LMFDB - Embedded newform 666.2.bs.b.611.2

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:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			611.2
Character	$\chi$	$=$	666.611
Dual form			666.2.bs.b.557.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-0.0741011 + 0.0345539i) q^{5} +(-1.92570 - 0.700897i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-0.0741011 + 0.0345539i) q^{5} +(-1.92570 - 0.700897i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.0408808 + 0.0708076i) q^{10} +(0.0467419 - 0.0809593i) q^{11} +(-3.00542 + 4.29219i) q^{13} +(-0.530394 + 1.97946i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-2.94921 - 4.21190i) q^{17} +(-7.61336 - 0.666082i) q^{19} +(0.0669751 - 0.0468965i) q^{20} +(-0.0847251 - 0.0395080i) q^{22} +(6.72256 + 1.80130i) q^{23} +(-3.20964 + 3.82510i) q^{25} +(4.53780 + 2.61990i) q^{26} +(2.01815 + 0.355855i) q^{28} +(-3.03735 + 0.813856i) q^{29} +(-0.356247 + 0.356247i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-3.93883 + 3.30507i) q^{34} +(0.166915 - 0.0146032i) q^{35} +(-6.08100 + 0.146577i) q^{37} +7.64244i q^{38} +(-0.0525553 - 0.0626330i) q^{40} +(0.847815 + 4.80820i) q^{41} +(5.17585 + 5.17585i) q^{43} +(-0.0319733 + 0.0878460i) q^{44} +(1.20854 - 6.85397i) q^{46} +(-7.78930 + 4.49715i) q^{47} +(-2.14525 - 1.80008i) q^{49} +(4.09028 + 2.86405i) q^{50} +(2.21443 - 4.74887i) q^{52} +(-2.03092 - 5.57992i) q^{53} +(-0.000666164 + 0.00761429i) q^{55} +(0.178607 - 2.04149i) q^{56} +(1.07548 + 2.95486i) q^{58} +(3.74133 - 8.02332i) q^{59} +(-4.71665 - 3.30264i) q^{61} +(0.385940 + 0.323842i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(0.0743933 - 0.421905i) q^{65} +(1.89197 - 5.19815i) q^{67} +(3.63579 + 3.63579i) q^{68} +(-0.0290952 - 0.165007i) q^{70} +(6.74204 + 8.03485i) q^{71} +4.72714i q^{73} +(0.676013 + 6.04508i) q^{74} +(7.61336 - 0.666082i) q^{76} +(-0.146755 + 0.123142i) q^{77} +(5.96506 + 12.7921i) q^{79} +(-0.0578141 + 0.0578141i) q^{80} +(4.71601 - 1.26365i) q^{82} +(-11.2270 - 1.97962i) q^{83} +(0.364077 + 0.210200i) q^{85} +(4.70505 - 5.60726i) q^{86} +(0.0902984 + 0.0241954i) q^{88} +(5.09003 + 2.37352i) q^{89} +(8.79593 - 6.15898i) q^{91} +(-6.93322 - 0.606578i) q^{92} +(5.15892 + 7.36770i) q^{94} +(0.587174 - 0.213714i) q^{95} +(0.309796 - 1.15618i) q^{97} +(-1.60626 + 2.29398i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{35}{36}\right)$

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 $

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$		0			0
$3$		0			0
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$	−0.0741011	+	0.0345539i	−0.0331390	+	0.0154530i	−0.439117	−	0.898430i	$-0.644709\pi$
$5$	−0.0741011	+	0.0345539i	−0.0331390	+	0.0154530i	0.405978	+	0.913883i	$0.366931\pi$
$6$		0			0
$7$	−1.92570	−	0.700897i	−0.727846	−	0.264914i	−0.0485931	−	0.998819i	$-0.515474\pi$
$7$	−1.92570	−	0.700897i	−0.727846	−	0.264914i	−0.679253	+	0.733904i	$0.737696\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$		0			0
$10$	0.0408808	+	0.0708076i	0.0129276	+	0.0223913i
$11$	0.0467419	−	0.0809593i	0.0140932	−	0.0244102i	−0.858893	−	0.512155i	$-0.828847\pi$
$11$	0.0467419	−	0.0809593i	0.0140932	−	0.0244102i	0.872986	+	0.487745i	$0.162181\pi$
$12$		0			0
$13$	−3.00542	+	4.29219i	−0.833555	+	1.19044i	0.146004	+	0.989284i	$0.453359\pi$
$13$	−3.00542	+	4.29219i	−0.833555	+	1.19044i	−0.979559	+	0.201156i	$0.935530\pi$
$14$	−0.530394	+	1.97946i	−0.141754	+	0.529033i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−2.94921	−	4.21190i	−0.715287	−	1.02154i	−0.998054	−	0.0623477i	$-0.980141\pi$
$17$	−2.94921	−	4.21190i	−0.715287	−	1.02154i	0.282767	−	0.959189i	$-0.408748\pi$
$18$		0			0
$19$	−7.61336	−	0.666082i	−1.74662	−	0.152810i	−0.831379	−	0.555707i	$-0.812448\pi$
$19$	−7.61336	−	0.666082i	−1.74662	−	0.152810i	−0.915245	+	0.402897i	$0.868003\pi$
$20$	0.0669751	−	0.0468965i	0.0149761	−	0.0104864i
$21$		0			0
$22$	−0.0847251	−	0.0395080i	−0.0180634	−	0.00842312i
$23$	6.72256	+	1.80130i	1.40175	+	0.375598i	0.878973	−	0.476871i	$-0.158229\pi$
$23$	6.72256	+	1.80130i	1.40175	+	0.375598i	0.522777	+	0.852469i	$0.324896\pi$
$24$		0			0
$25$	−3.20964	+	3.82510i	−0.641928	+	0.765020i
$26$	4.53780	+	2.61990i	0.889935	+	0.513805i
$27$		0			0
$28$	2.01815	+	0.355855i	0.381395	+	0.0672502i
$29$	−3.03735	+	0.813856i	−0.564022	+	0.151129i	−0.529554	−	0.848277i	$-0.677641\pi$
$29$	−3.03735	+	0.813856i	−0.564022	+	0.151129i	−0.0344685	+	0.999406i	$0.510974\pi$
$30$		0			0
$31$	−0.356247	+	0.356247i	−0.0639838	+	0.0639838i	−0.738375	−	0.674391i	$-0.764406\pi$
$31$	−0.356247	+	0.356247i	−0.0639838	+	0.0639838i	0.674391	+	0.738375i	$0.264406\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$		0			0
$34$	−3.93883	+	3.30507i	−0.675504	+	0.566816i
$35$	0.166915	−	0.0146032i	0.0282138	−	0.00246839i
$36$		0			0
$37$	−6.08100	+	0.146577i	−0.999710	+	0.0240971i
$37$	−6.08100	+	0.146577i	−0.999710	+	0.0240971i
$38$			7.64244i			1.23977i
$39$		0			0
$40$	−0.0525553	−	0.0626330i	−0.00830972	−	0.00990314i
$41$	0.847815	+	4.80820i	0.132406	+	0.750915i	0.976631	+	0.214924i	$0.0689505\pi$
$41$	0.847815	+	4.80820i	0.132406	+	0.750915i	−0.844224	+	0.535990i	$0.819938\pi$
$42$		0			0
$43$	5.17585	+	5.17585i	0.789310	+	0.789310i	0.981381	−	0.192071i	$-0.0615205\pi$
$43$	5.17585	+	5.17585i	0.789310	+	0.789310i	−0.192071	+	0.981381i	$0.561520\pi$
$44$	−0.0319733	+	0.0878460i	−0.00482016	+	0.0132433i
$45$		0			0
$46$	1.20854	−	6.85397i	0.178190	−	1.01056i
$47$	−7.78930	+	4.49715i	−1.13619	+	0.655977i	−0.945483	−	0.325671i	$-0.894410\pi$
$47$	−7.78930	+	4.49715i	−1.13619	+	0.655977i	−0.190702	+	0.981648i	$0.561077\pi$
$48$		0			0
$49$	−2.14525	−	1.80008i	−0.306464	−	0.257154i
$50$	4.09028	+	2.86405i	0.578454	+	0.405038i
$51$		0			0
$52$	2.21443	−	4.74887i	0.307087	−	0.658550i
$53$	−2.03092	−	5.57992i	−0.278969	−	0.766461i	−0.997480	−	0.0709454i	$-0.977398\pi$
$53$	−2.03092	−	5.57992i	−0.278969	−	0.766461i	0.718511	−	0.695515i	$-0.244824\pi$
$54$		0			0
$55$	−0.000666164		0.00761429i	−8.98255e−5		0.00102671i
$56$	0.178607	−	2.04149i	0.0238674	−	0.272805i
$57$		0			0
$58$	1.07548	+	2.95486i	0.141218	+	0.387992i
$59$	3.74133	−	8.02332i	0.487080	−	1.04455i	−0.497152	−	0.867664i	$-0.665621\pi$
$59$	3.74133	−	8.02332i	0.487080	−	1.04455i	0.984232	−	0.176883i	$-0.0566015\pi$
$60$		0			0
$61$	−4.71665	−	3.30264i	−0.603906	−	0.422859i	0.231233	−	0.972898i	$-0.425724\pi$
$61$	−4.71665	−	3.30264i	−0.603906	−	0.422859i	−0.835139	+	0.550039i	$0.814613\pi$
$62$	0.385940	+	0.323842i	0.0490145	+	0.0411280i
$63$		0			0
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	0.0743933	−	0.421905i	0.00922735	−	0.0523309i
$66$		0			0
$67$	1.89197	−	5.19815i	0.231141	−	0.635055i	−0.768849	−	0.639430i	$-0.779170\pi$
$67$	1.89197	−	5.19815i	0.231141	−	0.635055i	0.999990	+	0.00437504i	$0.00139262\pi$
$68$	3.63579	+	3.63579i	0.440904	+	0.440904i
$69$		0			0
$70$	−0.0290952	−	0.165007i	−0.00347755	−	0.0197221i
$71$	6.74204	+	8.03485i	0.800133	+	0.953561i	0.999653	−	0.0263324i	$-0.00838284\pi$
$71$	6.74204	+	8.03485i	0.800133	+	0.953561i	−0.199520	+	0.979894i	$0.563938\pi$
$72$		0			0
$73$			4.72714i			0.553270i	0.960975	+	0.276635i	$0.0892192\pi$
$73$			4.72714i			0.553270i	−0.960975	+	0.276635i	$0.910781\pi$
$74$	0.676013	+	6.04508i	0.0785849	+	0.702726i
$75$		0			0
$76$	7.61336	−	0.666082i	0.873312	−	0.0764049i
$77$	−0.146755	+	0.123142i	−0.0167243	+	0.0140333i
$78$		0			0
$79$	5.96506	+	12.7921i	0.671122	+	1.43922i	0.886516	+	0.462698i	$0.153118\pi$
$79$	5.96506	+	12.7921i	0.671122	+	1.43922i	−0.215394	+	0.976527i	$0.569104\pi$
$80$	−0.0578141	+	0.0578141i	−0.00646382	+	0.00646382i
$81$		0			0
$82$	4.71601	−	1.26365i	0.520796	−	0.139547i
$83$	−11.2270	−	1.97962i	−1.23232	−	0.217291i	−0.480699	−	0.876886i	$-0.659617\pi$
$83$	−11.2270	−	1.97962i	−1.23232	−	0.217291i	−0.751622	+	0.659594i	$0.770728\pi$
$84$		0			0
$85$	0.364077	+	0.210200i	0.0394897	+	0.0227994i
$86$	4.70505	−	5.60726i	0.507359	−	0.604646i
$87$		0			0
$88$	0.0902984	+	0.0241954i	0.00962584	+	0.00257924i
$89$	5.09003	+	2.37352i	0.539542	+	0.251593i	0.673233	−	0.739430i	$-0.264905\pi$
$89$	5.09003	+	2.37352i	0.539542	+	0.251593i	−0.133691	+	0.991023i	$0.542683\pi$
$90$		0			0
$91$	8.79593	−	6.15898i	0.922064	−	0.645636i
$92$	−6.93322	−	0.606578i	−0.722838	−	0.0632402i
$93$		0			0
$94$	5.15892	+	7.36770i	0.532102	+	0.759921i
$95$	0.587174	−	0.213714i	0.0602428	−	0.0219266i
$96$		0			0
$97$	0.309796	−	1.15618i	0.0314551	−	0.117392i	−0.948413	−	0.317037i	$-0.897312\pi$
$97$	0.309796	−	1.15618i	0.0314551	−	0.117392i	0.979868	+	0.199645i	$0.0639788\pi$
$98$	−1.60626	+	2.29398i	−0.162257	+	0.231726i
$99$		0			0
$100$	2.49666	−	4.32434i	0.249666	−	0.432434i
$101$	−4.65686	−	8.06592i	−0.463375	−	0.802589i	0.535752	−	0.844376i	$-0.320028\pi$
$101$	−4.65686	−	8.06592i	−0.463375	−	0.802589i	−0.999127	+	0.0417866i	$0.986695\pi$
$102$		0			0
$103$	−5.00217	−	18.6684i	−0.492879	−	1.83945i	−0.541600	−	0.840636i	$-0.682181\pi$
$103$	−5.00217	−	18.6684i	−0.492879	−	1.83945i	0.0487214	−	0.998812i	$-0.484485\pi$
$104$	−4.92380	−	1.79212i	−0.482818	−	0.175731i
$105$		0			0
$106$	−5.38168	+	2.50952i	−0.522715	+	0.243746i
$107$	6.82200	−	1.20290i	0.659508	−	0.116289i	0.166130	−	0.986104i	$-0.446873\pi$
$107$	6.82200	−	1.20290i	0.659508	−	0.116289i	0.493378	+	0.869815i	$0.335762\pi$
$108$		0			0
$109$	−0.415060	−	4.74416i	−0.0397556	−	0.454408i	−0.989817	−	0.142346i	$-0.954536\pi$
$109$	−0.415060	−	4.74416i	−0.0397556	−	0.454408i	0.950061	−	0.312063i	$-0.101020\pi$
$110$	0.00764338			0.000728767
$111$		0			0
$112$	−2.04929			−0.193639
$113$	−1.75594	−	20.0705i	−0.165185	−	1.88808i	−0.400704	−	0.916207i	$-0.631235\pi$
$113$	−1.75594	−	20.0705i	−0.165185	−	1.88808i	0.235519	−	0.971870i	$-0.424321\pi$
$114$		0			0
$115$	−0.560391	+	0.0988121i	−0.0522568	+	0.00921427i
$116$	2.84988	−	1.32892i	0.264605	−	0.123387i
$117$		0			0
$118$	−8.31886	−	3.02782i	−0.765813	−	0.278733i
$119$	2.72717	+	10.1779i	0.249999	+	0.933011i
$120$		0			0
$121$	5.49563	+	9.51871i	0.499603	+	0.865337i
$122$	−2.87899	+	4.98655i	−0.260651	+	0.451461i
$123$		0			0
$124$	0.288973	−	0.412696i	0.0259505	−	0.0370612i
$125$	0.211473	−	0.789228i	0.0189147	−	0.0705907i
$126$		0			0
$127$	11.9540	−	4.35091i	1.06075	−	0.386081i	0.248040	−	0.968750i	$-0.420214\pi$
$127$	11.9540	−	4.35091i	1.06075	−	0.386081i	0.812710	+	0.582669i	$0.197991\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$		0			0
$130$	−0.426784	−	0.0373387i	−0.0374314	−	0.00327482i
$131$	−1.32503	+	0.927796i	−0.115768	+	0.0810619i	−0.630027	−	0.776573i	$-0.716956\pi$
$131$	−1.32503	+	0.927796i	−0.115768	+	0.0810619i	0.514258	+	0.857635i	$0.328067\pi$
$132$		0			0
$133$	14.1942	+	6.61885i	1.23079	+	0.573927i
$134$	−5.34326	−	1.43172i	−0.461588	−	0.123682i
$135$		0			0
$136$	3.30507	−	3.93883i	0.283408	−	0.337752i
$137$	−13.7839	−	7.95811i	−1.17763	−	0.679908i	−0.222168	−	0.975008i	$-0.571313\pi$
$137$	−13.7839	−	7.95811i	−1.17763	−	0.679908i	−0.955466	+	0.295101i	$0.904647\pi$
$138$		0			0
$139$	−5.21477	−	0.919504i	−0.442311	−	0.0779913i	−0.0519424	−	0.998650i	$-0.516541\pi$
$139$	−5.21477	−	0.919504i	−0.442311	−	0.0779913i	−0.390368	+	0.920659i	$0.627652\pi$
$140$	−0.161844	+	0.0433658i	−0.0136783	+	0.00366508i
$141$		0			0
$142$	7.41667	−	7.41667i	0.622393	−	0.622393i
$143$	0.207014	+	0.443942i	0.0173114	+	0.0371243i
$144$		0			0
$145$	0.196949	−	0.165260i	0.0163557	−	0.0137241i
$146$	4.70915	−	0.411997i	0.389732	−	0.0340971i
$147$		0			0
$148$	5.96316	−	1.20030i	0.490169	−	0.0986644i
$149$		−	4.75836i		−	0.389820i	−0.980821	−	0.194910i	$-0.937559\pi$
$149$		−	4.75836i		−	0.389820i	0.980821	−	0.194910i	$-0.0624414\pi$
$150$		0			0
$151$	2.62654	+	3.13019i	0.213745	+	0.254731i	0.862254	−	0.506475i	$-0.169052\pi$
$151$	2.62654	+	3.13019i	0.213745	+	0.254731i	−0.648510	+	0.761206i	$0.724607\pi$
$152$	−1.32710	−	7.52633i	−0.107642	−	0.610466i
$153$		0			0
$154$	0.135464	+	0.135464i	0.0109160	+	0.0109160i
$155$	0.0140886	−	0.0387080i	0.00113162	−	0.00310910i
$156$		0			0
$157$	−0.745032	+	4.22529i	−0.0594600	+	0.337215i	−0.999997	−	0.00247695i	$-0.999212\pi$
$157$	−0.745032	+	4.22529i	−0.0594600	+	0.337215i	0.940537	+	0.339692i	$0.110323\pi$
$158$	12.2235	−	7.05727i	0.972453	−	0.561446i
$159$		0			0
$160$	0.0626330	+	0.0525553i	0.00495157	+	0.00415486i
$161$	−11.6831	−	8.18059i	−0.920757	−	0.644721i
$162$		0			0
$163$	−1.73199	+	3.71427i	−0.135660	+	0.290924i	−0.962388	−	0.271677i	$-0.912422\pi$
$163$	−1.73199	+	3.71427i	−0.135660	+	0.290924i	0.826728	+	0.562601i	$0.190199\pi$
$164$	−1.66987	−	4.58793i	−0.130395	−	0.358257i
$165$		0			0
$166$	−0.993590	+	11.3568i	−0.0771176	+	0.881458i
$167$	−0.228078	+	2.60695i	−0.0176492	+	0.201732i	0.982251	+	0.187574i	$0.0600623\pi$
$167$	−0.228078	+	2.60695i	−0.0176492	+	0.201732i	−0.999900	+	0.0141579i	$0.995493\pi$
$168$		0			0
$169$	−4.94407	−	13.5837i	−0.380313	−	1.04490i
$170$	0.177669	−	0.381012i	0.0136266	−	0.0292223i
$171$		0			0
$172$	−5.99599	−	4.19844i	−0.457190	−	0.320128i
$173$	−0.932633	−	0.782572i	−0.0709068	−	0.0594978i	0.606645	−	0.794973i	$-0.292515\pi$
$173$	−0.932633	−	0.782572i	−0.0709068	−	0.0594978i	−0.677552	+	0.735475i	$0.736959\pi$
$174$		0			0
$175$	8.86181	−	5.11637i	0.669890	−	0.386761i
$176$	0.0162333	−	0.0920635i	0.00122363	−	0.00693955i
$177$		0			0
$178$	1.92086	−	5.27753i	0.143975	−	0.395567i
$179$	−5.10868	−	5.10868i	−0.381840	−	0.381840i	0.489924	−	0.871765i	$-0.337024\pi$
$179$	−5.10868	−	5.10868i	−0.381840	−	0.381840i	−0.871765	+	0.489924i	$0.837024\pi$
$180$		0			0
$181$	−1.95114	−	11.0655i	−0.145027	−	0.822490i	−0.967345	−	0.253462i	$-0.918431\pi$
$181$	−1.95114	−	11.0655i	−0.145027	−	0.822490i	0.822318	−	0.569028i	$-0.192680\pi$
$182$	−6.90215	−	8.22567i	−0.511622	−	0.609727i
$183$		0			0
$184$			6.95971i			0.513076i
$185$	0.445544	−	0.220984i	0.0327570	−	0.0162470i
$186$		0			0
$187$	−0.478844	+	0.0418934i	−0.0350166	+	0.00306355i
$188$	6.89004	−	5.78143i	0.502508	−	0.421654i
$189$		0			0
$190$	−0.264076	−	0.566313i	−0.0191581	−	0.0410847i
$191$	7.95827	−	7.95827i	0.575840	−	0.575840i	−0.357914	−	0.933754i	$-0.616512\pi$
$191$	7.95827	−	7.95827i	0.575840	−	0.575840i	0.933754	+	0.357914i	$0.116512\pi$
$192$		0			0
$193$	−18.8822	+	5.05946i	−1.35917	+	0.364188i	−0.863511	−	0.504330i	$-0.831740\pi$
$193$	−18.8822	+	5.05946i	−1.35917	+	0.364188i	−0.495658	+	0.868518i	$0.665073\pi$
$194$	−1.17878	−	0.207850i	−0.0846313	−	0.0149228i
$195$		0			0
$196$	2.42524	+	1.40021i	0.173231	+	0.100015i
$197$	−5.28637	+	6.30005i	−0.376638	+	0.448860i	−0.920750	−	0.390153i	$-0.872422\pi$
$197$	−5.28637	+	6.30005i	−0.376638	+	0.448860i	0.544112	+	0.839013i	$0.316867\pi$
$198$		0			0
$199$	6.27114	+	1.68035i	0.444549	+	0.119117i	0.474148	−	0.880445i	$-0.342756\pi$
$199$	6.27114	+	1.68035i	0.444549	+	0.119117i	−0.0295987	+	0.999562i	$0.509423\pi$
$200$	−4.52548	−	2.11027i	−0.320000	−	0.149218i
$201$		0			0
$202$	−7.62936	+	5.34213i	−0.536800	+	0.375871i
$203$	6.41945	+	0.561630i	0.450557	+	0.0394187i
$204$		0			0
$205$	−0.228966	−	0.326998i	−0.0159917	−	0.0228385i
$206$	−18.1614	+	6.61019i	−1.26536	+	0.460554i
$207$		0			0
$208$	−1.35616	+	5.06126i	−0.0940327	+	0.350935i
$209$	−0.409788	+	0.585238i	−0.0283456	+	0.0404818i
$210$		0			0
$211$	−6.66962	+	11.5521i	−0.459156	+	0.795281i	−0.998917	−	0.0465376i	$-0.985181\pi$
$211$	−6.66962	+	11.5521i	−0.459156	+	0.795281i	0.539761	+	0.841818i	$0.318515\pi$
$212$	2.96901	+	5.14248i	0.203913	+	0.353187i
$213$		0			0
$214$	−1.79290	−	6.69120i	−0.122560	−	0.457401i
$215$	−0.562382	−	0.204690i	−0.0383541	−	0.0139598i
$216$		0			0
$217$	0.935717	−	0.436332i	0.0635206	−	0.0296201i
$218$	−4.68994	+	0.826962i	−0.317642	+	0.0560089i
$219$		0			0
$220$	−0.000666164	−	0.00761429i	−4.49128e−5	−	0.000513355i
$221$	26.9419			1.81231
$222$		0			0
$223$	−8.61963			−0.577213			−0.288606	−	0.957448i	$-0.593192\pi$
$223$	−8.61963			−0.577213			−0.288606	+	0.957448i	$0.593192\pi$
$224$	0.178607	+	2.04149i	0.0119337	+	0.136403i
$225$		0			0
$226$	−19.8411	+	3.49852i	−1.31981	+	0.232718i
$227$	−1.54260	+	0.719325i	−0.102386	+	0.0477433i	−0.473136	−	0.880989i	$-0.656878\pi$
$227$	−1.54260	+	0.719325i	−0.102386	+	0.0477433i	0.370751	+	0.928732i	$0.379100\pi$
$228$		0			0
$229$	20.2839	+	7.38274i	1.34040	+	0.487865i	0.909938	−	0.414744i	$-0.136129\pi$
$229$	20.2839	+	7.38274i	1.34040	+	0.487865i	0.430461	+	0.902609i	$0.358351\pi$
$230$	0.147277	+	0.549647i	0.00971118	+	0.0362426i
$231$		0			0
$232$	−1.57225	−	2.72322i	−0.103223	−	0.178788i
$233$	−7.87150	+	13.6338i	−0.515679	+	0.893182i	0.484155	+	0.874982i	$0.339127\pi$
$233$	−7.87150	+	13.6338i	−0.515679	+	0.893182i	−0.999834	+	0.0182000i	$0.994206\pi$
$234$		0			0
$235$	0.421801	−	0.602395i	0.0275153	−	0.0392959i
$236$	−2.29126	+	8.55110i	−0.149148	+	0.556629i
$237$		0			0
$238$	9.90153	−	3.60386i	0.641821	−	0.233604i
$239$	6.16633	+	8.80642i	0.398866	+	0.569640i	0.967475	−	0.252968i	$-0.0814068\pi$
$239$	6.16633	+	8.80642i	0.398866	+	0.569640i	−0.568608	+	0.822609i	$0.692518\pi$
$240$		0			0
$241$	7.12164	+	0.623063i	0.458745	+	0.0401350i	0.314187	−	0.949361i	$-0.398268\pi$
$241$	7.12164	+	0.623063i	0.458745	+	0.0401350i	0.144558	+	0.989496i	$0.453824\pi$
$242$	9.00351	−	6.30433i	0.578768	−	0.405258i
$243$		0			0
$244$	5.21849	+	2.43342i	0.334080	+	0.155784i
$245$	0.221165	+	0.0592611i	0.0141297	+	0.00378605i
$246$		0			0
$247$	25.7403	−	30.6761i	1.63782	−	1.95188i
$248$	−0.436312	−	0.251905i	−0.0277058	−	0.0159960i
$249$		0			0
$250$	−0.804656	−	0.141882i	−0.0508909	−	0.00897344i
$251$	11.9186	−	3.19357i	0.752292	−	0.201576i	0.137758	−	0.990466i	$-0.456010\pi$
$251$	11.9186	−	3.19357i	0.752292	−	0.201576i	0.614535	+	0.788890i	$0.289344\pi$
$252$		0			0
$253$	0.460058	−	0.460058i	0.0289236	−	0.0289236i
$254$	−5.37622	−	11.5293i	−0.337334	−	0.723415i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−21.8099	+	1.90812i	−1.36046	+	0.119025i	−0.743906	−	0.668285i	$-0.767029\pi$
$257$	−21.8099	+	1.90812i	−1.36046	+	0.119025i	−0.616558	+	0.787310i	$0.711473\pi$
$258$		0			0
$259$	11.8129	+	3.97989i	0.734018	+	0.247298i
$260$			0.428414i			0.0265691i
$261$		0			0
$262$	1.03975	+	1.23913i	0.0642360	+	0.0765534i
$263$	1.66000	+	9.41434i	0.102360	+	0.580513i	0.992242	+	0.124322i	$0.0396755\pi$
$263$	1.66000	+	9.41434i	0.102360	+	0.580513i	−0.889882	+	0.456191i	$0.849213\pi$
$264$		0			0
$265$	0.343302	+	0.343302i	0.0210889	+	0.0210889i
$266$	5.35656	−	14.7170i	0.328432	−	0.902359i
$267$		0			0
$268$	−0.960579	+	5.44771i	−0.0586767	+	0.332772i
$269$	24.6295	−	14.2199i	1.50169	−	0.867001i	0.501692	−	0.865046i	$-0.332711\pi$
$269$	24.6295	−	14.2199i	1.50169	−	0.867001i	0.999998	−	0.00195476i	$-0.000622219\pi$
$270$		0			0
$271$	0.258733	+	0.217103i	0.0157169	+	0.0131881i	0.650612	−	0.759410i	$-0.274512\pi$
$271$	0.258733	+	0.217103i	0.0157169	+	0.0131881i	−0.634895	+	0.772598i	$0.718957\pi$
$272$	−4.21190	−	2.94921i	−0.255384	−	0.178822i
$273$		0			0
$274$	−6.72649	+	14.4250i	−0.406362	+	0.871446i
$275$	0.159653	+	0.438643i	0.00962743	+	0.0264512i
$276$		0			0
$277$	−0.787339	+	8.99932i	−0.0473066	+	0.540717i	0.935153	+	0.354243i	$0.115261\pi$
$277$	−0.787339	+	8.99932i	−0.0473066	+	0.540717i	−0.982460	+	0.186474i	$0.940294\pi$
$278$	−0.461508	+	5.27506i	−0.0276794	+	0.316377i
$279$		0			0
$280$	0.0573064	+	0.157448i	0.00342471	+	0.00940932i
$281$	−11.8672	+	25.4492i	−0.707936	+	1.51817i	0.141189	+	0.989983i	$0.454907\pi$
$281$	−11.8672	+	25.4492i	−0.707936	+	1.51817i	−0.849125	+	0.528191i	$0.822870\pi$
$282$		0			0
$283$	−11.1429	−	7.80236i	−0.662378	−	0.463802i	0.193417	−	0.981117i	$-0.438043\pi$
$283$	−11.1429	−	7.80236i	−0.662378	−	0.463802i	−0.855796	+	0.517314i	$0.826932\pi$
$284$	−8.03485	−	6.74204i	−0.476781	−	0.400066i
$285$		0			0
$286$	0.424211	−	0.244918i	0.0250841	−	0.0144823i
$287$	1.73742	−	9.85338i	0.102556	−	0.581626i
$288$		0			0
$289$	−3.22796	+	8.86875i	−0.189880	+	0.521691i
$290$	−0.181796	−	0.181796i	−0.0106755	−	0.0106755i
$291$		0			0
$292$	−0.820859	−	4.65532i	−0.0480371	−	0.272432i
$293$	16.0120	+	19.0823i	0.935430	+	1.11480i	0.993194	+	0.116472i	$0.0371585\pi$
$293$	16.0120	+	19.0823i	0.935430	+	1.11480i	−0.0577640	+	0.998330i	$0.518397\pi$
$294$		0			0
$295$			0.723814i			0.0421421i
$296$	−1.71546	−	5.83585i	−0.0997091	−	0.339202i
$297$		0			0
$298$	−4.74025	+	0.414718i	−0.274595	+	0.0240240i
$299$	−27.9357	+	23.4408i	−1.61556	+	1.35562i
$300$		0			0
$301$	−6.33939	−	13.5949i	−0.365396	−	0.783595i
$302$	2.88936	−	2.88936i	0.166264	−	0.166264i
$303$		0			0
$304$	−7.38203	+	1.97801i	−0.423388	+	0.113447i
$305$	0.463628	+	0.0817502i	0.0265473	+	0.00468100i
$306$		0			0
$307$	−5.88777	−	3.39930i	−0.336033	−	0.194008i	0.322484	−	0.946575i	$-0.395482\pi$
$307$	−5.88777	−	3.39930i	−0.336033	−	0.194008i	−0.658516	+	0.752567i	$0.728816\pi$
$308$	0.123142	−	0.146755i	0.00701667	−	0.00836214i
$309$		0			0
$310$	−0.0397886	−	0.0106613i	−0.00225984	−	0.000605523i
$311$	31.8564	+	14.8549i	1.80641	+	0.842344i	0.938140	+	0.346256i	$0.112547\pi$
$311$	31.8564	+	14.8549i	1.80641	+	0.842344i	0.868272	+	0.496088i	$0.165231\pi$
$312$		0			0
$313$	−24.1676	+	16.9223i	−1.36603	+	0.956506i	−0.366371	+	0.930469i	$0.619400\pi$
$313$	−24.1676	+	16.9223i	−1.36603	+	0.956506i	−0.999661	+	0.0260366i	$0.991711\pi$
$314$	4.27414	+	0.373939i	0.241204	+	0.0211026i
$315$		0			0
$316$	−8.09576	−	11.5619i	−0.455422	−	0.650410i
$317$	−32.0131	+	11.6518i	−1.79804	+	0.654432i	−0.799483	+	0.600689i	$0.794893\pi$
$317$	−32.0131	+	11.6518i	−1.79804	+	0.654432i	−0.998555	+	0.0537429i	$0.982885\pi$
$318$		0			0
$319$	−0.0760823	+	0.283943i	−0.00425979	+	0.0158978i
$320$	0.0468965	−	0.0669751i	0.00262159	−	0.00374402i
$321$		0			0
$322$	−7.13121	+	12.3516i	−0.397407	+	0.688329i
$323$	19.6479	+	34.0311i	1.09324	+	1.89354i
$324$		0			0
$325$	−6.77173	−	25.2724i	−0.375628	−	1.40186i
$326$	3.85109	+	1.40168i	0.213292	+	0.0776320i
$327$		0			0
$328$	−4.42493	+	2.06338i	−0.244326	+	0.113931i
$329$	18.1519	−	3.20067i	1.00075	−	0.176458i
$330$		0			0
$331$	0.437724	+	5.00321i	0.0240595	+	0.275001i	0.998689	+	0.0511790i	$0.0162979\pi$
$331$	0.437724	+	5.00321i	0.0240595	+	0.275001i	−0.974630	+	0.223822i	$0.928147\pi$
$332$	11.4002			0.625666
$333$		0			0
$334$	2.61690			0.143191
$335$	0.0394192	+	0.450564i	0.00215370	+	0.0246169i
$336$		0			0
$337$	−22.3573	+	3.94219i	−1.21788	+	0.214745i	−0.745412	−	0.666604i	$-0.767747\pi$
$337$	−22.3573	+	3.94219i	−1.21788	+	0.214745i	−0.472466	+	0.881349i	$0.656636\pi$
$338$	−13.1011	+	6.10915i	−0.712607	+	0.332294i
$339$		0			0
$340$	−0.395047	−	0.143785i	−0.0214244	−	0.00779785i
$341$	0.0121899	+	0.0454932i	0.000660118	+	0.00246359i
$342$		0			0
$343$	10.0419	+	17.3931i	0.542214	+	0.939142i
$344$	−3.65988	+	6.33910i	−0.197327	+	0.341781i
$345$		0			0
$346$	−0.698310	+	0.997290i	−0.0375414	+	0.0536146i
$347$	−3.97719	+	14.8431i	−0.213507	+	0.796817i	0.773180	+	0.634186i	$0.218665\pi$
$347$	−3.97719	+	14.8431i	−0.213507	+	0.796817i	−0.986687	+	0.162631i	$0.948002\pi$
$348$		0			0
$349$	−6.38284	+	2.32316i	−0.341666	+	0.124356i	−0.507154	−	0.861856i	$-0.669302\pi$
$349$	−6.38284	+	2.32316i	−0.341666	+	0.124356i	0.165488	+	0.986212i	$0.447080\pi$
$350$	−5.86925	−	8.38216i	−0.313725	−	0.448045i
$351$		0			0
$352$	−0.0931280	−	0.00814765i	−0.00496374	−	0.000434271i
$353$	13.7006	−	9.59325i	0.729209	−	0.510597i	−0.149023	−	0.988834i	$-0.547613\pi$
$353$	13.7006	−	9.59325i	0.729209	−	0.510597i	0.878231	+	0.478236i	$0.158724\pi$
$354$		0			0
$355$	−0.777228	−	0.362427i	−0.0412510	−	0.0192356i
$356$	−5.42486	−	1.45359i	−0.287517	−	0.0770399i
$357$		0			0
$358$	−4.64399	+	5.53449i	−0.245442	+	0.292507i
$359$	21.3335	+	12.3169i	1.12594	+	0.650062i	0.942911	−	0.333045i	$-0.108076\pi$
$359$	21.3335	+	12.3169i	1.12594	+	0.650062i	0.183030	+	0.983107i	$0.441409\pi$
$360$		0			0
$361$	38.8082	+	6.84293i	2.04254	+	0.360154i
$362$	−10.8533	+	2.90813i	−0.570437	+	0.152848i
$363$		0			0
$364$	−7.59280	+	7.59280i	−0.397971	+	0.397971i
$365$	−0.163341	−	0.350286i	−0.00854966	−	0.0183348i
$366$		0			0
$367$	6.82666	−	5.72824i	0.356349	−	0.299012i	−0.446985	−	0.894542i	$-0.647502\pi$
$367$	6.82666	−	5.72824i	0.356349	−	0.299012i	0.803333	+	0.595530i	$0.203058\pi$
$368$	6.93322	−	0.606578i	0.361419	−	0.0316201i
$369$		0			0
$370$	−0.258974	−	0.424588i	−0.0134634	−	0.0220733i
$371$			12.1687i			0.631768i
$372$		0			0
$373$	17.9693	+	21.4149i	0.930413	+	1.10882i	0.993839	+	0.110836i	$0.0353530\pi$
$373$	17.9693	+	21.4149i	0.930413	+	1.10882i	−0.0634257	+	0.997987i	$0.520203\pi$
$374$	0.0834680	+	0.473371i	0.00431603	+	0.0244774i
$375$		0			0
$376$	−6.35993	−	6.35993i	−0.327989	−	0.327989i
$377$	5.63531	−	15.4829i	0.290233	−	0.797409i
$378$		0			0
$379$	−1.67165	+	9.48042i	−0.0858671	+	0.486977i	0.911299	+	0.411745i	$0.135081\pi$
$379$	−1.67165	+	9.48042i	−0.0858671	+	0.486977i	−0.997166	+	0.0752313i	$0.976030\pi$
$380$	−0.541142	+	0.312429i	−0.0277600	+	0.0160273i
$381$		0			0
$382$	−8.62159	−	7.23437i	−0.441119	−	0.370143i
$383$	7.69620	+	5.38893i	0.393257	+	0.275362i	0.753436	−	0.657522i	$-0.228395\pi$
$383$	7.69620	+	5.38893i	0.393257	+	0.275362i	−0.360178	+	0.932884i	$0.617284\pi$
$384$		0			0
$385$	0.00661967	−	0.0141959i	0.000337369	−	0.000723491i
$386$	6.68590	+	18.3694i	0.340303	+	0.934976i
$387$		0			0
$388$	−0.104322	+	1.19241i	−0.00529615	+	0.0605353i
$389$	0.198208	−	2.26553i	0.0100496	−	0.114867i	−0.989513	−	0.144444i	$-0.953861\pi$
$389$	0.198208	−	2.26553i	0.0100496	−	0.114867i	0.999562	+	0.0295773i	$0.00941610\pi$
$390$		0			0
$391$	−12.2393	−	33.6272i	−0.618968	−	1.70060i
$392$	1.18351	−	2.53805i	0.0597763	−	0.128191i
$393$		0			0
$394$	6.73682	+	4.71717i	0.339396	+	0.237648i
$395$	−0.884035	−	0.741793i	−0.0444806	−	0.0373237i
$396$		0			0
$397$	−33.3296	+	19.2428i	−1.67276	+	0.965770i	−0.706681	+	0.707532i	$0.749809\pi$
$397$	−33.3296	+	19.2428i	−1.67276	+	0.965770i	−0.966081	+	0.258238i	$0.916858\pi$
$398$	1.12739	−	6.39372i	0.0565108	−	0.320488i
$399$		0			0
$400$	−1.70781	+	4.69218i	−0.0853907	+	0.234609i
$401$	−19.6027	−	19.6027i	−0.978914	−	0.978914i	0.0208684	−	0.999782i	$-0.493357\pi$
$401$	−19.6027	−	19.6027i	−0.978914	−	0.978914i	−0.999782	+	0.0208684i	$0.993357\pi$
$402$		0			0
$403$	−0.458407	−	2.59975i	−0.0228349	−	0.129503i
$404$	5.98675	+	7.13473i	0.297852	+	0.354966i
$405$		0			0
$406$		−	6.44398i		−	0.319809i
$407$	−0.272370	+	0.499165i	−0.0135009	+	0.0247427i
$408$		0			0
$409$	−20.3493	+	1.78033i	−1.00621	+	0.0880319i	−0.578329	−	0.815804i	$-0.696295\pi$
$409$	−20.3493	+	1.78033i	−1.00621	+	0.0880319i	−0.427880	+	0.903835i	$0.640739\pi$
$410$	−0.305797	+	0.256595i	−0.0151023	+	0.0126723i
$411$		0			0
$412$	8.16791	+	17.5161i	0.402404	+	0.862958i
$413$	−12.8282	+	12.8282i	−0.631235	+	0.631235i
$414$		0			0
$415$	0.900335	−	0.241244i	0.0441957	−	0.0118422i
$416$	5.16019	+	0.909881i	0.252999	+	0.0446106i
$417$		0			0
$418$	0.618727	+	0.357222i	0.0302629	+	0.0174723i
$419$	15.8623	−	18.9040i	0.774925	−	0.923520i	−0.223767	−	0.974643i	$-0.571836\pi$
$419$	15.8623	−	18.9040i	0.774925	−	0.923520i	0.998692	+	0.0511230i	$0.0162801\pi$
$420$		0			0
$421$	−34.0718	−	9.12952i	−1.66056	−	0.444945i	−0.698018	−	0.716080i	$-0.745934\pi$
$421$	−34.0718	−	9.12952i	−1.66056	−	0.444945i	−0.962541	+	0.271135i	$0.912601\pi$
$422$	12.0895	+	5.63741i	0.588505	+	0.274425i
$423$		0			0
$424$	4.86414	−	3.40591i	0.236224	−	0.165406i
$425$	25.5768	+	2.23768i	1.24066	+	0.108544i
$426$		0			0
$427$	6.76805	+	9.66577i	0.327529	+	0.467760i
$428$	−6.50948	+	2.36926i	−0.314648	+	0.114522i
$429$		0			0
$430$	−0.154897	+	0.578082i	−0.00746978	+	0.0278776i
$431$	−13.0562	+	18.6462i	−0.628897	+	0.898158i	−0.999531	−	0.0306209i	$-0.990252\pi$
$431$	−13.0562	+	18.6462i	−0.628897	+	0.898158i	0.370634	+	0.928779i	$0.379140\pi$
$432$		0			0
$433$	−13.3867	+	23.1864i	−0.643322	+	1.11427i	0.341364	+	0.939931i	$0.389111\pi$
$433$	−13.3867	+	23.1864i	−0.643322	+	1.11427i	−0.984686	+	0.174336i	$0.944222\pi$
$434$	−0.516225	−	0.894127i	−0.0247796	−	0.0429195i
$435$		0			0
$436$	1.23257	+	4.60001i	0.0590294	+	0.220301i
$437$	−49.9814	−	18.1918i	−2.39094	−	0.870230i
$438$		0			0
$439$	−13.6646	+	6.37192i	−0.652177	+	0.304115i	−0.720404	−	0.693555i	$-0.756044\pi$
$439$	−13.6646	+	6.37192i	−0.652177	+	0.304115i	0.0682269	+	0.997670i	$0.478266\pi$
$440$	−0.00752726	+	0.00132726i	−0.000358848	+	6.32746e-5i
$441$		0			0
$442$	−2.34814	−	26.8394i	−0.111690	−	1.27662i
$443$	−16.9338			−0.804548			−0.402274	−	0.915519i	$-0.631780\pi$
$443$	−16.9338			−0.804548			−0.402274	+	0.915519i	$0.631780\pi$
$444$		0			0
$445$	−0.459191			−0.0217678
$446$	0.751250	+	8.58683i	0.0355727	+	0.406598i
$447$		0			0
$448$	2.01815	−	0.355855i	0.0953488	−	0.0168126i
$449$	21.3254	−	9.94421i	1.00641	−	0.469296i	0.151713	−	0.988425i	$-0.451521\pi$
$449$	21.3254	−	9.94421i	1.00641	−	0.469296i	0.854696	+	0.519129i	$0.173743\pi$
$450$		0			0
$451$	0.428897	+	0.156106i	0.0201960	+	0.00735073i
$452$	5.21448	+	19.4607i	0.245268	+	0.915354i
$453$		0			0
$454$	0.851034	+	1.47403i	0.0399410	+	0.0691798i
$455$	−0.438971	+	0.760321i	−0.0205793	+	0.0356444i
$456$		0			0
$457$	20.3937	−	29.1252i	0.953978	−	1.36242i	0.0220584	−	0.999757i	$-0.492978\pi$
$457$	20.3937	−	29.1252i	0.953978	−	1.36242i	0.931920	−	0.362665i	$-0.118133\pi$
$458$	5.58679	−	20.8502i	0.261053	−	0.974265i
$459$		0			0
$460$	0.534719	−	0.194622i	0.0249314	−	0.00907429i
$461$	−10.6754	−	15.2460i	−0.497202	−	0.710078i	0.489612	−	0.871941i	$-0.337139\pi$
$461$	−10.6754	−	15.2460i	−0.497202	−	0.710078i	−0.986813	+	0.161863i	$0.948250\pi$
$462$		0			0
$463$	−9.07890	−	0.794301i	−0.421932	−	0.0369143i	−0.125787	−	0.992057i	$-0.540146\pi$
$463$	−9.07890	−	0.794301i	−0.421932	−	0.0369143i	−0.296145	+	0.955143i	$0.595701\pi$
$464$	−2.57582	+	1.80361i	−0.119580	+	0.0837305i
$465$		0			0
$466$	14.2680	+	6.65328i	0.660952	+	0.308207i
$467$	−6.23587	−	1.67090i	−0.288562	−	0.0773199i	0.111635	−	0.993749i	$-0.464391\pi$
$467$	−6.23587	−	1.67090i	−0.288562	−	0.0773199i	−0.400196	+	0.916429i	$0.631058\pi$
$468$		0			0
$469$	−7.28674	+	8.68399i	−0.336470	+	0.400990i
$470$	−0.636865	−	0.367694i	−0.0293764	−	0.0169605i
$471$		0			0
$472$	8.71826	+	1.53726i	0.401290	+	0.0707583i
$473$	0.660962	−	0.177104i	0.0303911	−	0.00814327i
$474$		0			0
$475$	26.9840	−	26.9840i	1.23811	−	1.23811i
$476$	−4.45312	−	9.54975i	−0.204109	−	0.437712i
$477$		0			0
$478$	8.23548	−	6.91039i	0.376682	−	0.316074i
$479$	21.2061	−	1.85530i	0.968933	−	0.0847707i	0.408311	−	0.912843i	$-0.366118\pi$
$479$	21.2061	−	1.85530i	0.968933	−	0.0847707i	0.560622	+	0.828072i	$0.310562\pi$
$480$		0			0
$481$	17.6468	−	26.5413i	0.804627	−	1.21018i
$482$		−	7.14884i		−	0.325621i
$483$		0			0
$484$	−7.06505	−	8.41979i	−0.321138	−	0.382718i
$485$	0.0169941	+	0.0963786i	0.000771664	+	0.00437633i
$486$		0			0
$487$	9.59314	+	9.59314i	0.434707	+	0.434707i	0.890226	−	0.455519i	$-0.150546\pi$
$487$	9.59314	+	9.59314i	0.434707	+	0.434707i	−0.455519	+	0.890226i	$0.650546\pi$
$488$	1.96934	−	5.41072i	0.0891479	−	0.244932i
$489$		0			0
$490$	0.0397597	−	0.225489i	0.00179616	−	0.0101865i
$491$	−23.0346	+	13.2990i	−1.03954	+	0.600177i	−0.919702	−	0.392616i	$-0.871570\pi$
$491$	−23.0346	+	13.2990i	−1.03954	+	0.600177i	−0.119835	+	0.992794i	$0.538237\pi$
$492$		0			0
$493$	12.3857	+	10.3928i	0.557822	+	0.468068i
$494$	−32.8028	−	22.9688i	−1.47587	−	1.03341i
$495$		0			0
$496$	−0.212919	+	0.456606i	−0.00956034	+	0.0205022i
$497$	−7.35154	−	20.1982i	−0.329761	−	0.906012i
$498$		0			0
$499$	−0.583121	+	6.66511i	−0.0261041	+	0.298371i	0.971909	+	0.235358i	$0.0756264\pi$
$499$	−0.583121	+	6.66511i	−0.0261041	+	0.298371i	−0.998013	+	0.0630127i	$0.979929\pi$
$500$	−0.0712122	+	0.813959i	−0.00318471	+	0.0364014i
$501$		0			0
$502$	−4.22018	−	11.5949i	−0.188356	−	0.517504i
$503$	13.8860	−	29.7785i	0.619144	−	1.32776i	−0.307403	−	0.951579i	$-0.599460\pi$
$503$	13.8860	−	29.7785i	0.619144	−	1.32776i	0.926547	−	0.376179i	$-0.122762\pi$
$504$		0			0
$505$	0.623788	+	0.436781i	0.0277582	+	0.0194365i
$506$	−0.498404	−	0.418210i	−0.0221567	−	0.0185917i
$507$		0			0
$508$	−11.0169	+	6.36061i	−0.488796	+	0.282206i
$509$	−0.923450	+	5.23715i	−0.0409312	+	0.232132i	−0.998410	−	0.0563717i	$-0.982047\pi$
$509$	−0.923450	+	5.23715i	−0.0409312	+	0.232132i	0.957479	+	0.288504i	$0.0931579\pi$
$510$		0			0
$511$	3.31324	−	9.10305i	0.146569	−	0.402695i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	3.80171	+	21.5606i	0.167686	+	0.950997i
$515$	1.01573	+	1.21050i	0.0447585	+	0.0533411i
$516$		0			0
$517$			0.840822i			0.0369793i
$518$	2.93518	−	12.1148i	0.128965	−	0.532295i
$519$		0			0
$520$	0.426784	−	0.0373387i	0.0187157	−	0.00163741i
$521$	8.93876	−	7.50051i	0.391614	−	0.328603i	−0.425627	−	0.904898i	$-0.639947\pi$
$521$	8.93876	−	7.50051i	0.391614	−	0.328603i	0.817242	+	0.576295i	$0.195502\pi$
$522$		0			0
$523$	16.5894	+	35.5761i	0.725405	+	1.55564i	0.827883	+	0.560901i	$0.189545\pi$
$523$	16.5894	+	35.5761i	0.725405	+	1.55564i	−0.102478	+	0.994735i	$0.532677\pi$
$524$	1.14379	−	1.14379i	0.0499667	−	0.0499667i
$525$		0			0
$526$	9.23383	−	2.47420i	0.402614	−	0.107880i
$527$	2.55112	+	0.449832i	0.111129	+	0.0195950i
$528$		0			0
$529$	22.0295	+	12.7188i	0.957806	+	0.552989i
$530$	0.312075	−	0.371916i	0.0135557	−	0.0161550i
$531$		0			0
$532$	−15.1279	−	4.05351i	−0.655877	−	0.175742i
$533$	−23.1858	−	10.8117i	−1.00429	−	0.468307i
$534$		0			0
$535$	−0.463953	+	0.324863i	−0.0200584	+	0.0140451i
$536$	5.51070	+	0.482124i	0.238026	+	0.0208246i
$537$		0			0
$538$	−16.3124	−	23.2965i	−0.703276	−	1.00438i
$539$	−0.246006	+	0.0895390i	−0.0105962	+	0.00385672i
$540$		0			0
$541$	−1.59701	+	5.96011i	−0.0686607	+	0.256245i	−0.991721	−	0.128410i	$-0.959013\pi$
$541$	−1.59701	+	5.96011i	−0.0686607	+	0.256245i	0.923061	+	0.384655i	$0.125679\pi$
$542$	0.193727	−	0.276671i	0.00832128	−	0.0118840i
$543$		0			0
$544$	−2.57089	+	4.45291i	−0.110226	+	0.190917i
$545$	0.194686	+	0.337206i	0.00833942	+	0.0144443i
$546$		0			0
$547$	−5.17369	−	19.3085i	−0.221211	−	0.825571i	−0.983887	−	0.178791i	$-0.942782\pi$
$547$	−5.17369	−	19.3085i	−0.221211	−	0.825571i	0.762676	−	0.646781i	$-0.223885\pi$
$548$	14.9564	+	5.44367i	0.638904	+	0.232542i
$549$		0			0
$550$	0.423059	−	0.197276i	0.0180393	−	0.00841186i
$551$	23.6665	−	4.17305i	1.00823	−	0.177778i
$552$		0			0
$553$	−2.52096	−	28.8146i	−0.107202	−	1.22532i
$554$	9.03370			0.383805
$555$		0			0
$556$	5.29521			0.224567
$557$	−3.31456	−	37.8856i	−0.140442	−	1.60526i	−0.660294	−	0.751007i	$-0.729568\pi$
$557$	−3.31456	−	37.8856i	−0.140442	−	1.60526i	0.519852	−	0.854256i	$-0.325987\pi$
$558$		0			0
$559$	−37.7714	+	6.66011i	−1.59756	+	0.281693i
$560$	0.151854	−	0.0708109i	0.00641702	−	0.00299230i
$561$		0			0
$562$	26.3867	+	9.60397i	1.11306	+	0.405119i
$563$	−10.5776	−	39.4761i	−0.445792	−	1.66372i	−0.713837	−	0.700312i	$-0.753044\pi$
$563$	−10.5776	−	39.4761i	−0.445792	−	1.66372i	0.268045	−	0.963407i	$-0.413623\pi$
$564$		0			0
$565$	0.823633	+	1.42657i	0.0346505	+	0.0600164i
$566$	−6.80150	+	11.7805i	−0.285888	+	0.495173i
$567$		0			0
$568$	−6.01610	+	8.59188i	−0.252430	+	0.360507i
$569$	−9.76404	+	36.4399i	−0.409330	+	1.52764i	0.386598	+	0.922248i	$0.373650\pi$
$569$	−9.76404	+	36.4399i	−0.409330	+	1.52764i	−0.795928	+	0.605392i	$0.793017\pi$
$570$		0			0
$571$	−13.6730	+	4.97657i	−0.572198	+	0.208263i	−0.611882	−	0.790949i	$-0.709587\pi$
$571$	−13.6730	+	4.97657i	−0.572198	+	0.208263i	0.0396837	+	0.999212i	$0.487365\pi$
$572$	−0.280958	−	0.401250i	−0.0117475	−	0.0167771i
$573$		0			0
$574$	−9.96731	−	0.872026i	−0.416027	−	0.0363977i
$575$	−28.4672	+	19.9329i	−1.18716	+	0.831261i
$576$		0			0
$577$	28.4758	+	13.2785i	1.18546	+	0.552791i	0.912438	−	0.409216i	$-0.134198\pi$
$577$	28.4758	+	13.2785i	1.18546	+	0.552791i	0.273026	+	0.962007i	$0.411976\pi$
$578$	9.11634	+	2.44272i	0.379190	+	0.101604i
$579$		0			0
$580$	−0.165260	+	0.196949i	−0.00686205	+	0.00817787i
$581$	20.2323	+	11.6811i	0.839376	+	0.484614i
$582$		0			0
$583$	−0.546676	−	0.0963936i	−0.0226410	−	0.00399222i
$584$	−4.56607	+	1.22347i	−0.188945	+	0.0506277i
$585$		0			0
$586$	17.6142	−	17.6142i	0.727635	−	0.727635i
$587$	−18.7182	−	40.1414i	−0.772584	−	1.65681i	−0.753903	−	0.656986i	$-0.771831\pi$
$587$	−18.7182	−	40.1414i	−0.772584	−	1.65681i	−0.0186807	−	0.999826i	$-0.505947\pi$
$588$		0			0
$589$	2.94952	−	2.47494i	0.121533	−	0.101978i
$590$	0.721060	−	0.0630846i	0.0296856	−	0.00259715i
$591$		0			0
$592$	−5.66414	+	2.21756i	−0.232795	+	0.0911412i
$593$			28.5125i			1.17087i	0.810721	+	0.585433i	$0.199076\pi$
$593$			28.5125i			1.17087i	−0.810721	+	0.585433i	$0.800924\pi$
$594$		0			0
$595$	−0.553774	−	0.659962i	−0.0227025	−	0.0270558i
$596$	0.826280	+	4.68607i	0.0338457	+	0.191949i
$597$		0			0
$598$	25.7864	+	25.7864i	1.05448	+	1.05448i
$599$	4.98253	−	13.6894i	0.203581	−	0.559333i	−0.795321	−	0.606188i	$-0.792698\pi$
$599$	4.98253	−	13.6894i	0.203581	−	0.559333i	0.998902	+	0.0468554i	$0.0149200\pi$
$600$		0			0
$601$	1.16812	−	6.62472i	0.0476485	−	0.270228i	−0.951671	−	0.307120i	$-0.900635\pi$
$601$	1.16812	−	6.62472i	0.0476485	−	0.270228i	0.999319	+	0.0368922i	$0.0117458\pi$
$602$	−12.9906	+	7.50014i	−0.529458	+	0.305683i
$603$		0			0
$604$	−3.13019	−	2.62654i	−0.127366	−	0.106872i
$605$	−0.736141	−	0.515451i	−0.0299284	−	0.0209561i
$606$		0			0
$607$	10.2261	−	21.9300i	0.415066	−	0.890112i	−0.581972	−	0.813209i	$-0.697719\pi$
$607$	10.2261	−	21.9300i	0.415066	−	0.890112i	0.997039	−	0.0769037i	$-0.0245034\pi$
$608$	2.61387	+	7.18154i	0.106006	+	0.291250i
$609$		0			0
$610$	0.0410312	−	0.468989i	0.00166131	−	0.0189888i
$611$	4.10751	−	46.9490i	0.166172	−	1.89935i
$612$		0			0
$613$	−0.234258	−	0.643620i	−0.00946161	−	0.0259956i	0.934872	−	0.354985i	$-0.115514\pi$
$613$	−0.234258	−	0.643620i	−0.00946161	−	0.0259956i	−0.944334	+	0.328990i	$0.893292\pi$
$614$	−2.87322	+	6.16163i	−0.115954	+	0.248663i
$615$		0			0
$616$	−0.156929	−	0.109883i	−0.00632285	−	0.00442731i
$617$	5.94794	+	4.99091i	0.239455	+	0.200927i	0.754616	−	0.656167i	$-0.227823\pi$
$617$	5.94794	+	4.99091i	0.239455	+	0.200927i	−0.515161	+	0.857094i	$0.672268\pi$
$618$		0			0
$619$	−24.3094	+	14.0350i	−0.977076	+	0.564115i	−0.901386	−	0.433016i	$-0.857449\pi$
$619$	−24.3094	+	14.0350i	−0.977076	+	0.564115i	−0.0756901	+	0.997131i	$0.524116\pi$
$620$	−0.00715295	+	0.0405664i	−0.000287269	+	0.00162919i
$621$		0			0
$622$	12.0219	−	33.0299i	0.482034	−	1.32438i
$623$	−8.13827	−	8.13827i	−0.326053	−	0.326053i
$624$		0			0
$625$	−4.32380	−	24.5215i	−0.172952	−	0.980859i
$626$	18.9643	+	22.6007i	0.757964	+	0.903307i
$627$		0			0
$628$		−	4.29047i		−	0.171208i
$629$	18.5515	+	25.1803i	0.739696	+	1.00400i
$630$		0			0
$631$	31.9009	−	2.79097i	1.26996	−	0.111107i	0.567821	−	0.823152i	$-0.307786\pi$
$631$	31.9009	−	2.79097i	1.26996	−	0.111107i	0.702134	+	0.712045i	$0.252231\pi$
$632$	−10.8124	+	9.07265i	−0.430093	+	0.360891i
$633$		0			0
$634$	14.3976	+	30.8758i	0.571803	+	1.22623i
$635$	−0.735466	+	0.735466i	−0.0291861	+	0.0291861i
$636$		0			0
$637$	14.1737	−	3.79783i	0.561582	−	0.150475i
$638$	0.289494	+	0.0510455i	0.0114612	+	0.00202091i
$639$		0			0
$640$	−0.0708076	−	0.0408808i	−0.00279891	−	0.00161595i
$641$	−8.62878	+	10.2834i	−0.340816	+	0.406169i	−0.909043	−	0.416703i	$-0.863185\pi$
$641$	−8.62878	+	10.2834i	−0.340816	+	0.406169i	0.568226	+	0.822872i	$0.307630\pi$
$642$		0			0
$643$	5.56362	+	1.49077i	0.219408	+	0.0587902i	0.366848	−	0.930281i	$-0.380437\pi$
$643$	5.56362	+	1.49077i	0.219408	+	0.0587902i	−0.147440	+	0.989071i	$0.547103\pi$
$644$	12.9262	+	6.02756i	0.509362	+	0.237519i
$645$		0			0
$646$	32.1892	−	22.5391i	1.26647	−	0.886790i
$647$	−27.5548	−	2.41073i	−1.08329	−	0.0947757i	−0.468498	−	0.883464i	$-0.655205\pi$
$647$	−27.5548	−	2.41073i	−1.08329	−	0.0947757i	−0.614793	+	0.788689i	$0.710760\pi$
$648$		0			0
$649$	−0.474685	−	0.677921i	−0.0186330	−	0.0266107i
$650$	−24.5861	+	8.94860i	−0.964346	+	0.350993i
$651$		0			0
$652$	1.06070	−	3.95860i	0.0415404	−	0.155031i
$653$	13.5295	−	19.3221i	0.529451	−	0.756134i	−0.461963	−	0.886899i	$-0.652855\pi$
$653$	13.5295	−	19.3221i	0.529451	−	0.756134i	0.991413	+	0.130765i	$0.0417434\pi$
$654$		0			0
$655$	0.0661272	−	0.114536i	0.00258380	−	0.00447528i
$656$	2.44119	+	4.22826i	0.0953123	+	0.165086i
$657$		0			0
$658$	−4.77053	−	17.8039i	−0.185975	−	0.694066i
$659$	−15.3229	−	5.57707i	−0.596895	−	0.217252i	0.0258646	−	0.999665i	$-0.491766\pi$
$659$	−15.3229	−	5.57707i	−0.596895	−	0.217252i	−0.622759	+	0.782414i	$0.713988\pi$
$660$		0			0
$661$	−2.49678	+	1.16427i	−0.0971135	+	0.0452848i	−0.470568	−	0.882364i	$-0.655951\pi$
$661$	−2.49678	+	1.16427i	−0.0971135	+	0.0452848i	0.373455	+	0.927648i	$0.378173\pi$
$662$	4.94602	−	0.872116i	0.192232	−	0.0338958i
$663$		0			0
$664$	−0.993590	−	11.3568i	−0.0385588	−	0.440729i
$665$	−1.28051			−0.0496561
$666$		0			0
$667$	−21.8848			−0.847382
$668$	−0.228078	−	2.60695i	−0.00882461	−	0.100866i
$669$		0			0
$670$	0.445413	−	0.0785384i	0.0172078	−	0.00303420i
$671$	−0.487845	+	0.227486i	−0.0188330	+	0.00878199i
$672$		0			0
$673$	−14.8999	−	5.42313i	−0.574350	−	0.209046i	0.0384821	−	0.999259i	$-0.487748\pi$
$673$	−14.8999	−	5.42313i	−0.574350	−	0.209046i	−0.612832	+	0.790213i	$0.709970\pi$
$674$	5.87575	+	21.9286i	0.226325	+	0.844658i
$675$		0			0
$676$	7.22774	+	12.5188i	0.277990	+	0.481493i
$677$	−2.29819	+	3.98058i	−0.0883266	+	0.152986i	−0.906804	−	0.421553i	$-0.861485\pi$
$677$	−2.29819	+	3.98058i	−0.0883266	+	0.152986i	0.818477	+	0.574539i	$0.194819\pi$
$678$		0			0
$679$	−1.40694	+	2.00931i	−0.0539932	+	0.0771103i
$680$	−0.108808	+	0.406075i	−0.00417258	+	0.0155723i
$681$		0			0
$682$	0.0442576	−	0.0161085i	0.00169471	−	0.000616825i
$683$	−27.1672	−	38.7988i	−1.03952	−	1.48459i	−0.866179	−	0.499734i	$-0.833431\pi$
$683$	−27.1672	−	38.7988i	−1.03952	−	1.48459i	−0.173346	−	0.984861i	$-0.555458\pi$
$684$		0			0
$685$	1.29638	+	0.113419i	0.0495322	+	0.00433351i
$686$	16.4517	−	11.5196i	0.628131	−	0.439822i
$687$		0			0
$688$	6.63395	+	3.09346i	0.252917	+	0.117937i
$689$	30.0539	+	8.05291i	1.14496	+	0.306791i
$690$		0			0
$691$	−10.0433	+	11.9691i	−0.382065	+	0.455327i	−0.922465	−	0.386081i	$-0.873828\pi$
$691$	−10.0433	+	11.9691i	−0.382065	+	0.455327i	0.540400	+	0.841408i	$0.318273\pi$
$692$	1.05436	+	0.608733i	0.0400806	+	0.0231406i
$693$		0			0
$694$	15.1332	+	2.66839i	0.574449	+	0.101291i
$695$	0.418192	−	0.112054i	0.0158629	−	0.00425046i
$696$		0			0
$697$	17.7513	−	17.7513i	0.672378	−	0.672378i
$698$	2.87062	+	6.15607i	0.108655	+	0.233011i
$699$		0			0
$700$	−7.83873	+	6.57747i	−0.296276	+	0.248605i
$701$	1.81313	−	0.158628i	0.0684810	−	0.00599131i	−0.0528638	−	0.998602i	$-0.516835\pi$
$701$	1.81313	−	0.158628i	0.0684810	−	0.00599131i	0.121345	+	0.992610i	$0.461279\pi$
$702$		0			0
$703$	46.3944	+	2.93450i	1.74980	+	0.110677i
$704$			0.0934838i			0.00352330i
$705$		0			0
$706$	−10.7508	−	12.8123i	−0.404613	−	0.482199i
$707$	3.31433	+	18.7965i	0.124648	+	0.706916i
$708$		0			0
$709$	30.3617	+	30.3617i	1.14026	+	1.14026i	0.988402	+	0.151857i	$0.0485253\pi$
$709$	30.3617	+	30.3617i	1.14026	+	1.14026i	0.151857	+	0.988402i	$0.451475\pi$
$710$	−0.293308	+	0.805858i	−0.0110077	+	0.0302433i
$711$		0			0
$712$	−0.975248	+	5.53090i	−0.0365490	+	0.207279i
$713$	−3.03660	+	1.75318i	−0.113722	+	0.0656572i
$714$		0			0
$715$	−0.0306799	−	0.0257435i	−0.00114736	−	0.000962752i
$716$	5.91818	+	4.14395i	0.221173	+	0.154867i
$717$		0			0
$718$	10.4107	−	22.3258i	0.388524	−	0.833193i
$719$	−0.175409	−	0.481933i	−0.00654166	−	0.0179731i	0.936379	−	0.350991i	$-0.114155\pi$
$719$	−0.175409	−	0.481933i	−0.00654166	−	0.0179731i	−0.942920	+	0.333018i	$0.891933\pi$
$720$		0			0
$721$	−3.45192	+	39.4557i	−0.128556	+	1.46941i
$722$	3.43454	−	39.2569i	0.127820	−	1.46099i
$723$		0			0
$724$	3.84300	+	10.5585i	0.142824	+	0.392405i
$725$	6.63573	−	14.2304i	0.246445	−	0.528502i
$726$		0			0
$727$	−7.88484	−	5.52102i	−0.292432	−	0.204763i	0.418149	−	0.908379i	$-0.362679\pi$
$727$	−7.88484	−	5.52102i	−0.292432	−	0.204763i	−0.710581	+	0.703615i	$0.751568\pi$
$728$	8.22567	+	6.90215i	0.304864	+	0.255811i
$729$		0			0
$730$	−0.334717	+	0.193249i	−0.0123884	+	0.00715247i
$731$	6.53553	−	37.0648i	0.241725	−	1.37089i
$732$		0			0
$733$	11.6456	−	31.9960i	0.430139	−	1.18180i	−0.515588	−	0.856836i	$-0.672427\pi$
$733$	11.6456	−	31.9960i	0.430139	−	1.18180i	0.945727	−	0.324961i	$-0.105351\pi$
$734$	−6.30143	−	6.30143i	−0.232590	−	0.232590i
$735$		0			0
$736$	−1.20854	−	6.85397i	−0.0445474	−	0.252641i
$737$	−0.332404	−	0.396144i	−0.0122443	−	0.0145922i
$738$		0			0
$739$		−	21.9621i		−	0.807888i	−0.914784	−	0.403944i	$-0.867639\pi$
$739$		−	21.9621i		−	0.807888i	0.914784	−	0.403944i	$-0.132361\pi$
$740$	−0.400401	+	0.294994i	−0.0147191	+	0.0108442i
$741$		0			0
$742$	12.1224	−	1.06057i	0.445027	−	0.0389349i
$743$	−22.7466	+	19.0867i	−0.834492	+	0.700222i	−0.956318	−	0.292329i	$-0.905570\pi$
$743$	−22.7466	+	19.0867i	−0.834492	+	0.700222i	0.121825	+	0.992552i	$0.461125\pi$
$744$		0			0
$745$	0.164420	+	0.352599i	0.00602388	+	0.0129182i
$746$	19.7673	−	19.7673i	0.723733	−	0.723733i
$747$		0			0
$748$	0.464295	−	0.124407i	0.0169763	−	0.00454878i
$749$	−13.9802	−	2.46509i	−0.510827	−	0.0900726i
$750$		0			0
$751$	−37.0006	−	21.3623i	−1.35017	−	0.779521i	−0.361897	−	0.932218i	$-0.617871\pi$
$751$	−37.0006	−	21.3623i	−1.35017	−	0.779521i	−0.988273	+	0.152697i	$0.951204\pi$
$752$	−5.78143	+	6.89004i	−0.210827	+	0.251254i
$753$		0			0
$754$	−15.9151	−	4.26444i	−0.579594	−	0.155302i
$755$	−0.302790	−	0.141193i	−0.0110196	−	0.00513854i
$756$		0			0
$757$	5.26333	−	3.68542i	0.191299	−	0.133949i	−0.474003	−	0.880523i	$-0.657192\pi$
$757$	5.26333	−	3.68542i	0.191299	−	0.133949i	0.665302	+	0.746574i	$0.268303\pi$
$758$	9.59004	+	0.839020i	0.348326	+	0.0304746i
$759$		0			0
$760$	0.358404	+	0.511853i	0.0130007	+	0.0185669i
$761$	14.9673	−	5.44766i	0.542565	−	0.197477i	−0.0561751	−	0.998421i	$-0.517891\pi$
$761$	14.9673	−	5.44766i	0.542565	−	0.197477i	0.598740	+	0.800943i	$0.295668\pi$
$762$		0			0
$763$	−2.52589	+	9.42674i	−0.0914433	+	0.341271i
$764$	−6.45542	+	9.21930i	−0.233549	+	0.333543i
$765$		0			0
$766$	4.69766	−	8.13659i	0.169733	−	0.293987i
$767$	23.1933	+	40.1720i	0.837462	+	1.45053i
$768$		0			0
$769$	1.24915	+	4.66189i	0.0450455	+	0.168112i	0.984784	−	0.173781i	$-0.0555986\pi$
$769$	1.24915	+	4.66189i	0.0450455	+	0.168112i	−0.939739	+	0.341893i	$0.888932\pi$
$770$	−0.0147188	−	0.00535722i	−0.000530430	−	0.000193061i
$771$		0			0
$772$	17.7167	−	8.26146i	0.637640	−	0.297336i
$773$	−35.3635	+	6.23554i	−1.27194	+	0.224277i	−0.768553	−	0.639786i	$-0.779023\pi$
$773$	−35.3635	+	6.23554i	−1.27194	+	0.224277i	−0.503384	+	0.864063i	$0.667912\pi$
$774$		0			0
$775$	−0.219256	−	2.50610i	−0.00787590	−	0.0900219i
$776$	1.19696			0.0429684
$777$		0			0
$778$	−2.27419			−0.0815335
$779$	−3.25206	−	37.1713i	−0.116517	−	1.33180i
$780$		0			0
$781$	0.965632	−	0.170267i	0.0345530	−	0.00609263i
$782$	−32.4325	+	15.1235i	−1.15978	+	0.540816i
$783$		0			0
$784$	−2.63154	−	0.957802i	−0.0939836	−	0.0342072i
$785$	−0.0907925	−	0.338842i	−0.00324052	−	0.0120938i
$786$		0			0
$787$	19.2152	+	33.2817i	0.684948	+	1.18636i	0.973453	+	0.228886i	$0.0735084\pi$
$787$	19.2152	+	33.2817i	0.684948	+	1.18636i	−0.288505	+	0.957478i	$0.593158\pi$
$788$	4.11207	−	7.12231i	0.146486	−	0.253722i
$789$		0			0
$790$	−0.661922	+	0.945322i	−0.0235501	+	0.0336331i
$791$	−10.6860	+	39.8805i	−0.379949	+	1.41799i
$792$		0			0
$793$	28.3511	−	10.3190i	1.00678	−	0.366437i
$794$	22.0745	+	31.5256i	0.783394	+	1.11880i
$795$		0			0
$796$	−6.46765	−	0.565846i	−0.229240	−	0.0200559i
$797$	−23.8024	+	16.6666i	−0.843125	+	0.590363i	−0.913353	−	0.407168i	$-0.866516\pi$
$797$	−23.8024	+	16.6666i	−0.843125	+	0.590363i	0.0702280	+	0.997531i	$0.477627\pi$
$798$		0			0
$799$	41.9138	+	19.5447i	1.48280	+	0.691443i
$800$	4.82317	+	1.29237i	0.170525	+	0.0456920i
$801$		0			0
$802$	−17.8196	+	21.2366i	−0.629234	+	0.749891i
$803$	0.382706	+	0.220955i	0.0135054	+	0.00779735i
$804$		0			0
$805$	1.14840	+	0.202494i	0.0404758	+	0.00713698i
$806$	−2.54991	+	0.683246i	−0.0898167	+	0.0240663i
$807$		0			0
$808$	6.58580	−	6.58580i	0.231688	−	0.231688i
$809$	−6.01017	−	12.8888i	−0.211306	−	0.453148i	0.771876	−	0.635773i	$-0.219318\pi$
$809$	−6.01017	−	12.8888i	−0.211306	−	0.453148i	−0.983183	+	0.182625i	$0.941541\pi$
$810$		0			0
$811$	−32.3636	+	27.1563i	−1.13644	+	0.953586i	−0.999316	−	0.0369680i	$-0.988230\pi$
$811$	−32.3636	+	27.1563i	−1.13644	+	0.953586i	−0.137123	+	0.990554i	$0.543786\pi$
$812$	−6.41945	+	0.561630i	−0.225279	+	0.0197093i
$813$		0			0
$814$	0.521004	+	0.227829i	0.0182612	+	0.00798540i
$815$		−	0.335079i		−	0.0117373i
$816$		0			0
$817$	−35.9581	−	42.8531i	−1.25801	−	1.49924i
$818$	3.54712	+	20.1167i	0.124022	+	0.703365i
$819$		0			0
$820$	0.282270	+	0.282270i	0.00985730	+	0.00985730i
$821$	4.31086	−	11.8440i	0.150450	−	0.413358i	−0.841457	−	0.540324i	$-0.818302\pi$
$821$	4.31086	−	11.8440i	0.150450	−	0.413358i	0.991907	+	0.126966i	$0.0405240\pi$
$822$		0			0
$823$	−0.150089	+	0.851197i	−0.00523177	+	0.0296708i	−0.987312	−	0.158793i	$-0.949240\pi$
$823$	−0.150089	+	0.851197i	−0.00523177	+	0.0296708i	0.982080	+	0.188464i	$0.0603508\pi$
$824$	16.7376	−	9.66346i	0.583082	−	0.336642i
$825$		0			0
$826$	13.8974	+	11.6613i	0.483554	+	0.405750i
$827$	5.81588	+	4.07233i	0.202238	+	0.141609i	0.670309	−	0.742083i	$-0.266162\pi$
$827$	5.81588	+	4.07233i	0.202238	+	0.141609i	−0.468070	+	0.883691i	$0.655051\pi$
$828$		0			0
$829$	−0.850573	+	1.82406i	−0.0295416	+	0.0633522i	−0.920525	−	0.390684i	$-0.872239\pi$
$829$	−0.850573	+	1.82406i	−0.0295416	+	0.0633522i	0.890983	+	0.454036i	$0.150016\pi$
$830$	−0.318795	−	0.875883i	−0.0110655	−	0.0304023i
$831$		0			0
$832$	0.456679	−	5.21986i	0.0158325	−	0.180966i
$833$	−1.25497	+	14.3444i	−0.0434822	+	0.497004i
$834$		0			0
$835$	−0.0731793	−	0.201059i	−0.00253248	−	0.00695792i
$836$	0.301937	−	0.647506i	0.0104427	−	0.0223945i
$837$		0			0
$838$	−20.2145	−	14.1544i	−0.698299	−	0.488954i
$839$	24.9072	+	20.8996i	0.859891	+	0.721534i	0.961945	−	0.273245i	$-0.0880969\pi$
$839$	24.9072	+	20.8996i	0.859891	+	0.721534i	−0.102054	+	0.994779i	$0.532541\pi$
$840$		0			0
$841$	−16.5516	+	9.55607i	−0.570745	+	0.329520i
$842$	−6.12522	+	34.7379i	−0.211089	+	1.19715i
$843$		0			0
$844$	4.56229	−	12.5348i	0.157040	−	0.431465i
$845$	0.835731	+	0.835731i	0.0287500	+	0.0287500i
$846$		0			0
$847$	−3.91129	−	22.1820i	−0.134394	−	0.762184i
$848$	−3.81689	−	4.54879i	−0.131072	−	0.156206i
$849$		0			0
$850$		−	25.6745i		−	0.880630i
$851$	−41.1439	−	9.96836i	−1.41039	−	0.341711i
$852$		0			0
$853$	−38.0428	+	3.32832i	−1.30256	+	0.113959i	−0.717231	−	0.696835i	$-0.754591\pi$
$853$	−38.0428	+	3.32832i	−1.30256	+	0.113959i	−0.585331	+	0.810795i	$0.699035\pi$
$854$	9.03912	−	7.58472i	0.309312	−	0.259544i
$855$		0			0
$856$	2.92758	+	6.27822i	0.100063	+	0.214585i
$857$	38.0032	−	38.0032i	1.29817	−	1.29817i	0.368564	−	0.929602i	$-0.379850\pi$
$857$	38.0032	−	38.0032i	1.29817	−	1.29817i	0.929602	−	0.368564i	$-0.120150\pi$
$858$		0			0
$859$	−47.6652	+	12.7718i	−1.62631	+	0.435770i	−0.952848	−	0.303448i	$-0.901862\pi$
$859$	−47.6652	+	12.7718i	−1.62631	+	0.435770i	−0.673467	+	0.739218i	$0.735196\pi$
$860$	0.589382	+	0.103924i	0.0200978	+	0.00354378i
$861$		0			0
$862$	19.7132	+	11.3814i	0.671435	+	0.387653i
$863$	8.87652	−	10.5786i	0.302160	−	0.360101i	−0.593504	−	0.804831i	$-0.702256\pi$
$863$	8.87652	−	10.5786i	0.302160	−	0.360101i	0.895665	+	0.444730i	$0.146700\pi$
$864$		0			0
$865$	0.0961501	+	0.0257633i	0.00326920	+	0.000875979i
$866$	24.2649	+	11.3149i	0.824554	+	0.384496i
$867$		0			0
$868$	−0.845733	+	0.592188i	−0.0287060	+	0.0201002i
$869$	1.31446	+	0.115000i	0.0445900	+	0.00390112i
$870$		0			0
$871$	16.6253	+	23.7433i	0.563326	+	0.804513i
$872$	4.47508	−	1.62880i	0.151545	−	0.0551580i
$873$		0			0
$874$	−13.7664	+	51.3768i	−0.465654	+	1.73784i
$875$	−0.960401	+	1.37159i	−0.0324675	+	0.0463683i
$876$		0			0
$877$	−5.44868	+	9.43740i	−0.183989	+	0.318678i	−0.943235	−	0.332125i	$-0.892234\pi$
$877$	−5.44868	+	9.43740i	−0.183989	+	0.318678i	0.759246	+	0.650803i	$0.225568\pi$
$878$	7.53862	+	13.0573i	0.254416	+	0.440662i
$879$		0			0
$880$	0.00197825	+	0.00738293i	6.66868e−5	+	0.000248879i
$881$	−25.2957	−	9.20690i	−0.852235	−	0.310188i	−0.121284	−	0.992618i	$-0.538701\pi$
$881$	−25.2957	−	9.20690i	−0.852235	−	0.310188i	−0.730951	+	0.682430i	$0.760923\pi$
$882$		0			0
$883$	8.46271	−	3.94623i	0.284793	−	0.132801i	−0.274973	−	0.961452i	$-0.588669\pi$
$883$	8.46271	−	3.94623i	0.284793	−	0.132801i	0.559766	+	0.828651i	$0.310891\pi$
$884$	−26.5326	+	4.67841i	−0.892388	+	0.157352i
$885$		0			0
$886$	1.47588	+	16.8693i	0.0495830	+	0.566736i
$887$	27.3636			0.918778			0.459389	−	0.888235i	$-0.348068\pi$
$887$	27.3636			0.918778			0.459389	+	0.888235i	$0.348068\pi$
$888$		0			0
$889$	−26.0694			−0.874340
$890$	0.0400212	+	0.457444i	0.00134151	+	0.0153336i
$891$		0			0
$892$	8.48868	−	1.49678i	0.284222	−	0.0501160i
$893$	62.2982	−	29.0501i	2.08473	−	0.972125i
$894$		0			0
$895$	0.555083	+	0.202034i	0.0185544	+	0.00675324i
$896$	−0.530394	−	1.97946i	−0.0177192	−	0.0661291i
$897$		0			0
$898$	−11.7650	−	20.3776i	−0.392603	−	0.680008i
$899$	0.792113	−	1.37198i	0.0264185	−	0.0457581i
$900$		0			0
$901$	−17.5125	+	25.0104i	−0.583424	+	0.833216i
$902$	0.118131	−	0.440870i	0.00393333	−	0.0146794i
$903$		0			0
$904$	18.9322	−	6.89075i	0.629675	−	0.229183i
$905$	0.526937	+	0.752544i	0.0175160	+	0.0250154i
$906$		0			0
$907$	−6.07713	−	0.531680i	−0.201788	−	0.0176541i	−0.0141862	−	0.999899i	$-0.504516\pi$
$907$	−6.07713	−	0.531680i	−0.201788	−	0.0176541i	−0.187601	+	0.982245i	$0.560071\pi$
$908$	1.39425	−	0.976266i	0.0462699	−	0.0323985i
$909$		0			0
$910$	0.795686	+	0.371035i	0.0263767	+	0.0122997i
$911$	27.6749	+	7.41548i	0.916912	+	0.245686i	0.686265	−	0.727352i	$-0.259249\pi$
$911$	27.6749	+	7.41548i	0.916912	+	0.245686i	0.230647	+	0.973038i	$0.425916\pi$
$912$		0			0
$913$	−0.685039	+	0.816397i	−0.0226715	+	0.0270188i
$914$	−30.7918	−	17.7777i	−1.01850	−	0.588033i
$915$		0			0
$916$	−21.2578	−	3.74832i	−0.702376	−	0.123848i
$917$	3.20190	−	0.857946i	0.105736	−	0.0283319i
$918$		0			0
$919$	−0.782463	+	0.782463i	−0.0258111	+	0.0258111i	−0.719895	−	0.694083i	$-0.755810\pi$
$919$	−0.782463	+	0.782463i	−0.0258111	+	0.0258111i	0.694083	+	0.719895i	$0.255810\pi$
$920$	−0.240485	−	0.515722i	−0.00792856	−	0.0170028i
$921$		0			0
$922$	−14.2576	+	11.9635i	−0.469548	+	0.393998i
$923$	−54.7498	+	4.78999i	−1.80211	+	0.157664i
$924$		0			0
$925$	18.9571	−	23.7309i	0.623307	−	0.780267i
$926$			9.11358i			0.299491i
$927$		0			0
$928$	2.02124	+	2.40883i	0.0663506	+	0.0790736i
$929$	6.55049	+	37.1497i	0.214914	+	1.21884i	0.881055	+	0.473014i	$0.156834\pi$
$929$	6.55049	+	37.1497i	0.214914	+	1.21884i	−0.666140	+	0.745826i	$0.732055\pi$
$930$		0			0
$931$	15.1336	+	15.1336i	0.495982	+	0.495982i
$932$	5.38442	−	14.7936i	0.176373	−	0.484580i
$933$		0			0
$934$	−1.12105	+	6.35777i	−0.0366818	+	0.208033i
$935$	0.0340353	−	0.0196503i	0.00111307	−	0.000642633i
$936$		0			0
$937$	−10.1252	−	8.49605i	−0.330776	−	0.277554i	0.462240	−	0.886755i	$-0.347046\pi$
$937$	−10.1252	−	8.49605i	−0.330776	−	0.277554i	−0.793016	+	0.609201i	$0.791490\pi$
$938$	9.28603	+	6.50215i	0.303200	+	0.212303i
$939$		0			0
$940$	−0.310788	+	0.666488i	−0.0101368	+	0.0217384i
$941$	7.10934	+	19.5327i	0.231758	+	0.636749i	0.999994	−	0.00341701i	$-0.00108767\pi$
$941$	7.10934	+	19.5327i	0.231758	+	0.636749i	−0.768236	+	0.640166i	$0.778865\pi$
$942$		0			0
$943$	−2.96154	+	33.8506i	−0.0964411	+	1.10233i
$944$	0.771568	−	8.81906i	0.0251124	−	0.287036i
$945$		0			0
$946$	−0.234037	−	0.643012i	−0.00760920	−	0.0209061i
$947$	16.3956	−	35.1604i	0.532785	−	1.14256i	−0.437193	−	0.899368i	$-0.644027\pi$
$947$	16.3956	−	35.1604i	0.532785	−	1.14256i	0.969978	−	0.243193i	$-0.0781948\pi$
$948$		0			0
$949$	−20.2898	−	14.2071i	−0.658634	−	0.461181i
$950$	−29.2331	−	24.5295i	−0.948447	−	0.795842i
$951$		0			0
$952$	−9.12530	+	5.26849i	−0.295753	+	0.170753i
$953$	−4.07400	+	23.1048i	−0.131970	+	0.748437i	0.844952	+	0.534842i	$0.179629\pi$
$953$	−4.07400	+	23.1048i	−0.131970	+	0.748437i	−0.976922	+	0.213596i	$0.931482\pi$
$954$		0			0
$955$	−0.314727	+	0.864706i	−0.0101843	+	0.0279812i
$956$	−7.60186	−	7.60186i	−0.245862	−	0.245862i
$957$		0			0
$958$	−3.69647	−	20.9637i	−0.119428	−	0.677308i
$959$	20.9657	+	24.9860i	0.677019	+	0.806840i
$960$		0			0
$961$			30.7462i			0.991812i
$962$	−27.9784	−	15.2665i	−0.902058	−	0.492210i
$963$		0			0
$964$	−7.12164	+	0.623063i	−0.229373	+	0.0200675i
$965$	1.22437	−	1.02737i	0.0394137	−	0.0330721i
$966$		0			0
$967$	−12.4019	−	26.5961i	−0.398820	−	0.855272i	−0.998485	−	0.0550208i	$-0.982477\pi$
$967$	−12.4019	−	26.5961i	−0.398820	−	0.855272i	0.599666	−	0.800251i	$-0.295300\pi$
$968$	−7.77200	+	7.77200i	−0.249801	+	0.249801i
$969$		0			0
$970$	0.0945307	−	0.0253294i	0.00303520	−	0.000813279i
$971$	−50.3879	−	8.88475i	−1.61702	−	0.285125i	−0.709368	−	0.704838i	$-0.751020\pi$
$971$	−50.3879	−	8.88475i	−1.61702	−	0.285125i	−0.907657	+	0.419713i	$0.862131\pi$
$972$		0			0
$973$	9.39759	+	5.42570i	0.301273	+	0.173940i
$974$	8.72054	−	10.3927i	0.279424	−	0.333005i
$975$		0			0
$976$	−5.56177	−	1.49027i	−0.178028	−	0.0477025i
$977$	0.184364	+	0.0859704i	0.00589833	+	0.00275044i	0.425565	−	0.904928i	$-0.360075\pi$
$977$	0.184364	+	0.0859704i	0.00589833	+	0.00275044i	−0.419667	+	0.907678i	$0.637853\pi$
$978$		0			0
$979$	0.430076	−	0.301143i	0.0137453	−	0.00962456i
$980$	−0.228096	−	0.0199558i	−0.00728625	−	0.000637465i
$981$		0			0
$982$	15.2560	+	21.7879i	0.486840	+	0.695279i
$983$	−49.1848	+	17.9018i	−1.56875	+	0.570979i	−0.972720	−	0.231981i	$-0.925479\pi$
$983$	−49.1848	+	17.9018i	−1.56875	+	0.570979i	−0.596032	+	0.802961i	$0.703257\pi$
$984$		0			0
$985$	0.174035	−	0.649506i	0.00554520	−	0.0206950i
$986$	9.27377	−	13.2443i	0.295337	−	0.421785i
$987$		0			0
$988$	−20.0224	+	34.6798i	−0.636998	+	1.10331i
$989$	25.4717	+	44.1182i	0.809952	+	1.40288i
$990$		0			0
$991$	−8.67555	−	32.3776i	−0.275588	−	1.02851i	−0.955446	−	0.295165i	$-0.904626\pi$
$991$	−8.67555	−	32.3776i	−0.275588	−	1.02851i	0.679859	−	0.733343i	$-0.262041\pi$
$992$	0.473426	+	0.172313i	0.0150313	+	0.00547094i
$993$		0			0
$994$	−19.4806	+	9.08395i	−0.617887	+	0.288125i
$995$	−0.522761	+	0.0921768i	−0.0165726	+	0.00292220i
$996$		0			0
$997$	−2.99983	−	34.2882i	−0.0950056	−	1.08592i	−0.882727	−	0.469887i	$-0.844295\pi$
$997$	−2.99983	−	34.2882i	−0.0950056	−	1.08592i	0.787721	−	0.616032i	$-0.211261\pi$
$998$	6.69057			0.211786
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.611.2	yes	96
3.2	odd	2	inner	666.2.bs.b.611.7	yes	96
37.2	odd	36	inner	666.2.bs.b.557.7	yes	96
111.2	even	36	inner	666.2.bs.b.557.2	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.557.2	✓	96	111.2	even	36	inner
666.2.bs.b.557.7	yes	96	37.2	odd	36	inner
666.2.bs.b.611.2	yes	96	1.1	even	1	trivial
666.2.bs.b.611.7	yes	96	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)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-0.0741011 + 0.0345539i) q^{5} +(-1.92570 - 0.700897i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(-0.0741011 + 0.0345539i) q^{5} +(-1.92570 - 0.700897i) q^{7} +(0.258819 + 0.965926i) q^{8} +(0.0408808 + 0.0708076i) q^{10} +(0.0467419 - 0.0809593i) q^{11} +(-3.00542 + 4.29219i) q^{13} +(-0.530394 + 1.97946i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-2.94921 - 4.21190i) q^{17} +(-7.61336 - 0.666082i) q^{19} +(0.0669751 - 0.0468965i) q^{20} +(-0.0847251 - 0.0395080i) q^{22} +(6.72256 + 1.80130i) q^{23} +(-3.20964 + 3.82510i) q^{25} +(4.53780 + 2.61990i) q^{26} +(2.01815 + 0.355855i) q^{28} +(-3.03735 + 0.813856i) q^{29} +(-0.356247 + 0.356247i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-3.93883 + 3.30507i) q^{34} +(0.166915 - 0.0146032i) q^{35} +(-6.08100 + 0.146577i) q^{37} +7.64244i q^{38} +(-0.0525553 - 0.0626330i) q^{40} +(0.847815 + 4.80820i) q^{41} +(5.17585 + 5.17585i) q^{43} +(-0.0319733 + 0.0878460i) q^{44} +(1.20854 - 6.85397i) q^{46} +(-7.78930 + 4.49715i) q^{47} +(-2.14525 - 1.80008i) q^{49} +(4.09028 + 2.86405i) q^{50} +(2.21443 - 4.74887i) q^{52} +(-2.03092 - 5.57992i) q^{53} +(-0.000666164 + 0.00761429i) q^{55} +(0.178607 - 2.04149i) q^{56} +(1.07548 + 2.95486i) q^{58} +(3.74133 - 8.02332i) q^{59} +(-4.71665 - 3.30264i) q^{61} +(0.385940 + 0.323842i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(0.0743933 - 0.421905i) q^{65} +(1.89197 - 5.19815i) q^{67} +(3.63579 + 3.63579i) q^{68} +(-0.0290952 - 0.165007i) q^{70} +(6.74204 + 8.03485i) q^{71} +4.72714i q^{73} +(0.676013 + 6.04508i) q^{74} +(7.61336 - 0.666082i) q^{76} +(-0.146755 + 0.123142i) q^{77} +(5.96506 + 12.7921i) q^{79} +(-0.0578141 + 0.0578141i) q^{80} +(4.71601 - 1.26365i) q^{82} +(-11.2270 - 1.97962i) q^{83} +(0.364077 + 0.210200i) q^{85} +(4.70505 - 5.60726i) q^{86} +(0.0902984 + 0.0241954i) q^{88} +(5.09003 + 2.37352i) q^{89} +(8.79593 - 6.15898i) q^{91} +(-6.93322 - 0.606578i) q^{92} +(5.15892 + 7.36770i) q^{94} +(0.587174 - 0.213714i) q^{95} +(0.309796 - 1.15618i) q^{97} +(-1.60626 + 2.29398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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