LMFDB - Embedded newform 666.2.bs.a.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.1
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.a.611.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-1.35125 - 0.630098i) q^{5} +(-0.533399 + 0.194141i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-1.35125 - 0.630098i) q^{5} +(-0.533399 + 0.194141i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.745469 - 1.29119i) q^{10} +(2.06935 + 3.58421i) q^{11} +(-1.18979 - 1.69919i) q^{13} +(-0.146914 - 0.548290i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.83004 + 5.46987i) q^{17} +(0.576069 - 0.0503995i) q^{19} +(1.22130 + 0.855167i) q^{20} +(-3.75093 + 1.74909i) q^{22} +(-8.94253 + 2.39614i) q^{23} +(-1.78509 - 2.12738i) q^{25} +(1.79642 - 1.03716i) q^{26} +(0.559008 - 0.0985682i) q^{28} +(-7.66914 - 2.05494i) q^{29} +(-2.71305 - 2.71305i) q^{31} +(-0.422618 + 0.906308i) q^{32} +(-5.11524 - 4.29220i) q^{34} +(0.843083 + 0.0737602i) q^{35} +(5.73193 - 2.03594i) q^{37} +0.578269i q^{38} +(-0.958357 + 1.14212i) q^{40} +(-0.166732 + 0.945584i) q^{41} +(-6.19601 + 6.19601i) q^{43} +(-1.41552 - 3.88910i) q^{44} +(-1.60763 - 9.11734i) q^{46} +(7.18392 + 4.14764i) q^{47} +(-5.11549 + 4.29240i) q^{49} +(2.27487 - 1.59288i) q^{50} +(0.876649 + 1.87998i) q^{52} +(-1.62845 + 4.47413i) q^{53} +(-0.537798 - 6.14706i) q^{55} +(0.0494723 + 0.565471i) q^{56} +(2.71553 - 7.46085i) q^{58} +(-0.589710 - 1.26464i) q^{59} +(0.953625 - 0.667735i) q^{61} +(2.93919 - 2.46627i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.537041 + 3.04571i) q^{65} +(1.02770 + 2.82358i) q^{67} +(4.72169 - 4.72169i) q^{68} +(-0.146959 + 0.833446i) q^{70} +(8.44934 - 10.0695i) q^{71} +2.55653i q^{73} +(1.52862 + 5.88756i) q^{74} +(-0.576069 - 0.0503995i) q^{76} +(-1.79963 - 1.51007i) q^{77} +(0.0758092 - 0.162573i) q^{79} +(-1.05425 - 1.05425i) q^{80} +(-0.927454 - 0.248511i) q^{82} +(8.12772 - 1.43314i) q^{83} +(8.62189 - 4.97785i) q^{85} +(-5.63242 - 6.71245i) q^{86} +(3.99767 - 1.07117i) q^{88} +(-10.1024 + 4.71081i) q^{89} +(0.964514 + 0.675360i) q^{91} +(9.22276 - 0.806887i) q^{92} +(-4.75798 + 6.79509i) q^{94} +(-0.810169 - 0.294877i) q^{95} +(4.90685 + 18.3126i) q^{97} +(-3.83023 - 5.47013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.35125	−	0.630098i	−0.604297	−	0.281788i	0.0962923	−	0.995353i	$-0.469302\pi$
$5$	−1.35125	−	0.630098i	−0.604297	−	0.281788i	−0.700589	+	0.713565i	$0.747079\pi$
$6$		0			0
$7$	−0.533399	+	0.194141i	−0.201606	+	0.0733786i	−0.440850	−	0.897581i	$-0.645323\pi$
$7$	−0.533399	+	0.194141i	−0.201606	+	0.0733786i	0.239244	+	0.970960i	$0.423101\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	0.745469	−	1.29119i	0.235738	−	0.408310i
$11$	2.06935	+	3.58421i	0.623932	+	1.08068i	0.988746	+	0.149601i	$0.0477990\pi$
$11$	2.06935	+	3.58421i	0.623932	+	1.08068i	−0.364815	+	0.931080i	$0.618868\pi$
$12$		0			0
$13$	−1.18979	−	1.69919i	−0.329987	−	0.471271i	0.619536	−	0.784969i	$-0.287321\pi$
$13$	−1.18979	−	1.69919i	−0.329987	−	0.471271i	−0.949523	+	0.313698i	$0.898432\pi$
$14$	−0.146914	−	0.548290i	−0.0392644	−	0.146537i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−3.83004	+	5.46987i	−0.928922	+	1.32664i	0.0161826	+	0.999869i	$0.494849\pi$
$17$	−3.83004	+	5.46987i	−0.928922	+	1.32664i	−0.945104	+	0.326769i	$0.894040\pi$
$18$		0			0
$19$	0.576069	−	0.0503995i	0.132159	−	0.0115624i	−0.0208842	−	0.999782i	$-0.506648\pi$
$19$	0.576069	−	0.0503995i	0.132159	−	0.0115624i	0.153043	+	0.988219i	$0.451093\pi$
$20$	1.22130	+	0.855167i	0.273092	+	0.191221i
$21$		0			0
$22$	−3.75093	+	1.74909i	−0.799701	+	0.372907i
$23$	−8.94253	+	2.39614i	−1.86465	+	0.499631i	−0.999996	−	0.00274350i	$-0.999127\pi$
$23$	−8.94253	+	2.39614i	−1.86465	+	0.499631i	−0.864650	+	0.502374i	$0.832460\pi$
$24$		0			0
$25$	−1.78509	−	2.12738i	−0.357018	−	0.425477i
$26$	1.79642	−	1.03716i	0.352307	−	0.203405i
$27$		0			0
$28$	0.559008	−	0.0985682i	0.105643	−	0.0186276i
$29$	−7.66914	−	2.05494i	−1.42412	−	0.381593i	−0.537179	−	0.843469i	$-0.680510\pi$
$29$	−7.66914	−	2.05494i	−1.42412	−	0.381593i	−0.886945	+	0.461876i	$0.847177\pi$
$30$		0			0
$31$	−2.71305	−	2.71305i	−0.487279	−	0.487279i	0.420168	−	0.907446i	$-0.361971\pi$
$31$	−2.71305	−	2.71305i	−0.487279	−	0.487279i	−0.907446	+	0.420168i	$0.861971\pi$
$32$	−0.422618	+	0.906308i	−0.0747091	+	0.160214i
$33$		0			0
$34$	−5.11524	−	4.29220i	−0.877257	−	0.736106i
$35$	0.843083	+	0.0737602i	0.142507	+	0.0124677i
$36$		0			0
$37$	5.73193	−	2.03594i	0.942323	−	0.334706i
$37$	5.73193	−	2.03594i	0.942323	−	0.334706i
$38$			0.578269i			0.0938076i
$39$		0			0
$40$	−0.958357	+	1.14212i	−0.151529	+	0.180586i
$41$	−0.166732	+	0.945584i	−0.0260392	+	0.147675i	−0.995055	−	0.0993217i	$-0.968333\pi$
$41$	−0.166732	+	0.945584i	−0.0260392	+	0.147675i	0.969016	+	0.246997i	$0.0794438\pi$
$42$		0			0
$43$	−6.19601	+	6.19601i	−0.944883	+	0.944883i	−0.998558	−	0.0536752i	$-0.982906\pi$
$43$	−6.19601	+	6.19601i	−0.944883	+	0.944883i	0.0536752	+	0.998558i	$0.482906\pi$
$44$	−1.41552	−	3.88910i	−0.213397	−	0.586304i
$45$		0			0
$46$	−1.60763	−	9.11734i	−0.237033	−	1.34428i
$47$	7.18392	+	4.14764i	1.04788	+	0.604995i	0.922056	−	0.387057i	$-0.126508\pi$
$47$	7.18392	+	4.14764i	1.04788	+	0.604995i	0.125827	+	0.992052i	$0.459842\pi$
$48$		0			0
$49$	−5.11549	+	4.29240i	−0.730784	+	0.613201i
$50$	2.27487	−	1.59288i	0.321715	−	0.225267i
$51$		0			0
$52$	0.876649	+	1.87998i	0.121569	+	0.260706i
$53$	−1.62845	+	4.47413i	−0.223685	+	0.614569i	−0.999873	−	0.0159324i	$-0.994928\pi$
$53$	−1.62845	+	4.47413i	−0.223685	+	0.614569i	0.776188	+	0.630501i	$0.217151\pi$
$54$		0			0
$55$	−0.537798	−	6.14706i	−0.0725166	−	0.828869i
$56$	0.0494723	+	0.565471i	0.00661102	+	0.0755643i
$57$		0			0
$58$	2.71553	−	7.46085i	0.356566	−	0.979658i
$59$	−0.589710	−	1.26464i	−0.0767736	−	0.164642i	0.864175	−	0.503192i	$-0.167841\pi$
$59$	−0.589710	−	1.26464i	−0.0767736	−	0.164642i	−0.940948	+	0.338550i	$0.890063\pi$
$60$		0			0
$61$	0.953625	−	0.667735i	0.122099	−	0.0854947i	−0.510932	−	0.859621i	$-0.670700\pi$
$61$	0.953625	−	0.667735i	0.122099	−	0.0854947i	0.633031	+	0.774127i	$0.281811\pi$
$62$	2.93919	−	2.46627i	0.373277	−	0.313217i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	0.537041	+	3.04571i	0.0666117	+	0.377774i
$66$		0			0
$67$	1.02770	+	2.82358i	0.125554	+	0.344956i	0.986505	−	0.163732i	$-0.0523532\pi$
$67$	1.02770	+	2.82358i	0.125554	+	0.344956i	−0.860951	+	0.508687i	$0.830131\pi$
$68$	4.72169	−	4.72169i	0.572589	−	0.572589i
$69$		0			0
$70$	−0.146959	+	0.833446i	−0.0175650	+	0.0996159i
$71$	8.44934	−	10.0695i	1.00275	−	1.19503i	0.0220039	−	0.999758i	$-0.492995\pi$
$71$	8.44934	−	10.0695i	1.00275	−	1.19503i	0.980748	−	0.195276i	$-0.0625602\pi$
$72$		0			0
$73$			2.55653i			0.299220i	0.988745	+	0.149610i	$0.0478018\pi$
$73$			2.55653i			0.299220i	−0.988745	+	0.149610i	$0.952198\pi$
$74$	1.52862	+	5.88756i	0.177698	+	0.684415i
$75$		0			0
$76$	−0.576069	−	0.0503995i	−0.0660796	−	0.00578122i
$77$	−1.79963	−	1.51007i	−0.205087	−	0.172089i
$78$		0			0
$79$	0.0758092	−	0.162573i	0.00852920	−	0.0182909i	−0.901997	−	0.431742i	$-0.857899\pi$
$79$	0.0758092	−	0.162573i	0.00852920	−	0.0182909i	0.910526	+	0.413451i	$0.135677\pi$
$80$	−1.05425	−	1.05425i	−0.117869	−	0.117869i
$81$		0			0
$82$	−0.927454	−	0.248511i	−0.102420	−	0.0274434i
$83$	8.12772	−	1.43314i	0.892133	−	0.157307i	0.291253	−	0.956646i	$-0.405928\pi$
$83$	8.12772	−	1.43314i	0.892133	−	0.157307i	0.600880	+	0.799339i	$0.294817\pi$
$84$		0			0
$85$	8.62189	−	4.97785i	0.935175	−	0.539924i
$86$	−5.63242	−	6.71245i	−0.607359	−	0.723823i
$87$		0			0
$88$	3.99767	−	1.07117i	0.426153	−	0.114187i
$89$	−10.1024	+	4.71081i	−1.07085	+	0.499345i	−0.876408	−	0.481570i	$-0.840067\pi$
$89$	−10.1024	+	4.71081i	−1.07085	+	0.499345i	−0.194440	+	0.980914i	$0.562289\pi$
$90$		0			0
$91$	0.964514	+	0.675360i	0.101109	+	0.0707970i
$92$	9.22276	−	0.806887i	0.961539	−	0.0841238i
$93$		0			0
$94$	−4.75798	+	6.79509i	−0.490748	+	0.700860i
$95$	−0.810169	−	0.294877i	−0.0831216	−	0.0302538i
$96$		0			0
$97$	4.90685	+	18.3126i	0.498215	+	1.85936i	0.511224	+	0.859448i	$0.329192\pi$
$97$	4.90685	+	18.3126i	0.498215	+	1.85936i	−0.0130091	+	0.999915i	$0.504141\pi$
$98$	−3.83023	−	5.47013i	−0.386911	−	0.552566i
$99$		0			0
$100$	1.38855	+	2.40504i	0.138855	+	0.240504i
$101$	1.87568	−	3.24877i	0.186637	−	0.323265i	−0.757490	−	0.652847i	$-0.773574\pi$
$101$	1.87568	−	3.24877i	0.186637	−	0.323265i	0.944127	+	0.329582i	$0.106908\pi$
$102$		0			0
$103$	1.83995	−	6.86677i	0.181295	−	0.676603i	−0.814098	−	0.580727i	$-0.802768\pi$
$103$	1.83995	−	6.86677i	0.181295	−	0.676603i	0.995393	−	0.0958757i	$-0.0305651\pi$
$104$	−1.94923	+	0.709462i	−0.191138	+	0.0695685i
$105$		0			0
$106$	−4.31517	−	2.01220i	−0.419127	−	0.195442i
$107$	−7.67030	−	1.35248i	−0.741516	−	0.130749i	−0.209886	−	0.977726i	$-0.567309\pi$
$107$	−7.67030	−	1.35248i	−0.741516	−	0.130749i	−0.531630	+	0.846977i	$0.678420\pi$
$108$		0			0
$109$	−0.105496	+	1.20582i	−0.0101046	+	0.115497i	−0.999572	−	0.0292608i	$-0.990685\pi$
$109$	−0.105496	+	1.20582i	−0.0101046	+	0.115497i	0.989467	+	0.144758i	$0.0462402\pi$
$110$	6.17054			0.588338
$111$		0			0
$112$	−0.567631			−0.0536361
$113$	0.300237	−	3.43173i	0.0282440	−	0.322830i	−0.968909	−	0.247419i	$-0.920418\pi$
$113$	0.300237	−	3.43173i	0.0282440	−	0.322830i	0.997153	−	0.0754109i	$-0.0240269\pi$
$114$		0			0
$115$	13.5934	+	2.39688i	1.26759	+	0.223510i
$116$	7.19579	+	3.35545i	0.668112	+	0.311546i
$117$		0			0
$118$	1.31122	−	0.477245i	0.120708	−	0.0439340i
$119$	0.981014	−	3.66119i	0.0899294	−	0.335621i
$120$		0			0
$121$	−3.06439	+	5.30769i	−0.278581	+	0.482517i
$122$	0.582080	+	1.00819i	0.0526991	+	0.0912775i
$123$		0			0
$124$	2.20072	+	3.14295i	0.197630	+	0.282245i
$125$	3.00105	+	11.2001i	0.268422	+	1.00177i
$126$		0			0
$127$	−12.4729	−	4.53975i	−1.10679	−	0.402838i	−0.276973	−	0.960878i	$-0.589331\pi$
$127$	−12.4729	−	4.53975i	−1.10679	−	0.402838i	−0.829814	+	0.558040i	$0.811554\pi$
$128$	0.573576	−	0.819152i	0.0506975	−	0.0724035i
$129$		0			0
$130$	−3.08093	+	0.269546i	−0.270215	+	0.0236408i
$131$	−6.43188	−	4.50365i	−0.561956	−	0.393486i	0.257800	−	0.966198i	$-0.417002\pi$
$131$	−6.43188	−	4.50365i	−0.561956	−	0.393486i	−0.819757	+	0.572712i	$0.805891\pi$
$132$		0			0
$133$	−0.297490	+	0.138722i	−0.0257956	+	0.0120287i
$134$	−2.90241	+	0.777698i	−0.250730	+	0.0671829i
$135$		0			0
$136$	4.29220	+	5.11524i	0.368053	+	0.438628i
$137$	12.8370	−	7.41147i	1.09674	−	0.633205i	0.161379	−	0.986892i	$-0.448406\pi$
$137$	12.8370	−	7.41147i	1.09674	−	0.633205i	0.935364	+	0.353688i	$0.115072\pi$
$138$		0			0
$139$	9.82735	−	1.73283i	0.833545	−	0.146977i	0.259441	−	0.965759i	$-0.416462\pi$
$139$	9.82735	−	1.73283i	0.833545	−	0.146977i	0.574104	+	0.818782i	$0.305350\pi$
$140$	−0.817466	−	0.219039i	−0.0690885	−	0.0185122i
$141$		0			0
$142$	9.29481	+	9.29481i	0.780003	+	0.780003i
$143$	3.62818	−	7.78066i	0.303404	−	0.650652i
$144$		0			0
$145$	9.06810	+	7.60904i	0.753065	+	0.631896i
$146$	−2.54681	−	0.222817i	−0.210775	−	0.0184404i
$147$		0			0
$148$	−5.99838	+	1.00967i	−0.493064	+	0.0829941i
$149$		−	2.96089i		−	0.242566i	−0.992618	−	0.121283i	$-0.961299\pi$
$149$		−	2.96089i		−	0.242566i	0.992618	−	0.121283i	$-0.0387008\pi$
$150$		0			0
$151$	1.34587	−	1.60394i	0.109525	−	0.130527i	−0.708497	−	0.705714i	$-0.750626\pi$
$151$	1.34587	−	1.60394i	0.109525	−	0.130527i	0.818022	+	0.575187i	$0.195071\pi$
$152$	0.100415	−	0.569484i	0.00814476	−	0.0461912i
$153$		0			0
$154$	1.66117	−	1.66117i	0.133861	−	0.133861i
$155$	1.95652	+	5.37550i	0.157152	+	0.431770i
$156$		0			0
$157$	2.14318	+	12.1546i	0.171044	+	0.970039i	0.942611	+	0.333892i	$0.108362\pi$
$157$	2.14318	+	12.1546i	0.171044	+	0.970039i	−0.771567	+	0.636148i	$0.780527\pi$
$158$	0.155347	+	0.0896899i	0.0123588	+	0.00713534i
$159$		0			0
$160$	1.14212	−	0.958357i	0.0902929	−	0.0757647i
$161$	4.30475	−	3.01422i	0.339262	−	0.237554i
$162$		0			0
$163$	3.17088	+	6.79997i	0.248362	+	0.532615i	0.990480	−	0.137654i	$-0.0439563\pi$
$163$	3.17088	+	6.79997i	0.248362	+	0.532615i	−0.742118	+	0.670269i	$0.766179\pi$
$164$	0.328398	−	0.902266i	0.0256436	−	0.0704551i
$165$		0			0
$166$	0.719305	+	8.22170i	0.0558289	+	0.638128i
$167$	−0.722547	−	8.25874i	−0.0559123	−	0.639081i	−0.971512	−	0.236990i	$-0.923839\pi$
$167$	−0.722547	−	8.25874i	−0.0559123	−	0.639081i	0.915600	−	0.402091i	$-0.131716\pi$
$168$		0			0
$169$	2.97460	−	8.17266i	0.228816	−	0.628666i
$170$	4.20746	+	9.02293i	0.322698	+	0.692027i
$171$		0			0
$172$	7.17781	−	5.02596i	0.547303	−	0.383226i
$173$	−17.5668	+	14.7403i	−1.33558	+	1.12068i	−0.352838	+	0.935685i	$0.614783\pi$
$173$	−17.5668	+	14.7403i	−1.33558	+	1.12068i	−0.982739	+	0.184997i	$0.940772\pi$
$174$		0			0
$175$	1.36518	+	0.788186i	0.103198	+	0.0595812i
$176$	0.718677	+	4.07582i	0.0541723	+	0.307226i
$177$		0			0
$178$	−3.81240	−	10.4745i	−0.285752	−	0.785096i
$179$	−3.17951	+	3.17951i	−0.237648	+	0.237648i	−0.815875	−	0.578228i	$-0.803745\pi$
$179$	−3.17951	+	3.17951i	−0.237648	+	0.237648i	0.578228	+	0.815875i	$0.303745\pi$
$180$		0			0
$181$	−2.48308	+	14.0823i	−0.184566	+	1.04673i	0.741945	+	0.670460i	$0.233903\pi$
$181$	−2.48308	+	14.0823i	−0.184566	+	1.04673i	−0.926511	+	0.376266i	$0.877208\pi$
$182$	−0.756853	+	0.901982i	−0.0561017	+	0.0668594i
$183$		0			0
$184$			9.25799i			0.682508i
$185$	−9.02810	−	0.860616i	−0.663759	−	0.0632738i
$186$		0			0
$187$	−27.5309	−	2.40864i	−2.01326	−	0.176137i
$188$	−6.35455	−	5.33210i	−0.463453	−	0.388883i
$189$		0			0
$190$	0.364366	−	0.781385i	0.0264339	−	0.0566877i
$191$	15.9622	+	15.9622i	1.15499	+	1.15499i	0.985539	+	0.169449i	$0.0541987\pi$
$191$	15.9622	+	15.9622i	1.15499	+	1.15499i	0.169449	+	0.985539i	$0.445801\pi$
$192$		0			0
$193$	17.3955	+	4.66112i	1.25216	+	0.335515i	0.823170	−	0.567795i	$-0.192204\pi$
$193$	17.3955	+	4.66112i	1.25216	+	0.335515i	0.428988	+	0.903310i	$0.358870\pi$
$194$	−18.6706	+	3.29213i	−1.34047	+	0.236361i
$195$		0			0
$196$	5.78314	−	3.33890i	0.413081	−	0.238493i
$197$	−5.23245	−	6.23579i	−0.372796	−	0.444281i	0.546730	−	0.837309i	$-0.315872\pi$
$197$	−5.23245	−	6.23579i	−0.372796	−	0.444281i	−0.919527	+	0.393027i	$0.871428\pi$
$198$		0			0
$199$	26.5509	−	7.11430i	1.88215	−	0.504320i	0.882740	−	0.469862i	$-0.155696\pi$
$199$	26.5509	−	7.11430i	1.88215	−	0.504320i	0.999406	−	0.0344580i	$-0.0109705\pi$
$200$	−2.51691	+	1.17365i	−0.177972	+	0.0829899i
$201$		0			0
$202$	3.07293	+	2.15169i	0.216211	+	0.151393i
$203$	4.48966	−	0.392794i	0.315112	−	0.0275688i
$204$		0			0
$205$	0.821107	−	1.17266i	0.0573486	−	0.0819022i
$206$	6.68028	+	2.43142i	0.465437	+	0.169405i
$207$		0			0
$208$	−0.536876	−	2.00365i	−0.0372256	−	0.138928i
$209$	1.37273	+	1.96046i	0.0949536	+	0.135608i
$210$		0			0
$211$	−3.39338	−	5.87750i	−0.233610	−	0.404624i	0.725258	−	0.688477i	$-0.241720\pi$
$211$	−3.39338	−	5.87750i	−0.233610	−	0.404624i	−0.958868	+	0.283853i	$0.908387\pi$
$212$	2.38063	−	4.12338i	0.163503	−	0.283195i
$213$		0			0
$214$	2.01584	−	7.52324i	0.137800	−	0.514278i
$215$	12.2765	−	4.46826i	0.837247	−	0.304733i
$216$		0			0
$217$	1.97386	+	0.920424i	0.133994	+	0.0624824i
$218$	−1.19204	−	0.210188i	−0.0807350	−	0.0142358i
$219$		0			0
$220$	−0.537798	+	6.14706i	−0.0362583	+	0.414434i
$221$	13.8513			0.931738
$222$		0			0
$223$	−8.12603			−0.544159			−0.272080	−	0.962275i	$-0.587711\pi$
$223$	−8.12603			−0.544159			−0.272080	+	0.962275i	$0.587711\pi$
$224$	0.0494723	−	0.565471i	0.00330551	−	0.0377822i
$225$		0			0
$226$	3.39250	+	0.598190i	0.225666	+	0.0397910i
$227$	21.4944	+	10.0230i	1.42663	+	0.665250i	0.974021	−	0.226458i	$-0.0727145\pi$
$227$	21.4944	+	10.0230i	1.42663	+	0.665250i	0.452612	+	0.891708i	$0.350492\pi$
$228$		0			0
$229$	−5.77966	+	2.10362i	−0.381930	+	0.139011i	−0.525848	−	0.850578i	$-0.676252\pi$
$229$	−5.77966	+	2.10362i	−0.381930	+	0.139011i	0.143918	+	0.989590i	$0.454030\pi$
$230$	−3.57250	+	13.3328i	−0.235564	+	0.879136i
$231$		0			0
$232$	−3.96984	+	6.87596i	−0.260633	+	0.451429i
$233$	−4.71515	−	8.16689i	−0.308900	−	0.535031i	0.669222	−	0.743063i	$-0.266628\pi$
$233$	−4.71515	−	8.16689i	−0.308900	−	0.535031i	−0.978122	+	0.208032i	$0.933294\pi$
$234$		0			0
$235$	−7.09385	−	10.1311i	−0.462752	−	0.660878i
$236$	0.361149	+	1.34783i	0.0235088	+	0.0877360i
$237$		0			0
$238$	3.56176	+	1.29637i	0.230875	+	0.0840315i
$239$	14.3623	−	20.5116i	0.929023	−	1.32678i	−0.0160322	−	0.999871i	$-0.505103\pi$
$239$	14.3623	−	20.5116i	0.929023	−	1.32678i	0.945055	−	0.326911i	$-0.106008\pi$
$240$		0			0
$241$	6.56077	−	0.573993i	0.422616	−	0.0369742i	0.126136	−	0.992013i	$-0.459743\pi$
$241$	6.56077	−	0.573993i	0.422616	−	0.0369742i	0.296481	+	0.955039i	$0.404187\pi$
$242$	−5.02041	−	3.51533i	−0.322724	−	0.225974i
$243$		0			0
$244$	−1.05509	+	0.491996i	−0.0675451	+	0.0314968i
$245$	9.61693	−	2.57685i	0.614403	−	0.164629i
$246$		0			0
$247$	−0.771037	−	0.918886i	−0.0490599	−	0.0584673i
$248$	−3.32280	+	1.91842i	−0.210998	+	0.121820i
$249$		0			0
$250$	−11.4190	+	2.01348i	−0.722202	+	0.127344i
$251$	−22.5136	−	6.03250i	−1.42105	−	0.380768i	−0.535191	−	0.844731i	$-0.679760\pi$
$251$	−22.5136	−	6.03250i	−1.42105	−	0.380768i	−0.885855	+	0.463963i	$0.846427\pi$
$252$		0			0
$253$	−27.0935	−	27.0935i	−1.70335	−	1.70335i
$254$	5.60956	−	12.0297i	0.351975	−	0.754812i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−21.8775	−	1.91403i	−1.36468	−	0.119394i	−0.618839	−	0.785518i	$-0.712397\pi$
$257$	−21.8775	−	1.91403i	−1.36468	−	0.119394i	−0.745841	+	0.666124i	$0.767952\pi$
$258$		0			0
$259$	−2.66214	+	2.19877i	−0.165418	+	0.136625i
$260$		−	3.09270i		−	0.191801i
$261$		0			0
$262$	5.04709	−	6.01489i	0.311810	−	0.371601i
$263$	3.73956	−	21.2081i	0.230591	−	1.30775i	−0.621112	−	0.783722i	$-0.713319\pi$
$263$	3.73956	−	21.2081i	0.230591	−	1.30775i	0.851703	−	0.524024i	$-0.175570\pi$
$264$		0			0
$265$	5.01958	−	5.01958i	0.308350	−	0.308350i
$266$	−0.112266	−	0.308448i	−0.00688347	−	0.0189122i
$267$		0			0
$268$	−0.521777	−	2.95914i	−0.0318726	−	0.180759i
$269$	−0.820827	−	0.473905i	−0.0500467	−	0.0288945i	0.474768	−	0.880111i	$-0.342532\pi$
$269$	−0.820827	−	0.473905i	−0.0500467	−	0.0288945i	−0.524815	+	0.851217i	$0.675865\pi$
$270$		0			0
$271$	−8.10200	+	6.79838i	−0.492161	+	0.412972i	−0.854800	−	0.518957i	$-0.826320\pi$
$271$	−8.10200	+	6.79838i	−0.492161	+	0.412972i	0.362639	+	0.931930i	$0.381876\pi$
$272$	−5.46987	+	3.83004i	−0.331659	+	0.232230i
$273$		0			0
$274$	6.26445	+	13.4341i	0.378449	+	0.811586i
$275$	3.93104	−	10.8004i	0.237050	−	0.651291i
$276$		0			0
$277$	2.70463	+	30.9141i	0.162505	+	1.85745i	0.441638	+	0.897193i	$0.354398\pi$
$277$	2.70463	+	30.9141i	0.162505	+	1.85745i	−0.279133	+	0.960253i	$0.590047\pi$
$278$	0.869723	+	9.94098i	0.0521625	+	0.596221i
$279$		0			0
$280$	0.289453	−	0.795265i	0.0172981	−	0.0475262i
$281$	8.11324	+	17.3989i	0.483995	+	1.03793i	0.985011	+	0.172493i	$0.0551821\pi$
$281$	8.11324	+	17.3989i	0.483995	+	1.03793i	−0.501016	+	0.865438i	$0.667040\pi$
$282$		0			0
$283$	4.08648	−	2.86138i	0.242916	−	0.170092i	−0.445778	−	0.895143i	$-0.647073\pi$
$283$	4.08648	−	2.86138i	0.242916	−	0.170092i	0.688694	+	0.725052i	$0.258184\pi$
$284$	−10.0695	+	8.44934i	−0.597517	+	0.501376i
$285$		0			0
$286$	7.43484	+	4.29251i	0.439631	+	0.253821i
$287$	−0.0946423	−	0.536743i	−0.00558656	−	0.0316829i
$288$		0			0
$289$	−9.43588	−	25.9249i	−0.555052	−	1.52499i
$290$	−8.37042	+	8.37042i	−0.491528	+	0.491528i
$291$		0			0
$292$	0.443937	−	2.51769i	0.0259795	−	0.147337i
$293$	−14.8241	+	17.6667i	−0.866035	+	1.03210i	0.133124	+	0.991099i	$0.457499\pi$
$293$	−14.8241	+	17.6667i	−0.866035	+	1.03210i	−0.999159	+	0.0410010i	$0.986945\pi$
$294$		0			0
$295$			2.08041i			0.121126i
$296$	−0.483032	−	6.06355i	−0.0280757	−	0.352437i
$297$		0			0
$298$	2.94963	+	0.258059i	0.170867	+	0.0149489i
$299$	14.7112	+	12.3442i	0.850771	+	0.713882i
$300$		0			0
$301$	2.10205	−	4.50785i	0.121160	−	0.259828i
$302$	1.48054	+	1.48054i	0.0851955	+	0.0851955i
$303$		0			0
$304$	0.558565	+	0.149667i	0.0320359	+	0.00858400i
$305$	−1.70932	+	0.301400i	−0.0978755	+	0.0172581i
$306$		0			0
$307$	−15.7332	+	9.08356i	−0.897940	+	0.518426i	−0.876531	−	0.481345i	$-0.840149\pi$
$307$	−15.7332	+	9.08356i	−0.897940	+	0.518426i	−0.0214090	+	0.999771i	$0.506815\pi$
$308$	1.51007	+	1.79963i	0.0860443	+	0.102544i
$309$		0			0
$310$	−5.52556	+	1.48057i	−0.313831	+	0.0840907i
$311$	−1.27088	+	0.592622i	−0.0720651	+	0.0336045i	−0.458317	−	0.888789i	$-0.651547\pi$
$311$	−1.27088	+	0.592622i	−0.0720651	+	0.0336045i	0.386252	+	0.922393i	$0.373770\pi$
$312$		0			0
$313$	−23.1580	−	16.2154i	−1.30897	−	0.916550i	−0.309559	−	0.950880i	$-0.600181\pi$
$313$	−23.1580	−	16.2154i	−1.30897	−	0.916550i	−0.999411	+	0.0343298i	$0.989070\pi$
$314$	−12.2951	+	1.07568i	−0.693852	+	0.0607042i
$315$		0			0
$316$	−0.102888	+	0.146939i	−0.00578790	+	0.00826598i
$317$	−4.49409	−	1.63572i	−0.252413	−	0.0918710i	0.212715	−	0.977114i	$-0.431770\pi$
$317$	−4.49409	−	1.63572i	−0.252413	−	0.0918710i	−0.465128	+	0.885243i	$0.653992\pi$
$318$		0			0
$319$	−8.50476	−	31.7402i	−0.476175	−	1.77711i
$320$	0.855167	+	1.22130i	0.0478053	+	0.0682730i
$321$		0			0
$322$	2.62756	+	4.55107i	0.146428	+	0.253621i
$323$	−1.93069	+	3.34405i	−0.107426	+	0.186068i
$324$		0			0
$325$	−1.49096	+	5.56434i	−0.0827036	+	0.308654i
$326$	−7.05046	+	2.56616i	−0.390489	+	0.142126i
$327$		0			0
$328$	0.870210	+	0.405786i	0.0480493	+	0.0224058i
$329$	−4.63713	−	0.817650i	−0.255653	−	0.0450785i
$330$		0			0
$331$	1.60444	−	18.3388i	0.0881878	−	1.00799i	−0.815204	−	0.579174i	$-0.803375\pi$
$331$	1.60444	−	18.3388i	0.0881878	−	1.00799i	0.903392	−	0.428817i	$-0.141069\pi$
$332$	−8.25310			−0.452948
$333$		0			0
$334$	8.29029			0.453625
$335$	0.390454	−	4.46291i	0.0213328	−	0.243835i
$336$		0			0
$337$	−10.8790	−	1.91826i	−0.592617	−	0.104494i	−0.130707	−	0.991421i	$-0.541725\pi$
$337$	−10.8790	−	1.91826i	−0.592617	−	0.104494i	−0.461910	+	0.886927i	$0.652836\pi$
$338$	7.88230	+	3.67558i	0.428741	+	0.199925i
$339$		0			0
$340$	−9.35530	+	3.40505i	−0.507362	+	0.184665i
$341$	4.10991	−	15.3384i	0.222564	−	0.830621i
$342$		0			0
$343$	3.88197	−	6.72378i	0.209607	−	0.363050i
$344$	4.38124	+	7.58854i	0.236221	+	0.409146i
$345$		0			0
$346$	−13.1531	−	18.7846i	−0.707117	−	1.00987i
$347$	−3.60973	−	13.4717i	−0.193780	−	0.723198i	−0.992579	−	0.121600i	$-0.961197\pi$
$347$	−3.60973	−	13.4717i	−0.193780	−	0.723198i	0.798799	−	0.601598i	$-0.205469\pi$
$348$		0			0
$349$	−21.4352	−	7.80179i	−1.14740	−	0.417620i	−0.302821	−	0.953048i	$-0.597928\pi$
$349$	−21.4352	−	7.80179i	−1.14740	−	0.417620i	−0.844581	+	0.535427i	$0.820151\pi$
$350$	−0.904170	+	1.29129i	−0.0483299	+	0.0690222i
$351$		0			0
$352$	−4.12295	+	0.360711i	−0.219754	+	0.0192260i
$353$	−0.357438	−	0.250281i	−0.0190245	−	0.0133211i	0.564026	−	0.825757i	$-0.309252\pi$
$353$	−0.357438	−	0.250281i	−0.0190245	−	0.0133211i	−0.583050	+	0.812436i	$0.698141\pi$
$354$		0			0
$355$	−17.7619	+	8.28253i	−0.942706	+	0.439591i
$356$	10.7669	−	2.88498i	0.570645	−	0.152904i
$357$		0			0
$358$	−2.89030	−	3.44452i	−0.152757	−	0.182049i
$359$	6.28925	−	3.63110i	0.331934	−	0.191642i	−0.324765	−	0.945795i	$-0.605285\pi$
$359$	6.28925	−	3.63110i	0.331934	−	0.191642i	0.656699	+	0.754152i	$0.271952\pi$
$360$		0			0
$361$	−18.3820	+	3.24125i	−0.967475	+	0.170592i
$362$	−13.8123	−	3.70099i	−0.725957	−	0.194520i
$363$		0			0
$364$	−0.832586	−	0.832586i	−0.0436394	−	0.0436394i
$365$	1.61087	−	3.45451i	0.0843166	−	0.180817i
$366$		0			0
$367$	13.9275	+	11.6866i	0.727011	+	0.610035i	0.929315	−	0.369288i	$-0.120398\pi$
$367$	13.9275	+	11.6866i	0.727011	+	0.610035i	−0.202304	+	0.979323i	$0.564843\pi$
$368$	−9.22276	−	0.806887i	−0.480770	−	0.0420619i
$369$		0			0
$370$	1.64419	−	8.91873i	0.0854775	−	0.463663i
$371$		−	2.70265i		−	0.140314i
$372$		0			0
$373$	8.84095	−	10.5362i	0.457767	−	0.545546i	−0.486951	−	0.873429i	$-0.661891\pi$
$373$	8.84095	−	10.5362i	0.457767	−	0.545546i	0.944718	+	0.327884i	$0.106335\pi$
$374$	4.79895	−	27.2162i	0.248148	−	1.40731i
$375$		0			0
$376$	5.86565	−	5.86565i	0.302498	−	0.302498i
$377$	5.63290	+	15.4763i	0.290109	+	0.797068i
$378$		0			0
$379$	−2.38561	−	13.5295i	−0.122541	−	0.694962i	−0.982738	−	0.185001i	$-0.940771\pi$
$379$	−2.38561	−	13.5295i	−0.122541	−	0.694962i	0.860198	−	0.509961i	$-0.170340\pi$
$380$	0.746655	+	0.431082i	0.0383026	+	0.0221140i
$381$		0			0
$382$	−17.2927	+	14.5103i	−0.884772	+	0.742412i
$383$	3.32095	−	2.32535i	0.169693	−	0.118820i	−0.485645	−	0.874156i	$-0.661415\pi$
$383$	3.32095	−	2.32535i	0.169693	−	0.118820i	0.655338	+	0.755336i	$0.272526\pi$
$384$		0			0
$385$	1.48026	+	3.17443i	0.0754410	+	0.161784i
$386$	−6.15950	+	16.9231i	−0.313510	+	0.861363i
$387$		0			0
$388$	−1.65235	−	18.8865i	−0.0838854	−	0.958815i
$389$	1.64859	+	18.8435i	0.0835868	+	0.955401i	0.915982	+	0.401219i	$0.131413\pi$
$389$	1.64859	+	18.8435i	0.0835868	+	0.955401i	−0.832395	+	0.554182i	$0.813031\pi$
$390$		0			0
$391$	21.1437	−	58.0918i	1.06928	−	2.93783i
$392$	2.82216	+	6.05214i	0.142540	+	0.305679i
$393$		0			0
$394$	6.66810	−	4.66905i	0.335934	−	0.235223i
$395$	−0.204874	+	0.171910i	−0.0103083	+	0.00864972i
$396$		0			0
$397$	27.4156	+	15.8284i	1.37595	+	0.794403i	0.991669	−	0.128814i	$-0.0411170\pi$
$397$	27.4156	+	15.8284i	1.37595	+	0.794403i	0.384278	+	0.923217i	$0.374450\pi$
$398$	4.77316	+	27.0700i	0.239257	+	1.35689i
$399$		0			0
$400$	−0.949825	−	2.60962i	−0.0474913	−	0.130481i
$401$	−13.4549	+	13.4549i	−0.671908	+	0.671908i	−0.958156	−	0.286248i	$-0.907592\pi$
$401$	−13.4549	+	13.4549i	−0.671908	+	0.671908i	0.286248	+	0.958156i	$0.407592\pi$
$402$		0			0
$403$	−1.38204	+	7.83794i	−0.0688444	+	0.390436i
$404$	−2.41133	+	2.87371i	−0.119968	+	0.142972i
$405$		0			0
$406$			4.50681i			0.223669i
$407$	19.1586	+	16.3314i	0.949655	+	0.809517i
$408$		0			0
$409$	−6.46698	−	0.565787i	−0.319772	−	0.0279764i	−0.0738599	−	0.997269i	$-0.523532\pi$
$409$	−6.46698	−	0.565787i	−0.319772	−	0.0279764i	−0.245912	+	0.969292i	$0.579087\pi$
$410$	1.09664	+	0.920186i	0.0541590	+	0.0454448i
$411$		0			0
$412$	−3.00440	+	6.44295i	−0.148016	+	0.317421i
$413$	0.560069	+	0.560069i	0.0275592	+	0.0275592i
$414$		0			0
$415$	−11.8856	−	3.18473i	−0.583441	−	0.156332i
$416$	2.04282	−	0.360203i	0.100157	−	0.0176604i
$417$		0			0
$418$	−2.07264	+	1.19664i	−0.101376	+	0.0585296i
$419$	5.75740	+	6.86141i	0.281268	+	0.335202i	0.888119	−	0.459614i	$-0.152012\pi$
$419$	5.75740	+	6.86141i	0.281268	+	0.335202i	−0.606851	+	0.794815i	$0.707568\pi$
$420$		0			0
$421$	−8.95933	+	2.40065i	−0.436651	+	0.117000i	−0.470447	−	0.882428i	$-0.655907\pi$
$421$	−8.95933	+	2.40065i	−0.436651	+	0.117000i	0.0337954	+	0.999429i	$0.489241\pi$
$422$	6.15089	−	2.86821i	0.299421	−	0.139622i
$423$		0			0
$424$	3.90020	+	2.73095i	0.189411	+	0.132627i
$425$	18.4735	−	1.61622i	0.896095	−	0.0783982i
$426$		0			0
$427$	−0.379028	+	0.541307i	−0.0183424	+	0.0261957i
$428$	7.31891	+	2.66387i	0.353773	+	0.128763i
$429$		0			0
$430$	3.38130	+	12.6192i	0.163061	+	0.608550i
$431$	−7.06898	−	10.0956i	−0.340501	−	0.486286i	0.611985	−	0.790870i	$-0.290371\pi$
$431$	−7.06898	−	10.0956i	−0.340501	−	0.486286i	−0.952485	+	0.304584i	$0.901483\pi$
$432$		0			0
$433$	19.4481	+	33.6851i	0.934617	+	1.61880i	0.775316	+	0.631573i	$0.217590\pi$
$433$	19.4481	+	33.6851i	0.934617	+	1.61880i	0.159300	+	0.987230i	$0.449076\pi$
$434$	−1.08895	+	1.88612i	−0.0522715	+	0.0905368i
$435$		0			0
$436$	0.313281	−	1.16918i	0.0150035	−	0.0559937i
$437$	−5.03075	+	1.83104i	−0.240653	+	0.0875906i
$438$		0			0
$439$	−30.3395	−	14.1475i	−1.44802	−	0.675225i	−0.469800	−	0.882773i	$-0.655674\pi$
$439$	−30.3395	−	14.1475i	−1.44802	−	0.675225i	−0.978225	+	0.207548i	$0.933452\pi$
$440$	−6.07679	−	1.07150i	−0.289700	−	0.0510819i
$441$		0			0
$442$	−1.20722	+	13.7986i	−0.0574215	+	0.656331i
$443$	−30.7055			−1.45886			−0.729431	−	0.684055i	$-0.760215\pi$
$443$	−30.7055			−1.45886			−0.729431	+	0.684055i	$0.760215\pi$
$444$		0			0
$445$	16.6191			0.787819
$446$	0.708230	−	8.09511i	0.0335357	−	0.383314i
$447$		0			0
$448$	0.559008	+	0.0985682i	0.0264106	+	0.00465691i
$449$	−22.0448	−	10.2797i	−1.04036	−	0.485128i	−0.174104	−	0.984727i	$-0.555703\pi$
$449$	−22.0448	−	10.2797i	−1.04036	−	0.485128i	−0.866257	+	0.499599i	$0.833481\pi$
$450$		0			0
$451$	−3.73420	+	1.35914i	−0.175837	+	0.0639993i
$452$	−0.891590	+	3.32746i	−0.0419369	+	0.156510i
$453$		0			0
$454$	−11.8582	+	20.5390i	−0.556534	+	0.963945i
$455$	−0.877756	−	1.52032i	−0.0411498	−	0.0712736i
$456$		0			0
$457$	10.4063	+	14.8617i	0.486785	+	0.695201i	0.985136	−	0.171774i	$-0.0549499\pi$
$457$	10.4063	+	14.8617i	0.486785	+	0.695201i	−0.498351	+	0.866975i	$0.666061\pi$
$458$	−1.59189	−	5.94101i	−0.0743840	−	0.277605i
$459$		0			0
$460$	−12.9707	−	4.72093i	−0.604760	−	0.220115i
$461$	4.55000	−	6.49808i	0.211915	−	0.302646i	−0.699096	−	0.715028i	$-0.746414\pi$
$461$	4.55000	−	6.49808i	0.211915	−	0.302646i	0.911011	+	0.412382i	$0.135303\pi$
$462$		0			0
$463$	13.6915	−	1.19785i	0.636300	−	0.0556690i	0.235558	−	0.971860i	$-0.424308\pi$
$463$	13.6915	−	1.19785i	0.636300	−	0.0556690i	0.400742	+	0.916191i	$0.368753\pi$
$464$	−6.50380	−	4.55401i	−0.301931	−	0.211415i
$465$		0			0
$466$	8.54676	−	3.98542i	0.395921	−	0.184621i
$467$	−19.7618	+	5.29515i	−0.914465	+	0.245030i	−0.685218	−	0.728338i	$-0.740293\pi$
$467$	−19.7618	+	5.29515i	−0.914465	+	0.245030i	−0.229247	+	0.973368i	$0.573626\pi$
$468$		0			0
$469$	−1.09635	−	1.30658i	−0.0506247	−	0.0603321i
$470$	10.7108	−	6.18387i	0.494051	−	0.285241i
$471$		0			0
$472$	−1.37417	+	0.242304i	−0.0632514	+	0.0111529i
$473$	−35.0295	−	9.38614i	−1.61066	−	0.431575i
$474$		0			0
$475$	−1.13555	−	1.13555i	−0.0521027	−	0.0521027i
$476$	−1.60187	+	3.43522i	−0.0734216	+	0.157453i
$477$		0			0
$478$	19.1817	+	16.0954i	0.877353	+	0.736186i
$479$	−13.1575	−	1.15114i	−0.601183	−	0.0525967i	−0.217498	−	0.976061i	$-0.569790\pi$
$479$	−13.1575	−	1.15114i	−0.601183	−	0.0525967i	−0.383685	+	0.923464i	$0.625345\pi$
$480$		0			0
$481$	−10.2792	−	7.31730i	−0.468692	−	0.333640i
$482$			6.58583i			0.299976i
$483$		0			0
$484$	3.93951	−	4.69493i	0.179069	−	0.213406i
$485$	4.90836	−	27.8367i	0.222877	−	1.26400i
$486$		0			0
$487$	−23.6767	+	23.6767i	−1.07290	+	1.07290i	−0.0757701	+	0.997125i	$0.524142\pi$
$487$	−23.6767	+	23.6767i	−1.07290	+	1.07290i	−0.997125	+	0.0757701i	$0.975858\pi$
$488$	−0.398166	−	1.09395i	−0.0180241	−	0.0495209i
$489$		0			0
$490$	1.72887	+	9.80492i	0.0781025	+	0.442941i
$491$	12.3141	+	7.10956i	0.555728	+	0.320850i	0.751429	−	0.659814i	$-0.229365\pi$
$491$	12.3141	+	7.10956i	0.555728	+	0.320850i	−0.195701	+	0.980664i	$0.562698\pi$
$492$		0			0
$493$	40.6134	−	34.0787i	1.82913	−	1.53483i
$494$	0.982590	−	0.688017i	0.0442088	−	0.0309553i
$495$		0			0
$496$	−1.62152	−	3.47735i	−0.0728082	−	0.156138i
$497$	−2.55196	+	7.01145i	−0.114471	+	0.314506i
$498$		0			0
$499$	0.978789	+	11.1876i	0.0438166	+	0.500826i	0.986116	+	0.166056i	$0.0531032\pi$
$499$	0.978789	+	11.1876i	0.0438166	+	0.500826i	−0.942300	+	0.334770i	$0.891341\pi$
$500$	−1.01059	−	11.5511i	−0.0451948	−	0.516579i
$501$		0			0
$502$	7.97173	−	21.9022i	0.355796	−	0.977541i
$503$	13.3777	+	28.6885i	0.596482	+	1.27916i	0.940372	+	0.340149i	$0.110477\pi$
$503$	13.3777	+	28.6885i	0.596482	+	1.27916i	−0.343890	+	0.939010i	$0.611745\pi$
$504$		0			0
$505$	−4.58156	+	3.20804i	−0.203877	+	0.142756i
$506$	29.3517	−	24.6290i	1.30484	−	1.09489i
$507$		0			0
$508$	11.4950	+	6.63667i	0.510010	+	0.294455i
$509$	4.78209	+	27.1206i	0.211962	+	1.20210i	0.886101	+	0.463493i	$0.153404\pi$
$509$	4.78209	+	27.1206i	0.211962	+	1.20210i	−0.674138	+	0.738605i	$0.735485\pi$
$510$		0			0
$511$	−0.496329	−	1.36365i	−0.0219563	−	0.0603244i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	3.81350	−	21.6274i	0.168206	−	0.953945i
$515$	−6.81296	+	8.11937i	−0.300215	+	0.357782i
$516$		0			0
$517$			34.3316i			1.50990i
$518$	−1.95838	−	2.84365i	−0.0860464	−	0.124943i
$519$		0			0
$520$	3.08093	+	0.269546i	0.135108	+	0.0118204i
$521$	28.3664	+	23.8022i	1.24275	+	1.04279i	0.997304	+	0.0733856i	$0.0233804\pi$
$521$	28.3664	+	23.8022i	1.24275	+	1.04279i	0.245451	+	0.969409i	$0.421064\pi$
$522$		0			0
$523$	−17.2775	+	37.0517i	−0.755491	+	1.62016i	0.0286623	+	0.999589i	$0.490875\pi$
$523$	−17.2775	+	37.0517i	−0.755491	+	1.62016i	−0.784154	+	0.620567i	$0.786903\pi$
$524$	5.55212	+	5.55212i	0.242545	+	0.242545i
$525$		0			0
$526$	20.8014	+	5.57373i	0.906986	+	0.243026i
$527$	25.2311	−	4.44893i	1.09909	−	0.193798i
$528$		0			0
$529$	54.3088	−	31.3552i	2.36125	−	1.36327i
$530$	4.56299	+	5.43796i	0.198204	+	0.236210i
$531$		0			0
$532$	0.317059	−	0.0849557i	0.0137463	−	0.00368330i
$533$	1.80510	−	0.841733i	0.0781877	−	0.0364595i
$534$		0			0
$535$	9.51229	+	6.66058i	0.411252	+	0.287962i
$536$	2.99336	−	0.261885i	0.129293	−	0.0113117i
$537$		0			0
$538$	0.543641	−	0.776400i	0.0234380	−	0.0334730i
$539$	−25.9706	−	9.45253i	−1.11863	−	0.407149i
$540$		0			0
$541$	8.77377	+	32.7441i	0.377214	+	1.40778i	0.850083	+	0.526648i	$0.176552\pi$
$541$	8.77377	+	32.7441i	0.377214	+	1.40778i	−0.472869	+	0.881132i	$0.656782\pi$
$542$	−6.06638	−	8.66369i	−0.260573	−	0.372137i
$543$		0			0
$544$	−3.33874	−	5.78286i	−0.143147	−	0.247938i
$545$	0.902336	−	1.56289i	0.0386518	−	0.0669469i
$546$		0			0
$547$	−3.82129	+	14.2613i	−0.163387	+	0.609768i	0.834854	+	0.550472i	$0.185552\pi$
$547$	−3.82129	+	14.2613i	−0.163387	+	0.609768i	−0.998240	+	0.0592958i	$0.981114\pi$
$548$	−13.9290	+	5.06974i	−0.595018	+	0.216569i
$549$		0			0
$550$	10.4167	+	4.85740i	0.444171	+	0.207120i
$551$	−4.52152	−	0.797266i	−0.192623	−	0.0339647i
$552$		0			0
$553$	−0.00887434	+	0.101434i	−0.000377375	+	0.00431342i
$554$	−31.0321			−1.31843
$555$		0			0
$556$	−9.97896			−0.423202
$557$	3.45643	−	39.5072i	0.146454	−	1.67397i	−0.467012	−	0.884251i	$-0.654670\pi$
$557$	3.45643	−	39.5072i	0.146454	−	1.67397i	0.613466	−	0.789721i	$-0.289775\pi$
$558$		0			0
$559$	17.9001	+	3.15628i	0.757095	+	0.133496i
$560$	0.767011	+	0.357663i	0.0324121	+	0.0151140i
$561$		0			0
$562$	−18.0398	+	6.56595i	−0.760963	+	0.276968i
$563$	1.05157	−	3.92451i	0.0443184	−	0.165399i	−0.940220	−	0.340568i	$-0.889381\pi$
$563$	1.05157	−	3.92451i	0.0443184	−	0.165399i	0.984538	+	0.175169i	$0.0560473\pi$
$564$		0			0
$565$	−2.56802	+	4.44794i	−0.108037	+	0.187126i
$566$	2.49433	+	4.32031i	0.104845	+	0.181596i
$567$		0			0
$568$	−7.53957	−	10.7676i	−0.316353	−	0.451799i
$569$	−6.67935	−	24.9277i	−0.280013	−	1.04502i	−0.952407	−	0.304829i	$-0.901401\pi$
$569$	−6.67935	−	24.9277i	−0.280013	−	1.04502i	0.672394	−	0.740193i	$-0.265266\pi$
$570$		0			0
$571$	38.1326	+	13.8791i	1.59580	+	0.580824i	0.978562	−	0.205952i	$-0.0660291\pi$
$571$	38.1326	+	13.8791i	1.59580	+	0.580824i	0.617239	+	0.786776i	$0.288251\pi$
$572$	−4.92416	+	7.03243i	−0.205890	+	0.294041i
$573$		0			0
$574$	0.542949	−	0.0475019i	0.0226623	−	0.00198269i
$575$	21.0607	+	14.7469i	0.878293	+	0.614987i
$576$		0			0
$577$	−15.9806	+	7.45185i	−0.665279	+	0.310225i	−0.725763	−	0.687944i	$-0.758513\pi$
$577$	−15.9806	+	7.45185i	−0.665279	+	0.310225i	0.0604842	+	0.998169i	$0.480736\pi$
$578$	26.6486	−	7.14048i	1.10844	−	0.297005i
$579$		0			0
$580$	−7.60904	−	9.06810i	−0.315948	−	0.376532i
$581$	−4.05709	+	2.34236i	−0.168316	+	0.0971775i
$582$		0			0
$583$	−19.4061	+	3.42181i	−0.803717	+	0.141717i
$584$	2.46942	+	0.661680i	0.102185	+	0.0273805i
$585$		0			0
$586$	−16.3075	−	16.3075i	−0.673656	−	0.673656i
$587$	−3.88092	+	8.32267i	−0.160183	+	0.343513i	−0.969975	−	0.243203i	$-0.921802\pi$
$587$	−3.88092	+	8.32267i	−0.160183	+	0.343513i	0.809793	+	0.586716i	$0.199580\pi$
$588$		0			0
$589$	−1.69964	−	1.42617i	−0.0700325	−	0.0587642i
$590$	−2.07250	−	0.181320i	−0.0853233	−	0.00746482i
$591$		0			0
$592$	6.08258	+	0.0472797i	0.249992	+	0.00194318i
$593$		−	20.2228i		−	0.830452i	−0.909718	−	0.415226i	$-0.863703\pi$
$593$		−	20.2228i		−	0.830452i	0.909718	−	0.415226i	$-0.136297\pi$
$594$		0			0
$595$	−3.63250	+	4.32905i	−0.148918	+	0.177474i
$596$	−0.514154	+	2.91591i	−0.0210606	+	0.119440i
$597$		0			0
$598$	−13.5794	+	13.5794i	−0.555301	+	0.555301i
$599$	1.13881	+	3.12886i	0.0465307	+	0.127842i	0.960781	−	0.277307i	$-0.0894419\pi$
$599$	1.13881	+	3.12886i	0.0465307	+	0.127842i	−0.914251	+	0.405149i	$0.867220\pi$
$600$		0			0
$601$	−2.30338	−	13.0631i	−0.0939569	−	0.532856i	−0.995062	−	0.0992553i	$-0.968354\pi$
$601$	−2.30338	−	13.0631i	−0.0939569	−	0.532856i	0.901105	−	0.433601i	$-0.142757\pi$
$602$	4.30749	+	2.48693i	0.175560	+	0.101360i
$603$		0			0
$604$	−1.60394	+	1.34587i	−0.0652635	+	0.0547626i
$605$	7.48512	−	5.24114i	0.304313	−	0.213083i
$606$		0			0
$607$	7.57926	+	16.2538i	0.307633	+	0.659720i	0.997964	−	0.0637727i	$-0.0203133\pi$
$607$	7.57926	+	16.2538i	0.307633	+	0.659720i	−0.690332	+	0.723493i	$0.742535\pi$
$608$	−0.197780	+	0.543395i	−0.00802103	+	0.0220376i
$609$		0			0
$610$	−0.151275	−	1.72909i	−0.00612497	−	0.0700087i
$611$	−1.49970	−	17.1417i	−0.0606714	−	0.693477i
$612$		0			0
$613$	−4.41513	+	12.1305i	−0.178326	+	0.489945i	−0.996362	−	0.0852209i	$-0.972840\pi$
$613$	−4.41513	+	12.1305i	−0.178326	+	0.489945i	0.818037	+	0.575166i	$0.195063\pi$
$614$	−7.67776	−	16.4650i	−0.309849	−	0.664473i
$615$		0			0
$616$	−1.92440	+	1.34748i	−0.0775361	+	0.0542914i
$617$	−5.32526	+	4.46842i	−0.214387	+	0.179892i	−0.743657	−	0.668562i	$-0.766910\pi$
$617$	−5.32526	+	4.46842i	−0.214387	+	0.179892i	0.529270	+	0.848453i	$0.322466\pi$
$618$		0			0
$619$	38.2628	+	22.0910i	1.53791	+	0.887914i	0.998961	+	0.0455774i	$0.0145128\pi$
$619$	38.2628	+	22.0910i	1.53791	+	0.887914i	0.538952	+	0.842337i	$0.318821\pi$
$620$	−0.993351	−	5.63358i	−0.0398940	−	0.226250i
$621$		0			0
$622$	−0.479602	−	1.31770i	−0.0192303	−	0.0528348i
$623$	4.47403	−	4.47403i	0.179248	−	0.179248i
$624$		0			0
$625$	0.590782	−	3.35049i	0.0236313	−	0.134020i
$626$	18.1721	−	21.6566i	0.726303	−	0.865574i
$627$		0			0
$628$		−	12.3421i		−	0.492502i
$629$	−10.8172	+	39.1506i	−0.431311	+	1.56104i
$630$		0			0
$631$	−36.4874	−	3.19223i	−1.45254	−	0.127081i	−0.666614	−	0.745403i	$-0.732257\pi$
$631$	−36.4874	−	3.19223i	−1.45254	−	0.127081i	−0.785925	+	0.618322i	$0.787813\pi$
$632$	−0.137413	−	0.115303i	−0.00546599	−	0.00458651i
$633$		0			0
$634$	2.02118	−	4.33443i	0.0802712	−	0.172142i
$635$	13.9934	+	13.9934i	0.555313	+	0.555313i
$636$		0			0
$637$	13.3799	+	3.58515i	0.530133	+	0.142049i
$638$	32.3607	−	5.70606i	1.28117	−	0.225905i
$639$		0			0
$640$	−1.29119	+	0.745469i	−0.0510388	+	0.0294673i
$641$	6.57479	+	7.83553i	0.259689	+	0.309485i	0.880097	−	0.474794i	$-0.157477\pi$
$641$	6.57479	+	7.83553i	0.259689	+	0.309485i	−0.620408	+	0.784279i	$0.713033\pi$
$642$		0			0
$643$	31.4471	−	8.42623i	1.24015	−	0.332298i	0.421629	−	0.906769i	$-0.361459\pi$
$643$	31.4471	−	8.42623i	1.24015	−	0.332298i	0.818525	+	0.574470i	$0.194792\pi$
$644$	−4.76276	+	2.22091i	−0.187679	+	0.0875162i
$645$		0			0
$646$	−3.16306	−	2.21480i	−0.124449	−	0.0871400i
$647$	41.9721	−	3.67209i	1.65009	−	0.144365i	0.776202	−	0.630484i	$-0.217144\pi$
$647$	41.9721	−	3.67209i	1.65009	−	0.144365i	0.873892	+	0.486119i	$0.161588\pi$
$648$		0			0
$649$	3.31241	−	4.73062i	0.130024	−	0.185693i
$650$	−5.41322	−	1.97025i	−0.212324	−	0.0772796i
$651$		0			0
$652$	−1.94190	−	7.24728i	−0.0760508	−	0.283826i
$653$	−15.3663	−	21.9453i	−0.601329	−	0.858786i	0.396926	−	0.917851i	$-0.370077\pi$
$653$	−15.3663	−	21.9453i	−0.601329	−	0.858786i	−0.998254	+	0.0590646i	$0.981188\pi$
$654$		0			0
$655$	5.85333	+	10.1383i	0.228709	+	0.396135i
$656$	−0.480086	+	0.831533i	−0.0187442	+	0.0324659i
$657$		0			0
$658$	1.21869	−	4.54822i	0.0475095	−	0.177308i
$659$	−19.9299	+	7.25388i	−0.776358	+	0.282571i	−0.699653	−	0.714483i	$-0.746662\pi$
$659$	−19.9299	+	7.25388i	−0.776358	+	0.282571i	−0.0767046	+	0.997054i	$0.524440\pi$
$660$		0			0
$661$	−27.0163	−	12.5979i	−1.05081	−	0.490001i	−0.181050	−	0.983474i	$-0.557949\pi$
$661$	−27.0163	−	12.5979i	−1.05081	−	0.490001i	−0.869761	+	0.493473i	$0.835727\pi$
$662$	18.1292	+	3.19666i	0.704610	+	0.124242i
$663$		0			0
$664$	0.719305	−	8.22170i	0.0279145	−	0.319064i
$665$	0.489391			0.0189778
$666$		0			0
$667$	73.5054			2.84614
$668$	−0.722547	+	8.25874i	−0.0279562	+	0.319540i
$669$		0			0
$670$	4.41190	+	0.777937i	0.170447	+	0.0300543i
$671$	4.36669	+	2.03622i	0.168574	+	0.0786074i
$672$		0			0
$673$	−32.2689	+	11.7449i	−1.24387	+	0.452733i	−0.878327	−	0.478060i	$-0.841340\pi$
$673$	−32.2689	+	11.7449i	−1.24387	+	0.452733i	−0.365547	+	0.930793i	$0.619118\pi$
$674$	2.85913	−	10.6704i	0.110129	−	0.411009i
$675$		0			0
$676$	−4.34858	+	7.53196i	−0.167253	+	0.289691i
$677$	−0.605524	−	1.04880i	−0.0232722	−	0.0403086i	0.854155	−	0.520019i	$-0.174075\pi$
$677$	−0.605524	−	1.04880i	−0.0232722	−	0.0403086i	−0.877427	+	0.479710i	$0.840742\pi$
$678$		0			0
$679$	−6.17254	−	8.81530i	−0.236880	−	0.338300i
$680$	−2.57673	−	9.61647i	−0.0988129	−	0.368775i
$681$		0			0
$682$	14.9218	+	5.43110i	0.571387	+	0.207968i
$683$	−8.26908	+	11.8095i	−0.316407	+	0.451877i	−0.945580	−	0.325389i	$-0.894505\pi$
$683$	−8.26908	+	11.8095i	−0.316407	+	0.451877i	0.629173	+	0.777265i	$0.283394\pi$
$684$		0			0
$685$	−22.0160	+	1.92615i	−0.841188	+	0.0735944i
$686$	6.35985	+	4.45322i	0.242820	+	0.170025i
$687$		0			0
$688$	−7.94151	+	3.70319i	−0.302767	+	0.141183i
$689$	9.53990	−	2.55621i	0.363441	−	0.0973838i
$690$		0			0
$691$	8.11127	+	9.66663i	0.308567	+	0.367736i	0.897934	−	0.440129i	$-0.145067\pi$
$691$	8.11127	+	9.66663i	0.308567	+	0.367736i	−0.589367	+	0.807865i	$0.700623\pi$
$692$	19.8595	−	11.4659i	0.754945	−	0.435868i
$693$		0			0
$694$	13.7350	−	2.42186i	0.521375	−	0.0919325i
$695$	−14.3711	−	3.85071i	−0.545125	−	0.146066i
$696$		0			0
$697$	−4.53363	−	4.53363i	−0.171723	−	0.171723i
$698$	9.64030	−	20.6737i	0.364891	−	0.782511i
$699$		0			0
$700$	−1.20757	−	1.01327i	−0.0456419	−	0.0382981i
$701$	5.87122	+	0.513665i	0.221753	+	0.0194009i	0.197491	−	0.980305i	$-0.436721\pi$
$701$	5.87122	+	0.513665i	0.221753	+	0.0194009i	0.0242622	+	0.999706i	$0.492276\pi$
$702$		0			0
$703$	3.19937	−	1.46172i	0.120667	−	0.0551300i
$704$		−	4.13869i		−	0.155983i
$705$		0			0
$706$	0.280481	−	0.334264i	0.0105560	−	0.0125802i
$707$	−0.369765	+	2.09704i	−0.0139064	+	0.0788673i
$708$		0			0
$709$	−4.92670	+	4.92670i	−0.185026	+	0.185026i	−0.793542	−	0.608516i	$-0.791765\pi$
$709$	−4.92670	+	4.92670i	−0.185026	+	0.185026i	0.608516	+	0.793542i	$0.291765\pi$
$710$	−6.70296	−	18.4162i	−0.251558	−	0.691149i
$711$		0			0
$712$	1.93561	+	10.9774i	0.0725400	+	0.411395i
$713$	30.7624	+	17.7607i	1.15206	+	0.665143i
$714$		0			0
$715$	−9.80516	+	8.22750i	−0.366692	+	0.307691i
$716$	3.68332	−	2.57909i	0.137652	−	0.0963851i
$717$		0			0
$718$	3.06914	+	6.58179i	0.114539	+	0.245630i
$719$	2.19272	−	6.02445i	0.0817746	−	0.224674i	−0.892066	−	0.451904i	$-0.850745\pi$
$719$	2.19272	−	6.02445i	0.0817746	−	0.224674i	0.973841	+	0.227230i	$0.0729671\pi$
$720$		0			0
$721$	0.351699	+	4.01994i	0.0130980	+	0.149710i
$722$	−1.62681	−	18.5946i	−0.0605438	−	0.692018i
$723$		0			0
$724$	4.89072	−	13.4371i	0.181762	−	0.499388i
$725$	9.31844	+	19.9835i	0.346078	+	0.742167i
$726$		0			0
$727$	13.5564	−	9.49230i	0.502779	−	0.352050i	−0.294509	−	0.955649i	$-0.595156\pi$
$727$	13.5564	−	9.49230i	0.502779	−	0.352050i	0.797288	+	0.603599i	$0.206267\pi$
$728$	0.901982	−	0.756853i	0.0334297	−	0.0280508i
$729$		0			0
$730$	3.30097	+	1.90582i	0.122174	+	0.0705374i
$731$	−10.1604	−	57.6224i	−0.375795	−	2.13124i
$732$		0			0
$733$	−12.1194	−	33.2976i	−0.447638	−	1.22988i	−0.934363	−	0.356321i	$-0.884031\pi$
$733$	−12.1194	−	33.2976i	−0.447638	−	1.22988i	0.486725	−	0.873555i	$-0.338191\pi$
$734$	−12.8560	+	12.8560i	−0.474523	+	0.474523i
$735$		0			0
$736$	1.60763	−	9.11734i	0.0592581	−	0.336070i
$737$	−7.99366	+	9.52647i	−0.294450	+	0.350912i
$738$		0			0
$739$			0.499207i			0.0183636i	0.999958	+	0.00918181i	$0.00292270\pi$
$739$			0.499207i			0.0183636i	−0.999958	+	0.00918181i	$0.997077\pi$
$740$	8.74149	+	2.41525i	0.321344	+	0.0887865i
$741$		0			0
$742$	2.69236	+	0.235551i	0.0988397	+	0.00864735i
$743$	−22.8903	−	19.2073i	−0.839765	−	0.704646i	0.117746	−	0.993044i	$-0.462433\pi$
$743$	−22.8903	−	19.2073i	−0.839765	−	0.704646i	−0.957511	+	0.288397i	$0.906878\pi$
$744$		0			0
$745$	−1.86565	+	4.00090i	−0.0683522	+	0.146582i
$746$	9.72561	+	9.72561i	0.356080	+	0.356080i
$747$		0			0
$748$	26.6944	+	7.15273i	0.976042	+	0.261530i
$749$	4.35390	−	0.767711i	0.159088	−	0.0280515i
$750$		0			0
$751$	−14.7086	+	8.49201i	−0.536724	+	0.309878i	−0.743750	−	0.668458i	$-0.766955\pi$
$751$	−14.7086	+	8.49201i	−0.536724	+	0.309878i	0.207026	+	0.978335i	$0.433621\pi$
$752$	5.33210	+	6.35455i	0.194442	+	0.231727i
$753$		0			0
$754$	−15.9083	+	4.26262i	−0.579347	+	0.155235i
$755$	−2.82924	+	1.31930i	−0.102967	+	0.0480142i
$756$		0			0
$757$	0.540116	+	0.378193i	0.0196309	+	0.0137457i	0.583351	−	0.812220i	$-0.301741\pi$
$757$	0.540116	+	0.378193i	0.0196309	+	0.0137457i	−0.563720	+	0.825966i	$0.690630\pi$
$758$	13.6859	−	1.19736i	0.497094	−	0.0434901i
$759$		0			0
$760$	−0.494517	+	0.706243i	−0.0179380	+	0.0256181i
$761$	4.75422	+	1.73040i	0.172340	+	0.0627268i	0.426749	−	0.904370i	$-0.359659\pi$
$761$	4.75422	+	1.73040i	0.172340	+	0.0627268i	−0.254409	+	0.967097i	$0.581881\pi$
$762$		0			0
$763$	−0.177828	−	0.663665i	−0.00643782	−	0.0240263i
$764$	−12.9479	−	18.4916i	−0.468440	−	0.669001i
$765$		0			0
$766$	2.02707	+	3.51098i	0.0732409	+	0.126857i
$767$	−1.44723	+	2.50668i	−0.0522564	+	0.0905108i
$768$		0			0
$769$	12.0255	−	44.8798i	0.433651	−	1.61841i	−0.310624	−	0.950533i	$-0.600538\pi$
$769$	12.0255	−	44.8798i	0.433651	−	1.61841i	0.744275	−	0.667873i	$-0.232795\pi$
$770$	−3.29136	+	1.19796i	−0.118612	+	0.0431714i
$771$		0			0
$772$	−16.3219	−	7.61101i	−0.587437	−	0.273926i
$773$	−32.0478	−	5.65089i	−1.15268	−	0.203248i	−0.435534	−	0.900172i	$-0.643440\pi$
$773$	−32.0478	−	5.65089i	−1.15268	−	0.203248i	−0.717145	+	0.696924i	$0.754552\pi$
$774$		0			0
$775$	−0.928670	+	10.6147i	−0.0333588	+	0.381293i
$776$	18.9586			0.680574
$777$		0			0
$778$	−18.9154			−0.678151
$779$	−0.0483921	+	0.553124i	−0.00173383	+	0.0198177i
$780$		0			0
$781$	53.5760	+	9.44689i	1.91710	+	0.338036i
$782$	56.0279	+	26.1263i	2.00356	+	0.934273i
$783$		0			0
$784$	−6.27507	+	2.28394i	−0.224110	+	0.0815693i

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)

\(f(q)\)	\(=\)	\(q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-1.35125 - 0.630098i) q^{5} +(-0.533399 + 0.194141i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-1.35125 - 0.630098i) q^{5} +(-0.533399 + 0.194141i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.745469 - 1.29119i) q^{10} +(2.06935 + 3.58421i) q^{11} +(-1.18979 - 1.69919i) q^{13} +(-0.146914 - 0.548290i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.83004 + 5.46987i) q^{17} +(0.576069 - 0.0503995i) q^{19} +(1.22130 + 0.855167i) q^{20} +(-3.75093 + 1.74909i) q^{22} +(-8.94253 + 2.39614i) q^{23} +(-1.78509 - 2.12738i) q^{25} +(1.79642 - 1.03716i) q^{26} +(0.559008 - 0.0985682i) q^{28} +(-7.66914 - 2.05494i) q^{29} +(-2.71305 - 2.71305i) q^{31} +(-0.422618 + 0.906308i) q^{32} +(-5.11524 - 4.29220i) q^{34} +(0.843083 + 0.0737602i) q^{35} +(5.73193 - 2.03594i) q^{37} +0.578269i q^{38} +(-0.958357 + 1.14212i) q^{40} +(-0.166732 + 0.945584i) q^{41} +(-6.19601 + 6.19601i) q^{43} +(-1.41552 - 3.88910i) q^{44} +(-1.60763 - 9.11734i) q^{46} +(7.18392 + 4.14764i) q^{47} +(-5.11549 + 4.29240i) q^{49} +(2.27487 - 1.59288i) q^{50} +(0.876649 + 1.87998i) q^{52} +(-1.62845 + 4.47413i) q^{53} +(-0.537798 - 6.14706i) q^{55} +(0.0494723 + 0.565471i) q^{56} +(2.71553 - 7.46085i) q^{58} +(-0.589710 - 1.26464i) q^{59} +(0.953625 - 0.667735i) q^{61} +(2.93919 - 2.46627i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.537041 + 3.04571i) q^{65} +(1.02770 + 2.82358i) q^{67} +(4.72169 - 4.72169i) q^{68} +(-0.146959 + 0.833446i) q^{70} +(8.44934 - 10.0695i) q^{71} +2.55653i q^{73} +(1.52862 + 5.88756i) q^{74} +(-0.576069 - 0.0503995i) q^{76} +(-1.79963 - 1.51007i) q^{77} +(0.0758092 - 0.162573i) q^{79} +(-1.05425 - 1.05425i) q^{80} +(-0.927454 - 0.248511i) q^{82} +(8.12772 - 1.43314i) q^{83} +(8.62189 - 4.97785i) q^{85} +(-5.63242 - 6.71245i) q^{86} +(3.99767 - 1.07117i) q^{88} +(-10.1024 + 4.71081i) q^{89} +(0.964514 + 0.675360i) q^{91} +(9.22276 - 0.806887i) q^{92} +(-4.75798 + 6.79509i) q^{94} +(-0.810169 - 0.294877i) q^{95} +(4.90685 + 18.3126i) q^{97} +(-3.83023 - 5.47013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more