LMFDB - Embedded newform 507.2.t.b.127.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.11
Character	$\chi$	$=$	507.127
Dual form			507.2.t.b.4.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.992569 - 0.0399992i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.00992 + 0.0815293i) q^{4} +(-0.620050 + 0.235154i) q^{5} +(-0.314570 - 0.942252i) q^{6} +(1.02980 - 2.41704i) q^{7} +(-2.97142 + 0.360796i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})$	\(q+(0.992569 - 0.0399992i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.00992 + 0.0815293i) q^{4} +(-0.620050 + 0.235154i) q^{5} +(-0.314570 - 0.942252i) q^{6} +(1.02980 - 2.41704i) q^{7} +(-2.97142 + 0.360796i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-0.606036 + 0.258208i) q^{10} +(1.55666 - 2.46166i) q^{11} +(0.359288 + 0.947365i) q^{12} +(-3.60478 - 0.0747826i) q^{13} +(0.925470 - 2.44027i) q^{14} +(0.398378 + 0.530145i) q^{15} +(-0.934732 + 0.151909i) q^{16} +(0.0646290 + 0.0275358i) q^{17} +(-0.817531 + 0.564301i) q^{18} +(-5.66449 - 3.27039i) q^{19} +(0.607030 - 0.288039i) q^{20} +(-2.60812 - 0.316683i) q^{21} +(1.44663 - 2.50563i) q^{22} +(-3.99049 - 6.91173i) q^{23} +(1.17325 + 2.75372i) q^{24} +(-3.41339 + 3.02400i) q^{25} +(-3.58098 + 0.0699611i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-0.842961 + 2.52498i) q^{28} +(0.0439904 + 1.09161i) q^{29} +(0.416623 + 0.510271i) q^{30} +(3.08701 - 3.48452i) q^{31} +(4.94379 - 1.00928i) q^{32} +(-2.79756 - 0.810323i) q^{33} +(0.0652501 + 0.0247461i) q^{34} +(-0.0701537 + 1.74085i) q^{35} +(0.810001 - 0.608677i) q^{36} +(5.57663 + 1.13848i) q^{37} +(-5.75320 - 3.01951i) q^{38} +(0.931081 + 3.48326i) q^{39} +(1.75759 - 0.922452i) q^{40} +(3.72916 - 1.08016i) q^{41} +(-2.60140 - 0.210007i) q^{42} +(0.0239107 + 0.117122i) q^{43} +(-1.37141 + 2.61300i) q^{44} +(0.398378 - 0.530145i) q^{45} +(-4.23730 - 6.70075i) q^{46} +(2.25848 + 1.55892i) q^{47} +(0.405970 + 0.855564i) q^{48} +(0.0675030 + 0.0702781i) q^{49} +(-3.26707 + 3.13806i) q^{50} +(0.00846775 - 0.0697382i) q^{51} +(3.64664 - 0.218370i) q^{52} +(0.332216 + 2.73604i) q^{53} +(0.769473 + 0.628255i) q^{54} +(-0.386338 + 1.89241i) q^{55} +(-2.18792 + 7.55357i) q^{56} +(-1.56531 + 6.35072i) q^{57} +(0.0873271 + 1.08174i) q^{58} +(2.03239 - 12.5058i) q^{59} +(-0.445553 - 0.502926i) q^{60} +(4.57816 + 3.44026i) q^{61} +(2.92470 - 3.58210i) q^{62} +(0.421444 + 2.59325i) q^{63} +(6.70564 - 1.65279i) q^{64} +(2.25273 - 0.801308i) q^{65} +(-2.80918 - 0.692402i) q^{66} +(-0.338613 + 4.19447i) q^{67} +(-0.0675152 - 0.0225399i) q^{68} +(-5.52862 + 5.75590i) q^{69} +1.73071i q^{70} +(2.03517 + 1.95481i) q^{71} +(2.31858 - 1.89306i) q^{72} +(0.0695838 + 0.132581i) q^{73} +(5.58073 + 0.906957i) q^{74} +(3.85427 + 2.43729i) q^{75} +(5.98732 + 2.84102i) q^{76} +(-4.34687 - 6.29753i) q^{77} +(1.06349 + 3.42013i) q^{78} +(-2.14011 + 3.10048i) q^{79} +(0.543859 - 0.313997i) q^{80} +(0.428693 - 0.903450i) q^{81} +(3.65824 - 1.22130i) q^{82} +(-0.951144 - 3.85894i) q^{83} +(2.65981 + 0.107187i) q^{84} +(-0.0465483 - 0.00187583i) q^{85} +(0.0284178 + 0.115295i) q^{86} +(1.03627 - 0.345959i) q^{87} +(-3.73733 + 7.87626i) q^{88} +(9.78311 - 5.64828i) q^{89} +(0.374213 - 0.542141i) q^{90} +(-3.89296 + 8.63586i) q^{91} +(4.59359 + 6.65497i) q^{92} +(-4.20580 - 1.99568i) q^{93} +(2.30405 + 1.45700i) q^{94} +(4.28131 + 0.695781i) q^{95} +(-2.34488 - 4.46780i) q^{96} +(-14.5015 + 11.8401i) q^{97} +(0.0698124 + 0.0670558i) q^{98} +2.91255i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

Coefficient data

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

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

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

$2$	0.992569	−	0.0399992i	0.701852	−	0.0282837i	0.313225	−	0.949679i	$-0.398591\pi$
$2$	0.992569	−	0.0399992i	0.701852	−	0.0282837i	0.388627	+	0.921395i	$0.372950\pi$
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$4$	−1.00992	+	0.0815293i	−0.504961	+	0.0407647i
$5$	−0.620050	+	0.235154i	−0.277295	+	0.105164i	−0.489332	−	0.872098i	$-0.662759\pi$
$5$	−0.620050	+	0.235154i	−0.277295	+	0.105164i	0.212037	+	0.977262i	$0.431990\pi$
$6$	−0.314570	−	0.942252i	−0.128423	−	0.384673i
$7$	1.02980	−	2.41704i	0.389229	−	0.913554i	−0.603958	−	0.797016i	$-0.706410\pi$
$7$	1.02980	−	2.41704i	0.389229	−	0.913554i	0.993186	−	0.116537i	$-0.0371794\pi$
$8$	−2.97142	+	0.360796i	−1.05056	+	0.127560i
$9$	−0.845190	+	0.534466i	−0.281730	+	0.178155i
$10$	−0.606036	+	0.258208i	−0.191646	+	0.0816525i
$11$	1.55666	−	2.46166i	0.469351	−	0.742219i	−0.524682	−	0.851298i	$-0.675816\pi$
$11$	1.55666	−	2.46166i	0.469351	−	0.742219i	0.994033	+	0.109079i	$0.0347902\pi$
$12$	0.359288	+	0.947365i	0.103718	+	0.273481i
$13$	−3.60478	−	0.0747826i	−0.999785	−	0.0207410i
$13$	−3.60478	−	0.0747826i	−0.999785	−	0.0207410i
$14$	0.925470	−	2.44027i	0.247342	−	0.652188i
$15$	0.398378	+	0.530145i	0.102861	+	0.136883i
$16$	−0.934732	+	0.151909i	−0.233683	+	0.0379772i
$17$	0.0646290	+	0.0275358i	0.0156748	+	0.00667842i	0.399790	−	0.916607i	$-0.369083\pi$
$17$	0.0646290	+	0.0275358i	0.0156748	+	0.00667842i	−0.384115	+	0.923285i	$0.625493\pi$
$18$	−0.817531	+	0.564301i	−0.192694	+	0.133007i
$19$	−5.66449	−	3.27039i	−1.29952	−	0.750279i	−0.319201	−	0.947687i	$-0.603414\pi$
$19$	−5.66449	−	3.27039i	−1.29952	−	0.750279i	−0.980321	+	0.197408i	$0.936748\pi$
$20$	0.607030	−	0.288039i	0.135736	−	0.0644076i
$21$	−2.60812	−	0.316683i	−0.569137	−	0.0691058i
$22$	1.44663	−	2.50563i	0.308422	−	0.534203i
$23$	−3.99049	−	6.91173i	−0.832075	−	1.44120i	−0.896390	−	0.443266i	$-0.853820\pi$
$23$	−3.99049	−	6.91173i	−0.832075	−	1.44120i	0.0643152	−	0.997930i	$-0.479514\pi$
$24$	1.17325	+	2.75372i	0.239489	+	0.562101i
$25$	−3.41339	+	3.02400i	−0.682678	+	0.604800i
$26$	−3.58098	+	0.0699611i	−0.702288	+	0.0137205i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	−0.842961	+	2.52498i	−0.159305	+	0.477176i
$29$	0.0439904	+	1.09161i	0.00816882	+	0.202707i	0.998120	+	0.0612953i	$0.0195231\pi$
$29$	0.0439904	+	1.09161i	0.00816882	+	0.202707i	−0.989951	+	0.141412i	$0.954836\pi$
$30$	0.416623	+	0.510271i	0.0760647	+	0.0931623i
$31$	3.08701	−	3.48452i	0.554444	−	0.625838i	−0.402741	−	0.915314i	$-0.631943\pi$
$31$	3.08701	−	3.48452i	0.554444	−	0.625838i	0.957185	+	0.289476i	$0.0934810\pi$
$32$	4.94379	−	1.00928i	0.873947	−	0.178418i
$33$	−2.79756	−	0.810323i	−0.486993	−	0.141059i
$34$	0.0652501	+	0.0247461i	0.0111903	+	0.00424392i
$35$	−0.0701537	+	1.74085i	−0.0118581	+	0.294257i
$36$	0.810001	−	0.608677i	0.135000	−	0.101446i
$37$	5.57663	+	1.13848i	0.916793	+	0.187165i	0.635181	−	0.772364i	$-0.280926\pi$
$37$	5.57663	+	1.13848i	0.916793	+	0.187165i	0.281612	+	0.959528i	$0.409131\pi$
$38$	−5.75320	−	3.01951i	−0.933293	−	0.489830i
$39$	0.931081	+	3.48326i	0.149092	+	0.557768i
$40$	1.75759	−	0.922452i	0.277899	−	0.145853i
$41$	3.72916	−	1.08016i	0.582397	−	0.168693i	0.0260747	−	0.999660i	$-0.491699\pi$
$41$	3.72916	−	1.08016i	0.582397	−	0.168693i	0.556322	+	0.830967i	$0.312212\pi$
$42$	−2.60140	−	0.210007i	−0.401405	−	0.0324048i
$43$	0.0239107	+	0.117122i	0.00364634	+	0.0178610i	0.981573	−	0.191087i	$-0.0612012\pi$
$43$	0.0239107	+	0.117122i	0.00364634	+	0.0178610i	−0.977927	+	0.208948i	$0.932996\pi$
$44$	−1.37141	+	2.61300i	−0.206748	+	0.393925i
$45$	0.398378	−	0.530145i	0.0593867	−	0.0790294i
$46$	−4.23730	−	6.70075i	−0.624756	−	0.987972i
$47$	2.25848	+	1.55892i	0.329433	+	0.227391i	0.721287	−	0.692636i	$-0.243551\pi$
$47$	2.25848	+	1.55892i	0.329433	+	0.227391i	−0.391854	+	0.920027i	$0.628166\pi$
$48$	0.405970	+	0.855564i	0.0585967	+	0.123490i
$49$	0.0675030	+	0.0702781i	0.00964329	+	0.0100397i
$50$	−3.26707	+	3.13806i	−0.462033	+	0.443789i
$51$	0.00846775	−	0.0697382i	0.00118572	−	0.00976531i
$52$	3.64664	−	0.218370i	0.505698	−	0.0302825i
$53$	0.332216	+	2.73604i	0.0456334	+	0.375824i	0.997578	+	0.0695548i	$0.0221579\pi$
$53$	0.332216	+	2.73604i	0.0456334	+	0.375824i	−0.951945	+	0.306270i	$0.900919\pi$
$54$	0.769473	+	0.628255i	0.104712	+	0.0854947i
$55$	−0.386338	+	1.89241i	−0.0520938	+	0.255172i
$56$	−2.18792	+	7.55357i	−0.292373	+	1.00939i
$57$	−1.56531	+	6.35072i	−0.207331	+	0.841174i
$58$	0.0873271	+	1.08174i	0.0114666	+	0.142039i
$59$	2.03239	−	12.5058i	0.264595	−	1.62812i	−0.425893	−	0.904774i	$-0.640040\pi$
$59$	2.03239	−	12.5058i	0.264595	−	1.62812i	0.690488	−	0.723344i	$-0.257396\pi$
$60$	−0.445553	−	0.502926i	−0.0575207	−	0.0649275i
$61$	4.57816	+	3.44026i	0.586173	+	0.440481i	0.852001	−	0.523540i	$-0.175389\pi$
$61$	4.57816	+	3.44026i	0.586173	+	0.440481i	−0.265828	+	0.964020i	$0.585645\pi$
$62$	2.92470	−	3.58210i	0.371437	−	0.454927i
$63$	0.421444	+	2.59325i	0.0530969	+	0.326719i
$64$	6.70564	−	1.65279i	0.838205	−	0.206599i
$65$	2.25273	−	0.801308i	0.279416	−	0.0993901i
$66$	−2.80918	−	0.692402i	−0.345787	−	0.0852287i
$67$	−0.338613	+	4.19447i	−0.0413682	+	0.512437i	0.942580	+	0.333981i	$0.108392\pi$
$67$	−0.338613	+	4.19447i	−0.0413682	+	0.512437i	−0.983948	+	0.178456i	$0.942890\pi$
$68$	−0.0675152	−	0.0225399i	−0.00818742	−	0.00273336i
$69$	−5.52862	+	5.75590i	−0.665568	+	0.692929i
$70$			1.73071i			0.206860i
$71$	2.03517	+	1.95481i	0.241530	+	0.231993i	0.803709	−	0.595023i	$-0.202857\pi$
$71$	2.03517	+	1.95481i	0.241530	+	0.231993i	−0.562178	+	0.827016i	$0.690037\pi$
$72$	2.31858	−	1.89306i	0.273247	−	0.223100i
$73$	0.0695838	+	0.132581i	0.00814416	+	0.0155174i	0.889494	−	0.456947i	$-0.151057\pi$
$73$	0.0695838	+	0.132581i	0.00814416	+	0.0155174i	−0.881350	+	0.472464i	$0.843365\pi$
$74$	5.58073	+	0.906957i	0.648747	+	0.105432i
$75$	3.85427	+	2.43729i	0.445053	+	0.281434i
$76$	5.98732	+	2.84102i	0.686793	+	0.325887i
$77$	−4.34687	−	6.29753i	−0.495372	−	0.717670i
$78$	1.06349	+	3.42013i	0.120416	+	0.387254i
$79$	−2.14011	+	3.10048i	−0.240781	+	0.348831i	−0.924680	−	0.380745i	$-0.875667\pi$
$79$	−2.14011	+	3.10048i	−0.240781	+	0.348831i	0.683899	+	0.729577i	$0.260283\pi$
$80$	0.543859	−	0.313997i	0.0608053	−	0.0351059i
$81$	0.428693	−	0.903450i	0.0476325	−	0.100383i
$82$	3.65824	−	1.22130i	0.403985	−	0.134870i
$83$	−0.951144	−	3.85894i	−0.104402	−	0.423574i	0.895361	−	0.445340i	$-0.146917\pi$
$83$	−0.951144	−	3.85894i	−0.104402	−	0.423574i	−0.999763	+	0.0217661i	$0.993071\pi$
$84$	2.65981	+	0.107187i	0.290209	+	0.0116950i
$85$	−0.0465483	−	0.00187583i	−0.00504888	−	0.000203463i
$86$	0.0284178	+	0.115295i	0.00306437	+	0.0124326i
$87$	1.03627	−	0.345959i	0.111100	−	0.0370907i
$88$	−3.73733	+	7.87626i	−0.398401	+	0.839613i
$89$	9.78311	−	5.64828i	1.03701	−	0.598717i	0.118023	−	0.993011i	$-0.462344\pi$
$89$	9.78311	−	5.64828i	1.03701	−	0.598717i	0.918984	+	0.394294i	$0.129011\pi$
$90$	0.374213	−	0.542141i	0.0394455	−	0.0571466i
$91$	−3.89296	+	8.63586i	−0.408093	+	0.905284i
$92$	4.59359	+	6.65497i	0.478915	+	0.693828i
$93$	−4.20580	−	1.99568i	−0.436122	−	0.206942i
$94$	2.30405	+	1.45700i	0.237645	+	0.150278i
$95$	4.28131	+	0.695781i	0.439253	+	0.0713856i
$96$	−2.34488	−	4.46780i	−0.239324	−	0.455993i
$97$	−14.5015	+	11.8401i	−1.47240	+	1.20218i	−0.539530	+	0.841966i	$0.681398\pi$
$97$	−14.5015	+	11.8401i	−1.47240	+	1.20218i	−0.932871	+	0.360211i	$0.882705\pi$
$98$	0.0698124	+	0.0670558i	0.00705212	+	0.00677365i
$99$			2.91255i			0.292723i
$100$	3.20071	−	3.33229i	0.320071	−	0.333229i
$101$	−1.45537	−	0.485872i	−0.144814	−	0.0483461i	0.243337	−	0.969942i	$-0.421758\pi$
$101$	−1.45537	−	0.485872i	−0.144814	−	0.0483461i	−0.388151	+	0.921596i	$0.626886\pi$
$102$	0.00561536	−	0.0695587i	0.000556003	−	0.00688734i
$103$	6.68561	+	1.64785i	0.658753	+	0.162368i	0.554501	−	0.832183i	$-0.312909\pi$
$103$	6.68561	+	1.64785i	0.658753	+	0.162368i	0.104252	+	0.994551i	$0.466755\pi$
$104$	10.7383	−	1.07838i	1.05297	−	0.105744i
$105$	1.69163	−	0.416950i	0.165086	−	0.0406901i
$106$	0.439186	+	2.70242i	0.0426576	+	0.262482i
$107$	6.57404	−	8.05174i	0.635537	−	0.778391i	−0.351963	−	0.936014i	$-0.614486\pi$
$107$	6.57404	−	8.05174i	0.635537	−	0.778391i	0.987499	+	0.157623i	$0.0503830\pi$
$108$	−0.810001	−	0.608677i	−0.0779424	−	0.0585699i
$109$	−7.92468	−	8.94511i	−0.759046	−	0.856786i	0.234275	−	0.972170i	$-0.424729\pi$
$109$	−7.92468	−	8.94511i	−0.759046	−	0.856786i	−0.993321	+	0.115384i	$0.963190\pi$
$110$	−0.307772	+	1.89380i	−0.0293449	+	0.180567i
$111$	−0.457988	−	5.67320i	−0.0434703	−	0.538477i
$112$	−0.595421	+	2.41572i	−0.0562620	+	0.228264i
$113$	5.64557	−	19.4908i	0.531090	−	1.83354i	−0.0210412	−	0.999779i	$-0.506698\pi$
$113$	5.64557	−	19.4908i	0.531090	−	1.83354i	0.552131	−	0.833757i	$-0.313815\pi$
$114$	−1.29966	+	6.36614i	−0.121724	+	0.596243i
$115$	4.09963	+	3.34724i	0.382292	+	0.312132i
$116$	−0.133425	−	1.09886i	−0.0123882	−	0.102026i
$117$	3.08669	−	1.86342i	0.285365	−	0.172274i
$118$	1.51707	−	12.4942i	0.139657	−	1.15018i
$119$	0.133110	−	0.127854i	0.0122022	−	0.0117204i
$120$	−1.37502	−	1.43155i	−0.125522	−	0.130682i
$121$	1.07903	+	2.27401i	0.0980938	+	0.206728i
$122$	4.68175	+	3.23158i	0.423865	+	0.292573i
$123$	−2.07503	−	3.28140i	−0.187100	−	0.295874i
$124$	−2.83355	+	3.77077i	−0.254461	+	0.338626i
$125$	2.94626	−	5.61363i	0.263521	−	0.502098i
$126$	0.522040	+	2.55712i	0.0465070	+	0.227806i
$127$	−6.26926	−	0.506107i	−0.556307	−	0.0449097i	−0.200883	−	0.979615i	$-0.564381\pi$
$127$	−6.26926	−	0.506107i	−0.556307	−	0.0449097i	−0.355423	+	0.934705i	$0.615663\pi$
$128$	−3.10340	+	0.898910i	−0.274304	+	0.0794532i
$129$	0.105846	−	0.0555520i	0.00931918	−	0.00489109i
$130$	2.20393	−	0.885461i	0.193298	−	0.0776600i
$131$	−4.74789	−	2.49189i	−0.414825	−	0.217717i	0.244381	−	0.969679i	$-0.421415\pi$
$131$	−4.74789	−	2.49189i	−0.414825	−	0.217717i	−0.659206	+	0.751962i	$0.729108\pi$
$132$	2.89138	+	0.590280i	0.251663	+	0.0513773i
$133$	−13.7380	+	10.3234i	−1.19123	+	0.895153i
$134$	−0.168321	+	4.17685i	−0.0145407	+	0.360825i
$135$	−0.620050	−	0.235154i	−0.0533654	−	0.0202388i
$136$	−0.201975	−	0.0585026i	−0.0173192	−	0.00501656i
$137$	7.02733	−	1.43464i	0.600386	−	0.122570i	0.109787	−	0.993955i	$-0.464983\pi$
$137$	7.02733	−	1.43464i	0.600386	−	0.122570i	0.490599	+	0.871386i	$0.336778\pi$
$138$	−5.25730	+	5.93427i	−0.447531	+	0.505159i
$139$	−2.33620	−	2.86132i	−0.198154	−	0.242694i	0.665964	−	0.745984i	$-0.268020\pi$
$139$	−2.33620	−	2.86132i	−0.198154	−	0.242694i	−0.864118	+	0.503290i	$0.832123\pi$
$140$	−0.0710802	−	1.76384i	−0.00600737	−	0.149071i
$141$	0.869019	−	2.60303i	0.0731846	−	0.219215i
$142$	2.09824	+	1.85888i	0.176080	+	0.155993i
$143$	−5.79550	+	8.75733i	−0.484644	+	0.732324i
$144$	0.708837	−	0.627974i	0.0590697	−	0.0523312i
$145$	−0.283973	−	0.666509i	−0.0235827	−	0.0553506i
$146$	0.0743698	+	0.128812i	0.00615489	+	0.0106606i
$147$	0.0487228	−	0.0843905i	0.00401859	−	0.00696041i
$148$	−5.72478	−	0.695115i	−0.470574	−	0.0571381i
$149$	−8.54961	+	4.05684i	−0.700412	+	0.332350i	−0.745381	−	0.666639i	$-0.767732\pi$
$149$	−8.54961	+	4.05684i	−0.700412	+	0.332350i	0.0449691	+	0.998988i	$0.485681\pi$
$150$	3.92312	+	2.26501i	0.320321	+	0.184938i
$151$	−2.87137	+	1.98197i	−0.233669	+	0.161290i	−0.679146	−	0.734003i	$-0.737650\pi$
$151$	−2.87137	+	1.98197i	−0.233669	+	0.161290i	0.445477	+	0.895294i	$0.353034\pi$
$152$	18.0115	+	7.67398i	1.46093	+	0.622442i
$153$	−0.0693407	+	0.0112690i	−0.00560586	+	0.000911042i
$154$	−4.56646	−	6.07686i	−0.367976	−	0.489687i
$155$	−1.09470	+	2.88650i	−0.0879288	+	0.231849i
$156$	−1.22431	−	3.44191i	−0.0980230	−	0.275573i
$157$	−2.66526	−	7.02771i	−0.212711	−	0.560872i	0.785615	−	0.618716i	$-0.212347\pi$
$157$	−2.66526	−	7.02771i	−0.212711	−	0.560872i	−0.998326	+	0.0578434i	$0.981578\pi$
$158$	−2.00019	+	3.16304i	−0.159126	+	0.251638i
$159$	2.53559	−	1.08031i	0.201085	−	0.0856745i
$160$	−2.82806	+	1.78836i	−0.223578	+	0.141382i
$161$	−20.8153	+	2.52744i	−1.64048	+	0.199190i
$162$	0.389370	−	0.913884i	0.0305918	−	0.0718015i
$163$	4.60113	+	13.7821i	0.360388	+	1.07950i	0.960190	+	0.279347i	$0.0901178\pi$
$163$	4.60113	+	13.7821i	0.360388	+	1.07950i	−0.599802	+	0.800149i	$0.704754\pi$
$164$	−3.67809	+	1.39492i	−0.287211	+	0.108925i
$165$	1.92518	−	0.155416i	0.149875	−	0.0120992i
$166$	−1.09843	−	3.79222i	−0.0852547	−	0.294333i
$167$	6.32972	−	0.255079i	0.489808	−	0.0197386i	0.205866	−	0.978580i	$-0.433999\pi$
$167$	6.32972	−	0.255079i	0.489808	−	0.0197386i	0.283942	+	0.958841i	$0.408358\pi$
$168$	7.86406			0.606725
$169$	12.9888	+	0.539149i	0.999140	+	0.0414730i
$170$	−0.0462775			−0.00354932
$171$	6.53548	−	0.263371i	0.499781	−	0.0201405i
$172$	−0.0336968	−	0.116335i	−0.00256936	−	0.00887045i
$173$	−21.8184	+	1.76136i	−1.65882	+	0.133914i	−0.874037	−	0.485859i	$-0.838507\pi$
$173$	−21.8184	+	1.76136i	−1.65882	+	0.133914i	−0.784782	+	0.619772i	$0.787225\pi$
$174$	1.01473	−	0.384838i	0.0769268	−	0.0291745i
$175$	3.79400	+	11.3644i	0.286799	+	0.859068i
$176$	−1.08111	+	2.53747i	−0.0814920	+	0.191269i
$177$	−12.5775	+	1.52719i	−0.945383	+	0.114790i
$178$	9.48448	−	5.99762i	0.710892	−	0.449541i
$179$	5.13461	−	2.18765i	0.383779	−	0.163513i	−0.191456	−	0.981501i	$-0.561321\pi$
$179$	5.13461	−	2.18765i	0.383779	−	0.163513i	0.575235	+	0.817988i	$0.304911\pi$
$180$	−0.359109	+	0.567885i	−0.0267664	+	0.0423276i
$181$	−8.79165	−	23.1817i	−0.653478	−	1.72308i	−0.690063	−	0.723749i	$-0.742417\pi$
$181$	−8.79165	−	23.1817i	−0.653478	−	1.72308i	0.0365848	−	0.999331i	$-0.488352\pi$
$182$	−3.51860	+	8.72740i	−0.260816	+	0.646918i
$183$	2.03071	−	5.35455i	0.150115	−	0.395819i
$184$	14.3511	+	19.0979i	1.05798	+	1.40792i
$185$	−3.72551	+	0.605454i	−0.273905	+	0.0445139i
$186$	−4.25438	−	1.81262i	−0.311946	−	0.132908i
$187$	0.168389	−	0.116231i	0.0123138	−	0.00849963i
$188$	−2.40799	−	1.39025i	−0.175621	−	0.101395i
$189$	2.37361	−	1.12629i	0.172655	−	0.0819257i
$190$	4.27733	+	0.519361i	0.310310	+	0.0376784i
$191$	10.5088	−	18.2018i	0.760389	−	1.31703i	−0.182261	−	0.983250i	$-0.558341\pi$
$191$	10.5088	−	18.2018i	0.760389	−	1.31703i	0.942650	−	0.333783i	$-0.108325\pi$
$192$	−3.45316	−	5.98105i	−0.249211	−	0.431645i
$193$	9.89189	+	23.2171i	0.712034	+	1.67121i	0.740894	+	0.671622i	$0.234402\pi$
$193$	9.89189	+	23.2171i	0.712034	+	1.67121i	−0.0288602	+	0.999583i	$0.509188\pi$
$194$	−13.9201	+	12.3321i	−0.999405	+	0.885396i
$195$	−1.39642	−	1.94085i	−0.0999996	−	0.138987i
$196$	−0.0739025	−	0.0654719i	−0.00527875	−	0.00467656i
$197$	−3.96291	+	11.8704i	−0.282345	+	0.845728i	0.707890	+	0.706323i	$0.249647\pi$
$197$	−3.96291	+	11.8704i	−0.282345	+	0.845728i	−0.990235	+	0.139405i	$0.955481\pi$
$198$	0.116500	+	2.89091i	0.00827927	+	0.205448i
$199$	9.65077	+	11.8200i	0.684125	+	0.837901i	0.993594	−	0.113009i	$-0.0360488\pi$
$199$	9.65077	+	11.8200i	0.684125	+	0.837901i	−0.309469	+	0.950909i	$0.600151\pi$
$200$	9.05156	−	10.2171i	0.640042	−	0.722458i
$201$	4.12308	−	0.841732i	0.290819	−	0.0593712i
$202$	−1.46398	−	0.424048i	−0.103006	−	0.0298359i
$203$	2.68376	+	1.01782i	0.188363	+	0.0714368i
$204$	−0.00286606	+	0.0711205i	−0.000200664	+	0.00497943i
$205$	−2.05826	+	1.54668i	−0.143755	+	0.108025i
$206$	6.70184	+	1.36819i	0.466939	+	0.0953263i
$207$	7.06681	+	3.70895i	0.491177	+	0.257790i
$208$	3.38086	−	0.477695i	0.234421	−	0.0331222i
$209$	−16.8683	+	8.85316i	−1.16680	+	0.612386i
$210$	1.66238	−	0.481515i	0.114715	−	0.0332277i
$211$	−3.02030	−	0.243824i	−0.207926	−	0.0167855i	−0.0239353	−	0.999714i	$-0.507620\pi$
$211$	−3.02030	−	0.243824i	−0.207926	−	0.0167855i	−0.183991	+	0.982928i	$0.558902\pi$
$212$	−0.558580	−	2.73610i	−0.0383634	−	0.187916i
$213$	1.31141	−	2.49868i	0.0898562	−	0.171207i
$214$	6.20313	−	8.25486i	0.424037	−	0.564291i
$215$	−0.0423675	−	0.0669989i	−0.00288944	−	0.00456929i
$216$	−2.46339	−	1.70036i	−0.167613	−	0.115695i
$217$	−5.24319	−	11.0498i	−0.355931	−	0.750109i
$218$	−8.22358	−	8.56166i	−0.556971	−	0.579869i
$219$	0.107987	−	0.103723i	0.00729707	−	0.00700893i
$220$	0.235884	−	1.94268i	0.0159033	−	0.130976i
$221$	−0.230914	−	0.104094i	−0.0155329	−	0.00700209i
$222$	−0.681508	−	5.61272i	−0.0457398	−	0.376701i
$223$	−19.0464	−	15.5509i	−1.27544	−	1.04137i	−0.996715	−	0.0809947i	$-0.974190\pi$
$223$	−19.0464	−	15.5509i	−1.27544	−	1.04137i	−0.278726	−	0.960371i	$-0.589912\pi$
$224$	2.65166	−	12.9887i	0.177171	−	0.867843i
$225$	1.26874	−	4.38019i	0.0845826	−	0.292013i
$226$	4.82400	−	19.5717i	0.320888	−	1.30189i
$227$	1.12645	+	13.9536i	0.0747651	+	0.926133i	0.920046	+	0.391810i	$0.128151\pi$
$227$	1.12645	+	13.9536i	0.0747651	+	0.926133i	−0.845281	+	0.534322i	$0.820567\pi$
$228$	1.06307	−	6.54135i	0.0704037	−	0.433212i
$229$	−18.0316	−	20.3534i	−1.19156	−	1.34499i	−0.924439	−	0.381330i	$-0.875466\pi$
$229$	−18.0316	−	20.3534i	−1.19156	−	1.34499i	−0.267121	−	0.963663i	$-0.586072\pi$
$230$	4.20305	+	3.15838i	0.277141	+	0.208258i
$231$	−4.83952	+	5.92733i	−0.318417	+	0.389990i
$232$	−0.524563	−	3.22776i	−0.0344392	−	0.211913i
$233$	7.01723	−	1.72959i	0.459714	−	0.113309i	−0.00265577	−	0.999996i	$-0.500845\pi$
$233$	7.01723	−	1.72959i	0.459714	−	0.113309i	0.462370	+	0.886687i	$0.346999\pi$
$234$	2.98922	−	1.97304i	0.195411	−	0.128982i
$235$	−1.76696	−	0.435516i	−0.115264	−	0.0284099i
$236$	−1.03297	+	12.7956i	−0.0672404	+	0.832922i
$237$	3.57348	+	1.19300i	0.232123	+	0.0774939i
$238$	0.127007	−	0.132228i	0.00823264	−	0.00857108i
$239$		−	22.6744i		−	1.46669i	−0.679858	−	0.733344i	$-0.737959\pi$
$239$		−	22.6744i		−	1.46669i	0.679858	−	0.733344i	$-0.262041\pi$
$240$	−0.452911	−	0.435027i	−0.0292353	−	0.0280809i
$241$	15.0011	−	12.2480i	0.966304	−	0.788963i	−0.0111873	−	0.999937i	$-0.503561\pi$
$241$	15.0011	−	12.2480i	0.966304	−	0.788963i	0.977492	+	0.210974i	$0.0676637\pi$
$242$	1.16197	+	2.21395i	0.0746944	+	0.142318i
$243$	−0.987050	−	0.160411i	−0.0633193	−	0.0102904i
$244$	−4.90407	−	3.10114i	−0.313951	−	0.198530i
$245$	−0.0583814	−	0.0277023i	−0.00372985	−	0.00176984i
$246$	−2.19087	−	3.17402i	−0.139685	−	0.202368i
$247$	20.1746	+	12.2126i	1.28368	+	0.777071i
$248$	−7.91561	+	11.4677i	−0.502642	+	0.728203i
$249$	−3.44196	+	1.98722i	−0.218125	+	0.125935i
$250$	2.69982	−	5.68976i	0.170752	−	0.359852i
$251$	−14.5175	+	4.84666i	−0.916337	+	0.305918i	−0.735445	−	0.677585i	$-0.763027\pi$
$251$	−14.5175	+	4.84666i	−0.916337	+	0.305918i	−0.180892	+	0.983503i	$0.557899\pi$
$252$	−0.637051	−	2.58462i	−0.0401305	−	0.162816i
$253$	−23.2262	−	0.935983i	−1.46022	−	0.0588448i
$254$	−6.24291	−	0.251581i	−0.391715	−	0.0157856i
$255$	0.0111488	+	0.0452324i	0.000698164	+	0.00283256i
$256$	−16.1462	+	5.39039i	−1.00914	+	0.336899i
$257$	7.38067	−	15.5544i	0.460394	−	0.970259i	−0.531953	−	0.846774i	$-0.678542\pi$
$257$	7.38067	−	15.5544i	0.460394	−	0.970259i	0.992346	−	0.123485i	$-0.0394071\pi$
$258$	0.102837	−	0.0593730i	0.00640235	−	0.00369640i
$259$	8.49457	−	12.3065i	0.527827	−	0.764690i
$260$	−2.20975	+	0.992922i	−0.137043	+	0.0615784i
$261$	−0.620609	−	0.899108i	−0.0384147	−	0.0556534i
$262$	−4.81228	−	2.28346i	−0.297304	−	0.141072i
$263$	19.5336	+	12.3523i	1.20449	+	0.761674i	0.977235	−	0.212161i	$-0.0680500\pi$
$263$	19.5336	+	12.3523i	1.20449	+	0.761674i	0.227257	+	0.973835i	$0.427024\pi$
$264$	8.60509	+	1.39846i	0.529606	+	0.0860694i
$265$	−0.849382	−	1.61836i	−0.0521771	−	0.0994152i
$266$	−13.2229	+	10.7962i	−0.810750	+	0.661957i
$267$	−8.14711	−	7.82540i	−0.498595	−	0.478907i
$268$		−	4.26370i		−	0.260447i
$269$	1.18054	−	1.22907i	0.0719789	−	0.0749380i	−0.684239	−	0.729258i	$-0.739865\pi$
$269$	1.18054	−	1.22907i	0.0719789	−	0.0749380i	0.756218	+	0.654320i	$0.227045\pi$
$270$	−0.624848	−	0.208605i	−0.0380271	−	0.0126953i
$271$	−0.957897	+	11.8657i	−0.0581881	+	0.720789i	0.900229	+	0.435417i	$0.143399\pi$
$271$	−0.957897	+	11.8657i	−0.0581881	+	0.720789i	−0.958417	+	0.285372i	$0.907883\pi$
$272$	−0.0645937	−	0.0159209i	−0.00391657	−	0.000965348i
$273$	9.37799	+	1.33661i	0.567582	+	0.0808954i
$274$	6.91773	−	1.70507i	0.417915	−	0.103007i
$275$	2.13057	+	13.1099i	0.128478	+	0.790560i
$276$	5.11420	−	6.26376i	0.307839	−	0.377034i
$277$	10.9926	+	8.26038i	0.660480	+	0.496318i	0.877331	−	0.479886i	$-0.159322\pi$
$277$	10.9926	+	8.26038i	0.660480	+	0.496318i	−0.216851	+	0.976205i	$0.569579\pi$
$278$	−2.43329	−	2.74661i	−0.145939	−	0.164731i
$279$	−0.746758	+	4.59498i	−0.0447072	+	0.275095i
$280$	−0.419633	−	5.19809i	−0.0250779	−	0.310645i
$281$	1.80718	−	7.33203i	0.107808	−	0.437392i	−0.892088	−	0.451862i	$-0.850760\pi$
$281$	1.80718	−	7.33203i	0.107808	−	0.437392i	0.999895	+	0.0144698i	$0.00460603\pi$
$282$	0.758442	−	2.61845i	0.0451646	−	0.155926i
$283$	−4.96979	+	24.3437i	−0.295423	+	1.44708i	0.512954	+	0.858416i	$0.328551\pi$
$283$	−4.96979	+	24.3437i	−0.295423	+	1.44708i	−0.808378	+	0.588664i	$0.799654\pi$
$284$	−2.21474	−	1.80828i	−0.131420	−	0.107302i
$285$	−0.522825	−	4.30585i	−0.0309695	−	0.255057i
$286$	−5.40215	+	8.92406i	−0.319436	+	0.527691i
$287$	1.22950	−	10.1259i	0.0725753	−	0.597711i
$288$	−3.63902	+	3.49532i	−0.214431	+	0.205964i
$289$	−11.7729	−	12.2569i	−0.692523	−	0.720993i
$290$	−0.308523	−	0.650197i	−0.0181171	−	0.0381809i
$291$	15.4072	+	10.6348i	0.903184	+	0.623423i
$292$	−0.0810834	−	0.128223i	−0.00474505	−	0.00750369i
$293$	2.00204	−	2.66423i	0.116960	−	0.155646i	−0.737166	−	0.675712i	$-0.763836\pi$
$293$	2.00204	−	2.66423i	0.116960	−	0.155646i	0.854126	+	0.520066i	$0.174093\pi$
$294$	0.0449852	−	0.0857122i	0.00262359	−	0.00499884i
$295$	1.68061	+	8.23215i	0.0978487	+	0.479294i
$296$	−16.9813	−	1.37087i	−0.987016	−	0.0796802i
$297$	2.79756	−	0.810323i	0.162331	−	0.0470197i
$298$	−8.32381	+	4.36867i	−0.482185	+	0.253070i
$299$	13.8679	+	25.2137i	0.802004	+	1.45814i
$300$	−4.09122	−	2.14724i	−0.236207	−	0.123971i
$301$	0.307712	+	0.0628198i	0.0177362	+	0.00362087i
$302$	−2.77076	+	2.08209i	−0.159439	+	0.119811i
$303$	−0.0617811	+	1.53308i	−0.00354923	+	0.0880733i
$304$	5.79158	+	2.19646i	0.332170	+	0.125975i
$305$	−3.64768	−	1.05656i	−0.208866	−	0.0604986i
$306$	−0.0683747	+	0.0139588i	−0.00390872	+	0.000797971i
$307$	9.80588	−	11.0686i	0.559651	−	0.631716i	−0.398777	−	0.917048i	$-0.630565\pi$
$307$	9.80588	−	11.0686i	0.559651	−	0.631716i	0.958429	+	0.285332i	$0.0921039\pi$
$308$	4.90343	+	6.00562i	0.279399	+	0.342202i
$309$	−0.277259	−	6.88011i	−0.0157727	−	0.391396i
$310$	−0.971112	+	2.90884i	−0.0551555	+	0.165211i
$311$	−22.3146	−	19.7690i	−1.26535	−	1.12100i	−0.987035	−	0.160507i	$-0.948687\pi$
$311$	−22.3146	−	19.7690i	−1.26535	−	1.12100i	−0.278310	−	0.960491i	$-0.589774\pi$
$312$	−4.02338	−	10.0143i	−0.227779	−	0.566947i
$313$	−4.60777	+	4.08213i	−0.260447	+	0.230736i	−0.783233	−	0.621728i	$-0.786431\pi$
$313$	−4.60777	+	4.08213i	−0.260447	+	0.230736i	0.522786	+	0.852464i	$0.324893\pi$
$314$	−2.92656	−	6.86888i	−0.165155	−	0.387633i
$315$	−0.871129	−	1.50884i	−0.0490826	−	0.0850135i
$316$	1.90856	−	3.30573i	0.107365	−	0.185962i
$317$	3.73078	+	0.452999i	0.209541	+	0.0254429i	0.224634	−	0.974443i	$-0.427881\pi$
$317$	3.73078	+	0.452999i	0.209541	+	0.0254429i	−0.0150927	+	0.999886i	$0.504804\pi$
$318$	2.47354	−	1.17371i	0.138709	−	0.0658183i
$319$	2.75566	+	1.59098i	0.154287	+	0.0890777i
$320$	−3.76917	+	2.60167i	−0.210703	+	0.145438i
$321$	−9.56286	−	4.07435i	−0.533747	−	0.227408i
$322$	−20.5595	+	3.34125i	−1.14574	+	0.186201i
$323$	−0.276037	−	0.367338i	−0.0153591	−	0.0204393i
$324$	−0.359288	+	0.947365i	−0.0199605	+	0.0526314i
$325$	12.5306	−	10.6456i	0.695075	−	0.590510i
$326$	5.11821	+	13.4956i	0.283471	+	0.747453i
$327$	−6.38716	+	10.1005i	−0.353211	+	0.558558i
$328$	−10.6912	+	4.55508i	−0.590321	+	0.251512i
$329$	6.09375	−	3.85345i	0.335959	−	0.212448i
$330$	1.90466	−	0.231267i	0.104848	−	0.0127308i
$331$	2.38965	−	5.60872i	0.131347	−	0.308283i	−0.841301	−	0.540567i	$-0.818210\pi$
$331$	2.38965	−	5.60872i	0.131347	−	0.308283i	0.972648	+	0.232284i	$0.0746199\pi$
$332$	1.27520	+	3.81968i	0.0699856	+	0.209632i
$333$	−5.32179	+	2.01829i	−0.291632	+	0.110602i
$334$	6.27248	−	0.506367i	0.343215	−	0.0277072i
$335$	−0.776390	−	2.68041i	−0.0424187	−	0.146446i
$336$	2.48600	−	0.100182i	0.135622	−	0.00546539i
$337$	−20.3151			−1.10663			−0.553317	−	0.832970i	$-0.686638\pi$
$337$	−20.3151			−1.10663			−0.553317	+	0.832970i	$0.686638\pi$
$338$	12.9139	+	0.0156010i	0.702421	+	0.000848583i
$339$	−20.2919			−1.10211
$340$	0.0471631	−	0.00190061i	0.00255778	−	0.000103075i
$341$	−3.77227	−	13.0234i	−0.204280	−	0.705257i
$342$	6.47638	−	0.522827i	0.350202	−	0.0282713i
$343$	17.4352	−	6.61229i	0.941411	−	0.357030i
$344$	−0.113306	−	0.339392i	−0.00610904	−	0.0182988i
$345$	2.07450	−	4.86902i	0.111687	−	0.262139i
$346$	−21.5858	+	2.62099i	−1.16046	+	0.140905i
$347$	−19.4545	+	12.3023i	−1.04437	+	0.660420i	−0.942441	−	0.334371i	$-0.891476\pi$
$347$	−19.4545	+	12.3023i	−1.04437	+	0.660420i	−0.101930	+	0.994792i	$0.532502\pi$
$348$	−1.01835	+	0.433878i	−0.0545893	+	0.0232583i
$349$	17.6185	−	27.8614i	0.943097	−	1.49139i	0.0736965	−	0.997281i	$-0.476520\pi$
$349$	17.6185	−	27.8614i	0.943097	−	1.49139i	0.869401	−	0.494108i	$-0.164505\pi$
$350$	4.22037	+	11.1282i	0.225588	+	0.594827i
$351$	−2.64862	−	2.44638i	−0.141373	−	0.130578i
$352$	5.21130	−	13.7411i	0.277763	−	0.732401i
$353$	13.1494	+	17.4986i	0.699869	+	0.931357i	0.999744	−	0.0226217i	$-0.00720131\pi$
$353$	13.1494	+	17.4986i	0.699869	+	0.931357i	−0.299875	+	0.953979i	$0.596945\pi$
$354$	−12.4229	+	2.01893i	−0.660272	+	0.107305i
$355$	−1.72159	−	0.733500i	−0.0913724	−	0.0389302i
$356$	−9.41968	+	6.50193i	−0.499242	+	0.344602i
$357$	−0.159840	−	0.0922835i	−0.00845961	−	0.00488416i
$358$	5.00895	−	2.37678i	0.264731	−	0.125616i
$359$	−10.3188	−	1.25293i	−0.544605	−	0.0661270i	−0.156389	−	0.987695i	$-0.549985\pi$
$359$	−10.3188	−	1.25293i	−0.544605	−	0.0661270i	−0.388216	+	0.921568i	$0.626909\pi$
$360$	−0.992475	+	1.71902i	−0.0523080	+	0.0906002i
$361$	11.8909	+	20.5957i	0.625838	+	1.08398i
$362$	−9.65356	−	22.6577i	−0.507380	−	1.19086i
$363$	1.88402	−	1.66910i	0.0988856	−	0.0876050i
$364$	3.22751	−	9.03893i	0.169167	−	0.473769i
$365$	−0.0743223	−	0.0658438i	−0.00389021	−	0.00344642i
$366$	1.80144	−	5.39598i	0.0941630	−	0.282052i
$367$	−1.05414	−	26.1582i	−0.0550257	−	1.36545i	−0.757078	−	0.653324i	$-0.773374\pi$
$367$	−1.05414	−	26.1582i	−0.0550257	−	1.36545i	0.702053	−	0.712125i	$-0.252267\pi$
$368$	4.77999	+	5.85443i	0.249174	+	0.305183i
$369$	−2.57454	+	2.90605i	−0.134025	+	0.151283i
$370$	−3.67361	+	0.749972i	−0.190982	+	0.0389892i
$371$	6.95523	+	2.01461i	0.361098	+	0.104593i
$372$	4.41024	+	1.67258i	0.228660	+	0.0867194i
$373$	0.910784	−	22.6009i	0.0471586	−	1.17023i	−0.786371	−	0.617755i	$-0.788043\pi$
$373$	0.910784	−	22.6009i	0.0471586	−	1.17023i	0.833530	−	0.552475i	$-0.186316\pi$
$374$	0.162489	−	0.122102i	0.00840209	−	0.00631376i
$375$	−6.21169	−	1.26813i	−0.320770	−	0.0654857i
$376$	−7.27334	−	3.81735i	−0.375094	−	0.196865i
$377$	−0.0769421	−	3.93830i	−0.00396272	−	0.202833i
$378$	2.31092	−	1.21286i	0.118861	−	0.0623830i
$379$	−5.97397	+	1.73038i	−0.306862	+	0.0888837i	−0.428076	−	0.903743i	$-0.640808\pi$
$379$	−5.97397	+	1.73038i	−0.306862	+	0.0888837i	0.121214	+	0.992626i	$0.461321\pi$
$380$	−4.38052	−	0.353632i	−0.224716	−	0.0181409i
$381$	1.25809	+	6.16254i	0.0644540	+	0.315717i
$382$	9.70264	−	18.4868i	0.496430	−	0.945869i
$383$	−8.31585	+	11.0664i	−0.424920	+	0.565466i	−0.960237	−	0.279185i	$-0.909936\pi$
$383$	−8.31585	+	11.0664i	−0.424920	+	0.565466i	0.535317	+	0.844651i	$0.320192\pi$
$384$	1.72684	+	2.73078i	0.0881224	+	0.139354i
$385$	4.17617	+	2.88260i	0.212837	+	0.146911i
$386$	10.7470	+	22.6489i	0.547010	+	1.15280i
$387$	−0.0828068	−	0.0862111i	−0.00420931	−	0.00438235i
$388$	13.6800	−	13.1399i	0.694498	−	0.667075i
$389$	−2.71950	+	22.3971i	−0.137884	+	1.13558i	0.745360	+	0.666662i	$0.232278\pi$
$389$	−2.71950	+	22.3971i	−0.137884	+	1.13558i	−0.883244	+	0.468914i	$0.844645\pi$
$390$	−1.46367	−	1.87057i	−0.0741160	−	0.0947199i
$391$	−0.0675810	−	0.556580i	−0.00341772	−	0.0281474i
$392$	−0.225936	−	0.184471i	−0.0114115	−	0.00931718i
$393$	−1.07255	+	5.25372i	−0.0541032	+	0.265015i
$394$	−3.45865	+	11.9407i	−0.174244	+	0.601561i
$395$	0.597883	−	2.42571i	0.0300828	−	0.122051i
$396$	−0.237459	−	2.94145i	−0.0119327	−	0.147814i
$397$	2.58321	−	15.8951i	0.129647	−	0.797753i	−0.838042	−	0.545606i	$-0.816299\pi$
$397$	2.58321	−	15.8951i	0.129647	−	0.797753i	0.967689	−	0.252146i	$-0.0811365\pi$
$398$	10.0518	+	11.3462i	0.503853	+	0.568733i
$399$	13.7380	+	10.3234i	0.687758	+	0.516817i
$400$	2.73123	−	3.34515i	0.136562	−	0.167258i
$401$	2.41874	+	14.8831i	0.120786	+	0.743225i	0.974817	+	0.223004i	$0.0715864\pi$
$401$	2.41874	+	14.8831i	0.120786	+	0.743225i	−0.854032	+	0.520221i	$0.825850\pi$
$402$	4.05877	−	1.00040i	0.202433	−	0.0498953i
$403$	−11.3886	+	12.3301i	−0.567305	+	0.614204i
$404$	1.50942	+	0.372038i	0.0750963	+	0.0185096i
$405$	−0.0533609	+	0.660993i	−0.00265152	+	0.0328450i
$406$	2.70453	+	0.902906i	0.134224	+	0.0448105i
$407$	11.4835	−	11.9556i	0.569215	−	0.592615i
$408$			0.210277i			0.0104102i
$409$	6.32123	+	6.07163i	0.312565	+	0.300223i	0.832547	−	0.553955i	$-0.186882\pi$
$409$	6.32123	+	6.07163i	0.312565	+	0.300223i	−0.519982	+	0.854177i	$0.674061\pi$
$410$	−1.98110	+	1.61752i	−0.0978395	+	0.0798835i
$411$	−3.33313	−	6.35074i	−0.164411	−	0.313259i
$412$	−6.88629	−	1.11913i	−0.339263	−	0.0551356i
$413$	−28.1340	−	17.7909i	−1.38438	−	0.875432i
$414$	7.16265	+	3.39872i	0.352025	+	0.167038i
$415$	1.49720	+	2.16907i	0.0734948	+	0.106476i
$416$	−17.8967	+	3.26853i	−0.877460	+	0.160253i
$417$	−2.09838	+	3.04003i	−0.102758	+	0.148871i
$418$	−16.3888	+	9.46208i	−0.801603	+	0.462806i
$419$	11.4179	−	24.0628i	0.557802	−	1.17554i	−0.407209	−	0.913335i	$-0.633498\pi$
$419$	11.4179	−	24.0628i	0.557802	−	1.17554i	0.965011	−	0.262209i	$-0.0844509\pi$
$420$	−1.67442	+	0.559004i	−0.0817034	+	0.0272766i
$421$	8.82212	+	35.7927i	0.429964	+	1.74443i	0.641559	+	0.767074i	$0.278288\pi$
$421$	8.82212	+	35.7927i	0.429964	+	1.74443i	−0.211595	+	0.977357i	$0.567866\pi$
$422$	−3.00761	−	0.121202i	−0.146408	−	0.00590004i
$423$	−2.74203	−	0.110500i	−0.133322	−	0.00537270i
$424$	−1.97430	−	8.01007i	−0.0958807	−	0.389003i
$425$	−0.303872	+	0.101447i	−0.0147400	+	0.00492092i
$426$	1.20172	−	2.53257i	0.0582234	−	0.122703i
$427$	13.0298	−	7.52278i	0.630558	−	0.364053i
$428$	−5.98282	+	8.66761i	−0.289190	+	0.418965i
$429$	10.0240	+	3.13024i	0.483962	+	0.151130i
$430$	−0.0447326	−	0.0648064i	−0.00215720	−	0.00312524i
$431$	22.6361	+	10.7409i	1.09034	+	0.517373i	0.887016	−	0.461738i	$-0.152774\pi$
$431$	22.6361	+	10.7409i	1.09034	+	0.517373i	0.203324	+	0.979111i	$0.434825\pi$
$432$	−0.800391	−	0.506137i	−0.0385089	−	0.0243515i
$433$	−4.32493	−	0.702870i	−0.207843	−	0.0337778i	0.0555983	−	0.998453i	$-0.482293\pi$
$433$	−4.32493	−	0.702870i	−0.207843	−	0.0337778i	−0.263441	+	0.964675i	$0.584857\pi$
$434$	−5.64621	−	10.7580i	−0.271027	−	0.516398i
$435$	−0.561188	+	0.458196i	−0.0269069	+	0.0219688i
$436$	8.73259	+	8.38777i	0.418215	+	0.401701i
$437$			52.2019i			2.49715i
$438$	0.103036	−	0.107271i	0.00492323	−	0.00512562i
$439$	27.1580	+	9.06667i	1.29618	+	0.432728i	0.879315	−	0.476240i	$-0.158001\pi$
$439$	27.1580	+	9.06667i	1.29618	+	0.432728i	0.416865	+	0.908969i	$0.363129\pi$
$440$	0.465199	−	5.76253i	0.0221775	−	0.274718i
$441$	−0.0946141	−	0.0233203i	−0.00450543	−	0.00111049i
$442$	−0.233361	−	0.0940837i	−0.0110999	−	0.00447511i
$443$	2.61408	−	0.644312i	0.124199	−	0.0306122i	−0.176726	−	0.984260i	$-0.556551\pi$
$443$	2.61408	−	0.644312i	0.124199	−	0.0306122i	0.300925	+	0.953648i	$0.402705\pi$
$444$	0.925065	+	5.69215i	0.0439016	+	0.270138i
$445$	−4.73780	+	5.80275i	−0.224593	+	0.275077i
$446$	−19.5269	−	14.6735i	−0.924624	−	0.694810i
$447$	6.27532	+	7.08338i	0.296813	+	0.335032i
$448$	2.91063	−	17.9098i	0.137514	−	0.846159i
$449$	2.07925	+	25.7561i	0.0981258	+	1.21551i	0.839102	+	0.543975i	$0.183081\pi$
$449$	2.07925	+	25.7561i	0.0981258	+	1.21551i	−0.740976	+	0.671532i	$0.765637\pi$
$450$	1.08411	−	4.39839i	0.0511053	−	0.207342i
$451$	3.14604	−	10.8614i	0.148141	−	0.511442i
$452$	−4.11251	+	20.1444i	−0.193436	+	0.947514i
$453$	2.70258	+	2.20659i	0.126978	+	0.103675i
$454$	1.67621	+	13.8048i	0.0786685	+	0.647893i
$455$	0.383073	−	6.27011i	0.0179587	−	0.293947i
$456$	2.35989	−	19.4354i	0.110512	−	0.910146i
$457$	23.5507	−	22.6208i	1.10166	−	1.05815i	0.103676	−	0.994611i	$-0.466939\pi$
$457$	23.5507	−	22.6208i	1.10166	−	1.05815i	0.997979	−	0.0635433i	$-0.0202401\pi$
$458$	−18.7117	−	19.4809i	−0.874340	−	0.910284i
$459$	0.0301158	+	0.0634678i	0.00140569	+	0.00296242i
$460$	−4.41320	−	3.04621i	−0.205766	−	0.142030i
$461$	5.68951	+	8.99724i	0.264987	+	0.419043i	0.951302	−	0.308261i	$-0.0997471\pi$
$461$	5.68951	+	8.99724i	0.264987	+	0.419043i	−0.686315	+	0.727305i	$0.740773\pi$
$462$	−4.56646	+	6.07686i	−0.212451	+	0.282721i
$463$	−13.5693	+	25.8541i	−0.630618	+	1.20154i	0.335158	+	0.942162i	$0.391210\pi$
$463$	−13.5693	+	25.8541i	−0.630618	+	1.20154i	−0.965775	+	0.259380i	$0.916482\pi$
$464$	−0.206945	−	1.01368i	−0.00960716	−	0.0470590i
$465$	3.07710	+	0.248409i	0.142697	+	0.0115197i
$466$	6.89590	−	1.99742i	0.319447	−	0.0925288i
$467$	−3.83885	+	2.01478i	−0.177641	+	0.0932331i	−0.551200	−	0.834373i	$-0.685830\pi$
$467$	−3.83885	+	2.01478i	−0.177641	+	0.0932331i	0.373559	+	0.927607i	$0.378137\pi$
$468$	−2.96539	+	2.13357i	−0.137075	+	0.0986242i
$469$	9.78949	+	5.13792i	0.452037	+	0.237247i
$470$	−1.77125	−	0.361603i	−0.0817015	−	0.0166795i
$471$	−6.00872	+	4.51526i	−0.276867	+	0.208052i
$472$	−1.52705	+	37.8933i	−0.0702880	+	1.74418i
$473$	0.325536	+	0.123459i	0.0149682	+	0.00567667i
$474$	3.59465	+	1.04120i	0.165108	+	0.0478240i
$475$	29.2248	−	5.96628i	1.34092	−	0.273752i
$476$	−0.124007	+	0.139975i	−0.00568385	+	0.00641574i
$477$	−1.74311	−	2.13492i	−0.0798114	−	0.0977512i
$478$	−0.906958	−	22.5059i	−0.0414833	−	1.02940i
$479$	−3.59359	+	10.7641i	−0.164195	+	0.491825i	−0.998203	−	0.0599285i	$-0.980913\pi$
$479$	−3.59359	+	10.7641i	−0.164195	+	0.491825i	0.834007	+	0.551753i	$0.186041\pi$
$480$	2.50457	+	2.21885i	0.114317	+	0.101276i
$481$	−20.0174	−	4.52099i	−0.912714	−	0.206140i
$482$	14.3997	−	12.7570i	0.655888	−	0.581066i
$483$	8.21884	+	19.2903i	0.373970	+	0.877740i
$484$	−1.27514	−	2.20860i	−0.0579608	−	0.100391i
$485$	6.20739	−	10.7515i	0.281863	−	0.488201i
$486$	−0.986132	−	0.119738i	−0.0447318	−	0.00543143i
$487$	5.12305	−	2.43092i	0.232148	−	0.110155i	−0.309066	−	0.951041i	$-0.600016\pi$
$487$	5.12305	−	2.43092i	0.232148	−	0.110155i	0.541213	+	0.840885i	$0.317965\pi$
$488$	−14.8449	−	8.57068i	−0.671995	−	0.387977i
$489$	11.9578	−	8.25388i	0.540751	−	0.373253i
$490$	−0.0590556	−	0.0251613i	−0.00266786	−	0.00113667i
$491$	34.9188	−	5.67486i	1.57586	−	0.256103i	0.691316	−	0.722552i	$-0.257031\pi$
$491$	34.9188	−	5.67486i	1.57586	−	0.256103i	0.884548	+	0.466450i	$0.154467\pi$
$492$	2.36315	+	3.14479i	0.106539	+	0.141778i
$493$	−0.0272154	+	0.0717610i	−0.00122572	+	0.00323195i
$494$	20.5132	+	11.3149i	0.922933	+	0.509082i
$495$	−0.684899	−	1.80593i	−0.0307839	−	0.0811705i
$496$	−2.35620	+	3.72604i	−0.105797	+	0.167304i
$497$	6.82066	−	2.90601i	0.305949	−	0.130353i
$498$	−3.33689	+	2.11012i	−0.149530	+	0.0945569i
$499$	33.4075	−	4.05640i	1.49552	−	0.181589i	0.668481	−	0.743729i	$-0.266945\pi$
$499$	33.4075	−	4.05640i	1.49552	−	0.181589i	0.827043	+	0.562139i	$0.190022\pi$
$500$	−2.51782	+	5.90953i	−0.112600	+	0.264282i
$501$	−2.00605	−	6.00884i	−0.0896235	−	0.268455i
$502$	−14.2158	+	5.39133i	−0.634481	+	0.240627i
$503$	10.7762	−	0.869941i	0.480485	−	0.0387888i	0.162148	−	0.986766i	$-0.448158\pi$
$503$	10.7762	−	0.869941i	0.480485	−	0.0387888i	0.318337	+	0.947978i	$0.396876\pi$
$504$	−2.18792	−	7.55357i	−0.0974577	−	0.336463i
$505$	1.01665	−	0.0409698i	0.0452405	−	0.00182313i
$506$	−23.0910			−1.02652
$507$	−3.09585	−	12.6260i	−0.137492	−	0.560740i
$508$	6.37272			0.282744
$509$	34.5375	−	1.39181i	1.53085	−	0.0616911i	0.739541	−	0.673111i	$-0.235042\pi$
$509$	34.5375	−	1.39181i	1.53085	−	0.0616911i	0.791306	+	0.611420i	$0.209401\pi$
$510$	0.0128752	+	0.0444503i	0.000570123	+	0.00196829i
$511$	0.392110	−	0.0316544i	0.0173459	−	0.00140031i
$512$	−9.76858	+	3.70473i	−0.431714	+	0.163728i
$513$	−2.07126	−	6.20417i	−0.0914482	−	0.273921i
$514$	6.70366	−	15.7341i	0.295686	−	0.694000i
$515$	−4.53291	+	0.550395i	−0.199744	+	0.0242533i
$516$	−0.102367	+	0.0647328i	−0.00450644	+	0.00284970i
$517$	7.35322	−	3.13291i	0.323394	−	0.137785i
$518$	7.93920	−	12.5548i	0.348828	−	0.551628i
$519$	7.76207	+	20.4669i	0.340717	+	0.898397i
$520$	−6.40469	+	3.19380i	−0.280864	+	0.140057i
$521$	10.2160	−	26.9373i	0.447570	−	1.18014i	−0.501522	−	0.865145i	$-0.667226\pi$
$521$	10.2160	−	26.9373i	0.447570	−	1.18014i	0.949092	−	0.314999i	$-0.102004\pi$
$522$	−0.651961	−	0.867602i	−0.0285356	−	0.0379739i
$523$	−13.1712	+	2.14054i	−0.575938	+	0.0935991i	−0.441402	−	0.897310i	$-0.645519\pi$
$523$	−13.1712	+	2.14054i	−0.575938	+	0.0935991i	−0.134536	+	0.990909i	$0.542955\pi$
$524$	4.99816	+	2.12952i	0.218346	+	0.0930284i
$525$	9.86016	−	6.80598i	0.430333	−	0.297037i
$526$	19.8825	+	11.4792i	0.866918	+	0.500515i
$527$	0.295460	−	0.140197i	0.0128704	−	0.00610709i
$528$	2.73807	+	0.332461i	0.119159	+	0.0144685i
$529$	−20.3480	+	35.2438i	−0.884697	+	1.53234i
$530$	−0.907803	−	1.57236i	−0.0394324	−	0.0682990i
$531$	4.96617	+	11.6560i	0.215513	+	0.505829i
$532$	13.0326	−	11.5459i	0.565035	−	0.500577i
$533$	−13.5236	+	3.61487i	−0.585770	+	0.156578i
$534$	−8.39957	−	7.44137i	−0.363485	−	0.322020i
$535$	−2.18284	+	6.53839i	−0.0943723	+	0.282679i
$536$	−0.507187	−	12.5857i	−0.0219071	−	0.543620i
$537$	−3.52982	−	4.32324i	−0.152323	−	0.186562i
$538$	1.12261	−	1.26716i	0.0483990	−	0.0546312i
$539$	0.278080	−	0.0567705i	0.0119778	−	0.00244528i
$540$	0.645374	+	0.186935i	0.0277725	+	0.00804440i
$541$	9.45232	+	3.58479i	0.406387	+	0.154122i	0.549324	−	0.835610i	$-0.314885\pi$
$541$	9.45232	+	3.58479i	0.406387	+	0.154122i	−0.142937	+	0.989732i	$0.545655\pi$
$542$	−0.476161	+	11.8158i	−0.0204529	+	0.507533i
$543$	−19.8204	+	14.8941i	−0.850576	+	0.639166i
$544$	0.347304	+	0.0709025i	0.0148905	+	0.00303992i
$545$	7.01718	+	3.68290i	0.300583	+	0.157758i
$546$	9.36176	+	0.951567i	0.400646	+	0.0407233i
$547$	−28.3810	+	14.8955i	−1.21348	+	0.636885i	−0.945211	−	0.326459i	$-0.894145\pi$
$547$	−28.3810	+	14.8955i	−1.21348	+	0.636885i	−0.268271	+	0.963343i	$0.586452\pi$
$548$	−6.98009	+	2.02181i	−0.298175	+	0.0863674i
$549$	−5.70812	−	0.460807i	−0.243617	−	0.0196668i
$550$	2.63913	+	12.9273i	0.112533	+	0.551222i
$551$	3.32081	−	6.32728i	0.141471	−	0.269551i
$552$	14.3511	−	19.0979i	0.610825	−	0.812861i
$553$	5.29008	+	8.36560i	0.224957	+	0.355741i
$554$	11.2413	+	7.75930i	0.477597	+	0.329661i
$555$	1.61805	+	3.40997i	0.0686825	+	0.144745i
$556$	2.59266	+	2.69924i	0.109953	+	0.114473i
$557$	−17.5738	+	16.8799i	−0.744626	+	0.715223i	−0.965593	−	0.260058i	$-0.916258\pi$
$557$	−17.5738	+	16.8799i	−0.744626	+	0.715223i	0.220967	+	0.975281i	$0.429079\pi$
$558$	−0.557413	+	4.59071i	−0.0235972	+	0.194340i
$559$	−0.0774339	−	0.423987i	−0.00327510	−	0.0179327i
$560$	−0.198875	−	1.63788i	−0.00840399	−	0.0692131i
$561$	−0.158491	−	0.129404i	−0.00669147	−	0.00546342i
$562$	1.50048	−	7.34983i	0.0632939	−	0.310034i
$563$	−1.47106	+	5.07869i	−0.0619978	+	0.214041i	−0.985536	−	0.169464i	$-0.945796\pi$
$563$	−1.47106	+	5.07869i	−0.0619978	+	0.214041i	0.923538	+	0.383506i	$0.125283\pi$
$564$	−0.665418	+	2.69971i	−0.0280192	+	0.113678i
$565$	1.08279	+	13.4128i	0.0455535	+	0.564282i
$566$	−3.95913	+	24.3615i	−0.166415	+	1.02399i
$567$	−1.74220	−	1.96654i	−0.0731657	−	0.0825869i
$568$	−6.75263	−	5.07427i	−0.283334	−	0.212912i
$569$	6.32147	−	7.74240i	0.265010	−	0.324578i	−0.624908	−	0.780698i	$-0.714864\pi$
$569$	6.32147	−	7.74240i	0.265010	−	0.324578i	0.889918	+	0.456120i	$0.150761\pi$
$570$	−0.691171	−	4.25294i	−0.0289500	−	0.178136i
$571$	−17.9153	+	4.41573i	−0.749733	+	0.184793i	−0.595626	−	0.803262i	$-0.703096\pi$
$571$	−17.9153	+	4.41573i	−0.749733	+	0.184793i	−0.154107	+	0.988054i	$0.549250\pi$
$572$	5.13903	−	9.31672i	0.214873	−	0.389552i
$573$	−20.4068	−	5.02984i	−0.852508	−	0.210124i
$574$	0.815340	−	10.0998i	0.0340316	−	0.421557i
$575$	34.5222	+	11.5252i	1.43967	+	0.480634i
$576$	−4.78418	+	4.98086i	−0.199341	+	0.207536i
$577$		−	14.6029i		−	0.607925i	−0.952684	−	0.303963i	$-0.901690\pi$
$577$		−	14.6029i		−	0.607925i	0.952684	−	0.303963i	$-0.0983098\pi$
$578$	−12.1757	−	11.6949i	−0.506441	−	0.486443i
$579$	19.5484	−	15.9608i	0.812403	−	0.663306i
$580$	0.341131	+	0.649970i	0.0141647	+	0.0269885i
$581$	−10.3067	−	1.67500i	−0.427594	−	0.0694907i
$582$	15.7181	+	9.93950i	0.651535	+	0.412005i
$583$	7.25236	+	3.44129i	0.300362	+	0.142524i
$584$	−0.254597	−	0.368847i	−0.0105353	−	0.0152630i
$585$	−1.47571	+	1.88126i	−0.0610131	+	0.0777807i
$586$	1.88060	−	2.72451i	0.0776867	−	0.112549i
$587$	20.9471	−	12.0938i	0.864580	−	0.499165i	−0.000963630	−	1.00000i	$-0.500307\pi$
$587$	20.9471	−	12.0938i	0.864580	−	0.499165i	0.865543	+	0.500834i	$0.166973\pi$
$588$	−0.0423260	+	0.0892001i	−0.00174549	+	0.00367855i
$589$	−28.8821	+	9.64226i	−1.19007	+	0.397302i
$590$	1.99740	+	8.10375i	0.0822315	+	0.333626i
$591$	12.5042	+	0.503904i	0.514356	+	0.0207278i
$592$	−5.38561	−	0.217032i	−0.221347	−	0.00891998i
$593$	7.49419	+	30.4051i	0.307750	+	1.24859i	0.897504	+	0.441006i	$0.145378\pi$
$593$	7.49419	+	30.4051i	0.307750	+	1.24859i	−0.589754	+	0.807583i	$0.700775\pi$
$594$	2.74436	−	0.916202i	0.112602	−	0.0375922i
$595$	−0.0524696	+	0.110577i	−0.00215104	+	0.00453323i
$596$	8.30369	−	4.79414i	0.340132	−	0.196376i
$597$	8.66836	−	12.5583i	0.354772	−	0.513976i
$598$	14.7734	+	24.4716i	0.604130	+	1.00072i
$599$	10.9349	+	15.8420i	0.446790	+	0.647286i	0.980070	−	0.198652i	$-0.0636564\pi$
$599$	10.9349	+	15.8420i	0.446790	+	0.647286i	−0.533281	+	0.845938i	$0.679041\pi$
$600$	−12.3320	−	5.85161i	−0.503452	−	0.238891i
$601$	0.482596	+	0.305175i	0.0196855	+	0.0124483i	0.544272	−	0.838909i	$-0.316806\pi$
$601$	0.482596	+	0.305175i	0.0196855	+	0.0124483i	−0.524587	+	0.851357i	$0.675780\pi$
$602$	0.307938	+	0.0500447i	0.0125506	+	0.00203967i
$603$	−1.95561	−	3.72611i	−0.0796386	−	0.151739i
$604$	2.73827	−	2.23573i	0.111419	−	0.0909706i
$605$	−1.20380	−	1.15626i	−0.0489413	−	0.0470088i
$606$			1.52416i			0.0619148i
$607$	−10.9211	+	11.3701i	−0.443274	+	0.461497i	−0.904929	−	0.425562i	$-0.860076\pi$
$607$	−10.9211	+	11.3701i	−0.443274	+	0.461497i	0.461655	+	0.887060i	$0.347256\pi$
$608$	−31.3048	−	10.4511i	−1.26958	−	0.423847i
$609$	0.230962	−	2.86098i	0.00935906	−	0.115933i
$610$	−3.66283	−	0.902808i	−0.148304	−	0.0365536i
$611$	−8.02474	−	5.78844i	−0.324646	−	0.234175i
$612$	0.0691100	−	0.0170341i	0.00279360	−	0.000688562i
$613$	−4.84303	−	29.8004i	−0.195608	−	1.20363i	−0.880166	−	0.474667i	$-0.842569\pi$
$613$	−4.84303	−	29.8004i	−0.195608	−	1.20363i	0.684557	−	0.728959i	$-0.259996\pi$
$614$	9.29028	−	11.3785i	0.374925	−	0.459200i
$615$	2.05826	+	1.54668i	0.0829971	+	0.0623683i
$616$	15.1885	+	17.1443i	0.611962	+	0.690762i
$617$	−6.47560	+	39.8459i	−0.260698	+	1.60414i	0.444937	+	0.895562i	$0.353226\pi$
$617$	−6.47560	+	39.8459i	−0.260698	+	1.60414i	−0.705635	+	0.708576i	$0.749338\pi$
$618$	−0.550397	−	6.81789i	−0.0221402	−	0.274256i
$619$	2.37072	−	9.61838i	0.0952872	−	0.386595i	−0.903863	−	0.427823i	$-0.859281\pi$
$619$	2.37072	−	9.61838i	0.0952872	−	0.386595i	0.999150	+	0.0412275i	$0.0131269\pi$
$620$	0.870232	−	3.00439i	0.0349494	−	0.120659i
$621$	1.59640	−	7.81969i	0.0640614	−	0.313793i
$622$	−22.9395	−	18.7295i	−0.919791	−	0.750986i
$623$	−3.57742	−	29.4627i	−0.143326	−	1.18040i
$624$	−1.39945	−	3.11447i	−0.0560228	−	0.124679i
$625$	2.24162	−	18.4614i	0.0896648	−	0.738456i
$626$	−4.41025	+	4.23610i	−0.176269	+	0.169309i
$627$	13.1967	+	13.7392i	0.527024	+	0.548690i
$628$	3.26467	+	6.88014i	0.130274	+	0.274548i
$629$	0.329063	+	0.227136i	0.0131206	+	0.00905650i
$630$	−0.925008	−	1.46278i	−0.0368532	−	0.0582787i
$631$	−19.3403	+	25.7372i	−0.769924	+	1.02458i	0.228770	+	0.973481i	$0.426530\pi$
$631$	−19.3403	+	25.7372i	−0.769924	+	1.02458i	−0.998693	+	0.0511020i	$0.983727\pi$
$632$	5.24052	−	9.98497i	0.208457	−	0.397181i
$633$	0.606103	+	2.96889i	0.0240904	+	0.118003i
$634$	3.72118	+	0.300404i	0.147787	+	0.0119306i
$635$	4.00627	−	1.16043i	0.158984	−	0.0460502i
$636$	−2.47267	+	1.29776i	−0.0980478	+	0.0514595i
$637$	−0.238078	−	0.258385i	−0.00943298	−	0.0102376i
$638$	2.79882	+	1.46893i	0.110806	+	0.0581556i
$639$	−2.76488	−	0.564455i	−0.109377	−	0.0223295i
$640$	1.71288	−	1.28715i	0.0677075	−	0.0508789i
$641$	−0.0918861	+	2.28013i	−0.00362928	+	0.0900597i	0.996359	+	0.0852549i	$0.0271705\pi$
$641$	−0.0918861	+	2.28013i	−0.00362928	+	0.0900597i	−0.999988	+	0.00480481i	$0.998471\pi$
$642$	−9.65476	−	3.66157i	−0.381043	−	0.144511i
$643$	−8.36321	−	2.42243i	−0.329813	−	0.0955314i	0.109180	−	0.994022i	$-0.465177\pi$
$643$	−8.36321	−	2.42243i	−0.329813	−	0.0955314i	−0.438993	+	0.898491i	$0.644665\pi$
$644$	20.8158	−	4.24957i	0.820257	−	0.167457i
$645$	−0.0525663	+	0.0593351i	−0.00206980	+	0.00233632i
$646$	−0.288679	−	0.353567i	−0.0113579	−	0.0139109i
$647$	−0.0740413	−	1.83732i	−0.00291086	−	0.0722323i	0.997081	−	0.0763558i	$-0.0243285\pi$
$647$	−0.0740413	−	1.83732i	−0.00291086	−	0.0722323i	−0.999991	+	0.00412346i	$0.998687\pi$
$648$	−0.947864	+	2.83920i	−0.0372356	+	0.111534i
$649$	−27.6213	−	24.4704i	−1.08423	−	0.960546i
$650$	12.0117	−	11.0677i	0.471138	−	0.434110i
$651$	−9.15478	+	8.11042i	−0.358804	+	0.317873i
$652$	−5.77043	−	13.5437i	−0.225987	−	0.530412i
$653$	−24.6104	−	42.6264i	−0.963079	−	1.66810i	−0.714691	−	0.699441i	$-0.753433\pi$
$653$	−24.6104	−	42.6264i	−0.963079	−	1.66810i	−0.248388	−	0.968661i	$-0.579901\pi$
$654$	−5.93568	+	10.2809i	−0.232104	+	0.402015i
$655$	3.52991	+	0.428608i	0.137925	+	0.0167471i
$656$	−3.32168	+	1.57616i	−0.129690	+	0.0615386i
$657$	−0.129671	−	0.0748658i	−0.00505896	−	0.00292079i
$658$	5.89433	−	4.06856i	0.229785	−	0.158609i
$659$	14.3486	+	6.11336i	0.558941	+	0.238143i	0.652914	−	0.757432i	$-0.273546\pi$
$659$	14.3486	+	6.11336i	0.558941	+	0.238143i	−0.0939726	+	0.995575i	$0.529957\pi$
$660$	−1.93161	+	0.313917i	−0.0751878	+	0.0122192i
$661$	13.2012	+	17.5676i	0.513468	+	0.683302i	0.979495	−	0.201469i	$-0.0645714\pi$
$661$	13.2012	+	17.5676i	0.513468	+	0.683302i	−0.466027	+	0.884771i	$0.654315\pi$
$662$	2.14755	−	5.66263i	0.0834669	−	0.220084i
$663$	−0.0357396	+	0.250757i	−0.00138801	+	0.00973861i
$664$	4.21854	+	11.1234i	0.163711	+	0.431670i
$665$	6.09063	−	9.63156i	0.236185	−	0.373496i
$666$	−5.20152	+	2.21616i	−0.201555	+	0.0858744i
$667$	7.36938	−	4.66011i	0.285344	−	0.180440i
$668$	−6.37173	+	0.773668i	−0.246529	+	0.0299341i
$669$	−9.63788	+	22.6209i	−0.372622	+	0.874576i
$670$	−0.877835	−	2.62944i	−0.0339137	−	0.101584i
$671$	15.5954	−	5.91456i	0.602054	−	0.228329i
$672$	−13.2136	+	1.06671i	−0.509726	+	0.0411493i
$673$	9.82658	+	33.9253i	0.378787	+	1.30772i	0.892998	+	0.450060i	$0.148597\pi$
$673$	9.82658	+	33.9253i	0.378787	+	1.30772i	−0.514212	+	0.857663i	$0.671915\pi$
$674$	−20.1641	+	0.812587i	−0.776694	+	0.0312997i
$675$	−4.56024			−0.175524
$676$	−13.1616	+	0.514471i	−0.506217	+	0.0197873i
$677$	−45.3764			−1.74396			−0.871978	−	0.489545i	$-0.837163\pi$
$677$	−45.3764			−1.74396			−0.871978	+	0.489545i	$0.837163\pi$
$678$	−20.1411	+	0.811659i	−0.773515	+	0.0311716i
$679$	13.6842	+	47.2435i	0.525153	+	1.81304i
$680$	0.138991	−	0.0112205i	0.00533008	−	0.000430288i
$681$	13.0893	−	4.96411i	0.501582	−	0.190225i
$682$	−4.26517	−	12.7757i	−0.163322	−	0.489208i
$683$	−8.84830	+	20.7677i	−0.338571	+	0.794655i	0.660469	+	0.750853i	$0.270357\pi$
$683$	−8.84830	+	20.7677i	−0.338571	+	0.794655i	−0.999040	+	0.0438019i	$0.986053\pi$
$684$	−6.57885	+	0.798817i	−0.251549	+	0.0305435i
$685$	−4.01994	+	2.54205i	−0.153594	+	0.0971269i
$686$	17.0411	−	7.26054i	0.650633	−	0.277209i
$687$	−14.5331	+	22.9823i	−0.554474	+	0.876831i
$688$	−0.0401420	−	0.105846i	−0.00153040	−	0.00403533i
$689$	−0.992955	−	9.88767i	−0.0378286	−	0.376690i
$690$	1.86432	−	4.91582i	0.0709736	−	0.187142i
$691$	22.4068	+	29.8180i	0.852394	+	1.13433i	0.989608	+	0.143789i	$0.0459286\pi$
$691$	22.4068	+	29.8180i	0.852394	+	1.13433i	−0.137214	+	0.990541i	$0.543815\pi$
$692$	21.8912	−	3.55767i	0.832180	−	0.135242i
$693$	7.03975	+	2.99936i	0.267418	+	0.113936i
$694$	−18.8178	+	12.9890i	−0.714315	+	0.493056i
$695$	2.12141	+	1.22480i	0.0804697	+	0.0464592i
$696$	−2.95438	+	1.40187i	−0.111986	+	0.0531378i
$697$	0.270755	+	0.0328756i	0.0102556	+	0.00124525i
$698$	16.3731	−	28.3591i	0.619733	−	1.07341i
$699$	−3.61362	−	6.25898i	−0.136680	−	0.236736i
$700$	−4.75817	−	11.1678i	−0.179842	−	0.422105i
$701$	5.93035	−	5.25384i	0.223986	−	0.198435i	−0.543665	−	0.839302i	$-0.682964\pi$
$701$	5.93035	−	5.25384i	0.223986	−	0.198435i	0.767651	+	0.640868i	$0.221425\pi$
$702$	−2.72679	−	2.32226i	−0.102916	−	0.0876481i
$703$	−27.8655	−	24.6867i	−1.05097	−	0.931075i
$704$	6.36979	−	19.0799i	0.240070	−	0.719099i
$705$	0.0732775	+	1.81836i	0.00275979	+	0.0684835i
$706$	13.7516	+	16.8426i	0.517547	+	0.633880i
$707$	−2.67311	+	3.01732i	−0.100533	+	0.113478i
$708$	12.5778	−	2.56777i	0.472702	−	0.0965028i
$709$	−0.951997	−	0.275749i	−0.0357530	−	0.0103560i	0.260293	−	0.965530i	$-0.416181\pi$
$709$	−0.951997	−	0.275749i	−0.0357530	−	0.0103560i	−0.296046	+	0.955174i	$0.595668\pi$
$710$	−1.73813	−	0.659187i	−0.0652310	−	0.0247389i
$711$	0.151697	−	3.76431i	0.00568906	−	0.141173i
$712$	−27.0318	+	20.3131i	−1.01306	+	0.761266i
$713$	−36.4028	−	7.43168i	−1.36329	−	0.278318i
$714$	−0.162343	−	0.0852042i	−0.00607554	−	0.00318869i
$715$	1.53418	−	6.79282i	0.0573751	−	0.254037i
$716$	−5.00720	+	2.62798i	−0.187128	+	0.0982122i
$717$	−21.7792	+	6.30843i	−0.813360	+	0.235592i
$718$	−10.2922	−	0.830875i	−0.384103	−	0.0310080i
$719$	−7.42229	−	36.3568i	−0.276805	−	1.35588i	−0.845783	−	0.533527i	$-0.820866\pi$
$719$	−7.42229	−	36.3568i	−0.276805	−	1.35588i	0.568979	−	0.822352i	$-0.307339\pi$
$720$	−0.291843	+	0.556061i	−0.0108764	+	0.0207232i
$721$	10.8678	−	14.4624i	0.404737	−	0.538607i
$722$	12.6264	+	19.9670i	0.469905	+	0.743095i
$723$	−15.9380	−	11.0012i	−0.592740	−	0.409139i
$724$	10.7689	+	22.6949i	0.400222	+	0.843449i
$725$	−3.45119	−	3.59307i	−0.128174	−	0.133443i
$726$	1.80326	−	1.73206i	0.0669253	−	0.0642826i
$727$	3.12751	−	25.7573i	0.115993	−	0.955286i	−0.812250	−	0.583310i	$-0.801757\pi$
$727$	3.12751	−	25.7573i	0.115993	−	0.955286i	0.928242	−	0.371976i	$-0.121320\pi$
$728$	8.45183	−	27.0653i	0.313246	−	1.00311i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−0.0764037	−	0.0623817i	−0.00282783	−	0.00230885i
$731$	−0.00167973	+	0.00822788i	−6.21272e−5	+	0.000304319i
$732$	−1.61431	+	5.57324i	−0.0596665	+	0.205993i
$733$	0.118667	−	0.481451i	0.00438307	−	0.0177828i	−0.968710	−	0.248197i	$-0.920162\pi$
$733$	0.118667	−	0.481451i	0.00438307	−	0.0177828i	0.973093	+	0.230414i	$0.0740081\pi$
$734$	−2.09262	−	25.9217i	−0.0772398	−	0.956787i
$735$	−0.0103659	+	0.0637837i	−0.000382350	+	0.00235270i
$736$	−26.7040	−	30.1426i	−0.984324	−	1.11107i
$737$	9.79827	+	7.36292i	0.360924	+	0.271217i
$738$	−2.43917	+	2.98744i	−0.0897869	+	0.109969i
$739$	0.764286	+	4.70284i	0.0281147	+	0.172997i	0.997310	−	0.0732958i	$-0.0233517\pi$
$739$	0.764286	+	4.70284i	0.0281147	+	0.172997i	−0.969196	+	0.246293i	$0.920788\pi$
$740$	3.71311	−	0.915200i	0.136497	−	0.0336434i
$741$	6.11752	−	22.7759i	0.224733	−	0.836692i
$742$	6.98413	+	1.72143i	0.256395	+	0.0631958i
$743$	4.13790	−	51.2570i	0.151805	−	1.88044i	−0.255025	−	0.966934i	$-0.582084\pi$
$743$	4.13790	−	51.2570i	0.151805	−	1.88044i	0.406830	−	0.913504i	$-0.366634\pi$
$744$	13.2172	+	4.41256i	0.484568	+	0.161772i
$745$	4.34721	−	4.52592i	0.159269	−	0.165817i
$746$		−	22.4694i		−	0.822662i
$747$	2.86637	+	2.75319i	0.104875	+	0.100734i
$748$	−0.160584	+	0.131113i	−0.00587152	+	0.00479395i
$749$	−12.6914	−	24.1814i	−0.463733	−	0.883569i
$750$	−6.21625	−	1.01024i	−0.226985	−	0.0368887i
$751$	−35.0095	−	22.1387i	−1.27752	−	0.807852i	−0.288762	−	0.957401i	$-0.593244\pi$
$751$	−35.0095	−	22.1387i	−1.27752	−	0.807852i	−0.988754	+	0.149549i	$0.952218\pi$
$752$	−2.34789	−	1.11409i	−0.0856187	−	0.0406266i
$753$	8.69433	+	12.5959i	0.316839	+	0.459020i
$754$	−0.233899	−	3.90596i	−0.00851810	−	0.142247i
$755$	1.31433	−	1.90413i	0.0478333	−	0.0692985i
$756$	−2.30533	+	1.33099i	−0.0838442	+	0.0484075i
$757$	10.6936	−	22.5362i	0.388664	−	0.819093i	−0.610959	−	0.791662i	$-0.709216\pi$
$757$	10.6936	−	22.5362i	0.388664	−	0.819093i	0.999624	−	0.0274308i	$-0.00873259\pi$
$758$	−5.86036	+	1.95648i	−0.212858	+	0.0710624i
$759$	5.56290	+	22.5696i	0.201921	+	0.819224i
$760$	−12.9726	−	0.522778i	−0.470566	−	0.0189631i
$761$	−7.62445	−	0.307255i	−0.276386	−	0.0111380i	−0.0983140	−	0.995155i	$-0.531345\pi$
$761$	−7.62445	−	0.307255i	−0.276386	−	0.0111380i	−0.178072	+	0.984017i	$0.556986\pi$
$762$	1.49524	+	6.06642i	0.0541668	+	0.219763i
$763$	−29.7815	+	9.94253i	−1.07816	+	0.359944i
$764$	−9.12908	+	19.2391i	−0.330279	+	0.696047i
$765$	0.0403448	−	0.0232931i	0.00145867	−	0.000842163i
$766$	−7.81141	+	11.3168i	−0.282238	+	0.408892i
$767$	−8.26153	+	44.9286i	−0.298307	+	1.62228i
$768$	9.66971	+	14.0090i	0.348926	+	0.505506i
$769$	−16.7203	−	7.93389i	−0.602950	−	0.286103i	0.102646	−	0.994718i	$-0.467269\pi$
$769$	−16.7203	−	7.93389i	−0.602950	−	0.286103i	−0.705596	+	0.708615i	$0.749320\pi$
$770$	4.26043	+	2.69414i	0.153535	+	0.0970899i
$771$	−16.9938	−	2.76175i	−0.612015	−	0.0994621i
$772$	−11.8829	−	22.6410i	−0.427675	−	0.814868i
$773$	−22.7084	+	18.5408i	−0.816763	+	0.666866i	−0.945791	−	0.324775i	$-0.894712\pi$
$773$	−22.7084	+	18.5408i	−0.816763	+	0.666866i	0.129029	+	0.991641i	$0.458814\pi$
$774$	−0.0856398	−	0.0822582i	−0.00307826	−	0.00295671i
$775$			21.2291i			0.762573i
$776$	38.8181	−	40.4139i	1.39349	−	1.45077i
$777$	−14.1840	−	4.73530i	−0.508847	−	0.169878i
$778$	−1.80342	+	22.3394i	−0.0646559	+	0.800907i
$779$	−24.6563	−	6.07724i	−0.883405	−	0.217740i
$780$	1.56851	+	1.84625i	0.0561617	+	0.0661065i
$781$	7.98014	−	1.96693i	0.285552	−	0.0703823i
$782$	−0.0893415	−	0.549740i	−0.00319484	−	0.0196587i
$783$	−0.690945	+	0.846254i	−0.0246924	+	0.0302426i
$784$	−0.0737731	−	0.0554369i	−0.00263475	−	0.00197989i
$785$	3.30519	+	3.73079i	0.117967	+	0.133157i
$786$	−0.854440	+	5.25758i	−0.0304769	+	0.187532i
$787$	−0.147332	−	1.82503i	−0.00525182	−	0.0650554i	0.993601	−	0.112951i	$-0.0360304\pi$
$787$	−0.147332	−	1.82503i	−0.00525182	−	0.0650554i	−0.998852	+	0.0478960i	$0.984748\pi$
$788$	3.03444	−	12.3112i	0.108098	−	0.438569i
$789$	6.43001	−	22.1990i	0.228914	−	0.790304i
$790$	0.496414	−	2.43160i	0.0176616	−	0.0865123i
$791$	−41.2960	−	33.7172i	−1.46832	−	1.19884i
$792$	−1.05084	−	8.65442i	−0.0373399	−	0.307521i
$793$	−16.2460	−	12.7437i	−0.576911	−	0.452544i
$794$	1.92822	−	15.8803i	0.0684299	−	0.563571i
$795$	−1.31815	+	1.26610i	−0.0467501	+	0.0449041i
$796$	−10.7102	−	11.1505i	−0.379613	−	0.395219i
$797$	−15.9503	−	33.6145i	−0.564987	−	1.19069i	−0.962045	−	0.272892i	$-0.912020\pi$
$797$	−15.9503	−	33.6145i	−0.564987	−	1.19069i	0.397057	−	0.917794i	$-0.370031\pi$
$798$	14.0488	+	9.69718i	0.497322	+	0.343276i
$799$	0.103037	+	0.162940i	0.00364520	+	0.00576442i
$800$	−13.8230	+	18.3951i	−0.488718	+	0.650365i
$801$	−5.24977	+	10.0026i	−0.185492	+	0.353425i
$802$	2.99607	+	14.6757i	0.105795	+	0.518218i
$803$	0.434687	+	0.0350916i	0.0153398	+	0.00123836i
$804$	−4.09536	+	1.18624i	−0.144432	+	0.0418353i
$805$	12.3122	−	6.46194i	0.433948	−	0.227754i
$806$	−10.8108	+	12.6940i	−0.380792	+	0.447126i
$807$	−1.50900	−	0.791982i	−0.0531192	−	0.0278791i
$808$	4.49980	+	0.918641i	0.158302	+	0.0323177i
$809$	36.4500	−	27.3904i	1.28151	−	0.962995i	0.281519	−	0.959556i	$-0.409162\pi$
$809$	36.4500	−	27.3904i	1.28151	−	0.962995i	0.999994	−	0.00343905i	$-0.00109469\pi$
$810$	−0.0265252	+	0.658216i	−0.000932000	+	0.0231273i
$811$	−10.5947	−	4.01803i	−0.372029	−	0.141092i	0.161502	−	0.986872i	$-0.448366\pi$
$811$	−10.5947	−	4.01803i	−0.372029	−	0.141092i	−0.533531	+	0.845780i	$0.679135\pi$
$812$	−2.79337	−	0.809111i	−0.0980282	−	0.0283942i
$813$	11.6637	−	2.38116i	0.409064	−	0.0835110i
$814$	10.9199	−	12.3260i	0.382743	−	0.432028i
$815$	−6.09384	−	7.46360i	−0.213458	−	0.261438i
$816$	0.00267877	+	0.0664729i	9.37756e−5	+	0.00232702i
$817$	0.247594	−	0.741634i	0.00866221	−	0.0259465i
$818$	6.51712	+	5.77366i	0.227866	+	0.201871i
$819$	−1.32528	−	9.37960i	−0.0463091	−	0.327750i
$820$	1.95258	−	1.72984i	0.0681871	−	0.0604085i
$821$	6.75595	+	15.8568i	0.235784	+	0.553406i	0.995273	−	0.0971143i	$-0.0309612\pi$
$821$	6.75595	+	15.8568i	0.235784	+	0.553406i	−0.759489	+	0.650520i	$0.774551\pi$
$822$	−3.56238	−	6.17022i	−0.124252	−	0.215211i
$823$	11.9018	−	20.6145i	0.414869	−	0.718575i	−0.580545	−	0.814228i	$-0.697161\pi$
$823$	11.9018	−	20.6145i	0.414869	−	0.718575i	0.995415	+	0.0956531i	$0.0304940\pi$
$824$	−20.4603	−	2.48433i	−0.712768	−	0.0865457i
$825$	11.9996	−	5.69387i	0.417772	−	0.198235i
$826$	−28.6366	−	16.5333i	−0.996394	−	0.575268i
$827$	−7.27630	+	5.02247i	−0.253022	+	0.174648i	−0.687824	−	0.725878i	$-0.741434\pi$
$827$	−7.27630	+	5.02247i	−0.253022	+	0.174648i	0.434802	+	0.900526i	$0.356818\pi$
$828$	−7.43931	−	3.16959i	−0.258534	−	0.110151i
$829$	3.20658	−	0.521121i	0.111369	−	0.0180993i	−0.104471	−	0.994528i	$-0.533315\pi$
$829$	3.20658	−	0.521121i	0.111369	−	0.0180993i	0.215840	+	0.976429i	$0.430751\pi$
$830$	1.57284	+	2.09307i	0.0545940	+	0.0726514i
$831$	4.87592	−	12.8567i	0.169144	−	0.445996i
$832$	−24.2959	+	5.45648i	−0.842310	+	0.189169i
$833$	0.00242748	+	0.00640075i	8.41073e−5	+	0.000221773i
$834$	−1.96119	+	3.10137i	−0.0679104	+	0.107392i
$835$	−3.86476	+	1.64662i	−0.133746	+	0.0569836i
$836$	16.3139	−	10.3163i	0.564226	−	0.356795i
$837$	4.62133	−	0.561131i	0.159736	−	0.0193955i
$838$	10.3706	−	24.3407i	0.358246	−	0.840835i
$839$	−12.4657	−	37.3394i	−0.430365	−	1.28910i	−0.911082	−	0.412224i	$-0.864752\pi$
$839$	−12.4657	−	37.3394i	−0.430365	−	1.28910i	0.480718	−	0.876875i	$-0.340376\pi$
$840$	−4.87611	+	1.84927i	−0.168242	+	0.0638057i
$841$	27.7163	−	2.23749i	0.955734	−	0.0771548i
$842$	10.1882	+	35.1739i	0.351110	+	1.21217i
$843$	−7.54534	+	0.304067i	−0.259875	+	0.0104726i
$844$	3.07015			0.105679
$845$	−8.18050	+	2.72007i	−0.281418	+	0.0935733i
$846$	−2.72608			−0.0937245
$847$	6.60756	−	0.266275i	0.227038	−	0.00914933i
$848$	−0.726162	−	2.50700i	−0.0249365	−	0.0860908i
$849$	24.7652	−	1.99925i	0.849940	−	0.0686142i
$850$	−0.297556	+	0.112848i	−0.0102061	+	0.00387066i
$851$	−14.3846	−	43.0873i	−0.493099	−	1.47701i
$852$	−1.12070	+	2.63039i	−0.0383947	+	0.0901157i
$853$	20.1031	−	2.44096i	0.688317	−	0.0835768i	0.231097	−	0.972931i	$-0.425768\pi$
$853$	20.1031	−	2.44096i	0.688317	−	0.0835768i	0.457220	+	0.889354i	$0.348845\pi$
$854$	12.6321	−	7.98806i	0.432262	−	0.273346i
$855$	−3.99039	+	1.70015i	−0.136469	+	0.0581438i
$856$	−16.6292	+	26.2970i	−0.568374	+	0.898812i
$857$	20.4241	+	53.8539i	0.697674	+	1.83961i	0.516797	+	0.856108i	$0.327124\pi$
$857$	20.4241	+	53.8539i	0.697674	+	1.83961i	0.180877	+	0.983506i	$0.442106\pi$
$858$	10.0747	+	2.70603i	0.343944	+	0.0923824i
$859$	3.63716	−	9.59040i	0.124098	−	0.327220i	−0.858541	−	0.512744i	$-0.828629\pi$
$859$	3.63716	−	9.59040i	0.124098	−	0.327220i	0.982640	+	0.185524i	$0.0593982\pi$
$860$	0.0482503	+	0.0642095i	0.00164532	+	0.00218952i
$861$	−10.0681	+	1.63623i	−0.343122	+	0.0557627i
$862$	22.8975	+	9.75570i	0.779891	+	0.332281i
$863$	−1.50820	+	1.04103i	−0.0513396	+	0.0354372i	−0.593458	−	0.804865i	$-0.702238\pi$
$863$	−1.50820	+	1.04103i	−0.0513396	+	0.0354372i	0.542119	+	0.840302i	$0.317622\pi$
$864$	4.36976	+	2.52288i	0.148662	+	0.0858302i
$865$	13.1143	−	6.22280i	0.445899	−	0.211582i
$866$	−4.32091	−	0.524653i	−0.146830	−	0.0178284i
$867$	−8.49753	+	14.7182i	−0.288591	+	0.499855i
$868$	6.19609	+	10.7320i	0.210309	+	0.364266i
$869$	4.30091	+	10.0946i	0.145899	+	0.342436i
$870$	−0.538690	+	0.477238i	−0.0182633	+	0.0161799i
$871$	1.53430	−	15.0948i	0.0519877	−	0.511468i
$872$	26.7749	+	23.7205i	0.906712	+	0.803277i
$873$	5.92838	−	17.7577i	0.200645	−	0.601006i
$874$	2.08803	+	51.8139i	0.0706287	+	1.75263i
$875$	−10.5343	−	12.9021i	−0.356123	−	0.436172i
$876$	−0.100602	+	0.113556i	−0.00339902	+	0.00383670i
$877$	−8.66999	+	1.76999i	−0.292765	+	0.0597683i	−0.344163	−	0.938910i	$-0.611837\pi$
$877$	−8.66999	+	1.76999i	−0.292765	+	0.0597683i	0.0513984	+	0.998678i	$0.483632\pi$
$878$	27.3188	+	7.91299i	0.921966	+	0.267051i
$879$	−3.11605	−	1.18176i	−0.105102	−	0.0398598i
$880$	0.0736491	−	1.82758i	0.00248271	−	0.0616078i
$881$	16.9668	−	12.7498i	0.571628	−	0.429550i	−0.275224	−	0.961380i	$-0.588752\pi$
$881$	16.9668	−	12.7498i	0.571628	−	0.429550i	0.846851	+	0.531830i	$0.178495\pi$
$882$	−0.0948438	−	0.0193625i	−0.00319356	−	0.000651969i
$883$	12.5993	+	6.61265i	0.424002	+	0.222533i	0.663207	−	0.748436i	$-0.269195\pi$
$883$	12.5993	+	6.61265i	0.424002	+	0.222533i	−0.239206	+	0.970969i	$0.576887\pi$
$884$	0.241691	+	0.0863002i	0.00812896	+	0.00290259i
$885$	7.43956	−	3.90458i	0.250078	−	0.131251i
$886$	2.56888	−	0.744085i	0.0863032	−	0.0249980i
$887$	36.1080	+	2.91494i	1.21239	+	0.0978741i	0.670069	−	0.742298i	$-0.266264\pi$
$887$	36.1080	+	2.91494i	1.21239	+	0.0978741i	0.542319	+	0.840173i	$0.317546\pi$
$888$	3.40774	+	16.6922i	0.114356	+	0.560154i
$889$	−7.67938	+	14.6318i	−0.257558	+	0.490736i
$890$	−4.47049	+	5.94914i	−0.149851	+	0.199416i
$891$	−1.55666	−	2.46166i	−0.0521501	−	0.0824688i
$892$	20.5032	+	14.1524i	0.686499	+	0.473856i
$893$	−7.69486	−	16.2166i	−0.257499	−	0.542667i
$894$	6.51202	+	6.77973i	0.217794	+	0.226748i
$895$	−2.66928	+	2.56388i	−0.0892242	+	0.0857010i
$896$	−1.02319	+	8.42673i	−0.0341824	+	0.281517i
$897$	20.3599	−	20.3353i	0.679796	−	0.678976i
$898$	3.09402	+	25.4815i	0.103249	+	0.850330i
$899$	3.93954	+	3.21653i	0.131391	+	0.107277i
$900$	−0.924213	+	4.52709i	−0.0308071	+	0.150903i
$901$	−0.0538685	+	0.185975i	−0.00179462	+	0.00619574i
$902$	2.68821	−	10.9065i	0.0895076	−	0.363147i
$903$	−0.0252712	−	0.313040i	−0.000840973	−	0.0104173i
$904$	−9.74316	+	59.9521i	−0.324053	+	1.99398i
$905$	10.9025	+	12.3064i	0.362412	+	0.409079i
$906$	2.77076	+	2.08209i	0.0920523	+	0.0691728i
$907$	−27.4800	+	33.6568i	−0.912457	+	1.11756i	0.0802219	+	0.996777i	$0.474437\pi$
$907$	−27.4800	+	33.6568i	−0.912457	+	1.11756i	−0.992679	+	0.120780i	$0.961460\pi$
$908$	−2.27525	−	14.0002i	−0.0755070	−	0.464613i
$909$	1.48974	−	0.367188i	0.0494116	−	0.0121789i
$910$	0.129427	−	6.23884i	0.00429048	−	0.206815i
$911$	0.493500	+	0.121637i	0.0163504	+	0.00403001i	0.247482	−	0.968892i	$-0.420397\pi$
$911$	0.493500	+	0.121637i	0.0163504	+	0.00403001i	−0.231132	+	0.972922i	$0.574243\pi$
$912$	0.498418	−	6.17401i	0.0165043	−	0.204442i
$913$	−10.9800	−	3.66567i	−0.363386	−	0.121316i
$914$	22.4709	−	23.3947i	0.743271	−	0.773827i
$915$			3.79762i			0.125545i
$916$	19.8699	+	19.0853i	0.656519	+	0.630595i
$917$	−10.9124	+	8.90967i	−0.360358	+	0.294223i
$918$	0.0324307	+	0.0617915i	0.00107037	+	0.00203942i
$919$	4.43426	+	0.720638i	0.146273	+	0.0237716i	0.233107	−	0.972451i	$-0.425111\pi$
$919$	4.43426	+	0.720638i	0.146273	+	0.0237716i	−0.0868339	+	0.996223i	$0.527675\pi$
$920$	−13.3894	−	8.46693i	−0.441435	−	0.279146i
$921$	−13.3597	−	6.33926i	−0.440217	−	0.208886i
$922$	6.00711	+	8.70280i	0.197834	+	0.286612i
$923$	−7.19015	−	7.19884i	−0.236667	−	0.236953i
$924$	4.40428	−	6.38070i	0.144890	−	0.209910i
$925$	−22.4780	+	12.9777i	−0.739071	+	0.426703i
$926$	−12.4343	+	26.2047i	−0.408616	+	0.861141i
$927$	−6.53133	+	2.18048i	−0.214517	+	0.0716163i
$928$	1.31922	+	5.35230i	0.0433056	+	0.175698i
$929$	32.5208	+	1.31054i	1.06697	+	0.0429975i	0.567532	−	0.823351i	$-0.307898\pi$
$929$	32.5208	+	1.31054i	1.06697	+	0.0429975i	0.499440	+	0.866349i	$0.333539\pi$
$930$	3.06417	+	0.123482i	0.100478	+	0.00404913i
$931$	−0.152533	−	0.618850i	−0.00499906	−	0.0202820i
$932$	−6.94584	+	2.31886i	−0.227519	+	0.0759569i
$933$	−12.7802	+	26.9337i	−0.418404	+	0.881769i
$934$	−3.72973	+	2.15336i	−0.122041	+	0.0704602i
$935$	−0.0770776	+	0.111666i	−0.00252071	+	0.00365188i
$936$	−8.49953	+	6.65068i	−0.277816	+	0.217384i
$937$	−25.9784	−	37.6362i	−0.848676	−	1.22952i	−0.971488	−	0.237090i	$-0.923806\pi$
$937$	−25.9784	−	37.6362i	−0.848676	−	1.22952i	0.122811	−	0.992430i	$-0.460809\pi$
$938$	9.92225	+	4.70817i	0.323973	+	0.153727i
$939$	5.20293	+	3.29013i	0.169791	+	0.107369i
$940$	1.82000	+	0.295778i	0.0593617	+	0.00964722i
$941$	−10.4843	−	19.9762i	−0.341779	−	0.651205i	0.652527	−	0.757765i	$-0.273709\pi$
$941$	−10.4843	−	19.9762i	−0.341779	−	0.651205i	−0.994306	+	0.106560i	$0.966016\pi$
$942$	−5.78346	+	4.72205i	−0.188435	+	0.153853i
$943$	−22.3470	−	21.4646i	−0.727718	−	0.698982i
$944$			11.9983i			0.390512i
$945$	−1.20690	+	1.25652i	−0.0392606	+	0.0408746i
$946$	0.328055	+	0.109521i	0.0106660	+	0.00356083i
$947$	−2.69088	+	33.3326i	−0.0874419	+	1.08316i	0.793067	+	0.609134i	$0.208483\pi$
$947$	−2.69088	+	33.3326i	−0.0874419	+	1.08316i	−0.880509	+	0.474029i	$0.842799\pi$
$948$	−3.70620	−	0.913497i	−0.120372	−	0.0296690i
$949$	−0.240919	−	0.483128i	−0.00782056	−	0.0156830i
$950$	28.7689	−	7.09090i	0.933387	−	0.230059i
$951$	−0.602855	−	3.70951i	−0.0195489	−	0.120289i
$952$	−0.349397	+	0.427933i	−0.0113240	+	0.0138694i
$953$	−20.5644	−	15.4531i	−0.666146	−	0.500576i	0.213047	−	0.977042i	$-0.431661\pi$
$953$	−20.5644	−	15.4531i	−0.666146	−	0.500576i	−0.879193	+	0.476465i	$0.841918\pi$
$954$	−1.81555	−	2.04933i	−0.0587806	−	0.0663495i
$955$	−2.23576	+	13.7572i	−0.0723475	+	0.445172i
$956$	1.84863	+	22.8994i	0.0597890	+	0.740620i
$957$	0.761492	−	3.08950i	0.0246155	−	0.0998692i
$958$	−3.13633	+	10.8279i	−0.101330	+	0.349832i
$959$	3.76919	−	18.4627i	0.121713	−	0.596192i
$960$	3.54760	+	2.89653i	0.114498	+	0.0934850i
$961$	1.12442	+	9.26046i	0.0362717	+	0.298724i
$962$	−20.0495	−	3.68672i	−0.646420	−	0.118865i
$963$	−1.25294	+	10.3189i	−0.0403753	+	0.332520i
$964$	−14.1513	+	13.5926i	−0.455784	+	0.437787i
$965$	−11.5931	−	12.0697i	−0.373194	−	0.388536i
$966$	8.92935	+	18.8182i	0.287297	+	0.605466i
$967$	10.6311	+	7.33810i	0.341872	+	0.235977i	0.726612	−	0.687048i	$-0.241094\pi$
$967$	10.6311	+	7.33810i	0.341872	+	0.235977i	−0.384740	+	0.923025i	$0.625709\pi$
$968$	−4.02671	−	6.36773i	−0.129423	−	0.204667i
$969$	−0.276037	+	0.367338i	−0.00886758	+	0.0118006i
$970$	5.73121	−	10.9199i	0.184018	−	0.350617i
$971$	−4.70245	−	23.0341i	−0.150909	−	0.739200i	−0.982860	−	0.184352i	$-0.940981\pi$
$971$	−4.70245	−	23.0341i	−0.150909	−	0.739200i	0.831951	−	0.554848i	$-0.187224\pi$
$972$	1.00992	+	0.0815293i	0.0323933	+	0.00261505i
$973$	−9.32174	+	2.70008i	−0.298841	+	0.0865604i
$974$	4.98774	−	2.61777i	0.159818	−	0.0838788i
$975$	−13.7115	−	9.07413i	−0.439120	−	0.290605i
$976$	−4.80196	−	2.52026i	−0.153707	−	0.0806717i
$977$	0.398471	+	0.0813484i	0.0127482	+	0.00260256i	0.206396	−	0.978469i	$-0.433827\pi$
$977$	0.398471	+	0.0813484i	0.0127482	+	0.00260256i	−0.193647	+	0.981071i	$0.562032\pi$
$978$	11.5388	−	8.67085i	0.368970	−	0.277263i
$979$	1.32482	−	32.8752i	0.0423415	−	1.05069i
$980$	0.0612192	+	0.0232174i	0.00195558	+	0.000741652i
$981$	11.4787	+	3.32485i	0.366487	+	0.106154i
$982$	34.4323	−	7.02941i	1.09878	−	0.224317i
$983$	21.9893	−	24.8208i	0.701351	−	0.791661i	−0.284609	−	0.958644i	$-0.591864\pi$
$983$	21.9893	−	24.8208i	0.701351	−	0.791661i	0.985960	+	0.166982i	$0.0534023\pi$
$984$	7.34971	+	9.00176i	0.234300	+	0.286966i
$985$	−0.334160	−	8.29211i	−0.0106472	−	0.264208i
$986$	−0.0241427	+	0.0723163i	−0.000768861	+	0.00230302i
$987$	−5.39670	−	4.78106i	−0.171779	−	0.152183i
$988$	−21.3705	−	10.6890i	−0.679886	−	0.340062i
$989$	0.714102	−	0.632639i	0.0227071	−	0.0201167i
$990$	−0.752045	−	1.76511i	−0.0239015	−	0.0560990i
$991$	29.0884	+	50.3827i	0.924025	+	1.60046i	0.793122	+	0.609063i	$0.208454\pi$
$991$	29.0884	+	50.3827i	0.924025	+	1.60046i	0.130903	+	0.991395i	$0.458212\pi$
$992$	11.7447	−	20.3424i	0.372894	−	0.645872i
$993$	−6.05212	−	0.734861i	−0.192058	−	0.0233201i
$994$	6.65374	−	3.15724i	0.211044	−	0.100142i
$995$	−8.76349	−	5.05960i	−0.277821	−	0.160400i
$996$	3.31409	−	2.28755i	0.105011	−	0.0724839i
$997$	−46.8136	−	19.9454i	−1.48260	−	0.631677i	−0.509172	−	0.860665i	$-0.670048\pi$
$997$	−46.8136	−	19.9454i	−1.48260	−	0.631677i	−0.973429	+	0.228987i	$0.926459\pi$
$998$	32.9970	−	5.36253i	1.04450	−	0.169748i
$999$	3.41922	+	4.55016i	0.108179	+	0.143961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.127.11	yes	360
169.4	even	78	inner	507.2.t.b.4.11	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.11	✓	360	169.4	even	78	inner
507.2.t.b.127.11	yes	360	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.992569 - 0.0399992i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.00992 + 0.0815293i) q^{4} +(-0.620050 + 0.235154i) q^{5} +(-0.314570 - 0.942252i) q^{6} +(1.02980 - 2.41704i) q^{7} +(-2.97142 + 0.360796i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})\)	\(q+(0.992569 - 0.0399992i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.00992 + 0.0815293i) q^{4} +(-0.620050 + 0.235154i) q^{5} +(-0.314570 - 0.942252i) q^{6} +(1.02980 - 2.41704i) q^{7} +(-2.97142 + 0.360796i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-0.606036 + 0.258208i) q^{10} +(1.55666 - 2.46166i) q^{11} +(0.359288 + 0.947365i) q^{12} +(-3.60478 - 0.0747826i) q^{13} +(0.925470 - 2.44027i) q^{14} +(0.398378 + 0.530145i) q^{15} +(-0.934732 + 0.151909i) q^{16} +(0.0646290 + 0.0275358i) q^{17} +(-0.817531 + 0.564301i) q^{18} +(-5.66449 - 3.27039i) q^{19} +(0.607030 - 0.288039i) q^{20} +(-2.60812 - 0.316683i) q^{21} +(1.44663 - 2.50563i) q^{22} +(-3.99049 - 6.91173i) q^{23} +(1.17325 + 2.75372i) q^{24} +(-3.41339 + 3.02400i) q^{25} +(-3.58098 + 0.0699611i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-0.842961 + 2.52498i) q^{28} +(0.0439904 + 1.09161i) q^{29} +(0.416623 + 0.510271i) q^{30} +(3.08701 - 3.48452i) q^{31} +(4.94379 - 1.00928i) q^{32} +(-2.79756 - 0.810323i) q^{33} +(0.0652501 + 0.0247461i) q^{34} +(-0.0701537 + 1.74085i) q^{35} +(0.810001 - 0.608677i) q^{36} +(5.57663 + 1.13848i) q^{37} +(-5.75320 - 3.01951i) q^{38} +(0.931081 + 3.48326i) q^{39} +(1.75759 - 0.922452i) q^{40} +(3.72916 - 1.08016i) q^{41} +(-2.60140 - 0.210007i) q^{42} +(0.0239107 + 0.117122i) q^{43} +(-1.37141 + 2.61300i) q^{44} +(0.398378 - 0.530145i) q^{45} +(-4.23730 - 6.70075i) q^{46} +(2.25848 + 1.55892i) q^{47} +(0.405970 + 0.855564i) q^{48} +(0.0675030 + 0.0702781i) q^{49} +(-3.26707 + 3.13806i) q^{50} +(0.00846775 - 0.0697382i) q^{51} +(3.64664 - 0.218370i) q^{52} +(0.332216 + 2.73604i) q^{53} +(0.769473 + 0.628255i) q^{54} +(-0.386338 + 1.89241i) q^{55} +(-2.18792 + 7.55357i) q^{56} +(-1.56531 + 6.35072i) q^{57} +(0.0873271 + 1.08174i) q^{58} +(2.03239 - 12.5058i) q^{59} +(-0.445553 - 0.502926i) q^{60} +(4.57816 + 3.44026i) q^{61} +(2.92470 - 3.58210i) q^{62} +(0.421444 + 2.59325i) q^{63} +(6.70564 - 1.65279i) q^{64} +(2.25273 - 0.801308i) q^{65} +(-2.80918 - 0.692402i) q^{66} +(-0.338613 + 4.19447i) q^{67} +(-0.0675152 - 0.0225399i) q^{68} +(-5.52862 + 5.75590i) q^{69} +1.73071i q^{70} +(2.03517 + 1.95481i) q^{71} +(2.31858 - 1.89306i) q^{72} +(0.0695838 + 0.132581i) q^{73} +(5.58073 + 0.906957i) q^{74} +(3.85427 + 2.43729i) q^{75} +(5.98732 + 2.84102i) q^{76} +(-4.34687 - 6.29753i) q^{77} +(1.06349 + 3.42013i) q^{78} +(-2.14011 + 3.10048i) q^{79} +(0.543859 - 0.313997i) q^{80} +(0.428693 - 0.903450i) q^{81} +(3.65824 - 1.22130i) q^{82} +(-0.951144 - 3.85894i) q^{83} +(2.65981 + 0.107187i) q^{84} +(-0.0465483 - 0.00187583i) q^{85} +(0.0284178 + 0.115295i) q^{86} +(1.03627 - 0.345959i) q^{87} +(-3.73733 + 7.87626i) q^{88} +(9.78311 - 5.64828i) q^{89} +(0.374213 - 0.542141i) q^{90} +(-3.89296 + 8.63586i) q^{91} +(4.59359 + 6.65497i) q^{92} +(-4.20580 - 1.99568i) q^{93} +(2.30405 + 1.45700i) q^{94} +(4.28131 + 0.695781i) q^{95} +(-2.34488 - 4.46780i) q^{96} +(-14.5015 + 11.8401i) q^{97} +(0.0698124 + 0.0670558i) q^{98} +2.91255i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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