LMFDB - Embedded newform 18.10.c.a.13.1

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			13.1
Root			$11.6557 + 20.1883i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.10.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(-128.927 - 55.3251i) q^{3} +(-128.000 + 221.703i) q^{4} +(897.758 - 1554.96i) q^{5} +(-264.808 - 2229.06i) q^{6} +(5590.83 + 9683.61i) q^{7} -4096.00 q^{8} +(13561.3 + 14265.8i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(-128.927 - 55.3251i) q^{3} +(-128.000 + 221.703i) q^{4} +(897.758 - 1554.96i) q^{5} +(-264.808 - 2229.06i) q^{6} +(5590.83 + 9683.61i) q^{7} -4096.00 q^{8} +(13561.3 + 14265.8i) q^{9} +28728.3 q^{10} +(9213.10 + 15957.6i) q^{11} +(28768.3 - 21501.8i) q^{12} +(-10588.5 + 18339.7i) q^{13} +(-89453.3 + 154938. i) q^{14} +(-201774. + 150808. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +660849. q^{17} +(-89182.3 + 302037. i) q^{18} +522089. q^{19} +(229826. + 398070. i) q^{20} +(-185062. - 1.55779e6i) q^{21} +(-147410. + 255321. i) q^{22} +(-524295. + 908105. i) q^{23} +(528084. + 226612. i) q^{24} +(-635377. - 1.10051e6i) q^{25} -338831. q^{26} +(-959156. - 2.58952e6i) q^{27} -2.86251e6 q^{28} +(-1.30249e6 - 2.25598e6i) q^{29} +(-3.70384e6 - 1.58939e6i) q^{30} +(26962.3 - 46700.1i) q^{31} +(524288. - 908093. i) q^{32} +(-304963. - 2.56707e6i) q^{33} +(5.28679e6 + 9.15699e6i) q^{34} +2.00769e7 q^{35} +(-4.89860e6 + 1.18055e6i) q^{36} -1.93749e7 q^{37} +(4.17672e6 + 7.23428e6i) q^{38} +(2.37978e6 - 1.77868e6i) q^{39} +(-3.67722e6 + 6.36913e6i) q^{40} +(648885. - 1.12390e6i) q^{41} +(2.01049e7 - 1.50266e7i) q^{42} +(7.35308e6 + 1.27359e7i) q^{43} -4.71711e6 q^{44} +(3.43575e7 - 8.28004e6i) q^{45} -1.67774e7 q^{46} +(1.53291e7 + 2.65507e7i) q^{47} +(1.08465e6 + 9.13024e6i) q^{48} +(-4.23380e7 + 7.33316e7i) q^{49} +(1.01660e7 - 1.76081e7i) q^{50} +(-8.52012e7 - 3.65615e7i) q^{51} +(-2.71064e6 - 4.69497e6i) q^{52} +5.86557e7 q^{53} +(2.82082e7 - 3.40066e7i) q^{54} +3.30845e7 q^{55} +(-2.29001e7 - 3.96641e7i) q^{56} +(-6.73114e7 - 2.88847e7i) q^{57} +(2.08398e7 - 3.60957e7i) q^{58} +(-1.14839e7 + 1.98906e7i) q^{59} +(-7.60747e6 - 6.40371e7i) q^{60} +(-9.03978e7 - 1.56574e8i) q^{61} +862794. q^{62} +(-6.23254e7 + 2.11080e8i) q^{63} +1.67772e7 q^{64} +(1.90117e7 + 3.29293e7i) q^{65} +(3.31307e7 - 2.47623e7i) q^{66} +(1.18973e8 - 2.06067e8i) q^{67} +(-8.45886e7 + 1.46512e8i) q^{68} +(1.17837e8 - 8.80725e7i) q^{69} +(1.60615e8 + 2.78193e8i) q^{70} +4.73186e7 q^{71} +(-5.55470e7 - 5.84326e7i) q^{72} -7.05287e7 q^{73} +(-1.55000e8 - 2.68467e8i) q^{74} +(2.10316e7 + 1.77037e8i) q^{75} +(-6.68275e7 + 1.15749e8i) q^{76} +(-1.03018e8 + 1.78432e8i) q^{77} +(4.36844e7 + 1.87458e7i) q^{78} +(1.28832e8 + 2.23143e8i) q^{79} -1.17671e8 q^{80} +(-1.96045e7 + 3.86924e8i) q^{81} +2.07643e7 q^{82} +(-1.46745e8 - 2.54170e8i) q^{83} +(3.69054e8 + 1.58368e8i) q^{84} +(5.93282e8 - 1.02760e9i) q^{85} +(-1.17649e8 + 2.03774e8i) q^{86} +(4.31137e7 + 3.62917e8i) q^{87} +(-3.77368e7 - 6.53621e7i) q^{88} +1.41522e8 q^{89} +(3.89592e8 + 4.09831e8i) q^{90} -2.36793e8 q^{91} +(-1.34219e8 - 2.32475e8i) q^{92} +(-6.05985e6 + 4.52920e6i) q^{93} +(-2.45265e8 + 4.24812e8i) q^{94} +(4.68710e8 - 8.11830e8i) q^{95} +(-1.17835e8 + 8.80713e7i) q^{96} +(-1.64320e8 - 2.84610e8i) q^{97} -1.35482e9 q^{98} +(-1.02706e8 + 3.47837e8i) 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
$3$	−128.927	−	55.3251i	−0.918962	−	0.394345i
$3$	−128.927	−	55.3251i	−0.918962	−	0.394345i
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	897.758	−	1554.96i	0.642383	−	1.11264i	−0.342516	−	0.939512i	$-0.611279\pi$
$5$	897.758	−	1554.96i	0.642383	−	1.11264i	0.984899	−	0.173129i	$-0.0553877\pi$
$6$	−264.808	−	2229.06i	−0.0834162	−	0.702169i
$7$	5590.83	+	9683.61i	0.880107	+	1.52439i	0.851221	+	0.524807i	$0.175863\pi$
$7$	5590.83	+	9683.61i	0.880107	+	1.52439i	0.0288856	+	0.999583i	$0.490804\pi$
$8$	−4096.00			−0.353553
$9$	13561.3	+	14265.8i	0.688984	+	0.724777i
$10$	28728.3			0.908467
$11$	9213.10	+	15957.6i	0.189731	+	0.328624i	0.945161	−	0.326606i	$-0.105905\pi$
$11$	9213.10	+	15957.6i	0.189731	+	0.328624i	−0.755429	+	0.655230i	$0.772572\pi$
$12$	28768.3	−	21501.8i	0.400497	−	0.299336i
$13$	−10588.5	+	18339.7i	−0.102822	+	0.178094i	−0.912846	−	0.408303i	$-0.866121\pi$
$13$	−10588.5	+	18339.7i	−0.102822	+	0.178094i	0.810024	+	0.586397i	$0.199454\pi$
$14$	−89453.3	+	154938.i	−0.622330	+	1.07791i
$15$	−201774.	+	150808.i	−1.02909	+	0.769154i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	660849.			1.91903			0.959515	−	0.281656i	$-0.0908838\pi$
$17$	660849.			1.91903			0.959515	+	0.281656i	$0.0908838\pi$
$18$	−89182.3	+	302037.i	−0.200241	+	0.678162i
$19$	522089.			0.919081			0.459540	−	0.888157i	$-0.348014\pi$
$19$	522089.			0.919081			0.459540	+	0.888157i	$0.348014\pi$
$20$	229826.	+	398070.i	0.321192	+	0.556320i
$21$	−185062.	−	1.55779e6i	−0.207649	−	1.74792i
$22$	−147410.	+	255321.i	−0.134160	+	0.232372i
$23$	−524295.	+	908105.i	−0.390661	+	0.676645i	−0.992537	−	0.121945i	$-0.961087\pi$
$23$	−524295.	+	908105.i	−0.390661	+	0.676645i	0.601876	+	0.798590i	$0.294420\pi$
$24$	528084.	+	226612.i	0.324902	+	0.139422i
$25$	−635377.	−	1.10051e6i	−0.325313	−	0.563459i
$26$	−338831.			−0.145413
$27$	−959156.	−	2.58952e6i	−0.347338	−	0.937740i
$28$	−2.86251e6			−0.880107
$29$	−1.30249e6	−	2.25598e6i	−0.341966	−	0.592303i	0.642831	−	0.766008i	$-0.277760\pi$
$29$	−1.30249e6	−	2.25598e6i	−0.341966	−	0.592303i	−0.984798	+	0.173705i	$0.944426\pi$
$30$	−3.70384e6	−	1.58939e6i	−0.834847	−	0.358250i
$31$	26962.3	−	46700.1i	0.00524360	−	0.00908218i	−0.863392	−	0.504534i	$-0.831664\pi$
$31$	26962.3	−	46700.1i	0.00524360	−	0.00908218i	0.868635	+	0.495452i	$0.164998\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	−304963.	−	2.56707e6i	−0.0447645	−	0.376813i
$34$	5.28679e6	+	9.15699e6i	0.678480	+	1.17516i
$35$	2.00769e7			2.26146
$36$	−4.89860e6	+	1.18055e6i	−0.486083	+	0.117145i
$37$	−1.93749e7			−1.69955			−0.849773	−	0.527150i	$-0.823261\pi$
$37$	−1.93749e7			−1.69955			−0.849773	+	0.527150i	$0.823261\pi$
$38$	4.17672e6	+	7.23428e6i	0.324944	+	0.562820i
$39$	2.37978e6	−	1.77868e6i	0.164720	−	0.123114i
$40$	−3.67722e6	+	6.36913e6i	−0.227117	+	0.393378i
$41$	648885.	−	1.12390e6i	0.0358625	−	0.0621156i	−0.847537	−	0.530736i	$-0.821916\pi$
$41$	648885.	−	1.12390e6i	0.0358625	−	0.0621156i	0.883400	+	0.468621i	$0.155249\pi$
$42$	2.01049e7	−	1.50266e7i	0.996965	−	0.745143i
$43$	7.35308e6	+	1.27359e7i	0.327990	+	0.568096i	0.982113	−	0.188293i	$-0.0602953\pi$
$43$	7.35308e6	+	1.27359e7i	0.327990	+	0.568096i	−0.654123	+	0.756388i	$0.726962\pi$
$44$	−4.71711e6			−0.189731
$45$	3.43575e7	−	8.28004e6i	1.24901	−	0.301007i
$46$	−1.67774e7			−0.552478
$47$	1.53291e7	+	2.65507e7i	0.458222	+	0.793663i	0.998867	−	0.0475872i	$-0.0151532\pi$
$47$	1.53291e7	+	2.65507e7i	0.458222	+	0.793663i	−0.540645	+	0.841251i	$0.681820\pi$
$48$	1.08465e6	+	9.13024e6i	0.0294921	+	0.248254i
$49$	−4.23380e7	+	7.33316e7i	−1.04918	+	1.81723i
$50$	1.01660e7	−	1.76081e7i	0.230031	−	0.398425i
$51$	−8.52012e7	−	3.65615e7i	−1.76352	−	0.756761i
$52$	−2.71064e6	−	4.69497e6i	−0.0514112	−	0.0890468i
$53$	5.86557e7			1.02110			0.510551	−	0.859848i	$-0.329442\pi$
$53$	5.86557e7			1.02110			0.510551	+	0.859848i	$0.329442\pi$
$54$	2.82082e7	−	3.40066e7i	0.451444	−	0.544241i
$55$	3.30845e7			0.487521
$56$	−2.29001e7	−	3.96641e7i	−0.311165	−	0.538953i
$57$	−6.73114e7	−	2.88847e7i	−0.844601	−	0.362435i
$58$	2.08398e7	−	3.60957e7i	0.241807	−	0.418821i
$59$	−1.14839e7	+	1.98906e7i	−0.123383	+	0.213705i	−0.921100	−	0.389327i	$-0.872708\pi$
$59$	−1.14839e7	+	1.98906e7i	−0.123383	+	0.213705i	0.797717	+	0.603032i	$0.206041\pi$
$60$	−7.60747e6	−	6.40371e7i	−0.0757809	−	0.637898i
$61$	−9.03978e7	−	1.56574e8i	−0.835937	−	1.44789i	−0.893265	−	0.449531i	$-0.851591\pi$
$61$	−9.03978e7	−	1.56574e8i	−0.835937	−	1.44789i	0.0573274	−	0.998355i	$-0.481742\pi$
$62$	862794.			0.00741557
$63$	−6.23254e7	+	2.11080e8i	−0.498463	+	1.68816i
$64$	1.67772e7			0.125000
$65$	1.90117e7	+	3.29293e7i	0.132103	+	0.228809i
$66$	3.31307e7	−	2.47623e7i	0.214923	−	0.160636i
$67$	1.18973e8	−	2.06067e8i	0.721294	−	1.24932i	−0.239188	−	0.970973i	$-0.576881\pi$
$67$	1.18973e8	−	2.06067e8i	0.721294	−	1.24932i	0.960481	−	0.278344i	$-0.0897855\pi$
$68$	−8.45886e7	+	1.46512e8i	−0.479758	+	0.830965i
$69$	1.17837e8	−	8.80725e7i	0.625834	−	0.467756i
$70$	1.60615e8	+	2.78193e8i	0.799548	+	1.38486i
$71$	4.73186e7			0.220988			0.110494	−	0.993877i	$-0.464757\pi$
$71$	4.73186e7			0.220988			0.110494	+	0.993877i	$0.464757\pi$
$72$	−5.55470e7	−	5.84326e7i	−0.243593	−	0.256247i
$73$	−7.05287e7			−0.290679			−0.145339	−	0.989382i	$-0.546427\pi$
$73$	−7.05287e7			−0.290679			−0.145339	+	0.989382i	$0.546427\pi$
$74$	−1.55000e8	−	2.68467e8i	−0.600880	−	1.04075i
$75$	2.10316e7	+	1.77037e8i	0.0767532	+	0.646083i
$76$	−6.68275e7	+	1.15749e8i	−0.229770	+	0.397974i
$77$	−1.03018e8	+	1.78432e8i	−0.333967	+	0.578448i
$78$	4.36844e7	+	1.87458e7i	0.133629	+	0.0573428i
$79$	1.28832e8	+	2.23143e8i	0.372136	+	0.644558i	0.989894	−	0.141810i	$-0.0452922\pi$
$79$	1.28832e8	+	2.23143e8i	0.372136	+	0.644558i	−0.617758	+	0.786368i	$0.711959\pi$
$80$	−1.17671e8			−0.321192
$81$	−1.96045e7	+	3.86924e8i	−0.0506028	+	0.998719i
$82$	2.07643e7			0.0507172
$83$	−1.46745e8	−	2.54170e8i	−0.339401	−	0.587860i	0.644919	−	0.764251i	$-0.276891\pi$
$83$	−1.46745e8	−	2.54170e8i	−0.339401	−	0.587860i	−0.984320	+	0.176391i	$0.943558\pi$
$84$	3.69054e8	+	1.58368e8i	0.808785	+	0.347066i
$85$	5.93282e8	−	1.02760e9i	1.23275	−	2.13519i
$86$	−1.17649e8	+	2.03774e8i	−0.231924	+	0.401704i
$87$	4.31137e7	+	3.62917e8i	0.0806823	+	0.679157i
$88$	−3.77368e7	−	6.53621e7i	−0.0670801	−	0.116186i
$89$	1.41522e8			0.239093			0.119547	−	0.992829i	$-0.461856\pi$
$89$	1.41522e8			0.239093			0.119547	+	0.992829i	$0.461856\pi$
$90$	3.89592e8	+	4.09831e8i	0.625919	+	0.658436i
$91$	−2.36793e8			−0.361979
$92$	−1.34219e8	−	2.32475e8i	−0.195331	−	0.338322i
$93$	−6.05985e6	+	4.52920e6i	−0.00840018	+	0.00627839i
$94$	−2.45265e8	+	4.24812e8i	−0.324012	+	0.561205i
$95$	4.68710e8	−	8.11830e8i	0.590402	−	1.02261i
$96$	−1.17835e8	+	8.80713e7i	−0.141597	+	0.105831i
$97$	−1.64320e8	−	2.84610e8i	−0.188459	−	0.326420i	0.756278	−	0.654251i	$-0.227016\pi$
$97$	−1.64320e8	−	2.84610e8i	−0.188459	−	0.326420i	−0.944737	+	0.327830i	$0.893683\pi$
$98$	−1.35482e9			−1.48376
$99$	−1.02706e8	+	3.47837e8i	−0.107457	+	0.363929i
$100$	3.25313e8			0.325313
$101$	−2.47471e8	−	4.28632e8i	−0.236635	−	0.409863i	0.723112	−	0.690731i	$-0.242711\pi$
$101$	−2.47471e8	−	4.28632e8i	−0.236635	−	0.409863i	−0.959746	+	0.280868i	$0.909378\pi$
$102$	−1.74998e8	−	1.47307e9i	−0.160078	−	1.34748i
$103$	1.99528e8	−	3.45593e8i	0.174677	−	0.302550i	−0.765372	−	0.643588i	$-0.777445\pi$
$103$	1.99528e8	−	3.45593e8i	0.174677	−	0.302550i	0.940050	+	0.341038i	$0.110778\pi$
$104$	4.33703e7	−	7.51196e7i	0.0363532	−	0.0629656i
$105$	−2.58845e9	−	1.11075e9i	−2.07820	−	0.891798i
$106$	4.69246e8	+	8.12757e8i	0.361014	+	0.625294i
$107$	−1.26980e8			−0.0936502			−0.0468251	−	0.998903i	$-0.514910\pi$
$107$	−1.26980e8			−0.0936502			−0.0468251	+	0.998903i	$0.514910\pi$
$108$	6.96875e8	+	1.18811e8i	0.492888	+	0.0840333i
$109$	−2.21053e9			−1.49995			−0.749974	−	0.661467i	$-0.769934\pi$
$109$	−2.21053e9			−1.49995			−0.749974	+	0.661467i	$0.769934\pi$
$110$	2.64676e8	+	4.58433e8i	0.172365	+	0.298544i
$111$	2.49795e9	+	1.07192e9i	1.56182	+	0.670207i
$112$	3.66401e8	−	6.34625e8i	0.220027	−	0.381097i
$113$	−3.33955e8	+	5.78427e8i	−0.192679	+	0.333730i	−0.946137	−	0.323766i	$-0.895051\pi$
$113$	−3.33955e8	+	5.78427e8i	−0.192679	+	0.333730i	0.753458	+	0.657496i	$0.228384\pi$
$114$	−1.38253e8	−	1.16377e9i	−0.0766662	−	0.645350i
$115$	9.41380e8	+	1.63052e9i	0.501908	+	0.869331i
$116$	6.66875e8			0.341966
$117$	−4.05224e8	+	9.76576e7i	−0.199921	+	0.0481803i
$118$	−3.67484e8			−0.174489
$119$	3.69470e9	+	6.39940e9i	1.68895	+	2.92535i
$120$	8.26465e8	−	6.17709e8i	0.363839	−	0.271937i
$121$	1.00921e9	−	1.74801e9i	0.428004	−	0.741325i
$122$	1.44637e9	−	2.50518e9i	0.591097	−	1.02381i
$123$	−1.45839e8	+	1.09001e8i	−0.0574512	+	0.0429397i
$124$	6.90235e6	+	1.19552e7i	0.00262180	+	0.00454109i
$125$	1.22521e9			0.448864
$126$	−3.42341e9	+	8.25030e8i	−1.21002	+	0.291610i
$127$	−2.12304e9			−0.724171			−0.362085	−	0.932145i	$-0.617935\pi$
$127$	−2.12304e9			−0.724171			−0.362085	+	0.932145i	$0.617935\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	−2.43394e8	−	2.04881e9i	−0.0773849	−	0.651400i
$130$	−3.04188e8	+	5.26869e8i	−0.0934108	+	0.161792i
$131$	2.48713e7	−	4.30783e7i	0.00737865	−	0.0127802i	−0.862313	−	0.506376i	$-0.830985\pi$
$131$	2.48713e7	−	4.30783e7i	0.00737865	−	0.0127802i	0.869691	+	0.493596i	$0.164318\pi$
$132$	6.08162e8	+	2.60974e8i	0.174356	+	0.0748196i
$133$	2.91892e9	+	5.05571e9i	0.808889	+	1.40104i
$134$	3.80714e9			1.02006
$135$	−4.88770e9	−	8.33312e8i	−1.26649	−	0.215926i
$136$	−2.70684e9			−0.678480
$137$	−3.38969e9	−	5.87112e9i	−0.822087	−	1.42390i	−0.904125	−	0.427267i	$-0.859476\pi$
$137$	−3.38969e9	−	5.87112e9i	−0.822087	−	1.42390i	0.0820385	−	0.996629i	$-0.473857\pi$
$138$	2.16306e9	+	9.28213e8i	0.507707	+	0.217867i
$139$	−2.37656e9	+	4.11632e9i	−0.539985	+	0.935282i	0.458919	+	0.888478i	$0.348237\pi$
$139$	−2.37656e9	+	4.11632e9i	−0.539985	+	0.935282i	−0.998904	+	0.0468036i	$0.985097\pi$
$140$	−2.56984e9	+	4.45109e9i	−0.565366	+	0.979243i
$141$	−5.07408e8	−	4.27119e9i	−0.108111	−	0.910044i
$142$	3.78549e8	+	6.55666e8i	0.0781312	+	0.135327i
$143$	−3.90210e8			−0.0780344
$144$	3.65291e8	−	1.23714e9i	0.0707958	−	0.239766i
$145$	−4.67728e9			−0.878694
$146$	−5.64230e8	−	9.77275e8i	−0.102770	−	0.178004i
$147$	9.51559e9	−	7.11206e9i	1.68077	−	1.25623i
$148$	2.47999e9	−	4.29547e9i	0.424886	−	0.735925i
$149$	3.60147e9	−	6.23793e9i	0.598606	−	1.03682i	−0.394421	−	0.918930i	$-0.629055\pi$
$149$	3.60147e9	−	6.23793e9i	0.598606	−	1.03682i	0.993027	−	0.117887i	$-0.0376120\pi$
$150$	−2.28484e9	+	1.70772e9i	−0.368507	+	0.275426i
$151$	−2.48682e9	−	4.30729e9i	−0.389267	−	0.674230i	0.603084	−	0.797678i	$-0.293938\pi$
$151$	−2.48682e9	−	4.30729e9i	−0.389267	−	0.674230i	−0.992351	+	0.123448i	$0.960605\pi$
$152$	−2.13848e9			−0.324944
$153$	8.96195e9	+	9.42752e9i	1.32218	+	1.39087i
$154$	−3.29657e9			−0.472301
$155$	−4.84112e7	−	8.38507e7i	−0.00673680	−	0.0116685i
$156$	8.97250e7	+	7.55275e8i	0.0121298	+	0.102104i
$157$	3.46761e8	−	6.00607e8i	0.0455493	−	0.0788936i	−0.842352	−	0.538928i	$-0.818830\pi$
$157$	3.46761e8	−	6.00607e8i	0.0455493	−	0.0788936i	0.887901	+	0.460034i	$0.152163\pi$
$158$	−2.06131e9	+	3.57029e9i	−0.263140	+	0.455771i
$159$	−7.56229e9	−	3.24513e9i	−0.938354	−	0.402666i
$160$	−9.41368e8	−	1.63050e9i	−0.113558	−	0.196689i
$161$	−1.17250e10			−1.37529
$162$	−5.51821e9	+	2.82374e9i	−0.629479	+	0.322113i
$163$	7.96784e9			0.884090			0.442045	−	0.896993i	$-0.354253\pi$
$163$	7.96784e9			0.884090			0.442045	+	0.896993i	$0.354253\pi$
$164$	1.66114e8	+	2.87719e8i	0.0179312	+	0.0310578i
$165$	−4.26548e9	−	1.83041e9i	−0.448013	−	0.192251i
$166$	2.34793e9	−	4.06673e9i	0.239993	−	0.415680i
$167$	3.06914e9	−	5.31590e9i	0.305346	−	0.528875i	−0.671992	−	0.740558i	$-0.734561\pi$
$167$	3.06914e9	−	5.31590e9i	0.305346	−	0.528875i	0.977338	+	0.211683i	$0.0678945\pi$
$168$	7.58014e8	+	6.38071e9i	0.0734151	+	0.617984i
$169$	5.07802e9	+	8.79539e9i	0.478855	+	0.829401i
$170$	1.89850e10			1.74338
$171$	7.08020e9	+	7.44801e9i	0.633232	+	0.666129i
$172$	−3.76477e9			−0.327990
$173$	1.87019e9	+	3.23926e9i	0.158737	+	0.274940i	0.934413	−	0.356190i	$-0.115925\pi$
$173$	1.87019e9	+	3.23926e9i	0.158737	+	0.274940i	−0.775677	+	0.631131i	$0.782591\pi$
$174$	−4.68381e9	+	3.50073e9i	−0.387371	+	0.289526i
$175$	7.10457e9	−	1.23055e10i	0.572620	−	0.991808i
$176$	6.03790e8	−	1.04579e9i	0.0474328	−	0.0821560i
$177$	2.58103e9	−	1.92909e9i	0.197657	−	0.147731i
$178$	1.13217e9	+	1.96098e9i	0.0845323	+	0.146414i
$179$	−2.42118e10			−1.76274			−0.881369	−	0.472429i	$-0.843377\pi$
$179$	−2.42118e10			−1.76274			−0.881369	+	0.472429i	$0.843377\pi$
$180$	−2.56205e9	+	8.67699e9i	−0.181912	+	0.616088i
$181$	1.15322e10			0.798657			0.399328	−	0.916808i	$-0.369243\pi$
$181$	1.15322e10			0.798657			0.399328	+	0.916808i	$0.369243\pi$
$182$	−1.89435e9	−	3.28110e9i	−0.127979	−	0.221666i
$183$	2.99226e9	+	2.51878e10i	0.197228	+	1.66020i
$184$	2.14751e9	−	3.71960e9i	0.138120	−	0.239230i
$185$	−1.73940e10	+	3.01273e10i	−1.09176	+	1.89098i
$186$	−1.11237e8	−	4.77341e7i	−0.00681463	−	0.00292429i
$187$	6.08846e9	+	1.05455e10i	0.364100	+	0.630639i
$188$	−7.84849e9			−0.458222
$189$	1.97134e10	−	2.37657e10i	1.12379	−	1.35479i
$190$	1.49987e10			0.834955
$191$	−9.08575e9	−	1.57370e10i	−0.493981	−	0.855601i	0.505995	−	0.862537i	$-0.331126\pi$
$191$	−9.08575e9	−	1.57370e10i	−0.493981	−	0.855601i	−0.999976	+	0.00693591i	$0.997792\pi$
$192$	−2.16303e9	−	9.28201e8i	−0.114870	−	0.0492931i
$193$	9.56069e9	−	1.65596e10i	0.496000	−	0.859097i	−0.503990	−	0.863710i	$-0.668135\pi$
$193$	9.56069e9	−	1.65596e10i	0.496000	−	0.859097i	0.999989	+	0.00461309i	$0.00146840\pi$
$194$	2.62911e9	−	4.55376e9i	0.133261	−	0.230814i
$195$	−6.29307e8	−	5.29730e9i	−0.0311679	−	0.262361i
$196$	−1.08385e10	−	1.87729e10i	−0.524588	−	0.908613i
$197$	1.18643e10			0.561233			0.280617	−	0.959820i	$-0.409461\pi$
$197$	1.18643e10			0.561233			0.280617	+	0.959820i	$0.409461\pi$
$198$	−5.64141e9	+	1.35956e9i	−0.260852	+	0.0628645i
$199$	−2.22347e10			−1.00506			−0.502530	−	0.864560i	$-0.667598\pi$
$199$	−2.22347e10			−1.00506			−0.502530	+	0.864560i	$0.667598\pi$
$200$	2.60250e9	+	4.50767e9i	0.115016	+	0.199213i
$201$	−2.67395e10	+	1.99854e10i	−1.15550	+	0.863637i
$202$	3.95954e9	−	6.85812e9i	0.167326	−	0.289817i
$203$	1.45640e10	−	2.52256e10i	0.601934	−	1.04258i
$204$	1.90115e10	−	1.42094e10i	0.768566	−	0.574435i
$205$	−1.16508e9	−	2.01798e9i	−0.0460749	−	0.0798041i
$206$	6.38490e9			0.247031
$207$	−2.00649e10	+	4.83558e9i	−0.759576	+	0.183055i
$208$	1.38785e9			0.0514112
$209$	4.81006e9	+	8.33127e9i	0.174378	+	0.302032i
$210$	−5.31651e9	−	4.47526e10i	−0.188643	−	1.58793i
$211$	−2.80343e10	+	4.85568e10i	−0.973686	+	1.68647i	−0.289479	+	0.957184i	$0.593482\pi$
$211$	−2.80343e10	+	4.85568e10i	−0.973686	+	1.68647i	−0.684206	+	0.729289i	$0.739851\pi$
$212$	−7.50793e9	+	1.30041e10i	−0.255275	+	0.442150i
$213$	−6.10064e9	−	2.61791e9i	−0.203080	−	0.0871457i
$214$	−1.01584e9	−	1.75949e9i	−0.0331103	−	0.0573488i
$215$	2.64051e10			0.842782
$216$	3.92870e9	+	1.06067e10i	0.122803	+	0.331541i
$217$	6.02967e8			0.0184597
$218$	−1.76842e10	−	3.06299e10i	−0.530312	−	0.918527i
$219$	9.09305e9	+	3.90201e9i	0.267123	+	0.114628i
$220$	−4.23482e9	+	7.33492e9i	−0.121880	+	0.211103i
$221$	−6.99737e9	+	1.21198e10i	−0.197319	+	0.341767i
$222$	5.13064e9	+	4.31880e10i	0.141770	+	1.19337i
$223$	−3.21706e10	−	5.57212e10i	−0.871139	−	1.50886i	−0.860819	−	0.508911i	$-0.830048\pi$
$223$	−3.21706e10	−	5.57212e10i	−0.871139	−	1.50886i	−0.0103203	−	0.999947i	$-0.503285\pi$
$224$	1.17248e10			0.311165
$225$	7.08305e9	−	2.39884e10i	0.184246	−	0.623993i
$226$	−1.06866e10			−0.272490
$227$	−6.18839e9	−	1.07186e10i	−0.154690	−	0.267930i	0.778256	−	0.627947i	$-0.216104\pi$
$227$	−6.18839e9	−	1.07186e10i	−0.154690	−	0.267930i	−0.932946	+	0.360016i	$0.882771\pi$
$228$	1.50197e10	−	1.12259e10i	0.368089	−	0.275114i
$229$	−2.12375e10	+	3.67844e10i	−0.510321	+	0.883901i	0.489608	+	0.871943i	$0.337140\pi$
$229$	−2.12375e10	+	3.67844e10i	−0.510321	+	0.883901i	−0.999928	+	0.0119584i	$0.996193\pi$
$230$	−1.50621e10	+	2.60883e10i	−0.354903	+	0.614710i
$231$	2.31535e10	−	1.73052e10i	0.535012	−	0.399874i
$232$	5.33500e9	+	9.24049e9i	0.120903	+	0.209411i
$233$	4.56572e9			0.101486			0.0507431	−	0.998712i	$-0.483841\pi$
$233$	4.56572e9			0.101486			0.0507431	+	0.998712i	$0.483841\pi$
$234$	−4.59497e9	−	4.83368e9i	−0.100187	−	0.105392i
$235$	5.50472e10			1.17742
$236$	−2.93987e9	−	5.09200e9i	−0.0616913	−	0.106852i
$237$	−4.26446e9	−	3.58968e10i	−0.0878004	−	0.739075i
$238$	−5.91151e10	+	1.02390e11i	−1.19427	+	2.06854i
$239$	3.22318e10	−	5.58270e10i	0.638989	−	1.10676i	−0.346666	−	0.937989i	$-0.612686\pi$
$239$	3.22318e10	−	5.58270e10i	0.638989	−	1.10676i	0.985655	−	0.168773i	$-0.0539804\pi$
$240$	1.51709e10	+	6.51016e9i	0.295163	+	0.126660i
$241$	3.08142e10	+	5.33717e10i	0.588401	+	1.01914i	0.994442	+	0.105286i	$0.0335757\pi$
$241$	3.08142e10	+	5.33717e10i	0.588401	+	1.01914i	−0.406041	+	0.913855i	$0.633091\pi$
$242$	3.22948e10			0.605289
$243$	2.39342e10	−	4.88003e10i	0.440342	−	0.897830i
$244$	4.62837e10			0.835937
$245$	7.60186e10	+	1.31668e11i	1.34795	+	2.33471i
$246$	−2.67708e9	−	1.14879e9i	−0.0466072	−	0.0200001i
$247$	−5.52812e9	+	9.57499e9i	−0.0945021	+	0.163682i
$248$	−1.10438e8	+	1.91283e8i	−0.00185389	+	0.00321103i
$249$	4.85742e9	+	4.08881e10i	0.0800771	+	0.674062i
$250$	9.80167e9	+	1.69770e10i	0.158697	+	0.274872i
$251$	1.50155e10			0.238785			0.119393	−	0.992847i	$-0.461905\pi$
$251$	1.50155e10			0.238785			0.119393	+	0.992847i	$0.461905\pi$
$252$	−3.88192e10	−	4.08359e10i	−0.606379	−	0.637881i
$253$	−1.93215e10			−0.296482
$254$	−1.69843e10	−	2.94177e10i	−0.256033	−	0.443462i
$255$	−1.33342e11	+	9.96612e10i	−1.97486	+	1.47603i
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	4.31146e10	−	7.46766e10i	0.616489	−	1.06779i	−0.373633	−	0.927577i	$-0.621888\pi$
$257$	4.31146e10	−	7.46766e10i	0.616489	−	1.06779i	0.990121	−	0.140213i	$-0.0447787\pi$
$258$	2.64420e10	−	1.97630e10i	0.371540	−	0.277693i
$259$	−1.08322e11	−	1.87619e11i	−1.49578	−	2.59077i
$260$	−9.73401e9			−0.132103
$261$	1.45199e10	−	4.91750e10i	0.193678	−	0.655936i
$262$	7.95880e8			0.0104350
$263$	5.72954e10	+	9.92386e10i	0.738446	+	1.27903i	0.953195	+	0.302357i	$0.0977735\pi$
$263$	5.72954e10	+	9.92386e10i	0.738446	+	1.27903i	−0.214748	+	0.976669i	$0.568893\pi$
$264$	1.24913e9	+	1.05147e10i	0.0158266	+	0.133223i
$265$	5.26586e10	−	9.12074e10i	0.655938	−	1.13612i
$266$	−4.67026e10	+	8.08914e10i	−0.571971	+	0.990683i
$267$	−1.82459e10	−	7.82969e9i	−0.219718	−	0.0942853i
$268$	3.04571e10	+	5.27533e10i	0.360647	+	0.624659i
$269$	−1.28269e11			−1.49361			−0.746806	−	0.665042i	$-0.768414\pi$
$269$	−1.28269e11			−1.49361			−0.746806	+	0.665042i	$0.768414\pi$
$270$	−2.75549e10	−	7.43924e10i	−0.315545	−	0.851906i
$271$	−7.44512e10			−0.838514			−0.419257	−	0.907868i	$-0.637709\pi$
$271$	−7.44512e10			−0.838514			−0.419257	+	0.907868i	$0.637709\pi$
$272$	−2.16547e10	−	3.75070e10i	−0.239879	−	0.415482i
$273$	3.05290e10	+	1.31006e10i	0.332645	+	0.142745i
$274$	5.42351e10	−	9.39379e10i	0.581303	−	1.00685i
$275$	1.17076e10	−	2.02781e10i	0.123444	−	0.213811i
$276$	4.44279e9	+	3.73980e10i	0.0460856	+	0.387933i
$277$	1.83059e10	+	3.17067e10i	0.186823	+	0.323588i	0.944189	−	0.329403i	$-0.106847\pi$
$277$	1.83059e10	+	3.17067e10i	0.186823	+	0.323588i	−0.757366	+	0.652991i	$0.773514\pi$
$278$	−7.60499e10			−0.763654
$279$	1.03186e9	−	2.48674e8i	0.0101953	−	0.00245703i
$280$	−8.22348e10			−0.799548
$281$	−3.75847e10	−	6.50987e10i	−0.359611	−	0.622865i	0.628285	−	0.777984i	$-0.283757\pi$
$281$	−3.75847e10	−	6.50987e10i	−0.359611	−	0.622865i	−0.987896	+	0.155119i	$0.950424\pi$
$282$	5.51240e10	−	4.12003e10i	0.519063	−	0.387954i
$283$	−1.69742e10	+	2.94001e10i	−0.157308	+	0.272465i	−0.933897	−	0.357542i	$-0.883615\pi$
$283$	−1.69742e10	+	2.94001e10i	−0.157308	+	0.272465i	0.776589	+	0.630007i	$0.216948\pi$
$284$	−6.05678e9	+	1.04907e10i	−0.0552471	+	0.0956908i
$285$	−1.05344e11	+	7.87352e10i	−0.945818	+	0.706915i
$286$	−3.12168e9	−	5.40691e9i	−0.0275893	−	0.0477861i
$287$	1.45112e10			0.126251
$288$	2.00647e10	−	4.83552e9i	0.171856	−	0.0414168i
$289$	3.18133e11			2.68268
$290$	−3.74183e10	−	6.48103e10i	−0.310665	−	0.538088i
$291$	5.43914e9	+	4.57848e10i	0.0444643	+	0.374286i
$292$	9.02768e9	−	1.56364e10i	0.0726697	−	0.125868i
$293$	4.22072e10	−	7.31050e10i	0.334566	−	0.579486i	−0.648835	−	0.760929i	$-0.724743\pi$
$293$	4.22072e10	−	7.31050e10i	0.334566	−	0.579486i	0.983401	+	0.181443i	$0.0580768\pi$
$294$	1.74672e11	+	7.49554e10i	1.36352	+	0.585113i
$295$	2.06195e10	+	3.57140e10i	0.158518	+	0.274561i
$296$	7.93598e10			0.600880
$297$	3.24856e10	−	3.91633e10i	0.242263	−	0.292062i
$298$	1.15247e11			0.846557
$299$	−1.11029e10	−	1.92309e10i	−0.0803374	−	0.139148i
$300$	−4.19416e10	−	1.79980e10i	−0.298950	−	0.128286i
$301$	−8.22196e10	+	1.42409e11i	−0.577333	+	0.999970i
$302$	3.97891e10	−	6.89167e10i	0.275253	−	0.476753i
$303$	8.19153e9	+	6.89536e10i	0.0558307	+	0.469964i
$304$	−1.71078e10	−	2.96316e10i	−0.114885	−	0.198987i
$305$	−3.24622e11			−2.14797
$306$	−5.89360e10	+	1.99601e11i	−0.384268	+	1.30141i
$307$	−2.60554e10			−0.167408			−0.0837039	−	0.996491i	$-0.526675\pi$
$307$	−2.60554e10			−0.167408			−0.0837039	+	0.996491i	$0.526675\pi$
$308$	−2.63726e10	−	4.56786e10i	−0.166984	−	0.289224i
$309$	−4.48445e10	+	3.35173e10i	−0.279831	+	0.209149i
$310$	7.74580e8	−	1.34161e9i	0.00476364	−	0.00825086i
$311$	−7.50063e10	+	1.29915e11i	−0.454648	+	0.787474i	−0.998668	−	0.0515984i	$-0.983568\pi$
$311$	−7.50063e10	+	1.29915e11i	−0.454648	+	0.787474i	0.544019	+	0.839073i	$0.316902\pi$
$312$	−9.74760e9	+	7.28547e9i	−0.0582374	+	0.0435273i
$313$	−8.67447e10	−	1.50246e11i	−0.510850	−	0.884818i	−0.999921	−	0.0125741i	$-0.995997\pi$
$313$	−8.67447e10	−	1.50246e11i	−0.510850	−	0.884818i	0.489071	−	0.872244i	$-0.337336\pi$
$314$	1.10963e10			0.0644164
$315$	2.72268e11	+	2.86412e11i	1.55811	+	1.63906i
$316$	−6.59619e10			−0.372136
$317$	9.58489e9	+	1.66015e10i	0.0533115	+	0.0923382i	0.891450	−	0.453120i	$-0.149689\pi$
$317$	9.58489e9	+	1.66015e10i	0.0533115	+	0.0923382i	−0.838138	+	0.545458i	$0.816356\pi$
$318$	−1.55325e10	−	1.30747e11i	−0.0851763	−	0.716986i
$319$	2.39999e10	−	4.15691e10i	0.129763	−	0.224757i
$320$	1.50619e10	−	2.60879e10i	0.0802979	−	0.139080i
$321$	1.63711e10	+	7.02518e9i	0.0860610	+	0.0369305i
$322$	−9.37998e10	−	1.62466e11i	−0.486240	−	0.842192i
$323$	3.45022e11			1.76374
$324$	−8.32727e10	−	5.38727e10i	−0.419807	−	0.271591i
$325$	2.69106e10			0.133798
$326$	6.37428e10	+	1.10406e11i	0.312573	+	0.541393i
$327$	2.84996e11	+	1.22298e11i	1.37840	+	0.591497i
$328$	−2.65783e9	+	4.60350e9i	−0.0126793	+	0.0219612i
$329$	−1.71405e11	+	2.96882e11i	−0.806568	+	1.39702i
$330$	−8.76104e9	−	7.37475e10i	−0.0406671	−	0.342322i
$331$	1.01835e11	+	1.76383e11i	0.466305	+	0.807663i	0.999259	−	0.0384806i	$-0.0122518\pi$
$331$	1.01835e11	+	1.76383e11i	0.466305	+	0.807663i	−0.532955	+	0.846144i	$0.678918\pi$
$332$	7.51336e10			0.339401
$333$	−2.62749e11	−	2.76399e11i	−1.17096	−	1.23179i
$334$	9.82125e10			0.431825
$335$	−2.13618e11	−	3.69997e11i	−0.926694	−	1.60508i
$336$	−8.23496e10	+	6.15490e10i	−0.352480	+	0.263448i
$337$	9.54368e10	−	1.65301e11i	0.403071	−	0.698139i	−0.591024	−	0.806654i	$-0.701276\pi$
$337$	9.54368e10	−	1.65301e11i	0.403071	−	0.698139i	0.994095	+	0.108515i	$0.0346095\pi$
$338$	−8.12483e10	+	1.40726e11i	−0.338602	+	0.586475i
$339$	7.50573e10	−	5.60987e10i	0.308670	−	0.230703i
$340$	1.51880e11	+	2.63064e11i	0.616377	+	1.06760i
$341$	9.93625e8			0.00397949
$342$	−4.65612e10	+	1.57690e11i	−0.184037	+	0.623286i
$343$	−4.95599e11			−1.93333
$344$	−3.01182e10	−	5.21663e10i	−0.115962	−	0.200852i
$345$	−3.11606e10	−	2.62299e11i	−0.118419	−	0.996808i
$346$	−2.99230e10	+	5.18282e10i	−0.112244	+	0.194412i
$347$	2.51960e11	−	4.36407e11i	0.932928	−	1.61588i	0.154641	−	0.987971i	$-0.450578\pi$
$347$	2.51960e11	−	4.36407e11i	0.932928	−	1.61588i	0.778287	−	0.627908i	$-0.216089\pi$
$348$	−8.59781e10	−	3.68949e10i	−0.314254	−	0.134853i
$349$	1.33958e11	+	2.32022e11i	0.483341	+	0.837171i	0.999817	−	0.0191305i	$-0.00608980\pi$
$349$	1.33958e11	+	2.32022e11i	0.483341	+	0.837171i	−0.516476	+	0.856302i	$0.672756\pi$
$350$	2.27346e11			0.809808
$351$	5.76471e10	+	9.82835e9i	0.202720	+	0.0345620i
$352$	1.93213e10			0.0670801
$353$	2.71507e10	+	4.70264e10i	0.0930668	+	0.161196i	0.908800	−	0.417232i	$-0.137000\pi$
$353$	2.71507e10	+	4.70264e10i	0.0930668	+	0.161196i	−0.815733	+	0.578428i	$0.803666\pi$
$354$	4.73785e10	+	2.03311e10i	0.160349	+	0.0688090i
$355$	4.24807e10	−	7.35787e10i	0.141959	−	0.245881i
$356$	−1.81148e10	+	3.13757e10i	−0.0597733	+	0.103530i
$357$	−1.22298e11	−	1.02946e12i	−0.398485	−	3.35432i
$358$	−1.93694e11	−	3.35488e11i	−0.623222	−	1.07945i
$359$	−2.39369e11			−0.760577			−0.380289	−	0.924868i	$-0.624175\pi$
$359$	−2.39369e11			−0.760577			−0.380289	+	0.924868i	$0.624175\pi$
$360$	−1.40728e11	+	3.39151e10i	−0.441591	+	0.106422i
$361$	−5.01103e10			−0.155290
$362$	9.22579e10	+	1.59795e11i	0.282368	+	0.489075i
$363$	−2.26823e11	+	1.69530e11i	−0.685658	+	0.512468i
$364$	3.03095e10	−	5.24976e10i	0.0904947	−	0.156741i
$365$	−6.33178e10	+	1.09670e11i	−0.186727	+	0.323421i
$366$	−3.25075e11	+	2.42964e11i	−0.946931	+	0.707747i
$367$	2.12436e11	+	3.67950e11i	0.611267	+	1.05875i	0.991027	+	0.133661i	$0.0426733\pi$
$367$	2.12436e11	+	3.67950e11i	0.611267	+	1.05875i	−0.379760	+	0.925085i	$0.623993\pi$
$368$	6.87203e10			0.195331
$369$	2.48330e10	−	5.98468e9i	0.0697286	−	0.0168044i
$370$	−5.56608e11			−1.54398
$371$	3.27934e11	+	5.67999e11i	0.898678	+	1.55656i
$372$	−2.28474e8	−	1.92322e9i	−0.000618578	−	0.00520698i
$373$	1.10701e11	−	1.91740e11i	0.296117	−	0.512889i	−0.679127	−	0.734021i	$-0.737642\pi$
$373$	1.10701e11	−	1.91740e11i	0.296117	−	0.512889i	0.975244	+	0.221131i	$0.0709749\pi$
$374$	−9.74154e10	+	1.68728e11i	−0.257457	+	0.445929i
$375$	−1.57962e11	−	6.77848e10i	−0.412489	−	0.177007i
$376$	−6.27879e10	−	1.08752e11i	−0.162006	−	0.280602i
$377$	5.51654e10			0.140647
$378$	4.87014e11	+	8.30319e10i	1.22695	+	0.209186i
$379$	−7.92760e10			−0.197363			−0.0986814	−	0.995119i	$-0.531462\pi$
$379$	−7.92760e10			−0.197363			−0.0986814	+	0.995119i	$0.531462\pi$
$380$	1.19990e11	+	2.07828e11i	0.295201	+	0.511303i
$381$	2.73717e11	+	1.17457e11i	0.665486	+	0.285573i
$382$	1.45372e11	−	2.51792e11i	0.349298	−	0.605001i
$383$	1.74198e11	−	3.01720e11i	0.413666	−	0.716490i	−0.581622	−	0.813460i	$-0.697582\pi$
$383$	1.74198e11	−	3.01720e11i	0.413666	−	0.716490i	0.995287	+	0.0969692i	$0.0309148\pi$
$384$	−4.44274e9	−	3.73975e10i	−0.0104270	−	0.0877712i
$385$	1.84970e11	+	3.20378e11i	0.429070	+	0.743171i
$386$	3.05942e11			0.701449
$387$	−8.19706e10	+	2.77612e11i	−0.185763	+	0.629129i
$388$	8.41316e10			0.188459
$389$	4.65041e10	+	8.05475e10i	0.102972	+	0.178352i	0.912908	−	0.408166i	$-0.133832\pi$
$389$	4.65041e10	+	8.05475e10i	0.102972	+	0.178352i	−0.809936	+	0.586518i	$0.800498\pi$
$390$	6.83671e10	−	5.10983e10i	0.149643	−	0.111845i
$391$	−3.46479e11	+	6.00120e11i	−0.749691	+	1.29850i
$392$	1.73417e11	−	3.00366e11i	0.370940	−	0.642487i
$393$	−5.58988e9	+	4.17794e9i	−0.0118205	+	0.00883478i
$394$	9.49142e10	+	1.64396e11i	0.198426	+	0.343684i
$395$	4.62640e11			0.956216
$396$	−6.39699e10	−	6.72932e10i	−0.130722	−	0.137513i
$397$	−2.16735e11			−0.437896			−0.218948	−	0.975737i	$-0.570262\pi$
$397$	−2.16735e11			−0.437896			−0.218948	+	0.975737i	$0.570262\pi$
$398$	−1.77878e11	−	3.08093e11i	−0.355343	−	0.615472i
$399$	−9.66190e10	−	8.13306e11i	−0.190847	−	1.60648i
$400$	−4.16401e10	+	7.21227e10i	−0.0813283	+	0.140865i
$401$	−2.98152e11	+	5.16415e11i	−0.575822	+	0.997353i	0.420130	+	0.907464i	$0.361985\pi$
$401$	−2.98152e11	+	5.16415e11i	−0.575822	+	0.997353i	−0.995952	+	0.0898892i	$0.971349\pi$
$402$	−4.90842e11	−	2.10630e11i	−0.937400	−	0.402257i
$403$	5.70978e8	+	9.88963e8i	0.00107832	+	0.00186770i
$404$	1.26705e11			0.236635
$405$	5.84053e11	+	3.77849e11i	1.07871	+	0.697863i
$406$	4.66048e11			0.851263
$407$	−1.78503e11	−	3.09177e11i	−0.322457	−	0.558511i
$408$	3.48984e11	+	1.49756e11i	0.623497	+	0.267555i
$409$	−2.45553e11	+	4.25310e11i	−0.433901	+	0.751538i	−0.997205	−	0.0747111i	$-0.976197\pi$
$409$	−2.45553e11	+	4.25310e11i	−0.433901	+	0.751538i	0.563304	+	0.826249i	$0.309530\pi$
$410$	1.86413e10	−	3.22877e10i	0.0325799	−	0.0564300i
$411$	1.12202e11	+	9.44480e11i	0.193960	+	1.63269i
$412$	5.10792e10	+	8.84717e10i	0.0873386	+	0.151275i
$413$	−2.56817e11			−0.434360
$414$	−2.27523e11	−	2.39343e11i	−0.380649	−	0.400423i
$415$	−5.26967e11			−0.872102
$416$	1.11028e10	+	1.92306e10i	0.0181766	+	0.0314828i
$417$	5.34138e11	−	3.99221e11i	0.865050	−	0.646548i
$418$	−7.69610e10	+	1.33300e11i	−0.123304	+	0.213569i
$419$	1.47003e11	−	2.54617e11i	0.233004	−	0.403575i	−0.725687	−	0.688025i	$-0.758478\pi$
$419$	1.47003e11	−	2.54617e11i	0.233004	−	0.403575i	0.958691	+	0.284450i	$0.0918111\pi$
$420$	5.77578e11	−	4.31689e11i	0.905710	−	0.676938i
$421$	4.84670e10	+	8.39473e10i	0.0751929	+	0.130238i	0.901170	−	0.433466i	$-0.142709\pi$
$421$	4.84670e10	+	8.39473e10i	0.0751929	+	0.130238i	−0.825977	+	0.563703i	$0.809376\pi$
$422$	−8.97098e11			−1.37700
$423$	−1.70885e11	+	5.78743e11i	−0.259521	+	0.878930i
$424$	−2.40254e11			−0.361014
$425$	−4.19888e11	−	7.27268e11i	−0.624286	−	1.08129i
$426$	−1.25303e10	−	1.05476e11i	−0.0184340	−	0.155171i
$427$	1.01080e12	−	1.75075e12i	1.47143	−	2.54859i
$428$	1.62534e10	−	2.81518e10i	0.0234125	−	0.0405517i
$429$	5.03085e10	+	2.15884e10i	0.0717107	+	0.0307725i
$430$	2.11241e11	+	3.65880e11i	0.297968	+	0.516097i
$431$	−1.11086e12			−1.55064			−0.775318	−	0.631571i	$-0.782410\pi$
$431$	−1.11086e12			−1.55064			−0.775318	+	0.631571i	$0.782410\pi$
$432$	−1.15541e11	+	1.39291e11i	−0.159609	+	0.192418i
$433$	2.51266e11			0.343509			0.171755	−	0.985140i	$-0.445056\pi$
$433$	2.51266e11			0.343509			0.171755	+	0.985140i	$0.445056\pi$
$434$	4.82374e9	+	8.35495e9i	0.00652649	+	0.0113042i
$435$	6.03027e11	+	2.58771e11i	0.807487	+	0.346509i
$436$	2.82947e11	−	4.90079e11i	0.374987	−	0.649497i
$437$	−2.73729e11	+	4.74112e11i	−0.359049	+	0.621891i
$438$	1.86766e10	+	1.57213e11i	0.0242473	+	0.204106i
$439$	−5.52531e11	−	9.57012e11i	−0.710013	−	1.22978i	−0.964852	−	0.262795i	$-0.915356\pi$
$439$	−5.52531e11	−	9.57012e11i	−0.710013	−	1.22978i	0.254838	−	0.966984i	$-0.417978\pi$
$440$	−1.35514e11			−0.172365
$441$	−1.62029e12	+	3.90485e11i	−2.03995	+	0.491621i
$442$	−2.23916e11			−0.279052
$443$	−7.66592e9	−	1.32778e10i	−0.00945687	−	0.0163798i	0.861258	−	0.508168i	$-0.169677\pi$
$443$	−7.66592e9	−	1.32778e10i	−0.00945687	−	0.0163798i	−0.870715	+	0.491788i	$0.836344\pi$
$444$	−5.57385e11	+	4.16596e11i	−0.680663	+	0.508735i
$445$	1.27052e11	−	2.20061e11i	0.153590	−	0.266025i
$446$	5.14730e11	−	8.91539e11i	0.615989	−	1.06692i
$447$	−8.09440e11	+	6.04985e11i	−0.958960	+	0.716738i
$448$	9.37986e10	+	1.62464e11i	0.110013	+	0.190549i
$449$	1.10134e12			1.27883			0.639415	−	0.768862i	$-0.279177\pi$
$449$	1.10134e12			1.27883			0.639415	+	0.768862i	$0.279177\pi$
$450$	3.89057e11	−	9.37615e10i	0.447257	−	0.107788i
$451$	2.39129e10			0.0272169
$452$	−8.54925e10	−	1.48077e11i	−0.0963396	−	0.166865i
$453$	8.23160e10	+	6.92909e11i	0.0918423	+	0.773098i
$454$	9.90143e10	−	1.71498e11i	0.109382	−	0.189455i
$455$	−2.12583e11	+	3.68205e11i	−0.232529	+	0.402752i
$456$	2.75707e11	+	1.18312e11i	0.298611	+	0.128140i
$457$	1.74031e11	+	3.01431e11i	0.186640	+	0.323270i	0.944128	−	0.329579i	$-0.106907\pi$
$457$	1.74031e11	+	3.01431e11i	0.186640	+	0.323270i	−0.757488	+	0.652849i	$0.773574\pi$
$458$	−6.79599e11			−0.721702
$459$	−6.33857e11	−	1.71128e12i	−0.666552	−	1.79955i
$460$	−4.81986e11			−0.501908
$461$	−8.85382e10	−	1.53353e11i	−0.0913013	−	0.158138i	0.816758	−	0.576981i	$-0.195769\pi$
$461$	−8.85382e10	−	1.53353e11i	−0.0913013	−	0.158138i	−0.908059	+	0.418842i	$0.862436\pi$
$462$	4.25016e11	+	1.82383e11i	0.434027	+	0.186250i
$463$	−2.14420e10	+	3.71386e10i	−0.0216846	+	0.0375588i	−0.876664	−	0.481103i	$-0.840236\pi$
$463$	−2.14420e10	+	3.71386e10i	−0.0216846	+	0.0375588i	0.854979	+	0.518662i	$0.173570\pi$
$464$	−8.53600e10	+	1.47848e11i	−0.0854916	+	0.148076i
$465$	1.60246e9	+	1.34890e10i	0.00158946	+	0.0133795i
$466$	3.65257e10	+	6.32644e10i	0.0358808	+	0.0621474i
$467$	1.23771e12			1.20419			0.602093	−	0.798426i	$-0.294334\pi$
$467$	1.23771e12			1.20419			0.602093	+	0.798426i	$0.294334\pi$
$468$	3.02177e10	−	1.02339e11i	0.0291176	−	0.0986134i
$469$	2.66064e12			2.53926
$470$	4.40378e11	+	7.62757e11i	0.416280	+	0.721017i
$471$	−7.79354e10	+	5.82498e10i	−0.0729694	+	0.0545382i
$472$	4.70379e10	−	8.14720e10i	0.0436223	−	0.0755561i
$473$	−1.35489e11	+	2.34674e11i	−0.124460	+	0.215571i
$474$	4.63285e11	−	3.46265e11i	0.421547	−	0.315069i
$475$	−3.31724e11	−	5.74562e11i	−0.298989	−	0.517864i
$476$	−1.89168e12			−1.68895
$477$	7.95446e11	+	8.36769e11i	0.703522	+	0.740070i
$478$	1.03142e12			0.903667
$479$	4.46116e11	+	7.72695e11i	0.387202	+	0.670654i	0.992072	−	0.125670i	$-0.0401082\pi$
$479$	4.46116e11	+	7.72695e11i	0.387202	+	0.670654i	−0.604870	+	0.796324i	$0.706775\pi$
$480$	3.11602e10	+	2.62296e11i	0.0267926	+	0.225531i
$481$	2.05151e11	−	3.55332e11i	0.174751	−	0.302678i
$482$	−4.93026e11	+	8.53947e11i	−0.416062	+	0.720641i
$483$	1.51166e12	+	6.48685e11i	1.26384	+	0.542341i
$484$	2.58358e11	+	4.47489e11i	0.214002	+	0.370663i
$485$	−5.90077e11			−0.484251
$486$	8.67670e11	−	5.87608e10i	0.705491	−	0.0477776i
$487$	−4.38243e11			−0.353049			−0.176524	−	0.984296i	$-0.556485\pi$
$487$	−4.38243e11			−0.353049			−0.176524	+	0.984296i	$0.556485\pi$
$488$	3.70270e11	+	6.41326e11i	0.295549	+	0.511905i
$489$	−1.02727e12	−	4.40822e11i	−0.812446	−	0.348637i
$490$	−1.21630e12	+	2.10669e12i	−0.953142	+	1.65089i
$491$	6.10106e11	−	1.05673e12i	0.473738	−	0.820539i	−0.525810	−	0.850602i	$-0.676238\pi$
$491$	6.10106e11	−	1.05673e12i	0.473738	−	0.820539i	0.999548	+	0.0300635i	$0.00957095\pi$
$492$	−5.49855e9	−	4.62850e10i	−0.00423063	−	0.0356120i
$493$	−8.60749e11	−	1.49086e12i	−0.656244	−	1.13665i
$494$	−1.76900e11			−0.133646
$495$	4.48668e11	+	4.71977e11i	0.335894	+	0.353344i
$496$	−3.53400e9			−0.00262180
$497$	2.64551e11	+	4.58215e11i	0.194493	+	0.336872i
$498$	−5.27703e11	+	3.94411e11i	−0.384465	+	0.287354i
$499$	−1.02247e12	+	1.77097e12i	−0.738242	+	1.27867i	0.215045	+	0.976604i	$0.431010\pi$
$499$	−1.02247e12	+	1.77097e12i	−0.738242	+	1.27867i	−0.953286	+	0.302068i	$0.902323\pi$
$500$	−1.56827e11	+	2.71632e11i	−0.112216	+	0.194364i
$501$	−6.89797e11	+	5.15562e11i	−0.489161	+	0.365604i
$502$	1.20124e11	+	2.08060e11i	0.0844233	+	0.146225i
$503$	2.19466e11			0.152866			0.0764329	−	0.997075i	$-0.475647\pi$
$503$	2.19466e11			0.152866			0.0764329	+	0.997075i	$0.475647\pi$
$504$	2.55285e11	−	8.64582e11i	0.176233	−	0.596855i
$505$	−8.88676e11			−0.608040
$506$	−1.54572e11	−	2.67727e11i	−0.104822	−	0.181558i
$507$	−1.68087e11	−	1.41490e12i	−0.112979	−	0.951023i
$508$	2.71749e11	−	4.70683e11i	0.181043	−	0.313575i
$509$	3.39312e11	−	5.87706e11i	0.224063	−	0.388088i	−0.731975	−	0.681331i	$-0.761401\pi$
$509$	3.39312e11	−	5.87706e11i	0.224063	−	0.388088i	0.956038	+	0.293243i	$0.0947346\pi$
$510$	−2.44768e12	−	1.05035e12i	−1.60210	−	0.687492i
$511$	−3.94314e11	−	6.82973e11i	−0.255828	−	0.443108i
$512$	−6.87195e10			−0.0441942
$513$	−5.00765e11	−	1.35196e12i	−0.319232	−	0.861859i
$514$	1.37967e12			0.871847
$515$	−3.58256e11	−	6.20517e11i	−0.224420	−	0.388706i
$516$	4.85381e11	+	2.08287e11i	0.301411	+	0.129341i
$517$	−2.82457e11	+	4.89229e11i	−0.173878	+	0.301165i
$518$	1.73315e12	−	3.00191e12i	1.05768	−	1.83195i
$519$	−6.19051e10	−	5.21096e11i	−0.0374518	−	0.315257i
$520$	−7.78721e10	−	1.34878e11i	−0.0467054	−	0.0808961i
$521$	3.00159e12			1.78477			0.892383	−	0.451279i	$-0.149032\pi$
$521$	3.00159e12			1.78477			0.892383	+	0.451279i	$0.149032\pi$
$522$	7.97547e11	−	1.92206e11i	0.470153	−	0.113305i
$523$	−1.25398e12			−0.732881			−0.366440	−	0.930442i	$-0.619424\pi$
$523$	−1.25398e12			−0.732881			−0.366440	+	0.930442i	$0.619424\pi$
$524$	6.36704e9	+	1.10280e10i	0.00368932	+	0.00639010i
$525$	−1.59677e12	+	1.19345e12i	−0.917331	+	0.685624i
$526$	−9.16727e11	+	1.58782e12i	−0.522160	+	0.904408i
$527$	1.78180e10	−	3.08617e10i	0.0100626	−	0.0174290i
$528$	−1.35703e11	+	1.01426e11i	−0.0759868	+	0.0567934i
$529$	3.50807e11	+	6.07615e11i	0.194768	+	0.337348i
$530$	1.68508e12			0.927637
$531$	−4.39491e11	+	1.05916e11i	−0.239897	+	0.0578144i
$532$	−1.49448e12			−0.808889
$533$	1.37414e10	+	2.38008e10i	0.00737493	+	0.0127737i
$534$	−3.74760e10	−	3.15460e11i	−0.0199442	−	0.167884i
$535$	−1.13997e11	+	1.97449e11i	−0.0601593	+	0.104199i
$536$	−4.87314e11	+	8.44052e11i	−0.255016	+	0.441700i
$537$	3.12155e12	+	1.33952e12i	1.61989	+	0.695127i
$538$	−1.02615e12	−	1.77735e12i	−0.528071	−	0.914647i
$539$	−1.56026e12			−0.796245
$540$	8.10373e11	−	9.76951e11i	0.410122	−	0.494426i
$541$	1.80539e11			0.0906113			0.0453056	−	0.998973i	$-0.485574\pi$
$541$	1.80539e11			0.0906113			0.0453056	+	0.998973i	$0.485574\pi$
$542$	−5.95610e11	−	1.03163e12i	−0.296459	−	0.513483i
$543$	−1.48682e12	−	6.38022e11i	−0.733936	−	0.314946i
$544$	3.46475e11	−	6.00112e11i	0.169620	−	0.293790i
$545$	−1.98452e12	+	3.43729e12i	−0.963542	+	1.66890i
$546$	6.27047e10	+	5.27827e11i	0.0301949	+	0.254170i
$547$	7.51495e11	+	1.30163e12i	0.358908	+	0.621647i	0.987779	−	0.155863i	$-0.0498159\pi$
$547$	7.51495e11	+	1.30163e12i	0.358908	+	0.621647i	−0.628871	+	0.777510i	$0.716483\pi$
$548$	1.73552e12			0.822087
$549$	1.00774e12	−	3.41293e12i	0.473447	−	1.60344i
$550$	3.74643e11			0.174576
$551$	−6.80016e11	−	1.17782e12i	−0.314295	−	0.544374i
$552$	−4.82659e11	+	3.60745e11i	−0.221266	+	0.165377i
$553$	−1.44056e12	+	2.49511e12i	−0.655039	+	1.13456i
$554$	−2.92894e11	+	5.07307e11i	−0.132104	+	0.228811i
$555$	3.90935e12	−	2.92189e12i	1.74899	−	1.30721i
$556$	−6.08399e11	−	1.05378e12i	−0.269993	−	0.467641i
$557$	1.28134e12			0.564047			0.282023	−	0.959408i	$-0.408994\pi$
$557$	1.28134e12			0.564047			0.282023	+	0.959408i	$0.408994\pi$
$558$	1.17006e10	+	1.23084e10i	0.00510920	+	0.00537463i
$559$	−3.11431e11			−0.134899
$560$	−6.57879e11	−	1.13948e12i	−0.282683	−	0.489621i
$561$	−2.01534e11	−	1.69645e12i	−0.0859044	−	0.723115i
$562$	6.01356e11	−	1.04158e12i	0.254283	−	0.440432i
$563$	−1.18810e12	+	2.05784e12i	−0.498384	+	0.863227i	−0.999998	−	0.00186484i	$-0.999406\pi$
$563$	−1.18810e12	+	2.05784e12i	−0.498384	+	0.863227i	0.501614	+	0.865091i	$0.332740\pi$
$564$	1.01188e12	+	4.34218e11i	0.421089	+	0.180698i
$565$	5.99622e11	+	1.03858e12i	0.247548	+	0.428766i
$566$	−5.43174e11			−0.222467
$567$	−3.85643e12	+	1.97339e12i	−1.56697	+	0.801841i
$568$	−1.93817e11			−0.0781312
$569$	−1.47643e11	−	2.55724e11i	−0.0590481	−	0.102274i	0.834990	−	0.550265i	$-0.185473\pi$
$569$	−1.47643e11	−	2.55724e11i	−0.0590481	−	0.102274i	−0.894038	+	0.447990i	$0.852140\pi$
$570$	−1.93374e12	−	8.29806e11i	−0.767292	−	0.329261i
$571$	−3.77029e11	+	6.53034e11i	−0.148427	+	0.257083i	−0.930646	−	0.365920i	$-0.880754\pi$
$571$	−3.77029e11	+	6.53034e11i	−0.148427	+	0.257083i	0.782219	+	0.623003i	$0.214088\pi$
$572$	4.99469e10	−	8.65105e10i	0.0195086	−	0.0337899i
$573$	3.00747e11	+	2.53159e12i	0.116548	+	0.981064i
$574$	1.16090e11	+	2.01073e11i	0.0446365	+	0.0773127i
$575$	1.33250e12			0.508349
$576$	2.27520e11	+	2.39340e11i	0.0861230	+	0.0905971i
$577$	−2.25656e12			−0.847532			−0.423766	−	0.905772i	$-0.639292\pi$
$577$	−2.25656e12			−0.847532			−0.423766	+	0.905772i	$0.639292\pi$
$578$	2.54507e12	+	4.40818e12i	0.948470	+	1.64280i
$579$	−2.14879e12	+	1.60603e12i	−0.794586	+	0.593882i
$580$	5.98692e11	−	1.03697e12i	0.219674	−	0.380486i
$581$	1.64086e12	−	2.84205e12i	0.597418	−	1.03476i
$582$	−5.90900e11	+	4.41646e11i	−0.213482	+	0.159559i
$583$	5.40401e11	+	9.36001e11i	0.193735	+	0.335558i
$584$	2.88886e11			0.102770
$585$	−2.11939e11	+	7.17781e11i	−0.0748186	+	0.253390i
$586$	1.35063e12			0.473148
$587$	−5.51711e11	−	9.55592e11i	−0.191796	−	0.332201i	0.754049	−	0.656818i	$-0.228098\pi$
$587$	−5.51711e11	−	9.55592e11i	−0.191796	−	0.332201i	−0.945846	+	0.324617i	$0.894765\pi$
$588$	3.58766e11	+	3.01997e12i	0.123769	+	1.04185i
$589$	1.40767e10	−	2.43816e10i	0.00481929	−	0.00834725i
$590$	−3.29911e11	+	5.71423e11i	−0.112089	+	0.194144i
$591$	−1.52962e12	−	6.56392e11i	−0.515752	−	0.221320i
$592$	6.34878e11	+	1.09964e12i	0.212443	+	0.367962i
$593$	8.96636e11			0.297763			0.148881	−	0.988855i	$-0.452433\pi$
$593$	8.96636e11			0.297763			0.148881	+	0.988855i	$0.452433\pi$
$594$	8.02547e11	+	1.36828e11i	0.264504	+	0.0450957i
$595$	1.32678e13			4.33982
$596$	9.21976e11	+	1.59691e12i	0.299303	+	0.518408i
$597$	2.86665e12	+	1.23014e12i	0.923613	+	0.396341i
$598$	1.77647e11	−	3.07694e11i	0.0568071	−	0.0983928i
$599$	−1.76747e12	+	3.06135e12i	−0.560959	+	0.971610i	0.436454	+	0.899727i	$0.356234\pi$
$599$	−1.76747e12	+	3.06135e12i	−0.560959	+	0.971610i	−0.997413	+	0.0718830i	$0.977099\pi$
$600$	−8.61454e10	−	7.25143e11i	−0.0271364	−	0.228425i
$601$	−2.23158e12	−	3.86522e12i	−0.697715	−	1.20848i	−0.969257	−	0.246052i	$-0.920867\pi$
$601$	−2.23158e12	−	3.86522e12i	−0.697715	−	1.20848i	0.271541	−	0.962427i	$-0.412467\pi$
$602$	−2.63103e12			−0.816472
$603$	4.55314e12	−	1.09729e12i	1.40244	−	0.337982i
$604$	1.27325e12			0.389267
$605$	−1.81206e12	−	3.13857e12i	−0.549886	−	0.952430i
$606$	−8.89917e11	+	6.65134e11i	−0.268054	+	0.200347i
$607$	9.84361e11	−	1.70496e12i	0.294310	−	0.509760i	−0.680514	−	0.732735i	$-0.738243\pi$
$607$	9.84361e11	−	1.70496e12i	0.294310	−	0.509760i	0.974824	+	0.222975i	$0.0715768\pi$
$608$	2.73725e11	−	4.74106e11i	0.0812360	−	0.140705i
$609$	−3.27330e12	+	2.44650e12i	−0.964291	+	0.720722i
$610$	−2.59697e12	−	4.49809e12i	−0.759422	−	1.31536i
$611$	−6.49245e11			−0.188462
$612$	−3.23723e12	+	7.80163e11i	−0.932809	+	0.224804i
$613$	−5.68828e12			−1.62708			−0.813540	−	0.581509i	$-0.802463\pi$
$613$	−5.68828e12			−1.62708			−0.813540	+	0.581509i	$0.802463\pi$
$614$	−2.08444e11	−	3.61035e11i	−0.0591876	−	0.102516i
$615$	3.85654e10	+	3.24630e11i	0.0108708	+	0.0915064i
$616$	4.21961e11	−	7.30858e11i	0.118075	−	0.204512i
$617$	1.36075e12	−	2.35689e12i	0.378003	−	0.654720i	−0.612769	−	0.790262i	$-0.709944\pi$
$617$	1.36075e12	−	2.35689e12i	0.378003	−	0.654720i	0.990772	+	0.135542i	$0.0432776\pi$
$618$	−8.23185e11	−	3.53245e11i	−0.227012	−	0.0974155i
$619$	4.27121e11	+	7.39795e11i	0.116935	+	0.202537i	0.918551	−	0.395301i	$-0.129360\pi$
$619$	4.27121e11	+	7.39795e11i	0.116935	+	0.202537i	−0.801617	+	0.597838i	$0.796027\pi$
$620$	2.47866e10			0.00673680
$621$	2.85444e12	+	4.86658e11i	0.770208	+	0.131314i
$622$	−2.40020e12			−0.642970
$623$	7.91223e11	+	1.37044e12i	0.210428	+	0.364471i
$624$	−1.78931e11	−	7.67829e10i	−0.0472449	−	0.0202738i
$625$	2.34091e12	−	4.05458e12i	0.613656	−	1.06288i
$626$	1.38791e12	−	2.40394e12i	0.361225	−	0.625661i
$627$	−1.59218e11	−	1.34024e12i	−0.0411422	−	0.346321i
$628$	8.87707e10	+	1.53755e11i	0.0227746	+	0.0394468i
$629$	−1.28039e13			−3.26148
$630$	−1.79050e12	+	6.06395e12i	−0.452837	+	1.53364i
$631$	1.82693e12			0.458764			0.229382	−	0.973336i	$-0.426330\pi$
$631$	1.82693e12			0.458764			0.229382	+	0.973336i	$0.426330\pi$
$632$	−5.27695e11	−	9.13995e11i	−0.131570	−	0.227886i
$633$	6.30079e12	−	4.70928e12i	1.55983	−	1.16584i
$634$	−1.53358e11	+	2.65624e11i	−0.0376969	+	0.0652929i
$635$	−1.90597e12	+	3.30124e12i	−0.465195	+	0.805742i
$636$	1.68743e12	−	1.26120e12i	0.408948	−	0.305652i
$637$	−8.96589e11	−	1.55294e12i	−0.215758	−	0.373703i
$638$	7.67998e11			0.183513
$639$	6.41701e11	+	6.75037e11i	0.152257	+	0.160167i
$640$	4.81980e11			0.113558
$641$	−3.56045e12	−	6.16687e12i	−0.832997	−	1.44279i	−0.895651	−	0.444757i	$-0.853290\pi$
$641$	−3.56045e12	−	6.16687e12i	−0.832997	−	1.44279i	0.0626545	−	0.998035i	$-0.480043\pi$
$642$	3.36253e10	+	2.83047e11i	0.00781194	+	0.0657583i
$643$	−3.01320e12	+	5.21902e12i	−0.695151	+	1.20404i	0.274979	+	0.961450i	$0.411329\pi$
$643$	−3.01320e12	+	5.21902e12i	−0.695151	+	1.20404i	−0.970130	+	0.242586i	$0.922004\pi$
$644$	1.50080e12	−	2.59946e12i	0.343823	−	0.595520i
$645$	−3.40433e12	−	1.46087e12i	−0.774485	−	0.332347i
$646$	2.76018e12	+	4.78077e12i	0.623578	+	1.08007i
$647$	−5.11089e12			−1.14664			−0.573320	−	0.819332i	$-0.694345\pi$
$647$	−5.11089e12			−1.14664			−0.573320	+	0.819332i	$0.694345\pi$
$648$	8.03002e10	−	1.58484e12i	0.0178908	−	0.353100i
$649$	−4.23208e11			−0.0936381
$650$	2.15285e11	+	3.72885e11i	0.0473047	+	0.0819341i
$651$	−7.77386e10	−	3.33592e10i	−0.0169638	−	0.00727949i
$652$	−1.01988e12	+	1.76649e12i	−0.221023	+	0.382822i
$653$	3.26957e12	−	5.66306e12i	0.703689	−	1.21883i	−0.263473	−	0.964667i	$-0.584868\pi$
$653$	3.26957e12	−	5.66306e12i	0.703689	−	1.21883i	0.967163	−	0.254159i	$-0.0817986\pi$
$654$	5.85364e11	+	4.92740e12i	0.125120	+	1.05322i
$655$	−4.46567e10	−	7.73478e10i	−0.00947984	−	0.0164196i
$656$	−8.50506e10			−0.0179312
$657$	−9.56459e11	−	1.00615e12i	−0.200273	−	0.210677i
$658$	−5.48495e12			−1.14066
$659$	9.73090e11	+	1.68544e12i	0.200987	+	0.348120i	0.948847	−	0.315737i	$-0.102252\pi$
$659$	9.73090e11	+	1.68544e12i	0.200987	+	0.348120i	−0.747860	+	0.663857i	$0.768918\pi$
$660$	9.51787e11	−	7.11377e11i	0.195251	−	0.145932i
$661$	8.94843e11	−	1.54991e12i	0.182323	−	0.315792i	−0.760348	−	0.649515i	$-0.774972\pi$
$661$	8.94843e11	−	1.54991e12i	0.182323	−	0.315792i	0.942671	+	0.333723i	$0.108305\pi$
$662$	−1.62935e12	+	2.82212e12i	−0.329727	+	0.571104i
$663$	1.57268e12	−	1.17544e12i	0.316103	−	0.236259i
$664$	6.01069e11	+	1.04108e12i	0.119996	+	0.207840i
$665$	1.04819e13			2.07847
$666$	1.72790e12	−	5.85194e12i	0.340318	−	1.15257i
$667$	2.73155e12			0.534372
$668$	7.85700e11	+	1.36087e12i	0.152673	+	0.264438i
$669$	1.06488e12	+	8.96380e12i	0.205534	+	1.73011i
$670$	3.41789e12	−	5.91996e12i	0.655272	−	1.13496i
$671$	1.66569e12	−	2.88506e12i	0.317207	−	0.549418i
$672$	−1.51165e12	−	6.48677e11i	−0.285949	−	0.122706i
$673$	2.62493e12	+	4.54651e12i	0.493230	+	0.854300i	0.999970	−	0.00779968i	$-0.00248274\pi$
$673$	2.62493e12	+	4.54651e12i	0.493230	+	0.854300i	−0.506740	+	0.862099i	$0.669149\pi$
$674$	3.05398e12			0.570028
$675$	−2.24036e12	+	2.70088e12i	−0.415384	+	0.500770i
$676$	−2.59995e12			−0.478855
$677$	5.01631e12	+	8.68851e12i	0.917774	+	1.58963i	0.802789	+	0.596263i	$0.203348\pi$
$677$	5.01631e12	+	8.68851e12i	0.917774	+	1.58963i	0.114984	+	0.993367i	$0.463318\pi$
$678$	1.37778e12	+	5.91235e11i	0.250408	+	0.107455i
$679$	1.83737e12	−	3.18241e12i	0.331728	−	0.574569i
$680$	−2.43008e12	+	4.20903e12i	−0.435844	+	0.754904i
$681$	2.04842e11	+	1.72429e12i	0.0364969	+	0.307219i
$682$	7.94900e9	+	1.37681e10i	0.00140696	+	0.00243693i
$683$	−2.26372e12			−0.398043			−0.199021	−	0.979995i	$-0.563776\pi$
$683$	−2.26372e12			−0.398043			−0.199021	+	0.979995i	$0.563776\pi$
$684$	−2.55751e12	+	6.16351e11i	−0.446750	+	0.107665i
$685$	−1.21725e13			−2.11238
$686$	−3.96479e12	−	6.86722e12i	−0.683537	−	1.18392i
$687$	4.77318e12	−	3.56753e12i	0.817527	−	0.611029i
$688$	4.81891e11	−	8.34660e11i	0.0819976	−	0.142024i
$689$	−6.21073e11	+	1.07573e12i	−0.104992	+	0.181852i
$690$	3.38524e12	−	2.53017e12i	0.568550	−	0.424941i
$691$	1.70919e12	+	2.96041e12i	0.285193	+	0.493970i	0.972656	−	0.232250i	$-0.0746088\pi$
$691$	1.70919e12	+	2.96041e12i	0.285193	+	0.493970i	−0.687463	+	0.726220i	$0.741275\pi$
$692$	−9.57536e11			−0.158737
$693$	−3.94252e12	+	9.50135e11i	−0.649344	+	0.156490i
$694$	8.06271e12			1.31936
$695$	4.26715e12	+	7.39092e12i	0.693755	+	1.20162i
$696$	−1.76594e11	−	1.48651e12i	−0.0285255	−	0.240118i
$697$	4.28815e11	−	7.42729e11i	0.0688212	−	0.119202i
$698$	−2.14333e12	+	3.71235e12i	−0.341774	+	0.591969i
$699$	−5.88643e11	−	2.52599e11i	−0.0932621	−	0.0400206i
$700$	1.81877e12	+	3.15020e12i	0.286310	+	0.495904i
$701$	6.70506e12			1.04875			0.524374	−	0.851488i	$-0.324299\pi$
$701$	6.70506e12			1.04875			0.524374	+	0.851488i	$0.324299\pi$
$702$	3.24991e11	+	8.77409e11i	0.0505074	+	0.136359i
$703$	−1.01155e13			−1.56202
$704$	1.54570e11	+	2.67723e11i	0.0237164	+	0.0410780i
$705$	−7.09707e12	−	3.04549e12i	−1.08200	−	0.464309i
$706$	−4.34411e11	+	7.52422e11i	−0.0658082	+	0.113983i
$707$	2.76714e12	−	4.79282e12i	0.416527	−	0.721447i
$708$	9.73125e10	+	8.19144e11i	0.0145552	+	0.122521i
$709$	2.50944e12	+	4.34647e12i	0.372965	+	0.645995i	0.990020	−	0.140925i	$-0.0450077\pi$
$709$	2.50944e12	+	4.34647e12i	0.372965	+	0.645995i	−0.617055	+	0.786920i	$0.711674\pi$
$710$	1.35938e12			0.200761
$711$	−1.43619e12	+	4.86399e12i	−0.210765	+	0.713805i
$712$	−5.79672e11			−0.0845323
$713$	2.82724e10	+	4.89692e10i	0.00409694	+	0.00709611i
$714$	1.32863e13	−	9.93032e12i	1.91321	−	1.42995i
$715$	−3.50314e11	+	6.06762e11i	−0.0501280	+	0.0868243i
$716$	3.09910e12	−	5.36781e12i	0.440684	−	0.763288i
$717$	−7.24418e12	+	5.41438e12i	−1.02365	+	0.765090i
$718$	−1.91495e12	−	3.31680e12i	−0.268905	−	0.465756i
$719$	−9.03791e11			−0.126121			−0.0630606	−	0.998010i	$-0.520086\pi$
$719$	−9.03791e11			−0.126121			−0.0630606	+	0.998010i	$0.520086\pi$
$720$	−1.59577e12	−	1.67867e12i	−0.221296	−	0.232792i
$721$	4.46211e12			0.614939
$722$	−4.00882e11	−	6.94348e11i	−0.0549034	−	0.0950955i
$723$	−1.01998e12	−	8.58584e12i	−0.138825	−	1.16859i
$724$	−1.47613e12	+	2.55673e12i	−0.199664	+	0.345829i
$725$	−1.65514e12	+	2.86679e12i	−0.222492	+	0.385368i
$726$	−4.16366e12	−	1.78671e12i	−0.556238	−	0.238693i
$727$	7.29367e12	+	1.26330e13i	0.968369	+	1.67727i	0.700276	+	0.713872i	$0.253060\pi$
$727$	7.29367e12	+	1.26330e13i	0.968369	+	1.67727i	0.268094	+	0.963393i	$0.413606\pi$
$728$	9.69905e11			0.127979
$729$	−5.78564e12	+	4.96751e12i	−0.758713	+	0.651425i
$730$	−2.02617e12			−0.264072
$731$	4.85927e12	+	8.41650e12i	0.629423	+	1.09019i
$732$	−5.96721e12	−	2.56065e12i	−0.768195	−	0.329648i
$733$	1.46865e12	−	2.54378e12i	0.187911	−	0.325471i	−0.756643	−	0.653828i	$-0.773162\pi$
$733$	1.46865e12	−	2.54378e12i	0.187911	−	0.325471i	0.944553	+	0.328358i	$0.106495\pi$
$734$	−3.39898e12	+	5.88720e12i	−0.432231	+	0.748646i
$735$	−2.51629e12	−	2.11813e13i	−0.318030	−	2.67707i
$736$	5.49763e11	+	9.52217e11i	0.0690598	+	0.119615i
$737$	4.38444e12			0.547407
$738$	2.81590e11	+	2.96219e11i	0.0349433	+	0.0367586i
$739$	−1.26838e13			−1.56441			−0.782206	−	0.623020i	$-0.785905\pi$
$739$	−1.26838e13			−1.56441			−0.782206	+	0.623020i	$0.785905\pi$
$740$	−4.45287e12	−	7.71259e12i	−0.545880	−	0.945492i
$741$	1.24246e12	−	9.28629e11i	0.151391	−	0.113152i
$742$	−5.24695e12	+	9.08798e12i	−0.635461	+	1.10065i
$743$	−5.84236e11	+	1.01193e12i	−0.0703296	+	0.121814i	−0.899046	−	0.437855i	$-0.855738\pi$
$743$	−5.84236e11	+	1.01193e12i	−0.0703296	+	0.121814i	0.828716	+	0.559669i	$0.189072\pi$
$744$	2.48211e10	−	1.85516e10i	0.00296991	−	0.00221975i
$745$	−6.46649e12	−	1.12003e13i	−0.769070	−	1.33207i
$746$	3.54244e12			0.418772
$747$	1.63589e12	−	5.54031e12i	0.192225	−	0.651016i
$748$	−3.11729e12			−0.364100
$749$	−7.09924e11	−	1.22963e12i	−0.0824221	−	0.142759i
$750$	−3.24445e11	−	2.73107e12i	−0.0374425	−	0.315179i
$751$	5.94877e12	−	1.03036e13i	0.682413	−	1.18197i	−0.291829	−	0.956471i	$-0.594264\pi$
$751$	5.94877e12	−	1.03036e13i	0.682413	−	1.18197i	0.974242	−	0.225504i	$-0.0724029\pi$
$752$	1.00461e12	−	1.74003e12i	0.114555	−	0.198416i
$753$	−1.93590e12	−	8.30732e11i	−0.219434	−	0.0941637i
$754$	4.41323e11	+	7.64395e11i	0.0497263	+	0.0861284i
$755$	−8.93024e12			−1.00023
$756$	2.74559e12	+	7.41252e12i	0.305694	+	0.825311i
$757$	5.40853e12			0.598615			0.299308	−	0.954157i	$-0.403244\pi$
$757$	5.40853e12			0.598615			0.299308	+	0.954157i	$0.403244\pi$
$758$	−6.34208e11	−	1.09848e12i	−0.0697783	−	0.120859i
$759$	2.49106e12	+	1.06896e12i	0.272456	+	0.116916i
$760$	−1.91984e12	+	3.32525e12i	−0.208739	+	0.361546i
$761$	1.70400e12	−	2.95141e12i	0.184178	−	0.319006i	−0.759121	−	0.650949i	$-0.774371\pi$
$761$	1.70400e12	−	2.95141e12i	0.184178	−	0.319006i	0.943299	+	0.331944i	$0.107704\pi$
$762$	5.62197e11	+	4.73239e12i	0.0604075	+	0.508490i
$763$	−1.23587e13	−	2.14059e13i	−1.32011	−	2.28651i
$764$	4.65190e12			0.493981
$765$	2.27051e13	−	5.47186e12i	2.39688	−	0.577641i
$766$	5.57435e12			0.585012
$767$	−2.43193e11	−	4.21222e11i	−0.0253730	−	0.0439473i
$768$	4.82653e11	−	3.60740e11i	0.0500621	−	0.0374170i
$769$	1.25469e12	−	2.17319e12i	0.129381	−	0.224094i	−0.794056	−	0.607844i	$-0.792034\pi$
$769$	1.25469e12	−	2.17319e12i	0.129381	−	0.224094i	0.923437	+	0.383751i	$0.125368\pi$
$770$	−2.95952e12	+	5.12604e12i	−0.303398	+	0.525501i
$771$	−9.69012e12	+	7.24251e12i	−0.987608	+	0.738149i
$772$	2.44754e12	+	4.23926e12i	0.248000	+	0.429548i
$773$	1.35883e13			1.36885			0.684427	−	0.729082i	$-0.260052\pi$
$773$	1.35883e13			1.36885			0.684427	+	0.729082i	$0.260052\pi$
$774$	−4.50247e12	+	1.08508e12i	−0.450938	+	0.108675i
$775$	−6.85249e10			−0.00682324
$776$	6.73053e11	+	1.16576e12i	0.0666303	+	0.115407i
$777$	3.58557e12	+	3.01821e13i	0.352909	+	2.97067i
$778$	−7.44066e11	+	1.28876e12i	−0.0728120	+	0.126114i
$779$	3.38776e11	−	5.86777e11i	0.0329605	−	0.0570893i
$780$	1.25498e12	+	5.38535e11i	0.121397	+	0.0520941i
$781$	4.35951e11	+	7.55089e11i	0.0419284	+	0.0726221i
$782$	−1.10873e13			−1.06022
$783$	−4.59261e12	+	5.53666e12i	−0.436648	+	0.526405i
$784$	5.54933e12			0.524588
$785$	−6.22614e11	−	1.07840e12i	−0.0585202	−	0.101360i
$786$	−1.02610e11	−	4.40321e10i	−0.00958936	−	0.00411499i
$787$	6.70949e10	−	1.16212e11i	0.00623452	−	0.0107985i	−0.862891	−	0.505390i	$-0.831349\pi$
$787$	6.70949e10	−	1.16212e11i	0.00623452	−	0.0107985i	0.869126	+	0.494591i	$0.164682\pi$
$788$	−1.51863e12	+	2.63034e12i	−0.140308	+	0.243021i
$789$	−1.89653e12	−	1.59644e13i	−0.174226	−	1.46658i
$790$	3.70112e12	+	6.41052e12i	0.338073	+	0.585560i
$791$	−7.46835e12			−0.678313
$792$	4.20682e11	−	1.42474e12i	0.0379919	−	0.128668i
$793$	3.82869e12			0.343812
$794$	−1.73388e12	−	3.00316e12i	−0.154820	−	0.268155i
$795$	−1.18352e13	+	8.84574e12i	−1.05081	+	0.785384i
$796$	2.84604e12	−	4.92949e12i	0.251265	−	0.435204i
$797$	7.58270e12	−	1.31336e13i	0.665674	−	1.15298i	−0.313428	−	0.949612i	$-0.601478\pi$
$797$	7.58270e12	−	1.31336e13i	0.665674	−	1.15298i	0.979102	−	0.203369i	$-0.0651891\pi$
$798$	1.04965e13	−	7.84524e12i	0.916291	−	0.684846i
$799$	1.01302e13	+	1.75460e13i	0.879342	+	1.52306i
$800$	−1.33248e12			−0.115016
$801$	1.91921e12	+	2.01892e12i	0.164731	+	0.173289i
$802$	−9.54087e12			−0.814336
$803$	−6.49788e11	−	1.12547e12i	−0.0551508	−	0.0955240i
$804$	−1.00816e12	−	8.48635e12i	−0.0850898	−	0.716257i
$805$	−1.05262e13	+	1.82319e13i	−0.883466	+	1.53021i
$806$	−9.13565e9	+	1.58234e10i	−0.000762486	+	0.00132066i
$807$	1.65374e13	+	7.09651e12i	1.37257	+	0.588999i
$808$	1.01364e12	+	1.75568e12i	0.0836629	+	0.144908i
$809$	−4.97475e12			−0.408322			−0.204161	−	0.978937i	$-0.565447\pi$
$809$	−4.97475e12			−0.408322			−0.204161	+	0.978937i	$0.565447\pi$
$810$	−5.63204e11	+	1.11157e13i	−0.0459710	+	0.907304i
$811$	1.46659e13			1.19046			0.595230	−	0.803555i	$-0.297061\pi$
$811$	1.46659e13			1.19046			0.595230	+	0.803555i	$0.297061\pi$
$812$	3.72839e12	+	6.45775e12i	0.300967	+	0.521290i
$813$	9.59876e12	+	4.11902e12i	0.770563	+	0.330664i
$814$	2.85605e12	−	4.94683e12i	0.228011	−	0.394927i
$815$	7.15320e12	−	1.23897e13i	0.567925	−	0.983675i
$816$	7.16791e11	+	6.03371e12i	0.0565962	+	0.476408i
$817$	3.83896e12	+	6.64928e12i	0.301450	+	0.522126i
$818$	−7.85770e12			−0.613628
$819$	−3.21122e12	−	3.37804e12i	−0.249397	−	0.262354i
$820$	5.96522e11			0.0460749
$821$	−1.22211e13	−	2.11675e13i	−0.938784	−	1.62602i	−0.767744	−	0.640757i	$-0.778621\pi$
$821$	−1.22211e13	−	2.11675e13i	−0.938784	−	1.62602i	−0.171040	−	0.985264i	$-0.554713\pi$
$822$	−1.21895e13	+	9.11056e12i	−0.931241	+	0.696020i
$823$	8.82302e12	−	1.52819e13i	0.670375	−	1.16112i	−0.307422	−	0.951573i	$-0.599466\pi$
$823$	8.82302e12	−	1.52819e13i	0.670375	−	1.16112i	0.977798	−	0.209551i	$-0.0672003\pi$
$824$	−8.17267e11	+	1.41555e12i	−0.0617577	+	0.106968i
$825$	−2.63131e12	+	1.96667e12i	−0.197756	+	0.147805i
$826$	−2.05454e12	−	3.55857e12i	−0.153569	−	0.265990i
$827$	−1.53876e13			−1.14392			−0.571959	−	0.820282i	$-0.693816\pi$
$827$	−1.53876e13			−1.14392			−0.571959	+	0.820282i	$0.693816\pi$
$828$	1.49625e12	−	5.06740e12i	0.110629	−	0.374670i
$829$	−1.22874e13			−0.903579			−0.451789	−	0.892125i	$-0.649214\pi$
$829$	−1.22874e13			−0.903579			−0.451789	+	0.892125i	$0.649214\pi$
$830$	−4.21574e12	−	7.30188e12i	−0.308335	−	0.534051i
$831$	−6.05942e11	−	5.10062e12i	−0.0440785	−	0.371038i
$832$	−1.77645e11	+	3.07690e11i	−0.0128528	+	0.0222617i
$833$	−2.79790e13	+	4.84611e13i	−2.01340	+	3.48731i
$834$	9.80487e12	+	4.20747e12i	0.701770	+	0.301143i
$835$	−5.51069e12	−	9.54479e12i	−0.392299	−	0.679481i
$836$	−2.46275e12			−0.174378
$837$	−1.46792e11	−	2.50268e10i	−0.0103380	−	0.00176255i
$838$	4.70410e12			0.329518
$839$	2.51427e12	+	4.35484e12i	0.175179	+	0.303419i	0.940223	−	0.340559i	$-0.110616\pi$
$839$	2.51427e12	+	4.35484e12i	0.175179	+	0.303419i	−0.765044	+	0.643978i	$0.777283\pi$
$840$	1.06023e13	+	4.54965e12i	0.734755	+	0.315298i
$841$	3.86061e12	−	6.68678e12i	0.266118	−	0.460930i
$842$	−7.75472e11	+	1.34316e12i	−0.0531694	+	0.0920921i
$843$	1.24409e12	+	1.04723e13i	0.0848454	+	0.714200i
$844$	−7.17678e12	−	1.24306e13i	−0.486843	−	0.843236i
$845$	1.82353e13			1.23043
$846$	−9.38638e12	+	2.26209e12i	−0.629987	+	0.151825i
$847$	2.25693e13			1.50676
$848$	−1.92203e12	−	3.32905e12i	−0.127638	−	0.221075i
$849$	3.81499e12	−	2.85137e12i	0.252005	−	0.188351i
$850$	6.71821e12	−	1.16363e13i	0.441437	−	0.764591i
$851$	1.01582e13	−	1.75945e13i	0.663946	−	1.14999i
$852$	1.36128e12	−	1.01744e12i	0.0885052	−	0.0661498i
$853$	−5.96108e12	−	1.03249e13i	−0.385526	−	0.667751i	0.606316	−	0.795224i	$-0.292647\pi$
$853$	−5.96108e12	−	1.03249e13i	−0.385526	−	0.667751i	−0.991842	+	0.127473i	$0.959313\pi$
$854$	3.23456e13			2.08091
$855$	1.79377e13	−	4.32292e12i	1.14794	−	0.276650i
$856$	5.20110e11			0.0331103
$857$	−2.85974e12	−	4.95321e12i	−0.181097	−	0.313670i	0.761157	−	0.648568i	$-0.224632\pi$
$857$	−2.85974e12	−	4.95321e12i	−0.181097	−	0.313670i	−0.942255	+	0.334898i	$0.891298\pi$
$858$	1.03331e11	+	8.69803e11i	0.00650933	+	0.0547934i
$859$	2.91056e12	−	5.04124e12i	0.182393	−	0.315914i	−0.760302	−	0.649570i	$-0.774949\pi$
$859$	2.91056e12	−	5.04124e12i	0.182393	−	0.315914i	0.942695	+	0.333656i	$0.108282\pi$
$860$	−3.37986e12	+	5.85408e12i	−0.210696	+	0.364935i
$861$	−1.87089e12	−	8.02835e11i	−0.116020	−	0.0497865i
$862$	−8.88685e12	−	1.53925e13i	−0.548233	−	0.949567i
$863$	−1.65530e13			−1.01585			−0.507924	−	0.861402i	$-0.669587\pi$
$863$	−1.65530e13			−1.01585			−0.507924	+	0.861402i	$0.669587\pi$
$864$	−2.85440e12	−	4.86652e11i	−0.174262	−	0.0297102i
$865$	6.71591e12			0.407880
$866$	2.01013e12	+	3.48164e12i	0.121449	+	0.210356i
$867$	−4.10159e13	−	1.76007e13i	−2.46528	−	1.05790i
$868$	−7.71798e10	+	1.33679e11i	−0.00461493	+	0.00799329i
$869$	−2.37388e12	+	4.11168e12i	−0.141211	+	0.244585i
$870$	1.23858e12	+	1.04260e13i	0.0732973	+	0.616992i
$871$	2.51948e12	+	4.36387e12i	0.148330	+	0.256915i
$872$	9.05431e12			0.530312
$873$	1.83180e12	−	6.20382e12i	0.106737	−	0.361489i
$874$	−8.75932e12			−0.507772
$875$	6.84994e12	+	1.18644e13i	0.395048	+	0.684244i
$876$	−2.02900e12	+	1.51649e12i	−0.116416	+	0.0870106i
$877$	−1.53953e13	+	2.66654e13i	−0.878799	+	1.52213i	−0.0261400	+	0.999658i	$0.508322\pi$
$877$	−1.53953e13	+	2.66654e13i	−0.878799	+	1.52213i	−0.852659	+	0.522467i	$0.825012\pi$
$878$	8.84050e12	−	1.53122e13i	0.502055	−	0.869585i
$879$	−9.48619e12	+	7.09009e12i	−0.535972	+	0.400591i
$880$	−1.08411e12	−	1.87774e12i	−0.0609401	−	0.105551i
$881$	−2.43879e13			−1.36390			−0.681949	−	0.731399i	$-0.738868\pi$
$881$	−2.43879e13			−1.36390			−0.681949	+	0.731399i	$0.738868\pi$
$882$	−1.83730e13	−	1.93275e13i	−1.02229	−	1.07539i
$883$	−5.39949e12			−0.298902			−0.149451	−	0.988769i	$-0.547751\pi$
$883$	−5.39949e12			−0.298902			−0.149451	+	0.988769i	$0.547751\pi$
$884$	−1.79133e12	−	3.10267e12i	−0.0986596	−	0.170883i
$885$	−6.82524e11	−	5.74526e12i	−0.0374002	−	0.314822i
$886$	1.22655e11	−	2.12444e11i	0.00668702	−	0.0115823i
$887$	−1.32250e12	+	2.29063e12i	−0.0717361	+	0.124251i	−0.899662	−	0.436587i	$-0.856187\pi$
$887$	−1.32250e12	+	2.29063e12i	−0.0717361	+	0.124251i	0.827926	+	0.560837i	$0.189521\pi$
$888$	−1.02316e13	−	4.39059e12i	−0.552186	−	0.236954i
$889$	−1.18696e13	−	2.05587e13i	−0.637348	−	1.10392i
$890$	4.06567e12			0.217209
$891$	−6.35498e12	+	3.25193e12i	−0.337804	+	0.172859i
$892$	1.64714e13			0.871139
$893$	8.00315e12	+	1.38619e13i	0.421143	+	0.729441i
$894$	−1.48584e13	−	6.37605e12i	−0.777954	−	0.333836i
$895$	−2.17363e13	+	3.76484e13i	−1.13235	+	1.96129i
$896$	−1.50078e12	+	2.59942e12i	−0.0777912	+	0.134738i
$897$	3.67518e11	+	3.09365e12i	0.0189545	+	0.159553i
$898$	8.81072e12	+	1.52606e13i	0.452135	+	0.783120i
$899$	−1.40472e11			−0.00717253
$900$	4.41166e12	+	4.64084e12i	0.224135	+	0.235779i
$901$	3.87625e13			1.95952
$902$	1.91304e11	+	3.31347e11i	0.00962263	+	0.0166669i
$903$	1.84791e13	−	1.38115e13i	0.924881	−	0.691266i
$904$	1.36788e12	−	2.36924e12i	0.0681224	−	0.117991i
$905$	1.03532e13	−	1.79322e13i	0.513044	−	0.888618i
$906$	−8.94270e12	+	6.68388e12i	−0.440952	+	0.329573i
$907$	−2.85590e12	−	4.94657e12i	−0.140123	−	0.242701i	0.787420	−	0.616417i	$-0.211417\pi$
$907$	−2.85590e12	−	4.94657e12i	−0.140123	−	0.242701i	−0.927543	+	0.373717i	$0.878083\pi$
$908$	3.16846e12			0.154690
$909$	2.75875e12	−	9.34316e12i	0.134022	−	0.453896i
$910$	−6.80266e12			−0.328846
$911$	−7.23101e12	−	1.25245e13i	−0.347829	−	0.602458i	0.638034	−	0.770008i	$-0.279748\pi$
$911$	−7.23101e12	−	1.25245e13i	−0.347829	−	0.602458i	−0.985864	+	0.167550i	$0.946414\pi$
$912$	5.66286e11	+	4.76680e12i	0.0271056	+	0.228166i
$913$	2.70396e12	−	4.68339e12i	0.128790	−	0.223071i
$914$	−2.78450e12	+	4.82290e12i	−0.131974	+	0.228586i
$915$	4.18524e13	+	1.79597e13i	1.97390	+	0.847041i
$916$	−5.43679e12	−	9.41680e12i	−0.255160	−	0.441951i
$917$	5.56204e11			0.0259760
$918$	1.86414e13	−	2.24732e13i	0.866334	−	1.04442i
$919$	−3.39599e13			−1.57053			−0.785266	−	0.619158i	$-0.787474\pi$
$919$	−3.39599e13			−1.57053			−0.785266	+	0.619158i	$0.787474\pi$
$920$	−3.85589e12	−	6.67860e12i	−0.177451	−	0.307355i
$921$	3.35925e12	+	1.44152e12i	0.153842	+	0.0660165i
$922$	1.41661e12	−	2.45364e12i	0.0645597	−	0.111821i
$923$	−5.01031e11	+	8.67811e11i	−0.0227226	+	0.0393566i
$924$	8.72957e11	+	7.34826e12i	0.0393975	+	0.331635i
$925$	1.23104e13	+	2.13222e13i	0.552884	+	0.957623i
$926$	−6.86144e11			−0.0306666
$927$	7.63600e12	−	1.84025e12i	0.339631	−	0.0818499i
$928$	−2.73152e12			−0.120903
$929$	1.14626e13	+	1.98538e13i	0.504908	+	0.874526i	0.999984	+	0.00567608i	$0.00180676\pi$
$929$	1.14626e13	+	1.98538e13i	0.504908	+	0.874526i	−0.495076	+	0.868849i	$0.664860\pi$
$930$	−1.74089e11	+	1.30116e11i	−0.00763129	+	0.00570371i
$931$	−2.21042e13	+	3.82857e13i	−0.964278	+	1.67018i
$932$	−5.84412e11	+	1.01223e12i	−0.0253716	+	0.0439448i
$933$	1.68579e13	−	1.25998e13i	0.728341	−	0.544371i
$934$	9.90169e12	+	1.71502e13i	0.425744	+	0.737410i
$935$	2.18639e13			0.935567
$936$	1.65980e12	−	4.00005e11i	0.0706827	−	0.0170343i
$937$	2.69013e13			1.14010			0.570052	−	0.821608i	$-0.306923\pi$
$937$	2.69013e13			1.14010			0.570052	+	0.821608i	$0.306923\pi$
$938$	2.12851e13	+	3.68668e13i	0.897765	+	1.55497i
$939$	2.87133e12	+	2.41699e13i	0.120528	+	1.01457i
$940$	−7.04605e12	+	1.22041e13i	−0.294354	+	0.509836i
$941$	−8.91220e12	+	1.54364e13i	−0.370537	+	0.641789i	−0.989648	−	0.143514i	$-0.954160\pi$
$941$	−8.91220e12	+	1.54364e13i	−0.370537	+	0.641789i	0.619111	+	0.785303i	$0.287493\pi$
$942$	−1.43062e12	−	6.13906e11i	−0.0591962	−	0.0254023i
$943$	6.80413e11	+	1.17851e12i	0.0280201	+	0.0485323i
$944$	1.50521e12			0.0616913
$945$	−1.92568e13	−	5.19895e13i	−0.785492	−	2.12067i
$946$	−4.33565e12			−0.176013
$947$	8.37750e12	+	1.45103e13i	0.338485	+	0.586274i	0.984148	−	0.177349i	$-0.0567521\pi$
$947$	8.37750e12	+	1.45103e13i	0.338485	+	0.586274i	−0.645663	+	0.763623i	$0.723419\pi$
$948$	8.50426e12	+	3.64935e12i	0.341979	+	0.146750i
$949$	7.46790e11	−	1.29348e12i	0.0298883	−	0.0517680i
$950$	5.30758e12	−	9.19300e12i	0.211417	−	0.366185i
$951$	−3.17269e11	−	2.67067e12i	−0.0125781	−	0.105878i
$952$	−1.51335e13	−	2.62119e13i	−0.597135	−	1.03427i
$953$	1.77293e13			0.696263			0.348131	−	0.937446i	$-0.386816\pi$
$953$	1.77293e13			0.696263			0.348131	+	0.937446i	$0.386816\pi$
$954$	−5.23105e12	+	1.77162e13i	−0.204466	+	0.692472i
$955$	−3.26272e13			−1.26930
$956$	8.25133e12	+	1.42917e13i	0.319495	+	0.553381i
$957$	−5.39405e12	+	4.03157e12i	−0.207879	+	0.155371i
$958$	−7.13785e12	+	1.23631e13i	−0.273793	+	0.474224i
$959$	3.79024e13	−	6.56489e13i	1.44705	−	2.50636i
$960$	−3.38520e12	+	2.53014e12i	−0.128636	+	0.0961443i
$961$	1.32184e13	+	2.28949e13i	0.499945	+	0.865930i
$962$	6.56482e12			0.247136
$963$	−1.72201e12	−	1.81147e12i	−0.0645234	−	0.0678755i
$964$	−1.57768e13			−0.588401
$965$	−1.71664e13	−	2.97330e13i	−0.637244	−	1.10374i
$966$	3.10487e12	+	2.61357e13i	0.114722	+	0.965689i
$967$	1.92667e13	−	3.33709e13i	0.708578	−	1.22729i	−0.256806	−	0.966463i	$-0.582670\pi$
$967$	1.92667e13	−	3.33709e13i	0.708578	−	1.22729i	0.965385	−	0.260831i	$-0.0839964\pi$
$968$	−4.13373e12	+	7.15983e12i	−0.151322	+	0.262098i
$969$	−4.44826e13	−	1.90884e13i	−1.62081	−	0.695524i
$970$	−4.72062e12	−	8.17635e12i	−0.171209	−	0.296542i
$971$	−1.91351e13			−0.690786			−0.345393	−	0.938458i	$-0.612254\pi$
$971$	−1.91351e13			−0.690786			−0.345393	+	0.938458i	$0.612254\pi$
$972$	7.75557e12	+	1.15527e13i	0.278686	+	0.415131i
$973$	−5.31478e13			−1.90098
$974$	−3.50595e12	−	6.07248e12i	−0.124822	−	0.216197i
$975$	−3.46951e12	−	1.48883e12i	−0.122955	−	0.0527625i
$976$	−5.92431e12	+	1.02612e13i	−0.208984	+	0.361972i
$977$	5.65903e12	−	9.80173e12i	0.198708	−	0.344173i	−0.749401	−	0.662116i	$-0.769659\pi$
$977$	5.65903e12	−	9.80173e12i	0.198708	−	0.344173i	0.948110	+	0.317943i	$0.102992\pi$
$978$	−2.10995e12	−	1.77608e13i	−0.0737474	−	0.620781i
$979$	1.30385e12	+	2.25834e12i	0.0453634	+	0.0785718i
$980$	−3.89215e13			−1.34795
$981$	−2.99775e13	−	3.15349e13i	−1.03344	−	1.08713i
$982$	1.95234e13			0.669967
$983$	1.36426e13	+	2.36297e13i	0.466023	+	0.807175i	0.999247	−	0.0387990i	$-0.0123532\pi$
$983$	1.36426e13	+	2.36297e13i	0.466023	+	0.807175i	−0.533224	+	0.845974i	$0.679020\pi$
$984$	5.97355e11	−	4.46470e11i	0.0203121	−	0.0151815i
$985$	1.06513e13	−	1.84485e13i	0.360527	−	0.624451i
$986$	1.37720e13	−	2.38538e13i	0.464034	−	0.803731i
$987$	3.85237e13	−	2.87930e13i	1.29211	−	0.965740i
$988$	−1.41520e12	−	2.45120e12i	−0.0472510	−	0.0818412i
$989$	−1.54207e13			−0.512532
$990$	−2.95056e12	+	9.99274e12i	−0.0976215	+	0.330618i
$991$	2.96159e13			0.975423			0.487711	−	0.873005i	$-0.337832\pi$
$991$	2.96159e13			0.975423			0.487711	+	0.873005i	$0.337832\pi$
$992$	−2.82720e10	−	4.89686e10i	−0.000926946	−	0.00160552i
$993$	−3.37083e12	−	2.83745e13i	−0.110018	−	0.926097i
$994$	−4.23281e12	+	7.33144e12i	−0.137528	+	0.238205i
$995$	−1.99614e13	+	3.45741e13i	−0.645634	+	1.11827i
$996$	−9.68674e12	−	4.15678e12i	−0.311897	−	0.133841i
$997$	−1.12148e13	−	1.94247e13i	−0.359471	−	0.622623i	0.628401	−	0.777889i	$-0.283710\pi$
$997$	−1.12148e13	−	1.94247e13i	−0.359471	−	0.622623i	−0.987873	+	0.155267i	$0.950376\pi$
$998$	−3.27191e13			−1.04403
$999$	1.85836e13	+	5.01718e13i	0.590316	+	1.59373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.10.c.a.13.1	yes	8
3.2	odd	2		54.10.c.a.37.1		8
9.2	odd	6		54.10.c.a.19.1		8
9.4	even	3		162.10.a.e.1.1		4
9.5	odd	6		162.10.a.h.1.4		4
9.7	even	3	inner	18.10.c.a.7.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.10.c.a.7.1	✓	8	9.7	even	3	inner
18.10.c.a.13.1	yes	8	1.1	even	1	trivial
54.10.c.a.19.1		8	9.2	odd	6
54.10.c.a.37.1		8	3.2	odd	2
162.10.a.e.1.1		4	9.4	even	3
162.10.a.h.1.4		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)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(-128.927 - 55.3251i) q^{3} +(-128.000 + 221.703i) q^{4} +(897.758 - 1554.96i) q^{5} +(-264.808 - 2229.06i) q^{6} +(5590.83 + 9683.61i) q^{7} -4096.00 q^{8} +(13561.3 + 14265.8i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(-128.927 - 55.3251i) q^{3} +(-128.000 + 221.703i) q^{4} +(897.758 - 1554.96i) q^{5} +(-264.808 - 2229.06i) q^{6} +(5590.83 + 9683.61i) q^{7} -4096.00 q^{8} +(13561.3 + 14265.8i) q^{9} +28728.3 q^{10} +(9213.10 + 15957.6i) q^{11} +(28768.3 - 21501.8i) q^{12} +(-10588.5 + 18339.7i) q^{13} +(-89453.3 + 154938. i) q^{14} +(-201774. + 150808. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +660849. q^{17} +(-89182.3 + 302037. i) q^{18} +522089. q^{19} +(229826. + 398070. i) q^{20} +(-185062. - 1.55779e6i) q^{21} +(-147410. + 255321. i) q^{22} +(-524295. + 908105. i) q^{23} +(528084. + 226612. i) q^{24} +(-635377. - 1.10051e6i) q^{25} -338831. q^{26} +(-959156. - 2.58952e6i) q^{27} -2.86251e6 q^{28} +(-1.30249e6 - 2.25598e6i) q^{29} +(-3.70384e6 - 1.58939e6i) q^{30} +(26962.3 - 46700.1i) q^{31} +(524288. - 908093. i) q^{32} +(-304963. - 2.56707e6i) q^{33} +(5.28679e6 + 9.15699e6i) q^{34} +2.00769e7 q^{35} +(-4.89860e6 + 1.18055e6i) q^{36} -1.93749e7 q^{37} +(4.17672e6 + 7.23428e6i) q^{38} +(2.37978e6 - 1.77868e6i) q^{39} +(-3.67722e6 + 6.36913e6i) q^{40} +(648885. - 1.12390e6i) q^{41} +(2.01049e7 - 1.50266e7i) q^{42} +(7.35308e6 + 1.27359e7i) q^{43} -4.71711e6 q^{44} +(3.43575e7 - 8.28004e6i) q^{45} -1.67774e7 q^{46} +(1.53291e7 + 2.65507e7i) q^{47} +(1.08465e6 + 9.13024e6i) q^{48} +(-4.23380e7 + 7.33316e7i) q^{49} +(1.01660e7 - 1.76081e7i) q^{50} +(-8.52012e7 - 3.65615e7i) q^{51} +(-2.71064e6 - 4.69497e6i) q^{52} +5.86557e7 q^{53} +(2.82082e7 - 3.40066e7i) q^{54} +3.30845e7 q^{55} +(-2.29001e7 - 3.96641e7i) q^{56} +(-6.73114e7 - 2.88847e7i) q^{57} +(2.08398e7 - 3.60957e7i) q^{58} +(-1.14839e7 + 1.98906e7i) q^{59} +(-7.60747e6 - 6.40371e7i) q^{60} +(-9.03978e7 - 1.56574e8i) q^{61} +862794. q^{62} +(-6.23254e7 + 2.11080e8i) q^{63} +1.67772e7 q^{64} +(1.90117e7 + 3.29293e7i) q^{65} +(3.31307e7 - 2.47623e7i) q^{66} +(1.18973e8 - 2.06067e8i) q^{67} +(-8.45886e7 + 1.46512e8i) q^{68} +(1.17837e8 - 8.80725e7i) q^{69} +(1.60615e8 + 2.78193e8i) q^{70} +4.73186e7 q^{71} +(-5.55470e7 - 5.84326e7i) q^{72} -7.05287e7 q^{73} +(-1.55000e8 - 2.68467e8i) q^{74} +(2.10316e7 + 1.77037e8i) q^{75} +(-6.68275e7 + 1.15749e8i) q^{76} +(-1.03018e8 + 1.78432e8i) q^{77} +(4.36844e7 + 1.87458e7i) q^{78} +(1.28832e8 + 2.23143e8i) q^{79} -1.17671e8 q^{80} +(-1.96045e7 + 3.86924e8i) q^{81} +2.07643e7 q^{82} +(-1.46745e8 - 2.54170e8i) q^{83} +(3.69054e8 + 1.58368e8i) q^{84} +(5.93282e8 - 1.02760e9i) q^{85} +(-1.17649e8 + 2.03774e8i) q^{86} +(4.31137e7 + 3.62917e8i) q^{87} +(-3.77368e7 - 6.53621e7i) q^{88} +1.41522e8 q^{89} +(3.89592e8 + 4.09831e8i) q^{90} -2.36793e8 q^{91} +(-1.34219e8 - 2.32475e8i) q^{92} +(-6.05985e6 + 4.52920e6i) q^{93} +(-2.45265e8 + 4.24812e8i) q^{94} +(4.68710e8 - 8.11830e8i) q^{95} +(-1.17835e8 + 8.80713e7i) q^{96} +(-1.64320e8 - 2.84610e8i) q^{97} -1.35482e9 q^{98} +(-1.02706e8 + 3.47837e8i) 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

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Database

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