LMFDB - Embedded newform 441.2.w.a.62.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			62.10
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.138369 + 0.0315817i) q^{2} +(-1.78379 + 0.859028i) q^{4} +(-0.192202 - 0.241014i) q^{5} +(0.709889 - 2.54874i) q^{7} +(0.441617 - 0.352178i) q^{8} +O(q^{10})$	\(q+(-0.138369 + 0.0315817i) q^{2} +(-1.78379 + 0.859028i) q^{4} +(-0.192202 - 0.241014i) q^{5} +(0.709889 - 2.54874i) q^{7} +(0.441617 - 0.352178i) q^{8} +(0.0342063 + 0.0272786i) q^{10} +(-3.20217 + 0.730874i) q^{11} +(0.890293 - 0.203204i) q^{13} +(-0.0177329 + 0.375084i) q^{14} +(2.41886 - 3.03315i) q^{16} +(-6.36412 - 3.06480i) q^{17} +1.38237i q^{19} +(0.549885 + 0.264811i) q^{20} +(0.419997 - 0.202260i) q^{22} +(-2.81540 - 5.84624i) q^{23} +(1.09146 - 4.78199i) q^{25} +(-0.116771 + 0.0562340i) q^{26} +(0.923142 + 5.15622i) q^{28} +(1.58724 - 3.29594i) q^{29} -8.97699i q^{31} +(-0.729059 + 1.51391i) q^{32} +(0.977386 + 0.223082i) q^{34} +(-0.750722 + 0.318779i) q^{35} +(4.12028 + 1.98422i) q^{37} +(-0.0436575 - 0.191276i) q^{38} +(-0.169759 - 0.0387464i) q^{40} +(-3.46729 - 4.34784i) q^{41} +(-2.74808 + 3.44598i) q^{43} +(5.08415 - 4.05447i) q^{44} +(0.574197 + 0.720020i) q^{46} +(1.61402 + 7.07149i) q^{47} +(-5.99211 - 3.61864i) q^{49} +0.696148i q^{50} +(-1.41354 + 1.12726i) q^{52} +(5.09945 + 10.5891i) q^{53} +(0.791613 + 0.631290i) q^{55} +(-0.584109 - 1.37557i) q^{56} +(-0.115533 + 0.506183i) q^{58} +(-5.11818 + 6.41799i) q^{59} +(-1.81339 + 3.76555i) q^{61} +(0.283509 + 1.24213i) q^{62} +(-1.67349 + 7.33205i) q^{64} +(-0.220091 - 0.175517i) q^{65} -12.5089 q^{67} +13.9850 q^{68} +(0.0938087 - 0.0678181i) q^{70} +(2.21314 + 4.59564i) q^{71} +(7.82141 + 1.78519i) q^{73} +(-0.632782 - 0.144428i) q^{74} +(-1.18749 - 2.46585i) q^{76} +(-0.410379 + 8.68032i) q^{77} +3.00380 q^{79} -1.19594 q^{80} +(0.617075 + 0.492101i) q^{82} +(2.42195 - 10.6113i) q^{83} +(0.484538 + 2.12290i) q^{85} +(0.271418 - 0.563604i) q^{86} +(-1.15673 + 1.45050i) q^{88} +(3.41674 - 14.9697i) q^{89} +(0.114097 - 2.41337i) q^{91} +(10.0442 + 8.00995i) q^{92} +(-0.446659 - 0.927498i) q^{94} +(0.333169 - 0.265694i) q^{95} +1.26073i q^{97} +(0.943403 + 0.311465i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$-1$

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 $

$2$	−0.138369	+	0.0315817i	−0.0978413	+	0.0223316i	−0.271161	−	0.962534i	$-0.587408\pi$
$2$	−0.138369	+	0.0315817i	−0.0978413	+	0.0223316i	0.173320	+	0.984866i	$0.444551\pi$
$3$		0			0
$3$		0			0
$4$	−1.78379	+	0.859028i	−0.891895	+	0.429514i
$5$	−0.192202	−	0.241014i	−0.0859553	−	0.107785i	0.736994	−	0.675899i	$-0.236244\pi$
$5$	−0.192202	−	0.241014i	−0.0859553	−	0.107785i	−0.822950	+	0.568115i	$0.807673\pi$
$6$		0			0
$7$	0.709889	−	2.54874i	0.268313	−	0.963332i
$7$	0.709889	−	2.54874i	0.268313	−	0.963332i
$8$	0.441617	−	0.352178i	0.156135	−	0.124514i
$9$		0			0
$10$	0.0342063	+	0.0272786i	0.0108170	+	0.00862626i
$11$	−3.20217	+	0.730874i	−0.965490	+	0.220367i	−0.676072	−	0.736836i	$-0.736319\pi$
$11$	−3.20217	+	0.730874i	−0.965490	+	0.220367i	−0.289418	+	0.957203i	$0.593462\pi$
$12$		0			0
$13$	0.890293	−	0.203204i	0.246923	−	0.0563585i	−0.0972680	−	0.995258i	$-0.531010\pi$
$13$	0.890293	−	0.203204i	0.246923	−	0.0563585i	0.344191	+	0.938900i	$0.388153\pi$
$14$	−0.0177329	+	0.375084i	−0.00473930	+	0.100246i
$15$		0			0
$16$	2.41886	−	3.03315i	0.604714	−	0.758288i
$17$	−6.36412	−	3.06480i	−1.54353	−	0.743323i	−0.547883	−	0.836555i	$-0.684566\pi$
$17$	−6.36412	−	3.06480i	−1.54353	−	0.743323i	−0.995644	+	0.0932318i	$0.970280\pi$
$18$		0			0
$19$			1.38237i			0.317137i	0.987348	+	0.158568i	$0.0506878\pi$
$19$			1.38237i			0.317137i	−0.987348	+	0.158568i	$0.949312\pi$
$20$	0.549885	+	0.264811i	0.122958	+	0.0592135i
$21$		0			0
$22$	0.419997	−	0.202260i	0.0895436	−	0.0431219i
$23$	−2.81540	−	5.84624i	−0.587051	−	1.21902i	−0.957031	−	0.289985i	$-0.906350\pi$
$23$	−2.81540	−	5.84624i	−0.587051	−	1.21902i	0.369980	−	0.929040i	$-0.379365\pi$
$24$		0			0
$25$	1.09146	−	4.78199i	0.218292	−	0.956399i
$26$	−0.116771	+	0.0562340i	−0.0229007	+	0.0110284i
$27$		0			0
$28$	0.923142	+	5.15622i	0.174458	+	0.974435i
$29$	1.58724	−	3.29594i	0.294743	−	0.612041i	−0.700034	−	0.714110i	$-0.746832\pi$
$29$	1.58724	−	3.29594i	0.294743	−	0.612041i	0.994777	+	0.102068i	$0.0325461\pi$
$30$		0			0
$31$		−	8.97699i		−	1.61231i	−0.591701	−	0.806157i	$-0.701544\pi$
$31$		−	8.97699i		−	1.61231i	0.591701	−	0.806157i	$-0.298456\pi$
$32$	−0.729059	+	1.51391i	−0.128881	+	0.267623i
$33$		0			0
$34$	0.977386	+	0.223082i	0.167620	+	0.0382583i
$35$	−0.750722	+	0.318779i	−0.126895	+	0.0538835i
$36$		0			0
$37$	4.12028	+	1.98422i	0.677370	+	0.326204i	0.740746	−	0.671786i	$-0.234472\pi$
$37$	4.12028	+	1.98422i	0.677370	+	0.326204i	−0.0633760	+	0.997990i	$0.520187\pi$
$38$	−0.0436575	−	0.191276i	−0.00708218	−	0.0310291i
$39$		0			0
$40$	−0.169759	−	0.0387464i	−0.0268413	−	0.00612635i
$41$	−3.46729	−	4.34784i	−0.541499	−	0.679018i	0.433519	−	0.901144i	$-0.357272\pi$
$41$	−3.46729	−	4.34784i	−0.541499	−	0.679018i	−0.975018	+	0.222126i	$0.928700\pi$
$42$		0			0
$43$	−2.74808	+	3.44598i	−0.419078	+	0.525507i	−0.945896	−	0.324471i	$-0.894814\pi$
$43$	−2.74808	+	3.44598i	−0.419078	+	0.525507i	0.526818	+	0.849978i	$0.323385\pi$
$44$	5.08415	−	4.05447i	0.766465	−	0.611235i
$45$		0			0
$46$	0.574197	+	0.720020i	0.0846607	+	0.106161i
$47$	1.61402	+	7.07149i	0.235429	+	1.03148i	0.945057	+	0.326906i	$0.106006\pi$
$47$	1.61402	+	7.07149i	0.235429	+	1.03148i	−0.709628	+	0.704577i	$0.751137\pi$
$48$		0			0
$49$	−5.99211	−	3.61864i	−0.856016	−	0.516949i
$50$			0.696148i			0.0984501i
$51$		0			0
$52$	−1.41354	+	1.12726i	−0.196022	+	0.156323i
$53$	5.09945	+	10.5891i	0.700463	+	1.45453i	0.882052	+	0.471151i	$0.156161\pi$
$53$	5.09945	+	10.5891i	0.700463	+	1.45453i	−0.181590	+	0.983374i	$0.558124\pi$
$54$		0			0
$55$	0.791613	+	0.631290i	0.106741	+	0.0851232i
$56$	−0.584109	−	1.37557i	−0.0780548	−	0.183818i
$57$		0			0
$58$	−0.115533	+	0.506183i	−0.0151702	+	0.0664650i
$59$	−5.11818	+	6.41799i	−0.666330	+	0.835551i	−0.994016	−	0.109235i	$-0.965160\pi$
$59$	−5.11818	+	6.41799i	−0.666330	+	0.835551i	0.327686	+	0.944787i	$0.393731\pi$
$60$		0			0
$61$	−1.81339	+	3.76555i	−0.232181	+	0.482129i	−0.984211	−	0.177000i	$-0.943361\pi$
$61$	−1.81339	+	3.76555i	−0.232181	+	0.482129i	0.752030	+	0.659129i	$0.229075\pi$
$62$	0.283509	+	1.24213i	0.0360056	+	0.157751i
$63$		0			0
$64$	−1.67349	+	7.33205i	−0.209187	+	0.916507i
$65$	−0.220091	−	0.175517i	−0.0272989	−	0.0217702i
$66$		0			0
$67$	−12.5089			−1.52820			−0.764102	−	0.645096i	$-0.776817\pi$
$67$	−12.5089			−1.52820			−0.764102	+	0.645096i	$0.776817\pi$
$68$	13.9850			1.69593
$69$		0			0
$70$	0.0938087	−	0.0678181i	0.0112123	−	0.00810581i
$71$	2.21314	+	4.59564i	0.262652	+	0.545402i	0.990034	−	0.140831i	$-0.0449774\pi$
$71$	2.21314	+	4.59564i	0.262652	+	0.545402i	−0.727382	+	0.686233i	$0.759263\pi$
$72$		0			0
$73$	7.82141	+	1.78519i	0.915427	+	0.208940i	0.654186	−	0.756333i	$-0.273011\pi$
$73$	7.82141	+	1.78519i	0.915427	+	0.208940i	0.261241	+	0.965274i	$0.415868\pi$
$74$	−0.632782	−	0.144428i	−0.0735594	−	0.0167895i
$75$		0			0
$76$	−1.18749	−	2.46585i	−0.136215	−	0.282853i
$77$	−0.410379	+	8.68032i	−0.0467670	+	0.989214i
$78$		0			0
$79$	3.00380			0.337954			0.168977	−	0.985620i	$-0.445954\pi$
$79$	3.00380			0.337954			0.168977	+	0.985620i	$0.445954\pi$
$80$	−1.19594			−0.133710
$81$		0			0
$82$	0.617075	+	0.492101i	0.0681446	+	0.0543435i
$83$	2.42195	−	10.6113i	0.265844	−	1.16474i	−0.648955	−	0.760827i	$-0.724794\pi$
$83$	2.42195	−	10.6113i	0.265844	−	1.16474i	0.914798	−	0.403911i	$-0.132349\pi$
$84$		0			0
$85$	0.484538	+	2.12290i	0.0525556	+	0.230261i
$86$	0.271418	−	0.563604i	0.0292677	−	0.0607750i
$87$		0			0
$88$	−1.15673	+	1.45050i	−0.123308	+	0.154624i
$89$	3.41674	−	14.9697i	0.362174	−	1.58679i	−0.385492	−	0.922711i	$-0.625968\pi$
$89$	3.41674	−	14.9697i	0.362174	−	1.58679i	0.747666	−	0.664075i	$-0.231174\pi$
$90$		0			0
$91$	0.114097	−	2.41337i	0.0119606	−	0.252990i
$92$	10.0442	+	8.00995i	1.04718	+	0.835095i
$93$		0			0
$94$	−0.446659	−	0.927498i	−0.0460694	−	0.0956641i
$95$	0.333169	−	0.265694i	0.0341824	−	0.0272596i
$96$		0			0
$97$			1.26073i			0.128008i	0.997950	+	0.0640040i	$0.0203870\pi$
$97$			1.26073i			0.128008i	−0.997950	+	0.0640040i	$0.979613\pi$
$98$	0.943403	+	0.311465i	0.0952981	+	0.0314627i
$99$		0			0
$100$	2.16093	+	9.46766i	0.216093	+	0.946766i
$101$	−5.79383	−	7.26523i	−0.576507	−	0.722917i	0.405005	−	0.914314i	$-0.367270\pi$
$101$	−5.79383	−	7.26523i	−0.576507	−	0.722917i	−0.981513	+	0.191397i	$0.938698\pi$
$102$		0			0
$103$	−0.261967	+	0.208911i	−0.0258123	+	0.0205847i	−0.636311	−	0.771433i	$-0.719540\pi$
$103$	−0.261967	+	0.208911i	−0.0258123	+	0.0205847i	0.610499	+	0.792017i	$0.290969\pi$
$104$	0.321604	−	0.403279i	0.0315359	−	0.0395448i
$105$		0			0
$106$	−1.04003	−	1.30415i	−0.101016	−	0.126670i
$107$	1.52607	+	0.348316i	0.147531	+	0.0336730i	0.295649	−	0.955297i	$-0.404464\pi$
$107$	1.52607	+	0.348316i	0.147531	+	0.0336730i	−0.148118	+	0.988970i	$0.547321\pi$
$108$		0			0
$109$	1.09437	+	4.79473i	0.104821	+	0.459252i	0.999911	+	0.0133651i	$0.00425438\pi$
$109$	1.09437	+	4.79473i	0.104821	+	0.459252i	−0.895089	+	0.445887i	$0.852888\pi$
$110$	−0.129472	−	0.0623502i	−0.0123446	−	0.00594486i
$111$		0			0
$112$	−6.01358	−	8.31823i	−0.568230	−	0.785999i
$113$	10.0382	+	2.29115i	0.944314	+	0.215533i	0.666841	−	0.745200i	$-0.267646\pi$
$113$	10.0382	+	2.29115i	0.944314	+	0.215533i	0.277473	+	0.960734i	$0.410503\pi$
$114$		0			0
$115$	−0.867897	+	1.80221i	−0.0809318	+	0.168057i
$116$			7.24275i			0.672473i
$117$		0			0
$118$	0.505504	−	1.04969i	0.0465354	−	0.0966317i
$119$	−12.3292	+	14.0448i	−1.13022	+	1.28749i
$120$		0			0
$121$	−0.190959	+	0.0919611i	−0.0173599	+	0.00836010i
$122$	0.131994	−	0.578303i	0.0119502	−	0.0523571i
$123$		0			0
$124$	7.71148	+	16.0131i	0.692511	+	1.43801i
$125$	−2.75100	+	1.32481i	−0.246057	+	0.118495i
$126$		0			0
$127$	−0.659753	−	0.317721i	−0.0585437	−	0.0281931i	0.404383	−	0.914590i	$-0.367486\pi$
$127$	−0.659753	−	0.317721i	−0.0585437	−	0.0281931i	−0.462927	+	0.886397i	$0.653201\pi$
$128$		−	4.42800i		−	0.391383i
$129$		0			0
$130$	0.0359968	+	0.0173351i	0.00315712	+	0.00152039i
$131$	−2.74720	+	3.44488i	−0.240024	+	0.300981i	−0.887223	−	0.461340i	$-0.847369\pi$
$131$	−2.74720	+	3.44488i	−0.240024	+	0.300981i	0.647199	+	0.762321i	$0.275940\pi$
$132$		0			0
$133$	3.52329	+	0.981327i	0.305508	+	0.0850919i
$134$	1.73084	−	0.395052i	0.149521	−	0.0341273i
$135$		0			0
$136$	−3.88986	+	0.887835i	−0.333553	+	0.0761312i
$137$	8.10295	+	6.46189i	0.692282	+	0.552076i	0.905196	−	0.424995i	$-0.139724\pi$
$137$	8.10295	+	6.46189i	0.692282	+	0.552076i	−0.212914	+	0.977071i	$0.568295\pi$
$138$		0			0
$139$	13.4286	−	10.7089i	1.13900	−	0.908320i	0.142324	−	0.989820i	$-0.454542\pi$
$139$	13.4286	−	10.7089i	1.13900	−	0.908320i	0.996673	+	0.0814998i	$0.0259710\pi$
$140$	1.06529	−	1.21353i	0.0900334	−	0.102562i
$141$		0			0
$142$	−0.451367	−	0.565997i	−0.0378779	−	0.0474974i
$143$	−2.70235	+	1.30138i	−0.225982	+	0.108827i
$144$		0			0
$145$	−1.09944	+	0.250939i	−0.0913033	+	0.0208394i
$146$	−1.13862			−0.0942326
$147$		0			0
$148$	−9.05421			−0.744251
$149$	21.7591	−	4.96636i	1.78257	−	0.406860i	0.801110	−	0.598517i	$-0.204243\pi$
$149$	21.7591	−	4.96636i	1.78257	−	0.406860i	0.981462	+	0.191657i	$0.0613861\pi$
$150$		0			0
$151$	−11.8815	+	5.72183i	−0.966903	+	0.465636i	−0.849581	−	0.527458i	$-0.823145\pi$
$151$	−11.8815	+	5.72183i	−0.966903	+	0.465636i	−0.117322	+	0.993094i	$0.537431\pi$
$152$	0.486839	+	0.610476i	0.0394878	+	0.0495162i
$153$		0			0
$154$	−0.217356	−	1.21404i	−0.0175150	−	0.0978304i
$155$	−2.16358	+	1.72539i	−0.173783	+	0.138587i
$156$		0			0
$157$	−12.6316	−	10.0734i	−1.00811	−	0.803943i	−0.0274451	−	0.999623i	$-0.508737\pi$
$157$	−12.6316	−	10.0734i	−1.00811	−	0.803943i	−0.980668	+	0.195680i	$0.937309\pi$
$158$	−0.415632	+	0.0948652i	−0.0330659	+	0.00754707i
$159$		0			0
$160$	0.504999	−	0.115263i	0.0399236	−	0.00911231i
$161$	−16.8991	+	3.02553i	−1.33184	+	0.238445i
$162$		0			0
$163$	1.23296	−	1.54609i	0.0965732	−	0.121099i	−0.731197	−	0.682167i	$-0.761038\pi$
$163$	1.23296	−	1.54609i	0.0965732	−	0.121099i	0.827770	+	0.561068i	$0.189609\pi$
$164$	9.91982	+	4.77713i	0.774608	+	0.373031i
$165$		0			0
$166$			1.54475i			0.119896i
$167$	−19.2265	−	9.25902i	−1.48779	−	0.716484i	−0.499117	−	0.866535i	$-0.666342\pi$
$167$	−19.2265	−	9.25902i	−1.48779	−	0.716484i	−0.988678	+	0.150051i	$0.952056\pi$
$168$		0			0
$169$	−10.9613	+	5.27867i	−0.843174	+	0.406051i
$170$	−0.134090	−	0.278440i	−0.0102842	−	0.0213554i
$171$		0			0
$172$	1.94180	−	8.50758i	0.148061	−	0.648697i
$173$	12.3806	−	5.96218i	0.941279	−	0.453296i	0.100659	−	0.994921i	$-0.467905\pi$
$173$	12.3806	−	5.96218i	0.941279	−	0.453296i	0.840620	+	0.541625i	$0.182191\pi$
$174$		0			0
$175$	−11.4132	−	6.17653i	−0.862759	−	0.466901i
$176$	−5.52874	+	11.4805i	−0.416744	+	0.865378i
$177$		0			0
$178$			2.17924i			0.163341i
$179$	3.54189	−	7.35481i	0.264733	−	0.549724i	−0.725652	−	0.688062i	$-0.758462\pi$
$179$	3.54189	−	7.35481i	0.264733	−	0.549724i	0.990385	+	0.138338i	$0.0441760\pi$
$180$		0			0
$181$	13.9311	+	3.17968i	1.03549	+	0.236344i	0.706295	−	0.707918i	$-0.250365\pi$
$181$	13.9311	+	3.17968i	1.03549	+	0.236344i	0.329196	+	0.944262i	$0.393222\pi$
$182$	0.0604311	+	0.337538i	0.00447945	+	0.0250200i
$183$		0			0
$184$	−3.30224	−	1.59028i	−0.243444	−	0.117237i
$185$	−0.313701	−	1.37441i	−0.0230638	−	0.101049i
$186$		0			0
$187$	22.6190	+	5.16263i	1.65406	+	0.377529i
$188$	−8.95368	−	11.2276i	−0.653014	−	0.818854i
$189$		0			0
$190$	−0.0377091	+	0.0472857i	−0.00273570	+	0.00343046i
$191$	2.02065	−	1.61142i	0.146209	−	0.116598i	−0.547654	−	0.836705i	$-0.684479\pi$
$191$	2.02065	−	1.61142i	0.146209	−	0.116598i	0.693863	+	0.720107i	$0.255907\pi$
$192$		0			0
$193$	8.62528	+	10.8158i	0.620861	+	0.778535i	0.988465	−	0.151447i	$-0.0483933\pi$
$193$	8.62528	+	10.8158i	0.620861	+	0.778535i	−0.367604	+	0.929982i	$0.619822\pi$
$194$	−0.0398161	−	0.174446i	−0.00285863	−	0.0125245i
$195$		0			0
$196$	13.7972	+	1.30750i	0.985513	+	0.0933929i
$197$			6.73817i			0.480075i	0.970764	+	0.240037i	$0.0771597\pi$
$197$			6.73817i			0.480075i	−0.970764	+	0.240037i	$0.922840\pi$
$198$		0			0
$199$	18.8469	−	15.0299i	1.33602	−	1.06544i	0.344050	−	0.938951i	$-0.388201\pi$
$199$	18.8469	−	15.0299i	1.33602	−	1.06544i	0.991968	−	0.126487i	$-0.0403703\pi$
$200$	−1.20210	−	2.49619i	−0.0850016	−	0.176508i
$201$		0			0
$202$	1.03113	+	0.822300i	0.0725502	+	0.0578568i
$203$	−7.27372	−	6.38522i	−0.510515	−	0.448154i
$204$		0			0
$205$	−0.381469	+	1.67133i	−0.0266430	+	0.116730i
$206$	0.0296502	−	0.0371801i	0.00206582	−	0.00259046i
$207$		0			0
$208$	1.53714	−	3.19191i	0.106582	−	0.221319i
$209$	−1.01034	−	4.42657i	−0.0698864	−	0.306192i
$210$		0			0
$211$	2.04736	−	8.97005i	0.140946	−	0.617524i	−0.854271	−	0.519829i	$-0.825996\pi$
$211$	2.04736	−	8.97005i	0.140946	−	0.617524i	0.995216	−	0.0976953i	$-0.0311471\pi$
$212$	−18.1927	−	14.5082i	−1.24948	−	0.996425i
$213$		0			0
$214$	−0.222161			−0.0151866
$215$	1.35871			0.0926635
$216$		0			0
$217$	−22.8800	−	6.37267i	−1.55319	−	0.432605i
$218$	−0.302852	−	0.628878i	−0.0205117	−	0.0425930i
$219$		0			0
$220$	−1.95437	−	0.446071i	−0.131763	−	0.0300741i
$221$	−6.28871	−	1.43536i	−0.423025	−	0.0965526i
$222$		0			0
$223$	−5.22344	−	10.8466i	−0.349787	−	0.726341i	0.649638	−	0.760244i	$-0.274921\pi$
$223$	−5.22344	−	10.8466i	−0.349787	−	0.726341i	−0.999425	+	0.0339029i	$0.989206\pi$
$224$	3.34100	+	2.93289i	0.223230	+	0.195962i
$225$		0			0
$226$	−1.46133			−0.0972061
$227$	−25.7976			−1.71224			−0.856122	−	0.516774i	$-0.827133\pi$
$227$	−25.7976			−1.71224			−0.856122	+	0.516774i	$0.827133\pi$
$228$		0			0
$229$	−10.5459	−	8.41010i	−0.696895	−	0.555755i	0.209696	−	0.977767i	$-0.432753\pi$
$229$	−10.5459	−	8.41010i	−0.696895	−	0.555755i	−0.906590	+	0.422012i	$0.861324\pi$
$230$	0.0631729	−	0.276778i	0.00416550	−	0.0182502i
$231$		0			0
$232$	−0.459804	−	2.01453i	−0.0301876	−	0.132261i
$233$	−2.64559	+	5.49362i	−0.173318	+	0.359899i	−0.969475	−	0.245192i	$-0.921149\pi$
$233$	−2.64559	+	5.49362i	−0.173318	+	0.359899i	0.796156	+	0.605091i	$0.206863\pi$
$234$		0			0
$235$	1.39411	−	1.74815i	0.0909415	−	0.114037i
$236$	3.61652	−	15.8450i	0.235415	−	1.03142i
$237$		0			0
$238$	1.26241	−	2.33274i	0.0818301	−	0.151209i
$239$	−6.92016	−	5.51864i	−0.447628	−	0.356971i	0.373582	−	0.927597i	$-0.378129\pi$
$239$	−6.92016	−	5.51864i	−0.447628	−	0.356971i	−0.821210	+	0.570626i	$0.806701\pi$
$240$		0			0
$241$	4.13861	+	8.59392i	0.266591	+	0.553583i	0.990694	−	0.136110i	$-0.0434600\pi$
$241$	4.13861	+	8.59392i	0.266591	+	0.553583i	−0.724102	+	0.689693i	$0.757746\pi$
$242$	0.0235184	−	0.0187553i	0.00151182	−	0.00120564i
$243$		0			0
$244$		−	8.27469i		−	0.529733i
$245$	0.279554	+	2.13969i	0.0178601	+	0.136700i
$246$		0			0
$247$	0.280902	+	1.23071i	0.0178734	+	0.0783083i
$248$	−3.16149	−	3.96439i	−0.200755	−	0.251739i
$249$		0			0
$250$	0.338813	−	0.270194i	0.0214284	−	0.0170886i
$251$	11.4848	−	14.4015i	0.724913	−	0.909012i	−0.273692	−	0.961817i	$-0.588245\pi$
$251$	11.4848	−	14.4015i	0.724913	−	0.909012i	0.998605	+	0.0528055i	$0.0168163\pi$
$252$		0			0
$253$	13.2882	+	16.6629i	0.835425	+	1.04759i
$254$	0.101323	+	0.0231264i	0.00635759	+	0.00145108i
$255$		0			0
$256$	−3.20714	−	14.0514i	−0.200446	−	0.878213i
$257$	−6.48591	−	3.12345i	−0.404580	−	0.194835i	0.220516	−	0.975383i	$-0.429226\pi$
$257$	−6.48591	−	3.12345i	−0.404580	−	0.194835i	−0.625096	+	0.780548i	$0.714940\pi$
$258$		0			0
$259$	7.98220	−	9.09293i	0.495990	−	0.565007i
$260$	0.543369	+	0.124020i	0.0336983	+	0.00769142i
$261$		0			0
$262$	0.271331	−	0.563425i	0.0167629	−	0.0348085i
$263$			20.8350i			1.28474i	0.766393	+	0.642372i	$0.222050\pi$
$263$			20.8350i			1.28474i	−0.766393	+	0.642372i	$0.777950\pi$
$264$		0			0
$265$	1.57200	−	3.26428i	0.0965669	−	0.200523i
$266$	−0.518504	−	0.0245133i	−0.0317915	−	0.00150301i
$267$		0			0
$268$	22.3132	−	10.7455i	1.36300	−	0.656384i
$269$	3.46371	−	15.1755i	0.211186	−	0.925268i	−0.752576	−	0.658505i	$-0.771189\pi$
$269$	3.46371	−	15.1755i	0.211186	−	0.925268i	0.963762	−	0.266762i	$-0.0859539\pi$
$270$		0			0
$271$	−6.68504	−	13.8816i	−0.406087	−	0.843248i	−0.999271	−	0.0381813i	$-0.987844\pi$
$271$	−6.68504	−	13.8816i	−0.406087	−	0.843248i	0.593184	−	0.805067i	$-0.297871\pi$
$272$	−24.6899	+	11.8900i	−1.49705	+	0.720939i
$273$		0			0
$274$	−1.32527	−	0.638217i	−0.0800625	−	0.0385561i
$275$			16.1105i			0.971497i
$276$		0			0
$277$	−4.77881	−	2.30135i	−0.287131	−	0.138275i	0.284775	−	0.958594i	$-0.408081\pi$
$277$	−4.77881	−	2.30135i	−0.287131	−	0.138275i	−0.571905	+	0.820320i	$0.693796\pi$
$278$	−1.51989	+	1.90588i	−0.0911568	+	0.114307i
$279$		0			0
$280$	−0.219265	+	0.405166i	−0.0131036	+	0.0242133i
$281$	13.0478	−	2.97807i	0.778365	−	0.177657i	0.185160	−	0.982708i	$-0.440720\pi$
$281$	13.0478	−	2.97807i	0.778365	−	0.177657i	0.593205	+	0.805052i	$0.297862\pi$
$282$		0			0
$283$	−0.244198	+	0.0557366i	−0.0145161	+	0.00331319i	−0.229773	−	0.973244i	$-0.573798\pi$
$283$	−0.244198	+	0.0557366i	−0.0145161	+	0.00331319i	0.215257	+	0.976557i	$0.430941\pi$
$284$	−7.89556	−	6.29650i	−0.468515	−	0.373628i
$285$		0			0
$286$	0.332820	−	0.265415i	0.0196801	−	0.0156943i
$287$	−13.5429	+	5.75071i	−0.799411	+	0.339454i
$288$		0			0
$289$	20.5098	+	25.7184i	1.20646	+	1.51285i
$290$	0.144202	−	0.0694443i	0.00846786	−	0.00407791i
$291$		0			0
$292$	−15.4853	+	3.53441i	−0.906207	+	0.206836i
$293$	29.6370			1.73141			0.865705	−	0.500554i	$-0.166870\pi$
$293$	29.6370			1.73141			0.865705	+	0.500554i	$0.166870\pi$
$294$		0			0
$295$	2.53055			0.147334
$296$	2.51838	−	0.574804i	0.146378	−	0.0334098i
$297$		0			0
$298$	−2.85392	+	1.37438i	−0.165323	+	0.0796155i
$299$	−3.69451	−	4.63276i	−0.213659	−	0.267920i
$300$		0			0
$301$	6.83207	+	9.45039i	0.393794	+	0.544711i
$302$	1.46332	−	1.16696i	0.0842047	−	0.0671510i
$303$		0			0
$304$	4.19293	+	3.34375i	0.240481	+	0.191777i
$305$	1.25608	−	0.286693i	0.0719232	−	0.0164160i
$306$		0			0
$307$	−18.3270	+	4.18302i	−1.04598	+	0.238737i	−0.710782	−	0.703412i	$-0.751659\pi$
$307$	−18.3270	+	4.18302i	−1.04598	+	0.238737i	−0.335194	+	0.942149i	$0.608802\pi$
$308$	−6.72460	−	15.8364i	−0.383170	−	0.902362i
$309$		0			0
$310$	0.244880	−	0.307070i	0.0139082	−	0.0174404i
$311$	3.01117	+	1.45010i	0.170748	+	0.0822277i	0.517305	−	0.855801i	$-0.326935\pi$
$311$	3.01117	+	1.45010i	0.170748	+	0.0822277i	−0.346558	+	0.938029i	$0.612649\pi$
$312$		0			0
$313$			12.6437i			0.714664i	0.933977	+	0.357332i	$0.116314\pi$
$313$			12.6437i			0.714664i	−0.933977	+	0.357332i	$0.883686\pi$
$314$	2.06595	+	0.994911i	0.116588	+	0.0561460i
$315$		0			0
$316$	−5.35815	+	2.58035i	−0.301419	+	0.145156i
$317$	−4.29054	−	8.90940i	−0.240981	−	0.500402i	0.745041	−	0.667019i	$-0.232430\pi$
$317$	−4.29054	−	8.90940i	−0.240981	−	0.500402i	−0.986022	+	0.166617i	$0.946716\pi$
$318$		0			0
$319$	−2.67370	+	11.7142i	−0.149698	+	0.655871i
$320$	2.08877	−	1.00590i	0.116766	−	0.0562315i
$321$		0			0
$322$	2.24276	−	0.952342i	0.124984	−	0.0530719i
$323$	4.23668	−	8.79756i	0.235735	−	0.489509i
$324$		0			0
$325$		−	4.47916i		−	0.248459i
$326$	−0.121775	+	0.252869i	−0.00674451	+	0.0140051i
$327$		0			0
$328$	−3.06242	−	0.698978i	−0.169094	−	0.0385946i
$329$	19.1691	+	0.906259i	1.05683	+	0.0499636i
$330$		0			0
$331$	−22.1135	−	10.6493i	−1.21547	−	0.585340i	−0.287423	−	0.957804i	$-0.592799\pi$
$331$	−22.1135	−	10.6493i	−1.21547	−	0.585340i	−0.928047	+	0.372464i	$0.878513\pi$
$332$	4.79512	+	21.0088i	0.263166	+	1.15301i
$333$		0			0
$334$	2.95276	+	0.673949i	0.161568	+	0.0368769i
$335$	2.40423	+	3.01481i	0.131357	+	0.164717i
$336$		0			0
$337$	7.46969	−	9.36670i	0.406900	−	0.510236i	−0.535587	−	0.844480i	$-0.679909\pi$
$337$	7.46969	−	9.36670i	0.406900	−	0.510236i	0.942487	+	0.334244i	$0.108481\pi$
$338$	1.34998	−	1.07658i	0.0734295	−	0.0585581i
$339$		0			0
$340$	−2.68794	−	3.37058i	−0.145774	−	0.182795i
$341$	6.56104	+	28.7458i	0.355300	+	1.55667i
$342$		0			0
$343$	−13.4767	+	12.7035i	−0.727673	+	0.685924i
$344$			2.48961i			0.134231i
$345$		0			0
$346$	−1.52479	+	1.21598i	−0.0819731	+	0.0653714i
$347$	11.8882	+	24.6862i	0.638194	+	1.32522i	0.929581	+	0.368618i	$0.120169\pi$
$347$	11.8882	+	24.6862i	0.638194	+	1.32522i	−0.291387	+	0.956605i	$0.594117\pi$
$348$		0			0
$349$	12.9684	+	10.3419i	0.694181	+	0.553591i	0.905771	−	0.423768i	$-0.139293\pi$
$349$	12.9684	+	10.3419i	0.694181	+	0.553591i	−0.211590	+	0.977359i	$0.567864\pi$
$350$	1.77430	+	0.494188i	0.0948401	+	0.0264154i
$351$		0			0
$352$	1.22809	−	5.38063i	0.0654577	−	0.286789i
$353$	1.73839	−	2.17988i	0.0925253	−	0.116023i	−0.733414	−	0.679783i	$-0.762074\pi$
$353$	1.73839	−	2.17988i	0.0925253	−	0.116023i	0.825939	+	0.563760i	$0.190646\pi$
$354$		0			0
$355$	0.682241	−	1.41669i	0.0362096	−	0.0751900i
$356$	6.76465	+	29.6379i	0.358526	+	1.57080i
$357$		0			0
$358$	−0.257809	+	1.12953i	−0.0136256	+	0.0596977i
$359$	−12.0446	−	9.60524i	−0.635689	−	0.506945i	0.251797	−	0.967780i	$-0.418979\pi$
$359$	−12.0446	−	9.60524i	−0.635689	−	0.506945i	−0.887486	+	0.460835i	$0.847550\pi$
$360$		0			0
$361$	17.0891			0.899424
$362$	−2.02805			−0.106592
$363$		0			0
$364$	1.86963	+	4.40296i	0.0979952	+	0.230778i
$365$	−1.07304	−	2.22818i	−0.0561653	−	0.116628i
$366$		0			0
$367$	−23.7121	−	5.41212i	−1.23776	−	0.282510i	−0.446942	−	0.894563i	$-0.647487\pi$
$367$	−23.7121	−	5.41212i	−1.23776	−	0.282510i	−0.790817	+	0.612053i	$0.790344\pi$
$368$	−24.5426	−	5.60168i	−1.27937	−	0.292008i
$369$		0			0
$370$	0.0868127	+	0.180268i	0.00451318	+	0.00937171i
$371$	30.6089	−	5.48005i	1.58913	−	0.284510i
$372$		0			0
$373$	−24.0321			−1.24433			−0.622166	−	0.782885i	$-0.713747\pi$
$373$	−24.0321			−1.24433			−0.622166	+	0.782885i	$0.713747\pi$
$374$	−3.29280			−0.170267
$375$		0			0
$376$	3.20320	+	2.55446i	0.165192	+	0.131736i
$377$	0.743363	−	3.25689i	0.0382852	−	0.167738i
$378$		0			0
$379$	3.33432	+	14.6086i	0.171273	+	0.750394i	0.985476	+	0.169815i	$0.0543169\pi$
$379$	3.33432	+	14.6086i	0.171273	+	0.750394i	−0.814203	+	0.580580i	$0.802826\pi$
$380$	−0.366065	+	0.760143i	−0.0187788	+	0.0389945i
$381$		0			0
$382$	−0.228703	+	0.286785i	−0.0117015	+	0.0146732i
$383$	1.47341	−	6.45544i	0.0752878	−	0.329857i	−0.923232	−	0.384242i	$-0.874463\pi$
$383$	1.47341	−	6.45544i	0.0752878	−	0.329857i	0.998520	+	0.0543850i	$0.0173198\pi$
$384$		0			0
$385$	2.17095	−	1.56947i	0.110642	−	0.0799874i
$386$	−1.53505	−	1.22416i	−0.0781319	−	0.0623081i
$387$		0			0
$388$	−1.08300	−	2.24888i	−0.0549812	−	0.114170i
$389$	23.3312	−	18.6060i	1.18294	−	0.943363i	0.183725	−	0.982978i	$-0.441184\pi$
$389$	23.3312	−	18.6060i	1.18294	−	0.943363i	0.999215	+	0.0396147i	$0.0126131\pi$
$390$		0			0
$391$			45.8348i			2.31797i
$392$	−3.92062	+	0.512236i	−0.198021	+	0.0258718i
$393$		0			0
$394$	−0.212803	−	0.932351i	−0.0107209	−	0.0469712i
$395$	−0.577336	−	0.723957i	−0.0290489	−	0.0364262i
$396$		0			0
$397$	6.45231	−	5.14554i	0.323832	−	0.258247i	−0.448057	−	0.894005i	$-0.647884\pi$
$397$	6.45231	−	5.14554i	0.323832	−	0.258247i	0.771889	+	0.635758i	$0.219312\pi$
$398$	−2.13314	+	2.67488i	−0.106925	+	0.134079i
$399$		0			0
$400$	−11.8644	−	14.8775i	−0.593221	−	0.743876i
$401$	17.5696	+	4.01014i	0.877382	+	0.200257i	0.637412	−	0.770523i	$-0.280005\pi$
$401$	17.5696	+	4.01014i	0.877382	+	0.200257i	0.239971	+	0.970780i	$0.422862\pi$
$402$		0			0
$403$	−1.82416	−	7.99215i	−0.0908677	−	0.398117i
$404$	16.5760	+	7.98258i	0.824687	+	0.397148i
$405$		0			0
$406$	1.20811	+	0.653796i	0.0599575	+	0.0324474i
$407$	−14.6440	−	3.34241i	−0.725878	−	0.165677i
$408$		0			0
$409$	4.63554	−	9.62580i	0.229213	−	0.475965i	−0.754364	−	0.656457i	$-0.772055\pi$
$409$	4.63554	−	9.62580i	0.229213	−	0.475965i	0.983577	+	0.180491i	$0.0577688\pi$
$410$		−	0.243306i		−	0.0120160i
$411$		0			0
$412$	0.287833	−	0.597690i	0.0141805	−	0.0294461i
$413$	12.7244	+	17.6009i	0.626128	+	0.866086i
$414$		0			0
$415$	−3.02296	+	1.45578i	−0.148391	+	0.0714615i
$416$	−0.341445	+	1.49597i	−0.0167407	+	0.0733459i
$417$		0			0
$418$	0.279597	+	0.580590i	0.0136756	+	0.0283976i
$419$	−3.14076	+	1.51251i	−0.153436	+	0.0738910i	−0.509026	−	0.860751i	$-0.669994\pi$
$419$	−3.14076	+	1.51251i	−0.153436	+	0.0738910i	0.355590	+	0.934642i	$0.384280\pi$
$420$		0			0
$421$	−3.00203	−	1.44570i	−0.146310	−	0.0704593i	0.359296	−	0.933224i	$-0.383017\pi$
$421$	−3.00203	−	1.44570i	−0.146310	−	0.0704593i	−0.505606	+	0.862764i	$0.668731\pi$
$422$			1.30583i			0.0635669i
$423$		0			0
$424$	5.98125	+	2.88042i	0.290475	+	0.139885i
$425$	−21.6020	+	27.0881i	−1.04785	+	1.31397i
$426$		0			0
$427$	8.31008	+	7.29498i	0.402153	+	0.353029i
$428$	−3.02140	+	0.689616i	−0.146045	+	0.0333338i
$429$		0			0
$430$	−0.188003	+	0.0429105i	−0.00906632	+	0.00206933i
$431$	−6.51912	−	5.19883i	−0.314015	−	0.250419i	0.453781	−	0.891113i	$-0.350075\pi$
$431$	−6.51912	−	5.19883i	−0.314015	−	0.250419i	−0.767796	+	0.640695i	$0.778646\pi$
$432$		0			0
$433$	−6.37738	+	5.08579i	−0.306477	+	0.244407i	−0.764635	−	0.644463i	$-0.777081\pi$
$433$	−6.37738	+	5.08579i	−0.306477	+	0.244407i	0.458158	+	0.888871i	$0.348509\pi$
$434$	3.36713	+	0.159188i	0.161627	+	0.00764125i
$435$		0			0
$436$	−6.07092	−	7.61270i	−0.290744	−	0.364582i
$437$	8.08164	−	3.89192i	0.386598	−	0.186176i
$438$		0			0
$439$	−28.9715	+	6.61256i	−1.38274	+	0.315600i	−0.848258	−	0.529583i	$-0.822348\pi$
$439$	−28.9715	+	6.61256i	−1.38274	+	0.315600i	−0.534477	+	0.845183i	$0.679491\pi$
$440$	0.571916			0.0272650
$441$		0			0
$442$	0.915491			0.0435455
$443$	15.0217	−	3.42860i	0.713701	−	0.162898i	0.149772	−	0.988721i	$-0.452146\pi$
$443$	15.0217	−	3.42860i	0.713701	−	0.162898i	0.563929	+	0.825823i	$0.309289\pi$
$444$		0			0
$445$	−4.26461	+	2.05373i	−0.202162	+	0.0973560i
$446$	1.06531	+	1.33586i	0.0504440	+	0.0632548i
$447$		0			0
$448$	17.4995	+	9.47024i	0.826773	+	0.447427i
$449$	17.7912	−	14.1880i	0.839620	−	0.669575i	−0.106172	−	0.994348i	$-0.533859\pi$
$449$	17.7912	−	14.1880i	0.839620	−	0.669575i	0.945792	+	0.324773i	$0.105288\pi$
$450$		0			0
$451$	14.2805	+	11.3884i	0.672445	+	0.536257i
$452$	−19.8742	+	4.53615i	−0.934803	+	0.213363i
$453$		0			0
$454$	3.56957	−	0.814731i	0.167528	−	0.0382372i
$455$	−0.603586	+	0.436356i	−0.0282965	+	0.0204567i
$456$		0			0
$457$	12.8282	−	16.0861i	0.600080	−	0.752477i	−0.385310	−	0.922787i	$-0.625906\pi$
$457$	12.8282	−	16.0861i	0.600080	−	0.752477i	0.985390	+	0.170310i	$0.0544771\pi$
$458$	1.72483	+	0.830635i	0.0805960	+	0.0388130i
$459$		0			0
$460$		−	3.96031i		−	0.184650i
$461$	21.2236	+	10.2207i	0.988481	+	0.476028i	0.857014	−	0.515293i	$-0.172317\pi$
$461$	21.2236	+	10.2207i	0.988481	+	0.476028i	0.131467	+	0.991321i	$0.458031\pi$
$462$		0			0
$463$	33.1523	−	15.9653i	1.54072	−	0.741972i	0.545361	−	0.838201i	$-0.316393\pi$
$463$	33.1523	−	15.9653i	1.54072	−	0.741972i	0.995359	+	0.0962299i	$0.0306784\pi$
$464$	−6.15778	−	12.7868i	−0.285868	−	0.593610i
$465$		0			0
$466$	0.192568	−	0.843697i	0.00892055	−	0.0390835i
$467$	−1.19638	+	0.576147i	−0.0553620	+	0.0266609i	−0.461360	−	0.887213i	$-0.652638\pi$
$467$	−1.19638	+	0.576147i	−0.0553620	+	0.0266609i	0.405998	+	0.913874i	$0.366924\pi$
$468$		0			0
$469$	−8.87992	+	31.8818i	−0.410037	+	1.47217i
$470$	−0.137691	+	0.285918i	−0.00635120	+	0.0131884i
$471$		0			0
$472$			4.63680i			0.213426i
$473$	6.28123	−	13.0431i	0.288811	−	0.599723i
$474$		0			0
$475$	6.61047	+	1.50880i	0.303309	+	0.0692283i
$476$	9.92780	−	35.6441i	0.455040	−	1.63374i
$477$		0			0
$478$	1.13182	+	0.545056i	0.0517683	+	0.0249303i
$479$	0.362159	+	1.58672i	0.0165475	+	0.0724992i	0.982527	−	0.186117i	$-0.0595905\pi$
$479$	0.362159	+	1.58672i	0.0165475	+	0.0724992i	−0.965980	+	0.258617i	$0.916733\pi$
$480$		0			0
$481$	4.07146	+	0.929283i	0.185642	+	0.0423717i
$482$	−0.844064	−	1.05842i	−0.0384461	−	0.0482099i
$483$		0			0
$484$	0.261634	−	0.328078i	0.0118924	−	0.0149127i
$485$	0.303854	−	0.242315i	0.0137973	−	0.0110030i
$486$		0			0
$487$	−3.19498	−	4.00637i	−0.144778	−	0.181546i	0.704155	−	0.710046i	$-0.251326\pi$
$487$	−3.19498	−	4.00637i	−0.144778	−	0.181546i	−0.848933	+	0.528500i	$0.822755\pi$
$488$	0.525317	+	2.30156i	0.0237800	+	0.104187i
$489$		0			0
$490$	−0.106257	−	0.287237i	−0.00480019	−	0.0129760i
$491$		−	23.8841i		−	1.07787i	−0.842346	−	0.538937i	$-0.818826\pi$
$491$		−	23.8841i		−	1.07787i	0.842346	−	0.538937i	$-0.181174\pi$
$492$		0			0
$493$	−20.2028	+	16.1112i	−0.909889	+	0.725612i
$494$	−0.0777360	−	0.161420i	−0.00349751	−	0.00726265i
$495$		0			0
$496$	−27.2286	−	21.7141i	−1.22260	−	0.974990i
$497$	13.2842	−	2.37832i	0.595876	−	0.106682i
$498$		0			0
$499$	−2.62275	+	11.4910i	−0.117410	+	0.514408i	0.881683	+	0.471842i	$0.156411\pi$
$499$	−2.62275	+	11.4910i	−0.117410	+	0.514408i	−0.999094	+	0.0425667i	$0.986447\pi$
$500$	3.76916	−	4.72638i	0.168562	−	0.211370i
$501$		0			0
$502$	−1.13431	+	2.35542i	−0.0506267	+	0.105127i
$503$	9.07175	+	39.7459i	0.404489	+	1.77218i	0.608848	+	0.793287i	$0.291632\pi$
$503$	9.07175	+	39.7459i	0.404489	+	1.77218i	−0.204359	+	0.978896i	$0.565511\pi$
$504$		0			0
$505$	−0.637434	+	2.79278i	−0.0283655	+	0.124277i
$506$	−2.36492	−	1.88596i	−0.105133	−	0.0838411i
$507$		0			0
$508$	1.44979			0.0643241
$509$	−37.9152			−1.68056			−0.840280	−	0.542153i	$-0.817609\pi$
$509$	−37.9152			−1.68056			−0.840280	+	0.542153i	$0.817609\pi$
$510$		0			0
$511$	10.1023	−	18.6674i	0.446900	−	0.825799i
$512$	4.73001	+	9.82196i	0.209039	+	0.434073i
$513$		0			0
$514$	0.996090	+	0.227351i	0.0439356	+	0.0100280i
$515$	0.100701	+	0.0229843i	0.00443741	+	0.00101281i
$516$		0			0
$517$	−10.3367	−	21.4644i	−0.454609	−	0.944005i
$518$	−0.817315	+	1.51027i	−0.0359108	+	0.0663573i
$519$		0			0
$520$	−0.159009			−0.00697300
$521$	30.2237			1.32412			0.662062	−	0.749449i	$-0.269681\pi$
$521$	30.2237			1.32412			0.662062	+	0.749449i	$0.269681\pi$
$522$		0			0
$523$	−22.9744	−	18.3215i	−1.00460	−	0.801141i	−0.0245105	−	0.999700i	$-0.507803\pi$
$523$	−22.9744	−	18.3215i	−1.00460	−	0.801141i	−0.980089	+	0.198558i	$0.936374\pi$
$524$	1.94118	−	8.50487i	0.0848009	−	0.371537i
$525$		0			0
$526$	−0.658007	−	2.88292i	−0.0286905	−	0.125701i
$527$	−27.5127	+	57.1307i	−1.19847	+	2.48865i
$528$		0			0
$529$	−11.9118	+	14.9369i	−0.517902	+	0.649429i
$530$	−0.114423	+	0.501320i	−0.00497022	+	0.0217760i
$531$		0			0
$532$	−7.12779	+	1.27612i	−0.309029	+	0.0553269i
$533$	−3.97040	−	3.16629i	−0.171977	−	0.137147i
$534$		0			0
$535$	−0.209365	−	0.434751i	−0.00905164	−	0.0187959i
$536$	−5.52413	+	4.40535i	−0.238606	+	0.190282i
$537$		0			0
$538$			2.20920i			0.0952456i
$539$	21.8325	+	7.20801i	0.940393	+	0.310471i
$540$		0			0
$541$	8.37790	+	36.7060i	0.360194	+	1.57811i	0.752700	+	0.658364i	$0.228751\pi$
$541$	8.37790	+	36.7060i	0.360194	+	1.57811i	−0.392505	+	0.919750i	$0.628392\pi$
$542$	1.36340	+	1.70965i	0.0585632	+	0.0734360i
$543$		0			0
$544$	9.27965	−	7.40027i	0.397862	−	0.317284i
$545$	0.945255	−	1.18531i	0.0404903	−	0.0507732i
$546$		0			0
$547$	−3.74553	−	4.69675i	−0.160147	−	0.200819i	0.695283	−	0.718736i	$-0.255279\pi$
$547$	−3.74553	−	4.69675i	−0.160147	−	0.200819i	−0.855431	+	0.517917i	$0.826707\pi$
$548$	−20.0049	−	4.56599i	−0.854567	−	0.195049i
$549$		0			0
$550$	−0.508796	−	2.22918i	−0.0216951	−	0.0950526i
$551$	4.55620	+	2.19415i	0.194101	+	0.0934740i
$552$		0			0
$553$	2.13237	−	7.65590i	0.0906774	−	0.325562i
$554$	0.733917	+	0.167512i	0.0311811	+	0.00711689i
$555$		0			0
$556$	−14.7545	+	30.6380i	−0.625730	+	1.29934i
$557$		−	19.0735i		−	0.808170i	−0.914721	−	0.404085i	$-0.867590\pi$
$557$		−	19.0735i		−	0.808170i	0.914721	−	0.404085i	$-0.132410\pi$
$558$		0			0
$559$	−1.74636	+	3.62635i	−0.0738631	+	0.153378i
$560$	−0.848985	+	3.04813i	−0.0358761	+	0.128807i
$561$		0			0
$562$	−1.71135	+	0.824142i	−0.0721889	+	0.0347643i
$563$	0.435284	−	1.90711i	0.0183451	−	0.0803749i	−0.964927	−	0.262519i	$-0.915447\pi$
$563$	0.435284	−	1.90711i	0.0183451	−	0.0803749i	0.983272	+	0.182144i	$0.0583038\pi$
$564$		0			0
$565$	−1.37716	−	2.85970i	−0.0579376	−	0.120309i
$566$	0.0320290	−	0.0154244i	0.00134628	−	0.000648335i
$567$		0			0
$568$	2.59584	+	1.25009i	0.108919	+	0.0524527i
$569$			38.8454i			1.62848i	0.580525	+	0.814242i	$0.302847\pi$
$569$			38.8454i			1.62848i	−0.580525	+	0.814242i	$0.697153\pi$
$570$		0			0
$571$	25.6912	+	12.3722i	1.07514	+	0.517761i	0.885760	−	0.464143i	$-0.153637\pi$
$571$	25.6912	+	12.3722i	1.07514	+	0.517761i	0.189381	+	0.981904i	$0.439352\pi$
$572$	3.70250	−	4.64279i	0.154809	−	0.194125i
$573$		0			0
$574$	1.69229	−	1.22343i	0.0706349	−	0.0510648i
$575$	−31.0296	+	7.08229i	−1.29402	+	0.295352i
$576$		0			0
$577$	28.3854	−	6.47877i	1.18170	−	0.269715i	0.413849	−	0.910346i	$-0.364184\pi$
$577$	28.3854	−	6.47877i	1.18170	−	0.269715i	0.767849	+	0.640631i	$0.221327\pi$
$578$	−3.65014	−	2.91089i	−0.151826	−	0.121077i
$579$		0			0
$580$	1.74560	−	1.39207i	0.0724822	−	0.0578026i
$581$	−25.3260	−	13.7057i	−1.05070	−	0.568610i
$582$		0			0
$583$	−24.0686	−	30.1810i	−0.996819	−	1.24997i
$584$	4.08277	−	1.96616i	0.168946	−	0.0813602i
$585$		0			0
$586$	−4.10082	+	0.935987i	−0.169404	+	0.0386652i
$587$	35.1074			1.44904			0.724518	−	0.689255i	$-0.242062\pi$
$587$	35.1074			1.44904			0.724518	+	0.689255i	$0.242062\pi$
$588$		0			0
$589$	12.4095			0.511324
$590$	−0.350148	+	0.0799190i	−0.0144154	+	0.00329021i
$591$		0			0
$592$	15.9848	−	7.69788i	0.656972	−	0.316381i
$593$	−26.2524	−	32.9195i	−1.07806	−	1.35184i	−0.931956	−	0.362571i	$-0.881899\pi$
$593$	−26.2524	−	32.9195i	−1.07806	−	1.35184i	−0.146101	−	0.989270i	$-0.546672\pi$
$594$		0			0
$595$	5.75468	+	0.272064i	0.235919	+	0.0111535i
$596$	−34.5473	+	27.5506i	−1.41511	+	1.12852i
$597$		0			0
$598$	0.657514	+	0.524350i	0.0268878	+	0.0214423i
$599$	31.3942	−	7.16552i	1.28273	−	0.292775i	0.473776	−	0.880645i	$-0.342891\pi$
$599$	31.3942	−	7.16552i	1.28273	−	0.292775i	0.808955	+	0.587870i	$0.200033\pi$
$600$		0			0
$601$	−38.2700	+	8.73487i	−1.56106	+	0.356303i	−0.913865	−	0.406018i	$-0.866917\pi$
$601$	−38.2700	+	8.73487i	−1.56106	+	0.356303i	−0.647199	+	0.762321i	$0.724060\pi$
$602$	−1.24380	−	1.09187i	−0.0506936	−	0.0445012i
$603$		0			0
$604$	16.2789	−	20.4131i	0.662379	−	0.830596i
$605$	0.0588666	+	0.0283486i	0.00239327	+	0.00115254i
$606$		0			0
$607$		−	23.4300i		−	0.950995i	−0.879717	−	0.475497i	$-0.842268\pi$
$607$		−	23.4300i		−	0.950995i	0.879717	−	0.475497i	$-0.157732\pi$
$608$	−2.09277	−	1.00783i	−0.0848732	−	0.0408728i
$609$		0			0
$610$	−0.164748	+	0.0793386i	−0.00667047	+	0.00321233i
$611$	2.87390	+	5.96772i	0.116266	+	0.241428i
$612$		0			0
$613$	6.44500	−	28.2374i	0.260311	−	1.14050i	−0.660604	−	0.750735i	$-0.729700\pi$
$613$	6.44500	−	28.2374i	0.260311	−	1.14050i	0.920915	−	0.389763i	$-0.127443\pi$
$614$	2.40377	−	1.15760i	0.0970083	−	0.0467167i
$615$		0			0
$616$	2.87578	+	3.97790i	0.115869	+	0.160274i
$617$	4.90112	−	10.1773i	0.197312	−	0.409722i	−0.778714	−	0.627380i	$-0.784127\pi$
$617$	4.90112	−	10.1773i	0.197312	−	0.409722i	0.976025	+	0.217658i	$0.0698417\pi$
$618$		0			0
$619$		−	3.36702i		−	0.135332i	−0.997708	−	0.0676659i	$-0.978445\pi$
$619$		−	3.36702i		−	0.135332i	0.997708	−	0.0676659i	$-0.0215552\pi$
$620$	2.37720	−	4.93631i	0.0954707	−	0.198247i
$621$		0			0
$622$	−0.462447	−	0.105551i	−0.0185424	−	0.00423219i
$623$	−35.7283	−	19.3352i	−1.43143	−	0.774648i
$624$		0			0
$625$	−21.2481	−	10.2325i	−0.849923	−	0.409302i
$626$	−0.399310	−	1.74949i	−0.0159596	−	0.0699237i
$627$		0			0
$628$	31.1855	+	7.11788i	1.24444	+	0.284034i
$629$	−20.1407	−	25.2557i	−0.803063	−	1.00701i
$630$		0			0
$631$	1.11552	−	1.39881i	0.0444080	−	0.0556859i	−0.759132	−	0.650937i	$-0.774376\pi$
$631$	1.11552	−	1.39881i	0.0444080	−	0.0556859i	0.803540	+	0.595251i	$0.202948\pi$
$632$	1.32653	−	1.05787i	0.0527665	−	0.0420799i
$633$		0			0
$634$	0.875050	+	1.09728i	0.0347527	+	0.0435785i
$635$	0.0502309	+	0.220076i	0.00199335	+	0.00873345i
$636$		0			0
$637$	−6.07006	−	2.00403i	−0.240504	−	0.0794026i
$638$		−	1.70532i		−	0.0675143i
$639$		0			0
$640$	−1.06721	+	0.851069i	−0.0421851	+	0.0336415i
$641$	−19.7285	−	40.9666i	−0.779229	−	1.61808i	−0.786093	−	0.618108i	$-0.787899\pi$
$641$	−19.7285	−	40.9666i	−0.779229	−	1.61808i	0.00686447	−	0.999976i	$-0.497815\pi$
$642$		0			0
$643$	26.7354	+	21.3208i	1.05434	+	0.840809i	0.987605	−	0.156962i	$-0.0501699\pi$
$643$	26.7354	+	21.3208i	1.05434	+	0.840809i	0.0667365	+	0.997771i	$0.478741\pi$
$644$	27.5455	−	19.9137i	1.08544	−	0.784711i
$645$		0			0
$646$	−0.308381	+	1.35111i	−0.0121331	+	0.0531586i
$647$	−18.5669	+	23.2822i	−0.729940	+	0.915316i	−0.998855	−	0.0478480i	$-0.984764\pi$
$647$	−18.5669	+	23.2822i	−0.729940	+	0.915316i	0.268914	+	0.963164i	$0.413335\pi$
$648$		0			0
$649$	11.6985	−	24.2922i	0.459207	−	0.953553i
$650$	0.141460	+	0.619775i	0.00554850	+	0.0243096i
$651$		0			0
$652$	−0.871216	+	3.81705i	−0.0341195	+	0.149487i
$653$	−13.0659	−	10.4197i	−0.511306	−	0.407753i	0.333561	−	0.942728i	$-0.391750\pi$
$653$	−13.0659	−	10.4197i	−0.511306	−	0.407753i	−0.844868	+	0.534975i	$0.820321\pi$
$654$		0			0
$655$	1.35828			0.0530724
$656$	−21.5745			−0.842344
$657$		0			0
$658$	−2.68103	+	0.479997i	−0.104517	+	0.0187122i
$659$	−18.7246	−	38.8821i	−0.729409	−	1.51463i	−0.852779	−	0.522272i	$-0.825085\pi$
$659$	−18.7246	−	38.8821i	−0.729409	−	1.51463i	0.123370	−	0.992361i	$-0.460630\pi$
$660$		0			0
$661$	40.2581	+	9.18865i	1.56586	+	0.357397i	0.915528	−	0.402255i	$-0.131773\pi$
$661$	40.2581	+	9.18865i	1.56586	+	0.357397i	0.650330	+	0.759651i	$0.274630\pi$
$662$	3.39614	+	0.775147i	0.131995	+	0.0301270i
$663$		0			0
$664$	−2.66747	−	5.53907i	−0.103518	−	0.214958i
$665$	−0.440670	−	1.03777i	−0.0170884	−	0.0402431i
$666$		0			0
$667$	−23.7376			−0.919123
$668$	42.2499			1.63470
$669$		0			0
$670$	−0.427883	−	0.341225i	−0.0165306	−	0.0131827i
$671$	3.05464	−	13.3833i	0.117923	−	0.516655i
$672$		0			0
$673$	−8.25636	−	36.1735i	−0.318259	−	1.39439i	−0.840604	−	0.541651i	$-0.817799\pi$
$673$	−8.25636	−	36.1735i	−0.318259	−	1.39439i	0.522344	−	0.852735i	$-0.325058\pi$
$674$	−0.737754	+	1.53196i	−0.0284172	+	0.0590090i
$675$		0			0
$676$	15.0181	−	18.8321i	0.577618	−	0.724310i
$677$	0.404227	−	1.77103i	0.0155357	−	0.0680663i	−0.966566	−	0.256418i	$-0.917457\pi$
$677$	0.404227	−	1.77103i	0.0155357	−	0.0680663i	0.982102	+	0.188352i	$0.0603146\pi$
$678$		0			0
$679$	3.21328	+	0.894981i	0.123314	+	0.0343462i
$680$	0.961618	+	0.766865i	0.0368764	+	0.0294079i
$681$		0			0
$682$	−1.81568	−	3.77031i	−0.0695261	−	0.144373i
$683$	3.01377	−	2.40340i	0.115319	−	0.0919636i	−0.564133	−	0.825684i	$-0.690789\pi$
$683$	3.01377	−	2.40340i	0.115319	−	0.0919636i	0.679451	+	0.733721i	$0.262218\pi$
$684$		0			0
$685$		−	3.19491i		−	0.122071i
$686$	1.46355	−	2.18338i	0.0558787	−	0.0833618i
$687$		0			0
$688$	3.80497	+	16.6707i	0.145063	+	0.635563i
$689$	6.69174	+	8.39118i	0.254935	+	0.319679i
$690$		0			0
$691$	14.8492	−	11.8418i	0.564890	−	0.450485i	−0.298938	−	0.954273i	$-0.596632\pi$
$691$	14.8492	−	11.8418i	0.564890	−	0.450485i	0.863827	+	0.503788i	$0.168061\pi$
$692$	−16.9627	+	21.2705i	−0.644825	+	0.808585i
$693$		0			0
$694$	−2.42459	−	3.04034i	−0.0920361	−	0.115410i
$695$	−5.16200	−	1.17819i	−0.195806	−	0.0446914i
$696$		0			0
$697$	8.74098	+	38.2967i	0.331088	+	1.45059i
$698$	−2.12103	−	1.02143i	−0.0802822	−	0.0386619i
$699$		0			0
$700$	25.6646	+	1.21334i	0.970031	+	0.0458601i
$701$	−33.2148	−	7.58107i	−1.25451	−	0.286333i	−0.456904	−	0.889516i	$-0.651042\pi$
$701$	−33.2148	−	7.58107i	−1.25451	−	0.286333i	−0.797603	+	0.603183i	$0.793899\pi$
$702$		0			0
$703$	−2.74292	+	5.69574i	−0.103451	+	0.214819i
$704$		−	24.7016i		−	0.930976i
$705$		0			0
$706$	−0.171695	+	0.356528i	−0.00646181	+	0.0134181i
$707$	−22.6301	+	9.60943i	−0.851094	+	0.361400i
$708$		0			0
$709$	−19.2392	+	9.26513i	−0.722545	+	0.347959i	−0.758747	−	0.651385i	$-0.774188\pi$
$709$	−19.2392	+	9.26513i	−0.722545	+	0.347959i	0.0362024	+	0.999344i	$0.488474\pi$
$710$	−0.0496592	+	0.217571i	−0.00186368	+	0.00816531i
$711$		0			0
$712$	−3.76311	−	7.81417i	−0.141028	−	0.292848i
$713$	−52.4816	+	25.2738i	−1.96545	+	0.946511i
$714$		0			0
$715$	0.833048	+	0.401175i	0.0311542	+	0.0150031i
$716$			16.1620i			0.604003i
$717$		0			0
$718$	1.96994	+	0.948675i	0.0735176	+	0.0354042i
$719$	−17.7207	+	22.2211i	−0.660871	+	0.828706i	−0.993438	−	0.114374i	$-0.963514\pi$
$719$	−17.7207	+	22.2211i	−0.660871	+	0.828706i	0.332567	+	0.943080i	$0.392085\pi$
$720$		0			0
$721$	0.346493	+	0.815988i	0.0129041	+	0.0303890i
$722$	−2.36459	+	0.539702i	−0.0880009	+	0.0200856i
$723$		0			0
$724$	−27.5816	+	6.29532i	−1.02506	+	0.233964i
$725$	−14.0288	−	11.1876i	−0.521015	−	0.415496i
$726$		0			0
$727$	30.3607	−	24.2119i	1.12602	−	0.897968i	0.130397	−	0.991462i	$-0.458375\pi$
$727$	30.3607	−	24.2119i	1.12602	−	0.897968i	0.995620	+	0.0934937i	$0.0298035\pi$
$728$	−0.799549	−	1.10597i	−0.0296333	−	0.0409899i
$729$		0			0
$730$	0.218844	+	0.274422i	0.00809979	+	0.0101568i
$731$	28.0504	−	13.5083i	1.03748	−	0.499624i
$732$		0			0
$733$	30.4061	−	6.93999i	1.12307	−	0.256334i	0.379634	−	0.925137i	$-0.376050\pi$
$733$	30.4061	−	6.93999i	1.12307	−	0.256334i	0.743440	+	0.668803i	$0.233193\pi$
$734$	3.45193			0.127413
$735$		0			0
$736$	10.9033			0.401899
$737$	40.0555	−	9.14241i	1.47546	−	0.336765i
$738$		0			0
$739$	35.1833	−	16.9434i	1.29424	−	0.623272i	0.345228	−	0.938519i	$-0.387802\pi$
$739$	35.1833	−	16.9434i	1.29424	−	0.623272i	0.949010	+	0.315247i	$0.102087\pi$
$740$	1.74024	+	2.18219i	0.0639724	+	0.0802188i
$741$		0			0
$742$	−4.06224	+	1.72495i	−0.149129	+	0.0633248i
$743$	−5.37604	+	4.28725i	−0.197228	+	0.157284i	−0.717124	−	0.696945i	$-0.754542\pi$
$743$	−5.37604	+	4.28725i	−0.197228	+	0.157284i	0.519896	+	0.854229i	$0.325971\pi$
$744$		0			0
$745$	−5.37909	−	4.28968i	−0.197075	−	0.157162i
$746$	3.32528	−	0.758974i	0.121747	−	0.0277880i
$747$		0			0
$748$	−44.7823	+	10.2213i	−1.63740	+	0.373727i
$749$	1.97111	−	3.64229i	0.0720227	−	0.133086i
$750$		0			0
$751$	13.8825	−	17.4081i	0.506580	−	0.635231i	−0.461120	−	0.887338i	$-0.652552\pi$
$751$	13.8825	−	17.4081i	0.506580	−	0.635231i	0.967699	+	0.252107i	$0.0811235\pi$
$752$	25.3530	+	12.2094i	0.924528	+	0.445229i
$753$		0			0
$754$			0.474127i			0.0172667i
$755$	3.66269	+	1.76386i	0.133299	+	0.0641933i
$756$		0			0
$757$	−22.5836	+	10.8757i	−0.820816	+	0.395284i	−0.796663	−	0.604424i	$-0.793403\pi$
$757$	−22.5836	+	10.8757i	−0.820816	+	0.395284i	−0.0241534	+	0.999708i	$0.507689\pi$
$758$	−0.922730	−	1.91607i	−0.0335151	−	0.0695948i
$759$		0			0
$760$	0.0535618	−	0.234669i	0.00194289	−	0.00851235i
$761$	−8.63094	+	4.15644i	−0.312871	+	0.150671i	−0.583729	−	0.811949i	$-0.698407\pi$
$761$	−8.63094	+	4.15644i	−0.312871	+	0.150671i	0.270858	+	0.962619i	$0.412693\pi$
$762$		0			0
$763$	12.9974	+	0.614477i	0.470537	+	0.0222455i
$764$	−2.22017	+	4.61022i	−0.0803228	+	0.166792i
$765$		0			0
$766$			0.939762i			0.0339550i
$767$	−3.25252	+	6.75392i	−0.117442	+	0.243870i
$768$		0			0
$769$	17.6246	+	4.02271i	0.635561	+	0.145063i	0.528148	−	0.849152i	$-0.322886\pi$
$769$	17.6246	+	4.02271i	0.635561	+	0.145063i	0.107412	+	0.994215i	$0.465744\pi$
$770$	−0.250825	+	0.285727i	−0.00903910	+	0.0102969i
$771$		0			0
$772$	−24.6767	−	11.8837i	−0.888135	−	0.427703i
$773$	−3.84244	−	16.8348i	−0.138203	−	0.605507i	−0.995829	−	0.0912341i	$-0.970919\pi$
$773$	−3.84244	−	16.8348i	−0.138203	−	0.605507i	0.857626	−	0.514273i	$-0.171938\pi$
$774$		0			0
$775$	−42.9279	−	9.79801i	−1.54202	−	0.351955i
$776$	0.444002	+	0.556761i	0.0159387	+	0.0199865i
$777$		0			0
$778$	−2.64070	+	3.31133i	−0.0946736	+	0.118717i
$779$	6.01031	−	4.79306i	0.215342	−	0.171729i
$780$		0			0
$781$	−10.4457	−	13.0985i	−0.373776	−	0.468700i
$782$	−1.44754	−	6.34210i	−0.0517640	−	0.226793i
$783$		0			0
$784$	−25.4700	+	9.42202i	−0.909641	+	0.336501i
$785$			4.98051i			0.177762i
$786$		0			0
$787$	−33.7413	+	26.9078i	−1.20275	+	0.959159i	−0.999799	−	0.0200303i	$-0.993624\pi$
$787$	−33.7413	+	26.9078i	−1.20275	+	0.959159i	−0.202948	+	0.979189i	$0.565052\pi$
$788$	−5.78828	−	12.0195i	−0.206199	−	0.428176i
$789$		0			0
$790$	0.102749	+	0.0819396i	0.00365564	+	0.00291528i
$791$	12.9655	−	23.9582i	0.461002	−	0.851857i
$792$		0			0
$793$	−0.849277	+	3.72093i	−0.0301587	+	0.132134i
$794$	−0.730291	+	0.915756i	−0.0259171	+	0.0324990i
$795$		0			0
$796$	−20.7077	+	43.0001i	−0.733967	+	1.52410i
$797$	7.60236	+	33.3081i	0.269289	+	1.17983i	0.910842	+	0.412755i	$0.135433\pi$
$797$	7.60236	+	33.3081i	0.269289	+	1.17983i	−0.641553	+	0.767079i	$0.721709\pi$
$798$		0			0
$799$	11.4009	−	49.9505i	0.403334	−	1.76712i
$800$	6.44375	+	5.13872i	0.227821	+	0.181681i
$801$		0			0
$802$	−2.55772			−0.0903163
$803$	−26.3502			−0.929879
$804$		0			0
$805$	3.97724	+	3.49141i	0.140179	+	0.123056i
$806$	0.504812	+	1.04825i	0.0177812	+	0.0369231i
$807$		0			0
$808$	−5.11730	−	1.16799i	−0.180026	−	0.0410898i
$809$	35.9385	+	8.20273i	1.26353	+	0.288393i	0.801244	−	0.598337i	$-0.204172\pi$
$809$	35.9385	+	8.20273i	1.26353	+	0.288393i	0.462287	+	0.886730i	$0.347029\pi$
$810$		0			0
$811$	−6.20209	−	12.8788i	−0.217785	−	0.452235i	0.763240	−	0.646115i	$-0.223607\pi$
$811$	−6.20209	−	12.8788i	−0.217785	−	0.452235i	−0.981025	+	0.193879i	$0.937893\pi$
$812$	18.4599	+	5.14155i	0.647814	+	0.180433i
$813$		0			0
$814$	2.13183			0.0747207
$815$	−0.609606			−0.0213536
$816$		0			0
$817$	−4.76361	−	3.79885i	−0.166658	−	0.132905i
$818$	−0.337414	+	1.47831i	−0.0117974	+	0.0516878i
$819$		0			0
$820$	−0.755254	−	3.30899i	−0.0263746	−	0.115555i
$821$	−21.5354	+	44.7187i	−0.751590	+	1.56069i	0.0745422	+	0.997218i	$0.476250\pi$
$821$	−21.5354	+	44.7187i	−0.751590	+	1.56069i	−0.826133	+	0.563476i	$0.809464\pi$
$822$		0			0
$823$	−0.398260	+	0.499403i	−0.0138825	+	0.0174081i	−0.788724	−	0.614747i	$-0.789258\pi$
$823$	−0.398260	+	0.499403i	−0.0138825	+	0.0174081i	0.774842	+	0.632155i	$0.217829\pi$
$824$	−0.0421149	+	0.184517i	−0.00146714	+	0.00642797i
$825$		0			0
$826$	−2.31653	−	2.03356i	−0.0806023	−	0.0707565i
$827$	−10.2077	−	8.14034i	−0.354955	−	0.283067i	0.429735	−	0.902955i	$-0.358607\pi$
$827$	−10.2077	−	8.14034i	−0.354955	−	0.283067i	−0.784691	+	0.619887i	$0.787178\pi$
$828$		0			0
$829$	7.09969	+	14.7427i	0.246582	+	0.512034i	0.987120	−	0.159981i	$-0.0511433\pi$
$829$	7.09969	+	14.7427i	0.246582	+	0.512034i	−0.740538	+	0.672015i	$0.765429\pi$
$830$	0.372307	−	0.296905i	0.0129230	−	0.0103057i
$831$		0			0
$832$			6.86774i			0.238096i
$833$	27.0442	+	41.3941i	0.937024	+	1.43422i
$834$		0			0
$835$	1.46383	+	6.41346i	0.0506579	+	0.221947i
$836$	5.60477	+	7.02816i	0.193845	+	0.243074i
$837$		0			0
$838$	0.386815	−	0.308475i	0.0133623	−	0.0106561i
$839$	27.1017	−	33.9844i	0.935654	−	1.17327i	−0.0490082	−	0.998798i	$-0.515606\pi$
$839$	27.1017	−	33.9844i	0.935654	−	1.17327i	0.984662	−	0.174474i	$-0.0558225\pi$
$840$		0			0
$841$	9.73731	+	12.2102i	0.335769	+	0.421041i
$842$	0.461045	+	0.105230i	0.0158887	+	0.00362648i
$843$		0			0
$844$	4.05347	+	17.7594i	0.139526	+	0.611304i
$845$	3.37901	+	1.62724i	0.116241	+	0.0559789i
$846$		0			0
$847$	0.0988247	+	0.551987i	0.00339566	+	0.0189665i
$848$	44.4532	+	10.1462i	1.52653	+	0.348420i
$849$		0			0
$850$	2.13355	−	4.43037i	0.0731803	−	0.151960i
$851$		−	29.6745i		−	1.01723i
$852$		0			0
$853$	−6.75414	+	14.0251i	−0.231257	+	0.480211i	−0.984015	−	0.178087i	$-0.943009\pi$
$853$	−6.75414	+	14.0251i	−0.231257	+	0.480211i	0.752757	+	0.658298i	$0.228723\pi$
$854$	−1.38024	−	0.746949i	−0.0472309	−	0.0255601i
$855$		0			0
$856$	0.796608	−	0.383626i	0.0272275	−	0.0131121i
$857$	−1.76798	+	7.74601i	−0.0603929	+	0.264599i	−0.996106	−	0.0881632i	$-0.971900\pi$
$857$	−1.76798	+	7.74601i	−0.0603929	+	0.264599i	0.935713	+	0.352762i	$0.114757\pi$
$858$		0			0
$859$	24.9783	+	51.8679i	0.852247	+	1.76971i	0.595763	+	0.803161i	$0.296850\pi$
$859$	24.9783	+	51.8679i	0.852247	+	1.76971i	0.256484	+	0.966548i	$0.417436\pi$
$860$	−2.42366	+	1.16717i	−0.0826461	+	0.0398003i
$861$		0			0
$862$	1.06623	+	0.513469i	0.0363159	+	0.0174888i
$863$			46.7125i			1.59011i	0.606536	+	0.795056i	$0.292558\pi$
$863$			46.7125i			1.59011i	−0.606536	+	0.795056i	$0.707442\pi$
$864$		0			0
$865$	−3.81654	−	1.83795i	−0.129766	−	0.0624921i
$866$	0.721811	−	0.905122i	0.0245281	−	0.0307573i
$867$		0			0
$868$	46.2874	−	8.28704i	1.57110	−	0.281280i
$869$	−9.61867	+	2.19540i	−0.326291	+	0.0744738i
$870$		0			0
$871$	−11.1366	+	2.54185i	−0.377348	+	0.0861273i
$872$	2.17189	+	1.73202i	0.0735493	+	0.0586536i
$873$		0			0
$874$	−0.995332	+	0.793751i	−0.0336676	+	0.0268490i
$875$	1.42369	+	7.95206i	0.0481296	+	0.268829i
$876$		0			0
$877$	0.757672	+	0.950091i	0.0255848	+	0.0320823i	0.794459	−	0.607317i	$-0.207754\pi$
$877$	0.757672	+	0.950091i	0.0255848	+	0.0320823i	−0.768875	+	0.639400i	$0.779183\pi$
$878$	3.79991	−	1.82994i	0.128241	−	0.0617575i
$879$		0			0
$880$	3.82960	−	0.874081i	0.129096	−	0.0294653i
$881$	35.6860			1.20229			0.601146	−	0.799139i	$-0.294711\pi$
$881$	35.6860			1.20229			0.601146	+	0.799139i	$0.294711\pi$
$882$		0			0
$883$	−33.6481			−1.13235			−0.566174	−	0.824286i	$-0.691577\pi$
$883$	−33.6481			−1.13235			−0.566174	+	0.824286i	$0.691577\pi$
$884$	12.4508	−	2.84180i	0.418764	−	0.0955802i
$885$		0			0
$886$	−1.97024	+	0.948820i	−0.0661917	+	0.0318762i
$887$	−15.6293	−	19.5986i	−0.524782	−	0.658056i	0.446835	−	0.894616i	$-0.352551\pi$
$887$	−15.6293	−	19.5986i	−0.524782	−	0.658056i	−0.971617	+	0.236561i	$0.923980\pi$
$888$		0			0
$889$	−1.27814	+	1.45599i	−0.0428674	+	0.0488324i
$890$	0.525227	−	0.418855i	0.0176057	−	0.0140400i
$891$		0			0
$892$	18.6350	+	14.8609i	0.623947	+	0.497581i
$893$	−9.77539	+	2.23117i	−0.327121	+	0.0746632i
$894$		0			0
$895$	−2.45337	+	0.559965i	−0.0820070	+	0.0187176i
$896$	−11.2858	−	3.14339i	−0.377032	−	0.105013i
$897$		0			0
$898$	−2.01366	+	2.52506i	−0.0671969	+	0.0842622i
$899$	−29.5876	−	14.2487i	−0.986803	−	0.475219i
$900$		0			0
$901$		−	83.0192i		−	2.76577i
$902$	−2.33564	−	1.12479i	−0.0777684	−	0.0374513i
$903$		0			0
$904$	5.23992	−	2.52341i	0.174277	−	0.0839275i
$905$	−1.91124	−	3.96873i	−0.0635317	−	0.131925i
$906$		0			0
$907$	−13.3522	+	58.4998i	−0.443353	+	1.94245i	−0.136813	+	0.990597i	$0.543686\pi$
$907$	−13.3522	+	58.4998i	−0.443353	+	1.94245i	−0.306540	+	0.951858i	$0.599171\pi$
$908$	46.0174	−	22.1608i	1.52714	−	0.735433i
$909$		0			0
$910$	0.0697364	−	0.0794402i	0.00231174	−	0.00263342i
$911$	−3.72897	+	7.74329i	−0.123546	+	0.256547i	−0.953564	−	0.301190i	$-0.902616\pi$
$911$	−3.72897	+	7.74329i	−0.123546	+	0.256547i	0.830018	+	0.557737i	$0.188330\pi$
$912$		0			0
$913$			35.7492i			1.18313i
$914$	−1.26700	+	2.63095i	−0.0419086	+	0.0870241i
$915$		0			0
$916$	26.0362	+	5.94260i	0.860261	+	0.196349i
$917$	6.82989	+	9.44738i	0.225543	+	0.311980i
$918$		0			0
$919$	−10.3340	−	4.97658i	−0.340886	−	0.164162i	0.255606	−	0.966781i	$-0.417725\pi$
$919$	−10.3340	−	4.97658i	−0.340886	−	0.164162i	−0.596492	+	0.802619i	$0.703439\pi$
$920$	0.251419	+	1.10154i	0.00828904	+	0.0363167i
$921$		0			0
$922$	−3.25947	−	0.743952i	−0.107345	−	0.0245008i
$923$	2.90420	+	3.64175i	0.0955928	+	0.119870i
$924$		0			0
$925$	13.9856	−	17.5374i	0.459845	−	0.576628i
$926$	−4.08303	+	3.25611i	−0.134177	+	0.107002i
$927$		0			0
$928$	3.83256	+	4.80587i	0.125810	+	0.157761i
$929$	2.34784	+	10.2865i	0.0770300	+	0.337491i	0.998728	−	0.0504171i	$-0.0160551\pi$
$929$	2.34784	+	10.2865i	0.0770300	+	0.337491i	−0.921698	+	0.387908i	$0.873198\pi$
$930$		0			0
$931$	5.00229	−	8.28330i	0.163943	−	0.271474i
$932$		−	12.0721i		−	0.395435i
$933$		0			0
$934$	0.147346	−	0.117504i	0.00482131	−	0.00384486i
$935$	−3.10315	−	6.44375i	−0.101484	−	0.210733i
$936$		0			0
$937$	−32.4952	−	25.9141i	−1.06157	−	0.846577i	−0.0730024	−	0.997332i	$-0.523258\pi$
$937$	−32.4952	−	25.9141i	−1.06157	−	0.846577i	−0.988571	+	0.150755i	$0.951829\pi$
$938$	0.221818	−	4.69189i	0.00724262	−	0.153196i
$939$		0			0
$940$	−0.985079	+	4.31592i	−0.0321298	+	0.140770i
$941$	25.7881	−	32.3373i	0.840668	−	1.05416i	−0.157112	−	0.987581i	$-0.550218\pi$
$941$	25.7881	−	32.3373i	0.840668	−	1.05416i	0.997781	−	0.0665841i	$-0.0212101\pi$
$942$		0			0
$943$	−15.6567	+	32.5115i	−0.509852	+	1.05872i
$944$	7.08660	+	31.0484i	0.230649	+	1.01054i
$945$		0			0
$946$	−0.457201	+	2.00313i	−0.0148649	+	0.0651273i
$947$	−37.8718	−	30.2018i	−1.23067	−	0.981426i	−0.999965	−	0.00840212i	$-0.997325\pi$
$947$	−37.8718	−	30.2018i	−1.23067	−	0.981426i	−0.230705	−	0.973024i	$-0.574103\pi$
$948$		0			0
$949$	7.32610			0.237815
$950$	−0.962331			−0.0312221
$951$		0			0
$952$	−0.498511	+	10.5445i	−0.0161568	+	0.341749i
$953$	12.2254	+	25.3863i	0.396019	+	0.822342i	0.999685	+	0.0251047i	$0.00799191\pi$
$953$	12.2254	+	25.3863i	0.396019	+	0.822342i	−0.603666	+	0.797238i	$0.706294\pi$
$954$		0			0
$955$	−0.776746	−	0.177287i	−0.0251349	−	0.00573688i
$956$	17.0848	+	3.89949i	0.552561	+	0.126118i
$957$		0			0
$958$	−0.100223	−	0.208115i	−0.00323805	−	0.00672388i
$959$	22.2218	−	16.0651i	0.717581	−	0.518768i
$960$		0			0
$961$	−49.5863			−1.59956
$962$	−0.592710			−0.0191097
$963$		0			0
$964$	−14.7648	−	11.7746i	−0.475543	−	0.379233i
$965$	0.948949	−	4.15762i	0.0305478	−	0.133838i
$966$		0			0
$967$	6.58547	+	28.8528i	0.211774	+	0.927845i	0.963361	+	0.268210i	$0.0864320\pi$
$967$	6.58547	+	28.8528i	0.211774	+	0.927845i	−0.751586	+	0.659635i	$0.770711\pi$
$968$	−0.0519441	+	0.107863i	−0.00166955	+	0.00346685i
$969$		0			0
$970$	−0.0343911	+	0.0431250i	−0.00110423	+	0.00138466i
$971$	−1.24821	+	5.46875i	−0.0400569	+	0.175501i	−0.990999	−	0.133867i	$-0.957260\pi$
$971$	−1.24821	+	5.46875i	−0.0400569	+	0.175501i	0.950942	+	0.309368i	$0.100118\pi$
$972$		0			0
$973$	−17.7615	−	41.8281i	−0.569406	−	1.34095i
$974$	0.568612	+	0.453453i	0.0182195	+	0.0145296i
$975$		0			0
$976$	7.03513	+	14.6086i	0.225189	+	0.467610i
$977$	−20.5994	+	16.4275i	−0.659035	+	0.525563i	−0.894925	−	0.446217i	$-0.852771\pi$
$977$	−20.5994	+	16.4275i	−0.659035	+	0.525563i	0.235890	+	0.971780i	$0.424199\pi$
$978$		0			0
$979$			50.4327i			1.61184i
$980$	−2.33672	−	3.57661i	−0.0746438	−	0.114251i
$981$		0			0
$982$	0.754301	+	3.30481i	0.0240707	+	0.105461i
$983$	23.7409	+	29.7701i	0.757217	+	0.949520i	0.999788	−	0.0206138i	$-0.00656205\pi$
$983$	23.7409	+	29.7701i	0.757217	+	0.949520i	−0.242571	+	0.970134i	$0.577991\pi$
$984$		0			0
$985$	1.62399	−	1.29509i	0.0517447	−	0.0412650i
$986$	2.28661	−	2.86732i	0.0728206	−	0.0913142i
$987$		0			0
$988$	−1.55828	−	1.95403i	−0.0495756	−	0.0621659i
$989$	27.8830	+	6.36410i	0.886626	+	0.202367i
$990$		0			0
$991$	−8.83419	−	38.7051i	−0.280627	−	1.22951i	−0.896992	−	0.442047i	$-0.854252\pi$
$991$	−8.83419	−	38.7051i	−0.280627	−	1.22951i	0.616365	−	0.787461i	$-0.288605\pi$
$992$	13.5903	+	6.54475i	0.431493	+	0.207796i
$993$		0			0
$994$	−1.76300	+	0.748622i	−0.0559189	+	0.0237448i
$995$	−7.24480	−	1.65358i	−0.229676	−	0.0524220i
$996$		0			0
$997$	15.3757	−	31.9279i	0.486952	−	1.01117i	−0.502266	−	0.864713i	$-0.667500\pi$
$997$	15.3757	−	31.9279i	0.486952	−	1.01117i	0.989218	−	0.146453i	$-0.0467857\pi$
$998$		−	1.67283i		−	0.0529524i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.10	✓	120
3.2	odd	2	inner	441.2.w.a.62.11	yes	120
49.34	odd	14	inner	441.2.w.a.377.11	yes	120
147.83	even	14	inner	441.2.w.a.377.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.10	✓	120	1.1	even	1	trivial
441.2.w.a.62.11	yes	120	3.2	odd	2	inner
441.2.w.a.377.10	yes	120	147.83	even	14	inner
441.2.w.a.377.11	yes	120	49.34	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.138369 + 0.0315817i) q^{2} +(-1.78379 + 0.859028i) q^{4} +(-0.192202 - 0.241014i) q^{5} +(0.709889 - 2.54874i) q^{7} +(0.441617 - 0.352178i) q^{8} +O(q^{10})\)	\(q+(-0.138369 + 0.0315817i) q^{2} +(-1.78379 + 0.859028i) q^{4} +(-0.192202 - 0.241014i) q^{5} +(0.709889 - 2.54874i) q^{7} +(0.441617 - 0.352178i) q^{8} +(0.0342063 + 0.0272786i) q^{10} +(-3.20217 + 0.730874i) q^{11} +(0.890293 - 0.203204i) q^{13} +(-0.0177329 + 0.375084i) q^{14} +(2.41886 - 3.03315i) q^{16} +(-6.36412 - 3.06480i) q^{17} +1.38237i q^{19} +(0.549885 + 0.264811i) q^{20} +(0.419997 - 0.202260i) q^{22} +(-2.81540 - 5.84624i) q^{23} +(1.09146 - 4.78199i) q^{25} +(-0.116771 + 0.0562340i) q^{26} +(0.923142 + 5.15622i) q^{28} +(1.58724 - 3.29594i) q^{29} -8.97699i q^{31} +(-0.729059 + 1.51391i) q^{32} +(0.977386 + 0.223082i) q^{34} +(-0.750722 + 0.318779i) q^{35} +(4.12028 + 1.98422i) q^{37} +(-0.0436575 - 0.191276i) q^{38} +(-0.169759 - 0.0387464i) q^{40} +(-3.46729 - 4.34784i) q^{41} +(-2.74808 + 3.44598i) q^{43} +(5.08415 - 4.05447i) q^{44} +(0.574197 + 0.720020i) q^{46} +(1.61402 + 7.07149i) q^{47} +(-5.99211 - 3.61864i) q^{49} +0.696148i q^{50} +(-1.41354 + 1.12726i) q^{52} +(5.09945 + 10.5891i) q^{53} +(0.791613 + 0.631290i) q^{55} +(-0.584109 - 1.37557i) q^{56} +(-0.115533 + 0.506183i) q^{58} +(-5.11818 + 6.41799i) q^{59} +(-1.81339 + 3.76555i) q^{61} +(0.283509 + 1.24213i) q^{62} +(-1.67349 + 7.33205i) q^{64} +(-0.220091 - 0.175517i) q^{65} -12.5089 q^{67} +13.9850 q^{68} +(0.0938087 - 0.0678181i) q^{70} +(2.21314 + 4.59564i) q^{71} +(7.82141 + 1.78519i) q^{73} +(-0.632782 - 0.144428i) q^{74} +(-1.18749 - 2.46585i) q^{76} +(-0.410379 + 8.68032i) q^{77} +3.00380 q^{79} -1.19594 q^{80} +(0.617075 + 0.492101i) q^{82} +(2.42195 - 10.6113i) q^{83} +(0.484538 + 2.12290i) q^{85} +(0.271418 - 0.563604i) q^{86} +(-1.15673 + 1.45050i) q^{88} +(3.41674 - 14.9697i) q^{89} +(0.114097 - 2.41337i) q^{91} +(10.0442 + 8.00995i) q^{92} +(-0.446659 - 0.927498i) q^{94} +(0.333169 - 0.265694i) q^{95} +1.26073i q^{97} +(0.943403 + 0.311465i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Introduction

L-functions

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