0.466052i
$543$	−4.02103e12	+	6.61707e10i	−1.98490	+	0.0326638i
$544$	−5.23830e9	+	9.07299e9i	−0.00256445	+	0.00444177i
$545$	3.07181e11	−	5.32053e11i	0.149146	−	0.258328i
$546$	−5.99816e11	−	1.00052e12i	−0.288836	−	0.481792i
$547$	2.06573e11	+	3.57795e11i	0.0986576	+	0.170880i	0.911129	−	0.412121i	$-0.135212\pi$
$547$	2.06573e11	+	3.57795e11i	0.0986576	+	0.170880i	−0.812472	+	0.583001i	$0.801878\pi$
$548$	9.36678e10			0.0443688
$549$	−1.61954e11	−	2.60335e11i	−0.0760878	−	0.122309i
$550$	−1.61633e11			−0.0753180
$551$	−2.11331e11	−	3.66036e11i	−0.0976745	−	0.169177i
$552$	−5.93510e11	+	1.06820e12i	−0.272084	+	0.489698i
$553$	−1.14225e12	+	1.97844e12i	−0.519396	+	0.899620i
$554$	4.08155e11	−	7.06945e11i	0.184090	−	0.318854i
$555$	−1.03550e12	+	1.86370e12i	−0.463268	+	0.833792i
$556$	7.64580e11	+	1.32429e12i	0.339302	+	0.587688i
$557$	−6.75242e11			−0.297243			−0.148621	−	0.988894i	$-0.547484\pi$
$557$	−6.75242e11			−0.297243			−0.148621	+	0.988894i	$0.547484\pi$
$558$	3.06203e12	−	1.00806e11i	1.33707	−	0.0440181i
$559$	−3.54429e12			−1.53524
$560$	1.57806e11	+	2.73329e11i	0.0678076	+	0.117446i
$561$	−1.04120e10	−	1.73677e10i	−0.00443812	−	0.00740302i
$562$	−6.46907e10	+	1.12048e11i	−0.0273545	+	0.0473793i
$563$	−6.71183e11	+	1.16252e12i	−0.281549	+	0.487656i	−0.971766	−	0.235945i	$-0.924181\pi$
$563$	−6.71183e11	+	1.16252e12i	−0.281549	+	0.487656i	0.690218	+	0.723602i	$0.257515\pi$
$564$	2.37095e12	−	3.90166e10i	0.986656	−	0.0162366i
$565$	7.89458e11	+	1.36738e12i	0.325920	+	0.564510i
$566$	−2.46752e12			−1.01062
$567$	9.26226e11	+	1.38509e12i	0.376351	+	0.562800i
$568$	2.13815e11			0.0861929
$569$	2.49278e11	+	4.31762e11i	0.0996961	+	0.172679i	0.911559	−	0.411170i	$-0.134880\pi$
$569$	2.49278e11	+	4.31762e11i	0.0996961	+	0.172679i	−0.811863	+	0.583848i	$0.801546\pi$
$570$	−2.49949e11	+	4.11320e9i	−0.0991777	+	0.00163208i
$571$	−4.15075e11	+	7.18932e11i	−0.163405	+	0.283025i	−0.936088	−	0.351767i	$-0.885581\pi$
$571$	−4.15075e11	+	7.18932e11i	−0.163405	+	0.283025i	0.772683	+	0.634792i	$0.218914\pi$
$572$	2.23429e11	−	3.86990e11i	0.0872685	−	0.151153i
$573$	−6.87410e11	−	1.14664e12i	−0.266391	−	0.444354i
$574$	−7.22989e11	−	1.25225e12i	−0.277989	−	0.481491i
$575$	1.48707e12			0.567317
$576$	3.30047e11	−	1.08656e10i	0.124932	−	0.00411292i
$577$	−1.32111e12			−0.496190			−0.248095	−	0.968736i	$-0.579805\pi$
$577$	−1.32111e12			−0.496190			−0.248095	+	0.968736i	$0.579805\pi$
$578$	−9.47904e11	−	1.64182e12i	−0.353256	−	0.611857i
$579$	−1.42095e12	+	2.55743e12i	−0.525442	+	0.945693i
$580$	−6.09112e11	+	1.05501e12i	−0.223497	+	0.387108i
$581$	−1.05134e12	+	1.82097e12i	−0.382781	+	0.662996i
$582$	−2.46554e11	+	4.43749e11i	−0.0890755	+	0.160319i
$583$	−1.29376e11	−	2.24085e11i	−0.0463814	−	0.0803349i
$584$	1.20194e12			0.427588
$585$	−1.40672e12	−	2.26126e12i	−0.496601	−	0.798270i
$586$	9.93801e11			0.348145
$587$	7.73375e11	+	1.33952e12i	0.268855	+	0.465671i	0.968567	−	0.248755i	$-0.0800213\pi$
$587$	7.73375e11	+	1.33952e12i	0.268855	+	0.465671i	−0.699711	+	0.714426i	$0.746688\pi$
$588$	4.03624e11	+	6.73265e11i	0.139245	+	0.232267i
$589$	4.83758e11	−	8.37894e11i	0.165619	−	0.286860i
$590$	−1.45112e11	+	2.51342e11i	−0.0493026	+	0.0853946i
$591$	1.98718e12	−	3.27013e10i	0.670029	−	0.0110261i
$592$	−4.44716e11	−	7.70271e11i	−0.148811	−	0.257748i
$593$	1.54444e12			0.512892			0.256446	−	0.966559i	$-0.417448\pi$
$593$	1.54444e12			0.512892			0.256446	+	0.966559i	$0.417448\pi$
$594$	−2.91473e11	+	5.67835e11i	−0.0960636	+	0.187147i
$595$	4.81166e10			0.0157387
$596$	9.26900e11	+	1.60544e12i	0.300902	+	0.521177i
$597$	2.36976e12	−	3.89972e10i	0.763521	−	0.0125646i
$598$	−2.05560e12	+	3.56041e12i	−0.657331	+	1.13853i
$599$	1.31256e12	−	2.27342e12i	0.416580	−	0.721539i	−0.579012	−	0.815319i	$-0.696562\pi$
$599$	1.31256e12	−	2.27342e12i	0.416580	−	0.721539i	0.995593	+	0.0937802i	$0.0298951\pi$
$600$	−2.06625e11	−	3.44661e11i	−0.0650883	−	0.108571i
$601$	−2.38290e12	−	4.12730e12i	−0.745024	−	1.29042i	−0.950184	−	0.311690i	$-0.899105\pi$
$601$	−2.38290e12	−	4.12730e12i	−0.745024	−	1.29042i	0.205160	−	0.978728i	$-0.434229\pi$
$602$	−2.01849e12			−0.626385
$603$	−1.77162e12	+	3.31593e12i	−0.545685	+	1.02136i
$604$	−1.16232e12			−0.355351
$605$	1.20331e12	+	2.08420e12i	0.365156	+	0.632469i
$606$	1.31420e12	−	2.36530e12i	0.395853	−	0.712460i
$607$	−1.94657e12	+	3.37155e12i	−0.581996	+	1.00805i	0.413246	+	0.910619i	$0.364395\pi$
$607$	−1.94657e12	+	3.37155e12i	−0.581996	+	1.00805i	−0.995243	+	0.0974281i	$0.968938\pi$
$608$	5.21429e10	−	9.03141e10i	0.0154749	−	0.0268034i
$609$	1.24544e12	−	2.24155e12i	0.366897	−	0.660344i
$610$	1.39537e11	+	2.41685e11i	0.0408043	+	0.0706751i
$611$	7.97764e12			2.31574
$612$	2.37240e10	−	4.44042e10i	0.00683607	−	0.0127951i
$613$	1.77922e12			0.508928			0.254464	−	0.967082i	$-0.418101\pi$
$613$	1.77922e12			0.508928			0.254464	+	0.967082i	$0.418101\pi$
$614$	4.65198e11	+	8.05746e11i	0.132093	+	0.228792i
$615$	−1.69733e12	−	2.83124e12i	−0.478442	−	0.798065i
$616$	1.27243e11	−	2.20392e11i	0.0356059	−	0.0616713i
$617$	−1.77947e12	+	3.08214e12i	−0.494320	+	0.856187i	−0.999979	−	0.00654663i	$-0.997916\pi$
$617$	−1.77947e12	+	3.08214e12i	−0.494320	+	0.856187i	0.505659	+	0.862734i	$0.331249\pi$
$618$	−3.65241e11	+	6.01047e9i	−0.100724	+	0.00165752i
$619$	−1.23981e12	−	2.14741e12i	−0.339427	−	0.587905i	0.644898	−	0.764269i	$-0.276900\pi$
$619$	−1.23981e12	−	2.14741e12i	−0.339427	−	0.587905i	−0.984325	+	0.176364i	$0.943566\pi$
$620$	−2.78864e12			−0.757931
$621$	2.68162e12	−	5.22423e12i	0.723578	−	1.40965i
$622$	−4.06982e12			−1.09023
$623$	1.32209e12	+	2.28993e12i	0.351614	+	0.609013i
$624$	1.11083e12	−	1.82799e10i	0.293303	−	0.00482663i
$625$	9.79935e11	−	1.69730e12i	0.256884	−	0.444936i
$626$	1.11598e12	−	1.93294e12i	0.290451	−	0.503076i
$627$	1.03642e11	+	1.72881e11i	0.0267814	+	0.0446727i
$628$	1.30460e12	+	2.25963e12i	0.334702	+	0.579720i
$629$	−1.35598e11			−0.0345402
$630$	−8.01133e11	−	1.28780e12i	−0.202615	−	0.325698i
$631$	−9.13591e11			−0.229414			−0.114707	−	0.993399i	$-0.536593\pi$
$631$	−9.13591e11			−0.229414			−0.114707	+	0.993399i	$0.536593\pi$
$632$	−1.08784e12	−	1.88420e12i	−0.271231	−	0.469786i
$633$	1.52509e12	−	2.74487e12i	0.377554	−	0.679525i
$634$	−1.95297e12	+	3.38264e12i	−0.480058	+	0.831485i
$635$	1.34038e12	−	2.32161e12i	0.327150	−	0.566640i
$636$	3.12443e11	−	5.62337e11i	0.0757205	−	0.136282i
$637$	1.32046e12	+	2.28710e12i	0.317758	+	0.550373i
$638$	9.82286e11			0.234717
$639$	−1.02692e12	+	3.38073e10i	−0.243658	+	0.00802153i
$640$	−3.00579e11			−0.0708189
$641$	−1.15646e12	−	2.00304e12i	−0.270563	−	0.468629i	0.698443	−	0.715666i	$-0.253877\pi$
$641$	−1.15646e12	−	2.00304e12i	−0.270563	−	0.468629i	−0.969006	+	0.247036i	$0.920543\pi$
$642$	−1.95143e12	−	3.25508e12i	−0.453361	−	0.756229i
$643$	3.22658e12	−	5.58859e12i	0.744376	−	1.28930i	−0.206109	−	0.978529i	$-0.566080\pi$
$643$	3.22658e12	−	5.58859e12i	0.744376	−	1.28930i	0.950486	−	0.310768i	$-0.100586\pi$
$644$	−1.17067e12	+	2.02766e12i	−0.268194	+	0.464526i
$645$	−4.60740e12	+	7.58201e10i	−1.04818	+	0.0172491i
$646$	−7.94941e9	−	1.37688e10i	−0.00179593	−	0.00311064i
$647$	−2.92956e12			−0.657253			−0.328627	−	0.944460i	$-0.606586\pi$
$647$	−2.92956e12			−0.657253			−0.328627	+	0.944460i	$0.606586\pi$
$648$	−1.58344e12	+	1.04371e11i	−0.352788	+	0.0232536i
$649$	2.34015e11			0.0517778
$650$	−6.75975e11	−	1.17082e12i	−0.148532	−	0.257265i
$651$	5.86916e12	−	9.65838e10i	1.28074	−	0.0210761i
$652$	9.34308e11	−	1.61827e12i	0.202477	−	0.350701i
$653$	4.82242e10	−	8.35267e10i	0.0103790	−	0.0179769i	−0.860789	−	0.508962i	$-0.830030\pi$
$653$	4.82242e10	−	8.35267e10i	0.0103790	−	0.0179769i	0.871168	+	0.490985i	$0.163363\pi$
$654$	−6.33268e11	−	1.05632e12i	−0.135359	−	0.225786i
$655$	−3.92823e11	−	6.80389e11i	−0.0833894	−	0.144435i
$656$	1.37710e12			0.290334
$657$	−5.77271e12	+	1.90045e11i	−1.20875	+	0.0397934i
$658$	4.54329e12			0.944831
$659$	1.35156e12	+	2.34096e12i	0.279158	+	0.483515i	0.971176	−	0.238365i	$-0.0766115\pi$
$659$	1.35156e12	+	2.34096e12i	0.279158	+	0.483515i	−0.692018	+	0.721880i	$0.743278\pi$
$660$	2.82168e11	−	5.07847e11i	0.0578841	−	0.104180i
$661$	9.75154e11	−	1.68902e12i	0.198686	−	0.344134i	−0.749417	−	0.662098i	$-0.769666\pi$
$661$	9.75154e11	−	1.68902e12i	0.198686	−	0.344134i	0.948103	+	0.317965i	$0.102999\pi$
$662$	−1.56838e12	+	2.71652e12i	−0.317389	+	0.549733i
$663$	8.22618e10	−	1.48055e11i	0.0165344	−	0.0297586i
$664$	−1.00126e12	−	1.73423e12i	−0.199890	−	0.346219i
$665$	−4.78961e11			−0.0949735
$666$	2.25768e12	+	3.62915e12i	0.444661	+	0.714778i
$667$	−9.03729e12			−1.76796
$668$	−4.50200e11	−	7.79769e11i	−0.0874805	−	0.151521i
$669$	2.16391e11	+	3.60951e11i	0.0417658	+	0.0696675i
$670$	1.71100e12	−	2.96355e12i	0.328031	−	0.568166i
$671$	1.12512e11	−	1.94877e11i	0.0214264	−	0.0371116i
$672$	6.32619e11	−	1.04105e10i	0.119669	−	0.00196929i
$673$	4.96134e12	+	8.59330e12i	0.932248	+	1.61470i	0.779469	+	0.626440i	$0.215489\pi$
$673$	4.96134e12	+	8.59330e12i	0.932248	+	1.61470i	0.152778	+	0.988260i	$0.451178\pi$
$674$	6.42989e12			1.20015
$675$	1.04688e12	+	1.62268e12i	0.194102	+	0.300860i
$676$	1.02290e12			0.188397
$677$	3.11762e12	+	5.39988e12i	0.570393	+	0.987950i	0.996525	+	0.0832892i	$0.0265425\pi$
$677$	3.11762e12	+	5.39988e12i	0.570393	+	0.987950i	−0.426132	+	0.904661i	$0.640124\pi$
$678$	3.16480e12	−	5.20805e10i	0.575192	−	0.00946545i
$679$	−4.86317e11	+	8.42325e11i	−0.0878022	+	0.152078i
$680$	−2.29123e10	+	3.96853e10i	−0.00410941	+	0.00711770i
$681$	−3.44884e11	−	5.75284e11i	−0.0614484	−	0.102499i
$682$	1.12428e12	+	1.94730e12i	0.198996	+	0.344671i
$683$	−7.81146e12			−1.37353			−0.686767	−	0.726878i	$-0.740971\pi$
$683$	−7.81146e12			−1.37353			−0.686767	+	0.726878i	$0.740971\pi$
$684$	−2.36153e11	+	4.42007e11i	−0.0412516	+	0.0772105i
$685$	4.09703e11			0.0710987
$686$	2.14045e12	+	3.70736e12i	0.369017	+	0.639155i
$687$	−4.07529e12	+	7.33474e12i	−0.697997	+	1.25626i
$688$	9.61170e11	−	1.66479e12i	0.163551	−	0.283278i
$689$	1.08214e12	−	1.87431e12i	0.182934	−	0.316852i
$690$	−2.59602e12	+	4.67233e12i	−0.436000	+	0.784716i
$691$	2.54209e12	+	4.40302e12i	0.424169	+	0.734683i	0.996342	−	0.0854501i	$-0.0272328\pi$
$691$	2.54209e12	+	4.40302e12i	0.424169	+	0.734683i	−0.572173	+	0.820133i	$0.693899\pi$
$692$	−3.64509e12			−0.604270
$693$	−5.76280e11	+	1.07862e12i	−0.0949148	+	0.177652i
$694$	−3.09589e12			−0.506603
$695$	3.34428e12	+	5.79245e12i	0.543714	+	0.941740i
$696$	1.25571e12	+	2.09459e12i	0.202838	+	0.338344i
$697$	1.04973e11	−	1.81818e11i	0.0168472	−	0.0291803i
$698$	1.55871e12	−	2.69976e12i	0.248551	−	0.430503i
$699$	−8.51389e12	+	1.40106e11i	−1.34890	+	0.0221978i
$700$	−3.84970e11	−	6.66787e11i	−0.0606018	−	0.104965i
$701$	−1.07821e13			−1.68645			−0.843226	−	0.537560i	$-0.819346\pi$
$701$	−1.07821e13			−1.68645			−0.843226	+	0.537560i	$0.819346\pi$
$702$	−5.33221e12	+	2.63433e11i	−0.828686	+	0.0409405i
$703$	1.34976e12			0.208429
$704$	1.21182e11	+	2.09894e11i	0.0185936	+	0.0322050i
$705$	1.03705e13	−	1.70659e11i	1.58107	−	0.0260182i
$706$	2.06839e12	−	3.58256e12i	0.313337	−	0.542715i
$707$	2.59220e12	−	4.48982e12i	0.390195	−	0.675837i
$708$	2.99155e11	+	4.99006e11i	0.0447453	+	0.0746374i
$709$	1.26372e12	+	2.18883e12i	0.187820	+	0.325314i	0.944523	−	0.328444i	$-0.106524\pi$
$709$	1.26372e12	+	2.18883e12i	0.187820	+	0.325314i	−0.756703	+	0.653759i	$0.773191\pi$
$710$	9.35229e11			0.138120
$711$	5.52263e12	+	8.87746e12i	0.810462	+	1.30279i
$712$	−2.51824e12			−0.367229
$713$	−1.03436e13	−	1.79157e13i	−1.49889	−	2.59616i
$714$	4.68483e10	−	8.43179e10i	0.00674609	−	0.0121417i
$715$	9.77279e11	−	1.69270e12i	0.139843	−	0.242216i
$716$	−7.60924e11	+	1.31796e12i	−0.108201	+	0.187410i
$717$	1.98546e12	−	3.57345e12i	0.280560	−	0.504954i
$718$	−2.53559e11	−	4.39177e11i	−0.0356057	−	0.0616708i
$719$	−2.52331e12			−0.352120			−0.176060	−	0.984379i	$-0.556335\pi$
$719$	−2.52331e12			−0.352120			−0.176060	+	0.984379i	$0.556335\pi$
$720$	1.44363e12	−	4.75260e10i	0.200198	−	0.00659075i
$721$	−6.99888e11			−0.0964539
$722$	−2.50237e12	−	4.33424e12i	−0.342716	−	0.593602i
$723$	−2.50922e12	−	4.18551e12i	−0.341521	−	0.569674i
$724$	3.66911e12	−	6.35508e12i	0.496291	−	0.859602i
$725$	1.48593e12	−	2.57371e12i	0.199746	−	0.345970i
$726$	4.82387e12	−	7.93823e10i	0.644437	−	0.0106050i
$727$	−2.41003e12	−	4.17429e12i	−0.319976	−	0.554214i	0.660507	−	0.750820i	$-0.270341\pi$
$727$	−2.41003e12	−	4.17429e12i	−0.319976	−	0.554214i	−0.980483	+	0.196606i	$0.937008\pi$
$728$	2.12861e12			0.280869
$729$	7.58846e12	−	7.51638e11i	0.995130	−	0.0985677i
$730$	5.25730e12			0.685188
$731$	−1.46535e11	−	2.53805e11i	−0.0189807	−	0.0328755i
$732$	5.59381e11	−	9.20526e9i	0.0720125	−	0.00118505i
$733$	−1.11409e12	+	1.92966e12i	−0.142545	+	0.246895i	−0.928454	−	0.371446i	$-0.878862\pi$
$733$	−1.11409e12	+	1.92966e12i	−0.142545	+	0.246895i	0.785909	+	0.618342i	$0.212195\pi$
$734$	−1.03246e12	+	1.78827e12i	−0.131292	+	0.227405i
$735$	1.76545e12	+	2.94486e12i	0.223132	+	0.372196i
$736$	−1.11491e12	−	1.93108e12i	−0.140052	−	0.242577i
$737$	−2.75926e12			−0.344499
$738$	−6.61396e12	+	2.17740e11i	−0.820745	+	0.0270199i
$739$	−6.00472e12			−0.740615			−0.370308	−	0.928909i	$-0.620748\pi$
$739$	−6.00472e12			−0.740615			−0.370308	+	0.928909i	$0.620748\pi$
$740$	−1.94519e12	−	3.36917e12i	−0.238462	−	0.413028i
$741$	−8.18848e11	+	1.47377e12i	−0.0997749	+	0.179575i
$742$	6.16280e11	−	1.06743e12i	0.0746381	−	0.129277i
$743$	7.42709e12	−	1.28641e13i	0.894065	−	1.54857i	0.0591079	−	0.998252i	$-0.481174\pi$
$743$	7.42709e12	−	1.28641e13i	0.894065	−	1.54857i	0.834957	−	0.550315i	$-0.185492\pi$
$744$	−2.71514e12	+	4.88672e12i	−0.324873	+	0.584708i
$745$	4.05426e12	+	7.02219e12i	0.482180	+	0.835159i
$746$	9.09713e12			1.07542
$747$	5.08308e12	+	8.17089e12i	0.597288	+	0.960123i
$748$	3.69496e10			0.00431572
$749$	−3.63576e12	−	6.29732e12i	−0.422111	−	0.731118i
$750$	−3.42802e12	−	5.71812e12i	−0.395611	−	0.659899i
$751$	3.33511e12	−	5.77659e12i	0.382588	−	0.662661i	−0.608844	−	0.793290i	$-0.708366\pi$
$751$	3.33511e12	−	5.77659e12i	0.382588	−	0.662661i	0.991431	+	0.130629i	$0.0416997\pi$
$752$	−2.16344e12	+	3.74719e12i	−0.246697	+	0.427292i
$753$	−1.37203e13	+	2.25783e11i	−1.55520	+	0.0255925i
$754$	4.10807e12	+	7.11539e12i	0.462878	+	0.801729i
$755$	−5.08397e12			−0.569432
$756$	−3.03671e12	+	1.50026e11i	−0.338108	+	0.0167039i
$757$	6.61576e12			0.732232			0.366116	−	0.930569i	$-0.380687\pi$
$757$	6.61576e12			0.732232			0.366116	+	0.930569i	$0.380687\pi$
$758$	3.30785e12	+	5.72936e12i	0.363944	+	0.630369i
$759$	4.30930e12	−	7.09145e10i	0.471323	−	0.00775616i
$760$	2.28073e11	−	3.95034e11i	0.0247978	−	0.0429510i
$761$	−5.96589e12	+	1.03332e13i	−0.644829	+	1.11688i	0.339512	+	0.940602i	$0.389738\pi$
$761$	−5.96589e12	+	1.03332e13i	−0.644829	+	1.11688i	−0.984341	+	0.176274i	$0.943595\pi$
$762$	−2.76326e12	−	4.60925e12i	−0.296910	−	0.495260i
$763$	−1.17986e12	−	2.04358e12i	−0.126029	−	0.218289i
$764$	2.43946e12			0.259044
$765$	1.03769e11	−	1.94224e11i	0.0109545	−	0.0205034i
$766$	−2.71860e12			−0.285309
$767$	9.78688e11	+	1.69514e12i	0.102109	+	0.176858i
$768$	−2.92657e11	+	5.26725e11i	−0.0303552	+	0.0546334i
$769$	−8.79021e11	+	1.52251e12i	−0.0906423	+	0.156997i	−0.907782	−	0.419443i	$-0.862225\pi$
$769$	−8.79021e11	+	1.52251e12i	−0.0906423	+	0.156997i	0.817139	+	0.576440i	$0.195559\pi$
$770$	5.56563e11	−	9.63996e11i	0.0570567	−	0.0988251i
$771$	8.12800e12	−	1.46288e13i	0.828398	−	1.49096i
$772$	−2.66925e12	−	4.62328e12i	−0.270465	−	0.468460i
$773$	1.11558e13			1.12381			0.561905	−	0.827202i	$-0.310069\pi$
$773$	1.11558e13			1.12381			0.561905	+	0.827202i	$0.310069\pi$
$774$	−4.35310e12	+	8.14768e12i	−0.435977	+	0.816018i
$775$	6.80291e12			0.677387
$776$	−4.63152e11	−	8.02203e11i	−0.0458507	−	0.0794157i
$777$	4.21067e12	+	7.02360e12i	0.414435	+	0.691298i
$778$	−1.40098e11	+	2.42657e11i	−0.0137096	+	0.0237457i
$779$	−1.04491e12	+	1.80985e12i	−0.101663	+	0.176085i
$780$	4.85876e12	−	7.99565e10i	0.470002	−	0.00773443i
$781$	−3.77050e11	−	6.53070e11i	−0.0362635	−	0.0628101i
$782$	−3.39946e11			−0.0325072
$783$	−6.36215e12	−	9.86140e12i	−0.604889	−	0.937585i
$784$	−1.43237e12			−0.135404
$785$	5.70631e12	+	9.88362e12i	0.536342	+	0.928972i
$786$	−1.57476e12	+	2.59145e10i	−0.147168	+	0.00242182i
$787$	9.39932e10	−	1.62801e11i	0.00873394	−	0.0151276i	−0.861625	−	0.507545i	$-0.830553\pi$
$787$	9.39932e10	−	1.62801e11i	0.00873394	−	0.0151276i	0.870359	+	0.492417i	$0.163887\pi$
$788$	−1.81326e12	+	3.14066e12i	−0.167530	+	0.290170i
$789$	−3.89507e12	−	6.49717e12i	−0.357823	−	0.596867i
$790$	−4.75823e12	−	8.24149e12i	−0.434633	−	0.752807i
$791$	6.06451e12			0.550809
$792$	−6.15205e11	−	9.88923e11i	−0.0555592	−	0.0893098i
$793$	1.88218e12			0.169017
$794$	−2.50633e12	−	4.34109e12i	−0.223793	−	0.387620i
$795$	1.36663e12	−	2.45966e12i	0.121338	−	0.218385i
$796$	−2.16236e12	+	3.74532e12i	−0.190906	+	0.330659i
$797$	−9.27647e12	+	1.60673e13i	−0.814368	+	1.41053i	0.0954134	+	0.995438i	$0.469583\pi$
$797$	−9.27647e12	+	1.60673e13i	−0.814368	+	1.41053i	−0.909781	+	0.415088i	$0.863751\pi$
$798$	−4.66336e11	+	8.39315e11i	−0.0407086	+	0.0732676i
$799$	3.29826e11	+	5.71275e11i	0.0286302	+	0.0495890i
$800$	7.33265e11			0.0632931
$801$	1.20946e13	−	3.98170e11i	1.03812	−	0.0341761i
$802$	−1.17297e13			−1.00115
$803$	−2.11955e12	−	3.67117e12i	−0.179897	−	0.311590i
$804$	−3.52732e12	−	5.88374e12i	−0.297709	−	0.496594i
$805$	−5.12053e12	+	8.86901e12i	−0.429767	+	0.744379i
$806$	−9.40379e12	+	1.62878e13i	−0.784866	+	1.35943i
$807$	9.68703e12	−	1.59411e11i	0.804006	−	0.0132309i
$808$	2.46873e12	+	4.27596e12i	0.203761	+	0.352925i
$809$	5.17529e11			0.0424783			0.0212391	−	0.999774i	$-0.493239\pi$
$809$	5.17529e11			0.0424783			0.0212391	+	0.999774i	$0.493239\pi$
$810$	−6.92597e12	+	4.56517e11i	−0.565324	+	0.0372627i
$811$	−1.09375e13			−0.887815			−0.443908	−	0.896073i	$-0.646408\pi$
$811$	−1.09375e13			−0.887815			−0.443908	+	0.896073i	$0.646408\pi$
$812$	2.33956e12	+	4.05223e12i	0.188856	+	0.327109i
$813$	−9.47911e12	+	1.55990e11i	−0.760957	+	0.0125224i
$814$	−1.56846e12	+	2.71665e12i	−0.125217	+	0.216882i
$815$	4.08667e12	−	7.07831e12i	0.324459	−	0.561980i
$816$	4.72348e10	+	7.87901e10i	0.00372955	+	0.00622108i
$817$	1.45863e12	+	2.52642e12i	0.114537	+	0.198384i
$818$	4.34373e12			0.339213
$819$	−1.02233e13	+	3.36564e11i	−0.793988	+	0.0261391i
$820$	6.02344e12			0.465246
$821$	8.33638e12	+	1.44390e13i	0.640374	+	1.10916i	0.985349	+	0.170548i	$0.0545539\pi$
$821$	8.33638e12	+	1.44390e13i	0.640374	+	1.10916i	−0.344976	+	0.938612i	$0.612113\pi$
$822$	3.98904e11	−	7.17950e11i	0.0304751	−	0.0548493i
$823$	−5.88624e12	+	1.01953e13i	−0.447238	+	0.774639i	−0.998205	−	0.0598878i	$-0.980926\pi$
$823$	−5.88624e12	+	1.01953e13i	−0.447238	+	0.774639i	0.550967	+	0.834527i	$0.314259\pi$
$824$	3.33275e11	−	5.77249e11i	0.0251843	−	0.0436205i
$825$	−6.88350e11	+	1.23890e12i	−0.0517329	+	0.0931092i
$826$	5.57366e11	+	9.65386e11i	0.0416610	+	0.0721590i
$827$	1.88793e12			0.140350			0.0701748	−	0.997535i	$-0.477644\pi$
$827$	1.88793e12			0.140350			0.0701748	+	0.997535i	$0.477644\pi$
$828$	5.66004e12	+	9.09835e12i	0.418488	+	0.672707i
$829$	−1.03119e13			−0.758301			−0.379151	−	0.925335i	$-0.623784\pi$
$829$	−1.03119e13			−0.758301			−0.379151	+	0.925335i	$0.623784\pi$
$830$	−4.37951e12	−	7.58554e12i	−0.320313	−	0.554798i
$831$	−3.68042e12	−	6.13912e12i	−0.267727	−	0.446583i
$832$	−1.01361e12	+	1.75562e12i	−0.0733356	+	0.127021i
$833$	−1.09185e11	+	1.89115e11i	−0.00785709	+	0.0136089i
$834$	1.34066e13	−	2.20622e11i	0.959561	−	0.0157907i
$835$	−1.96918e12	−	3.41071e12i	−0.140183	−	0.242804i
$836$	−3.67803e11			−0.0260427
$837$	1.22676e13	−	2.38993e13i	0.863966	−	1.68314i
$838$	4.63586e12			0.324737
$839$	6.91124e12	+	1.19706e13i	0.481534	+	0.834041i	0.999775	−	0.0211931i	$-0.00674648\pi$
$839$	6.91124e12	+	1.19706e13i	0.481534	+	0.834041i	−0.518241	+	0.855234i	$0.673413\pi$
$840$	2.76708e12	−	4.55355e10i	0.191763	−	0.00315568i
$841$	−1.77682e12	+	3.07753e12i	−0.122479	+	0.212139i
$842$	2.57143e12	−	4.45385e12i	0.176308	−	0.305374i
$843$	5.83330e11	+	9.73023e11i	0.0397823	+	0.0663589i
$844$	2.86489e12	+	4.96213e12i	0.194342	+	0.336610i
$845$	4.47418e12			0.301897
$846$	9.79812e12	−	1.83391e13i	0.657622	−	1.23087i
$847$	9.24367e12			0.617119
$848$	5.86924e11	+	1.01658e12i	0.0389763	+	0.0675090i
$849$	−1.05085e13	+	1.89132e13i	−0.694153	+	1.24934i
$850$	5.58948e10	−	9.68126e10i	0.00367271	−	0.00636131i
$851$	1.44302e13	−	2.49939e13i	0.943169	−	1.63362i
$852$	9.10578e11	−	1.63886e12i	0.0592024	−	0.106553i
$853$	−3.85923e12	−	6.68438e12i	−0.249591	−	0.432305i	0.713821	−	0.700328i	$-0.246963\pi$
$853$	−3.85923e12	−	6.68438e12i	−0.249591	−	0.432305i	−0.963412	+	0.268023i	$0.913630\pi$
$854$	1.07191e12			0.0689598
$855$	−1.03293e12	+	1.93334e12i	−0.0661035	+	0.123726i
$856$	6.92515e12			0.440857
$857$	4.42217e11	+	7.65943e11i	0.0280041	+	0.0485046i	0.879688	−	0.475552i	$-0.157752\pi$
$857$	4.42217e11	+	7.65943e11i	0.0280041	+	0.0485046i	−0.851684	+	0.524056i	$0.824418\pi$
$858$	−2.01471e12	−	3.36063e12i	−0.126917	−	0.211704i
$859$	1.27404e11	−	2.20670e11i	0.00798385	−	0.0138284i	−0.862006	−	0.506898i	$-0.830792\pi$
$859$	1.27404e11	−	2.20670e11i	0.00798385	−	0.0138284i	0.869990	+	0.493070i	$0.164125\pi$
$860$	4.20416e12	−	7.28182e12i	0.262081	−	0.453938i
$861$	−1.26773e13	+	2.08620e11i	−0.786166	+	0.0129373i
$862$	−6.04511e12	−	1.04704e13i	−0.372925	−	0.645925i
$863$	1.06270e12			0.0652172			0.0326086	−	0.999468i	$-0.489619\pi$
$863$	1.06270e12			0.0652172			0.0326086	+	0.999468i	$0.489619\pi$
$864$	1.32229e12	−	2.57604e12i	0.0807265	−	0.157268i
$865$	−1.59437e13			−0.968312
$866$	−4.15997e12	−	7.20527e12i	−0.251339	−	0.435331i
$867$	−1.66212e13	+	2.73520e11i	−0.999023	+	0.0164401i
$868$	−5.35549e12	+	9.27598e12i	−0.320229	+	0.554652i
$869$	−3.83668e12	+	6.64533e12i	−0.228227	+	0.395301i
$870$	5.49250e12	+	9.16176e12i	0.325037	+	0.542178i
$871$	−1.15396e13	−	1.99872e13i	−0.679376	−	1.17671i
$872$	2.24732e12			0.131626
$873$	2.35127e12	+	3.77960e12i	0.137006	+	0.220233i
$874$	3.38388e12			0.196161
$875$	−6.38686e12	−	1.10624e13i	−0.368342	−	0.637987i
$876$	5.11873e12	−	9.21272e12i	0.293693	−	0.528590i
$877$	9.91427e12	−	1.71720e13i	0.565930	−	0.980219i	−0.431033	−	0.902336i	$-0.641851\pi$
$877$	9.91427e12	−	1.71720e13i	0.565930	−	0.980219i	0.996963	−	0.0778829i	$-0.0248160\pi$
$878$	9.59907e12	−	1.66261e13i	0.545135	−	0.944201i
$879$	4.23232e12	−	7.61735e12i	0.239127	−	0.430382i
$880$	5.30053e11	+	9.18078e11i	0.0297952	+	0.0516069i
$881$	9.90161e12			0.553751			0.276875	−	0.960906i	$-0.410701\pi$
$881$	9.90161e12			0.553751			0.276875	+	0.960906i	$0.410701\pi$
$882$	6.87940e12	−	2.26478e11i	0.382773	−	0.0126014i
$883$	1.62458e13			0.899328			0.449664	−	0.893198i	$-0.351544\pi$
$883$	1.62458e13			0.899328			0.449664	+	0.893198i	$0.351544\pi$
$884$	1.54529e11	+	2.67652e11i	0.00851088	+	0.0147413i
$885$	1.30851e12	+	2.18266e12i	0.0717020	+	0.119603i
$886$	−6.25747e12	+	1.08383e13i	−0.341151	+	0.590892i
$887$	−1.24320e13	+	2.15329e13i	−0.674349	+	1.16801i	0.302310	+	0.953210i	$0.402242\pi$
$887$	−1.24320e13	+	2.15329e13i	−0.674349	+	1.16801i	−0.976659	+	0.214797i	$0.931091\pi$
$888$	−7.79794e12	+	1.28324e11i	−0.420844	+	0.00692548i
$889$	−5.14831e12	−	8.91714e12i	−0.276444	−	0.478815i
$890$	−1.10148e13			−0.588465
$891$	3.11108e12	+	4.65234e12i	0.165372	+	0.247299i
$892$	−7.67920e11			−0.0406139
$893$	−3.28314e12	−	5.68657e12i	−0.172766	−	0.299239i
$894$	1.62529e13	−	2.67460e11i	0.850963	−	0.0140036i
$895$	−3.32829e12	+	5.76476e12i	−0.173387	+	0.300315i
$896$	−5.77252e11	+	9.99830e11i	−0.0299212	+	0.0518251i
$897$	1.85358e13	+	3.09187e13i	0.955974	+	1.59461i
$898$	7.79298e12	+	1.34978e13i	0.399908	+	0.692661i
$899$	−4.13430e13			−2.11097
$900$	−3.52174e12	+	1.15940e11i	−0.178923	+	0.00589036i
$901$	1.78959e11			0.00904671
$902$	−2.42843e12	−	4.20617e12i	−0.122151	−	0.211571i
$903$	−8.59615e12	+	1.54714e13i	−0.430239	+	0.774346i
$904$	−2.88782e12	+	5.00185e12i	−0.143817	+	0.249099i
$905$	1.60487e13	−	2.77971e13i	0.795281	−	1.37747i
$906$	−4.94997e12	+	8.90899e12i	−0.244076	+	0.439290i
$907$	−4.66503e12	−	8.08007e12i	−0.228887	−	0.396444i	0.728591	−	0.684949i	$-0.240175\pi$
$907$	−4.66503e12	−	8.08007e12i	−0.228887	−	0.396444i	−0.957479	+	0.288504i	$0.906842\pi$
$908$	1.22391e12			0.0597536
$909$	−1.25329e13	−	2.01463e13i	−0.608857	−	0.978719i
$910$	9.31053e12			0.450078
$911$	1.73247e13	+	3.00072e13i	0.833360	+	1.44342i	0.895359	+	0.445346i	$0.146919\pi$
$911$	1.73247e13	+	3.00072e13i	0.833360	+	1.44342i	−0.0619982	+	0.998076i	$0.519747\pi$
$912$	−4.70183e11	−	7.84290e11i	−0.0225056	−	0.0375405i
$913$	−3.53132e12	+	6.11642e12i	−0.168197	+	0.291326i
$914$	−1.34151e13	+	2.32356e13i	−0.635821	+	1.10127i
$915$	2.44673e12	−	4.02638e10i	0.115396	−	0.00189898i
$916$	−7.65545e12	−	1.32596e13i	−0.359287	−	0.622302i
$917$	−3.01761e12			−0.140929
$918$	−2.39318e11	−	3.70946e11i	−0.0111220	−	0.0172393i
$919$	3.40721e13			1.57572			0.787860	−	0.615855i	$-0.211189\pi$
$919$	3.40721e13			1.57572			0.787860	+	0.615855i	$0.211189\pi$
$920$	−4.87662e12	−	8.44655e12i	−0.224426	−	0.388718i
$921$	8.15708e12	−	1.34234e11i	0.373565	−	0.00614744i
$922$	2.54614e12	−	4.41005e12i	0.116036	−	0.200981i
$923$	3.15376e12	−	5.46247e12i	0.143028	−	0.247732i
$924$	−1.14738e12	−	1.91389e12i	−0.0517826	−	0.0863760i
$925$	4.74530e12	+	8.21911e12i	0.213121	+	0.369136i
$926$	−1.02382e13			−0.457586
$927$	−1.50939e12	+	2.82512e12i	−0.0671339	+	0.125654i
$928$	−4.45624e12			−0.197243
$929$	−1.64478e13	−	2.84885e13i	−0.724500	−	1.25487i	−0.959180	−	0.282797i	$-0.908738\pi$
$929$	−1.64478e13	−	2.84885e13i	−0.724500	−	1.25487i	0.234680	−	0.972073i	$-0.424596\pi$
$930$	−1.18760e13	+	2.13745e13i	−0.520592	+	0.936965i
$931$	1.08685e12	−	1.88248e12i	0.0474128	−	0.0821214i
$932$	7.76875e12	−	1.34559e13i	0.337271	−	0.584171i
$933$	−1.73322e13	+	3.11946e13i	−0.748835	+	1.34776i
$934$	9.66988e12	+	1.67487e13i	0.415777	+	0.720146i
$935$	1.61618e11			0.00691571
$936$	4.59058e12	−	8.59218e12i	0.195491	−	0.365900i
$937$	2.49252e13			1.05636			0.528178	−	0.849134i	$-0.322875\pi$
$937$	2.49252e13			1.05636			0.528178	+	0.849134i	$0.322875\pi$
$938$	−6.57185e12	−	1.13828e13i	−0.277188	−	0.480104i
$939$	−1.00631e13	−	1.67857e13i	−0.422410	−	0.704602i
$940$	−9.46289e12	+	1.63902e13i	−0.395320	+	0.684714i
$941$	−2.02800e13	+	3.51260e13i	−0.843170	+	1.46041i	0.0440303	+	0.999030i	$0.485980\pi$
$941$	−2.02800e13	+	3.51260e13i	−0.843170	+	1.46041i	−0.887201	+	0.461384i	$0.847353\pi$
$942$	2.28756e13	−	3.76445e11i	0.946551	−	0.0155766i
$943$	2.23422e13	+	3.86978e13i	0.920075	+	1.59362i
$944$	−1.06163e12			−0.0435111
$945$	−1.32826e13	+	6.56214e11i	−0.541800	+	0.0267672i
$946$	−6.77985e12			−0.275239
$947$	2.18964e13	+	3.79257e13i	0.884705	+	1.53235i	0.846052	+	0.533101i	$0.178973\pi$
$947$	2.18964e13	+	3.79257e13i	0.884705	+	1.53235i	0.0386531	+	0.999253i	$0.487693\pi$
$948$	−1.90749e13	+	3.13900e11i	−0.767053	+	0.0126227i
$949$	1.77286e13	−	3.07068e13i	0.709537	−	1.22895i
$950$	−5.56386e11	+	9.63689e11i	−0.0221626	+	0.0383867i
$951$	1.76103e13	+	2.93749e13i	0.698161	+	1.16457i
$952$	8.80047e10	+	1.52429e11i	0.00347248	+	0.00601451i
$953$	3.57952e13			1.40575			0.702873	−	0.711316i	$-0.251900\pi$
$953$	3.57952e13			1.40575			0.702873	+	0.711316i	$0.251900\pi$
$954$	−2.97963e12	−	4.78966e12i	−0.116465	−	0.187213i
$955$	1.06702e13			0.415105
$956$	3.72970e12	+	6.46003e12i	0.144415	+	0.250135i
$957$	4.18328e12	−	7.52909e12i	0.161218	−	0.290161i
$958$	1.57267e13	−	2.72394e13i	0.603243	−	1.04485i
$959$	7.86821e11	−	1.36281e12i	0.0300395	−	0.0520299i
$960$	−1.28008e12	+	2.30390e12i	−0.0486426	+	0.0875473i
$961$	−3.40993e13	−	5.90617e13i	−1.28970	−	2.23383i
$962$	−2.62381e13			−0.987745
$963$	−3.32603e13	+	1.09497e12i	−1.24626	+	0.0410283i
$964$	8.90465e12			0.332101
$965$	−1.16753e13	−	2.02222e13i	−0.433407	−	0.750683i
$966$	1.05562e13	+	1.76083e13i	0.390042	+	0.650609i
$967$	−7.10321e12	+	1.23031e13i	−0.261238	+	0.452477i	−0.966571	−	0.256399i	$-0.917464\pi$
$967$	−7.10321e12	+	1.23031e13i	−0.261238	+	0.452477i	0.705333	+	0.708876i	$0.250797\pi$
$968$	−4.40168e12	+	7.62394e12i	−0.161131	+	0.279087i
$969$	−1.39390e11	+	2.29383e9i	−0.00507896	+	8.35802e-5i
$970$	−2.02583e12	−	3.50884e12i	−0.0734734	−	0.127260i
$971$	−4.96761e13			−1.79333			−0.896667	−	0.442706i	$-0.854019\pi$
$971$	−4.96761e13			−1.79333			−0.896667	+	0.442706i	$0.854019\pi$
$972$	−5.94342e12	+	1.25813e13i	−0.213569	+	0.452093i
$973$	2.56903e13			0.918884
$974$	1.12904e13	+	1.95556e13i	0.401972	+	0.696236i
$975$	−1.18530e13	+	1.95054e11i	−0.420056	+	0.00691250i
$976$	−5.10424e11	+	8.84080e11i	−0.0180056	+	0.0311865i
$977$	2.16585e13	−	3.75136e13i	0.760505	−	1.31723i	−0.182086	−	0.983283i	$-0.558285\pi$
$977$	2.16585e13	−	3.75136e13i	0.760505	−	1.31723i	0.942591	−	0.333951i	$-0.108382\pi$
$978$	−8.42485e12	−	1.40531e13i	−0.294468	−	0.491187i
$979$	4.44075e12	+	7.69161e12i	0.154502	+	0.267605i
$980$	−6.26518e12			−0.216978
$981$	−1.07935e13	+	3.55335e11i	−0.372093	+	0.0122497i
$982$	−9.12332e12			−0.313077
$983$	−1.89736e13	−	3.28632e13i	−0.648125	−	1.12259i	−0.983570	−	0.180526i	$-0.942220\pi$
$983$	−1.89736e13	−	3.28632e13i	−0.648125	−	1.12259i	0.335445	−	0.942060i	$-0.391113\pi$
$984$	5.86468e12	−	1.05553e13i	0.199419	−	0.358915i
$985$	−7.93121e12	+	1.37373e13i	−0.268458	+	0.464983i
$986$	−3.39687e11	+	5.88354e11i	−0.0114454	+	0.0198241i
$987$	1.93486e13	−	3.48237e13i	0.648966	−	1.16801i
$988$	−1.53821e12	−	2.66425e12i	−0.0513580	−	0.0889547i
$989$	6.23764e13			2.07318
$990$	−2.69091e12	−	4.32555e12i	−0.0890308	−	0.143114i
$991$	5.23655e12			0.172470			0.0862351	−	0.996275i	$-0.472516\pi$
$991$	5.23655e12			0.172470			0.0862351	+	0.996275i	$0.472516\pi$
$992$	−5.10039e12	−	8.83413e12i	−0.167225	−	0.289642i
$993$	1.41425e13	+	2.35903e13i	0.461587	+	0.769950i
$994$	1.79608e12	−	3.11089e12i	0.0583560	−	0.101076i
$995$	−9.45818e12	+	1.63820e13i	−0.305917	+	0.529864i
$996$	−1.75567e13	+	2.88916e11i	−0.565297	+	0.00930261i
$997$	−9.25267e12	−	1.60261e13i	−0.296578	−	0.513688i	0.678773	−	0.734348i	$-0.262512\pi$
$997$	−9.25267e12	−	1.60261e13i	−0.296578	−	0.513688i	−0.975351	+	0.220660i	$0.929179\pi$
$998$	−3.93090e12			−0.125431
$999$	3.74318e13	−	1.84928e12i	1.18904	−	0.0587434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.10.c.a.13.4	yes	8
3.2	odd	2		54.10.c.a.37.4		8
9.2	odd	6		54.10.c.a.19.4		8
9.4	even	3		162.10.a.e.1.4		4
9.5	odd	6		162.10.a.h.1.1		4
9.7	even	3	inner	18.10.c.a.7.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.10.c.a.7.4	✓	8	9.7	even	3	inner
18.10.c.a.13.4	yes	8	1.1	even	1	trivial
54.10.c.a.19.4		8	9.2	odd	6
54.10.c.a.37.4		8	3.2	odd	2
162.10.a.e.1.4		4	9.4	even	3
162.10.a.h.1.1		4	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(140.277 - 2.30842i) q^{3} +(-128.000 + 221.703i) q^{4} +(-559.872 + 969.728i) q^{5} +(1154.20 + 1925.27i) q^{6} +(2150.43 + 3724.66i) q^{7} -4096.00 q^{8} +(19672.3 - 647.638i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(140.277 - 2.30842i) q^{3} +(-128.000 + 221.703i) q^{4} +(-559.872 + 969.728i) q^{5} +(1154.20 + 1925.27i) q^{6} +(2150.43 + 3724.66i) q^{7} -4096.00 q^{8} +(19672.3 - 647.638i) q^{9} -17915.9 q^{10} +(7223.04 + 12510.7i) q^{11} +(-17443.7 + 31395.3i) q^{12} +(-60415.7 + 104643. i) q^{13} +(-34406.9 + 59594.5i) q^{14} +(-76298.8 + 137323. i) q^{15} +(-32768.0 - 56755.8i) q^{16} -9991.26 q^{17} +(166353. + 267407. i) q^{18} +99454.6 q^{19} +(-143327. - 248250. i) q^{20} +(310254. + 517520. i) q^{21} +(-115569. + 200171. i) q^{22} +(1.06326e6 - 1.84162e6i) q^{23} +(-574575. + 9455.30i) q^{24} +(349648. + 605608. i) q^{25} -1.93330e6 q^{26} +(2.75808e6 - 136261. i) q^{27} -1.10102e6 q^{28} +(-2.12490e6 - 3.68043e6i) q^{29} +(-2.51319e6 + 41357.5i) q^{30} +(4.86411e6 - 8.42488e6i) q^{31} +(524288. - 908093. i) q^{32} +(1.04211e6 + 1.73829e6i) q^{33} +(-79930.1 - 138443. i) q^{34} -4.81587e6 q^{35} +(-2.37448e6 + 4.44431e6i) q^{36} +1.35717e7 q^{37} +(795637. + 1.37808e6i) q^{38} +(-8.23338e6 + 1.48185e7i) q^{39} +(2.29324e6 - 3.97200e6i) q^{40} +(-1.05064e7 + 1.81977e7i) q^{41} +(-4.68893e6 + 8.43917e6i) q^{42} +(1.46663e7 + 2.54028e7i) q^{43} -3.69820e6 q^{44} +(-1.03860e7 + 1.94394e7i) q^{45} +3.40244e7 q^{46} +(-3.30115e7 - 5.71775e7i) q^{47} +(-4.72762e6 - 7.88590e6i) q^{48} +(1.09281e7 - 1.89280e7i) q^{49} +(-5.59437e6 + 9.68973e6i) q^{50} +(-1.40154e6 + 23064.0i) q^{51} +(-1.54664e7 - 2.67886e7i) q^{52} -1.79115e7 q^{53} +(2.39528e7 + 3.71271e7i) q^{54} -1.61759e7 q^{55} +(-8.80817e6 - 1.52562e7i) q^{56} +(1.39512e7 - 229583. i) q^{57} +(3.39984e7 - 5.88869e7i) q^{58} +(8.09962e6 - 1.40290e7i) q^{59} +(-2.06786e7 - 3.44930e7i) q^{60} +(-7.78845e6 - 1.34900e7i) q^{61} +1.55651e8 q^{62} +(4.47163e7 + 7.18800e7i) q^{63} +1.67772e7 q^{64} +(-6.76502e7 - 1.17174e8i) q^{65} +(-1.57496e7 + 2.83462e7i) q^{66} +(-9.55019e7 + 1.65414e8i) q^{67} +(1.27888e6 - 2.21509e6i) q^{68} +(1.44900e8 - 2.60792e8i) q^{69} +(-3.85270e7 - 6.67307e7i) q^{70} -5.22010e7 q^{71} +(-8.05779e7 + 2.65272e6i) q^{72} -2.93443e8 q^{73} +(1.08573e8 + 1.88054e8i) q^{74} +(5.04456e7 + 8.41458e7i) q^{75} +(-1.27302e7 + 2.20493e7i) q^{76} +(-3.10653e7 + 5.38067e7i) q^{77} +(-2.71198e8 + 4.46288e6i) q^{78} +(2.65586e8 + 4.60009e8i) q^{79} +7.33836e7 q^{80} +(3.86582e8 - 2.54811e7i) q^{81} -3.36206e8 q^{82} +(2.44448e8 + 4.23397e8i) q^{83} +(-1.54448e8 + 2.54162e6i) q^{84} +(5.59383e6 - 9.68880e6i) q^{85} +(-2.34661e8 + 4.06444e8i) q^{86} +(-3.06571e8 - 5.11375e8i) q^{87} +(-2.95856e7 - 5.12437e7i) q^{88} +6.14804e8 q^{89} +(-3.52448e8 + 1.16030e7i) q^{90} -5.19679e8 q^{91} +(2.72195e8 + 4.71455e8i) q^{92} +(6.62875e8 - 1.19305e9i) q^{93} +(5.28183e8 - 9.14841e8i) q^{94} +(-5.56819e7 + 9.64439e7i) q^{95} +(7.14493e7 - 1.28595e8i) q^{96} +(1.13074e8 + 1.95850e8i) q^{97} +3.49699e8 q^{98} +(1.50196e8 + 2.41436e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{2} - 81 q^{3} - 1024 q^{4} + 171 q^{5} + 1440 q^{6} + 7135 q^{7} - 32768 q^{8} + 8937 q^{9}+O(q^{10}) \) 8 * q + 64 * q^2 - 81 * q^3 - 1024 * q^4 + 171 * q^5 + 1440 * q^6 + 7135 * q^7 - 32768 * q^8 + 8937 * q^9	\( 8 q + 64 q^{2} - 81 q^{3} - 1024 q^{4} + 171 q^{5} + 1440 q^{6} + 7135 q^{7} - 32768 q^{8} + 8937 q^{9} + 5472 q^{10} - 26130 q^{11} + 43776 q^{12} - 4163 q^{13} - 114160 q^{14} - 665739 q^{15} - 262144 q^{16} + 1098510 q^{17} + 310608 q^{18} - 436382 q^{19} + 43776 q^{20} - 1515717 q^{21} + 418080 q^{22} - 289383 q^{23} + 331776 q^{24} + 2947937 q^{25} - 133216 q^{26} + 6980904 q^{27} - 3653120 q^{28} - 601707 q^{29} - 10990080 q^{30} + 5671315 q^{31} + 4194304 q^{32} - 551556 q^{33} + 8788080 q^{34} + 29787930 q^{35} + 2681856 q^{36} - 38737148 q^{37} - 3491056 q^{38} - 44596503 q^{39} - 700416 q^{40} - 18418410 q^{41} + 5424336 q^{42} + 35096140 q^{43} + 13378560 q^{44} + 69046263 q^{45} - 9260256 q^{46} - 79830825 q^{47} - 5898240 q^{48} - 40540299 q^{49} - 47166992 q^{50} - 107332533 q^{51} - 1065728 q^{52} + 330697236 q^{53} + 60357312 q^{54} + 56528442 q^{55} - 29224960 q^{56} - 118521549 q^{57} + 9627312 q^{58} - 90704166 q^{59} - 5412096 q^{60} - 122811677 q^{61} + 181482080 q^{62} + 26641197 q^{63} + 134217728 q^{64} - 116600103 q^{65} - 32628528 q^{66} + 221601736 q^{67} - 140609280 q^{68} + 162496665 q^{69} + 238303440 q^{70} + 276408240 q^{71} - 36605952 q^{72} - 988917014 q^{73} - 309897184 q^{74} + 203871807 q^{75} + 55856896 q^{76} - 548139525 q^{77} - 355557600 q^{78} + 592840885 q^{79} - 22413312 q^{80} + 1009312893 q^{81} - 589389120 q^{82} - 478410747 q^{83} + 474812928 q^{84} + 1468792818 q^{85} - 561538240 q^{86} - 2118569607 q^{87} + 107028480 q^{88} + 875519952 q^{89} + 200286432 q^{90} - 3695513062 q^{91} - 74082048 q^{92} + 2631169593 q^{93} + 1277293200 q^{94} + 813906756 q^{95} - 179306496 q^{96} + 2679512242 q^{97} - 1297289568 q^{98} - 46472697 q^{99}+O(q^{100}) \) 8 * q + 64 * q^2 - 81 * q^3 - 1024 * q^4 + 171 * q^5 + 1440 * q^6 + 7135 * q^7 - 32768 * q^8 + 8937 * q^9 + 5472 * q^10 - 26130 * q^11 + 43776 * q^12 - 4163 * q^13 - 114160 * q^14 - 665739 * q^15 - 262144 * q^16 + 1098510 * q^17 + 310608 * q^18 - 436382 * q^19 + 43776 * q^20 - 1515717 * q^21 + 418080 * q^22 - 289383 * q^23 + 331776 * q^24 + 2947937 * q^25 - 133216 * q^26 + 6980904 * q^27 - 3653120 * q^28 - 601707 * q^29 - 10990080 * q^30 + 5671315 * q^31 + 4194304 * q^32 - 551556 * q^33 + 8788080 * q^34 + 29787930 * q^35 + 2681856 * q^36 - 38737148 * q^37 - 3491056 * q^38 - 44596503 * q^39 - 700416 * q^40 - 18418410 * q^41 + 5424336 * q^42 + 35096140 * q^43 + 13378560 * q^44 + 69046263 * q^45 - 9260256 * q^46 - 79830825 * q^47 - 5898240 * q^48 - 40540299 * q^49 - 47166992 * q^50 - 107332533 * q^51 - 1065728 * q^52 + 330697236 * q^53 + 60357312 * q^54 + 56528442 * q^55 - 29224960 * q^56 - 118521549 * q^57 + 9627312 * q^58 - 90704166 * q^59 - 5412096 * q^60 - 122811677 * q^61 + 181482080 * q^62 + 26641197 * q^63 + 134217728 * q^64 - 116600103 * q^65 - 32628528 * q^66 + 221601736 * q^67 - 140609280 * q^68 + 162496665 * q^69 + 238303440 * q^70 + 276408240 * q^71 - 36605952 * q^72 - 988917014 * q^73 - 309897184 * q^74 + 203871807 * q^75 + 55856896 * q^76 - 548139525 * q^77 - 355557600 * q^78 + 592840885 * q^79 - 22413312 * q^80 + 1009312893 * q^81 - 589389120 * q^82 - 478410747 * q^83 + 474812928 * q^84 + 1468792818 * q^85 - 561538240 * q^86 - 2118569607 * q^87 + 107028480 * q^88 + 875519952 * q^89 + 200286432 * q^90 - 3695513062 * q^91 - 74082048 * q^92 + 2631169593 * q^93 + 1277293200 * q^94 + 813906756 * q^95 - 179306496 * q^96 + 2679512242 * q^97 - 1297289568 * q^98 - 46472697 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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