LMFDB - Embedded newform 672.2.bb.a.271.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.13
Character	$\chi$	$=$	672.271
Dual form			672.2.bb.a.367.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{3} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.79412 - 3.10751i) q^{11} +4.57992 q^{13} -0.257415i q^{15} +(6.92813 - 3.99996i) q^{17} +(-0.201988 - 0.116618i) q^{19} +(0.745237 + 2.53863i) q^{21} +(5.76102 + 3.32613i) q^{23} +(2.46687 + 4.27274i) q^{25} -1.00000i q^{27} +2.80806i q^{29} +(-1.03380 - 1.79060i) q^{31} +(-3.10751 - 1.79412i) q^{33} +(0.492874 + 0.470013i) q^{35} +(-6.46587 - 3.73307i) q^{37} +(3.96632 - 2.28996i) q^{39} -4.55693i q^{41} +5.42738 q^{43} +(-0.128707 - 0.222928i) q^{45} +(-1.42355 + 2.46565i) q^{47} +(-6.22145 - 3.20835i) q^{49} +(3.99996 - 6.92813i) q^{51} +(1.93137 - 1.11508i) q^{53} -0.923668 q^{55} -0.233235 q^{57} +(-2.14701 + 1.23958i) q^{59} +(-4.44251 + 7.69466i) q^{61} +(1.91471 + 1.82590i) q^{63} +(0.589469 - 1.02099i) q^{65} +(0.867859 + 1.50318i) q^{67} +6.65225 q^{69} -8.97302i q^{71} +(-6.57828 + 3.79797i) q^{73} +(4.27274 + 2.46687i) q^{75} +(9.10921 - 2.67409i) q^{77} +(-7.51791 - 4.34047i) q^{79} +(-0.500000 - 0.866025i) q^{81} +3.79017i q^{83} -2.05930i q^{85} +(1.40403 + 2.43185i) q^{87} +(-2.25065 - 1.29941i) q^{89} +(-2.85749 + 11.7756i) q^{91} +(-1.79060 - 1.03380i) q^{93} +(-0.0519946 + 0.0300191i) q^{95} +14.6024i q^{97} -3.58824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	0.128707	−	0.222928i	0.0575597	−	0.0996963i	−0.835810	−	0.549019i	$-0.815001\pi$
$5$	0.128707	−	0.222928i	0.0575597	−	0.0996963i	0.893369	+	0.449323i	$0.148335\pi$
$6$		0			0
$7$	−0.623918	+	2.57113i	−0.235819	+	0.971797i
$7$	−0.623918	+	2.57113i	−0.235819	+	0.971797i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.79412	−	3.10751i	−0.540948	−	0.936950i	−0.998850	−	0.0479470i	$-0.984732\pi$
$11$	−1.79412	−	3.10751i	−0.540948	−	0.936950i	0.457902	−	0.889003i	$-0.348601\pi$
$12$		0			0
$13$	4.57992			1.27024			0.635120	−	0.772413i	$-0.280951\pi$
$13$	4.57992			1.27024			0.635120	+	0.772413i	$0.280951\pi$
$14$		0			0
$15$		−	0.257415i		−	0.0664642i
$16$		0			0
$17$	6.92813	−	3.99996i	1.68032	−	0.970132i	0.718871	−	0.695143i	$-0.244659\pi$
$17$	6.92813	−	3.99996i	1.68032	−	0.970132i	0.961447	−	0.274989i	$-0.0886743\pi$
$18$		0			0
$19$	−0.201988	−	0.116618i	−0.0463391	−	0.0267539i	0.476651	−	0.879092i	$-0.341850\pi$
$19$	−0.201988	−	0.116618i	−0.0463391	−	0.0267539i	−0.522991	+	0.852338i	$0.675184\pi$
$20$		0			0
$21$	0.745237	+	2.53863i	0.162624	+	0.553974i
$22$		0			0
$23$	5.76102	+	3.32613i	1.20126	+	0.693545i	0.960834	−	0.277124i	$-0.0893811\pi$
$23$	5.76102	+	3.32613i	1.20126	+	0.693545i	0.240421	+	0.970669i	$0.422714\pi$
$24$		0			0
$25$	2.46687	+	4.27274i	0.493374	+	0.854548i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			2.80806i			0.521444i	0.965414	+	0.260722i	$0.0839605\pi$
$29$			2.80806i			0.521444i	−0.965414	+	0.260722i	$0.916039\pi$
$30$		0			0
$31$	−1.03380	−	1.79060i	−0.185676	−	0.321600i	0.758128	−	0.652106i	$-0.226114\pi$
$31$	−1.03380	−	1.79060i	−0.185676	−	0.321600i	−0.943804	+	0.330505i	$0.892781\pi$
$32$		0			0
$33$	−3.10751	−	1.79412i	−0.540948	−	0.312317i
$34$		0			0
$35$	0.492874	+	0.470013i	0.0833109	+	0.0794466i
$36$		0			0
$37$	−6.46587	−	3.73307i	−1.06298	−	0.613713i	−0.136726	−	0.990609i	$-0.543658\pi$
$37$	−6.46587	−	3.73307i	−1.06298	−	0.613713i	−0.926256	+	0.376896i	$0.876991\pi$
$38$		0			0
$39$	3.96632	−	2.28996i	0.635120	−	0.366687i
$40$		0			0
$41$		−	4.55693i		−	0.711673i	−0.934548	−	0.355837i	$-0.884196\pi$
$41$		−	4.55693i		−	0.711673i	0.934548	−	0.355837i	$-0.115804\pi$
$42$		0			0
$43$	5.42738			0.827667			0.413834	−	0.910353i	$-0.364190\pi$
$43$	5.42738			0.827667			0.413834	+	0.910353i	$0.364190\pi$
$44$		0			0
$45$	−0.128707	−	0.222928i	−0.0191866	−	0.0332321i
$46$		0			0
$47$	−1.42355	+	2.46565i	−0.207646	+	0.359653i	−0.950972	−	0.309276i	$-0.899913\pi$
$47$	−1.42355	+	2.46565i	−0.207646	+	0.359653i	0.743327	+	0.668928i	$0.233247\pi$
$48$		0			0
$49$	−6.22145	−	3.20835i	−0.888779	−	0.458336i
$50$		0			0
$51$	3.99996	−	6.92813i	0.560106	−	0.970132i
$52$		0			0
$53$	1.93137	−	1.11508i	0.265295	−	0.153168i	−0.361453	−	0.932390i	$-0.617719\pi$
$53$	1.93137	−	1.11508i	0.265295	−	0.153168i	0.626747	+	0.779222i	$0.284386\pi$
$54$		0			0
$55$	−0.923668			−0.124547
$56$		0			0
$57$	−0.233235			−0.0308928
$58$		0			0
$59$	−2.14701	+	1.23958i	−0.279517	+	0.161379i	−0.633205	−	0.773984i	$-0.718261\pi$
$59$	−2.14701	+	1.23958i	−0.279517	+	0.161379i	0.353688	+	0.935364i	$0.384928\pi$
$60$		0			0
$61$	−4.44251	+	7.69466i	−0.568806	+	0.985200i	0.427879	+	0.903836i	$0.359261\pi$
$61$	−4.44251	+	7.69466i	−0.568806	+	0.985200i	−0.996684	+	0.0813643i	$0.974072\pi$
$62$		0			0
$63$	1.91471	+	1.82590i	0.241230	+	0.230041i
$64$		0			0
$65$	0.589469	−	1.02099i	0.0731147	−	0.126638i
$66$		0			0
$67$	0.867859	+	1.50318i	0.106026	+	0.183642i	0.914157	−	0.405361i	$-0.132854\pi$
$67$	0.867859	+	1.50318i	0.106026	+	0.183642i	−0.808131	+	0.589003i	$0.799521\pi$
$68$		0			0
$69$	6.65225			0.800837
$70$		0			0
$71$		−	8.97302i		−	1.06490i	−0.846461	−	0.532451i	$-0.821271\pi$
$71$		−	8.97302i		−	1.06490i	0.846461	−	0.532451i	$-0.178729\pi$
$72$		0			0
$73$	−6.57828	+	3.79797i	−0.769929	+	0.444519i	−0.832849	−	0.553500i	$-0.813292\pi$
$73$	−6.57828	+	3.79797i	−0.769929	+	0.444519i	0.0629201	+	0.998019i	$0.479959\pi$
$74$		0			0
$75$	4.27274	+	2.46687i	0.493374	+	0.284849i
$76$		0			0
$77$	9.10921	−	2.67409i	1.03809	−	0.304741i
$78$		0			0
$79$	−7.51791	−	4.34047i	−0.845831	−	0.488341i	0.0134112	−	0.999910i	$-0.495731\pi$
$79$	−7.51791	−	4.34047i	−0.845831	−	0.488341i	−0.859242	+	0.511569i	$0.829064\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			3.79017i			0.416025i	0.978126	+	0.208012i	$0.0666994\pi$
$83$			3.79017i			0.416025i	−0.978126	+	0.208012i	$0.933301\pi$
$84$		0			0
$85$		−	2.05930i		−	0.223362i
$86$		0			0
$87$	1.40403	+	2.43185i	0.150528	+	0.260722i
$88$		0			0
$89$	−2.25065	−	1.29941i	−0.238569	−	0.137738i	0.375950	−	0.926640i	$-0.377316\pi$
$89$	−2.25065	−	1.29941i	−0.238569	−	0.137738i	−0.614519	+	0.788902i	$0.710650\pi$
$90$		0			0
$91$	−2.85749	+	11.7756i	−0.299547	+	1.23442i
$92$		0			0
$93$	−1.79060	−	1.03380i	−0.185676	−	0.107200i
$94$		0			0
$95$	−0.0519946	+	0.0300191i	−0.00533454	+	0.00307990i
$96$		0			0
$97$			14.6024i			1.48265i	0.671146	+	0.741325i	$0.265802\pi$
$97$			14.6024i			1.48265i	−0.671146	+	0.741325i	$0.734198\pi$
$98$		0			0
$99$	−3.58824			−0.360632
$100$		0			0
$101$	−0.709937	−	1.22965i	−0.0706414	−	0.122354i	0.828541	−	0.559928i	$-0.189171\pi$
$101$	−0.709937	−	1.22965i	−0.0706414	−	0.122354i	−0.899183	+	0.437574i	$0.855838\pi$
$102$		0			0
$103$	−4.42816	+	7.66981i	−0.436320	+	0.755728i	−0.997402	−	0.0720316i	$-0.977052\pi$
$103$	−4.42816	+	7.66981i	−0.436320	+	0.755728i	0.561082	+	0.827760i	$0.310385\pi$
$104$		0			0
$105$	0.661848	+	0.160606i	0.0645897	+	0.0156735i
$106$		0			0
$107$	6.00175	−	10.3953i	0.580211	−	1.00496i	−0.415243	−	0.909711i	$-0.636303\pi$
$107$	6.00175	−	10.3953i	0.580211	−	1.00496i	0.995454	−	0.0952445i	$-0.0303633\pi$
$108$		0			0
$109$	−10.8275	+	6.25126i	−1.03709	+	0.598762i	−0.919007	−	0.394242i	$-0.871007\pi$
$109$	−10.8275	+	6.25126i	−1.03709	+	0.598762i	−0.118080	+	0.993004i	$0.537674\pi$
$110$		0			0
$111$	−7.46614			−0.708655
$112$		0			0
$113$	0.143571			0.0135061			0.00675303	−	0.999977i	$-0.497850\pi$
$113$	0.143571			0.0135061			0.00675303	+	0.999977i	$0.497850\pi$
$114$		0			0
$115$	1.48297	−	0.856194i	0.138288	−	0.0798405i
$116$		0			0
$117$	2.28996	−	3.96632i	0.211707	−	0.366687i
$118$		0			0
$119$	5.96184	+	20.3088i	0.546521	+	1.86170i
$120$		0			0
$121$	−0.937751	+	1.62423i	−0.0852501	+	0.147657i
$122$		0			0
$123$	−2.27847	−	3.94642i	−0.205442	−	0.355837i
$124$		0			0
$125$	2.55709			0.228713
$126$		0			0
$127$		−	18.5252i		−	1.64385i	−0.569597	−	0.821924i	$-0.692901\pi$
$127$		−	18.5252i		−	1.64385i	0.569597	−	0.821924i	$-0.307099\pi$
$128$		0			0
$129$	4.70025	−	2.71369i	0.413834	−	0.238927i
$130$		0			0
$131$	−11.3578	−	6.55743i	−0.992336	−	0.572925i	−0.0863640	−	0.996264i	$-0.527525\pi$
$131$	−11.3578	−	6.55743i	−0.992336	−	0.572925i	−0.905972	+	0.423338i	$0.860858\pi$
$132$		0			0
$133$	0.425863	−	0.446577i	0.0369270	−	0.0387232i
$134$		0			0
$135$	−0.222928	−	0.128707i	−0.0191866	−	0.0110774i
$136$		0			0
$137$	1.26333	+	2.18816i	0.107934	+	0.186947i	0.914933	−	0.403606i	$-0.132243\pi$
$137$	1.26333	+	2.18816i	0.107934	+	0.186947i	−0.806999	+	0.590552i	$0.798910\pi$
$138$		0			0
$139$			16.8020i			1.42512i	0.701609	+	0.712562i	$0.252465\pi$
$139$			16.8020i			1.42512i	−0.701609	+	0.712562i	$0.747535\pi$
$140$		0			0
$141$			2.84709i			0.239768i
$142$		0			0
$143$	−8.21693	−	14.2321i	−0.687134	−	1.19015i
$144$		0			0
$145$	0.625995	+	0.361418i	0.0519860	+	0.0300141i
$146$		0			0
$147$	−6.99211	+	0.332209i	−0.576700	+	0.0274002i
$148$		0			0
$149$	−20.1564	−	11.6373i	−1.65128	−	0.953366i	−0.976547	−	0.215303i	$-0.930926\pi$
$149$	−20.1564	−	11.6373i	−1.65128	−	0.953366i	−0.674731	−	0.738064i	$-0.735740\pi$
$150$		0			0
$151$	10.6125	−	6.12714i	0.863634	−	0.498619i	−0.00159368	−	0.999999i	$-0.500507\pi$
$151$	10.6125	−	6.12714i	0.863634	−	0.498619i	0.865227	+	0.501380i	$0.167174\pi$
$152$		0			0
$153$		−	7.99992i		−	0.646755i
$154$		0			0
$155$	−0.532231			−0.0427498
$156$		0			0
$157$	−10.3040	−	17.8471i	−0.822352	−	1.42436i	−0.903926	−	0.427688i	$-0.859328\pi$
$157$	−10.3040	−	17.8471i	−0.822352	−	1.42436i	0.0815741	−	0.996667i	$-0.474005\pi$
$158$		0			0
$159$	1.11508	−	1.93137i	0.0884316	−	0.153168i
$160$		0			0
$161$	−12.1463	+	12.7371i	−0.957264	+	1.00383i
$162$		0			0
$163$	−7.21136	+	12.4904i	−0.564837	+	0.978326i	0.432228	+	0.901764i	$0.357728\pi$
$163$	−7.21136	+	12.4904i	−0.564837	+	0.978326i	−0.997065	+	0.0765619i	$0.975606\pi$
$164$		0			0
$165$	−0.799920	+	0.461834i	−0.0622737	+	0.0359537i
$166$		0			0
$167$	7.63662			0.590939			0.295470	−	0.955352i	$-0.404524\pi$
$167$	7.63662			0.590939			0.295470	+	0.955352i	$0.404524\pi$
$168$		0			0
$169$	7.97564			0.613510
$170$		0			0
$171$	−0.201988	+	0.116618i	−0.0154464	+	0.00891797i
$172$		0			0
$173$	−7.89966	+	13.6826i	−0.600600	+	1.04027i	0.392130	+	0.919910i	$0.371738\pi$
$173$	−7.89966	+	13.6826i	−0.600600	+	1.04027i	−0.992730	+	0.120360i	$0.961595\pi$
$174$		0			0
$175$	−12.5249	+	3.67681i	−0.946794	+	0.277940i
$176$		0			0
$177$	−1.23958	+	2.14701i	−0.0931723	+	0.161379i
$178$		0			0
$179$	11.4726	+	19.8711i	0.857500	+	1.48523i	0.874306	+	0.485374i	$0.161317\pi$
$179$	11.4726	+	19.8711i	0.857500	+	1.48523i	−0.0168065	+	0.999859i	$0.505350\pi$
$180$		0			0
$181$	15.1773			1.12812			0.564060	−	0.825734i	$-0.309239\pi$
$181$	15.1773			1.12812			0.564060	+	0.825734i	$0.309239\pi$
$182$		0			0
$183$			8.88503i			0.656800i
$184$		0			0
$185$	−1.66441	+	0.960948i	−0.122370	+	0.0706503i
$186$		0			0
$187$	−24.8598	−	14.3528i	−1.81793	−	1.04958i
$188$		0			0
$189$	2.57113	+	0.623918i	0.187022	+	0.0453834i
$190$		0			0
$191$	−18.5980	−	10.7376i	−1.34571	−	0.776944i	−0.358069	−	0.933695i	$-0.616565\pi$
$191$	−18.5980	−	10.7376i	−1.34571	−	0.776944i	−0.987638	+	0.156751i	$0.949898\pi$
$192$		0			0
$193$	3.58036	+	6.20137i	0.257720	+	0.446384i	0.965631	−	0.259918i	$-0.0836954\pi$
$193$	3.58036	+	6.20137i	0.257720	+	0.446384i	−0.707911	+	0.706302i	$0.750362\pi$
$194$		0			0
$195$		−	1.17894i		−	0.0844255i
$196$		0			0
$197$			9.29594i			0.662309i	0.943577	+	0.331154i	$0.107438\pi$
$197$			9.29594i			0.662309i	−0.943577	+	0.331154i	$0.892562\pi$
$198$		0			0
$199$	10.3895	+	17.9951i	0.736491	+	1.27564i	0.954066	+	0.299596i	$0.0968518\pi$
$199$	10.3895	+	17.9951i	0.736491	+	1.27564i	−0.217575	+	0.976043i	$0.569815\pi$
$200$		0			0
$201$	1.50318	+	0.867859i	0.106026	+	0.0612140i
$202$		0			0
$203$	−7.21989	−	1.75200i	−0.506737	−	0.122966i
$204$		0			0
$205$	−1.01587	−	0.586511i	−0.0709512	−	0.0409637i
$206$		0			0
$207$	5.76102	−	3.32613i	0.400418	−	0.231182i
$208$		0			0
$209$			0.836905i			0.0578899i
$210$		0			0
$211$	−5.13459			−0.353480			−0.176740	−	0.984258i	$-0.556555\pi$
$211$	−5.13459			−0.353480			−0.176740	+	0.984258i	$0.556555\pi$
$212$		0			0
$213$	−4.48651	−	7.77086i	−0.307411	−	0.532451i
$214$		0			0
$215$	0.698544	−	1.20991i	0.0476403	−	0.0825154i
$216$		0			0
$217$	5.24887	−	1.54085i	0.356316	−	0.104600i
$218$		0			0
$219$	−3.79797	+	6.57828i	−0.256643	+	0.444519i
$220$		0			0
$221$	31.7303	−	18.3195i	2.13441	−	1.23230i
$222$		0			0
$223$	−8.76372			−0.586862			−0.293431	−	0.955980i	$-0.594797\pi$
$223$	−8.76372			−0.586862			−0.293431	+	0.955980i	$0.594797\pi$
$224$		0			0
$225$	4.93374			0.328916
$226$		0			0
$227$	5.09712	−	2.94282i	0.338308	−	0.195322i	−0.321216	−	0.947006i	$-0.604091\pi$
$227$	5.09712	−	2.94282i	0.338308	−	0.195322i	0.659523	+	0.751684i	$0.270758\pi$
$228$		0			0
$229$	−7.90278	+	13.6880i	−0.522230	+	0.904529i	0.477435	+	0.878667i	$0.341566\pi$
$229$	−7.90278	+	13.6880i	−0.522230	+	0.904529i	−0.999666	+	0.0258624i	$0.991767\pi$
$230$		0			0
$231$	6.55176	−	6.87044i	0.431074	−	0.452042i
$232$		0			0
$233$	−0.159081	+	0.275536i	−0.0104217	+	0.0180510i	−0.871189	−	0.490947i	$-0.836651\pi$
$233$	−0.159081	+	0.275536i	−0.0104217	+	0.0180510i	0.860768	+	0.508998i	$0.169984\pi$
$234$		0			0
$235$	0.366442	+	0.634696i	0.0239040	+	0.0414030i
$236$		0			0
$237$	−8.68093			−0.563887
$238$		0			0
$239$		−	1.46820i		−	0.0949697i	−0.998872	−	0.0474849i	$-0.984879\pi$
$239$		−	1.46820i		−	0.0949697i	0.998872	−	0.0474849i	$-0.0151206\pi$
$240$		0			0
$241$	−12.8350	+	7.41030i	−0.826776	+	0.477339i	−0.852748	−	0.522323i	$-0.825065\pi$
$241$	−12.8350	+	7.41030i	−0.826776	+	0.477339i	0.0259714	+	0.999663i	$0.491732\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−1.51598	+	0.973995i	−0.0968523	+	0.0622263i
$246$		0			0
$247$	−0.925087	−	0.534099i	−0.0588619	−	0.0339839i
$248$		0			0
$249$	1.89508	+	3.28238i	0.120096	+	0.208012i
$250$		0			0
$251$		−	10.0773i		−	0.636074i	−0.948078	−	0.318037i	$-0.896976\pi$
$251$		−	10.0773i		−	0.636074i	0.948078	−	0.318037i	$-0.103024\pi$
$252$		0			0
$253$		−	23.8699i		−	1.50069i
$254$		0			0
$255$	−1.02965	−	1.78340i	−0.0644791	−	0.111681i
$256$		0			0
$257$	−15.8763	−	9.16617i	−0.990334	−	0.571770i	−0.0849601	−	0.996384i	$-0.527076\pi$
$257$	−15.8763	−	9.16617i	−0.990334	−	0.571770i	−0.905374	+	0.424615i	$0.860410\pi$
$258$		0			0
$259$	13.6324	−	14.2955i	0.847076	−	0.888278i
$260$		0			0
$261$	2.43185	+	1.40403i	0.150528	+	0.0869073i
$262$		0			0
$263$	2.62507	−	1.51558i	0.161869	−	0.0934549i	−0.416877	−	0.908963i	$-0.636876\pi$
$263$	2.62507	−	1.51558i	0.161869	−	0.0934549i	0.578746	+	0.815508i	$0.303542\pi$
$264$		0			0
$265$		−	0.574076i		−	0.0352652i
$266$		0			0
$267$	−2.59883			−0.159046
$268$		0			0
$269$	12.7236	+	22.0380i	0.775774	+	1.34368i	0.934358	+	0.356335i	$0.115974\pi$
$269$	12.7236	+	22.0380i	0.775774	+	1.34368i	−0.158584	+	0.987345i	$0.550693\pi$
$270$		0			0
$271$	−10.4445	+	18.0904i	−0.634458	+	1.09891i	0.352172	+	0.935935i	$0.385443\pi$
$271$	−10.4445	+	18.0904i	−0.634458	+	1.09891i	−0.986630	+	0.162978i	$0.947890\pi$
$272$		0			0
$273$	3.41313	+	11.6267i	0.206572	+	0.703680i
$274$		0			0
$275$	8.85173	−	15.3316i	0.533779	−	0.924533i
$276$		0			0
$277$	15.4661	−	8.92934i	0.929266	−	0.536512i	0.0426868	−	0.999089i	$-0.486408\pi$
$277$	15.4661	−	8.92934i	0.929266	−	0.536512i	0.886579	+	0.462576i	$0.153075\pi$
$278$		0			0
$279$	−2.06760			−0.123784
$280$		0			0
$281$	3.12507			0.186426			0.0932132	−	0.995646i	$-0.470286\pi$
$281$	3.12507			0.186426			0.0932132	+	0.995646i	$0.470286\pi$
$282$		0			0
$283$	13.3128	−	7.68615i	0.791364	−	0.456894i	−0.0490788	−	0.998795i	$-0.515629\pi$
$283$	13.3128	−	7.68615i	0.791364	−	0.456894i	0.840442	+	0.541901i	$0.182295\pi$
$284$		0			0
$285$	−0.0300191	+	0.0519946i	−0.00177818	+	0.00307990i
$286$		0			0
$287$	11.7165	+	2.84315i	0.691602	+	0.167826i
$288$		0			0
$289$	23.4993	−	40.7020i	1.38231	−	2.39424i
$290$		0			0
$291$	7.30121	+	12.6461i	0.428004	+	0.741325i
$292$		0			0
$293$	−23.0311			−1.34549			−0.672746	−	0.739873i	$-0.734885\pi$
$293$	−23.0311			−1.34549			−0.672746	+	0.739873i	$0.734885\pi$
$294$		0			0
$295$			0.638171i			0.0371557i
$296$		0			0
$297$	−3.10751	+	1.79412i	−0.180316	+	0.104106i
$298$		0			0
$299$	26.3850	+	15.2334i	1.52588	+	0.880969i
$300$		0			0
$301$	−3.38624	+	13.9545i	−0.195180	+	0.804325i
$302$		0			0
$303$	−1.22965	−	0.709937i	−0.0706414	−	0.0407848i
$304$		0			0
$305$	1.14357	+	1.98072i	0.0654806	+	0.113416i
$306$		0			0
$307$		−	4.16830i		−	0.237898i	−0.992900	−	0.118949i	$-0.962048\pi$
$307$		−	4.16830i		−	0.237898i	0.992900	−	0.118949i	$-0.0379524\pi$
$308$		0			0
$309$			8.85633i			0.503819i
$310$		0			0
$311$	−0.255482	−	0.442507i	−0.0144870	−	0.0250923i	0.858691	−	0.512494i	$-0.171278\pi$
$311$	−0.255482	−	0.442507i	−0.0144870	−	0.0250923i	−0.873178	+	0.487401i	$0.837945\pi$
$312$		0			0
$313$	−12.1966	−	7.04172i	−0.689393	−	0.398021i	0.113991	−	0.993482i	$-0.463636\pi$
$313$	−12.1966	−	7.04172i	−0.689393	−	0.398021i	−0.803385	+	0.595460i	$0.796970\pi$
$314$		0			0
$315$	0.653480	−	0.191835i	0.0368194	−	0.0108087i
$316$		0			0
$317$	−4.17009	−	2.40760i	−0.234216	−	0.135224i	0.378300	−	0.925683i	$-0.376509\pi$
$317$	−4.17009	−	2.40760i	−0.234216	−	0.135224i	−0.612515	+	0.790459i	$0.709842\pi$
$318$		0			0
$319$	8.72608	−	5.03800i	0.488566	−	0.282074i
$320$		0			0
$321$		−	12.0035i		−	0.669970i
$322$		0			0
$323$	−1.86586			−0.103819
$324$		0			0
$325$	11.2981	+	19.5688i	0.626703	+	1.08548i
$326$		0			0
$327$	−6.25126	+	10.8275i	−0.345695	+	0.598762i
$328$		0			0
$329$	−5.45135	−	5.19849i	−0.300543	−	0.286602i
$330$		0			0
$331$	10.5895	−	18.3415i	0.582049	−	1.00814i	−0.413187	−	0.910646i	$-0.635584\pi$
$331$	10.5895	−	18.3415i	0.582049	−	1.00814i	0.995236	−	0.0974930i	$-0.0310823\pi$
$332$		0			0
$333$	−6.46587	+	3.73307i	−0.354327	+	0.204571i
$334$		0			0
$335$	0.446800			0.0244113
$336$		0			0
$337$	13.0422			0.710454			0.355227	−	0.934780i	$-0.384404\pi$
$337$	13.0422			0.710454			0.355227	+	0.934780i	$0.384404\pi$
$338$		0			0
$339$	0.124336	−	0.0717857i	0.00675303	−	0.00389886i
$340$		0			0
$341$	−3.70953	+	6.42509i	−0.200882	+	0.347938i
$342$		0			0
$343$	12.1308	−	13.9944i	0.655001	−	0.755628i
$344$		0			0
$345$	0.856194	−	1.48297i	0.0460959	−	0.0798405i
$346$		0			0
$347$	2.51166	+	4.35032i	0.134833	+	0.233537i	0.925534	−	0.378665i	$-0.123617\pi$
$347$	2.51166	+	4.35032i	0.134833	+	0.233537i	−0.790701	+	0.612203i	$0.790284\pi$
$348$		0			0
$349$	13.9823			0.748455			0.374227	−	0.927337i	$-0.377908\pi$
$349$	13.9823			0.748455			0.374227	+	0.927337i	$0.377908\pi$
$350$		0			0
$351$		−	4.57992i		−	0.244458i
$352$		0			0
$353$	−2.00338	+	1.15665i	−0.106629	+	0.0615622i	−0.552366	−	0.833602i	$-0.686275\pi$
$353$	−2.00338	+	1.15665i	−0.106629	+	0.0615622i	0.445737	+	0.895164i	$0.352942\pi$
$354$		0			0
$355$	−2.00034	−	1.15489i	−0.106167	−	0.0612954i
$356$		0			0
$357$	15.3175	+	14.6070i	0.810688	+	0.773085i
$358$		0			0
$359$	8.33838	+	4.81417i	0.440083	+	0.254082i	0.703633	−	0.710564i	$-0.251560\pi$
$359$	8.33838	+	4.81417i	0.440083	+	0.254082i	−0.263550	+	0.964646i	$0.584893\pi$
$360$		0			0
$361$	−9.47280	−	16.4074i	−0.498568	−	0.863546i
$362$		0			0
$363$			1.87550i			0.0984383i
$364$		0			0
$365$			1.95531i			0.102346i
$366$		0			0
$367$	3.79729	+	6.57711i	0.198217	+	0.343322i	0.947950	−	0.318418i	$-0.103152\pi$
$367$	3.79729	+	6.57711i	0.198217	+	0.343322i	−0.749733	+	0.661740i	$0.769818\pi$
$368$		0			0
$369$	−3.94642	−	2.27847i	−0.205442	−	0.118612i
$370$		0			0
$371$	1.66200	+	5.66154i	0.0862866	+	0.293932i
$372$		0			0
$373$	17.6547	+	10.1929i	0.914124	+	0.527769i	0.881756	−	0.471707i	$-0.156362\pi$
$373$	17.6547	+	10.1929i	0.914124	+	0.527769i	0.0323679	+	0.999476i	$0.489695\pi$
$374$		0			0
$375$	2.21451	−	1.27855i	0.114357	−	0.0660238i
$376$		0			0
$377$			12.8607i			0.662359i
$378$		0			0
$379$	35.3247			1.81451			0.907253	−	0.420584i	$-0.138175\pi$
$379$	35.3247			1.81451			0.907253	+	0.420584i	$0.138175\pi$
$380$		0			0
$381$	−9.26261	−	16.0433i	−0.474538	−	0.821924i
$382$		0			0
$383$	7.06305	−	12.2336i	0.360905	−	0.625106i	−0.627205	−	0.778854i	$-0.715801\pi$
$383$	7.06305	−	12.2336i	0.360905	−	0.625106i	0.988110	+	0.153748i	$0.0491345\pi$
$384$		0			0
$385$	0.576293	−	2.37487i	0.0293706	−	0.121035i
$386$		0			0
$387$	2.71369	−	4.70025i	0.137945	−	0.238927i
$388$		0			0
$389$	−1.66609	+	0.961919i	−0.0844743	+	0.0487712i	−0.541642	−	0.840609i	$-0.682197\pi$
$389$	−1.66609	+	0.961919i	−0.0844743	+	0.0487712i	0.457168	+	0.889380i	$0.348864\pi$
$390$		0			0
$391$	53.2175			2.69132
$392$		0			0
$393$	−13.1149			−0.661557
$394$		0			0
$395$	−1.93522	+	1.11730i	−0.0973715	+	0.0562175i
$396$		0			0
$397$	−5.33766	+	9.24510i	−0.267890	+	0.463998i	−0.968317	−	0.249726i	$-0.919660\pi$
$397$	−5.33766	+	9.24510i	−0.267890	+	0.463998i	0.700427	+	0.713724i	$0.252993\pi$
$398$		0			0
$399$	0.145520	−	0.599679i	0.00728510	−	0.0300215i
$400$		0			0
$401$	6.90465	−	11.9592i	0.344802	−	0.597214i	−0.640516	−	0.767945i	$-0.721280\pi$
$401$	6.90465	−	11.9592i	0.344802	−	0.597214i	0.985318	+	0.170731i	$0.0546129\pi$
$402$		0			0
$403$	−4.73472	−	8.20078i	−0.235853	−	0.408510i
$404$		0			0
$405$	−0.257415			−0.0127910
$406$		0			0
$407$			26.7903i			1.32795i
$408$		0			0
$409$	19.5725	−	11.3002i	0.967797	−	0.558758i	0.0692334	−	0.997600i	$-0.477945\pi$
$409$	19.5725	−	11.3002i	0.967797	−	0.558758i	0.898564	+	0.438842i	$0.144611\pi$
$410$		0			0
$411$	2.18816	+	1.26333i	0.107934	+	0.0623156i
$412$		0			0
$413$	−1.84756	−	6.29364i	−0.0909124	−	0.309690i
$414$		0			0
$415$	0.844933	+	0.487823i	0.0414762	+	0.0239463i
$416$		0			0
$417$	8.40098	+	14.5509i	0.411398	+	0.712562i
$418$		0			0
$419$		−	18.9813i		−	0.927299i	−0.886019	−	0.463650i	$-0.846540\pi$
$419$		−	18.9813i		−	0.927299i	0.886019	−	0.463650i	$-0.153460\pi$
$420$		0			0
$421$		−	18.7332i		−	0.912999i	−0.889724	−	0.456499i	$-0.849103\pi$
$421$		−	18.7332i		−	0.912999i	0.889724	−	0.456499i	$-0.150897\pi$
$422$		0			0
$423$	1.42355	+	2.46565i	0.0692152	+	0.119884i
$424$		0			0
$425$	34.1816	+	19.7347i	1.65805	+	0.957276i
$426$		0			0
$427$	−17.0122	−	16.2231i	−0.823280	−	0.785093i
$428$		0			0
$429$	−14.2321	−	8.21693i	−0.687134	−	0.396717i
$430$		0			0
$431$	−22.2380	+	12.8391i	−1.07117	+	0.618439i	−0.928500	−	0.371331i	$-0.878901\pi$
$431$	−22.2380	+	12.8391i	−1.07117	+	0.618439i	−0.142668	+	0.989771i	$0.545568\pi$
$432$		0			0
$433$		−	9.18476i		−	0.441392i	−0.975343	−	0.220696i	$-0.929167\pi$
$433$		−	9.18476i		−	0.441392i	0.975343	−	0.220696i	$-0.0708328\pi$
$434$		0			0
$435$	0.722836			0.0346573
$436$		0			0
$437$	−0.775770	−	1.34367i	−0.0371101	−	0.0642766i
$438$		0			0
$439$	−9.86253	+	17.0824i	−0.470713	+	0.815298i	−0.999439	−	0.0334941i	$-0.989336\pi$
$439$	−9.86253	+	17.0824i	−0.470713	+	0.815298i	0.528726	+	0.848792i	$0.322670\pi$
$440$		0			0
$441$	−5.88924	+	3.78376i	−0.280440	+	0.180179i
$442$		0			0
$443$	−13.0143	+	22.5415i	−0.618330	+	1.07098i	0.371460	+	0.928449i	$0.378857\pi$
$443$	−13.0143	+	22.5415i	−0.618330	+	1.07098i	−0.989790	+	0.142531i	$0.954476\pi$
$444$		0			0
$445$	−0.579351	+	0.334489i	−0.0274639	+	0.0158563i
$446$		0			0
$447$	−23.2746			−1.10085
$448$		0			0
$449$	10.8554			0.512297			0.256148	−	0.966637i	$-0.417546\pi$
$449$	10.8554			0.512297			0.256148	+	0.966637i	$0.417546\pi$
$450$		0			0
$451$	−14.1607	+	8.17569i	−0.666802	+	0.384978i
$452$		0			0
$453$	6.12714	−	10.6125i	0.287878	−	0.498619i
$454$		0			0
$455$	2.25732	+	2.15262i	0.105825	+	0.100916i
$456$		0			0
$457$	−15.0321	+	26.0363i	−0.703171	+	1.21793i	0.264177	+	0.964474i	$0.414900\pi$
$457$	−15.0321	+	26.0363i	−0.703171	+	1.21793i	−0.967348	+	0.253453i	$0.918434\pi$
$458$		0			0
$459$	−3.99996	−	6.92813i	−0.186702	−	0.323377i
$460$		0			0
$461$	−9.23630			−0.430177			−0.215089	−	0.976595i	$-0.569004\pi$
$461$	−9.23630			−0.430177			−0.215089	+	0.976595i	$0.569004\pi$
$462$		0			0
$463$		−	17.3618i		−	0.806869i	−0.915008	−	0.403435i	$-0.867816\pi$
$463$		−	17.3618i		−	0.806869i	0.915008	−	0.403435i	$-0.132184\pi$
$464$		0			0
$465$	−0.460926	+	0.266116i	−0.0213749	+	0.0123408i
$466$		0			0
$467$	−18.8961	−	10.9097i	−0.874408	−	0.504840i	−0.00559766	−	0.999984i	$-0.501782\pi$
$467$	−18.8961	−	10.9097i	−0.874408	−	0.504840i	−0.868811	+	0.495144i	$0.835115\pi$
$468$		0			0
$469$	−4.40634	+	1.29352i	−0.203466	+	0.0597293i
$470$		0			0
$471$	−17.8471	−	10.3040i	−0.822352	−	0.474785i
$472$		0			0
$473$	−9.73738	−	16.8656i	−0.447725	−	0.775483i
$474$		0			0
$475$		−	1.15072i		−	0.0527987i
$476$		0			0
$477$		−	2.23016i		−	0.102112i
$478$		0			0
$479$	−10.2056	−	17.6766i	−0.466306	−	0.807665i	0.532954	−	0.846144i	$-0.321082\pi$
$479$	−10.2056	−	17.6766i	−0.466306	−	0.807665i	−0.999259	+	0.0384791i	$0.987749\pi$
$480$		0			0
$481$	−29.6131	−	17.0972i	−1.35024	−	0.779563i
$482$		0			0
$483$	−4.15046	+	17.1038i	−0.188853	+	0.778251i
$484$		0			0
$485$	3.25528	+	1.87944i	0.147815	+	0.0853409i
$486$		0			0
$487$	−7.32382	+	4.22841i	−0.331874	+	0.191608i	−0.656673	−	0.754176i	$-0.728037\pi$
$487$	−7.32382	+	4.22841i	−0.331874	+	0.191608i	0.324799	+	0.945783i	$0.394703\pi$
$488$		0			0
$489$			14.4227i			0.652218i
$490$		0			0
$491$	−37.4822			−1.69155			−0.845774	−	0.533541i	$-0.820861\pi$
$491$	−37.4822			−1.69155			−0.845774	+	0.533541i	$0.820861\pi$
$492$		0			0
$493$	11.2321	+	19.4546i	0.505869	+	0.876191i
$494$		0			0
$495$	−0.461834	+	0.799920i	−0.0207579	+	0.0359537i
$496$		0			0
$497$	23.0708	+	5.59843i	1.03487	+	0.251124i
$498$		0			0
$499$	6.23338	−	10.7965i	0.279045	−	0.483319i	−0.692103	−	0.721799i	$-0.743316\pi$
$499$	6.23338	−	10.7965i	0.279045	−	0.483319i	0.971148	+	0.238479i	$0.0766489\pi$
$500$		0			0
$501$	6.61351	−	3.81831i	0.295470	−	0.170590i
$502$		0			0
$503$	−13.8883			−0.619250			−0.309625	−	0.950859i	$-0.600203\pi$
$503$	−13.8883			−0.619250			−0.309625	+	0.950859i	$0.600203\pi$
$504$		0			0
$505$	−0.365497			−0.0162644
$506$		0			0
$507$	6.90710	−	3.98782i	0.306755	−	0.177105i
$508$		0			0
$509$	19.5215	−	33.8121i	0.865273	−	1.49870i	−0.00150245	−	0.999999i	$-0.500478\pi$
$509$	19.5215	−	33.8121i	0.865273	−	1.49870i	0.866776	−	0.498698i	$-0.166188\pi$
$510$		0			0
$511$	−5.66078	−	19.2833i	−0.250418	−	0.853041i
$512$		0			0
$513$	−0.116618	+	0.201988i	−0.00514879	+	0.00891797i
$514$		0			0
$515$	1.13988	+	1.97432i	0.0502289	+	0.0869990i
$516$		0			0
$517$	10.2161			0.449302
$518$		0			0
$519$			15.7993i			0.693514i
$520$		0			0
$521$	12.2354	−	7.06409i	0.536041	−	0.309483i	−0.207432	−	0.978249i	$-0.566511\pi$
$521$	12.2354	−	7.06409i	0.536041	−	0.309483i	0.743473	+	0.668766i	$0.233177\pi$
$522$		0			0
$523$	−9.63976	−	5.56552i	−0.421517	−	0.243363i	0.274209	−	0.961670i	$-0.411584\pi$
$523$	−9.63976	−	5.56552i	−0.421517	−	0.243363i	−0.695726	+	0.718307i	$0.744917\pi$
$524$		0			0
$525$	−9.00849	+	9.44666i	−0.393163	+	0.412286i
$526$		0			0
$527$	−14.3246	−	8.27032i	−0.623990	−	0.360261i
$528$		0			0
$529$	10.6262	+	18.4052i	0.462010	+	0.800224i
$530$		0			0
$531$			2.47915i			0.107586i
$532$		0			0
$533$		−	20.8704i		−	0.903996i
$534$		0			0
$535$	−1.54494	−	2.67591i	−0.0667936	−	0.115690i
$536$		0			0
$537$	19.8711	+	11.4726i	0.857500	+	0.495078i
$538$		0			0
$539$	1.19205	+	25.0894i	0.0513451	+	1.08068i
$540$		0			0
$541$	−11.0648	−	6.38829i	−0.475715	−	0.274654i	0.242914	−	0.970048i	$-0.421897\pi$
$541$	−11.0648	−	6.38829i	−0.475715	−	0.274654i	−0.718629	+	0.695394i	$0.755230\pi$
$542$		0			0
$543$	13.1439	−	7.58865i	0.564060	−	0.325660i
$544$		0			0
$545$			3.21833i			0.137858i
$546$		0			0
$547$	20.6852			0.884437			0.442218	−	0.896907i	$-0.354192\pi$
$547$	20.6852			0.884437			0.442218	+	0.896907i	$0.354192\pi$
$548$		0			0
$549$	4.44251	+	7.69466i	0.189602	+	0.328400i
$550$		0			0
$551$	0.327469	−	0.567193i	0.0139507	−	0.0241632i
$552$		0			0
$553$	15.8505	−	16.6214i	0.674031	−	0.706816i
$554$		0			0
$555$	−0.960948	+	1.66441i	−0.0407900	+	0.0706503i
$556$		0			0
$557$	4.75011	−	2.74248i	0.201268	−	0.116202i	−0.395979	−	0.918260i	$-0.629595\pi$
$557$	4.75011	−	2.74248i	0.201268	−	0.116202i	0.597247	+	0.802057i	$0.296261\pi$
$558$		0			0
$559$	24.8569			1.05134
$560$		0			0
$561$	−28.7057			−1.21195
$562$		0			0
$563$	−35.0039	+	20.2095i	−1.47524	+	0.851730i	−0.999610	−	0.0279158i	$-0.991113\pi$
$563$	−35.0039	+	20.2095i	−1.47524	+	0.851730i	−0.475629	+	0.879646i	$0.657780\pi$
$564$		0			0
$565$	0.0184787	−	0.0320060i	0.000777405	−	0.00134650i
$566$		0			0
$567$	2.53863	−	0.745237i	0.106612	−	0.0312970i
$568$		0			0
$569$	−8.93137	+	15.4696i	−0.374422	+	0.648519i	−0.990240	−	0.139370i	$-0.955492\pi$
$569$	−8.93137	+	15.4696i	−0.374422	+	0.648519i	0.615818	+	0.787888i	$0.288826\pi$
$570$		0			0
$571$	−4.38717	−	7.59881i	−0.183597	−	0.318000i	0.759506	−	0.650501i	$-0.225441\pi$
$571$	−4.38717	−	7.59881i	−0.183597	−	0.318000i	−0.943103	+	0.332501i	$0.892108\pi$
$572$		0			0
$573$	−21.4752			−0.897138
$574$		0			0
$575$			32.8205i			1.36871i
$576$		0			0
$577$	−3.76090	+	2.17135i	−0.156568	+	0.0903947i	−0.576237	−	0.817283i	$-0.695480\pi$
$577$	−3.76090	+	2.17135i	−0.156568	+	0.0903947i	0.419669	+	0.907677i	$0.362146\pi$
$578$		0			0
$579$	6.20137	+	3.58036i	0.257720	+	0.148795i
$580$		0			0
$581$	−9.74502	−	2.36475i	−0.404292	−	0.0981065i
$582$		0			0
$583$	−6.93024	−	4.00118i	−0.287021	−	0.165712i
$584$		0			0
$585$	−0.589469	−	1.02099i	−0.0243716	−	0.0422128i
$586$		0			0
$587$			10.5208i			0.434239i	0.976145	+	0.217119i	$0.0696661\pi$
$587$			10.5208i			0.434239i	−0.976145	+	0.217119i	$0.930334\pi$
$588$		0			0
$589$			0.482238i			0.0198703i
$590$		0			0
$591$	4.64797	+	8.05052i	0.191192	+	0.331154i
$592$		0			0
$593$	−13.0551	−	7.53735i	−0.536107	−	0.309522i	0.207392	−	0.978258i	$-0.433502\pi$
$593$	−13.0551	−	7.53735i	−0.536107	−	0.309522i	−0.743500	+	0.668736i	$0.766836\pi$
$594$		0			0
$595$	5.29473	+	1.28483i	0.217063	+	0.0526730i
$596$		0			0
$597$	17.9951	+	10.3895i	0.736491	+	0.425213i
$598$		0			0
$599$	6.10386	−	3.52407i	0.249397	−	0.143989i	−0.370091	−	0.928995i	$-0.620674\pi$
$599$	6.10386	−	3.52407i	0.249397	−	0.143989i	0.619488	+	0.785006i	$0.287340\pi$
$600$		0			0
$601$			0.706153i			0.0288046i	0.999896	+	0.0144023i	$0.00458455\pi$
$601$			0.706153i			0.0288046i	−0.999896	+	0.0144023i	$0.995415\pi$
$602$		0			0
$603$	1.73572			0.0706839
$604$		0			0
$605$	0.241391	+	0.418101i	0.00981394	+	0.0169982i
$606$		0			0
$607$	−3.09824	+	5.36632i	−0.125754	+	0.217812i	−0.922027	−	0.387125i	$-0.873468\pi$
$607$	−3.09824	+	5.36632i	−0.125754	+	0.217812i	0.796273	+	0.604937i	$0.206802\pi$
$608$		0			0
$609$	−7.12861	+	2.09267i	−0.288866	+	0.0847993i
$610$		0			0
$611$	−6.51972	+	11.2925i	−0.263760	+	0.456845i
$612$		0			0
$613$	−9.94156	+	5.73976i	−0.401536	+	0.231827i	−0.687146	−	0.726519i	$-0.741137\pi$
$613$	−9.94156	+	5.73976i	−0.401536	+	0.231827i	0.285611	+	0.958346i	$0.407804\pi$
$614$		0			0
$615$	−1.17302			−0.0473008
$616$		0			0
$617$	−48.1839			−1.93981			−0.969905	−	0.243485i	$-0.921709\pi$
$617$	−48.1839			−1.93981			−0.969905	+	0.243485i	$0.921709\pi$
$618$		0			0
$619$	−10.6872	+	6.17027i	−0.429556	+	0.248004i	−0.699157	−	0.714968i	$-0.746441\pi$
$619$	−10.6872	+	6.17027i	−0.429556	+	0.248004i	0.269602	+	0.962972i	$0.413108\pi$
$620$		0			0
$621$	3.32613	−	5.76102i	0.133473	−	0.231182i
$622$		0			0
$623$	4.74519	−	4.97600i	0.190112	−	0.199359i
$624$		0			0
$625$	−12.0052	+	20.7937i	−0.480209	+	0.831747i
$626$		0			0
$627$	0.418453	+	0.724781i	0.0167114	+	0.0289450i
$628$		0			0
$629$	−59.7285			−2.38153
$630$		0			0
$631$		−	2.33444i		−	0.0929326i	−0.998920	−	0.0464663i	$-0.985204\pi$
$631$		−	2.33444i		−	0.0929326i	0.998920	−	0.0464663i	$-0.0147960\pi$
$632$		0			0
$633$	−4.44669	+	2.56730i	−0.176740	+	0.102041i
$634$		0			0
$635$	−4.12979	−	2.38433i	−0.163886	−	0.0946194i
$636$		0			0
$637$	−28.4937	−	14.6940i	−1.12896	−	0.582197i
$638$		0			0
$639$	−7.77086	−	4.48651i	−0.307411	−	0.177484i
$640$		0			0
$641$	22.0146	+	38.1304i	0.869525	+	1.50606i	0.862483	+	0.506086i	$0.168908\pi$
$641$	22.0146	+	38.1304i	0.869525	+	1.50606i	0.00704191	+	0.999975i	$0.497758\pi$
$642$		0			0
$643$			0.391635i			0.0154446i	0.999970	+	0.00772228i	$0.00245810\pi$
$643$			0.391635i			0.0154446i	−0.999970	+	0.00772228i	$0.997542\pi$
$644$		0			0
$645$		−	1.39709i		−	0.0550103i
$646$		0			0
$647$	−13.1914	−	22.8482i	−0.518608	−	0.898256i	−0.999766	−	0.0216222i	$-0.993117\pi$
$647$	−13.1914	−	22.8482i	−0.518608	−	0.898256i	0.481158	−	0.876634i	$-0.340216\pi$
$648$		0			0
$649$	7.70400	+	4.44790i	0.302408	+	0.174596i
$650$		0			0
$651$	3.77522	−	3.95885i	0.147963	−	0.155160i
$652$		0			0
$653$	33.2271	+	19.1837i	1.30028	+	0.750715i	0.980451	−	0.196762i	$-0.0630426\pi$
$653$	33.2271	+	19.1837i	1.30028	+	0.750715i	0.319825	+	0.947477i	$0.396376\pi$
$654$		0			0
$655$	−2.92367	+	1.68798i	−0.114237	+	0.0659548i
$656$		0			0
$657$			7.59594i			0.296346i
$658$		0			0
$659$	27.8445			1.08467			0.542334	−	0.840163i	$-0.317541\pi$
$659$	27.8445			1.08467			0.542334	+	0.840163i	$0.317541\pi$
$660$		0			0
$661$	−10.0199	−	17.3549i	−0.389728	−	0.675029i	0.602685	−	0.797979i	$-0.294098\pi$
$661$	−10.0199	−	17.3549i	−0.389728	−	0.675029i	−0.992413	+	0.122951i	$0.960764\pi$
$662$		0			0
$663$	18.3195	−	31.7303i	0.711470	−	1.23230i
$664$		0			0
$665$	−0.0447427	−	0.152415i	−0.00173505	−	0.00591038i
$666$		0			0
$667$	−9.33996	+	16.1773i	−0.361645	+	0.626387i
$668$		0			0
$669$	−7.58960	+	4.38186i	−0.293431	+	0.169412i
$670$		0			0
$671$	31.8817			1.23078
$672$		0			0
$673$	−2.90485			−0.111974			−0.0559868	−	0.998432i	$-0.517830\pi$
$673$	−2.90485			−0.111974			−0.0559868	+	0.998432i	$0.517830\pi$
$674$		0			0
$675$	4.27274	−	2.46687i	0.164458	−	0.0949498i
$676$		0			0
$677$	−14.6961	+	25.4545i	−0.564819	+	0.978295i	0.432248	+	0.901755i	$0.357721\pi$
$677$	−14.6961	+	25.4545i	−0.564819	+	0.978295i	−0.997067	+	0.0765400i	$0.975613\pi$
$678$		0			0
$679$	−37.5448	−	9.11071i	−1.44084	−	0.349637i
$680$		0			0
$681$	2.94282	−	5.09712i	0.112769	−	0.195322i
$682$		0			0
$683$	0.120445	+	0.208616i	0.00460868	+	0.00798247i	0.868321	−	0.496003i	$-0.165200\pi$
$683$	0.120445	+	0.208616i	0.00460868	+	0.00798247i	−0.863712	+	0.503986i	$0.831866\pi$
$684$		0			0
$685$	0.650401			0.0248506
$686$		0			0
$687$			15.8056i			0.603020i
$688$		0			0
$689$	8.84553	−	5.10697i	0.336988	−	0.194560i
$690$		0			0
$691$	26.5759	+	15.3436i	1.01099	+	0.583698i	0.911483	−	0.411339i	$-0.134939\pi$
$691$	26.5759	+	15.3436i	1.01099	+	0.583698i	0.0995117	+	0.995036i	$0.468272\pi$
$692$		0			0
$693$	2.23877	−	9.22586i	0.0850439	−	0.350461i
$694$		0			0
$695$	3.74563	+	2.16254i	0.142080	+	0.0820297i
$696$		0			0
$697$	−18.2275	−	31.5710i	−0.690417	−	1.19584i
$698$		0			0
$699$			0.318161i			0.0120340i
$700$		0			0
$701$			1.90784i			0.0720581i	0.999351	+	0.0360290i	$0.0114709\pi$
$701$			1.90784i			0.0720581i	−0.999351	+	0.0360290i	$0.988529\pi$
$702$		0			0
$703$	0.870684	+	1.50807i	0.0328385	+	0.0568779i
$704$		0			0
$705$	0.634696	+	0.366442i	0.0239040	+	0.0138010i
$706$		0			0
$707$	3.60453	−	1.05814i	0.135562	−	0.0397956i
$708$		0			0
$709$	29.0031	+	16.7450i	1.08923	+	0.628870i	0.933373	−	0.358909i	$-0.116851\pi$
$709$	29.0031	+	16.7450i	1.08923	+	0.628870i	0.155862	+	0.987779i	$0.450184\pi$
$710$		0			0
$711$	−7.51791	+	4.34047i	−0.281944	+	0.162780i
$712$		0			0
$713$		−	13.7542i		−	0.515099i
$714$		0			0
$715$	−4.23032			−0.158205
$716$		0			0
$717$	−0.734098	−	1.27150i	−0.0274154	−	0.0474849i
$718$		0			0
$719$	−0.0121575	+	0.0210575i	−0.000453399	+	0.000785311i	−0.866252	−	0.499607i	$-0.833478\pi$
$719$	−0.0121575	+	0.0210575i	−0.000453399	+	0.000785311i	0.865799	+	0.500393i	$0.166811\pi$
$720$		0			0
$721$	−16.9573	−	16.1707i	−0.631522	−	0.602230i
$722$		0			0
$723$	−7.41030	+	12.8350i	−0.275592	+	0.477339i
$724$		0			0
$725$	−11.9981	+	6.92711i	−0.445599	+	0.257267i
$726$		0			0
$727$	−16.6521			−0.617593			−0.308797	−	0.951128i	$-0.599926\pi$
$727$	−16.6521			−0.617593			−0.308797	+	0.951128i	$0.599926\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	37.6016	−	21.7093i	1.39074	−	0.802947i
$732$		0			0
$733$	13.1766	−	22.8226i	0.486691	−	0.842973i	−0.513192	−	0.858274i	$-0.671537\pi$
$733$	13.1766	−	22.8226i	0.486691	−	0.842973i	0.999883	+	0.0153008i	$0.00487059\pi$
$734$		0			0
$735$	−0.825878	+	1.60149i	−0.0304630	+	0.0590720i
$736$		0			0
$737$	3.11409	−	5.39376i	0.114709	−	0.198682i
$738$		0			0
$739$	−2.67874	−	4.63971i	−0.0985390	−	0.170675i	0.812541	−	0.582904i	$-0.198084\pi$
$739$	−2.67874	−	4.63971i	−0.0985390	−	0.170675i	−0.911080	+	0.412229i	$0.864750\pi$
$740$		0			0
$741$	−1.06820			−0.0392412
$742$		0			0
$743$		−	33.1321i		−	1.21550i	−0.794129	−	0.607749i	$-0.792073\pi$
$743$		−	33.1321i		−	1.21550i	0.794129	−	0.607749i	$-0.207927\pi$
$744$		0			0
$745$	−5.18856	+	2.99562i	−0.190094	+	0.109751i
$746$		0			0
$747$	3.28238	+	1.89508i	0.120096	+	0.0693375i
$748$		0			0
$749$	22.9832	+	21.9171i	0.839788	+	0.800835i
$750$		0			0
$751$	13.6288	+	7.86861i	0.497323	+	0.287130i	0.727607	−	0.685994i	$-0.240632\pi$
$751$	13.6288	+	7.86861i	0.497323	+	0.287130i	−0.230284	+	0.973123i	$0.573966\pi$
$752$		0			0
$753$	−5.03865	−	8.72721i	−0.183619	−	0.318037i
$754$		0			0
$755$		−	3.15443i		−	0.114802i
$756$		0			0
$757$		−	17.9229i		−	0.651418i	−0.945470	−	0.325709i	$-0.894397\pi$
$757$		−	17.9229i		−	0.651418i	0.945470	−	0.325709i	$-0.105603\pi$
$758$		0			0
$759$	−11.9350	−	20.6719i	−0.433211	−	0.750344i
$760$		0			0
$761$	15.7934	+	9.11832i	0.572510	+	0.330539i	0.758151	−	0.652079i	$-0.226103\pi$
$761$	15.7934	+	9.11832i	0.572510	+	0.330539i	−0.185641	+	0.982618i	$0.559436\pi$
$762$		0			0
$763$	−9.31735	−	31.7392i	−0.337311	−	1.14904i
$764$		0			0
$765$	−1.78340	−	1.02965i	−0.0644791	−	0.0372270i
$766$		0			0
$767$	−9.83312	+	5.67716i	−0.355054	+	0.204990i
$768$		0			0
$769$			41.7710i			1.50630i	0.657847	+	0.753151i	$0.271467\pi$
$769$			41.7710i			1.50630i	−0.657847	+	0.753151i	$0.728533\pi$
$770$		0			0
$771$	−18.3323			−0.660223
$772$		0			0
$773$	−22.1831	−	38.4222i	−0.797870	−	1.38195i	−0.921001	−	0.389561i	$-0.872627\pi$
$773$	−22.1831	−	38.4222i	−0.797870	−	1.38195i	0.123131	−	0.992390i	$-0.460706\pi$
$774$		0			0
$775$	5.10050	−	8.83433i	0.183215	−	0.317338i
$776$		0			0
$777$	4.65826	−	19.1964i	0.167114	−	0.688669i
$778$		0			0
$779$	−0.531419	+	0.920444i	−0.0190400	+	0.0329783i
$780$		0			0
$781$	−27.8838	+	16.0987i	−0.997759	+	0.576057i
$782$		0			0
$783$	2.80806			0.100352
$784$		0			0
$785$	−5.30483			−0.189337
$786$		0			0
$787$	−25.7940	+	14.8922i	−0.919458	+	0.530849i	−0.883462	−	0.468503i	$-0.844794\pi$
$787$	−25.7940	+	14.8922i	−0.919458	+	0.530849i	−0.0359959	+	0.999352i	$0.511460\pi$
$788$		0			0
$789$	1.51558	−	2.62507i	0.0539562	−	0.0934549i
$790$		0			0
$791$	−0.0895768	+	0.369141i	−0.00318498	+	0.0131251i
$792$		0			0
$793$	−20.3463	+	35.2409i	−0.722520	+	1.25144i
$794$		0			0
$795$	−0.287038	−	0.497164i	−0.0101802	−	0.0176326i
$796$		0			0
$797$	34.1552			1.20984			0.604920	−	0.796286i	$-0.293205\pi$
$797$	34.1552			1.20984			0.604920	+	0.796286i	$0.293205\pi$
$798$		0			0
$799$			22.7765i			0.805775i
$800$		0			0
$801$	−2.25065	+	1.29941i	−0.0795229	+	0.0459126i
$802$		0			0
$803$	23.6045	+	13.6280i	0.832984	+	0.480923i
$804$		0			0
$805$	1.27614	+	4.34711i	0.0449779	+	0.153216i
$806$		0			0
$807$	22.0380	+	12.7236i	0.775774	+	0.447893i
$808$		0			0
$809$	−13.4152	−	23.2358i	−0.471653	−	0.816928i	0.527821	−	0.849356i	$-0.323009\pi$
$809$	−13.4152	−	23.2358i	−0.471653	−	0.816928i	−0.999474	+	0.0324281i	$0.989676\pi$
$810$		0			0
$811$			45.1596i			1.58577i	0.609372	+	0.792885i	$0.291422\pi$
$811$			45.1596i			1.58577i	−0.609372	+	0.792885i	$0.708578\pi$
$812$		0			0
$813$			20.8890i			0.732609i
$814$		0			0
$815$	1.85631	+	3.21522i	0.0650237	+	0.112624i
$816$		0			0
$817$	−1.09626	−	0.632928i	−0.0383534	−	0.0221433i
$818$		0			0
$819$	8.76920	+	8.36245i	0.306421	+	0.292208i
$820$		0			0
$821$	−17.5238	−	10.1174i	−0.611585	−	0.353099i	0.162000	−	0.986791i	$-0.448205\pi$
$821$	−17.5238	−	10.1174i	−0.611585	−	0.353099i	−0.773586	+	0.633692i	$0.781539\pi$
$822$		0			0
$823$	−40.5392	+	23.4053i	−1.41311	+	0.815858i	−0.995680	−	0.0928521i	$-0.970402\pi$
$823$	−40.5392	+	23.4053i	−1.41311	+	0.815858i	−0.417428	+	0.908710i	$0.637068\pi$
$824$		0			0
$825$		−	17.7035i		−	0.616355i
$826$		0			0
$827$	17.0446			0.592700			0.296350	−	0.955079i	$-0.404231\pi$
$827$	17.0446			0.592700			0.296350	+	0.955079i	$0.404231\pi$
$828$		0			0
$829$	6.94700	+	12.0325i	0.241279	+	0.417908i	0.961079	−	0.276274i	$-0.0890997\pi$
$829$	6.94700	+	12.0325i	0.241279	+	0.417908i	−0.719800	+	0.694182i	$0.755766\pi$
$830$		0			0
$831$	8.92934	−	15.4661i	0.309755	−	0.536512i
$832$		0			0
$833$	−55.9363	+	2.65765i	−1.93808	+	0.0920820i
$834$		0			0
$835$	0.982890	−	1.70242i	0.0340143	−	0.0589145i
$836$		0			0
$837$	−1.79060	+	1.03380i	−0.0618920	+	0.0357334i
$838$		0			0
$839$	−34.7647			−1.20021			−0.600105	−	0.799921i	$-0.704875\pi$
$839$	−34.7647			−1.20021			−0.600105	+	0.799921i	$0.704875\pi$
$840$		0			0
$841$	21.1148			0.728097
$842$		0			0
$843$	2.70639	−	1.56254i	0.0932132	−	0.0538166i
$844$		0			0
$845$	1.02652	−	1.77799i	0.0353135	−	0.0611648i
$846$		0			0
$847$	−3.59104	−	3.42447i	−0.123389	−	0.117666i
$848$		0			0
$849$	7.68615	−	13.3128i	0.263788	−	0.456894i
$850$		0			0
$851$	−24.8333	−	43.0126i	−0.851275	−	1.47445i
$852$		0			0
$853$	39.5354			1.35367			0.676834	−	0.736136i	$-0.263352\pi$
$853$	39.5354			1.35367			0.676834	+	0.736136i	$0.263352\pi$
$854$		0			0
$855$			0.0600382i			0.00205326i
$856$		0			0
$857$	−17.9608	+	10.3697i	−0.613530	+	0.354221i	−0.774346	−	0.632763i	$-0.781921\pi$
$857$	−17.9608	+	10.3697i	−0.613530	+	0.354221i	0.160816	+	0.986984i	$0.448587\pi$
$858$		0			0
$859$	41.7159	+	24.0847i	1.42333	+	0.821759i	0.996582	−	0.0826128i	$-0.0263265\pi$
$859$	41.7159	+	24.0847i	1.42333	+	0.821759i	0.426746	+	0.904371i	$0.359660\pi$
$860$		0			0
$861$	11.5683	−	3.39600i	0.394248	−	0.115735i
$862$		0			0
$863$	38.2263	+	22.0700i	1.30124	+	0.751271i	0.980617	−	0.195937i	$-0.0627747\pi$
$863$	38.2263	+	22.0700i	1.30124	+	0.751271i	0.320622	+	0.947207i	$0.396108\pi$
$864$		0			0
$865$	2.03349	+	3.52211i	0.0691408	+	0.119755i
$866$		0			0
$867$		−	46.9987i		−	1.59616i
$868$		0			0
$869$			31.1493i			1.05667i
$870$		0			0
$871$	3.97472	+	6.88442i	0.134678	+	0.233270i
$872$		0			0
$873$	12.6461	+	7.30121i	0.428004	+	0.247108i
$874$		0			0
$875$	−1.59542	+	6.57462i	−0.0539349	+	0.222263i
$876$		0			0
$877$	−1.21231	−	0.699930i	−0.0409369	−	0.0236350i	0.479392	−	0.877601i	$-0.340857\pi$
$877$	−1.21231	−	0.699930i	−0.0409369	−	0.0236350i	−0.520329	+	0.853966i	$0.674191\pi$
$878$		0			0
$879$	−19.9455	+	11.5156i	−0.672746	+	0.388410i
$880$		0			0
$881$			0.164680i			0.00554821i	0.999996	+	0.00277410i	$0.000883026\pi$
$881$			0.164680i			0.00554821i	−0.999996	+	0.00277410i	$0.999117\pi$
$882$		0			0
$883$	−28.9462			−0.974116			−0.487058	−	0.873370i	$-0.661930\pi$
$883$	−28.9462			−0.974116			−0.487058	+	0.873370i	$0.661930\pi$
$884$		0			0
$885$	0.319085	+	0.552672i	0.0107259	+	0.0185779i
$886$		0			0
$887$	20.3345	−	35.2204i	0.682766	−	1.18258i	−0.291368	−	0.956611i	$-0.594110\pi$
$887$	20.3345	−	35.2204i	0.682766	−	1.18258i	0.974133	−	0.225974i	$-0.0725564\pi$
$888$		0			0
$889$	47.6308	+	11.5582i	1.59749	+	0.387651i
$890$		0			0
$891$	−1.79412	+	3.10751i	−0.0601054	+	0.104106i
$892$		0			0
$893$	0.575078	−	0.332021i	0.0192442	−	0.0111107i
$894$		0			0
$895$	5.90642			0.197430
$896$		0			0
$897$	30.4668			1.01726
$898$		0			0
$899$	5.02810	−	2.90297i	0.167696	−	0.0968196i
$900$		0			0
$901$	8.92054	−	15.4508i	0.297186	−	0.514742i
$902$		0			0
$903$	4.04468	+	13.7781i	0.134599	+	0.458506i
$904$		0			0
$905$	1.95343	−	3.38344i	0.0649343	−	0.112469i
$906$		0			0
$907$	−6.57673	−	11.3912i	−0.218377	−	0.378240i	0.735935	−	0.677052i	$-0.236743\pi$
$907$	−6.57673	−	11.3912i	−0.218377	−	0.378240i	−0.954312	+	0.298813i	$0.903409\pi$
$908$		0			0
$909$	−1.41987			−0.0470942
$910$		0			0
$911$			4.58131i			0.151785i	0.997116	+	0.0758927i	$0.0241806\pi$
$911$			4.58131i			0.151785i	−0.997116	+	0.0758927i	$0.975819\pi$
$912$		0			0
$913$	11.7780	−	6.80002i	0.389794	−	0.225048i
$914$		0			0
$915$	1.98072	+	1.14357i	0.0654806	+	0.0378052i
$916$		0			0
$917$	23.9464	−	25.1111i	0.790779	−	0.829242i
$918$		0			0
$919$	22.6967	+	13.1039i	0.748694	+	0.432259i	0.825222	−	0.564809i	$-0.191050\pi$
$919$	22.6967	+	13.1039i	0.748694	+	0.432259i	−0.0765280	+	0.997067i	$0.524383\pi$
$920$		0			0
$921$	−2.08415	−	3.60986i	−0.0686751	−	0.118949i
$922$		0			0
$923$		−	41.0957i		−	1.35268i
$924$		0			0
$925$		−	36.8360i		−	1.21116i
$926$		0			0
$927$	4.42816	+	7.66981i	0.145440	+	0.251909i
$928$		0			0
$929$	4.55350	+	2.62897i	0.149396	+	0.0862536i	0.572834	−	0.819671i	$-0.305844\pi$
$929$	4.55350	+	2.62897i	0.149396	+	0.0862536i	−0.423439	+	0.905925i	$0.639177\pi$
$930$		0			0
$931$	0.882506	+	1.37358i	0.0289230	+	0.0450172i
$932$		0			0
$933$	−0.442507	−	0.255482i	−0.0144870	−	0.00836409i
$934$		0			0
$935$	−6.39929	+	3.69463i	−0.209279	+	0.120827i
$936$		0			0
$937$			4.17839i			0.136502i	0.997668	+	0.0682510i	$0.0217419\pi$
$937$			4.17839i			0.136502i	−0.997668	+	0.0682510i	$0.978258\pi$
$938$		0			0
$939$	−14.0834			−0.459596
$940$		0			0
$941$	9.55498	+	16.5497i	0.311483	+	0.539505i	0.978684	−	0.205373i	$-0.0658409\pi$
$941$	9.55498	+	16.5497i	0.311483	+	0.539505i	−0.667200	+	0.744878i	$0.732508\pi$
$942$		0			0
$943$	15.1569	−	26.2526i	0.493577	−	0.854901i
$944$		0			0
$945$	0.470013	−	0.492874i	0.0152895	−	0.0160332i
$946$		0			0
$947$	−1.20797	+	2.09227i	−0.0392539	+	0.0679897i	−0.884985	−	0.465620i	$-0.845831\pi$
$947$	−1.20797	+	2.09227i	−0.0392539	+	0.0679897i	0.845731	+	0.533610i	$0.179165\pi$
$948$		0			0
$949$	−30.1280	+	17.3944i	−0.977995	+	0.564646i
$950$		0			0
$951$	−4.81520			−0.156144
$952$		0			0
$953$	9.71810			0.314800			0.157400	−	0.987535i	$-0.449689\pi$
$953$	9.71810			0.314800			0.157400	+	0.987535i	$0.449689\pi$
$954$		0			0
$955$	−4.78741	+	2.76401i	−0.154917	+	0.0894414i
$956$		0			0
$957$	5.03800	−	8.72608i	0.162855	−	0.282074i
$958$		0			0
$959$	−6.41426	+	1.88297i	−0.207127	+	0.0608041i
$960$		0			0
$961$	13.3625	−	23.1446i	0.431049	−	0.746598i
$962$		0			0
$963$	−6.00175	−	10.3953i	−0.193404	−	0.334985i
$964$		0			0
$965$	1.84328			0.0593372
$966$		0			0
$967$		−	46.0680i		−	1.48145i	−0.671809	−	0.740724i	$-0.734483\pi$
$967$		−	46.0680i		−	1.48145i	0.671809	−	0.740724i	$-0.265517\pi$
$968$		0			0
$969$	−1.61588	+	0.932931i	−0.0519097	+	0.0299701i
$970$		0			0
$971$	−10.3074	−	5.95095i	−0.330779	−	0.190975i	0.325408	−	0.945574i	$-0.394498\pi$
$971$	−10.3074	−	5.95095i	−0.330779	−	0.190975i	−0.656187	+	0.754599i	$0.727832\pi$
$972$		0			0
$973$	−43.2001	−	10.4831i	−1.38493	−	0.336071i
$974$		0			0
$975$	19.5688	+	11.2981i	0.626703	+	0.361827i
$976$		0			0
$977$	−16.1299	−	27.9379i	−0.516042	−	0.893811i	−0.999827	−	0.0186241i	$-0.994071\pi$
$977$	−16.1299	−	27.9379i	−0.516042	−	0.893811i	0.483784	−	0.875187i	$-0.339262\pi$
$978$		0			0
$979$			9.32524i			0.298036i
$980$		0			0
$981$			12.5025i			0.399175i
$982$		0			0
$983$	25.6985	+	44.5110i	0.819653	+	1.41968i	0.905938	+	0.423411i	$0.139167\pi$
$983$	25.6985	+	44.5110i	0.819653	+	1.41968i	−0.0862842	+	0.996271i	$0.527499\pi$
$984$		0			0
$985$	2.07232	+	1.19646i	0.0660297	+	0.0381223i
$986$		0			0
$987$	−7.32025	−	1.77635i	−0.233006	−	0.0565420i
$988$		0			0
$989$	31.2672	+	18.0521i	0.994240	+	0.574025i
$990$		0			0
$991$	−10.5357	+	6.08280i	−0.334678	+	0.193226i	−0.657916	−	0.753091i	$-0.728562\pi$
$991$	−10.5357	+	6.08280i	−0.334678	+	0.193226i	0.323238	+	0.946318i	$0.395229\pi$
$992$		0			0
$993$		−	21.1789i		−	0.672093i
$994$		0			0
$995$	5.34881			0.169569
$996$		0			0
$997$	7.92001	+	13.7179i	0.250829	+	0.434449i	0.963754	−	0.266791i	$-0.0859634\pi$
$997$	7.92001	+	13.7179i	0.250829	+	0.434449i	−0.712925	+	0.701240i	$0.752630\pi$
$998$		0			0
$999$	−3.73307	+	6.46587i	−0.118109	+	0.204571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bb.a.271.13		32
3.2	odd	2		2016.2.bs.c.271.8		32
4.3	odd	2		168.2.t.a.19.2	✓	32
7.2	even	3		4704.2.p.a.3919.32		32
7.3	odd	6	inner	672.2.bb.a.367.12		32
7.5	odd	6		4704.2.p.a.3919.27		32
8.3	odd	2	inner	672.2.bb.a.271.12		32
8.5	even	2		168.2.t.a.19.11	yes	32
12.11	even	2		504.2.bk.c.19.15		32
21.17	even	6		2016.2.bs.c.1711.9		32
24.5	odd	2		504.2.bk.c.19.6		32
24.11	even	2		2016.2.bs.c.271.9		32
28.3	even	6		168.2.t.a.115.11	yes	32
28.19	even	6		1176.2.p.a.979.24		32
28.23	odd	6		1176.2.p.a.979.23		32
56.3	even	6	inner	672.2.bb.a.367.13		32
56.5	odd	6		1176.2.p.a.979.21		32
56.19	even	6		4704.2.p.a.3919.31		32
56.37	even	6		1176.2.p.a.979.22		32
56.45	odd	6		168.2.t.a.115.2	yes	32
56.51	odd	6		4704.2.p.a.3919.28		32
84.59	odd	6		504.2.bk.c.451.6		32
168.59	odd	6		2016.2.bs.c.1711.8		32
168.101	even	6		504.2.bk.c.451.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.2	✓	32	4.3	odd	2
168.2.t.a.19.11	yes	32	8.5	even	2
168.2.t.a.115.2	yes	32	56.45	odd	6
168.2.t.a.115.11	yes	32	28.3	even	6
504.2.bk.c.19.6		32	24.5	odd	2
504.2.bk.c.19.15		32	12.11	even	2
504.2.bk.c.451.6		32	84.59	odd	6
504.2.bk.c.451.15		32	168.101	even	6
672.2.bb.a.271.12		32	8.3	odd	2	inner
672.2.bb.a.271.13		32	1.1	even	1	trivial
672.2.bb.a.367.12		32	7.3	odd	6	inner
672.2.bb.a.367.13		32	56.3	even	6	inner
1176.2.p.a.979.21		32	56.5	odd	6
1176.2.p.a.979.22		32	56.37	even	6
1176.2.p.a.979.23		32	28.23	odd	6
1176.2.p.a.979.24		32	28.19	even	6
2016.2.bs.c.271.8		32	3.2	odd	2
2016.2.bs.c.271.9		32	24.11	even	2
2016.2.bs.c.1711.8		32	168.59	odd	6
2016.2.bs.c.1711.9		32	21.17	even	6
4704.2.p.a.3919.27		32	7.5	odd	6
4704.2.p.a.3919.28		32	56.51	odd	6
4704.2.p.a.3919.31		32	56.19	even	6
4704.2.p.a.3919.32		32	7.2	even	3

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(0.128707 - 0.222928i) q^{5} +(-0.623918 + 2.57113i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.79412 - 3.10751i) q^{11} +4.57992 q^{13} -0.257415i q^{15} +(6.92813 - 3.99996i) q^{17} +(-0.201988 - 0.116618i) q^{19} +(0.745237 + 2.53863i) q^{21} +(5.76102 + 3.32613i) q^{23} +(2.46687 + 4.27274i) q^{25} -1.00000i q^{27} +2.80806i q^{29} +(-1.03380 - 1.79060i) q^{31} +(-3.10751 - 1.79412i) q^{33} +(0.492874 + 0.470013i) q^{35} +(-6.46587 - 3.73307i) q^{37} +(3.96632 - 2.28996i) q^{39} -4.55693i q^{41} +5.42738 q^{43} +(-0.128707 - 0.222928i) q^{45} +(-1.42355 + 2.46565i) q^{47} +(-6.22145 - 3.20835i) q^{49} +(3.99996 - 6.92813i) q^{51} +(1.93137 - 1.11508i) q^{53} -0.923668 q^{55} -0.233235 q^{57} +(-2.14701 + 1.23958i) q^{59} +(-4.44251 + 7.69466i) q^{61} +(1.91471 + 1.82590i) q^{63} +(0.589469 - 1.02099i) q^{65} +(0.867859 + 1.50318i) q^{67} +6.65225 q^{69} -8.97302i q^{71} +(-6.57828 + 3.79797i) q^{73} +(4.27274 + 2.46687i) q^{75} +(9.10921 - 2.67409i) q^{77} +(-7.51791 - 4.34047i) q^{79} +(-0.500000 - 0.866025i) q^{81} +3.79017i q^{83} -2.05930i q^{85} +(1.40403 + 2.43185i) q^{87} +(-2.25065 - 1.29941i) q^{89} +(-2.85749 + 11.7756i) q^{91} +(-1.79060 - 1.03380i) q^{93} +(-0.0519946 + 0.0300191i) q^{95} +14.6024i q^{97} -3.58824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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