LMFDB - Embedded newform 603.2.z.c.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(10,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("603.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.z (of order $33$, degree $20$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	603.73
Dual form			603.2.z.c.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.260812 + 0.753567i) q^{2} +(1.07227 + 0.843239i) q^{4} +(1.62666 + 0.477630i) q^{5} +(1.76797 - 0.340749i) q^{7} +(-2.25677 + 1.45034i) q^{8} +O(q^{10})$	\(q+(-0.260812 + 0.753567i) q^{2} +(1.07227 + 0.843239i) q^{4} +(1.62666 + 0.477630i) q^{5} +(1.76797 - 0.340749i) q^{7} +(-2.25677 + 1.45034i) q^{8} +(-0.784178 + 1.10122i) q^{10} +(-2.86900 + 2.73558i) q^{11} +(-0.0951752 + 1.99797i) q^{13} +(-0.204332 + 1.42116i) q^{14} +(0.138870 + 0.572431i) q^{16} +(0.772123 - 0.607204i) q^{17} +(1.12934 + 0.217663i) q^{19} +(1.34145 + 1.88381i) q^{20} +(-1.31318 - 2.87545i) q^{22} +(6.55469 - 0.625897i) q^{23} +(-1.78839 - 1.14933i) q^{25} +(-1.48078 - 0.592817i) q^{26} +(2.18307 + 1.12545i) q^{28} +(-0.446677 + 0.773667i) q^{29} +(-0.291386 - 6.11694i) q^{31} +(-5.80854 - 0.554649i) q^{32} +(0.256190 + 0.740213i) q^{34} +(3.03864 + 0.290155i) q^{35} +(-0.715735 - 1.23969i) q^{37} +(-0.458569 + 0.794265i) q^{38} +(-4.36371 + 1.28130i) q^{40} +(5.64541 + 2.26008i) q^{41} +(1.31736 + 9.16244i) q^{43} +(-5.38308 + 0.514022i) q^{44} +(-1.23789 + 5.10264i) q^{46} +(-1.67196 - 2.34793i) q^{47} +(-3.48896 + 1.39677i) q^{49} +(1.33253 - 1.04791i) q^{50} +(-1.78682 + 2.06210i) q^{52} +(-0.356721 + 2.48105i) q^{53} +(-5.97347 + 3.07954i) q^{55} +(-3.49571 + 3.33315i) q^{56} +(-0.466511 - 0.538382i) q^{58} +(4.92775 - 3.16687i) q^{59} +(-2.89628 - 2.76160i) q^{61} +(4.68552 + 1.37579i) q^{62} +(1.44352 - 3.16086i) q^{64} +(-1.10911 + 3.20456i) q^{65} +(4.06799 + 7.10292i) q^{67} +1.33994 q^{68} +(-1.01116 + 2.21414i) q^{70} +(-0.665476 - 0.523336i) q^{71} +(-3.19057 - 3.04220i) q^{73} +(1.12086 - 0.216028i) q^{74} +(1.02741 + 1.18570i) q^{76} +(-4.14016 + 5.81404i) q^{77} +(13.5288 - 6.97460i) q^{79} +(-0.0475157 + 0.997477i) q^{80} +(-3.17552 + 3.66474i) q^{82} +(-1.93752 - 7.98658i) q^{83} +(1.54600 - 0.618924i) q^{85} +(-7.24809 - 1.39696i) q^{86} +(2.50714 - 10.3346i) q^{88} +(-3.81728 - 8.35868i) q^{89} +(0.512540 + 3.56479i) q^{91} +(7.55615 + 4.85604i) q^{92} +(2.20539 - 0.647561i) q^{94} +(1.73309 + 0.893469i) q^{95} +(-2.12978 - 3.68889i) q^{97} +(-0.142596 - 2.99346i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{20}{33}\right)$	$1$

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 $

$2$	−0.260812	+	0.753567i	−0.184422	+	0.532852i	−0.998877	−	0.0473741i	$-0.984915\pi$
$2$	−0.260812	+	0.753567i	−0.184422	+	0.532852i	0.814455	+	0.580226i	$0.197036\pi$
$3$		0			0
$3$		0			0
$4$	1.07227	+	0.843239i	0.536133	+	0.421620i
$5$	1.62666	+	0.477630i	0.727463	+	0.213602i	0.624436	−	0.781076i	$-0.285329\pi$
$5$	1.62666	+	0.477630i	0.727463	+	0.213602i	0.103027	+	0.994679i	$0.467147\pi$
$6$		0			0
$7$	1.76797	−	0.340749i	0.668231	−	0.128791i	0.156157	−	0.987732i	$-0.450089\pi$
$7$	1.76797	−	0.340749i	0.668231	−	0.128791i	0.512074	+	0.858941i	$0.328877\pi$
$8$	−2.25677	+	1.45034i	−0.797889	+	0.512772i
$9$		0			0
$10$	−0.784178	+	1.10122i	−0.247979	+	0.348237i
$11$	−2.86900	+	2.73558i	−0.865035	+	0.824809i	−0.985809	−	0.167871i	$-0.946311\pi$
$11$	−2.86900	+	2.73558i	−0.865035	+	0.824809i	0.120774	+	0.992680i	$0.461462\pi$
$12$		0			0
$13$	−0.0951752	+	1.99797i	−0.0263969	+	0.554138i	0.946473	+	0.322784i	$0.104619\pi$
$13$	−0.0951752	+	1.99797i	−0.0263969	+	0.554138i	−0.972870	+	0.231354i	$0.925684\pi$
$14$	−0.204332	+	1.42116i	−0.0546099	+	0.379820i
$15$		0			0
$16$	0.138870	+	0.572431i	0.0347175	+	0.143108i
$17$	0.772123	−	0.607204i	0.187267	−	0.147269i	−0.520124	−	0.854091i	$-0.674114\pi$
$17$	0.772123	−	0.607204i	0.187267	−	0.147269i	0.707391	+	0.706822i	$0.249872\pi$
$18$		0			0
$19$	1.12934	+	0.217663i	0.259088	+	0.0499352i	0.317141	−	0.948378i	$-0.397277\pi$
$19$	1.12934	+	0.217663i	0.259088	+	0.0499352i	−0.0580528	+	0.998314i	$0.518489\pi$
$20$	1.34145	+	1.88381i	0.299958	+	0.421232i
$21$		0			0
$22$	−1.31318	−	2.87545i	−0.279970	−	0.613049i
$23$	6.55469	−	0.625897i	1.36675	−	0.130508i	0.614253	−	0.789109i	$-0.289457\pi$
$23$	6.55469	−	0.625897i	1.36675	−	0.130508i	0.752493	+	0.658600i	$0.228851\pi$
$24$		0			0
$25$	−1.78839	−	1.14933i	−0.357677	−	0.229865i
$26$	−1.48078	−	0.592817i	−0.290406	−	0.116261i
$27$		0			0
$28$	2.18307	+	1.12545i	0.412561	+	0.212690i
$29$	−0.446677	+	0.773667i	−0.0829458	+	0.143666i	−0.904514	−	0.426444i	$-0.859766\pi$
$29$	−0.446677	+	0.773667i	−0.0829458	+	0.143666i	0.821568	+	0.570110i	$0.193099\pi$
$30$		0			0
$31$	−0.291386	−	6.11694i	−0.0523344	−	1.09864i	−0.860425	−	0.509577i	$-0.829802\pi$
$31$	−0.291386	−	6.11694i	−0.0523344	−	1.09864i	0.808091	−	0.589058i	$-0.200501\pi$
$32$	−5.80854	−	0.554649i	−1.02682	−	0.0980490i
$33$		0			0
$34$	0.256190	+	0.740213i	0.0439362	+	0.126945i
$35$	3.03864	+	0.290155i	0.513623	+	0.0490451i
$36$		0			0
$37$	−0.715735	−	1.23969i	−0.117666	−	0.203804i	0.801176	−	0.598428i	$-0.204208\pi$
$37$	−0.715735	−	1.23969i	−0.117666	−	0.203804i	−0.918842	+	0.394625i	$0.870875\pi$
$38$	−0.458569	+	0.794265i	−0.0743897	+	0.128847i
$39$		0			0
$40$	−4.36371	+	1.28130i	−0.689964	+	0.202592i
$41$	5.64541	+	2.26008i	0.881665	+	0.352966i	0.767921	−	0.640544i	$-0.221291\pi$
$41$	5.64541	+	2.26008i	0.881665	+	0.352966i	0.113744	+	0.993510i	$0.463716\pi$
$42$		0			0
$43$	1.31736	+	9.16244i	0.200895	+	1.39726i	0.801635	+	0.597814i	$0.203964\pi$
$43$	1.31736	+	9.16244i	0.200895	+	1.39726i	−0.600740	+	0.799445i	$0.705127\pi$
$44$	−5.38308	+	0.514022i	−0.811529	+	0.0774917i
$45$		0			0
$46$	−1.23789	+	5.10264i	−0.182516	+	0.752343i
$47$	−1.67196	−	2.34793i	−0.243880	−	0.342481i	0.674433	−	0.738336i	$-0.264388\pi$
$47$	−1.67196	−	2.34793i	−0.243880	−	0.342481i	−0.918313	+	0.395854i	$0.870449\pi$
$48$		0			0
$49$	−3.48896	+	1.39677i	−0.498423	+	0.199538i
$50$	1.33253	−	1.04791i	0.188448	−	0.148197i
$51$		0			0
$52$	−1.78682	+	2.06210i	−0.247788	+	0.285962i
$53$	−0.356721	+	2.48105i	−0.0489994	+	0.340798i	0.950544	+	0.310589i	$0.100526\pi$
$53$	−0.356721	+	2.48105i	−0.0489994	+	0.340798i	−0.999544	+	0.0302091i	$0.990383\pi$
$54$		0			0
$55$	−5.97347	+	3.07954i	−0.805462	+	0.415245i
$56$	−3.49571	+	3.33315i	−0.467133	+	0.445411i
$57$		0			0
$58$	−0.466511	−	0.538382i	−0.0612559	−	0.0706931i
$59$	4.92775	−	3.16687i	0.641539	−	0.412292i	−0.179027	−	0.983844i	$-0.557295\pi$
$59$	4.92775	−	3.16687i	0.641539	−	0.412292i	0.820566	+	0.571552i	$0.193659\pi$
$60$		0			0
$61$	−2.89628	−	2.76160i	−0.370830	−	0.353586i	0.481633	−	0.876373i	$-0.340044\pi$
$61$	−2.89628	−	2.76160i	−0.370830	−	0.353586i	−0.852463	+	0.522787i	$0.824892\pi$
$62$	4.68552	+	1.37579i	0.595062	+	0.174726i
$63$		0			0
$64$	1.44352	−	3.16086i	0.180439	−	0.395107i
$65$	−1.10911	+	3.20456i	−0.137568	+	0.397477i
$66$		0			0
$67$	4.06799	+	7.10292i	0.496984	+	0.867760i
$67$	4.06799	+	7.10292i	0.496984	+	0.867760i
$68$	1.33994			0.162492
$69$		0			0
$70$	−1.01116	+	2.21414i	−0.120857	+	0.264640i
$71$	−0.665476	−	0.523336i	−0.0789774	−	0.0621085i	0.577890	−	0.816115i	$-0.303876\pi$
$71$	−0.665476	−	0.523336i	−0.0789774	−	0.0621085i	−0.656867	+	0.754006i	$0.728119\pi$
$72$		0			0
$73$	−3.19057	−	3.04220i	−0.373428	−	0.356063i	0.480005	−	0.877266i	$-0.340635\pi$
$73$	−3.19057	−	3.04220i	−0.373428	−	0.356063i	−0.853433	+	0.521203i	$0.825483\pi$
$74$	1.12086	−	0.216028i	0.130297	−	0.0251128i
$75$		0			0
$76$	1.02741	+	1.18570i	0.117852	+	0.136009i
$77$	−4.14016	+	5.81404i	−0.471815	+	0.662571i
$78$		0			0
$79$	13.5288	−	6.97460i	1.52211	−	0.784704i	0.524347	−	0.851504i	$-0.324309\pi$
$79$	13.5288	−	6.97460i	1.52211	−	0.784704i	0.997766	+	0.0668004i	$0.0212791\pi$
$80$	−0.0475157	+	0.997477i	−0.00531241	+	0.111521i
$81$		0			0
$82$	−3.17552	+	3.66474i	−0.350677	+	0.404703i
$83$	−1.93752	−	7.98658i	−0.212671	−	0.876641i	−0.973684	−	0.227904i	$-0.926813\pi$
$83$	−1.93752	−	7.98658i	−0.212671	−	0.876641i	0.761013	−	0.648737i	$-0.224702\pi$
$84$		0			0
$85$	1.54600	−	0.618924i	0.167687	−	0.0671318i
$86$	−7.24809	−	1.39696i	−0.781582	−	0.150638i
$87$		0			0
$88$	2.50714	−	10.3346i	0.267263	−	1.10167i
$89$	−3.81728	−	8.35868i	−0.404631	−	0.886018i	−0.996780	−	0.0801895i	$-0.974447\pi$
$89$	−3.81728	−	8.35868i	−0.404631	−	0.886018i	0.592149	−	0.805829i	$-0.298280\pi$
$90$		0			0
$91$	0.512540	+	3.56479i	0.0537288	+	0.373692i
$92$	7.55615	+	4.85604i	0.787783	+	0.506277i
$93$		0			0
$94$	2.20539	−	0.647561i	0.227469	−	0.0667909i
$95$	1.73309	+	0.893469i	0.177811	+	0.0916679i
$96$		0			0
$97$	−2.12978	−	3.68889i	−0.216247	−	0.374550i	0.737411	−	0.675444i	$-0.236048\pi$
$97$	−2.12978	−	3.68889i	−0.216247	−	0.374550i	−0.953657	+	0.300894i	$0.902715\pi$
$98$	−0.142596	−	2.99346i	−0.0144044	−	0.302385i
$99$		0			0
$100$	−0.948468	−	2.74042i	−0.0948468	−	0.274042i
$101$	0.497672	+	1.43793i	0.0495203	+	0.143079i	0.967049	−	0.254590i	$-0.0819404\pi$
$101$	0.497672	+	1.43793i	0.0495203	+	0.143079i	−0.917529	+	0.397669i	$0.869819\pi$
$102$		0			0
$103$	−0.659576	−	13.8462i	−0.0649900	−	1.36431i	−0.762154	−	0.647396i	$-0.775858\pi$
$103$	−0.659576	−	13.8462i	−0.0649900	−	1.36431i	0.697164	−	0.716912i	$-0.254445\pi$
$104$	−2.68295	−	4.64700i	−0.263085	−	0.455676i
$105$		0			0
$106$	−1.77660	−	0.915901i	−0.172559	−	0.0889602i
$107$	3.63125	−	1.06623i	0.351047	−	0.103077i	−0.101455	−	0.994840i	$-0.532350\pi$
$107$	3.63125	−	1.06623i	0.351047	−	0.103077i	0.452502	+	0.891764i	$0.350532\pi$
$108$		0			0
$109$	−2.62784	−	1.68881i	−0.251701	−	0.161759i	0.408706	−	0.912666i	$-0.365980\pi$
$109$	−2.62784	−	1.68881i	−0.251701	−	0.161759i	−0.660407	+	0.750907i	$0.729616\pi$
$110$	−0.762685	−	5.30459i	−0.0727191	−	0.505773i
$111$		0			0
$112$	0.440574	+	0.964722i	0.0416303	+	0.0911576i
$113$	−0.0937820	+	0.386575i	−0.00882227	+	0.0363659i	−0.976053	−	0.217535i	$-0.930198\pi$
$113$	−0.0937820	+	0.386575i	−0.00882227	+	0.0363659i	0.967230	+	0.253901i	$0.0817136\pi$
$114$		0			0
$115$	10.9612	+	2.11259i	1.02213	+	0.197000i
$116$	−1.13134	+	0.452921i	−0.105042	+	0.0420527i
$117$		0			0
$118$	1.10123	+	4.53935i	0.101377	+	0.417881i
$119$	1.15819	−	1.33662i	0.106171	−	0.122528i
$120$		0			0
$121$	0.224327	−	4.70921i	0.0203934	−	0.428110i
$122$	2.83643	−	1.46228i	0.256798	−	0.132389i
$123$		0			0
$124$	4.84560	−	6.80470i	0.435148	−	0.611080i
$125$	−7.91116	−	9.12997i	−0.707596	−	0.816609i
$126$		0			0
$127$	−14.7985	+	2.85217i	−1.31315	+	0.253090i	−0.797298	−	0.603586i	$-0.793738\pi$
$127$	−14.7985	+	2.85217i	−1.31315	+	0.253090i	−0.515855	+	0.856676i	$0.672526\pi$
$128$	−6.44049	−	6.14100i	−0.569265	−	0.542793i
$129$		0			0
$130$	−2.12558	−	1.67158i	−0.186426	−	0.146607i
$131$	2.07017	−	4.53305i	0.180872	−	0.396054i	−0.797379	−	0.603479i	$-0.793781\pi$
$131$	2.07017	−	4.53305i	0.180872	−	0.396054i	0.978251	+	0.207425i	$0.0665082\pi$
$132$		0			0
$133$	2.07081			0.179562
$134$	−6.41351	+	1.21298i	−0.554043	+	0.104785i
$135$		0			0
$136$	−0.861853	+	2.49016i	−0.0739033	+	0.213529i
$137$	−0.532336	+	1.16565i	−0.0454806	+	0.0995885i	−0.931008	−	0.364998i	$-0.881070\pi$
$137$	−0.532336	+	1.16565i	−0.0454806	+	0.0995885i	0.885528	+	0.464586i	$0.153797\pi$
$138$		0			0
$139$	18.7522	+	5.50615i	1.59054	+	0.467025i	0.952894	−	0.303302i	$-0.0980892\pi$
$139$	18.7522	+	5.50615i	1.59054	+	0.467025i	0.637648	+	0.770328i	$0.279907\pi$
$140$	3.01356	+	2.87342i	0.254692	+	0.242848i
$141$		0			0
$142$	0.567933	−	0.364988i	0.0476599	−	0.0306291i
$143$	−5.19257	−	5.99254i	−0.434224	−	0.501121i
$144$		0			0
$145$	−1.09612	+	1.04514i	−0.0910274	+	0.0867945i
$146$	3.12464	−	1.61086i	0.258597	−	0.133316i
$147$		0			0
$148$	0.277896	−	1.93281i	0.0228429	−	0.158876i
$149$	5.34421	−	6.16755i	0.437815	−	0.505265i	−0.493367	−	0.869821i	$-0.664234\pi$
$149$	5.34421	−	6.16755i	0.437815	−	0.505265i	0.931181	+	0.364556i	$0.118779\pi$
$150$		0			0
$151$	17.1504	−	13.4872i	1.39568	−	1.09758i	0.413318	−	0.910587i	$-0.364370\pi$
$151$	17.1504	−	13.4872i	1.39568	−	1.09758i	0.982362	−	0.186989i	$-0.0598728\pi$
$152$	−2.86435	+	1.14671i	−0.232329	+	0.0930105i
$153$		0			0
$154$	−3.30147	−	4.63626i	−0.266040	−	0.373600i
$155$	2.44765	−	10.0893i	0.196600	−	0.810395i
$156$		0			0
$157$	−12.5116	+	1.19472i	−0.998537	+	0.0953487i	−0.581505	−	0.813543i	$-0.697536\pi$
$157$	−12.5116	+	1.19472i	−0.998537	+	0.0953487i	−0.417032	+	0.908892i	$0.636930\pi$
$158$	1.72735	+	12.0139i	0.137420	+	0.955778i
$159$		0			0
$160$	−9.18359	−	3.67656i	−0.726027	−	0.290657i
$161$	11.3752	−	3.34007i	0.896494	−	0.263234i
$162$		0			0
$163$	−1.38885	+	2.40555i	−0.108783	+	0.188417i	−0.915277	−	0.402824i	$-0.868029\pi$
$163$	−1.38885	+	2.40555i	−0.108783	+	0.188417i	0.806495	+	0.591241i	$0.201362\pi$
$164$	4.14759	+	7.18384i	0.323873	+	0.560964i
$165$		0			0
$166$	6.52375	+	0.622943i	0.506342	+	0.0483498i
$167$	−2.83954	−	8.20431i	−0.219730	−	0.634868i	−0.999956	−	0.00937069i	$-0.997017\pi$
$167$	−2.83954	−	8.20431i	−0.219730	−	0.634868i	0.780226	−	0.625498i	$-0.215104\pi$
$168$		0			0
$169$	8.95829	+	0.855413i	0.689099	+	0.0658010i
$170$	0.0631859	+	1.32644i	0.00484614	+	0.101733i
$171$		0			0
$172$	−6.31357	+	10.9354i	−0.481405	+	0.833818i
$173$	11.3427	+	5.84757i	0.862370	+	0.444582i	0.831882	−	0.554953i	$-0.187264\pi$
$173$	11.3427	+	5.84757i	0.862370	+	0.444582i	0.0304876	+	0.999535i	$0.490294\pi$
$174$		0			0
$175$	−3.55345	−	1.42259i	−0.268615	−	0.107537i
$176$	−1.96435	−	1.26241i	−0.148068	−	0.0951578i
$177$		0			0
$178$	7.29442	−	0.696532i	0.546740	−	0.0522073i
$179$	−6.84591	−	14.9905i	−0.511688	−	1.12044i	−0.972492	−	0.232938i	$-0.925166\pi$
$179$	−6.84591	−	14.9905i	−0.511688	−	1.12044i	0.460804	−	0.887502i	$-0.347561\pi$
$180$		0			0
$181$	−2.64882	−	3.71974i	−0.196885	−	0.276486i	0.704317	−	0.709886i	$-0.251253\pi$
$181$	−2.64882	−	3.71974i	−0.196885	−	0.276486i	−0.901202	+	0.433399i	$0.857314\pi$
$182$	−2.81999	−	0.543508i	−0.209031	−	0.0402875i
$183$		0			0
$184$	−13.8847	+	10.9190i	−1.02359	+	0.804960i
$185$	−0.572143	−	2.35840i	−0.0420648	−	0.173393i
$186$		0			0
$187$	−0.554161	+	3.85427i	−0.0405242	+	0.281852i
$188$	0.187088	−	3.92747i	0.0136448	−	0.286440i
$189$		0			0
$190$	−1.12530	+	1.07297i	−0.0816377	+	0.0778414i
$191$	9.38625	−	13.1811i	0.679165	−	0.953754i	−0.320813	−	0.947142i	$-0.603956\pi$
$191$	9.38625	−	13.1811i	0.679165	−	0.953754i	0.999978	−	0.00661125i	$-0.00210444\pi$
$192$		0			0
$193$	4.02039	−	2.58375i	0.289394	−	0.185982i	−0.387886	−	0.921707i	$-0.626795\pi$
$193$	4.02039	−	2.58375i	0.289394	−	0.185982i	0.677281	+	0.735725i	$0.263158\pi$
$194$	3.33530	−	0.642826i	0.239461	−	0.0461522i
$195$		0			0
$196$	−4.91890	−	1.44432i	−0.351350	−	0.103166i
$197$	6.41658	+	5.04606i	0.457163	+	0.359517i	0.820027	−	0.572326i	$-0.193959\pi$
$197$	6.41658	+	5.04606i	0.457163	+	0.359517i	−0.362864	+	0.931842i	$0.618201\pi$
$198$		0			0
$199$	−3.46352	+	10.0072i	−0.245523	+	0.709391i	0.753148	+	0.657851i	$0.228534\pi$
$199$	−3.46352	+	10.0072i	−0.245523	+	0.709391i	−0.998671	+	0.0515401i	$0.983587\pi$
$200$	5.70288			0.403255
$201$		0			0
$202$	−1.21338			−0.0853728
$203$	−0.526086	+	1.52003i	−0.0369240	+	0.106685i
$204$		0			0
$205$	8.10367	+	6.37280i	0.565985	+	0.445095i
$206$	10.6061	+	3.11422i	0.738960	+	0.216978i
$207$		0			0
$208$	−1.15692	+	0.222978i	−0.0802179	+	0.0154607i
$209$	−3.83551	+	2.46493i	−0.265308	+	0.170503i
$210$		0			0
$211$	−4.99586	+	7.01570i	−0.343929	+	0.482981i	−0.949921	−	0.312490i	$-0.898837\pi$
$211$	−4.99586	+	7.01570i	−0.343929	+	0.482981i	0.605992	+	0.795471i	$0.292776\pi$
$212$	−2.47462	+	2.35954i	−0.169958	+	0.162054i
$213$		0			0
$214$	−0.143597	+	3.01448i	−0.00981611	+	0.206066i
$215$	−2.23336	+	15.5334i	−0.152314	+	1.05937i
$216$		0			0
$217$	−2.59950	−	10.7153i	−0.176466	−	0.727402i
$218$	1.95800	−	1.53979i	0.132613	−	0.104288i
$219$		0			0
$220$	−9.00193	−	1.73498i	−0.606910	−	0.116972i
$221$	1.13969	+	1.60047i	0.0766639	+	0.107659i
$222$		0			0
$223$	−3.98989	−	8.73663i	−0.267183	−	0.585048i	0.727722	−	0.685873i	$-0.240579\pi$
$223$	−3.98989	−	8.73663i	−0.267183	−	0.585048i	−0.994904	+	0.100824i	$0.967852\pi$
$224$	−10.4583	+	0.998651i	−0.698777	+	0.0667252i
$225$		0			0
$226$	−0.266850	−	0.171494i	−0.0177506	−	0.0114076i
$227$	27.3033	+	10.9306i	1.81218	+	0.725489i	0.987021	+	0.160594i	$0.0513410\pi$
$227$	27.3033	+	10.9306i	1.81218	+	0.725489i	0.825163	+	0.564895i	$0.191083\pi$
$228$		0			0
$229$	1.15770	+	0.596836i	0.0765029	+	0.0394400i	0.496053	−	0.868292i	$-0.334782\pi$
$229$	1.15770	+	0.596836i	0.0765029	+	0.0394400i	−0.419551	+	0.907732i	$0.637812\pi$
$230$	−4.45079	+	7.70899i	−0.293476	+	0.508316i
$231$		0			0
$232$	−0.114032	−	2.39382i	−0.00748655	−	0.157162i
$233$	−14.1279	−	1.34905i	−0.925551	−	0.0883794i	−0.378615	−	0.925554i	$-0.623600\pi$
$233$	−14.1279	−	1.34905i	−0.925551	−	0.0883794i	−0.546935	+	0.837175i	$0.684206\pi$
$234$		0			0
$235$	−1.59826	−	4.61786i	−0.104259	−	0.301236i
$236$	7.95430	+	0.759543i	0.517781	+	0.0494420i
$237$		0			0
$238$	0.705164	+	1.22138i	0.0457090	+	0.0791702i
$239$	−7.37038	+	12.7659i	−0.476750	+	0.825755i	−0.999645	−	0.0266419i	$-0.991519\pi$
$239$	−7.37038	+	12.7659i	−0.476750	+	0.825755i	0.522895	+	0.852397i	$0.324852\pi$
$240$		0			0
$241$	24.2293	−	7.11437i	1.56075	−	0.458277i	0.616457	−	0.787388i	$-0.288567\pi$
$241$	24.2293	−	7.11437i	1.56075	−	0.458277i	0.944291	+	0.329111i	$0.106749\pi$
$242$	3.49020	+	1.39726i	0.224358	+	0.0898195i
$243$		0			0
$244$	−0.776895	−	5.40342i	−0.0497356	−	0.345919i
$245$	−6.34248	+	0.605633i	−0.405206	+	0.0386925i
$246$		0			0
$247$	−0.542369	+	2.23568i	−0.0345101	+	0.142253i
$248$	9.52922	+	13.3819i	0.605106	+	0.849753i
$249$		0			0
$250$	8.94337	−	3.58038i	0.565628	−	0.226443i
$251$	2.47759	−	1.94840i	0.156384	−	0.122982i	−0.536901	−	0.843645i	$-0.680405\pi$
$251$	2.47759	−	1.94840i	0.156384	−	0.122982i	0.693285	+	0.720663i	$0.256163\pi$
$252$		0			0
$253$	−17.0932	+	19.7266i	−1.07464	+	1.24020i
$254$	1.71032	−	11.8955i	0.107315	−	0.746392i
$255$		0			0
$256$	12.4846	−	6.43626i	0.780287	−	0.402266i
$257$	−13.6288	+	12.9951i	−0.850143	+	0.810610i	−0.983585	−	0.180447i	$-0.942246\pi$
$257$	−13.6288	+	12.9951i	−0.850143	+	0.810610i	0.133441	+	0.991057i	$0.457397\pi$
$258$		0			0
$259$	−1.68782	−	1.94785i	−0.104876	−	0.121033i
$260$	−3.89147	+	2.50090i	−0.241339	+	0.155099i
$261$		0			0
$262$	2.87603	+	2.74229i	0.177682	+	0.169419i
$263$	−25.0187	−	7.34615i	−1.54272	−	0.452983i	−0.603804	−	0.797133i	$-0.706349\pi$
$263$	−25.0187	−	7.34615i	−1.54272	−	0.452983i	−0.938915	+	0.344149i	$0.888167\pi$
$264$		0			0
$265$	−1.76529	+	3.86544i	−0.108441	+	0.237452i
$266$	−0.540092	+	1.56049i	−0.0331152	+	0.0956801i
$267$		0			0
$268$	−1.62749	+	11.0465i	−0.0994151	+	0.674773i
$269$	−20.0385			−1.22177			−0.610884	−	0.791720i	$-0.709186\pi$
$269$	−20.0385			−1.22177			−0.610884	+	0.791720i	$0.709186\pi$
$270$		0			0
$271$	−1.74726	+	3.82597i	−0.106139	+	0.232411i	−0.955248	−	0.295806i	$-0.904412\pi$
$271$	−1.74726	+	3.82597i	−0.106139	+	0.232411i	0.849109	+	0.528217i	$0.177139\pi$
$272$	0.454807	+	0.357664i	0.0275767	+	0.0216866i
$273$		0			0
$274$	−0.739559	−	0.705168i	−0.0446784	−	0.0426007i
$275$	8.27494	−	1.59486i	0.498998	−	0.0961740i
$276$		0			0
$277$	−19.5481	−	22.5597i	−1.17453	−	1.35548i	−0.921669	−	0.387978i	$-0.873174\pi$
$277$	−19.5481	−	22.5597i	−1.17453	−	1.35548i	−0.252862	−	0.967502i	$-0.581372\pi$
$278$	−9.04006	+	12.6950i	−0.542187	+	0.761394i
$279$		0			0
$280$	−7.27832	+	3.75224i	−0.434963	+	0.224239i
$281$	−0.0160485	+	0.336899i	−0.000957371	+	0.0200977i	−0.999295	−	0.0375307i	$-0.988051\pi$
$281$	−0.0160485	+	0.336899i	−0.000957371	+	0.0200977i	0.998338	+	0.0576284i	$0.0183538\pi$
$282$		0			0
$283$	−5.70955	+	6.58918i	−0.339398	+	0.391686i	−0.899632	−	0.436648i	$-0.856166\pi$
$283$	−5.70955	+	6.58918i	−0.339398	+	0.391686i	0.560235	+	0.828334i	$0.310711\pi$
$284$	−0.272270	−	1.12231i	−0.0161562	−	0.0665969i
$285$		0			0
$286$	5.87006	−	2.35002i	0.347104	−	0.138960i
$287$	10.7511	+	2.07210i	0.634615	+	0.122312i
$288$		0			0
$289$	−3.78042	+	15.5831i	−0.222378	+	0.916654i
$290$	−0.501706	−	1.09858i	−0.0294612	−	0.0645110i
$291$		0			0
$292$	−0.855835	−	5.95246i	−0.0500840	−	0.348342i
$293$	−6.37399	−	4.09631i	−0.372372	−	0.239309i	0.341047	−	0.940046i	$-0.389218\pi$
$293$	−6.37399	−	4.09631i	−0.372372	−	0.239309i	−0.713420	+	0.700737i	$0.752855\pi$
$294$		0			0
$295$	9.52836	−	2.79778i	0.554762	−	0.162893i
$296$	3.41322	+	1.75963i	0.198389	+	0.102277i
$297$		0			0
$298$	3.25383	+	5.63579i	0.188489	+	0.326473i
$299$	0.626681	+	13.1557i	0.0362419	+	0.760812i
$300$		0			0
$301$	5.45114	+	15.7500i	0.314199	+	0.907818i
$302$	5.69050	+	16.4416i	0.327451	+	0.946109i
$303$		0			0
$304$	0.0322350	+	0.676696i	0.00184880	+	0.0388112i
$305$	−3.39223	−	5.87552i	−0.194239	−	0.336431i
$306$		0			0
$307$	6.06481	+	3.12663i	0.346137	+	0.178446i	0.622525	−	0.782600i	$-0.286107\pi$
$307$	6.06481	+	3.12663i	0.346137	+	0.178446i	−0.276388	+	0.961046i	$0.589137\pi$
$308$	−9.34198	+	2.74305i	−0.532309	+	0.156300i
$309$		0			0
$310$	6.96462	+	4.47589i	0.395564	+	0.254213i
$311$	−1.01966	−	7.09190i	−0.0578197	−	0.402145i	−0.998093	−	0.0617248i	$-0.980340\pi$
$311$	−1.01966	−	7.09190i	−0.0578197	−	0.402145i	0.940274	−	0.340420i	$-0.110569\pi$
$312$		0			0
$313$	−7.51766	−	16.4614i	−0.424923	−	0.930452i	−0.994123	−	0.108253i	$-0.965474\pi$
$313$	−7.51766	−	16.4614i	−0.424923	−	0.930452i	0.569200	−	0.822199i	$-0.307253\pi$
$314$	2.36289	−	9.73995i	0.133345	−	0.549657i
$315$		0			0
$316$	20.3878	+	3.92942i	1.14690	+	0.221047i
$317$	−25.4729	+	10.1978i	−1.43070	+	0.572765i	−0.952242	−	0.305345i	$-0.901228\pi$
$317$	−25.4729	+	10.1978i	−1.43070	+	0.572765i	−0.478457	+	0.878111i	$0.658804\pi$
$318$		0			0
$319$	−0.834915	−	3.44157i	−0.0467463	−	0.192691i
$320$	3.85782	−	4.45217i	0.215659	−	0.248884i
$321$		0			0
$322$	−0.449832	+	9.44313i	−0.0250681	+	0.526245i
$323$	1.00416	−	0.517678i	0.0558727	−	0.0288044i
$324$		0			0
$325$	2.46653	−	3.46376i	0.136819	−	0.192135i
$326$	−1.45052	−	1.67399i	−0.0803367	−	0.0927135i
$327$		0			0
$328$	−16.0183	+	3.08727i	−0.884462	+	0.170466i
$329$	−3.75603	−	3.58137i	−0.207077	−	0.197447i
$330$		0			0
$331$	−1.98788	−	1.56329i	−0.109264	−	0.0859260i	0.562032	−	0.827115i	$-0.310020\pi$
$331$	−1.98788	−	1.56329i	−0.109264	−	0.0859260i	−0.671296	+	0.741189i	$0.734262\pi$
$332$	4.65706	−	10.1975i	0.255589	−	0.559663i
$333$		0			0
$334$	6.92308			0.378814
$335$	3.22466	+	13.4970i	0.176182	+	0.737420i
$336$		0			0
$337$	−8.11365	+	23.4428i	−0.441978	+	1.27701i	0.475671	+	0.879623i	$0.342205\pi$
$337$	−8.11365	+	23.4428i	−0.441978	+	1.27701i	−0.917650	+	0.397390i	$0.869916\pi$
$338$	−2.98104	+	6.52757i	−0.162147	+	0.355053i
$339$		0			0
$340$	2.17962	+	0.639995i	0.118207	+	0.0347086i
$341$	17.5694	+	16.7524i	0.951435	+	0.907192i
$342$		0			0
$343$	−16.2952	+	10.4723i	−0.879860	+	0.565452i
$344$	−16.2616	−	18.7669i	−0.876767	−	1.01184i
$345$		0			0
$346$	−7.36485	+	7.02237i	−0.395937	+	0.377525i
$347$	−1.54897	+	0.798549i	−0.0831530	+	0.0428683i	−0.499301	−	0.866428i	$-0.666410\pi$
$347$	−1.54897	+	0.798549i	−0.0831530	+	0.0428683i	0.416148	+	0.909297i	$0.363380\pi$
$348$		0			0
$349$	2.97063	−	20.6612i	0.159014	−	1.10597i	−0.741441	−	0.671018i	$-0.765857\pi$
$349$	2.97063	−	20.6612i	0.159014	−	1.10597i	0.900455	−	0.434949i	$-0.143234\pi$
$350$	1.99880	−	2.30673i	0.106840	−	0.123300i
$351$		0			0
$352$	18.1820	−	14.2985i	0.969103	−	0.762111i
$353$	−19.5376	+	7.82169i	−1.03988	+	0.416306i	−0.827846	−	0.560955i	$-0.810434\pi$
$353$	−19.5376	+	7.82169i	−1.03988	+	0.416306i	−0.212037	+	0.977262i	$0.568010\pi$
$354$		0			0
$355$	−0.832540	−	1.16914i	−0.0441866	−	0.0620514i
$356$	2.95523	−	12.1816i	0.156627	−	0.645624i
$357$		0			0
$358$	13.0818	−	1.24916i	0.691395	−	0.0660202i
$359$	4.17850	+	29.0621i	0.220533	+	1.53384i	0.736031	+	0.676947i	$0.236698\pi$
$359$	4.17850	+	29.0621i	0.220533	+	1.53384i	−0.515499	+	0.856890i	$0.672393\pi$
$360$		0			0
$361$	−16.4110	−	6.56996i	−0.863735	−	0.345787i
$362$	3.49392	−	1.02591i	0.183636	−	0.0539205i
$363$		0			0
$364$	−2.45640	+	4.25460i	−0.128750	+	0.223002i
$365$	−3.73692	−	6.47253i	−0.195599	−	0.338788i
$366$		0			0
$367$	11.0039	+	1.05074i	0.574398	+	0.0548483i	0.378213	−	0.925719i	$-0.376539\pi$
$367$	11.0039	+	1.05074i	0.574398	+	0.0548483i	0.196185	+	0.980567i	$0.437145\pi$
$368$	1.26853	+	3.66518i	0.0661268	+	0.191061i
$369$		0			0
$370$	1.92644	+	0.183952i	0.100151	+	0.00956323i
$371$	0.214742	+	4.50798i	0.0111488	+	0.234043i
$372$		0			0
$373$	0.979083	−	1.69582i	0.0506950	−	0.0878063i	−0.839564	−	0.543260i	$-0.817190\pi$
$373$	0.979083	−	1.69582i	0.0506950	−	0.0878063i	0.890259	+	0.455454i	$0.150523\pi$
$374$	−2.75992	−	1.42284i	−0.142712	−	0.0735732i
$375$		0			0
$376$	7.17852	+	2.87385i	0.370204	+	0.148207i
$377$	−1.50325	−	0.966082i	−0.0774215	−	0.0497558i
$378$		0			0
$379$	−18.6016	+	1.77624i	−0.955499	+	0.0912391i	−0.561143	−	0.827719i	$-0.689638\pi$
$379$	−18.6016	+	1.77624i	−0.955499	+	0.0912391i	−0.394356	+	0.918958i	$0.629032\pi$
$380$	1.10492	+	2.41944i	0.0566813	+	0.124115i
$381$		0			0
$382$	7.48482	+	10.5110i	0.382957	+	0.537788i
$383$	27.6189	+	5.32310i	1.41126	+	0.271998i	0.837236	−	0.546842i	$-0.184170\pi$
$383$	27.6189	+	5.32310i	1.41126	+	0.271998i	0.574022	+	0.818840i	$0.305382\pi$
$384$		0			0
$385$	−9.51158	+	7.47999i	−0.484755	+	0.381215i
$386$	0.898462	+	3.70351i	0.0457305	+	0.188504i
$387$		0			0
$388$	0.826925	−	5.75139i	0.0419807	−	0.291982i
$389$	−1.55279	+	32.5971i	−0.0787296	+	1.65274i	0.521751	+	0.853098i	$0.325279\pi$
$389$	−1.55279	+	32.5971i	−0.0787296	+	1.65274i	−0.600480	+	0.799639i	$0.705024\pi$
$390$		0			0
$391$	4.68098	−	4.46330i	0.236727	−	0.225719i
$392$	5.84799	−	8.21235i	0.295368	−	0.414786i
$393$		0			0
$394$	−5.47606	+	3.51925i	−0.275880	+	0.177297i
$395$	25.3381	−	4.88351i	1.27490	−	0.245716i
$396$		0			0
$397$	−2.40169	−	0.705199i	−0.120537	−	0.0353929i	0.220908	−	0.975295i	$-0.429098\pi$
$397$	−2.40169	−	0.705199i	−0.120537	−	0.0353929i	−0.341445	+	0.939902i	$0.610916\pi$
$398$	−6.63776	−	5.21999i	−0.332721	−	0.261654i
$399$		0			0
$400$	0.409556	−	1.18333i	0.0204778	−	0.0591667i
$401$	−4.59293			−0.229360			−0.114680	−	0.993402i	$-0.536584\pi$
$401$	−4.59293			−0.229360			−0.114680	+	0.993402i	$0.536584\pi$
$402$		0			0
$403$	12.2492			0.610177
$404$	−0.678882	+	1.96150i	−0.0337756	+	0.0975883i
$405$		0			0
$406$	−1.00823	−	0.792882i	−0.0500377	−	0.0393501i
$407$	5.44471	+	1.59871i	0.269884	+	0.0792452i
$408$		0			0
$409$	−2.52570	+	0.486789i	−0.124888	+	0.0240702i	−0.251312	−	0.967906i	$-0.580862\pi$
$409$	−2.52570	+	0.486789i	−0.124888	+	0.0240702i	0.126424	+	0.991976i	$0.459650\pi$
$410$	−6.91586	+	4.44455i	−0.341550	+	0.219501i
$411$		0			0
$412$	10.9684	−	15.4030i	0.540376	−	0.758852i
$413$	7.63302	−	7.27807i	0.375597	−	0.358131i
$414$		0			0
$415$	0.662941	−	13.9168i	0.0325425	−	0.683151i
$416$	1.66100	−	11.5525i	0.0814374	−	0.566410i
$417$		0			0
$418$	−0.857144	−	3.53319i	−0.0419243	−	0.172814i
$419$	0.195634	−	0.153848i	0.00955734	−	0.00751597i	−0.613369	−	0.789797i	$-0.710186\pi$
$419$	0.195634	−	0.153848i	0.00955734	−	0.00751597i	0.622926	+	0.782281i	$0.285944\pi$
$420$		0			0
$421$	5.62301	+	1.08375i	0.274049	+	0.0528186i	0.324424	−	0.945912i	$-0.394830\pi$
$421$	5.62301	+	1.08375i	0.274049	+	0.0528186i	−0.0503752	+	0.998730i	$0.516042\pi$
$422$	−3.98382	−	5.59449i	−0.193929	−	0.272336i
$423$		0			0
$424$	−2.79332	−	6.11653i	−0.135656	−	0.297045i
$425$	−2.07873	+	0.198495i	−0.100833	+	0.00962840i
$426$		0			0
$427$	−6.06155	−	3.89552i	−0.293339	−	0.188517i
$428$	4.79276	+	1.91873i	0.231667	+	0.0927454i
$429$		0			0
$430$	−11.1229	−	5.73427i	−0.536395	−	0.276531i
$431$	11.8157	−	20.4654i	0.569142	−	0.985784i	−0.427509	−	0.904011i	$-0.640609\pi$
$431$	11.8157	−	20.4654i	0.569142	−	0.985784i	0.996651	−	0.0817723i	$-0.0260580\pi$
$432$		0			0
$433$	0.796556	+	16.7218i	0.0382800	+	0.803596i	0.933631	+	0.358236i	$0.116622\pi$
$433$	0.796556	+	16.7218i	0.0382800	+	0.803596i	−0.895351	+	0.445361i	$0.853075\pi$
$434$	8.75267	+	0.835779i	0.420142	+	0.0401187i
$435$		0			0
$436$	−1.39367	−	4.02675i	−0.0667448	−	0.192846i
$437$	7.53871	+	0.719859i	0.360625	+	0.0344355i
$438$		0			0
$439$	11.2396	+	19.4676i	0.536437	+	0.929137i	0.999092	+	0.0425982i	$0.0135635\pi$
$439$	11.2396	+	19.4676i	0.536437	+	0.929137i	−0.462655	+	0.886538i	$0.653103\pi$
$440$	9.01437	−	15.6133i	0.429743	−	0.744337i
$441$		0			0
$442$	−1.50331	+	0.441411i	−0.0715051	+	0.0209958i
$443$	−6.86514	−	2.74839i	−0.326173	−	0.130580i	0.202796	−	0.979221i	$-0.434997\pi$
$443$	−6.86514	−	2.74839i	−0.326173	−	0.130580i	−0.528969	+	0.848641i	$0.677421\pi$
$444$		0			0
$445$	−2.21705	−	15.4199i	−0.105098	−	0.730976i
$446$	7.62425	−	0.728028i	0.361019	−	0.0344731i
$447$		0			0
$448$	1.47504	−	6.08019i	0.0696890	−	0.287262i
$449$	11.9642	+	16.8013i	0.564624	+	0.792903i	0.993902	−	0.110270i	$-0.0351714\pi$
$449$	11.9642	+	16.8013i	0.564624	+	0.792903i	−0.429278	+	0.903172i	$0.641232\pi$
$450$		0			0
$451$	−22.3793	+	8.95932i	−1.05380	+	0.421878i
$452$	−0.426534	+	0.335430i	−0.0200625	+	0.0157773i
$453$		0			0
$454$	−15.3580	+	17.7240i	−0.720785	+	0.831830i
$455$	−0.868924	+	6.04350i	−0.0407358	+	0.283324i
$456$		0			0
$457$	−26.8743	+	13.8547i	−1.25713	+	0.648094i	−0.952546	−	0.304393i	$-0.901546\pi$
$457$	−26.8743	+	13.8547i	−1.25713	+	0.648094i	−0.304580	+	0.952487i	$0.598516\pi$
$458$	−0.751697	+	0.716742i	−0.0351245	+	0.0334912i
$459$		0			0
$460$	9.97187	+	11.5082i	0.464941	+	0.536570i
$461$	31.8800	−	20.4881i	1.48480	−	0.954224i	0.488124	−	0.872774i	$-0.337681\pi$
$461$	31.8800	−	20.4881i	1.48480	−	0.954224i	0.996677	−	0.0814499i	$-0.0259551\pi$
$462$		0			0
$463$	15.9498	+	15.2081i	0.741252	+	0.706782i	0.963352	−	0.268242i	$-0.0864427\pi$
$463$	15.9498	+	15.2081i	0.741252	+	0.706782i	−0.222100	+	0.975024i	$0.571291\pi$
$464$	−0.504901	−	0.148252i	−0.0234394	−	0.00688243i
$465$		0			0
$466$	4.70133	−	10.2945i	0.217785	−	0.476883i
$467$	−10.4518	+	30.1986i	−0.483654	+	1.39743i	0.394433	+	0.918925i	$0.370941\pi$
$467$	−10.4518	+	30.1986i	−0.483654	+	1.39743i	−0.878087	+	0.478501i	$0.841180\pi$
$468$		0			0
$469$	9.61240	+	11.1716i	0.443860	+	0.515857i
$470$	3.89671			0.179742
$471$		0			0
$472$	−6.52777	+	14.2938i	−0.300465	+	0.657926i
$473$	−28.8441	−	22.6832i	−1.32625	−	1.04298i
$474$		0			0
$475$	−1.76953	−	1.68724i	−0.0811916	−	0.0774161i
$476$	2.36898	−	0.456583i	0.108582	−	0.0209274i
$477$		0			0
$478$	−7.69765	−	8.88356i	−0.352082	−	0.406325i
$479$	5.22756	−	7.34109i	0.238853	−	0.335423i	−0.677697	−	0.735341i	$-0.737022\pi$
$479$	5.22756	−	7.34109i	0.238853	−	0.335423i	0.916551	+	0.399918i	$0.130961\pi$
$480$		0			0
$481$	2.54499	−	1.31203i	0.116041	−	0.0598235i
$482$	−0.958145	+	20.1139i	−0.0436423	+	0.916165i
$483$		0			0
$484$	4.21153	−	4.86036i	0.191433	−	0.220926i
$485$	−1.70250	−	7.01781i	−0.0773066	−	0.318662i
$486$		0			0
$487$	39.3666	−	15.7600i	1.78387	−	0.714154i	0.788839	−	0.614601i	$-0.210683\pi$
$487$	39.3666	−	15.7600i	1.78387	−	0.714154i	0.995032	−	0.0995536i	$-0.0317415\pi$
$488$	10.5415	+	2.03170i	0.477190	+	0.0919709i
$489$		0			0
$490$	1.19781	−	4.93744i	0.0541115	−	0.223051i
$491$	−13.3344	−	29.1983i	−0.601775	−	1.31770i	−0.928060	−	0.372431i	$-0.878524\pi$
$491$	−13.3344	−	29.1983i	−0.601775	−	1.31770i	0.326285	−	0.945271i	$-0.394203\pi$
$492$		0			0
$493$	0.124884	+	0.868590i	0.00562451	+	0.0391193i
$494$	−1.54328	−	0.991803i	−0.0694353	−	0.0446233i
$495$		0			0
$496$	3.46106	−	1.01626i	0.155406	−	0.0456314i
$497$	−1.35487	−	0.698483i	−0.0607742	−	0.0313313i
$498$		0			0
$499$	−9.92481	−	17.1903i	−0.444295	−	0.769542i	0.553708	−	0.832711i	$-0.313213\pi$
$499$	−9.92481	−	17.1903i	−0.444295	−	0.769542i	−0.998003	+	0.0631692i	$0.979879\pi$
$500$	−0.784122	−	16.4608i	−0.0350670	−	0.736147i
$501$		0			0
$502$	0.822064	+	2.37520i	0.0366905	+	0.106010i
$503$	9.87679	+	28.5371i	0.440384	+	1.27241i	0.918957	+	0.394359i	$0.129033\pi$
$503$	9.87679	+	28.5371i	0.440384	+	1.27241i	−0.478572	+	0.878048i	$0.658845\pi$
$504$		0			0
$505$	0.122744	+	2.57672i	0.00546205	+	0.114663i
$506$	−10.4072	−	18.0258i	−0.462656	−	0.801344i
$507$		0			0
$508$	−18.2730	−	9.42037i	−0.810732	−	0.417961i
$509$	−39.0832	+	11.4759i	−1.73233	+	0.508658i	−0.987367	−	0.158447i	$-0.949351\pi$
$509$	−39.0832	+	11.4759i	−1.73233	+	0.508658i	−0.744963	+	0.667105i	$0.767533\pi$
$510$		0			0
$511$	−6.67747	−	4.29135i	−0.295394	−	0.189838i
$512$	−0.938896	−	6.53017i	−0.0414937	−	0.288595i
$513$		0			0
$514$	−6.23809	−	13.6595i	−0.275150	−	0.602495i
$515$	5.54046	−	22.8381i	0.244142	−	1.00637i
$516$		0			0
$517$	11.2198	+	2.16244i	0.493446	+	0.0951040i
$518$	1.90804	−	0.763864i	0.0838344	−	0.0335622i
$519$		0			0
$520$	−2.14469	−	8.84054i	−0.0940509	−	0.387683i
$521$	15.5949	−	17.9974i	0.683223	−	0.788482i	−0.303161	−	0.952939i	$-0.598042\pi$
$521$	15.5949	−	17.9974i	0.683223	−	0.788482i	0.986384	+	0.164458i	$0.0525874\pi$
$522$		0			0
$523$	0.889096	−	18.6644i	0.0388775	−	0.816138i	−0.892272	−	0.451499i	$-0.850889\pi$
$523$	0.889096	−	18.6644i	0.0388775	−	0.816138i	0.931149	−	0.364639i	$-0.118808\pi$
$524$	6.04222	−	3.11498i	0.263955	−	0.136079i
$525$		0			0
$526$	12.0610	−	16.9373i	0.525884	−	0.738501i
$527$	−3.93922	−	4.54610i	−0.171595	−	0.198031i
$528$		0			0
$529$	19.9878	−	3.85233i	0.869035	−	0.167493i
$530$	−2.45246	−	2.33841i	−0.106528	−	0.101574i
$531$		0			0
$532$	2.22046	+	1.74619i	0.0962692	+	0.0757069i
$533$	−5.05289	+	11.0643i	−0.218865	+	0.479247i
$534$		0			0
$535$	6.41607			0.277391
$536$	−19.4821	−	10.1297i	−0.841501	−	0.437536i
$537$		0			0
$538$	5.22628	−	15.1003i	0.225321	−	0.651022i
$539$	6.18883	−	13.5517i	0.266572	−	0.583711i
$540$		0			0
$541$	−8.31141	−	2.44045i	−0.357335	−	0.104923i	0.0981373	−	0.995173i	$-0.468712\pi$
$541$	−8.31141	−	2.44045i	−0.357335	−	0.104923i	−0.455473	+	0.890250i	$0.650530\pi$
$542$	−2.42742	−	2.31454i	−0.104267	−	0.0994180i
$543$		0			0
$544$	−4.82170	+	3.09872i	−0.206729	+	0.132856i
$545$	−3.46797	−	4.00225i	−0.148551	−	0.171437i
$546$		0			0
$547$	−13.0868	+	12.4782i	−0.559550	+	0.533529i	−0.916207	−	0.400706i	$-0.868765\pi$
$547$	−13.0868	+	12.4782i	−0.559550	+	0.533529i	0.356657	+	0.934235i	$0.383916\pi$
$548$	−1.55373	+	0.801004i	−0.0663721	+	0.0342172i
$549$		0			0
$550$	−0.956368	+	6.65168i	−0.0407797	+	0.283629i
$551$	−0.672848	+	0.776508i	−0.0286643	+	0.0330804i
$552$		0			0
$553$	21.5420	−	16.9408i	0.916060	−	0.720398i
$554$	22.0986	−	8.84695i	0.938880	−	0.375871i
$555$		0			0
$556$	15.4644	+	21.7167i	0.655835	+	0.920992i
$557$	1.30588	−	5.38292i	0.0553320	−	0.228082i	−0.937431	−	0.348171i	$-0.886803\pi$
$557$	1.30588	−	5.38292i	0.0553320	−	0.228082i	0.992763	+	0.120089i	$0.0383180\pi$
$558$		0			0
$559$	−18.4317	+	1.76001i	−0.779578	+	0.0744406i
$560$	0.255883	+	1.77970i	0.0108130	+	0.0752062i
$561$		0			0
$562$	−0.249690	−	0.0999608i	−0.0105325	−	0.00421659i
$563$	12.4854	−	3.66604i	0.526197	−	0.154505i	−0.00783564	−	0.999969i	$-0.502494\pi$
$563$	12.4854	−	3.66604i	0.526197	−	0.154505i	0.534032	+	0.845464i	$0.320676\pi$
$564$		0			0
$565$	−0.337191	+	0.584031i	−0.0141857	+	0.0245704i
$566$	−3.47627	−	6.02107i	−0.146118	−	0.253084i
$567$		0			0
$568$	2.26084	+	0.215884i	0.0948627	+	0.00905829i
$569$	−1.94273	−	5.61316i	−0.0814436	−	0.235316i	0.896926	−	0.442181i	$-0.145795\pi$
$569$	−1.94273	−	5.61316i	−0.0814436	−	0.235316i	−0.978369	+	0.206865i	$0.933674\pi$
$570$		0			0
$571$	36.3189	+	3.46803i	1.51990	+	0.145133i	0.821348	−	0.570428i	$-0.193223\pi$
$571$	36.3189	+	3.46803i	1.51990	+	0.145133i	0.698551	+	0.715560i	$0.253829\pi$
$572$	−0.514666	−	10.8042i	−0.0215193	−	0.451745i
$573$		0			0
$574$	−4.36547	+	7.56121i	−0.182211	+	0.315599i
$575$	−12.4417	−	6.41412i	−0.518853	−	0.267487i
$576$		0			0
$577$	−11.9557	−	4.78633i	−0.497721	−	0.199258i	0.109200	−	0.994020i	$-0.465171\pi$
$577$	−11.9557	−	4.78633i	−0.497721	−	0.199258i	−0.606921	+	0.794762i	$0.707595\pi$
$578$	−10.7569	−	6.91307i	−0.447430	−	0.287546i
$579$		0			0
$580$	−2.05663	+	0.196385i	−0.0853971	+	0.00815443i
$581$	−6.14691	−	13.4598i	−0.255017	−	0.558409i
$582$		0			0
$583$	−5.76368	−	8.09396i	−0.238707	−	0.335218i
$584$	11.6126	+	2.23815i	0.480533	+	0.0926151i
$585$		0			0
$586$	4.74926	−	3.73486i	0.196190	−	0.154286i
$587$	7.36197	+	30.3465i	0.303861	+	1.25253i	0.895038	+	0.445990i	$0.147148\pi$
$587$	7.36197	+	30.3465i	0.303861	+	1.25253i	−0.591177	+	0.806542i	$0.701336\pi$
$588$		0			0
$589$	1.00236	−	6.97153i	0.0413013	−	0.287257i
$590$	−0.376797	+	7.90995i	−0.0155125	+	0.325647i
$591$		0			0
$592$	0.610242	−	0.581864i	0.0250808	−	0.0239145i
$593$	−18.4923	+	25.9688i	−0.759389	+	1.06641i	0.236118	+	0.971724i	$0.424125\pi$
$593$	−18.4923	+	25.9688i	−0.759389	+	1.06641i	−0.995507	+	0.0946878i	$0.969815\pi$
$594$		0			0
$595$	2.52238	−	1.62104i	0.103408	−	0.0664561i
$596$	10.9311	−	2.10680i	0.447757	−	0.0862980i
$597$		0			0
$598$	−10.0771	−	2.95891i	−0.412084	−	0.120999i
$599$	−8.72831	−	6.86402i	−0.356629	−	0.280456i	0.423729	−	0.905789i	$-0.360721\pi$
$599$	−8.72831	−	6.86402i	−0.356629	−	0.280456i	−0.780358	+	0.625333i	$0.784963\pi$
$600$		0			0
$601$	4.75915	−	13.7507i	0.194130	−	0.560901i	−0.805362	−	0.592784i	$-0.798029\pi$
$601$	4.75915	−	13.7507i	0.194130	−	0.560901i	0.999492	+	0.0318824i	$0.0101502\pi$
$602$	−13.2904			−0.541678
$603$		0			0
$604$	29.7628			1.21103
$605$	2.61416	−	7.55312i	0.106281	−	0.307078i
$606$		0			0
$607$	−16.7794	−	13.1954i	−0.681054	−	0.535587i	0.216615	−	0.976257i	$-0.430498\pi$
$607$	−16.7794	−	13.1954i	−0.681054	−	0.535587i	−0.897669	+	0.440671i	$0.854741\pi$
$608$	−6.43910	−	1.89069i	−0.261140	−	0.0766776i
$609$		0			0
$610$	5.31233	−	1.02387i	0.215090	−	0.0414552i
$611$	4.85024	−	3.11706i	0.196220	−	0.126103i
$612$		0			0
$613$	−14.8946	+	20.9165i	−0.601586	+	0.844809i	−0.997290	−	0.0735692i	$-0.976561\pi$
$613$	−14.8946	+	20.9165i	−0.601586	+	0.844809i	0.395705	+	0.918378i	$0.370500\pi$
$614$	−3.93790	+	3.75478i	−0.158921	+	0.151530i
$615$		0			0
$616$	0.911064	−	19.1256i	0.0367078	−	0.770592i
$617$	3.84414	−	26.7366i	0.154759	−	1.07638i	−0.753343	−	0.657627i	$-0.771560\pi$
$617$	3.84414	−	26.7366i	0.154759	−	1.07638i	0.908103	−	0.418748i	$-0.137531\pi$
$618$		0			0
$619$	8.79217	+	36.2418i	0.353387	+	1.45668i	0.820074	+	0.572258i	$0.193932\pi$
$619$	8.79217	+	36.2418i	0.353387	+	1.45668i	−0.466687	+	0.884423i	$0.654552\pi$
$620$	11.1323	−	8.75450i	0.447082	−	0.351589i
$621$		0			0
$622$	5.61016	+	1.08127i	0.224947	+	0.0433550i
$623$	−9.59706	−	13.4772i	−0.384498	−	0.539952i
$624$		0			0
$625$	−4.09244	−	8.96119i	−0.163697	−	0.358448i
$626$	14.3654	−	1.37173i	0.574159	−	0.0548255i
$627$		0			0
$628$	−14.4232	−	9.26924i	−0.575549	−	0.369883i
$629$	−1.30538	−	0.522595i	−0.0520489	−	0.0208372i
$630$		0			0
$631$	−21.5625	−	11.1163i	−0.858390	−	0.442531i	−0.0279307	−	0.999610i	$-0.508892\pi$
$631$	−21.5625	−	11.1163i	−0.858390	−	0.442531i	−0.830460	+	0.557079i	$0.811922\pi$
$632$	−20.4160	+	35.3615i	−0.812103	+	1.40660i
$633$		0			0
$634$	−1.04109	−	21.8552i	−0.0413471	−	0.867982i
$635$	−25.4343	−	2.42868i	−1.00933	−	0.0963794i
$636$		0			0
$637$	−2.45864	−	7.10379i	−0.0974150	−	0.281462i
$638$	2.81121	+	0.268438i	0.111297	+	0.0106276i
$639$		0			0
$640$	−7.54335	−	13.0655i	−0.298177	−	0.516458i
$641$	−12.3566	+	21.4023i	−0.488057	+	0.845339i	−0.999906	−	0.0137365i	$-0.995627\pi$
$641$	−12.3566	+	21.4023i	−0.488057	+	0.845339i	0.511849	+	0.859075i	$0.328961\pi$
$642$		0			0
$643$	−11.5310	+	3.38581i	−0.454739	+	0.133524i	−0.501078	−	0.865402i	$-0.667063\pi$
$643$	−11.5310	+	3.38581i	−0.454739	+	0.133524i	0.0463384	+	0.998926i	$0.485245\pi$
$644$	15.0137	+	6.01060i	0.591625	+	0.236851i
$645$		0			0
$646$	0.128209	+	0.891715i	0.00504433	+	0.0350841i
$647$	−26.4715	+	2.52772i	−1.04070	+	0.0993749i	−0.601386	−	0.798958i	$-0.705385\pi$
$647$	−26.4715	+	2.52772i	−1.04070	+	0.0993749i	−0.439315	+	0.898333i	$0.644779\pi$
$648$		0			0
$649$	−5.47446	+	22.5660i	−0.214891	+	0.885794i
$650$	1.96687	+	2.76209i	0.0771471	+	0.108338i
$651$		0			0
$652$	−3.51767	+	1.40826i	−0.137762	+	0.0551518i
$653$	24.7455	−	19.4600i	0.968364	−	0.761530i	−0.00278650	−	0.999996i	$-0.500887\pi$
$653$	24.7455	−	19.4600i	0.968364	−	0.761530i	0.971151	+	0.238466i	$0.0766445\pi$
$654$		0			0
$655$	5.53258	−	6.38493i	0.216176	−	0.249480i
$656$	−0.509761	+	3.54547i	−0.0199028	+	0.138427i
$657$		0			0
$658$	3.67842	−	1.89636i	0.143400	−	0.0739276i
$659$	−14.5076	+	13.8330i	−0.565136	+	0.538856i	−0.917877	−	0.396865i	$-0.870098\pi$
$659$	−14.5076	+	13.8330i	−0.565136	+	0.538856i	0.352741	+	0.935721i	$0.385250\pi$
$660$		0			0
$661$	18.0142	+	20.7895i	0.700672	+	0.808619i	0.988843	−	0.148960i	$-0.0475926\pi$
$661$	18.0142	+	20.7895i	0.700672	+	0.808619i	−0.288171	+	0.957579i	$0.593047\pi$
$662$	1.69650	−	1.09028i	0.0659365	−	0.0423748i
$663$		0			0
$664$	15.9558	+	15.2138i	0.619205	+	0.590410i
$665$	3.36850	+	0.989081i	0.130625	+	0.0383549i
$666$		0			0
$667$	−2.44359	+	5.35071i	−0.0946162	+	0.207180i
$668$	3.87345	−	11.1916i	0.149868	−	0.433016i
$669$		0			0
$670$	−11.0119	−	1.09019i	−0.425428	−	0.0421176i
$671$	15.8640			0.612422
$672$		0			0
$673$	−10.8867	+	23.8385i	−0.419651	+	0.918907i	0.575243	+	0.817982i	$0.304907\pi$
$673$	−10.8867	+	23.8385i	−0.419651	+	0.918907i	−0.994894	+	0.100924i	$0.967820\pi$
$674$	−15.5496	−	12.2284i	−0.598949	−	0.471018i
$675$		0			0
$676$	8.88435	+	8.47121i	0.341706	+	0.325816i
$677$	−13.9230	+	2.68344i	−0.535104	+	0.103133i	−0.449642	−	0.893209i	$-0.648449\pi$
$677$	−13.9230	+	2.68344i	−0.535104	+	0.103133i	−0.0854616	+	0.996341i	$0.527236\pi$
$678$		0			0
$679$	−5.02238	−	5.79614i	−0.192741	−	0.222435i
$680$	−2.59131	+	3.63899i	−0.0993723	+	0.139549i
$681$		0			0
$682$	−17.2063	+	8.87049i	−0.658865	+	0.339668i
$683$	−0.0946502	+	1.98695i	−0.00362169	+	0.0760286i	−0.999955	−	0.00953313i	$-0.996965\pi$
$683$	−0.0946502	+	1.98695i	−0.00362169	+	0.0760286i	0.996333	+	0.0855618i	$0.0272685\pi$
$684$		0			0
$685$	−1.42268	+	1.64186i	−0.0543578	+	0.0627322i
$686$	−3.64159	−	15.0109i	−0.139037	−	0.573117i
$687$		0			0
$688$	−5.06192	+	2.02649i	−0.192984	+	0.0772591i
$689$	−4.92312	−	0.948854i	−0.187556	−	0.0361485i
$690$		0			0
$691$	−6.52466	+	26.8950i	−0.248210	+	1.02313i	0.702162	+	0.712018i	$0.252218\pi$
$691$	−6.52466	+	26.8950i	−0.248210	+	1.02313i	−0.950372	+	0.311117i	$0.899297\pi$
$692$	7.23149	+	15.8348i	0.274900	+	0.601947i
$693$		0			0
$694$	−0.197770	−	1.37552i	−0.00750726	−	0.0522141i
$695$	27.8735	+	17.9132i	1.05730	+	0.679487i
$696$		0			0
$697$	5.73129	−	1.68286i	0.217088	−	0.0637428i
$698$	14.7948	+	7.62725i	0.559992	+	0.288696i
$699$		0			0
$700$	−2.61066	−	4.52180i	−0.0986737	−	0.170908i
$701$	1.46443	+	30.7422i	0.0553107	+	1.16112i	0.840483	+	0.541838i	$0.182271\pi$
$701$	1.46443	+	30.7422i	0.0553107	+	1.16112i	−0.785172	+	0.619277i	$0.787426\pi$
$702$		0			0
$703$	−0.538474	−	1.55582i	−0.0203089	−	0.0586788i
$704$	4.50535	+	13.0173i	0.169802	+	0.490610i
$705$		0			0
$706$	−0.798516	−	16.7629i	−0.0300525	−	0.630880i
$707$	1.36984	+	2.37264i	0.0515183	+	0.0892323i
$708$		0			0
$709$	−7.00651	−	3.61211i	−0.263135	−	0.135656i	0.321611	−	0.946872i	$-0.395776\pi$
$709$	−7.00651	−	3.61211i	−0.263135	−	0.135656i	−0.584746	+	0.811216i	$0.698806\pi$
$710$	1.09816	−	0.322449i	0.0412132	−	0.0121013i
$711$		0			0
$712$	20.7376	+	13.3273i	0.777176	+	0.499460i
$713$	−5.73852	−	39.9123i	−0.214909	−	1.49473i
$714$		0			0
$715$	−5.58431	−	12.2279i	−0.208841	−	0.457299i
$716$	5.29990	−	21.8465i	0.198067	−	0.816442i
$717$		0			0
$718$	−22.9900	−	4.43096i	−0.857980	−	0.165362i
$719$	−39.2503	+	15.7135i	−1.46379	+	0.586013i	−0.960543	−	0.278130i	$-0.910285\pi$
$719$	−39.2503	+	15.7135i	−1.46379	+	0.586013i	−0.503246	+	0.864143i	$0.667861\pi$
$720$		0			0
$721$	−5.88419	−	24.2550i	−0.219139	−	0.903302i
$722$	9.23108	−	10.6532i	0.343545	−	0.396472i
$723$		0			0
$724$	0.296397	−	6.22214i	0.0110155	−	0.231244i
$725$	1.68802	−	0.870237i	0.0626916	−	0.0323198i
$726$		0			0
$727$	−6.47222	+	9.08896i	−0.240041	+	0.337091i	−0.916969	−	0.398959i	$-0.869372\pi$
$727$	−6.47222	+	9.08896i	−0.240041	+	0.337091i	0.676928	+	0.736050i	$0.263311\pi$
$728$	−6.32684	−	7.30156i	−0.234488	−	0.270614i
$729$		0			0
$730$	5.85212	−	1.12790i	0.216597	−	0.0417456i
$731$	6.58063	+	6.27462i	0.243394	+	0.232075i
$732$		0			0
$733$	40.0868	+	31.5246i	1.48064	+	1.16439i	0.948095	+	0.317988i	$0.103007\pi$
$733$	40.0868	+	31.5246i	1.48064	+	1.16439i	0.532546	+	0.846401i	$0.321235\pi$
$734$	−3.66175	+	8.01811i	−0.135158	+	0.295954i
$735$		0			0
$736$	−38.4203			−1.41619
$737$	−31.1017	−	9.24993i	−1.14564	−	0.340726i
$738$		0			0
$739$	9.62128	−	27.7989i	0.353924	−	1.02260i	−0.617771	−	0.786358i	$-0.711964\pi$
$739$	9.62128	−	27.7989i	0.353924	−	1.02260i	0.971695	−	0.236239i	$-0.0759148\pi$
$740$	1.37521	−	3.01129i	0.0505537	−	0.110697i
$741$		0			0
$742$	−3.45307	−	1.01391i	−0.126766	−	0.0372219i
$743$	22.3560	+	21.3164i	0.820162	+	0.782023i	0.978693	−	0.205331i	$-0.0658272\pi$
$743$	22.3560	+	21.3164i	0.820162	+	0.782023i	−0.158531	+	0.987354i	$0.550676\pi$
$744$		0			0
$745$	11.6390	−	7.47993i	0.426420	−	0.274043i
$746$	1.02256	+	1.18010i	0.0374385	+	0.0432064i
$747$		0			0
$748$	−3.84428	+	3.66552i	−0.140561	+	0.134025i
$749$	6.05664	−	3.12241i	0.221305	−	0.114091i
$750$		0			0
$751$	1.75932	−	12.2363i	0.0641984	−	0.446510i	−0.932216	−	0.361903i	$-0.882127\pi$
$751$	1.75932	−	12.2363i	0.0641984	−	0.446510i	0.996414	−	0.0846074i	$-0.0269636\pi$
$752$	1.11184	−	1.28314i	0.0405448	−	0.0467912i
$753$		0			0
$754$	1.12007	−	0.880836i	0.0407907	−	0.0320782i
$755$	34.3397	−	13.7476i	1.24975	−	0.500325i
$756$		0			0
$757$	−2.58494	−	3.63004i	−0.0939511	−	0.131936i	0.764925	−	0.644120i	$-0.222776\pi$
$757$	−2.58494	−	3.63004i	−0.0939511	−	0.131936i	−0.858876	+	0.512184i	$0.828837\pi$
$758$	3.51301	−	14.4808i	0.127598	−	0.525967i
$759$		0			0
$760$	−5.20701	+	0.497209i	−0.188878	+	0.0180357i
$761$	−1.07319	−	7.46422i	−0.0389032	−	0.270578i	0.961081	−	0.276268i	$-0.0890978\pi$
$761$	−1.07319	−	7.46422i	−0.0389032	−	0.270578i	−0.999984	+	0.00569042i	$0.998189\pi$
$762$		0			0
$763$	−5.22141	−	2.09034i	−0.189028	−	0.0756752i
$764$	21.1794	−	6.21883i	0.766244	−	0.224990i
$765$		0			0
$766$	−11.2146	+	19.4243i	−0.405201	+	0.701829i
$767$	5.85833	+	10.1469i	0.211532	+	0.366385i
$768$		0			0
$769$	2.90251	+	0.277156i	0.104667	+	0.00999449i	0.147258	−	0.989098i	$-0.452955\pi$
$769$	2.90251	+	0.277156i	0.104667	+	0.00999449i	−0.0425911	+	0.999093i	$0.513561\pi$
$770$	−3.15594	−	9.11848i	−0.113732	−	0.328607i
$771$		0			0
$772$	6.48965	+	0.619687i	0.233568	+	0.0223030i
$773$	−1.25003	−	26.2414i	−0.0449606	−	0.943839i	−0.902837	−	0.429983i	$-0.858520\pi$
$773$	−1.25003	−	26.2414i	−0.0449606	−	0.943839i	0.857876	−	0.513856i	$-0.171783\pi$
$774$		0			0
$775$	−6.50925	+	11.2743i	−0.233819	+	0.404986i
$776$	10.1566	+	5.23607i	0.364599	+	0.187964i
$777$		0			0
$778$	−24.1591	−	9.67184i	−0.866145	−	0.346752i
$779$	5.88366	+	3.78120i	0.210804	+	0.135475i
$780$		0			0
$781$	3.34088	−	0.319015i	0.119546	−	0.0114153i
$782$	2.14254	+	4.69151i	0.0766171	+	0.167768i
$783$		0			0
$784$	−1.28407	−	1.80322i	−0.0458595	−	0.0644006i
$785$	−20.9228	−	4.03253i	−0.746765	−	0.143927i
$786$		0			0
$787$	26.4269	−	20.7824i	0.942018	−	0.740811i	−0.0238851	−	0.999715i	$-0.507604\pi$
$787$	26.4269	−	20.7824i	0.942018	−	0.740811i	0.965903	+	0.258904i	$0.0833612\pi$
$788$	2.62525	+	10.8214i	0.0935207	+	0.385497i
$789$		0			0
$790$	−2.92842	+	20.3676i	−0.104188	+	0.724647i
$791$	−0.0340792	+	0.715409i	−0.00121172	+	0.0254370i
$792$		0			0
$793$	5.79325	−	5.52385i	0.205724	−	0.196158i
$794$	1.15780	−	1.62591i	0.0410889	−	0.0577013i
$795$		0			0
$796$	−12.1523	+	7.80979i	−0.430726	+	0.276811i
$797$	−8.46648	+	1.63178i	−0.299898	+	0.0578006i	−0.336981	−	0.941512i	$-0.609406\pi$
$797$	−8.46648	+	1.63178i	−0.299898	+	0.0578006i	0.0370825	+	0.999312i	$0.488194\pi$
$798$		0			0
$799$	−2.71663	−	0.797675i	−0.0961075	−	0.0282197i
$800$	9.75044	+	7.66783i	0.344730	+	0.271099i
$801$		0			0
$802$	1.19789	−	3.46108i	0.0422990	−	0.122215i
$803$	17.4759			0.616712
$804$		0			0
$805$	20.0989			0.708394
$806$	−3.19475	+	9.23061i	−0.112530	+	0.325134i
$807$		0			0
$808$	−3.20862	−	2.52328i	−0.112879	−	0.0887688i
$809$	16.5709	+	4.86565i	0.582602	+	0.171067i	0.559736	−	0.828671i	$-0.310903\pi$
$809$	16.5709	+	4.86565i	0.582602	+	0.171067i	0.0228660	+	0.999739i	$0.492721\pi$
$810$		0			0
$811$	39.9735	−	7.70427i	1.40366	−	0.270533i	0.569471	−	0.822011i	$-0.307148\pi$
$811$	39.9735	−	7.70427i	1.40366	−	0.270533i	0.834189	+	0.551478i	$0.185936\pi$
$812$	−1.84585	+	1.18626i	−0.0647766	+	0.0416294i
$813$		0			0
$814$	−2.62478	+	3.68599i	−0.0919986	+	0.129194i
$815$	−3.40814	+	3.24965i	−0.119382	+	0.113830i
$816$		0			0
$817$	−0.506572	+	10.6343i	−0.0177227	+	0.372045i
$818$	0.291905	−	2.03025i	0.0102062	−	0.0709859i
$819$		0			0
$820$	3.31550	+	13.6667i	0.115782	+	0.477261i
$821$	15.1688	−	11.9288i	0.529393	−	0.416319i	−0.317360	−	0.948305i	$-0.602796\pi$
$821$	15.1688	−	11.9288i	0.529393	−	0.416319i	0.846753	+	0.531986i	$0.178554\pi$
$822$		0			0
$823$	18.4579	+	3.55747i	0.643402	+	0.124006i	0.500507	−	0.865732i	$-0.333147\pi$
$823$	18.4579	+	3.55747i	0.643402	+	0.124006i	0.142895	+	0.989738i	$0.454359\pi$
$824$	21.5702	+	30.2911i	0.751433	+	1.05524i
$825$		0			0
$826$	3.49373	+	7.65020i	0.121562	+	0.266185i
$827$	−16.9098	+	1.61469i	−0.588010	+	0.0561482i	−0.384821	−	0.922991i	$-0.625737\pi$
$827$	−16.9098	+	1.61469i	−0.588010	+	0.0561482i	−0.203189	+	0.979139i	$0.565131\pi$
$828$		0			0
$829$	−5.46931	−	3.51491i	−0.189957	−	0.122078i	0.442206	−	0.896914i	$-0.354196\pi$
$829$	−5.46931	−	3.51491i	−0.189957	−	0.122078i	−0.632163	+	0.774836i	$0.717833\pi$
$830$	10.3144	+	4.12925i	0.358017	+	0.143328i
$831$		0			0
$832$	6.17793	+	3.18494i	0.214181	+	0.110418i
$833$	−1.84578	+	3.19699i	−0.0639525	+	0.110769i
$834$		0			0
$835$	−0.700335	−	14.7018i	−0.0242361	−	0.508778i
$836$	−6.19121	−	0.591189i	−0.214127	−	0.0204467i
$837$		0			0
$838$	0.0649112	+	0.187549i	0.00224232	+	0.00647876i
$839$	30.8653	+	2.94728i	1.06559	+	0.101752i	0.613090	−	0.790013i	$-0.289926\pi$
$839$	30.8653	+	2.94728i	1.06559	+	0.101752i	0.452500	+	0.891764i	$0.350532\pi$
$840$		0			0
$841$	14.1010	+	24.4236i	0.486240	+	0.842192i
$842$	−2.28322	+	3.95466i	−0.0786851	+	0.136287i
$843$		0			0
$844$	−11.2728	+	3.30999i	−0.388026	+	0.113935i
$845$	14.1635	+	5.67021i	0.487239	+	0.195061i
$846$		0			0
$847$	−1.20805	−	8.40219i	−0.0415092	−	0.288703i
$848$	−1.46977	+	0.140346i	−0.0504720	+	0.00481949i
$849$		0			0
$850$	0.392579	−	1.61823i	0.0134653	−	0.0555049i
$851$	−5.46733	−	7.67779i	−0.187418	−	0.263191i
$852$		0			0
$853$	−35.6389	+	14.2677i	−1.22025	+	0.488516i	−0.890254	−	0.455465i	$-0.849473\pi$
$853$	−35.6389	+	14.2677i	−1.22025	+	0.488516i	−0.330000	+	0.943981i	$0.607049\pi$
$854$	4.51646	−	3.55178i	0.154550	−	0.121540i
$855$		0			0
$856$	−6.64851	+	7.67279i	−0.227241	+	0.262250i
$857$	−4.26044	+	29.6320i	−0.145534	+	1.01221i	0.777883	+	0.628410i	$0.216294\pi$
$857$	−4.26044	+	29.6320i	−0.145534	+	1.01221i	−0.923416	+	0.383800i	$0.874615\pi$
$858$		0			0
$859$	−43.3134	+	22.3296i	−1.47783	+	0.761876i	−0.993589	−	0.113056i	$-0.963936\pi$
$859$	−43.3134	+	22.3296i	−1.47783	+	0.761876i	−0.484245	+	0.874933i	$0.660906\pi$
$860$	−15.4931	+	14.7726i	−0.528310	+	0.503742i
$861$		0			0
$862$	12.3404	+	14.2415i	0.420315	+	0.485069i
$863$	−6.41985	+	4.12579i	−0.218534	+	0.140444i	−0.645328	−	0.763905i	$-0.723279\pi$
$863$	−6.41985	+	4.12579i	−0.218534	+	0.140444i	0.426794	+	0.904349i	$0.359643\pi$
$864$		0			0
$865$	15.6577	+	14.9296i	0.532378	+	0.507621i
$866$	−12.8087	−	3.76098i	−0.435258	−	0.127803i
$867$		0			0
$868$	6.24820	−	13.6816i	0.212078	−	0.464385i
$869$	−19.7346	+	57.0194i	−0.669450	+	1.93425i
$870$		0			0
$871$	−14.5786	+	7.45172i	−0.493978	+	0.252492i
$872$	8.37977			0.283775
$873$		0			0
$874$	−2.50865	+	5.49317i	−0.0848563	+	0.185809i
$875$	−17.0977	−	13.4458i	−0.578009	−	0.454551i
$876$		0			0
$877$	16.2174	+	15.4633i	0.547623	+	0.522157i	0.912597	−	0.408860i	$-0.134074\pi$
$877$	16.2174	+	15.4633i	0.547623	+	0.522157i	−0.364974	+	0.931018i	$0.618922\pi$
$878$	−17.6015	+	3.39242i	−0.594023	+	0.114489i
$879$		0			0
$880$	−2.59236	−	2.99174i	−0.0873883	−	0.100852i
$881$	−12.0533	+	16.9265i	−0.406087	+	0.570269i	−0.966085	−	0.258225i	$-0.916863\pi$
$881$	−12.0533	+	16.9265i	−0.406087	+	0.570269i	0.559998	+	0.828494i	$0.310802\pi$
$882$		0			0
$883$	−21.1777	+	10.9178i	−0.712685	+	0.367415i	−0.776132	−	0.630570i	$-0.782821\pi$
$883$	−21.1777	+	10.9178i	−0.712685	+	0.367415i	0.0634468	+	0.997985i	$0.479791\pi$
$884$	−0.127529	+	2.67717i	−0.00428927	+	0.0900428i
$885$		0			0
$886$	3.86161	−	4.45653i	0.129733	−	0.149720i
$887$	12.9722	+	53.4720i	0.435563	+	1.79541i	0.589990	+	0.807411i	$0.299132\pi$
$887$	12.9722	+	53.4720i	0.435563	+	1.79541i	−0.154427	+	0.988004i	$0.549353\pi$
$888$		0			0
$889$	−25.1914	+	10.0851i	−0.844894	+	0.338244i
$890$	12.1982	+	2.35101i	0.408885	+	0.0788060i
$891$		0			0
$892$	3.08885	−	12.7324i	0.103422	−	0.426313i
$893$	−1.37715	−	3.01554i	−0.0460846	−	0.100911i
$894$		0			0
$895$	−3.97607	−	27.6541i	−0.132905	−	0.924376i
$896$	−13.4792	−	8.66253i	−0.450307	−	0.289395i
$897$		0			0
$898$	−15.7813	+	4.63381i	−0.526629	+	0.154632i
$899$	4.86263	+	2.50686i	0.162178	+	0.0836084i
$900$		0			0
$901$	1.23107	+	2.13228i	0.0410129	+	0.0710365i
$902$	−0.914657	−	19.2010i	−0.0304547	−	0.639324i
$903$		0			0
$904$	−0.349019	−	1.00843i	−0.0116082	−	0.0335397i
$905$	−2.53206	−	7.31590i	−0.0841684	−	0.243189i
$906$		0			0
$907$	−1.23414	−	25.9078i	−0.0409790	−	0.860254i	−0.922003	−	0.387183i	$-0.873448\pi$
$907$	−1.23414	−	25.9078i	−0.0409790	−	0.860254i	0.881024	−	0.473071i	$-0.156855\pi$
$908$	20.0593	+	34.7437i	0.665691	+	1.15301i
$909$		0			0
$910$	−4.32756	−	2.23101i	−0.143457	−	0.0739573i
$911$	18.7734	−	5.51238i	0.621992	−	0.182633i	0.0444731	−	0.999011i	$-0.485839\pi$
$911$	18.7734	−	5.51238i	0.621992	−	0.182633i	0.577519	+	0.816377i	$0.304021\pi$
$912$		0			0
$913$	27.4067	+	17.6132i	0.907029	+	0.582912i
$914$	−3.43127	−	23.8650i	−0.113496	−	0.789385i
$915$		0			0
$916$	0.738087	+	1.61618i	0.0243871	+	0.0534002i
$917$	2.11538	−	8.71971i	0.0698559	−	0.287950i
$918$		0			0
$919$	−6.52774	−	1.25812i	−0.215330	−	0.0415015i	0.0804451	−	0.996759i	$-0.474366\pi$
$919$	−6.52774	−	1.25812i	−0.215330	−	0.0415015i	−0.295775	+	0.955258i	$0.595578\pi$
$920$	−27.8008	+	11.1298i	−0.916566	+	0.366938i
$921$		0			0
$922$	7.12443	+	29.3673i	0.234630	+	0.967160i
$923$	1.10895	−	1.27979i	0.0365015	−	0.0421250i
$924$		0			0
$925$	−0.144796	+	3.03965i	−0.00476088	+	0.0999432i
$926$	−15.6203	+	8.05280i	−0.513313	+	0.264631i
$927$		0			0
$928$	3.02365	−	4.24613i	0.0992563	−	0.139386i
$929$	23.6421	+	27.2844i	0.775672	+	0.895174i	0.996789	−	0.0800738i	$-0.0255156\pi$
$929$	23.6421	+	27.2844i	0.775672	+	0.895174i	−0.221117	+	0.975247i	$0.570970\pi$
$930$		0			0
$931$	−4.24425	+	0.818011i	−0.139100	+	0.0268092i
$932$	−14.0113	−	13.3598i	−0.458956	−	0.437613i
$933$		0			0
$934$	−20.0307	−	15.7523i	−0.655425	−	0.515432i
$935$	−2.74234	+	6.00490i	−0.0896842	+	0.196381i
$936$		0			0
$937$	−10.5084			−0.343295			−0.171648	−	0.985158i	$-0.554909\pi$
$937$	−10.5084			−0.343295			−0.171648	+	0.985158i	$0.554909\pi$
$938$	−10.9256	+	4.32990i	−0.356733	+	0.141376i
$939$		0			0
$940$	2.18020	−	6.29929i	0.0711104	−	0.205460i
$941$	−4.43295	+	9.70681i	−0.144510	+	0.316433i	−0.968022	−	0.250866i	$-0.919285\pi$
$941$	−4.43295	+	9.70681i	−0.144510	+	0.316433i	0.823512	+	0.567299i	$0.192012\pi$
$942$		0			0
$943$	38.4185	+	11.2807i	1.25108	+	0.367350i
$944$	2.49713	+	2.38101i	0.0812748	+	0.0774954i
$945$		0			0
$946$	24.6162	−	15.8199i	0.800343	−	0.514349i
$947$	−29.4392	−	33.9747i	−0.956646	−	1.10403i	−0.994499	−	0.104745i	$-0.966597\pi$
$947$	−29.4392	−	33.9747i	−0.956646	−	1.10403i	0.0378533	−	0.999283i	$-0.487948\pi$
$948$		0			0
$949$	6.38191	−	6.08513i	0.207165	−	0.197532i
$950$	1.73297	−	0.893406i	0.0562248	−	0.0289859i
$951$		0			0
$952$	−0.675213	+	4.69621i	−0.0218838	+	0.152205i
$953$	5.38429	−	6.21381i	0.174414	−	0.201285i	−0.661811	−	0.749671i	$-0.730212\pi$
$953$	5.38429	−	6.21381i	0.174414	−	0.201285i	0.836226	+	0.548386i	$0.184757\pi$
$954$		0			0
$955$	21.5639	−	16.9580i	0.697792	−	0.548749i
$956$	−18.6677	+	7.47341i	−0.603756	+	0.241707i
$957$		0			0
$958$	4.16859	+	5.85396i	0.134681	+	0.189133i
$959$	−0.543961	+	2.24224i	−0.0175654	+	0.0724056i
$960$		0			0
$961$	−6.47244	+	0.618043i	−0.208789	+	0.0199369i
$962$	0.324941	+	2.26001i	0.0104765	+	0.0728657i
$963$		0			0
$964$	31.9794	+	12.8026i	1.02999	+	0.412345i
$965$	7.77388	−	2.28262i	0.250250	−	0.0734800i
$966$		0			0
$967$	−9.60249	+	16.6320i	−0.308795	+	0.534849i	−0.978099	−	0.208140i	$-0.933259\pi$
$967$	−9.60249	+	16.6320i	−0.308795	+	0.534849i	0.669304	+	0.742989i	$0.266593\pi$
$968$	6.32369	+	10.9529i	0.203251	+	0.352041i
$969$		0			0
$970$	5.73242	+	0.547380i	0.184057	+	0.0175753i
$971$	−14.1833	−	40.9800i	−0.455164	−	1.31511i	−0.906293	−	0.422651i	$-0.861100\pi$
$971$	−14.1833	−	40.9800i	−0.455164	−	1.31511i	0.451129	−	0.892459i	$-0.351022\pi$
$972$		0			0
$973$	35.0296	+	3.34492i	1.12300	+	0.107233i
$974$	1.60894	+	33.7758i	0.0515537	+	1.08225i
$975$		0			0
$976$	1.17862	−	2.04142i	0.0377266	−	0.0653443i
$977$	−44.0726	−	22.7210i	−1.41001	−	0.726910i	−0.425948	−	0.904748i	$-0.640059\pi$
$977$	−44.0726	−	22.7210i	−1.41001	−	0.726910i	−0.984060	+	0.177838i	$0.943090\pi$
$978$		0			0
$979$	33.8176	+	13.5385i	1.08082	+	0.432693i
$980$	−7.31152	−	4.69883i	−0.233558	−	0.150098i
$981$		0			0
$982$	25.4807	−	2.43311i	0.813121	−	0.0776437i
$983$	−6.42734	−	14.0739i	−0.205000	−	0.448888i	0.779007	−	0.627015i	$-0.215724\pi$
$983$	−6.42734	−	14.0739i	−0.205000	−	0.448888i	−0.984008	+	0.178127i	$0.942996\pi$
$984$		0			0
$985$	8.02743	+	11.2729i	0.255775	+	0.359186i
$986$	−0.687112	−	0.132430i	−0.0218821	−	0.00421743i
$987$		0			0
$988$	−2.46677	+	1.93989i	−0.0784786	+	0.0617162i
$989$	14.3696	+	59.2324i	0.456927	+	1.88348i
$990$		0			0
$991$	5.75037	−	39.9947i	0.182667	−	1.27047i	−0.667758	−	0.744378i	$-0.732746\pi$
$991$	5.75037	−	39.9947i	0.182667	−	1.27047i	0.850425	−	0.526096i	$-0.176345\pi$
$992$	−1.70023	+	35.6921i	−0.0539822	+	1.13323i
$993$		0			0
$994$	0.879720	−	0.838811i	0.0279030	−	0.0266055i
$995$	−10.4137	+	14.6240i	−0.330136	+	0.463611i
$996$		0			0
$997$	−17.8929	+	11.4990i	−0.566673	+	0.364178i	−0.792390	−	0.610014i	$-0.791164\pi$
$997$	−17.8929	+	11.4990i	−0.566673	+	0.364178i	0.225718	+	0.974193i	$0.427527\pi$
$998$	15.5425	−	2.99558i	0.491990	−	0.0948233i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.73.2		100
3.2	odd	2		67.2.g.a.6.4	✓	100
67.56	even	33	inner	603.2.z.c.190.2		100
201.56	odd	66		67.2.g.a.56.4	yes	100
201.116	odd	66		4489.2.a.p.1.22		50
201.152	even	66		4489.2.a.q.1.29		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.6.4	✓	100	3.2	odd	2
67.2.g.a.56.4	yes	100	201.56	odd	66
603.2.z.c.73.2		100	1.1	even	1	trivial
603.2.z.c.190.2		100	67.56	even	33	inner
4489.2.a.p.1.22		50	201.116	odd	66
4489.2.a.q.1.29		50	201.152	even	66

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.z (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.260812 + 0.753567i) q^{2} +(1.07227 + 0.843239i) q^{4} +(1.62666 + 0.477630i) q^{5} +(1.76797 - 0.340749i) q^{7} +(-2.25677 + 1.45034i) q^{8} +O(q^{10})\)	\(q+(-0.260812 + 0.753567i) q^{2} +(1.07227 + 0.843239i) q^{4} +(1.62666 + 0.477630i) q^{5} +(1.76797 - 0.340749i) q^{7} +(-2.25677 + 1.45034i) q^{8} +(-0.784178 + 1.10122i) q^{10} +(-2.86900 + 2.73558i) q^{11} +(-0.0951752 + 1.99797i) q^{13} +(-0.204332 + 1.42116i) q^{14} +(0.138870 + 0.572431i) q^{16} +(0.772123 - 0.607204i) q^{17} +(1.12934 + 0.217663i) q^{19} +(1.34145 + 1.88381i) q^{20} +(-1.31318 - 2.87545i) q^{22} +(6.55469 - 0.625897i) q^{23} +(-1.78839 - 1.14933i) q^{25} +(-1.48078 - 0.592817i) q^{26} +(2.18307 + 1.12545i) q^{28} +(-0.446677 + 0.773667i) q^{29} +(-0.291386 - 6.11694i) q^{31} +(-5.80854 - 0.554649i) q^{32} +(0.256190 + 0.740213i) q^{34} +(3.03864 + 0.290155i) q^{35} +(-0.715735 - 1.23969i) q^{37} +(-0.458569 + 0.794265i) q^{38} +(-4.36371 + 1.28130i) q^{40} +(5.64541 + 2.26008i) q^{41} +(1.31736 + 9.16244i) q^{43} +(-5.38308 + 0.514022i) q^{44} +(-1.23789 + 5.10264i) q^{46} +(-1.67196 - 2.34793i) q^{47} +(-3.48896 + 1.39677i) q^{49} +(1.33253 - 1.04791i) q^{50} +(-1.78682 + 2.06210i) q^{52} +(-0.356721 + 2.48105i) q^{53} +(-5.97347 + 3.07954i) q^{55} +(-3.49571 + 3.33315i) q^{56} +(-0.466511 - 0.538382i) q^{58} +(4.92775 - 3.16687i) q^{59} +(-2.89628 - 2.76160i) q^{61} +(4.68552 + 1.37579i) q^{62} +(1.44352 - 3.16086i) q^{64} +(-1.10911 + 3.20456i) q^{65} +(4.06799 + 7.10292i) q^{67} +1.33994 q^{68} +(-1.01116 + 2.21414i) q^{70} +(-0.665476 - 0.523336i) q^{71} +(-3.19057 - 3.04220i) q^{73} +(1.12086 - 0.216028i) q^{74} +(1.02741 + 1.18570i) q^{76} +(-4.14016 + 5.81404i) q^{77} +(13.5288 - 6.97460i) q^{79} +(-0.0475157 + 0.997477i) q^{80} +(-3.17552 + 3.66474i) q^{82} +(-1.93752 - 7.98658i) q^{83} +(1.54600 - 0.618924i) q^{85} +(-7.24809 - 1.39696i) q^{86} +(2.50714 - 10.3346i) q^{88} +(-3.81728 - 8.35868i) q^{89} +(0.512540 + 3.56479i) q^{91} +(7.55615 + 4.85604i) q^{92} +(2.20539 - 0.647561i) q^{94} +(1.73309 + 0.893469i) q^{95} +(-2.12978 - 3.68889i) q^{97} +(-0.142596 - 2.99346i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Introduction

L-functions

Modular forms

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