LMFDB - Embedded newform 416.2.bf.a.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	416.157
Dual form			416.2.bf.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40600 - 0.152175i) q^{2} +(-0.435996 - 0.180596i) q^{3} +(1.95369 + 0.427917i) q^{4} +(0.326436 + 0.788085i) q^{5} +(0.585530 + 0.320266i) q^{6} +(1.89112 - 1.89112i) q^{7} +(-2.68177 - 0.898955i) q^{8} +(-1.96384 - 1.96384i) q^{9} +O(q^{10})$	\(q+(-1.40600 - 0.152175i) q^{2} +(-0.435996 - 0.180596i) q^{3} +(1.95369 + 0.427917i) q^{4} +(0.326436 + 0.788085i) q^{5} +(0.585530 + 0.320266i) q^{6} +(1.89112 - 1.89112i) q^{7} +(-2.68177 - 0.898955i) q^{8} +(-1.96384 - 1.96384i) q^{9} +(-0.339042 - 1.15773i) q^{10} +(1.20781 - 0.500292i) q^{11} +(-0.774520 - 0.539397i) q^{12} +(-0.382683 + 0.923880i) q^{13} +(-2.94669 + 2.37113i) q^{14} -0.402555i q^{15} +(3.63377 + 1.67203i) q^{16} -1.89137i q^{17} +(2.46232 + 3.06001i) q^{18} +(0.478039 - 1.15409i) q^{19} +(0.300517 + 1.67936i) q^{20} +(-1.16605 + 0.482992i) q^{21} +(-1.77432 + 0.519613i) q^{22} +(-0.331773 - 0.331773i) q^{23} +(1.00689 + 0.876256i) q^{24} +(3.02102 - 3.02102i) q^{25} +(0.678645 - 1.24074i) q^{26} +(1.04335 + 2.51888i) q^{27} +(4.50389 - 2.88540i) q^{28} +(0.842762 + 0.349083i) q^{29} +(-0.0612588 + 0.565993i) q^{30} +6.24842 q^{31} +(-4.85465 - 2.90385i) q^{32} -0.616952 q^{33} +(-0.287819 + 2.65927i) q^{34} +(2.10769 + 0.873033i) q^{35} +(-2.99637 - 4.67709i) q^{36} +(-4.38186 - 10.5787i) q^{37} +(-0.847748 + 1.54991i) q^{38} +(0.333697 - 0.333697i) q^{39} +(-0.166972 - 2.40691i) q^{40} +(-8.18241 - 8.18241i) q^{41} +(1.71296 - 0.501645i) q^{42} +(9.38353 - 3.88678i) q^{43} +(2.57377 - 0.460570i) q^{44} +(0.906607 - 2.18874i) q^{45} +(0.415986 + 0.516962i) q^{46} -4.42878i q^{47} +(-1.28235 - 1.38524i) q^{48} -0.152637i q^{49} +(-4.70728 + 3.78783i) q^{50} +(-0.341572 + 0.824628i) q^{51} +(-1.14299 + 1.64121i) q^{52} +(1.51278 - 0.626614i) q^{53} +(-1.08365 - 3.70032i) q^{54} +(0.788546 + 0.788546i) q^{55} +(-6.77156 + 3.37151i) q^{56} +(-0.416847 + 0.416847i) q^{57} +(-1.13180 - 0.619059i) q^{58} +(4.71439 + 11.3815i) q^{59} +(0.172260 - 0.786466i) q^{60} +(10.2441 + 4.24324i) q^{61} +(-8.78530 - 0.950854i) q^{62} -7.42771 q^{63} +(6.38376 + 4.82158i) q^{64} -0.853018 q^{65} +(0.867437 + 0.0938848i) q^{66} +(-0.969976 - 0.401777i) q^{67} +(0.809348 - 3.69513i) q^{68} +(0.0847351 + 0.204569i) q^{69} +(-2.83056 - 1.54822i) q^{70} +(5.81076 - 5.81076i) q^{71} +(3.50117 + 7.03198i) q^{72} +(-6.10137 - 6.10137i) q^{73} +(4.55108 + 15.5405i) q^{74} +(-1.86273 + 0.771569i) q^{75} +(1.42779 - 2.05017i) q^{76} +(1.33800 - 3.23022i) q^{77} +(-0.519959 + 0.418398i) q^{78} +4.79900i q^{79} +(-0.131509 + 3.40953i) q^{80} +7.04523i q^{81} +(10.2593 + 12.7496i) q^{82} +(-4.15991 + 10.0429i) q^{83} +(-2.48477 + 0.444644i) q^{84} +(1.49056 - 0.617409i) q^{85} +(-13.7847 + 4.03689i) q^{86} +(-0.304398 - 0.304398i) q^{87} +(-3.68881 + 0.255900i) q^{88} +(-2.78966 + 2.78966i) q^{89} +(-1.60776 + 2.93942i) q^{90} +(1.02346 + 2.47086i) q^{91} +(-0.506209 - 0.790152i) q^{92} +(-2.72429 - 1.12844i) q^{93} +(-0.673950 + 6.22688i) q^{94} +1.06557 q^{95} +(1.59219 + 2.14280i) q^{96} -15.0464 q^{97} +(-0.0232275 + 0.214608i) q^{98} +(-3.35445 - 1.38946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51} - 32 q^{53} - 24 q^{54} + 32 q^{55} + 16 q^{56} - 64 q^{58} - 56 q^{60} - 64 q^{61} + 24 q^{62} + 80 q^{63} + 72 q^{64} + 96 q^{66} + 80 q^{67} - 32 q^{68} - 64 q^{69} - 120 q^{72} - 32 q^{74} + 32 q^{75} + 64 q^{76} - 32 q^{77} - 56 q^{80} - 80 q^{82} - 80 q^{83} + 112 q^{84} - 112 q^{87} - 88 q^{88} - 120 q^{90} + 144 q^{92} + 40 q^{94} + 136 q^{96} + 56 q^{98}+O(q^{100}) $ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

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 $

$2$	−1.40600	−	0.152175i	−0.994194	−	0.107604i
$2$	−1.40600	−	0.152175i	−0.994194	−	0.107604i
$3$	−0.435996	−	0.180596i	−0.251723	−	0.104267i	0.253254	−	0.967400i	$-0.418499\pi$
$3$	−0.435996	−	0.180596i	−0.251723	−	0.104267i	−0.504977	+	0.863133i	$0.668499\pi$
$4$	1.95369	+	0.427917i	0.976843	+	0.213959i
$5$	0.326436	+	0.788085i	0.145986	+	0.352443i	0.979911	−	0.199436i	$-0.0639111\pi$
$5$	0.326436	+	0.788085i	0.145986	+	0.352443i	−0.833924	+	0.551879i	$0.813911\pi$
$6$	0.585530	+	0.320266i	0.239041	+	0.130748i
$7$	1.89112	−	1.89112i	0.714775	−	0.714775i	−0.252756	−	0.967530i	$-0.581337\pi$
$7$	1.89112	−	1.89112i	0.714775	−	0.714775i	0.967530	+	0.252756i	$0.0813369\pi$
$8$	−2.68177	−	0.898955i	−0.948148	−	0.317828i
$9$	−1.96384	−	1.96384i	−0.654614	−	0.654614i
$10$	−0.339042	−	1.15773i	−0.107215	−	0.366105i
$11$	1.20781	−	0.500292i	0.364169	−	0.150844i	−0.193093	−	0.981180i	$-0.561852\pi$
$11$	1.20781	−	0.500292i	0.364169	−	0.150844i	0.557262	+	0.830337i	$0.311852\pi$
$12$	−0.774520	−	0.539397i	−0.223585	−	0.155711i
$13$	−0.382683	+	0.923880i	−0.106137	+	0.256238i
$13$	−0.382683	+	0.923880i	−0.106137	+	0.256238i
$14$	−2.94669	+	2.37113i	−0.787537	+	0.633712i
$15$		−	0.402555i		−	0.103939i
$16$	3.63377	+	1.67203i	0.908444	+	0.418008i
$17$		−	1.89137i		−	0.458724i	−0.973341	−	0.229362i	$-0.926336\pi$
$17$		−	1.89137i		−	0.458724i	0.973341	−	0.229362i	$-0.0736639\pi$
$18$	2.46232	+	3.06001i	0.580374	+	0.721252i
$19$	0.478039	−	1.15409i	0.109670	−	0.264766i	−0.859511	−	0.511118i	$-0.829232\pi$
$19$	0.478039	−	1.15409i	0.109670	−	0.264766i	0.969181	+	0.246351i	$0.0792317\pi$
$20$	0.300517	+	1.67936i	0.0671978	+	0.375516i
$21$	−1.16605	+	0.482992i	−0.254452	+	0.105398i
$22$	−1.77432	+	0.519613i	−0.378286	+	0.110782i
$23$	−0.331773	−	0.331773i	−0.0691795	−	0.0691795i	0.671670	−	0.740850i	$-0.265577\pi$
$23$	−0.331773	−	0.331773i	−0.0691795	−	0.0691795i	−0.740850	+	0.671670i	$0.765577\pi$
$24$	1.00689	+	0.876256i	0.205531	+	0.178865i
$25$	3.02102	−	3.02102i	0.604203	−	0.604203i
$26$	0.678645	−	1.24074i	0.133093	−	0.243330i
$27$	1.04335	+	2.51888i	0.200793	+	0.484758i
$28$	4.50389	−	2.88540i	0.851154	−	0.545290i
$29$	0.842762	+	0.349083i	0.156497	+	0.0648231i	0.459557	−	0.888148i	$-0.348008\pi$
$29$	0.842762	+	0.349083i	0.156497	+	0.0648231i	−0.303060	+	0.952971i	$0.598008\pi$
$30$	−0.0612588	+	0.565993i	−0.0111843	+	0.103336i
$31$	6.24842			1.12225			0.561125	−	0.827731i	$-0.310369\pi$
$31$	6.24842			1.12225			0.561125	+	0.827731i	$0.310369\pi$
$32$	−4.85465	−	2.90385i	−0.858190	−	0.513333i
$33$	−0.616952			−0.107398
$34$	−0.287819	+	2.65927i	−0.0493605	+	0.456060i
$35$	2.10769	+	0.873033i	0.356264	+	0.147570i
$36$	−2.99637	−	4.67709i	−0.499395	−	0.779515i
$37$	−4.38186	−	10.5787i	−0.720373	−	1.73913i	−0.672288	−	0.740290i	$-0.734688\pi$
$37$	−4.38186	−	10.5787i	−0.720373	−	1.73913i	−0.0480850	−	0.998843i	$-0.515312\pi$
$38$	−0.847748	+	1.54991i	−0.137523	+	0.251428i
$39$	0.333697	−	0.333697i	0.0534343	−	0.0534343i
$40$	−0.166972	−	2.40691i	−0.0264006	−	0.380566i
$41$	−8.18241	−	8.18241i	−1.27788	−	1.27788i	−0.941853	−	0.336025i	$-0.890917\pi$
$41$	−8.18241	−	8.18241i	−1.27788	−	1.27788i	−0.336025	−	0.941853i	$-0.609083\pi$
$42$	1.71296	−	0.501645i	0.264316	−	0.0774055i
$43$	9.38353	−	3.88678i	1.43097	−	0.592729i	0.473383	−	0.880857i	$-0.343033\pi$
$43$	9.38353	−	3.88678i	1.43097	−	0.592729i	0.957592	+	0.288128i	$0.0930328\pi$
$44$	2.57377	−	0.460570i	0.388010	−	0.0694336i
$45$	0.906607	−	2.18874i	0.135149	−	0.326279i
$46$	0.415986	+	0.516962i	0.0613339	+	0.0762218i
$47$		−	4.42878i		−	0.646004i	−0.946398	−	0.323002i	$-0.895308\pi$
$47$		−	4.42878i		−	0.646004i	0.946398	−	0.323002i	$-0.104692\pi$
$48$	−1.28235	−	1.38524i	−0.185091	−	0.199943i
$49$		−	0.152637i		−	0.0218053i
$50$	−4.70728	+	3.78783i	−0.665710	+	0.535680i
$51$	−0.341572	+	0.824628i	−0.0478297	+	0.115471i
$52$	−1.14299	+	1.64121i	−0.158504	+	0.227595i
$53$	1.51278	−	0.626614i	0.207796	−	0.0860720i	−0.276358	−	0.961055i	$-0.589127\pi$
$53$	1.51278	−	0.626614i	0.207796	−	0.0860720i	0.484154	+	0.874983i	$0.339127\pi$
$54$	−1.08365	−	3.70032i	−0.147466	−	0.503550i
$55$	0.788546	+	0.788546i	0.106328	+	0.106328i
$56$	−6.77156	+	3.37151i	−0.904888	+	0.450537i
$57$	−0.416847	+	0.416847i	−0.0552127	+	0.0552127i
$58$	−1.13180	−	0.619059i	−0.148613	−	0.0812865i
$59$	4.71439	+	11.3815i	0.613761	+	1.48175i	0.858838	+	0.512247i	$0.171187\pi$
$59$	4.71439	+	11.3815i	0.613761	+	1.48175i	−0.245077	+	0.969504i	$0.578813\pi$
$60$	0.172260	−	0.786466i	0.0222387	−	0.101532i
$61$	10.2441	+	4.24324i	1.31162	+	0.543291i	0.925357	−	0.379097i	$-0.123765\pi$
$61$	10.2441	+	4.24324i	1.31162	+	0.543291i	0.386264	+	0.922388i	$0.373765\pi$
$62$	−8.78530	−	0.950854i	−1.11573	−	0.120759i
$63$	−7.42771			−0.935803
$64$	6.38376	+	4.82158i	0.797970	+	0.602697i
$65$	−0.853018			−0.105804
$66$	0.867437	+	0.0938848i	0.106774	+	0.0115564i
$67$	−0.969976	−	0.401777i	−0.118501	−	0.0490849i	0.322645	−	0.946520i	$-0.395428\pi$
$67$	−0.969976	−	0.401777i	−0.118501	−	0.0490849i	−0.441146	+	0.897435i	$0.645428\pi$
$68$	0.809348	−	3.69513i	0.0981478	−	0.448101i
$69$	0.0847351	+	0.204569i	0.0102009	+	0.0246272i
$70$	−2.83056	−	1.54822i	−0.338317	−	0.185048i
$71$	5.81076	−	5.81076i	0.689610	−	0.689610i	−0.272536	−	0.962146i	$-0.587862\pi$
$71$	5.81076	−	5.81076i	0.689610	−	0.689610i	0.962146	+	0.272536i	$0.0878622\pi$
$72$	3.50117	+	7.03198i	0.412616	+	0.828726i
$73$	−6.10137	−	6.10137i	−0.714111	−	0.714111i	0.253282	−	0.967393i	$-0.418490\pi$
$73$	−6.10137	−	6.10137i	−0.714111	−	0.714111i	−0.967393	+	0.253282i	$0.918490\pi$
$74$	4.55108	+	15.5405i	0.529052	+	1.80655i
$75$	−1.86273	+	0.771569i	−0.215090	+	0.0890932i
$76$	1.42779	−	2.05017i	0.163779	−	0.235170i
$77$	1.33800	−	3.23022i	0.152480	−	0.368118i
$78$	−0.519959	+	0.418398i	−0.0588738	+	0.0473743i
$79$			4.79900i			0.539930i	0.962870	+	0.269965i	$0.0870122\pi$
$79$			4.79900i			0.539930i	−0.962870	+	0.269965i	$0.912988\pi$
$80$	−0.131509	+	3.40953i	−0.0147032	+	0.381198i
$81$			7.04523i			0.782804i
$82$	10.2593	+	12.7496i	1.13295	+	1.40796i
$83$	−4.15991	+	10.0429i	−0.456610	+	1.10235i	0.513152	+	0.858298i	$0.328478\pi$
$83$	−4.15991	+	10.0429i	−0.456610	+	1.10235i	−0.969761	+	0.244055i	$0.921522\pi$
$84$	−2.48477	+	0.444644i	−0.271110	+	0.0485146i
$85$	1.49056	−	0.617409i	0.161674	−	0.0669674i
$86$	−13.7847	+	4.03689i	−1.48645	+	0.435309i
$87$	−0.304398	−	0.304398i	−0.0326349	−	0.0326349i
$88$	−3.68881	+	0.255900i	−0.393229	+	0.0272790i
$89$	−2.78966	+	2.78966i	−0.295703	+	0.295703i	−0.839328	−	0.543625i	$-0.817051\pi$
$89$	−2.78966	+	2.78966i	−0.295703	+	0.295703i	0.543625	+	0.839328i	$0.317051\pi$
$90$	−1.60776	+	2.93942i	−0.169473	+	0.309842i
$91$	1.02346	+	2.47086i	0.107288	+	0.259017i
$92$	−0.506209	−	0.790152i	−0.0527760	−	0.0823791i
$93$	−2.72429	−	1.12844i	−0.282496	−	0.117014i
$94$	−0.673950	+	6.22688i	−0.0695127	+	0.642253i
$95$	1.06557			0.109325
$96$	1.59219	+	2.14280i	0.162502	+	0.218698i
$97$	−15.0464			−1.52773			−0.763864	−	0.645377i	$-0.776700\pi$
$97$	−15.0464			−1.52773			−0.763864	+	0.645377i	$0.776700\pi$
$98$	−0.0232275	+	0.214608i	−0.00234634	+	0.0216787i
$99$	−3.35445	−	1.38946i	−0.337135	−	0.139646i
$100$	7.19486	−	4.60937i	0.719486	−	0.460937i
$101$	2.47303	+	5.97043i	0.246076	+	0.594080i	0.997864	−	0.0653249i	$-0.0208084\pi$
$101$	2.47303	+	5.97043i	0.246076	+	0.594080i	−0.751788	+	0.659405i	$0.770808\pi$
$102$	0.605739	−	1.10745i	0.0599771	−	0.109654i
$103$	−0.0846203	+	0.0846203i	−0.00833788	+	0.00833788i	−0.711263	−	0.702926i	$-0.751877\pi$
$103$	−0.0846203	+	0.0846203i	−0.00833788	+	0.00833788i	0.702926	+	0.711263i	$0.251877\pi$
$104$	1.85679	−	2.13362i	0.182074	−	0.209218i
$105$	−0.761278	−	0.761278i	−0.0742931	−	0.0742931i
$106$	−2.22233	+	0.650813i	−0.215851	+	0.0632126i
$107$	−7.87870	+	3.26346i	−0.761662	+	0.315491i	−0.729490	−	0.683991i	$-0.760243\pi$
$107$	−7.87870	+	3.26346i	−0.761662	+	0.315491i	−0.0321723	+	0.999482i	$0.510243\pi$
$108$	0.960514	+	5.36756i	0.0924255	+	0.516494i
$109$	1.60640	−	3.87819i	0.153865	−	0.371463i	−0.828085	−	0.560602i	$-0.810570\pi$
$109$	1.60640	−	3.87819i	0.153865	−	0.371463i	0.981950	+	0.189139i	$0.0605697\pi$
$110$	−0.988701	−	1.22870i	−0.0942689	−	0.117151i
$111$			5.40363i			0.512890i
$112$	10.0339	−	3.70988i	0.948113	−	0.350551i
$113$			12.5875i			1.18413i	0.805889	+	0.592066i	$0.201688\pi$
$113$			12.5875i			1.18413i	−0.805889	+	0.592066i	$0.798312\pi$
$114$	0.649521	−	0.522654i	0.0608332	−	0.0489510i
$115$	0.153163	−	0.369768i	0.0142825	−	0.0344811i
$116$	1.49711	+	1.04263i	0.139003	+	0.0968059i
$117$	2.56588	−	1.06282i	0.237216	−	0.0982581i
$118$	−4.89645	−	16.7199i	−0.450755	−	1.53919i
$119$	−3.57679	−	3.57679i	−0.327884	−	0.327884i
$120$	−0.361879	+	1.07956i	−0.0330349	+	0.0985498i
$121$	−6.56966	+	6.56966i	−0.597241	+	0.597241i
$122$	−13.7575	−	7.52490i	−1.24554	−	0.681272i
$123$	2.08979	+	5.04521i	0.188430	+	0.454911i
$124$	12.2075	+	2.67381i	1.09626	+	0.240115i
$125$	7.30741	+	3.02683i	0.653595	+	0.270728i
$126$	10.4434	+	1.13031i	0.930370	+	0.100696i
$127$	−3.55894			−0.315805			−0.157902	−	0.987455i	$-0.550473\pi$
$127$	−3.55894			−0.315805			−0.157902	+	0.987455i	$0.550473\pi$
$128$	−8.24186	−	7.75060i	−0.728484	−	0.685062i
$129$	−4.79312			−0.422011
$130$	1.19934	+	0.129808i	0.105189	+	0.0113849i
$131$	3.99354	+	1.65418i	0.348917	+	0.144526i	0.550257	−	0.834995i	$-0.314530\pi$
$131$	3.99354	+	1.65418i	0.348917	+	0.144526i	−0.201340	+	0.979521i	$0.564530\pi$
$132$	−1.20533	−	0.264004i	−0.104911	−	0.0229786i
$133$	−1.27849	−	3.08654i	−0.110859	−	0.267637i
$134$	1.30265	+	0.712506i	0.112532	+	0.0615511i
$135$	−1.64450	+	1.64450i	−0.141536	+	0.141536i
$136$	−1.70025	+	5.07221i	−0.145795	+	0.434938i
$137$	1.59393	+	1.59393i	0.136179	+	0.136179i	0.771910	−	0.635731i	$-0.219301\pi$
$137$	1.59393	+	1.59393i	0.136179	+	0.136179i	−0.635731	+	0.771910i	$0.719301\pi$
$138$	−0.0880075	−	0.300519i	−0.00749170	−	0.0255818i
$139$	−6.37823	+	2.64195i	−0.540994	+	0.224087i	−0.636411	−	0.771350i	$-0.719582\pi$
$139$	−6.37823	+	2.64195i	−0.540994	+	0.224087i	0.0954166	+	0.995437i	$0.469582\pi$
$140$	3.74417	+	2.60755i	0.316440	+	0.220378i
$141$	−0.799818	+	1.93093i	−0.0673569	+	0.162614i
$142$	−9.05419	+	7.28569i	−0.759811	+	0.611401i
$143$			1.30733i			0.109324i
$144$	−3.85256	−	10.4198i	−0.321046	−	0.868314i
$145$			0.778121i			0.0646195i
$146$	7.65006	+	9.50701i	0.633124	+	0.786806i
$147$	−0.0275655	+	0.0665491i	−0.00227357	+	0.00548888i
$148$	−4.03395	−	22.5426i	−0.331588	−	1.85299i
$149$	−8.00860	+	3.31727i	−0.656090	+	0.271761i	−0.685792	−	0.727798i	$-0.740544\pi$
$149$	−8.00860	+	3.31727i	−0.656090	+	0.271761i	0.0297023	+	0.999559i	$0.490544\pi$
$150$	2.73642	−	0.801367i	0.223428	−	0.0654313i
$151$	4.88458	+	4.88458i	0.397501	+	0.397501i	0.877351	−	0.479849i	$-0.159309\pi$
$151$	4.88458	+	4.88458i	0.397501	+	0.397501i	−0.479849	+	0.877351i	$0.659309\pi$
$152$	−2.31947	+	2.66526i	−0.188133	+	0.216182i
$153$	−3.71434	+	3.71434i	−0.300287	+	0.300287i
$154$	−2.37279	+	4.33809i	−0.191205	+	0.349574i
$155$	2.03971	+	4.92429i	0.163833	+	0.395529i
$156$	0.794734	−	0.509144i	0.0636296	−	0.0407642i
$157$	6.86294	+	2.84272i	0.547722	+	0.226874i	0.639345	−	0.768920i	$-0.279206\pi$
$157$	6.86294	+	2.84272i	0.547722	+	0.226874i	−0.0916232	+	0.995794i	$0.529206\pi$
$158$	0.730289	−	6.74741i	0.0580987	−	0.536795i
$159$	−0.772730			−0.0612815
$160$	0.703749	−	4.77380i	0.0556362	−	0.377402i
$161$	−1.25484			−0.0988955
$162$	1.07211	−	9.90561i	0.0842328	−	0.778258i
$163$	14.0013	+	5.79952i	1.09666	+	0.454253i	0.856326	−	0.516436i	$-0.172741\pi$
$163$	14.0013	+	5.79952i	1.09666	+	0.454253i	0.240339	+	0.970689i	$0.422741\pi$
$164$	−12.4845	−	19.4873i	−0.974873	−	1.52170i
$165$	−0.201395	−	0.486211i	−0.0156786	−	0.0378515i
$166$	7.37713	−	13.4873i	0.572576	−	1.04682i
$167$	10.9841	−	10.9841i	0.849978	−	0.849978i	−0.140152	−	0.990130i	$-0.544759\pi$
$167$	10.9841	−	10.9841i	0.849978	−	0.849978i	0.990130	+	0.140152i	$0.0447592\pi$
$168$	3.56125	−	0.247050i	0.274757	−	0.0190604i
$169$	−0.707107	−	0.707107i	−0.0543928	−	0.0543928i
$170$	−2.18968	+	0.641253i	−0.167941	+	0.0491819i
$171$	−3.20524	+	1.32766i	−0.245111	+	0.101528i
$172$	19.9957	−	3.57818i	1.52466	−	0.272834i
$173$	−1.95183	+	4.71214i	−0.148395	+	0.358257i	−0.980545	−	0.196293i	$-0.937110\pi$
$173$	−1.95183	+	4.71214i	−0.148395	+	0.358257i	0.832150	+	0.554550i	$0.187110\pi$
$174$	0.381663	+	0.474306i	0.0289338	+	0.0359571i
$175$		−	11.4262i		−	0.863738i
$176$	5.22542	+	0.201550i	0.393881	+	0.0151924i
$177$		−	5.81371i		−	0.436985i
$178$	4.34679	−	3.49775i	0.325805	−	0.262168i
$179$	2.61944	−	6.32389i	0.195786	−	0.472670i	−0.795247	−	0.606286i	$-0.792659\pi$
$179$	2.61944	−	6.32389i	0.195786	−	0.472670i	0.991033	+	0.133616i	$0.0426588\pi$
$180$	2.70783	−	3.88816i	0.201829	−	0.289807i
$181$	−1.26352	+	0.523366i	−0.0939164	+	0.0389015i	−0.429147	−	0.903235i	$-0.641186\pi$
$181$	−1.26352	+	0.523366i	−0.0939164	+	0.0389015i	0.335231	+	0.942136i	$0.391186\pi$
$182$	−1.06299	−	3.62978i	−0.0787941	−	0.269057i
$183$	−3.70007	−	3.70007i	−0.273517	−	0.273517i
$184$	0.591490	+	1.18799i	0.0436052	+	0.0875797i
$185$	6.90655	−	6.90655i	0.507780	−	0.507780i
$186$	3.65864	+	2.00115i	0.268264	+	0.146732i
$187$	−0.946236	−	2.28442i	−0.0691956	−	0.167053i
$188$	1.89515	−	8.65245i	0.138218	−	0.631045i
$189$	6.73659	+	2.79039i	0.490015	+	0.202971i
$190$	−1.49819	−	0.162153i	−0.108690	−	0.0117638i
$191$	−1.79823			−0.130116			−0.0650578	−	0.997881i	$-0.520723\pi$
$191$	−1.79823			−0.130116			−0.0650578	+	0.997881i	$0.520723\pi$
$192$	−1.91254	−	3.25507i	−0.138026	−	0.234914i
$193$	−8.22843			−0.592295			−0.296148	−	0.955142i	$-0.595702\pi$
$193$	−8.22843			−0.592295			−0.296148	+	0.955142i	$0.595702\pi$
$194$	21.1553	+	2.28968i	1.51886	+	0.164390i
$195$	0.371912	+	0.154051i	0.0266332	+	0.0110318i
$196$	0.0653159	−	0.298205i	0.00466542	−	0.0213003i
$197$	−6.34220	−	15.3114i	−0.451863	−	1.09089i	−0.971613	−	0.236575i	$-0.923975\pi$
$197$	−6.34220	−	15.3114i	−0.451863	−	1.09089i	0.519750	−	0.854318i	$-0.326025\pi$
$198$	4.50492	+	2.46405i	0.320151	+	0.175112i
$199$	11.2876	−	11.2876i	0.800155	−	0.800155i	−0.182964	−	0.983120i	$-0.558569\pi$
$199$	11.2876	−	11.2876i	0.800155	−	0.800155i	0.983120	+	0.182964i	$0.0585692\pi$
$200$	−10.8174	+	5.38591i	−0.764907	+	0.380841i
$201$	0.350347	+	0.350347i	0.0247116	+	0.0247116i
$202$	−2.56854	−	8.77077i	−0.180722	−	0.617109i
$203$	2.25392	−	0.933603i	0.158194	−	0.0655261i
$204$	−1.02020	+	1.46490i	−0.0714281	+	0.102564i
$205$	3.77741	−	9.11947i	0.263826	−	0.636931i
$206$	0.131853	−	0.106099i	0.00918666	−	0.00739228i
$207$			1.30310i			0.0905718i
$208$	−2.93534	+	2.71731i	−0.203529	+	0.188412i
$209$		−	1.63308i		−	0.112963i
$210$	0.954511	+	1.18621i	0.0658675	+	0.0818560i
$211$	−8.31570	+	20.0759i	−0.572476	+	1.38208i	0.326964	+	0.945037i	$0.393974\pi$
$211$	−8.31570	+	20.0759i	−0.572476	+	1.38208i	−0.899440	+	0.437043i	$0.856026\pi$
$212$	3.22363	−	0.576862i	0.221400	−	0.0396191i
$213$	−3.58287	+	1.48407i	−0.245494	+	0.101687i
$214$	11.5741	−	3.38950i	0.791188	−	0.231701i
$215$	6.12624	+	6.12624i	0.417806	+	0.417806i
$216$	−0.533675	−	7.69297i	−0.0363120	−	0.523441i
$217$	11.8165	−	11.8165i	0.802156	−	0.802156i
$218$	−2.84876	+	5.20829i	−0.192943	+	0.352750i
$219$	1.55829	+	3.76205i	0.105300	+	0.254216i
$220$	1.20314	+	1.87800i	0.0811156	+	0.126615i
$221$	1.74739	+	0.723794i	0.117542	+	0.0486877i
$222$	0.822298	−	7.59752i	0.0551890	−	0.509912i
$223$	−24.6250			−1.64901			−0.824506	−	0.565854i	$-0.808547\pi$
$223$	−24.6250			−1.64901			−0.824506	+	0.565854i	$0.808547\pi$
$224$	−14.6722	+	3.68920i	−0.980329	+	0.246495i
$225$	−11.8656			−0.791040
$226$	1.91550	−	17.6981i	0.127417	−	1.17726i
$227$	−16.5634	−	6.86077i	−1.09935	−	0.455365i	−0.242092	−	0.970253i	$-0.577833\pi$
$227$	−16.5634	−	6.86077i	−1.09935	−	0.455365i	−0.857257	+	0.514888i	$0.827833\pi$
$228$	−0.992763	+	0.636012i	−0.0657474	+	0.0421209i
$229$	8.77120	+	21.1756i	0.579617	+	1.39932i	0.893157	+	0.449745i	$0.148485\pi$
$229$	8.77120	+	21.1756i	0.579617	+	1.39932i	−0.313540	+	0.949575i	$0.601515\pi$
$230$	−0.271617	+	0.496588i	−0.0179099	+	0.0327440i
$231$	−1.16673	+	1.16673i	−0.0767651	+	0.0767651i
$232$	−1.94628	−	1.69376i	−0.127780	−	0.111201i
$233$	−4.01218	−	4.01218i	−0.262847	−	0.262847i	0.563363	−	0.826210i	$-0.309507\pi$
$233$	−4.01218	−	4.01218i	−0.262847	−	0.262847i	−0.826210	+	0.563363i	$0.809507\pi$
$234$	−3.76937	+	1.10387i	−0.246412	+	0.0721622i
$235$	3.49026	−	1.44571i	0.227679	−	0.0943079i
$236$	4.34008	+	24.2533i	0.282515	+	1.57876i
$237$	0.866679	−	2.09235i	0.0562968	−	0.135913i
$238$	4.48468	+	5.57328i	0.290699	+	0.361262i
$239$		−	1.30948i		−	0.0847032i	−0.999103	−	0.0423516i	$-0.986515\pi$
$239$		−	1.30948i		−	0.0847032i	0.999103	−	0.0423516i	$-0.0134850\pi$
$240$	0.673084	−	1.46279i	0.0434474	−	0.0944230i
$241$			23.0868i			1.48715i	0.668653	+	0.743575i	$0.266871\pi$
$241$			23.0868i			1.48715i	−0.668653	+	0.743575i	$0.733129\pi$
$242$	10.2367	−	8.23721i	0.658039	−	0.529508i
$243$	4.40240	−	10.6283i	0.282414	−	0.681808i
$244$	18.1980	+	12.6736i	1.16501	+	0.811342i
$245$	0.120291	−	0.0498261i	0.00768511	−	0.00318328i
$246$	−2.17050	−	7.41159i	−0.138386	−	0.472546i
$247$	0.883302	+	0.883302i	0.0562031	+	0.0562031i
$248$	−16.7568	−	5.61705i	−1.06406	−	0.356683i
$249$	3.62741	−	3.62741i	0.229878	−	0.229878i
$250$	−9.81363	−	5.36774i	−0.620669	−	0.339485i
$251$	5.31497	+	12.8315i	0.335478	+	0.809915i	0.998138	+	0.0609951i	$0.0194274\pi$
$251$	5.31497	+	12.8315i	0.335478	+	0.809915i	−0.662660	+	0.748920i	$0.730573\pi$
$252$	−14.5114	−	3.17844i	−0.914132	−	0.200223i
$253$	−0.566704	−	0.234736i	−0.0356284	−	0.0147578i
$254$	5.00388	+	0.541582i	0.313971	+	0.0339819i
$255$	−0.761379			−0.0476794
$256$	10.4086	+	12.1516i	0.650539	+	0.759473i
$257$	6.64916			0.414763			0.207382	−	0.978260i	$-0.433506\pi$
$257$	6.64916			0.414763			0.207382	+	0.978260i	$0.433506\pi$
$258$	6.73914	+	0.729393i	0.419560	+	0.0454100i
$259$	−28.2922	−	11.7190i	−1.75799	−	0.728184i
$260$	−1.66653	−	0.365021i	−0.103354	−	0.0226376i
$261$	−0.969506	−	2.34060i	−0.0600109	−	0.144879i
$262$	−5.36320	−	2.93350i	−0.331340	−	0.181232i
$263$	21.6756	−	21.6756i	1.33658	−	1.33658i	0.437226	−	0.899352i	$-0.355961\pi$
$263$	21.6756	−	21.6756i	1.33658	−	1.33658i	0.899352	−	0.437226i	$-0.144039\pi$
$264$	1.65452	+	0.554612i	0.101829	+	0.0341340i
$265$	0.987650	+	0.987650i	0.0606709	+	0.0606709i
$266$	1.32786	+	4.53424i	0.0814165	+	0.278012i
$267$	1.72008	−	0.712481i	0.105267	−	0.0436031i
$268$	−1.72310	−	1.20002i	−0.105255	−	0.0733026i
$269$	−1.06032	+	2.55984i	−0.0646488	+	0.156076i	−0.952902	−	0.303278i	$-0.901919\pi$
$269$	−1.06032	+	2.55984i	−0.0646488	+	0.156076i	0.888253	+	0.459354i	$0.151919\pi$
$270$	2.56243	−	2.06192i	0.155944	−	0.125485i
$271$			15.1395i			0.919662i	0.888007	+	0.459831i	$0.152090\pi$
$271$			15.1395i			0.919662i	−0.888007	+	0.459831i	$0.847910\pi$
$272$	3.16242	−	6.87280i	0.191750	−	0.416725i
$273$		−	1.26212i		−	0.0763869i
$274$	−1.99852	−	2.48363i	−0.120735	−	0.150041i
$275$	2.13743	−	5.16021i	0.128892	−	0.311173i
$276$	0.0780074	+	0.435922i	0.00469549	+	0.0262395i
$277$	−4.77488	+	1.97782i	−0.286895	+	0.118836i	−0.521490	−	0.853257i	$-0.674624\pi$
$277$	−4.77488	+	1.97782i	−0.286895	+	0.118836i	0.234595	+	0.972093i	$0.424624\pi$
$278$	9.36984	−	2.74398i	0.561966	−	0.164573i
$279$	−12.2709	−	12.2709i	−0.734641	−	0.734641i
$280$	−4.86751	−	4.23599i	−0.290890	−	0.253149i
$281$	−0.645943	+	0.645943i	−0.0385337	+	0.0385337i	−0.726111	−	0.687577i	$-0.758674\pi$
$281$	−0.645943	+	0.645943i	−0.0385337	+	0.0385337i	0.687577	+	0.726111i	$0.258674\pi$
$282$	1.41839	−	2.59318i	0.0844637	−	0.154422i
$283$	9.27341	+	22.3880i	0.551247	+	1.33083i	0.916543	+	0.399936i	$0.130968\pi$
$283$	9.27341	+	22.3880i	0.551247	+	1.33083i	−0.365296	+	0.930891i	$0.619032\pi$
$284$	13.8389	−	8.86587i	0.821189	−	0.526093i
$285$	−0.464585	−	0.192437i	−0.0275196	−	0.0113990i
$286$	0.198943	−	1.83811i	0.0117637	−	0.108689i
$287$	−30.9478			−1.82679
$288$	3.83107	+	15.2365i	0.225748	+	0.897818i
$289$	13.4227			0.789573
$290$	0.118411	−	1.09404i	0.00695331	−	0.0642443i
$291$	6.56017	+	2.71731i	0.384564	+	0.159292i
$292$	−9.30927	−	14.5310i	−0.544784	−	0.850364i
$293$	2.50450	+	6.04640i	0.146314	+	0.353234i	0.979998	−	0.199008i	$-0.0637721\pi$
$293$	2.50450	+	6.04640i	0.146314	+	0.353234i	−0.833683	+	0.552243i	$0.813772\pi$
$294$	0.0488843	−	0.0893734i	0.00285099	−	0.00521236i
$295$	−7.43068	+	7.43068i	−0.432631	+	0.432631i
$296$	2.24132	+	32.3088i	0.130274	+	1.87791i
$297$	2.52035	+	2.52035i	0.146246	+	0.146246i
$298$	11.7649	−	3.44538i	0.681523	−	0.199585i
$299$	0.433483	−	0.179554i	0.0250690	−	0.0103839i
$300$	−3.96936	+	0.710309i	−0.229171	+	0.0410097i
$301$	10.3950	−	25.0957i	0.599157	−	1.44649i
$302$	−6.12442	−	7.61104i	−0.352421	−	0.437966i
$303$		−	3.04970i		−	0.175201i
$304$	3.66676	−	3.39440i	0.210303	−	0.194682i
$305$			9.45836i			0.541584i
$306$	5.78761	−	4.65715i	0.330856	−	0.266231i
$307$	0.837331	−	2.02149i	0.0477890	−	0.115373i	−0.898182	−	0.439623i	$-0.855112\pi$
$307$	0.837331	−	2.02149i	0.0477890	−	0.115373i	0.945971	+	0.324250i	$0.105112\pi$
$308$	3.99630	−	5.73829i	0.227711	−	0.326969i
$309$	0.0521762	−	0.0216121i	0.00296820	−	0.00122947i
$310$	−2.11848	−	7.23396i	−0.120322	−	0.410861i
$311$	−15.3119	−	15.3119i	−0.868261	−	0.868261i	0.124019	−	0.992280i	$-0.460422\pi$
$311$	−15.3119	−	15.3119i	−0.868261	−	0.868261i	−0.992280	+	0.124019i	$0.960422\pi$
$312$	−1.19488	+	0.594920i	−0.0676466	+	0.0336807i
$313$	3.74611	−	3.74611i	0.211743	−	0.211743i	−0.593265	−	0.805007i	$-0.702161\pi$
$313$	3.74611	−	3.74611i	0.211743	−	0.211743i	0.805007	+	0.593265i	$0.202161\pi$
$314$	−9.21671	−	5.04124i	−0.520129	−	0.284494i
$315$	−2.42467	−	5.85367i	−0.136615	−	0.329817i
$316$	−2.05358	+	9.37575i	−0.115523	+	0.527427i
$317$	28.5085	+	11.8086i	1.60120	+	0.663238i	0.991585	−	0.129460i	$-0.0413245\pi$
$317$	28.5085	+	11.8086i	1.60120	+	0.663238i	0.609614	+	0.792698i	$0.291324\pi$
$318$	1.08646	+	0.117590i	0.0609257	+	0.00659413i
$319$	1.19254			0.0667695
$320$	−1.71593	+	6.60488i	−0.0959232	+	0.369224i
$321$	4.02445			0.224623
$322$	1.76431	+	0.190956i	0.0983213	+	0.0106416i
$323$	−2.18281	−	0.904148i	−0.121455	−	0.0503081i
$324$	−3.01477	+	13.7642i	−0.167487	+	0.764676i
$325$	1.63496	+	3.94715i	0.0906914	+	0.218948i
$326$	−18.8033	−	10.2848i	−1.04142	−	0.569622i
$327$	−1.40077	+	1.40077i	−0.0774626	+	0.0774626i
$328$	14.5877	+	29.2989i	0.805472	+	1.61776i
$329$	−8.37534	−	8.37534i	−0.461747	−	0.461747i
$330$	0.209173	+	0.714261i	0.0115146	+	0.0393188i
$331$	−6.83272	+	2.83020i	−0.375560	+	0.155562i	−0.562476	−	0.826814i	$-0.690151\pi$
$331$	−6.83272	+	2.83020i	−0.375560	+	0.155562i	0.186915	+	0.982376i	$0.440151\pi$
$332$	−12.4247	+	17.8406i	−0.681894	+	0.979130i
$333$	−12.1697	+	29.3802i	−0.666895	+	1.61003i
$334$	−17.1152	+	13.7722i	−0.936504	+	0.753582i
$335$		−	0.895579i		−	0.0489307i
$336$	−5.04473	−	0.194580i	−0.275212	−	0.0106152i
$337$		−	27.9598i		−	1.52307i	−0.648127	−	0.761533i	$-0.724447\pi$
$337$		−	27.9598i		−	1.52307i	0.648127	−	0.761533i	$-0.275553\pi$
$338$	0.886590	+	1.10180i	0.0482241	+	0.0599299i
$339$	2.27325	−	5.48810i	0.123466	−	0.298073i
$340$	3.17628	−	0.568389i	0.172258	−	0.0308252i
$341$	7.54693	−	3.12604i	0.408689	−	0.169285i
$342$	4.70862	−	1.37893i	0.254613	−	0.0745639i
$343$	12.9492	+	12.9492i	0.699189	+	0.699189i
$344$	−28.6585	+	1.98809i	−1.54516	+	0.107191i
$345$	−0.133557	+	0.133557i	−0.00719047	+	0.00719047i
$346$	3.46135	−	6.32825i	0.186083	−	0.340209i
$347$	3.07392	+	7.42110i	0.165017	+	0.398385i	0.984659	−	0.174490i	$-0.0558278\pi$
$347$	3.07392	+	7.42110i	0.165017	+	0.398385i	−0.819642	+	0.572876i	$0.805828\pi$
$348$	−0.464441	−	0.724955i	−0.0248966	−	0.0388617i
$349$	−8.95514	−	3.70934i	−0.479358	−	0.198556i	0.129903	−	0.991527i	$-0.458534\pi$
$349$	−8.95514	−	3.70934i	−0.479358	−	0.198556i	−0.609260	+	0.792970i	$0.708534\pi$
$350$	−1.73878	+	16.0652i	−0.0929417	+	0.858723i
$351$	−2.72641			−0.145525
$352$	−7.31629	−	1.07856i	−0.389959	−	0.0574874i
$353$	0.746473			0.0397308			0.0198654	−	0.999803i	$-0.493676\pi$
$353$	0.746473			0.0397308			0.0198654	+	0.999803i	$0.493676\pi$
$354$	−0.884701	+	8.17408i	−0.0470213	+	0.434448i
$355$	6.47621	+	2.68254i	0.343722	+	0.142374i
$356$	−6.64386	+	4.25638i	−0.352124	+	0.225587i
$357$	0.913515	+	2.20542i	0.0483483	+	0.116723i
$358$	−4.64528	+	8.49279i	−0.245511	+	0.448858i
$359$	20.4669	−	20.4669i	1.08020	−	1.08020i	0.0837107	−	0.996490i	$-0.473323\pi$
$359$	20.4669	−	20.4669i	1.08020	−	1.08020i	0.996490	−	0.0837107i	$-0.0266772\pi$
$360$	−4.39889	+	5.05470i	−0.231842	+	0.266406i
$361$	12.3316	+	12.3316i	0.649033	+	0.649033i
$362$	1.85615	−	0.543578i	0.0975571	−	0.0285698i
$363$	4.05080	−	1.67789i	0.212612	−	0.0880666i
$364$	0.942204	+	5.26524i	0.0493849	+	0.275974i
$365$	2.81669	−	6.80010i	0.147433	−	0.355934i
$366$	4.63925	+	5.76537i	0.242498	+	0.301361i
$367$			7.14000i			0.372705i	0.982483	+	0.186352i	$0.0596666\pi$
$367$			7.14000i			0.372705i	−0.982483	+	0.186352i	$0.940333\pi$
$368$	−0.650854	−	1.76032i	−0.0339281	−	0.0917633i
$369$			32.1379i			1.67303i
$370$	−10.7616	+	8.65962i	−0.559471	+	0.450192i
$371$	1.67584	−	4.04584i	0.0870054	−	0.210050i
$372$	−4.83953	−	3.37038i	−0.250918	−	0.174746i
$373$	−14.2097	+	5.88585i	−0.735751	+	0.304758i	−0.718913	−	0.695100i	$-0.755360\pi$
$373$	−14.2097	+	5.88585i	−0.735751	+	0.304758i	−0.0168380	+	0.999858i	$0.505360\pi$
$374$	0.982779	+	3.35589i	0.0508183	+	0.173529i
$375$	−2.63937	−	2.63937i	−0.136297	−	0.136297i
$376$	−3.98127	+	11.8770i	−0.205319	+	0.612508i
$377$	−0.645022	+	0.645022i	−0.0332203	+	0.0332203i
$378$	−9.04704	−	4.94843i	−0.465329	−	0.254520i
$379$	−11.8203	−	28.5367i	−0.607167	−	1.46583i	−0.866067	−	0.499928i	$-0.833360\pi$
$379$	−11.8203	−	28.5367i	−0.607167	−	1.46583i	0.258900	−	0.965904i	$-0.416640\pi$
$380$	2.08179	+	0.455976i	0.106794	+	0.0233911i
$381$	1.55168	+	0.642729i	0.0794952	+	0.0329280i
$382$	2.52832	+	0.273646i	0.129360	+	0.0140010i
$383$	30.6123			1.56422			0.782108	−	0.623143i	$-0.214145\pi$
$383$	30.6123			1.56422			0.782108	+	0.623143i	$0.214145\pi$
$384$	2.19370	+	4.86767i	0.111947	+	0.248402i
$385$	2.98246			0.152000
$386$	11.5692	+	1.25216i	0.588856	+	0.0637333i
$387$	−26.0608	−	10.7947i	−1.32475	−	0.548727i
$388$	−29.3959	−	6.43860i	−1.49235	−	0.326871i
$389$	3.48037	+	8.40236i	0.176462	+	0.426017i	0.987220	−	0.159365i	$-0.0509447\pi$
$389$	3.48037	+	8.40236i	0.176462	+	0.426017i	−0.810758	+	0.585382i	$0.800945\pi$
$390$	−0.499467	−	0.273192i	−0.0252915	−	0.0138336i
$391$	−0.627505	+	0.627505i	−0.0317343	+	0.0317343i
$392$	−0.137214	+	0.409337i	−0.00693034	+	0.0206746i
$393$	−1.44243	−	1.44243i	−0.0727610	−	0.0727610i
$394$	6.58713	+	22.4930i	0.331855	+	1.13318i
$395$	−3.78203	+	1.56657i	−0.190294	+	0.0788225i
$396$	−5.95897	−	4.14999i	−0.299449	−	0.208545i
$397$	2.32388	−	5.61034i	0.116632	−	0.281575i	−0.854773	−	0.519002i	$-0.826304\pi$
$397$	2.32388	−	5.61034i	0.116632	−	0.281575i	0.971406	+	0.237426i	$0.0763039\pi$
$398$	−17.5881	+	14.1527i	−0.881610	+	0.709410i
$399$			1.57661i			0.0789293i
$400$	16.0289	−	5.92646i	0.801446	−	0.296323i
$401$			34.7591i			1.73578i	0.496753	+	0.867892i	$0.334526\pi$
$401$			34.7591i			1.73578i	−0.496753	+	0.867892i	$0.665474\pi$
$402$	−0.439274	−	0.545902i	−0.0219090	−	0.0272271i
$403$	−2.39117	+	5.77279i	−0.119113	+	0.287563i
$404$	2.27668	+	12.7226i	0.113269	+	0.632973i
$405$	−5.55224	+	2.29981i	−0.275893	+	0.114279i
$406$	−3.31108	+	0.969658i	−0.164326	+	0.0481233i
$407$	−10.5849	−	10.5849i	−0.524675	−	0.524675i
$408$	1.65732	−	1.90440i	0.0820496	−	0.0942821i
$409$	0.734114	−	0.734114i	0.0362996	−	0.0362996i	−0.688724	−	0.725024i	$-0.741829\pi$
$409$	0.734114	−	0.734114i	0.0362996	−	0.0362996i	0.725024	+	0.688724i	$0.241829\pi$
$410$	−6.69880	+	12.2472i	−0.330830	+	0.604845i
$411$	−0.407091	−	0.982805i	−0.0200803	−	0.0484782i
$412$	−0.201532	+	0.129111i	−0.00992876	+	0.00636084i
$413$	30.4393	+	12.6084i	1.49782	+	0.620417i
$414$	0.198299	−	1.83216i	0.00974589	−	0.0900459i
$415$	−9.27262			−0.455175
$416$	4.54060	−	3.37386i	0.222621	−	0.165417i
$417$	3.25801			0.159545
$418$	−0.248515	+	2.29612i	−0.0121552	+	0.112307i
$419$	−27.0719	−	11.2135i	−1.32255	−	0.547817i	−0.394028	−	0.919099i	$-0.628919\pi$
$419$	−27.0719	−	11.2135i	−1.32255	−	0.547817i	−0.928520	+	0.371281i	$0.878919\pi$
$420$	−1.16153	−	1.81306i	−0.0566771	−	0.0884684i
$421$	−6.09413	−	14.7125i	−0.297010	−	0.717044i	−0.999983	−	0.00582837i	$-0.998145\pi$
$421$	−6.09413	−	14.7125i	−0.297010	−	0.717044i	0.702973	−	0.711216i	$-0.251855\pi$
$422$	14.7469	−	26.9613i	0.717870	−	1.31245i
$423$	−8.69743	+	8.69743i	−0.422884	+	0.422884i
$424$	−4.62022	+	0.320513i	−0.224378	+	0.0155655i
$425$	−5.71385	−	5.71385i	−0.277162	−	0.277162i
$426$	5.26336	−	1.54139i	0.255010	−	0.0746804i
$427$	27.3972	−	11.3483i	1.32584	−	0.549182i
$428$	−16.7890	+	3.00435i	−0.811526	+	0.145221i
$429$	0.236097	−	0.569990i	0.0113989	−	0.0275194i
$430$	−7.68124	−	9.54576i	−0.370422	−	0.460338i
$431$		−	20.6647i		−	0.995384i	−0.867354	−	0.497692i	$-0.834181\pi$
$431$		−	20.6647i		−	0.995384i	0.867354	−	0.497692i	$-0.165819\pi$
$432$	−0.420330	+	10.8976i	−0.0202231	+	0.524309i
$433$			15.9772i			0.767814i	0.923372	+	0.383907i	$0.125422\pi$
$433$			15.9772i			0.767814i	−0.923372	+	0.383907i	$0.874578\pi$
$434$	−18.4122	+	14.8158i	−0.883813	+	0.711183i
$435$	0.140525	−	0.339258i	0.00673767	−	0.0162662i
$436$	4.79794	−	6.88936i	0.229780	−	0.329940i
$437$	−0.541497	+	0.224295i	−0.0259033	+	0.0107295i
$438$	−1.61847	−	5.52659i	−0.0773336	−	0.264071i
$439$	4.84235	+	4.84235i	0.231113	+	0.231113i	0.813157	−	0.582044i	$-0.197747\pi$
$439$	4.84235	+	4.84235i	0.231113	+	0.231113i	−0.582044	+	0.813157i	$0.697747\pi$
$440$	−1.40583	−	2.82357i	−0.0670204	−	0.134608i
$441$	−0.299755	+	0.299755i	−0.0142740	+	0.0142740i
$442$	−2.34670	−	1.28357i	−0.111621	−	0.0610530i
$443$	8.43892	+	20.3734i	0.400945	+	0.967967i	0.987437	+	0.158012i	$0.0505086\pi$
$443$	8.43892	+	20.3734i	0.400945	+	0.967967i	−0.586492	+	0.809955i	$0.699491\pi$
$444$	−2.31231	+	10.5570i	−0.109737	+	0.501013i
$445$	−3.10914	−	1.28785i	−0.147387	−	0.0610498i
$446$	34.6228	+	3.74731i	1.63944	+	0.177440i
$447$	4.09080			0.193488
$448$	21.1906	−	2.95427i	1.00116	−	0.139576i
$449$	20.1039			0.948762			0.474381	−	0.880320i	$-0.342672\pi$
$449$	20.1039			0.948762			0.474381	+	0.880320i	$0.342672\pi$
$450$	16.6831	+	1.80565i	0.786447	+	0.0851191i
$451$	−13.9764	−	5.78922i	−0.658124	−	0.272604i
$452$	−5.38641	+	24.5920i	−0.253355	+	1.15671i
$453$	−1.24752	−	3.01179i	−0.0586138	−	0.141506i
$454$	22.2441	+	12.1668i	1.04397	+	0.571016i
$455$	−1.61315	+	1.61315i	−0.0756259	+	0.0756259i
$456$	1.49261	−	0.743160i	0.0698980	−	0.0348017i
$457$	−21.5865	−	21.5865i	−1.00977	−	1.00977i	−0.999952	−	0.00982233i	$-0.996873\pi$
$457$	−21.5865	−	21.5865i	−1.00977	−	1.00977i	−0.00982233	−	0.999952i	$-0.503127\pi$
$458$	−9.10994	−	31.1076i	−0.425679	−	1.45356i
$459$	4.76412	−	1.97336i	0.222370	−	0.0921087i
$460$	0.457463	−	0.656870i	0.0213293	−	0.0306267i
$461$	10.1508	−	24.5063i	0.472772	−	1.14137i	−0.490161	−	0.871632i	$-0.663062\pi$
$461$	10.1508	−	24.5063i	0.472772	−	1.14137i	0.962933	−	0.269740i	$-0.0869378\pi$
$462$	1.81797	−	1.46288i	0.0845796	−	0.0680591i
$463$			33.1902i			1.54248i	0.636545	+	0.771239i	$0.280363\pi$
$463$			33.1902i			1.54248i	−0.636545	+	0.771239i	$0.719637\pi$
$464$	2.47873	+	2.67761i	0.115072	+	0.124305i
$465$		−	2.51533i		−	0.116646i
$466$	5.03059	+	6.25170i	0.233037	+	0.289604i
$467$	11.5203	−	27.8126i	0.533098	−	1.28701i	−0.396364	−	0.918094i	$-0.629728\pi$
$467$	11.5203	−	27.8126i	0.533098	−	1.28701i	0.929462	−	0.368919i	$-0.120272\pi$
$468$	5.46773	−	0.978438i	0.252746	−	0.0452283i
$469$	−2.59414	+	1.07453i	−0.119786	+	0.0496172i
$470$	−5.12731	+	1.50154i	−0.236505	+	0.0692611i
$471$	−2.47883	−	2.47883i	−0.114219	−	0.114219i
$472$	−2.41141	−	34.7607i	−0.110994	−	1.59999i
$473$	9.38902	−	9.38902i	0.431707	−	0.431707i
$474$	−1.53696	+	2.80996i	−0.0705947	+	0.129066i
$475$	−2.04236	−	4.93069i	−0.0937098	−	0.226235i
$476$	−5.45736	−	8.51850i	−0.250138	−	0.390445i
$477$	−4.20143	−	1.74029i	−0.192370	−	0.0796824i
$478$	−0.199270	+	1.84113i	−0.00911440	+	0.0842114i
$479$	9.47447			0.432900			0.216450	−	0.976294i	$-0.430552\pi$
$479$	9.47447			0.432900			0.216450	+	0.976294i	$0.430552\pi$
$480$	−1.16896	+	1.95427i	−0.0533554	+	0.0891996i
$481$	11.4503			0.522091
$482$	3.51323	−	32.4601i	0.160023	−	1.47852i
$483$	0.547107	+	0.226619i	0.0248942	+	0.0103115i
$484$	−15.6463	+	10.0238i	−0.711196	+	0.455626i
$485$	−4.91168	−	11.8578i	−0.223028	−	0.538437i
$486$	−7.80715	+	14.2735i	−0.354139	+	0.647460i
$487$	−15.2705	+	15.2705i	−0.691972	+	0.691972i	−0.962666	−	0.270693i	$-0.912747\pi$
$487$	−15.2705	+	15.2705i	−0.691972	+	0.691972i	0.270693	+	0.962666i	$0.412747\pi$
$488$	−23.6578	−	20.5883i	−1.07094	−	0.931991i
$489$	−5.05714	−	5.05714i	−0.228692	−	0.228692i
$490$	−0.176712	+	0.0517504i	−0.00798302	+	0.00233784i
$491$	6.94908	−	2.87840i	0.313608	−	0.129901i	−0.220328	−	0.975426i	$-0.570713\pi$
$491$	6.94908	−	2.87840i	0.313608	−	0.129901i	0.533935	+	0.845525i	$0.320713\pi$
$492$	1.92387	+	10.7510i	0.0867347	+	0.484693i
$493$	0.660244	−	1.59397i	0.0297359	−	0.0717888i
$494$	−1.10751	−	1.37634i	−0.0498291	−	0.0619245i
$495$		−	3.09716i		−	0.139207i
$496$	22.7054	+	10.4476i	1.01950	+	0.469109i
$497$		−	21.9776i		−	0.985832i
$498$	−5.65215	+	4.54815i	−0.253279	+	0.203807i
$499$	−1.96137	+	4.73518i	−0.0878032	+	0.211976i	−0.961681	−	0.274169i	$-0.911597\pi$
$499$	−1.96137	+	4.73518i	−0.0878032	+	0.211976i	0.873878	+	0.486145i	$0.161597\pi$
$500$	12.9812	+	9.04044i	0.580535	+	0.404301i
$501$	−6.77273	+	2.80536i	−0.302583	+	0.125334i
$502$	−5.52023	−	18.8499i	−0.246380	−	0.841312i
$503$	11.8213	+	11.8213i	0.527084	+	0.527084i	0.919702	−	0.392618i	$-0.128430\pi$
$503$	11.8213	+	11.8213i	0.527084	+	0.527084i	−0.392618	+	0.919702i	$0.628430\pi$
$504$	19.9194	+	6.67717i	0.887280	+	0.297425i
$505$	−3.89792	+	3.89792i	−0.173455	+	0.173455i
$506$	0.761066	+	0.416278i	0.0338335	+	0.0185058i
$507$	0.180596	+	0.435996i	0.00802053	+	0.0193633i
$508$	−6.95305	−	1.52293i	−0.308492	−	0.0675692i
$509$	29.7054	+	12.3044i	1.31667	+	0.545382i	0.926823	−	0.375498i	$-0.122528\pi$
$509$	29.7054	+	12.3044i	1.31667	+	0.545382i	0.389845	+	0.920880i	$0.372528\pi$
$510$	1.07050	+	0.115863i	0.0474026	+	0.00513050i
$511$	−23.0768			−1.02086
$512$	−12.7854	−	18.6691i	−0.565040	−	0.825064i
$513$	3.40577			0.150369
$514$	−9.34873	−	1.01184i	−0.412355	−	0.0446302i
$515$	−0.0943111	−	0.0390649i	−0.00415584	−	0.00172141i
$516$	−9.36425	−	2.05106i	−0.412238	−	0.0902927i
$517$	−2.21569	−	5.34914i	−0.0974458	−	0.235255i
$518$	37.9956	+	20.7823i	1.66943	+	0.913123i
$519$	1.70198	−	1.70198i	0.0747087	−	0.0747087i
$520$	2.28760	+	0.766824i	0.100318	+	0.0336275i
$521$	14.3141	+	14.3141i	0.627110	+	0.627110i	0.947340	−	0.320230i	$-0.103760\pi$
$521$	14.3141	+	14.3141i	0.627110	+	0.627110i	−0.320230	+	0.947340i	$0.603760\pi$
$522$	1.00695	+	3.43842i	0.0440729	+	0.150495i
$523$	−7.12247	+	2.95022i	−0.311444	+	0.129004i	−0.532930	−	0.846159i	$-0.678909\pi$
$523$	−7.12247	+	2.95022i	−0.311444	+	0.129004i	0.221486	+	0.975163i	$0.428909\pi$
$524$	7.09427	+	4.94065i	0.309915	+	0.215833i
$525$	−2.06352	+	4.98177i	−0.0900593	+	0.217422i
$526$	−33.7745	+	27.1775i	−1.47264	+	1.18500i
$527$		−	11.8181i		−	0.514803i
$528$	−2.24187	−	1.03156i	−0.0975647	−	0.0448930i
$529$		−	22.7799i		−	0.990428i
$530$	−1.23834	−	1.53893i	−0.0537902	−	0.0668471i
$531$	13.0932	−	31.6099i	0.568198	−	1.37175i
$532$	−1.17698	−	6.57722i	−0.0510285	−	0.285159i
$533$	10.6908	−	4.42829i	0.463071	−	0.191810i
$534$	−2.52686	+	0.739997i	−0.109348	+	0.0320228i
$535$	−5.14378	−	5.14378i	−0.222385	−	0.222385i
$536$	2.24007	+	1.94944i	0.0967564	+	0.0842029i
$537$	−2.28413	+	2.28413i	−0.0985676	+	0.0985676i
$538$	1.88036	−	3.43779i	0.0810679	−	0.148213i
$539$	−0.0763631	−	0.184357i	−0.00328919	−	0.00794081i
$540$	−3.91655	+	2.50913i	−0.168542	+	0.107976i
$541$	−30.5832	−	12.6680i	−1.31488	−	0.544640i	−0.388573	−	0.921418i	$-0.627032\pi$
$541$	−30.5832	−	12.6680i	−1.31488	−	0.544640i	−0.926303	+	0.376779i	$0.877032\pi$
$542$	2.30386	−	21.2862i	0.0989593	−	0.914322i
$543$	0.645406			0.0276970
$544$	−5.49224	+	9.18193i	−0.235478	+	0.393672i
$545$	3.58073			0.153382
$546$	−0.192063	+	1.77454i	−0.00821954	+	0.0759434i
$547$	−26.6325	−	11.0315i	−1.13872	−	0.471675i	−0.267986	−	0.963423i	$-0.586358\pi$
$547$	−26.6325	−	11.0315i	−1.13872	−	0.471675i	−0.870738	+	0.491748i	$0.836358\pi$
$548$	2.43197	+	3.79611i	0.103889	+	0.162162i
$549$	−11.7847	−	28.4508i	−0.502959	−	1.21425i
$550$	−3.79049	+	6.93001i	−0.161627	+	0.295497i
$551$	0.805747	−	0.805747i	0.0343260	−	0.0343260i
$552$	−0.0433420	−	0.624779i	−0.00184476	−	0.0265924i
$553$	9.07547	+	9.07547i	0.385928	+	0.385928i
$554$	7.01447	−	2.05420i	0.298016	−	0.0872747i
$555$	−4.25852	+	1.76394i	−0.180764	+	0.0748750i
$556$	−13.5916	+	2.43218i	−0.576412	+	0.103148i
$557$	−9.67109	+	23.3481i	−0.409777	+	0.989290i	0.575419	+	0.817859i	$0.304839\pi$
$557$	−9.67109	+	23.3481i	−0.409777	+	0.989290i	−0.985196	+	0.171431i	$0.945161\pi$
$558$	15.3856	+	19.1203i	0.651325	+	0.809426i
$559$			10.1567i			0.429581i
$560$	6.19913	+	6.69652i	0.261961	+	0.282980i
$561$			1.16688i			0.0492658i
$562$	1.00649	−	0.809901i	0.0424564	−	0.0341636i
$563$	15.9053	−	38.3988i	0.670329	−	1.61832i	−0.110722	−	0.993851i	$-0.535316\pi$
$563$	15.9053	−	38.3988i	0.670329	−	1.61832i	0.781052	−	0.624467i	$-0.214684\pi$
$564$	−2.38887	+	3.43018i	−0.100590	+	0.144437i
$565$	−9.92003	+	4.10901i	−0.417339	+	0.172867i
$566$	−9.63154	−	32.8887i	−0.404844	−	1.38242i
$567$	13.3233	+	13.3233i	0.559528	+	0.559528i
$568$	−20.8067	+	10.3595i	−0.873030	+	0.434675i
$569$	24.8201	−	24.8201i	1.04051	−	1.04051i	0.0413677	−	0.999144i	$-0.486828\pi$
$569$	24.8201	−	24.8201i	1.04051	−	1.04051i	0.999144	−	0.0413677i	$-0.0131715\pi$
$570$	0.623923	+	0.341265i	0.0261333	+	0.0142940i
$571$	−2.05341	−	4.95737i	−0.0859325	−	0.207459i	0.875072	−	0.483993i	$-0.160814\pi$
$571$	−2.05341	−	4.95737i	−0.0859325	−	0.207459i	−0.961004	+	0.276534i	$0.910814\pi$
$572$	−0.559428	+	2.55411i	−0.0233908	+	0.106793i
$573$	0.784023	+	0.324753i	0.0327530	+	0.0135668i
$574$	43.5126	+	4.70948i	1.81618	+	0.196570i
$575$	−2.00458			−0.0835970
$576$	−3.06789	−	22.0055i	−0.127829	−	0.916896i
$577$	18.4008			0.766034			0.383017	−	0.923741i	$-0.374885\pi$
$577$	18.4008			0.766034			0.383017	+	0.923741i	$0.374885\pi$
$578$	−18.8724	−	2.04261i	−0.784988	−	0.0849612i
$579$	3.58756	+	1.48602i	0.149094	+	0.0617568i
$580$	−0.332971	+	1.52020i	−0.0138259	+	0.0631231i
$581$	11.1254	+	26.8592i	0.461561	+	1.11431i
$582$	−8.81010	−	4.81884i	−0.365191	−	0.199747i
$583$	1.51366	−	1.51366i	0.0626896	−	0.0626896i
$584$	10.8776	+	21.8473i	0.450118	+	0.904048i
$585$	1.67519	+	1.67519i	0.0692607	+	0.0692607i
$586$	−2.60122	−	8.88237i	−0.107456	−	0.366927i
$587$	−18.6100	+	7.70853i	−0.768119	+	0.318165i	−0.732110	−	0.681186i	$-0.761464\pi$
$587$	−18.6100	+	7.70853i	−0.768119	+	0.318165i	−0.0360086	+	0.999351i	$0.511464\pi$
$588$	−0.0823319	+	0.118220i	−0.00339531	+	0.00487532i
$589$	2.98699	−	7.21124i	0.123077	−	0.297134i
$590$	11.5783	−	9.31679i	0.476672	−	0.383566i
$591$			7.82109i			0.321717i
$592$	1.76529	−	45.7673i	0.0725532	−	1.88103i
$593$		−	7.52341i		−	0.308950i	−0.987997	−	0.154475i	$-0.950631\pi$
$593$		−	7.52341i		−	0.308950i	0.987997	−	0.154475i	$-0.0493685\pi$
$594$	−3.16009	−	3.92715i	−0.129660	−	0.161133i
$595$	1.65123	−	3.98641i	0.0676936	−	0.163427i
$596$	−17.0658	+	3.05389i	−0.699042	+	0.125092i
$597$	−6.95983	+	2.88286i	−0.284847	+	0.117987i
$598$	−0.636801	+	0.186489i	−0.0260407	+	0.00762609i
$599$	25.6912	+	25.6912i	1.04972	+	1.04972i	0.998698	+	0.0510181i	$0.0162466\pi$
$599$	25.6912	+	25.6912i	1.04972	+	1.04972i	0.0510181	+	0.998698i	$0.483753\pi$
$600$	5.68902	−	0.394658i	0.232253	−	0.0161118i
$601$	13.6537	−	13.6537i	0.556948	−	0.556948i	−0.371490	−	0.928437i	$-0.621153\pi$
$601$	13.6537	−	13.6537i	0.556948	−	0.556948i	0.928437	+	0.371490i	$0.121153\pi$
$602$	−18.4343	+	33.7028i	−0.751326	+	1.37362i
$603$	1.11585	+	2.69391i	0.0454410	+	0.109704i
$604$	7.45274	+	11.6331i	0.303248	+	0.473345i
$605$	−7.32202	−	3.03288i	−0.297682	−	0.123304i
$606$	−0.464089	+	4.28789i	−0.0188523	+	0.174184i
$607$	43.0071			1.74561			0.872803	−	0.488073i	$-0.162300\pi$
$607$	43.0071			1.74561			0.872803	+	0.488073i	$0.162300\pi$
$608$	−5.67202	+	4.21455i	−0.230031	+	0.170923i
$609$	−1.15130			−0.0466532
$610$	1.43933	−	13.2985i	0.0582766	−	0.538439i
$611$	4.09166	+	1.69482i	0.165531	+	0.0685651i
$612$	−8.84609	+	5.66723i	−0.357582	+	0.229084i
$613$	−5.87719	−	14.1888i	−0.237377	−	0.573080i	0.759633	−	0.650352i	$-0.225379\pi$
$613$	−5.87719	−	14.1888i	−0.237377	−	0.573080i	−0.997010	+	0.0772729i	$0.975379\pi$
$614$	−1.48491	+	2.71481i	−0.0599261	+	0.109561i
$615$	−3.29387	+	3.29387i	−0.132822	+	0.132822i
$616$	−6.49204	+	7.45991i	−0.261572	+	0.300568i
$617$	12.0440	+	12.0440i	0.484875	+	0.484875i	0.906685	−	0.421809i	$-0.138605\pi$
$617$	12.0440	+	12.0440i	0.484875	+	0.484875i	−0.421809	+	0.906685i	$0.638605\pi$
$618$	−0.0766486	+	0.0224467i	−0.00308326	+	0.000902939i
$619$	13.8040	−	5.71780i	0.554829	−	0.229818i	−0.0876095	−	0.996155i	$-0.527923\pi$
$619$	13.8040	−	5.71780i	0.554829	−	0.229818i	0.642439	+	0.766337i	$0.277923\pi$
$620$	1.87776	+	10.4933i	0.0754127	+	0.421423i
$621$	0.489540	−	1.18185i	0.0196445	−	0.0474261i
$622$	19.1985	+	23.8587i	0.769791	+	0.956648i
$623$			10.5511i			0.422723i
$624$	1.77053	−	0.654628i	0.0708780	−	0.0262061i
$625$		−	14.6149i		−	0.584595i
$626$	−5.83710	+	4.69697i	−0.233298	+	0.187729i
$627$	−0.294928	+	0.712018i	−0.0117783	+	0.0284353i
$628$	12.1916	+	8.49055i	0.486497	+	0.338810i
$629$	−20.0083	+	8.28769i	−0.797782	+	0.330452i
$630$	2.51831	+	8.59924i	0.100332	+	0.342602i
$631$	−33.1762	−	33.1762i	−1.32072	−	1.32072i	−0.913191	−	0.407533i	$-0.866389\pi$
$631$	−33.1762	−	33.1762i	−1.32072	−	1.32072i	−0.407533	−	0.913191i	$-0.633611\pi$
$632$	4.31409	−	12.8698i	0.171605	−	0.511934i
$633$	7.25123	−	7.25123i	0.288210	−	0.288210i
$634$	−38.2861	−	20.9412i	−1.52053	−	0.831683i
$635$	−1.16177	−	2.80475i	−0.0461033	−	0.111303i
$636$	−1.50967	−	0.330664i	−0.0598624	−	0.0131117i
$637$	0.141018	+	0.0584116i	0.00558734	+	0.00231435i
$638$	−1.67672	−	0.181475i	−0.0663819	−	0.00718467i
$639$	−22.8228			−0.902857
$640$	3.41769	−	9.02536i	0.135096	−	0.356759i
$641$	−22.4652			−0.887321			−0.443660	−	0.896195i	$-0.646320\pi$
$641$	−22.4652			−0.887321			−0.443660	+	0.896195i	$0.646320\pi$
$642$	−5.65838	−	0.612421i	−0.223319	−	0.0241703i
$643$	43.9429	+	18.2017i	1.73294	+	0.717806i	0.999266	+	0.0383022i	$0.0121950\pi$
$643$	43.9429	+	18.2017i	1.73294	+	0.717806i	0.733672	+	0.679504i	$0.237805\pi$
$644$	−2.45157	−	0.536969i	−0.0966054	−	0.0211595i
$645$	−1.56464	−	3.77739i	−0.0616078	−	0.148734i
$646$	2.93144	+	1.60340i	0.115336	+	0.0630850i
$647$	−14.9835	+	14.9835i	−0.589061	+	0.589061i	−0.937377	−	0.348316i	$-0.886754\pi$
$647$	−14.9835	+	14.9835i	−0.589061	+	0.589061i	0.348316	+	0.937377i	$0.386754\pi$
$648$	6.33334	−	18.8937i	0.248797	−	0.742214i
$649$	11.3882	+	11.3882i	0.447026	+	0.447026i
$650$	−1.69810	−	5.79850i	−0.0666051	−	0.227436i
$651$	−7.28595	+	3.01794i	−0.285559	+	0.118282i
$652$	24.8724	+	17.3218i	0.974078	+	0.678375i
$653$	−13.9669	+	33.7191i	−0.546567	+	1.31953i	0.373449	+	0.927651i	$0.378175\pi$
$653$	−13.9669	+	33.7191i	−0.546567	+	1.31953i	−0.920017	+	0.391880i	$0.871825\pi$
$654$	2.18264	−	1.75632i	0.0853481	−	0.0686776i
$655$			3.68723i			0.144072i
$656$	−16.0518	−	43.4143i	−0.626717	−	1.69504i
$657$			23.9642i			0.934934i
$658$	10.5012	+	13.0503i	0.409381	+	0.508752i
$659$	−4.44676	+	10.7354i	−0.173221	+	0.418193i	−0.986517	−	0.163657i	$-0.947671\pi$
$659$	−4.44676	+	10.7354i	−0.173221	+	0.418193i	0.813296	+	0.581850i	$0.197671\pi$
$660$	−0.185405	−	1.03608i	−0.00721688	−	0.0403295i
$661$	−3.85527	+	1.59691i	−0.149953	+	0.0621124i	−0.456398	−	0.889776i	$-0.650861\pi$
$661$	−3.85527	+	1.59691i	−0.149953	+	0.0621124i	0.306445	+	0.951888i	$0.400861\pi$
$662$	10.0375	−	2.93950i	0.390119	−	0.114247i
$663$	−0.631143	−	0.631143i	−0.0245116	−	0.0245116i
$664$	20.1840	−	23.1932i	0.783293	−	0.900071i
$665$	2.01512	−	2.01512i	0.0781429	−	0.0781429i
$666$	21.5816	−	39.4568i	0.836268	−	1.52892i
$667$	−0.163789	−	0.395422i	−0.00634195	−	0.0153108i
$668$	26.1598	−	16.7592i	1.01215	−	0.648435i
$669$	10.7364	+	4.44716i	0.415093	+	0.171937i
$670$	−0.136285	+	1.25919i	−0.00526514	+	0.0486466i
$671$	14.4958			0.559604
$672$	7.06329	+	1.04126i	0.272472	+	0.0401676i
$673$	−29.8300			−1.14986			−0.574931	−	0.818202i	$-0.694971\pi$
$673$	−29.8300			−1.14986			−0.574931	+	0.818202i	$0.694971\pi$
$674$	−4.25478	+	39.3115i	−0.163888	+	1.51422i
$675$	10.7616	+	4.45758i	0.414212	+	0.171572i
$676$	−1.07888	−	1.68405i	−0.0414954	−	0.0647710i
$677$	7.95995	+	19.2170i	0.305926	+	0.738570i	0.999829	+	0.0185018i	$0.00588964\pi$
$677$	7.95995	+	19.2170i	0.305926	+	0.738570i	−0.693903	+	0.720068i	$0.744110\pi$
$678$	−4.03134	+	7.37035i	−0.154823	+	0.283057i
$679$	−28.4545	+	28.4545i	−1.09198	+	1.09198i
$680$	−4.55235	+	0.315805i	−0.174575	+	0.0121106i
$681$	5.98254	+	5.98254i	0.229251	+	0.229251i
$682$	−11.0867	+	3.24676i	−0.424532	+	0.124325i
$683$	7.41331	−	3.07069i	0.283662	−	0.117497i	−0.236316	−	0.971676i	$-0.575940\pi$
$683$	7.41331	−	3.07069i	0.283662	−	0.117497i	0.519978	+	0.854179i	$0.325940\pi$
$684$	−6.83017	+	1.22224i	−0.261158	+	0.0467336i
$685$	−0.735838	+	1.77647i	−0.0281149	+	0.0678754i
$686$	−16.2360	−	20.1771i	−0.619894	−	0.770365i
$687$		−	10.8165i		−	0.412675i
$688$	40.5964	+	1.56585i	1.54772	+	0.0596974i
$689$			1.63742i			0.0623808i
$690$	0.208106	−	0.167457i	0.00792244	−	0.00637500i
$691$	−16.6012	+	40.0788i	−0.631538	+	1.52467i	0.206151	+	0.978520i	$0.433906\pi$
$691$	−16.6012	+	40.0788i	−0.631538	+	1.52467i	−0.837689	+	0.546148i	$0.816094\pi$
$692$	−5.82967	+	8.37081i	−0.221611	+	0.318210i
$693$	−8.97128	+	3.71603i	−0.340791	+	0.141160i
$694$	−3.19263	−	10.9019i	−0.121191	−	0.413829i
$695$	−4.16416	−	4.16416i	−0.157956	−	0.157956i
$696$	0.542685	+	1.08996i	0.0205704	+	0.0413150i
$697$	−15.4759	+	15.4759i	−0.586193	+	0.586193i
$698$	12.0265	+	6.57809i	0.455209	+	0.248984i
$699$	1.02471	+	2.47388i	0.0387583	+	0.0935707i
$700$	4.88946	−	22.3232i	0.184804	−	0.843736i
$701$	−40.3595	−	16.7175i	−1.52436	−	0.631410i	−0.545899	−	0.837851i	$-0.683812\pi$
$701$	−40.3595	−	16.7175i	−1.52436	−	0.631410i	−0.978459	+	0.206441i	$0.933812\pi$
$702$	3.83334	+	0.414892i	0.144680	+	0.0156591i
$703$	−14.3035			−0.539467
$704$	10.1226	+	2.62981i	0.381509	+	0.0991148i
$705$	−1.78283			−0.0671452
$706$	−1.04954	−	0.113595i	−0.0395001	−	0.00427519i
$707$	15.9676	+	6.61398i	0.600522	+	0.248744i
$708$	2.48778	−	11.3582i	0.0934966	−	0.426866i
$709$	−11.2543	−	27.1702i	−0.422663	−	1.02040i	−0.981559	−	0.191161i	$-0.938775\pi$
$709$	−11.2543	−	27.1702i	−0.422663	−	1.02040i	0.558896	−	0.829238i	$-0.311225\pi$
$710$	−8.69736	−	4.75717i	−0.326406	−	0.178533i
$711$	9.42449	−	9.42449i	0.353446	−	0.353446i
$712$	9.98900	−	4.97344i	0.374354	−	0.186388i
$713$	−2.07306	−	2.07306i	−0.0776367	−	0.0776367i
$714$	−0.948794	−	3.23984i	−0.0355077	−	0.121248i
$715$	−1.03029	+	0.426758i	−0.0385305	+	0.0159599i
$716$	7.82366	−	11.2340i	0.292384	−	0.419834i
$717$	−0.236486	+	0.570928i	−0.00883174	+	0.0213217i
$718$	−31.8910	+	25.6619i	−1.19016	+	0.957695i
$719$		−	30.7164i		−	1.14553i	−0.819720	−	0.572764i	$-0.805871\pi$
$719$		−	30.7164i		−	1.14553i	0.819720	−	0.572764i	$-0.194129\pi$
$720$	6.95405	−	6.43753i	0.259162	−	0.239912i
$721$			0.320053i			0.0119194i
$722$	−15.4617	−	19.2149i	−0.575426	−	0.715103i
$723$	4.16937	−	10.0657i	0.155060	−	0.374349i
$724$	−2.69247	+	0.481812i	−0.100065	+	0.0179064i
$725$	3.60058	−	1.49141i	0.133722	−	0.0553896i
$726$	−5.95076	+	1.74269i	−0.220853	+	0.0646774i
$727$	13.2713	+	13.2713i	0.492205	+	0.492205i	0.909000	−	0.416795i	$-0.136847\pi$
$727$	13.2713	+	13.2713i	0.492205	+	0.492205i	−0.416795	+	0.909000i	$0.636847\pi$
$728$	−0.523502	−	7.54633i	−0.0194023	−	0.279685i
$729$	11.1063	−	11.1063i	0.411346	−	0.411346i
$730$	−4.99509	+	9.13233i	−0.184876	+	0.338003i
$731$	−7.35133	−	17.7477i	−0.271899	−	0.656422i
$732$	−5.64545	−	8.81210i	−0.208662	−	0.325705i
$733$	−0.117704	−	0.0487546i	−0.00434750	−	0.00180079i	0.380509	−	0.924777i	$-0.375749\pi$
$733$	−0.117704	−	0.0487546i	−0.00434750	−	0.00180079i	−0.384856	+	0.922977i	$0.625749\pi$
$734$	1.08653	−	10.0389i	0.0401045	−	0.370541i
$735$	−0.0614448			−0.00226642
$736$	0.647225	+	2.57406i	0.0238570	+	0.0948813i
$737$	−1.37256			−0.0505587
$738$	4.89059	−	45.1860i	0.180025	−	1.66332i
$739$	17.7594	+	7.35619i	0.653291	+	0.270602i	0.684612	−	0.728908i	$-0.259972\pi$
$739$	17.7594	+	7.35619i	0.653291	+	0.270602i	−0.0313215	+	0.999509i	$0.509972\pi$
$740$	16.4487	−	10.5378i	0.604665	−	0.387377i
$741$	−0.225596	−	0.544637i	−0.00828747	−	0.0200077i
$742$	−2.97191	+	5.43344i	−0.109102	+	0.199468i
$743$	−15.0526	+	15.0526i	−0.552226	+	0.552226i	−0.927083	−	0.374856i	$-0.877692\pi$
$743$	−15.0526	+	15.0526i	−0.552226	+	0.552226i	0.374856	+	0.927083i	$0.377692\pi$
$744$	6.29150	+	5.47522i	0.230657	+	0.200731i
$745$	−5.22858	−	5.22858i	−0.191560	−	0.191560i
$746$	20.8746	−	6.11316i	0.764272	−	0.223819i
$747$	27.8921	−	11.5533i	1.02052	−	0.422713i
$748$	−0.871107	−	4.86794i	−0.0318508	−	0.177990i
$749$	−8.72794	+	21.0711i	−0.318912	+	0.769922i
$750$	3.30932	+	4.11261i	0.120839	+	0.150171i
$751$			38.7660i			1.41459i	0.706918	+	0.707295i	$0.250085\pi$
$751$			38.7660i			1.41459i	−0.706918	+	0.707295i	$0.749915\pi$
$752$	7.40506	−	16.0932i	0.270035	−	0.586858i
$753$		−	6.55433i		−	0.238853i
$754$	1.00506	−	0.808746i	0.0366021	−	0.0294528i
$755$	−2.25497	+	5.44397i	−0.0820666	+	0.198126i
$756$	11.9671	+	8.33424i	0.435240	+	0.303113i
$757$	−14.1943	+	5.87947i	−0.515900	+	0.213693i	−0.625415	−	0.780292i	$-0.715070\pi$
$757$	−14.1943	+	5.87947i	−0.515900	+	0.213693i	0.109515	+	0.993985i	$0.465070\pi$
$758$	12.2768	+	41.9214i	0.445913	+	1.52265i
$759$	0.204688	+	0.204688i	0.00742972	+	0.00742972i
$760$	−2.85761	−	0.957899i	−0.103656	−	0.0347467i
$761$	−4.67975	+	4.67975i	−0.169641	+	0.169641i	−0.786822	−	0.617181i	$-0.788275\pi$
$761$	−4.67975	+	4.67975i	−0.169641	+	0.169641i	0.617181	+	0.786822i	$0.288275\pi$
$762$	−2.08387	−	1.13981i	−0.0754905	−	0.0412908i
$763$	−4.29622	−	10.3720i	−0.155534	−	0.375491i
$764$	−3.51318	−	0.769495i	−0.127103	−	0.0278394i
$765$	−4.13972	−	1.71473i	−0.149672	−	0.0619961i
$766$	−43.0410	−	4.65843i	−1.55513	−	0.168316i
$767$	−12.3193			−0.444824
$768$	−2.34360	−	7.17779i	−0.0845675	−	0.259006i
$769$	25.5231			0.920388			0.460194	−	0.887818i

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bf (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40600 - 0.152175i) q^{2} +(-0.435996 - 0.180596i) q^{3} +(1.95369 + 0.427917i) q^{4} +(0.326436 + 0.788085i) q^{5} +(0.585530 + 0.320266i) q^{6} +(1.89112 - 1.89112i) q^{7} +(-2.68177 - 0.898955i) q^{8} +(-1.96384 - 1.96384i) q^{9} +O(q^{10})\)	\(q+(-1.40600 - 0.152175i) q^{2} +(-0.435996 - 0.180596i) q^{3} +(1.95369 + 0.427917i) q^{4} +(0.326436 + 0.788085i) q^{5} +(0.585530 + 0.320266i) q^{6} +(1.89112 - 1.89112i) q^{7} +(-2.68177 - 0.898955i) q^{8} +(-1.96384 - 1.96384i) q^{9} +(-0.339042 - 1.15773i) q^{10} +(1.20781 - 0.500292i) q^{11} +(-0.774520 - 0.539397i) q^{12} +(-0.382683 + 0.923880i) q^{13} +(-2.94669 + 2.37113i) q^{14} -0.402555i q^{15} +(3.63377 + 1.67203i) q^{16} -1.89137i q^{17} +(2.46232 + 3.06001i) q^{18} +(0.478039 - 1.15409i) q^{19} +(0.300517 + 1.67936i) q^{20} +(-1.16605 + 0.482992i) q^{21} +(-1.77432 + 0.519613i) q^{22} +(-0.331773 - 0.331773i) q^{23} +(1.00689 + 0.876256i) q^{24} +(3.02102 - 3.02102i) q^{25} +(0.678645 - 1.24074i) q^{26} +(1.04335 + 2.51888i) q^{27} +(4.50389 - 2.88540i) q^{28} +(0.842762 + 0.349083i) q^{29} +(-0.0612588 + 0.565993i) q^{30} +6.24842 q^{31} +(-4.85465 - 2.90385i) q^{32} -0.616952 q^{33} +(-0.287819 + 2.65927i) q^{34} +(2.10769 + 0.873033i) q^{35} +(-2.99637 - 4.67709i) q^{36} +(-4.38186 - 10.5787i) q^{37} +(-0.847748 + 1.54991i) q^{38} +(0.333697 - 0.333697i) q^{39} +(-0.166972 - 2.40691i) q^{40} +(-8.18241 - 8.18241i) q^{41} +(1.71296 - 0.501645i) q^{42} +(9.38353 - 3.88678i) q^{43} +(2.57377 - 0.460570i) q^{44} +(0.906607 - 2.18874i) q^{45} +(0.415986 + 0.516962i) q^{46} -4.42878i q^{47} +(-1.28235 - 1.38524i) q^{48} -0.152637i q^{49} +(-4.70728 + 3.78783i) q^{50} +(-0.341572 + 0.824628i) q^{51} +(-1.14299 + 1.64121i) q^{52} +(1.51278 - 0.626614i) q^{53} +(-1.08365 - 3.70032i) q^{54} +(0.788546 + 0.788546i) q^{55} +(-6.77156 + 3.37151i) q^{56} +(-0.416847 + 0.416847i) q^{57} +(-1.13180 - 0.619059i) q^{58} +(4.71439 + 11.3815i) q^{59} +(0.172260 - 0.786466i) q^{60} +(10.2441 + 4.24324i) q^{61} +(-8.78530 - 0.950854i) q^{62} -7.42771 q^{63} +(6.38376 + 4.82158i) q^{64} -0.853018 q^{65} +(0.867437 + 0.0938848i) q^{66} +(-0.969976 - 0.401777i) q^{67} +(0.809348 - 3.69513i) q^{68} +(0.0847351 + 0.204569i) q^{69} +(-2.83056 - 1.54822i) q^{70} +(5.81076 - 5.81076i) q^{71} +(3.50117 + 7.03198i) q^{72} +(-6.10137 - 6.10137i) q^{73} +(4.55108 + 15.5405i) q^{74} +(-1.86273 + 0.771569i) q^{75} +(1.42779 - 2.05017i) q^{76} +(1.33800 - 3.23022i) q^{77} +(-0.519959 + 0.418398i) q^{78} +4.79900i q^{79} +(-0.131509 + 3.40953i) q^{80} +7.04523i q^{81} +(10.2593 + 12.7496i) q^{82} +(-4.15991 + 10.0429i) q^{83} +(-2.48477 + 0.444644i) q^{84} +(1.49056 - 0.617409i) q^{85} +(-13.7847 + 4.03689i) q^{86} +(-0.304398 - 0.304398i) q^{87} +(-3.68881 + 0.255900i) q^{88} +(-2.78966 + 2.78966i) q^{89} +(-1.60776 + 2.93942i) q^{90} +(1.02346 + 2.47086i) q^{91} +(-0.506209 - 0.790152i) q^{92} +(-2.72429 - 1.12844i) q^{93} +(-0.673950 + 6.22688i) q^{94} +1.06557 q^{95} +(1.59219 + 2.14280i) q^{96} -15.0464 q^{97} +(-0.0232275 + 0.214608i) q^{98} +(-3.35445 - 1.38946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51} - 32 q^{53} - 24 q^{54} + 32 q^{55} + 16 q^{56} - 64 q^{58} - 56 q^{60} - 64 q^{61} + 24 q^{62} + 80 q^{63} + 72 q^{64} + 96 q^{66} + 80 q^{67} - 32 q^{68} - 64 q^{69} - 120 q^{72} - 32 q^{74} + 32 q^{75} + 64 q^{76} - 32 q^{77} - 56 q^{80} - 80 q^{82} - 80 q^{83} + 112 q^{84} - 112 q^{87} - 88 q^{88} - 120 q^{90} + 144 q^{92} + 40 q^{94} + 136 q^{96} + 56 q^{98}+O(q^{100}) \) 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Introduction

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