LMFDB - Embedded newform 507.2.q.b.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48832 - 0.120150i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(0.226569 + 0.0368210i) q^{4} +(1.90213 + 1.68514i) q^{5} +(1.19370 + 0.897007i) q^{6} +(3.62894 - 3.77813i) q^{7} +(2.56677 + 0.632652i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-2.62851 - 2.73657i) q^{10} +(-1.92044 + 4.04724i) q^{11} +(-0.171814 - 0.152214i) q^{12} +(-2.87984 + 2.16945i) q^{13} +(-5.85498 + 5.18706i) q^{14} +(-0.707011 - 2.44089i) q^{15} +(-4.17962 - 1.39536i) q^{16} +(4.91868 - 5.12088i) q^{17} +(-0.529484 - 1.39613i) q^{18} +(-2.12592 + 3.68219i) q^{19} +(0.368914 + 0.451838i) q^{20} +(-5.08643 + 1.25369i) q^{21} +(3.34451 - 5.79286i) q^{22} +(0.921815 + 1.59663i) q^{23} +(-1.83128 - 1.90656i) q^{24} +(0.175717 + 1.44716i) q^{25} +(4.54679 - 2.88284i) q^{26} +(0.120537 - 0.992709i) q^{27} +(0.961320 - 0.722385i) q^{28} +(5.88857 + 0.475375i) q^{29} +(0.758989 + 3.71777i) q^{30} +(-0.669659 + 5.51514i) q^{31} +(1.18889 + 0.506538i) q^{32} +(3.78625 - 2.39428i) q^{33} +(-7.93585 + 7.03055i) q^{34} +(13.2694 - 1.07122i) q^{35} +(0.0638624 + 0.220479i) q^{36} +(10.0608 - 4.28652i) q^{37} +(3.60646 - 5.22487i) q^{38} +(3.59351 - 0.294427i) q^{39} +(3.81622 + 5.52875i) q^{40} +(5.88012 + 3.71836i) q^{41} +(7.72088 - 1.25476i) q^{42} +(0.0615556 + 0.0262264i) q^{43} +(-0.584135 + 0.846266i) q^{44} +(-0.707011 + 2.44089i) q^{45} +(-1.18012 - 2.48706i) q^{46} +(-1.58671 + 4.18381i) q^{47} +(2.78680 + 3.41321i) q^{48} +(-0.823176 - 20.4269i) q^{49} +(-0.0876474 - 2.17495i) q^{50} +(-6.89415 + 1.69926i) q^{51} +(-0.732363 + 0.385492i) q^{52} +(-0.758399 - 0.186929i) q^{53} +(-0.298671 + 1.46299i) q^{54} +(-10.4731 + 4.46217i) q^{55} +(11.7049 - 7.40173i) q^{56} +(3.76481 - 1.97592i) q^{57} +(-8.70698 - 1.41502i) q^{58} +(-1.81294 + 0.605249i) q^{59} +(-0.0703108 - 0.579061i) q^{60} +(0.774448 - 2.67370i) q^{61} +(1.65931 - 8.12785i) q^{62} +(4.96905 + 1.65891i) q^{63} +(6.09475 + 3.19877i) q^{64} +(-9.13365 - 0.726344i) q^{65} +(-5.92284 + 3.10854i) q^{66} +(6.57428 - 1.06842i) q^{67} +(1.30297 - 0.979122i) q^{68} +(0.0742355 - 1.84214i) q^{69} -19.8778 q^{70} +(0.307329 - 7.62629i) q^{71} +(0.528785 + 2.59016i) q^{72} +(-3.13654 - 4.54406i) q^{73} +(-15.4888 + 5.17092i) q^{74} +(0.624942 - 1.31704i) q^{75} +(-0.617248 + 0.755992i) q^{76} +(8.32184 + 21.9429i) q^{77} +(-5.38368 + 0.00644285i) q^{78} +(0.244908 - 0.645770i) q^{79} +(-5.59880 - 9.69741i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-8.30476 - 6.24062i) q^{82} +(4.23194 + 2.22110i) q^{83} +(-1.19859 + 0.0967600i) q^{84} +(17.9854 - 1.45193i) q^{85} +(-0.0884635 - 0.0464292i) q^{86} +(-4.72289 - 3.54902i) q^{87} +(-7.48982 + 9.17337i) q^{88} +(7.34601 + 12.7237i) q^{89} +(1.34553 - 3.54788i) q^{90} +(-2.25428 + 18.7532i) q^{91} +(0.150065 + 0.395689i) q^{92} +(3.51364 - 4.30343i) q^{93} +(2.86422 - 6.03621i) q^{94} +(-10.2488 + 3.42154i) q^{95} +(-0.734109 - 1.06354i) q^{96} +(-1.81227 - 8.87709i) q^{97} +(-1.22914 + 30.5007i) q^{98} -4.47976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	−1.48832	−	0.120150i	−1.05240	−	0.0849588i	−0.457862	−	0.889024i	$-0.651384\pi$
$2$	−1.48832	−	0.120150i	−1.05240	−	0.0849588i	−0.594542	+	0.804065i	$0.702667\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	0.226569	+	0.0368210i	0.113284	+	0.0184105i
$5$	1.90213	+	1.68514i	0.850658	+	0.753617i	0.970991	−	0.239117i	$-0.0768578\pi$
$5$	1.90213	+	1.68514i	0.850658	+	0.753617i	−0.120333	+	0.992734i	$0.538396\pi$
$6$	1.19370	+	0.897007i	0.487326	+	0.366202i
$7$	3.62894	−	3.77813i	1.37161	−	1.42800i	0.584130	−	0.811660i	$-0.301436\pi$
$7$	3.62894	−	3.77813i	1.37161	−	1.42800i	0.787481	−	0.616339i	$-0.211385\pi$
$8$	2.56677	+	0.632652i	0.907490	+	0.223676i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−2.62851	−	2.73657i	−0.831209	−	0.865380i
$11$	−1.92044	+	4.04724i	−0.579035	+	1.22029i	0.376775	+	0.926305i	$0.377033\pi$
$11$	−1.92044	+	4.04724i	−0.579035	+	1.22029i	−0.955810	+	0.293985i	$0.905018\pi$
$12$	−0.171814	−	0.152214i	−0.0495985	−	0.0439404i
$13$	−2.87984	+	2.16945i	−0.798723	+	0.601699i
$13$	−2.87984	+	2.16945i	−0.798723	+	0.601699i
$14$	−5.85498	+	5.18706i	−1.56481	+	1.38630i
$15$	−0.707011	−	2.44089i	−0.182549	−	0.630234i
$16$	−4.17962	−	1.39536i	−1.04491	−	0.348841i
$17$	4.91868	−	5.12088i	1.19295	−	1.24200i	0.229743	−	0.973251i	$-0.426211\pi$
$17$	4.91868	−	5.12088i	1.19295	−	1.24200i	0.963211	−	0.268745i	$-0.0866090\pi$
$18$	−0.529484	−	1.39613i	−0.124800	−	0.329072i
$19$	−2.12592	+	3.68219i	−0.487718	+	0.844753i	−0.999900	−	0.0141239i	$-0.995504\pi$
$19$	−2.12592	+	3.68219i	−0.487718	+	0.844753i	0.512182	+	0.858877i	$0.328837\pi$
$20$	0.368914	+	0.451838i	0.0824918	+	0.101034i
$21$	−5.08643	+	1.25369i	−1.10995	+	0.273578i
$22$	3.34451	−	5.79286i	0.713052	−	1.23504i
$23$	0.921815	+	1.59663i	0.192212	+	0.332920i	0.945983	−	0.324216i	$-0.105101\pi$
$23$	0.921815	+	1.59663i	0.192212	+	0.332920i	−0.753771	+	0.657137i	$0.771767\pi$
$24$	−1.83128	−	1.90656i	−0.373808	−	0.389175i
$25$	0.175717	+	1.44716i	0.0351433	+	0.289431i
$26$	4.54679	−	2.88284i	0.891699	−	0.565371i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	0.961320	−	0.722385i	0.181672	−	0.136518i
$29$	5.88857	+	0.475375i	1.09348	+	0.0882749i	0.614021	−	0.789289i	$-0.289551\pi$
$29$	5.88857	+	0.475375i	1.09348	+	0.0882749i	0.479459	+	0.877564i	$0.340833\pi$
$30$	0.758989	+	3.71777i	0.138572	+	0.678769i
$31$	−0.669659	+	5.51514i	−0.120274	+	0.990548i	0.800197	+	0.599737i	$0.204728\pi$
$31$	−0.669659	+	5.51514i	−0.120274	+	0.990548i	−0.920471	+	0.390811i	$0.872195\pi$
$32$	1.18889	+	0.506538i	0.210168	+	0.0895441i
$33$	3.78625	−	2.39428i	0.659102	−	0.416791i
$34$	−7.93585	+	7.03055i	−1.36099	+	1.20573i
$35$	13.2694	−	1.07122i	2.24294	−	0.181068i
$36$	0.0638624	+	0.220479i	0.0106437	+	0.0367464i
$37$	10.0608	−	4.28652i	1.65399	−	0.704700i	0.655276	−	0.755389i	$-0.272552\pi$
$37$	10.0608	−	4.28652i	1.65399	−	0.704700i	0.998714	+	0.0506898i	$0.0161420\pi$
$38$	3.60646	−	5.22487i	0.585046	−	0.847585i
$39$	3.59351	−	0.294427i	0.575422	−	0.0471461i
$40$	3.81622	+	5.52875i	0.603397	+	0.874172i
$41$	5.88012	+	3.71836i	0.918321	+	0.580711i	0.907878	−	0.419235i	$-0.137702\pi$
$41$	5.88012	+	3.71836i	0.918321	+	0.580711i	0.0104429	+	0.999945i	$0.496676\pi$
$42$	7.72088	−	1.25476i	1.19136	−	0.193614i
$43$	0.0615556	+	0.0262264i	0.00938714	+	0.00399948i	0.396655	−	0.917968i	$-0.370171\pi$
$43$	0.0615556	+	0.0262264i	0.00938714	+	0.00399948i	−0.387268	+	0.921967i	$0.626581\pi$
$44$	−0.584135	+	0.846266i	−0.0880617	+	0.127579i
$45$	−0.707011	+	2.44089i	−0.105395	+	0.363866i
$46$	−1.18012	−	2.48706i	−0.174000	−	0.366697i
$47$	−1.58671	+	4.18381i	−0.231445	+	0.610271i	−0.999548	−	0.0300555i	$-0.990432\pi$
$47$	−1.58671	+	4.18381i	−0.231445	+	0.610271i	0.768103	+	0.640326i	$0.221201\pi$
$48$	2.78680	+	3.41321i	0.402240	+	0.492655i
$49$	−0.823176	−	20.4269i	−0.117597	−	2.91813i
$50$	−0.0876474	−	2.17495i	−0.0123952	−	0.307584i
$51$	−6.89415	+	1.69926i	−0.965375	+	0.237943i
$52$	−0.732363	+	0.385492i	−0.101560	+	0.0534582i
$53$	−0.758399	−	0.186929i	−0.104174	−	0.0256766i	0.186884	−	0.982382i	$-0.440161\pi$
$53$	−0.758399	−	0.186929i	−0.104174	−	0.0256766i	−0.291058	+	0.956705i	$0.594007\pi$
$54$	−0.298671	+	1.46299i	−0.0406440	+	0.199088i
$55$	−10.4731	+	4.46217i	−1.41219	+	0.601678i
$56$	11.7049	−	7.40173i	1.56413	−	0.989098i
$57$	3.76481	−	1.97592i	0.498661	−	0.261718i
$58$	−8.70698	−	1.41502i	−1.14328	−	0.185802i
$59$	−1.81294	+	0.605249i	−0.236025	+	0.0787967i	−0.432220	−	0.901768i	$-0.642270\pi$
$59$	−1.81294	+	0.605249i	−0.236025	+	0.0787967i	0.196195	+	0.980565i	$0.437141\pi$
$60$	−0.0703108	−	0.579061i	−0.00907708	−	0.0747565i
$61$	0.774448	−	2.67370i	0.0991579	−	0.342333i	−0.895565	−	0.444931i	$-0.853228\pi$
$61$	0.774448	−	2.67370i	0.0991579	−	0.342333i	0.994723	+	0.102598i	$0.0327155\pi$
$62$	1.65931	−	8.12785i	0.210733	−	1.03224i
$63$	4.96905	+	1.65891i	0.626042	+	0.209003i
$64$	6.09475	+	3.19877i	0.761843	+	0.399846i
$65$	−9.13365	−	0.726344i	−1.13289	−	0.0900919i
$66$	−5.92284	+	3.10854i	−0.729051	+	0.382635i
$67$	6.57428	−	1.06842i	0.803176	−	0.130529i	0.255054	−	0.966927i	$-0.417907\pi$
$67$	6.57428	−	1.06842i	0.803176	−	0.130529i	0.548123	+	0.836398i	$0.315343\pi$
$68$	1.30297	−	0.979122i	0.158009	−	0.118736i
$69$	0.0742355	−	1.84214i	0.00893690	−	0.221767i
$70$	−19.8778			−2.37586
$71$	0.307329	−	7.62629i	0.0364733	−	0.905074i	−0.872599	−	0.488437i	$-0.837567\pi$
$71$	0.307329	−	7.62629i	0.0364733	−	0.905074i	0.909073	−	0.416638i	$-0.136792\pi$
$72$	0.528785	+	2.59016i	0.0623179	+	0.305253i
$73$	−3.13654	−	4.54406i	−0.367104	−	0.531842i	0.595286	−	0.803514i	$-0.297039\pi$
$73$	−3.13654	−	4.54406i	−0.367104	−	0.531842i	−0.962390	+	0.271672i	$0.912423\pi$
$74$	−15.4888	+	5.17092i	−1.80054	+	0.601107i
$75$	0.624942	−	1.31704i	0.0721620	−	0.152078i
$76$	−0.617248	+	0.755992i	−0.0708032	+	0.0867182i
$77$	8.32184	+	21.9429i	0.948361	+	2.50062i
$78$	−5.38368	+	0.00644285i	−0.609582	+	0.000729509i
$79$	0.244908	−	0.645770i	0.0275543	−	0.0726548i	−0.920533	−	0.390665i	$-0.872245\pi$
$79$	0.244908	−	0.645770i	0.0275543	−	0.0726548i	0.948087	+	0.318010i	$0.103014\pi$
$80$	−5.59880	−	9.69741i	−0.625965	−	1.08420i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−8.30476	−	6.24062i	−0.917107	−	0.689161i
$83$	4.23194	+	2.22110i	0.464516	+	0.243797i	0.680709	−	0.732554i	$-0.261672\pi$
$83$	4.23194	+	2.22110i	0.464516	+	0.243797i	−0.216193	+	0.976351i	$0.569364\pi$
$84$	−1.19859	+	0.0967600i	−0.130777	+	0.0105574i
$85$	17.9854	−	1.45193i	1.95079	−	0.157484i
$86$	−0.0884635	−	0.0464292i	−0.00953926	−	0.00500659i
$87$	−4.72289	−	3.54902i	−0.506347	−	0.380495i
$88$	−7.48982	+	9.17337i	−0.798418	+	0.977884i
$89$	7.34601	+	12.7237i	0.778676	+	1.34871i	0.932705	+	0.360640i	$0.117442\pi$
$89$	7.34601	+	12.7237i	0.778676	+	1.34871i	−0.154029	+	0.988066i	$0.549225\pi$
$90$	1.34553	−	3.54788i	0.141832	−	0.373979i
$91$	−2.25428	+	18.7532i	−0.236313	+	1.96587i
$92$	0.150065	+	0.395689i	0.0156454	+	0.0412534i
$93$	3.51364	−	4.30343i	0.364348	−	0.446245i
$94$	2.86422	−	6.03621i	0.295421	−	0.622588i
$95$	−10.2488	+	3.42154i	−1.05150	+	0.351043i
$96$	−0.734109	−	1.06354i	−0.0749247	−	0.108547i
$97$	−1.81227	−	8.87709i	−0.184008	−	0.901332i	−0.961998	−	0.273055i	$-0.911966\pi$
$97$	−1.81227	−	8.87709i	−0.184008	−	0.901332i	0.777990	−	0.628277i	$-0.216239\pi$
$98$	−1.22914	+	30.5007i	−0.124162	+	3.08104i
$99$	−4.47976			−0.450233
$100$	−0.0134739	+	0.334351i	−0.00134739	+	0.0334351i
$101$	−0.671450	+	0.504562i	−0.0668118	+	0.0502058i	−0.633623	−	0.773642i	$-0.718433\pi$
$101$	−0.671450	+	0.504562i	−0.0668118	+	0.0502058i	0.566812	+	0.823847i	$0.308177\pi$
$102$	10.4649	−	1.70071i	1.03618	−	0.168395i
$103$	5.18217	−	2.71982i	0.510615	−	0.267991i	−0.189679	−	0.981846i	$-0.560745\pi$
$103$	5.18217	−	2.71982i	0.510615	−	0.267991i	0.700294	+	0.713855i	$0.253052\pi$
$104$	−8.76439	+	3.74656i	−0.859419	+	0.367380i
$105$	−11.7877	−	6.18665i	−1.15036	−	0.603756i
$106$	1.10628	+	0.369332i	0.107452	+	0.0358727i
$107$	−3.02698	+	14.8271i	−0.292630	+	1.43339i	0.521768	+	0.853087i	$0.325273\pi$
$107$	−3.02698	+	14.8271i	−0.292630	+	1.43339i	−0.814398	+	0.580307i	$0.802933\pi$
$108$	0.0638624	−	0.220479i	0.00614516	−	0.0212156i
$109$	−0.572947	−	4.71865i	−0.0548784	−	0.451964i	−0.994084	−	0.108610i	$-0.965360\pi$
$109$	−0.572947	−	4.71865i	−0.0548784	−	0.451964i	0.939206	−	0.343354i	$-0.111563\pi$
$110$	16.1235	−	5.38280i	1.53731	−	0.513230i
$111$	−10.7943	−	1.75425i	−1.02455	−	0.166506i
$112$	−20.4395	+	10.7275i	−1.93135	+	1.01365i
$113$	−4.33936	+	2.74405i	−0.408213	+	0.258138i	−0.722754	−	0.691106i	$-0.757124\pi$
$113$	−4.33936	+	2.74405i	−0.408213	+	0.258138i	0.314541	+	0.949244i	$0.398149\pi$
$114$	−5.84066	+	2.48847i	−0.547028	+	0.233067i
$115$	−0.937133	+	4.59038i	−0.0873881	+	0.428055i
$116$	1.31666	+	0.324528i	0.122249	+	0.0301317i
$117$	−3.19456	−	1.67176i	−0.295337	−	0.154554i
$118$	2.77097	−	0.682982i	0.255088	−	0.0628736i
$119$	−1.49777	−	37.1668i	−0.137300	−	3.40707i
$120$	−0.270504	−	6.71248i	−0.0246935	−	0.612763i
$121$	−5.73518	−	7.02432i	−0.521380	−	0.638575i
$122$	−1.47387	+	3.88629i	−0.133438	+	0.351848i
$123$	−2.98248	−	6.28545i	−0.268921	−	0.566740i
$124$	−0.354797	+	1.22490i	−0.0318617	+	0.109999i
$125$	5.11346	−	7.40812i	0.457361	−	0.662602i
$126$	−7.19624	−	3.06603i	−0.641092	−	0.273144i
$127$	−11.9071	+	1.93509i	−1.05658	+	0.171711i	−0.663792	−	0.747918i	$-0.731054\pi$
$127$	−11.9071	+	1.93509i	−1.05658	+	0.171711i	−0.392789	+	0.919629i	$0.628490\pi$
$128$	−10.8711	−	6.87446i	−0.960878	−	0.607623i
$129$	−0.0380091	−	0.0550656i	−0.00334651	−	0.00484826i
$130$	13.5066	+	2.17844i	1.18460	+	0.191062i
$131$	−0.600626	+	0.870157i	−0.0524770	+	0.0760260i	−0.848344	−	0.529445i	$-0.822400\pi$
$131$	−0.600626	+	0.870157i	−0.0524770	+	0.0760260i	0.795867	+	0.605471i	$0.207015\pi$
$132$	0.946006	−	0.403055i	0.0823392	−	0.0350815i
$133$	6.19698	+	21.3945i	0.537346	+	1.85513i
$134$	−9.91303	+	0.800262i	−0.856355	+	0.0691321i
$135$	1.90213	−	1.68514i	0.163709	−	0.145034i
$136$	15.8648	−	10.0323i	1.36040	−	0.860264i
$137$	−5.98742	−	2.55100i	−0.511540	−	0.217947i	0.120744	−	0.992684i	$-0.461472\pi$
$137$	−5.98742	−	2.55100i	−0.511540	−	0.217947i	−0.632284	+	0.774737i	$0.717882\pi$
$138$	−0.331819	+	2.73277i	−0.0282463	+	0.232629i
$139$	1.59460	+	7.81085i	0.135252	+	0.662507i	0.989722	+	0.143007i	$0.0456770\pi$
$139$	1.59460	+	7.81085i	0.135252	+	0.662507i	−0.854470	+	0.519501i	$0.826118\pi$
$140$	3.04587	+	0.245888i	0.257423	+	0.0207813i
$141$	3.57717	−	2.68807i	0.301252	−	0.226376i
$142$	−1.37370	+	11.3135i	−0.115279	+	0.949405i
$143$	−3.24975	−	15.8217i	−0.271758	−	1.32308i
$144$	−0.531132	−	4.37427i	−0.0442610	−	0.364522i
$145$	10.3997	+	10.8273i	0.863652	+	0.899157i
$146$	4.12221	+	7.13988i	0.341157	+	0.590900i
$147$	−10.2217	+	17.7046i	−0.843075	+	1.46025i
$148$	2.43730	−	0.600742i	0.200345	−	0.0493807i
$149$	−4.48190	−	5.48934i	−0.367172	−	0.449704i	0.557666	−	0.830065i	$-0.311697\pi$
$149$	−4.48190	−	5.48934i	−0.367172	−	0.449704i	−0.924838	+	0.380362i	$0.875800\pi$
$150$	−1.08836	+	1.88509i	−0.0888640	+	0.153917i
$151$	−0.695114	−	1.83287i	−0.0565676	−	0.149156i	0.903753	−	0.428053i	$-0.140800\pi$
$151$	−0.695114	−	1.83287i	−0.0565676	−	0.149156i	−0.960321	+	0.278897i	$0.910031\pi$
$152$	−7.78628	+	8.10638i	−0.631551	+	0.657514i
$153$	6.73506	+	2.24849i	0.544498	+	0.181780i
$154$	−9.74915	−	33.6580i	−0.785609	−	2.71224i
$155$	−10.5676	+	9.36203i	−0.848806	+	0.751977i
$156$	0.825018	+	0.0656087i	0.0660543	+	0.00525290i
$157$	−13.5273	−	11.9841i	−1.07959	−	0.956436i	−0.0804065	−	0.996762i	$-0.525622\pi$
$157$	−13.5273	−	11.9841i	−1.07959	−	0.956436i	−0.999187	+	0.0403261i	$0.987160\pi$
$158$	−0.442092	+	0.931689i	−0.0351709	+	0.0741212i
$159$	0.541084	+	0.563329i	0.0429108	+	0.0446749i
$160$	1.40783	+	2.96694i	0.111299	+	0.234557i
$161$	9.37749	+	2.31134i	0.739050	+	0.182159i
$162$	1.03435	−	1.07687i	0.0812663	−	0.0846072i
$163$	6.79824	+	5.10855i	0.532479	+	0.400132i	0.832689	−	0.553741i	$-0.186800\pi$
$163$	6.79824	+	5.10855i	0.532479	+	0.400132i	−0.300210	+	0.953873i	$0.597057\pi$
$164$	1.19534	+	1.05898i	0.0933402	+	0.0826922i
$165$	11.2366	+	1.82613i	0.874770	+	0.142164i
$166$	−6.03164	−	3.81418i	−0.468146	−	0.296037i
$167$	5.80080	+	0.468289i	0.448880	+	0.0362373i	0.302840	−	0.953041i	$-0.402065\pi$
$167$	5.80080	+	0.468289i	0.448880	+	0.0362373i	0.146040	+	0.989279i	$0.453347\pi$
$168$	−13.8488			−1.06846
$169$	3.58693	−	12.4954i	0.275918	−	0.961181i
$170$	−26.9425			−2.06639
$171$	−4.23804	−	0.342130i	−0.324091	−	0.0261634i
$172$	0.0129809	+	0.00820862i	0.000989783	+	0.000625901i
$173$	2.71598	+	0.441390i	0.206492	+	0.0335583i	0.262778	−	0.964856i	$-0.415361\pi$
$173$	2.71598	+	0.441390i	0.206492	+	0.0335583i	−0.0562851	+	0.998415i	$0.517926\pi$
$174$	6.60277	+	5.84955i	0.500555	+	0.443453i
$175$	6.10521	+	4.58777i	0.461510	+	0.346803i
$176$	13.6741	−	14.2362i	1.03072	−	1.07310i
$177$	1.85577	+	0.457405i	0.139488	+	0.0343807i
$178$	−9.40450	−	19.8196i	−0.704897	−	1.48554i
$179$	−7.06156	−	7.35186i	−0.527806	−	0.549504i	0.402914	−	0.915238i	$-0.367998\pi$
$179$	−7.06156	−	7.35186i	−0.527806	−	0.549504i	−0.930719	+	0.365734i	$0.880818\pi$
$180$	−0.250063	+	0.526996i	−0.0186386	+	0.0392799i
$181$	−3.41819	−	3.02825i	−0.254072	−	0.225088i	0.526466	−	0.850196i	$-0.323517\pi$
$181$	−3.41819	−	3.02825i	−0.254072	−	0.225088i	−0.780539	+	0.625108i	$0.785055\pi$
$182$	5.60830	−	27.6400i	0.415715	−	2.04881i
$183$	−2.08356	+	1.84587i	−0.154021	+	0.136451i
$184$	1.35598	+	4.68137i	0.0999638	+	0.345115i
$185$	26.3604	+	8.80039i	1.93805	+	0.647017i
$186$	−5.74649	+	5.98273i	−0.421353	+	0.438675i
$187$	11.2794	+	29.7414i	0.824834	+	2.17491i
$188$	−0.513550	+	0.889496i	−0.0374545	+	0.0648731i
$189$	−3.31316	−	4.05789i	−0.240997	−	0.295168i
$190$	15.6646	−	3.86097i	1.13643	−	0.280104i
$191$	−3.41392	+	5.91308i	−0.247022	+	0.427855i	−0.962698	−	0.270577i	$-0.912785\pi$
$191$	−3.41392	+	5.91308i	−0.247022	+	0.427855i	0.715676	+	0.698433i	$0.246119\pi$
$192$	−3.44159	−	5.96100i	−0.248375	−	0.430198i
$193$	8.10608	+	8.43932i	0.583488	+	0.607475i	0.945867	−	0.324556i	$-0.105215\pi$
$193$	8.10608	+	8.43932i	0.583488	+	0.607475i	−0.362379	+	0.932031i	$0.618035\pi$
$194$	1.63066	+	13.4297i	0.117075	+	0.964198i
$195$	7.33147	+	5.49552i	0.525017	+	0.393543i
$196$	0.565633	−	4.65841i	0.0404024	−	0.332744i
$197$	−11.7045	+	8.79537i	−0.833912	+	0.626644i	−0.929519	−	0.368775i	$-0.879777\pi$
$197$	−11.7045	+	8.79537i	−0.833912	+	0.626644i	0.0956067	+	0.995419i	$0.469521\pi$
$198$	6.66733	+	0.538243i	0.473827	+	0.0382512i
$199$	−3.94266	−	19.3124i	−0.279488	−	1.36902i	−0.840767	−	0.541397i	$-0.817896\pi$
$199$	−3.94266	−	19.3124i	−0.279488	−	1.36902i	0.561279	−	0.827627i	$-0.310309\pi$
$200$	−0.464522	+	3.82568i	−0.0328467	+	0.270517i
$201$	−6.12755	−	2.61071i	−0.432204	−	0.184145i
$202$	1.05996	−	0.670277i	0.0745783	−	0.0471605i
$203$	23.1653	−	20.5227i	1.62589	−	1.44041i
$204$	−1.62457	+	0.131149i	−0.113743	+	0.00918225i
$205$	4.91879	+	16.9816i	0.343543	+	1.18605i
$206$	−8.03954	+	3.42533i	−0.560141	+	0.238654i
$207$	−1.04730	+	1.51728i	−0.0727925	+	0.105458i
$208$	15.0638	−	5.04909i	1.04449	−	0.350091i
$209$	−10.8200	−	15.6755i	−0.748438	−	1.08430i
$210$	16.8006	+	10.6240i	1.15935	+	0.733127i
$211$	6.84107	−	1.11178i	0.470958	−	0.0765382i	0.0796997	−	0.996819i	$-0.474604\pi$
$211$	6.84107	−	1.11178i	0.470958	−	0.0765382i	0.391259	+	0.920281i	$0.372040\pi$
$212$	−0.164947	−	0.0702772i	−0.0113286	−	0.00482666i
$213$	−4.33574	+	6.28141i	−0.297080	+	0.430395i
$214$	6.28661	−	21.7039i	0.429744	−	1.48365i
$215$	0.0728915	+	0.153616i	0.00497116	+	0.0104765i
$216$	0.937429	−	2.47180i	0.0637839	−	0.168184i
$217$	18.4068	+	22.5442i	1.24953	+	1.53040i
$218$	0.285786	+	7.09171i	0.0193559	+	0.480311i
$219$	0.222326	+	5.51696i	0.0150234	+	0.372802i
$220$	−2.53718	+	0.625358i	−0.171056	+	0.0421616i
$221$	−3.05546	+	25.4182i	−0.205533	+	1.70981i
$222$	15.8547	+	3.90782i	1.06409	+	0.262276i
$223$	1.99218	−	9.75834i	0.133406	−	0.653467i	−0.857004	−	0.515310i	$-0.827677\pi$
$223$	1.99218	−	9.75834i	0.133406	−	0.653467i	0.990410	−	0.138157i	$-0.0441180\pi$
$224$	6.22817	−	2.65358i	0.416137	−	0.177299i
$225$	−1.23211	+	0.779136i	−0.0821404	+	0.0519424i
$226$	6.78807	−	3.56265i	0.451536	−	0.236984i
$227$	−10.7019	−	1.73923i	−0.710311	−	0.115437i	−0.205488	−	0.978660i	$-0.565878\pi$
$227$	−10.7019	−	1.73923i	−0.710311	−	0.115437i	−0.504823	+	0.863223i	$0.668442\pi$
$228$	0.925744	−	0.309059i	0.0613089	−	0.0204679i
$229$	3.39749	+	27.9809i	0.224512	+	1.84903i	0.473844	+	0.880609i	$0.342866\pi$
$229$	3.39749	+	27.9809i	0.224512	+	1.84903i	−0.249332	+	0.968418i	$0.580211\pi$
$230$	1.94629	−	6.71938i	0.128335	−	0.443063i
$231$	4.69419	−	22.9936i	0.308855	−	1.51287i
$232$	14.8139	+	4.94559i	0.972577	+	0.324694i
$233$	3.74819	+	1.96720i	0.245552	+	0.128876i	0.583010	−	0.812465i	$-0.301875\pi$
$233$	3.74819	+	1.96720i	0.245552	+	0.128876i	−0.337458	+	0.941341i	$0.609567\pi$
$234$	4.55368	+	2.87195i	0.297683	+	0.187745i
$235$	−10.0684	+	5.28431i	−0.656791	+	0.344710i
$236$	−0.433042	+	0.0703762i	−0.0281886	+	0.00458110i
$237$	−0.552136	+	0.414903i	−0.0358651	+	0.0269509i
$238$	−2.23642	+	55.4961i	−0.144965	+	3.59728i
$239$	−22.9532			−1.48472			−0.742361	−	0.670000i	$-0.766294\pi$
$239$	−22.9532			−1.48472			−0.742361	+	0.670000i	$0.766294\pi$
$240$	−0.450882	+	11.1885i	−0.0291043	+	0.722216i
$241$	0.986428	+	4.83185i	0.0635414	+	0.311247i	0.999123	−	0.0418632i	$-0.0133294\pi$
$241$	0.986428	+	4.83185i	0.0635414	+	0.311247i	−0.935582	+	0.353110i	$0.885124\pi$
$242$	7.69183	+	11.1435i	0.494450	+	0.716334i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	0.273914	−	0.577262i	0.0175356	−	0.0369554i
$245$	32.8564	−	40.2418i	2.09912	−	2.57095i
$246$	3.68370	+	9.71312i	0.234864	+	0.619286i
$247$	−1.86606	−	15.2162i	−0.118735	−	0.968184i
$248$	−5.20802	+	13.7324i	−0.330710	+	0.872010i
$249$	−2.38970	−	4.13908i	−0.151441	−	0.262303i
$250$	−8.50056	+	10.4113i	−0.537623	+	0.658468i
$251$	−14.7630	−	11.0937i	−0.931831	−	0.700226i	0.0222570	−	0.999752i	$-0.492915\pi$
$251$	−14.7630	−	11.0937i	−0.931831	−	0.700226i	−0.954088	+	0.299527i	$0.903171\pi$
$252$	1.06475	+	0.558824i	0.0670729	+	0.0352026i
$253$	−8.23224	+	0.664575i	−0.517557	+	0.0417815i
$254$	17.9540	−	1.44940i	1.12654	−	0.0909435i
$255$	−15.9770	−	8.38540i	−1.00052	−	0.525114i
$256$	4.34833	+	3.26756i	0.271771	+	0.204222i
$257$	−14.9606	+	18.3234i	−0.933214	+	1.14298i	0.0562808	+	0.998415i	$0.482076\pi$
$257$	−14.9606	+	18.3234i	−0.933214	+	1.14298i	−0.989495	+	0.144565i	$0.953822\pi$
$258$	0.0499536	+	0.0865222i	0.00310998	+	0.00538664i
$259$	20.3152	−	53.5667i	1.26232	−	3.32847i
$260$	−2.04266	−	0.500877i	−0.126680	−	0.0310631i
$261$	2.09491	+	5.52382i	0.129672	+	0.341916i
$262$	0.998475	−	1.22291i	0.0616860	−	0.0755516i
$263$	6.04324	−	12.7359i	0.372642	−	0.785327i	−0.627336	−	0.778748i	$-0.715855\pi$
$263$	6.04324	−	12.7359i	0.372642	−	0.785327i	0.999978	−	0.00657808i	$-0.00209388\pi$
$264$	11.2332	−	3.75018i	0.691354	−	0.230808i
$265$	−1.12757	−	1.63357i	−0.0692662	−	0.100349i
$266$	−6.65257	−	32.5864i	−0.407895	−	1.99800i
$267$	0.591588	−	14.6801i	0.0362046	−	0.898408i
$268$	1.52887			0.0933905
$269$	−0.272664	+	6.76608i	−0.0166246	+	0.412535i	0.969355	+	0.245666i	$0.0790067\pi$
$269$	−0.272664	+	6.76608i	−0.0166246	+	0.412535i	−0.985979	+	0.166869i	$0.946634\pi$
$270$	−3.03345	+	2.27949i	−0.184610	+	0.138725i
$271$	−30.1028	+	4.89218i	−1.82861	+	0.297179i	−0.974747	−	0.223314i	$-0.928313\pi$
$271$	−30.1028	+	4.89218i	−1.82861	+	0.297179i	−0.853866	+	0.520492i	$0.825748\pi$
$272$	−27.7037	+	14.5400i	−1.67978	+	0.881619i
$273$	11.9283	−	14.6452i	0.721931	−	0.886368i
$274$	8.60471	+	4.51610i	0.519830	+	0.272828i
$275$	−6.19445	−	2.06801i	−0.373539	−	0.124706i
$276$	0.0846487	−	0.414637i	0.00509525	−	0.0249582i
$277$	−2.75061	+	9.49620i	−0.165268	+	0.570571i	0.834539	+	0.550948i	$0.185734\pi$
$277$	−2.75061	+	9.49620i	−0.165268	+	0.570571i	−0.999807	+	0.0196231i	$0.993753\pi$
$278$	−1.43480	−	11.8167i	−0.0860537	−	0.708716i
$279$	−5.26973	+	1.75930i	−0.315491	+	0.105326i
$280$	34.7372	+	5.64534i	2.07594	+	0.337373i
$281$	−6.59857	+	3.46319i	−0.393637	+	0.206597i	−0.649916	−	0.760006i	$-0.725196\pi$
$281$	−6.59857	+	3.46319i	−0.393637	+	0.206597i	0.256278	+	0.966603i	$0.417504\pi$
$282$	−5.64696	+	3.57092i	−0.336271	+	0.212645i
$283$	−22.0401	+	9.39043i	−1.31015	+	0.558203i	−0.930285	−	0.366839i	$-0.880440\pi$
$283$	−22.0401	+	9.39043i	−1.31015	+	0.558203i	−0.379866	+	0.925042i	$0.624030\pi$
$284$	0.350439	−	1.71656i	0.0207947	−	0.101859i
$285$	10.4909	+	2.58576i	0.621425	+	0.153167i
$286$	2.93571	+	23.9383i	0.173592	+	1.41550i
$287$	35.3871	−	8.72213i	2.08883	−	0.514851i
$288$	0.0520356	+	1.29125i	0.00306623	+	0.0760877i
$289$	−1.34556	−	33.3897i	−0.0791506	−	1.96410i
$290$	−14.1773	−	17.3640i	−0.832519	−	1.01965i
$291$	−3.21279	+	8.47143i	−0.188337	+	0.496604i
$292$	−0.543324	−	1.14503i	−0.0317956	−	0.0670079i
$293$	5.01464	−	17.3125i	0.292958	−	1.01141i	−0.670135	−	0.742239i	$-0.733764\pi$
$293$	5.01464	−	17.3125i	0.292958	−	1.01141i	0.963093	−	0.269169i	$-0.0867491\pi$
$294$	17.3405	−	25.1220i	1.01132	−	1.46514i
$295$	−4.46838	−	1.90380i	−0.260159	−	0.110843i
$296$	28.5357	−	4.63750i	1.65860	−	0.269549i
$297$	3.78625	+	2.39428i	0.219701	+	0.138930i
$298$	6.01098	+	8.70841i	0.348207	+	0.504464i
$299$	−6.11850	−	2.59820i	−0.353842	−	0.150258i
$300$	0.190087	−	0.275388i	0.0109747	−	0.0158996i
$301$	0.322468	−	0.137391i	0.0185868	−	0.00791908i
$302$	0.814336	+	2.81141i	0.0468598	+	0.161779i
$303$	0.837174	−	0.0675837i	0.0480944	−	0.00388258i
$304$	14.0235	−	12.4238i	0.804305	−	0.712552i
$305$	5.97866	−	3.78068i	0.342337	−	0.216481i
$306$	−9.75380	−	4.15570i	−0.557587	−	0.237566i
$307$	0.952857	−	7.84748i	0.0543824	−	0.447879i	−0.939929	−	0.341369i	$-0.889109\pi$
$307$	0.952857	−	7.84748i	0.0543824	−	0.447879i	0.994312	−	0.106510i	$-0.0339676\pi$
$308$	1.07751	+	5.27799i	0.0613968	+	0.300741i
$309$	−5.83357	−	0.470935i	−0.331860	−	0.0267905i
$310$	16.8528	−	12.6640i	0.957173	−	0.719269i
$311$	−1.97355	+	16.2536i	−0.111910	+	0.921659i	0.823310	+	0.567592i	$0.192125\pi$
$311$	−1.97355	+	16.2536i	−0.111910	+	0.921659i	−0.935220	+	0.354067i	$0.884798\pi$
$312$	9.40998	+	1.51771i	0.532735	+	0.0859236i
$313$	−0.162775	−	1.34057i	−0.00920058	−	0.0757736i	0.987385	−	0.158336i	$-0.0506128\pi$
$313$	−0.162775	−	1.34057i	−0.00920058	−	0.0757736i	−0.996586	+	0.0825621i	$0.973690\pi$
$314$	18.6930	+	19.4615i	1.05491	+	1.09828i
$315$	6.65628	+	11.5290i	0.375039	+	0.649586i
$316$	0.0792665	−	0.137294i	0.00445909	−	0.00772336i
$317$	0.957616	−	0.236031i	0.0537851	−	0.0132568i	−0.212331	−	0.977198i	$-0.568106\pi$
$317$	0.957616	−	0.236031i	0.0537851	−	0.0132568i	0.266116	+	0.963941i	$0.414259\pi$
$318$	−0.737625	−	0.903426i	−0.0413639	−	0.0506616i
$319$	−13.2326	+	22.9196i	−0.740884	+	1.28325i
$320$	6.20262	+	16.3550i	0.346737	+	0.914270i
$321$	10.4830	−	10.9139i	0.585103	−	0.609157i
$322$	−13.6790	−	4.56673i	−0.762302	−	0.254494i
$323$	8.39940	+	28.9981i	0.467355	+	1.61350i
$324$	−0.171814	+	0.152214i	−0.00954523	+	0.00845634i
$325$	−3.64558	−	3.78637i	−0.202220	−	0.210030i
$326$	−9.50419	−	8.41998i	−0.526388	−	0.466339i
$327$	−2.03771	+	4.29437i	−0.112685	+	0.237479i
$328$	12.7405	+	13.2643i	0.703476	+	0.732396i
$329$	10.0489	+	21.1776i	0.554013	+	1.16756i
$330$	−16.5043	−	4.06795i	−0.908533	−	0.223933i
$331$	18.6984	−	19.4671i	1.02776	−	1.07001i	0.0302448	−	0.999543i	$-0.490371\pi$
$331$	18.6984	−	19.4671i	1.02776	−	1.07001i	0.997514	−	0.0704678i	$-0.0224492\pi$
$332$	0.877044	+	0.659055i	0.0481340	+	0.0361704i
$333$	8.18566	+	7.25186i	0.448572	+	0.397400i
$334$	−8.57720	−	1.39393i	−0.469324	−	0.0762725i
$335$	14.3056	+	9.04630i	0.781597	+	0.494252i
$336$	23.0087	+	1.85746i	1.25523	+	0.101332i
$337$	−23.4519			−1.27750			−0.638752	−	0.769412i	$-0.720549\pi$
$337$	−23.4519			−1.27750			−0.638752	+	0.769412i	$0.720549\pi$
$338$	−6.83983	+	18.1662i	−0.372037	+	0.988109i
$339$	5.13419			0.278851
$340$	4.12838	+	0.333277i	0.223893	+	0.0180745i
$341$	−21.0351	−	13.3018i	−1.13911	−	0.720331i
$342$	6.26647	+	1.01840i	0.338852	+	0.0550688i
$343$	−52.7144	−	46.7009i	−2.84631	−	2.52161i
$344$	0.141407	+	0.106260i	0.00762414	+	0.00572917i
$345$	3.24546	−	3.37888i	0.174730	−	0.181913i
$346$	−3.98923	−	0.983257i	−0.214462	−	0.0528602i
$347$	5.46670	+	11.5208i	0.293468	+	0.618470i	0.995613	−	0.0935633i	$-0.0298257\pi$
$347$	5.46670	+	11.5208i	0.293468	+	0.618470i	−0.702146	+	0.712033i	$0.747774\pi$
$348$	−0.939381	−	0.977999i	−0.0503561	−	0.0524263i
$349$	5.10167	−	10.7515i	0.273086	−	0.575517i	−0.719855	−	0.694125i	$-0.755792\pi$
$349$	5.10167	−	10.7515i	0.273086	−	0.575517i	0.992941	+	0.118607i	$0.0378430\pi$
$350$	−8.53530	−	7.56162i	−0.456231	−	0.404186i
$351$	1.80651	+	3.12034i	0.0964244	+	0.166551i
$352$	−4.33327	+	3.83894i	−0.230964	+	0.204616i
$353$	−2.11950	−	7.31737i	−0.112810	−	0.389464i	0.884167	−	0.467172i	$-0.154727\pi$
$353$	−2.11950	−	7.31737i	−0.112810	−	0.389464i	−0.996976	+	0.0777077i	$0.975240\pi$
$354$	−2.70702	−	0.903737i	−0.143877	−	0.0480331i
$355$	13.4359	−	13.9883i	0.713106	−	0.742422i
$356$	1.19588	+	3.15327i	0.0633815	+	0.167123i
$357$	−18.5985	+	32.2135i	−0.984336	+	1.70492i
$358$	9.62656	+	11.7904i	0.508779	+	0.623142i
$359$	−21.9850	+	5.41881i	−1.16032	+	0.285994i	−0.772057	−	0.635553i	$-0.780772\pi$
$359$	−21.9850	+	5.41881i	−1.16032	+	0.285994i	−0.388266	+	0.921547i	$0.626926\pi$
$360$	−3.35896	+	5.81790i	−0.177033	+	0.306630i
$361$	0.460966	+	0.798417i	0.0242614	+	0.0420220i
$362$	4.72353	+	4.91772i	0.248263	+	0.258469i
$363$	1.09306	+	9.00215i	0.0573707	+	0.472490i
$364$	−1.20126	+	4.16589i	−0.0629633	+	0.218352i
$365$	1.69127	−	13.9289i	0.0885252	−	0.729071i
$366$	3.32279	−	2.49692i	0.173685	−	0.130516i
$367$	16.1812	+	1.30628i	0.844653	+	0.0681875i	0.495213	−	0.868771i	$-0.335090\pi$
$367$	16.1812	+	1.30628i	0.844653	+	0.0681875i	0.349440	+	0.936959i	$0.386372\pi$
$368$	−1.62496	−	7.95958i	−0.0847069	−	0.414922i
$369$	−0.838593	+	6.90643i	−0.0436554	+	0.359535i
$370$	−38.1754	−	16.2650i	−1.98464	−	0.845578i
$371$	−3.45843	+	2.18698i	−0.179553	+	0.113542i
$372$	0.954538	−	0.845647i	0.0494905	−	0.0438448i
$373$	−27.6058	+	2.22857i	−1.42937	+	0.115391i	−0.770777	−	0.637105i	$-0.780132\pi$
$373$	−27.6058	+	2.22857i	−1.42937	+	0.115391i	−0.658596	+	0.752496i	$0.728850\pi$
$374$	−13.2140	−	45.6201i	−0.683280	−	2.35896i
$375$	−8.28123	+	3.52830i	−0.427641	+	0.182201i
$376$	−6.71960	+	9.73503i	−0.346537	+	0.502046i
$377$	−17.9894	+	11.4060i	−0.926503	+	0.587438i
$378$	4.44350	+	6.43752i	0.228549	+	0.331110i
$379$	−0.795615	−	0.503117i	−0.0408680	−	0.0258434i	0.513876	−	0.857865i	$-0.328209\pi$
$379$	−0.795615	−	0.503117i	−0.0408680	−	0.0258434i	−0.554744	+	0.832021i	$0.687184\pi$
$380$	−2.44804	+	0.397845i	−0.125582	+	0.0204090i
$381$	11.0980	+	4.72840i	0.568566	+	0.242243i
$382$	5.79147	−	8.39039i	0.296317	−	0.429290i
$383$	−4.98340	+	17.2047i	−0.254640	+	0.879120i	0.726719	+	0.686935i	$0.241044\pi$
$383$	−4.98340	+	17.2047i	−0.254640	+	0.879120i	−0.981359	+	0.192184i	$0.938443\pi$
$384$	5.51398	+	11.6205i	0.281384	+	0.593004i
$385$	−21.1476	+	55.7616i	−1.07778	+	2.84188i
$386$	−11.0505	−	13.5344i	−0.562454	−	0.688882i
$387$	0.00269418	+	0.0668555i	0.000136953	+	0.00339845i
$388$	−0.0837406	−	2.07800i	−0.00425129	−	0.105495i
$389$	−12.2768	+	3.02597i	−0.622460	+	0.153423i	−0.537918	−	0.842997i	$-0.680789\pi$
$389$	−12.2768	+	3.02597i	−0.622460	+	0.153423i	−0.0845420	+	0.996420i	$0.526943\pi$
$390$	−10.2513	−	9.05999i	−0.519095	−	0.458770i
$391$	12.7103	+	3.13280i	0.642786	+	0.158433i
$392$	10.8102	−	52.9519i	0.545998	−	2.67448i
$393$	0.972713	−	0.414434i	0.0490669	−	0.0209054i
$394$	18.4769	−	11.6841i	0.930851	−	0.588634i
$395$	1.55406	−	0.815633i	0.0781932	−	0.0410389i
$396$	−1.01497	−	0.164949i	−0.0510044	−	0.00828902i
$397$	10.6267	−	3.54770i	0.533336	−	0.178054i	−0.0372279	−	0.999307i	$-0.511853\pi$
$397$	10.6267	−	3.54770i	0.533336	−	0.178054i	0.570564	+	0.821253i	$0.306725\pi$
$398$	3.54757	+	29.2169i	0.177824	+	1.46451i
$399$	6.19698	−	21.3945i	0.310237	−	1.07106i
$400$	1.28488	−	6.29376i	0.0642440	−	0.314688i
$401$	24.7731	+	8.27046i	1.23711	+	0.413007i	0.858627	−	0.512602i	$-0.171318\pi$
$401$	24.7731	+	8.27046i	1.23711	+	0.413007i	0.378481	+	0.925609i	$0.376446\pi$
$402$	8.80610	+	4.62180i	0.439209	+	0.230514i
$403$	−10.0363	−	17.3355i	−0.499945	−	0.863543i
$404$	−0.170708	+	0.0895945i	−0.00849305	+	0.00445749i
$405$	−2.50831	+	0.407640i	−0.124639	+	0.0202558i
$406$	−36.9433	+	27.7611i	−1.83346	+	1.37776i
$407$	−1.97264	+	48.9506i	−0.0977803	+	2.42639i
$408$	−18.7707			−0.929290
$409$	−0.315693	+	7.83385i	−0.0156100	+	0.387359i	0.972433	+	0.233182i	$0.0749137\pi$
$409$	−0.315693	+	7.83385i	−0.0156100	+	0.387359i	−0.988043	+	0.154177i	$0.950727\pi$
$410$	−5.28041	−	25.8651i	−0.260781	−	1.27739i
$411$	3.69709	+	5.35615i	0.182364	+	0.264200i
$412$	1.27427	−	0.425412i	0.0627786	−	0.0209586i
$413$	−4.29236	+	9.04595i	−0.211213	+	0.445122i
$414$	1.74102	−	2.13237i	0.0855666	−	0.104800i
$415$	4.30685	+	11.3562i	0.211415	+	0.557455i
$416$	−4.52271	+	1.12049i	−0.221744	+	0.0549366i
$417$	2.82689	−	7.45391i	0.138434	−	0.365019i
$418$	14.2203	+	24.6303i	0.695537	+	1.20471i
$419$	−7.93647	+	9.72041i	−0.387722	+	0.474873i	−0.931178	−	0.364564i	$-0.881218\pi$
$419$	−7.93647	+	9.72041i	−0.387722	+	0.474873i	0.543456	+	0.839437i	$0.317115\pi$
$420$	−2.44292	−	1.83574i	−0.119202	−	0.0895748i
$421$	−16.0728	−	8.43567i	−0.783342	−	0.411130i	0.0251152	−	0.999685i	$-0.492005\pi$
$421$	−16.0728	−	8.43567i	−0.783342	−	0.411130i	−0.808457	+	0.588555i	$0.799697\pi$
$422$	−10.3153	+	0.832737i	−0.502141	+	0.0405370i
$423$	−4.46007	+	0.360054i	−0.216856	+	0.0175064i
$424$	−1.82837	−	0.959605i	−0.0887937	−	0.0466025i
$425$	8.27501	+	6.21827i	0.401397	+	0.301630i
$426$	7.20770	−	8.82783i	0.349214	−	0.427710i
$427$	−7.29118	−	12.6287i	−0.352845	−	0.611145i
$428$	−1.23177	+	3.24791i	−0.0595399	+	0.156994i
$429$	−5.70950	+	15.1092i	−0.275657	+	0.729481i
$430$	−0.0900292	−	0.237388i	−0.00434159	−	0.0114478i
$431$	15.5921	−	19.0968i	0.751043	−	0.919860i	−0.247758	−	0.968822i	$-0.579694\pi$
$431$	15.5921	−	19.0968i	0.751043	−	0.919860i	0.998801	+	0.0489617i	$0.0155912\pi$
$432$	−1.88899	+	3.98096i	−0.0908840	+	0.191534i
$433$	−8.37198	+	2.79498i	−0.402332	+	0.134318i	−0.510630	−	0.859800i	$-0.670588\pi$
$433$	−8.37198	+	2.79498i	−0.402332	+	0.134318i	0.108299	+	0.994118i	$0.465460\pi$
$434$	−24.6865	−	35.7646i	−1.18499	−	1.71676i
$435$	−3.00295	−	14.7094i	−0.143980	−	0.705263i
$436$	0.0439333	−	1.09019i	0.00210402	−	0.0522108i
$437$	−7.83880			−0.374981
$438$	0.331969	−	8.23773i	0.0158621	−	0.393614i
$439$	1.84898	−	1.38942i	0.0882471	−	0.0663134i	−0.555703	−	0.831381i	$-0.687551\pi$
$439$	1.84898	−	1.38942i	0.0882471	−	0.0663134i	0.643950	+	0.765067i	$0.277294\pi$
$440$	−29.7050	+	4.82753i	−1.41613	+	0.230144i
$441$	18.1018	−	9.50056i	0.861991	−	0.452408i
$442$	7.60150	−	37.4633i	0.361567	−	1.78195i
$443$	−6.72347	−	3.52875i	−0.319442	−	0.167656i	0.297379	−	0.954759i	$-0.403887\pi$
$443$	−6.72347	−	3.52875i	−0.319442	−	0.167656i	−0.616821	+	0.787104i	$0.711580\pi$
$444$	−2.38106	−	0.794915i	−0.113000	−	0.0377250i
$445$	−7.46809	+	36.5811i	−0.354021	+	1.73411i
$446$	−4.13747	+	14.2842i	−0.195915	+	0.676377i
$447$	0.854198	+	7.03496i	0.0404022	+	0.332742i
$448$	34.2029	−	11.4186i	1.61593	−	0.539478i
$449$	4.72600	+	0.768050i	0.223034	+	0.0362465i	0.270901	−	0.962607i	$-0.412678\pi$
$449$	4.72600	+	0.768050i	0.223034	+	0.0362465i	−0.0478673	+	0.998854i	$0.515242\pi$
$450$	1.92738	−	1.01157i	0.0908578	−	0.0476858i
$451$	−26.3415	+	16.6574i	−1.24037	+	0.784366i
$452$	−1.08420	+	0.461936i	−0.0509966	+	0.0217276i
$453$	−0.392100	+	1.92063i	−0.0184225	+	0.0902393i
$454$	15.7189	+	3.87437i	0.737726	+	0.181833i
$455$	−35.8897	+	31.8723i	−1.68254	+	1.49419i
$456$	10.9135	−	2.68993i	0.511070	−	0.125967i
$457$	−0.00461250	−	0.114458i	−0.000215763	−	0.00535412i	0.999078	−	0.0429429i	$-0.0136733\pi$
$457$	−0.00461250	−	0.114458i	−0.000215763	−	0.00535412i	−0.999293	+	0.0375887i	$0.988032\pi$
$458$	−1.69467	−	42.0528i	−0.0791866	−	1.96500i
$459$	−4.49067	−	5.50007i	−0.209606	−	0.256721i
$460$	−0.381348	+	1.00553i	−0.0177804	+	0.0468831i
$461$	−3.11958	−	6.57438i	−0.145293	−	0.306199i	0.817737	−	0.575592i	$-0.195228\pi$
$461$	−3.11958	−	6.57438i	−0.145293	−	0.306199i	−0.963030	+	0.269393i	$0.913177\pi$
$462$	−9.74915	+	33.6580i	−0.453571	+	1.56591i
$463$	20.0545	−	29.0540i	0.932012	−	1.35025i	−0.00463864	−	0.999989i	$-0.501477\pi$
$463$	20.0545	−	29.0540i	0.932012	−	1.35025i	0.936651	−	0.350264i	$-0.113908\pi$
$464$	−23.9487	−	10.2036i	−1.11179	−	0.473690i
$465$	13.9353	−	2.26470i	0.646233	−	0.105023i
$466$	−5.34215	−	3.37817i	−0.247471	−	0.156491i
$467$	−24.3036	−	35.2099i	−1.12464	−	1.62932i	−0.679072	−	0.734072i	$-0.737618\pi$
$467$	−24.3036	−	35.2099i	−1.12464	−	1.62932i	−0.445567	−	0.895249i	$-0.646998\pi$
$468$	−0.662232	−	0.496396i	−0.0306117	−	0.0229459i
$469$	19.8210	−	28.7157i	0.915251	−	1.32597i
$470$	15.6200	−	6.65504i	0.720495	−	0.306974i
$471$	5.02801	+	17.3587i	0.231679	+	0.799847i
$472$	−5.03632	+	0.406574i	−0.231815	+	0.0187141i
$473$	−0.224358	+	0.198764i	−0.0103160	+	0.00913918i
$474$	0.871607	−	0.551171i	0.0400342	−	0.0253161i
$475$	−5.70227	−	2.42951i	−0.261638	−	0.111474i
$476$	1.02917	−	8.47598i	0.0471720	−	0.388496i
$477$	−0.156239	−	0.765311i	−0.00715371	−	0.0350412i
$478$	34.1618	+	2.75783i	1.56253	+	0.126140i
$479$	13.0466	−	9.80389i	0.596114	−	0.447951i	−0.259371	−	0.965778i	$-0.583515\pi$
$479$	13.0466	−	9.80389i	0.596114	−	0.447951i	0.855485	+	0.517827i	$0.173259\pi$
$480$	0.395844	−	3.26007i	0.0180677	−	0.148801i
$481$	−19.6742	+	34.1710i	−0.897064	+	1.55806i
$482$	−0.887578	−	7.30987i	−0.0404281	−	0.332955i
$483$	−6.69043	−	6.96547i	−0.304425	−	0.316940i
$484$	−1.04077	−	1.80267i	−0.0473078	−	0.0819394i
$485$	11.5120	−	19.9393i	0.522731	−	0.905397i
$486$	−1.44978	+	0.357338i	−0.0657632	+	0.0162092i
$487$	−2.31144	−	2.83101i	−0.104742	−	0.128285i	0.719574	−	0.694416i	$-0.244337\pi$
$487$	−2.31144	−	2.83101i	−0.104742	−	0.128285i	−0.824315	+	0.566131i	$0.808440\pi$
$488$	3.67935	−	6.37283i	0.166556	−	0.288484i
$489$	−3.01546	−	7.95112i	−0.136364	−	0.359562i
$490$	−53.7360	+	55.9451i	−2.42754	+	2.52734i
$491$	−26.7940	−	8.94514i	−1.20919	−	0.403688i	−0.360594	−	0.932723i	$-0.617426\pi$
$491$	−26.7940	−	8.94514i	−1.20919	−	0.403688i	−0.848600	+	0.529035i	$0.822554\pi$
$492$	−0.444301	−	1.53390i	−0.0200306	−	0.0691538i
$493$	31.3983	−	27.8165i	1.41411	−	1.25279i
$494$	0.949079	+	22.8708i	0.0427011	+	1.02901i
$495$	−8.52108	−	7.54902i	−0.382994	−	0.339303i
$496$	10.4945	−	22.1168i	0.471219	−	0.993073i
$497$	−27.6978	−	28.8365i	−1.24242	−	1.29349i
$498$	3.05933	+	6.44741i	0.137092	+	0.288915i
$499$	−16.2743	−	4.01125i	−0.728538	−	0.179568i	−0.142434	−	0.989804i	$-0.545493\pi$
$499$	−16.2743	−	4.01125i	−0.728538	−	0.179568i	−0.586104	+	0.810236i	$0.699339\pi$
$500$	1.43132	−	1.49017i	0.0640108	−	0.0666423i
$501$	−4.65250	−	3.49612i	−0.207858	−	0.156195i
$502$	20.6392	+	18.2847i	0.921172	+	0.816087i
$503$	22.4125	+	3.64238i	0.999322	+	0.162406i	0.638001	−	0.770036i	$-0.279762\pi$
$503$	22.4125	+	3.64238i	0.999322	+	0.162406i	0.361321	+	0.932441i	$0.382326\pi$
$504$	11.7049	+	7.40173i	0.521378	+	0.329699i
$505$	−2.12744	−	0.171745i	−0.0946699	−	0.00764254i
$506$	12.3321			0.548228
$507$	−9.70998	+	8.64386i	−0.431235	+	0.383887i
$508$	−2.76902			−0.122855
$509$	−6.57147	−	0.530504i	−0.291275	−	0.0235142i	−0.0660345	−	0.997817i	$-0.521035\pi$
$509$	−6.57147	−	0.530504i	−0.291275	−	0.0235142i	−0.225241	+	0.974303i	$0.572317\pi$
$510$	22.7715	+	14.3998i	1.00834	+	0.637635i
$511$	−28.5503	−	4.63988i	−1.26299	−	0.205256i
$512$	13.1760	+	11.6729i	0.582304	+	0.515876i
$513$	3.39910	+	2.55425i	0.150074	+	0.112773i
$514$	24.4677	−	25.4736i	1.07922	−	1.12359i
$515$	14.4404	+	3.55925i	0.636321	+	0.156839i
$516$	−0.00658409	−	0.0138757i	−0.000289849	−	0.000610843i
$517$	−13.8857	−	14.4565i	−0.610692	−	0.635798i
$518$	−36.6715	+	77.2836i	−1.61125	+	3.39565i
$519$	−2.05962	−	1.82466i	−0.0904071	−	0.0800937i
$520$	−22.9845	−	7.64278i	−1.00794	−	0.335158i
$521$	−17.7735	+	15.7459i	−0.778671	+	0.689842i	−0.955693	−	0.294365i	$-0.904892\pi$
$521$	−17.7735	+	15.7459i	−0.778671	+	0.689842i	0.177022	+	0.984207i	$0.443354\pi$
$522$	−2.45422	−	8.47294i	−0.107418	−	0.370850i
$523$	38.3116	+	12.7903i	1.67525	+	0.559280i	0.986218	−	0.165453i	$-0.0529085\pi$
$523$	38.3116	+	12.7903i	1.67525	+	0.559280i	0.689030	+	0.724733i	$0.258037\pi$
$524$	−0.168123	+	0.175035i	−0.00734450	+	0.00764643i
$525$	−2.70806	−	7.14056i	−0.118189	−	0.311640i
$526$	−10.5245	+	18.2290i	−0.458890	+	0.794821i
$527$	24.9485	+	30.5564i	1.08678	+	1.33106i
$528$	−19.1660	+	4.72399i	−0.834093	+	0.205585i
$529$	9.80051	−	16.9750i	0.426109	−	0.738043i
$530$	1.48192	+	2.56676i	0.0643704	+	0.111493i
$531$	−1.32401	−	1.37844i	−0.0574570	−	0.0598191i
$532$	0.616277	+	5.07549i	0.0267190	+	0.220051i
$533$	−25.0006	+	2.04838i	−1.08290	+	0.0887250i
$534$	−2.64429	+	21.7777i	−0.114430	+	0.942412i
$535$	−30.7435	+	23.1022i	−1.32916	+	0.998797i
$536$	17.5506	+	1.41683i	0.758071	+	0.0611978i
$537$	2.03904	+	9.98789i	0.0879911	+	0.431009i
$538$	1.21875	−	10.0373i	0.0525442	−	0.432741i
$539$	84.2535	+	35.8971i	3.62906	+	1.54620i
$540$	0.493011	−	0.311762i	0.0212158	−	0.0134161i
$541$	−2.08708	+	1.84899i	−0.0897305	+	0.0794943i	−0.706796	−	0.707418i	$-0.749860\pi$
$541$	−2.08708	+	1.84899i	−0.0897305	+	0.0794943i	0.617065	+	0.786912i	$0.288322\pi$
$542$	45.3904	−	3.66429i	1.94969	−	0.157395i
$543$	1.27052	+	4.38636i	0.0545234	+	0.188237i
$544$	8.44168	−	3.59666i	0.361934	−	0.154206i
$545$	6.86175	−	9.94096i	0.293925	−	0.425824i
$546$	−19.5127	+	20.3636i	−0.835067	+	0.871482i
$547$	2.03997	+	2.95540i	0.0872227	+	0.126364i	0.864166	−	0.503206i	$-0.167846\pi$
$547$	2.03997	+	2.95540i	0.0872227	+	0.126364i	−0.776944	+	0.629570i	$0.783231\pi$
$548$	−1.26263	−	0.798440i	−0.0539370	−	0.0341077i
$549$	2.74756	−	0.446522i	0.117263	−	0.0190571i
$550$	8.97087	+	3.82213i	0.382519	+	0.162976i
$551$	−14.2690	+	20.6723i	−0.607881	+	0.880668i
$552$	1.35598	−	4.68137i	0.0577141	−	0.199252i
$553$	−1.55104	−	3.26876i	−0.0659571	−	0.139002i
$554$	5.23476	−	13.8029i	0.222404	−	0.586430i
$555$	−17.5760	−	21.5267i	−0.746061	−	0.913758i
$556$	0.0736824	+	1.82841i	0.00312483	+	0.0775418i
$557$	−0.0449102	−	1.11444i	−0.00190291	−	0.0472202i	0.997959	−	0.0638648i	$-0.0203426\pi$
$557$	−0.0449102	−	1.11444i	−0.00190291	−	0.0472202i	−0.999861	+	0.0166446i	$0.994702\pi$
$558$	8.05444	−	1.98524i	0.340972	−	0.0840420i
$559$	−0.234167	+	0.0580143i	−0.00990421	+	0.00245374i
$560$	−56.9558	−	14.0383i	−2.40682	−	0.593228i
$561$	6.36251	−	31.1656i	0.268625	−	1.31581i
$562$	10.2369	−	4.36153i	0.431818	−	0.183980i
$563$	15.3468	−	9.70474i	0.646792	−	0.409006i	−0.170398	−	0.985375i	$-0.554505\pi$
$563$	15.3468	−	9.70474i	0.646792	−	0.409006i	0.817189	+	0.576369i	$0.195531\pi$
$564$	0.909453	−	0.477318i	0.0382949	−	0.0200987i
$565$	−12.8781	−	2.09290i	−0.541787	−	0.0880489i
$566$	33.9311	−	11.3279i	1.42623	−	0.476146i
$567$	0.631450	+	5.20046i	0.0265184	+	0.218399i
$568$	5.61363	−	19.3805i	0.235543	−	0.813188i
$569$	−2.75009	+	13.4708i	−0.115290	+	0.564726i	0.880577	+	0.473903i	$0.157155\pi$
$569$	−2.75009	+	13.4708i	−0.115290	+	0.564726i	−0.995867	+	0.0908238i	$0.971050\pi$
$570$	−15.3031	−	5.10893i	−0.640977	−	0.213989i
$571$	31.3807	+	16.4699i	1.31324	+	0.689242i	0.968396	−	0.249417i	$-0.0802391\pi$
$571$	31.3807	+	16.4699i	1.31324	+	0.689242i	0.344845	+	0.938660i	$0.387931\pi$
$572$	−0.153721	−	3.70437i	−0.00642741	−	0.154887i
$573$	6.04575	−	3.17305i	0.252565	−	0.132556i
$574$	−53.7154	+	8.72960i	−2.24204	+	0.364366i
$575$	−2.14860	+	1.61456i	−0.0896026	+	0.0673320i
$576$	−0.277157	+	6.87759i	−0.0115482	+	0.286566i
$577$	37.1229			1.54544			0.772722	−	0.634744i	$-0.218894\pi$
$577$	37.1229			1.54544			0.772722	+	0.634744i	$0.218894\pi$
$578$	−2.00914	+	49.8564i	−0.0835693	+	2.07375i
$579$	−2.34065	−	11.4652i	−0.0972740	−	0.476479i
$580$	1.95759	+	2.83605i	0.0812844	+	0.117761i
$581$	23.7491	−	7.92860i	0.985277	−	0.328934i
$582$	5.79951	−	12.2222i	0.240397	−	0.506627i
$583$	2.21301	−	2.71044i	0.0916533	−	0.112255i
$584$	−5.17596	−	13.6479i	−0.214183	−	0.564753i
$585$	−3.25931	−	8.56318i	−0.134756	−	0.354044i
$586$	−9.54350	+	25.1641i	−0.394238	+	1.03952i
$587$	−12.4521	−	21.5677i	−0.513954	−	0.890194i	−0.999869	−	0.0161878i	$-0.994847\pi$
$587$	−12.4521	−	21.5677i	−0.513954	−	0.890194i	0.485915	−	0.874006i	$-0.338486\pi$
$588$	−2.96783	+	3.63493i	−0.122391	+	0.149902i
$589$	−18.8842	−	14.1905i	−0.778109	−	0.584711i
$590$	6.42165	+	3.37034i	0.264375	+	0.138755i
$591$	14.5934	−	1.17810i	0.600291	−	0.0484605i
$592$	−48.0318	+	3.87752i	−1.97409	+	0.159365i
$593$	−35.5610	−	18.6638i	−1.46031	−	0.766432i	−0.467264	−	0.884118i	$-0.654760\pi$
$593$	−35.5610	−	18.6638i	−1.46031	−	0.766432i	−0.993051	+	0.117685i	$0.962453\pi$
$594$	−5.34749	−	4.01838i	−0.219410	−	0.164876i
$595$	59.7822	−	73.2200i	2.45083	−	3.00173i
$596$	−0.813337	−	1.40874i	−0.0333156	−	0.0577043i
$597$	−6.98954	+	18.4299i	−0.286063	+	0.754286i
$598$	8.79412	+	4.60210i	0.359619	+	0.188194i
$599$	6.91718	+	18.2391i	0.282628	+	0.745230i	0.998877	+	0.0473843i	$0.0150885\pi$
$599$	6.91718	+	18.2391i	0.282628	+	0.745230i	−0.716248	+	0.697845i	$0.754142\pi$
$600$	2.43731	−	2.98516i	0.0995026	−	0.121869i
$601$	−19.5547	+	41.2106i	−0.797651	+	1.68101i	−0.0675088	+	0.997719i	$0.521505\pi$
$601$	−19.5547	+	41.2106i	−0.797651	+	1.68101i	−0.730142	+	0.683295i	$0.760546\pi$
$602$	−0.496444	+	0.165737i	−0.0202336	+	0.00675496i
$603$	3.78361	+	5.48151i	0.154081	+	0.223224i
$604$	−0.0900032	−	0.440865i	−0.00366218	−	0.0179385i
$605$	0.927906	−	23.0257i	0.0377247	−	0.936130i
$606$	−1.25411			−0.0509446
$607$	−1.09662	+	27.2124i	−0.0445105	+	1.10452i	0.810444	+	0.585815i	$0.199226\pi$
$607$	−1.09662	+	27.2124i	−0.0445105	+	1.10452i	−0.854955	+	0.518702i	$0.826415\pi$
$608$	−4.39265	+	3.30086i	−0.178145	+	0.133868i
$609$	−30.5478	+	4.96450i	−1.23786	+	0.201172i
$610$	−9.35243	+	4.90853i	−0.378669	+	0.198741i
$611$	−4.50712	−	15.4910i	−0.182338	−	0.626698i
$612$	1.44316	+	0.757431i	0.0583364	+	0.0306173i
$613$	26.9497	+	8.99714i	1.08849	+	0.363391i	0.803600	−	0.595169i	$-0.202915\pi$
$613$	26.9497	+	8.99714i	1.08849	+	0.363391i	0.284889	+	0.958560i	$0.408043\pi$
$614$	−2.36103	+	11.5651i	−0.0952835	+	0.466730i
$615$	4.91879	−	16.9816i	0.198345	−	0.684765i
$616$	7.47803	+	61.5871i	0.301299	+	2.48142i
$617$	18.9303	−	6.31988i	0.762107	−	0.254429i	0.0910619	−	0.995845i	$-0.470974\pi$
$617$	18.9303	−	6.31988i	0.762107	−	0.254429i	0.671045	+	0.741417i	$0.265846\pi$
$618$	8.62566	+	1.40181i	0.346975	+	0.0563889i
$619$	−1.72946	+	0.907691i	−0.0695129	+	0.0364832i	−0.499121	−	0.866532i	$-0.666344\pi$
$619$	−1.72946	+	0.907691i	−0.0695129	+	0.0364832i	0.429609	+	0.903015i	$0.358652\pi$
$620$	−2.73900	+	1.73204i	−0.110001	+	0.0695603i
$621$	1.69610	−	0.722641i	0.0680622	−	0.0289986i
$622$	4.89015	−	23.9535i	0.196077	−	0.960449i
$623$	74.7299	+	18.4193i	2.99399	+	0.737953i
$624$	−15.4304	−	3.78366i	−0.617709	−	0.151468i
$625$	29.2873	−	7.21867i	1.17149	−	0.288747i
$626$	0.0811921	+	2.01476i	0.00324509	+	0.0805260i
$627$	0.766953	+	19.0317i	0.0306292	+	0.760055i
$628$	−2.62359	−	3.21331i	−0.104693	−	0.128225i
$629$	27.5352	−	72.6044i	1.09790	−	2.89493i
$630$	−8.52148	−	17.9586i	−0.339504	−	0.715489i
$631$	2.08318	−	7.19199i	0.0829302	−	0.286308i	−0.908325	−	0.418264i	$-0.862639\pi$
$631$	2.08318	−	7.19199i	0.0829302	−	0.286308i	0.991256	+	0.131956i	$0.0421257\pi$
$632$	1.03717	−	1.50260i	0.0412564	−	0.0597702i
$633$	−6.37621	−	2.71665i	−0.253432	−	0.107977i
$634$	−1.45360	+	0.236233i	−0.0577299	+	0.00938202i
$635$	−25.9096	−	16.3843i	−1.02819	−	0.650190i
$636$	0.101851	+	0.147556i	0.00403864	+	0.00585097i
$637$	46.6859	+	57.0403i	1.84976	+	2.26002i
$638$	22.4482	−	32.5218i	0.888732	−	1.28755i
$639$	7.02173	−	2.99168i	0.277775	−	0.118349i
$640$	−9.09379	−	31.3954i	−0.359464	−	1.24101i
$641$	41.2275	−	3.32823i	1.62839	−	0.131457i	0.767776	−	0.640719i	$-0.221364\pi$
$641$	41.2275	−	3.32823i	1.62839	−	0.131457i	0.860612	+	0.509262i	$0.170082\pi$
$642$	−16.9134	+	14.9839i	−0.667517	+	0.591369i
$643$	−31.2315	+	19.7496i	−1.23165	+	0.778848i	−0.981889	−	0.189459i	$-0.939327\pi$
$643$	−31.2315	+	19.7496i	−1.23165	+	0.778848i	−0.249761	+	0.968307i	$0.580352\pi$
$644$	2.03954	+	0.868967i	0.0803692	+	0.0342421i
$645$	0.0204951	−	0.168792i	0.000806994	−	0.00664619i
$646$	−9.01690	−	44.1677i	−0.354765	−	1.73775i
$647$	−40.8920	−	3.30114i	−1.60763	−	0.129781i	−0.756232	−	0.654303i	$-0.772962\pi$
$647$	−40.8920	−	3.30114i	−1.60763	−	0.129781i	−0.851397	+	0.524522i	$0.824244\pi$
$648$	−2.11340	+	1.58811i	−0.0830220	+	0.0623870i
$649$	1.03206	−	8.49977i	0.0405118	−	0.333645i
$650$	4.97086	+	6.07335i	0.194973	+	0.238216i
$651$	−3.50811	−	28.8919i	−0.137494	−	1.13236i
$652$	1.35217	+	1.40776i	0.0529550	+	0.0551320i
$653$	−12.9800	−	22.4820i	−0.507947	−	0.879789i	−0.999958	−	0.00920048i	$-0.997071\pi$
$653$	−12.9800	−	22.4820i	−0.507947	−	0.879789i	0.492011	−	0.870589i	$-0.336262\pi$
$654$	3.54873	−	6.14658i	0.138766	−	0.240350i
$655$	−2.60880	+	0.643012i	−0.101934	+	0.0251246i
$656$	−19.3882	−	23.7463i	−0.756983	−	0.927136i
$657$	2.76072	−	4.78171i	0.107706	−	0.186552i
$658$	−12.4115	−	32.7264i	−0.483851	−	1.27581i
$659$	5.88650	−	6.12849i	0.229305	−	0.238732i	−0.596603	−	0.802536i	$-0.703483\pi$
$659$	5.88650	−	6.12849i	0.229305	−	0.238732i	0.825908	+	0.563804i	$0.190663\pi$
$660$	2.47863	+	0.827488i	0.0964805	+	0.0322099i
$661$	−8.59391	−	29.6696i	−0.334265	−	1.15402i	−0.935024	−	0.354585i	$-0.884622\pi$
$661$	−8.59391	−	29.6696i	−0.334265	−	1.15402i	0.600759	−	0.799430i	$-0.294865\pi$
$662$	−30.1683	+	26.7268i	−1.17252	+	1.03877i
$663$	16.1676	−	19.8501i	0.627897	−	0.770915i
$664$	9.45724	+	8.37839i	0.367012	+	0.325144i
$665$	−24.2652	+	51.1378i	−0.940963	+	1.98304i
$666$	−11.3116	−	11.7766i	−0.438316	−	0.456335i
$667$	4.66918	+	9.84008i	0.180791	+	0.381009i
$668$	1.29704	+	0.319691i	0.0501839	+	0.0123692i
$669$	−6.89927	+	7.18290i	−0.266741	+	0.277707i
$670$	−20.2044	−	15.1826i	−0.780564	−	0.586556i
$671$	9.33385	+	8.26907i	0.360329	+	0.319224i
$672$	−6.68223	−	1.08597i	−0.257773	−	0.0418922i
$673$	−43.3619	−	27.4204i	−1.67148	−	1.05698i	−0.915440	−	0.402455i	$-0.868157\pi$
$673$	−43.3619	−	27.4204i	−1.67148	−	1.05698i	−0.756041	−	0.654525i	$-0.772869\pi$
$674$	34.9040	+	2.81774i	1.34445	+	0.108535i
$675$	1.45779			0.0561102
$676$	1.27278	−	2.69898i	0.0489530	−	0.103807i
$677$	19.1026			0.734173			0.367086	−	0.930187i	$-0.380355\pi$
$677$	19.1026			0.734173			0.367086	+	0.930187i	$0.380355\pi$
$678$	−7.64133	−	0.616872i	−0.293463	−	0.0236908i
$679$	−40.1154	−	25.3675i	−1.53949	−	0.973514i
$680$	47.0828	+	7.65170i	1.80554	+	0.293429i
$681$	8.11559	+	7.18979i	0.310990	+	0.275513i
$682$	29.7088	+	22.3247i	1.13761	+	0.854856i
$683$	−28.8920	+	30.0797i	−1.10552	+	1.15097i	−0.118076	+	0.993005i	$0.537673\pi$
$683$	−28.8920	+	30.0797i	−1.10552	+	1.15097i	−0.987445	+	0.157965i	$0.949507\pi$
$684$	−0.947611	−	0.233565i	−0.0362328	−	0.00893058i
$685$	−7.09005	−	14.9420i	−0.270897	−	0.570903i
$686$	72.8450	+	75.8397i	2.78123	+	2.89557i
$687$	12.0833	−	25.4650i	0.461006	−	0.971550i
$688$	−0.220684	−	0.195509i	−0.00841349	−	0.00745370i
$689$	2.58960	−	1.10699i	0.0986559	−	0.0421729i
$690$	−5.23626	+	4.63892i	−0.199341	+	0.176601i
$691$	9.97904	+	34.4516i	0.379621	+	1.31060i	0.892075	+	0.451888i	$0.149249\pi$
$691$	9.97904	+	34.4516i	0.379621	+	1.31060i	−0.512454	+	0.858715i	$0.671264\pi$
$692$	0.599105	+	0.200011i	0.0227746	+	0.00760326i
$693$	−16.2568	+	16.9251i	−0.617545	+	0.642932i
$694$	−6.75199	−	17.8035i	−0.256302	−	0.675813i
$695$	−10.1292	+	17.5444i	−0.384224	+	0.665495i
$696$	−9.87728	−	12.0975i	−0.374397	−	0.458553i
$697$	47.9637	−	11.8220i	1.81676	−	0.447790i
$698$	−8.88473	+	15.3888i	−0.336292	+	0.582475i
$699$	−2.11653	−	3.66594i	−0.0800545	−	0.138658i
$700$	1.21432	+	1.26424i	0.0458971	+	0.0477840i
$701$	−4.40048	−	36.2412i	−0.166204	−	1.36881i	−0.802171	−	0.597095i	$-0.796322\pi$
$701$	−4.40048	−	36.2412i	−0.166204	−	1.36881i	0.635967	−	0.771716i	$-0.280602\pi$
$702$	−2.31376	−	4.86112i	−0.0873274	−	0.183471i
$703$	−5.60468	+	46.1587i	−0.211385	+	1.74091i
$704$	−24.6508	+	18.5239i	−0.929062	+	0.698145i
$705$	11.3340	+	0.914976i	0.426863	+	0.0344600i
$706$	2.27532	+	11.1453i	0.0856329	+	0.419458i
$707$	−0.530353	+	4.36785i	−0.0199460	+	0.164270i
$708$	0.403617	+	0.171965i	0.0151688	+	0.00646284i
$709$	−36.1344	+	22.8500i	−1.35706	+	0.858151i	−0.997194	−	0.0748544i	$-0.976151\pi$
$709$	−36.1344	+	22.8500i	−1.35706	+	0.858151i	−0.359863	+	0.933005i	$0.617176\pi$
$710$	−21.6777	+	19.2048i	−0.813550	+	0.720742i
$711$	0.688411	−	0.0555743i	0.0258174	−	0.00208420i
$712$	10.8059	+	37.3062i	0.404967	+	1.39811i
$713$	−9.42294	+	4.01474i	−0.352892	+	0.150353i
$714$	31.5510	−	45.7095i	1.18077	−	1.71063i
$715$	20.4803	−	35.5712i	0.765921	−	1.33029i
$716$	−1.32923	−	1.92572i	−0.0496755	−	0.0719674i
$717$	19.3999	+	12.2677i	0.724501	+	0.458147i
$718$	33.3718	−	5.42345i	1.24543	−	0.202401i
$719$	−19.1474	−	8.15795i	−0.714078	−	0.304240i	0.00420531	−	0.999991i	$-0.498661\pi$
$719$	−19.1474	−	8.15795i	−0.714078	−	0.304240i	−0.718283	+	0.695751i	$0.755072\pi$
$720$	6.36096	−	9.21545i	0.237059	−	0.343439i
$721$	8.53000	−	29.4490i	0.317674	−	1.09674i
$722$	−0.590137	−	1.24369i	−0.0219626	−	0.0462853i
$723$	1.74874	−	4.61104i	0.0650362	−	0.171486i
$724$	−0.662952	−	0.811969i	−0.0246384	−	0.0301766i
$725$	0.346778	+	8.60522i	0.0128790	+	0.319590i
$726$	−0.545217	−	13.5294i	−0.0202349	−	0.502124i
$727$	20.6099	−	5.07989i	0.764380	−	0.188403i	0.162195	−	0.986759i	$-0.448143\pi$
$727$	20.6099	−	5.07989i	0.764380	−	0.188403i	0.602186	+	0.798356i	$0.294297\pi$
$728$	−17.6505	+	46.7090i	−0.654171	+	1.73115i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−4.19071	+	20.5275i	−0.155105	+	0.759755i
$731$	0.437074	−	0.186220i	0.0161658	−	0.00688759i
$732$	−0.540037	+	0.341498i	−0.0199603	+	0.0126221i
$733$	4.90737	−	2.57559i	0.181258	−	0.0951314i	−0.371654	−	0.928371i	$-0.621209\pi$
$733$	4.90737	−	2.57559i	0.181258	−	0.0951314i	0.552911	+	0.833240i	$0.313517\pi$
$734$	−23.9259	−	3.88834i	−0.883123	−	0.143521i
$735$	−49.2777	+	16.4513i	−1.81764	+	0.606816i
$736$	0.287181	+	2.36515i	0.0105856	+	0.0871805i
$737$	−8.30134	+	28.6596i	−0.305784	+	1.05569i
$738$	2.07790	−	10.1782i	0.0764887	−	0.374666i
$739$	−13.5764	−	4.53246i	−0.499414	−	0.166729i	0.0557907	−	0.998442i	$-0.482232\pi$
$739$	−13.5764	−	4.53246i	−0.499414	−	0.166729i	−0.555205	+	0.831713i	$0.687360\pi$
$740$	5.64840	+	2.96451i	0.207639	+	0.108978i
$741$	−6.55536	+	13.8579i	−0.240817	+	0.509084i
$742$	5.41002	−	2.83940i	0.198608	−	0.104238i
$743$	12.4710	−	2.02673i	0.457516	−	0.0743536i	0.0727142	−	0.997353i	$-0.476834\pi$
$743$	12.4710	−	2.02673i	0.457516	−	0.0743536i	0.384802	+	0.922999i	$0.374270\pi$
$744$	11.7413	−	8.82300i	0.430456	−	0.323467i
$745$	0.725136	−	17.9941i	0.0265669	−	0.659251i
$746$	41.3541			1.51408
$747$	−0.192447	+	4.77552i	−0.00704126	+	0.174727i
$748$	1.46046	+	7.15380i	0.0533997	+	0.261569i
$749$	45.0341	+	65.2432i	1.64551	+	2.38393i
$750$	12.7491	−	4.25626i	0.465530	−	0.155417i
$751$	−5.64809	+	11.9031i	−0.206102	+	0.434350i	−0.980010	−	0.198947i	$-0.936248\pi$
$751$	−5.64809	+	11.9031i	−0.206102	+	0.434350i	0.773908	+	0.633297i	$0.218299\pi$
$752$	12.4698	−	15.2727i	0.454726	−	0.556938i
$753$	6.54834	+	17.2666i	0.238635	+	0.629228i
$754$	28.1445	−	14.8144i	1.02496	−	0.539508i
$755$	1.76644	−	4.65771i	0.0642872	−	0.169511i
$756$	−0.601244	−	1.04138i	−0.0218670	−	0.0378748i
$757$	−5.67422	+	6.94966i	−0.206233	+	0.252590i	−0.867356	−	0.497688i	$-0.834183\pi$
$757$	−5.67422	+	6.94966i	−0.206233	+	0.252590i	0.661123	+	0.750277i	$0.270080\pi$
$758$	1.12368	+	0.844393i	0.0408140	+	0.0306697i
$759$	7.31300	+	3.83816i	0.265445	+	0.139316i
$760$	−28.4709	+	2.29841i	−1.03275	+	0.0833720i
$761$	18.9783	−	1.53209i	0.687962	−	0.0555381i	0.268458	−	0.963291i	$-0.413486\pi$
$761$	18.9783	−	1.53209i	0.687962	−	0.0555381i	0.419504	+	0.907753i	$0.362204\pi$
$762$	−15.9492	−	8.37081i	−0.577780	−	0.303242i
$763$	−19.9068	−	14.9590i	−0.720676	−	0.541553i
$764$	−0.991213	+	1.21402i	−0.0358608	+	0.0439215i
$765$	9.02193	+	15.6264i	0.326189	+	0.564975i
$766$	9.48406	−	25.0074i	0.342673	−	0.903554i
$767$	3.90792	−	5.67612i	0.141107	−	0.204953i
$768$	−1.92877	−	5.08574i	−0.0695984	−	0.183516i
$769$	32.2545	−	39.5047i	1.16313	−	1.42457i	0.277163	−	0.960823i	$-0.410606\pi$
$769$	32.2545	−	39.5047i	1.16313	−	1.42457i	0.885965	−	0.463751i	$-0.153497\pi$
$770$	38.1742	−	80.4504i	1.37570	−	2.89923i
$771$	22.4377	−	7.49082i	0.808075	−	0.269775i
$772$	1.52584	+	2.21056i	0.0549162	+	0.0795598i
$773$	5.74090	+	28.1208i	0.206486	+	1.01144i	0.942433	+	0.334396i	$0.108532\pi$
$773$	5.74090	+	28.1208i	0.206486	+	1.01144i	−0.735947	+	0.677039i	$0.763263\pi$
$774$	0.00402286	−	0.0998262i	0.000144599	−	0.00358818i
$775$	−8.09894			−0.290922
$776$	0.964426	−	23.9320i	0.0346209	−	0.859108i
$777$	−45.7997	+	34.4163i	−1.64306	+	1.23468i
$778$	18.6354	−	3.02856i	0.668113	−	0.108579i
$779$	−26.1924	+	13.7468i	−0.938439	+	0.492531i
$780$	1.45873	+	1.51507i	0.0522309	+	0.0542481i
$781$	30.2753	+	15.8897i	1.08333	+	0.568577i
$782$	−18.5406	−	6.18976i	−0.663010	−	0.221345i
$783$	1.18170	−	5.78834i	0.0422304	−	0.206858i
$784$	−25.0624	+	86.5254i	−0.895086	+	3.09019i
$785$	−5.53570	−	45.5906i	−0.197578	−	1.62720i
$786$	−1.49750	+	0.499941i	−0.0534142	+	0.0178323i
$787$	−35.8175	−	5.82091i	−1.27676	−	0.207493i	−0.516033	−	0.856569i	$-0.672592\pi$
$787$	−35.8175	−	5.82091i	−1.27676	−	0.207493i	−0.760724	+	0.649076i	$0.775156\pi$
$788$	−2.97573	+	1.56178i	−0.106006	+	0.0556363i
$789$	−11.9146	+	7.53431i	−0.424170	+	0.268229i
$790$	−2.41094	+	1.02721i	−0.0857774	+	0.0365463i
$791$	−5.37993	+	26.3527i	−0.191288	+	0.936993i
$792$	−11.4985	−	2.83413i	−0.408582	−	0.100706i
$793$	3.57020	+	9.37997i	0.126781	+	0.333092i
$794$	−16.2421	+	4.00333i	−0.576412	+	0.142073i
$795$	0.0799253	+	1.98333i	0.00283466	+	0.0703413i
$796$	−0.182181	−	4.52077i	−0.00645723	−	0.160234i
$797$	11.2123	+	13.7326i	0.397160	+	0.486432i	0.934011	−	0.357245i	$-0.116284\pi$
$797$	11.2123	+	13.7326i	0.397160	+	0.486432i	−0.536851	+	0.843677i	$0.680386\pi$
$798$	−11.7936	+	31.0973i	−0.417491	+	1.10083i
$799$	13.6203	+	28.7041i	0.481851	+	1.01548i
$800$	−0.524132	+	1.80951i	−0.0185309	+	0.0639760i
$801$	−8.34602	+	12.0913i	−0.294892	+	0.427225i
$802$	−35.8766	−	15.2856i	−1.26685	−	0.539753i
$803$	24.4144	−	3.96773i	0.861566	−	0.140018i
$804$	−1.29218	−	0.817128i	−0.0455718	−	0.0288179i
$805$	13.9423	+	20.1988i	0.491400	+	0.711916i
$806$	12.8545	+	27.0067i	0.452779	+	0.951270i
$807$	3.84669	−	5.57289i	0.135410	−	0.196175i
$808$	−2.04267	+	0.870300i	−0.0718608	+	0.0306170i
$809$	−14.3172	−	49.4288i	−0.503367	−	1.73782i	−0.661057	−	0.750336i	$-0.729892\pi$
$809$	−14.3172	−	49.4288i	−0.503367	−	1.73782i	0.157690	−	0.987489i	$-0.449595\pi$
$810$	3.78215	−	0.305327i	0.132891	−	0.0107281i
$811$	12.6040	−	11.1662i	0.442587	−	0.392098i	−0.412186	−	0.911100i	$-0.635235\pi$
$811$	12.6040	−	11.1662i	0.442587	−	0.392098i	0.854773	+	0.519002i	$0.173696\pi$
$812$	6.00420	−	3.79683i	0.210706	−	0.133243i
$813$	28.0573	+	11.9541i	0.984011	+	0.419248i
$814$	8.81734	−	72.6173i	0.309048	−	2.54524i
$815$	4.32252	+	21.1731i	0.151411	+	0.741661i
$816$	31.1861	+	2.51760i	1.09173	+	0.0881336i
$817$	−0.227433	+	0.170904i	−0.00795686	+	0.00597919i
$818$	1.41109	−	11.6214i	0.0493376	−	0.406332i
$819$	−17.9090	+	6.00274i	−0.625791	+	0.209753i
$820$	0.489163	+	4.02862i	0.0170823	+	0.140686i
$821$	−7.06491	−	7.35535i	−0.246567	−	0.256704i	0.586406	−	0.810018i	$-0.300542\pi$
$821$	−7.06491	−	7.35535i	−0.246567	−	0.256704i	−0.832973	+	0.553314i	$0.813363\pi$
$822$	−4.85892	−	8.41589i	−0.169474	−	0.293538i
$823$	14.7029	−	25.4662i	0.512510	−	0.887694i	−0.487384	−	0.873188i	$-0.662049\pi$
$823$	14.7029	−	25.4662i	0.512510	−	0.887694i	0.999895	−	0.0145066i	$-0.00461777\pi$
$824$	15.0221	−	3.70263i	0.523321	−	0.128987i
$825$	4.13020	+	5.05858i	0.143795	+	0.176117i
$826$	7.47528	−	12.9476i	0.260098	−	0.450503i
$827$	−8.62814	−	22.7505i	−0.300030	−	0.791114i	−0.997240	−	0.0742470i	$-0.976345\pi$
$827$	−8.62814	−	22.7505i	−0.300030	−	0.791114i	0.697210	−	0.716867i	$-0.254425\pi$
$828$	−0.293154	+	0.305205i	−0.0101878	+	0.0106066i
$829$	7.38047	+	2.46396i	0.256334	+	0.0855770i	0.441931	−	0.897049i	$-0.354294\pi$
$829$	7.38047	+	2.46396i	0.256334	+	0.0855770i	−0.185597	+	0.982626i	$0.559422\pi$
$830$	−5.04553	−	17.4192i	−0.175133	−	0.604629i
$831$	7.40018	−	6.55599i	0.256709	−	0.227425i
$832$	−24.4915	+	4.01034i	−0.849089	+	0.139034i
$833$	−108.653	−	96.2579i	−3.76459	−	3.33514i
$834$	−5.10292	+	10.7542i	−0.176700	+	0.372387i
$835$	10.2447	+	10.6659i	0.354534	+	0.369109i
$836$	−1.87429	−	3.94999i	−0.0648238	−	0.136613i
$837$	5.39421	+	1.32955i	0.186451	+	0.0459561i
$838$	12.9799	−	13.5135i	0.448384	−	0.466818i
$839$	−13.4994	−	10.1442i	−0.466053	−	0.350216i	0.341629	−	0.939835i	$-0.389021\pi$
$839$	−13.4994	−	10.1442i	−0.466053	−	0.350216i	−0.807681	+	0.589619i	$0.799278\pi$
$840$	−26.3423	−	23.3372i	−0.908894	−	0.805210i
$841$	5.82484	+	0.946629i	0.200857	+	0.0326424i
$842$	22.9080	+	14.4862i	0.789463	+	0.499226i
$843$	7.42800	+	0.599650i	0.255834	+	0.0206531i
$844$	1.59091			0.0547614
$845$	27.8792	−	17.7233i	0.959074	−	0.609700i
$846$	6.68129			0.229707
$847$	−47.3514	−	3.82260i	−1.62701	−	0.131346i
$848$	2.90899	+	1.83953i	0.0998951	+	0.0631699i
$849$	23.6470	+	3.84301i	0.811562	+	0.131892i
$850$	−11.5688	−	10.2490i	−0.396805	−	0.351539i
$851$	16.1182	+	12.1121i	0.552525	+	0.415196i
$852$	−1.21363	+	1.26353i	−0.0415784	+	0.0432877i
$853$	3.27298	+	0.806718i	0.112065	+	0.0276215i	0.294949	−	0.955513i	$-0.404697\pi$
$853$	3.27298	+	0.806718i	0.112065	+	0.0276215i	−0.182884	+	0.983134i	$0.558543\pi$
$854$	9.33429	+	19.6716i	0.319413	+	0.673148i
$855$	−7.48477	−	7.79247i	−0.255974	−	0.266497i
$856$	−17.1500	+	36.1428i	−0.586174	+	1.23534i
$857$	−29.1646	−	25.8376i	−0.996245	−	0.882596i	−0.00316015	−	0.999995i	$-0.501006\pi$
$857$	−29.1646	−	25.8376i	−0.996245	−	0.882596i	−0.993085	+	0.117399i	$0.962544\pi$
$858$	10.3130	−	21.8014i	0.352079	−	0.744288i
$859$	4.33327	−	3.83894i	0.147849	−	0.130983i	−0.585956	−	0.810343i	$-0.699281\pi$
$859$	4.33327	−	3.83894i	0.147849	−	0.130983i	0.733805	+	0.679360i	$0.237742\pi$
$860$	0.0108587	+	0.0374884i	0.000370277	+	0.00127835i
$861$	−34.5705	−	11.5413i	−1.17816	−	0.393327i
$862$	−25.5005	+	26.5488i	−0.868550	+	0.904256i
$863$	9.93214	+	26.1889i	0.338094	+	0.891481i	0.990978	+	0.134023i	$0.0427896\pi$
$863$	9.93214	+	26.1889i	0.338094	+	0.891481i	−0.652884	+	0.757458i	$0.726441\pi$
$864$	0.646149	−	1.11916i	0.0219824	−	0.0380747i
$865$	4.42235	+	5.41639i	0.150364	+	0.184163i
$866$	12.7960	−	3.15394i	0.434827	−	0.107175i
$867$	−16.7084	+	28.9398i	−0.567447	+	0.982848i
$868$	3.34030	+	5.78556i	0.113377	+	0.196375i
$869$	2.14326	+	2.23137i	0.0727050	+	0.0756939i
$870$	2.70202	+	22.2532i	0.0916072	+	0.754453i
$871$	−16.6150	+	17.3395i	−0.562977	+	0.587527i
$872$	1.51464	−	12.4741i	0.0512920	−	0.422428i
$873$	7.24311	−	5.44284i	0.245142	−	0.184212i
$874$	11.6667	+	0.941831i	0.394631	+	0.0318579i
$875$	−9.43240	−	46.2029i	−0.318873	−	1.56194i
$876$	−0.152768	+	1.25816i	−0.00516155	+	0.0425092i
$877$	20.3691	+	8.67848i	0.687817	+	0.293051i	0.707458	−	0.706756i	$-0.249842\pi$
$877$	20.3691	+	8.67848i	0.687817	+	0.293051i	−0.0196406	+	0.999807i	$0.506252\pi$
$878$	−2.91882	+	1.84575i	−0.0985054	+	0.0622911i
$879$	−13.4913	+	11.9522i	−0.455049	+	0.403139i
$880$	49.9999	−	4.03641i	1.68550	−	0.136067i
$881$	13.3697	+	46.1575i	0.450436	+	1.55509i	0.789152	+	0.614198i	$0.210520\pi$
$881$	13.3697	+	46.1575i	0.450436	+	1.55509i	−0.338716	+	0.940889i	$0.609993\pi$
$882$	−28.0828	+	11.9650i	−0.945598	+	0.402882i
$883$	−8.59201	+	12.4477i	−0.289144	+	0.418898i	−0.940458	−	0.339911i	$-0.889603\pi$
$883$	−8.59201	+	12.4477i	−0.289144	+	0.418898i	0.651313	+	0.758809i	$0.274218\pi$
$884$	−1.62819	+	5.64646i	−0.0547621	+	0.189911i
$885$	2.75911	+	3.99727i	0.0927466	+	0.134367i
$886$	9.58271	+	6.05974i	0.321937	+	0.203581i
$887$	51.5684	−	8.38068i	1.73150	−	0.281396i	0.788703	−	0.614774i	$-0.210753\pi$
$887$	51.5684	−	8.38068i	1.73150	−	0.281396i	0.942793	+	0.333378i	$0.108189\pi$
$888$	−26.5967	−	11.3318i	−0.892526	−	0.380270i
$889$	−35.8990	+	52.0087i	−1.20401	+	1.74432i
$890$	15.5101	−	53.5472i	0.519901	−	1.79491i
$891$	−1.92044	−	4.04724i	−0.0643372	−	0.135588i
$892$	0.810678	−	2.13758i	0.0271435	−	0.0715715i
$893$	−12.0324	−	14.7370i	−0.402648	−	0.493154i
$894$	−0.426074	−	10.5729i	−0.0142500	−	0.353611i
$895$	−1.04309	−	25.8839i	−0.0348665	−	0.865203i
$896$	−65.4232	+	16.1254i	−2.18564	+	0.538711i
$897$	3.78264	+	5.46610i	0.126299	+	0.182508i
$898$	−6.94153	−	1.71093i	−0.231642	−	0.0570946i
$899$	−6.56509	+	32.1580i	−0.218958	+	1.07253i
$900$	−0.307845	+	0.131161i	−0.0102615	+	0.00437202i
$901$	−4.68756	+	2.96423i	−0.156165	+	0.0987529i
$902$	41.2061	−	21.6266i	1.37201	−	0.720088i
$903$	−0.345978	−	0.0562268i	−0.0115134	−	0.00187111i
$904$	−12.8742	+	4.29803i	−0.428188	+	0.142950i
$905$	−1.39881	−	11.5203i	−0.0464981	−	0.382946i
$906$	0.814336	−	2.81141i	0.0270545	−	0.0934030i
$907$	5.33919	−	26.1531i	0.177285	−	0.868398i	−0.789686	−	0.613511i	$-0.789757\pi$
$907$	5.33919	−	26.1531i	0.177285	−	0.868398i	0.966971	−	0.254887i	$-0.0820383\pi$
$908$	−2.36068	−	0.788111i	−0.0783419	−	0.0261544i
$909$	−0.743692	−	0.390320i	−0.0246667	−	0.0129461i
$910$	57.2450	−	43.1241i	1.89765	−	1.42955i
$911$	37.3763	−	19.6166i	1.23833	−	0.649927i	0.286952	−	0.957945i	$-0.407358\pi$
$911$	37.3763	−	19.6166i	1.23833	−	0.649927i	0.951381	+	0.308018i	$0.0996656\pi$
$912$	−18.4926	+	3.00534i	−0.612352	+	0.0995169i
$913$	−17.1165	+	12.8622i	−0.566474	+	0.425677i
$914$	−0.00688722	+	0.170905i	−0.000227809	+	0.00565302i
$915$	−7.07375			−0.233851
$916$	−0.260518	+	6.46469i	−0.00860776	+	0.213599i
$917$	1.10793	+	5.42699i	0.0365870	+	0.179215i
$918$	6.02273	+	8.72543i	0.198780	+	0.287982i
$919$	−54.7124	+	18.2657i	−1.80480	+	0.602530i	−0.804838	+	0.593495i	$0.797748\pi$
$919$	−54.7124	+	18.2657i	−1.80480	+	0.602530i	−0.999959	+	0.00903464i	$0.997124\pi$
$920$	−5.30952	+	11.1896i	−0.175050	+	0.368909i
$921$	−4.99956	+	6.12334i	−0.164741	+	0.201771i
$922$	3.85303	+	10.1596i	0.126893	+	0.334589i
$923$	15.6598	+	22.6292i	0.515450	+	0.744850i
$924$	1.91021	−	5.03680i	0.0628411	−	0.165698i
$925$	7.97112	+	13.8064i	0.262089	+	0.453951i
$926$	−33.3384	+	40.8322i	−1.09557	+	1.34183i
$927$	4.67878	+	3.51587i	0.153671	+	0.115476i
$928$	6.76006	+	3.54795i	0.221910	+	0.116467i
$929$	37.3667	−	3.01655i	1.22596	−	0.0989699i	0.549530	−	0.835474i	$-0.314807\pi$
$929$	37.3667	−	3.01655i	1.22596	−	0.0989699i	0.676433	+	0.736504i	$0.263525\pi$
$930$	−21.0123	+	1.69629i	−0.689020	+	0.0556235i
$931$	76.9658	+	40.3948i	2.52245	+	1.32389i
$932$	0.776788	+	0.583718i	0.0254445	+	0.0191203i
$933$	10.3550	−	12.6826i	0.339009	−	0.415210i
$934$	31.9412	+	55.3238i	1.04515	+	1.81025i
$935$	−28.6635	+	75.5794i	−0.937397	+	2.47171i
$936$	−7.14205	−	6.31207i	−0.233445	−	0.206316i
$937$	−2.90594	−	7.66233i	−0.0949329	−	0.250317i	0.879135	−	0.476572i	$-0.158121\pi$
$937$	−2.90594	−	7.66233i	−0.0949329	−	0.250317i	−0.974068	+	0.226255i	$0.927352\pi$
$938$	−32.9503	+	40.3568i	−1.07587	+	1.31770i
$939$	−0.578914	+	1.22004i	−0.0188921	+	0.0398143i
$940$	−2.47576	+	0.826531i	−0.0807505	+	0.0269585i
$941$	13.4421	+	19.4743i	0.438200	+	0.634843i	0.978406	−	0.206690i	$-0.0662692\pi$
$941$	13.4421	+	19.4743i	0.438200	+	0.634843i	−0.540206	+	0.841533i	$0.681654\pi$
$942$	−5.39766	−	26.4395i	−0.175865	−	0.861445i
$943$	−0.516468	+	12.8160i	−0.0168185	+	0.417347i
$944$	8.42196			0.274112
$945$	0.536043	−	13.3018i	0.0174375	−	0.432706i
$946$	0.357799	−	0.268869i	0.0116331	−	0.00874167i
$947$	47.8587	−	7.77780i	1.55520	−	0.252744i	0.678797	−	0.734326i	$-0.262501\pi$
$947$	47.8587	−	7.77780i	1.55520	−	0.252744i	0.876401	+	0.481581i	$0.159937\pi$
$948$	−0.140374	+	0.0736739i	−0.00455913	+	0.00239282i
$949$	18.8908	+	6.28157i	0.613223	+	0.203908i
$950$	8.19491	+	4.30102i	0.265878	+	0.139544i
$951$	−0.935519	−	0.312322i	−0.0303363	−	0.0101277i
$952$	19.6692	−	96.3461i	0.637482	−	3.12260i
$953$	0.447773	−	1.54589i	0.0145048	−	0.0500763i	−0.952939	−	0.303161i	$-0.901958\pi$
$953$	0.447773	−	1.54589i	0.0145048	−	0.0500763i	0.967444	+	0.253085i	$0.0814452\pi$
$954$	0.140583	+	1.15780i	0.00455153	+	0.0374852i
$955$	−16.4581	+	5.49451i	−0.532571	+	0.177798i
$956$	−5.20049	−	0.845162i	−0.168196	−	0.0273345i
$957$	23.4338	−	12.2990i	0.757507	−	0.397570i
$958$	−20.5955	+	13.0238i	−0.665410	+	0.420780i
$959$	−31.3660	+	13.3638i	−1.01286	+	0.431540i
$960$	3.49878	−	17.1381i	0.112923	−	0.553131i
$961$	0.130889	+	0.0322613i	0.00422223	+	0.00104069i
$962$	33.3871	−	48.4936i	1.07644	−	1.56350i
$963$	−14.6932	+	3.62156i	−0.473483	+	0.116703i
$964$	0.0455804	+	1.13107i	0.00146805	+	0.0364292i
$965$	1.19737	+	29.7125i	0.0385448	+	0.956480i
$966$	9.12062	+	11.1707i	0.293451	+	0.359412i
$967$	21.4604	−	56.5863i	0.690118	−	1.81969i	0.129572	−	0.991570i	$-0.458640\pi$
$967$	21.4604	−	56.5863i	0.690118	−	1.81969i	0.560547	−	0.828123i	$-0.310591\pi$
$968$	−10.2769	−	21.6582i	−0.330313	−	0.696120i
$969$	8.39940	−	28.9981i	0.269828	−	0.931553i
$970$	−19.5292	+	28.2930i	−0.627045	+	0.908432i
$971$	−29.2934	−	12.4808i	−0.940072	−	0.400527i	−0.133090	−	0.991104i	$-0.542490\pi$
$971$	−29.2934	−	12.4808i	−0.940072	−	0.400527i	−0.806981	+	0.590577i	$0.798900\pi$
$972$	0.226569	−	0.0368210i	0.00726720	−	0.00118103i
$973$	35.2971	+	22.3205i	1.13157	+	0.715563i
$974$	3.10003	+	4.49117i	0.0993314	+	0.143906i
$975$	1.05752	+	5.14863i	0.0338678	+	0.164888i
$976$	−6.96769	+	10.0944i	−0.223030	+	0.323115i
$977$	31.3432	−	13.3541i	1.00276	−	0.427235i	0.172737	−	0.984968i	$-0.444739\pi$
$977$	31.3432	−	13.3541i	1.00276	−	0.427235i	0.830020	+	0.557733i	$0.188329\pi$
$978$	3.53266	+	12.1961i	0.112962	+	0.389990i
$979$	−65.6034	+	5.29605i	−2.09669	+	0.169263i
$980$	8.92597	−	7.90772i	0.285130	−	0.252603i
$981$	4.01744	−	2.54048i	0.128267	−	0.0811112i
$982$	38.8033	+	16.5325i	1.23826	+	0.527575i
$983$	−1.58779	+	13.0766i	−0.0506427	+	0.417080i	0.945236	+	0.326387i	$0.105831\pi$
$983$	−1.58779	+	13.0766i	−0.0506427	+	0.417080i	−0.995879	+	0.0906929i	$0.971092\pi$
$984$	−3.67884	−	18.0202i	−0.117277	−	0.574462i
$985$	−37.0849	−	2.99380i	−1.18162	−	0.0953905i
$986$	−50.0730	+	37.6274i	−1.59465	+	1.19830i
$987$	2.82547	−	23.2699i	0.0899358	−	0.740688i
$988$	0.137484	−	3.51623i	0.00437396	−	0.111866i
$989$	0.0148690	+	0.122457i	0.000472807	+	0.00389392i
$990$	11.7751	+	12.2592i	0.374238	+	0.389623i
$991$	−14.5050	−	25.1234i	−0.460766	−	0.798070i	0.538234	−	0.842796i	$-0.319092\pi$
$991$	−14.5050	−	25.1234i	−0.460766	−	0.798070i	−0.998999	+	0.0447260i	$0.985759\pi$
$992$	−3.58978	+	6.21767i	−0.113975	+	0.197411i
$993$	−26.2082	+	6.45975i	−0.831694	+	0.204994i
$994$	37.7586	+	46.2459i	1.19763	+	1.46683i
$995$	25.0447	−	43.3787i	0.793970	−	1.37520i
$996$	−0.389026	−	1.02578i	−0.0123268	−	0.0325030i
$997$	37.6520	−	39.1998i	1.19245	−	1.24147i	0.229046	−	0.973416i	$-0.426439\pi$
$997$	37.6520	−	39.1998i	1.19245	−	1.24147i	0.963403	−	0.268056i	$-0.0863812\pi$
$998$	23.7395	+	7.92540i	0.751459	+	0.250874i
$999$	−3.04257	−	10.5042i	−0.0962626	−	0.332337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.16.5	✓	384
169.74	even	39	inner	507.2.q.b.412.5	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.16.5	✓	384	1.1	even	1	trivial
507.2.q.b.412.5	yes	384	169.74	even	39	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48832 - 0.120150i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(0.226569 + 0.0368210i) q^{4} +(1.90213 + 1.68514i) q^{5} +(1.19370 + 0.897007i) q^{6} +(3.62894 - 3.77813i) q^{7} +(2.56677 + 0.632652i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-2.62851 - 2.73657i) q^{10} +(-1.92044 + 4.04724i) q^{11} +(-0.171814 - 0.152214i) q^{12} +(-2.87984 + 2.16945i) q^{13} +(-5.85498 + 5.18706i) q^{14} +(-0.707011 - 2.44089i) q^{15} +(-4.17962 - 1.39536i) q^{16} +(4.91868 - 5.12088i) q^{17} +(-0.529484 - 1.39613i) q^{18} +(-2.12592 + 3.68219i) q^{19} +(0.368914 + 0.451838i) q^{20} +(-5.08643 + 1.25369i) q^{21} +(3.34451 - 5.79286i) q^{22} +(0.921815 + 1.59663i) q^{23} +(-1.83128 - 1.90656i) q^{24} +(0.175717 + 1.44716i) q^{25} +(4.54679 - 2.88284i) q^{26} +(0.120537 - 0.992709i) q^{27} +(0.961320 - 0.722385i) q^{28} +(5.88857 + 0.475375i) q^{29} +(0.758989 + 3.71777i) q^{30} +(-0.669659 + 5.51514i) q^{31} +(1.18889 + 0.506538i) q^{32} +(3.78625 - 2.39428i) q^{33} +(-7.93585 + 7.03055i) q^{34} +(13.2694 - 1.07122i) q^{35} +(0.0638624 + 0.220479i) q^{36} +(10.0608 - 4.28652i) q^{37} +(3.60646 - 5.22487i) q^{38} +(3.59351 - 0.294427i) q^{39} +(3.81622 + 5.52875i) q^{40} +(5.88012 + 3.71836i) q^{41} +(7.72088 - 1.25476i) q^{42} +(0.0615556 + 0.0262264i) q^{43} +(-0.584135 + 0.846266i) q^{44} +(-0.707011 + 2.44089i) q^{45} +(-1.18012 - 2.48706i) q^{46} +(-1.58671 + 4.18381i) q^{47} +(2.78680 + 3.41321i) q^{48} +(-0.823176 - 20.4269i) q^{49} +(-0.0876474 - 2.17495i) q^{50} +(-6.89415 + 1.69926i) q^{51} +(-0.732363 + 0.385492i) q^{52} +(-0.758399 - 0.186929i) q^{53} +(-0.298671 + 1.46299i) q^{54} +(-10.4731 + 4.46217i) q^{55} +(11.7049 - 7.40173i) q^{56} +(3.76481 - 1.97592i) q^{57} +(-8.70698 - 1.41502i) q^{58} +(-1.81294 + 0.605249i) q^{59} +(-0.0703108 - 0.579061i) q^{60} +(0.774448 - 2.67370i) q^{61} +(1.65931 - 8.12785i) q^{62} +(4.96905 + 1.65891i) q^{63} +(6.09475 + 3.19877i) q^{64} +(-9.13365 - 0.726344i) q^{65} +(-5.92284 + 3.10854i) q^{66} +(6.57428 - 1.06842i) q^{67} +(1.30297 - 0.979122i) q^{68} +(0.0742355 - 1.84214i) q^{69} -19.8778 q^{70} +(0.307329 - 7.62629i) q^{71} +(0.528785 + 2.59016i) q^{72} +(-3.13654 - 4.54406i) q^{73} +(-15.4888 + 5.17092i) q^{74} +(0.624942 - 1.31704i) q^{75} +(-0.617248 + 0.755992i) q^{76} +(8.32184 + 21.9429i) q^{77} +(-5.38368 + 0.00644285i) q^{78} +(0.244908 - 0.645770i) q^{79} +(-5.59880 - 9.69741i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-8.30476 - 6.24062i) q^{82} +(4.23194 + 2.22110i) q^{83} +(-1.19859 + 0.0967600i) q^{84} +(17.9854 - 1.45193i) q^{85} +(-0.0884635 - 0.0464292i) q^{86} +(-4.72289 - 3.54902i) q^{87} +(-7.48982 + 9.17337i) q^{88} +(7.34601 + 12.7237i) q^{89} +(1.34553 - 3.54788i) q^{90} +(-2.25428 + 18.7532i) q^{91} +(0.150065 + 0.395689i) q^{92} +(3.51364 - 4.30343i) q^{93} +(2.86422 - 6.03621i) q^{94} +(-10.2488 + 3.42154i) q^{95} +(-0.734109 - 1.06354i) q^{96} +(-1.81227 - 8.87709i) q^{97} +(-1.22914 + 30.5007i) q^{98} -4.47976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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