LMFDB - Embedded newform 441.2.w.a.62.11

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			62.11
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.11

$q$-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	−0.173320	−	0.984866i	$-0.555449\pi$
$2$	0.138369	−	0.0315817i	0.0978413	−	0.0223316i	0.271161	+	0.962534i	$0.412592\pi$
$3$		0			0
$3$		0			0
$4$	−1.78379	+	0.859028i	−0.891895	+	0.429514i
$5$	0.192202	+	0.241014i	0.0859553	+	0.107785i	0.822950	−	0.568115i	$-0.192327\pi$
$5$	0.192202	+	0.241014i	0.0859553	+	0.107785i	−0.736994	+	0.675899i	$0.763756\pi$
$6$		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	0.289418	−	0.957203i	$-0.406538\pi$
$11$	3.20217	−	0.730874i	0.965490	−	0.220367i	0.676072	+	0.736836i	$0.263681\pi$
$12$		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	0.995644	−	0.0932318i	$-0.0297198\pi$
$17$	6.36412	+	3.06480i	1.54353	+	0.743323i	0.547883	+	0.836555i	$0.315434\pi$
$18$		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	$0.0936503\pi$
$23$	2.81540	+	5.84624i	0.587051	+	1.21902i	−0.369980	+	0.929040i	$0.620635\pi$
$24$		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	−0.994777	−	0.102068i	$-0.967454\pi$
$29$	−1.58724	+	3.29594i	−0.294743	+	0.612041i	0.700034	+	0.714110i	$0.253168\pi$
$30$		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	0.975018	−	0.222126i	$-0.0712997\pi$
$41$	3.46729	+	4.34784i	0.541499	+	0.679018i	−0.433519	+	0.901144i	$0.642728\pi$
$42$		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	$-0.893994\pi$
$47$	−1.61402	−	7.07149i	−0.235429	−	1.03148i	0.709628	−	0.704577i	$-0.248863\pi$
$48$		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	$-0.843839\pi$
$53$	−5.09945	−	10.5891i	−0.700463	−	1.45453i	0.181590	−	0.983374i	$-0.441876\pi$
$54$		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	−0.327686	−	0.944787i	$-0.606269\pi$
$59$	5.11818	−	6.41799i	0.666330	−	0.835551i	0.994016	+	0.109235i	$0.0348402\pi$
$60$		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	0.727382	−	0.686233i	$-0.240737\pi$
$71$	−2.21314	−	4.59564i	−0.262652	−	0.545402i	−0.990034	+	0.140831i	$0.955023\pi$
$72$		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	$0.275206\pi$
$83$	−2.42195	+	10.6113i	−0.265844	+	1.16474i	−0.914798	+	0.403911i	$0.867651\pi$
$84$		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	$0.374032\pi$
$89$	−3.41674	+	14.9697i	−0.362174	+	1.58679i	−0.747666	+	0.664075i	$0.768826\pi$
$90$		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	0.981513	−	0.191397i	$-0.0613018\pi$
$101$	5.79383	+	7.26523i	0.576507	+	0.722917i	−0.405005	+	0.914314i	$0.632730\pi$
$102$		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	0.148118	−	0.988970i	$-0.452679\pi$
$107$	−1.52607	−	0.348316i	−0.147531	−	0.0336730i	−0.295649	+	0.955297i	$0.595536\pi$
$108$		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	−0.277473	−	0.960734i	$-0.589497\pi$
$113$	−10.0382	−	2.29115i	−0.944314	−	0.215533i	−0.666841	+	0.745200i	$0.732354\pi$
$114$		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	−0.647199	−	0.762321i	$-0.724060\pi$
$131$	2.74720	−	3.44488i	0.240024	−	0.300981i	0.887223	+	0.461340i	$0.152631\pi$
$132$		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	0.212914	−	0.977071i	$-0.431705\pi$
$137$	−8.10295	−	6.46189i	−0.692282	−	0.552076i	−0.905196	+	0.424995i	$0.860276\pi$
$138$		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	−0.981462	−	0.191657i	$-0.938614\pi$
$149$	−21.7591	+	4.96636i	−1.78257	+	0.406860i	−0.801110	+	0.598517i	$0.795757\pi$
$150$		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	0.988678	−	0.150051i	$-0.0479437\pi$
$167$	19.2265	+	9.25902i	1.48779	+	0.716484i	0.499117	+	0.866535i	$0.333658\pi$
$168$		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	−0.840620	−	0.541625i	$-0.817809\pi$
$173$	−12.3806	+	5.96218i	−0.941279	+	0.453296i	−0.100659	+	0.994921i	$0.532095\pi$
$174$		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	−0.990385	−	0.138338i	$-0.955824\pi$
$179$	−3.54189	+	7.35481i	−0.264733	+	0.549724i	0.725652	+	0.688062i	$0.241538\pi$
$180$		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	−0.693863	−	0.720107i	$-0.744093\pi$
$191$	−2.02065	+	1.61142i	−0.146209	+	0.116598i	0.547654	+	0.836705i	$0.315521\pi$
$192$		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	$-0.922840\pi$
$197$		−	6.73817i		−	0.480075i	0.970764	−	0.240037i	$-0.0771597\pi$
$198$		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	$-0.172867\pi$
$227$	25.7976			1.71224			0.856122	+	0.516774i	$0.172867\pi$
$228$		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	−0.796156	−	0.605091i	$-0.793137\pi$
$233$	2.64559	−	5.49362i	0.173318	−	0.359899i	0.969475	+	0.245192i	$0.0788510\pi$
$234$		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	0.821210	−	0.570626i	$-0.193299\pi$
$239$	6.92016	+	5.51864i	0.447628	+	0.356971i	−0.373582	+	0.927597i	$0.621871\pi$
$240$		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	−0.998605	−	0.0528055i	$-0.983184\pi$
$251$	−11.4848	+	14.4015i	−0.724913	+	0.909012i	0.273692	+	0.961817i	$0.411755\pi$
$252$		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	0.625096	−	0.780548i	$-0.285060\pi$
$257$	6.48591	+	3.12345i	0.404580	+	0.194835i	−0.220516	+	0.975383i	$0.570774\pi$
$258$		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	$-0.777950\pi$
$263$		−	20.8350i		−	1.28474i	0.766393	−	0.642372i	$-0.222050\pi$
$264$		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	$0.228811\pi$
$269$	−3.46371	+	15.1755i	−0.211186	+	0.925268i	−0.963762	+	0.266762i	$0.914046\pi$
$270$		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	−0.593205	−	0.805052i	$-0.702138\pi$
$281$	−13.0478	+	2.97807i	−0.778365	+	0.177657i	−0.185160	+	0.982708i	$0.559280\pi$
$282$		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	$-0.833130\pi$
$293$	−29.6370			−1.73141			−0.865705	+	0.500554i	$0.833130\pi$
$294$		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	0.346558	−	0.938029i	$-0.387351\pi$
$311$	−3.01117	−	1.45010i	−0.170748	−	0.0822277i	−0.517305	+	0.855801i	$0.673065\pi$
$312$		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	0.986022	−	0.166617i	$-0.0532844\pi$
$317$	4.29054	+	8.90940i	0.240981	+	0.500402i	−0.745041	+	0.667019i	$0.767570\pi$
$318$		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	$-0.879831\pi$
$347$	−11.8882	−	24.6862i	−0.638194	−	1.32522i	0.291387	−	0.956605i	$-0.405883\pi$
$348$		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	−0.825939	−	0.563760i	$-0.809354\pi$
$353$	−1.73839	+	2.17988i	−0.0925253	+	0.116023i	0.733414	+	0.679783i	$0.237926\pi$
$354$		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	0.887486	−	0.460835i	$-0.152450\pi$
$359$	12.0446	+	9.60524i	0.635689	+	0.506945i	−0.251797	+	0.967780i	$0.581021\pi$
$360$		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	−0.998520	−	0.0543850i	$-0.982680\pi$
$383$	−1.47341	+	6.45544i	−0.0752878	+	0.329857i	0.923232	+	0.384242i	$0.125537\pi$
$384$		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	−0.999215	−	0.0396147i	$-0.987387\pi$
$389$	−23.3312	+	18.6060i	−1.18294	+	0.943363i	−0.183725	+	0.982978i	$0.558816\pi$
$390$		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	−0.239971	−	0.970780i	$-0.577138\pi$
$401$	−17.5696	−	4.01014i	−0.877382	−	0.200257i	−0.637412	+	0.770523i	$0.719995\pi$
$402$		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	−0.355590	−	0.934642i	$-0.615720\pi$
$419$	3.14076	−	1.51251i	0.153436	−	0.0738910i	0.509026	+	0.860751i	$0.330006\pi$
$420$		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	0.767796	−	0.640695i	$-0.221354\pi$
$431$	6.51912	+	5.19883i	0.314015	+	0.250419i	−0.453781	+	0.891113i	$0.649925\pi$
$432$		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	−0.563929	−	0.825823i	$-0.690711\pi$
$443$	−15.0217	+	3.42860i	−0.713701	+	0.162898i	−0.149772	+	0.988721i	$0.547854\pi$
$444$		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	−0.945792	−	0.324773i	$-0.894712\pi$
$449$	−17.7912	+	14.1880i	−0.839620	+	0.669575i	0.106172	+	0.994348i	$0.466141\pi$
$450$		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	−0.131467	−	0.991321i	$-0.541969\pi$
$461$	−21.2236	−	10.2207i	−0.988481	−	0.476028i	−0.857014	+	0.515293i	$0.827683\pi$
$462$		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	−0.405998	−	0.913874i	$-0.633076\pi$
$467$	1.19638	−	0.576147i	0.0553620	−	0.0266609i	0.461360	+	0.887213i	$0.347362\pi$
$468$		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	0.965980	−	0.258617i	$-0.0832666\pi$
$479$	−0.362159	−	1.58672i	−0.0165475	−	0.0724992i	−0.982527	+	0.186117i	$0.940409\pi$
$480$		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	$0.181174\pi$
$491$			23.8841i			1.07787i	−0.842346	+	0.538937i	$0.818826\pi$
$492$		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	$-0.708368\pi$
$503$	−9.07175	−	39.7459i	−0.404489	−	1.77218i	0.204359	−	0.978896i	$-0.434489\pi$
$504$		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	$-0.182391\pi$
$509$	37.9152			1.68056			0.840280	+	0.542153i	$0.182391\pi$
$510$		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	$-0.730319\pi$
$521$	−30.2237			−1.32412			−0.662062	+	0.749449i	$0.730319\pi$
$522$		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	$0.132410\pi$
$557$			19.0735i			0.808170i	−0.914721	+	0.404085i	$0.867590\pi$
$558$		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	−0.983272	−	0.182144i	$-0.941696\pi$
$563$	−0.435284	+	1.90711i	−0.0183451	+	0.0803749i	0.964927	+	0.262519i	$0.0845533\pi$
$564$		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	$-0.697153\pi$
$569$		−	38.8454i		−	1.62848i	0.580525	−	0.814242i	$-0.302847\pi$
$570$		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	$-0.757938\pi$
$587$	−35.1074			−1.44904			−0.724518	+	0.689255i	$0.757938\pi$
$588$		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	$0.118101\pi$
$593$	26.2524	+	32.9195i	1.07806	+	1.35184i	0.146101	+	0.989270i	$0.453328\pi$
$594$		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	−0.808955	−	0.587870i	$-0.799967\pi$
$599$	−31.3942	+	7.16552i	−1.28273	+	0.292775i	−0.473776	+	0.880645i	$0.657109\pi$
$600$		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	−0.976025	−	0.217658i	$-0.930158\pi$
$617$	−4.90112	+	10.1773i	−0.197312	+	0.409722i	0.778714	+	0.627380i	$0.215873\pi$
$618$		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	$0.212101\pi$
$641$	19.7285	+	40.9666i	0.779229	+	1.61808i	−0.00686447	+	0.999976i	$0.502185\pi$
$642$		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	−0.268914	−	0.963164i	$-0.586665\pi$
$647$	18.5669	−	23.2822i	0.729940	−	0.915316i	0.998855	+	0.0478480i	$0.0152363\pi$
$648$		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	0.844868	−	0.534975i	$-0.179679\pi$
$653$	13.0659	+	10.4197i	0.511306	+	0.407753i	−0.333561	+	0.942728i	$0.608250\pi$
$654$		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	$0.174915\pi$
$659$	18.7246	+	38.8821i	0.729409	+	1.51463i	−0.123370	+	0.992361i	$0.539370\pi$
$660$		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	−0.982102	−	0.188352i	$-0.939685\pi$
$677$	−0.404227	+	1.77103i	−0.0155357	+	0.0680663i	0.966566	+	0.256418i	$0.0825425\pi$
$678$		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	−0.679451	−	0.733721i	$-0.737782\pi$
$683$	−3.01377	+	2.40340i	−0.115319	+	0.0919636i	0.564133	+	0.825684i	$0.309211\pi$
$684$		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	0.797603	−	0.603183i	$-0.206101\pi$
$701$	33.2148	+	7.58107i	1.25451	+	0.286333i	0.456904	+	0.889516i	$0.348958\pi$
$702$		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	−0.332567	−	0.943080i	$-0.607915\pi$
$719$	17.7207	−	22.2211i	0.660871	−	0.828706i	0.993438	+	0.114374i	$0.0364862\pi$
$720$		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	−0.519896	−	0.854229i	$-0.674029\pi$
$743$	5.37604	−	4.28725i	0.197228	−	0.157284i	0.717124	+	0.696945i	$0.245458\pi$
$744$		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	−0.270858	−	0.962619i	$-0.587307\pi$
$761$	8.63094	−	4.15644i	0.312871	−	0.150671i	0.583729	+	0.811949i	$0.301593\pi$
$762$		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	$0.0290812\pi$
$773$	3.84244	+	16.8348i	0.138203	+	0.605507i	−0.857626	+	0.514273i	$0.828062\pi$
$774$		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	$-0.864567\pi$
$797$	−7.60236	−	33.3081i	−0.269289	−	1.17983i	0.641553	−	0.767079i	$-0.278291\pi$
$798$		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	−0.462287	−	0.886730i	$-0.652971\pi$
$809$	−35.9385	−	8.20273i	−1.26353	−	0.288393i	−0.801244	+	0.598337i	$0.795828\pi$
$810$		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	$-0.523750\pi$
$821$	21.5354	−	44.7187i	0.751590	−	1.56069i	0.826133	−	0.563476i	$-0.190536\pi$
$822$		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	0.784691	−	0.619887i	$-0.212822\pi$
$827$	10.2077	+	8.14034i	0.354955	+	0.283067i	−0.429735	+	0.902955i	$0.641393\pi$
$828$		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	$0.484394\pi$
$839$	−27.1017	+	33.9844i	−0.935654	+	1.17327i	−0.984662	+	0.174474i	$0.944177\pi$
$840$		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	−0.935713	−	0.352762i	$-0.885243\pi$
$857$	1.76798	−	7.74601i	0.0603929	−	0.264599i	0.996106	+	0.0881632i	$0.0280997\pi$
$858$		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	$-0.707442\pi$
$863$		−	46.7125i		−	1.59011i	0.606536	−	0.795056i	$-0.292558\pi$
$864$		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	$-0.705289\pi$
$881$	−35.6860			−1.20229			−0.601146	+	0.799139i	$0.705289\pi$
$882$		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	0.971617	−	0.236561i	$-0.0760203\pi$
$887$	15.6293	+	19.5986i	0.524782	+	0.658056i	−0.446835	+	0.894616i	$0.647449\pi$
$888$		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	−0.830018	−	0.557737i	$-0.811670\pi$
$911$	3.72897	−	7.74329i	0.123546	−	0.256547i	0.953564	+	0.301190i	$0.0973840\pi$
$912$		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	0.921698	−	0.387908i	$-0.126802\pi$
$929$	−2.34784	−	10.2865i	−0.0770300	−	0.337491i	−0.998728	+	0.0504171i	$0.983945\pi$
$930$		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	$0.449782\pi$
$941$	−25.7881	+	32.3373i	−0.840668	+	1.05416i	−0.997781	+	0.0665841i	$0.978790\pi$
$942$		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	$0.00267451\pi$
$947$	37.8718	+	30.2018i	1.23067	+	0.981426i	0.230705	+	0.973024i	$0.425897\pi$
$948$		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	$-0.992008\pi$
$953$	−12.2254	−	25.3863i	−0.396019	−	0.822342i	0.603666	−	0.797238i	$-0.293706\pi$
$954$		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	−0.950942	−	0.309368i	$-0.899882\pi$
$971$	1.24821	−	5.46875i	0.0400569	−	0.175501i	0.990999	+	0.133867i	$0.0427396\pi$
$972$		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	−0.235890	−	0.971780i	$-0.575801\pi$
$977$	20.5994	−	16.4275i	0.659035	−	0.525563i	0.894925	+	0.446217i	$0.147229\pi$
$978$		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	0.242571	−	0.970134i	$-0.422009\pi$
$983$	−23.7409	−	29.7701i	−0.757217	−	0.949520i	−0.999788	+	0.0206138i	$0.993438\pi$
$984$		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.62.11	yes	120
3.2	odd	2	inner	441.2.w.a.62.10	✓	120
49.34	odd	14	inner	441.2.w.a.377.10	yes	120
147.83	even	14	inner	441.2.w.a.377.11	yes	120

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

Modular forms

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