LMFDB - Embedded newform 507.2.q.b.412.5

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			412.5
Character	$\chi$	$=$	507.412
Dual form			507.2.q.b.16.5

$q$-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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{38}{39}\right)$

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	−0.594542	−	0.804065i	$-0.702667\pi$
$2$	−1.48832	+	0.120150i	−1.05240	+	0.0849588i	−0.457862	+	0.889024i	$0.651384\pi$
$3$	−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	−0.120333	−	0.992734i	$-0.538396\pi$
$5$	1.90213	−	1.68514i	0.850658	−	0.753617i	0.970991	+	0.239117i	$0.0768578\pi$
$6$	1.19370	−	0.897007i	0.487326	−	0.366202i
$7$	3.62894	+	3.77813i	1.37161	+	1.42800i	0.787481	+	0.616339i	$0.211385\pi$
$7$	3.62894	+	3.77813i	1.37161	+	1.42800i	0.584130	+	0.811660i	$0.301436\pi$
$8$	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	−0.955810	−	0.293985i	$-0.905018\pi$
$11$	−1.92044	−	4.04724i	−0.579035	−	1.22029i	0.376775	−	0.926305i	$-0.377033\pi$
$12$	−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	0.963211	+	0.268745i	$0.0866090\pi$
$17$	4.91868	+	5.12088i	1.19295	+	1.24200i	0.229743	+	0.973251i	$0.426211\pi$
$18$	−0.529484	+	1.39613i	−0.124800	+	0.329072i
$19$	−2.12592	−	3.68219i	−0.487718	−	0.844753i	0.512182	−	0.858877i	$-0.328837\pi$
$19$	−2.12592	−	3.68219i	−0.487718	−	0.844753i	−0.999900	+	0.0141239i	$0.995504\pi$
$20$	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	−0.753771	−	0.657137i	$-0.771767\pi$
$23$	0.921815	−	1.59663i	0.192212	−	0.332920i	0.945983	+	0.324216i	$0.105101\pi$
$24$	−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	0.479459	−	0.877564i	$-0.340833\pi$
$29$	5.88857	−	0.475375i	1.09348	−	0.0882749i	0.614021	+	0.789289i	$0.289551\pi$
$30$	0.758989	−	3.71777i	0.138572	−	0.678769i
$31$	−0.669659	−	5.51514i	−0.120274	−	0.990548i	−0.920471	−	0.390811i	$-0.872195\pi$
$31$	−0.669659	−	5.51514i	−0.120274	−	0.990548i	0.800197	−	0.599737i	$-0.204728\pi$
$32$	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	0.998714	−	0.0506898i	$-0.0161420\pi$
$37$	10.0608	+	4.28652i	1.65399	+	0.704700i	0.655276	+	0.755389i	$0.272552\pi$
$38$	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	0.0104429	−	0.999945i	$-0.496676\pi$
$41$	5.88012	−	3.71836i	0.918321	−	0.580711i	0.907878	+	0.419235i	$0.137702\pi$
$42$	7.72088	+	1.25476i	1.19136	+	0.193614i
$43$	0.0615556	−	0.0262264i	0.00938714	−	0.00399948i	−0.387268	−	0.921967i	$-0.626581\pi$
$43$	0.0615556	−	0.0262264i	0.00938714	−	0.00399948i	0.396655	+	0.917968i	$0.370171\pi$
$44$	−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	0.768103	−	0.640326i	$-0.221201\pi$
$47$	−1.58671	−	4.18381i	−0.231445	−	0.610271i	−0.999548	+	0.0300555i	$0.990432\pi$
$48$	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	−0.291058	−	0.956705i	$-0.594007\pi$
$53$	−0.758399	+	0.186929i	−0.104174	+	0.0256766i	0.186884	+	0.982382i	$0.440161\pi$
$54$	−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	0.196195	−	0.980565i	$-0.437141\pi$
$59$	−1.81294	−	0.605249i	−0.236025	−	0.0787967i	−0.432220	+	0.901768i	$0.642270\pi$
$60$	−0.0703108	+	0.579061i	−0.00907708	+	0.0747565i
$61$	0.774448	+	2.67370i	0.0991579	+	0.342333i	0.994723	−	0.102598i	$-0.0327155\pi$
$61$	0.774448	+	2.67370i	0.0991579	+	0.342333i	−0.895565	+	0.444931i	$0.853228\pi$
$62$	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	0.548123	−	0.836398i	$-0.315343\pi$
$67$	6.57428	+	1.06842i	0.803176	+	0.130529i	0.255054	+	0.966927i	$0.417907\pi$
$68$	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	0.909073	+	0.416638i	$0.136792\pi$
$71$	0.307329	+	7.62629i	0.0364733	+	0.905074i	−0.872599	+	0.488437i	$0.837567\pi$
$72$	0.528785	−	2.59016i	0.0623179	−	0.305253i
$73$	−3.13654	+	4.54406i	−0.367104	+	0.531842i	−0.962390	−	0.271672i	$-0.912423\pi$
$73$	−3.13654	+	4.54406i	−0.367104	+	0.531842i	0.595286	+	0.803514i	$0.297039\pi$
$74$	−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	0.948087	−	0.318010i	$-0.103014\pi$
$79$	0.244908	+	0.645770i	0.0275543	+	0.0726548i	−0.920533	+	0.390665i	$0.872245\pi$
$80$	−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	−0.216193	−	0.976351i	$-0.569364\pi$
$83$	4.23194	−	2.22110i	0.464516	−	0.243797i	0.680709	+	0.732554i	$0.261672\pi$
$84$	−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	−0.154029	−	0.988066i	$-0.549225\pi$
$89$	7.34601	−	12.7237i	0.778676	−	1.34871i	0.932705	−	0.360640i	$-0.117442\pi$
$90$	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	0.777990	+	0.628277i	$0.216239\pi$
$97$	−1.81227	+	8.87709i	−0.184008	+	0.901332i	−0.961998	+	0.273055i	$0.911966\pi$
$98$	−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	0.566812	−	0.823847i	$-0.308177\pi$
$101$	−0.671450	−	0.504562i	−0.0668118	−	0.0502058i	−0.633623	+	0.773642i	$0.718433\pi$
$102$	10.4649	+	1.70071i	1.03618	+	0.168395i
$103$	5.18217	+	2.71982i	0.510615	+	0.267991i	0.700294	−	0.713855i	$-0.253052\pi$
$103$	5.18217	+	2.71982i	0.510615	+	0.267991i	−0.189679	+	0.981846i	$0.560745\pi$
$104$	−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	−0.814398	−	0.580307i	$-0.802933\pi$
$107$	−3.02698	−	14.8271i	−0.292630	−	1.43339i	0.521768	−	0.853087i	$-0.325273\pi$
$108$	0.0638624	+	0.220479i	0.00614516	+	0.0212156i
$109$	−0.572947	+	4.71865i	−0.0548784	+	0.451964i	0.939206	+	0.343354i	$0.111563\pi$
$109$	−0.572947	+	4.71865i	−0.0548784	+	0.451964i	−0.994084	+	0.108610i	$0.965360\pi$
$110$	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	0.314541	−	0.949244i	$-0.398149\pi$
$113$	−4.33936	−	2.74405i	−0.408213	−	0.258138i	−0.722754	+	0.691106i	$0.757124\pi$
$114$	−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	−0.392789	−	0.919629i	$-0.628490\pi$
$127$	−11.9071	−	1.93509i	−1.05658	−	0.171711i	−0.663792	+	0.747918i	$0.731054\pi$
$128$	−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	0.795867	−	0.605471i	$-0.207015\pi$
$131$	−0.600626	−	0.870157i	−0.0524770	−	0.0760260i	−0.848344	+	0.529445i	$0.822400\pi$
$132$	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	−0.632284	−	0.774737i	$-0.717882\pi$
$137$	−5.98742	+	2.55100i	−0.511540	+	0.217947i	0.120744	+	0.992684i	$0.461472\pi$
$138$	−0.331819	−	2.73277i	−0.0282463	−	0.232629i
$139$	1.59460	−	7.81085i	0.135252	−	0.662507i	−0.854470	−	0.519501i	$-0.826118\pi$
$139$	1.59460	−	7.81085i	0.135252	−	0.662507i	0.989722	−	0.143007i	$-0.0456770\pi$
$140$	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	−0.924838	−	0.380362i	$-0.875800\pi$
$149$	−4.48190	+	5.48934i	−0.367172	+	0.449704i	0.557666	+	0.830065i	$0.311697\pi$
$150$	−1.08836	−	1.88509i	−0.0888640	−	0.153917i
$151$	−0.695114	+	1.83287i	−0.0565676	+	0.149156i	−0.960321	−	0.278897i	$-0.910031\pi$
$151$	−0.695114	+	1.83287i	−0.0565676	+	0.149156i	0.903753	+	0.428053i	$0.140800\pi$
$152$	−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	−0.999187	−	0.0403261i	$-0.987160\pi$
$157$	−13.5273	+	11.9841i	−1.07959	+	0.956436i	−0.0804065	+	0.996762i	$0.525622\pi$
$158$	−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	−0.300210	−	0.953873i	$-0.597057\pi$
$163$	6.79824	−	5.10855i	0.532479	−	0.400132i	0.832689	+	0.553741i	$0.186800\pi$
$164$	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	0.146040	−	0.989279i	$-0.453347\pi$
$167$	5.80080	−	0.468289i	0.448880	−	0.0362373i	0.302840	+	0.953041i	$0.402065\pi$
$168$	−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	−0.0562851	−	0.998415i	$-0.517926\pi$
$173$	2.71598	−	0.441390i	0.206492	−	0.0335583i	0.262778	+	0.964856i	$0.415361\pi$
$174$	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	−0.930719	−	0.365734i	$-0.880818\pi$
$179$	−7.06156	+	7.35186i	−0.527806	+	0.549504i	0.402914	+	0.915238i	$0.367998\pi$
$180$	−0.250063	−	0.526996i	−0.0186386	−	0.0392799i
$181$	−3.41819	+	3.02825i	−0.254072	+	0.225088i	−0.780539	−	0.625108i	$-0.785055\pi$
$181$	−3.41819	+	3.02825i	−0.254072	+	0.225088i	0.526466	+	0.850196i	$0.323517\pi$
$182$	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	0.715676	−	0.698433i	$-0.246119\pi$
$191$	−3.41392	−	5.91308i	−0.247022	−	0.427855i	−0.962698	+	0.270577i	$0.912785\pi$
$192$	−3.44159	+	5.96100i	−0.248375	+	0.430198i
$193$	8.10608	−	8.43932i	0.583488	−	0.607475i	−0.362379	−	0.932031i	$-0.618035\pi$
$193$	8.10608	−	8.43932i	0.583488	−	0.607475i	0.945867	+	0.324556i	$0.105215\pi$
$194$	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	0.0956067	−	0.995419i	$-0.469521\pi$
$197$	−11.7045	−	8.79537i	−0.833912	−	0.626644i	−0.929519	+	0.368775i	$0.879777\pi$
$198$	6.66733	−	0.538243i	0.473827	−	0.0382512i
$199$	−3.94266	+	19.3124i	−0.279488	+	1.36902i	0.561279	+	0.827627i	$0.310309\pi$
$199$	−3.94266	+	19.3124i	−0.279488	+	1.36902i	−0.840767	+	0.541397i	$0.817896\pi$
$200$	−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	0.391259	−	0.920281i	$-0.372040\pi$
$211$	6.84107	+	1.11178i	0.470958	+	0.0765382i	0.0796997	+	0.996819i	$0.474604\pi$
$212$	−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	0.990410	+	0.138157i	$0.0441180\pi$
$223$	1.99218	+	9.75834i	0.133406	+	0.653467i	−0.857004	+	0.515310i	$0.827677\pi$
$224$	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	−0.504823	−	0.863223i	$-0.668442\pi$
$227$	−10.7019	+	1.73923i	−0.710311	+	0.115437i	−0.205488	+	0.978660i	$0.565878\pi$
$228$	0.925744	+	0.309059i	0.0613089	+	0.0204679i
$229$	3.39749	−	27.9809i	0.224512	−	1.84903i	−0.249332	−	0.968418i	$-0.580211\pi$
$229$	3.39749	−	27.9809i	0.224512	−	1.84903i	0.473844	−	0.880609i	$-0.342866\pi$
$230$	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	−0.337458	−	0.941341i	$-0.609567\pi$
$233$	3.74819	−	1.96720i	0.245552	−	0.128876i	0.583010	+	0.812465i	$0.301875\pi$
$234$	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	−0.935582	−	0.353110i	$-0.885124\pi$
$241$	0.986428	−	4.83185i	0.0635414	−	0.311247i	0.999123	+	0.0418632i	$0.0133294\pi$
$242$	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	−0.954088	−	0.299527i	$-0.903171\pi$
$251$	−14.7630	+	11.0937i	−0.931831	+	0.700226i	0.0222570	+	0.999752i	$0.492915\pi$
$252$	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	−0.989495	−	0.144565i	$-0.953822\pi$
$257$	−14.9606	−	18.3234i	−0.933214	−	1.14298i	0.0562808	−	0.998415i	$-0.482076\pi$
$258$	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	0.999978	+	0.00657808i	$0.00209388\pi$
$263$	6.04324	+	12.7359i	0.372642	+	0.785327i	−0.627336	+	0.778748i	$0.715855\pi$
$264$	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	−0.985979	−	0.166869i	$-0.946634\pi$
$269$	−0.272664	−	6.76608i	−0.0166246	−	0.412535i	0.969355	−	0.245666i	$-0.0790067\pi$
$270$	−3.03345	−	2.27949i	−0.184610	−	0.138725i
$271$	−30.1028	−	4.89218i	−1.82861	−	0.297179i	−0.853866	−	0.520492i	$-0.825748\pi$
$271$	−30.1028	−	4.89218i	−1.82861	−	0.297179i	−0.974747	+	0.223314i	$0.928313\pi$
$272$	−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	−0.999807	−	0.0196231i	$-0.993753\pi$
$277$	−2.75061	−	9.49620i	−0.165268	−	0.570571i	0.834539	−	0.550948i	$-0.185734\pi$
$278$	−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	0.256278	−	0.966603i	$-0.417504\pi$
$281$	−6.59857	−	3.46319i	−0.393637	−	0.206597i	−0.649916	+	0.760006i	$0.725196\pi$
$282$	−5.64696	−	3.57092i	−0.336271	−	0.212645i
$283$	−22.0401	−	9.39043i	−1.31015	−	0.558203i	−0.379866	−	0.925042i	$-0.624030\pi$
$283$	−22.0401	−	9.39043i	−1.31015	−	0.558203i	−0.930285	+	0.366839i	$0.880440\pi$
$284$	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	0.963093	+	0.269169i	$0.0867491\pi$
$293$	5.01464	+	17.3125i	0.292958	+	1.01141i	−0.670135	+	0.742239i	$0.733764\pi$
$294$	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	0.994312	+	0.106510i	$0.0339676\pi$
$307$	0.952857	+	7.84748i	0.0543824	+	0.447879i	−0.939929	+	0.341369i	$0.889109\pi$
$308$	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	−0.935220	−	0.354067i	$-0.884798\pi$
$311$	−1.97355	−	16.2536i	−0.111910	−	0.921659i	0.823310	−	0.567592i	$-0.192125\pi$
$312$	9.40998	−	1.51771i	0.532735	−	0.0859236i
$313$	−0.162775	+	1.34057i	−0.00920058	+	0.0757736i	−0.996586	−	0.0825621i	$-0.973690\pi$
$313$	−0.162775	+	1.34057i	−0.00920058	+	0.0757736i	0.987385	+	0.158336i	$0.0506128\pi$
$314$	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	0.266116	−	0.963941i	$-0.414259\pi$
$317$	0.957616	+	0.236031i	0.0537851	+	0.0132568i	−0.212331	+	0.977198i	$0.568106\pi$
$318$	−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	0.997514	+	0.0704678i	$0.0224492\pi$
$331$	18.6984	+	19.4671i	1.02776	+	1.07001i	0.0302448	+	0.999543i	$0.490371\pi$
$332$	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	−0.702146	−	0.712033i	$-0.747774\pi$
$347$	5.46670	−	11.5208i	0.293468	−	0.618470i	0.995613	+	0.0935633i	$0.0298257\pi$
$348$	−0.939381	+	0.977999i	−0.0503561	+	0.0524263i
$349$	5.10167	+	10.7515i	0.273086	+	0.575517i	0.992941	−	0.118607i	$-0.0378430\pi$
$349$	5.10167	+	10.7515i	0.273086	+	0.575517i	−0.719855	+	0.694125i	$0.755792\pi$
$350$	−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	−0.996976	−	0.0777077i	$-0.975240\pi$
$353$	−2.11950	+	7.31737i	−0.112810	+	0.389464i	0.884167	+	0.467172i	$0.154727\pi$
$354$	−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	−0.388266	−	0.921547i	$-0.626926\pi$
$359$	−21.9850	−	5.41881i	−1.16032	−	0.285994i	−0.772057	+	0.635553i	$0.780772\pi$
$360$	−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	0.349440	−	0.936959i	$-0.386372\pi$
$367$	16.1812	−	1.30628i	0.844653	−	0.0681875i	0.495213	+	0.868771i	$0.335090\pi$
$368$	−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	−0.658596	−	0.752496i	$-0.728850\pi$
$373$	−27.6058	−	2.22857i	−1.42937	−	0.115391i	−0.770777	+	0.637105i	$0.780132\pi$
$374$	−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	−0.554744	−	0.832021i	$-0.687184\pi$
$379$	−0.795615	+	0.503117i	−0.0408680	+	0.0258434i	0.513876	+	0.857865i	$0.328209\pi$
$380$	−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	−0.981359	−	0.192184i	$-0.938443\pi$
$383$	−4.98340	−	17.2047i	−0.254640	−	0.879120i	0.726719	−	0.686935i	$-0.241044\pi$
$384$	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	−0.0845420	−	0.996420i	$-0.526943\pi$
$389$	−12.2768	−	3.02597i	−0.622460	−	0.153423i	−0.537918	+	0.842997i	$0.680789\pi$
$390$	−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	0.570564	−	0.821253i	$-0.306725\pi$
$397$	10.6267	+	3.54770i	0.533336	+	0.178054i	−0.0372279	+	0.999307i	$0.511853\pi$
$398$	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	0.378481	−	0.925609i	$-0.376446\pi$
$401$	24.7731	−	8.27046i	1.23711	−	0.413007i	0.858627	+	0.512602i	$0.171318\pi$
$402$	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	−0.988043	−	0.154177i	$-0.950727\pi$
$409$	−0.315693	−	7.83385i	−0.0156100	−	0.387359i	0.972433	−	0.233182i	$-0.0749137\pi$
$410$	−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	0.543456	−	0.839437i	$-0.317115\pi$
$419$	−7.93647	−	9.72041i	−0.387722	−	0.474873i	−0.931178	+	0.364564i	$0.881218\pi$
$420$	−2.44292	+	1.83574i	−0.119202	+	0.0895748i
$421$	−16.0728	+	8.43567i	−0.783342	+	0.411130i	−0.808457	−	0.588555i	$-0.799697\pi$
$421$	−16.0728	+	8.43567i	−0.783342	+	0.411130i	0.0251152	+	0.999685i	$0.492005\pi$
$422$	−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	0.998801	−	0.0489617i	$-0.0155912\pi$
$431$	15.5921	+	19.0968i	0.751043	+	0.919860i	−0.247758	+	0.968822i	$0.579694\pi$
$432$	−1.88899	−	3.98096i	−0.0908840	−	0.191534i
$433$	−8.37198	−	2.79498i	−0.402332	−	0.134318i	0.108299	−	0.994118i	$-0.465460\pi$
$433$	−8.37198	−	2.79498i	−0.402332	−	0.134318i	−0.510630	+	0.859800i	$0.670588\pi$
$434$	−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	0.643950	−	0.765067i	$-0.277294\pi$
$439$	1.84898	+	1.38942i	0.0882471	+	0.0663134i	−0.555703	+	0.831381i	$0.687551\pi$
$440$	−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	−0.616821	−	0.787104i	$-0.711580\pi$
$443$	−6.72347	+	3.52875i	−0.319442	+	0.167656i	0.297379	+	0.954759i	$0.403887\pi$
$444$	−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	−0.0478673	−	0.998854i	$-0.515242\pi$
$449$	4.72600	−	0.768050i	0.223034	−	0.0362465i	0.270901	+	0.962607i	$0.412678\pi$
$450$	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	−0.999293	−	0.0375887i	$-0.988032\pi$
$457$	−0.00461250	+	0.114458i	−0.000215763	+	0.00535412i	0.999078	+	0.0429429i	$0.0136733\pi$
$458$	−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	−0.963030	−	0.269393i	$-0.913177\pi$
$461$	−3.11958	+	6.57438i	−0.145293	+	0.306199i	0.817737	+	0.575592i	$0.195228\pi$
$462$	−9.74915	−	33.6580i	−0.453571	−	1.56591i
$463$	20.0545	+	29.0540i	0.932012	+	1.35025i	0.936651	+	0.350264i	$0.113908\pi$
$463$	20.0545	+	29.0540i	0.932012	+	1.35025i	−0.00463864	+	0.999989i	$0.501477\pi$
$464$	−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	−0.445567	+	0.895249i	$0.646998\pi$
$467$	−24.3036	+	35.2099i	−1.12464	+	1.62932i	−0.679072	+	0.734072i	$0.737618\pi$
$468$	−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	0.855485	−	0.517827i	$-0.173259\pi$
$479$	13.0466	+	9.80389i	0.596114	+	0.447951i	−0.259371	+	0.965778i	$0.583515\pi$
$480$	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	−0.824315	−	0.566131i	$-0.808440\pi$
$487$	−2.31144	+	2.83101i	−0.104742	+	0.128285i	0.719574	+	0.694416i	$0.244337\pi$
$488$	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	−0.848600	−	0.529035i	$-0.822554\pi$
$491$	−26.7940	+	8.94514i	−1.20919	+	0.403688i	−0.360594	+	0.932723i	$0.617426\pi$
$492$	−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	−0.586104	−	0.810236i	$-0.699339\pi$
$499$	−16.2743	+	4.01125i	−0.728538	+	0.179568i	−0.142434	+	0.989804i	$0.545493\pi$
$500$	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	0.361321	−	0.932441i	$-0.382326\pi$
$503$	22.4125	−	3.64238i	0.999322	−	0.162406i	0.638001	+	0.770036i	$0.279762\pi$
$504$	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	−0.225241	−	0.974303i	$-0.572317\pi$
$509$	−6.57147	+	0.530504i	−0.291275	+	0.0235142i	−0.0660345	+	0.997817i	$0.521035\pi$
$510$	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	0.177022	−	0.984207i	$-0.443354\pi$
$521$	−17.7735	−	15.7459i	−0.778671	−	0.689842i	−0.955693	+	0.294365i	$0.904892\pi$
$522$	−2.45422	+	8.47294i	−0.107418	+	0.370850i
$523$	38.3116	−	12.7903i	1.67525	−	0.559280i	0.689030	−	0.724733i	$-0.258037\pi$
$523$	38.3116	−	12.7903i	1.67525	−	0.559280i	0.986218	+	0.165453i	$0.0529085\pi$
$524$	−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	0.617065	−	0.786912i	$-0.288322\pi$
$541$	−2.08708	−	1.84899i	−0.0897305	−	0.0794943i	−0.706796	+	0.707418i	$0.749860\pi$
$542$	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	−0.776944	−	0.629570i	$-0.783231\pi$
$547$	2.03997	−	2.95540i	0.0872227	−	0.126364i	0.864166	+	0.503206i	$0.167846\pi$
$548$	−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	−0.999861	−	0.0166446i	$-0.994702\pi$
$557$	−0.0449102	+	1.11444i	−0.00190291	+	0.0472202i	0.997959	+	0.0638648i	$0.0203426\pi$
$558$	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	0.817189	−	0.576369i	$-0.195531\pi$
$563$	15.3468	+	9.70474i	0.646792	+	0.409006i	−0.170398	+	0.985375i	$0.554505\pi$
$564$	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	−0.995867	−	0.0908238i	$-0.971050\pi$
$569$	−2.75009	−	13.4708i	−0.115290	−	0.564726i	0.880577	−	0.473903i	$-0.157155\pi$
$570$	−15.3031	+	5.10893i	−0.640977	+	0.213989i
$571$	31.3807	−	16.4699i	1.31324	−	0.689242i	0.344845	−	0.938660i	$-0.387931\pi$
$571$	31.3807	−	16.4699i	1.31324	−	0.689242i	0.968396	+	0.249417i	$0.0802391\pi$
$572$	−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	0.485915	+	0.874006i	$0.338486\pi$
$587$	−12.4521	+	21.5677i	−0.513954	+	0.890194i	−0.999869	+	0.0161878i	$0.994847\pi$
$588$	−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	−0.993051	−	0.117685i	$-0.962453\pi$
$593$	−35.5610	+	18.6638i	−1.46031	+	0.766432i	−0.467264	+	0.884118i	$0.654760\pi$
$594$	−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	−0.716248	−	0.697845i	$-0.754142\pi$
$599$	6.91718	−	18.2391i	0.282628	−	0.745230i	0.998877	−	0.0473843i	$-0.0150885\pi$
$600$	2.43731	+	2.98516i	0.0995026	+	0.121869i
$601$	−19.5547	−	41.2106i	−0.797651	−	1.68101i	−0.730142	−	0.683295i	$-0.760546\pi$
$601$	−19.5547	−	41.2106i	−0.797651	−	1.68101i	−0.0675088	−	0.997719i	$-0.521505\pi$
$602$	−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	−0.854955	−	0.518702i	$-0.826415\pi$
$607$	−1.09662	−	27.2124i	−0.0445105	−	1.10452i	0.810444	−	0.585815i	$-0.199226\pi$
$608$	−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	0.284889	−	0.958560i	$-0.408043\pi$
$613$	26.9497	−	8.99714i	1.08849	−	0.363391i	0.803600	+	0.595169i	$0.202915\pi$
$614$	−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	0.671045	−	0.741417i	$-0.265846\pi$
$617$	18.9303	+	6.31988i	0.762107	+	0.254429i	0.0910619	+	0.995845i	$0.470974\pi$
$618$	8.62566	−	1.40181i	0.346975	−	0.0563889i
$619$	−1.72946	−	0.907691i	−0.0695129	−	0.0364832i	0.429609	−	0.903015i	$-0.358652\pi$
$619$	−1.72946	−	0.907691i	−0.0695129	−	0.0364832i	−0.499121	+	0.866532i	$0.666344\pi$
$620$	−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	0.991256	−	0.131956i	$-0.0421257\pi$
$631$	2.08318	+	7.19199i	0.0829302	+	0.286308i	−0.908325	+	0.418264i	$0.862639\pi$
$632$	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	0.860612	−	0.509262i	$-0.170082\pi$
$641$	41.2275	+	3.32823i	1.62839	+	0.131457i	0.767776	+	0.640719i	$0.221364\pi$
$642$	−16.9134	−	14.9839i	−0.667517	−	0.591369i
$643$	−31.2315	−	19.7496i	−1.23165	−	0.778848i	−0.249761	−	0.968307i	$-0.580352\pi$
$643$	−31.2315	−	19.7496i	−1.23165	−	0.778848i	−0.981889	+	0.189459i	$0.939327\pi$
$644$	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	−0.851397	−	0.524522i	$-0.824244\pi$
$647$	−40.8920	+	3.30114i	−1.60763	+	0.129781i	−0.756232	+	0.654303i	$0.772962\pi$
$648$	−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	0.492011	+	0.870589i	$0.336262\pi$
$653$	−12.9800	+	22.4820i	−0.507947	+	0.879789i	−0.999958	+	0.00920048i	$0.997071\pi$
$654$	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	0.825908	−	0.563804i	$-0.190663\pi$
$659$	5.88650	+	6.12849i	0.229305	+	0.238732i	−0.596603	+	0.802536i	$0.703483\pi$
$660$	2.47863	−	0.827488i	0.0964805	−	0.0322099i
$661$	−8.59391	+	29.6696i	−0.334265	+	1.15402i	0.600759	+	0.799430i	$0.294865\pi$
$661$	−8.59391	+	29.6696i	−0.334265	+	1.15402i	−0.935024	+	0.354585i	$0.884622\pi$
$662$	−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	−0.756041	+	0.654525i	$0.772869\pi$
$673$	−43.3619	+	27.4204i	−1.67148	+	1.05698i	−0.915440	+	0.402455i	$0.868157\pi$
$674$	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	−0.987445	−	0.157965i	$-0.949507\pi$
$683$	−28.8920	−	30.0797i	−1.10552	−	1.15097i	−0.118076	−	0.993005i	$-0.537673\pi$
$684$	−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	−0.512454	−	0.858715i	$-0.671264\pi$
$691$	9.97904	−	34.4516i	0.379621	−	1.31060i	0.892075	−	0.451888i	$-0.149249\pi$
$692$	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	0.635967	+	0.771716i	$0.280602\pi$
$701$	−4.40048	+	36.2412i	−0.166204	+	1.36881i	−0.802171	+	0.597095i	$0.796322\pi$
$702$	−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	−0.359863	−	0.933005i	$-0.617176\pi$
$709$	−36.1344	−	22.8500i	−1.35706	−	0.858151i	−0.997194	+	0.0748544i	$0.976151\pi$
$710$	−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	−0.718283	−	0.695751i	$-0.755072\pi$
$719$	−19.1474	+	8.15795i	−0.714078	+	0.304240i	0.00420531	+	0.999991i	$0.498661\pi$
$720$	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	0.602186	−	0.798356i	$-0.294297\pi$
$727$	20.6099	+	5.07989i	0.764380	+	0.188403i	0.162195	+	0.986759i	$0.448143\pi$
$728$	−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	0.552911	−	0.833240i	$-0.313517\pi$
$733$	4.90737	+	2.57559i	0.181258	+	0.0951314i	−0.371654	+	0.928371i	$0.621209\pi$
$734$	−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	−0.555205	−	0.831713i	$-0.687360\pi$
$739$	−13.5764	+	4.53246i	−0.499414	+	0.166729i	0.0557907	+	0.998442i	$0.482232\pi$
$740$	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	0.384802	−	0.922999i	$-0.374270\pi$
$743$	12.4710	+	2.02673i	0.457516	+	0.0743536i	0.0727142	+	0.997353i	$0.476834\pi$
$744$	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	0.773908	−	0.633297i	$-0.218299\pi$
$751$	−5.64809	−	11.9031i	−0.206102	−	0.434350i	−0.980010	+	0.198947i	$0.936248\pi$
$752$	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	0.661123	−	0.750277i	$-0.270080\pi$
$757$	−5.67422	−	6.94966i	−0.206233	−	0.252590i	−0.867356	+	0.497688i	$0.834183\pi$
$758$	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	0.419504	−	0.907753i	$-0.362204\pi$
$761$	18.9783	+	1.53209i	0.687962	+	0.0555381i	0.268458	+	0.963291i	$0.413486\pi$
$762$	−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	0.885965	+	0.463751i	$0.153497\pi$
$769$	32.2545	+	39.5047i	1.16313	+	1.42457i	0.277163	+	0.960823i	$0.410606\pi$
$770$	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	−0.735947	−	0.677039i	$-0.763263\pi$
$773$	5.74090	−	28.1208i	0.206486	−	1.01144i	0.942433	−	0.334396i	$-0.108532\pi$
$774$	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	−0.760724	−	0.649076i	$-0.775156\pi$
$787$	−35.8175	+	5.82091i	−1.27676	+	0.207493i	−0.516033	+	0.856569i	$0.672592\pi$
$788$	−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	−0.536851	−	0.843677i	$-0.680386\pi$
$797$	11.2123	−	13.7326i	0.397160	−	0.486432i	0.934011	+	0.357245i	$0.116284\pi$
$798$	−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	0.157690	+	0.987489i	$0.449595\pi$
$809$	−14.3172	+	49.4288i	−0.503367	+	1.73782i	−0.661057	+	0.750336i	$0.729892\pi$
$810$	3.78215	+	0.305327i	0.132891	+	0.0107281i
$811$	12.6040	+	11.1662i	0.442587	+	0.392098i	0.854773	−	0.519002i	$-0.173696\pi$
$811$	12.6040	+	11.1662i	0.442587	+	0.392098i	−0.412186	+	0.911100i	$0.635235\pi$
$812$	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	−0.832973	−	0.553314i	$-0.813363\pi$
$821$	−7.06491	+	7.35535i	−0.246567	+	0.256704i	0.586406	+	0.810018i	$0.300542\pi$
$822$	−4.85892	+	8.41589i	−0.169474	+	0.293538i
$823$	14.7029	+	25.4662i	0.512510	+	0.887694i	0.999895	+	0.0145066i	$0.00461777\pi$
$823$	14.7029	+	25.4662i	0.512510	+	0.887694i	−0.487384	+	0.873188i	$0.662049\pi$
$824$	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	0.697210	+	0.716867i	$0.254425\pi$
$827$	−8.62814	+	22.7505i	−0.300030	+	0.791114i	−0.997240	+	0.0742470i	$0.976345\pi$
$828$	−0.293154	−	0.305205i	−0.0101878	−	0.0106066i
$829$	7.38047	−	2.46396i	0.256334	−	0.0855770i	−0.185597	−	0.982626i	$-0.559422\pi$
$829$	7.38047	−	2.46396i	0.256334	−	0.0855770i	0.441931	+	0.897049i	$0.354294\pi$
$830$	−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	−0.807681	−	0.589619i	$-0.799278\pi$
$839$	−13.4994	+	10.1442i	−0.466053	+	0.350216i	0.341629	+	0.939835i	$0.389021\pi$
$840$	−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	−0.182884	−	0.983134i	$-0.558543\pi$
$853$	3.27298	−	0.806718i	0.112065	−	0.0276215i	0.294949	+	0.955513i	$0.404697\pi$
$854$	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	−0.993085	−	0.117399i	$-0.962544\pi$
$857$	−29.1646	+	25.8376i	−0.996245	+	0.882596i	−0.00316015	+	0.999995i	$0.501006\pi$
$858$	10.3130	+	21.8014i	0.352079	+	0.744288i
$859$	4.33327	+	3.83894i	0.147849	+	0.130983i	0.733805	−	0.679360i	$-0.237742\pi$
$859$	4.33327	+	3.83894i	0.147849	+	0.130983i	−0.585956	+	0.810343i	$0.699281\pi$
$860$	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	−0.652884	−	0.757458i	$-0.726441\pi$
$863$	9.93214	−	26.1889i	0.338094	−	0.891481i	0.990978	−	0.134023i	$-0.0427896\pi$
$864$	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	−0.0196406	−	0.999807i	$-0.506252\pi$
$877$	20.3691	−	8.67848i	0.687817	−	0.293051i	0.707458	+	0.706756i	$0.249842\pi$
$878$	−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	−0.338716	−	0.940889i	$-0.609993\pi$
$881$	13.3697	−	46.1575i	0.450436	−	1.55509i	0.789152	−	0.614198i	$-0.210520\pi$
$882$	−28.0828	−	11.9650i	−0.945598	−	0.402882i
$883$	−8.59201	−	12.4477i	−0.289144	−	0.418898i	0.651313	−	0.758809i	$-0.274218\pi$
$883$	−8.59201	−	12.4477i	−0.289144	−	0.418898i	−0.940458	+	0.339911i	$0.889603\pi$
$884$	−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	0.942793	−	0.333378i	$-0.108189\pi$
$887$	51.5684	+	8.38068i	1.73150	+	0.281396i	0.788703	+	0.614774i	$0.210753\pi$
$888$	−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	0.966971	+	0.254887i	$0.0820383\pi$
$907$	5.33919	+	26.1531i	0.177285	+	0.868398i	−0.789686	+	0.613511i	$0.789757\pi$
$908$	−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	0.951381	−	0.308018i	$-0.0996656\pi$
$911$	37.3763	+	19.6166i	1.23833	+	0.649927i	0.286952	+	0.957945i	$0.407358\pi$
$912$	−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	−0.999959	−	0.00903464i	$-0.997124\pi$
$919$	−54.7124	−	18.2657i	−1.80480	−	0.602530i	−0.804838	−	0.593495i	$-0.797748\pi$
$920$	−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	0.676433	−	0.736504i	$-0.263525\pi$
$929$	37.3667	+	3.01655i	1.22596	+	0.0989699i	0.549530	+	0.835474i	$0.314807\pi$
$930$	−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	−0.974068	−	0.226255i	$-0.927352\pi$
$937$	−2.90594	+	7.66233i	−0.0949329	+	0.250317i	0.879135	+	0.476572i	$0.158121\pi$
$938$	−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	−0.540206	−	0.841533i	$-0.681654\pi$
$941$	13.4421	−	19.4743i	0.438200	−	0.634843i	0.978406	+	0.206690i	$0.0662692\pi$
$942$	−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	0.876401	−	0.481581i	$-0.159937\pi$
$947$	47.8587	+	7.77780i	1.55520	+	0.252744i	0.678797	+	0.734326i	$0.262501\pi$
$948$	−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	0.967444	−	0.253085i	$-0.0814452\pi$
$953$	0.447773	+	1.54589i	0.0145048	+	0.0500763i	−0.952939	+	0.303161i	$0.901958\pi$
$954$	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	0.560547	+	0.828123i	$0.310591\pi$
$967$	21.4604	+	56.5863i	0.690118	+	1.81969i	0.129572	+	0.991570i	$0.458640\pi$
$968$	−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	−0.806981	−	0.590577i	$-0.798900\pi$
$971$	−29.2934	+	12.4808i	−0.940072	+	0.400527i	−0.133090	+	0.991104i	$0.542490\pi$
$972$	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	0.830020	−	0.557733i	$-0.188329\pi$
$977$	31.3432	+	13.3541i	1.00276	+	0.427235i	0.172737	+	0.984968i	$0.444739\pi$
$978$	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	−0.995879	−	0.0906929i	$-0.971092\pi$
$983$	−1.58779	−	13.0766i	−0.0506427	−	0.417080i	0.945236	−	0.326387i	$-0.105831\pi$
$984$	−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	−0.998999	−	0.0447260i	$-0.985759\pi$
$991$	−14.5050	+	25.1234i	−0.460766	+	0.798070i	0.538234	+	0.842796i	$0.319092\pi$
$992$	−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	0.963403	+	0.268056i	$0.0863812\pi$
$997$	37.6520	+	39.1998i	1.19245	+	1.24147i	0.229046	+	0.973416i	$0.426439\pi$
$998$	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.412.5	yes	384
169.16	even	39	inner	507.2.q.b.16.5	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.16.5	✓	384	169.16	even	39	inner
507.2.q.b.412.5	yes	384	1.1	even	1	trivial

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

Fields

Representations

Groups

Database

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