LMFDB - Embedded newform 71.9.e.a.14.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,9,Mod(14,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("71.14");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	71.e (of order $10$, degree $4$, 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:	$28.9238813143$
Analytic rank:	$0$
Dimension:	$188$
Relative dimension:	$47$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.9
Character	$\chi$	$=$	71.14
Dual form			71.9.e.a.66.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.53857 + 20.1236i) q^{2} +(1.61600 - 4.97354i) q^{3} +(-155.100 - 112.687i) q^{4} +(-471.892 + 342.850i) q^{5} +(89.5195 + 65.0397i) q^{6} +(2413.84 + 784.305i) q^{7} +(-1100.46 + 799.529i) q^{8} +(5285.84 + 3840.38i) q^{9} +O(q^{10})$	\(q+(-6.53857 + 20.1236i) q^{2} +(1.61600 - 4.97354i) q^{3} +(-155.100 - 112.687i) q^{4} +(-471.892 + 342.850i) q^{5} +(89.5195 + 65.0397i) q^{6} +(2413.84 + 784.305i) q^{7} +(-1100.46 + 799.529i) q^{8} +(5285.84 + 3840.38i) q^{9} +(-3813.89 - 11737.9i) q^{10} +(17999.0 + 5848.22i) q^{11} +(-811.094 + 589.295i) q^{12} +(25841.3 - 8396.35i) q^{13} +(-31566.1 + 43447.1i) q^{14} +(942.600 + 2901.02i) q^{15} +(-24060.2 - 74049.7i) q^{16} +(127726. - 41500.6i) q^{17} +(-111844. + 81259.7i) q^{18} +(-67337.1 + 207242. i) q^{19} +111825. q^{20} +(7801.55 - 10737.9i) q^{21} +(-235375. + 323966. i) q^{22} +36343.6i q^{23} +(2198.15 + 6765.21i) q^{24} +(-15573.4 + 47929.8i) q^{25} +574922. i q^{26} +(55400.2 - 40250.6i) q^{27} +(-286006. - 393654. i) q^{28} +(60931.6 - 44269.4i) q^{29} -64542.4 q^{30} +(435108. + 141375. i) q^{31} +1.29925e6 q^{32} +(58172.7 - 80067.9i) q^{33} +2.84166e6i q^{34} +(-1.40797e6 + 457478. i) q^{35} +(-387073. - 1.19129e6i) q^{36} -867579. q^{37} +(-3.73018e6 - 2.71014e6i) q^{38} -142091. i q^{39} +(245179. - 754584. i) q^{40} -4.28319e6i q^{41} +(165075. + 227206. i) q^{42} +(-4.75437e6 + 3.45425e6i) q^{43} +(-2.13262e6 - 2.93530e6i) q^{44} -3.81102e6 q^{45} +(-731365. - 237635. i) q^{46} +(439187. - 142701. i) q^{47} -407171. q^{48} +(547677. + 397911. i) q^{49} +(-862696. - 626785. i) q^{50} -702314. i q^{51} +(-4.95414e6 - 1.60970e6i) q^{52} +(-2.14848e6 - 2.95714e6i) q^{53} +(447751. + 1.37804e6i) q^{54} +(-1.04986e7 + 3.41121e6i) q^{55} +(-3.28341e6 + 1.06684e6i) q^{56} +(921912. + 669808. i) q^{57} +(492456. + 1.51562e6i) q^{58} +(-2.09764e6 - 2.88715e6i) q^{59} +(180710. - 556167. i) q^{60} +(1.66491e7 - 5.40961e6i) q^{61} +(-5.68997e6 + 7.83157e6i) q^{62} +(9.74714e6 + 1.34158e7i) q^{63} +(-2.33581e6 + 7.18890e6i) q^{64} +(-9.31563e6 + 1.28219e7i) q^{65} +(1.23089e6 + 1.69418e6i) q^{66} +(1.75126e7 - 2.41040e7i) q^{67} +(-2.44868e7 - 7.95625e6i) q^{68} +(180756. + 58731.3i) q^{69} -3.13248e7i q^{70} +(2.03883e6 + 2.53298e7i) q^{71} -8.88734e6 q^{72} +(-1.25869e7 + 3.87386e7i) q^{73} +(5.67273e6 - 1.74589e7i) q^{74} +(213215. + 154909. i) q^{75} +(3.37975e7 - 2.45553e7i) q^{76} +(3.88599e7 + 2.82333e7i) q^{77} +(2.85940e6 + 929074. i) q^{78} +(-2.87984e7 + 2.09233e7i) q^{79} +(3.67418e7 + 2.66945e7i) q^{80} +(1.31361e7 + 4.04286e7i) q^{81} +(8.61934e7 + 2.80059e7i) q^{82} +(4.09196e7 - 2.97298e7i) q^{83} +(-2.42004e6 + 786319. i) q^{84} +(-4.60443e7 + 6.33745e7i) q^{85} +(-3.84254e7 - 1.18261e8i) q^{86} +(-121710. - 374585. i) q^{87} +(-2.44829e7 + 7.95498e6i) q^{88} +(-1.76064e7 + 1.27918e7i) q^{89} +(2.49186e7 - 7.66917e7i) q^{90} +6.89621e7 q^{91} +(4.09544e6 - 5.63689e6i) q^{92} +(1.40627e6 - 1.93557e6i) q^{93} +9.77111e6i q^{94} +(-3.92772e7 - 1.20883e8i) q^{95} +(2.09959e6 - 6.46187e6i) q^{96} +7.99800e7i q^{97} +(-1.15884e7 + 8.41949e6i) q^{98} +(7.26801e7 + 1.00036e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 188 q + 6 q^{2} - 73 q^{3} - 6170 q^{4} + 291 q^{5} - 4342 q^{6} - 5 q^{7} - 4231 q^{8} - 103462 q^{9}+O(q^{10}) $ 188 * q + 6 * q^2 - 73 * q^3 - 6170 * q^4 + 291 * q^5 - 4342 * q^6 - 5 * q^7 - 4231 * q^8 - 103462 * q^9	\( 188 q + 6 q^{2} - 73 q^{3} - 6170 q^{4} + 291 q^{5} - 4342 q^{6} - 5 q^{7} - 4231 q^{8} - 103462 q^{9} - 39605 q^{10} + 28465 q^{11} + 87226 q^{12} - 5 q^{13} - 270305 q^{14} - 273057 q^{15} - 607702 q^{16} + 267190 q^{17} - 595620 q^{18} - 164489 q^{19} + 1380836 q^{20} - 5 q^{21} + 1441620 q^{22} + 1594977 q^{24} - 3158228 q^{25} + 2482310 q^{27} + 1860770 q^{28} + 2583153 q^{29} + 780472 q^{30} - 1534580 q^{31} - 6084580 q^{32} - 5198730 q^{33} + 10938955 q^{35} - 12158488 q^{36} - 4992382 q^{37} + 305303 q^{38} - 8681861 q^{40} + 30641485 q^{42} - 9988337 q^{43} - 32861225 q^{44} - 21060496 q^{45} + 19044385 q^{46} + 23015995 q^{47} - 53495300 q^{48} + 25425264 q^{49} - 4315274 q^{50} - 45871475 q^{52} + 75873220 q^{53} + 18140888 q^{54} - 11520710 q^{55} + 42589435 q^{56} + 9074010 q^{57} + 40460737 q^{58} + 32264995 q^{59} - 158115870 q^{60} + 9916960 q^{61} - 41573135 q^{62} - 20329385 q^{63} - 173398207 q^{64} - 29584700 q^{65} + 144000740 q^{66} - 128145130 q^{67} - 164559375 q^{68} - 6139445 q^{69} + 23495669 q^{71} + 775956446 q^{72} + 162484067 q^{73} - 71216283 q^{74} + 39808021 q^{75} + 234840675 q^{76} - 257706146 q^{77} + 42725920 q^{78} + 86434027 q^{79} - 407918718 q^{80} + 89998907 q^{81} - 401066875 q^{82} + 201744669 q^{83} - 650053825 q^{84} - 238358045 q^{85} + 120450107 q^{86} + 243937047 q^{87} + 8458490 q^{88} + 121627626 q^{89} + 542716852 q^{90} + 213723098 q^{91} + 377149290 q^{92} - 564095080 q^{93} - 185902021 q^{95} + 133775573 q^{96} + 803758296 q^{98} - 824163320 q^{99}+O(q^{100}) \) 188 * q + 6 * q^2 - 73 * q^3 - 6170 * q^4 + 291 * q^5 - 4342 * q^6 - 5 * q^7 - 4231 * q^8 - 103462 * q^9 - 39605 * q^10 + 28465 * q^11 + 87226 * q^12 - 5 * q^13 - 270305 * q^14 - 273057 * q^15 - 607702 * q^16 + 267190 * q^17 - 595620 * q^18 - 164489 * q^19 + 1380836 * q^20 - 5 * q^21 + 1441620 * q^22 + 1594977 * q^24 - 3158228 * q^25 + 2482310 * q^27 + 1860770 * q^28 + 2583153 * q^29 + 780472 * q^30 - 1534580 * q^31 - 6084580 * q^32 - 5198730 * q^33 + 10938955 * q^35 - 12158488 * q^36 - 4992382 * q^37 + 305303 * q^38 - 8681861 * q^40 + 30641485 * q^42 - 9988337 * q^43 - 32861225 * q^44 - 21060496 * q^45 + 19044385 * q^46 + 23015995 * q^47 - 53495300 * q^48 + 25425264 * q^49 - 4315274 * q^50 - 45871475 * q^52 + 75873220 * q^53 + 18140888 * q^54 - 11520710 * q^55 + 42589435 * q^56 + 9074010 * q^57 + 40460737 * q^58 + 32264995 * q^59 - 158115870 * q^60 + 9916960 * q^61 - 41573135 * q^62 - 20329385 * q^63 - 173398207 * q^64 - 29584700 * q^65 + 144000740 * q^66 - 128145130 * q^67 - 164559375 * q^68 - 6139445 * q^69 + 23495669 * q^71 + 775956446 * q^72 + 162484067 * q^73 - 71216283 * q^74 + 39808021 * q^75 + 234840675 * q^76 - 257706146 * q^77 + 42725920 * q^78 + 86434027 * q^79 - 407918718 * q^80 + 89998907 * q^81 - 401066875 * q^82 + 201744669 * q^83 - 650053825 * q^84 - 238358045 * q^85 + 120450107 * q^86 + 243937047 * q^87 + 8458490 * q^88 + 121627626 * q^89 + 542716852 * q^90 + 213723098 * q^91 + 377149290 * q^92 - 564095080 * q^93 - 185902021 * q^95 + 133775573 * q^96 + 803758296 * q^98 - 824163320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−6.53857	+	20.1236i	−0.408661	+	1.25773i	0.509139	+	0.860684i	$0.329964\pi$
$2$	−6.53857	+	20.1236i	−0.408661	+	1.25773i	−0.917800	+	0.397044i	$0.870036\pi$
$3$	1.61600	−	4.97354i	0.0199506	−	0.0614018i	−0.940586	−	0.339557i	$-0.889723\pi$
$3$	1.61600	−	4.97354i	0.0199506	−	0.0614018i	0.960536	+	0.278155i	$0.0897229\pi$
$4$	−155.100	−	112.687i	−0.605859	−	0.440183i
$5$	−471.892	+	342.850i	−0.755028	+	0.548560i	−0.897381	−	0.441256i	$-0.854533\pi$
$5$	−471.892	+	342.850i	−0.755028	+	0.548560i	0.142353	+	0.989816i	$0.454533\pi$
$6$	89.5195	+	65.0397i	0.0690737	+	0.0501850i
$7$	2413.84	+	784.305i	1.00535	+	0.326658i	0.765001	−	0.644029i	$-0.222739\pi$
$7$	2413.84	+	784.305i	1.00535	+	0.326658i	0.240348	+	0.970687i	$0.422739\pi$
$8$	−1100.46	+	799.529i	−0.268666	+	0.195198i
$9$	5285.84	+	3840.38i	0.805645	+	0.585335i
$10$	−3813.89	−	11737.9i	−0.381389	−	1.17379i
$11$	17999.0	+	5848.22i	1.22935	+	0.399441i	0.850480	−	0.526008i	$-0.176312\pi$
$11$	17999.0	+	5848.22i	1.22935	+	0.399441i	0.378873	+	0.925449i	$0.376312\pi$
$12$	−811.094	+	589.295i	−0.0391153	+	0.0284189i
$13$	25841.3	−	8396.35i	0.904776	−	0.293980i	0.180569	−	0.983562i	$-0.442206\pi$
$13$	25841.3	−	8396.35i	0.904776	−	0.293980i	0.724207	+	0.689583i	$0.242206\pi$
$14$	−31566.1	+	43447.1i	−0.821693	+	1.13096i
$15$	942.600	+	2901.02i	0.0186193	+	0.0573042i
$16$	−24060.2	−	74049.7i	−0.367130	−	1.12991i
$17$	127726.	−	41500.6i	1.52926	−	0.496888i	0.580873	−	0.813994i	$-0.302711\pi$
$17$	127726.	−	41500.6i	1.52926	−	0.496888i	0.948390	+	0.317106i	$0.102711\pi$
$18$	−111844.	+	81259.7i	−1.06543	+	0.774079i
$19$	−67337.1	+	207242.i	−0.516702	+	1.59025i	0.263461	+	0.964670i	$0.415136\pi$
$19$	−67337.1	+	207242.i	−0.516702	+	1.59025i	−0.780163	+	0.625576i	$0.784864\pi$
$20$	111825.			0.698907
$21$	7801.55	−	10737.9i	0.0401147	−	0.0552132i
$22$	−235375.	+	323966.i	−1.00478	+	1.38296i
$23$			36343.6i			0.129872i	0.997889	+	0.0649361i	$0.0206844\pi$
$23$			36343.6i			0.129872i	−0.997889	+	0.0649361i	$0.979316\pi$
$24$	2198.15	+	6765.21i	0.00662541	+	0.0203909i
$25$	−15573.4	+	47929.8i	−0.0398678	+	0.122700i
$26$			574922.i			1.25810i
$27$	55400.2	−	40250.6i	0.104245	−	0.0757386i
$28$	−286006.	−	393654.i	−0.465311	−	0.640446i
$29$	60931.6	−	44269.4i	0.0861490	−	0.0625909i	−0.543877	−	0.839165i	$-0.683044\pi$
$29$	60931.6	−	44269.4i	0.0861490	−	0.0625909i	0.630026	+	0.776574i	$0.283044\pi$
$30$	−64542.4			−0.0796820
$31$	435108.	+	141375.i	0.471140	+	0.153083i	0.534958	−	0.844879i	$-0.320328\pi$
$31$	435108.	+	141375.i	0.471140	+	0.153083i	−0.0638174	+	0.997962i	$0.520328\pi$
$32$	1.29925e6			1.23906
$33$	58172.7	−	80067.9i	0.0490528	−	0.0675153i
$34$			2.84166e6i			2.12646i
$35$	−1.40797e6	+	457478.i	−0.938258	+	0.304858i
$36$	−387073.	−	1.19129e6i	−0.230453	−	0.709262i
$37$	−867579.			−0.462916			−0.231458	−	0.972845i	$-0.574350\pi$
$37$	−867579.			−0.462916			−0.231458	+	0.972845i	$0.574350\pi$
$38$	−3.73018e6	−	2.71014e6i	−1.78894	−	1.29974i
$39$		−	142091.i		−	0.0614199i
$40$	245179.	−	754584.i	0.0957731	−	0.294759i
$41$		−	4.28319e6i		−	1.51577i	−0.652391	−	0.757883i	$-0.726234\pi$
$41$		−	4.28319e6i		−	1.51577i	0.652391	−	0.757883i	$-0.273766\pi$
$42$	165075.	+	227206.i	0.0530498	+	0.0730168i
$43$	−4.75437e6	+	3.45425e6i	−1.39065	+	1.01037i	−0.394860	+	0.918741i	$0.629207\pi$
$43$	−4.75437e6	+	3.45425e6i	−1.39065	+	1.01037i	−0.995793	+	0.0916276i	$0.970793\pi$
$44$	−2.13262e6	−	2.93530e6i	−0.568988	−	0.783145i
$45$	−3.81102e6			−0.929376
$46$	−731365.	−	237635.i	−0.163344	−	0.0530736i
$47$	439187.	−	142701.i	0.0900033	−	0.0292438i	−0.263669	−	0.964613i	$-0.584933\pi$
$47$	439187.	−	142701.i	0.0900033	−	0.0292438i	0.353673	+	0.935369i	$0.384933\pi$
$48$	−407171.			−0.0767029
$49$	547677.	+	397911.i	0.0950036	+	0.0690242i
$50$	−862696.	−	626785.i	−0.138031	−	0.100286i
$51$		−	702314.i		−	0.103813i
$52$	−4.95414e6	−	1.60970e6i	−0.677572	−	0.220156i
$53$	−2.14848e6	−	2.95714e6i	−0.272288	−	0.374773i	0.650872	−	0.759187i	$-0.274403\pi$
$53$	−2.14848e6	−	2.95714e6i	−0.272288	−	0.374773i	−0.923161	+	0.384415i	$0.874403\pi$
$54$	447751.	+	1.37804e6i	0.0526576	+	0.162064i
$55$	−1.04986e7	+	3.41121e6i	−1.14731	+	0.372785i
$56$	−3.28341e6	+	1.06684e6i	−0.333866	+	0.108480i
$57$	921912.	+	669808.i	0.0873354	+	0.0634528i
$58$	492456.	+	1.51562e6i	0.0435167	+	0.133931i
$59$	−2.09764e6	−	2.88715e6i	−0.173110	−	0.238265i	0.713642	−	0.700510i	$-0.247044\pi$
$59$	−2.09764e6	−	2.88715e6i	−0.173110	−	0.238265i	−0.886752	+	0.462245i	$0.847044\pi$
$60$	180710.	−	556167.i	0.0139437	−	0.0429142i
$61$	1.66491e7	−	5.40961e6i	1.20246	−	0.390703i	0.361795	−	0.932258i	$-0.382164\pi$
$61$	1.66491e7	−	5.40961e6i	1.20246	−	0.390703i	0.840666	+	0.541555i	$0.182164\pi$
$62$	−5.68997e6	+	7.83157e6i	−0.385073	+	0.530008i
$63$	9.74714e6	+	1.34158e7i	0.618750	+	0.851636i
$64$	−2.33581e6	+	7.18890e6i	−0.139225	+	0.428492i
$65$	−9.31563e6	+	1.28219e7i	−0.521866	+	0.718287i
$66$	1.23089e6	+	1.69418e6i	0.0648700	+	0.0892859i
$67$	1.75126e7	−	2.41040e7i	0.869061	−	1.19616i	−0.110271	−	0.993902i	$-0.535172\pi$
$67$	1.75126e7	−	2.41040e7i	0.869061	−	1.19616i	0.979332	−	0.202258i	$-0.0648280\pi$
$68$	−2.44868e7	−	7.95625e6i	−1.14524	−	0.372111i
$69$	180756.	+	58731.3i	0.00797438	+	0.00259103i
$70$		−	3.13248e7i		−	1.30466i
$71$	2.03883e6	+	2.53298e7i	0.0802320	+	0.996776i
$71$	2.03883e6	+	2.53298e7i	0.0802320	+	0.996776i
$72$	−8.88734e6			−0.330706
$73$	−1.25869e7	+	3.87386e7i	−0.443230	+	1.36412i	0.441184	+	0.897417i	$0.354559\pi$
$73$	−1.25869e7	+	3.87386e7i	−0.443230	+	1.36412i	−0.884413	+	0.466704i	$0.845441\pi$
$74$	5.67273e6	−	1.74589e7i	0.189176	−	0.582223i
$75$	213215.	+	154909.i	0.00673863	+	0.00489590i
$76$	3.37975e7	−	2.45553e7i	1.01305	−	0.736022i
$77$	3.88599e7	+	2.82333e7i	1.10545	+	0.803155i
$78$	2.85940e6	+	929074.i	0.0772496	+	0.0250999i
$79$	−2.87984e7	+	2.09233e7i	−0.739368	+	0.537182i	−0.892513	−	0.451021i	$-0.851060\pi$
$79$	−2.87984e7	+	2.09233e7i	−0.739368	+	0.537182i	0.153145	+	0.988204i	$0.451060\pi$
$80$	3.67418e7	+	2.66945e7i	0.897016	+	0.651720i
$81$	1.31361e7	+	4.04286e7i	0.305158	+	0.939180i
$82$	8.61934e7	+	2.80059e7i	1.90642	+	0.619434i
$83$	4.09196e7	−	2.97298e7i	0.862221	−	0.626440i	−0.0662673	−	0.997802i	$-0.521109\pi$
$83$	4.09196e7	−	2.97298e7i	0.862221	−	0.626440i	0.928488	+	0.371362i	$0.121109\pi$
$84$	−2.42004e6	+	786319.i	−0.0486077	+	0.0157936i
$85$	−4.60443e7	+	6.33745e7i	−0.882064	+	1.21406i
$86$	−3.84254e7	−	1.18261e8i	−0.702464	−	2.16196i
$87$	−121710.	−	374585.i	−0.00212447	−	0.00653843i
$88$	−2.44829e7	+	7.95498e6i	−0.408256	+	0.132650i
$89$	−1.76064e7	+	1.27918e7i	−0.280614	+	0.203878i	−0.719185	−	0.694818i	$-0.755485\pi$
$89$	−1.76064e7	+	1.27918e7i	−0.280614	+	0.203878i	0.438571	+	0.898697i	$0.355485\pi$
$90$	2.49186e7	−	7.66917e7i	0.379799	−	1.16890i
$91$	6.89621e7			1.00565
$92$	4.09544e6	−	5.63689e6i	0.0571675	−	0.0786843i
$93$	1.40627e6	−	1.93557e6i	0.0187991	−	0.0258747i
$94$			9.77111e6i			0.125150i
$95$	−3.92772e7	−	1.20883e8i	−0.482220	−	1.48412i
$96$	2.09959e6	−	6.46187e6i	0.0247201	−	0.0760805i
$97$			7.99800e7i			0.903430i	0.892162	+	0.451715i	$0.149188\pi$
$97$			7.99800e7i			0.903430i	−0.892162	+	0.451715i	$0.850812\pi$
$98$	−1.15884e7	+	8.41949e6i	−0.125638	+	0.0912813i
$99$	7.26801e7	+	1.00036e8i	0.756615	+	1.04139i
$100$	7.81649e6	−	5.67901e6i	0.0781649	−	0.0567901i
$101$	1.39365e8			1.33927			0.669635	−	0.742690i	$-0.266451\pi$
$101$	1.39365e8			1.33927			0.669635	+	0.742690i	$0.266451\pi$
$102$	1.41331e7	+	4.59213e6i	0.130568	+	0.0424242i
$103$	−1.29522e8			−1.15079			−0.575394	−	0.817876i	$-0.695151\pi$
$103$	−1.29522e8			−1.15079			−0.575394	+	0.817876i	$0.695151\pi$
$104$	−2.17241e7	+	2.99007e7i	−0.185699	+	0.255592i
$105$			7.74190e6i			0.0636928i
$106$	7.35564e7	−	2.38999e7i	0.582635	−	0.189310i
$107$	−6.99211e7	−	2.15195e8i	−0.533425	−	1.64171i	−0.747028	−	0.664792i	$-0.768520\pi$
$107$	−6.99211e7	−	2.15195e8i	−0.533425	−	1.64171i	0.213603	−	0.976921i	$-0.431480\pi$
$108$	−1.31283e7			−0.0964968
$109$	−6.00719e7	−	4.36448e7i	−0.425564	−	0.309191i	0.354308	−	0.935129i	$-0.384716\pi$
$109$	−6.00719e7	−	4.36448e7i	−0.425564	−	0.309191i	−0.779873	+	0.625938i	$0.784716\pi$
$110$		−	2.33575e8i		−	1.59535i
$111$	−1.40201e6	+	4.31494e6i	−0.00923547	+	0.0284239i
$112$		−	1.97615e8i		−	1.25588i
$113$	−3.04094e7	−	4.18550e7i	−0.186507	−	0.256705i	0.705517	−	0.708693i	$-0.250715\pi$
$113$	−3.04094e7	−	4.18550e7i	−0.186507	−	0.256705i	−0.892024	+	0.451988i	$0.850715\pi$
$114$	−1.95070e7	+	1.41726e7i	−0.115497	+	0.0839134i
$115$	−1.24604e7	−	1.71503e7i	−0.0712427	−	0.0980571i
$116$	−1.44391e7			−0.0797457
$117$	1.68838e8	+	5.48588e7i	0.901005	+	0.292754i
$118$	7.18155e7	−	2.33343e7i	0.370416	−	0.120356i
$119$	3.40859e8			1.69975
$120$	−3.35674e6	−	2.43882e6i	−0.0161880	−	0.0117613i
$121$	1.16341e8	+	8.45265e7i	0.542738	+	0.394323i
$122$			3.70411e8i			1.67203i
$123$	−2.13026e7	−	6.92165e6i	−0.0930707	−	0.0302405i
$124$	−5.15541e7	−	7.09582e7i	−0.218060	−	0.300134i
$125$	−7.94927e7	−	2.44653e8i	−0.325602	−	1.00210i
$126$	−3.33707e8	+	1.08428e8i	−1.32399	+	0.430189i
$127$	−3.78500e8	+	1.22982e8i	−1.45496	+	0.472744i	−0.926526	−	0.376231i	$-0.877220\pi$
$127$	−3.78500e8	+	1.22982e8i	−1.45496	+	0.472744i	−0.528432	+	0.848976i	$0.677220\pi$
$128$	1.39691e8	+	1.01492e8i	0.520391	+	0.378086i
$129$	9.49679e6	+	2.92281e7i	0.0342940	+	0.105546i
$130$	−1.97112e8	−	2.71301e8i	−0.690143	−	0.949901i
$131$	−1.23834e8	+	3.81123e8i	−0.420491	+	1.29414i	0.486756	+	0.873538i	$0.338180\pi$
$131$	−1.23834e8	+	3.81123e8i	−0.420491	+	1.29414i	−0.907247	+	0.420599i	$0.861820\pi$
$132$	−1.80452e7	+	5.86323e6i	−0.0594382	+	0.0193126i
$133$	−3.25082e8	+	4.47438e8i	−1.03893	+	1.42997i
$134$	3.70553e8	+	5.10022e8i	1.14929	+	1.58187i
$135$	−1.23430e7	+	3.79879e7i	−0.0371609	+	0.114369i
$136$	−1.07376e8	+	1.47790e8i	−0.313870	+	0.432006i
$137$	−1.85179e7	−	2.54877e7i	−0.0525666	−	0.0723517i	0.781924	−	0.623373i	$-0.214238\pi$
$137$	−1.85179e7	−	2.54877e7i	−0.0525666	−	0.0723517i	−0.834491	+	0.551021i	$0.814238\pi$
$138$	−2.36378e6	+	3.25346e6i	−0.00651763	+	0.00897075i
$139$	2.06987e8	+	6.72542e7i	0.554478	+	0.180161i	0.572835	−	0.819671i	$-0.305844\pi$
$139$	2.06987e8	+	6.72542e7i	0.554478	+	0.180161i	−0.0183572	+	0.999831i	$0.505844\pi$
$140$	2.69928e8	+	8.77050e7i	0.702646	+	0.228303i
$141$		−	2.41492e6i		−	0.00610979i
$142$	−5.23058e8	−	1.24592e8i	−1.28646	−	0.306433i
$143$	5.14220e8			1.22972
$144$	1.57201e8	−	4.83815e8i	0.365600	−	1.12520i
$145$	−1.35754e7	+	4.17808e7i	−0.0307101	+	0.0945158i
$146$	−6.97262e8	−	5.06591e8i	−1.53456	−	1.11493i
$147$	2.86407e6	−	2.08087e6i	0.00613359	−	0.00445631i
$148$	1.34562e8	+	9.77647e7i	0.280462	+	0.203768i
$149$	−2.01655e7	−	6.55217e6i	−0.0409132	−	0.0132935i	0.288489	−	0.957483i	$-0.406847\pi$
$149$	−2.01655e7	−	6.55217e6i	−0.0409132	−	0.0132935i	−0.329402	+	0.944190i	$0.606847\pi$
$150$	−4.51146e6	+	3.27777e6i	−0.00891153	+	0.00647461i
$151$	−6.88865e7	−	5.00490e7i	−0.132503	−	0.0962692i	0.519559	−	0.854434i	$-0.326096\pi$
$151$	−6.88865e7	−	5.00490e7i	−0.132503	−	0.0962692i	−0.652063	+	0.758165i	$0.726096\pi$
$152$	−9.15947e7	−	2.81899e8i	−0.171592	−	0.528105i
$153$	8.34515e8	+	2.71150e8i	1.52289	+	0.494817i
$154$	−8.22246e8	+	5.97396e8i	−1.46190	+	1.06213i
$155$	−2.53795e8	+	8.24629e7i	−0.439699	+	0.142867i
$156$	−1.60118e7	+	2.20384e7i	−0.0270360	+	0.0372118i
$157$	1.48340e8	+	4.56544e8i	0.244152	+	0.751422i	0.995775	+	0.0918292i	$0.0292714\pi$
$157$	1.48340e8	+	4.56544e8i	0.244152	+	0.751422i	−0.751623	+	0.659593i	$0.770729\pi$
$158$	−2.32752e8	−	7.16338e8i	−0.373479	−	1.14945i
$159$	−1.81794e7	+	5.90684e6i	−0.0284440	+	0.00924202i
$160$	−6.13106e8	+	4.45447e8i	−0.935525	+	0.679699i
$161$	−2.85044e7	+	8.77276e7i	−0.0424237	+	0.130567i
$162$	−8.99463e8			−1.30594
$163$	7.21986e8	−	9.93728e8i	1.02277	−	1.40772i	0.112527	−	0.993649i	$-0.464105\pi$
$163$	7.21986e8	−	9.93728e8i	1.02277	−	1.40772i	0.910243	−	0.414074i	$-0.135895\pi$
$164$	−4.82659e8	+	6.64323e8i	−0.667214	+	0.918341i
$165$			5.77279e7i			0.0778843i
$166$	3.30717e8	+	1.01784e9i	0.435536	+	1.34044i
$167$	3.37340e8	−	1.03822e9i	0.433712	−	1.33483i	−0.460689	−	0.887562i	$-0.652398\pi$
$167$	3.37340e8	−	1.03822e9i	0.433712	−	1.33483i	0.894401	−	0.447266i	$-0.147602\pi$
$168$			1.80542e7i			0.0226642i
$169$	−6.26656e7	+	4.55292e7i	−0.0768214	+	0.0558140i
$170$	−9.74263e8	−	1.34096e9i	−1.16649	−	1.60553i
$171$	−1.15182e9	+	8.36849e8i	−1.34711	+	0.978729i
$172$	1.12665e9			1.28729
$173$	−2.61698e8	−	8.50309e7i	−0.292157	−	0.0949276i	0.159272	−	0.987235i	$-0.449085\pi$
$173$	−2.61698e8	−	8.50309e7i	−0.292157	−	0.0949276i	−0.451429	+	0.892307i	$0.649085\pi$
$174$	8.33383e6			0.00909176
$175$	−7.51832e7	+	1.03481e8i	−0.0801620	+	0.110334i
$176$		−	1.47353e9i		−	1.53570i
$177$	−1.77491e7	+	5.76705e6i	−0.0180836	+	0.00587571i
$178$	−1.42297e8	−	4.37944e8i	−0.141747	−	0.436253i
$179$	8.18745e8			0.797511			0.398755	−	0.917057i	$-0.369442\pi$
$179$	8.18745e8			0.797511			0.398755	+	0.917057i	$0.369442\pi$
$180$	5.91090e8	+	4.29452e8i	0.563071	+	0.409095i
$181$		−	1.88989e9i		−	1.76085i	−0.474189	−	0.880423i	$-0.657259\pi$
$181$		−	1.88989e9i		−	1.76085i	0.474189	−	0.880423i	$-0.342741\pi$
$182$	−4.50914e8	+	1.38777e9i	−0.410968	+	1.26483i
$183$		−	9.15468e7i		−	0.0816280i
$184$	−2.90577e7	−	3.99945e7i	−0.0253507	−	0.0348923i
$185$	4.09404e8	−	2.97450e8i	0.349515	−	0.253937i
$186$	2.97556e7	+	4.09551e7i	0.0248609	+	0.0342182i
$187$	2.54163e9			2.07848
$188$	−8.41984e7	−	2.73577e7i	−0.0674020	−	0.0219002i
$189$	1.65296e8	−	5.37079e7i	0.129543	−	0.0420912i
$190$	2.68942e9			2.06369
$191$	−4.57674e8	−	3.32519e8i	−0.343892	−	0.249852i	0.402410	−	0.915460i	$-0.368173\pi$
$191$	−4.57674e8	−	3.32519e8i	−0.343892	−	0.249852i	−0.746302	+	0.665607i	$0.768173\pi$
$192$	3.19796e7	+	2.32345e7i	0.0235325	+	0.0170974i
$193$			6.21547e8i			0.447965i	0.974593	+	0.223983i	$0.0719059\pi$
$193$			6.21547e8i			0.447965i	−0.974593	+	0.223983i	$0.928094\pi$
$194$	−1.60949e9	−	5.22955e8i	−1.13627	−	0.369196i
$195$	4.87160e7	+	6.70518e7i	0.0336925	+	0.0463738i
$196$	−4.01054e7	−	1.23432e8i	−0.0271756	−	0.0836379i
$197$	5.41938e8	−	1.76086e8i	0.359819	−	0.116912i	−0.123528	−	0.992341i	$-0.539421\pi$
$197$	5.41938e8	−	1.76086e8i	0.359819	−	0.116912i	0.483347	+	0.875429i	$0.339421\pi$
$198$	−2.48831e9	+	8.08500e8i	−1.61899	+	0.526040i
$199$	−2.13669e9	−	1.55240e9i	−1.36248	−	0.989897i	−0.998283	−	0.0585739i	$-0.981345\pi$
$199$	−2.13669e9	−	1.55240e9i	−1.36248	−	0.989897i	−0.364194	−	0.931323i	$-0.618655\pi$
$200$	−2.11835e7	−	6.51961e7i	−0.0132397	−	0.0407476i
$201$	−9.15818e7	−	1.26051e8i	−0.0561080	−	0.0772260i
$202$	−9.11248e8	+	2.80453e9i	−0.547307	+	1.68444i
$203$	1.81800e8	−	5.90704e7i	0.107056	−	0.0347845i
$204$	−7.91415e7	+	1.08929e8i	−0.0456966	+	0.0628959i
$205$	1.46849e9	+	2.02121e9i	0.831488	+	1.14445i
$206$	8.46891e8	−	2.60646e9i	0.470282	−	1.44738i
$207$	−1.39573e8	+	1.92106e8i	−0.0760188	+	0.104631i
$208$	−1.24349e9	−	1.71152e9i	−0.664340	−	0.914386i
$209$	−2.42400e9	+	3.33634e9i	−1.27042	+	1.74858i
$210$	−1.55795e8	−	5.06209e7i	−0.0801082	−	0.0260287i
$211$	2.03115e9	+	6.59962e8i	1.02474	+	0.332958i	0.772708	−	0.634762i	$-0.218902\pi$
$211$	2.03115e9	+	6.59962e8i	1.02474	+	0.332958i	0.252030	+	0.967719i	$0.418902\pi$
$212$			7.00758e8i			0.346916i
$213$	1.29273e8	+	3.07927e7i	0.0628045	+	0.0149599i
$214$	4.78769e9			2.28282
$215$	1.05926e9	−	3.26007e9i	0.495734	−	1.52571i
$216$	−2.87840e7	+	8.85881e7i	−0.0132232	+	0.0406968i
$217$	9.39401e8	+	6.82515e8i	0.423655	+	0.307803i
$218$	1.27108e9	−	9.23491e8i	0.562789	−	0.408890i
$219$	1.72328e8	+	1.25203e8i	0.0749167	+	0.0544302i
$220$	2.01274e9	+	6.53978e8i	0.859204	+	0.279172i
$221$	2.95214e9	−	2.14486e9i	1.23757	−	0.899144i
$222$	−7.76653e7	−	5.64271e7i	−0.0319753	−	0.0232314i
$223$	9.25045e8	+	2.84700e9i	0.374062	+	1.15124i	0.944109	+	0.329632i	$0.106925\pi$
$223$	9.25045e8	+	2.84700e9i	0.374062	+	1.15124i	−0.570047	+	0.821612i	$0.693075\pi$
$224$	3.13618e9	+	1.01901e9i	1.24569	+	0.404748i
$225$	−2.66387e8	+	1.93542e8i	−0.103940	+	0.0755169i
$226$	1.04111e9	−	3.38277e8i	0.399083	−	0.129670i
$227$	−3.04641e8	+	4.19302e8i	−0.114732	+	0.157915i	−0.862521	−	0.506022i	$-0.831116\pi$
$227$	−3.04641e8	+	4.19302e8i	−0.114732	+	0.157915i	0.747789	+	0.663937i	$0.231116\pi$
$228$	−6.75101e7	−	2.07775e8i	−0.0249821	−	0.0768870i
$229$	−1.23897e9	−	3.81315e9i	−0.450524	−	1.38657i	−0.876310	−	0.481747i	$-0.840002\pi$
$229$	−1.23897e9	−	3.81315e9i	−0.450524	−	1.38657i	0.425786	−	0.904824i	$-0.359998\pi$
$230$	4.26599e8	−	1.38610e8i	0.152443	−	0.0495318i
$231$	2.03217e8	−	1.47646e8i	0.0713695	−	0.0518530i
$232$	−3.16580e7	+	9.74332e7i	−0.0109278	+	0.0336322i
$233$	3.97379e9			1.34828			0.674141	−	0.738602i	$-0.264514\pi$
$233$	3.97379e9			1.34828			0.674141	+	0.738602i	$0.264514\pi$
$234$	−2.20792e9	+	3.03894e9i	−0.736410	+	1.01358i
$235$	−1.58324e8	+	2.17915e8i	−0.0519130	+	0.0714521i
$236$			6.84173e8i			0.220555i
$237$	5.75246e7	+	1.77042e8i	0.0182331	+	0.0561156i
$238$	−2.22873e9	+	6.85932e9i	−0.694623	+	2.13783i
$239$			2.06135e9i			0.631772i	0.948797	+	0.315886i	$0.102302\pi$
$239$			2.06135e9i			0.631772i	−0.948797	+	0.315886i	$0.897698\pi$
$240$	1.92141e8	−	1.39599e8i	0.0579128	−	0.0420761i
$241$	−3.39015e9	−	4.66614e9i	−1.00496	−	1.38321i	−0.922230	−	0.386643i	$-0.873635\pi$
$241$	−3.39015e9	−	4.66614e9i	−1.00496	−	1.38321i	−0.0827344	−	0.996572i	$-0.526365\pi$
$242$	−2.46168e9	+	1.78852e9i	−0.717746	+	0.521473i
$243$	6.71588e8			0.192610
$244$	−3.19186e9	−	1.03710e9i	−0.900503	−	0.292591i
$245$	−3.94868e8			−0.109594
$246$	2.78578e8	−	3.83429e8i	0.0760687	−	0.104700i
$247$			5.92080e9i			1.59072i
$248$	−5.91851e8	+	1.92304e8i	−0.156461	+	0.0508372i
$249$	−8.17364e7	−	2.51559e8i	−0.0212627	−	0.0654398i
$250$	5.44309e9			1.39343
$251$	−1.26106e9	−	9.16211e8i	−0.317716	−	0.230834i	0.417484	−	0.908684i	$-0.362912\pi$
$251$	−1.26106e9	−	9.16211e8i	−0.317716	−	0.230834i	−0.735200	+	0.677850i	$0.762912\pi$
$252$		−	3.17916e9i		−	0.788335i
$253$	−2.12545e8	+	6.54146e8i	−0.0518763	+	0.159659i
$254$		−	8.42092e9i		−	2.02313i
$255$	2.40788e8	+	3.31417e8i	0.0569475	+	0.0783815i
$256$	−4.52127e9	+	3.28489e9i	−1.05269	+	0.764824i
$257$	9.67159e8	+	1.33118e9i	0.221700	+	0.305144i	0.905350	−	0.424666i	$-0.139609\pi$
$257$	9.67159e8	+	1.33118e9i	0.221700	+	0.305144i	−0.683650	+	0.729810i	$0.739609\pi$
$258$	−6.50272e8			−0.146763
$259$	−2.09420e9	−	6.80447e8i	−0.465392	−	0.151215i
$260$	2.88971e9	−	9.38923e8i	0.632355	−	0.205464i
$261$	4.92086e8			0.106042
$262$	−6.85989e9	−	4.98400e9i	−1.45583	−	1.05773i
$263$	2.12625e9	+	1.54481e9i	0.444417	+	0.322888i	0.787387	−	0.616458i	$-0.211433\pi$
$263$	2.12625e9	+	1.54481e9i	0.444417	+	0.322888i	−0.342971	+	0.939346i	$0.611433\pi$
$264$			1.34622e8i			0.0277141i
$265$	2.02771e9	+	6.58842e8i	0.411170	+	0.133597i
$266$	−6.87850e9	−	9.46745e9i	−1.37394	−	1.89106i
$267$	3.51685e7	+	1.08238e8i	0.00692005	+	0.0212977i
$268$	−5.43239e9	+	1.76509e9i	−1.05306	+	0.342159i
$269$	−5.59415e9	+	1.81765e9i	−1.06838	+	0.347137i	−0.789856	−	0.613293i	$-0.789845\pi$
$269$	−5.59415e9	+	1.81765e9i	−1.06838	+	0.347137i	−0.278522	+	0.960430i	$0.589845\pi$
$270$	−6.83749e8	−	4.96773e8i	−0.128660	−	0.0934766i
$271$	5.58917e8	+	1.72017e9i	0.103626	+	0.318929i	0.989406	−	0.145178i	$-0.0463753\pi$
$271$	5.58917e8	+	1.72017e9i	0.103626	+	0.318929i	−0.885779	+	0.464107i	$0.846375\pi$
$272$	−6.14621e9	−	8.45954e9i	−1.12288	−	1.54551i
$273$	1.11443e8	−	3.42986e8i	0.0200633	−	0.0617484i
$274$	6.33987e8	−	2.05995e8i	0.112481	−	0.0365472i
$275$	−5.60608e8	+	7.71611e8i	−0.0980231	+	0.134917i
$276$	−2.14171e7	−	2.94781e7i	−0.00369083	−	0.00507999i
$277$	−5.59688e8	+	1.72254e9i	−0.0950664	+	0.292584i	−0.987271	−	0.159047i	$-0.949158\pi$
$277$	−5.59688e8	+	1.72254e9i	−0.0950664	+	0.292584i	0.892205	+	0.451631i	$0.149158\pi$
$278$	−2.70680e9	+	3.72559e9i	−0.453186	+	0.623758i
$279$	1.75697e9	+	2.41827e9i	0.289967	+	0.399105i
$280$	1.18365e9	−	1.62915e9i	0.192571	−	0.265051i
$281$	−9.60947e9	−	3.12231e9i	−1.54125	−	0.500784i	−0.589532	−	0.807745i	$-0.700688\pi$
$281$	−9.60947e9	−	3.12231e9i	−1.54125	−	0.500784i	−0.951722	+	0.306961i	$0.900688\pi$
$282$	4.85970e7	+	1.57901e7i	0.00768446	+	0.00249683i
$283$			7.06865e9i			1.10202i	0.834497	+	0.551012i	$0.185758\pi$
$283$			7.06865e9i			1.10202i	−0.834497	+	0.551012i	$0.814242\pi$
$284$	2.53811e9	−	4.15840e9i	0.390154	−	0.639223i
$285$	−6.64687e8			−0.100748
$286$	−3.36226e9	+	1.03480e10i	−0.502537	+	1.54665i
$287$	3.35933e9	−	1.03389e10i	0.495136	−	1.52387i
$288$	6.86762e9	+	4.98962e9i	0.998243	+	0.725266i
$289$	8.94803e9	−	6.50112e9i	1.28273	−	0.931959i
$290$	−7.52018e8	−	5.46373e8i	−0.106325	−	0.0772498i
$291$	3.97784e8	+	1.29248e8i	0.0554722	+	0.0180240i
$292$	6.31757e9	−	4.58998e9i	0.868997	−	0.631364i
$293$	−2.93216e9	−	2.13034e9i	−0.397849	−	0.289054i	0.370816	−	0.928707i	$-0.379078\pi$
$293$	−2.93216e9	−	2.13034e9i	−0.397849	−	0.289054i	−0.768664	+	0.639653i	$0.779078\pi$
$294$	2.31478e7	+	7.12415e7i	0.00309827	+	0.00953551i
$295$	1.97972e9	+	6.43249e8i	0.261406	+	0.0849359i
$296$	9.54734e8	−	6.93655e8i	0.124370	−	0.0903601i
$297$	1.23254e9	−	4.00476e8i	0.158407	−	0.0514696i
$298$	2.63707e8	−	3.62962e8i	0.0334393	−	0.0460252i
$299$	3.05153e8	+	9.39165e8i	0.0381798	+	0.117505i
$300$	−1.56133e7	−	4.80529e7i	−0.00192757	−	0.00593246i
$301$	−1.41855e10	+	4.60914e9i	−1.72814	+	0.561505i
$302$	1.45759e9	−	1.05900e9i	0.175229	−	0.127312i
$303$	2.25214e8	−	6.93138e8i	0.0267193	−	0.0822335i
$304$	1.69664e10			1.98653
$305$	−6.00189e9	+	8.26089e9i	−0.693567	+	0.954613i
$306$	−1.09131e10	+	1.50205e10i	−1.24469	+	1.71317i
$307$			1.03492e9i			0.116507i	0.998302	+	0.0582534i	$0.0185532\pi$
$307$			1.03492e9i			0.116507i	−0.998302	+	0.0582534i	$0.981447\pi$
$308$	−2.84564e9	−	8.75798e9i	−0.316211	−	0.973198i
$309$	−2.09308e8	+	6.44185e8i	−0.0229590	+	0.0706605i
$310$		−	5.64646e9i		−	0.611406i
$311$	−2.86451e9	+	2.08119e9i	−0.306203	+	0.222469i	−0.730265	−	0.683163i	$-0.760604\pi$
$311$	−2.86451e9	+	2.08119e9i	−0.306203	+	0.222469i	0.424063	+	0.905633i	$0.360604\pi$
$312$	1.13606e8	+	1.56366e8i	0.0119890	+	0.0165015i
$313$	−5.01175e8	+	3.64125e8i	−0.0522170	+	0.0379379i	−0.613588	−	0.789627i	$-0.710274\pi$
$313$	−5.01175e8	+	3.64125e8i	−0.0522170	+	0.0379379i	0.561371	+	0.827565i	$0.310274\pi$
$314$	−1.01573e10			−1.04486
$315$	−9.19920e9	−	2.98900e9i	−0.934347	−	0.303588i
$316$	6.82442e9			0.684412
$317$	7.32587e9	−	1.00832e10i	0.725474	−	0.998529i	−0.273850	−	0.961772i	$-0.588297\pi$
$317$	7.32587e9	−	1.00832e10i	0.725474	−	0.998529i	0.999324	−	0.0367570i	$-0.0117028\pi$
$318$		−	4.04458e8i		−	0.0395517i
$319$	1.35560e9	−	4.40462e8i	0.130909	−	0.0425349i
$320$	−1.36246e9	−	4.19322e9i	−0.129934	−	0.399897i
$321$	−1.18327e9			−0.111446
$322$	−1.57902e9	−	1.14723e9i	−0.146881	−	0.106715i
$323$			2.92647e10i			2.68865i
$324$	2.51837e9	−	7.75074e9i	0.228528	−	0.703337i
$325$			1.36933e9i			0.122737i
$326$	1.52767e10	+	2.10265e10i	1.35257	+	1.86165i
$327$	−3.14145e8	+	2.28240e8i	−0.0274751	+	0.0199619i
$328$	3.42454e9	+	4.71347e9i	0.295874	+	0.407235i
$329$	1.17205e9			0.100037
$330$	−1.16170e9	−	3.77458e8i	−0.0979573	−	0.0318283i
$331$	2.51107e9	−	8.15896e8i	0.209193	−	0.0679708i	−0.202546	−	0.979273i	$-0.564922\pi$
$331$	2.51107e9	−	8.15896e8i	0.209193	−	0.0679708i	0.411739	+	0.911302i	$0.364922\pi$
$332$	−9.69678e9			−0.798133
$333$	−4.58588e9	−	3.33184e9i	−0.372946	−	0.270961i
$334$	1.86871e10	+	1.35770e10i	1.50161	+	1.09098i
$335$			1.73787e10i			1.37987i
$336$	−9.82846e8	−	3.19346e8i	−0.0771132	−	0.0250556i
$337$	1.02559e10	+	1.41160e10i	0.795158	+	1.09444i	0.993447	+	0.114297i	$0.0364616\pi$
$337$	1.02559e10	+	1.41160e10i	0.795158	+	1.09444i	−0.198289	+	0.980144i	$0.563538\pi$
$338$	−5.06471e8	−	1.55876e9i	−0.0388050	−	0.119429i
$339$	−2.57309e8	+	8.36049e7i	−0.0194830	+	0.00633043i
$340$	1.42829e10	−	4.64081e9i	1.06881	−	0.347279i
$341$	7.00470e9	+	5.08921e9i	0.518050	+	0.376385i
$342$	−9.30917e9	−	2.86507e10i	−0.680466	−	2.09426i
$343$	−7.59022e9	−	1.04470e10i	−0.548375	−	0.754774i
$344$	2.47021e9	−	7.60251e9i	0.176400	−	0.542904i
$345$	−1.05434e8	+	3.42574e7i	−0.00744222	+	0.00241812i
$346$	3.42226e9	−	4.71034e9i	0.238786	−	0.328661i
$347$	−1.18008e10	−	1.62424e10i	−0.813942	−	1.12029i	−0.990703	−	0.136041i	$-0.956562\pi$
$347$	−1.18008e10	−	1.62424e10i	−0.813942	−	1.12029i	0.176761	−	0.984254i	$-0.443438\pi$
$348$	−2.33336e7	+	7.18133e7i	−0.00159098	+	0.00489653i
$349$	−4.88903e9	+	6.72917e9i	−0.329550	+	0.453586i	−0.941353	−	0.337424i	$-0.890444\pi$
$349$	−4.88903e9	+	6.72917e9i	−0.329550	+	0.453586i	0.611803	+	0.791010i	$0.290444\pi$
$350$	−1.59082e9	−	2.18958e9i	−0.106011	−	0.145911i
$351$	1.09366e9	−	1.50529e9i	0.0720530	−	0.0991724i
$352$	2.33851e10	+	7.59829e9i	1.52324	+	0.494931i
$353$	2.70038e10	+	8.77407e9i	1.73911	+	0.565070i	0.994715	−	0.102674i	$-0.0327399\pi$
$353$	2.70038e10	+	8.77407e9i	1.73911	+	0.565070i	0.744391	+	0.667744i	$0.232740\pi$
$354$		−	3.94886e8i		−	0.0251454i
$355$	−9.64642e9	−	1.12539e10i	−0.607369	−	0.708582i
$356$	4.17221e9			0.259756
$357$	5.50828e8	−	1.69527e9i	0.0339112	−	0.104368i
$358$	−5.35342e9	+	1.64761e10i	−0.325911	+	1.00305i
$359$	1.46865e9	+	1.06704e9i	0.0884181	+	0.0642395i	0.631116	−	0.775688i	$-0.282597\pi$
$359$	1.46865e9	+	1.06704e9i	0.0884181	+	0.0642395i	−0.542698	+	0.839928i	$0.682597\pi$
$360$	4.19387e9	−	3.04702e9i	0.249692	−	0.181412i
$361$	−2.46751e10	−	1.79275e10i	−1.45288	−	1.05558i
$362$	3.80314e10	+	1.23572e10i	2.21467	+	0.719589i
$363$	6.08403e8	−	4.42031e8i	0.0350401	−	0.0254581i
$364$	−1.06960e10	−	7.77112e9i	−0.609280	−	0.442668i
$365$	−7.34186e9	−	2.25959e10i	−0.413651	−	1.27309i
$366$	1.84226e9	+	5.98585e8i	0.102666	+	0.0333581i
$367$	1.85071e10	−	1.34462e10i	1.02018	−	0.741201i	0.0538569	−	0.998549i	$-0.482849\pi$
$367$	1.85071e10	−	1.34462e10i	1.02018	−	0.741201i	0.966319	+	0.257348i	$0.0828485\pi$
$368$	2.69123e9	−	8.74434e8i	0.146744	−	0.0476799i
$369$	1.64491e10	−	2.26402e10i	0.887231	−	1.22117i
$370$	3.30885e9	+	1.01836e10i	0.176551	+	0.543368i
$371$	−2.86681e9	−	8.82312e9i	−0.151322	−	0.465722i
$372$	−4.36225e8	+	1.41738e8i	−0.0227792	+	0.00740142i
$373$	2.61173e10	−	1.89753e10i	1.34925	−	0.980287i	0.350201	−	0.936675i	$-0.386113\pi$
$373$	2.61173e10	−	1.89753e10i	1.34925	−	0.980287i	0.999049	−	0.0436125i	$-0.0138867\pi$
$374$	−1.66186e10	+	5.11469e10i	−0.849394	+	2.61416i
$375$	−1.34526e9			−0.0680267
$376$	−3.69214e8	+	5.08179e8i	−0.0184725	+	0.0254253i
$377$	1.20285e9	−	1.65558e9i	0.0595451	−	0.0819568i
$378$			3.67753e9i			0.180131i
$379$	−2.51055e9	−	7.72667e9i	−0.121678	−	0.374486i	0.871603	−	0.490212i	$-0.163081\pi$
$379$	−2.51055e9	−	7.72667e9i	−0.121678	−	0.374486i	−0.993281	+	0.115726i	$0.963081\pi$
$380$	−7.52999e9	+	2.31749e10i	−0.361127	+	1.11143i
$381$			2.08122e9i			0.0987685i
$382$	9.68404e9	−	7.03586e9i	0.454782	−	0.330418i
$383$	−7.42165e9	−	1.02150e10i	−0.344910	−	0.474727i	0.600958	−	0.799281i	$-0.294786\pi$
$383$	−7.42165e9	−	1.02150e10i	−0.344910	−	0.474727i	−0.945867	+	0.324553i	$0.894786\pi$
$384$	7.30515e8	−	5.30750e8i	0.0335973	−	0.0244099i
$385$	−2.80175e10			−1.27522
$386$	−1.25078e10	−	4.06403e9i	−0.563419	−	0.183066i
$387$	−3.83965e10			−1.71178
$388$	9.01269e9	−	1.24049e10i	0.397674	−	0.547352i
$389$			5.77825e9i			0.252347i	0.992008	+	0.126173i	$0.0402696\pi$
$389$			5.77825e9i			0.252347i	−0.992008	+	0.126173i	$0.959730\pi$
$390$	−1.66786e9	+	5.41921e8i	−0.0720944	+	0.0234249i
$391$	1.50828e9	+	4.64200e9i	0.0645319	+	0.198609i
$392$	−9.20836e8			−0.0389976
$393$	1.69542e9	+	1.23179e9i	0.0710732	+	0.0516377i
$394$			1.20571e10i			0.500332i
$395$	6.41622e9	−	1.97471e10i	0.263567	−	0.811175i
$396$		−	2.37056e10i		−	0.963985i
$397$	−7.41646e9	−	1.02079e10i	−0.298562	−	0.410935i	0.633210	−	0.773980i	$-0.281737\pi$
$397$	−7.41646e9	−	1.02079e10i	−0.298562	−	0.410935i	−0.931772	+	0.363045i	$0.881737\pi$
$398$	4.52108e10	−	3.28475e10i	1.80181	−	1.30909i
$399$	1.70002e9	+	2.33987e9i	0.0670751	+	0.0923210i
$400$	3.92389e9			0.153277
$401$	2.23988e9	+	7.27781e8i	0.0866257	+	0.0281464i	0.352009	−	0.935997i	$-0.385499\pi$
$401$	2.23988e9	+	7.27781e8i	0.0866257	+	0.0281464i	−0.265384	+	0.964143i	$0.585499\pi$
$402$	3.13543e9	−	1.01876e9i	0.120058	−	0.0390094i
$403$	1.24308e10			0.471280
$404$	−2.16155e10	−	1.57046e10i	−0.811409	−	0.589523i
$405$	−2.00598e10	−	1.45743e10i	−0.745600	−	0.541710i
$406$			4.04471e9i			0.148862i
$407$	−1.56155e10	−	5.07379e9i	−0.569087	−	0.184908i
$408$	5.61520e8	+	7.72867e8i	0.0202640	+	0.0278910i
$409$	1.15015e10	+	3.53979e10i	0.411018	+	1.26498i	0.915765	+	0.401715i	$0.131586\pi$
$409$	1.15015e10	+	3.53979e10i	0.411018	+	1.26498i	−0.504747	+	0.863268i	$0.668414\pi$
$410$	−5.02759e10	+	1.63356e10i	−1.77920	+	0.578096i
$411$	−1.56689e8	+	5.09114e7i	−0.00549126	+	0.00178422i
$412$	2.00889e10	+	1.45954e10i	0.697216	+	0.506557i
$413$	−2.79896e9	−	8.61431e9i	−0.0962047	−	0.296088i
$414$	−2.95327e9	−	4.06482e9i	−0.100531	−	0.138369i
$415$	−9.11677e9	+	2.80585e10i	−0.307361	+	0.945960i
$416$	3.35743e10	−	1.09089e10i	1.12107	−	0.364258i
$417$	6.68983e8	−	9.20777e8i	0.0221244	−	0.0304516i
$418$	−5.12900e10	−	7.05946e10i	−1.68007	−	2.31242i
$419$	−6.18789e9	+	1.90444e10i	−0.200764	+	0.617889i	0.799097	+	0.601203i	$0.205312\pi$
$419$	−6.18789e9	+	1.90444e10i	−0.200764	+	0.617889i	−0.999861	+	0.0166860i	$0.994688\pi$
$420$	8.72410e8	−	1.20077e9i	0.0280365	−	0.0385889i
$421$	1.17768e10	+	1.62094e10i	0.374886	+	0.515986i	0.954221	−	0.299104i	$-0.0966877\pi$
$421$	1.17768e10	+	1.62094e10i	0.374886	+	0.515986i	−0.579335	+	0.815090i	$0.696688\pi$
$422$	−2.65617e10	+	3.65590e10i	−0.837541	+	1.15278i
$423$	2.86950e9	+	9.32356e8i	0.0896281	+	0.0291219i
$424$	4.72863e9	+	1.53643e9i	0.146309	+	0.0475388i
$425$			6.76817e9i			0.207451i
$426$	−1.46493e9	+	2.40011e9i	−0.0444813	+	0.0728775i
$427$	4.44310e10			1.33652
$428$	−1.34049e10	+	4.12559e10i	−0.399473	+	1.22945i
$429$	8.30981e8	−	2.55750e9i	0.0245336	−	0.0755068i
$430$	5.86784e10	+	4.26324e10i	1.71635	+	1.24700i
$431$	−4.65509e10	+	3.38212e10i	−1.34902	+	0.980122i	−0.349963	+	0.936764i	$0.613806\pi$
$431$	−4.65509e10	+	3.38212e10i	−1.34902	+	0.980122i	−0.999060	+	0.0433583i	$0.986194\pi$
$432$	−4.31349e9	−	3.13393e9i	−0.123849	−	0.0899818i
$433$	−3.90070e10	−	1.26742e10i	−1.10966	−	0.360552i	−0.303850	−	0.952720i	$-0.598272\pi$
$433$	−3.90070e10	−	1.26742e10i	−1.10966	−	0.360552i	−0.805814	+	0.592168i	$0.798272\pi$
$434$	−1.98770e10	+	1.44415e10i	−0.560264	+	0.407055i
$435$	1.85861e8	+	1.35036e8i	0.00519075	+	0.00377130i
$436$	4.39896e9	+	1.35386e10i	0.121732	+	0.374652i
$437$	−7.53193e9	−	2.44727e9i	−0.206529	−	0.0671052i
$438$	−3.64633e9	+	2.64921e9i	−0.0990739	+	0.0719814i
$439$	3.43363e10	−	1.11565e10i	0.924475	−	0.300380i	0.192174	−	0.981361i	$-0.438446\pi$
$439$	3.43363e10	−	1.11565e10i	0.924475	−	0.300380i	0.732301	+	0.680981i	$0.238446\pi$
$440$	8.82593e9	−	1.21479e10i	0.235478	−	0.324107i
$441$	1.36680e9	+	4.20658e9i	0.0361369	+	0.111218i
$442$	2.38596e10	+	7.34322e10i	0.625135	+	1.92397i
$443$	1.21933e10	−	3.96184e9i	0.316597	−	0.102868i	−0.146408	−	0.989224i	$-0.546771\pi$
$443$	1.21933e10	−	3.96184e9i	0.316597	−	0.102868i	0.463005	+	0.886356i	$0.346771\pi$
$444$	7.03689e8	−	5.11260e8i	0.0181071	−	0.0131556i
$445$	3.92265e9	−	1.20727e10i	0.100032	−	0.307867i
$446$	−6.33404e10			−1.60082
$447$	−6.51750e7	+	8.97057e7i	−0.00163249	+	0.00224693i
$448$	−1.12766e10	+	1.55209e10i	−0.279940	+	0.385304i
$449$		−	1.03973e10i		−	0.255820i	−0.991786	−	0.127910i	$-0.959173\pi$
$449$		−	1.03973e10i		−	0.255820i	0.991786	−	0.127910i	$-0.0408269\pi$
$450$	−2.15297e9	−	6.62617e9i	−0.0525035	−	0.161589i
$451$	2.50490e10	−	7.70930e10i	0.605459	−	1.86341i
$452$			9.91845e9i			0.237624i
$453$	−3.60242e8	+	2.61731e8i	−0.00855463	+	0.00621530i
$454$	−6.44598e9	−	8.87213e9i	−0.151728	−	0.208835i
$455$	−3.25427e10	+	2.36437e10i	−0.759291	+	0.551657i
$456$	−1.55006e9			−0.0358499
$457$	1.56005e8	+	5.06890e7i	0.00357662	+	0.00116211i	0.310805	−	0.950474i	$-0.399401\pi$
$457$	1.56005e8	+	5.06890e7i	0.00357662	+	0.00116211i	−0.307228	+	0.951636i	$0.599401\pi$
$458$	8.48356e10			1.92804
$459$	5.40560e9	−	7.44017e9i	0.121785	−	0.167622i
$460$			4.06413e9i			0.0907686i
$461$	−2.27376e10	+	7.38788e9i	−0.503431	+	0.163575i	−0.549713	−	0.835354i	$-0.685263\pi$
$461$	−2.27376e10	+	7.38788e9i	−0.503431	+	0.163575i	0.0462816	+	0.998928i	$0.485263\pi$
$462$	1.64243e9	+	5.05487e9i	0.0360511	+	0.110954i
$463$	−6.56622e9			−0.142887			−0.0714433	−	0.997445i	$-0.522760\pi$
$463$	−6.56622e9			−0.142887			−0.0714433	+	0.997445i	$0.522760\pi$
$464$	−4.74416e9	−	3.44684e9i	−0.102350	−	0.0743616i
$465$			1.39552e9i			0.0298486i
$466$	−2.59829e10	+	7.99671e10i	−0.550990	+	1.69577i
$467$			1.65437e10i			0.347829i	0.984761	+	0.173914i	$0.0556416\pi$
$467$			1.65437e10i			0.347829i	−0.984761	+	0.173914i	$0.944358\pi$
$468$	−2.00049e10	−	2.75344e10i	−0.417017	−	0.573975i
$469$	6.11774e10	−	4.44480e10i	1.26444	−	0.918672i
$470$	−3.35002e9	−	4.61091e9i	−0.0686525	−	0.0944921i
$471$	2.51036e9			0.0510096
$472$	4.61672e9	+	1.50006e9i	0.0930177	+	0.0302233i
$473$	−1.05775e11	+	3.43683e10i	−2.11319	+	0.686616i
$474$	−3.93887e9			−0.0780294
$475$	−8.88443e9	−	6.45492e9i	−0.174524	−	0.126799i
$476$	−5.28672e10	−	3.84102e10i	−1.02981	−	0.748203i
$477$		−	2.38819e10i		−	0.461313i
$478$	−4.14819e10	−	1.34783e10i	−0.794598	−	0.258180i
$479$	3.16821e10	+	4.36066e10i	0.601827	+	0.828343i	0.995874	−	0.0907468i	$-0.0289254\pi$
$479$	3.16821e10	+	4.36066e10i	0.601827	+	0.828343i	−0.394047	+	0.919090i	$0.628925\pi$
$480$	1.22467e9	+	3.76915e9i	0.0230704	+	0.0710033i
$481$	−2.24194e10	+	7.28450e9i	−0.418835	+	0.136088i
$482$	1.16066e11	−	3.77123e10i	2.15040	−	0.698706i
$483$	3.90254e8	+	2.83536e8i	0.00717065	+	0.00520978i
$484$	−8.51944e9	−	2.62201e10i	−0.155249	−	0.477808i
$485$	−2.74211e10	−	3.77420e10i	−0.495585	−	0.682115i
$486$	−4.39123e9	+	1.35148e10i	−0.0787120	+	0.242251i
$487$	7.54893e10	−	2.45279e10i	1.34205	−	0.436059i	0.452041	−	0.891997i	$-0.350696\pi$
$487$	7.54893e10	−	2.45279e10i	1.34205	−	0.436059i	0.890011	+	0.455938i	$0.150696\pi$
$488$	−1.39965e10	+	1.92645e10i	−0.246796	+	0.339686i
$489$	−3.77562e9	−	5.19669e9i	−0.0660317	−	0.0908849i
$490$	2.58187e9	−	7.94619e9i	0.0447869	−	0.137840i
$491$	3.74862e9	−	5.15953e9i	0.0644979	−	0.0887737i	−0.775550	−	0.631287i	$-0.782527\pi$
$491$	3.74862e9	−	5.15953e9i	0.0644979	−	0.0887737i	0.840047	+	0.542513i	$0.182527\pi$
$492$	2.52406e9	+	3.47407e9i	0.0430764	+	0.0592896i
$493$	5.94532e9	−	8.18303e9i	0.100644	−	0.138524i
$494$	−1.19148e11	−	3.87136e10i	−2.00069	−	0.650063i
$495$	−6.85944e10	−	2.22877e10i	−1.14253	−	0.371231i
$496$		−	3.56211e10i		−	0.588547i
$497$	−1.49448e10	+	6.27411e10i	−0.244943	+	1.02832i
$498$	5.59672e9			0.0909947
$499$	2.36759e10	−	7.28670e10i	0.381861	−	1.17525i	−0.556872	−	0.830599i	$-0.687998\pi$
$499$	2.36759e10	−	7.28670e10i	0.381861	−	1.17525i	0.938732	−	0.344648i	$-0.112002\pi$
$500$	−1.52399e10	+	4.69035e10i	−0.243838	+	0.750457i
$501$	−4.61851e9	−	3.35555e9i	−0.0733080	−	0.0532614i
$502$	2.66830e10	−	1.93863e10i	0.420165	−	0.305268i
$503$	9.09110e10	+	6.60507e10i	1.42018	+	1.03182i	0.991741	+	0.128255i	$0.0409377\pi$
$503$	9.09110e10	+	6.60507e10i	1.42018	+	1.03182i	0.428443	+	0.903569i	$0.359062\pi$
$504$	−2.14526e10	−	6.97038e9i	−0.332474	−	0.108028i
$505$	−6.57653e10	+	4.77813e10i	−1.01119	+	0.734670i
$506$	−1.17741e10	−	8.55436e9i	−0.179607	−	0.130492i
$507$	1.25174e8	+	3.85245e8i	0.00189444	+	0.00583050i
$508$	7.25637e10	+	2.35774e10i	1.08959	+	0.354031i
$509$	1.42236e10	−	1.03340e10i	0.211903	−	0.153957i	−0.476771	−	0.879027i	$-0.658193\pi$
$509$	1.42236e10	−	1.03340e10i	0.211903	−	0.153957i	0.688674	+	0.725071i	$0.258193\pi$
$510$	−8.24372e9	+	2.67855e9i	−0.121855	+	0.0395930i
$511$	−6.07658e10	+	8.36370e10i	−0.891201	+	1.22663i
$512$	−2.28819e10	−	7.04233e10i	−0.332976	−	1.02479i
$513$	4.61114e9	+	1.41916e10i	0.0665792	+	0.204910i
$514$	−3.31120e10	+	1.07588e10i	−0.474388	+	0.154138i
$515$	6.11206e10	−	4.44067e10i	0.868878	−	0.631277i
$516$	1.82067e9	−	5.60345e9i	0.0256822	−	0.0790417i
$517$	8.73946e9			0.122327
$518$	2.73861e10	−	3.76938e10i	0.380375	−	0.523541i
$519$	−8.45810e8	+	1.16416e9i	−0.0116574	+	0.0160451i
$520$		−	2.15580e10i		−	0.294846i
$521$	−3.43610e10	−	1.05752e11i	−0.466353	−	1.43529i	−0.857273	−	0.514861i	$-0.827843\pi$
$521$	−3.43610e10	−	1.05752e11i	−0.466353	−	1.43529i	0.390921	−	0.920424i	$-0.372157\pi$
$522$	−3.21754e9	+	9.90256e9i	−0.0433353	+	0.133372i
$523$			8.74364e10i			1.16865i	0.811519	+	0.584327i	$0.198641\pi$
$523$			8.74364e10i			1.16865i	−0.811519	+	0.584327i	$0.801359\pi$
$524$	6.21543e10	−	4.51577e10i	0.824415	−	0.598972i
$525$	3.93170e8	+	5.41152e8i	0.00517539	+	0.00712332i
$526$	−4.49898e10	+	3.26870e10i	−0.587720	+	0.427004i
$527$	6.14416e10			0.796563
$528$	−7.32865e9	−	2.38122e9i	−0.0942949	−	0.0306383i
$529$	7.69901e10			0.983133
$530$	−2.65166e10	+	3.64970e10i	−0.336058	+	0.462545i
$531$		−	2.33167e10i		−	0.293285i
$532$	1.00841e11	−	3.27651e10i	1.25889	−	0.409039i
$533$	−3.59632e10	−	1.10683e11i	−0.445604	−	1.37143i
$534$	−2.40809e9			−0.0296147
$535$	1.06775e11	+	7.75765e10i	1.30333	+	0.946924i
$536$			4.05272e10i			0.491006i
$537$	1.32309e9	−	4.07206e9i	0.0159109	−	0.0489686i
$538$		−	1.24460e11i		−	1.48559i
$539$	7.53055e9	+	1.03649e10i	0.0892219	+	0.122803i
$540$	6.19514e9	−	4.50103e9i	0.0728578	−	0.0529343i
$541$	−2.91088e10	−	4.00649e10i	−0.339810	−	0.467708i	0.604576	−	0.796547i	$-0.293343\pi$
$541$	−2.91088e10	−	4.00649e10i	−0.339810	−	0.467708i	−0.944386	+	0.328839i	$0.893343\pi$
$542$	−3.82706e10			−0.443474
$543$	−9.39943e9	−	3.05406e9i	−0.108119	−	0.0351300i
$544$	1.65947e11	−	5.39196e10i	1.89485	−	0.615674i
$545$	4.33111e10			0.490923
$546$	6.17345e9	+	4.48528e9i	0.0694637	+	0.0504683i
$547$	9.28753e10	+	6.74778e10i	1.03741	+	0.753723i	0.969778	−	0.243987i	$-0.0784555\pi$
$547$	9.28753e10	+	6.74778e10i	1.03741	+	0.753723i	0.0676324	+	0.997710i	$0.478455\pi$
$548$			6.03987e9i			0.0669739i
$549$	1.08779e11	+	3.53445e10i	1.19745	+	0.389075i
$550$	−1.18621e10	−	1.63267e10i	−0.129631	−	0.178422i
$551$	5.07154e9	+	1.56086e10i	0.0550216	+	0.169339i
$552$	−2.45872e8	+	7.98886e7i	−0.00264821	+	0.000860456i
$553$	−8.59251e10	+	2.79188e10i	−0.918797	+	0.298535i
$554$	−3.10043e10	−	2.25259e10i	−0.329142	−	0.239135i
$555$	−8.17780e8	−	2.51687e9i	−0.00861915	−	0.0265270i
$556$	−2.45251e10	−	3.37558e10i	−0.256632	−	0.353224i
$557$	3.34223e10	−	1.02863e11i	0.347229	−	1.06866i	−0.613151	−	0.789966i	$-0.710098\pi$
$557$	3.34223e10	−	1.02863e11i	0.347229	−	1.06866i	0.960380	−	0.278695i	$-0.0899018\pi$
$558$	−6.01525e10	+	1.95447e10i	−0.620464	+	0.201601i
$559$	−9.38560e10	+	1.29182e11i	−0.961202	+	1.32298i
$560$	6.77523e10	+	9.32530e10i	0.688925	+	0.948223i
$561$	4.10728e9	−	1.26409e10i	0.0414670	−	0.127622i
$562$	1.25664e11	−	1.72962e11i	1.25970	−	1.73383i
$563$	1.12634e10	+	1.55028e10i	0.112108	+	0.154304i	0.861384	−	0.507955i	$-0.169598\pi$
$563$	1.12634e10	+	1.55028e10i	0.112108	+	0.154304i	−0.749276	+	0.662258i	$0.769598\pi$
$564$	−2.72130e8	+	3.74554e8i	−0.00268943	+	0.00370168i
$565$	2.87000e10	+	9.32519e9i	0.281636	+	0.0915090i
$566$	−1.42247e11	−	4.62189e10i	−1.38605	−	0.450354i
$567$			1.07891e11i			1.04389i
$568$	−2.24955e10	−	2.62442e10i	−0.216124	−	0.252139i
$569$	6.67017e10			0.636338			0.318169	−	0.948034i	$-0.396932\pi$
$569$	6.67017e10			0.636338			0.318169	+	0.948034i	$0.396932\pi$
$570$	4.34610e9	−	1.33759e10i	0.0411719	−	0.126714i
$571$	−3.71122e10	+	1.14220e11i	−0.349118	+	1.07448i	0.610224	+	0.792229i	$0.291080\pi$
$571$	−3.71122e10	+	1.14220e11i	−0.349118	+	1.07448i	−0.959342	+	0.282246i	$0.908920\pi$
$572$	−7.97556e10	−	5.79458e10i	−0.745035	−	0.541300i
$573$	−2.39340e9	+	1.73891e9i	−0.0222023	+	0.0161309i
$574$	1.86092e11	+	1.35204e11i	1.71427	+	1.24549i
$575$	−1.74194e9	−	5.65991e8i	−0.0159354	−	0.00517772i
$576$	−3.99549e10	+	2.90289e10i	−0.362977	+	0.263719i
$577$	1.84226e10	+	1.33848e10i	0.166207	+	0.120756i	0.667779	−	0.744359i	$-0.267245\pi$
$577$	1.84226e10	+	1.33848e10i	0.166207	+	0.120756i	−0.501573	+	0.865116i	$0.667245\pi$
$578$	7.23190e10	+	2.22575e11i	0.647949	+	1.99418i
$579$	3.09129e9	+	1.00442e9i	0.0275059	+	0.00893720i
$580$	6.81369e9	−	4.95043e9i	0.0602102	−	0.0437453i
$581$	1.22091e11	−	3.96696e10i	1.07146	−	0.348140i
$582$	−5.20188e9	+	7.15977e9i	−0.0453386	+	0.0624032i
$583$	−2.13765e10	−	6.57901e10i	−0.185039	−	0.569491i
$584$	−1.71213e10	−	5.26939e10i	−0.147192	−	0.453011i
$585$	−9.84818e10	+	3.19987e10i	−0.840877	+	0.273217i
$586$	6.20424e10	−	4.50765e10i	0.526136	−	0.382260i
$587$	−1.16179e10	+	3.57562e10i	−0.0978531	+	0.301161i	−0.987987	−	0.154539i	$-0.950611\pi$
$587$	−1.16179e10	+	3.57562e10i	−0.0978531	+	0.301161i	0.890134	+	0.455700i	$0.150611\pi$
$588$	−6.78704e8			−0.00567769
$589$	−5.85979e10	+	8.06530e10i	−0.486878	+	0.670131i
$590$	−2.58890e10	+	3.56332e10i	−0.213653	+	0.294067i
$591$		−	2.97991e9i		−	0.0244260i
$592$	2.08741e10	+	6.42440e10i	0.169950	+	0.523053i
$593$	2.74373e10	−	8.44435e10i	0.221883	−	0.682884i	−0.776710	−	0.629858i	$-0.783113\pi$
$593$	2.74373e10	−	8.44435e10i	0.221883	−	0.682884i	0.998593	−	0.0530267i	$-0.0168868\pi$
$594$			2.74217e10i			0.220267i
$595$	−1.60849e11	+	1.16863e11i	−1.28336	+	0.932417i
$596$	2.38933e9	+	3.28863e9i	0.0189361	+	0.0260633i
$597$	−1.11738e10	+	8.11824e9i	−0.0879637	+	0.0639094i
$598$	−2.08947e10			−0.163392
$599$	3.80662e10	+	1.23685e10i	0.295687	+	0.0960745i	0.453104	−	0.891458i	$-0.350317\pi$
$599$	3.80662e10	+	1.23685e10i	0.295687	+	0.0960745i	−0.157417	+	0.987532i	$0.550317\pi$
$600$	−3.58488e8			−0.00276611
$601$	−1.20193e11	+	1.65431e11i	−0.921257	+	1.26800i	0.0419164	+	0.999121i	$0.486654\pi$
$601$	−1.20193e11	+	1.65431e11i	−0.921257	+	1.26800i	−0.963174	+	0.268881i	$0.913346\pi$
$602$		−	3.15601e11i		−	2.40299i
$603$	1.85137e11	−	6.01546e10i	1.40031	−	0.454988i
$604$	5.04444e9	+	1.55252e10i	0.0379023	+	0.116651i
$605$	−8.38803e10			−0.626092
$606$	1.24759e10	+	9.06426e9i	0.0925083	+	0.0672112i
$607$			8.91183e10i			0.656466i	0.944597	+	0.328233i	$0.106453\pi$
$607$			8.91183e10i			0.656466i	−0.944597	+	0.328233i	$0.893547\pi$
$608$	−8.74877e10	+	2.69259e11i	−0.640225	+	1.97041i
$609$		−	9.99648e8i		−	0.00726738i
$610$	−1.26995e11	−	1.74794e11i	−0.917210	−	1.26243i
$611$	1.01510e10	−	7.37514e9i	0.0728357	−	0.0529182i
$612$	−9.88782e10	−	1.36094e11i	−0.704847	−	0.970139i
$613$	1.18449e11			0.838857			0.419429	−	0.907788i	$-0.362230\pi$
$613$	1.18449e11			0.838857			0.419429	+	0.907788i	$0.362230\pi$
$614$	−2.08263e10	−	6.76687e9i	−0.146534	−	0.0476118i
$615$	1.24256e10	−	4.03734e9i	0.0868597	−	0.0282224i
$616$	−6.53370e10			−0.453771
$617$	9.04881e10	+	6.57435e10i	0.624383	+	0.453641i	0.854450	−	0.519534i	$-0.173895\pi$
$617$	9.04881e10	+	6.57435e10i	0.624383	+	0.453641i	−0.230067	+	0.973175i	$0.573895\pi$
$618$	−1.15948e10	−	8.42409e9i	−0.0794892	−	0.0577523i
$619$			4.87577e9i			0.0332109i	0.999862	+	0.0166055i	$0.00528593\pi$
$619$			4.87577e9i			0.0332109i	−0.999862	+	0.0166055i	$0.994714\pi$
$620$	4.86560e10	+	1.58093e10i	0.329283	+	0.106991i
$621$	1.46285e9	+	2.01344e9i	0.00983634	+	0.0135386i
$622$	−2.31513e10	−	7.12525e10i	−0.154673	−	0.476034i
$623$	−5.25316e10	+	1.70686e10i	−0.348713	+	0.113304i
$624$	−1.05218e10	+	3.41875e9i	−0.0693989	+	0.0225491i
$625$	1.05465e11	+	7.66249e10i	0.691176	+	0.502169i
$626$	−4.05055e9	−	1.24663e10i	−0.0263765	−	0.0811785i
$627$	1.26763e10	+	1.74474e10i	0.0820203	+	0.112891i
$628$	2.84389e10	−	8.75260e10i	0.182841	−	0.562728i
$629$	−1.10812e11	+	3.60050e10i	−0.707921	+	0.230017i
$630$	1.20299e11	−	1.65578e11i	0.763661	−	1.05109i
$631$	1.36115e11	+	1.87347e11i	0.858597	+	1.18176i	0.981902	+	0.189389i	$0.0606508\pi$
$631$	1.36115e11	+	1.87347e11i	0.858597	+	1.18176i	−0.123305	+	0.992369i	$0.539349\pi$
$632$	1.49627e10	−	4.60504e10i	0.0937867	−	0.288646i
$633$	6.56470e9	−	9.03553e9i	0.0408884	−	0.0562780i
$634$	1.55010e11	+	2.13353e11i	0.959406	+	1.32051i
$635$	1.36447e11	−	1.87803e11i	0.839205	−	1.15507i
$636$	3.48525e9	+	1.13243e9i	0.0213013	+	0.00692120i
$637$	1.74937e10	+	5.68404e9i	0.106249	+	0.0345223i
$638$			3.01596e10i			0.182030i
$639$	−8.64991e10	+	1.41719e11i	−0.518810	+	0.850010i
$640$	−1.00716e11			−0.600312
$641$	2.87287e10	−	8.84179e10i	0.170170	−	0.523731i	−0.829210	−	0.558938i	$-0.811209\pi$
$641$	2.87287e10	−	8.84179e10i	0.170170	−	0.523731i	0.999380	+	0.0352071i	$0.0112091\pi$
$642$	7.73692e9	−	2.38118e10i	0.0455437	−	0.140169i
$643$	−2.44856e11	−	1.77898e11i	−1.43241	−	1.04071i	−0.989562	−	0.144110i	$-0.953968\pi$
$643$	−2.44856e11	−	1.77898e11i	−1.43241	−	1.04071i	−0.442848	−	0.896597i	$-0.646032\pi$
$644$	1.43068e10	−	1.03945e10i	0.0831761	−	0.0604310i
$645$	−1.45023e10	−	1.05366e10i	−0.0837913	−	0.0608779i
$646$	−5.88912e11	−	1.91349e11i	−3.38159	−	1.09874i
$647$	1.01560e11	−	7.37880e10i	0.579572	−	0.421084i	−0.258998	−	0.965878i	$-0.583392\pi$
$647$	1.01560e11	−	7.37880e10i	0.579572	−	0.421084i	0.838570	+	0.544794i	$0.183392\pi$
$648$	−4.67796e10	−	3.39873e10i	−0.265311	−	0.192760i
$649$	−2.08706e10	−	6.42331e10i	−0.117640	−	0.362060i
$650$	−2.75559e10	−	8.95345e9i	−0.154369	−	0.0501576i
$651$	4.91259e9	−	3.56920e9i	0.0273518	−	0.0198723i
$652$	−2.23960e11	+	7.27690e10i	−1.23931	+	0.402676i
$653$	1.66895e11	−	2.29711e11i	0.917889	−	1.26337i	−0.0465112	−	0.998918i	$-0.514810\pi$
$653$	1.66895e11	−	2.29711e11i	0.917889	−	1.26337i	0.964400	−	0.264448i	$-0.0851897\pi$
$654$	−2.53896e9	−	7.81412e9i	−0.0138786	−	0.0427139i
$655$	−7.22315e10	−	2.22306e11i	−0.392429	−	1.20777i
$656$	−3.17169e11	+	1.03055e11i	−1.71268	+	0.556483i
$657$	−2.15304e11	+	1.56427e11i	−1.15555	+	0.839559i
$658$	−7.66353e9	+	2.35859e10i	−0.0408813	+	0.125820i
$659$	−3.02057e11			−1.60158			−0.800788	−	0.598948i	$-0.795585\pi$
$659$	−3.02057e11			−1.60158			−0.800788	+	0.598948i	$0.795585\pi$
$660$	6.50517e9	−	8.95360e9i	0.0342833	−	0.0471870i
$661$	9.06978e10	−	1.24835e11i	0.475106	−	0.653928i	−0.502449	−	0.864607i	$-0.667567\pi$
$661$	9.06978e10	−	1.24835e11i	0.475106	−	0.653928i	0.977555	+	0.210679i	$0.0675675\pi$
$662$			5.58666e10i			0.290885i
$663$	−5.89687e9	−	1.81487e10i	−0.0305188	−	0.0939272i
$664$	−2.12604e10	+	6.54328e10i	−0.109370	+	0.336607i
$665$		−	3.22597e11i		−	1.64958i
$666$	9.70338e10	−	7.04992e10i	0.493204	−	0.358333i
$667$	1.60891e9	+	2.21447e9i	0.00812882	+	0.0111884i
$668$	−1.69316e11	+	1.23015e11i	−0.850337	+	0.617806i
$669$	1.56545e10			0.0781512
$670$	−3.49722e11	−	1.13632e11i	−1.73550	−	0.563897i
$671$	3.31303e11			1.63431
$672$	1.01362e10	−	1.39512e10i	0.0497045	−	0.0684124i
$673$			9.27964e9i			0.0452346i	0.999744	+	0.0226173i	$0.00719993\pi$
$673$			9.27964e9i			0.0452346i	−0.999744	+	0.0226173i	$0.992800\pi$
$674$	−3.51124e11	+	1.14087e11i	−1.70146	+	0.552837i
$675$	1.06644e9	+	3.28216e9i	0.00513713	+	0.0158105i
$676$	1.48500e10			0.0711114
$677$	3.03917e11	+	2.20809e11i	1.44677	+	1.05114i	0.986572	+	0.163328i	$0.0522228\pi$
$677$	3.03917e11	+	2.20809e11i	1.44677	+	1.05114i	0.460201	+	0.887815i	$0.347777\pi$
$678$		−	5.72466e9i		−	0.0270914i
$679$	−6.27287e10	+	1.93059e11i	−0.295112	+	0.908262i
$680$		−	1.06555e11i		−	0.498353i
$681$	1.59312e9	+	2.19274e9i	0.00740729	+	0.0101953i
$682$	−1.48214e11	+	1.07684e11i	−0.685097	+	0.497752i
$683$	1.19576e10	+	1.64582e10i	0.0549492	+	0.0756311i	0.835607	−	0.549327i	$-0.185116\pi$
$683$	1.19576e10	+	1.64582e10i	0.0549492	+	0.0756311i	−0.780658	+	0.624958i	$0.785116\pi$
$684$	2.72950e11			1.24698
$685$	1.74769e10	+	5.67860e9i	0.0793785	+	0.0257916i
$686$	2.59862e11	−	8.44342e10i	1.17340	−	0.381261i
$687$	−2.09670e10			−0.0941262
$688$	3.70177e11	+	2.68950e11i	1.65218	+	1.20038i
$689$	−8.03488e10	−	5.83768e10i	−0.356535	−	0.259038i
$690$		−	2.34570e9i		−	0.0103485i
$691$	9.11419e10	+	2.96138e10i	0.399766	+	0.129892i	0.501998	−	0.864869i	$-0.332598\pi$
$691$	9.11419e10	+	2.96138e10i	0.399766	+	0.129892i	−0.102232	+	0.994761i	$0.532598\pi$
$692$	3.10075e10	+	4.26782e10i	0.135221	+	0.186115i
$693$	9.69799e10	+	2.98474e11i	0.420483	+	1.29412i
$694$	4.04017e11	−	1.31273e11i	1.74165	−	0.565897i
$695$	−1.20734e11	+	3.92288e10i	−0.517475	+	0.168138i
$696$	4.33429e8	+	3.14904e8i	0.00184706	+	0.00134197i
$697$	−1.77755e11	−	5.47073e11i	−0.753165	−	2.31800i
$698$	−1.03448e11	−	1.42384e11i	−0.435814	−	0.599846i
$699$	6.42165e9	−	1.97638e10i	0.0268991	−	0.0827869i
$700$	2.33218e10	−	7.57772e9i	0.0971338	−	0.0315607i
$701$	−1.22760e11	+	1.68965e11i	−0.508376	+	0.699720i	−0.983644	−	0.180121i	$-0.942351\pi$
$701$	−1.22760e11	+	1.68965e11i	−0.508376	+	0.699720i	0.475268	+	0.879841i	$0.342351\pi$
$702$	2.31409e10	+	3.18508e10i	0.0952867	+	0.131151i
$703$	5.84203e10	−	1.79799e11i	0.239190	−	0.736150i
$704$	−8.40844e10	+	1.15732e11i	−0.342314	+	0.471155i
$705$	8.27956e8	+	1.13958e9i	0.00335159	+	0.00461307i
$706$	−3.53132e11	+	4.86045e11i	−1.42141	+	1.95640i
$707$	3.36405e11	+	1.09305e11i	1.34643	+	0.437483i
$708$	3.40276e9	+	1.10562e9i	0.0135425	+	0.00440022i
$709$		−	4.03229e11i		−	1.59576i	−0.602818	−	0.797879i	$-0.705955\pi$
$709$		−	4.03229e11i		−	1.59576i	0.602818	−	0.797879i	$-0.294045\pi$
$710$	2.89543e11	−	1.20537e11i	1.13941	−	0.474335i
$711$	−2.32577e11			−0.910100
$712$	9.14766e9	−	2.81536e10i	0.0355951	−	0.109550i
$713$	−5.13808e9	+	1.58134e10i	−0.0198812	+	0.0611880i
$714$	3.05135e10	+	2.21693e10i	0.117408	+	0.0853022i
$715$	−2.42657e11	+	1.76300e11i	−0.928470	+	0.674573i
$716$	−1.26987e11	−	9.22617e10i	−0.483179	−	0.351050i
$717$	1.02522e10	+	3.33115e9i	0.0387919	+	0.0126043i
$718$	−3.10756e10	+	2.25777e10i	−0.116929	+	0.0849538i
$719$	−5.71163e10	−	4.14974e10i	−0.213720	−	0.155276i	0.475775	−	0.879567i	$-0.342168\pi$
$719$	−5.71163e10	−	4.14974e10i	−0.213720	−	0.155276i	−0.689495	+	0.724290i	$0.742168\pi$
$720$	9.16940e10	+	2.82205e11i	0.341202	+	1.05011i
$721$	−3.12646e11	−	1.01585e11i	−1.15694	−	0.375914i
$722$	5.22107e11	−	3.79333e11i	1.92137	−	1.39596i
$723$	−2.86857e10	+	9.32056e9i	−0.104981	+	0.0341106i
$724$	−2.12965e11	+	2.93122e11i	−0.775094	+	1.06683i
$725$	1.17292e9	+	3.60986e9i	0.00424536	+	0.0130659i
$726$	4.91719e9	+	1.51335e10i	0.0176999	+	0.0544746i
$727$	4.35591e11	−	1.41532e11i	1.55934	−	0.506661i	0.602711	−	0.797960i	$-0.294087\pi$
$727$	4.35591e11	−	1.41532e11i	1.55934	−	0.506661i	0.956632	+	0.291299i	$0.0940873\pi$
$728$	−7.58899e10	+	5.51372e10i	−0.270183	+	0.196300i
$729$	−8.51004e10	+	2.61912e11i	−0.301316	+	0.927354i
$730$	5.02717e11			1.77024
$731$	−4.63901e11	+	6.38505e11i	−1.62464	+	2.23612i
$732$	−1.03161e10	+	1.41989e10i	−0.0359312	+	0.0494551i
$733$			1.11838e10i			0.0387411i	0.999812	+	0.0193706i	$0.00616623\pi$
$733$			1.11838e10i			0.0387411i	−0.999812	+	0.0193706i	$0.993834\pi$
$734$	1.49577e11	+	4.60350e11i	0.515324	+	1.58600i
$735$	−6.38108e8	+	1.96389e9i	−0.00218648	+	0.00672928i
$736$			4.72193e10i			0.160919i
$737$	4.56173e11	−	3.31429e11i	1.54618	−	1.12336i
$738$	3.48051e11	+	4.79051e11i	1.17332	+	1.61494i
$739$	−1.23831e11	+	8.99687e10i	−0.415195	+	0.301657i	−0.775702	−	0.631100i	$-0.782604\pi$
$739$	−1.23831e11	+	8.99687e10i	−0.415195	+	0.301657i	0.360506	+	0.932757i	$0.382604\pi$
$740$	−9.70172e10			−0.323535
$741$	2.94474e10	+	9.56803e9i	0.0976728	+	0.0317358i
$742$	1.96298e11			0.647591
$743$	3.01038e11	−	4.14343e11i	0.987792	−	1.35958i	0.0552678	−	0.998472i	$-0.482399\pi$
$743$	3.01038e11	−	4.14343e11i	0.987792	−	1.35958i	0.932524	−	0.361107i	$-0.117601\pi$
$744$			3.25436e9i			0.0106212i
$745$	1.17624e10	−	3.82182e9i	0.0381829	−	0.0124064i
$746$	2.11083e11	+	6.49646e11i	0.681550	+	2.09759i
$747$	3.30468e11			1.06132
$748$	−3.94207e11	−	2.86408e11i	−1.25927	−	0.914912i
$749$		−	5.74286e11i		−	1.82474i
$750$	8.79605e9	−	2.70714e10i	0.0277998	−	0.0855591i
$751$			3.19349e10i			0.100394i	0.998739	+	0.0501968i	$0.0159849\pi$
$751$			3.19349e10i			0.100394i	−0.998739	+	0.0501968i	$0.984015\pi$
$752$	−2.11339e10	−	2.90883e10i	−0.0660858	−	0.0909593i
$753$	−6.59468e9	+	4.79132e9i	−0.0205123	+	0.0149030i
$754$	2.54514e10	+	3.50309e10i	0.0787457	+	0.108384i
$755$	4.96663e10			0.152853
$756$	−3.16896e10	−	1.02966e10i	−0.0970129	−	0.0315214i
$757$	−3.29813e11	+	1.07163e11i	−1.00435	+	0.326333i	−0.764602	−	0.644502i	$-0.777065\pi$
$757$	−3.29813e11	+	1.07163e11i	−1.00435	+	0.326333i	−0.239747	+	0.970835i	$0.577065\pi$
$758$	1.71904e11			0.520726
$759$	2.90995e9	+	2.11420e9i	0.00876836	+	0.00637059i
$760$	1.39872e11	+	1.01623e11i	0.419253	+	0.304605i
$761$		−	4.51472e11i		−	1.34614i	−0.739577	−	0.673072i	$-0.764974\pi$
$761$		−	4.51472e11i		−	1.34614i	0.739577	−	0.673072i	$-0.235026\pi$
$762$	−4.18818e10	−	1.36082e10i	−0.124224	−	0.0403628i
$763$	−1.10773e11	−	1.52466e11i	−0.326841	−	0.449858i
$764$	3.35147e10	+	1.03148e11i	0.0983697	+	0.302751i
$765$	−4.86765e11	+	1.58160e11i	−1.42126	+	0.461795i
$766$	2.54091e11	−	8.25590e10i	0.738029	−	0.239800i
$767$	−7.84472e10	−	5.69952e10i	−0.226671	−	0.164686i
$768$	9.03118e9	+	2.77951e10i	0.0259597	+	0.0798957i
$769$	8.67760e10	+	1.19437e11i	0.248138	+	0.341533i	0.914858	−	0.403775i	$-0.132302\pi$
$769$	8.67760e10	+	1.19437e11i	0.248138	+	0.341533i	−0.666720	+	0.745308i	$0.732302\pi$
$770$	1.83194e11	−	5.63814e11i	0.521133	−	1.60388i
$771$	8.18361e9	−	2.65902e9i	0.0231594	−	0.00752495i
$772$	7.00401e10	−	9.64019e10i	0.197187	−	0.271404i
$773$	−6.74251e10	−	9.28026e10i	−0.188844	−	0.259922i	0.704088	−	0.710112i	$-0.251356\pi$
$773$	−6.74251e10	−	9.28026e10i	−0.188844	−	0.259922i	−0.892932	+	0.450191i	$0.851356\pi$
$774$	2.51058e11	−	7.72677e11i	0.699536	−	2.15295i
$775$	−1.35522e10	+	1.86530e10i	−0.0375666	+	0.0517060i
$776$	−6.39464e10	−	8.80146e10i	−0.176347	−	0.242721i
$777$	−6.76846e9	+	9.31599e9i	−0.0185697	+	0.0255591i
$778$	−1.16279e11	−	3.77815e10i	−0.317384	−	0.103124i
$779$	8.87659e11	+	2.88418e11i	2.41044	+	0.783199i
$780$		−	1.58894e10i		−	0.0429268i
$781$	−1.11437e11	+	4.67833e11i	−0.299520	+	1.25744i
$782$	−1.03276e11			−0.276167
$783$	1.59375e9	−	4.90506e9i	0.00424008	−	0.0130496i
$784$	1.62879e10	−	5.01291e10i	0.0431124	−	0.132686i
$785$	−2.26527e11	−	1.64581e11i	−0.596542	−	0.433413i
$786$	−3.58737e10	+	2.60638e10i	−0.0939910	+	0.0682885i
$787$	3.07985e11	+	2.23764e11i	0.802842	+	0.583299i	0.911747	−	0.410753i	$-0.134734\pi$
$787$	3.07985e11	+	2.23764e11i	0.802842	+	0.583299i	−0.108904	+	0.994052i	$0.534734\pi$
$788$	−1.03897e11	−	3.37582e10i	−0.269463	−	0.0875538i
$789$	1.11192e10	−	8.07856e9i	0.0286923	−	0.0208462i
$790$	3.55431e11	+	2.58235e11i	0.912529	+	0.662991i
$791$	−4.05765e10	−	1.24882e11i	−0.103650	−	0.319001i
$792$	−1.59963e11	−	5.19751e10i	−0.406554	−	0.132097i
$793$	3.84813e11	−	2.79583e11i	0.973099	−	0.706998i
$794$	2.53913e11	−	8.25013e10i	0.638856	−	0.207577i
$795$	6.55356e9	−	9.02020e9i	0.0164062	−	0.0225812i
$796$	1.56466e11	+	4.81553e11i	0.389734	+	1.19948i
$797$	−1.12100e11	−	3.45008e11i	−0.277825	−	0.855059i	−0.988458	−	0.151495i	$-0.951591\pi$
$797$	−1.12100e11	−	3.45008e11i	−0.277825	−	0.855059i	0.710633	−	0.703563i	$-0.248409\pi$
$798$	−5.82024e10	+	1.89111e10i	−0.143526	+	0.0466343i
$799$	5.01733e10	−	3.64530e10i	0.123108	−	0.0894431i
$800$	−2.02337e10	+	6.22728e10i	−0.0493986	+	0.152033i
$801$	−1.42190e11			−0.345412
$802$	−2.92912e10	+	4.03159e10i	−0.0708011	+	0.0974493i
$803$	−4.53104e11	+	6.23644e11i	−1.08977	+	1.49994i
$804$			2.98706e10i			0.0714859i
$805$	−1.66264e10	−	5.11707e10i	−0.0395926	−	0.121854i
$806$	−8.12796e10	+	2.50153e11i	−0.192593	+	0.592742i
$807$			3.07601e10i			0.0725259i
$808$	−1.53365e11	+	1.11426e11i	−0.359817	+	0.261422i
$809$	−2.21937e11	−	3.05470e11i	−0.518127	−	0.713140i	0.467137	−	0.884185i	$-0.345286\pi$
$809$	−2.21937e11	−	3.05470e11i	−0.518127	−	0.713140i	−0.985263	+	0.171045i	$0.945286\pi$
$810$	4.24450e11	−	3.08381e11i	0.986021	−	0.716386i
$811$	−2.78999e11			−0.644941			−0.322470	−	0.946580i	$-0.604513\pi$
$811$	−2.78999e11			−0.644941			−0.322470	+	0.946580i	$0.604513\pi$
$812$	−3.48536e10	−	1.13246e10i	−0.0801722	−	0.0260495i
$813$	9.45856e9			0.0216502
$814$	2.04206e11	−	2.81066e11i	0.465127	−	0.640193i
$815$			7.16466e11i			1.62392i
$816$	−5.20062e10	+	1.68978e10i	−0.117299	+	0.0381127i
$817$	−3.95722e11	−	1.21791e12i	−0.888181	−	2.73354i
$818$	−7.87539e11			−1.75897
$819$	3.64522e11	+	2.64841e11i	0.810193	+	0.588640i
$820$		−	4.78969e11i		−	1.05938i
$821$	2.55410e11	−	7.86072e11i	0.562168	−	1.73017i	−0.114052	−	0.993475i	$-0.536383\pi$
$821$	2.55410e11	−	7.86072e11i	0.562168	−	1.73017i	0.676220	−	0.736700i	$-0.263617\pi$
$822$		−	3.48605e9i		−	0.00763565i
$823$	1.41334e11	+	1.94530e11i	0.308069	+	0.424020i	0.934778	−	0.355233i	$-0.115599\pi$
$823$	1.41334e11	+	1.94530e11i	0.308069	+	0.424020i	−0.626709	+	0.779253i	$0.715599\pi$
$824$	1.42534e11	−	1.03557e11i	0.309178	−	0.224631i
$825$	2.93170e9	+	4.03513e9i	0.00632853	+	0.00871048i
$826$	1.91652e11			0.411713
$827$	2.27807e11	+	7.40191e10i	0.487019	+	0.158242i	0.542226	−	0.840233i	$-0.317582\pi$
$827$	2.27807e11	+	7.40191e10i	0.487019	+	0.158242i	−0.0552067	+	0.998475i	$0.517582\pi$
$828$	4.32956e10	−	1.40676e10i	0.0921134	−	0.0299295i
$829$	−8.33857e11			−1.76552			−0.882762	−	0.469821i	$-0.844318\pi$
$829$	−8.33857e11			−1.76552			−0.882762	+	0.469821i	$0.844318\pi$
$830$	−5.05030e11	−	3.66925e11i	−1.06415	−	0.773153i
$831$	7.66269e9	+	5.56727e9i	0.0160686	+	0.0116745i
$832$			2.05383e11i			0.428618i
$833$	8.64659e10	+	2.80945e10i	0.179583	+	0.0583500i
$834$	1.41552e10	+	1.94829e10i	0.0292585	+	0.0402708i
$835$	1.96767e11	+	6.05587e11i	0.404769	+	1.24575i
$836$	7.51924e11	−	2.44315e11i	1.53939	−	0.500178i
$837$	2.97955e10	−	9.68114e9i	0.0607084	−	0.0197254i
$838$	−3.42782e11	−	2.49046e11i	−0.695091	−	0.505014i
$839$	1.77991e11	+	5.47799e11i	0.359211	+	1.10554i	0.953527	+	0.301306i	$0.0974227\pi$
$839$	1.77991e11	+	5.47799e11i	0.359211	+	1.10554i	−0.594316	+	0.804231i	$0.702577\pi$
$840$	−6.18987e9	−	8.51963e9i	−0.0124327	−	0.0171121i
$841$	−1.52832e11	+	4.70368e11i	−0.305513	+	0.940272i
$842$	−4.03195e11	+	1.31006e11i	−0.802171	+	0.260641i
$843$	−3.10579e10	+	4.27475e10i	−0.0614980	+	0.0846448i
$844$	−2.40663e11	−	3.31244e11i	−0.474285	−	0.652798i
$845$	1.39617e10	−	4.29698e10i	0.0273850	−	0.0842823i
$846$	−3.75248e10	+	5.16485e10i	−0.0732550	+	0.100827i
$847$	2.14534e11	+	2.95280e11i	0.416833	+	0.573721i
$848$	−1.67282e11	+	2.30244e11i	−0.323494	+	0.445251i
$849$	3.51563e10	+	1.14230e10i	0.0676662	+	0.0219861i
$850$	−1.36200e11	−	4.42542e10i	−0.260917	−	0.0847771i
$851$		−	3.15309e10i		−	0.0601199i
$852$	−1.65804e10	−	1.93434e10i	−0.0314656	−	0.0367091i
$853$	−4.94432e10			−0.0933921			−0.0466961	−	0.998909i	$-0.514869\pi$
$853$	−4.94432e10			−0.0933921			−0.0466961	+	0.998909i	$0.514869\pi$
$854$	−2.90515e11	+	8.94114e11i	−0.546182	+	1.68098i
$855$	2.56623e11	−	7.89805e11i	0.480210	−	1.47794i
$856$	2.49000e11	+	1.80909e11i	0.463772	+	0.336950i
$857$	−7.70977e11	+	5.60147e11i	−1.42928	+	1.03843i	−0.439132	+	0.898423i	$0.644714\pi$
$857$	−7.70977e11	+	5.60147e11i	−1.42928	+	1.03843i	−0.990150	+	0.140012i	$0.955286\pi$
$858$	4.60327e10	+	3.34447e10i	0.0849410	+	0.0617133i
$859$	−5.50697e11	−	1.78932e11i	−1.01144	−	0.328637i	−0.244012	−	0.969772i	$-0.578464\pi$
$859$	−5.50697e11	−	1.78932e11i	−1.01144	−	0.328637i	−0.767428	+	0.641136i	$0.778464\pi$
$860$	−5.31658e11	+	3.86272e11i	−0.971938	+	0.706154i
$861$	−4.59925e10	−	3.34155e10i	−0.0836902	−	0.0608045i
$862$	−3.76230e11	−	1.15792e12i	−0.681435	−	2.09724i
$863$	−3.96085e11	−	1.28696e11i	−0.714077	−	0.232018i	−0.0706236	−	0.997503i	$-0.522499\pi$
$863$	−3.96085e11	−	1.28696e11i	−0.714077	−	0.232018i	−0.643453	+	0.765485i	$0.722499\pi$
$864$	7.19786e10	−	5.22955e10i	0.129166	−	0.0938447i
$865$	1.52646e11	−	4.95978e10i	0.272660	−	0.0885927i
$866$	5.10101e11	−	7.02093e11i	0.906952	−	1.24831i
$867$	−1.78736e10	−	5.50092e10i	−0.0316326	−	0.0973552i
$868$	−6.87907e10	−	2.11716e11i	−0.121186	−	0.372971i
$869$	−6.40706e11	+	2.08178e11i	−1.12352	+	0.365053i
$870$	−3.93267e9	+	2.85725e9i	−0.00686453	+	0.00498737i
$871$	2.50162e11	−	7.69919e11i	0.434659	−	1.33774i
$872$	1.01002e11			0.174688
$873$	−3.07154e11	+	4.22761e11i	−0.528809	+	0.727844i
$874$	9.84961e10	−	1.35568e11i	0.168800	−	0.232334i
$875$		−	6.52901e11i		−	1.11382i
$876$	−1.26193e10	−	3.88381e10i	−0.0214298	−	0.0659541i
$877$	1.17202e11	−	3.60710e11i	0.198123	−	0.609761i	−0.801803	−	0.597589i	$-0.796125\pi$
$877$	1.17202e11	−	3.60710e11i	0.198123	−	0.609761i	0.999926	−	0.0121720i	$-0.00387457\pi$
$878$			7.63919e11i			1.28549i
$879$	−1.53337e10	+	1.11406e10i	−0.0256858	+	0.0186618i
$880$	5.05199e11	+	6.95346e11i	0.842426	+	1.15950i
$881$	7.74290e10	−	5.62554e10i	0.128529	−	0.0933815i	−0.521664	−	0.853151i	$-0.674688\pi$
$881$	7.74290e10	−	5.62554e10i	0.128529	−	0.0933815i	0.650192	+	0.759770i	$0.274688\pi$
$882$	−9.35887e10			−0.154650
$883$	2.91775e11	+	9.48034e10i	0.479960	+	0.155948i	0.538998	−	0.842307i	$-0.318803\pi$
$883$	2.91775e11	+	9.48034e10i	0.479960	+	0.155948i	−0.0590377	+	0.998256i	$0.518803\pi$
$884$	−6.99575e11			−1.14558
$885$	6.39846e9	−	8.80672e9i	0.0104304	−	0.0143563i
$886$			2.71278e11i			0.440231i
$887$	4.85890e11	−	1.57875e11i	0.784952	−	0.255046i	0.110999	−	0.993821i	$-0.464595\pi$
$887$	4.85890e11	−	1.57875e11i	0.784952	−	0.255046i	0.673953	+	0.738774i	$0.264595\pi$
$888$	−1.90707e9	−	5.86936e9i	−0.00306701	−	0.00943928i
$889$	−1.01009e12			−1.61717
$890$	2.17298e11	+	1.57876e11i	0.346334	+	0.251627i
$891$			8.04496e11i			1.27648i
$892$	1.77344e11	−	5.45810e11i	0.280129	−	0.862148i
$893$			1.00627e11i			0.158238i
$894$	−1.37905e9	−	1.89811e9i	−0.00215889	−	0.00297146i
$895$	−3.86360e11	+	2.80707e11i	−0.602143	+	0.437482i
$896$	2.57592e11	+	3.54546e11i	0.399669	+	0.550098i
$897$	5.16411e9			0.00797674
$898$	2.09232e11	+	6.79835e10i	0.321753	+	0.104544i
$899$	3.27704e10	−	1.06478e10i	0.0501699	−	0.0163012i
$900$	6.31262e10			0.0962144
$901$	−3.97139e11	−	2.88539e11i	−0.602620	−	0.437829i
$902$	1.38761e12	+	1.00816e12i	2.09624	+	1.52301i
$903$			7.80005e10i			0.117313i
$904$	6.69286e10	+	2.17464e10i	0.100216	+	0.0325622i
$905$	6.47948e11	+	8.91823e11i	0.965930	+	1.32949i
$906$	−2.91151e9	−	8.96072e9i	−0.00432122	−	0.0132993i
$907$	−4.82116e11	+	1.56649e11i	−0.712397	+	0.231472i	−0.642724	−	0.766098i	$-0.722196\pi$
$907$	−4.82116e11	+	1.56649e11i	−0.712397	+	0.231472i	−0.0696736	+	0.997570i	$0.522196\pi$
$908$	9.44996e10	−	3.07048e10i	0.139023	−	0.0451713i
$909$	7.36660e11	+	5.35215e11i	1.07898	+	0.783922i
$910$	−2.63014e11	−	8.09474e11i	−0.383542	−	1.18042i
$911$	−6.39585e11	−	8.80314e11i	−0.928592	−	1.27810i	−0.960406	−	0.278604i	$-0.910128\pi$
$911$	−6.39585e11	−	8.80314e11i	−0.928592	−	1.27810i	0.0318141	−	0.999494i	$-0.489872\pi$
$912$	2.74177e10	−	8.43831e10i	0.0396326	−	0.121976i
$913$	9.10376e11	−	2.95799e11i	1.31020	−	0.425710i
$914$	−2.04010e9	+	2.80795e9i	−0.00292325	+	0.00402351i
$915$	3.13868e10	+	4.32003e10i	0.0447778	+	0.0616314i
$916$	−2.37528e11	+	7.31035e11i	−0.337390	+	1.03838i
$917$	−5.97833e11	+	8.22847e11i	−0.845479	+	1.16370i
$918$	1.14378e11	+	1.57428e11i	0.161055	+	0.221673i
$919$	−6.76411e10	+	9.31000e10i	−0.0948306	+	0.130523i	−0.853796	−	0.520608i	$-0.825705\pi$
$919$	−6.76411e10	+	9.31000e10i	−0.0948306	+	0.130523i	0.758965	+	0.651131i	$0.225705\pi$
$920$	2.74243e10	+	8.91068e9i	0.0382810	+	0.0124383i
$921$	5.14720e9	+	1.67243e9i	0.00715373	+	0.00232439i
$922$		−	5.05869e11i		−	0.700026i
$923$	2.65364e11	+	6.37435e11i	0.365624	+	0.878273i
$924$	−4.81568e10			−0.0660647
$925$	1.35111e10	−	4.15829e10i	0.0184554	−	0.0568000i
$926$	4.29337e10	−	1.32136e11i	0.0583921	−	0.179712i
$927$	−6.84634e11	−	4.97415e11i	−0.927127	−	0.673597i
$928$	7.91653e10	−	5.75170e10i	0.106744	−	0.0775540i
$929$	6.45962e11	+	4.69319e11i	0.867250	+	0.630094i	0.929848	−	0.367945i	$-0.119938\pi$
$929$	6.45962e11	+	4.69319e11i	0.867250	+	0.630094i	−0.0625975	+	0.998039i	$0.519938\pi$
$930$	−2.80829e10	−	9.12470e9i	−0.0375414	−	0.0121979i
$931$	−1.19343e11	+	8.67077e10i	−0.158854	+	0.115414i
$932$	−6.16335e11	−	4.47793e11i	−0.816870	−	0.593491i
$933$	5.72183e9	+	1.76100e10i	0.00755107	+	0.0232398i
$934$	−3.32920e11	−	1.08172e11i	−0.437474	−	0.142144i
$935$	−1.19938e12	+	8.71398e11i	−1.56931	+	1.14017i
$936$	−2.29660e11	+	7.46212e10i	−0.299215	+	0.0972207i
$937$	−4.51982e11	+	6.22100e11i	−0.586358	+	0.807053i	−0.994374	−	0.105922i	$-0.966221\pi$
$937$	−4.51982e11	+	6.22100e11i	−0.586358	+	0.807053i	0.408016	+	0.912975i	$0.366221\pi$
$938$	4.94443e11	+	1.52174e12i	0.638711	+	1.96575i
$939$	1.00109e9	+	3.08104e9i	0.00128769	+	0.00396310i
$940$	4.91122e10	−	1.59575e10i	0.0629040	−	0.0204387i
$941$	5.84918e11	−	4.24968e11i	0.745996	−	0.541998i	−0.148587	−	0.988899i	$-0.547473\pi$
$941$	5.84918e11	−	4.24968e11i	0.745996	−	0.541998i	0.894583	+	0.446901i	$0.147473\pi$
$942$	−1.64142e10	+	5.05176e10i	−0.0208456	+	0.0641563i
$943$	1.55666e11			0.196856
$944$	−1.63323e11	+	2.24795e11i	−0.205665	+	0.283073i
$945$	−5.95882e10	+	8.20161e10i	−0.0747193	+	0.102842i
$946$		−	2.35330e12i		−	2.93841i
$947$	−1.96312e11	−	6.04186e11i	−0.244088	−	0.751226i	−0.995785	−	0.0917176i	$-0.970764\pi$
$947$	−1.96312e11	−	6.04186e11i	−0.244088	−	0.751226i	0.751697	−	0.659509i	$-0.229236\pi$
$948$	1.10283e10	−	3.39415e10i	0.0136545	−	0.0420241i
$949$			1.10674e12i			1.36452i
$950$	1.87988e11	−	1.36581e11i	0.230800	−	0.167686i
$951$	−3.83106e10	−	5.27300e10i	−0.0468378	−	0.0644667i
$952$	−3.75100e11	+	2.72526e11i	−0.456667	+	0.331788i
$953$	4.08633e11			0.495407			0.247703	−	0.968836i	$-0.420324\pi$
$953$	4.08633e11			0.495407			0.247703	+	0.968836i	$0.420324\pi$
$954$	4.80592e11	+	1.56154e11i	0.580207	+	0.188521i
$955$	3.29977e11			0.396707
$956$	2.32287e11	−	3.19716e11i	0.278095	−	0.382765i
$957$		−	7.45393e9i		−	0.00888664i
$958$	−1.08468e12	+	3.52434e11i	−1.28777	+	0.418423i
$959$	−2.47092e10	−	7.60470e10i	−0.0292135	−	0.0899099i
$960$	−2.30569e10			−0.0271466
$961$	−5.20671e11	−	3.78290e11i	−0.610478	−	0.443538i
$962$		−	4.98790e11i		−	0.582395i
$963$	4.56840e11	−	1.40601e12i	0.531201	−	1.63487i
$964$			1.10574e12i			1.28040i
$965$	−2.13097e11	−	2.93303e11i	−0.245736	−	0.338226i
$966$	−8.25748e9	+	5.99941e9i	−0.00948286	+	0.00688970i
$967$	−5.06457e11	−	6.97078e11i	−0.579211	−	0.797215i	0.414398	−	0.910096i	$-0.363992\pi$
$967$	−5.06457e11	−	6.97078e11i	−0.579211	−	0.797215i	−0.993609	+	0.112881i	$0.963992\pi$
$968$	−1.95610e11			−0.222786
$969$	1.45549e11	+	4.72918e10i	0.165088	+	0.0536402i
$970$	9.38801e11	−	3.05035e11i	1.06044	−	0.344558i
$971$	7.52046e11			0.845994			0.422997	−	0.906131i	$-0.360978\pi$
$971$	7.52046e11			0.845994			0.422997	+	0.906131i	$0.360978\pi$
$972$	−1.04163e11	−	7.56791e10i	−0.116694	−	0.0847834i
$973$	4.46886e11	+	3.24682e11i	0.498593	+	0.362249i
$974$			1.67950e12i			1.86614i
$975$	6.81042e9	+	2.21284e9i	0.00753625	+	0.00244868i
$976$	−8.01161e11	−	1.10270e12i	−0.882918	−	1.21523i
$977$	3.78458e10	+	1.16477e11i	0.0415374	+	0.127839i	0.969675	−	0.244399i	$-0.0785906\pi$
$977$	3.78458e10	+	1.16477e11i	0.0415374	+	0.127839i	−0.928137	+	0.372238i	$0.878591\pi$
$978$	1.29264e11	−	4.20003e10i	0.141293	−	0.0459089i
$979$	−3.91705e11	+	1.27273e11i	−0.426411	+	0.138549i
$980$	6.12441e10	+	4.44964e10i	0.0663987	+	0.0482415i
$981$	−1.49917e11	−	4.61398e11i	−0.161874	−	0.498196i
$982$	7.93180e10	+	1.09172e11i	0.0852954	+	0.117399i
$983$	−2.15355e10	+	6.62795e10i	−0.0230644	+	0.0709848i	−0.961926	−	0.273309i	$-0.911882\pi$
$983$	−2.15355e10	+	6.62795e10i	−0.0230644	+	0.0709848i	0.938862	+	0.344294i	$0.111882\pi$
$984$	2.89767e10	−	9.41510e9i	0.0309078	−	0.0100426i
$985$	−1.95365e11	+	2.68897e11i	−0.207540	+	0.285655i
$986$	1.25799e11	+	1.73147e11i	0.133097	+	0.183192i
$987$	1.89403e9	−	5.82924e9i	0.00199581	−	0.00614247i
$988$	6.67196e11	−	9.18316e11i	0.700206	−	0.963750i
$989$	−1.25540e11	−	1.72791e11i	−0.131219	−	0.180607i
$990$	8.97019e11	−	1.23464e12i	0.933815	−	1.28529i
$991$	−1.41868e12	−	4.60957e11i	−1.47092	−	0.477932i	−0.539536	−	0.841962i	$-0.681400\pi$
$991$	−1.41868e12	−	4.60957e11i	−1.47092	−	0.477932i	−0.931387	+	0.364030i	$0.881400\pi$
$992$	5.65314e11	+	1.83682e11i	0.583771	+	0.189679i
$993$		−	1.38074e10i		−	0.0142009i
$994$	−1.16486e12	−	7.10982e11i	−1.19324	−	0.728304i
$995$	1.54053e12			1.57173
$996$	−1.56700e10	+	4.82274e10i	−0.0159233	+	0.0490068i
$997$	4.22849e11	−	1.30139e12i	0.427961	−	1.31713i	−0.472169	−	0.881508i	$-0.656529\pi$
$997$	4.22849e11	−	1.30139e12i	0.427961	−	1.31713i	0.900130	−	0.435621i	$-0.143471\pi$
$998$	1.31154e12	+	9.52892e11i	1.32209	+	0.960554i
$999$	−4.80641e10	+	3.49206e10i	−0.0482568	+	0.0350606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.9.e.a.14.9	✓	188
71.66	odd	10	inner	71.9.e.a.66.9	yes	188

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.9.e.a.14.9	✓	188	1.1	even	1	trivial
71.9.e.a.66.9	yes	188	71.66	odd	10	inner

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	71.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.53857 + 20.1236i) q^{2} +(1.61600 - 4.97354i) q^{3} +(-155.100 - 112.687i) q^{4} +(-471.892 + 342.850i) q^{5} +(89.5195 + 65.0397i) q^{6} +(2413.84 + 784.305i) q^{7} +(-1100.46 + 799.529i) q^{8} +(5285.84 + 3840.38i) q^{9} +O(q^{10})\)	\(q+(-6.53857 + 20.1236i) q^{2} +(1.61600 - 4.97354i) q^{3} +(-155.100 - 112.687i) q^{4} +(-471.892 + 342.850i) q^{5} +(89.5195 + 65.0397i) q^{6} +(2413.84 + 784.305i) q^{7} +(-1100.46 + 799.529i) q^{8} +(5285.84 + 3840.38i) q^{9} +(-3813.89 - 11737.9i) q^{10} +(17999.0 + 5848.22i) q^{11} +(-811.094 + 589.295i) q^{12} +(25841.3 - 8396.35i) q^{13} +(-31566.1 + 43447.1i) q^{14} +(942.600 + 2901.02i) q^{15} +(-24060.2 - 74049.7i) q^{16} +(127726. - 41500.6i) q^{17} +(-111844. + 81259.7i) q^{18} +(-67337.1 + 207242. i) q^{19} +111825. q^{20} +(7801.55 - 10737.9i) q^{21} +(-235375. + 323966. i) q^{22} +36343.6i q^{23} +(2198.15 + 6765.21i) q^{24} +(-15573.4 + 47929.8i) q^{25} +574922. i q^{26} +(55400.2 - 40250.6i) q^{27} +(-286006. - 393654. i) q^{28} +(60931.6 - 44269.4i) q^{29} -64542.4 q^{30} +(435108. + 141375. i) q^{31} +1.29925e6 q^{32} +(58172.7 - 80067.9i) q^{33} +2.84166e6i q^{34} +(-1.40797e6 + 457478. i) q^{35} +(-387073. - 1.19129e6i) q^{36} -867579. q^{37} +(-3.73018e6 - 2.71014e6i) q^{38} -142091. i q^{39} +(245179. - 754584. i) q^{40} -4.28319e6i q^{41} +(165075. + 227206. i) q^{42} +(-4.75437e6 + 3.45425e6i) q^{43} +(-2.13262e6 - 2.93530e6i) q^{44} -3.81102e6 q^{45} +(-731365. - 237635. i) q^{46} +(439187. - 142701. i) q^{47} -407171. q^{48} +(547677. + 397911. i) q^{49} +(-862696. - 626785. i) q^{50} -702314. i q^{51} +(-4.95414e6 - 1.60970e6i) q^{52} +(-2.14848e6 - 2.95714e6i) q^{53} +(447751. + 1.37804e6i) q^{54} +(-1.04986e7 + 3.41121e6i) q^{55} +(-3.28341e6 + 1.06684e6i) q^{56} +(921912. + 669808. i) q^{57} +(492456. + 1.51562e6i) q^{58} +(-2.09764e6 - 2.88715e6i) q^{59} +(180710. - 556167. i) q^{60} +(1.66491e7 - 5.40961e6i) q^{61} +(-5.68997e6 + 7.83157e6i) q^{62} +(9.74714e6 + 1.34158e7i) q^{63} +(-2.33581e6 + 7.18890e6i) q^{64} +(-9.31563e6 + 1.28219e7i) q^{65} +(1.23089e6 + 1.69418e6i) q^{66} +(1.75126e7 - 2.41040e7i) q^{67} +(-2.44868e7 - 7.95625e6i) q^{68} +(180756. + 58731.3i) q^{69} -3.13248e7i q^{70} +(2.03883e6 + 2.53298e7i) q^{71} -8.88734e6 q^{72} +(-1.25869e7 + 3.87386e7i) q^{73} +(5.67273e6 - 1.74589e7i) q^{74} +(213215. + 154909. i) q^{75} +(3.37975e7 - 2.45553e7i) q^{76} +(3.88599e7 + 2.82333e7i) q^{77} +(2.85940e6 + 929074. i) q^{78} +(-2.87984e7 + 2.09233e7i) q^{79} +(3.67418e7 + 2.66945e7i) q^{80} +(1.31361e7 + 4.04286e7i) q^{81} +(8.61934e7 + 2.80059e7i) q^{82} +(4.09196e7 - 2.97298e7i) q^{83} +(-2.42004e6 + 786319. i) q^{84} +(-4.60443e7 + 6.33745e7i) q^{85} +(-3.84254e7 - 1.18261e8i) q^{86} +(-121710. - 374585. i) q^{87} +(-2.44829e7 + 7.95498e6i) q^{88} +(-1.76064e7 + 1.27918e7i) q^{89} +(2.49186e7 - 7.66917e7i) q^{90} +6.89621e7 q^{91} +(4.09544e6 - 5.63689e6i) q^{92} +(1.40627e6 - 1.93557e6i) q^{93} +9.77111e6i q^{94} +(-3.92772e7 - 1.20883e8i) q^{95} +(2.09959e6 - 6.46187e6i) q^{96} +7.99800e7i q^{97} +(-1.15884e7 + 8.41949e6i) q^{98} +(7.26801e7 + 1.00036e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 188 q + 6 q^{2} - 73 q^{3} - 6170 q^{4} + 291 q^{5} - 4342 q^{6} - 5 q^{7} - 4231 q^{8} - 103462 q^{9}+O(q^{10}) \) 188 * q + 6 * q^2 - 73 * q^3 - 6170 * q^4 + 291 * q^5 - 4342 * q^6 - 5 * q^7 - 4231 * q^8 - 103462 * q^9	\( 188 q + 6 q^{2} - 73 q^{3} - 6170 q^{4} + 291 q^{5} - 4342 q^{6} - 5 q^{7} - 4231 q^{8} - 103462 q^{9} - 39605 q^{10} + 28465 q^{11} + 87226 q^{12} - 5 q^{13} - 270305 q^{14} - 273057 q^{15} - 607702 q^{16} + 267190 q^{17} - 595620 q^{18} - 164489 q^{19} + 1380836 q^{20} - 5 q^{21} + 1441620 q^{22} + 1594977 q^{24} - 3158228 q^{25} + 2482310 q^{27} + 1860770 q^{28} + 2583153 q^{29} + 780472 q^{30} - 1534580 q^{31} - 6084580 q^{32} - 5198730 q^{33} + 10938955 q^{35} - 12158488 q^{36} - 4992382 q^{37} + 305303 q^{38} - 8681861 q^{40} + 30641485 q^{42} - 9988337 q^{43} - 32861225 q^{44} - 21060496 q^{45} + 19044385 q^{46} + 23015995 q^{47} - 53495300 q^{48} + 25425264 q^{49} - 4315274 q^{50} - 45871475 q^{52} + 75873220 q^{53} + 18140888 q^{54} - 11520710 q^{55} + 42589435 q^{56} + 9074010 q^{57} + 40460737 q^{58} + 32264995 q^{59} - 158115870 q^{60} + 9916960 q^{61} - 41573135 q^{62} - 20329385 q^{63} - 173398207 q^{64} - 29584700 q^{65} + 144000740 q^{66} - 128145130 q^{67} - 164559375 q^{68} - 6139445 q^{69} + 23495669 q^{71} + 775956446 q^{72} + 162484067 q^{73} - 71216283 q^{74} + 39808021 q^{75} + 234840675 q^{76} - 257706146 q^{77} + 42725920 q^{78} + 86434027 q^{79} - 407918718 q^{80} + 89998907 q^{81} - 401066875 q^{82} + 201744669 q^{83} - 650053825 q^{84} - 238358045 q^{85} + 120450107 q^{86} + 243937047 q^{87} + 8458490 q^{88} + 121627626 q^{89} + 542716852 q^{90} + 213723098 q^{91} + 377149290 q^{92} - 564095080 q^{93} - 185902021 q^{95} + 133775573 q^{96} + 803758296 q^{98} - 824163320 q^{99}+O(q^{100}) \) 188 * q + 6 * q^2 - 73 * q^3 - 6170 * q^4 + 291 * q^5 - 4342 * q^6 - 5 * q^7 - 4231 * q^8 - 103462 * q^9 - 39605 * q^10 + 28465 * q^11 + 87226 * q^12 - 5 * q^13 - 270305 * q^14 - 273057 * q^15 - 607702 * q^16 + 267190 * q^17 - 595620 * q^18 - 164489 * q^19 + 1380836 * q^20 - 5 * q^21 + 1441620 * q^22 + 1594977 * q^24 - 3158228 * q^25 + 2482310 * q^27 + 1860770 * q^28 + 2583153 * q^29 + 780472 * q^30 - 1534580 * q^31 - 6084580 * q^32 - 5198730 * q^33 + 10938955 * q^35 - 12158488 * q^36 - 4992382 * q^37 + 305303 * q^38 - 8681861 * q^40 + 30641485 * q^42 - 9988337 * q^43 - 32861225 * q^44 - 21060496 * q^45 + 19044385 * q^46 + 23015995 * q^47 - 53495300 * q^48 + 25425264 * q^49 - 4315274 * q^50 - 45871475 * q^52 + 75873220 * q^53 + 18140888 * q^54 - 11520710 * q^55 + 42589435 * q^56 + 9074010 * q^57 + 40460737 * q^58 + 32264995 * q^59 - 158115870 * q^60 + 9916960 * q^61 - 41573135 * q^62 - 20329385 * q^63 - 173398207 * q^64 - 29584700 * q^65 + 144000740 * q^66 - 128145130 * q^67 - 164559375 * q^68 - 6139445 * q^69 + 23495669 * q^71 + 775956446 * q^72 + 162484067 * q^73 - 71216283 * q^74 + 39808021 * q^75 + 234840675 * q^76 - 257706146 * q^77 + 42725920 * q^78 + 86434027 * q^79 - 407918718 * q^80 + 89998907 * q^81 - 401066875 * q^82 + 201744669 * q^83 - 650053825 * q^84 - 238358045 * q^85 + 120450107 * q^86 + 243937047 * q^87 + 8458490 * q^88 + 121627626 * q^89 + 542716852 * q^90 + 213723098 * q^91 + 377149290 * q^92 - 564095080 * q^93 - 185902021 * q^95 + 133775573 * q^96 + 803758296 * q^98 - 824163320 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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