LMFDB - Embedded newform 512.2.o.a.157.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			157.51
Character	$\chi$	$=$	512.157
Dual form			512.2.o.a.437.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15864 + 0.810897i) q^{2} +(2.35125 - 0.906977i) q^{3} +(0.684893 + 1.87907i) q^{4} +(-2.18371 + 2.79817i) q^{5} +(3.45971 + 0.855760i) q^{6} +(-0.0220573 + 0.0616461i) q^{7} +(-0.730190 + 2.73255i) q^{8} +(2.48291 - 2.25038i) q^{9} +O(q^{10})$	\(q+(1.15864 + 0.810897i) q^{2} +(2.35125 - 0.906977i) q^{3} +(0.684893 + 1.87907i) q^{4} +(-2.18371 + 2.79817i) q^{5} +(3.45971 + 0.855760i) q^{6} +(-0.0220573 + 0.0616461i) q^{7} +(-0.730190 + 2.73255i) q^{8} +(2.48291 - 2.25038i) q^{9} +(-4.79916 + 1.47130i) q^{10} +(-0.212957 - 0.948342i) q^{11} +(3.31463 + 3.79699i) q^{12} +(0.277178 - 0.0767054i) q^{13} +(-0.0755451 + 0.0535394i) q^{14} +(-2.59658 + 8.55976i) q^{15} +(-3.06184 + 2.57393i) q^{16} +(6.31477 - 1.91557i) q^{17} +(4.70162 - 0.593995i) q^{18} +(-0.163819 - 0.325453i) q^{19} +(-6.75357 - 2.18691i) q^{20} +(0.00404931 + 0.164951i) q^{21} +(0.522266 - 1.27147i) q^{22} +(1.56318 - 0.231875i) q^{23} +(0.761499 + 7.08717i) q^{24} +(-1.84624 - 7.37062i) q^{25} +(0.383349 + 0.135889i) q^{26} +(0.397681 - 0.790056i) q^{27} +(-0.130944 + 0.000773647i) q^{28} +(-1.49083 - 8.59184i) q^{29} +(-9.94958 + 7.81213i) q^{30} +(-2.16534 + 3.24065i) q^{31} +(-5.63477 + 0.499423i) q^{32} +(-1.36084 - 2.03664i) q^{33} +(8.86988 + 2.90118i) q^{34} +(-0.124329 - 0.196337i) q^{35} +(5.92916 + 3.12430i) q^{36} +(-1.25344 + 1.08122i) q^{37} +(0.0741012 - 0.509923i) q^{38} +(0.582144 - 0.431747i) q^{39} +(-6.05160 - 8.01029i) q^{40} +(1.88294 - 7.51712i) q^{41} +(-0.129066 + 0.194402i) q^{42} +(-2.39385 - 5.40045i) q^{43} +(1.63615 - 1.04968i) q^{44} +(0.874977 + 11.8618i) q^{45} +(1.99918 + 0.998914i) q^{46} +(0.711720 + 0.867233i) q^{47} +(-4.86466 + 8.82897i) q^{48} +(5.40776 + 4.43803i) q^{49} +(3.83768 - 10.0370i) q^{50} +(13.1102 - 10.2313i) q^{51} +(0.333972 + 0.468303i) q^{52} +(1.15498 - 6.65633i) q^{53} +(1.10142 - 0.592913i) q^{54} +(3.11866 + 1.47501i) q^{55} +(-0.152345 - 0.105286i) q^{56} +(-0.680358 - 0.616641i) q^{57} +(5.23976 - 11.1638i) q^{58} +(1.89886 - 6.86159i) q^{59} +(-17.8628 + 0.983366i) q^{60} +(6.90000 + 0.169385i) q^{61} +(-5.13668 + 1.99889i) q^{62} +(0.0839606 + 0.202699i) q^{63} +(-6.93364 - 3.99056i) q^{64} +(-0.390641 + 0.943092i) q^{65} +(0.0747815 - 3.46323i) q^{66} +(-9.87936 + 9.40593i) q^{67} +(7.92444 + 10.5540i) q^{68} +(3.46511 - 1.96296i) q^{69} +(0.0151564 - 0.328302i) q^{70} +(-12.2112 + 0.599897i) q^{71} +(4.33627 + 8.42787i) q^{72} +(2.20466 + 6.16161i) q^{73} +(-2.32904 + 0.236339i) q^{74} +(-11.0260 - 15.6557i) q^{75} +(0.499352 - 0.530729i) q^{76} +(0.0631588 + 0.00778990i) q^{77} +(1.02460 - 0.0281812i) q^{78} +(14.1574 - 1.39438i) q^{79} +(-0.516112 - 14.1883i) q^{80} +(-0.766875 + 7.78621i) q^{81} +(8.27726 - 7.18277i) q^{82} +(-5.57164 - 4.80613i) q^{83} +(-0.307181 + 0.120583i) q^{84} +(-8.42957 + 21.8528i) q^{85} +(1.60559 - 8.19834i) q^{86} +(-11.2979 - 18.8494i) q^{87} +(2.74689 + 0.110554i) q^{88} +(-14.5702 - 2.16128i) q^{89} +(-8.60489 + 14.4530i) q^{90} +(-0.00138521 + 0.0187788i) q^{91} +(1.50632 + 2.77851i) q^{92} +(-2.15205 + 9.58349i) q^{93} +(0.121391 + 1.58194i) q^{94} +(1.26841 + 0.252302i) q^{95} +(-12.7958 + 6.28487i) q^{96} +(-2.31313 + 0.460110i) q^{97} +(2.66686 + 9.52722i) q^{98} +(-2.66288 - 1.87541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{91}{128}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.15864	+	0.810897i	0.819282	+	0.573390i
$2$	1.15864	+	0.810897i	0.819282	+	0.573390i
$3$	2.35125	−	0.906977i	1.35749	−	0.523643i	0.431818	−	0.901961i	$-0.357872\pi$
$3$	2.35125	−	0.906977i	1.35749	−	0.523643i	0.925676	+	0.378318i	$0.123497\pi$
$4$	0.684893	+	1.87907i	0.342447	+	0.939537i
$5$	−2.18371	+	2.79817i	−0.976585	+	1.25138i	−0.00870620	+	0.999962i	$0.502771\pi$
$5$	−2.18371	+	2.79817i	−0.976585	+	1.25138i	−0.967879	+	0.251416i	$0.919104\pi$
$6$	3.45971	+	0.855760i	1.41242	+	0.349363i
$7$	−0.0220573	+	0.0616461i	−0.00833688	+	0.0233000i	−0.945640	−	0.325214i	$-0.894564\pi$
$7$	−0.0220573	+	0.0616461i	−0.00833688	+	0.0233000i	0.937304	+	0.348514i	$0.113314\pi$
$8$	−0.730190	+	2.73255i	−0.258161	+	0.966102i
$9$	2.48291	−	2.25038i	0.827636	−	0.750126i
$10$	−4.79916	+	1.47130i	−1.51763	+	0.465267i
$11$	−0.212957	−	0.948342i	−0.0642090	−	0.285936i	0.933066	−	0.359704i	$-0.117122\pi$
$11$	−0.212957	−	0.948342i	−0.0642090	−	0.285936i	−0.997275	+	0.0737685i	$0.976497\pi$
$12$	3.31463	+	3.79699i	0.956852	+	1.09610i
$13$	0.277178	−	0.0767054i	0.0768753	−	0.0212743i	−0.228063	−	0.973646i	$-0.573239\pi$
$13$	0.277178	−	0.0767054i	0.0768753	−	0.0212743i	0.304938	+	0.952372i	$0.401364\pi$
$14$	−0.0755451	+	0.0535394i	−0.0201903	+	0.0143090i
$15$	−2.59658	+	8.55976i	−0.670433	+	2.21012i
$16$	−3.06184	+	2.57393i	−0.765460	+	0.643483i
$17$	6.31477	−	1.91557i	1.53156	−	0.464593i	0.591700	−	0.806158i	$-0.298457\pi$
$17$	6.31477	−	1.91557i	1.53156	−	0.464593i	0.939858	+	0.341565i	$0.110957\pi$
$18$	4.70162	−	0.593995i	1.10818	−	0.140006i
$19$	−0.163819	−	0.325453i	−0.0375827	−	0.0746641i	0.873652	−	0.486550i	$-0.161745\pi$
$19$	−0.163819	−	0.325453i	−0.0375827	−	0.0746641i	−0.911235	+	0.411886i	$0.864870\pi$
$20$	−6.75357	−	2.18691i	−1.51014	−	0.489008i
$21$	0.00404931	+	0.164951i	0.000883633	+	0.0359952i
$22$	0.522266	−	1.27147i	0.111348	−	0.271079i
$23$	1.56318	−	0.231875i	0.325945	−	0.0483493i	0.0182470	−	0.999834i	$-0.494191\pi$
$23$	1.56318	−	0.231875i	0.325945	−	0.0483493i	0.307698	+	0.951484i	$0.400441\pi$
$24$	0.761499	+	7.08717i	0.155440	+	1.44666i
$25$	−1.84624	−	7.37062i	−0.369249	−	1.47412i
$26$	0.383349	+	0.135889i	0.0751810	+	0.0266499i
$27$	0.397681	−	0.790056i	0.0765337	−	0.152046i
$28$	−0.130944		0.000773647i	−0.0247462		0.000146206i
$29$	−1.49083	−	8.59184i	−0.276839	−	1.59546i	−0.716689	−	0.697393i	$-0.754343\pi$
$29$	−1.49083	−	8.59184i	−0.276839	−	1.59546i	0.439850	−	0.898071i	$-0.355032\pi$
$30$	−9.94958	+	7.81213i	−1.81654	+	1.42629i
$31$	−2.16534	+	3.24065i	−0.388906	+	0.582039i	−0.973330	−	0.229410i	$-0.926320\pi$
$31$	−2.16534	+	3.24065i	−0.388906	+	0.582039i	0.584424	+	0.811448i	$0.301320\pi$
$32$	−5.63477	+	0.499423i	−0.996095	+	0.0882863i
$33$	−1.36084	−	2.03664i	−0.236892	−	0.354533i
$34$	8.86988	+	2.90118i	1.52117	+	0.497548i
$35$	−0.124329	−	0.196337i	−0.0210155	−	0.0331871i
$36$	5.92916	+	3.12430i	0.988193	+	0.520717i
$37$	−1.25344	+	1.08122i	−0.206064	+	0.177752i	−0.750130	−	0.661291i	$-0.770009\pi$
$37$	−1.25344	+	1.08122i	−0.206064	+	0.177752i	0.544066	+	0.839042i	$0.316884\pi$
$38$	0.0741012	−	0.509923i	0.0120208	−	0.0827205i
$39$	0.582144	−	0.431747i	0.0932176	−	0.0691349i
$40$	−6.05160	−	8.01029i	−0.956843	−	1.26654i
$41$	1.88294	−	7.51712i	0.294066	−	1.17398i	−0.625239	−	0.780433i	$-0.714999\pi$
$41$	1.88294	−	7.51712i	0.294066	−	1.17398i	0.919305	−	0.393545i	$-0.128751\pi$
$42$	−0.129066	+	0.194402i	−0.0199154	+	0.0299969i
$43$	−2.39385	−	5.40045i	−0.365059	−	0.823560i	−0.998751	−	0.0499743i	$-0.984086\pi$
$43$	−2.39385	−	5.40045i	−0.365059	−	0.823560i	0.633691	−	0.773586i	$-0.281539\pi$
$44$	1.63615	−	1.04968i	0.246659	−	0.158245i
$45$	0.874977	+	11.8618i	0.130434	+	1.76825i
$46$	1.99918	+	0.998914i	0.294764	+	0.147282i
$47$	0.711720	+	0.867233i	0.103815	+	0.126499i	0.822326	−	0.569017i	$-0.192676\pi$
$47$	0.711720	+	0.867233i	0.103815	+	0.126499i	−0.718511	+	0.695516i	$0.755176\pi$
$48$	−4.86466	+	8.82897i	−0.702153	+	1.27435i
$49$	5.40776	+	4.43803i	0.772537	+	0.634005i
$50$	3.83768	−	10.0370i	0.542730	−	1.41945i
$51$	13.1102	−	10.2313i	1.83580	−	1.43267i
$52$	0.333972	+	0.468303i	0.0463136	+	0.0649419i
$53$	1.15498	−	6.65633i	0.158649	−	0.914318i	−0.793474	−	0.608604i	$-0.791730\pi$
$53$	1.15498	−	6.65633i	0.158649	−	0.914318i	0.952123	−	0.305714i	$-0.0988951\pi$
$54$	1.10142	−	0.592913i	0.149885	−	0.0806852i
$55$	3.11866	+	1.47501i	0.420519	+	0.198891i
$56$	−0.152345	−	0.105286i	−0.0203579	−	0.0140694i
$57$	−0.680358	−	0.616641i	−0.0901157	−	0.0816761i
$58$	5.23976	−	11.1638i	0.688014	−	1.46587i
$59$	1.89886	−	6.86159i	0.247210	−	0.893302i	−0.730425	−	0.682993i	$-0.760678\pi$
$59$	1.89886	−	6.86159i	0.247210	−	0.893302i	0.977635	−	0.210309i	$-0.0674471\pi$
$60$	−17.8628	+	0.983366i	−2.30608	+	0.126952i
$61$	6.90000	+	0.169385i	0.883454	+	0.0216876i	0.463743	−	0.885970i	$-0.346506\pi$
$61$	6.90000	+	0.169385i	0.883454	+	0.0216876i	0.419712	+	0.907658i	$0.362131\pi$
$62$	−5.13668	+	1.99889i	−0.652359	+	0.253859i
$63$	0.0839606	+	0.202699i	0.0105780	+	0.0255377i
$64$	−6.93364	−	3.99056i	−0.866706	−	0.498820i
$65$	−0.390641	+	0.943092i	−0.0484531	+	0.116976i
$66$	0.0747815	−	3.46323i	0.00920497	−	0.426294i
$67$	−9.87936	+	9.40593i	−1.20696	+	1.14912i	−0.222232	+	0.974994i	$0.571334\pi$
$67$	−9.87936	+	9.40593i	−1.20696	+	1.14912i	−0.984724	+	0.174124i	$0.944291\pi$
$68$	7.92444	+	10.5540i	0.960979	+	1.27986i
$69$	3.46511	−	1.96296i	0.417150	−	0.236313i
$70$	0.0151564	−	0.328302i	0.00181154	−	0.0392396i
$71$	−12.2112	+	0.599897i	−1.44920	+	0.0711946i	−0.758371	−	0.651823i	$-0.774004\pi$
$71$	−12.2112	+	0.599897i	−1.44920	+	0.0711946i	−0.690829	+	0.723018i	$0.742754\pi$
$72$	4.33627	+	8.42787i	0.511034	+	0.993235i
$73$	2.20466	+	6.16161i	0.258036	+	0.721162i	0.998780	+	0.0493750i	$0.0157230\pi$
$73$	2.20466	+	6.16161i	0.258036	+	0.721162i	−0.740744	+	0.671787i	$0.765527\pi$
$74$	−2.32904	+	0.236339i	−0.270746	+	0.0274739i
$75$	−11.0260	−	15.6557i	−1.27317	−	1.80776i
$76$	0.499352	−	0.530729i	0.0572796	−	0.0608788i
$77$	0.0631588	+	0.00778990i	0.00719762	+	0.000887741i
$78$	1.02460	−	0.0281812i	0.116013	−	0.00319090i
$79$	14.1574	−	1.39438i	1.59283	−	0.156880i	0.737639	−	0.675195i	$-0.235940\pi$
$79$	14.1574	−	1.39438i	1.59283	−	0.156880i	0.855190	+	0.518315i	$0.173440\pi$
$80$	−0.516112	−	14.1883i	−0.0577031	−	1.58630i
$81$	−0.766875	+	7.78621i	−0.0852084	+	0.865135i
$82$	8.27726	−	7.18277i	0.914071	−	0.793204i
$83$	−5.57164	−	4.80613i	−0.611567	−	0.527541i	0.291761	−	0.956491i	$-0.405759\pi$
$83$	−5.57164	−	4.80613i	−0.611567	−	0.527541i	−0.903328	+	0.428950i	$0.858884\pi$
$84$	−0.307181	+	0.120583i	−0.0335162	+	0.0131566i
$85$	−8.42957	+	21.8528i	−0.914315	+	2.37027i
$86$	1.60559	−	8.19834i	0.173135	−	0.884050i
$87$	−11.2979	−	18.8494i	−1.21126	−	2.02087i
$88$	2.74689	+	0.110554i	0.292819	+	0.0117851i
$89$	−14.5702	−	2.16128i	−1.54443	−	0.229095i	−0.680518	−	0.732732i	$-0.738245\pi$
$89$	−14.5702	−	2.16128i	−1.54443	−	0.229095i	−0.863916	+	0.503637i	$0.831995\pi$
$90$	−8.60489	+	14.4530i	−0.907035	+	1.52348i
$91$	−0.00138521	+	0.0187788i	−0.000145209	+	0.00196856i
$92$	1.50632	+	2.77851i	0.157045	+	0.289680i
$93$	−2.15205	+	9.58349i	−0.223157	+	0.993762i
$94$	0.121391	+	1.58194i	0.0125205	+	0.163165i
$95$	1.26841	+	0.252302i	0.130136	+	0.0258856i
$96$	−12.7958	+	6.28487i	−1.30596	+	0.641447i
$97$	−2.31313	+	0.460110i	−0.234863	+	0.0467171i	−0.311118	−	0.950371i	$-0.600704\pi$
$97$	−2.31313	+	0.460110i	−0.234863	+	0.0467171i	0.0762555	+	0.997088i	$0.475704\pi$
$98$	2.66686	+	9.52722i	0.269394	+	0.962394i
$99$	−2.66288	−	1.87541i	−0.267630	−	0.188486i
$100$	12.5855	−	8.51732i	1.25855	−	0.851732i
$101$	0.319799	−	0.105647i	0.0318211	−	0.0105123i	−0.297727	−	0.954651i	$-0.596229\pi$
$101$	0.319799	−	0.105647i	0.0318211	−	0.0105123i	0.329548	+	0.944139i	$0.393104\pi$
$102$	23.4866	−	1.22338i	2.32552	−	0.121133i
$103$	−3.78459	−	2.26839i	−0.372906	−	0.223512i	0.315356	−	0.948974i	$-0.397876\pi$
$103$	−3.78459	−	2.26839i	−0.372906	−	0.223512i	−0.688262	+	0.725462i	$0.741626\pi$
$104$	0.00720880	+	0.813411i	0.000706881	+	0.0797615i
$105$	−0.470402	−	0.348874i	−0.0459066	−	0.0340466i
$106$	6.73581	−	6.77572i	0.654239	−	0.658116i
$107$	8.85588	+	8.43150i	0.856131	+	0.815104i	0.984273	−	0.176652i	$-0.0565266\pi$
$107$	8.85588	+	8.43150i	0.856131	+	0.815104i	−0.128143	+	0.991756i	$0.540902\pi$
$108$	1.75694	+	0.206168i	0.169062	+	0.0198385i
$109$	−5.00185	+	15.1408i	−0.479090	+	1.45023i	0.373491	+	0.927634i	$0.378161\pi$
$109$	−5.00185	+	15.1408i	−0.479090	+	1.45023i	−0.852582	+	0.522594i	$0.824964\pi$
$110$	2.41732	+	4.23792i	0.230482	+	0.404070i
$111$	−1.96650	+	3.67906i	−0.186652	+	0.349201i
$112$	−0.0911368	−	0.245525i	−0.00861161	−	0.0231999i
$113$	−3.47185	+	1.85574i	−0.326604	+	0.174573i	−0.626547	−	0.779384i	$-0.715532\pi$
$113$	−3.47185	+	1.85574i	−0.326604	+	0.174573i	0.299943	+	0.953957i	$0.403032\pi$
$114$	−0.288258	−	1.26616i	−0.0269979	−	0.118587i
$115$	−2.76470	+	4.88037i	−0.257809	+	0.455097i
$116$	15.1236	−	8.68586i	1.40420	−	0.806462i
$117$	0.515591	−	0.814207i	0.0476664	−	0.0752735i
$118$	7.76413	−	6.41033i	0.714746	−	0.590119i
$119$	−0.0211999	+	0.431533i	−0.00194339	+	0.0395586i
$120$	−21.4940	−	13.3455i	−1.96212	−	1.21827i
$121$	9.08988	−	4.29919i	0.826353	−	0.390836i
$122$	7.85726	+	5.79144i	0.711363	+	0.524333i
$123$	−2.39059	−	19.3824i	−0.215552	−	1.74765i
$124$	−7.57246	−	1.84932i	−0.680027	−	0.166074i
$125$	8.43135	+	3.73736i	0.754123	+	0.334280i
$126$	−0.0670877	+	0.302939i	−0.00597665	+	0.0269879i
$127$	−10.4787	+	10.4787i	−0.929836	+	0.929836i	−0.997695	−	0.0678592i	$-0.978383\pi$
$127$	−10.4787	+	10.4787i	−0.929836	+	0.929836i	0.0678592	+	0.997695i	$0.478383\pi$
$128$	−4.79767	−	10.2461i	−0.424058	−	0.905635i
$129$	−10.5266	−	10.5266i	−0.926817	−	0.926817i
$130$	−1.21736	+	0.775934i	−0.106770	+	0.0680539i
$131$	−2.79274	+	6.30032i	−0.244003	+	0.550462i	−0.993797	−	0.111210i	$-0.964528\pi$
$131$	−2.79274	+	6.30032i	−0.244003	+	0.550462i	0.749794	+	0.661671i	$0.230153\pi$
$132$	2.89497	−	3.95200i	0.251975	−	0.343977i
$133$	0.0236763	−	0.00292020i	0.00205300	−	0.000253213i
$134$	−19.0739	+	2.88695i	−1.64773	+	0.249395i
$135$	1.34229	+	2.83803i	0.115526	+	0.244259i
$136$	0.623391	+	18.6542i	0.0534553	+	1.59958i
$137$	14.3785	+	0.706369i	1.22844	+	0.0603492i	0.652911	−	0.757435i	$-0.273548\pi$
$137$	14.3785	+	0.706369i	1.22844	+	0.0603492i	0.575525	+	0.817784i	$0.304798\pi$
$138$	5.60657	+	0.535481i	0.477263	+	0.0455832i
$139$	−14.9524	−	9.46853i	−1.26825	−	0.803110i	−0.280606	−	0.959823i	$-0.590535\pi$
$139$	−14.9524	−	9.46853i	−1.26825	−	0.803110i	−0.987644	+	0.156713i	$0.949910\pi$
$140$	0.283780	−	0.368094i	0.0239838	−	0.0311096i
$141$	2.45999	+	1.39357i	0.207169	+	0.117360i
$142$	−14.6348	−	9.20694i	−1.22813	−	0.772629i
$143$	−0.131770	−	0.246524i	−0.0110192	−	0.0206154i
$144$	−1.80996	+	13.2811i	−0.150830	+	1.10676i
$145$	27.2969	+	14.5905i	2.26689	+	1.21168i
$146$	−2.44202	+	8.92684i	−0.202103	+	0.738790i
$147$	16.7402	+	5.53021i	1.38071	+	0.456124i
$148$	−2.89017	−	1.61478i	−0.237570	−	0.132734i
$149$	−10.2806	+	10.7981i	−0.842220	+	0.884612i	−0.994608	−	0.103709i	$-0.966929\pi$
$149$	−10.2806	+	10.7981i	−0.842220	+	0.884612i	0.152387	+	0.988321i	$0.451304\pi$
$150$	−0.0799969	−	27.0802i	−0.00653172	−	2.21109i
$151$	14.1390	−	19.0643i	1.15062	−	1.55143i	0.366964	−	0.930235i	$-0.380397\pi$
$151$	14.1390	−	19.0643i	1.15062	−	1.55143i	0.783656	−	0.621196i	$-0.213353\pi$
$152$	1.00894	−	0.210002i	0.0818355	−	0.0170334i
$153$	11.3683	−	18.9668i	0.919070	−	1.53338i
$154$	0.0668615	+	0.0602410i	0.00538786	+	0.00485435i
$155$	−4.33942	−	13.1356i	−0.348551	−	1.05508i
$156$	1.20999	+	0.798191i	0.0968768	+	0.0639064i
$157$	−2.51814	+	3.57549i	−0.200970	+	0.285355i	−0.905524	−	0.424295i	$-0.860522\pi$
$157$	−2.51814	+	3.57549i	−0.200970	+	0.285355i	0.704554	+	0.709650i	$0.251147\pi$
$158$	17.5340	+	9.86458i	1.39493	+	0.784784i
$159$	−3.32148	−	16.6982i	−0.263411	−	1.32426i
$160$	10.9072	−	16.8576i	0.862292	−	1.33271i
$161$	−0.0201853	+	0.101478i	−0.00159082	+	0.00799760i
$162$	−7.20235	+	8.39956i	−0.565870	+	0.659932i
$163$	2.37018	+	0.532243i	0.185647	+	0.0416885i	0.310931	−	0.950432i	$-0.399359\pi$
$163$	2.37018	+	0.532243i	0.185647	+	0.0416885i	−0.125284	+	0.992121i	$0.539984\pi$
$164$	15.4149	−	1.61024i	1.20370	−	0.125739i
$165$	8.67054	+	0.639577i	0.675000	+	0.0497910i
$166$	−2.55825	−	10.0866i	−0.198559	−	0.782872i
$167$	1.51207	−	10.1935i	0.117007	−	0.788800i	−0.848645	−	0.528963i	$-0.822581\pi$
$167$	1.51207	−	10.1935i	0.117007	−	0.788800i	0.965652	−	0.259837i	$-0.0836690\pi$
$168$	−0.453693	−	0.109380i	−0.0350031	−	0.00843889i
$169$	−11.0795	+	6.64081i	−0.852271	+	0.510832i
$170$	−27.4872	+	18.4841i	−2.10817	+	1.41766i
$171$	−1.13914	−	0.439415i	−0.0871123	−	0.0336029i
$172$	8.50831	−	8.19696i	0.648752	−	0.625012i
$173$	9.59098	−	11.1186i	0.729189	−	0.845333i	−0.263672	−	0.964612i	$-0.584934\pi$
$173$	9.59098	−	11.1186i	0.729189	−	0.845333i	0.992861	+	0.119280i	$0.0380586\pi$
$174$	2.19472	−	31.0011i	0.166381	−	2.35019i
$175$	0.495093	+	0.0487624i	0.0374255	+	0.00368609i
$176$	3.09301	+	2.35553i	0.233144	+	0.177555i
$177$	−1.75861	−	17.8555i	−0.132186	−	1.34210i
$178$	−15.1290	−	14.3190i	−1.13397	−	1.07326i
$179$	−1.54480	+	12.5249i	−0.115463	+	0.936153i	0.817437	+	0.576018i	$0.195394\pi$
$179$	−1.54480	+	12.5249i	−0.115463	+	0.936153i	−0.932900	+	0.360135i	$0.882731\pi$
$180$	−21.6899	+	9.76819i	−1.61667	+	0.728078i
$181$	16.9631	−	11.9467i	1.26085	−	0.887994i	0.263791	−	0.964580i	$-0.415027\pi$
$181$	16.9631	−	11.9467i	1.26085	−	0.887994i	0.997063	+	0.0765864i	$0.0244021\pi$
$182$	−0.0168327	+	0.0206346i	−0.00124772	+	0.00152954i
$183$	16.3772	−	5.85987i	1.21064	−	0.433174i
$184$	−0.507805	+	4.44077i	−0.0374359	+	0.327378i
$185$	−0.288296	−	5.86840i	−0.0211960	−	0.431453i
$186$	−10.2647	+	9.35873i	−0.752642	+	0.686216i
$187$	−3.16139	−	5.58063i	−0.231184	−	0.408096i
$188$	−1.14214	+	1.93134i	−0.0832994	+	0.140857i
$189$	0.0399321	+	0.0419420i	0.00290463	+	0.00305083i
$190$	1.26504	+	1.32087i	0.0917753	+	0.0958262i
$191$	14.4942	+	6.00369i	1.04876	+	0.434412i	0.839450	−	0.543437i	$-0.182877\pi$
$191$	14.4942	+	6.00369i	1.04876	+	0.434412i	0.209313	+	0.977849i	$0.432877\pi$
$192$	−19.9221	−	3.09415i	−1.43775	−	0.223301i
$193$	10.7321	−	4.44538i	0.772514	−	0.319986i	0.0386235	−	0.999254i	$-0.487703\pi$
$193$	10.7321	−	4.44538i	0.772514	−	0.319986i	0.733890	+	0.679268i	$0.237703\pi$
$194$	−3.05319	−	1.34261i	−0.219206	−	0.0963936i
$195$	−0.0631328	+	2.57175i	−0.00452104	+	0.184167i
$196$	−4.63566	+	13.2012i	−0.331118	+	0.942940i
$197$	−4.83628	−	1.33838i	−0.344571	−	0.0953556i	0.0901312	−	0.995930i	$-0.471271\pi$
$197$	−4.83628	−	1.33838i	−0.344571	−	0.0953556i	−0.434702	+	0.900574i	$0.643146\pi$
$198$	−1.56455	−	4.33225i	−0.111188	−	0.307879i
$199$	−10.2894	+	11.3526i	−0.729393	+	0.804761i	−0.986869	−	0.161523i	$-0.948359\pi$
$199$	−10.2894	+	11.3526i	−0.729393	+	0.804761i	0.257476	+	0.966285i	$0.417109\pi$
$200$	21.4887	+	0.337002i	1.51948	+	0.0238297i
$201$	−14.6979	+	31.0760i	−1.03671	+	2.19193i
$202$	0.456200	+	0.136917i	0.0320981	+	0.00963341i
$203$	0.562537	+	0.0976094i	0.0394823	+	0.00685083i
$204$	28.2045	+	17.6277i	1.97471	+	1.23419i
$205$	16.9224	+	21.6840i	1.18191	+	1.51448i
$206$	−2.54554	−	5.69716i	−0.177356	−	0.396940i
$207$	3.35942	−	4.09346i	0.233496	−	0.284515i
$208$	−0.651240	+	0.948296i	−0.0451554	+	0.0657525i
$209$	−0.273754	+	0.224664i	−0.0189360	+	0.0155404i
$210$	−0.262126	−	0.785667i	−0.0180884	−	0.0542162i
$211$	−14.1077	+	1.04065i	−0.971214	+	0.0716411i	−0.549862	−	0.835256i	$-0.685320\pi$
$211$	−14.1077	+	1.04065i	−0.971214	+	0.0716411i	−0.421353	+	0.906897i	$0.638445\pi$
$212$	13.2988	−	2.38858i	0.913364	−	0.164048i
$213$	−28.1674	+	12.4858i	−1.93000	+	0.855510i
$214$	3.42371	+	16.9503i	0.234040	+	1.15870i
$215$	20.3388	+	5.09461i	1.38710	+	0.347450i
$216$	1.86848	+	1.66357i	0.127134	+	0.113192i
$217$	−0.152012	−	0.204965i	−0.0103193	−	0.0139139i
$218$	−18.0730	+	13.4868i	−1.22406	+	0.913440i
$219$	10.7721	+	12.4879i	0.727914	+	0.843854i
$220$	−0.635715	+	6.87041i	−0.0428599	+	0.463203i
$221$	1.60338	−	1.01533i	0.107855	−	0.0682985i
$222$	−5.26180	+	2.66808i	−0.353149	+	0.179070i
$223$	−16.6368	+	11.1164i	−1.11408	+	0.744407i	−0.969501	−	0.245086i	$-0.921184\pi$
$223$	−16.6368	+	11.1164i	−1.11408	+	0.744407i	−0.144582	+	0.989493i	$0.546184\pi$
$224$	0.0935004	−	0.358377i	0.00624726	−	0.0239451i
$225$	−21.1707	−	14.1458i	−1.41138	−	0.943056i
$226$	−5.52744	−	0.665173i	−0.367680	−	0.0442467i
$227$	−29.0304	+	5.03726i	−1.92682	+	0.334335i	−0.999229	−	0.0392688i	$-0.987497\pi$
$227$	−29.0304	+	5.03726i	−1.92682	+	0.334335i	−0.927589	+	0.373603i	$0.878122\pi$
$228$	0.692741	−	1.70078i	0.0458779	−	0.112637i
$229$	−12.6445	−	6.36473i	−0.835575	−	0.420593i	−0.0203886	−	0.999792i	$-0.506490\pi$
$229$	−12.6445	−	6.36473i	−0.835575	−	0.420593i	−0.815186	+	0.579199i	$0.803365\pi$
$230$	−7.16077	+	3.41271i	−0.472167	+	0.225028i
$231$	0.155567	−	0.0389676i	0.0102356	−	0.00256388i
$232$	24.5662	+	2.19992i	1.61285	+	0.144432i
$233$	3.22362	+	21.7319i	0.211186	+	1.42370i	0.792425	+	0.609969i	$0.208818\pi$
$233$	3.22362	+	21.7319i	0.211186	+	1.42370i	−0.581239	+	0.813733i	$0.697432\pi$
$234$	1.25762	−	0.525282i	0.0822133	−	0.0343388i
$235$	−3.98085	+	0.0977245i	−0.259682	+	0.00637484i
$236$	14.1939	−	1.13136i	0.923947	−	0.0736454i
$237$	32.0228	−	16.1189i	2.08011	−	1.04704i
$238$	−0.374492	+	0.482801i	−0.0242747	+	0.0312953i
$239$	−3.76386	−	12.4078i	−0.243464	−	0.802592i	−0.990464	−	0.137769i	$-0.956007\pi$
$239$	−3.76386	−	12.4078i	−0.243464	−	0.802592i	0.747001	−	0.664823i	$-0.231493\pi$
$240$	−14.0819	−	32.8920i	−0.908985	−	2.12317i
$241$	18.6135	+	5.64635i	1.19900	+	0.363713i	0.825761	−	0.564021i	$-0.190746\pi$
$241$	18.6135	+	5.64635i	1.19900	+	0.363713i	0.373242	+	0.927734i	$0.378246\pi$
$242$	14.0181	+	2.38974i	0.901118	+	0.153618i
$243$	5.96652	+	21.5602i	0.382753	+	1.38309i
$244$	4.40748	+	13.0816i	0.282160	+	0.837465i
$245$	−24.2273	+	5.44043i	−1.54783	+	0.347576i
$246$	12.9473	−	24.3958i	0.825489	−	1.55542i
$247$	−0.0703711	−	0.0776425i	−0.00447760	−	0.00494027i
$248$	−7.27414	−	8.28318i	−0.461908	−	0.525982i
$249$	−17.4594	−	6.24706i	−1.10644	−	0.395891i
$250$	6.73829	+	11.1672i	0.426167	+	0.706276i
$251$	17.0186	+	13.2814i	1.07420	+	0.838316i	0.987453	−	0.157914i	$-0.0504768\pi$
$251$	17.0186	+	13.2814i	1.07420	+	0.838316i	0.0867503	+	0.996230i	$0.472352\pi$
$252$	−0.323382	+	0.296595i	−0.0203712	+	0.0186838i
$253$	−0.552786	−	1.43304i	−0.0347534	−	0.0900948i
$254$	−20.6382	+	3.64390i	−1.29496	+	0.228639i
$255$			59.0269i			3.69641i
$256$	2.74975	−	15.7619i	0.171860	−	0.985121i
$257$		−	1.46532i		−	0.0914041i	−0.998955	−	0.0457020i	$-0.985448\pi$
$257$		−	1.46532i		−	0.0914041i	0.998955	−	0.0457020i	$-0.0145525\pi$
$258$	−3.66056	−	20.7326i	−0.227897	−	1.29075i
$259$	−0.0390056	−	0.101118i	−0.00242369	−	0.00628319i
$260$	−2.03969	−	0.0881270i	−0.126496	−	0.00546540i
$261$	−23.0365	−	17.9778i	−1.42592	−	1.11280i
$262$	−8.34469	+	5.03518i	−0.515537	+	0.311075i
$263$	14.3012	+	5.11705i	0.881850	+	0.315531i	0.738591	−	0.674154i	$-0.235492\pi$
$263$	14.3012	+	5.11705i	0.881850	+	0.315531i	0.143259	+	0.989685i	$0.454242\pi$
$264$	6.55889	−	2.23142i	0.403672	−	0.137335i
$265$	16.1034	+	17.7673i	0.989223	+	1.09144i
$266$	0.0298003	+	0.0158156i	0.00182717	+	0.000969716i
$267$	−36.2183	+	8.13309i	−2.21652	+	0.497737i
$268$	−24.4408	−	12.1220i	−1.49296	−	0.740469i
$269$	−2.71847	−	9.82330i	−0.165748	−	0.598937i	−0.998943	−	0.0459581i	$-0.985366\pi$
$269$	−2.71847	−	9.82330i	−0.165748	−	0.598937i	0.833195	−	0.552979i	$-0.186509\pi$
$270$	−0.746120	+	4.37671i	−0.0454074	+	0.266358i
$271$	9.38926	+	2.84820i	0.570357	+	0.173016i	0.562273	−	0.826951i	$-0.309927\pi$
$271$	9.38926	+	2.84820i	0.570357	+	0.173016i	0.00808351	+	0.999967i	$0.497427\pi$
$272$	−14.4043	+	22.1190i	−0.873389	+	1.34116i
$273$	0.0137750	+	0.0454101i	0.000833700	+	0.00274834i
$274$	16.0867	+	12.4779i	0.971832	+	0.753817i
$275$	−6.59670	+	3.32050i	−0.397796	+	0.200234i
$276$	6.06178	+	5.16678i	0.364876	+	0.311004i
$277$	−18.4712	+	0.453442i	−1.10983	+	0.0272447i	−0.575327	−	0.817924i	$-0.695125\pi$
$277$	−18.4712	+	0.453442i	−1.10983	+	0.0272447i	−0.534500	+	0.845169i	$0.679500\pi$
$278$	−9.64650	−	23.0955i	−0.578559	−	1.38518i
$279$	1.91636	+	12.9191i	0.114730	+	0.773445i
$280$	0.627285	−	0.196372i	0.0374875	−	0.0117355i
$281$	1.84843	−	0.463007i	0.110268	−	0.0276207i	−0.187453	−	0.982273i	$-0.560023\pi$
$281$	1.84843	−	0.463007i	0.110268	−	0.0276207i	0.297721	+	0.954653i	$0.403773\pi$
$282$	1.72020	+	3.60944i	0.102437	+	0.214939i
$283$	−6.77719	−	3.41135i	−0.402862	−	0.202784i	0.236599	−	0.971607i	$-0.423967\pi$
$283$	−6.77719	−	3.41135i	−0.402862	−	0.202784i	−0.639461	+	0.768824i	$0.720842\pi$
$284$	−9.49060	−	22.5348i	−0.563164	−	1.33720i
$285$	3.21117	−	0.557191i	0.190213	−	0.0330051i
$286$	0.0472317	−	0.392485i	0.00279287	−	0.0232081i
$287$	0.421869	+	0.281884i	0.0249021	+	0.0166391i
$288$	−12.8667	+	13.9204i	−0.758179	+	0.820266i
$289$	22.0720	−	14.7480i	1.29835	−	0.867532i
$290$	19.7959	+	39.0401i	1.16246	+	2.29252i
$291$	−5.02143	+	3.17979i	−0.294362	+	0.186402i
$292$	−10.0682	+	8.36277i	−0.589195	+	0.489394i
$293$	−3.02880	−	3.51122i	−0.176944	−	0.205128i	0.661758	−	0.749717i	$-0.269810\pi$
$293$	−3.02880	−	3.51122i	−0.176944	−	0.205128i	−0.838703	+	0.544589i	$0.816685\pi$
$294$	14.9114	+	19.9821i	0.869651	+	1.16538i
$295$	15.0533	+	20.2970i	0.876438	+	1.18174i
$296$	−2.03924	−	4.21457i	−0.118529	−	0.244967i
$297$	−0.833932	−	0.208889i	−0.0483896	−	0.0121210i
$298$	−20.6676	+	4.17456i	−1.19724	+	0.241825i
$299$	0.415491	−	0.184175i	0.0240285	−	0.0106511i
$300$	21.8665	−	31.4411i	1.26247	−	1.81525i
$301$	0.385718	−	0.0284523i	0.0222324	−	0.00163996i
$302$	31.8412	−	10.6234i	1.83226	−	0.611305i
$303$	0.656106	−	0.538453i	0.0376923	−	0.0309333i
$304$	1.33928	+	0.574826i	0.0768131	+	0.0329685i
$305$	−15.5416	+	18.9375i	−0.889908	+	1.08436i
$306$	28.5518	−	12.7572i	1.63220	−	0.729281i
$307$	−2.82707	−	3.62255i	−0.161349	−	0.206750i	0.700865	−	0.713294i	$-0.252798\pi$
$307$	−2.82707	−	3.62255i	−0.161349	−	0.206750i	−0.862214	+	0.506544i	$0.830923\pi$
$308$	0.0286193	+	0.124015i	0.00163073	+	0.00706643i
$309$	−10.9559	−	1.90103i	−0.623258	−	0.108146i
$310$	5.62380	−	18.7383i	0.319411	−	1.06426i
$311$	−1.37232	+	2.90153i	−0.0778173	+	0.164531i	−0.939147	−	0.343516i	$-0.888382\pi$
$311$	−1.37232	+	2.90153i	−0.0778173	+	0.164531i	0.861330	+	0.508046i	$0.169632\pi$
$312$	0.754695	+	1.90599i	0.0427262	+	0.107906i
$313$	−11.7097	+	12.9196i	−0.661870	+	0.730261i	−0.975674	−	0.219227i	$-0.929647\pi$
$313$	−11.7097	+	12.9196i	−0.661870	+	0.730261i	0.313804	+	0.949488i	$0.398397\pi$
$314$	−5.81697	+	2.10075i	−0.328271	+	0.118552i
$315$	−0.750531	−	0.207700i	−0.0422876	−	0.0117026i
$316$	12.3164	+	25.6478i	0.692854	+	1.44280i
$317$	0.530724	−	21.6193i	0.0298084	−	1.21426i	−0.779319	−	0.626628i	$-0.784435\pi$
$317$	0.530724	−	21.6193i	0.0298084	−	1.21426i	0.809127	−	0.587634i	$-0.199940\pi$
$318$	9.69213	−	22.0406i	0.543508	−	1.23598i
$319$	−7.83051	+	3.24351i	−0.438425	+	0.181601i
$320$	26.3073	−	10.6873i	1.47062	−	0.597436i
$321$	28.4696	+	11.7925i	1.58902	+	0.658192i
$322$	−0.105676	+	0.101209i	−0.00588908	+	0.00564013i
$323$	−1.65791	−	1.74136i	−0.0922485	−	0.0968917i
$324$	−15.1561	+	3.89171i	−0.842006	+	0.216206i
$325$	−1.07710	−	1.90135i	−0.0597470	−	0.105468i
$326$	2.31460	+	2.53865i	0.128194	+	0.140603i
$327$	1.97177	+	40.1364i	0.109039	+	2.21955i
$328$	19.1660	+	10.6342i	1.05827	+	0.587173i
$329$	−0.0691602	+	0.0247459i	−0.00381292	+	0.00136429i
$330$	9.52740	+	7.77195i	0.524466	+	0.427832i
$331$	−9.48093	+	6.67723i	−0.521119	+	0.367014i	−0.806344	−	0.591447i	$-0.798557\pi$
$331$	−9.48093	+	6.67723i	−0.521119	+	0.367014i	0.285225	+	0.958461i	$0.407932\pi$
$332$	5.21510	−	13.7612i	0.286216	−	0.755245i
$333$	−0.679012	+	5.50528i	−0.0372096	+	0.301688i
$334$	10.0179	−	10.5845i	0.548153	−	0.579159i
$335$	−4.74570	−	48.1839i	−0.259286	−	2.63257i
$336$	−0.436970	−	0.494630i	−0.0238387	−	0.0269843i
$337$	−7.90207	−	0.778286i	−0.430453	−	0.0423959i	−0.119529	−	0.992831i	$-0.538138\pi$
$337$	−7.90207	−	0.778286i	−0.430453	−	0.0423959i	−0.310924	+	0.950435i	$0.600638\pi$
$338$	−18.2222	−	1.29004i	−0.991157	−	0.0701689i
$339$	−6.48006	+	7.51219i	−0.351949	+	0.408006i
$340$	−46.8365	−	0.872925i	−2.54006	−	0.0473410i
$341$	3.53437	+	1.36336i	0.191397	+	0.0738300i
$342$	−0.963534	−	1.43285i	−0.0521020	−	0.0774796i
$343$	−0.785977	+	0.471096i	−0.0424388	+	0.0254368i
$344$	16.5049	−	2.59797i	0.889887	−	0.140073i
$345$	−2.07411	+	13.9825i	−0.111666	+	0.752792i
$346$	20.1285	−	5.10518i	1.08212	−	0.274456i
$347$	−7.64835	−	0.564176i	−0.410585	−	0.0302866i	−0.133303	−	0.991075i	$-0.542558\pi$
$347$	−7.64835	−	0.564176i	−0.410585	−	0.0302866i	−0.277281	+	0.960789i	$0.589433\pi$
$348$	27.6816	−	34.1394i	1.48389	−	1.83006i
$349$	−20.8493	−	4.68187i	−1.11604	−	0.250615i	−0.378288	−	0.925688i	$-0.623487\pi$
$349$	−20.8493	−	4.68187i	−1.11604	−	0.250615i	−0.737751	+	0.675073i	$0.764112\pi$
$350$	0.534093	+	0.457967i	0.0285485	+	0.0244794i
$351$	0.0496267	−	0.249490i	0.00264888	−	0.0133168i
$352$	1.67359	+	5.23733i	0.0892025	+	0.279150i
$353$	−5.94889	−	29.9071i	−0.316627	−	1.59179i	−0.731453	−	0.681892i	$-0.761157\pi$
$353$	−5.94889	−	29.9071i	−0.316627	−	1.59179i	0.414825	−	0.909901i	$-0.363843\pi$
$354$	12.4414	−	22.1142i	0.661252	−	1.17535i
$355$	24.9871	−	35.4789i	1.32618	−	1.88302i
$356$	−5.91780	−	28.8586i	−0.313643	−	1.52951i
$357$	0.341545	+	1.03387i	0.0180765	+	0.0547182i
$358$	−11.9462	+	13.2592i	−0.631378	+	0.700768i
$359$	11.9607	−	19.9551i	0.631259	−	1.05319i	−0.361419	−	0.932403i	$-0.617708\pi$
$359$	11.9607	−	19.9551i	0.631259	−	1.05319i	0.992678	−	0.120789i	$-0.0385423\pi$
$360$	−33.0518	−	6.27043i	−1.74198	−	0.330481i
$361$	11.2392	−	15.1543i	0.591537	−	0.797595i
$362$	29.3416	−	0.0866774i	1.54216	−	0.00455567i
$363$	17.4733	−	18.3528i	0.917110	−	0.963271i
$364$	−0.0362356	+	0.0102586i	−0.00189926	+	0.000537696i
$365$	−22.0556	−	7.28617i	−1.15444	−	0.381376i
$366$	23.7271	+	6.49077i	1.24023	+	0.339278i
$367$	0.518729	+	0.277267i	0.0270774	+	0.0144732i	0.484880	−	0.874581i	$-0.338863\pi$
$367$	0.518729	+	0.277267i	0.0270774	+	0.0144732i	−0.457802	+	0.889054i	$0.651363\pi$
$368$	−4.18937	+	4.73347i	−0.218386	+	0.246749i
$369$	−12.2412	−	22.9017i	−0.637251	−	1.19221i
$370$	4.42464	−	7.03314i	0.230026	−	0.365636i
$371$	0.384861	+	0.218021i	0.0199810	+	0.0113191i
$372$	−19.4820	+	2.51982i	−1.01010	+	0.130646i
$373$	15.2358	+	9.64799i	0.788882	+	0.499554i	0.867552	−	0.497347i	$-0.165692\pi$
$373$	15.2358	+	9.64799i	0.788882	+	0.499554i	−0.0786698	+	0.996901i	$0.525067\pi$
$374$	0.862403	−	9.02950i	0.0445938	−	0.466904i
$375$	23.2139	+	1.14043i	1.19876	+	0.0588913i
$376$	−2.88945	+	1.31156i	−0.149012	+	0.0676387i
$377$	−1.07226	−	2.26711i	−0.0552244	−	0.116762i
$378$	0.0122563	+	0.0809765i	0.000630396	+	0.00416498i
$379$	23.6084	−	2.91182i	1.21268	−	0.149570i	0.509432	−	0.860511i	$-0.329856\pi$
$379$	23.6084	−	2.91182i	1.21268	−	0.149570i	0.703252	+	0.710941i	$0.251731\pi$
$380$	0.394629	+	2.55623i	0.0202441	+	0.131132i
$381$	−15.1341	+	34.1420i	−0.775344	+	1.74915i
$382$	11.9252	+	18.7094i	0.610145	+	0.957256i
$383$	4.16992	+	4.16992i	0.213073	+	0.213073i	0.805571	−	0.592499i	$-0.201858\pi$
$383$	4.16992	+	4.16992i	0.213073	+	0.213073i	−0.592499	+	0.805571i	$0.701858\pi$
$384$	−20.5735	−	19.7397i	−1.04989	−	1.00734i
$385$	−0.159718	+	0.159718i	−0.00813998	+	0.00813998i
$386$	16.0394	+	3.55203i	0.816383	+	0.180793i
$387$	−18.0968	−	8.02174i	−0.919910	−	0.407768i
$388$	−2.44883	−	4.03142i	−0.124320	−	0.204664i
$389$	3.90601	+	31.6691i	0.198043	+	1.60569i	0.682508	+	0.730878i	$0.260889\pi$
$389$	3.90601	+	31.6691i	0.198043	+	1.60569i	−0.484465	+	0.874810i	$0.660986\pi$
$390$	−2.15857	+	2.92853i	−0.109303	+	0.148292i
$391$	9.42693	−	4.45861i	0.476740	−	0.225481i
$392$	−16.0758	+	11.5364i	−0.811952	+	0.582674i
$393$	−0.852183	+	17.3466i	−0.0429869	+	0.875019i
$394$	−4.51822	−	5.47243i	−0.227625	−	0.275697i
$395$	−27.0139	+	42.6596i	−1.35922	+	2.14644i
$396$	1.70025	−	6.28821i	0.0854408	−	0.315994i
$397$	−3.78395	+	6.67960i	−0.189911	+	0.335239i	−0.948744	−	0.316046i	$-0.897645\pi$
$397$	−3.78395	+	6.67960i	−0.189911	+	0.335239i	0.758833	+	0.651285i	$0.225770\pi$
$398$	−21.1274	+	4.80992i	−1.05902	+	0.241100i
$399$	0.0530204	−	0.0283400i	0.00265434	−	0.00141877i
$400$	24.6244	+	17.8156i	1.23122	+	0.890778i
$401$	6.32050	−	11.8248i	0.315631	−	0.590504i	−0.673215	−	0.739447i	$-0.735087\pi$
$401$	6.32050	−	11.8248i	0.315631	−	0.590504i	0.988846	+	0.148943i	$0.0475872\pi$
$402$	−42.2290	+	24.0875i	−2.10619	+	1.20137i
$403$	−0.351607	+	1.06433i	−0.0175148	+	0.0530181i
$404$	0.417547	+	0.528568i	0.0207737	+	0.0262973i
$405$	−20.1125	−	19.1487i	−0.999398	−	0.951506i
$406$	0.572626	+	0.569253i	0.0284190	+	0.0282516i
$407$	1.29230	+	0.958432i	0.0640567	+	0.0475077i
$408$	18.3846	+	43.2952i	0.910175	+	2.14343i
$409$	22.6302	+	13.5640i	1.11899	+	0.670696i	0.949165	−	0.314778i	$-0.101930\pi$
$409$	22.6302	+	13.5640i	1.11899	+	0.670696i	0.169824	+	0.985474i	$0.445680\pi$
$410$	2.02344	+	38.8463i	0.0999307	+	1.91848i
$411$	34.4480	−	11.3801i	1.69920	−	0.561339i
$412$	1.67044	−	8.66513i	0.0822968	−	0.426900i
$413$	0.381106	+	0.268405i	0.0187530	+	0.0132074i
$414$	7.21173	−	2.01871i	0.354437	−	0.0992141i
$415$	25.6152	−	5.09518i	1.25740	−	0.250113i
$416$	−1.52352	+	0.570646i	−0.0746969	+	0.0279782i
$417$	−43.7447	−	8.70135i	−2.14218	−	0.426107i
$418$	−0.499362	+	0.0383187i	−0.0244246	+	0.00187423i
$419$	−5.29402	+	23.5753i	−0.258630	+	1.15173i	0.658323	+	0.752736i	$0.271266\pi$
$419$	−5.29402	+	23.5753i	−0.258630	+	1.15173i	−0.916953	+	0.398995i	$0.869359\pi$
$420$	0.333385	−	1.12286i	0.0162675	−	0.0547901i
$421$	−2.32511	+	31.5208i	−0.113319	+	1.53623i	0.579413	+	0.815034i	$0.303282\pi$
$421$	−2.32511	+	31.5208i	−0.113319	+	1.53623i	−0.692733	+	0.721195i	$0.743593\pi$
$422$	−17.1896	−	10.2342i	−0.836777	−	0.498191i
$423$	3.71874	+	0.551623i	0.180811	+	0.0268208i
$424$	17.3454	+	8.01644i	0.842367	+	0.389313i
$425$	−25.7775	−	43.0072i	−1.25039	−	2.08616i
$426$	−42.7605	−	8.37436i	−2.07176	−	0.405739i
$427$	−0.162637	+	0.421622i	−0.00787058	+	0.0204037i
$428$	−9.77809	+	22.4155i	−0.472642	+	1.08350i
$429$	−0.533416	−	0.460127i	−0.0257535	−	0.0222152i
$430$	19.4342	+	22.3955i	0.937199	+	1.08001i
$431$	0.121661	−	1.23524i	0.00586020	−	0.0594996i	−0.991810	−	0.127723i	$-0.959233\pi$
$431$	0.121661	−	1.23524i	0.00586020	−	0.0594996i	0.997670	+	0.0682235i	$0.0217331\pi$
$432$	0.815914	+	3.44263i	0.0392557	+	0.165634i
$433$	34.4036	−	3.38846i	1.65333	−	0.162839i	0.772092	−	0.635511i	$-0.219210\pi$
$433$	34.4036	−	3.38846i	1.65333	−	0.162839i	0.881238	+	0.472672i	$0.156710\pi$
$434$	−0.00992222	−	0.360746i	−0.000476282	−	0.0173164i
$435$	77.4151	+	9.54824i	3.71177	+	0.457803i
$436$	−31.8765	+	0.970997i	−1.52661	+	0.0465023i
$437$	−0.331543	−	0.470755i	−0.0158598	−	0.0225192i
$438$	2.35463	+	23.2041i	0.112509	+	1.10873i
$439$	−9.30900	−	26.0169i	−0.444294	−	1.24172i	−0.929988	−	0.367590i	$-0.880183\pi$
$439$	−9.30900	−	26.0169i	−0.444294	−	1.24172i	0.485694	−	0.874129i	$-0.338567\pi$
$440$	−6.30776	+	7.44484i	−0.300711	+	0.354919i
$441$	23.4142	−	1.15027i	1.11496	−	0.0547746i
$442$	2.68107	+	0.123774i	0.127525	+	0.00588735i
$443$	9.27376	−	5.25352i	0.440610	−	0.249602i	−0.256532	−	0.966536i	$-0.582580\pi$
$443$	9.27376	−	5.25352i	0.440610	−	0.249602i	0.697142	+	0.716933i	$0.254455\pi$
$444$	−8.26007	−	1.17543i	−0.392005	−	0.0557836i
$445$	37.8646	−	36.0501i	1.79496	−	1.70894i
$446$	−28.2903	−	0.610872i	−1.33958	−	0.0289256i
$447$	−14.3787	+	34.7132i	−0.680088	+	1.64188i
$448$	0.398940	−	0.339411i	0.0188481	−	0.0160357i
$449$	0.732154	+	1.76758i	0.0345525	+	0.0834171i	0.940214	−	0.340585i	$-0.110625\pi$
$449$	0.732154	+	1.76758i	0.0345525	+	0.0834171i	−0.905661	+	0.424002i	$0.860625\pi$
$450$	−13.0585	−	33.5572i	−0.615581	−	1.58190i
$451$	−7.52979	−	0.184846i	−0.354564	−	0.00870406i
$452$	−5.86492	−	5.25288i	−0.275863	−	0.247075i
$453$	15.9535	−	57.6487i	0.749563	−	2.70857i
$454$	−37.7205	−	17.7043i	−1.77031	−	0.830904i
$455$	−0.0495214	−	0.0448836i	−0.00232160	−	0.00210418i
$456$	2.18179	−	1.40885i	0.102172	−	0.0659753i
$457$	26.7343	+	12.6444i	1.25058	+	0.591480i	0.934063	−	0.357107i	$-0.116237\pi$
$457$	26.7343	+	12.6444i	1.25058	+	0.591480i	0.316516	+	0.948587i	$0.397487\pi$
$458$	−9.48933	−	17.6278i	−0.443407	−	0.823695i
$459$	0.997860	−	5.75081i	0.0465761	−	0.268425i
$460$	−11.0641	−	1.85254i	−0.515867	−	0.0863750i
$461$	−4.10559	+	3.20404i	−0.191217	+	0.149227i	−0.706299	−	0.707914i	$-0.749636\pi$
$461$	−4.10559	+	3.20404i	−0.191217	+	0.149227i	0.515082	+	0.857141i	$0.327761\pi$
$462$	0.211845	+	0.0809996i	0.00985593	+	0.00376844i
$463$	−2.66889	−	2.19030i	−0.124034	−	0.101792i	0.570331	−	0.821415i	$-0.306815\pi$
$463$	−2.66889	−	2.19030i	−0.124034	−	0.101792i	−0.694365	+	0.719623i	$0.744315\pi$
$464$	26.6795	+	22.4696i	1.23856	+	1.04312i
$465$	−22.1168	−	26.9494i	−1.02564	−	1.24975i
$466$	−13.8873	+	27.7934i	−0.643316	+	1.28751i
$467$	−2.29055	−	31.0523i	−0.105994	−	1.43693i	−0.744661	−	0.667443i	$-0.767389\pi$
$467$	−2.29055	−	31.0523i	−0.105994	−	1.43693i	0.638667	−	0.769484i	$-0.279486\pi$
$468$	1.88308	+	0.411189i	0.0870454	+	0.0190072i
$469$	−0.361927	−	0.816494i	−0.0167122	−	0.0377022i
$470$	−4.69162	−	3.11483i	−0.216408	−	0.143677i
$471$	−2.67790	+	10.6908i	−0.123391	+	0.492604i
$472$	17.3631	+	10.1990i	0.799201	+	0.469446i
$473$	−4.61168	+	3.42025i	−0.212045	+	0.157263i
$474$	50.1737	+	7.29116i	2.30456	+	0.334894i
$475$	−2.09634	+	1.80832i	−0.0961867	+	0.0829712i
$476$	−0.825403	+	0.255718i	−0.0378323	+	0.0117208i
$477$	−12.1115	−	19.1262i	−0.554549	−	0.875729i
$478$	5.70046	−	17.4282i	0.260733	−	0.797149i
$479$	−11.6501	−	17.4356i	−0.532305	−	0.796651i	0.463696	−	0.885994i	$-0.346523\pi$
$479$	−11.6501	−	17.4356i	−0.532305	−	0.796651i	−0.996001	+	0.0893437i	$0.971523\pi$
$480$	10.3562	−	49.5290i	0.472691	−	2.26068i
$481$	−0.264489	+	0.395836i	−0.0120597	+	0.0180486i
$482$	16.9878	+	21.6357i	0.773771	+	0.985480i
$483$	0.0445778	+	0.256908i	0.00202836	+	0.0116897i
$484$	14.3041	+	14.1361i	0.650187	+	0.642549i
$485$	3.76374	−	7.47727i	0.170903	−	0.339525i
$486$	−10.5701	+	29.8188i	−0.479468	+	1.35261i
$487$	0.0255177	+	0.101872i	0.00115632	+	0.00461628i	0.970607	−	0.240671i	$-0.0773676\pi$
$487$	0.0255177	+	0.101872i	0.00115632	+	0.00461628i	−0.969450	+	0.245288i	$0.921118\pi$
$488$	−5.50117	+	18.7309i	−0.249026	+	0.847908i
$489$	6.05563	−	0.898267i	0.273845	−	0.0406210i
$490$	−32.4824	−	13.3424i	−1.46741	−	0.602747i
$491$	−0.844121	−	34.3857i	−0.0380946	−	1.55180i	−0.649423	−	0.760427i	$-0.724990\pi$
$491$	−0.844121	−	34.3857i	−0.0380946	−	1.55180i	0.611329	−	0.791377i	$-0.290635\pi$
$492$	34.7837	−	17.7670i	1.56817	−	0.800998i
$493$	−25.8725	−	51.3997i	−1.16524	−	2.31493i
$494$	−0.0185747	−	0.147023i	−0.000835715	−	0.00661490i
$495$	11.0627	−	3.35583i	0.497230	−	0.150833i
$496$	−1.71131	−	15.4958i	−0.0768399	−	0.695782i
$497$	0.232365	−	0.766003i	0.0104230	−	0.0343599i
$498$	−15.1634	−	21.3958i	−0.679488	−	0.958770i
$499$	−8.43443	+	2.33412i	−0.377577	+	0.104490i	−0.450334	−	0.892860i	$-0.648695\pi$
$499$	−8.43443	+	2.33412i	−0.377577	+	0.104490i	0.0727573	+	0.997350i	$0.476820\pi$
$500$	−1.24820	+	18.4028i	−0.0558213	+	0.823000i
$501$	−5.69006	−	25.3390i	−0.254213	−	1.13206i
$502$	8.94854	+	29.1887i	0.399393	+	1.30276i
$503$	−28.8648	+	26.1616i	−1.28702	+	1.16649i	−0.310615	+	0.950536i	$0.600535\pi$
$503$	−28.8648	+	26.1616i	−1.28702	+	1.16649i	−0.976404	+	0.215950i	$0.930715\pi$
$504$	−0.615192	+	0.0814178i	−0.0274028	+	0.00362664i
$505$	−0.402729	+	1.12555i	−0.0179212	+	0.0500864i
$506$	0.521571	−	2.10864i	0.0231866	−	0.0937403i
$507$	−20.0277	+	25.6631i	−0.889460	+	1.13974i
$508$	−26.8671	−	12.5135i	−1.19203	−	0.555196i
$509$	−1.14109	+	0.440168i	−0.0505781	+	0.0195101i	−0.385052	−	0.922895i	$-0.625816\pi$
$509$	−1.14109	+	0.440168i	−0.0505781	+	0.0195101i	0.334474	+	0.942405i	$0.391441\pi$
$510$	−47.8647	+	68.3909i	−2.11948	+	3.02840i
$511$	−0.428468			−0.0189543
$512$	15.9673	−	16.0327i	0.705661	−	0.708550i
$513$	−0.322274			−0.0142287
$514$	1.18822	−	1.69778i	0.0524102	−	0.0748858i
$515$	14.6118	−	5.63639i	0.643872	−	0.248369i
$516$	12.5707	−	26.9899i	0.553394	−	1.18816i
$517$	0.670867	−	0.859637i	0.0295047	−	0.0378068i
$518$	0.0368030	−	0.148789i	0.00161703	−	0.00653743i
$519$	12.4665	−	34.8414i	0.547217	−	1.52937i
$520$	−2.29180	−	1.75608i	−0.100502	−	0.0770094i
$521$	8.69705	−	7.88255i	0.381025	−	0.345341i	−0.458469	−	0.888711i	$-0.651602\pi$
$521$	8.69705	−	7.88255i	0.381025	−	0.345341i	0.839493	+	0.543370i	$0.182852\pi$
$522$	−12.1128	−	39.5100i	−0.530163	−	1.72931i
$523$	2.12443	+	9.46051i	0.0928948	+	0.413679i	0.999973	−	0.00728176i	$-0.00231788\pi$
$523$	2.12443	+	9.46051i	0.0928948	+	0.413679i	−0.907079	+	0.420961i	$0.861693\pi$
$524$	−13.7515	−	0.932719i	−0.600737	−	0.0407460i
$525$	1.20831	−	0.334385i	0.0527351	−	0.0145938i
$526$	12.4205	+	17.5256i	0.541561	+	0.764153i
$527$	−7.46592	+	24.6118i	−0.325221	+	1.07211i
$528$	9.40885	+	2.73316i	0.409467	+	0.118946i
$529$	−19.6199	+	5.95162i	−0.853038	+	0.258766i
$530$	4.25054	+	33.6441i	0.184632	+	1.46141i
$531$	−10.7265	−	21.3098i	−0.465489	−	0.924768i
$532$	0.0217030	+	0.0424896i	0.000940945	+	0.00184216i
$533$	−0.0546946	−	2.22801i	−0.00236909	−	0.0965059i
$534$	−48.5590	−	19.9460i	−2.10136	−	0.863146i
$535$	−42.9314	+	6.36828i	−1.85609	+	0.275325i
$536$	−18.4884	−	33.8640i	−0.798575	−	1.46270i
$537$	7.72757	+	30.8502i	0.333469	+	1.33128i
$538$	4.81595	−	13.5861i	0.207630	−	0.585737i
$539$	3.05715	−	6.07351i	0.131681	−	0.261605i
$540$	−4.41355	+	4.46601i	−0.189929	+	0.192186i
$541$	1.30875	+	7.54249i	0.0562674	+	0.324277i	0.999979	−	0.00649269i	$-0.00206670\pi$
$541$	1.30875	+	7.54249i	0.0562674	+	0.324277i	−0.943712	+	0.330770i	$0.892692\pi$
$542$	8.56917	+	10.9138i	0.368078	+	0.468786i
$543$	29.0489	−	43.4748i	1.24661	−	1.86568i
$544$	−34.6256	+	13.9475i	−1.48456	+	0.597994i
$545$	−31.4439	−	47.0592i	−1.34691	−	2.01579i
$546$	−0.0208626	+	0.0637840i	−0.000892837	+	0.00272970i
$547$	21.4869	+	33.9315i	0.918714	+	1.45081i	0.892447	+	0.451153i	$0.148987\pi$
$547$	21.4869	+	33.9315i	0.918714	+	1.45081i	0.0262676	+	0.999655i	$0.491638\pi$
$548$	8.52040	+	27.5020i	0.363974	+	1.17483i
$549$	17.5133	−	15.1070i	0.747447	−	0.644753i
$550$	−10.3358	−	1.50198i	−0.440719	−	0.0640445i
$551$	−2.55201	+	1.89270i	−0.108719	+	0.0806318i
$552$	2.83369	+	10.9019i	0.120610	+	0.464016i
$553$	−0.226316	+	0.903503i	−0.00962392	+	0.0384209i
$554$	−21.7692	−	14.4529i	−0.924883	−	0.614043i
$555$	−6.00036	−	13.5366i	−0.254701	−	0.574596i
$556$	7.55125	−	34.5817i	0.320244	−	1.46659i
$557$	−0.585542	−	7.93800i	−0.0248102	−	0.336344i	−0.995414	−	0.0956609i	$-0.969504\pi$
$557$	−0.585542	−	7.93800i	−0.0248102	−	0.336344i	0.970604	−	0.240683i	$-0.0773714\pi$
$558$	−8.25566	+	16.5225i	−0.349490	+	0.699454i
$559$	−1.07777	−	1.31326i	−0.0455846	−	0.0555451i
$560$	0.886035	+	0.281139i	0.0374418	+	0.0118803i
$561$	−12.4947	−	10.2541i	−0.527527	−	0.432930i
$562$	2.51711	+	0.962424i	0.106178	+	0.0405974i
$563$	−3.78350	+	2.95267i	−0.159455	+	0.124440i	−0.691805	−	0.722084i	$-0.743184\pi$
$563$	−3.78350	+	2.95267i	−0.159455	+	0.124440i	0.532350	+	0.846525i	$0.321309\pi$
$564$	−0.933786	+	5.57695i	−0.0393195	+	0.234832i
$565$	2.38884	−	13.7672i	0.100499	−	0.579191i
$566$	−5.08607	−	9.44812i	−0.213783	−	0.397134i
$567$	−0.463074	−	0.219018i	−0.0194473	−	0.00919789i
$568$	7.27723	−	33.8057i	0.305346	−	1.41845i
$569$	7.00317	+	6.34730i	0.293588	+	0.266093i	0.805042	−	0.593218i	$-0.202143\pi$
$569$	7.00317	+	6.34730i	0.293588	+	0.266093i	−0.511454	+	0.859311i	$0.670893\pi$
$570$	4.17241	+	1.95834i	0.174763	+	0.0820260i
$571$	−5.53168	+	19.9889i	−0.231494	+	0.836511i	0.752543	+	0.658544i	$0.228827\pi$
$571$	−5.53168	+	19.9889i	−0.231494	+	0.836511i	−0.984036	+	0.177967i	$0.943048\pi$
$572$	0.372989	−	0.416448i	0.0155955	−	0.0174126i
$573$	39.5246	+	0.970276i	1.65117	+	0.0405338i
$574$	0.260215	+	0.668694i	0.0108612	+	0.0279107i
$575$	−4.59507	−	11.0935i	−0.191628	−	0.462630i
$576$	−26.1959	+	5.69512i	−1.09149	+	0.237297i
$577$	12.6087	−	30.4401i	0.524907	−	1.26724i	−0.409916	−	0.912123i	$-0.634442\pi$
$577$	12.6087	−	30.4401i	0.524907	−	1.26724i	0.934823	−	0.355115i	$-0.115558\pi$
$578$	37.5326	+	0.810442i	1.56115	+	0.0337099i
$579$	21.2020	−	20.1860i	0.881124	−	0.838900i
$580$	−8.72117	+	61.2859i	−0.362127	+	2.54476i
$581$	0.419174	−	0.237459i	0.0173903	−	0.00985148i
$582$	−8.39651	−	0.387634i	−0.348047	−	0.0160679i
$583$	−6.55844	+	0.322195i	−0.271623	+	0.0133440i
$584$	−18.4467	+	1.52519i	−0.763331	+	0.0631129i
$585$	1.15239	+	3.22070i	0.0476453	+	0.133160i
$586$	−0.662052	−	6.52428i	−0.0273491	−	0.269516i
$587$	−13.8675	−	19.6903i	−0.572373	−	0.812707i	0.423265	−	0.906006i	$-0.360884\pi$
$587$	−13.8675	−	19.6903i	−0.572373	−	0.812707i	−0.995638	+	0.0932986i	$0.970259\pi$
$588$	1.07357	+	35.2436i	0.0442731	+	1.45342i
$589$	1.40940	+	0.173834i	0.0580735	+	0.00716268i
$590$	0.982568	+	35.7236i	0.0404517	+	1.47072i
$591$	−12.5852	+	1.23953i	−0.517685	+	0.0509876i
$592$	1.05483	−	6.53679i	0.0433534	−	0.268660i
$593$	0.372103	−	3.77803i	0.0152804	−	0.155145i	−0.984517	−	0.175291i	$-0.943913\pi$
$593$	0.372103	−	3.77803i	0.0152804	−	0.155145i	0.999797	+	0.0201464i	$0.00641324\pi$
$594$	−0.796840	−	0.918260i	−0.0326947	−	0.0376767i
$595$	−1.16121	−	1.00167i	−0.0476049	−	0.0410643i
$596$	−27.3315	−	11.9225i	−1.11954	−	0.488365i
$597$	−13.8963	+	36.0249i	−0.568739	+	1.47440i
$598$	0.630751	+	0.123528i	0.0257933	+	0.00505145i
$599$	−12.4901	−	20.8384i	−0.510331	−	0.851436i	0.489457	−	0.872027i	$-0.337195\pi$
$599$	−12.4901	−	20.8384i	−0.510331	−	0.851436i	−0.999788	+	0.0205917i	$0.993445\pi$
$600$	50.8309	−	18.6974i	2.07516	−	0.763317i
$601$	−37.2137	−	5.52013i	−1.51798	−	0.225171i	−0.664892	−	0.746940i	$-0.731522\pi$
$601$	−37.2137	−	5.52013i	−1.51798	−	0.225171i	−0.853087	+	0.521769i	$0.825272\pi$
$602$	0.469981	+	0.279812i	0.0191550	+	0.0114043i
$603$	−3.36265	+	45.5864i	−0.136938	+	1.85642i
$604$	45.5070	+	13.5113i	1.85165	+	0.549768i
$605$	−7.81981	+	34.8232i	−0.317921	+	1.41576i
$606$	1.19682	−	0.0918383i	0.0486175	−	0.00373068i
$607$	−7.56466	−	1.50471i	−0.307040	−	0.0610741i	0.0391654	−	0.999233i	$-0.487530\pi$
$607$	−7.56466	−	1.50471i	−0.307040	−	0.0610741i	−0.346206	+	0.938159i	$0.612530\pi$
$608$	1.08562	+	1.75204i	0.0440278	+	0.0710545i
$609$	1.41119	−	0.280704i	0.0571844	−	0.0113747i
$610$	−33.3634	+	9.33909i	−1.35085	+	0.378129i
$611$	0.263794	+	0.185785i	0.0106720	+	0.00751605i
$612$	43.4261	+	8.37158i	1.75540	+	0.338401i
$613$	44.3258	−	14.6433i	1.79030	−	0.591436i	0.790523	−	0.612432i	$-0.209809\pi$
$613$	44.3258	−	14.6433i	1.79030	−	0.591436i	0.999780	+	0.0209964i	$0.00668386\pi$
$614$	−0.338038	−	6.48969i	−0.0136421	−	0.261903i
$615$	59.4556	+	35.6363i	2.39748	+	1.43699i
$616$	−0.0674042	+	0.166896i	−0.00271579	+	0.00672445i
$617$	34.3201	+	25.4535i	1.38167	+	1.02472i	0.994721	+	0.102621i	$0.0327228\pi$
$617$	34.3201	+	25.4535i	1.38167	+	1.02472i	0.386954	+	0.922099i	$0.373527\pi$
$618$	−11.1524	−	11.0867i	−0.448615	−	0.445972i
$619$	4.86037	+	4.62746i	0.195355	+	0.185993i	0.780918	−	0.624634i	$-0.214752\pi$
$619$	4.86037	+	4.62746i	0.195355	+	0.185993i	−0.585563	+	0.810627i	$0.699127\pi$
$620$	21.7108	−	17.1506i	0.871926	−	0.688785i
$621$	0.438450	−	1.32721i	0.0175944	−	0.0532590i
$622$	−3.94287	+	2.24902i	−0.158095	+	0.0901775i
$623$	0.454613	−	0.850521i	0.0182137	−	0.0340754i
$624$	−0.671144	+	2.82034i	−0.0268673	+	0.112904i
$625$	4.63626	−	2.47813i	0.185450	−	0.0991253i
$626$	−24.0438	+	5.47387i	−0.960983	+	0.218780i
$627$	−0.439899	+	0.776530i	−0.0175679	+	0.0310116i
$628$	−8.44327	−	2.28295i	−0.336923	−	0.0910996i
$629$	−5.84402	+	9.22871i	−0.233016	+	0.367973i
$630$	−0.701172	−	0.849253i	−0.0279354	−	0.0338350i
$631$	−1.31389	+	26.7448i	−0.0523051	+	1.06469i	0.818951	+	0.573864i	$0.194556\pi$
$631$	−1.31389	+	26.7448i	−0.0523051	+	1.06469i	−0.871256	+	0.490830i	$0.836694\pi$
$632$	−6.52737	+	39.7039i	−0.259645	+	1.57934i
$633$	−32.2269	+	15.2422i	−1.28090	+	0.605822i
$634$	18.1459	−	24.6186i	0.720667	−	0.977731i
$635$	−6.43871	−	52.2037i	−0.255512	−	2.07164i
$636$	29.1024	−	17.6778i	1.15398	−	0.700971i
$637$	1.83933	+	0.815320i	0.0728770	+	0.0323041i
$638$	−11.7029	−	2.59168i	−0.463322	−	0.102606i
$639$	−28.9692	+	28.9692i	−1.14601	+	1.14601i
$640$	39.1470	+	8.94983i	1.54742	+	0.353773i
$641$	−8.12224	−	8.12224i	−0.320809	−	0.320809i	0.528268	−	0.849078i	$-0.322842\pi$
$641$	−8.12224	−	8.12224i	−0.320809	−	0.320809i	−0.849078	+	0.528268i	$0.822842\pi$
$642$	23.4235	+	36.7491i	0.924452	+	1.45037i
$643$	11.0037	−	24.8240i	0.433945	−	0.978963i	−0.555159	−	0.831744i	$-0.687343\pi$
$643$	11.0037	−	24.8240i	0.433945	−	0.978963i	0.989104	−	0.147219i	$-0.0470323\pi$
$644$	−0.204510	+	0.0315721i	−0.00805882	+	0.00124412i
$645$	52.4423	−	6.46815i	2.06492	−	0.254683i
$646$	−0.508860	−	3.36200i	−0.0200208	−	0.132276i
$647$	−11.9330	−	25.2302i	−0.469135	−	0.991903i	−0.990364	−	0.138486i	$-0.955776\pi$
$647$	−11.9330	−	25.2302i	−0.469135	−	0.991903i	0.521229	−	0.853417i	$-0.325474\pi$
$648$	−20.7162	−	7.78094i	−0.813811	−	0.305664i
$649$	−6.91150	−	0.339540i	−0.271300	−	0.0133281i
$650$	0.293826	−	3.07641i	0.0115248	−	0.120667i
$651$	−0.543316	−	0.344051i	−0.0212942	−	0.0134844i
$652$	0.623200	+	4.81828i	0.0244064	+	0.188699i
$653$	8.93696	+	5.06273i	0.349730	+	0.198120i	0.657707	−	0.753274i	$-0.271527\pi$
$653$	8.93696	+	5.06273i	0.349730	+	0.198120i	−0.307976	+	0.951394i	$0.599652\pi$
$654$	−30.2619	+	48.1025i	−1.18333	+	1.88096i
$655$	−11.5308	−	21.5726i	−0.450546	−	0.842913i
$656$	13.5833	+	27.8628i	0.530339	+	1.08786i
$657$	19.3399	+	10.3374i	0.754522	+	0.403300i
$658$	−0.100198	−	0.0274101i	−0.00390613	−	0.00106856i
$659$	−6.70891	−	2.21633i	−0.261342	−	0.0863358i	0.180026	−	0.983662i	$-0.442382\pi$
$659$	−6.70891	−	2.21633i	−0.261342	−	0.0863358i	−0.441368	+	0.897326i	$0.645507\pi$
$660$	4.73658	+	16.7306i	0.184371	+	0.651239i
$661$	11.3240	−	11.8940i	0.440453	−	0.462622i	−0.466089	−	0.884738i	$-0.654337\pi$
$661$	11.3240	−	11.8940i	0.440453	−	0.462622i	0.906542	+	0.422115i	$0.138712\pi$
$662$	−16.3995	+	0.0484455i	−0.637386	+	0.00188289i
$663$	2.84907	−	3.84152i	0.110649	−	0.149192i
$664$	17.2013	−	11.7154i	0.667541	−	0.454645i
$665$	−0.0435311	+	0.0726272i	−0.00168806	+	0.00281636i
$666$	−5.25094	+	5.82803i	−0.203470	+	0.225832i
$667$	−4.32265	−	13.0849i	−0.167374	−	0.506648i
$668$	20.1900	−	4.14020i	0.781176	−	0.160189i
$669$	−29.0350	+	41.2265i	−1.12256	+	1.59391i
$670$	33.5736	−	59.6761i	1.29706	−	2.30549i
$671$	−1.30877	−	6.57963i	−0.0505245	−	0.254004i
$672$	−0.105197	−	0.927436i	−0.00405807	−	0.0357766i
$673$	−6.57938	+	33.0768i	−0.253617	+	1.27502i	0.618526	+	0.785764i	$0.287730\pi$
$673$	−6.57938	+	33.0768i	−0.253617	+	1.27502i	−0.872142	+	0.489252i	$0.837270\pi$
$674$	−8.52454	−	7.30951i	−0.328353	−	0.281552i
$675$	−6.55742	−	1.47252i	−0.252395	−	0.0566772i
$676$	−20.0669	−	16.2710i	−0.771803	−	0.625808i
$677$	7.21418	+	0.532150i	0.277264	+	0.0204522i	0.211482	−	0.977382i	$-0.432171\pi$
$677$	7.21418	+	0.532150i	0.277264	+	0.0204522i	0.0657814	+	0.997834i	$0.479046\pi$
$678$	−13.5997	+	3.44927i	−0.522292	+	0.132468i
$679$	0.0226575	−	0.152744i	0.000869514	−	0.00586178i
$680$	−53.5588	−	38.9909i	−2.05388	−	1.49523i
$681$	−63.6891	+	38.1738i	−2.44057	+	1.46282i
$682$	2.98952	+	4.44565i	0.114475	+	0.170233i
$683$	11.6957	+	4.51153i	0.447524	+	0.172629i	0.573153	−	0.819448i	$-0.305720\pi$
$683$	11.6957	+	4.51153i	0.447524	+	0.172629i	−0.125629	+	0.992077i	$0.540095\pi$
$684$	0.0455037	−	2.44148i	0.00173988	−	0.0933524i
$685$	−33.3750	+	38.6909i	−1.27519	+	1.47830i
$686$	−1.29267	−	0.0915148i	−0.0493546	−	0.00349405i
$687$	−35.5031	−	3.49675i	−1.35453	−	0.133409i
$688$	21.2300	+	10.3737i	0.809385	+	0.395494i
$689$	−0.190441	−	1.93358i	−0.00725523	−	0.0736635i
$690$	−13.7415	+	14.5188i	−0.523130	+	0.552721i
$691$	0.320315	−	2.59704i	0.0121854	−	0.0987962i	−0.985157	−	0.171657i	$-0.945088\pi$
$691$	0.320315	−	2.59704i	0.0121854	−	0.0987962i	0.997342	+	0.0728609i	$0.0232129\pi$
$692$	27.4615	+	10.4071i	1.04393	+	0.395619i
$693$	0.174348	−	0.122790i	0.00662293	−	0.00466439i
$694$	−8.40419	−	6.85570i	−0.319019	−	0.260239i
$695$	59.1464	−	21.1629i	2.24355	−	0.802755i
$696$	59.7565	−	17.1084i	2.26506	−	0.648492i
$697$	−2.50920	−	51.0759i	−0.0950426	−	1.93464i
$698$	−20.3604	−	22.3313i	−0.770651	−	0.845251i
$699$	27.2898	+	48.1733i	1.03220	+	1.82208i
$700$	0.247458	+	0.963714i	0.00935303	+	0.0364250i
$701$	13.3391	+	14.0105i	0.503811	+	0.529170i	0.926093	−	0.377295i	$-0.123146\pi$
$701$	13.3391	+	14.0105i	0.503811	+	0.529170i	−0.422282	+	0.906465i	$0.638771\pi$
$702$	0.259810	−	0.248827i	0.00980590	−	0.00939138i
$703$	0.557224	+	0.230810i	0.0210161	+	0.00870516i
$704$	−2.30784	+	7.42528i	−0.0869802	+	0.279851i
$705$	−9.27134	+	3.84032i	−0.349179	+	0.144635i
$706$	17.3589	−	39.4755i	0.653312	−	1.48568i
$707$	−0.000541165		0.0220446i	−2.03526e−5		0.000829073i
$708$	32.3474	−	15.5337i	1.21569	−	0.583792i
$709$	−32.5092	−	8.99652i	−1.22091	−	0.337871i	−0.404066	−	0.914730i	$-0.632403\pi$
$709$	−32.5092	−	8.99652i	−1.22091	−	0.337871i	−0.816844	+	0.576859i	$0.804278\pi$
$710$	57.7207	−	20.8454i	2.16622	−	0.782312i
$711$	32.0136	−	35.3216i	1.20060	−	1.32466i
$712$	16.5448	−	38.2355i	0.620042	−	1.43294i
$713$	−2.63337	+	5.56780i	−0.0986206	+	0.208516i
$714$	−0.442635	+	1.47484i	−0.0165652	+	0.0551945i
$715$	0.977563	+	0.169623i	0.0365588	+	0.00634355i
$716$	−24.5932	+	5.67542i	−0.919091	+	0.212100i
$717$	−20.1033	−	25.7600i	−0.750772	−	0.962025i
$718$	30.0396	−	13.4220i	1.12107	−	0.500904i
$719$	−24.8713	+	30.3058i	−0.927543	+	1.13021i	0.0636738	+	0.997971i	$0.479718\pi$
$719$	−24.8713	+	30.3058i	−0.927543	+	1.13021i	−0.991217	+	0.132244i	$0.957782\pi$
$720$	−33.2104	−	34.0667i	−1.23768	−	1.26959i
$721$	0.223315	−	0.183270i	0.00831670	−	0.00682534i
$722$	25.3108	−	8.44456i	0.941969	−	0.314274i
$723$	48.8861	−	3.60606i	1.81809	−	0.134111i
$724$	34.0667	+	23.6926i	1.26608	+	0.880529i
$725$	−60.5747	+	26.8509i	−2.24969	+	0.997219i
$726$	35.1275	−	7.09523i	1.30370	−	0.263329i
$727$	−43.7613	−	10.9616i	−1.62302	−	0.406545i	−0.678394	−	0.734699i	$-0.737324\pi$
$727$	−43.7613	−	10.9616i	−1.62302	−	0.406545i	−0.944624	+	0.328154i	$0.893574\pi$
$728$	−0.0503026	−	0.0174973i	−0.00186434	−	0.000648492i
$729$	19.6014	+	26.4294i	0.725976	+	0.978865i
$730$	−19.6461	−	26.3268i	−0.727135	−	0.974399i
$731$	−25.4616	−	29.5170i	−0.941730	−	1.09173i
$732$	22.2278	+	26.7607i	0.821563	+	0.989103i
$733$	31.4284	−	19.9018i	1.16083	−	0.735090i	0.191659	−	0.981462i	$-0.438613\pi$
$733$	31.4284	−	19.9018i	1.16083	−	0.735090i	0.969176	+	0.246371i	$0.0792382\pi$
$734$	0.376186	+	0.741888i	0.0138853	+	0.0273836i
$735$	−52.0302	+	34.7654i	−1.91916	+	1.28234i
$736$	−8.69232	+	2.08725i	−0.320403	+	0.0769370i
$737$	11.0239	+	7.36595i	0.406071	+	0.271328i
$738$	4.38774	−	36.4611i	0.161515	−	1.34215i
$739$	16.8393	−	2.92190i	0.619444	−	0.107484i	0.147427	−	0.989073i	$-0.452901\pi$
$739$	16.8393	−	2.92190i	0.619444	−	0.107484i	0.472017	+	0.881589i	$0.343526\pi$
$740$	10.8297	−	4.56096i	0.398108	−	0.167664i
$741$	−0.235880	−	0.118732i	−0.00866526	−	0.00436173i
$742$	0.269123	+	0.564690i	0.00987981	+	0.0207304i
$743$	−0.761301	+	0.190696i	−0.0279294	+	0.00699595i	−0.256920	−	0.966433i	$-0.582708\pi$
$743$	−0.761301	+	0.190696i	−0.0279294	+	0.00699595i	0.228990	+	0.973429i	$0.426458\pi$
$744$	−24.6160	−	12.8783i	−0.902465	−	0.472143i
$745$	−7.76490	−	52.3467i	−0.284484	−	1.91783i
$746$	9.82934	+	23.5332i	0.359878	+	0.861613i
$747$	−24.6495	+	0.605111i	−0.901877	+	0.0221398i
$748$	8.32121	−	9.76262i	0.304253	−	0.356957i
$749$	−0.715106	+	0.359954i	−0.0261294	+	0.0131524i
$750$	25.9718	+	20.1454i	0.948356	+	0.735607i
$751$	−9.36026	−	30.8567i	−0.341561	−	1.12598i	−0.944589	−	0.328255i	$-0.893539\pi$
$751$	−9.36026	−	30.8567i	−0.341561	−	1.12598i	0.603028	−	0.797720i	$-0.293961\pi$
$752$	−4.41137	−	0.823413i	−0.160866	−	0.0300268i
$753$	52.0609	+	15.7925i	1.89720	+	0.575510i
$754$	0.596025	−	3.49626i	0.0217060	−	0.127326i
$755$	22.4695	+	81.1943i	0.817749	+	2.95496i
$756$	−0.0514629	+	0.103761i	−0.00187169	+	0.00377376i
$757$	22.5214	−	5.05734i	0.818552	−	0.183812i	0.210383	−	0.977619i	$-0.432529\pi$
$757$	22.5214	−	5.05734i	0.818552	−	0.183812i	0.608170	+	0.793807i	$0.291904\pi$
$758$	29.7149	+	15.7702i	1.07929	+	0.572801i
$759$	−2.59948	−	2.86808i	−0.0943550	−	0.104105i
$760$	−1.61560	+	3.28175i	−0.0586041	+	0.119042i
$761$	−3.64623	−	1.30464i	−0.132176	−	0.0472933i	0.269971	−	0.962868i	$-0.412986\pi$
$761$	−3.64623	−	1.30464i	−0.132176	−	0.0472933i	−0.402147	+	0.915575i	$0.631736\pi$
$762$	−45.2206	+	27.2861i	−1.63817	+	0.988471i
$763$	−0.823045	−	0.642310i	−0.0297962	−	0.0232532i
$764$	−1.35441	+	31.3476i	−0.0490007	+	1.13411i
$765$	28.2473	+	73.2283i	1.02128	+	2.64758i
$766$	1.45006	+	8.21281i	0.0523929	+	0.296741i
$767$		−	2.04753i		−	0.0739321i
$768$	−7.83036	−	39.5542i	−0.282554	−	1.42729i
$769$			2.18672i			0.0788550i	0.999222	+	0.0394275i	$0.0125534\pi$
$769$			2.18672i			0.0788550i	−0.999222	+	0.0394275i	$0.987447\pi$
$770$	−0.314571	+	0.0555409i	−0.0113363	+	0.00200156i
$771$	−1.32901	−	3.44533i	−0.0478631	−	0.124081i
$772$	15.7036	+	17.1218i	0.565183	+	0.616227i
$773$	41.7482	+	32.5806i	1.50158	+	1.17184i	0.938421	+	0.345494i	$0.112289\pi$
$773$	41.7482	+	32.5806i	1.50158	+	1.17184i	0.563158	+	0.826349i	$0.309586\pi$
$774$	−14.4628	−	23.9689i	−0.519856	−	0.861545i
$775$	27.8834	+	9.97683i	1.00160	+	0.358378i
$776$	0.431751	−	6.65671i	0.0154990	−	0.238962i
$777$	−0.183424	−	0.202377i	−0.00658030	−	0.00726024i
$778$	−21.1547	+	39.8605i	−0.758434	+	1.42907i
$779$	−2.75493	+	0.618641i	−0.0987057	+	0.0221651i
$780$	−4.87574	+	1.64274i	−0.174580	+	0.0588196i
$781$	3.16936	+	11.4526i	0.113409	+	0.409807i
$782$	14.5379	+	2.47835i	0.519874	+	0.0886255i
$783$	−7.38090	−	2.23897i	−0.263772	−	0.0800144i
$784$	−27.9809	+	0.330645i	−0.999318	+	0.0118088i
$785$	−4.50592	−	14.8540i	−0.160823	−	0.530163i
$786$	−15.0537	+	19.4074i	−0.536946	+	0.692239i
$787$	−43.5929	+	21.9428i	−1.55392	+	0.782177i	−0.998770	−	0.0495746i	$-0.984213\pi$
$787$	−43.5929	+	21.9428i	−1.55392	+	0.782177i	−0.555148	+	0.831751i	$0.687338\pi$
$788$	−0.797423	−	10.0044i	−0.0284070	−	0.356392i
$789$	38.2667	−	0.939395i	1.36233	−	0.0334434i
$790$	−65.8919	+	27.5217i	−2.34433	+	0.979177i
$791$	−0.0378195	−	0.254959i	−0.00134471	−	0.00906528i
$792$	7.06906	−	5.90704i	0.251188	−	0.209898i
$793$	1.92552	−	0.482317i	0.0683772	−	0.0171276i
$794$	−9.80070	+	4.67086i	−0.347814	+	0.165763i
$795$	53.9776	+	27.1700i	1.91439	+	0.963622i
$796$	−28.3794	−	11.5592i	−1.00588	−	0.409704i
$797$	31.7200	−	5.50394i	1.12358	−	0.194960i	0.421342	−	0.906902i	$-0.361559\pi$
$797$	31.7200	−	5.50394i	1.12358	−	0.194960i	0.702238	+	0.711942i	$0.252184\pi$
$798$	0.0844123	+	0.0101582i	0.00298816	+	0.000359597i
$799$	6.15559	+	4.11304i	0.217769	+	0.145509i
$800$	14.0842	+	40.6097i	0.497952	+	1.43577i
$801$	−41.0401	+	27.4221i	−1.45008	+	0.968912i
$802$	16.9119	−	8.57544i	0.597180	−	0.302809i
$803$	5.37381	−	3.40293i	0.189638	−	0.120087i
$804$	−68.4607	−	6.33462i	−2.41442	−	0.223405i
$805$	−0.239874	−	0.278081i	−0.00845445	−	0.00980106i
$806$	−1.27045	+	0.948058i	−0.0447496	+	0.0333939i
$807$	−15.3013	−	20.6314i	−0.538632	−	0.726261i
$808$	0.0551723	+	0.951008i	0.00194095	+	0.0334563i
$809$	−4.18488	−	1.04826i	−0.147133	−	0.0368548i	0.168714	−	0.985665i	$-0.446039\pi$
$809$	−4.18488	−	1.04826i	−0.147133	−	0.0368548i	−0.315847	+	0.948810i	$0.602289\pi$
$810$	−7.77554	−	38.4956i	−0.273205	−	1.35260i
$811$	22.3166	−	9.89228i	0.783643	−	0.347365i	0.0256863	−	0.999670i	$-0.491823\pi$
$811$	22.3166	−	9.89228i	0.783643	−	0.347365i	0.757957	+	0.652305i	$0.226198\pi$
$812$	0.201862	+	1.12390i	0.00708398	+	0.0394412i
$813$	24.6597	−	1.81901i	0.864854	−	0.0637955i
$814$	0.720117	+	2.15840i	0.0252401	+	0.0756518i
$815$	−6.66510	+	5.46991i	−0.233468	+	0.191603i
$816$	−13.8067	+	65.0715i	−0.483332	+	2.27796i
$817$	−1.36543	+	1.66378i	−0.0477704	+	0.0582084i
$818$	15.2212	+	34.0665i	0.532197	+	1.19111i
$819$	0.0388201	+	0.0497434i	0.00135648	+	0.00173817i
$820$	−29.1559	+	46.6496i	−1.01817	+	1.62908i
$821$	−33.6045	−	5.83094i	−1.17281	−	0.203501i	−0.449017	−	0.893523i	$-0.648226\pi$
$821$	−33.6045	−	5.83094i	−1.17281	−	0.203501i	−0.723788	+	0.690022i	$0.757601\pi$
$822$	49.1410	+	14.7484i	1.71399	+	0.514408i
$823$	−6.88337	+	14.5537i	−0.239939	+	0.507309i	−0.987642	−	0.156724i	$-0.949907\pi$
$823$	−6.88337	+	14.5537i	−0.239939	+	0.507309i	0.747703	+	0.664033i	$0.231157\pi$
$824$	8.96197	−	8.68521i	0.312205	−	0.302564i
$825$	−12.4989	+	13.7904i	−0.435154	+	0.480119i
$826$	0.223916	+	0.620023i	0.00779103	+	0.0215734i
$827$	6.54992	+	1.81261i	0.227763	+	0.0630306i	0.378726	−	0.925509i	$-0.376362\pi$
$827$	6.54992	+	1.81261i	0.227763	+	0.0630306i	−0.150963	+	0.988539i	$0.548237\pi$
$828$	9.99276	+	3.50901i	0.347272	+	0.121946i
$829$	−0.665006	+	27.0894i	−0.0230966	+	0.940852i	0.870550	+	0.492080i	$0.163763\pi$
$829$	−0.665006	+	27.0894i	−0.0230966	+	0.940852i	−0.893646	+	0.448772i	$0.851862\pi$
$830$	33.8105	+	14.8678i	1.17358	+	0.516069i
$831$	−43.0191	+	17.8191i	−1.49232	+	0.618138i
$832$	−2.22795	−	0.574246i	−0.0772402	−	0.0199084i
$833$	42.6501	+	17.6663i	1.47774	+	0.612100i
$834$	−43.6284	−	45.5541i	−1.51073	−	1.57741i
$835$	25.2213	+	26.4908i	0.872820	+	0.916751i
$836$	−0.609653	−	0.360533i	−0.0210853	−	0.0124693i
$837$	1.69919	+	2.99948i	0.0587325	+	0.103677i
$838$	−25.2510	+	23.0224i	−0.872282	+	0.795297i
$839$	0.927879	+	18.8874i	0.0320339	+	0.652066i	0.960101	+	0.279653i	$0.0902194\pi$
$839$	0.927879	+	18.8874i	0.0320339	+	0.652066i	−0.928067	+	0.372413i	$0.878531\pi$
$840$	1.29680	−	1.03065i	0.0447438	−	0.0355609i
$841$	−44.2923	+	15.8480i	−1.52732	+	0.546484i
$842$	−28.2541	+	34.6358i	−0.973699	+	1.19363i
$843$	3.92617	−	2.76512i	0.135225	−	0.0952359i
$844$	−11.6177	−	25.7967i	−0.399899	−	0.887959i
$845$	5.61238	−	45.5040i	0.193072	−	1.56538i
$846$	3.86137	+	3.65464i	0.132757	+	0.125649i
$847$	0.0645300	+	0.655184i	0.00221728	+	0.0225124i
$848$	13.5966	+	23.3535i	0.466908	+	0.801962i
$849$	−19.0289	−	1.87418i	−0.653069	−	0.0643217i
$850$	5.00752	−	70.7328i	0.171757	−	2.42611i
$851$	−1.70863	+	1.98078i	−0.0585712	+	0.0679003i
$852$	−42.7533	−	44.3773i	−1.46471	−	1.52034i
$853$	17.7488	+	6.84647i	0.607708	+	0.234419i	0.644128	−	0.764918i	$-0.277220\pi$
$853$	17.7488	+	6.84647i	0.607708	+	0.234419i	−0.0364201	+	0.999337i	$0.511595\pi$
$854$	−0.530330	+	0.356626i	−0.0181475	+	0.0122035i
$855$	3.71711	−	2.22795i	0.127123	−	0.0761943i
$856$	−29.5060	+	18.0425i	−1.00849	+	0.616681i
$857$	5.02102	−	33.8489i	0.171515	−	1.15626i	−0.716887	−	0.697190i	$-0.754433\pi$
$857$	5.02102	−	33.8489i	0.171515	−	1.15626i	0.888401	−	0.459068i	$-0.151817\pi$
$858$	−0.244921	−	0.965667i	−0.00836146	−	0.0329673i
$859$	−0.716243	−	0.0528332i	−0.0244379	−	0.00180265i	0.0613401	−	0.998117i	$-0.480463\pi$
$859$	−0.716243	−	0.0528332i	−0.0244379	−	0.00180265i	−0.0857780	+	0.996314i	$0.527338\pi$
$860$	4.35678	+	41.7074i	0.148565	+	1.42221i
$861$	1.24758	+	0.280153i	0.0425174	+	0.00954760i
$862$	1.14262	−	1.33255i	0.0389177	−	0.0453868i
$863$	−0.247483	+	1.24418i	−0.00842440	+	0.0423523i	−0.984769	−	0.173869i	$-0.944373\pi$
$863$	−0.247483	+	1.24418i	−0.00842440	+	0.0423523i	0.976344	+	0.216221i	$0.0693732\pi$
$864$	−1.84627	+	4.65039i	−0.0628112	+	0.158210i
$865$	10.1678	+	51.1170i	0.345716	+	1.73803i
$866$	42.6090	+	23.9717i	1.44791	+	0.814593i
$867$	38.5206	−	54.6951i	1.30823	−	1.85754i
$868$	0.281032	−	0.426021i	0.00953884	−	0.0144601i
$869$	−4.33726	−	13.1291i	−0.147132	−	0.445374i
$870$	81.9536	+	73.8386i	2.77849	+	2.50336i
$871$	−2.01685	+	3.36492i	−0.0683384	+	0.114016i
$872$	−37.7207	−	24.7235i	−1.27738	−	0.837243i
$873$	−4.70787	+	6.34783i	−0.159337	+	0.214841i
$874$	−0.00240545	−	0.814282i	−8.13656e−5	−	0.0275435i
$875$	−0.416367	+	0.437324i	−0.0140758	+	0.0147842i
$876$	−16.0879	+	28.7945i	−0.543561	+	0.972877i
$877$	−2.11955	−	0.700203i	−0.0715720	−	0.0236442i	0.277673	−	0.960676i	$-0.410437\pi$
$877$	−2.11955	−	0.700203i	−0.0715720	−	0.0236442i	−0.349245	+	0.937031i	$0.613562\pi$
$878$	10.3112	−	37.6929i	0.347988	−	1.27207i
$879$	−10.3061	−	5.50870i	−0.347615	−	0.185804i
$880$	−13.3454	+	3.51095i	−0.449874	+	0.118354i
$881$	−7.59306	−	14.2056i	−0.255817	−	0.478599i	0.720927	−	0.693011i	$-0.243716\pi$
$881$	−7.59306	−	14.2056i	−0.255817	−	0.478599i	−0.976743	+	0.214412i	$0.931216\pi$
$882$	28.0614	+	17.6538i	0.944877	+	0.594433i
$883$	−25.2467	−	14.3021i	−0.849618	−	0.481302i	0.00534883	−	0.999986i	$-0.498297\pi$
$883$	−25.2467	−	14.3021i	−0.849618	−	0.481302i	−0.854966	+	0.518683i	$0.826422\pi$
$884$	3.00602	+	2.31748i	0.101104	+	0.0779453i
$885$	53.8030	+	34.0704i	1.80857	+	1.14526i
$886$	15.0050	+	1.43312i	0.504103	+	0.0481467i
$887$	12.3957	+	0.608959i	0.416205	+	0.0204469i	0.256093	−	0.966652i	$-0.417565\pi$
$887$	12.3957	+	0.608959i	0.416205	+	0.0204469i	0.160112	+	0.987099i	$0.448815\pi$
$888$	−8.61729	−	8.05996i	−0.289177	−	0.270475i
$889$	−0.414839	−	0.877104i	−0.0139133	−	0.0294171i
$890$	73.1044	−	11.0648i	2.45046	−	0.370893i
$891$	7.54730	−	0.930871i	0.252844	−	0.0311854i
$892$	−32.2829	−	23.6483i	−1.08091	−	0.791803i
$893$	0.165650	−	0.373701i	0.00554327	−	0.0125054i
$894$	−44.8085	+	28.5605i	−1.49862	+	0.955205i
$895$	−31.6733	−	31.6733i	−1.05872	−	1.05872i
$896$	0.737455	−	0.0697560i	0.0246366	−	0.00233038i
$897$	0.809881	−	0.809881i	0.0270411	−	0.0270411i
$898$	−0.585019	+	2.64169i	−0.0195223	+	0.0881542i
$899$	31.0713	+	13.7730i	1.03629	+	0.459354i
$900$	12.0814	−	49.4698i	0.402713	−	1.64899i
$901$	−5.45718	−	44.2457i	−0.181805	−	1.47404i
$902$	−8.57442	−	6.32005i	−0.285497	−	0.210435i
$903$	0.881114	−	0.416736i	0.0293216	−	0.0138681i
$904$	−2.53579	−	10.8420i	−0.0843393	−	0.360601i
$905$	−3.61346	+	73.5537i	−0.120115	+	2.44501i
$906$	65.2315	−	53.8574i	2.16717	−	1.78929i
$907$	−23.8817	+	37.7134i	−0.792980	+	1.25225i	0.170734	+	0.985317i	$0.445386\pi$
$907$	−23.8817	+	37.7134i	−0.792980	+	1.25225i	−0.963714	+	0.266935i	$0.913989\pi$
$908$	−29.3481	−	51.1004i	−0.973952	−	1.69582i
$909$	0.556285	−	0.981980i	0.0184508	−	0.0325702i
$910$	−0.0209815	−	0.0921607i	−0.000695531	−	0.00305510i
$911$	39.3192	−	21.0166i	1.30270	−	0.696310i	0.333543	−	0.942735i	$-0.391756\pi$
$911$	39.3192	−	21.0166i	1.30270	−	0.696310i	0.969162	+	0.246425i	$0.0792559\pi$
$912$	3.67034	+	0.136861i	0.121537	+	0.00453192i
$913$	−3.37133	+	6.30732i	−0.111575	+	0.208742i
$914$	20.7222	+	36.3291i	0.685428	+	1.20166i
$915$	−19.3663	+	58.6225i	−0.640229	+	1.93800i
$916$	3.29963	−	28.1192i	0.109023	−	0.929084i
$917$	−0.326790	−	0.311130i	−0.0107916	−	0.0102744i
$918$	5.81947	−	5.85396i	0.192071	−	0.193209i
$919$	−42.8558	−	31.7840i	−1.41368	−	1.04846i	−0.989757	−	0.142762i	$-0.954402\pi$
$919$	−42.8558	−	31.7840i	−1.41368	−	1.04846i	−0.423926	−	0.905697i	$-0.639348\pi$
$920$	−11.3171	−	11.1183i	−0.373114	−	0.366559i
$921$	−9.93271	−	5.95344i	−0.327294	−	0.196172i
$922$	−7.35505	+	0.383113i	−0.242226	+	0.0126172i
$923$	−3.33865	+	1.10294i	−0.109893	+	0.0363037i
$924$	0.179770	+	0.265634i	0.00591400	+	0.00873872i
$925$	10.2834	+	7.24241i	0.338117	+	0.238129i
$926$	−1.31618	−	4.70197i	−0.0432522	−	0.154516i
$927$	−14.5015	+	2.88453i	−0.476293	+	0.0947405i
$928$	12.6914	+	47.6684i	0.416616	+	1.56479i
$929$	−0.318165	−	0.0632870i	−0.0104387	−	0.00207638i	0.189868	−	0.981810i	$-0.439194\pi$
$929$	−0.318165	−	0.0632870i	−0.0104387	−	0.00207638i	−0.200307	+	0.979733i	$0.564194\pi$
$930$	−3.77223	−	49.1590i	−0.123696	−	1.61199i
$931$	0.558476	−	2.48701i	0.0183033	−	0.0815084i
$932$	−38.6280	+	20.9414i	−1.26530	+	0.685959i
$933$	−0.595050	+	8.06689i	−0.0194811	+	0.264098i
$934$	22.5262	−	37.8358i	0.737081	−	1.23802i
$935$	22.5191	+	3.34039i	0.736453	+	0.109243i
$936$	1.84838	+	2.00340i	0.0604162	+	0.0654833i
$937$	−4.30158	−	7.17675i	−0.140527	−	0.234454i	0.779417	−	0.626506i	$-0.215516\pi$
$937$	−4.30158	−	7.17675i	−0.140527	−	0.234454i	−0.919943	+	0.392051i	$0.871766\pi$
$938$	0.242749	−	1.23951i	0.00792604	−	0.0404713i
$939$	−15.8145	+	40.9977i	−0.516088	+	1.33791i
$940$	−2.91009	−	7.41339i	−0.0949167	−	0.241798i
$941$	−10.5194	−	9.07407i	−0.342921	−	0.295806i	0.464746	−	0.885444i	$-0.346146\pi$
$941$	−10.5194	−	9.07407i	−0.342921	−	0.295806i	−0.807668	+	0.589638i	$0.799271\pi$
$942$	−11.7718	+	10.2152i	−0.383547	+	0.332831i
$943$	1.20033	−	12.1872i	0.0390882	−	0.396870i
$944$	11.8473	+	25.8966i	0.385595	+	0.842863i
$945$	−0.204561	+	0.0201475i	−0.00665436	+	0.000655398i
$946$	−8.11675	+	0.223249i	−0.263898	+	0.00725844i
$947$	30.0216	+	3.70281i	0.975571	+	0.120325i	0.594391	−	0.804176i	$-0.297393\pi$
$947$	30.0216	+	3.70281i	0.975571	+	0.120325i	0.381180	+	0.924501i	$0.375518\pi$
$948$	52.2209	+	49.1335i	1.69606	+	1.59578i
$949$	1.08371	+	1.53875i	0.0351788	+	0.0499500i
$950$	−3.89526	+	0.395272i	−0.126379	+	0.0128243i
$951$	−18.3603	−	51.3137i	−0.595375	−	1.66396i
$952$	−1.16371	−	0.373031i	−0.0377159	−	0.0120900i
$953$	−3.48726	+	0.171318i	−0.112963	+	0.00554953i	−0.105471	−	0.994422i	$-0.533635\pi$
$953$	−3.48726	+	0.171318i	−0.112963	+	0.00554953i	−0.00749252	+	0.999972i	$0.502385\pi$
$954$	1.47647	−	31.9816i	0.0478023	−	1.03544i
$955$	−48.4505	+	27.4468i	−1.56782	+	0.888159i
$956$	20.7373	−	15.5706i	0.670692	−	0.503588i
$957$	−15.4697	+	14.7284i	−0.500064	+	0.476101i
$958$	0.640200	−	29.6485i	0.0206839	−	0.957900i
$959$	−0.360696	+	0.870796i	−0.0116475	+	0.0281195i
$960$	52.1620	−	48.9885i	1.68352	−	1.58110i
$961$	6.05003	+	14.6061i	0.195162	+	0.471163i
$962$	−0.627430	+	0.244158i	−0.0202291	+	0.00787197i
$963$	40.9624	+	1.00557i	1.32000	+	0.0324041i
$964$	2.13837	+	38.8433i	0.0688721	+	1.25106i
$965$	−10.9969	+	39.7376i	−0.354002	+	1.27920i
$966$	−0.156676	+	0.333812i	−0.00504098	+	0.0107402i
$967$	−20.4771	−	18.5594i	−0.658501	−	0.596830i	0.272364	−	0.962194i	$-0.412194\pi$
$967$	−20.4771	−	18.5594i	−0.658501	−	0.596830i	−0.930865	+	0.365364i	$0.880944\pi$
$968$	5.11041	+	27.9778i	0.164255	+	0.899240i
$969$	−5.47753	−	2.59068i	−0.175963	−	0.0832245i
$970$	10.4241	−	5.61146i	0.334698	−	0.180173i
$971$	1.27662	−	7.35735i	0.0409687	−	0.236109i	−0.957695	−	0.287785i	$-0.907081\pi$
$971$	1.27662	−	7.35735i	0.0409687	−	0.236109i	0.998664	+	0.0516759i	$0.0164563\pi$
$972$	−36.4269	+	25.9780i	−1.16839	+	0.833245i
$973$	0.913509	−	0.712909i	0.0292857	−	0.0228548i
$974$	−0.0530421	+	0.138726i	−0.00169958	+	0.00444505i
$975$	−4.25702	−	3.49365i	−0.136334	−	0.111886i
$976$	−21.5627	+	17.2415i	−0.690205	+	0.551887i
$977$	−7.31914	−	8.91840i	−0.234160	−	0.285325i	0.642652	−	0.766158i	$-0.277834\pi$
$977$	−7.31914	−	8.91840i	−0.234160	−	0.285325i	−0.876812	+	0.480833i	$0.840334\pi$
$978$	7.74469	+	3.86972i	0.247648	+	0.123740i
$979$	1.05319	+	14.2777i	0.0336601	+	0.456319i
$980$	−26.8161	−	41.7989i	−0.856610	−	1.33522i
$981$	21.6534	+	48.8493i	0.691340	+	1.55964i
$982$	26.9052	−	40.5251i	0.858579	−	1.29321i
$983$	4.96412	−	19.8179i	0.158331	−	0.632092i	−0.837936	−	0.545768i	$-0.816238\pi$
$983$	4.96412	−	19.8179i	0.158331	−	0.632092i	0.996267	−	0.0863238i	$-0.0275119\pi$
$984$	54.7090	+	7.62044i	1.74406	+	0.242931i
$985$	14.3061	−	10.6101i	0.455829	−	0.338066i
$986$	11.7030	−	80.5337i	0.372700	−	2.56471i
$987$	−0.140169	+	0.120910i	−0.00446162	+	0.00384862i
$988$	0.0976994	−	0.185409i	0.00310823	−	0.00589866i
$989$	−4.99424	−	7.88677i	−0.158808	−	0.250785i
$990$	15.5389	+	5.08249i	0.493858	+	0.161532i
$991$	12.2726	+	18.3673i	0.389853	+	0.583457i	0.973538	−	0.228523i	$-0.0733897\pi$
$991$	12.2726	+	18.3673i	0.389853	+	0.583457i	−0.583685	+	0.811980i	$0.698390\pi$
$992$	10.5827	−	19.3417i	0.336001	−	0.614101i
$993$	−16.2359	+	24.2988i	−0.515232	+	0.771099i
$994$	0.890376	−	0.699098i	0.0282410	−	0.0221741i
$995$	−9.29737	−	53.5821i	−0.294746	−	1.69867i
$996$	−0.219112	−	37.0860i	−0.00694282	−	1.17511i
$997$	23.1430	−	45.9773i	0.732947	−	1.45612i	−0.151002	−	0.988533i	$-0.548250\pi$
$997$	23.1430	−	45.9773i	0.732947	−	1.45612i	0.883949	−	0.467583i	$-0.154875\pi$
$998$	−11.6652	−	4.13504i	−0.369255	−	0.130893i
$999$	0.355758	+	1.42027i	0.0112557	+	0.0449352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.157.51	✓	4032
512.437	even	128	inner	512.2.o.a.437.51	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.157.51	✓	4032	1.1	even	1	trivial
512.2.o.a.437.51	yes	4032	512.437	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15864 + 0.810897i) q^{2} +(2.35125 - 0.906977i) q^{3} +(0.684893 + 1.87907i) q^{4} +(-2.18371 + 2.79817i) q^{5} +(3.45971 + 0.855760i) q^{6} +(-0.0220573 + 0.0616461i) q^{7} +(-0.730190 + 2.73255i) q^{8} +(2.48291 - 2.25038i) q^{9} +O(q^{10})\)	\(q+(1.15864 + 0.810897i) q^{2} +(2.35125 - 0.906977i) q^{3} +(0.684893 + 1.87907i) q^{4} +(-2.18371 + 2.79817i) q^{5} +(3.45971 + 0.855760i) q^{6} +(-0.0220573 + 0.0616461i) q^{7} +(-0.730190 + 2.73255i) q^{8} +(2.48291 - 2.25038i) q^{9} +(-4.79916 + 1.47130i) q^{10} +(-0.212957 - 0.948342i) q^{11} +(3.31463 + 3.79699i) q^{12} +(0.277178 - 0.0767054i) q^{13} +(-0.0755451 + 0.0535394i) q^{14} +(-2.59658 + 8.55976i) q^{15} +(-3.06184 + 2.57393i) q^{16} +(6.31477 - 1.91557i) q^{17} +(4.70162 - 0.593995i) q^{18} +(-0.163819 - 0.325453i) q^{19} +(-6.75357 - 2.18691i) q^{20} +(0.00404931 + 0.164951i) q^{21} +(0.522266 - 1.27147i) q^{22} +(1.56318 - 0.231875i) q^{23} +(0.761499 + 7.08717i) q^{24} +(-1.84624 - 7.37062i) q^{25} +(0.383349 + 0.135889i) q^{26} +(0.397681 - 0.790056i) q^{27} +(-0.130944 + 0.000773647i) q^{28} +(-1.49083 - 8.59184i) q^{29} +(-9.94958 + 7.81213i) q^{30} +(-2.16534 + 3.24065i) q^{31} +(-5.63477 + 0.499423i) q^{32} +(-1.36084 - 2.03664i) q^{33} +(8.86988 + 2.90118i) q^{34} +(-0.124329 - 0.196337i) q^{35} +(5.92916 + 3.12430i) q^{36} +(-1.25344 + 1.08122i) q^{37} +(0.0741012 - 0.509923i) q^{38} +(0.582144 - 0.431747i) q^{39} +(-6.05160 - 8.01029i) q^{40} +(1.88294 - 7.51712i) q^{41} +(-0.129066 + 0.194402i) q^{42} +(-2.39385 - 5.40045i) q^{43} +(1.63615 - 1.04968i) q^{44} +(0.874977 + 11.8618i) q^{45} +(1.99918 + 0.998914i) q^{46} +(0.711720 + 0.867233i) q^{47} +(-4.86466 + 8.82897i) q^{48} +(5.40776 + 4.43803i) q^{49} +(3.83768 - 10.0370i) q^{50} +(13.1102 - 10.2313i) q^{51} +(0.333972 + 0.468303i) q^{52} +(1.15498 - 6.65633i) q^{53} +(1.10142 - 0.592913i) q^{54} +(3.11866 + 1.47501i) q^{55} +(-0.152345 - 0.105286i) q^{56} +(-0.680358 - 0.616641i) q^{57} +(5.23976 - 11.1638i) q^{58} +(1.89886 - 6.86159i) q^{59} +(-17.8628 + 0.983366i) q^{60} +(6.90000 + 0.169385i) q^{61} +(-5.13668 + 1.99889i) q^{62} +(0.0839606 + 0.202699i) q^{63} +(-6.93364 - 3.99056i) q^{64} +(-0.390641 + 0.943092i) q^{65} +(0.0747815 - 3.46323i) q^{66} +(-9.87936 + 9.40593i) q^{67} +(7.92444 + 10.5540i) q^{68} +(3.46511 - 1.96296i) q^{69} +(0.0151564 - 0.328302i) q^{70} +(-12.2112 + 0.599897i) q^{71} +(4.33627 + 8.42787i) q^{72} +(2.20466 + 6.16161i) q^{73} +(-2.32904 + 0.236339i) q^{74} +(-11.0260 - 15.6557i) q^{75} +(0.499352 - 0.530729i) q^{76} +(0.0631588 + 0.00778990i) q^{77} +(1.02460 - 0.0281812i) q^{78} +(14.1574 - 1.39438i) q^{79} +(-0.516112 - 14.1883i) q^{80} +(-0.766875 + 7.78621i) q^{81} +(8.27726 - 7.18277i) q^{82} +(-5.57164 - 4.80613i) q^{83} +(-0.307181 + 0.120583i) q^{84} +(-8.42957 + 21.8528i) q^{85} +(1.60559 - 8.19834i) q^{86} +(-11.2979 - 18.8494i) q^{87} +(2.74689 + 0.110554i) q^{88} +(-14.5702 - 2.16128i) q^{89} +(-8.60489 + 14.4530i) q^{90} +(-0.00138521 + 0.0187788i) q^{91} +(1.50632 + 2.77851i) q^{92} +(-2.15205 + 9.58349i) q^{93} +(0.121391 + 1.58194i) q^{94} +(1.26841 + 0.252302i) q^{95} +(-12.7958 + 6.28487i) q^{96} +(-2.31313 + 0.460110i) q^{97} +(2.66686 + 9.52722i) q^{98} +(-2.66288 - 1.87541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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