LMFDB - Embedded newform 666.2.bs.a.431.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			431.2
Character	$\chi$	$=$	666.431
Dual form			666.2.bs.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-0.718088 - 0.0628246i) q^{5} +(-2.07081 + 1.73762i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-0.718088 - 0.0628246i) q^{5} +(-2.07081 + 1.73762i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.360415 + 0.624258i) q^{10} +(2.14666 - 3.71813i) q^{11} +(0.0350998 - 0.0163673i) q^{13} +(2.61114 + 0.699652i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(-1.26227 - 0.588607i) q^{17} +(-1.15999 - 0.812232i) q^{19} +(0.304636 - 0.653295i) q^{20} +(-4.27699 + 0.374188i) q^{22} +(1.21793 - 4.54537i) q^{23} +(-4.41234 - 0.778014i) q^{25} +(-0.0335397 - 0.0193642i) q^{26} +(-0.924566 - 2.54022i) q^{28} +(-2.18568 - 8.15709i) q^{29} +(-3.19999 - 3.19999i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(0.241851 + 1.37160i) q^{34} +(1.59619 - 1.11766i) q^{35} +(6.02223 - 0.856003i) q^{37} +1.41608i q^{38} +(-0.709880 + 0.125171i) q^{40} +(-8.42883 - 3.06784i) q^{41} +(-0.673546 + 0.673546i) q^{43} +(2.75969 + 3.28888i) q^{44} +(-4.42192 + 1.60945i) q^{46} +(2.04440 - 1.18033i) q^{47} +(0.0534066 - 0.302884i) q^{49} +(1.89350 + 4.06062i) q^{50} +(0.00337540 + 0.0385810i) q^{52} +(-0.385452 + 0.459364i) q^{53} +(-1.77508 + 2.53508i) q^{55} +(-1.55052 + 2.21437i) q^{56} +(-5.42824 + 6.46912i) q^{58} +(0.273822 + 3.12980i) q^{59} +(-4.73693 - 10.1584i) q^{61} +(-0.785839 + 4.45671i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-0.0262330 + 0.00954803i) q^{65} +(5.48130 + 6.53235i) q^{67} +(0.984832 - 0.984832i) q^{68} +(-1.83107 - 0.666456i) q^{70} +(0.759603 - 0.133939i) q^{71} -9.36628i q^{73} +(-4.15541 - 4.44214i) q^{74} +(1.15999 - 0.812232i) q^{76} +(2.01535 + 11.4296i) q^{77} +(-0.124024 + 1.41760i) q^{79} +(0.509704 + 0.509704i) q^{80} +(2.32155 + 8.66414i) q^{82} +(-2.84370 - 7.81299i) q^{83} +(0.869443 + 0.501973i) q^{85} +(0.938067 + 0.165407i) q^{86} +(1.11119 - 4.14703i) q^{88} +(-10.6799 + 0.934373i) q^{89} +(-0.0442449 + 0.0948835i) q^{91} +(3.85469 + 2.69909i) q^{92} +(-2.13949 - 0.997660i) q^{94} +(0.781945 + 0.656130i) q^{95} +(-2.87161 - 0.769446i) q^{97} +(-0.278741 + 0.129979i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{29}{36}\right)$

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 $

$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	−0.718088	−	0.0628246i	−0.321139	−	0.0280960i	−0.0745532	−	0.997217i	$-0.523753\pi$
$5$	−0.718088	−	0.0628246i	−0.321139	−	0.0280960i	−0.246586	+	0.969121i	$0.579309\pi$
$6$		0			0
$7$	−2.07081	+	1.73762i	−0.782692	+	0.656757i	−0.943925	−	0.330160i	$-0.892897\pi$
$7$	−2.07081	+	1.73762i	−0.782692	+	0.656757i	0.161233	+	0.986916i	$0.448453\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$		0			0
$10$	0.360415	+	0.624258i	0.113973	+	0.197408i
$11$	2.14666	−	3.71813i	0.647243	−	1.12106i	−0.336536	−	0.941671i	$-0.609255\pi$
$11$	2.14666	−	3.71813i	0.647243	−	1.12106i	0.983779	−	0.179387i	$-0.0574113\pi$
$12$		0			0
$13$	0.0350998	−	0.0163673i	0.00973493	−	0.00453947i	−0.417745	−	0.908564i	$-0.637179\pi$
$13$	0.0350998	−	0.0163673i	0.00973493	−	0.00453947i	0.427480	+	0.904025i	$0.359402\pi$
$14$	2.61114	+	0.699652i	0.697856	+	0.186990i
$15$		0			0
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−1.26227	−	0.588607i	−0.306146	−	0.142758i	0.263474	−	0.964667i	$-0.415132\pi$
$17$	−1.26227	−	0.588607i	−0.306146	−	0.142758i	−0.569620	+	0.821908i	$0.692910\pi$
$18$		0			0
$19$	−1.15999	−	0.812232i	−0.266119	−	0.186339i	0.432899	−	0.901442i	$-0.357491\pi$
$19$	−1.15999	−	0.812232i	−0.266119	−	0.186339i	−0.699018	+	0.715104i	$0.746380\pi$
$20$	0.304636	−	0.653295i	0.0681188	−	0.146081i
$21$		0			0
$22$	−4.27699	+	0.374188i	−0.911856	+	0.0797771i
$23$	1.21793	−	4.54537i	0.253955	−	0.947775i	−0.714713	−	0.699418i	$-0.753443\pi$
$23$	1.21793	−	4.54537i	0.253955	−	0.947775i	0.968669	−	0.248357i	$-0.0798906\pi$
$24$		0			0
$25$	−4.41234	−	0.778014i	−0.882467	−	0.155603i
$26$	−0.0335397	−	0.0193642i	−0.00657768	−	0.00379763i
$27$		0			0
$28$	−0.924566	−	2.54022i	−0.174726	−	0.480057i
$29$	−2.18568	−	8.15709i	−0.405871	−	1.51473i	−0.802443	−	0.596729i	$-0.796467\pi$
$29$	−2.18568	−	8.15709i	−0.405871	−	1.51473i	0.396571	−	0.918004i	$-0.370200\pi$
$30$		0			0
$31$	−3.19999	−	3.19999i	−0.574735	−	0.574735i	0.358713	−	0.933448i	$-0.383216\pi$
$31$	−3.19999	−	3.19999i	−0.574735	−	0.574735i	−0.933448	+	0.358713i	$0.883216\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$		0			0
$34$	0.241851	+	1.37160i	0.0414771	+	0.235228i
$35$	1.59619	−	1.11766i	0.269805	−	0.188920i
$36$		0			0
$37$	6.02223	−	0.856003i	0.990049	−	0.140726i
$37$	6.02223	−	0.856003i	0.990049	−	0.140726i
$38$			1.41608i			0.229719i
$39$		0			0
$40$	−0.709880	+	0.125171i	−0.112242	+	0.0197913i
$41$	−8.42883	−	3.06784i	−1.31636	−	0.479117i	−0.414071	−	0.910244i	$-0.635894\pi$
$41$	−8.42883	−	3.06784i	−1.31636	−	0.479117i	−0.902291	+	0.431128i	$0.858116\pi$
$42$		0			0
$43$	−0.673546	+	0.673546i	−0.102715	+	0.102715i	−0.756597	−	0.653882i	$-0.773139\pi$
$43$	−0.673546	+	0.673546i	−0.102715	+	0.102715i	0.653882	+	0.756597i	$0.273139\pi$
$44$	2.75969	+	3.28888i	0.416040	+	0.495817i
$45$		0			0
$46$	−4.42192	+	1.60945i	−0.651977	+	0.237300i
$47$	2.04440	−	1.18033i	0.298206	−	0.172169i	−0.343431	−	0.939178i	$-0.611589\pi$
$47$	2.04440	−	1.18033i	0.298206	−	0.172169i	0.641637	+	0.767009i	$0.278256\pi$
$48$		0			0
$49$	0.0534066	−	0.302884i	0.00762951	−	0.0432691i
$50$	1.89350	+	4.06062i	0.267781	+	0.574259i
$51$		0			0
$52$	0.00337540	+	0.0385810i	0.000468083	+	0.00535022i
$53$	−0.385452	+	0.459364i	−0.0529459	+	0.0630985i	−0.791867	−	0.610693i	$-0.790891\pi$
$53$	−0.385452	+	0.459364i	−0.0529459	+	0.0630985i	0.738922	+	0.673791i	$0.235335\pi$
$54$		0			0
$55$	−1.77508	+	2.53508i	−0.239352	+	0.341830i
$56$	−1.55052	+	2.21437i	−0.207197	+	0.295908i
$57$		0			0
$58$	−5.42824	+	6.46912i	−0.712762	+	0.849437i
$59$	0.273822	+	3.12980i	0.0356486	+	0.407465i	0.992964	+	0.118419i	$0.0377826\pi$
$59$	0.273822	+	3.12980i	0.0356486	+	0.407465i	−0.957315	+	0.289046i	$0.906662\pi$
$60$		0			0
$61$	−4.73693	−	10.1584i	−0.606501	−	1.30065i	−0.934498	−	0.355967i	$-0.884151\pi$
$61$	−4.73693	−	10.1584i	−0.606501	−	1.30065i	0.327997	−	0.944679i	$-0.393626\pi$
$62$	−0.785839	+	4.45671i	−0.0998016	+	0.566003i
$63$		0			0
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−0.0262330	+	0.00954803i	−0.00325380	+	0.00118429i
$66$		0			0
$67$	5.48130	+	6.53235i	0.669647	+	0.798054i	0.988736	−	0.149671i	$-0.0478213\pi$
$67$	5.48130	+	6.53235i	0.669647	+	0.798054i	−0.319089	+	0.947725i	$0.603377\pi$
$68$	0.984832	−	0.984832i	0.119428	−	0.119428i
$69$		0			0
$70$	−1.83107	−	0.666456i	−0.218855	−	0.0796567i
$71$	0.759603	−	0.133939i	0.0901483	−	0.0158956i	−0.128392	−	0.991723i	$-0.540982\pi$
$71$	0.759603	−	0.133939i	0.0901483	−	0.0158956i	0.218540	+	0.975828i	$0.429870\pi$
$72$		0			0
$73$		−	9.36628i		−	1.09624i	−0.836400	−	0.548120i	$-0.815344\pi$
$73$		−	9.36628i		−	1.09624i	0.836400	−	0.548120i	$-0.184656\pi$
$74$	−4.15541	−	4.44214i	−0.483056	−	0.516388i
$75$		0			0
$76$	1.15999	−	0.812232i	0.133060	−	0.0931694i
$77$	2.01535	+	11.4296i	0.229670	+	1.30252i
$78$		0			0
$79$	−0.124024	+	1.41760i	−0.0139538	+	0.159493i	−0.999975	−	0.00712971i	$-0.997731\pi$
$79$	−0.124024	+	1.41760i	−0.0139538	+	0.159493i	0.986021	+	0.166622i	$0.0532861\pi$
$80$	0.509704	+	0.509704i	0.0569867	+	0.0569867i
$81$		0			0
$82$	2.32155	+	8.66414i	0.256372	+	0.956794i
$83$	−2.84370	−	7.81299i	−0.312136	−	0.857588i	−0.992225	−	0.124458i	$-0.960281\pi$
$83$	−2.84370	−	7.81299i	−0.312136	−	0.857588i	0.680089	−	0.733130i	$-0.261941\pi$
$84$		0			0
$85$	0.869443	+	0.501973i	0.0943044	+	0.0544467i
$86$	0.938067	+	0.165407i	0.101154	+	0.0178362i
$87$		0			0
$88$	1.11119	−	4.14703i	0.118454	−	0.442075i
$89$	−10.6799	+	0.934373i	−1.13207	+	0.0990433i	−0.637755	−	0.770239i	$-0.720137\pi$
$89$	−10.6799	+	0.934373i	−1.13207	+	0.0990433i	−0.494315	+	0.869283i	$0.664581\pi$
$90$		0			0
$91$	−0.0442449	+	0.0948835i	−0.00463813	+	0.00994649i
$92$	3.85469	+	2.69909i	0.401880	+	0.281399i
$93$		0			0
$94$	−2.13949	−	0.997660i	−0.220671	−	0.102901i
$95$	0.781945	+	0.656130i	0.0802258	+	0.0673175i
$96$		0			0
$97$	−2.87161	−	0.769446i	−0.291568	−	0.0781254i	0.110070	−	0.993924i	$-0.464892\pi$
$97$	−2.87161	−	0.769446i	−0.291568	−	0.0781254i	−0.401638	+	0.915798i	$0.631559\pi$
$98$	−0.278741	+	0.129979i	−0.0281570	+	0.0131298i
$99$		0			0
$100$	2.24020	−	3.88014i	0.224020	−	0.388014i
$101$	−3.35666	−	5.81391i	−0.334000	−	0.578505i	0.649292	−	0.760539i	$-0.275065\pi$
$101$	−3.35666	−	5.81391i	−0.334000	−	0.578505i	−0.983292	+	0.182034i	$0.941732\pi$
$102$		0			0
$103$	9.58937	−	2.56946i	0.944869	−	0.253177i	0.246685	−	0.969096i	$-0.420659\pi$
$103$	9.58937	−	2.56946i	0.944869	−	0.253177i	0.698183	+	0.715919i	$0.253992\pi$
$104$	0.0296676	−	0.0248941i	0.00290915	−	0.00244107i
$105$		0			0
$106$	0.597375	+	0.0522635i	0.0580222	+	0.00507628i
$107$	−3.18517	+	8.75119i	−0.307922	+	0.846010i	0.685139	+	0.728412i	$0.259741\pi$
$107$	−3.18517	+	8.75119i	−0.307922	+	0.846010i	−0.993061	+	0.117597i	$0.962481\pi$
$108$		0			0
$109$	5.93207	+	8.47187i	0.568189	+	0.811458i	0.995708	−	0.0925480i	$-0.0295012\pi$
$109$	5.93207	+	8.47187i	0.568189	+	0.811458i	−0.427519	+	0.904006i	$0.640612\pi$
$110$	3.09476			0.295074
$111$		0			0
$112$	2.70325			0.255433
$113$	1.82365	+	2.60444i	0.171554	+	0.245005i	0.895717	−	0.444624i	$-0.146663\pi$
$113$	1.82365	+	2.60444i	0.171554	+	0.245005i	−0.724163	+	0.689629i	$0.757774\pi$
$114$		0			0
$115$	−1.16014	+	3.18746i	−0.108184	+	0.297232i
$116$	8.41270	+	0.736016i	0.781100	+	0.0683374i
$117$		0			0
$118$	2.40672	−	2.01948i	0.221557	−	0.185908i
$119$	3.63670	−	0.974450i	0.333375	−	0.0893277i
$120$		0			0
$121$	−3.71631	−	6.43684i	−0.337846	−	0.585167i
$122$	−5.60426	+	9.70686i	−0.507386	+	0.878818i
$123$		0			0
$124$	4.10147	−	1.91254i	0.368322	−	0.171752i
$125$	6.60091	+	1.76871i	0.590404	+	0.158198i
$126$		0			0
$127$	13.2744	+	11.1386i	1.17792	+	0.988389i	0.999991	+	0.00434519i	$0.00138312\pi$
$127$	13.2744	+	11.1386i	1.17792	+	0.988389i	0.177926	+	0.984044i	$0.443061\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$		0			0
$130$	0.0228679	+	0.0160123i	0.00200565	+	0.00140437i
$131$	−7.18594	+	15.4103i	−0.627838	+	1.34640i	0.292870	+	0.956152i	$0.405390\pi$
$131$	−7.18594	+	15.4103i	−0.627838	+	1.34640i	−0.920708	+	0.390252i	$0.872388\pi$
$132$		0			0
$133$	3.81346	−	0.333634i	0.330669	−	0.0289298i
$134$	2.20705	−	8.23682i	0.190660	−	0.711553i
$135$		0			0
$136$	−1.37160	−	0.241851i	−0.117614	−	0.0207385i
$137$	−7.25301	−	4.18752i	−0.619666	−	0.357764i	0.157073	−	0.987587i	$-0.449794\pi$
$137$	−7.25301	−	4.18752i	−0.619666	−	0.357764i	−0.776739	+	0.629823i	$0.783128\pi$
$138$		0			0
$139$	−2.79536	−	7.68019i	−0.237099	−	0.651425i	−0.999988	−	0.00489532i	$-0.998442\pi$
$139$	−2.79536	−	7.68019i	−0.237099	−	0.651425i	0.762889	−	0.646530i	$-0.223780\pi$
$140$	0.504331	+	1.88219i	0.0426238	+	0.159074i
$141$		0			0
$142$	−0.545406	−	0.545406i	−0.0457695	−	0.0457695i
$143$	0.0144917	−	0.165641i	0.00121185	−	0.0138516i
$144$		0			0
$145$	1.05705	+	5.99482i	0.0877831	+	0.497843i
$146$	−7.67241	+	5.37228i	−0.634973	+	0.444613i
$147$		0			0
$148$	−1.25534	+	5.95182i	−0.103189	+	0.489236i
$149$			10.1731i			0.833417i	0.909040	+	0.416708i	$0.136816\pi$
$149$			10.1731i			0.833417i	−0.909040	+	0.416708i	$0.863184\pi$
$150$		0			0
$151$	16.5269	−	2.91414i	1.34494	−	0.237149i	0.545609	−	0.838040i	$-0.316298\pi$
$151$	16.5269	−	2.91414i	1.34494	−	0.237149i	0.799332	+	0.600890i	$0.205187\pi$
$152$	−1.33068	−	0.484329i	−0.107933	−	0.0392843i
$153$		0			0
$154$	8.20663	−	8.20663i	0.661309	−	0.661309i
$155$	2.09684	+	2.49891i	0.168422	+	0.200717i
$156$		0			0
$157$	22.5615	−	8.21170i	1.80060	−	0.655365i	0.802310	−	0.596907i	$-0.203604\pi$
$157$	22.5615	−	8.21170i	1.80060	−	0.655365i	0.998290	−	0.0584573i	$-0.0186182\pi$
$158$	1.23237	−	0.711508i	0.0980420	−	0.0566046i
$159$		0			0
$160$	0.125171	−	0.709880i	0.00989564	−	0.0561209i
$161$	5.37600	+	11.5289i	0.423689	+	0.908603i
$162$		0			0
$163$	0.660979	+	7.55502i	0.0517718	+	0.591755i	0.977127	+	0.212655i	$0.0682109\pi$
$163$	0.660979	+	7.55502i	0.0517718	+	0.591755i	−0.925356	+	0.379100i	$0.876234\pi$
$164$	5.76566	−	6.87125i	0.450222	−	0.536554i
$165$		0			0
$166$	−4.76895	+	6.81077i	−0.370142	+	0.528618i
$167$	12.3723	−	17.6695i	0.957398	−	1.36731i	0.0274467	−	0.999623i	$-0.491262\pi$
$167$	12.3723	−	17.6695i	0.957398	−	1.36731i	0.929951	−	0.367683i	$-0.119849\pi$
$168$		0			0
$169$	−8.35527	+	9.95743i	−0.642713	+	0.765956i
$170$	−0.0874997	−	1.00013i	−0.00671092	−	0.0767062i
$171$		0			0
$172$	−0.402560	−	0.863293i	−0.0306949	−	0.0658255i
$173$	0.812529	−	4.60808i	0.0617755	−	0.350346i	−0.938215	−	0.346052i	$-0.887522\pi$
$173$	0.812529	−	4.60808i	0.0617755	−	0.350346i	0.999991	−	0.00429404i	$-0.00136684\pi$
$174$		0			0
$175$	10.4890	−	6.05582i	0.792893	−	0.457777i
$176$	−4.03440	+	1.46840i	−0.304105	+	0.110685i
$177$		0			0
$178$	6.89115	+	8.21255i	0.516514	+	0.615557i
$179$	18.2887	−	18.2887i	1.36696	−	1.36696i	0.502225	−	0.864737i	$-0.332515\pi$
$179$	18.2887	−	18.2887i	1.36696	−	1.36696i	0.864737	−	0.502225i	$-0.167485\pi$
$180$		0			0
$181$	−2.37927	−	0.865985i	−0.176850	−	0.0643681i	0.252078	−	0.967707i	$-0.418886\pi$
$181$	−2.37927	−	0.865985i	−0.176850	−	0.0643681i	−0.428928	+	0.903339i	$0.641108\pi$
$182$	0.103102	−	0.0181796i	0.00764242	−	0.00134756i
$183$		0			0
$184$		−	4.70571i		−	0.346910i
$185$	−4.37827	+	0.236342i	−0.321897	+	0.0173762i
$186$		0			0
$187$	−4.89819	+	3.42975i	−0.358191	+	0.250808i
$188$	0.409925	+	2.32480i	0.0298969	+	0.169553i
$189$		0			0
$190$	0.0889648	−	1.01687i	0.00645418	−	0.0737717i
$191$	−0.163885	−	0.163885i	−0.0118583	−	0.0118583i	0.701153	−	0.713011i	$-0.252669\pi$
$191$	−0.163885	−	0.163885i	−0.0118583	−	0.0118583i	−0.713011	+	0.701153i	$0.752669\pi$
$192$		0			0
$193$	−4.08217	−	15.2349i	−0.293841	−	1.09663i	−0.942133	−	0.335239i	$-0.891183\pi$
$193$	−4.08217	−	15.2349i	−0.293841	−	1.09663i	0.648292	−	0.761392i	$-0.275484\pi$
$194$	1.01680	+	2.79362i	0.0730017	+	0.200571i
$195$		0			0
$196$	0.266351	+	0.153778i	0.0190251	+	0.0109841i
$197$	−0.409273	−	0.0721659i	−0.0291595	−	0.00514161i	0.159049	−	0.987271i	$-0.449157\pi$
$197$	−0.409273	−	0.0721659i	−0.0291595	−	0.00514161i	−0.188209	+	0.982129i	$0.560268\pi$
$198$		0			0
$199$	−0.265434	+	0.990613i	−0.0188161	+	0.0702227i	−0.974696	−	0.223537i	$-0.928240\pi$
$199$	−0.265434	+	0.990613i	−0.0188161	+	0.0702227i	0.955879	+	0.293759i	$0.0949064\pi$
$200$	−4.46335	+	0.390493i	−0.315607	+	0.0276120i
$201$		0			0
$202$	−2.83717	+	6.08434i	−0.199623	+	0.428092i
$203$	18.7000	+	13.0939i	1.31248	+	0.919011i
$204$		0			0
$205$	5.85991	+	2.73252i	0.409274	+	0.190847i
$206$	−7.60502	−	6.38137i	−0.529867	−	0.444611i
$207$		0			0
$208$	−0.0374087	−	0.0100236i	−0.00259383	−	0.000695014i
$209$	−5.51008	+	2.56939i	−0.381140	+	0.177729i
$210$		0			0
$211$	−5.73085	+	9.92613i	−0.394528	+	0.683343i	−0.993041	−	0.117771i	$-0.962425\pi$
$211$	−5.73085	+	9.92613i	−0.394528	+	0.683343i	0.598513	+	0.801113i	$0.295759\pi$
$212$	−0.299828	−	0.519318i	−0.0205923	−	0.0356669i
$213$		0			0
$214$	8.99550	−	2.41034i	0.614920	−	0.164767i
$215$	0.525981	−	0.441350i	0.0358716	−	0.0300998i
$216$		0			0
$217$	12.1869	+	1.06622i	0.827301	+	0.0723795i
$218$	3.53726	−	9.71854i	0.239573	−	0.658222i
$219$		0			0
$220$	−1.77508	−	2.53508i	−0.119676	−	0.170915i
$221$	−0.0539394			−0.00362836
$222$		0			0
$223$	−3.10179			−0.207711			−0.103856	−	0.994592i	$-0.533118\pi$
$223$	−3.10179			−0.207711			−0.103856	+	0.994592i	$0.533118\pi$
$224$	−1.55052	−	2.21437i	−0.103598	−	0.147954i
$225$		0			0
$226$	1.08743	−	2.98769i	0.0723348	−	0.198738i
$227$	−4.72486	−	0.413372i	−0.313600	−	0.0274365i	−0.0707307	−	0.997495i	$-0.522533\pi$
$227$	−4.72486	−	0.413372i	−0.313600	−	0.0274365i	−0.242869	+	0.970059i	$0.578089\pi$
$228$		0			0
$229$	−19.3753	+	16.2578i	−1.28035	+	1.07434i	−0.287158	+	0.957883i	$0.592711\pi$
$229$	−19.3753	+	16.2578i	−1.28035	+	1.07434i	−0.993195	+	0.116461i	$0.962845\pi$
$230$	3.27644	−	0.877920i	0.216042	−	0.0578883i
$231$		0			0
$232$	−4.22242	−	7.31344i	−0.277215	−	0.480151i
$233$	−5.20016	+	9.00695i	−0.340674	+	0.590065i	−0.984558	−	0.175058i	$-0.943989\pi$
$233$	−5.20016	+	9.00695i	−0.340674	+	0.590065i	0.643884	+	0.765123i	$0.277322\pi$
$234$		0			0
$235$	−1.54221	+	0.719144i	−0.100603	+	0.0469118i
$236$	−3.03470	−	0.813146i	−0.197542	−	0.0529313i
$237$		0			0
$238$	−2.88415	−	2.42009i	−0.186951	−	0.156871i
$239$	11.3149	+	5.27620i	0.731897	+	0.341289i	0.752584	−	0.658497i	$-0.228807\pi$
$239$	11.3149	+	5.27620i	0.731897	+	0.341289i	−0.0206863	+	0.999786i	$0.506585\pi$
$240$		0			0
$241$	−7.21834	−	5.05434i	−0.464974	−	0.325578i	0.317503	−	0.948257i	$-0.397155\pi$
$241$	−7.21834	−	5.05434i	−0.464974	−	0.325578i	−0.782478	+	0.622679i	$0.786044\pi$
$242$	−3.14116	+	6.73624i	−0.201921	+	0.433022i
$243$		0			0
$244$	11.1659	−	0.976887i	0.714821	−	0.0625388i
$245$	−0.0573792	+	0.214142i	−0.00366582	+	0.0136810i
$246$		0			0
$247$	−0.0540094	−	0.00952331i	−0.00343653	−	0.000605954i
$248$	−3.91917	−	2.26273i	−0.248867	−	0.143684i
$249$		0			0
$250$	−2.33729	−	6.42164i	−0.147823	−	0.406140i
$251$	2.12374	+	7.92590i	0.134049	+	0.500279i	1.00000		0.000149336i	$4.75350e-5\pi$
$251$	2.12374	+	7.92590i	0.134049	+	0.500279i	−0.865951	+	0.500129i	$0.833286\pi$
$252$		0			0
$253$	−14.2858	−	14.2858i	−0.898139	−	0.898139i
$254$	1.51028	−	17.2626i	0.0947636	−	1.08315i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−6.57242	+	4.60206i	−0.409976	+	0.287068i	−0.760315	−	0.649555i	$-0.774955\pi$
$257$	−6.57242	+	4.60206i	−0.409976	+	0.287068i	0.350339	+	0.936623i	$0.386067\pi$
$258$		0			0
$259$	−10.9835	+	12.2369i	−0.682481	+	0.760366i
$260$		−	0.0279166i		−	0.00173131i
$261$		0			0
$262$	16.7451	−	2.95261i	1.03451	−	0.182413i
$263$	−18.2632	−	6.64726i	−1.12616	−	0.409888i	−0.289261	−	0.957250i	$-0.593410\pi$
$263$	−18.2632	−	6.64726i	−1.12616	−	0.409888i	−0.836896	+	0.547363i	$0.815632\pi$
$264$		0			0
$265$	0.305648	−	0.305648i	0.0187758	−	0.0187758i
$266$	−2.46061	−	2.93244i	−0.150870	−	0.179799i
$267$		0			0
$268$	−8.01312	+	2.91654i	−0.489479	+	0.178156i
$269$	−17.0791	+	9.86062i	−1.04133	+	0.601212i	−0.920210	−	0.391425i	$-0.871982\pi$
$269$	−17.0791	+	9.86062i	−1.04133	+	0.601212i	−0.121121	+	0.992638i	$0.538649\pi$
$270$		0			0
$271$	−4.40413	+	24.9771i	−0.267532	+	1.51725i	0.494195	+	0.869351i	$0.335463\pi$
$271$	−4.40413	+	24.9771i	−0.267532	+	1.51725i	−0.761727	+	0.647898i	$0.775648\pi$
$272$	0.588607	+	1.26227i	0.0356895	+	0.0765365i
$273$		0			0
$274$	0.729934	+	8.34318i	0.0440969	+	0.504030i
$275$	−12.3645	+	14.7355i	−0.745610	+	0.888583i
$276$		0			0
$277$	−3.96790	+	5.66675i	−0.238408	+	0.340482i	−0.920471	−	0.390812i	$-0.872194\pi$
$277$	−3.96790	+	5.66675i	−0.238408	+	0.340482i	0.682063	+	0.731294i	$0.261083\pi$
$278$	−4.68789	+	6.69500i	−0.281161	+	0.401540i
$279$		0			0
$280$	1.25253	−	1.49270i	0.0748528	−	0.0892061i
$281$	−0.564702	−	6.45458i	−0.0336873	−	0.385048i	−0.994258	−	0.107011i	$-0.965872\pi$
$281$	−0.564702	−	6.45458i	−0.0336873	−	0.385048i	0.960571	−	0.278037i	$-0.0896836\pi$
$282$		0			0
$283$	−10.1227	−	21.7081i	−0.601729	−	1.29041i	−0.937341	−	0.348413i	$-0.886721\pi$
$283$	−10.1227	−	21.7081i	−0.601729	−	1.29041i	0.335612	−	0.942000i	$-0.391057\pi$
$284$	−0.133939	+	0.759603i	−0.00794779	+	0.0450742i
$285$		0			0
$286$	−0.143997	+	0.0831366i	−0.00851471	+	0.00491597i
$287$	22.7852	−	8.29315i	1.34497	−	0.489529i
$288$		0			0
$289$	−9.68052	−	11.5368i	−0.569442	−	0.678635i
$290$	4.30437	−	4.30437i	0.252761	−	0.252761i
$291$		0			0
$292$	8.80143	+	3.20346i	0.515064	+	0.187468i
$293$	13.7242	−	2.41994i	0.801775	−	0.141375i	0.242278	−	0.970207i	$-0.422105\pi$
$293$	13.7242	−	2.41994i	0.801775	−	0.141375i	0.559497	+	0.828832i	$0.310994\pi$
$294$		0			0
$295$		−	2.26467i		−	0.131854i
$296$	5.59548	−	2.38550i	0.325231	−	0.138655i
$297$		0			0
$298$	8.33335	−	5.83508i	0.482738	−	0.338017i
$299$	−0.0316464	−	0.179476i	−0.00183016	−	0.0103793i
$300$		0			0
$301$	0.224421	−	2.56515i	0.0129354	−	0.147853i
$302$	−11.8666	−	11.8666i	−0.682844	−	0.682844i
$303$		0			0
$304$	0.366509	+	1.36783i	0.0210207	+	0.0784505i
$305$	2.76333	+	7.59220i	0.158228	+	0.434728i
$306$		0			0
$307$	14.6235	+	8.44288i	0.834607	+	0.481860i	0.855427	−	0.517923i	$-0.173295\pi$
$307$	14.6235	+	8.44288i	0.834607	+	0.481860i	−0.0208206	+	0.999783i	$0.506628\pi$
$308$	−11.4296	−	2.01535i	−0.651262	−	0.114835i
$309$		0			0
$310$	0.844293	−	3.15094i	0.0479526	−	0.178962i
$311$	8.86433	−	0.775528i	0.502650	−	0.0439762i	0.166988	−	0.985959i	$-0.446596\pi$
$311$	8.86433	−	0.775528i	0.502650	−	0.0439762i	0.335662	+	0.941983i	$0.391040\pi$
$312$		0			0
$313$	−8.21984	+	17.6275i	−0.464613	+	0.996365i	0.524799	+	0.851226i	$0.324141\pi$
$313$	−8.21984	+	17.6275i	−0.464613	+	0.996365i	−0.989411	+	0.145139i	$0.953637\pi$
$314$	−19.6673	−	13.7712i	−1.10989	−	0.777155i
$315$		0			0
$316$	−1.28969	−	0.601393i	−0.0725508	−	0.0338310i
$317$	−17.2721	−	14.4930i	−0.970100	−	0.814011i	0.0124662	−	0.999922i	$-0.496032\pi$
$317$	−17.2721	−	14.4930i	−0.970100	−	0.814011i	−0.982566	+	0.185912i	$0.940476\pi$
$318$		0			0
$319$	−35.0210	−	9.38385i	−1.96080	−	0.525395i
$320$	−0.653295	+	0.304636i	−0.0365203	+	0.0170297i
$321$		0			0
$322$	6.36036	−	11.0165i	0.354449	−	0.613923i
$323$	0.986134	+	1.70803i	0.0548700	+	0.0950376i
$324$		0			0
$325$	−0.167606	+	0.0449099i	−0.00929711	+	0.00249115i
$326$	5.80959	−	4.87482i	0.321763	−	0.269992i
$327$		0			0
$328$	−8.93564	−	0.781767i	−0.493388	−	0.0431659i
$329$	−2.18259	+	5.99661i	−0.120330	+	0.330604i
$330$		0			0
$331$	−4.31602	−	6.16391i	−0.237230	−	0.338799i	0.682830	−	0.730577i	$-0.260749\pi$
$331$	−4.31602	−	6.16391i	−0.237230	−	0.338799i	−0.920060	+	0.391778i	$0.871860\pi$
$332$	8.31441			0.456313
$333$		0			0
$334$	−21.5705			−1.18028
$335$	−3.52566	−	5.03517i	−0.192627	−	0.275100i
$336$		0			0
$337$	−3.76826	+	10.3532i	−0.205270	+	0.563976i	−0.999020	−	0.0442695i	$-0.985904\pi$
$337$	−3.76826	+	10.3532i	−0.205270	+	0.563976i	0.793749	+	0.608245i	$0.208126\pi$
$338$	12.9490	+	1.13289i	0.704335	+	0.0616213i
$339$		0			0
$340$	−0.769068	+	0.645324i	−0.0417086	+	0.0349976i
$341$	−18.7672	+	5.02867i	−1.01630	+	0.272318i
$342$		0			0
$343$	−9.04567	−	15.6676i	−0.488420	−	0.845969i
$344$	−0.476269	+	0.824922i	−0.0256787	+	0.0444768i
$345$		0			0
$346$	−4.24077	+	1.97750i	−0.227985	+	0.106311i
$347$	19.7758	+	5.29892i	1.06162	+	0.284461i	0.747047	−	0.664772i	$-0.231471\pi$
$347$	19.7758	+	5.29892i	1.06162	+	0.284461i	0.314576	+	0.949232i	$0.398138\pi$
$348$		0			0
$349$	−20.4583	−	17.1665i	−1.09511	−	0.918903i	−0.0980196	−	0.995184i	$-0.531251\pi$
$349$	−20.4583	−	17.1665i	−1.09511	−	0.918903i	−0.997086	+	0.0762816i	$0.975695\pi$
$350$	−10.9769	−	5.11860i	−0.586739	−	0.273601i
$351$		0			0
$352$	3.51688	+	2.46255i	0.187451	+	0.131254i
$353$	1.23427	−	2.64689i	0.0656933	−	0.140880i	−0.870720	−	0.491780i	$-0.836347\pi$
$353$	1.23427	−	2.64689i	0.0656933	−	0.140880i	0.936413	+	0.350900i	$0.114124\pi$
$354$		0			0
$355$	−0.553877	+	0.0484579i	−0.0293967	+	0.00257188i
$356$	2.77473	−	10.3554i	0.147060	−	0.548837i
$357$		0			0
$358$	−25.4712	−	4.49126i	−1.34619	−	0.237370i
$359$	26.8112	+	15.4795i	1.41504	+	0.816975i	0.995858	−	0.0909267i	$-0.0289829\pi$
$359$	26.8112	+	15.4795i	1.41504	+	0.816975i	0.419184	+	0.907901i	$0.362316\pi$
$360$		0			0
$361$	−5.81253	−	15.9698i	−0.305923	−	0.840516i
$362$	0.655322	+	2.44570i	0.0344430	+	0.128543i
$363$		0			0
$364$	−0.0740287	−	0.0740287i	−0.00388016	−	0.00388016i
$365$	−0.588433	+	6.72581i	−0.0308000	+	0.352045i
$366$		0			0
$367$	1.71660	+	9.73534i	0.0896059	+	0.508180i	0.996267	+	0.0863214i	$0.0275112\pi$
$367$	1.71660	+	9.73534i	0.0896059	+	0.508180i	−0.906661	+	0.421859i	$0.861378\pi$
$368$	−3.85469	+	2.69909i	−0.200940	+	0.140700i
$369$		0			0
$370$	2.70487	+	3.45091i	0.140620	+	0.179404i
$371$		−	1.62102i		−	0.0841592i
$372$		0			0
$373$	3.04917	−	0.537652i	0.157880	−	0.0278386i	−0.0941493	−	0.995558i	$-0.530013\pi$
$373$	3.04917	−	0.537652i	0.157880	−	0.0278386i	0.252030	+	0.967720i	$0.418902\pi$
$374$	5.61897	+	2.04514i	0.290550	+	0.105752i
$375$		0			0
$376$	1.66924	−	1.66924i	0.0860846	−	0.0860846i
$377$	−0.210227	−	0.250538i	−0.0108272	−	0.0129034i
$378$		0			0
$379$	−25.9424	+	9.44226i	−1.33257	+	0.485016i	−0.907465	−	0.420127i	$-0.861985\pi$
$379$	−25.9424	+	9.44226i	−1.33257	+	0.485016i	−0.425106	+	0.905144i	$0.639763\pi$
$380$	−0.884001	+	0.510378i	−0.0453483	+	0.0261819i
$381$		0			0
$382$	−0.0402462	+	0.228247i	−0.00205917	+	0.0116782i
$383$	−4.97953	−	10.6786i	−0.254442	−	0.545653i	0.737047	−	0.675841i	$-0.236219\pi$
$383$	−4.97953	−	10.6786i	−0.254442	−	0.545653i	−0.991489	+	0.130189i	$0.958442\pi$
$384$		0			0
$385$	−0.729137	−	8.33407i	−0.0371603	−	0.424744i
$386$	−10.1382	+	12.0823i	−0.516023	+	0.614972i
$387$		0			0
$388$	1.70519	−	2.43527i	0.0865680	−	0.123632i
$389$	13.8852	−	19.8301i	0.704006	−	1.00543i	−0.294750	−	0.955574i	$-0.595236\pi$
$389$	13.8852	−	19.8301i	0.704006	−	1.00543i	0.998757	−	0.0498511i	$-0.0158747\pi$
$390$		0			0
$391$	−4.21279	+	5.02061i	−0.213050	+	0.253903i
$392$	−0.0268053	−	0.306386i	−0.00135387	−	0.0154748i
$393$		0			0
$394$	0.175635	+	0.376650i	0.00884835	+	0.0189753i
$395$	0.178120	−	1.01017i	0.00896221	−	0.0508272i
$396$		0			0
$397$	−12.1780	+	7.03099i	−0.611198	+	0.352875i	−0.773434	−	0.633877i	$-0.781463\pi$
$397$	−12.1780	+	7.03099i	−0.611198	+	0.352875i	0.162236	+	0.986752i	$0.448129\pi$
$398$	0.963709	−	0.350761i	0.0483064	−	0.0175821i
$399$		0			0
$400$	2.87995	+	3.43219i	0.143997	+	0.171609i
$401$	12.7350	−	12.7350i	0.635955	−	0.635955i	−0.313600	−	0.949555i	$-0.601535\pi$
$401$	12.7350	−	12.7350i	0.635955	−	0.635955i	0.949555	+	0.313600i	$0.101535\pi$
$402$		0			0
$403$	−0.164694	−	0.0599437i	−0.00820400	−	0.00298601i
$404$	6.61133	−	1.16576i	0.328926	−	0.0579985i
$405$		0			0
$406$		−	22.8285i		−	1.13296i
$407$	9.74496	−	24.2290i	0.483040	−	1.20099i
$408$		0			0
$409$	19.7209	−	13.8087i	0.975135	−	0.682797i	0.0266586	−	0.999645i	$-0.491513\pi$
$409$	19.7209	−	13.8087i	0.975135	−	0.682797i	0.948476	+	0.316848i	$0.102624\pi$
$410$	−1.12276	−	6.36746i	−0.0554489	−	0.314467i
$411$		0			0
$412$	−0.865251	+	9.88987i	−0.0426279	+	0.487239i
$413$	−6.00542	−	6.00542i	−0.295507	−	0.295507i
$414$		0			0
$415$	1.55118	+	5.78907i	0.0761443	+	0.284174i
$416$	0.0132459	+	0.0363927i	0.000649432	+	0.00178430i
$417$		0			0
$418$	5.26518	+	3.03985i	0.257528	+	0.148684i
$419$	−4.19000	−	0.738811i	−0.204695	−	0.0360933i	0.0703603	−	0.997522i	$-0.477585\pi$
$419$	−4.19000	−	0.738811i	−0.204695	−	0.0360933i	−0.275055	+	0.961428i	$0.588696\pi$
$420$		0			0
$421$	2.60289	−	9.71413i	0.126857	−	0.473438i	−0.873042	−	0.487645i	$-0.837856\pi$
$421$	2.60289	−	9.71413i	0.126857	−	0.473438i	0.999899	+	0.0142075i	$0.00452255\pi$
$422$	11.4181	−	0.998953i	0.555824	−	0.0486283i
$423$		0			0
$424$	−0.253426	+	0.543474i	−0.0123074	+	0.0263934i
$425$	5.11162	+	3.57920i	0.247950	+	0.173617i
$426$		0			0
$427$	27.4606	+	12.8051i	1.32891	+	0.619682i
$428$	−7.13404	−	5.98617i	−0.344837	−	0.289352i
$429$		0			0
$430$	−0.663223	−	0.177710i	−0.0319835	−	0.00856994i
$431$	−10.0279	+	4.67606i	−0.483025	+	0.225238i	−0.648849	−	0.760917i	$-0.724749\pi$
$431$	−10.0279	+	4.67606i	−0.483025	+	0.225238i	0.165824	+	0.986155i	$0.446972\pi$
$432$		0			0
$433$	−8.87524	+	15.3724i	−0.426517	+	0.738748i	−0.996561	−	0.0828656i	$-0.973593\pi$
$433$	−8.87524	+	15.3724i	−0.426517	+	0.738748i	0.570044	+	0.821614i	$0.306926\pi$
$434$	−6.11673	−	10.5945i	−0.293613	−	0.508552i
$435$		0			0
$436$	−9.98985	+	2.67677i	−0.478427	+	0.128194i
$437$	−5.10467	+	4.28333i	−0.244190	+	0.204899i
$438$		0			0
$439$	10.2965	+	0.900824i	0.491424	+	0.0429940i	0.330175	−	0.943920i	$-0.392892\pi$
$439$	10.2965	+	0.900824i	0.491424	+	0.0429940i	0.161249	+	0.986914i	$0.448448\pi$
$440$	−1.05847	+	2.90812i	−0.0504606	+	0.138639i
$441$		0			0
$442$	0.0309384	+	0.0441846i	0.00147159	+	0.00210165i
$443$	19.7759			0.939580			0.469790	−	0.882778i	$-0.344330\pi$
$443$	19.7759			0.939580			0.469790	+	0.882778i	$0.344330\pi$
$444$		0			0
$445$	7.72783			0.366334
$446$	1.77911	+	2.54084i	0.0842434	+	0.120312i
$447$		0			0
$448$	−0.924566	+	2.54022i	−0.0436816	+	0.120014i
$449$	−17.1146	−	1.49733i	−0.807686	−	0.0706633i	−0.324170	−	0.945999i	$-0.605085\pi$
$449$	−17.1146	−	1.49733i	−0.807686	−	0.0706633i	−0.483516	+	0.875336i	$0.660640\pi$
$450$		0			0
$451$	−29.5005	+	24.7538i	−1.38912	+	1.16561i
$452$	−3.07110	+	0.822898i	−0.144452	+	0.0387058i
$453$		0			0
$454$	2.37146	+	4.10748i	0.111298	+	0.192774i
$455$	0.0377327	−	0.0653550i	0.00176894	−	0.00306389i
$456$		0			0
$457$	36.0382	−	16.8049i	1.68579	−	0.786099i	0.687597	−	0.726093i	$-0.258666\pi$
$457$	36.0382	−	16.8049i	1.68579	−	0.786099i	0.998198	−	0.0600060i	$-0.0191120\pi$
$458$	24.4308	+	6.54621i	1.14158	+	0.305884i
$459$		0			0
$460$	−2.59844	−	2.18035i	−0.121153	−	0.101659i
$461$	−37.4798	−	17.4771i	−1.74561	−	0.813991i	−0.986650	−	0.162853i	$-0.947930\pi$
$461$	−37.4798	−	17.4771i	−1.74561	−	0.813991i	−0.758959	−	0.651138i	$-0.774292\pi$
$462$		0			0
$463$	31.8270	+	22.2855i	1.47913	+	1.03570i	0.986188	+	0.165632i	$0.0529665\pi$
$463$	31.8270	+	22.2855i	1.47913	+	1.03570i	0.492939	+	0.870064i	$0.335922\pi$
$464$	−3.56894	+	7.65362i	−0.165684	+	0.355310i
$465$		0			0
$466$	10.3608	−	0.906448i	0.479953	−	0.0419904i
$467$	−5.38963	+	20.1144i	−0.249403	+	0.930783i	0.721717	+	0.692188i	$0.243353\pi$
$467$	−5.38963	+	20.1144i	−0.249403	+	0.930783i	−0.971119	+	0.238594i	$0.923313\pi$
$468$		0			0
$469$	−22.7014	−	4.00288i	−1.04825	−	0.184836i
$470$	1.47366	+	0.850820i	0.0679750	+	0.0392454i
$471$		0			0
$472$	1.07454	+	2.95228i	0.0494599	+	0.135890i
$473$	1.05845	+	3.95021i	0.0486678	+	0.181631i
$474$		0			0
$475$	4.48633	+	4.48633i	0.205847	+	0.205847i
$476$	−0.328140	+	3.75066i	−0.0150403	+	0.171911i
$477$		0			0
$478$	−2.16792	−	12.2949i	−0.0991584	−	0.562355i
$479$	16.4408	−	11.5120i	0.751201	−	0.525996i	−0.134127	−	0.990964i	$-0.542823\pi$
$479$	16.4408	−	11.5120i	0.751201	−	0.525996i	0.885328	+	0.464968i	$0.153934\pi$
$480$		0			0
$481$	0.197369	−	0.128613i	0.00899923	−	0.00586426i
$482$			8.81197i			0.401374i
$483$		0			0
$484$	7.31970	−	1.29066i	0.332714	−	0.0586664i
$485$	2.01373	+	0.732938i	0.0914388	+	0.0332810i
$486$		0			0
$487$	10.4440	−	10.4440i	0.473261	−	0.473261i	−0.429708	−	0.902968i	$-0.641383\pi$
$487$	10.4440	−	10.4440i	0.473261	−	0.473261i	0.902968	+	0.429708i	$0.141383\pi$
$488$	−7.20470	−	8.58622i	−0.326141	−	0.388680i
$489$		0			0
$490$	0.208326	−	0.0758245i	0.00941121	−	0.00342540i
$491$	−19.9822	+	11.5367i	−0.901785	+	0.520646i	−0.877779	−	0.479066i	$-0.840976\pi$
$491$	−19.9822	+	11.5367i	−0.901785	+	0.520646i	−0.0240064	+	0.999712i	$0.507642\pi$
$492$		0			0
$493$	−2.04239	+	11.5830i	−0.0919846	+	0.521671i
$494$	0.0231775	+	0.0497042i	0.00104280	+	0.00223630i
$495$		0			0
$496$	0.394420	+	4.50825i	0.0177100	+	0.202426i
$497$	−1.34026	+	1.59726i	−0.0601189	+	0.0716469i
$498$		0			0
$499$	9.48381	−	13.5443i	0.424554	−	0.606326i	−0.548711	−	0.836012i	$-0.684881\pi$
$499$	9.48381	−	13.5443i	0.424554	−	0.606326i	0.973265	+	0.229687i	$0.0737701\pi$
$500$	−3.91969	+	5.59790i	−0.175294	+	0.250345i
$501$		0			0
$502$	5.27439	−	6.28578i	0.235408	−	0.280548i
$503$	−3.72021	−	42.5222i	−0.165876	−	1.89597i	−0.389086	−	0.921201i	$-0.627209\pi$
$503$	−3.72021	−	42.5222i	−0.165876	−	1.89597i	0.223210	−	0.974770i	$-0.428346\pi$
$504$		0			0
$505$	2.04512	+	4.38578i	0.0910067	+	0.195165i
$506$	−3.50824	+	19.8962i	−0.155960	+	0.884494i
$507$		0			0
$508$	−15.0070	+	8.66428i	−0.665827	+	0.384415i
$509$	18.5564	−	6.75400i	0.822500	−	0.299366i	0.103723	−	0.994606i	$-0.466924\pi$
$509$	18.5564	−	6.75400i	0.822500	−	0.299366i	0.718777	+	0.695241i	$0.244702\pi$
$510$		0			0
$511$	16.2750	+	19.3958i	0.719963	+	0.858019i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	7.53957	+	2.74418i	0.332556	+	0.121041i
$515$	−7.04744	+	1.24265i	−0.310547	+	0.0547578i
$516$		0			0
$517$		−	10.1351i		−	0.445741i
$518$	16.3238	+	1.97833i	0.717226	+	0.0869226i
$519$		0			0
$520$	−0.0228679	+	0.0160123i	−0.00100283	+	0.000702186i
$521$	4.14458	+	23.5051i	0.181577	+	1.02978i	0.930275	+	0.366864i	$0.119569\pi$
$521$	4.14458	+	23.5051i	0.181577	+	1.02978i	−0.748697	+	0.662912i	$0.769320\pi$
$522$		0			0
$523$	−2.11764	+	24.2048i	−0.0925981	+	1.05840i	0.797709	+	0.603042i	$0.206045\pi$
$523$	−2.11764	+	24.2048i	−0.0925981	+	1.05840i	−0.890308	+	0.455360i	$0.849511\pi$
$524$	−12.0232	−	12.0232i	−0.525236	−	0.525236i
$525$		0			0
$526$	5.03022	+	18.7730i	0.219328	+	0.818544i
$527$	2.15572	+	5.92279i	0.0939046	+	0.258001i
$528$		0			0
$529$	0.741561	+	0.428140i	0.0322418	+	0.0186148i
$530$	−0.425684	−	0.0750596i	−0.0184905	−	0.00326038i
$531$		0			0
$532$	−0.990766	+	3.69759i	−0.0429551	+	0.160311i
$533$	−0.346063	+	0.0302766i	−0.0149896	+	0.00131142i
$534$		0			0
$535$	2.83703	−	6.08402i	0.122655	−	0.263035i
$536$	6.98522	+	4.89111i	0.301716	+	0.211264i
$537$		0			0
$538$	17.8735	+	8.33455i	0.770582	+	0.359328i
$539$	−1.01151	−	0.848761i	−0.0435690	−	0.0365587i
$540$		0			0
$541$	−18.3170	−	4.90803i	−0.787510	−	0.211013i	−0.157417	−	0.987532i	$-0.550317\pi$
$541$	−18.3170	−	4.90803i	−0.787510	−	0.211013i	−0.630093	+	0.776520i	$0.716983\pi$
$542$	22.9861	−	10.7186i	0.987338	−	0.460403i
$543$		0			0
$544$	0.696381	−	1.20617i	0.0298571	−	0.0517140i
$545$	−3.72751	−	6.45623i	−0.159669	−	0.276555i
$546$		0			0
$547$	17.5071	−	4.69100i	0.748548	−	0.200573i	0.135674	−	0.990754i	$-0.456680\pi$
$547$	17.5071	−	4.69100i	0.748548	−	0.200573i	0.612874	+	0.790181i	$0.290013\pi$
$548$	6.41566	−	5.38338i	0.274063	−	0.229967i
$549$		0			0
$550$	19.1626	+	1.67651i	0.817097	+	0.0714867i
$551$	−4.09008	+	11.2374i	−0.174243	+	0.478729i
$552$		0			0
$553$	−2.20642	−	3.15109i	−0.0938264	−	0.133998i
$554$	6.91782			0.293910
$555$		0			0
$556$	8.17309			0.346616
$557$	7.83666	+	11.1919i	0.332050	+	0.474216i	0.950110	−	0.311914i	$-0.100970\pi$
$557$	7.83666	+	11.1919i	0.332050	+	0.474216i	−0.618060	+	0.786131i	$0.712081\pi$
$558$		0			0
$559$	−0.0126172	+	0.0346655i	−0.000533651	+	0.00146619i
$560$	−1.94117	−	0.169830i	−0.0820294	−	0.00717665i
$561$		0			0
$562$	−4.96338	+	4.16477i	−0.209368	+	0.175680i
$563$	−8.05397	+	2.15805i	−0.339434	+	0.0909512i	−0.424510	−	0.905423i	$-0.639554\pi$
$563$	−8.05397	+	2.15805i	−0.339434	+	0.0909512i	0.0850754	+	0.996375i	$0.472887\pi$
$564$		0			0
$565$	−1.14592	−	1.98479i	−0.0482091	−	0.0835006i
$566$	−11.9761	+	20.7433i	−0.503394	+	0.871904i
$567$		0			0
$568$	0.699054	−	0.325974i	0.0293317	−	0.0136776i
$569$	40.1145	+	10.7487i	1.68169	+	0.450607i	0.968224	−	0.250084i	$-0.0804582\pi$
$569$	40.1145	+	10.7487i	1.68169	+	0.450607i	0.713465	+	0.700691i	$0.247125\pi$
$570$		0			0
$571$	−27.7990	−	23.3261i	−1.16335	−	0.976168i	−0.163406	−	0.986559i	$-0.552248\pi$
$571$	−27.7990	−	23.3261i	−1.16335	−	0.976168i	−0.999946	+	0.0103904i	$0.996693\pi$
$572$	0.150695	+	0.0702701i	0.00630086	+	0.00293814i
$573$		0			0
$574$	−19.8624	−	13.9078i	−0.829041	−	0.580501i
$575$	−8.91026	+	19.1081i	−0.371584	+	0.796864i
$576$		0			0
$577$	43.0103	−	3.76291i	1.79054	−	0.156652i	0.857045	−	0.515241i	$-0.172298\pi$
$577$	43.0103	−	3.76291i	1.79054	−	0.156652i	0.933495	+	0.358590i	$0.116742\pi$
$578$	−3.89787	+	14.5470i	−0.162130	+	0.605077i
$579$		0			0
$580$	−5.99482	−	1.05705i	−0.248921	−	0.0438916i
$581$	19.4647	+	11.2380i	0.807533	+	0.466229i
$582$		0			0
$583$	0.880538	+	2.41926i	0.0364681	+	0.100195i
$584$	−2.42417	−	9.04713i	−0.100313	−	0.374373i
$585$		0			0
$586$	−9.85416	−	9.85416i	−0.407072	−	0.407072i
$587$	−3.51806	+	40.2116i	−0.145206	+	1.65971i	0.478529	+	0.878072i	$0.341170\pi$
$587$	−3.51806	+	40.2116i	−0.145206	+	1.65971i	−0.623734	+	0.781636i	$0.714385\pi$
$588$		0			0
$589$	1.11281	+	6.31108i	0.0458527	+	0.260043i
$590$	−1.85511	+	1.29896i	−0.0763738	+	0.0534775i
$591$		0			0
$592$	−5.16352	−	3.21528i	−0.212220	−	0.132147i
$593$		−	34.1575i		−	1.40268i	−0.712827	−	0.701340i	$-0.752585\pi$
$593$		−	34.1575i		−	1.40268i	0.712827	−	0.701340i	$-0.247415\pi$
$594$		0			0
$595$	−2.67269	+	0.471267i	−0.109570	+	0.0193201i
$596$	−9.55963	−	3.47942i	−0.391578	−	0.142523i
$597$		0			0
$598$	−0.128866	+	0.128866i	−0.00526973	+	0.00526973i
$599$	−22.3960	−	26.6906i	−0.915078	−	1.09055i	−0.995592	−	0.0937937i	$-0.970101\pi$
$599$	−22.3960	−	26.6906i	−0.915078	−	1.09055i	0.0805140	−	0.996753i	$-0.474344\pi$
$600$		0			0
$601$	32.7398	−	11.9163i	1.33549	−	0.486077i	0.427098	−	0.904206i	$-0.359536\pi$
$601$	32.7398	−	11.9163i	1.33549	−	0.486077i	0.908388	+	0.418129i	$0.137314\pi$
$602$	−2.22997	+	1.28747i	−0.0908868	+	0.0524735i
$603$		0			0
$604$	−2.91414	+	16.5269i	−0.118575	+	0.672471i
$605$	2.26425	+	4.85569i	0.0920547	+	0.197412i
$606$		0			0
$607$	−2.11297	−	24.1513i	−0.0857626	−	0.980271i	−0.910159	−	0.414259i	$-0.864041\pi$
$607$	−2.11297	−	24.1513i	−0.0857626	−	0.980271i	0.824397	−	0.566013i	$-0.191515\pi$
$608$	0.910241	−	1.08478i	0.0369151	−	0.0439937i
$609$		0			0
$610$	4.63418	−	6.61830i	0.187633	−	0.267967i
$611$	0.0524390	−	0.0748906i	0.00212145	−	0.00302975i
$612$		0			0
$613$	8.25283	−	9.83534i	0.333329	−	0.397246i	−0.573182	−	0.819428i	$-0.694291\pi$
$613$	8.25283	−	9.83534i	0.333329	−	0.397246i	0.906511	+	0.422182i	$0.138736\pi$
$614$	−1.47169	−	16.8215i	−0.0593926	−	0.678860i
$615$		0			0
$616$	4.90487	+	10.5185i	0.197623	+	0.423804i
$617$	0.996744	−	5.65281i	0.0401274	−	0.227574i	−0.958148	−	0.286272i	$-0.907584\pi$
$617$	0.996744	−	5.65281i	0.0401274	−	0.227574i	0.998276	+	0.0586983i	$0.0186950\pi$
$618$		0			0
$619$	6.45138	−	3.72470i	0.259303	−	0.149709i	−0.364714	−	0.931120i	$-0.618833\pi$
$619$	6.45138	−	3.72470i	0.259303	−	0.149709i	0.624016	+	0.781411i	$0.285500\pi$
$620$	−3.06537	+	1.11570i	−0.123108	+	0.0448077i
$621$		0			0
$622$	−5.71965	−	6.81641i	−0.229337	−	0.273313i
$623$	20.4925	−	20.4925i	0.821015	−	0.821015i
$624$		0			0
$625$	16.4221	+	5.97715i	0.656884	+	0.239086i
$626$	19.1543	−	3.37742i	0.765560	−	0.134989i
$627$		0			0
$628$			24.0094i			0.958079i
$629$	−8.10554	−	2.46422i	−0.323189	−	0.0982548i
$630$		0			0
$631$	34.6175	−	24.2394i	1.37810	−	0.964955i	0.378880	−	0.925446i	$-0.376309\pi$
$631$	34.6175	−	24.2394i	1.37810	−	0.964955i	0.999219	−	0.0395094i	$-0.0125795\pi$
$632$	0.247104	+	1.40140i	0.00982928	+	0.0557446i
$633$		0			0
$634$	−1.96512	+	22.4614i	−0.0780447	+	0.892056i
$635$	−8.83244	−	8.83244i	−0.350505	−	0.350505i
$636$		0			0
$637$	−0.00308283	−	0.0115053i	−0.000122146	−	0.000455856i
$638$	12.4004	+	34.0699i	0.490937	+	1.34884i
$639$		0			0
$640$	0.624258	+	0.360415i	0.0246760	+	0.0142467i
$641$	3.53559	+	0.623420i	0.139647	+	0.0246236i	0.243035	−	0.970018i	$-0.421857\pi$
$641$	3.53559	+	0.623420i	0.139647	+	0.0246236i	−0.103387	+	0.994641i	$0.532968\pi$
$642$		0			0
$643$	10.9454	−	40.8489i	0.431646	−	1.61092i	−0.317322	−	0.948318i	$-0.602784\pi$
$643$	10.9454	−	40.8489i	0.431646	−	1.61092i	0.748968	−	0.662606i	$-0.230550\pi$
$644$	−12.6723	+	1.10868i	−0.499359	+	0.0436882i
$645$		0			0
$646$	0.833516	−	1.78748i	0.0327943	−	0.0703275i
$647$	−10.5382	−	7.37894i	−0.414300	−	0.290096i	0.347783	−	0.937575i	$-0.386934\pi$
$647$	−10.5382	−	7.37894i	−0.414300	−	0.290096i	−0.762083	+	0.647479i	$0.775823\pi$
$648$		0			0
$649$	12.2248	+	5.70051i	0.479865	+	0.223765i
$650$	0.132923	+	0.111536i	0.00521367	+	0.00437479i
$651$		0			0
$652$	−7.32547	−	1.96285i	−0.286887	−	0.0768712i
$653$	−20.0068	+	9.32931i	−0.782926	+	0.365084i	−0.772625	−	0.634863i	$-0.781057\pi$
$653$	−20.0068	+	9.32931i	−0.782926	+	0.365084i	−0.0103006	+	0.999947i	$0.503279\pi$
$654$		0			0
$655$	6.12828	−	10.6145i	0.239452	−	0.414743i
$656$	4.48489	+	7.76805i	0.175105	+	0.303292i
$657$		0			0
$658$	6.16402	−	1.65164i	0.240299	−	0.0643878i
$659$	−4.14058	+	3.47436i	−0.161294	+	0.135342i	−0.719863	−	0.694117i	$-0.755795\pi$
$659$	−4.14058	+	3.47436i	−0.161294	+	0.135342i	0.558569	+	0.829458i	$0.311351\pi$
$660$		0			0
$661$	37.3375	+	3.26660i	1.45226	+	0.127056i	0.785798	−	0.618484i	$-0.212253\pi$
$661$	37.3375	+	3.26660i	1.45226	+	0.127056i	0.666461	+	0.745540i	$0.267808\pi$
$662$	−2.57361	+	7.07095i	−0.100026	+	0.274820i
$663$		0			0
$664$	−4.76895	−	6.81077i	−0.185071	−	0.264309i
$665$	−2.75936			−0.107003
$666$		0			0
$667$	−39.7390			−1.53870
$668$	12.3723	+	17.6695i	0.478699	+	0.683653i
$669$		0			0
$670$	−2.10233	+	5.77610i	−0.0812201	+	0.223150i
$671$	−47.9387	−	4.19409i	−1.85065	−	0.161911i
$672$		0			0
$673$	−32.0178	+	26.8661i	−1.23420	+	1.03561i	−0.236240	+	0.971695i	$0.575915\pi$
$673$	−32.0178	+	26.8661i	−1.23420	+	1.03561i	−0.997955	+	0.0639180i	$0.979640\pi$
$674$	10.6422	−	2.85158i	0.409924	−	0.109839i
$675$		0			0
$676$	−6.49925	−	11.2570i	−0.249971	−	0.432963i
$677$	−19.7100	+	34.1388i	−0.757518	+	1.31206i	0.186594	+	0.982437i	$0.440255\pi$
$677$	−19.7100	+	34.1388i	−0.757518	+	1.31206i	−0.944113	+	0.329623i	$0.893078\pi$
$678$		0			0
$679$	7.28356	−	3.39638i	0.279518	−	0.130341i
$680$	0.969738	+	0.259841i	0.0371878	+	0.00996443i
$681$		0			0
$682$	14.8837	+	12.4889i	0.569926	+	0.478225i
$683$	15.4128	+	7.18709i	0.589753	+	0.275006i	0.694500	−	0.719492i	$-0.255626\pi$
$683$	15.4128	+	7.18709i	0.589753	+	0.275006i	−0.104747	+	0.994499i	$0.533403\pi$
$684$		0			0
$685$	4.94522	+	3.46268i	0.188947	+	0.132302i
$686$	−7.64573	+	16.3963i	−0.291915	+	0.626015i
$687$		0			0
$688$	0.948913	−	0.0830192i	0.0361770	−	0.00316508i
$689$	−0.00601074	+	0.0224324i	−0.000228991	+	0.000854606i
$690$		0			0
$691$	8.02015	+	1.41417i	0.305101	+	0.0537975i	0.324103	−	0.946022i	$-0.394938\pi$
$691$	8.02015	+	1.41417i	0.305101	+	0.0537975i	−0.0190017	+	0.999819i	$0.506049\pi$
$692$	4.05228	+	2.33959i	0.154045	+	0.0889377i
$693$		0			0
$694$	−7.00233	−	19.2387i	−0.265805	−	0.730293i
$695$	1.52481	+	5.69067i	0.0578394	+	0.215859i
$696$		0			0
$697$	8.83372	+	8.83372i	0.334601	+	0.334601i
$698$	−2.32761	+	26.6047i	−0.0881015	+	1.00700i
$699$		0			0
$700$	2.10317	+	11.9276i	0.0794922	+	0.450822i
$701$	13.8128	−	9.67182i	0.521702	−	0.365299i	−0.282867	−	0.959159i	$-0.591285\pi$
$701$	13.8128	−	9.67182i	0.521702	−	0.365299i	0.804569	+	0.593860i	$0.202397\pi$
$702$		0			0
$703$	−7.68098	−	3.89849i	−0.289694	−	0.147035i
$704$		−	4.29332i		−	0.161811i
$705$		0			0
$706$	−2.87615	+	0.507143i	−0.108245	+	0.0190866i
$707$	17.0533	+	6.20691i	0.641357	+	0.233435i
$708$		0			0
$709$	−11.8507	+	11.8507i	−0.445064	+	0.445064i	−0.893710	−	0.448646i	$-0.851906\pi$
$709$	−11.8507	+	11.8507i	−0.445064	+	0.445064i	0.448646	+	0.893710i	$0.351906\pi$
$710$	0.357385	+	0.425915i	0.0134124	+	0.0159843i
$711$		0			0
$712$	−10.0742	+	3.66670i	−0.377546	+	0.137416i
$713$	−18.4425	+	10.6478i	−0.690676	+	0.398762i
$714$		0			0
$715$	−0.0208126	+	0.118034i	−0.000778347	+	0.00441422i
$716$	10.9307	+	23.4409i	0.408498	+	0.876026i
$717$		0			0
$718$	−2.69825	−	30.8411i	−0.100698	−	1.15098i
$719$	−1.15668	+	1.37848i	−0.0431370	+	0.0514086i	−0.787182	−	0.616721i	$-0.788461\pi$
$719$	−1.15668	+	1.37848i	−0.0431370	+	0.0514086i	0.744045	+	0.668130i	$0.232905\pi$
$720$		0			0
$721$	−15.3930	+	21.9835i	−0.573266	+	0.818708i
$722$	−9.74776	+	13.9213i	−0.362774	+	0.518095i
$723$		0			0
$724$	1.62752	−	1.93960i	0.0604863	−	0.0720847i
$725$	3.29765	+	37.6923i	0.122472	+	1.39986i
$726$		0			0
$727$	15.3139	+	32.8407i	0.567960	+	1.21800i	0.955185	+	0.296010i	$0.0956561\pi$
$727$	15.3139	+	32.8407i	0.567960	+	1.21800i	−0.387224	+	0.921985i	$0.626566\pi$
$728$	−0.0181796	+	0.103102i	−0.000673782	+	0.00382121i
$729$		0			0
$730$	5.84698	−	3.37575i	0.216406	−	0.124942i
$731$	1.24665	−	0.453744i	0.0461091	−	0.0167823i
$732$		0			0
$733$	24.6964	+	29.4320i	0.912182	+	1.08710i	0.995887	+	0.0906055i	$0.0288802\pi$
$733$	24.6964	+	29.4320i	0.912182	+	1.08710i	−0.0837050	+	0.996491i	$0.526675\pi$
$734$	6.99012	−	6.99012i	0.258010	−	0.258010i
$735$		0			0
$736$	4.42192	+	1.60945i	0.162994	+	0.0593250i
$737$	36.0546	−	6.35740i	1.32809	−	0.234178i
$738$		0			0
$739$		−	45.9953i		−	1.69196i	−0.533211	−	0.845982i	$-0.679015\pi$
$739$		−	45.9953i		−	1.69196i	0.533211	−	0.845982i	$-0.320985\pi$
$740$	1.27537	−	4.19506i	0.0468835	−	0.154214i
$741$		0			0
$742$	−1.32786	+	0.929780i	−0.0487474	+	0.0341333i
$743$	−0.372254	−	2.11116i	−0.0136567	−	0.0774508i	0.977218	−	0.212239i	$-0.0680756\pi$
$743$	−0.372254	−	2.11116i	−0.0136567	−	0.0774508i	−0.990874	+	0.134788i	$0.956965\pi$
$744$		0			0
$745$	0.639123	−	7.30521i	0.0234157	−	0.267642i
$746$	−2.18935	−	2.18935i	−0.0801579	−	0.0801579i
$747$		0			0
$748$	−1.54763	−	5.77583i	−0.0565869	−	0.211185i
$749$	−8.61032	−	23.6567i	−0.314614	−	0.864395i
$750$		0			0
$751$	23.4439	+	13.5354i	0.855481	+	0.493912i	0.862496	−	0.506063i	$-0.168900\pi$
$751$	23.4439	+	13.5354i	0.855481	+	0.493912i	−0.00701548	+	0.999975i	$0.502233\pi$
$752$	−2.32480	−	0.409925i	−0.0847767	−	0.0149484i
$753$		0			0
$754$	−0.0846479	+	0.315910i	−0.00308270	+	0.0115048i
$755$	−12.0509	+	1.05431i	−0.438576	+	0.0383704i
$756$		0			0
$757$	−12.5183	+	26.8457i	−0.454987	+	0.975723i	0.536303	+	0.844026i	$0.319820\pi$
$757$	−12.5183	+	26.8457i	−0.454987	+	0.975723i	−0.991290	+	0.131697i	$0.957957\pi$
$758$	22.6146	+	15.8349i	0.821399	+	0.575150i
$759$		0			0
$760$	0.925120	+	0.431390i	0.0335576	+	0.0156482i
$761$	−33.4303	−	28.0514i	−1.21185	−	1.01686i	−0.999210	−	0.0397296i	$-0.987350\pi$
$761$	−33.4303	−	28.0514i	−1.21185	−	1.01686i	−0.212637	−	0.977131i	$-0.568205\pi$
$762$		0			0
$763$	−27.0050	−	7.23598i	−0.977648	−	0.261960i
$764$	0.210054	−	0.0979496i	0.00759947	−	0.00354369i
$765$		0			0
$766$	−5.89128	+	10.2040i	−0.212861	+	0.368686i
$767$	0.0608375	+	0.105374i	0.00219671	+	0.00380482i
$768$		0			0
$769$	16.6847	−	4.47064i	0.601664	−	0.161215i	0.0548856	−	0.998493i	$-0.482521\pi$
$769$	16.6847	−	4.47064i	0.601664	−	0.161215i	0.546779	+	0.837277i	$0.315854\pi$
$770$	−6.40866	+	5.37750i	−0.230952	+	0.193792i
$771$		0			0
$772$	15.7123	+	1.37465i	0.565498	+	0.0494746i
$773$	3.90275	−	10.7227i	0.140372	−	0.385669i	−0.849508	−	0.527576i	$-0.823101\pi$
$773$	3.90275	−	10.7227i	0.140372	−	0.385669i	0.989880	+	0.141907i	$0.0453233\pi$
$774$		0			0
$775$	11.6298	+	16.6091i	0.417754	+	0.596615i
$776$	−2.97291			−0.106721
$777$		0			0
$778$	−24.2081			−0.867901
$779$	7.28554	+	10.4048i	0.261031	+	0.372792i
$780$		0			0
$781$	1.13261	−	3.11182i	0.0405280	−	0.111350i
$782$	6.52900	+	0.571214i	0.233477	+	0.0204266i
$783$		0			0
$784$	−0.235602	+	0.197693i	−0.00841435	+	0.00706048i
$785$	−16.7170	+	4.47931i	−0.596656	+	0.159873i
$786$		0			0
$787$	−20.1358	−	34.8762i	−0.717763	−	1.24320i	−0.961884	−	0.273457i	$-0.911833\pi$
$787$	−20.1358	−	34.8762i	−0.717763	−	1.24320i	0.244122	−	0.969745i	$-0.421500\pi$
$788$	0.207793	−	0.359909i	0.00740234	−	0.0128212i
$789$		0			0
$790$	−0.929649	+	0.433503i	−0.0330754	+	0.0154233i
$791$	−8.30194	−	2.22450i	−0.295183	−	0.0790940i
$792$		0			0
$793$	−0.332530	−	0.279026i	−0.0118085	−	0.00990850i
$794$	12.7445	+	5.94285i	0.452284	+	0.210904i
$795$		0			0
$796$	−0.840088	−	0.588236i	−0.0297761	−	0.0208495i
$797$	−12.0198	+	25.7765i	−0.425762	+	0.913049i	0.570049	+	0.821611i	$0.306924\pi$
$797$	−12.0198	+	25.7765i	−0.425762	+	0.913049i	−0.995811	+	0.0914383i	$0.970854\pi$
$798$		0			0
$799$	−3.27533	+	0.286555i	−0.115873	+	0.0101376i
$800$	1.15961	−	4.32774i	0.0409985	−	0.153009i
$801$		0			0
$802$	−17.7364	−	3.12740i	−0.626293	−	0.110432i
$803$	−34.8250	−	20.1062i	−1.22895	−	0.709534i
$804$		0			0
$805$	−3.13615	−	8.61649i	−0.110535	−	0.303692i
$806$	0.0453616	+	0.169292i	0.00159779	+	0.00596305i
$807$		0			0
$808$	−4.74704	−	4.74704i	−0.167000	−	0.167000i
$809$	2.70079	−	30.8702i	0.0949548	−	1.08534i	−0.787935	−	0.615758i	$-0.788850\pi$
$809$	2.70079	−	30.8702i	0.0949548	−	1.08534i	0.882890	−	0.469580i	$-0.155595\pi$
$810$		0			0
$811$	−8.59939	−	48.7696i	−0.301965	−	1.71253i	−0.637455	−	0.770487i	$-0.720013\pi$
$811$	−8.59939	−	48.7696i	−0.301965	−	1.71253i	0.335490	−	0.942044i	$-0.391098\pi$
$812$	−18.7000	+	13.0939i	−0.656242	+	0.459505i
$813$		0			0
$814$	−25.4367	+	5.91456i	−0.891555	+	0.207305i
$815$		−	5.46670i		−	0.191490i
$816$		0			0
$817$	1.32838	−	0.234229i	0.0464742	−	0.00819465i
$818$	−22.6229	−	8.23405i	−0.790990	−	0.287897i
$819$		0			0
$820$	−4.57193	+	4.57193i	−0.159659	+	0.159659i
$821$	29.0896	+	34.6676i	1.01523	+	1.20991i	0.977569	+	0.210616i	$0.0675471\pi$
$821$	29.0896	+	34.6676i	1.01523	+	1.20991i	0.0376635	+	0.999290i	$0.488008\pi$
$822$		0			0
$823$	34.7330	−	12.6418i	1.21072	−	0.440665i	0.343764	−	0.939056i	$-0.388298\pi$
$823$	34.7330	−	12.6418i	1.21072	−	0.440665i	0.866952	+	0.498391i	$0.166076\pi$
$824$	8.59759	−	4.96382i	0.299511	−	0.172923i
$825$		0			0
$826$	−1.47478	+	8.36392i	−0.0513143	+	0.291018i
$827$	0.198441	+	0.425559i	0.00690048	+	0.0147981i	0.909728	−	0.415205i	$-0.136290\pi$
$827$	0.198441	+	0.425559i	0.00690048	+	0.0147981i	−0.902827	+	0.430003i	$0.858512\pi$
$828$		0			0
$829$	−2.00427	−	22.9089i	−0.0696113	−	0.795661i	−0.948116	−	0.317926i	$-0.897014\pi$
$829$	−2.00427	−	22.9089i	−0.0696113	−	0.795661i	0.878504	−	0.477735i	$-0.158542\pi$
$830$	3.85241	−	4.59112i	0.133719	−	0.159360i
$831$		0			0
$832$	0.0222137	−	0.0317244i	0.000770120	−	0.00109985i
$833$	−0.245693	+	0.350886i	−0.00851276	+	0.0121575i
$834$		0			0
$835$	−9.99448	+	11.9110i	−0.345873	+	0.412196i
$836$	−0.529881	−	6.05657i	−0.0183263	−	0.209471i
$837$		0			0
$838$	1.79809	+	3.85601i	0.0621140	+	0.133204i
$839$	5.55488	−	31.5033i	0.191776	−	1.08761i	−0.725160	−	0.688580i	$-0.758234\pi$
$839$	5.55488	−	31.5033i	0.191776	−	1.08761i	0.916936	−	0.399034i	$-0.130655\pi$
$840$		0			0
$841$	−36.6461	+	21.1576i	−1.26366	+	0.729574i
$842$	−9.45031	+	3.43963i	−0.325679	+	0.118538i
$843$		0			0
$844$	−7.36744	−	8.78017i	−0.253598	−	0.302226i
$845$	6.62539	−	6.62539i	0.227920	−	0.227920i
$846$		0			0
$847$	18.8805	+	6.87194i	0.648742	+	0.236123i
$848$	0.590547	−	0.104129i	0.0202795	−	0.00357581i
$849$		0			0
$850$		−	6.24014i		−	0.214035i
$851$	3.44379	−	28.4158i	0.118052	−	0.974081i
$852$		0			0
$853$	31.1942	−	21.8424i	1.06807	−	0.747871i	0.0991071	−	0.995077i	$-0.468401\pi$
$853$	31.1942	−	21.8424i	1.06807	−	0.747871i	0.968963	+	0.247206i	$0.0795125\pi$
$854$	−5.26144	−	29.8391i	−0.180043	−	1.02107i
$855$		0			0
$856$	−0.811666	+	9.27739i	−0.0277422	+	0.317095i
$857$	−2.16381	−	2.16381i	−0.0739144	−	0.0739144i	0.669183	−	0.743098i	$-0.266644\pi$
$857$	−2.16381	−	2.16381i	−0.0739144	−	0.0739144i	−0.743098	+	0.669183i	$0.766644\pi$
$858$		0			0
$859$	8.14097	+	30.3825i	0.277766	+	1.03664i	0.953965	+	0.299918i	$0.0969595\pi$
$859$	8.14097	+	30.3825i	0.277766	+	1.03664i	−0.676199	+	0.736719i	$0.736374\pi$
$860$	0.234838	+	0.645211i	0.00800789	+	0.0220015i
$861$		0			0
$862$	9.58215	+	5.53225i	0.326369	+	0.188429i
$863$	−49.9048	−	8.79957i	−1.69878	−	0.299541i	−0.761512	−	0.648150i	$-0.775543\pi$
$863$	−49.9048	−	8.79957i	−1.69878	−	0.299541i	−0.937268	+	0.348609i	$0.886654\pi$
$864$		0			0
$865$	−0.872968	+	3.25796i	−0.0296818	+	0.110774i
$866$	17.6829	−	1.54706i	0.600890	−	0.0525711i
$867$		0			0
$868$	−5.17008	+	11.0873i	−0.175484	+	0.376327i
$869$	5.00459	+	3.50425i	0.169769	+	0.118873i
$870$		0			0
$871$	0.299309	+	0.139570i	0.0101417	+	0.00472916i
$872$	7.92262	+	6.64787i	0.268294	+	0.225125i
$873$		0			0
$874$	6.43662	+	1.72469i	0.217722	+	0.0583384i
$875$	−16.7426	+	7.80719i	−0.566002	+	0.263931i
$876$		0			0
$877$	15.1689	−	26.2733i	0.512217	−	0.887186i	−0.487682	−	0.873021i	$-0.662158\pi$
$877$	15.1689	−	26.2733i	0.512217	−	0.887186i	0.999900	−	0.0141652i	$-0.00450908\pi$
$878$	−5.16790	−	8.95107i	−0.174408	−	0.302084i
$879$		0			0
$880$	2.98931	−	0.800983i	0.100770	−	0.0270011i
$881$	30.1668	−	25.3130i	1.01635	−	0.852816i	0.0271823	−	0.999630i	$-0.491347\pi$
$881$	30.1668	−	25.3130i	1.01635	−	0.852816i	0.989164	+	0.146815i	$0.0469021\pi$
$882$		0			0
$883$	−30.3080	−	2.65161i	−1.01995	−	0.0892337i	−0.435103	−	0.900381i	$-0.643288\pi$
$883$	−30.3080	−	2.65161i	−1.01995	−	0.0892337i	−0.584843	+	0.811147i	$0.698844\pi$
$884$	0.0184484	−	0.0506865i	0.000620485	−	0.00170477i
$885$		0			0
$886$	−11.3430	−	16.1994i	−0.381075	−	0.544231i
$887$	6.29614			0.211404			0.105702	−	0.994398i	$-0.466291\pi$
$887$	6.29614			0.211404			0.105702	+	0.994398i	$0.466291\pi$
$888$		0			0
$889$	−46.8434			−1.57108
$890$	−4.43250	−	6.33027i	−0.148578	−	0.212191i
$891$		0			0
$892$	1.06087	−	2.91473i	0.0355207	−	0.0975923i
$893$	−3.33018	−	0.291353i	−0.111440	−	0.00974974i
$894$		0			0
$895$	−14.2819	+	11.9839i	−0.477391	+	0.400578i
$896$	2.61114	−	0.699652i	0.0872320	−	0.0233737i
$897$		0			0
$898$	8.58996	+	14.8783i	0.286651	+	0.496494i
$899$	−19.1084	+	33.0967i	−0.637301	+	1.10384i
$900$		0			0
$901$	0.756930	−	0.352962i	0.0252170	−	0.0117589i
$902$	37.1979	+	9.96716i	1.23856	+	0.331870i
$903$		0			0
$904$	2.43559	+	2.04370i	0.0810064	+	0.0679724i
$905$	1.65412	+	0.771330i	0.0549849	+	0.0256399i
$906$		0			0
$907$	29.8378	+	20.8927i	0.990749	+	0.693730i	0.952184	−	0.305526i	$-0.0988325\pi$
$907$	29.8378	+	20.8927i	0.990749	+	0.693730i	0.0385650	+	0.999256i	$0.487721\pi$
$908$	2.00444	−	4.29854i	0.0665197	−	0.142652i
$909$		0			0
$910$	−0.0751783	+	0.00657725i	−0.00249214	+	0.000218034i
$911$	3.46558	−	12.9337i	0.114820	−	0.428514i	−0.884453	−	0.466628i	$-0.845469\pi$
$911$	3.46558	−	12.9337i	0.114820	−	0.428514i	0.999273	+	0.0381146i	$0.0121352\pi$
$912$		0			0
$913$	−35.1542	−	6.19863i	−1.16343	−	0.205145i
$914$	−34.4364	−	19.8819i	−1.13905	−	0.657634i
$915$		0			0
$916$	−8.65058	−	23.7673i	−0.285823	−	0.785293i
$917$	−11.8965	−	44.3982i	−0.392856	−	1.46616i
$918$		0			0
$919$	−35.2453	−	35.2453i	−1.16263	−	1.16263i	−0.983897	−	0.178737i	$-0.942799\pi$
$919$	−35.2453	−	35.2453i	−1.16263	−	1.16263i	−0.178737	−	0.983897i	$-0.557201\pi$
$920$	−0.295634	+	3.37911i	−0.00974677	+	0.111406i
$921$		0			0
$922$	7.18112	+	40.7262i	0.236498	+	1.34124i
$923$	0.0244697	−	0.0171339i	0.000805430	−	0.000563968i
$924$		0			0
$925$	−27.2381	−	0.908406i	−0.895583	−	0.0298682i
$926$		−	38.8536i		−	1.27681i
$927$		0			0
$928$	8.31654	−	1.46643i	0.273004	−	0.0481379i
$929$	39.6302	+	14.4242i	1.30023	+	0.473243i	0.897070	−	0.441888i	$-0.145691\pi$
$929$	39.6302	+	14.4242i	1.30023	+	0.473243i	0.403155	+	0.915132i	$0.367913\pi$
$930$		0			0
$931$	−0.307963	+	0.307963i	−0.0100931	+	0.0100931i
$932$	−6.68520	−	7.96711i	−0.218981	−	0.260971i
$933$		0			0
$934$	19.5681	−	7.12221i	0.640288	−	0.233046i
$935$	3.73280	−	2.15513i	0.122076	−	0.0704804i
$936$		0			0
$937$	−5.72780	+	32.4839i	−0.187119	+	1.06120i	0.736084	+	0.676891i	$0.236673\pi$
$937$	−5.72780	+	32.4839i	−0.187119	+	1.06120i	−0.923203	+	0.384314i	$0.874438\pi$
$938$	9.74204	+	20.8919i	0.318089	+	0.682144i
$939$		0			0
$940$	−0.148308	−	1.69516i	−0.00483726	−	0.0552902i
$941$	33.9498	−	40.4598i	1.10673	−	1.31895i	0.163600	−	0.986527i	$-0.447689\pi$
$941$	33.9498	−	40.4598i	1.10673	−	1.31895i	0.943130	−	0.332424i	$-0.107866\pi$
$942$		0			0
$943$	−24.2102	+	34.5757i	−0.788392	+	1.12594i
$944$	1.80204	−	2.57358i	0.0586513	−	0.0837627i
$945$		0			0
$946$	2.62871	−	3.13278i	0.0854669	−	0.101855i
$947$	3.74383	+	42.7922i	0.121658	+	1.39056i	0.774265	+	0.632862i	$0.218120\pi$
$947$	3.74383	+	42.7922i	0.121658	+	1.39056i	−0.652607	+	0.757697i	$0.726325\pi$
$948$		0			0
$949$	−0.153301	−	0.328755i	−0.00497635	−	0.0106718i
$950$	1.10173	−	6.24823i	0.0357449	−	0.202719i
$951$		0			0
$952$	3.26057	−	1.88249i	0.105676	−	0.0610119i
$953$	48.5522	−	17.6716i	1.57276	−	0.572438i	0.599146	−	0.800640i	$-0.295507\pi$
$953$	48.5522	−	17.6716i	1.57276	−	0.572438i	0.973614	+	0.228202i	$0.0732846\pi$
$954$		0			0
$955$	0.107388	+	0.127980i	0.00347499	+	0.00414133i
$956$	−8.82792	+	8.82792i	−0.285515	+	0.285515i
$957$		0			0
$958$	−18.8601	−	6.86453i	−0.609343	−	0.221783i
$959$	22.2959	−	3.93137i	0.719972	−	0.126950i
$960$		0			0
$961$		−	10.5202i		−	0.339360i
$962$	−0.218560	−	0.0879054i	−0.00704665	−	0.00283418i
$963$		0			0
$964$	7.21834	−	5.05434i	0.232487	−	0.162789i
$965$	1.97423	+	11.1964i	0.0635529	+	0.360426i
$966$		0			0
$967$	1.24942	−	14.2810i	0.0401787	−	0.459245i	−0.949280	−	0.314431i	$-0.898186\pi$
$967$	1.24942	−	14.2810i	0.0401787	−	0.459245i	0.989459	−	0.144814i	$-0.0462582\pi$
$968$	−5.25565	−	5.25565i	−0.168923	−	0.168923i
$969$		0			0
$970$	−0.554641	−	2.06995i	−0.0178084	−	0.0664620i
$971$	3.86825	+	10.6279i	0.124138	+	0.341067i	0.986158	−	0.165807i	$-0.0530230\pi$
$971$	3.86825	+	10.6279i	0.124138	+	0.341067i	−0.862020	+	0.506874i	$0.830801\pi$
$972$		0			0
$973$	19.1339	+	11.0469i	0.613404	+	0.354149i
$974$	−14.5456	−	2.56478i	−0.466071	−	0.0821808i
$975$		0			0
$976$	−2.90098	+	10.8266i	−0.0928581	+	0.346551i
$977$	−2.74072	+	0.239782i	−0.0876835	+	0.00767131i	−0.130913	−	0.991394i	$-0.541791\pi$
$977$	−2.74072	+	0.239782i	−0.0876835	+	0.00767131i	0.0432295	+	0.999065i	$0.486235\pi$
$978$		0			0
$979$	−19.4521	+	41.7151i	−0.621691	+	1.33322i
$980$	−0.181603	−	0.127160i	−0.00580109	−	0.00406197i
$981$		0			0
$982$	20.9117	+	9.75128i	0.667319	+	0.311176i
$983$	−12.8151	−	10.7531i	−0.408738	−	0.342972i	0.415121	−	0.909766i	$-0.363739\pi$
$983$	−12.8151	−	10.7531i	−0.408738	−	0.342972i	−0.823860	+	0.566794i	$0.808184\pi$
$984$		0			0
$985$	0.289360	+	0.0775339i	0.00921979	+	0.00247044i
$986$	10.6597	−	4.97069i	0.339473	−	0.158299i
$987$		0			0
$988$	0.0274213	−	0.0474950i	0.000872387	−	0.00151102i
$989$	2.24118	+	3.88185i	0.0712655	+	0.123436i
$990$		0			0
$991$	4.43450	−	1.18822i	0.140867	−	0.0377451i	−0.187697	−	0.982227i	$-0.560102\pi$
$991$	4.43450	−	1.18822i	0.140867	−	0.0377451i	0.328563	+	0.944482i	$0.393436\pi$
$992$	3.46671	−	2.90891i	0.110068	−	0.0923581i
$993$		0			0
$994$	2.07714	+	0.181726i	0.0658829	+	0.00576400i
$995$	0.252840	−	0.694671i	0.00801556	−	0.0220226i
$996$		0			0
$997$	−2.56338	−	3.66088i	−0.0811829	−	0.115941i	0.776507	−	0.630109i	$-0.216990\pi$
$997$	−2.56338	−	3.66088i	−0.0811829	−	0.115941i	−0.857690	+	0.514168i	$0.828101\pi$
$998$	−16.5345			−0.523391
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.431.2	yes	72
3.2	odd	2	inner	666.2.bs.a.431.5	yes	72
37.17	odd	36	inner	666.2.bs.a.17.5	yes	72
111.17	even	36	inner	666.2.bs.a.17.2	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.17.2	✓	72	111.17	even	36	inner
666.2.bs.a.17.5	yes	72	37.17	odd	36	inner
666.2.bs.a.431.2	yes	72	1.1	even	1	trivial
666.2.bs.a.431.5	yes	72	3.2	odd	2	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-0.718088 - 0.0628246i) q^{5} +(-2.07081 + 1.73762i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-0.718088 - 0.0628246i) q^{5} +(-2.07081 + 1.73762i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.360415 + 0.624258i) q^{10} +(2.14666 - 3.71813i) q^{11} +(0.0350998 - 0.0163673i) q^{13} +(2.61114 + 0.699652i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(-1.26227 - 0.588607i) q^{17} +(-1.15999 - 0.812232i) q^{19} +(0.304636 - 0.653295i) q^{20} +(-4.27699 + 0.374188i) q^{22} +(1.21793 - 4.54537i) q^{23} +(-4.41234 - 0.778014i) q^{25} +(-0.0335397 - 0.0193642i) q^{26} +(-0.924566 - 2.54022i) q^{28} +(-2.18568 - 8.15709i) q^{29} +(-3.19999 - 3.19999i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(0.241851 + 1.37160i) q^{34} +(1.59619 - 1.11766i) q^{35} +(6.02223 - 0.856003i) q^{37} +1.41608i q^{38} +(-0.709880 + 0.125171i) q^{40} +(-8.42883 - 3.06784i) q^{41} +(-0.673546 + 0.673546i) q^{43} +(2.75969 + 3.28888i) q^{44} +(-4.42192 + 1.60945i) q^{46} +(2.04440 - 1.18033i) q^{47} +(0.0534066 - 0.302884i) q^{49} +(1.89350 + 4.06062i) q^{50} +(0.00337540 + 0.0385810i) q^{52} +(-0.385452 + 0.459364i) q^{53} +(-1.77508 + 2.53508i) q^{55} +(-1.55052 + 2.21437i) q^{56} +(-5.42824 + 6.46912i) q^{58} +(0.273822 + 3.12980i) q^{59} +(-4.73693 - 10.1584i) q^{61} +(-0.785839 + 4.45671i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-0.0262330 + 0.00954803i) q^{65} +(5.48130 + 6.53235i) q^{67} +(0.984832 - 0.984832i) q^{68} +(-1.83107 - 0.666456i) q^{70} +(0.759603 - 0.133939i) q^{71} -9.36628i q^{73} +(-4.15541 - 4.44214i) q^{74} +(1.15999 - 0.812232i) q^{76} +(2.01535 + 11.4296i) q^{77} +(-0.124024 + 1.41760i) q^{79} +(0.509704 + 0.509704i) q^{80} +(2.32155 + 8.66414i) q^{82} +(-2.84370 - 7.81299i) q^{83} +(0.869443 + 0.501973i) q^{85} +(0.938067 + 0.165407i) q^{86} +(1.11119 - 4.14703i) q^{88} +(-10.6799 + 0.934373i) q^{89} +(-0.0442449 + 0.0948835i) q^{91} +(3.85469 + 2.69909i) q^{92} +(-2.13949 - 0.997660i) q^{94} +(0.781945 + 0.656130i) q^{95} +(-2.87161 - 0.769446i) q^{97} +(-0.278741 + 0.129979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

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Database

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