LMFDB - Embedded newform 666.2.bs.b.557.2

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			557.2
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.b.611.2

$q$-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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

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

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	0.405978	−	0.913883i	$-0.366931\pi$
$5$	−0.0741011	−	0.0345539i	−0.0331390	−	0.0154530i	−0.439117	+	0.898430i	$0.644709\pi$
$6$		0			0
$7$	−1.92570	+	0.700897i	−0.727846	+	0.264914i	−0.679253	−	0.733904i	$-0.737696\pi$
$7$	−1.92570	+	0.700897i	−0.727846	+	0.264914i	−0.0485931	+	0.998819i	$0.515474\pi$
$8$	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	0.872986	−	0.487745i	$-0.162181\pi$
$11$	0.0467419	+	0.0809593i	0.0140932	+	0.0244102i	−0.858893	+	0.512155i	$0.828847\pi$
$12$		0			0
$13$	−3.00542	−	4.29219i	−0.833555	−	1.19044i	−0.979559	−	0.201156i	$-0.935530\pi$
$13$	−3.00542	−	4.29219i	−0.833555	−	1.19044i	0.146004	−	0.989284i	$-0.453359\pi$
$14$	−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	0.282767	+	0.959189i	$0.408748\pi$
$17$	−2.94921	+	4.21190i	−0.715287	+	1.02154i	−0.998054	+	0.0623477i	$0.980141\pi$
$18$		0			0
$19$	−7.61336	+	0.666082i	−1.74662	+	0.152810i	−0.915245	−	0.402897i	$-0.868003\pi$
$19$	−7.61336	+	0.666082i	−1.74662	+	0.152810i	−0.831379	+	0.555707i	$0.812448\pi$
$20$	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	0.522777	−	0.852469i	$-0.324896\pi$
$23$	6.72256	−	1.80130i	1.40175	−	0.375598i	0.878973	+	0.476871i	$0.158229\pi$
$24$		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	−0.0344685	−	0.999406i	$-0.510974\pi$
$29$	−3.03735	−	0.813856i	−0.564022	−	0.151129i	−0.529554	+	0.848277i	$0.677641\pi$
$30$		0			0
$31$	−0.356247	−	0.356247i	−0.0639838	−	0.0639838i	0.674391	−	0.738375i	$-0.264406\pi$
$31$	−0.356247	−	0.356247i	−0.0639838	−	0.0639838i	−0.738375	+	0.674391i	$0.764406\pi$
$32$	−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	−0.844224	−	0.535990i	$-0.819938\pi$
$41$	0.847815	−	4.80820i	0.132406	−	0.750915i	0.976631	−	0.214924i	$-0.0689505\pi$
$42$		0			0
$43$	5.17585	−	5.17585i	0.789310	−	0.789310i	−0.192071	−	0.981381i	$-0.561520\pi$
$43$	5.17585	−	5.17585i	0.789310	−	0.789310i	0.981381	+	0.192071i	$0.0615205\pi$
$44$	−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	−0.190702	−	0.981648i	$-0.561077\pi$
$47$	−7.78930	−	4.49715i	−1.13619	−	0.655977i	−0.945483	+	0.325671i	$0.894410\pi$
$48$		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	0.718511	+	0.695515i	$0.244824\pi$
$53$	−2.03092	+	5.57992i	−0.278969	+	0.766461i	−0.997480	+	0.0709454i	$0.977398\pi$
$54$		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	0.984232	+	0.176883i	$0.0566015\pi$
$59$	3.74133	+	8.02332i	0.487080	+	1.04455i	−0.497152	+	0.867664i	$0.665621\pi$
$60$		0			0
$61$	−4.71665	+	3.30264i	−0.603906	+	0.422859i	−0.835139	−	0.550039i	$-0.814613\pi$
$61$	−4.71665	+	3.30264i	−0.603906	+	0.422859i	0.231233	+	0.972898i	$0.425724\pi$
$62$	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	0.999990	−	0.00437504i	$-0.00139262\pi$
$67$	1.89197	+	5.19815i	0.231141	+	0.635055i	−0.768849	+	0.639430i	$0.779170\pi$
$68$	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	−0.199520	−	0.979894i	$-0.563938\pi$
$71$	6.74204	−	8.03485i	0.800133	−	0.953561i	0.999653	+	0.0263324i	$0.00838284\pi$
$72$		0			0
$73$		−	4.72714i		−	0.553270i	−0.960975	−	0.276635i	$-0.910781\pi$
$73$		−	4.72714i		−	0.553270i	0.960975	−	0.276635i	$-0.0892192\pi$
$74$	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	−0.215394	−	0.976527i	$-0.569104\pi$
$79$	5.96506	−	12.7921i	0.671122	−	1.43922i	0.886516	−	0.462698i	$-0.153118\pi$
$80$	−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	−0.751622	−	0.659594i	$-0.770728\pi$
$83$	−11.2270	+	1.97962i	−1.23232	+	0.217291i	−0.480699	+	0.876886i	$0.659617\pi$
$84$		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	−0.133691	−	0.991023i	$-0.542683\pi$
$89$	5.09003	−	2.37352i	0.539542	−	0.251593i	0.673233	+	0.739430i	$0.264905\pi$
$90$		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	0.979868	−	0.199645i	$-0.0639788\pi$
$97$	0.309796	+	1.15618i	0.0314551	+	0.117392i	−0.948413	+	0.317037i	$0.897312\pi$
$98$	−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	−0.999127	−	0.0417866i	$-0.986695\pi$
$101$	−4.65686	+	8.06592i	−0.463375	+	0.802589i	0.535752	+	0.844376i	$0.320028\pi$
$102$		0			0
$103$	−5.00217	+	18.6684i	−0.492879	+	1.83945i	0.0487214	+	0.998812i	$0.484485\pi$
$103$	−5.00217	+	18.6684i	−0.492879	+	1.83945i	−0.541600	+	0.840636i	$0.682181\pi$
$104$	−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	0.493378	−	0.869815i	$-0.335762\pi$
$107$	6.82200	+	1.20290i	0.659508	+	0.116289i	0.166130	+	0.986104i	$0.446873\pi$
$108$		0			0
$109$	−0.415060	+	4.74416i	−0.0397556	+	0.454408i	0.950061	+	0.312063i	$0.101020\pi$
$109$	−0.415060	+	4.74416i	−0.0397556	+	0.454408i	−0.989817	+	0.142346i	$0.954536\pi$
$110$	0.00764338			0.000728767
$111$		0			0
$112$	−2.04929			−0.193639
$113$	−1.75594	+	20.0705i	−0.165185	+	1.88808i	0.235519	+	0.971870i	$0.424321\pi$
$113$	−1.75594	+	20.0705i	−0.165185	+	1.88808i	−0.400704	+	0.916207i	$0.631235\pi$
$114$		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	0.812710	−	0.582669i	$-0.197991\pi$
$127$	11.9540	+	4.35091i	1.06075	+	0.386081i	0.248040	+	0.968750i	$0.420214\pi$
$128$	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	0.514258	−	0.857635i	$-0.328067\pi$
$131$	−1.32503	−	0.927796i	−0.115768	−	0.0810619i	−0.630027	+	0.776573i	$0.716956\pi$
$132$		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	−0.955466	−	0.295101i	$-0.904647\pi$
$137$	−13.7839	+	7.95811i	−1.17763	+	0.679908i	−0.222168	+	0.975008i	$0.571313\pi$
$138$		0			0
$139$	−5.21477	+	0.919504i	−0.442311	+	0.0779913i	−0.390368	−	0.920659i	$-0.627652\pi$
$139$	−5.21477	+	0.919504i	−0.442311	+	0.0779913i	−0.0519424	+	0.998650i	$0.516541\pi$
$140$	−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	$0.0624414\pi$
$149$			4.75836i			0.389820i	−0.980821	+	0.194910i	$0.937559\pi$
$150$		0			0
$151$	2.62654	−	3.13019i	0.213745	−	0.254731i	−0.648510	−	0.761206i	$-0.724607\pi$
$151$	2.62654	−	3.13019i	0.213745	−	0.254731i	0.862254	+	0.506475i	$0.169052\pi$
$152$	−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	0.940537	−	0.339692i	$-0.110323\pi$
$157$	−0.745032	−	4.22529i	−0.0594600	−	0.337215i	−0.999997	+	0.00247695i	$0.999212\pi$
$158$	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	0.826728	−	0.562601i	$-0.190199\pi$
$163$	−1.73199	−	3.71427i	−0.135660	−	0.290924i	−0.962388	+	0.271677i	$0.912422\pi$
$164$	−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	−0.999900	−	0.0141579i	$-0.995493\pi$
$167$	−0.228078	−	2.60695i	−0.0176492	−	0.201732i	0.982251	−	0.187574i	$-0.0600623\pi$
$168$		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	−0.677552	−	0.735475i	$-0.736959\pi$
$173$	−0.932633	+	0.782572i	−0.0709068	+	0.0594978i	0.606645	+	0.794973i	$0.292515\pi$
$174$		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	−0.871765	−	0.489924i	$-0.837024\pi$
$179$	−5.10868	+	5.10868i	−0.381840	+	0.381840i	0.489924	+	0.871765i	$0.337024\pi$
$180$		0			0
$181$	−1.95114	+	11.0655i	−0.145027	+	0.822490i	0.822318	+	0.569028i	$0.192680\pi$
$181$	−1.95114	+	11.0655i	−0.145027	+	0.822490i	−0.967345	+	0.253462i	$0.918431\pi$
$182$	−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	0.933754	−	0.357914i	$-0.116512\pi$
$191$	7.95827	+	7.95827i	0.575840	+	0.575840i	−0.357914	+	0.933754i	$0.616512\pi$
$192$		0			0
$193$	−18.8822	−	5.05946i	−1.35917	−	0.364188i	−0.495658	−	0.868518i	$-0.665073\pi$
$193$	−18.8822	−	5.05946i	−1.35917	−	0.364188i	−0.863511	+	0.504330i	$0.831740\pi$
$194$	−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	0.544112	−	0.839013i	$-0.316867\pi$
$197$	−5.28637	−	6.30005i	−0.376638	−	0.448860i	−0.920750	+	0.390153i	$0.872422\pi$
$198$		0			0
$199$	6.27114	−	1.68035i	0.444549	−	0.119117i	−0.0295987	−	0.999562i	$-0.509423\pi$
$199$	6.27114	−	1.68035i	0.444549	−	0.119117i	0.474148	+	0.880445i	$0.342756\pi$
$200$	−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	0.539761	−	0.841818i	$-0.318515\pi$
$211$	−6.66962	−	11.5521i	−0.459156	−	0.795281i	−0.998917	+	0.0465376i	$0.985181\pi$
$212$	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	0.370751	−	0.928732i	$-0.379100\pi$
$227$	−1.54260	−	0.719325i	−0.102386	−	0.0477433i	−0.473136	+	0.880989i	$0.656878\pi$
$228$		0			0
$229$	20.2839	−	7.38274i	1.34040	−	0.487865i	0.430461	−	0.902609i	$-0.358351\pi$
$229$	20.2839	−	7.38274i	1.34040	−	0.487865i	0.909938	+	0.414744i	$0.136129\pi$
$230$	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	−0.999834	−	0.0182000i	$-0.994206\pi$
$233$	−7.87150	−	13.6338i	−0.515679	−	0.893182i	0.484155	−	0.874982i	$-0.339127\pi$
$234$		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	−0.568608	−	0.822609i	$-0.692518\pi$
$239$	6.16633	−	8.80642i	0.398866	−	0.569640i	0.967475	+	0.252968i	$0.0814068\pi$
$240$		0			0
$241$	7.12164	−	0.623063i	0.458745	−	0.0401350i	0.144558	−	0.989496i	$-0.453824\pi$
$241$	7.12164	−	0.623063i	0.458745	−	0.0401350i	0.314187	+	0.949361i	$0.398268\pi$
$242$	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	0.614535	−	0.788890i	$-0.289344\pi$
$251$	11.9186	+	3.19357i	0.752292	+	0.201576i	0.137758	+	0.990466i	$0.456010\pi$
$252$		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	−0.616558	−	0.787310i	$-0.711473\pi$
$257$	−21.8099	−	1.90812i	−1.36046	−	0.119025i	−0.743906	+	0.668285i	$0.767029\pi$
$258$		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	−0.889882	−	0.456191i	$-0.849213\pi$
$263$	1.66000	−	9.41434i	0.102360	−	0.580513i	0.992242	−	0.124322i	$-0.0396755\pi$
$264$		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	0.999998	+	0.00195476i	$0.000622219\pi$
$269$	24.6295	+	14.2199i	1.50169	+	0.867001i	0.501692	+	0.865046i	$0.332711\pi$
$270$		0			0
$271$	0.258733	−	0.217103i	0.0157169	−	0.0131881i	−0.634895	−	0.772598i	$-0.718957\pi$
$271$	0.258733	−	0.217103i	0.0157169	−	0.0131881i	0.650612	+	0.759410i	$0.274512\pi$
$272$	−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	−0.982460	−	0.186474i	$-0.940294\pi$
$277$	−0.787339	−	8.99932i	−0.0473066	−	0.540717i	0.935153	−	0.354243i	$-0.115261\pi$
$278$	−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	−0.849125	−	0.528191i	$-0.822870\pi$
$281$	−11.8672	−	25.4492i	−0.707936	−	1.51817i	0.141189	−	0.989983i	$-0.454907\pi$
$282$		0			0
$283$	−11.1429	+	7.80236i	−0.662378	+	0.463802i	−0.855796	−	0.517314i	$-0.826932\pi$
$283$	−11.1429	+	7.80236i	−0.662378	+	0.463802i	0.193417	+	0.981117i	$0.438043\pi$
$284$	−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	−0.0577640	−	0.998330i	$-0.518397\pi$
$293$	16.0120	−	19.0823i	0.935430	−	1.11480i	0.993194	−	0.116472i	$-0.0371585\pi$
$294$		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	−0.658516	−	0.752567i	$-0.728816\pi$
$307$	−5.88777	+	3.39930i	−0.336033	+	0.194008i	0.322484	+	0.946575i	$0.395482\pi$
$308$	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	0.868272	−	0.496088i	$-0.165231\pi$
$311$	31.8564	−	14.8549i	1.80641	−	0.842344i	0.938140	−	0.346256i	$-0.112547\pi$
$312$		0			0
$313$	−24.1676	−	16.9223i	−1.36603	−	0.956506i	−0.999661	−	0.0260366i	$-0.991711\pi$
$313$	−24.1676	−	16.9223i	−1.36603	−	0.956506i	−0.366371	−	0.930469i	$-0.619400\pi$
$314$	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	−0.998555	−	0.0537429i	$-0.982885\pi$
$317$	−32.0131	−	11.6518i	−1.79804	−	0.654432i	−0.799483	−	0.600689i	$-0.794893\pi$
$318$		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	−0.974630	−	0.223822i	$-0.928147\pi$
$331$	0.437724	−	5.00321i	0.0240595	−	0.275001i	0.998689	−	0.0511790i	$-0.0162979\pi$
$332$	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	−0.472466	−	0.881349i	$-0.656636\pi$
$337$	−22.3573	−	3.94219i	−1.21788	−	0.214745i	−0.745412	+	0.666604i	$0.767747\pi$
$338$	−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	−0.986687	−	0.162631i	$-0.948002\pi$
$347$	−3.97719	−	14.8431i	−0.213507	−	0.796817i	0.773180	−	0.634186i	$-0.218665\pi$
$348$		0			0
$349$	−6.38284	−	2.32316i	−0.341666	−	0.124356i	0.165488	−	0.986212i	$-0.447080\pi$
$349$	−6.38284	−	2.32316i	−0.341666	−	0.124356i	−0.507154	+	0.861856i	$0.669302\pi$
$350$	−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	0.878231	−	0.478236i	$-0.158724\pi$
$353$	13.7006	+	9.59325i	0.729209	+	0.510597i	−0.149023	+	0.988834i	$0.547613\pi$
$354$		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	0.183030	−	0.983107i	$-0.441409\pi$
$359$	21.3335	−	12.3169i	1.12594	−	0.650062i	0.942911	+	0.333045i	$0.108076\pi$
$360$		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	0.803333	−	0.595530i	$-0.203058\pi$
$367$	6.82666	+	5.72824i	0.356349	+	0.299012i	−0.446985	+	0.894542i	$0.647502\pi$
$368$	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	−0.0634257	−	0.997987i	$-0.520203\pi$
$373$	17.9693	−	21.4149i	0.930413	−	1.10882i	0.993839	−	0.110836i	$-0.0353530\pi$
$374$	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	−0.997166	−	0.0752313i	$-0.976030\pi$
$379$	−1.67165	−	9.48042i	−0.0858671	−	0.486977i	0.911299	−	0.411745i	$-0.135081\pi$
$380$	−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	−0.360178	−	0.932884i	$-0.617284\pi$
$383$	7.69620	−	5.38893i	0.393257	−	0.275362i	0.753436	+	0.657522i	$0.228395\pi$
$384$		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	0.999562	−	0.0295773i	$-0.00941610\pi$
$389$	0.198208	+	2.26553i	0.0100496	+	0.114867i	−0.989513	+	0.144444i	$0.953861\pi$
$390$		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	−0.966081	−	0.258238i	$-0.916858\pi$
$397$	−33.3296	−	19.2428i	−1.67276	−	0.965770i	−0.706681	−	0.707532i	$-0.749809\pi$
$398$	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	−0.999782	−	0.0208684i	$-0.993357\pi$
$401$	−19.6027	+	19.6027i	−0.978914	+	0.978914i	0.0208684	+	0.999782i	$0.493357\pi$
$402$		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	−0.427880	−	0.903835i	$-0.640739\pi$
$409$	−20.3493	−	1.78033i	−1.00621	−	0.0880319i	−0.578329	+	0.815804i	$0.696295\pi$
$410$	−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	0.998692	−	0.0511230i	$-0.0162801\pi$
$419$	15.8623	+	18.9040i	0.774925	+	0.923520i	−0.223767	+	0.974643i	$0.571836\pi$
$420$		0			0
$421$	−34.0718	+	9.12952i	−1.66056	+	0.444945i	−0.962541	−	0.271135i	$-0.912601\pi$
$421$	−34.0718	+	9.12952i	−1.66056	+	0.444945i	−0.698018	+	0.716080i	$0.745934\pi$
$422$	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	0.370634	−	0.928779i	$-0.379140\pi$
$431$	−13.0562	−	18.6462i	−0.628897	−	0.898158i	−0.999531	+	0.0306209i	$0.990252\pi$
$432$		0			0
$433$	−13.3867	−	23.1864i	−0.643322	−	1.11427i	−0.984686	−	0.174336i	$-0.944222\pi$
$433$	−13.3867	−	23.1864i	−0.643322	−	1.11427i	0.341364	−	0.939931i	$-0.389111\pi$
$434$	−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	0.0682269	−	0.997670i	$-0.478266\pi$
$439$	−13.6646	−	6.37192i	−0.652177	−	0.304115i	−0.720404	+	0.693555i	$0.756044\pi$
$440$	−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	0.854696	−	0.519129i	$-0.173743\pi$
$449$	21.3254	+	9.94421i	1.00641	+	0.469296i	0.151713	+	0.988425i	$0.451521\pi$
$450$		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	0.931920	+	0.362665i	$0.118133\pi$
$457$	20.3937	+	29.1252i	0.953978	+	1.36242i	0.0220584	+	0.999757i	$0.492978\pi$
$458$	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	−0.986813	−	0.161863i	$-0.948250\pi$
$461$	−10.6754	+	15.2460i	−0.497202	+	0.710078i	0.489612	+	0.871941i	$0.337139\pi$
$462$		0			0
$463$	−9.07890	+	0.794301i	−0.421932	+	0.0369143i	−0.296145	−	0.955143i	$-0.595701\pi$
$463$	−9.07890	+	0.794301i	−0.421932	+	0.0369143i	−0.125787	+	0.992057i	$0.540146\pi$
$464$	−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	−0.400196	−	0.916429i	$-0.631058\pi$
$467$	−6.23587	+	1.67090i	−0.288562	+	0.0773199i	0.111635	+	0.993749i	$0.464391\pi$
$468$		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	0.560622	−	0.828072i	$-0.310562\pi$
$479$	21.2061	+	1.85530i	0.968933	+	0.0847707i	0.408311	+	0.912843i	$0.366118\pi$
$480$		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	−0.455519	−	0.890226i	$-0.650546\pi$
$487$	9.59314	−	9.59314i	0.434707	−	0.434707i	0.890226	+	0.455519i	$0.150546\pi$
$488$	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	−0.119835	−	0.992794i	$-0.538237\pi$
$491$	−23.0346	−	13.2990i	−1.03954	−	0.600177i	−0.919702	+	0.392616i	$0.871570\pi$
$492$		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	−0.998013	−	0.0630127i	$-0.979929\pi$
$499$	−0.583121	−	6.66511i	−0.0261041	−	0.298371i	0.971909	−	0.235358i	$-0.0756264\pi$
$500$	−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	0.926547	+	0.376179i	$0.122762\pi$
$503$	13.8860	+	29.7785i	0.619144	+	1.32776i	−0.307403	+	0.951579i	$0.599460\pi$
$504$		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	0.957479	−	0.288504i	$-0.0931579\pi$
$509$	−0.923450	−	5.23715i	−0.0409312	−	0.232132i	−0.998410	+	0.0563717i	$0.982047\pi$
$510$		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	0.817242	−	0.576295i	$-0.195502\pi$
$521$	8.93876	+	7.50051i	0.391614	+	0.328603i	−0.425627	+	0.904898i	$0.639947\pi$
$522$		0			0
$523$	16.5894	−	35.5761i	0.725405	−	1.55564i	−0.102478	−	0.994735i	$-0.532677\pi$
$523$	16.5894	−	35.5761i	0.725405	−	1.55564i	0.827883	−	0.560901i	$-0.189545\pi$
$524$	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	0.923061	−	0.384655i	$-0.125679\pi$
$541$	−1.59701	−	5.96011i	−0.0686607	−	0.256245i	−0.991721	+	0.128410i	$0.959013\pi$
$542$	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	0.762676	+	0.646781i	$0.223885\pi$
$547$	−5.17369	+	19.3085i	−0.221211	+	0.825571i	−0.983887	+	0.178791i	$0.942782\pi$
$548$	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	0.519852	+	0.854256i	$0.325987\pi$
$557$	−3.31456	+	37.8856i	−0.140442	+	1.60526i	−0.660294	+	0.751007i	$0.729568\pi$
$558$		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	0.268045	+	0.963407i	$0.413623\pi$
$563$	−10.5776	+	39.4761i	−0.445792	+	1.66372i	−0.713837	+	0.700312i	$0.753044\pi$
$564$		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	−0.795928	−	0.605392i	$-0.793017\pi$
$569$	−9.76404	−	36.4399i	−0.409330	−	1.52764i	0.386598	−	0.922248i	$-0.373650\pi$
$570$		0			0
$571$	−13.6730	−	4.97657i	−0.572198	−	0.208263i	0.0396837	−	0.999212i	$-0.487365\pi$
$571$	−13.6730	−	4.97657i	−0.572198	−	0.208263i	−0.611882	+	0.790949i	$0.709587\pi$
$572$	−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	0.273026	−	0.962007i	$-0.411976\pi$
$577$	28.4758	−	13.2785i	1.18546	−	0.552791i	0.912438	+	0.409216i	$0.134198\pi$
$578$	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	−0.0186807	+	0.999826i	$0.505947\pi$
$587$	−18.7182	+	40.1414i	−0.772584	+	1.65681i	−0.753903	+	0.656986i	$0.771831\pi$
$588$		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	$-0.800924\pi$
$593$		−	28.5125i		−	1.17087i	0.810721	−	0.585433i	$-0.199076\pi$
$594$		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	0.998902	−	0.0468554i	$-0.0149200\pi$
$599$	4.98253	+	13.6894i	0.203581	+	0.559333i	−0.795321	+	0.606188i	$0.792698\pi$
$600$		0			0
$601$	1.16812	+	6.62472i	0.0476485	+	0.270228i	0.999319	−	0.0368922i	$-0.0117458\pi$
$601$	1.16812	+	6.62472i	0.0476485	+	0.270228i	−0.951671	+	0.307120i	$0.900635\pi$
$602$	−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	0.997039	+	0.0769037i	$0.0245034\pi$
$607$	10.2261	+	21.9300i	0.415066	+	0.890112i	−0.581972	+	0.813209i	$0.697719\pi$
$608$	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	−0.944334	−	0.328990i	$-0.893292\pi$
$613$	−0.234258	+	0.643620i	−0.00946161	+	0.0259956i	0.934872	+	0.354985i	$0.115514\pi$
$614$	−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	−0.515161	−	0.857094i	$-0.672268\pi$
$617$	5.94794	−	4.99091i	0.239455	−	0.200927i	0.754616	+	0.656167i	$0.227823\pi$
$618$		0			0
$619$	−24.3094	−	14.0350i	−0.977076	−	0.564115i	−0.0756901	−	0.997131i	$-0.524116\pi$
$619$	−24.3094	−	14.0350i	−0.977076	−	0.564115i	−0.901386	+	0.433016i	$0.857449\pi$
$620$	−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	0.702134	−	0.712045i	$-0.252231\pi$
$631$	31.9009	+	2.79097i	1.26996	+	0.111107i	0.567821	+	0.823152i	$0.307786\pi$
$632$	−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	0.568226	−	0.822872i	$-0.307630\pi$
$641$	−8.62878	−	10.2834i	−0.340816	−	0.406169i	−0.909043	+	0.416703i	$0.863185\pi$
$642$		0			0
$643$	5.56362	−	1.49077i	0.219408	−	0.0587902i	−0.147440	−	0.989071i	$-0.547103\pi$
$643$	5.56362	−	1.49077i	0.219408	−	0.0587902i	0.366848	+	0.930281i	$0.380437\pi$
$644$	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	−0.614793	−	0.788689i	$-0.710760\pi$
$647$	−27.5548	+	2.41073i	−1.08329	+	0.0947757i	−0.468498	+	0.883464i	$0.655205\pi$
$648$		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	0.991413	−	0.130765i	$-0.0417434\pi$
$653$	13.5295	+	19.3221i	0.529451	+	0.756134i	−0.461963	+	0.886899i	$0.652855\pi$
$654$		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	−0.622759	−	0.782414i	$-0.713988\pi$
$659$	−15.3229	+	5.57707i	−0.596895	+	0.217252i	0.0258646	+	0.999665i	$0.491766\pi$
$660$		0			0
$661$	−2.49678	−	1.16427i	−0.0971135	−	0.0452848i	0.373455	−	0.927648i	$-0.378173\pi$
$661$	−2.49678	−	1.16427i	−0.0971135	−	0.0452848i	−0.470568	+	0.882364i	$0.655951\pi$
$662$	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	−0.612832	−	0.790213i	$-0.709970\pi$
$673$	−14.8999	+	5.42313i	−0.574350	+	0.209046i	0.0384821	+	0.999259i	$0.487748\pi$
$674$	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	0.818477	−	0.574539i	$-0.194819\pi$
$677$	−2.29819	−	3.98058i	−0.0883266	−	0.152986i	−0.906804	+	0.421553i	$0.861485\pi$
$678$		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	−0.173346	+	0.984861i	$0.555458\pi$
$683$	−27.1672	+	38.7988i	−1.03952	+	1.48459i	−0.866179	+	0.499734i	$0.833431\pi$
$684$		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	0.540400	−	0.841408i	$-0.318273\pi$
$691$	−10.0433	−	11.9691i	−0.382065	−	0.455327i	−0.922465	+	0.386081i	$0.873828\pi$
$692$	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	0.121345	−	0.992610i	$-0.461279\pi$
$701$	1.81313	+	0.158628i	0.0684810	+	0.00599131i	−0.0528638	+	0.998602i	$0.516835\pi$
$702$		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	0.151857	−	0.988402i	$-0.451475\pi$
$709$	30.3617	−	30.3617i	1.14026	−	1.14026i	0.988402	−	0.151857i	$-0.0485253\pi$
$710$	−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	−0.942920	−	0.333018i	$-0.891933\pi$
$719$	−0.175409	+	0.481933i	−0.00654166	+	0.0179731i	0.936379	+	0.350991i	$0.114155\pi$
$720$		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	−0.710581	−	0.703615i	$-0.751568\pi$
$727$	−7.88484	+	5.52102i	−0.292432	+	0.204763i	0.418149	+	0.908379i	$0.362679\pi$
$728$	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	0.945727	+	0.324961i	$0.105351\pi$
$733$	11.6456	+	31.9960i	0.430139	+	1.18180i	−0.515588	+	0.856836i	$0.672427\pi$
$734$	−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	$0.132361\pi$
$739$			21.9621i			0.807888i	−0.914784	+	0.403944i	$0.867639\pi$
$740$	−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	0.121825	−	0.992552i	$-0.461125\pi$
$743$	−22.7466	−	19.0867i	−0.834492	−	0.700222i	−0.956318	+	0.292329i	$0.905570\pi$
$744$		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	−0.988273	−	0.152697i	$-0.951204\pi$
$751$	−37.0006	+	21.3623i	−1.35017	+	0.779521i	−0.361897	+	0.932218i	$0.617871\pi$
$752$	−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	0.665302	−	0.746574i	$-0.268303\pi$
$757$	5.26333	+	3.68542i	0.191299	+	0.133949i	−0.474003	+	0.880523i	$0.657192\pi$
$758$	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	0.598740	−	0.800943i	$-0.295668\pi$
$761$	14.9673	+	5.44766i	0.542565	+	0.197477i	−0.0561751	+	0.998421i	$0.517891\pi$
$762$		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	−0.939739	−	0.341893i	$-0.888932\pi$
$769$	1.24915	−	4.66189i	0.0450455	−	0.168112i	0.984784	+	0.173781i	$0.0555986\pi$
$770$	−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	−0.503384	−	0.864063i	$-0.667912\pi$
$773$	−35.3635	−	6.23554i	−1.27194	−	0.224277i	−0.768553	+	0.639786i	$0.779023\pi$
$774$		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
$784$

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

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