LMFDB - Embedded newform 456.2.bk.a.253.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(61,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 0, 2]))

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

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

chi := DirichletCharacter("456.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.34
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16921 + 0.795584i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(0.734092 + 1.86041i) q^{4} +(-0.853481 + 0.150492i) q^{5} +(-1.14750 + 0.826590i) q^{6} +(0.0398455 - 0.0690145i) q^{7} +(-0.621803 + 2.75923i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(1.16921 + 0.795584i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(0.734092 + 1.86041i) q^{4} +(-0.853481 + 0.150492i) q^{5} +(-1.14750 + 0.826590i) q^{6} +(0.0398455 - 0.0690145i) q^{7} +(-0.621803 + 2.75923i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-1.11763 - 0.503060i) q^{10} +(-0.739964 + 0.427218i) q^{11} +(-1.99928 + 0.0535249i) q^{12} +(2.18874 + 6.01350i) q^{13} +(0.101494 - 0.0489918i) q^{14} +(0.150492 - 0.853481i) q^{15} +(-2.92222 + 2.73142i) q^{16} +(0.464046 - 0.389381i) q^{17} +(-0.384273 - 1.36100i) q^{18} +(-3.00818 + 3.15450i) q^{19} +(-0.906510 - 1.47735i) q^{20} +(0.0512244 + 0.0610469i) q^{21} +(-1.20506 - 0.0891965i) q^{22} +(0.655519 - 3.71764i) q^{23} +(-2.38016 - 1.52802i) q^{24} +(-3.99268 + 1.45322i) q^{25} +(-2.22516 + 8.77236i) q^{26} +(0.866025 - 0.500000i) q^{27} +(0.157645 + 0.0234658i) q^{28} +(4.15179 - 4.94791i) q^{29} +(0.854972 - 0.878168i) q^{30} +(5.02093 - 8.69651i) q^{31} +(-5.58975 + 0.868726i) q^{32} +(-0.148371 - 0.841456i) q^{33} +(0.852352 - 0.0860795i) q^{34} +(-0.0236213 + 0.0648990i) q^{35} +(0.633498 - 1.89702i) q^{36} +0.193804i q^{37} +(-6.02685 + 1.29500i) q^{38} -6.39944 q^{39} +(0.115455 - 2.44853i) q^{40} +(5.97913 + 2.17623i) q^{41} +(0.0113240 + 0.112130i) q^{42} +(3.40642 - 0.600643i) q^{43} +(-1.33800 - 1.06301i) q^{44} +(0.750539 + 0.433324i) q^{45} +(3.72413 - 3.82517i) q^{46} +(2.84962 + 2.39111i) q^{47} +(-1.56724 - 3.68019i) q^{48} +(3.49682 + 6.05668i) q^{49} +(-5.82443 - 1.47740i) q^{50} +(0.207185 + 0.569237i) q^{51} +(-9.58082 + 8.48640i) q^{52} +(10.2634 + 1.80971i) q^{53} +(1.41036 + 0.104392i) q^{54} +(0.567252 - 0.475981i) q^{55} +(0.165651 + 0.152856i) q^{56} +(-1.93540 - 3.90567i) q^{57} +(8.79078 - 2.48204i) q^{58} +(-6.74111 - 8.03375i) q^{59} +(1.69830 - 0.346558i) q^{60} +(8.93080 + 1.57474i) q^{61} +(12.7893 - 6.17345i) q^{62} +(-0.0748851 + 0.0272559i) q^{63} +(-7.22672 - 3.43140i) q^{64} +(-2.77303 - 4.80302i) q^{65} +(0.495972 - 1.10188i) q^{66} +(-7.25150 + 8.64200i) q^{67} +(1.06506 + 0.577473i) q^{68} +(3.26923 + 1.88749i) q^{69} +(-0.0792508 + 0.0570876i) q^{70} +(-0.0904163 - 0.512777i) q^{71} +(2.24993 - 1.71401i) q^{72} +(3.99052 + 1.45243i) q^{73} +(-0.154187 + 0.226597i) q^{74} -4.24892i q^{75} +(-8.07693 - 3.28074i) q^{76} +0.0680909i q^{77} +(-7.48227 - 5.09129i) q^{78} +(-0.598224 - 0.217736i) q^{79} +(2.08300 - 2.77098i) q^{80} +(0.173648 + 0.984808i) q^{81} +(5.25947 + 7.30136i) q^{82} +(1.07179 + 0.618800i) q^{83} +(-0.0759685 + 0.140112i) q^{84} +(-0.337456 + 0.402165i) q^{85} +(4.46067 + 2.00781i) q^{86} +(3.22952 + 5.59369i) q^{87} +(-0.718683 - 2.30738i) q^{88} +(12.6054 - 4.58799i) q^{89} +(0.532790 + 1.10376i) q^{90} +(0.502230 + 0.0885567i) q^{91} +(7.39752 - 1.50956i) q^{92} +(6.45479 + 7.69252i) q^{93} +(1.42946 + 5.06282i) q^{94} +(2.09270 - 3.14501i) q^{95} +(1.09547 - 5.54977i) q^{96} +(3.79612 - 3.18533i) q^{97} +(-0.730082 + 9.86353i) q^{98} +(0.841456 + 0.148371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6}+O(q^{10}) $ 240 * q + 6 * q^4 + 6 * q^6	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48} - 120 q^{49} + 18 q^{50} + 6 q^{52} - 6 q^{54} + 72 q^{58} - 12 q^{60} + 12 q^{62} + 30 q^{64} - 48 q^{66} - 78 q^{68} - 108 q^{70} - 36 q^{72} - 24 q^{73} - 96 q^{74} - 48 q^{76} - 96 q^{78} - 114 q^{80} - 66 q^{82} - 36 q^{84} - 24 q^{86} - 24 q^{88} + 6 q^{90} - 108 q^{94} + 120 q^{95} - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	1.16921	+	0.795584i	0.826755	+	0.562563i
$2$	1.16921	+	0.795584i	0.826755	+	0.562563i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$4$	0.734092	+	1.86041i	0.367046	+	0.930203i
$5$	−0.853481	+	0.150492i	−0.381688	+	0.0673020i	−0.361201	−	0.932488i	$-0.617633\pi$
$5$	−0.853481	+	0.150492i	−0.381688	+	0.0673020i	−0.0204878	+	0.999790i	$0.506522\pi$
$6$	−1.14750	+	0.826590i	−0.468464	+	0.337454i
$7$	0.0398455	−	0.0690145i	0.0150602	−	0.0260850i	−0.858397	−	0.512986i	$-0.828539\pi$
$7$	0.0398455	−	0.0690145i	0.0150602	−	0.0260850i	0.873457	+	0.486901i	$0.161873\pi$
$8$	−0.621803	+	2.75923i	−0.219840	+	0.975536i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−1.11763	−	0.503060i	−0.353424	−	0.159081i
$11$	−0.739964	+	0.427218i	−0.223107	+	0.128811i	−0.607388	−	0.794405i	$-0.707783\pi$
$11$	−0.739964	+	0.427218i	−0.223107	+	0.128811i	0.384281	+	0.923216i	$0.374449\pi$
$12$	−1.99928	+	0.0535249i	−0.577143	+	0.0154513i
$13$	2.18874	+	6.01350i	0.607046	+	1.66785i	0.736645	+	0.676279i	$0.236409\pi$
$13$	2.18874	+	6.01350i	0.607046	+	1.66785i	−0.129599	+	0.991566i	$0.541369\pi$
$14$	0.101494	−	0.0489918i	0.0271255	−	0.0130936i
$15$	0.150492	−	0.853481i	0.0388568	−	0.220368i
$16$	−2.92222	+	2.73142i	−0.730554	+	0.682855i
$17$	0.464046	−	0.389381i	0.112548	−	0.0944388i	−0.584777	−	0.811194i	$-0.698818\pi$
$17$	0.464046	−	0.389381i	0.112548	−	0.0944388i	0.697325	+	0.716755i	$0.254374\pi$
$18$	−0.384273	−	1.36100i	−0.0905741	−	0.320792i
$19$	−3.00818	+	3.15450i	−0.690124	+	0.723691i
$19$	−3.00818	+	3.15450i	−0.690124	+	0.723691i
$20$	−0.906510	−	1.47735i	−0.202702	−	0.330345i
$21$	0.0512244	+	0.0610469i	0.0111781	+	0.0133215i
$22$	−1.20506	−	0.0891965i	−0.256919	−	0.0190168i
$23$	0.655519	−	3.71764i	0.136685	−	0.775181i	−0.836986	−	0.547224i	$-0.815685\pi$
$23$	0.655519	−	3.71764i	0.136685	−	0.775181i	0.973671	−	0.227956i	$-0.0732044\pi$
$24$	−2.38016	−	1.52802i	−0.485848	−	0.311905i
$25$	−3.99268	+	1.45322i	−0.798536	+	0.290643i
$26$	−2.22516	+	8.77236i	−0.436390	+	1.72040i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	0.157645	+	0.0234658i	0.0297921	+	0.00443463i
$29$	4.15179	−	4.94791i	0.770968	−	0.918804i	−0.227520	−	0.973773i	$-0.573062\pi$
$29$	4.15179	−	4.94791i	0.770968	−	0.918804i	0.998488	+	0.0549694i	$0.0175061\pi$
$30$	0.854972	−	0.878168i	0.156096	−	0.160331i
$31$	5.02093	−	8.69651i	0.901786	−	1.56194i	0.0766128	−	0.997061i	$-0.475589\pi$
$31$	5.02093	−	8.69651i	0.901786	−	1.56194i	0.825174	−	0.564879i	$-0.191077\pi$
$32$	−5.58975	+	0.868726i	−0.988138	+	0.153571i
$33$	−0.148371	−	0.841456i	−0.0258281	−	0.146479i
$34$	0.852352	−	0.0860795i	0.146177	−	0.0147625i
$35$	−0.0236213	+	0.0648990i	−0.00399273	+	0.0109699i
$36$	0.633498	−	1.89702i	0.105583	−	0.316170i
$37$			0.193804i			0.0318612i	0.999873	+	0.0159306i	$0.00507107\pi$
$37$			0.193804i			0.0318612i	−0.999873	+	0.0159306i	$0.994929\pi$
$38$	−6.02685	+	1.29500i	−0.977685	+	0.210077i
$39$	−6.39944			−1.02473
$40$	0.115455	−	2.44853i	0.0182551	−	0.387146i
$41$	5.97913	+	2.17623i	0.933783	+	0.339869i	0.763708	−	0.645562i	$-0.223377\pi$
$41$	5.97913	+	2.17623i	0.933783	+	0.339869i	0.170075	+	0.985431i	$0.445599\pi$
$42$	0.0113240	+	0.112130i	0.00174734	+	0.0173020i
$43$	3.40642	−	0.600643i	0.519474	−	0.0915973i	0.0922372	−	0.995737i	$-0.470598\pi$
$43$	3.40642	−	0.600643i	0.519474	−	0.0915973i	0.427237	+	0.904140i	$0.359487\pi$
$44$	−1.33800	−	1.06301i	−0.201711	−	0.160256i
$45$	0.750539	+	0.433324i	0.111884	+	0.0645961i
$46$	3.72413	−	3.82517i	0.549093	−	0.563990i
$47$	2.84962	+	2.39111i	0.415660	+	0.348780i	0.826509	−	0.562923i	$-0.190323\pi$
$47$	2.84962	+	2.39111i	0.415660	+	0.348780i	−0.410850	+	0.911703i	$0.634768\pi$
$48$	−1.56724	−	3.68019i	−0.226211	−	0.531189i
$49$	3.49682	+	6.05668i	0.499546	+	0.865240i
$50$	−5.82443	−	1.47740i	−0.823699	−	0.208936i
$51$	0.207185	+	0.569237i	0.0290118	+	0.0797091i
$52$	−9.58082	+	8.48640i	−1.32862	+	1.17685i
$53$	10.2634	+	1.80971i	1.40979	+	0.248583i	0.826158	−	0.563438i	$-0.190522\pi$
$53$	10.2634	+	1.80971i	1.40979	+	0.248583i	0.583628	+	0.812021i	$0.301633\pi$
$54$	1.41036	+	0.104392i	0.191925	+	0.0142060i
$55$	0.567252	−	0.475981i	0.0764883	−	0.0641813i
$56$	0.165651	+	0.152856i	0.0221360	+	0.0204263i
$57$	−1.93540	−	3.90567i	−0.256350	−	0.517318i
$58$	8.79078	−	2.48204i	1.15429	−	0.325907i
$59$	−6.74111	−	8.03375i	−0.877618	−	1.04590i	−0.998581	−	0.0532477i	$-0.983043\pi$
$59$	−6.74111	−	8.03375i	−0.877618	−	1.04590i	0.120963	−	0.992657i	$-0.461402\pi$
$60$	1.69830	−	0.346558i	0.219249	−	0.0447405i
$61$	8.93080	+	1.57474i	1.14347	+	0.201625i	0.713124	−	0.701038i	$-0.247280\pi$
$61$	8.93080	+	1.57474i	1.14347	+	0.201625i	0.430348	+	0.902663i	$0.358391\pi$
$62$	12.7893	−	6.17345i	1.62425	−	0.784029i
$63$	−0.0748851	+	0.0272559i	−0.00943463	+	0.00343393i
$64$	−7.22672	−	3.43140i	−0.903340	−	0.428924i
$65$	−2.77303	−	4.80302i	−0.343952	−	0.595742i
$66$	0.495972	−	1.10188i	0.0610499	−	0.135632i
$67$	−7.25150	+	8.64200i	−0.885912	+	1.05579i	0.112158	+	0.993690i	$0.464224\pi$
$67$	−7.25150	+	8.64200i	−0.885912	+	1.05579i	−0.998070	+	0.0620982i	$0.980221\pi$
$68$	1.06506	+	0.577473i	0.129157	+	0.0700289i
$69$	3.26923	+	1.88749i	0.393569	+	0.227227i
$70$	−0.0792508	+	0.0570876i	−0.00947228	+	0.00682328i
$71$	−0.0904163	−	0.512777i	−0.0107304	−	0.0608554i	0.978972	−	0.203993i	$-0.0653920\pi$
$71$	−0.0904163	−	0.512777i	−0.0107304	−	0.0608554i	−0.989703	+	0.143138i	$0.954281\pi$
$72$	2.24993	−	1.71401i	0.265157	−	0.201998i
$73$	3.99052	+	1.45243i	0.467055	+	0.169994i	0.564818	−	0.825215i	$-0.308946\pi$
$73$	3.99052	+	1.45243i	0.467055	+	0.169994i	−0.0977626	+	0.995210i	$0.531169\pi$
$74$	−0.154187	+	0.226597i	−0.0179239	+	0.0263414i
$75$		−	4.24892i		−	0.490623i
$76$	−8.07693	−	3.28074i	−0.926487	−	0.376327i
$77$			0.0680909i			0.00775968i
$78$	−7.48227	−	5.09129i	−0.847200	−	0.576475i
$79$	−0.598224	−	0.217736i	−0.0673055	−	0.0244972i	0.308148	−	0.951338i	$-0.400291\pi$
$79$	−0.598224	−	0.217736i	−0.0673055	−	0.0244972i	−0.375453	+	0.926841i	$0.622513\pi$
$80$	2.08300	−	2.77098i	0.232887	−	0.309805i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	5.25947	+	7.30136i	0.580812	+	0.806300i
$83$	1.07179	+	0.618800i	0.117645	+	0.0679221i	0.557668	−	0.830064i	$-0.311696\pi$
$83$	1.07179	+	0.618800i	0.117645	+	0.0679221i	−0.440023	+	0.897986i	$0.645030\pi$
$84$	−0.0759685	+	0.140112i	−0.00828884	+	0.0152875i
$85$	−0.337456	+	0.402165i	−0.0366023	+	0.0436209i
$86$	4.46067	+	2.00781i	0.481007	+	0.216508i
$87$	3.22952	+	5.59369i	0.346241	+	0.599707i
$88$	−0.718683	−	2.30738i	−0.0766119	−	0.245967i
$89$	12.6054	−	4.58799i	1.33617	−	0.486326i	0.427565	−	0.903985i	$-0.359372\pi$
$89$	12.6054	−	4.58799i	1.33617	−	0.486326i	0.908604	+	0.417659i	$0.137149\pi$
$90$	0.532790	+	1.10376i	0.0561610	+	0.116347i
$91$	0.502230	+	0.0885567i	0.0526480	+	0.00928326i
$92$	7.39752	−	1.50956i	0.771245	−	0.157382i
$93$	6.45479	+	7.69252i	0.669330	+	0.797677i
$94$	1.42946	+	5.06282i	0.147438	+	0.522190i
$95$	2.09270	−	3.14501i	0.214706	−	0.322671i
$96$	1.09547	−	5.54977i	0.111806	−	0.566421i
$97$	3.79612	−	3.18533i	0.385438	−	0.323421i	−0.429395	−	0.903117i	$-0.641273\pi$
$97$	3.79612	−	3.18533i	0.385438	−	0.323421i	0.814833	+	0.579696i	$0.196829\pi$
$98$	−0.730082	+	9.86353i	−0.0737495	+	0.996367i
$99$	0.841456	+	0.148371i	0.0845695	+	0.0149119i
$100$	−5.63457	−	6.36121i	−0.563457	−	0.636121i
$101$	−4.44180	−	12.2038i	−0.441976	−	1.21432i	−0.938190	−	0.346119i	$-0.887499\pi$
$101$	−4.44180	−	12.2038i	−0.441976	−	1.21432i	0.496214	−	0.868200i	$-0.334723\pi$
$102$	−0.210633	+	0.830390i	−0.0208558	+	0.0822208i
$103$	0.0275674	+	0.0477482i	0.00271630	+	0.00470477i	0.867380	−	0.497646i	$-0.165802\pi$
$103$	0.0275674	+	0.0477482i	0.00271630	+	0.00470477i	−0.864664	+	0.502351i	$0.832469\pi$
$104$	−17.9536	+	2.30002i	−1.76050	+	0.225535i
$105$	−0.0529061	−	0.0443935i	−0.00516311	−	0.00433236i
$106$	10.5603	+	10.2813i	1.02570	+	0.998611i
$107$	−9.86290	−	5.69435i	−0.953483	−	0.550493i	−0.0593215	−	0.998239i	$-0.518894\pi$
$107$	−9.86290	−	5.69435i	−0.953483	−	0.550493i	−0.894161	+	0.447746i	$0.852227\pi$
$108$	1.56595	+	1.24411i	0.150683	+	0.119715i
$109$	−11.6753	+	2.05867i	−1.11829	+	0.197184i	−0.702089	−	0.712089i	$-0.747749\pi$
$109$	−11.6753	+	2.05867i	−1.11829	+	0.197184i	−0.416199	+	0.909273i	$0.636638\pi$
$110$	1.04192	−	0.105224i	0.0993430	−	0.0100327i
$111$	−0.182116	−	0.0662848i	−0.0172857	−	0.00629148i
$112$	0.0720701	+	0.310510i	0.00680999	+	0.0293404i
$113$	−8.83638			−0.831257			−0.415628	−	0.909535i	$-0.636438\pi$
$113$	−8.83638			−0.831257			−0.415628	+	0.909535i	$0.636438\pi$
$114$	0.844401	−	6.10631i	0.0790854	−	0.571908i
$115$			3.27158i			0.305077i
$116$	12.2529	+	4.09179i	1.13765	+	0.379913i
$117$	2.18874	−	6.01350i	0.202349	−	0.555949i
$118$	−1.49024	−	14.7562i	−0.137188	−	1.35842i
$119$	−0.00838276	−	0.0475410i	−0.000768446	−	0.00435808i
$120$	2.26138	+	0.945939i	0.206434	+	0.0863520i
$121$	−5.13497	+	8.89403i	−0.466815	+	0.808548i
$122$	9.18912	+	8.94640i	0.831943	+	0.809969i
$123$	−4.08997	+	4.87423i	−0.368780	+	0.439495i
$124$	19.8649	+	2.95693i	1.78392	+	0.265540i
$125$	6.94167	−	4.00778i	0.620882	−	0.358467i
$126$	−0.109241	−	0.0277095i	−0.00973192	−	0.00246856i
$127$	15.1089	−	5.49917i	1.34069	−	0.487973i	0.430663	−	0.902513i	$-0.358280\pi$
$127$	15.1089	−	5.49917i	1.34069	−	0.487973i	0.910031	+	0.414540i	$0.136058\pi$
$128$	−5.71958	−	9.76148i	−0.505544	−	0.862801i
$129$	−0.600643	+	3.40642i	−0.0528837	+	0.299918i
$130$	0.578965	−	7.82191i	0.0507786	−	0.686027i
$131$	−14.1207	−	16.8284i	−1.23373	−	1.47030i	−0.832218	−	0.554448i	$-0.812929\pi$
$131$	−14.1207	−	16.8284i	−1.23373	−	1.47030i	−0.401512	−	0.915854i	$-0.631515\pi$
$132$	1.45653	−	0.893737i	0.126775	−	0.0777898i
$133$	0.0978434	+	0.333300i	0.00848410	+	0.0289008i
$134$	−15.3539	+	4.33512i	−1.32638	+	0.374497i
$135$	−0.663891	+	0.557070i	−0.0571386	+	0.0479450i
$136$	0.785848	+	1.52253i	0.0673859	+	0.130556i
$137$	0.953914	−	5.40992i	0.0814984	−	0.462200i	−0.916559	−	0.399899i	$-0.869045\pi$
$137$	0.953914	−	5.40992i	0.0814984	−	0.462200i	0.998057	−	0.0623009i	$-0.0198438\pi$
$138$	2.32075	+	4.80782i	0.197556	+	0.409269i
$139$	0.378827	+	1.04082i	0.0321317	+	0.0882810i	0.954721	−	0.297502i	$-0.0961535\pi$
$139$	0.378827	+	1.04082i	0.0321317	+	0.0882810i	−0.922590	+	0.385783i	$0.873931\pi$
$140$	−0.138079	+	0.00369665i	−0.0116698	+	0.000312424i
$141$	−3.22154	+	1.85996i	−0.271302	+	0.156637i
$142$	0.302241	−	0.671476i	0.0253635	−	0.0563490i
$143$	−4.18866	−	3.51471i	−0.350274	−	0.293914i
$144$	3.99427	−	0.214023i	0.332856	−	0.0178353i
$145$	−2.79886	+	4.84776i	−0.232432	+	0.402585i
$146$	3.51022	+	4.87299i	0.290508	+	0.403292i
$147$	−6.88740	+	1.21443i	−0.568063	+	0.100165i
$148$	−0.360554	+	0.142270i	−0.0296373	+	0.0116945i
$149$	−3.95902	+	10.8773i	−0.324335	+	0.891104i	0.665181	+	0.746682i	$0.268354\pi$
$149$	−3.95902	+	10.8773i	−0.324335	+	0.891104i	−0.989516	+	0.144422i	$0.953868\pi$
$150$	3.38037	−	4.96787i	0.276006	−	0.405625i
$151$	−5.70537			−0.464297			−0.232148	−	0.972680i	$-0.574576\pi$
$151$	−5.70537			−0.464297			−0.232148	+	0.972680i	$0.574576\pi$
$152$	−6.83350	−	10.2617i	−0.554270	−	0.832337i
$153$	−0.605770			−0.0489736
$154$	−0.0541720	+	0.0796124i	−0.00436531	+	0.00641535i
$155$	−2.97652	+	8.17792i	−0.239080	+	0.656866i
$156$	−4.69778	−	11.9055i	−0.376123	−	0.953207i
$157$	9.79596	−	1.72729i	0.781803	−	0.137853i	0.231519	−	0.972830i	$-0.425631\pi$
$157$	9.79596	−	1.72729i	0.781803	−	0.137853i	0.550284	+	0.834978i	$0.314519\pi$
$158$	−0.526221	−	0.730516i	−0.0418639	−	0.0581167i
$159$	−5.21086	+	9.02548i	−0.413248	+	0.715767i
$160$	4.64001	−	1.58265i	0.366825	−	0.125120i
$161$	−0.230451	−	0.193371i	−0.0181621	−	0.0152398i
$162$	−0.580467	+	1.28960i	−0.0456058	+	0.101320i
$163$	10.2687	−	5.92863i	0.804306	−	0.464366i	−0.0406687	−	0.999173i	$-0.512949\pi$
$163$	10.2687	−	5.92863i	0.804306	−	0.464366i	0.844975	+	0.534806i	$0.179615\pi$
$164$	0.340572	+	12.7212i	0.0265942	+	0.993355i
$165$	0.253264	+	0.695838i	0.0197166	+	0.0541709i
$166$	0.760841	+	1.57621i	0.0590527	+	0.122337i
$167$	−2.83673	+	16.0879i	−0.219513	+	1.24492i	0.653389	+	0.757023i	$0.273347\pi$
$167$	−2.83673	+	16.0879i	−0.219513	+	1.24492i	−0.872902	+	0.487896i	$0.837764\pi$
$168$	−0.200294	+	0.103381i	−0.0154530	+	0.00797601i
$169$	−21.4131	+	17.9677i	−1.64716	+	1.38213i
$170$	−0.714512	+	0.201739i	−0.0548006	+	0.0154727i
$171$	4.33207	−	0.482864i	0.331282	−	0.0369256i
$172$	3.61807	+	5.89639i	0.275875	+	0.449596i
$173$	−7.28322	−	8.67980i	−0.553733	−	0.659913i	0.414475	−	0.910061i	$-0.363965\pi$
$173$	−7.28322	−	8.67980i	−0.553733	−	0.659913i	−0.968208	+	0.250148i	$0.919521\pi$
$174$	−0.674273	+	9.10954i	−0.0511165	+	0.690593i
$175$	−0.0587974	+	0.333457i	−0.00444467	+	0.0252070i
$176$	0.995423	−	3.26957i	0.0750328	−	0.246453i
$177$	9.85485	−	3.58687i	0.740736	−	0.269606i
$178$	18.3884	+	4.66434i	1.37827	+	0.349607i
$179$	−4.29325	+	2.47871i	−0.320893	+	0.185268i	−0.651790	−	0.758399i	$-0.725982\pi$
$179$	−4.29325	+	2.47871i	−0.320893	+	0.185268i	0.330898	+	0.943667i	$0.392649\pi$
$180$	−0.255193	+	1.71441i	−0.0190210	+	0.127784i
$181$	9.22112	−	10.9893i	0.685400	−	0.816828i	−0.305391	−	0.952227i	$-0.598787\pi$
$181$	9.22112	−	10.9893i	0.685400	−	0.816828i	0.990791	+	0.135399i	$0.0432316\pi$
$182$	0.516757	+	0.503107i	0.0383046	+	0.0372928i
$183$	−4.53428	+	7.85361i	−0.335184	+	0.580556i
$184$	9.85022	+	4.12037i	0.726168	+	0.303757i
$185$	−0.0291659	−	0.165408i	−0.00214432	−	0.0121610i
$186$	1.42694	+	14.1295i	0.104629	+	1.03602i
$187$	−0.177027	+	0.486377i	−0.0129455	+	0.0355674i
$188$	−2.35656	+	7.05674i	−0.171870	+	0.514666i
$189$		−	0.0796910i		−	0.00579667i
$190$	4.94892	−	2.01225i	0.359032	−	0.145984i
$191$	−0.928822			−0.0672072			−0.0336036	−	0.999435i	$-0.510698\pi$
$191$	−0.928822			−0.0672072			−0.0336036	+	0.999435i	$0.510698\pi$
$192$	5.69614	−	5.61729i	0.411084	−	0.405393i
$193$	−5.19857	−	1.89212i	−0.374201	−	0.136198i	0.148071	−	0.988977i	$-0.452693\pi$
$193$	−5.19857	−	1.89212i	−0.374201	−	0.136198i	−0.522273	+	0.852779i	$0.674916\pi$
$194$	6.97265	−	0.704172i	0.500607	−	0.0505566i
$195$	5.46180	−	0.963062i	0.391128	−	0.0689663i
$196$	−8.70088	+	10.9517i	−0.621492	+	0.782262i
$197$	−6.64743	−	3.83790i	−0.473610	−	0.273439i	0.244140	−	0.969740i	$-0.421494\pi$
$197$	−6.64743	−	3.83790i	−0.473610	−	0.273439i	−0.717750	+	0.696301i	$0.754828\pi$
$198$	0.865794	+	0.842925i	0.0615293	+	0.0599041i
$199$	−1.11643	−	0.936793i	−0.0791414	−	0.0664075i	0.602359	−	0.798225i	$-0.294228\pi$
$199$	−1.11643	−	0.936793i	−0.0791414	−	0.0664075i	−0.681500	+	0.731818i	$0.738672\pi$
$200$	−1.52710	−	11.9203i	−0.107983	−	0.842896i
$201$	−5.64067	−	9.76992i	−0.397862	−	0.689117i
$202$	4.51572	−	17.8026i	0.317725	−	1.25258i
$203$	−0.176047	−	0.483686i	−0.0123561	−	0.0339481i
$204$	−0.906919	+	0.803321i	−0.0634970	+	0.0562437i
$205$	−5.43058	−	0.957557i	−0.379288	−	0.0668787i
$206$	−0.00575565	+	0.0777597i	−0.000401015	+	0.00541778i
$207$	−2.89181	+	2.42651i	−0.200994	+	0.168654i
$208$	−22.8214	−	11.5944i	−1.58238	−	0.803927i
$209$	0.878285	−	3.61936i	0.0607522	−	0.250357i
$210$	−0.0265395	−	0.0939965i	−0.00183140	−	0.00648637i
$211$	−8.33027	−	9.92763i	−0.573479	−	0.683446i	0.398862	−	0.917011i	$-0.369405\pi$
$211$	−8.33027	−	9.92763i	−0.573479	−	0.683446i	−0.972341	+	0.233565i	$0.924961\pi$
$212$	4.16748	+	20.4226i	0.286224	+	1.40263i
$213$	0.512777	+	0.0904163i	0.0351349	+	0.00619523i
$214$	−7.00144	−	14.5046i	−0.478609	−	0.991517i
$215$	−2.81692	+	1.02528i	−0.192112	+	0.0699232i
$216$	0.841119	+	2.70047i	0.0572309	+	0.183743i
$217$	−0.400123	−	0.693034i	−0.0271621	−	0.0470462i
$218$	−15.2887	−	6.88165i	−1.03548	−	0.466084i
$219$	−2.72968	+	3.25310i	−0.184455	+	0.219824i
$220$	1.30193	+	0.705905i	0.0877763	+	0.0475921i
$221$	3.35722	+	1.93829i	0.225831	+	0.130384i
$222$	−0.160196	−	0.222389i	−0.0107517	−	0.0149258i
$223$	−0.0663808	−	0.376464i	−0.00444519	−	0.0252099i	0.982504	−	0.186239i	$-0.0596298\pi$
$223$	−0.0663808	−	0.376464i	−0.00444519	−	0.0252099i	−0.986950	+	0.161029i	$0.948519\pi$
$224$	−0.162772	+	0.420388i	−0.0108757	+	0.0280884i
$225$	3.99268	+	1.45322i	0.266179	+	0.0968811i
$226$	−10.3316	−	7.03008i	−0.687245	−	0.467634i
$227$		−	0.301405i		−	0.0200050i	−0.999950	−	0.0100025i	$-0.996816\pi$
$227$		−	0.301405i		−	0.0200050i	0.999950	−	0.0100025i	$-0.00318395\pi$
$228$	5.84536	−	6.46775i	0.387118	−	0.428337i
$229$			5.13829i			0.339547i	0.985483	+	0.169774i	$0.0543037\pi$
$229$			5.13829i			0.339547i	−0.985483	+	0.169774i	$0.945696\pi$
$230$	−2.60282	+	3.82516i	−0.171625	+	0.252223i
$231$	−0.0639845	−	0.0232885i	−0.00420987	−	0.00153227i
$232$	11.0708	+	14.5324i	0.726836	+	0.954097i
$233$	−3.39093	−	19.2309i	−0.222147	−	1.25986i	−0.868064	−	0.496452i	$-0.834636\pi$
$233$	−3.39093	−	19.2309i	−0.222147	−	1.25986i	0.645917	−	0.763408i	$-0.276475\pi$
$234$	7.34333	−	5.28971i	0.480049	−	0.345799i
$235$	−2.79194	−	1.61193i	−0.182126	−	0.105150i
$236$	9.99743	−	18.4387i	0.650777	−	1.20026i
$237$	0.409210	−	0.487677i	0.0265810	−	0.0316780i
$238$	0.0280217	−	0.0622545i	0.00181638	−	0.00403536i
$239$	10.1872	+	17.6447i	0.658952	+	1.14134i	0.980887	+	0.194577i	$0.0623334\pi$
$239$	10.1872	+	17.6447i	0.658952	+	1.14134i	−0.321935	+	0.946762i	$0.604333\pi$
$240$	1.89144	+	2.90511i	0.122092	+	0.187524i
$241$	−15.7349	+	5.72704i	−1.01357	+	0.368911i	−0.794805	−	0.606865i	$-0.792427\pi$
$241$	−15.7349	+	5.72704i	−1.01357	+	0.368911i	−0.218770	+	0.975776i	$0.570204\pi$
$242$	−13.0798	+	6.31366i	−0.840801	+	0.405858i
$243$	−0.984808	−	0.173648i	−0.0631754	−	0.0111395i
$244$	3.62637	+	17.7709i	0.232155	+	1.13767i
$245$	−3.89595	−	4.64302i	−0.248903	−	0.296632i
$246$	−8.65988	+	2.44508i	−0.552134	+	0.155892i
$247$	−25.5537	−	11.1853i	−1.62594	−	0.711706i
$248$	20.8737	+	19.2614i	1.32548	+	1.22310i
$249$	−0.948056	+	0.795514i	−0.0600806	+	0.0504136i
$250$	11.3048	+	0.836761i	0.714977	+	0.0529214i
$251$	23.1200	+	4.07668i	1.45932	+	0.257318i	0.846282	−	0.532735i	$-0.178836\pi$
$251$	23.1200	+	4.07668i	1.45932	+	0.257318i	0.613039	+	0.790052i	$0.289947\pi$
$252$	−0.105680	−	0.119308i	−0.00665719	−	0.00751571i
$253$	1.10318	+	3.03096i	0.0693564	+	0.190555i
$254$	22.0404	+	5.59069i	1.38294	+	0.350791i
$255$	−0.262494	−	0.454653i	−0.0164380	−	0.0284715i
$256$	1.07871	−	15.9636i	0.0674191	−	0.997725i
$257$	7.41252	+	6.21984i	0.462380	+	0.387983i	0.844006	−	0.536334i	$-0.180191\pi$
$257$	7.41252	+	6.21984i	0.462380	+	0.387983i	−0.381626	+	0.924317i	$0.624636\pi$
$258$	−3.41237	+	3.50495i	−0.212445	+	0.218208i
$259$	0.0133753	+	0.00772221i	0.000831098	+	0.000479835i
$260$	6.89992	−	8.68482i	0.427915	−	0.538610i
$261$	−6.36091	+	1.12160i	−0.393731	+	0.0694253i
$262$	−3.12162	−	30.9101i	−0.192855	−	1.90963i
$263$	−12.4568	−	4.53391i	−0.768120	−	0.279573i	−0.0719103	−	0.997411i	$-0.522910\pi$
$263$	−12.4568	−	4.53391i	−0.768120	−	0.279573i	−0.696210	+	0.717838i	$0.745132\pi$
$264$	2.41403	+	0.113828i	0.148573	+	0.00700565i
$265$	−9.03196			−0.554829
$266$	−0.150769	+	0.467540i	−0.00924425	+	0.0286667i
$267$			13.4144i			0.820947i
$268$	−21.4009	−	7.14670i	−1.30727	−	0.436554i
$269$	−4.18131	+	11.4881i	−0.254939	+	0.700439i	0.744522	+	0.667598i	$0.232678\pi$
$269$	−4.18131	+	11.4881i	−0.254939	+	0.700439i	−0.999461	+	0.0328407i	$0.989545\pi$
$270$	−1.21942	+	0.123150i	−0.0742117	+	0.00749468i
$271$	−4.32557	−	24.5315i	−0.262759	−	1.49018i	−0.775340	−	0.631544i	$-0.782422\pi$
$271$	−4.32557	−	24.5315i	−0.262759	−	1.49018i	0.512581	−	0.858639i	$-0.328690\pi$
$272$	−0.292481	+	2.40536i	−0.0177343	+	0.145846i
$273$	−0.254989	+	0.441654i	−0.0154326	+	0.0267301i
$274$	5.41937	−	5.56640i	0.327396	−	0.336278i
$275$	2.33360	−	2.78107i	0.140721	−	0.167705i
$276$	−1.11158	+	7.46769i	−0.0669094	+	0.449502i
$277$	−9.98757	+	5.76633i	−0.600095	+	0.346465i	−0.769079	−	0.639154i	$-0.779285\pi$
$277$	−9.98757	+	5.76633i	−0.600095	+	0.346465i	0.168984	+	0.985619i	$0.445951\pi$
$278$	−0.385131	+	1.51832i	−0.0230986	+	0.0910628i
$279$	−9.43627	+	3.43452i	−0.564935	+	0.205619i
$280$	−0.164384	−	0.105531i	−0.00982379	−	0.00630668i
$281$	−3.49151	+	19.8013i	−0.208286	+	1.18125i	0.683898	+	0.729577i	$0.260283\pi$
$281$	−3.49151	+	19.8013i	−0.208286	+	1.18125i	−0.892184	+	0.451671i	$0.850828\pi$
$282$	−5.24640	−	0.388330i	−0.312418	−	0.0231247i
$283$	15.8660	+	18.9083i	0.943135	+	1.12398i	0.992133	+	0.125185i	$0.0399525\pi$
$283$	15.8660	+	18.9083i	0.943135	+	1.12398i	−0.0489989	+	0.998799i	$0.515603\pi$
$284$	0.887598	−	0.544636i	0.0526693	−	0.0323182i
$285$	2.23960	+	3.04215i	0.132662	+	0.180201i
$286$	−2.10117	−	7.44185i	−0.124245	−	0.440046i
$287$	0.388432	−	0.325934i	0.0229284	−	0.0192392i
$288$	4.84040	+	2.92754i	0.285224	+	0.172507i
$289$	−2.88830	+	16.3803i	−0.169900	+	0.963550i
$290$	−7.12924	+	3.44131i	−0.418644	+	0.202081i
$291$	1.69488	+	4.65663i	0.0993554	+	0.272977i
$292$	0.227300	+	8.49021i	0.0133018	+	0.496852i
$293$	−16.4553	+	9.50046i	−0.961327	+	0.555023i	−0.896581	−	0.442879i	$-0.853957\pi$
$293$	−16.4553	+	9.50046i	−0.961327	+	0.555023i	−0.0647460	+	0.997902i	$0.520624\pi$
$294$	−9.01898	−	4.05958i	−0.525998	−	0.236759i
$295$	6.96243	+	5.84217i	0.405368	+	0.340144i
$296$	−0.534750	−	0.120508i	−0.0310817	−	0.00700437i
$297$	−0.427218	+	0.739964i	−0.0247897	+	0.0429370i
$298$	−13.2827	+	9.56810i	−0.769447	+	0.554265i
$299$	23.7908	−	4.19495i	1.37586	−	0.242601i
$300$	7.90472	−	3.11910i	0.456379	−	0.180081i
$301$	0.0942774	−	0.259025i	0.00543406	−	0.0149300i
$302$	−6.67077	−	4.53910i	−0.383859	−	0.261196i
$303$	12.9870			0.746082
$304$	0.174302	−	17.4347i	0.00999690	−	0.999950i
$305$	−7.85925			−0.450019
$306$	−0.708270	−	0.481941i	−0.0404891	−	0.0275507i
$307$	6.10510	−	16.7736i	0.348437	−	0.957322i	−0.634426	−	0.772983i	$-0.718764\pi$
$307$	6.10510	−	16.7736i	0.348437	−	0.957322i	0.982863	−	0.184338i	$-0.0590142\pi$
$308$	−0.126677	+	0.0499850i	−0.00721808	+	0.00284816i
$309$	−0.0542972	+	0.00957407i	−0.00308886	+	0.000544650i
$310$	−9.98639	+	7.19361i	−0.567189	+	0.408570i
$311$	−2.64928	+	4.58869i	−0.150227	+	0.260201i	−0.931311	−	0.364225i	$-0.881334\pi$
$311$	−2.64928	+	4.58869i	−0.150227	+	0.260201i	0.781084	+	0.624426i	$0.214667\pi$
$312$	3.97919	−	17.6575i	0.225277	−	0.999661i
$313$	22.5070	+	18.8856i	1.27217	+	1.06748i	0.994273	+	0.106868i	$0.0340822\pi$
$313$	22.5070	+	18.8856i	1.27217	+	1.06748i	0.277898	+	0.960611i	$0.410362\pi$
$314$	12.8277	+	5.77395i	0.723910	+	0.325843i
$315$	0.0598112	−	0.0345320i	0.00336998	−	0.00194566i
$316$	−0.0340749	−	1.27278i	−0.00191686	−	0.0715994i
$317$	2.06659	+	5.67791i	0.116071	+	0.318903i	0.984101	−	0.177609i	$-0.0568362\pi$
$317$	2.06659	+	5.67791i	0.116071	+	0.318903i	−0.868030	+	0.496512i	$0.834614\pi$
$318$	−13.2731	+	6.40698i	−0.744319	+	0.359286i
$319$	−0.958336	+	5.43500i	−0.0536565	+	0.304301i
$320$	6.68427	+	1.84107i	0.373662	+	0.102919i
$321$	8.72425	−	7.32051i	0.486940	−	0.408591i
$322$	−0.115602	−	0.409434i	−0.00644224	−	0.0228169i
$323$	−0.167633	+	2.63516i	−0.00932736	+	0.146624i
$324$	−1.70467	+	1.04600i	−0.0947038	+	0.0581109i
$325$	−17.4778	−	20.8293i	−0.969497	−	1.15540i
$326$	16.7230	+	1.23781i	0.926199	+	0.0685557i
$327$	2.05867	−	11.6753i	0.113844	−	0.645644i
$328$	−9.72255	+	15.1446i	−0.536838	+	0.836222i
$329$	0.278566	−	0.101390i	0.0153578	−	0.00558979i
$330$	−0.257479	+	1.01507i	−0.0141738	+	0.0558779i
$331$	−9.60547	+	5.54572i	−0.527964	+	0.304820i	−0.740187	−	0.672401i	$-0.765263\pi$
$331$	−9.60547	+	5.54572i	−0.527964	+	0.304820i	0.212223	+	0.977221i	$0.431930\pi$
$332$	−0.364424	+	2.44822i	−0.0200003	+	0.134364i
$333$	0.124575	−	0.148462i	0.00682665	−	0.00813569i
$334$	−16.1160	+	16.5532i	−0.881828	+	0.905753i
$335$	4.88847	−	8.46708i	0.267086	−	0.462606i
$336$	−0.316433	−	0.0384769i	−0.0172629	−	0.00209909i
$337$	1.46380	+	8.30160i	0.0797380	+	0.452217i	0.998369	+	0.0570991i	$0.0181851\pi$
$337$	1.46380	+	8.30160i	0.0797380	+	0.452217i	−0.918630	+	0.395118i	$0.870704\pi$
$338$	−39.3311	+	3.97207i	−2.13933	+	0.216052i
$339$	3.02222	−	8.30348i	0.164144	−	0.450983i
$340$	−0.995913	−	0.332579i	−0.0540110	−	0.0180367i
$341$			8.58014i			0.464641i
$342$	5.44925	+	2.88196i	0.294662	+	0.155838i
$343$	1.11517			0.0602134
$344$	−0.460805	+	9.77258i	−0.0248449	+	0.526902i
$345$	−3.07428	−	1.11895i	−0.165514	−	0.0602421i
$346$	−1.61008	−	15.9429i	−0.0865585	−	0.857095i
$347$	−0.895766	+	0.157948i	−0.0480872	+	0.00847907i	−0.197640	−	0.980275i	$-0.563328\pi$
$347$	−0.895766	+	0.157948i	−0.0480872	+	0.00847907i	0.149553	+	0.988754i	$0.452217\pi$
$348$	−8.03577	+	10.1145i	−0.430762	+	0.542194i
$349$	−8.00061	−	4.61915i	−0.428263	−	0.247258i	0.270343	−	0.962764i	$-0.412863\pi$
$349$	−8.00061	−	4.61915i	−0.428263	−	0.247258i	−0.698606	+	0.715506i	$0.746196\pi$
$350$	−0.334039	+	0.343102i	−0.0178552	+	0.0183396i
$351$	4.90225	+	4.11348i	0.261663	+	0.219561i
$352$	3.76508	−	3.03087i	0.200679	−	0.161546i
$353$	−6.12429	−	10.6076i	−0.325963	−	0.564584i	0.655744	−	0.754983i	$-0.272355\pi$
$353$	−6.12429	−	10.6076i	−0.325963	−	0.564584i	−0.981707	+	0.190399i	$0.939022\pi$
$354$	14.3760	+	3.64656i	0.764077	+	0.193813i
$355$	0.154337	+	0.424038i	0.00819137	+	0.0225056i
$356$	17.7890	+	20.0831i	0.942817	+	1.06440i
$357$	0.0475410	+	0.00838276i	0.00251614	+	0.000443663i
$358$	−6.99173	−	0.517516i	−0.369524	−	0.0273516i
$359$	−20.7320	+	17.3962i	−1.09419	+	0.918136i	−0.997021	−	0.0771321i	$-0.975424\pi$
$359$	−20.7320	+	17.3962i	−1.09419	+	0.918136i	−0.0971706	+	0.995268i	$0.530979\pi$
$360$	−1.66233	+	1.80147i	−0.0876124	+	0.0949457i
$361$	−0.901707	−	18.9786i	−0.0474583	−	0.998873i
$362$	19.5243	−	5.51260i	1.02618	−	0.289736i
$363$	−6.60139	−	7.86723i	−0.346483	−	0.412922i
$364$	0.203932	+	0.999360i	0.0106889	+	0.0523807i
$365$	−3.62442	−	0.639082i	−0.189711	−	0.0334511i
$366$	−11.5497	+	5.57510i	−0.603714	+	0.291415i
$367$	29.4510	−	10.7193i	1.53733	−	0.559542i	0.571926	−	0.820305i	$-0.306197\pi$
$367$	29.4510	−	10.7193i	1.53733	−	0.559542i	0.965403	+	0.260764i	$0.0839743\pi$
$368$	8.23885	+	12.6542i	0.429480	+	0.659648i
$369$	−3.18143	−	5.51040i	−0.165619	−	0.286860i
$370$	0.0974949	−	0.216600i	0.00506852	−	0.0112605i
$371$	0.533847	−	0.636214i	0.0277159	−	0.0330306i
$372$	−9.57279	+	17.6555i	−0.496326	+	0.915397i
$373$	−29.7709	−	17.1883i	−1.54148	−	0.889974i	−0.998746	−	0.0500701i	$-0.984056\pi$
$373$	−29.7709	−	17.1883i	−1.54148	−	0.889974i	−0.542735	−	0.839904i	$-0.682611\pi$
$374$	−0.593935	+	0.427836i	−0.0307116	+	0.0221229i
$375$	1.39189	+	7.89378i	0.0718767	+	0.407633i
$376$	−8.36954	+	6.37596i	−0.431626	+	0.328815i
$377$	38.8415	+	14.1371i	2.00044	+	0.728099i
$378$	0.0634009	−	0.0931753i	0.00326099	−	0.00479242i
$379$		−	3.76359i		−	0.193323i	−0.995317	−	0.0966614i	$-0.969184\pi$
$379$		−	3.76359i		−	0.193323i	0.995317	−	0.0966614i	$-0.0308164\pi$
$380$	7.38723	+	1.58454i	0.378957	+	0.0812852i
$381$			16.0785i			0.823727i
$382$	−1.08599	−	0.738956i	−0.0555638	−	0.0378083i
$383$	22.8903	+	8.33139i	1.16964	+	0.425714i	0.852532	−	0.522675i	$-0.175066\pi$
$383$	22.8903	+	8.33139i	1.16964	+	0.425714i	0.317108	+	0.948389i	$0.397288\pi$
$384$	11.1290	−	2.03602i	0.567924	−	0.103900i
$385$	−0.0102471	−	0.0581143i	−0.000522242	−	0.00296178i
$386$	−4.57286	−	6.34819i	−0.232753	−	0.323114i
$387$	−2.99555	−	1.72948i	−0.152273	−	0.0879146i
$388$	8.71270	+	4.72401i	0.442320	+	0.239825i
$389$	13.0586	−	15.5626i	0.662098	−	0.789058i	−0.325587	−	0.945512i	$-0.605562\pi$
$389$	13.0586	−	15.5626i	0.662098	−	0.789058i	0.987685	+	0.156454i	$0.0500064\pi$
$390$	7.15217	+	3.21930i	0.362164	+	0.163016i
$391$	−1.14339	−	1.98040i	−0.0578235	−	0.100153i
$392$	−18.8861	+	5.88249i	−0.953893	+	0.297111i
$393$	20.6431	−	7.51346i	1.04130	−	0.379004i
$394$	−4.71886	−	9.77589i	−0.237733	−	0.492502i
$395$	0.543341	+	0.0958056i	0.0273384	+	0.00482050i
$396$	0.341675	+	1.67437i	0.0171698	+	0.0841401i
$397$	−0.478608	−	0.570383i	−0.0240207	−	0.0286267i	0.753900	−	0.656989i	$-0.228170\pi$
$397$	−0.478608	−	0.570383i	−0.0240207	−	0.0286267i	−0.777921	+	0.628362i	$0.783726\pi$
$398$	−0.560037	−	1.98352i	−0.0280721	−	0.0994247i
$399$	−0.346664	−	0.0220527i	−0.0173549	−	0.00110402i
$400$	7.69814	−	15.1523i	0.384907	−	0.757615i
$401$	22.3757	−	18.7754i	1.11739	−	0.937601i	0.118919	−	0.992904i	$-0.462057\pi$
$401$	22.3757	−	18.7754i	1.11739	−	0.937601i	0.998470	+	0.0553034i	$0.0176126\pi$
$402$	1.17768	−	15.9107i	0.0587375	−	0.793553i
$403$	63.2860	+	11.1590i	3.15250	+	0.555871i
$404$	19.4432	−	17.2222i	0.967338	−	0.856839i
$405$	−0.296411	−	0.814382i	−0.0147288	−	0.0404670i
$406$	0.178977	−	0.705589i	0.00888247	−	0.0350178i
$407$	−0.0827965	−	0.143408i	−0.00410407	−	0.00710846i
$408$	−1.69949	+	0.217719i	−0.0841371	+	0.0107787i
$409$	−26.8178	−	22.5028i	−1.32606	−	1.11269i	−0.984982	−	0.172656i	$-0.944765\pi$
$409$	−26.8178	−	22.5028i	−1.32606	−	1.11269i	−0.341073	−	0.940037i	$-0.610790\pi$
$410$	−5.58766	−	5.44006i	−0.275955	−	0.268666i
$411$	4.75740	+	2.74669i	0.234665	+	0.135484i
$412$	−0.0685939	+	0.0863382i	−0.00337938	+	0.00425358i
$413$	−0.823048	+	0.145126i	−0.0404995	+	0.00714116i
$414$	−5.31162	+	0.536423i	−0.261052	+	0.0263638i
$415$	−1.00788	−	0.366838i	−0.0494748	−	0.0180074i
$416$	−17.4586	−	31.7126i	−0.855977	−	1.55484i
$417$	−1.10762			−0.0542402
$418$	3.90640	−	3.53304i	0.191068	−	0.172806i
$419$			32.4478i			1.58518i	0.609756	+	0.792589i	$0.291268\pi$
$419$			32.4478i			1.58518i	−0.609756	+	0.792589i	$0.708732\pi$
$420$	0.0437519	−	0.131016i	0.00213488	−	0.00639291i
$421$	0.276256	−	0.759008i	0.0134639	−	0.0369918i	−0.932779	−	0.360450i	$-0.882623\pi$
$421$	0.276256	−	0.759008i	0.0134639	−	0.0369918i	0.946243	+	0.323458i	$0.104845\pi$
$422$	−1.84155	−	18.2349i	−0.0896453	−	0.887660i
$423$	−0.645956	−	3.66340i	−0.0314075	−	0.178121i
$424$	−11.3752	+	27.1938i	−0.552430	+	1.32065i
$425$	−1.28693	+	2.22903i	−0.0624255	+	0.108124i
$426$	0.527608	+	0.513672i	0.0255627	+	0.0248875i
$427$	0.464532	−	0.553608i	0.0224803	−	0.0267910i
$428$	3.35352	−	22.5292i	0.162098	−	1.08899i
$429$	4.73535	−	2.73396i	0.228625	−	0.131997i
$430$	−4.10926	−	1.04234i	−0.198166	−	0.0502660i
$431$	10.9424	−	3.98272i	0.527078	−	0.191841i	−0.0647551	−	0.997901i	$-0.520627\pi$
$431$	10.9424	−	3.98272i	0.527078	−	0.191841i	0.591833	+	0.806060i	$0.298404\pi$
$432$	−1.16500	+	3.82659i	−0.0560513	+	0.184107i
$433$	4.94840	−	28.0638i	0.237805	−	1.34866i	−0.598821	−	0.800883i	$-0.704364\pi$
$433$	4.94840	−	28.0638i	0.237805	−	1.34866i	0.836626	−	0.547775i	$-0.184525\pi$
$434$	0.0835395	−	1.12863i	0.00401003	−	0.0541761i
$435$	−3.59814	−	4.28809i	−0.172518	−	0.205598i
$436$	−12.4007	−	20.2095i	−0.593885	−	0.967859i
$437$	9.75535	+	13.2512i	0.466662	+	0.633888i
$438$	−5.77968	+	1.63187i	−0.276164	+	0.0779735i
$439$	−16.4605	+	13.8120i	−0.785617	+	0.659211i	−0.944656	−	0.328061i	$-0.893605\pi$
$439$	−16.4605	+	13.8120i	−0.785617	+	0.659211i	0.159040	+	0.987272i	$0.449160\pi$
$440$	0.960624	+	1.86115i	0.0457959	+	0.0887267i
$441$	1.21443	−	6.88740i	0.0578302	−	0.327971i
$442$	2.38321	+	4.93722i	0.113358	+	0.234839i
$443$	−5.56932	−	15.3016i	−0.264607	−	0.727000i	−0.998842	−	0.0481058i	$-0.984682\pi$
$443$	−5.56932	−	15.3016i	−0.264607	−	0.727000i	0.734236	−	0.678895i	$-0.237541\pi$
$444$	−0.0103733	−	0.387469i	−0.000492297	−	0.0183885i
$445$	−10.0680	+	5.81277i	−0.477269	+	0.275552i
$446$	0.221896	−	0.492976i	0.0105071	−	0.0233431i
$447$	−8.86726	−	7.44052i	−0.419407	−	0.351924i
$448$	−0.524768	+	0.362023i	−0.0247930	+	0.0171040i
$449$	0.0188285	−	0.0326119i	0.000888571	−	0.00153905i	−0.865581	−	0.500769i	$-0.833050\pi$
$449$	0.0188285	−	0.0326119i	0.000888571	−	0.00153905i	0.866469	+	0.499230i	$0.166384\pi$
$450$	3.51212	+	4.87562i	0.165563	+	0.229839i
$451$	−5.35406	+	0.944065i	−0.252113	+	0.0444543i
$452$	−6.48672	−	16.4392i	−0.305110	−	0.773237i
$453$	1.95135	−	5.36130i	0.0916826	−	0.251896i
$454$	0.239793	−	0.352406i	0.0112541	−	0.0165392i
$455$	−0.441971			−0.0207199
$456$	11.9801	−	2.91166i	0.561018	−	0.136351i
$457$	35.4201			1.65688			0.828441	−	0.560077i	$-0.189228\pi$
$457$	35.4201			1.65688			0.828441	+	0.560077i	$0.189228\pi$
$458$	−4.08794	+	6.00772i	−0.191017	+	0.280722i
$459$	0.207185	−	0.569237i	0.00967059	−	0.0265697i
$460$	−6.08647	+	2.40164i	−0.283783	+	0.111977i
$461$	14.6593	−	2.58482i	0.682750	−	0.120387i	0.178493	−	0.983941i	$-0.442878\pi$
$461$	14.6593	−	2.58482i	0.682750	−	0.120387i	0.504256	+	0.863554i	$0.331767\pi$
$462$	−0.0562833	−	0.0781341i	−0.00261853	−	0.00363513i
$463$	11.0131	−	19.0753i	0.511823	−	0.886503i	−0.488084	−	0.872797i	$-0.662304\pi$
$463$	11.0131	−	19.0753i	0.511823	−	0.886503i	0.999906	−	0.0137057i	$-0.00436281\pi$
$464$	1.38238	+	25.7991i	0.0641756	+	1.19770i
$465$	−6.66670	−	5.59403i	−0.309161	−	0.259417i
$466$	11.3351	−	25.1827i	0.525089	−	1.16657i
$467$	17.2579	−	9.96384i	0.798600	−	0.461072i	−0.0443816	−	0.999015i	$-0.514132\pi$
$467$	17.2579	−	9.96384i	0.798600	−	0.461072i	0.842981	+	0.537943i	$0.180798\pi$
$468$	12.7943	−	0.342529i	0.591416	−	0.0158334i
$469$	0.307483	+	0.844803i	0.0141983	+	0.0390094i
$470$	−1.98193	−	4.10590i	−0.0914197	−	0.189391i
$471$	−1.72729	+	9.79596i	−0.0795894	+	0.451374i
$472$	26.3586	−	13.6049i	1.21325	−	0.626216i
$473$	−2.26402	+	1.89974i	−0.104100	+	0.0873501i
$474$	0.866439	−	0.244635i	0.0397969	−	0.0112365i
$475$	7.42653	−	16.9664i	0.340753	−	0.778474i
$476$	0.0822918	−	0.0504948i	0.00377184	−	0.00231443i
$477$	−6.69896	−	7.98351i	−0.306724	−	0.365540i
$478$	−2.12692	+	28.7350i	−0.0972830	+	1.31431i
$479$	4.10260	−	23.2670i	0.187453	−	1.06310i	−0.735311	−	0.677730i	$-0.762964\pi$
$479$	4.10260	−	23.2670i	0.187453	−	1.06310i	0.922764	−	0.385367i	$-0.125925\pi$
$480$	−0.0997702	+	4.90148i	−0.00455386	+	0.223721i
$481$	−1.16544	+	0.424185i	−0.0531395	+	0.0193412i
$482$	−22.9537	−	5.82235i	−1.04551	−	0.265201i
$483$	0.260529	−	0.150416i	0.0118545	−	0.00684418i
$484$	−20.3160	−	3.02409i	−0.923456	−	0.137459i
$485$	−2.76055	+	3.28990i	−0.125350	+	0.149387i
$486$	−1.01329	−	0.986528i	−0.0459639	−	0.0447498i
$487$	18.2176	−	31.5538i	0.825518	−	1.42984i	−0.0760048	−	0.997107i	$-0.524216\pi$
$487$	18.2176	−	31.5538i	0.825518	−	1.42984i	0.901523	−	0.432732i	$-0.142450\pi$
$488$	−9.89827	+	23.6630i	−0.448073	+	1.07117i
$489$	2.05899	+	11.6771i	0.0931108	+	0.528058i
$490$	−0.861269	−	8.52821i	−0.0389081	−	0.385265i
$491$	−7.64935	+	21.0164i	−0.345210	+	0.948458i	0.638646	+	0.769500i	$0.279495\pi$
$491$	−7.64935	+	21.0164i	−0.345210	+	0.948458i	−0.983857	+	0.178957i	$0.942728\pi$
$492$	−12.0705	−	4.03086i	−0.544178	−	0.181725i
$493$		−	3.91269i		−	0.176219i
$494$	−20.9787	−	33.4081i	−0.943876	−	1.50310i
$495$	−0.740495			−0.0332828
$496$	9.08156	+	39.1274i	0.407774	+	1.75687i
$497$	−0.0389917	−	0.0141918i	−0.00174902	−	0.000636590i
$498$	−1.74137	+	0.175862i	−0.0780327	+	0.00788057i
$499$	−10.5987	+	1.86884i	−0.474464	+	0.0836608i	−0.405766	−	0.913977i	$-0.632995\pi$
$499$	−10.5987	+	1.86884i	−0.474464	+	0.0836608i	−0.0686973	+	0.997638i	$0.521884\pi$
$500$	12.5519	+	9.97225i	0.561339	+	0.445973i
$501$	−14.1475	−	8.16804i	−0.632062	−	0.364921i
$502$	23.7887	+	23.1604i	1.06174	+	1.03370i
$503$	6.36887	+	5.34412i	0.283974	+	0.238282i	0.773637	−	0.633630i	$-0.218436\pi$
$503$	6.36887	+	5.34412i	0.283974	+	0.238282i	−0.489663	+	0.871912i	$0.662880\pi$
$504$	−0.0286417	−	0.223573i	−0.00127580	−	0.00995874i
$505$	5.62756	+	9.74722i	0.250423	+	0.433746i
$506$	−1.12154	+	4.42150i	−0.0498585	+	0.196560i
$507$	−9.56041	−	26.2670i	−0.424593	−	1.16656i
$508$	21.3220	+	24.0717i	0.946010	+	1.06801i
$509$	−20.8281	−	3.67256i	−0.923191	−	0.162783i	−0.308203	−	0.951320i	$-0.599728\pi$
$509$	−20.8281	−	3.67256i	−0.923191	−	0.162783i	−0.614987	+	0.788537i	$0.710839\pi$
$510$	0.0548047	−	0.740421i	0.00242679	−	0.0327864i
$511$	0.259243	−	0.217531i	0.0114682	−	0.00962300i
$512$	13.9616	−	17.8066i	0.617022	−	0.786946i
$513$	−1.02791	+	4.23596i	−0.0453834	+	0.187022i
$514$	3.71837	+	13.1696i	0.164010	+	0.580885i
$515$	−0.0307140	−	0.0366035i	−0.00135342	−	0.00161294i
$516$	−6.77825	+	1.38318i	−0.298396	+	0.0608913i
$517$	−3.13014	−	0.551928i	−0.137663	−	0.0242738i
$518$	0.00949479	+	0.0196700i	0.000417177	+	0.000864251i
$519$	10.6473	−	3.87532i	0.467367	−	0.170108i
$520$	14.9769	−	4.66489i	0.656782	−	0.204569i
$521$	−22.7067	−	39.3292i	−0.994801	−	1.72305i	−0.585598	−	0.810602i	$-0.699140\pi$
$521$	−22.7067	−	39.3292i	−0.994801	−	1.72305i	−0.409203	−	0.912444i	$-0.634193\pi$
$522$	−8.32955	−	3.74926i	−0.364575	−	0.164100i
$523$	16.3448	−	19.4790i	0.714709	−	0.851757i	−0.279396	−	0.960176i	$-0.590134\pi$
$523$	16.3448	−	19.4790i	0.714709	−	0.851757i	0.994105	+	0.108419i	$0.0345787\pi$
$524$	20.9417	−	38.6238i	0.914843	−	1.68729i
$525$	−0.293237	−	0.169300i	−0.0127979	−	0.00738888i
$526$	−10.9575	−	15.2115i	−0.477770	−	0.663254i
$527$	−1.05631	−	5.99064i	−0.0460137	−	0.260957i
$528$	2.73194	+	2.05365i	0.118892	+	0.0893737i
$529$	8.22182	+	2.99250i	0.357471	+	0.130109i
$530$	−10.5602	−	7.18569i	−0.458707	−	0.312126i
$531$			10.4873i			0.455111i
$532$	−0.548248	+	0.426702i	−0.0237696	+	0.0184999i
$533$			40.7187i			1.76372i
$534$	−10.6723	+	15.6842i	−0.461834	+	0.678721i
$535$	9.27475	+	3.37573i	0.400983	+	0.145946i
$536$	−19.3363	−	25.3822i	−0.835200	−	1.09634i
$537$	−0.860847	−	4.88211i	−0.0371483	−	0.210678i
$538$	−14.0285	+	10.1053i	−0.604813	+	0.435672i
$539$	−5.17505	−	2.98781i	−0.222905	−	0.128694i
$540$	−1.52373	−	0.826165i	−0.0655710	−	0.0355525i
$541$	19.8725	−	23.6831i	0.854384	−	1.01821i	−0.145201	−	0.989402i	$-0.546383\pi$
$541$	19.8725	−	23.6831i	0.854384	−	1.01821i	0.999585	−	0.0288125i	$-0.00917258\pi$
$542$	14.4594	−	32.1238i	0.621084	−	1.37983i
$543$	7.17276	+	12.4236i	0.307812	+	0.533147i
$544$	−2.25564	+	2.57967i	−0.0967097	+	0.110603i
$545$	9.65481	−	3.51406i	0.413567	−	0.150526i
$546$	−0.649507	+	0.313520i	−0.0277963	+	0.0134174i
$547$	2.00088	+	0.352809i	0.0855514	+	0.0150850i	0.216260	−	0.976336i	$-0.430614\pi$
$547$	2.00088	+	0.352809i	0.0855514	+	0.0150850i	−0.130709	+	0.991421i	$0.541725\pi$
$548$	10.7649	−	2.19671i	0.459854	−	0.0938388i
$549$	−5.82916	−	6.94693i	−0.248783	−	0.296488i
$550$	4.94104	−	1.39508i	0.210687	−	0.0594864i
$551$	3.11884	+	27.9810i	0.132867	+	1.19203i
$552$	−7.24085	+	7.84693i	−0.308191	+	0.333987i
$553$	−0.0388635	+	0.0326103i	−0.00165264	+	0.00138673i
$554$	−16.2651	−	1.20392i	−0.691039	−	0.0511496i
$555$	0.165408	+	0.0291659i	0.00702117	+	0.00123802i
$556$	−1.65825	+	1.46883i	−0.0703255	+	0.0622922i
$557$	−10.5838	−	29.0788i	−0.448451	−	1.23211i	−0.933802	−	0.357790i	$-0.883530\pi$
$557$	−10.5838	−	29.0788i	−0.448451	−	1.23211i	0.485351	−	0.874319i	$-0.338692\pi$
$558$	−13.7654	−	3.49168i	−0.582736	−	0.147814i
$559$	11.0677	+	19.1699i	0.468115	+	0.810799i
$560$	−0.108240	−	0.254168i	−0.00457396	−	0.0107406i
$561$	−0.396498	−	0.332701i	−0.0167402	−	0.0140467i
$562$	−19.8359	+	20.3741i	−0.836728	+	0.859429i
$563$	33.2767	+	19.2123i	1.40245	+	0.809704i	0.994643	−	0.103366i	$-0.0329613\pi$
$563$	33.2767	+	19.2123i	1.40245	+	0.809704i	0.407804	+	0.913069i	$0.366295\pi$
$564$	−5.82518	−	4.62799i	−0.245284	−	0.194873i
$565$	7.54168	−	1.32980i	0.317281	−	0.0559452i
$566$	3.50745	+	34.7305i	0.147429	+	1.45983i
$567$	0.0748851	+	0.0272559i	0.00314488	+	0.00114464i
$568$	1.47109	+	0.0693661i	0.0617256	+	0.00291054i
$569$	−42.4854			−1.78108			−0.890541	−	0.454902i	$-0.849674\pi$
$569$	−42.4854			−1.78108			−0.890541	+	0.454902i	$0.849674\pi$
$570$	0.198268	+	5.33869i	0.00830454	+	0.223613i
$571$			1.39778i			0.0584953i	0.999572	+	0.0292476i	$0.00931114\pi$
$571$			1.39778i			0.0584953i	−0.999572	+	0.0292476i	$0.990689\pi$
$572$	3.46391	−	10.3727i	0.144833	−	0.433706i
$573$	0.317676	−	0.872807i	0.0132711	−	0.0364620i
$574$	0.713466	−	0.0720533i	0.0297795	−	0.00300745i
$575$	2.78525	+	15.7959i	0.116153	+	0.658736i
$576$	3.33033	+	7.27385i	0.138764	+	0.303077i
$577$	−0.383467	+	0.664184i	−0.0159639	+	0.0276503i	−0.873897	−	0.486111i	$-0.838415\pi$
$577$	−0.383467	+	0.664184i	−0.0159639	+	0.0276503i	0.857933	+	0.513761i	$0.171748\pi$
$578$	−16.4090	+	16.8541i	−0.682523	+	0.701040i
$579$	3.55603	−	4.23791i	0.147784	−	0.176122i
$580$	−11.0734	−	1.64830i	−0.459799	−	0.0684420i
$581$	0.0854122	−	0.0493128i	0.00354350	−	0.00204584i
$582$	−1.72308	+	6.79299i	−0.0714240	+	0.281578i
$583$	−8.36768	+	3.04559i	−0.346554	+	0.126135i
$584$	−6.48891	+	10.1077i	−0.268513	+	0.418258i
$585$	−0.963062	+	5.46180i	−0.0398177	+	0.225818i
$586$	−26.7980	−	1.98355i	−1.10702	−	0.0819396i
$587$	17.8491	+	21.2717i	0.736710	+	0.877977i	0.996139	−	0.0877852i	$-0.0279789\pi$
$587$	17.8491	+	21.2717i	0.736710	+	0.877977i	−0.259429	+	0.965762i	$0.583534\pi$
$588$	−7.31533	−	11.9218i	−0.301679	−	0.491649i
$589$	12.3293	+	41.9992i	0.508018	+	1.73055i
$590$	3.49258	+	12.3699i	0.143787	+	0.509261i
$591$	5.88000	−	4.93390i	0.241871	−	0.202954i
$592$	−0.529359	−	0.566337i	−0.0217565	−	0.0232763i
$593$	−3.71341	+	21.0598i	−0.152492	+	0.864823i	0.808552	+	0.588425i	$0.200252\pi$
$593$	−3.71341	+	21.0598i	−0.152492	+	0.864823i	−0.961043	+	0.276398i	$0.910859\pi$
$594$	−1.08821	+	0.525283i	−0.0446498	+	0.0215526i
$595$	0.0143091	+	0.0393138i	0.000586614	+	0.00161171i
$596$	−23.1425	+	0.619572i	−0.947953	+	0.0253787i
$597$	1.26214	−	0.728696i	0.0516559	−	0.0298235i
$598$	31.1538	+	14.0228i	1.27397	+	0.573434i
$599$	−26.2995	−	22.0679i	−1.07457	−	0.901671i	−0.0791106	−	0.996866i	$-0.525208\pi$
$599$	−26.2995	−	22.0679i	−1.07457	−	0.901671i	−0.995459	+	0.0951952i	$0.969652\pi$
$600$	11.7238	+	2.64199i	0.478621	+	0.107859i
$601$	−6.55072	+	11.3462i	−0.267210	+	0.462821i	−0.968140	−	0.250409i	$-0.919435\pi$
$601$	−6.55072	+	11.3462i	−0.267210	+	0.462821i	0.700931	+	0.713230i	$0.252768\pi$
$602$	0.316306	−	0.227848i	0.0128917	−	0.00928641i
$603$	11.1099	−	1.95898i	0.452432	−	0.0797759i
$604$	−4.18827	−	10.6143i	−0.170418	−	0.431890i
$605$	3.04412	−	8.36366i	0.123761	−	0.340031i
$606$	15.1845	+	10.3322i	0.616827	+	0.419718i
$607$	8.98116			0.364534			0.182267	−	0.983249i	$-0.441656\pi$
$607$	8.98116			0.364534			0.182267	+	0.983249i	$0.441656\pi$
$608$	14.0746	−	20.2461i	0.570800	−	0.821089i
$609$	0.514727			0.0208578
$610$	−9.18910	−	6.25269i	−0.372056	−	0.253164i
$611$	−8.14191	+	22.3697i	−0.329386	+	0.904981i
$612$	−0.444691	−	1.12698i	−0.0179756	−	0.0455553i
$613$	12.3457	−	2.17688i	0.498638	−	0.0879234i	0.0813278	−	0.996687i	$-0.474084\pi$
$613$	12.3457	−	2.17688i	0.498638	−	0.0879234i	0.417310	+	0.908764i	$0.362973\pi$
$614$	20.4830	−	14.7547i	0.826625	−	0.595453i
$615$	2.75718	−	4.77557i	0.111180	−	0.192570i
$616$	−0.187879	−	0.0423391i	−0.00756985	−	0.00170589i
$617$	−19.3210	−	16.2122i	−0.777833	−	0.652679i	0.164869	−	0.986315i	$-0.447280\pi$
$617$	−19.3210	−	16.2122i	−0.777833	−	0.652679i	−0.942702	+	0.333636i	$0.891724\pi$
$618$	−0.0711017	−	0.0320039i	−0.00286013	−	0.00128739i
$619$	−30.0838	+	17.3689i	−1.20917	+	0.698114i	−0.962578	−	0.271005i	$-0.912644\pi$
$619$	−30.0838	+	17.3689i	−1.20917	+	0.698114i	−0.246592	+	0.969119i	$0.579311\pi$
$620$	−17.3993	+	0.465815i	−0.698772	+	0.0187076i
$621$	−1.29112	−	3.54733i	−0.0518109	−	0.142349i
$622$	−6.74825	+	3.25741i	−0.270580	+	0.130610i
$623$	0.185631	−	1.05277i	0.00743714	−	0.0421781i
$624$	18.7005	−	17.4795i	0.748621	−	0.699742i
$625$	10.9529	−	9.19054i	0.438115	−	0.367622i
$626$	11.2903	+	39.9874i	0.451250	+	1.59822i
$627$	3.10070	+	2.06321i	0.123830	+	0.0823968i
$628$	10.4046	+	16.9565i	0.415189	+	0.676637i
$629$	0.0754635	+	0.0899340i	0.00300893	+	0.00358590i
$630$	0.0974048	+	0.00720975i	0.00388070	+	0.000287243i
$631$	−3.50313	+	19.8673i	−0.139458	+	0.790903i	0.832194	+	0.554485i	$0.187085\pi$
$631$	−3.50313	+	19.8673i	−0.139458	+	0.790903i	−0.971651	+	0.236418i	$0.924026\pi$
$632$	0.972761	−	1.51525i	0.0386944	−	0.0602735i
$633$	12.1780	−	4.43244i	0.484033	−	0.176174i
$634$	−2.10098	+	8.28280i	−0.0834406	+	0.328952i
$635$	−12.0675	+	6.96720i	−0.478886	+	0.276485i
$636$	−20.6163	−	3.06878i	−0.817490	−	0.121685i
$637$	−28.7682	+	34.2846i	−1.13984	+	1.35841i
$638$	−5.44449	+	5.59220i	−0.215549	+	0.221397i
$639$	−0.260343	+	0.450928i	−0.0102990	+	0.0178384i
$640$	6.35057	+	7.47049i	0.251028	+	0.295297i
$641$	−0.560476	−	3.17862i	−0.0221375	−	0.125548i	0.971736	−	0.236069i	$-0.0758591\pi$
$641$	−0.560476	−	3.17862i	−0.0221375	−	0.125548i	−0.993874	+	0.110521i	$0.964748\pi$
$642$	16.0245	−	1.61833i	0.632438	−	0.0638703i
$643$	−12.5650	+	34.5220i	−0.495514	+	1.36141i	0.400055	+	0.916491i	$0.368991\pi$
$643$	−12.5650	+	34.5220i	−0.495514	+	1.36141i	−0.895569	+	0.444922i	$0.853231\pi$
$644$	0.190577	−	0.570685i	0.00750978	−	0.0224881i
$645$		−	2.99771i		−	0.118035i
$646$	−2.29249	+	2.94768i	−0.0901968	+	0.115975i
$647$	−49.8275			−1.95892			−0.979461	−	0.201636i	$-0.935374\pi$
$647$	−49.8275			−1.95892			−0.979461	+	0.201636i	$0.935374\pi$
$648$	−2.82529	−	0.133220i	−0.110988	−	0.00523339i
$649$	8.42034	+	3.06475i	0.330527	+	0.120302i
$650$	−3.86378	−	38.2589i	−0.151550	−	1.50064i
$651$	0.788089	−	0.138961i	0.0308877	−	0.00544633i
$652$	18.5678	+	14.7518i	0.727172	+	0.577724i
$653$	12.7155	+	7.34130i	0.497596	+	0.287287i	0.727720	−	0.685874i	$-0.240580\pi$
$653$	12.7155	+	7.34130i	0.497596	+	0.287287i	−0.230124	+	0.973161i	$0.573913\pi$
$654$	11.6957	−	12.0130i	0.457337	−	0.469744i
$655$	14.5843	+	12.2377i	0.569855	+	0.478165i
$656$	−23.4165	+	9.97210i	−0.914261	+	0.389345i
$657$	−2.12331	−	3.67769i	−0.0828383	−	0.143480i
$658$	0.406365	+	0.103077i	0.0158418	+	0.00401836i
$659$	−1.81168	−	4.97755i	−0.0705731	−	0.193898i	0.899392	−	0.437144i	$-0.144010\pi$
$659$	−1.81168	−	4.97755i	−0.0705731	−	0.193898i	−0.969965	+	0.243246i	$0.921788\pi$
$660$	−1.10862	+	0.981983i	−0.0431530	+	0.0382237i
$661$	25.6644	+	4.52532i	0.998228	+	0.176015i	0.648808	−	0.760952i	$-0.275268\pi$
$661$	25.6644	+	4.52532i	0.998228	+	0.176015i	0.349420	+	0.936966i	$0.386379\pi$
$662$	−15.6429	−	1.15786i	−0.607978	−	0.0450015i
$663$	−2.96964	+	2.49182i	−0.115331	+	0.0967743i
$664$	−2.37386	+	2.57255i	−0.0921234	+	0.0998344i
$665$	−0.133667	−	0.269741i	−0.00518336	−	0.0104601i
$666$	0.263768	−	0.0744736i	0.0102208	−	0.00288580i
$667$	−15.6730	−	18.6783i	−0.606859	−	0.723226i
$668$	−32.0124	+	6.53253i	−1.23860	+	0.252751i
$669$	0.376464	+	0.0663808i	0.0145550	+	0.00256643i
$670$	12.4519	−	6.01058i	0.481059	−	0.232209i
$671$	−7.28122	+	2.65015i	−0.281088	+	0.102308i
$672$	−0.339365	−	0.296737i	−0.0130913	−	0.0114469i
$673$	−19.5272	−	33.8221i	−0.752719	−	1.30375i	−0.946501	−	0.322702i	$-0.895409\pi$
$673$	−19.5272	−	33.8221i	−0.752719	−	1.30375i	0.193782	−	0.981045i	$-0.437925\pi$
$674$	−4.89314	+	10.8709i	−0.188477	+	0.418730i
$675$	−2.73115	+	3.25486i	−0.105122	+	0.125280i
$676$	−49.1464	−	26.6470i	−1.89025	−	1.02489i
$677$	20.9589	+	12.1006i	0.805517	+	0.465065i	0.845397	−	0.534139i	$-0.179364\pi$
$677$	20.9589	+	12.1006i	0.805517	+	0.465065i	−0.0398797	+	0.999204i	$0.512697\pi$
$678$	10.1397	−	7.30406i	0.389413	−	0.280511i
$679$	−0.0685750	−	0.388908i	−0.00263167	−	0.0149249i
$680$	−0.899834	−	1.18119i	−0.0345071	−	0.0452965i
$681$	0.283229	+	0.103087i	0.0108533	+	0.00395029i
$682$	−6.82622	+	10.0320i	−0.261390	+	0.384144i
$683$		−	24.5420i		−	0.939073i	−0.882913	−	0.469537i	$-0.844421\pi$
$683$		−	24.5420i		−	0.939073i	0.882913	−	0.469537i	$-0.155579\pi$
$684$	4.07846	+	7.70494i	0.155944	+	0.294606i
$685$			4.76082i			0.181901i
$686$	1.30386	+	0.887210i	0.0497817	+	0.0338738i
$687$	−4.82841	−	1.75740i	−0.184215	−	0.0670489i
$688$	−8.31368	+	11.0596i	−0.316956	+	0.421642i
$689$	11.5811	+	65.6800i	0.441207	+	2.50221i
$690$	−2.70426	−	3.75413i	−0.102949	−	0.142917i
$691$	−35.4405	−	20.4616i	−1.34822	−	0.778395i	−0.360223	−	0.932866i	$-0.617299\pi$
$691$	−35.4405	−	20.4616i	−1.34822	−	0.778395i	−0.987997	+	0.154471i	$0.950633\pi$
$692$	10.8014	−	19.9215i	0.410607	−	0.757302i
$693$	0.0437680	−	0.0521607i	0.00166261	−	0.00198142i
$694$	−1.17300	−	0.527983i	−0.0445263	−	0.0200420i
$695$	−0.479956	−	0.831308i	−0.0182058	−	0.0315333i
$696$	−17.4424	+	5.43282i	−0.661153	+	0.205931i
$697$	3.62197	−	1.31829i	0.137192	−	0.0499338i
$698$	−5.67945	−	11.7659i	−0.214970	−	0.445346i
$699$	19.2309	+	3.39093i	0.727380	+	0.128257i
$700$	−0.663528	+	0.135401i	−0.0250790	+	0.00511768i
$701$	−1.73020	−	2.06197i	−0.0653488	−	0.0778797i	0.732380	−	0.680896i	$-0.238410\pi$
$701$	−1.73020	−	2.06197i	−0.0653488	−	0.0778797i	−0.797728	+	0.603017i	$0.793965\pi$
$702$	2.45913	+	8.70966i	0.0928140	+	0.328725i
$703$	−0.611354	−	0.582997i	−0.0230576	−	0.0219881i
$704$	6.81347	−	0.548280i	0.256792	−	0.0206641i
$705$	2.46961	−	2.07225i	0.0930111	−	0.0780455i
$706$	1.27866	−	17.2748i	0.0481228	−	0.650147i
$707$	−1.01922	−	0.179716i	−0.0383318	−	0.00675893i
$708$	13.9074	+	15.7009i	0.522672	+	0.590077i
$709$	0.531132	+	1.45927i	0.0199471	+	0.0548041i	0.949267	−	0.314473i	$-0.101828\pi$
$709$	0.531132	+	1.45927i	0.0199471	+	0.0548041i	−0.929319	+	0.369277i	$0.879605\pi$
$710$	−0.156906	+	0.618577i	−0.00588857	+	0.0232148i
$711$	0.318309	+	0.551327i	0.0119375	+	0.0206764i
$712$	4.82126	+	37.6340i	0.180684	+	1.41039i
$713$	−29.0391	−	24.3667i	−1.08752	−	0.912542i
$714$	0.0489161	+	0.0476240i	0.00183064	+	0.00178229i
$715$	4.10388	+	2.36938i	0.153476	+	0.0886096i
$716$	−7.76305	−	6.16759i	−0.290119	−	0.230494i
$717$	−20.0648	+	3.53796i	−0.749333	+	0.132128i
$718$	−38.0801	+	3.84573i	−1.42114	+	0.143521i
$719$	−9.59825	−	3.49348i	−0.357954	−	0.130285i	0.156782	−	0.987633i	$-0.449888\pi$
$719$	−9.59825	−	3.49348i	−0.357954	−	0.130285i	−0.514736	+	0.857349i	$0.672110\pi$
$720$	−3.37683	+	0.783769i	−0.125847	+	0.0292094i
$721$	0.00439375			0.000163632
$722$	14.0448	−	22.9073i	0.522693	−	0.852521i
$723$		−	16.7447i		−	0.622744i
$724$	27.2137	+	9.08786i	1.01139	+	0.337748i
$725$	−9.38639	+	25.7889i	−0.348602	+	0.957775i
$726$	−1.45935	−	14.4504i	−0.0541616	−	0.536304i
$727$	0.134279	+	0.761535i	0.00498014	+	0.0282438i	0.987197	−	0.159508i	$-0.0509909\pi$
$727$	0.134279	+	0.761535i	0.00498014	+	0.0282438i	−0.982216	+	0.187752i	$0.939880\pi$
$728$	−0.556636	+	1.33070i	−0.0206303	+	0.0493192i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−3.72925	−	3.63075i	−0.138026	−	0.134380i
$731$	1.34686	−	1.60512i	0.0498153	−	0.0593676i
$732$	−17.9395	−	2.67033i	−0.663062	−	0.0986983i
$733$	−3.19062	+	1.84211i	−0.117848	+	0.0680397i	−0.557765	−	0.829999i	$-0.688341\pi$
$733$	−3.19062	+	1.84211i	−0.117848	+	0.0680397i	0.439917	+	0.898038i	$0.355008\pi$
$734$	42.9624	+	10.8977i	1.58577	+	0.402240i
$735$	5.69550	−	2.07299i	0.210082	−	0.0764635i
$736$	−0.434584	+	21.3501i	−0.0160190	+	0.786976i
$737$	1.67383	−	9.49274i	0.0616562	−	0.349670i
$738$	0.664233	−	8.97389i	0.0244507	−	0.330333i
$739$	3.98056	+	4.74385i	0.146427	+	0.174505i	0.834273	−	0.551352i	$-0.185888\pi$
$739$	3.98056	+	4.74385i	0.146427	+	0.174505i	−0.687846	+	0.725857i	$0.741443\pi$
$740$	0.286315	−	0.175685i	0.0105252	−	0.00645831i
$741$	19.2507	−	20.1870i	0.707190	−	0.741588i
$742$	1.13034	−	0.319146i	0.0414961	−	0.0117162i
$743$	−38.8102	+	32.5656i	−1.42381	+	1.19472i	−0.474547	+	0.880230i	$0.657388\pi$
$743$	−38.8102	+	32.5656i	−1.42381	+	1.19472i	−0.949262	+	0.314488i	$0.898167\pi$
$744$	−25.2390	+	13.0270i	−0.925308	+	0.477594i
$745$	1.74200	−	9.87938i	0.0638220	−	0.361952i
$746$	−21.1337	−	43.7819i	−0.773760	−	1.60297i
$747$	−0.423284	−	1.16296i	−0.0154871	−	0.0425506i
$748$	−1.03481	+	0.0277041i	−0.0378365	+	0.00101296i
$749$	−0.785985	+	0.453788i	−0.0287193	+	0.0165811i
$750$	−4.65276	+	10.3368i	−0.169895	+	0.377448i
$751$	4.60784	+	3.86644i	0.168142	+	0.141088i	0.722976	−	0.690873i	$-0.242774\pi$
$751$	4.60784	+	3.86644i	0.168142	+	0.141088i	−0.554834	+	0.831961i	$0.687218\pi$
$752$	−14.8583	+	0.796147i	−0.541828	+	0.0290325i
$753$	−11.7383	+	20.3314i	−0.427769	+	0.740917i
$754$	34.1664	+	47.4309i	1.24427	+	1.72733i
$755$	4.86943	−	0.858612i	0.177217	−	0.0312481i
$756$	0.148258	−	0.0585006i	0.00539208	−	0.00212765i
$757$	5.33299	−	14.6523i	0.193831	−	0.532545i	−0.804262	−	0.594275i	$-0.797439\pi$
$757$	5.33299	−	14.6523i	0.193831	−	0.532545i	0.998093	+	0.0617291i	$0.0196615\pi$
$758$	2.99425	−	4.40042i	0.108756	−	0.159830i
$759$	−3.22549			−0.117078
$760$	7.37657	+	7.72982i	0.267576	+	0.280390i
$761$	14.6867			0.532393			0.266197	−	0.963919i	$-0.414233\pi$
$761$	14.6867			0.532393			0.266197	+	0.963919i	$0.414233\pi$
$762$	−12.7918	+	18.7991i	−0.463398	+	0.681020i
$763$	−0.323130	+	0.887791i	−0.0116981	+	0.0321402i
$764$	−0.681841	−	1.72798i	−0.0246681	−	0.0625163i
$765$	0.517013	−	0.0911633i	0.0186926	−	0.00329602i
$766$	20.1352	+	27.9523i	0.727515	+	1.00996i
$767$	33.5564	−	58.1215i	1.21165	−	2.09864i
$768$	14.6319	+	6.47352i	0.527984	+	0.233593i
$769$	22.5902	+	18.9554i	0.814623	+	0.683550i	0.951706	−	0.307010i	$-0.0993284\pi$
$769$	22.5902	+	18.9554i	0.814623	+	0.683550i	−0.137084	+	0.990559i	$0.543773\pi$
$770$	0.0342538	−	0.0761001i	0.00123442	−	0.00274246i
$771$	−8.37997	+	4.83818i	−0.301797	+	0.174243i
$772$	−0.296111	−	11.0604i	−0.0106573	−	0.398074i
$773$	12.5561	+	34.4977i	0.451613	+	1.24080i	0.931589	+	0.363514i	$0.118423\pi$
$773$	12.5561	+	34.4977i	0.451613	+	1.24080i	−0.479976	+	0.877281i	$0.659355\pi$
$774$	−2.12647	−	4.40534i	−0.0764345	−	0.158347i
$775$	−7.40907	+	42.0189i	−0.266142	+	1.50936i
$776$	6.42861	+	12.4550i	0.230774	+	0.447109i
$777$	−0.0118311	+	0.00992749i	−0.000424439	+	0.000356147i
$778$	27.6496	−	7.80674i	0.991287	−	0.279885i
$779$	−24.8512	+	12.3147i	−0.890386	+	0.441219i
$780$	5.80115	+	9.45418i	0.207715	+	0.338514i
$781$	0.285972	+	0.340808i	0.0102329	+	0.0121951i
$782$	0.238721	−	3.22516i	0.00853665	−	0.115331i
$783$	1.12160	−	6.36091i	0.0400827	−	0.227320i
$784$	−26.7618	−	8.14764i	−0.955779	−	0.290987i
$785$	−8.10072	+	2.94842i	−0.289127	+	0.105234i
$786$	30.1136	+	7.63849i	1.07412	+	0.272456i
$787$	−22.2471	+	12.8444i	−0.793024	+	0.457853i	−0.841026	−	0.540995i	$-0.818048\pi$
$787$	−22.2471	+	12.8444i	−0.793024	+	0.457853i	0.0480020	+	0.998847i	$0.484715\pi$
$788$	2.26022	−	15.1843i	0.0805168	−	0.540918i
$789$	8.52096	−	10.1549i	0.303354	−	0.361524i
$790$	0.559057	+	0.544290i	0.0198903	+	0.0193650i
$791$	−0.352090	+	0.609838i	−0.0125189	+	0.0216833i
$792$	−0.932610	+	2.22951i	−0.0331389	+	0.0792223i
$793$	10.0774	+	57.1521i	0.357861	+	2.02953i
$794$	−0.105805	−	1.04767i	−0.00375487	−	0.0371804i
$795$	3.08911	−	8.48727i	0.109560	−	0.301012i
$796$	0.923255	−	2.76470i	0.0327239	−	0.0979921i
$797$		−	39.3711i		−	1.39460i	−0.716781	−	0.697298i	$-0.754385\pi$
$797$		−	39.3711i		−	1.39460i	0.716781	−	0.697298i	$-0.245615\pi$
$798$	−0.387778	−	0.301585i	−0.0137272	−	0.0106760i
$799$	2.25341			0.0797199
$800$	21.0556	−	11.5917i	0.744429	−	0.409827i
$801$	−12.6054	−	4.58799i	−0.445390	−	0.162109i
$802$	41.0993	−	4.15064i	1.45127	−	0.146564i
$803$	−3.57335	+	0.630078i	−0.126101	+	0.0222350i
$804$	14.0352	−	17.6659i	0.494985	−	0.623030i
$805$	0.225786	+	0.130358i	0.00795793	+	0.00459451i
$806$	65.1165	+	63.3966i	2.29363	+	2.23305i
$807$	−9.36515	−	7.85829i	−0.329669	−	0.276625i
$808$	36.4349	−	4.66764i	1.28178	−	0.164207i
$809$	9.37318	+	16.2348i	0.329544	+	0.570786i	0.982421	−	0.186677i	$-0.0597718\pi$
$809$	9.37318	+	16.2348i	0.329544	+	0.570786i	−0.652878	+	0.757463i	$0.726438\pi$
$810$	0.301344	−	1.18800i	0.0105881	−	0.0417421i
$811$	−0.334643	−	0.919425i	−0.0117509	−	0.0322854i	0.933678	−	0.358112i	$-0.116580\pi$
$811$	−0.334643	−	0.919425i	−0.0117509	−	0.0322854i	−0.945429	+	0.325827i	$0.894357\pi$
$812$	0.770617	−	0.682589i	0.0270433	−	0.0239542i
$813$	24.5315	+	4.32557i	0.860358	+	0.151704i
$814$	0.0172866	−	0.233545i	0.000605896	−	0.00818575i
$815$	−7.87192	+	6.60533i	−0.275741	+	0.231375i
$816$	−2.16027	−	1.09752i	−0.0756244	−	0.0384210i
$817$	−8.35239	+	12.5524i	−0.292213	+	0.439152i
$818$	−13.4527	−	47.6463i	−0.470363	−	1.66591i
$819$	−0.327807	−	0.390666i	−0.0114545	−	0.0136510i
$820$	−2.20510	−	10.8060i	−0.0770054	−	0.377362i
$821$	23.6551	+	4.17104i	0.825570	+	0.145570i	0.570443	−	0.821337i	$-0.306772\pi$
$821$	23.6551	+	4.17104i	0.825570	+	0.145570i	0.255127	+	0.966908i	$0.417883\pi$
$822$	3.37717	+	6.99636i	0.117792	+	0.244026i
$823$	−12.9369	+	4.70866i	−0.450953	+	0.164134i	−0.557505	−	0.830174i	$-0.688241\pi$
$823$	−12.9369	+	4.70866i	−0.450953	+	0.164134i	0.106552	+	0.994307i	$0.466019\pi$
$824$	−0.148890	+	0.0463750i	−0.00518682	+	0.00161555i
$825$	1.81522	+	3.14405i	0.0631977	+	0.109462i
$826$	−1.07777	−	0.485122i	−0.0375005	−	0.0168795i
$827$	−21.4855	+	25.6055i	−0.747126	+	0.890390i	−0.996961	−	0.0778986i	$-0.975179\pi$
$827$	−21.4855	+	25.6055i	−0.747126	+	0.890390i	0.249836	+	0.968288i	$0.419623\pi$
$828$	−6.63715	−	3.59865i	−0.230657	−	0.125062i
$829$	−33.2032	−	19.1699i	−1.15319	−	0.665797i	−0.203531	−	0.979069i	$-0.565242\pi$
$829$	−33.2032	−	19.1699i	−1.15319	−	0.665797i	−0.949664	+	0.313271i	$0.898575\pi$
$830$	−0.886569	−	1.23076i	−0.0307733	−	0.0427204i
$831$	−2.00262	−	11.3574i	−0.0694703	−	0.393985i
$832$	4.81732	−	50.9683i	0.167010	−	1.76701i
$833$	3.98104	+	1.44898i	0.137935	+	0.0502042i
$834$	−1.29503	−	0.881201i	−0.0448433	−	0.0305135i
$835$		−	14.1576i		−	0.489945i
$836$	7.37822	−	1.02298i	0.255181	−	0.0353805i
$837$		−	10.0419i		−	0.347098i
$838$	−25.8150	+	37.9382i	−0.891763	+	1.31055i
$839$	8.46409	+	3.08068i	0.292213	+	0.106357i	0.483967	−	0.875086i	$-0.339195\pi$
$839$	8.46409	+	3.08068i	0.292213	+	0.106357i	−0.191754	+	0.981443i	$0.561418\pi$
$840$	0.155389	−	0.118376i	0.00536143	−	0.00408437i
$841$	−2.20866	−	12.5260i	−0.0761608	−	0.431930i
$842$	0.926855	−	0.667652i	0.0319415	−	0.0230088i
$843$	−17.4130	−	10.0534i	−0.599736	−	0.346257i
$844$	12.3542	−	22.7855i	0.425250	−	0.784308i
$845$	15.5717	−	18.5576i	0.535682	−	0.638400i
$846$	2.15928	−	4.79719i	0.0742377	−	0.164931i
$847$	0.409211	+	0.708774i	0.0140607	+	0.0243538i
$848$	−34.9350	+	22.7453i	−1.19967	+	0.781075i
$849$	−23.1945	+	8.44211i	−0.796033	+	0.289732i
$850$	−3.27808	+	1.58234i	−0.112437	+	0.0542738i
$851$	0.720492	+	0.127042i	0.0246981	+	0.00435495i
$852$	0.208214	+	1.02035i	0.00713330	+	0.0349565i
$853$	−1.08057	−	1.28778i	−0.0369981	−	0.0440927i	0.747228	−	0.664568i	$-0.231384\pi$
$853$	−1.08057	−	1.28778i	−0.0369981	−	0.0440927i	−0.784226	+	0.620475i	$0.786940\pi$
$854$	0.983576	−	0.277708i	0.0336573	−	0.00950297i
$855$	−3.62467	+	1.06406i	−0.123961	+	0.0363900i
$856$	21.8448	−	23.6733i	0.746640	−	0.809136i
$857$	−40.0143	+	33.5760i	−1.36686	+	1.14693i	−0.393065	+	0.919511i	$0.628585\pi$
$857$	−40.0143	+	33.5760i	−1.36686	+	1.14693i	−0.973796	+	0.227422i	$0.926970\pi$
$858$	7.71170	+	0.570807i	0.263273	+	0.0194870i
$859$	5.03590	+	0.887965i	0.171823	+	0.0302970i	0.258898	−	0.965905i	$-0.416641\pi$
$859$	5.03590	+	0.887965i	0.171823	+	0.0302970i	−0.0870748	+	0.996202i	$0.527752\pi$
$860$	−3.97531	−	4.48797i	−0.135557	−	0.153039i
$861$	0.173426	+	0.476483i	0.00591033	+	0.0162385i
$862$	15.9626	+	4.04900i	0.543687	+	0.137909i
$863$	−13.6811	−	23.6964i	−0.465710	−	0.806634i	0.533523	−	0.845785i	$-0.320868\pi$
$863$	−13.6811	−	23.6964i	−0.465710	−	0.806634i	−0.999233	+	0.0391518i	$0.987534\pi$
$864$	−4.40650	+	3.54721i	−0.149912	+	0.120679i
$865$	7.52233	+	6.31198i	0.255767	+	0.214614i
$866$	28.1128	−	28.8755i	0.955311	−	0.981229i
$867$	−14.4046	−	8.31652i	−0.489207	−	0.282444i
$868$	0.995597	−	1.25314i	0.0337928	−	0.0425344i
$869$	0.535685	−	0.0944557i	0.0181719	−	0.00320419i
$870$	−0.795431	−	7.87629i	−0.0269676	−	0.267031i
$871$	−67.8403	−	24.6919i	−2.29868	−	0.836652i
$872$	1.57938	−	33.4949i	0.0534845	−	1.13428i
$873$	−4.95549			−0.167718
$874$	0.863626	+	23.2545i	0.0292126	+	0.786597i
$875$		−	0.638768i		−	0.0215943i
$876$	−8.05593	−	2.69023i	−0.272185	−	0.0908945i
$877$	7.22846	−	19.8600i	0.244088	−	0.670626i	−0.755787	−	0.654817i	$-0.772746\pi$
$877$	7.22846	−	19.8600i	0.244088	−	0.670626i	0.999875	−	0.0158084i	$-0.00503219\pi$
$878$	−30.2343	+	3.05338i	−1.02036	+	0.103047i
$879$	−3.29947	−	18.7122i	−0.111288	−	0.631148i
$880$	−0.357530	+	2.94032i	−0.0120523	+	0.0991183i
$881$	11.3816	−	19.7135i	0.383456	−	0.664165i	−0.608098	−	0.793862i	$-0.708067\pi$
$881$	11.3816	−	19.7135i	0.383456	−	0.664165i	0.991554	+	0.129697i	$0.0414005\pi$
$882$	6.89943	−	7.08662i	0.232316	−	0.238619i
$883$	18.5752	−	22.1370i	0.625105	−	0.744971i	−0.356834	−	0.934168i	$-0.616144\pi$
$883$	18.5752	−	22.1370i	0.625105	−	0.744971i	0.981939	+	0.189197i	$0.0605884\pi$
$884$	−1.14150	+	7.66867i	−0.0383928	+	0.257925i
$885$	−7.87113	+	4.54440i	−0.264585	+	0.152758i
$886$	5.66200	−	22.3216i	0.190219	−	0.749909i
$887$	32.3773	−	11.7844i	1.08712	−	0.395680i	0.264568	−	0.964367i	$-0.414771\pi$
$887$	32.3773	−	11.7844i	1.08712	−	0.395680i	0.822554	+	0.568687i	$0.192548\pi$
$888$	0.296135	−	0.461284i	0.00993765	−	0.0154797i
$889$	0.222498	−	1.26185i	0.00746233	−	0.0423210i
$890$	−16.3961	−	1.21362i	−0.549600	−	0.0406805i
$891$	−0.549221	−	0.654536i	−0.0183996	−	0.0219278i
$892$	0.651647	−	0.399855i	0.0218187	−	0.0133881i
$893$	−16.1149	+	1.79621i	−0.539265	+	0.0601080i
$894$	−4.44811	−	15.7542i	−0.148767	−	0.526898i
$895$	3.29119	−	2.76163i	0.110012	−	0.0923112i
$896$	−0.901583	+	0.00578227i	−0.0301198	+	0.000193172i
$897$	−4.19495	+	23.7908i	−0.140065	+	0.794351i
$898$	0.0479599	−	0.0231504i	0.00160044	−	0.000772540i
$899$	−22.1837	−	60.9492i	−0.739868	−	2.03277i
$900$	0.227423	+	8.49480i	0.00758078	+	0.283160i
$901$	5.46736	−	3.15658i	0.182144	−	0.105161i
$902$	−7.01109	−	3.15580i	−0.233444	−	0.105077i
$903$	0.211159	+	0.177184i	0.00702694	+	0.00589630i
$904$	5.49448	−	24.3816i	0.182744	−	0.810921i
$905$	−6.21625	+	10.7669i	−0.206635	+	0.357903i
$906$	6.54690	−	4.71600i	0.217506	−	0.156679i
$907$	−20.3307	+	3.58486i	−0.675071	+	0.119033i	−0.500666	−	0.865641i	$-0.666911\pi$
$907$	−20.3307	+	3.58486i	−0.675071	+	0.119033i	−0.174405	+	0.984674i	$0.555800\pi$
$908$	0.560736	−	0.221259i	0.0186087	−	0.00734275i
$909$	−4.44180	+	12.2038i	−0.147325	+	0.404773i
$910$	−0.516756	−	0.351625i	−0.0171303	−	0.0116563i
$911$	52.1946			1.72928			0.864642	−	0.502388i	$-0.167545\pi$
$911$	52.1946			1.72928			0.864642	+	0.502388i	$0.167545\pi$
$912$	16.3237	+	6.12682i	0.540531	+	0.202879i
$913$	−1.05745			−0.0349965
$914$	41.4134	+	28.1796i	1.36983	+	0.932100i
$915$	2.68802	−	7.38528i	0.0888633	−	0.244150i
$916$	−9.55929	+	3.77198i	−0.315848	+	0.124630i
$917$	−1.72405	+	0.303996i	−0.0569331	+	0.0100388i
$918$	0.695119	−	0.500723i	0.0229423	−	0.0165263i
$919$	−11.8587	+	20.5399i	−0.391183	+	0.677549i	−0.992606	−	0.121382i	$-0.961267\pi$
$919$	−11.8587	+	20.5399i	−0.391183	+	0.677549i	0.601423	+	0.798931i	$0.294601\pi$
$920$	−9.02705	−	2.03428i	−0.297613	−	0.0670682i
$921$	13.6740	+	11.4738i	0.450573	+	0.378076i
$922$	19.1962	+	8.64048i	0.632192	+	0.284559i
$923$	2.88569	−	1.66605i	0.0949835	−	0.0548388i
$924$	−0.00364456	−	0.136133i	−0.000119897	−	0.00447845i
$925$	−0.281639	−	0.773797i	−0.00926023	−	0.0254423i
$926$	28.0526	−	13.5411i	0.921865	−	0.444988i
$927$	0.00957407	−	0.0542972i	0.000314454	−	0.00178335i
$928$	−18.9091	+	31.2644i	−0.620721	+	1.02630i
$929$	−26.1364	+	21.9310i	−0.857506	+	0.719533i	−0.961429	−	0.275052i	$-0.911305\pi$
$929$	−26.1364	+	21.9310i	−0.857506	+	0.719533i	0.103923	+	0.994585i	$0.466860\pi$
$930$	−3.34424	−	11.8445i	−0.109662	−	0.388396i
$931$	−29.6249	−	7.18885i	−0.970915	−	0.235605i
$932$	33.2881	−	20.4258i	1.09039	−	0.669068i
$933$	−3.40585	−	4.05893i	−0.111503	−	0.132884i
$934$	28.1051	+	2.08030i	0.919628	+	0.0680693i
$935$	0.0778933	−	0.441755i	0.00254738	−	0.0144469i
$936$	15.2317	+	9.77844i	0.497863	+	0.319618i
$937$	17.7233	−	6.45076i	0.578996	−	0.210737i	−0.0358868	−	0.999356i	$-0.511426\pi$
$937$	17.7233	−	6.45076i	0.578996	−	0.210737i	0.614883	+	0.788619i	$0.289203\pi$
$938$	−0.312600	+	1.23238i	−0.0102068	+	0.0402386i
$939$	−25.4445	+	14.6904i	−0.830351	+	0.479403i
$940$	0.949296	−	6.37744i	0.0309626	−	0.208009i
$941$	14.4066	−	17.1691i	0.469641	−	0.559697i	−0.478278	−	0.878209i	$-0.658739\pi$
$941$	14.4066	−	17.1691i	0.469641	−	0.559697i	0.947919	+	0.318512i	$0.103183\pi$
$942$	−9.81307	+	10.0793i	−0.319727	+	0.328401i
$943$	12.0098	−	20.8017i	0.391094	−	0.677395i
$944$	41.6425	+	5.06355i	1.35535	+	0.164804i
$945$	0.0119928	+	0.0680148i	0.000390127	+	0.00221252i
$946$	−4.15851	+	0.419970i	−0.135205	+	0.0136544i
$947$	17.1531	−	47.1278i	0.557401	−	1.53145i	−0.265992	−	0.963975i	$-0.585699\pi$
$947$	17.1531	−	47.1278i	0.557401	−	1.53145i	0.823393	−	0.567472i	$-0.192078\pi$
$948$	1.20767	+	0.403296i	0.0392234	+	0.0130984i
$949$			27.1760i			0.882171i
$950$	22.1814	−	13.9289i	0.719659	−	0.451912i
$951$	−6.04230			−0.195935
$952$	0.136389	+	0.00643113i	0.00442040	+	0.000208434i
$953$	43.3830	+	15.7901i	1.40531	+	0.511492i	0.929750	−	0.368191i	$-0.120023\pi$
$953$	43.3830	+	15.7901i	1.40531	+	0.511492i	0.475562	+	0.879682i	$0.342245\pi$
$954$	−1.48092	−	14.6640i	−0.0479466	−	0.474763i
$955$	0.792732	−	0.139780i	0.0256522	−	0.00452317i
$956$	−25.3479	+	31.9051i	−0.819811	+	1.03188i
$957$	−4.77945	−	2.75942i	−0.154498	−	0.0891994i
$958$	23.3076	−	23.9400i	0.753036	−	0.773466i
$959$	−0.335353	−	0.281395i	−0.0108291	−	0.00908671i
$960$	−4.01619	+	5.65148i	−0.129622	+	0.182401i
$961$	−34.9196	−	60.4825i	−1.12644	−	1.95105i
$962$	−1.70012	−	0.431244i	−0.0548139	−	0.0139039i
$963$	3.89516	+	10.7019i	0.125520	+	0.344863i
$964$	−22.2055	−	25.0691i	−0.715191	−	0.807423i
$965$	4.72163	+	0.832551i	0.151995	+	0.0268008i
$966$	0.424281	+	0.0314046i	0.0136510	+	0.00101043i
$967$	−10.8934	+	9.14064i	−0.350308	+	0.293943i	−0.800914	−	0.598780i	$-0.795652\pi$
$967$	−10.8934	+	9.14064i	−0.350308	+	0.293943i	0.450606	+	0.892723i	$0.351208\pi$
$968$	−21.3477	−	19.6989i	−0.686143	−	0.633147i
$969$	−2.41891	−	1.05880i	−0.0777065	−	0.0340136i
$970$	−5.84505	+	1.65032i	−0.187673	+	0.0529887i
$971$	−11.3741	−	13.5551i	−0.365011	−	0.435003i	0.552013	−	0.833836i	$-0.313860\pi$
$971$	−11.3741	−	13.5551i	−0.365011	−	0.435003i	−0.917024	+	0.398832i	$0.869416\pi$
$972$	−0.399884	−	1.95962i	−0.0128263	−	0.0628547i
$973$	0.0869260	+	0.0153274i	0.00278672	+	0.000491374i
$974$	46.4038	−	22.3993i	1.48688	−	0.717720i
$975$	25.5509	−	9.29977i	0.818284	−	0.297831i
$976$	−30.3990	+	19.7920i	−0.973048	+	0.633527i
$977$	2.96540	+	5.13622i	0.0948715	+	0.164322i	0.909555	−	0.415584i	$-0.136423\pi$
$977$	2.96540	+	5.13622i	0.0948715	+	0.164322i	−0.814683	+	0.579906i	$0.803089\pi$
$978$	−6.88274	+	15.2911i	−0.220086	+	0.488955i
$979$	−7.36746	+	8.78020i	−0.235465	+	0.280616i
$980$	5.77791	−	10.6565i	0.184568	−	0.340408i
$981$	10.2671	+	5.92769i	0.327802	+	0.189257i
$982$	−25.6640	+	18.4869i	−0.818971	+	0.589939i
$983$	−5.57583	−	31.6221i	−0.177841	−	1.00859i	−0.934813	−	0.355141i	$-0.884433\pi$
$983$	−5.57583	−	31.6221i	−0.177841	−	1.00859i	0.756972	−	0.653448i	$-0.226678\pi$
$984$	−10.9060	−	14.3160i	−0.347670	−	0.456377i
$985$	6.25103	+	2.27519i	0.199174	+	0.0724935i
$986$	3.11287	−	4.57475i	0.0991341	−	0.145690i
$987$			0.296444i			0.00943590i
$988$	2.05049	−	55.7513i	0.0652349	−	1.77369i
$989$		−	13.0576i		−	0.415206i
$990$	−0.865793	−	0.589126i	−0.0275167	−	0.0187237i
$991$	32.9890	+	12.0070i	1.04793	+	0.381415i	0.807881	−	0.589345i	$-0.200614\pi$
$991$	32.9890	+	12.0070i	1.04793	+	0.381415i	0.240049	+	0.970761i	$0.422836\pi$
$992$	−20.5109	+	52.9732i	−0.651221	+	1.68190i
$993$	−1.92601	−	10.9229i	−0.0611200	−	0.346629i
$994$	−0.0342986	−	0.0476143i	−0.00108789	−	0.00151023i
$995$	1.09383	+	0.631522i	0.0346767	+	0.0200206i
$996$	−2.17594	−	1.17979i	−0.0689472	−	0.0373830i
$997$	35.6614	−	42.4996i	1.12941	−	1.34598i	0.198767	−	0.980047i	$-0.436306\pi$
$997$	35.6614	−	42.4996i	1.12941	−	1.34598i	0.930642	−	0.365930i	$-0.119249\pi$
$998$	−13.8789	−	6.24711i	−0.439329	−	0.197749i
$999$	0.0969019	+	0.167839i	0.00306584	+	0.00531019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.34	yes	240
8.5	even	2	inner	456.2.bk.a.253.15	✓	240
19.16	even	9	inner	456.2.bk.a.301.15	yes	240
152.149	even	18	inner	456.2.bk.a.301.34	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.15	✓	240	8.5	even	2	inner
456.2.bk.a.253.34	yes	240	1.1	even	1	trivial
456.2.bk.a.301.15	yes	240	19.16	even	9	inner
456.2.bk.a.301.34	yes	240	152.149	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16921 + 0.795584i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(0.734092 + 1.86041i) q^{4} +(-0.853481 + 0.150492i) q^{5} +(-1.14750 + 0.826590i) q^{6} +(0.0398455 - 0.0690145i) q^{7} +(-0.621803 + 2.75923i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(1.16921 + 0.795584i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(0.734092 + 1.86041i) q^{4} +(-0.853481 + 0.150492i) q^{5} +(-1.14750 + 0.826590i) q^{6} +(0.0398455 - 0.0690145i) q^{7} +(-0.621803 + 2.75923i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-1.11763 - 0.503060i) q^{10} +(-0.739964 + 0.427218i) q^{11} +(-1.99928 + 0.0535249i) q^{12} +(2.18874 + 6.01350i) q^{13} +(0.101494 - 0.0489918i) q^{14} +(0.150492 - 0.853481i) q^{15} +(-2.92222 + 2.73142i) q^{16} +(0.464046 - 0.389381i) q^{17} +(-0.384273 - 1.36100i) q^{18} +(-3.00818 + 3.15450i) q^{19} +(-0.906510 - 1.47735i) q^{20} +(0.0512244 + 0.0610469i) q^{21} +(-1.20506 - 0.0891965i) q^{22} +(0.655519 - 3.71764i) q^{23} +(-2.38016 - 1.52802i) q^{24} +(-3.99268 + 1.45322i) q^{25} +(-2.22516 + 8.77236i) q^{26} +(0.866025 - 0.500000i) q^{27} +(0.157645 + 0.0234658i) q^{28} +(4.15179 - 4.94791i) q^{29} +(0.854972 - 0.878168i) q^{30} +(5.02093 - 8.69651i) q^{31} +(-5.58975 + 0.868726i) q^{32} +(-0.148371 - 0.841456i) q^{33} +(0.852352 - 0.0860795i) q^{34} +(-0.0236213 + 0.0648990i) q^{35} +(0.633498 - 1.89702i) q^{36} +0.193804i q^{37} +(-6.02685 + 1.29500i) q^{38} -6.39944 q^{39} +(0.115455 - 2.44853i) q^{40} +(5.97913 + 2.17623i) q^{41} +(0.0113240 + 0.112130i) q^{42} +(3.40642 - 0.600643i) q^{43} +(-1.33800 - 1.06301i) q^{44} +(0.750539 + 0.433324i) q^{45} +(3.72413 - 3.82517i) q^{46} +(2.84962 + 2.39111i) q^{47} +(-1.56724 - 3.68019i) q^{48} +(3.49682 + 6.05668i) q^{49} +(-5.82443 - 1.47740i) q^{50} +(0.207185 + 0.569237i) q^{51} +(-9.58082 + 8.48640i) q^{52} +(10.2634 + 1.80971i) q^{53} +(1.41036 + 0.104392i) q^{54} +(0.567252 - 0.475981i) q^{55} +(0.165651 + 0.152856i) q^{56} +(-1.93540 - 3.90567i) q^{57} +(8.79078 - 2.48204i) q^{58} +(-6.74111 - 8.03375i) q^{59} +(1.69830 - 0.346558i) q^{60} +(8.93080 + 1.57474i) q^{61} +(12.7893 - 6.17345i) q^{62} +(-0.0748851 + 0.0272559i) q^{63} +(-7.22672 - 3.43140i) q^{64} +(-2.77303 - 4.80302i) q^{65} +(0.495972 - 1.10188i) q^{66} +(-7.25150 + 8.64200i) q^{67} +(1.06506 + 0.577473i) q^{68} +(3.26923 + 1.88749i) q^{69} +(-0.0792508 + 0.0570876i) q^{70} +(-0.0904163 - 0.512777i) q^{71} +(2.24993 - 1.71401i) q^{72} +(3.99052 + 1.45243i) q^{73} +(-0.154187 + 0.226597i) q^{74} -4.24892i q^{75} +(-8.07693 - 3.28074i) q^{76} +0.0680909i q^{77} +(-7.48227 - 5.09129i) q^{78} +(-0.598224 - 0.217736i) q^{79} +(2.08300 - 2.77098i) q^{80} +(0.173648 + 0.984808i) q^{81} +(5.25947 + 7.30136i) q^{82} +(1.07179 + 0.618800i) q^{83} +(-0.0759685 + 0.140112i) q^{84} +(-0.337456 + 0.402165i) q^{85} +(4.46067 + 2.00781i) q^{86} +(3.22952 + 5.59369i) q^{87} +(-0.718683 - 2.30738i) q^{88} +(12.6054 - 4.58799i) q^{89} +(0.532790 + 1.10376i) q^{90} +(0.502230 + 0.0885567i) q^{91} +(7.39752 - 1.50956i) q^{92} +(6.45479 + 7.69252i) q^{93} +(1.42946 + 5.06282i) q^{94} +(2.09270 - 3.14501i) q^{95} +(1.09547 - 5.54977i) q^{96} +(3.79612 - 3.18533i) q^{97} +(-0.730082 + 9.86353i) q^{98} +(0.841456 + 0.148371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6}+O(q^{10}) \) 240 * q + 6 * q^4 + 6 * q^6	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48} - 120 q^{49} + 18 q^{50} + 6 q^{52} - 6 q^{54} + 72 q^{58} - 12 q^{60} + 12 q^{62} + 30 q^{64} - 48 q^{66} - 78 q^{68} - 108 q^{70} - 36 q^{72} - 24 q^{73} - 96 q^{74} - 48 q^{76} - 96 q^{78} - 114 q^{80} - 66 q^{82} - 36 q^{84} - 24 q^{86} - 24 q^{88} + 6 q^{90} - 108 q^{94} + 120 q^{95} - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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