LMFDB - Embedded newform 819.2.gh.d.262.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(19,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.1
Character	$\chi$	$=$	819.262
Dual form			819.2.gh.d.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.680470 - 2.53955i) q^{2} +(-4.25421 + 2.45617i) q^{4} +(-0.134776 + 0.502992i) q^{5} +(-2.56445 - 0.650845i) q^{7} +(5.41427 + 5.41427i) q^{8} +O(q^{10})$	\(q+(-0.680470 - 2.53955i) q^{2} +(-4.25421 + 2.45617i) q^{4} +(-0.134776 + 0.502992i) q^{5} +(-2.56445 - 0.650845i) q^{7} +(5.41427 + 5.41427i) q^{8} +1.36908 q^{10} +(-1.41413 - 1.41413i) q^{11} +(-2.40655 + 2.68487i) q^{13} +(0.0921792 + 6.95542i) q^{14} +(5.15321 - 8.92562i) q^{16} +(-2.54630 - 4.41032i) q^{17} +(5.09679 + 5.09679i) q^{19} +(-0.662067 - 2.47087i) q^{20} +(-2.62897 + 4.55351i) q^{22} +(4.14570 + 2.39352i) q^{23} +(4.09529 + 2.36442i) q^{25} +(8.45594 + 4.28458i) q^{26} +(12.5083 - 3.52989i) q^{28} +(1.35547 + 2.34774i) q^{29} +(3.23806 - 0.867635i) q^{31} +(-11.3816 - 3.04969i) q^{32} +(-9.46754 + 9.46754i) q^{34} +(0.672997 - 1.20218i) q^{35} +(7.17752 - 1.92321i) q^{37} +(9.47532 - 16.4117i) q^{38} +(-3.45305 + 1.99362i) q^{40} +(0.938828 - 3.50375i) q^{41} +(-3.62298 - 2.09173i) q^{43} +(9.48933 + 2.54266i) q^{44} +(3.25743 - 12.1569i) q^{46} +(-0.0803226 - 0.0215224i) q^{47} +(6.15280 + 3.33812i) q^{49} +(3.21783 - 12.0091i) q^{50} +(3.64348 - 17.3329i) q^{52} +(-6.85585 + 11.8747i) q^{53} +(0.901885 - 0.520704i) q^{55} +(-10.3608 - 17.4085i) q^{56} +(5.03985 - 5.03985i) q^{58} +(5.34294 + 1.43164i) q^{59} +0.753473i q^{61} +(-4.40680 - 7.63280i) q^{62} +10.3665i q^{64} +(-1.02612 - 1.57233i) q^{65} +(-7.68466 + 7.68466i) q^{67} +(21.6650 + 12.5083i) q^{68} +(-3.51095 - 0.891061i) q^{70} +(1.34000 + 5.00093i) q^{71} +(0.551150 + 2.05692i) q^{73} +(-9.76817 - 16.9190i) q^{74} +(-34.2014 - 9.16424i) q^{76} +(2.70608 + 4.54683i) q^{77} +(6.17212 + 10.6904i) q^{79} +(3.79499 + 3.79499i) q^{80} -9.53679 q^{82} +(7.09696 + 7.09696i) q^{83} +(2.56154 - 0.686362i) q^{85} +(-2.84672 + 10.6241i) q^{86} -15.3129i q^{88} +(-3.53214 - 13.1821i) q^{89} +(7.91891 - 5.31892i) q^{91} -23.5156 q^{92} +0.218629i q^{94} +(-3.25057 + 1.87672i) q^{95} +(3.28692 - 0.880729i) q^{97} +(4.29051 - 17.8968i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.680470	−	2.53955i	−0.481165	−	1.79573i	−0.596742	−	0.802433i	$-0.703539\pi$
$2$	−0.680470	−	2.53955i	−0.481165	−	1.79573i	0.115577	−	0.993298i	$-0.463128\pi$
$3$		0			0
$3$		0			0
$4$	−4.25421	+	2.45617i	−2.12711	+	1.22809i
$5$	−0.134776	+	0.502992i	−0.0602738	+	0.224945i	−0.989492	−	0.144586i	$-0.953815\pi$
$5$	−0.134776	+	0.502992i	−0.0602738	+	0.224945i	0.929218	+	0.369531i	$0.120482\pi$
$6$		0			0
$7$	−2.56445	−	0.650845i	−0.969271	−	0.245996i
$7$	−2.56445	−	0.650845i	−0.969271	−	0.245996i
$8$	5.41427	+	5.41427i	1.91423	+	1.91423i
$9$		0			0
$10$	1.36908			0.432942
$11$	−1.41413	−	1.41413i	−0.426375	−	0.426375i	0.461016	−	0.887392i	$-0.347485\pi$
$11$	−1.41413	−	1.41413i	−0.426375	−	0.426375i	−0.887392	+	0.461016i	$0.847485\pi$
$12$		0			0
$13$	−2.40655	+	2.68487i	−0.667457	+	0.744648i
$13$	−2.40655	+	2.68487i	−0.667457	+	0.744648i
$14$	0.0921792	+	6.95542i	0.0246359	+	1.85891i
$15$		0			0
$16$	5.15321	−	8.92562i	1.28830	−	2.23141i
$17$	−2.54630	−	4.41032i	−0.617569	−	1.06966i	−0.989928	−	0.141572i	$-0.954784\pi$
$17$	−2.54630	−	4.41032i	−0.617569	−	1.06966i	0.372359	−	0.928089i	$-0.378549\pi$
$18$		0			0
$19$	5.09679	+	5.09679i	1.16928	+	1.16928i	0.982378	+	0.186905i	$0.0598457\pi$
$19$	5.09679	+	5.09679i	1.16928	+	1.16928i	0.186905	+	0.982378i	$0.440154\pi$
$20$	−0.662067	−	2.47087i	−0.148043	−	0.552503i
$21$		0			0
$22$	−2.62897	+	4.55351i	−0.560499	+	0.970812i
$23$	4.14570	+	2.39352i	0.864437	+	0.499083i	0.865496	−	0.500916i	$-0.167004\pi$
$23$	4.14570	+	2.39352i	0.864437	+	0.499083i	−0.00105850	+	0.999999i	$0.500337\pi$
$24$		0			0
$25$	4.09529	+	2.36442i	0.819058	+	0.472883i
$26$	8.45594	+	4.28458i	1.65835	+	0.840275i
$27$		0			0
$28$	12.5083	−	3.52989i	2.36385	−	0.667087i
$29$	1.35547	+	2.34774i	0.251704	+	0.435965i	0.963995	−	0.265920i	$-0.0856756\pi$
$29$	1.35547	+	2.34774i	0.251704	+	0.435965i	−0.712291	+	0.701884i	$0.752342\pi$
$30$		0			0
$31$	3.23806	−	0.867635i	0.581572	−	0.155832i	0.0439736	−	0.999033i	$-0.485998\pi$
$31$	3.23806	−	0.867635i	0.581572	−	0.155832i	0.537599	+	0.843201i	$0.319332\pi$
$32$	−11.3816	−	3.04969i	−2.01200	−	0.539114i
$33$		0			0
$34$	−9.46754	+	9.46754i	−1.62367	+	1.62367i
$35$	0.672997	−	1.20218i	0.113757	−	0.203205i
$36$		0			0
$37$	7.17752	−	1.92321i	1.17998	−	0.316174i	0.385060	−	0.922892i	$-0.374181\pi$
$37$	7.17752	−	1.92321i	1.17998	−	0.316174i	0.794917	+	0.606718i	$0.207514\pi$
$38$	9.47532	−	16.4117i	1.53710	−	2.66234i
$39$		0			0
$40$	−3.45305	+	1.99362i	−0.545975	+	0.315219i
$41$	0.938828	−	3.50375i	0.146620	−	0.547194i	−0.853058	−	0.521817i	$-0.825255\pi$
$41$	0.938828	−	3.50375i	0.146620	−	0.547194i	0.999678	−	0.0253776i	$-0.00807880\pi$
$42$		0			0
$43$	−3.62298	−	2.09173i	−0.552500	−	0.318986i	0.197630	−	0.980277i	$-0.436676\pi$
$43$	−3.62298	−	2.09173i	−0.552500	−	0.318986i	−0.750130	+	0.661291i	$0.770009\pi$
$44$	9.48933	+	2.54266i	1.43057	+	0.383320i
$45$		0			0
$46$	3.25743	−	12.1569i	0.480282	−	1.79244i
$47$	−0.0803226	−	0.0215224i	−0.0117163	−	0.00313936i	0.252956	−	0.967478i	$-0.418597\pi$
$47$	−0.0803226	−	0.0215224i	−0.0117163	−	0.00313936i	−0.264672	+	0.964338i	$0.585264\pi$
$48$		0			0
$49$	6.15280	+	3.33812i	0.878972	+	0.476874i
$50$	3.21783	−	12.0091i	0.455070	−	1.69834i
$51$		0			0
$52$	3.64348	−	17.3329i	0.505260	−	2.40364i
$53$	−6.85585	+	11.8747i	−0.941723	+	1.63111i	−0.179541	+	0.983751i	$0.557461\pi$
$53$	−6.85585	+	11.8747i	−0.941723	+	1.63111i	−0.762183	+	0.647362i	$0.775872\pi$
$54$		0			0
$55$	0.901885	−	0.520704i	0.121610	−	0.0702117i
$56$	−10.3608	−	17.4085i	−1.38452	−	2.32631i
$57$		0			0
$58$	5.03985	−	5.03985i	0.661764	−	0.661764i
$59$	5.34294	+	1.43164i	0.695591	+	0.186383i	0.589255	−	0.807947i	$-0.299421\pi$
$59$	5.34294	+	1.43164i	0.695591	+	0.186383i	0.106336	+	0.994330i	$0.466088\pi$
$60$		0			0
$61$			0.753473i			0.0964723i	0.998836	+	0.0482361i	$0.0153600\pi$
$61$			0.753473i			0.0964723i	−0.998836	+	0.0482361i	$0.984640\pi$
$62$	−4.40680	−	7.63280i	−0.559664	−	0.969367i
$63$		0			0
$64$			10.3665i			1.29581i
$65$	−1.02612	−	1.57233i	−0.127275	−	0.195024i
$66$		0			0
$67$	−7.68466	+	7.68466i	−0.938831	+	0.938831i	−0.998234	−	0.0594033i	$-0.981080\pi$
$67$	−7.68466	+	7.68466i	−0.938831	+	0.938831i	0.0594033	+	0.998234i	$0.481080\pi$
$68$	21.6650	+	12.5083i	2.62727	+	1.51685i
$69$		0			0
$70$	−3.51095	−	0.891061i	−0.419638	−	0.106502i
$71$	1.34000	+	5.00093i	0.159028	+	0.593502i	0.998727	+	0.0504485i	$0.0160651\pi$
$71$	1.34000	+	5.00093i	0.159028	+	0.593502i	−0.839698	+	0.543053i	$0.817268\pi$
$72$		0			0
$73$	0.551150	+	2.05692i	0.0645072	+	0.240744i	0.990650	−	0.136429i	$-0.0435627\pi$
$73$	0.551150	+	2.05692i	0.0645072	+	0.240744i	−0.926143	+	0.377174i	$0.876896\pi$
$74$	−9.76817	−	16.9190i	−1.13553	−	1.96679i
$75$		0			0
$76$	−34.2014	−	9.16424i	−3.92317	−	1.05121i
$77$	2.70608	+	4.54683i	0.308386	+	0.518160i
$78$		0			0
$79$	6.17212	+	10.6904i	0.694418	+	1.20277i	0.970377	+	0.241597i	$0.0776713\pi$
$79$	6.17212	+	10.6904i	0.694418	+	1.20277i	−0.275959	+	0.961169i	$0.588995\pi$
$80$	3.79499	+	3.79499i	0.424292	+	0.424292i
$81$		0			0
$82$	−9.53679			−1.05316
$83$	7.09696	+	7.09696i	0.778993	+	0.778993i	0.979660	−	0.200667i	$-0.0643109\pi$
$83$	7.09696	+	7.09696i	0.778993	+	0.778993i	−0.200667	+	0.979660i	$0.564311\pi$
$84$		0			0
$85$	2.56154	−	0.686362i	0.277838	−	0.0744464i
$86$	−2.84672	+	10.6241i	−0.306970	+	1.14563i
$87$		0			0
$88$		−	15.3129i		−	1.63236i
$89$	−3.53214	−	13.1821i	−0.374406	−	1.39730i	−0.854211	−	0.519927i	$-0.825959\pi$
$89$	−3.53214	−	13.1821i	−0.374406	−	1.39730i	0.479805	−	0.877375i	$-0.340707\pi$
$90$		0			0
$91$	7.91891	−	5.31892i	0.830127	−	0.557574i
$92$	−23.5156			−2.45167
$93$		0			0
$94$			0.218629i			0.0225498i
$95$	−3.25057	+	1.87672i	−0.333501	+	0.192547i
$96$		0			0
$97$	3.28692	−	0.880729i	0.333737	−	0.0894244i	−0.0880594	−	0.996115i	$-0.528067\pi$
$97$	3.28692	−	0.880729i	0.333737	−	0.0894244i	0.421796	+	0.906691i	$0.361400\pi$
$98$	4.29051	−	17.8968i	0.433407	−	1.80785i
$99$		0			0
$100$	−23.2297			−2.32297
$101$	−12.0952			−1.20352			−0.601760	−	0.798677i	$-0.705534\pi$
$101$	−12.0952			−1.20352			−0.601760	+	0.798677i	$0.705534\pi$
$102$		0			0
$103$	−4.04418	−	7.00473i	−0.398485	−	0.690196i	0.595054	−	0.803686i	$-0.297131\pi$
$103$	−4.04418	−	7.00473i	−0.398485	−	0.690196i	−0.993539	+	0.113489i	$0.963797\pi$
$104$	−27.5663	+	1.50689i	−2.70310	+	0.147762i
$105$		0			0
$106$	34.8215	+	9.33040i	3.38216	+	0.906248i
$107$	−2.82363	+	4.89066i	−0.272970	+	0.472798i	−0.969621	−	0.244612i	$-0.921339\pi$
$107$	−2.82363	+	4.89066i	−0.272970	+	0.472798i	0.696651	+	0.717410i	$0.254673\pi$
$108$		0			0
$109$	2.50644	+	9.35415i	0.240073	+	0.895965i	0.975796	+	0.218682i	$0.0701758\pi$
$109$	2.50644	+	9.35415i	0.240073	+	0.895965i	−0.735723	+	0.677282i	$0.763158\pi$
$110$	−1.93606	−	1.93606i	−0.184596	−	0.184596i
$111$		0			0
$112$	−19.0243	+	19.5354i	−1.79763	+	1.84592i
$113$	−9.60923	+	16.6437i	−0.903960	+	1.56570i	−0.0816525	+	0.996661i	$0.526020\pi$
$113$	−9.60923	+	16.6437i	−0.903960	+	1.56570i	−0.822307	+	0.569044i	$0.807314\pi$
$114$		0			0
$115$	−1.76266	+	1.76266i	−0.164369	+	0.164369i
$116$	−11.5329	−	6.65853i	−1.07080	−	0.618229i
$117$		0			0
$118$		−	14.5428i		−	1.33878i
$119$	3.65942	+	12.9673i	0.335459	+	1.18871i
$120$		0			0
$121$		−	7.00049i		−	0.636408i
$122$	1.91348	−	0.512715i	0.173238	−	0.0464191i
$123$		0			0
$124$	−11.6443	+	11.6443i	−1.04569	+	1.04569i
$125$	−3.58231	+	3.58231i	−0.320411	+	0.320411i
$126$		0			0
$127$	−5.78281	+	3.33871i	−0.513141	+	0.296262i	−0.734124	−	0.679015i	$-0.762407\pi$
$127$	−5.78281	+	3.33871i	−0.513141	+	0.296262i	0.220983	+	0.975278i	$0.429074\pi$
$128$	3.56294	−	0.954687i	0.314923	−	0.0843832i
$129$		0			0
$130$	−3.29477	+	3.67581i	−0.288970	+	0.322390i
$131$	0.269003	−	0.155309i	0.0235029	−	0.0135694i	−0.488203	−	0.872730i	$-0.662347\pi$
$131$	0.269003	−	0.155309i	0.0235029	−	0.0135694i	0.511705	+	0.859161i	$0.329014\pi$
$132$		0			0
$133$	−9.75324	−	16.3877i	−0.845713	−	1.42099i
$134$	24.7447	+	14.2864i	2.13762	+	1.23416i
$135$		0			0
$136$	10.0923	−	37.6650i	0.865409	−	3.22975i
$137$	1.25362	−	4.67858i	0.107104	−	0.399718i	−0.891471	−	0.453077i	$-0.850326\pi$
$137$	1.25362	−	4.67858i	0.107104	−	0.399718i	0.998575	+	0.0533594i	$0.0169929\pi$
$138$		0			0
$139$	9.26980	+	5.35192i	0.786254	+	0.453944i	0.838642	−	0.544683i	$-0.183350\pi$
$139$	9.26980	+	5.35192i	0.786254	+	0.453944i	−0.0523882	+	0.998627i	$0.516683\pi$
$140$	0.0896863	+	6.76732i	0.00757988	+	0.571943i
$141$		0			0
$142$	11.7883	−	6.80597i	0.989251	−	0.571144i
$143$	7.19991	−	0.393577i	0.602087	−	0.0329125i
$144$		0			0
$145$	−1.36358	+	0.365370i	−0.113239	+	0.0303424i
$146$	4.84860	−	2.79934i	0.401273	−	0.231675i
$147$		0			0
$148$	−25.8110	+	25.8110i	−2.12165	+	2.12165i
$149$	12.0380	−	12.0380i	0.986188	−	0.986188i	−0.0137184	−	0.999906i	$-0.504367\pi$
$149$	12.0380	−	12.0380i	0.986188	−	0.986188i	0.999906	+	0.0137184i	$0.00436683\pi$
$150$		0			0
$151$	17.6453	−	4.72803i	1.43595	−	0.384762i	0.544837	−	0.838542i	$-0.316592\pi$
$151$	17.6453	−	4.72803i	1.43595	−	0.384762i	0.891114	+	0.453780i	$0.149925\pi$
$152$			55.1908i			4.47656i
$153$		0			0
$154$	9.70549	−	9.96620i	0.782091	−	0.803099i
$155$			1.74565i			0.140214i
$156$		0			0
$157$	−4.25722	−	2.45791i	−0.339763	−	0.196162i	0.320404	−	0.947281i	$-0.396181\pi$
$157$	−4.25722	−	2.45791i	−0.339763	−	0.196162i	−0.660167	+	0.751119i	$0.729515\pi$
$158$	22.9489	−	22.9489i	1.82572	−	1.82572i
$159$		0			0
$160$	3.06794	−	5.31382i	0.242542	−	0.420094i
$161$	−9.07362	−	8.83626i	−0.715101	−	0.696395i
$162$		0			0
$163$	2.14574	+	2.14574i	0.168067	+	0.168067i	0.786129	−	0.618062i	$-0.212082\pi$
$163$	2.14574	+	2.14574i	0.168067	+	0.168067i	−0.618062	+	0.786129i	$0.712082\pi$
$164$	4.61184	+	17.2116i	0.360124	+	1.34400i
$165$		0			0
$166$	13.1938	−	22.8523i	1.02404	−	1.77369i
$167$	9.12053	+	2.44384i	0.705768	+	0.189110i	0.593813	−	0.804603i	$-0.297622\pi$
$167$	9.12053	+	2.44384i	0.705768	+	0.189110i	0.111955	+	0.993713i	$0.464289\pi$
$168$		0			0
$169$	−1.41703	−	12.9225i	−0.109002	−	0.994041i
$170$	−3.48610	−	6.03810i	−0.267372	−	0.463101i
$171$		0			0
$172$	20.5506			1.56697
$173$	−21.9790			−1.67103			−0.835515	−	0.549468i	$-0.814831\pi$
$173$	−21.9790			−1.67103			−0.835515	+	0.549468i	$0.814831\pi$
$174$		0			0
$175$	−8.96330	−	8.72883i	−0.677562	−	0.659837i
$176$	−19.9093	+	5.33467i	−1.50072	+	0.402116i
$177$		0			0
$178$	−31.0731	+	17.9401i	−2.32903	+	1.34467i
$179$			17.0783i			1.27649i	0.769832	+	0.638247i	$0.220340\pi$
$179$			17.0783i			1.27649i	−0.769832	+	0.638247i	$0.779660\pi$
$180$		0			0
$181$	−18.0173			−1.33922			−0.669608	−	0.742714i	$-0.733538\pi$
$181$	−18.0173			−1.33922			−0.669608	+	0.742714i	$0.733538\pi$
$182$	−18.8962	−	16.4911i	−1.40068	−	1.22240i
$183$		0			0
$184$	9.48676	+	35.4051i	0.699373	+	2.61010i
$185$			3.86944i			0.284487i
$186$		0			0
$187$	−2.63596	+	9.83755i	−0.192761	+	0.719393i
$188$	0.394572	−	0.105725i	0.0287771	−	0.00771081i
$189$		0			0
$190$	6.97793	+	6.97793i	0.506232	+	0.506232i
$191$	22.0698			1.59692			0.798458	−	0.602050i	$-0.205649\pi$
$191$	22.0698			1.59692			0.798458	+	0.602050i	$0.205649\pi$
$192$		0			0
$193$	5.16659	+	5.16659i	0.371899	+	0.371899i	0.868169	−	0.496269i	$-0.165297\pi$
$193$	5.16659	+	5.16659i	0.371899	+	0.371899i	−0.496269	+	0.868169i	$0.665297\pi$
$194$	−4.47330	−	7.74799i	−0.321165	−	0.556273i
$195$		0			0
$196$	−34.3743	+	0.911276i	−2.45531	+	0.0650911i
$197$	22.5188	+	6.03390i	1.60440	+	0.429898i	0.946368	−	0.323092i	$-0.104722\pi$
$197$	22.5188	+	6.03390i	1.60440	+	0.429898i	0.658033	+	0.752989i	$0.271389\pi$
$198$		0			0
$199$	8.87911	+	15.3791i	0.629423	+	1.09019i	0.987668	+	0.156565i	$0.0500421\pi$
$199$	8.87911	+	15.3791i	0.629423	+	1.09019i	−0.358244	+	0.933628i	$0.616625\pi$
$200$	9.37142	+	34.9746i	0.662659	+	2.47308i
$201$		0			0
$202$	8.23044	+	30.7164i	0.579092	+	2.16120i
$203$	−1.94802	−	6.90287i	−0.136724	−	0.484486i
$204$		0			0
$205$	1.63583	+	0.944445i	0.114251	+	0.0659629i
$206$	−15.0369	+	15.0369i	−1.04767	+	1.04767i
$207$		0			0
$208$	11.5627	+	35.3156i	0.801726	+	2.44870i
$209$		−	14.4150i		−	0.997107i
$210$		0			0
$211$	−2.69516	−	4.66816i	−0.185543	−	0.321370i	0.758217	−	0.652003i	$-0.226071\pi$
$211$	−2.69516	−	4.66816i	−0.185543	−	0.321370i	−0.943759	+	0.330633i	$0.892738\pi$
$212$		−	67.3566i		−	4.62607i
$213$		0			0
$214$	14.3415	+	3.84278i	0.980362	+	0.262687i
$215$	1.54042	−	1.54042i	0.105055	−	0.105055i
$216$		0			0
$217$	−8.86853	+	0.117533i	−0.602035	+	0.00797868i
$218$	22.0497	−	12.7304i	1.49340	−	0.862213i
$219$		0			0
$220$	−2.55787	+	4.43037i	−0.172452	+	0.298695i
$221$	17.9689	+	3.77718i	1.20872	+	0.254081i
$222$		0			0
$223$	−3.70617	+	13.8316i	−0.248183	+	0.926233i	0.723573	+	0.690248i	$0.242498\pi$
$223$	−3.70617	+	13.8316i	−0.248183	+	0.926233i	−0.971757	+	0.235986i	$0.924168\pi$
$224$	27.2026	+	15.2284i	1.81755	+	1.01749i
$225$		0			0
$226$	48.8062	+	13.0776i	3.24654	+	0.869907i
$227$	1.53180	−	5.71677i	0.101669	−	0.379435i	−0.896277	−	0.443495i	$-0.853738\pi$
$227$	1.53180	−	5.71677i	0.101669	−	0.379435i	0.997946	+	0.0640600i	$0.0204049\pi$
$228$		0			0
$229$	28.5531	+	7.65078i	1.88684	+	0.505578i	0.998964	+	0.0454971i	$0.0144872\pi$
$229$	28.5531	+	7.65078i	1.88684	+	0.505578i	0.887877	+	0.460081i	$0.152179\pi$
$230$	5.67580	+	3.27693i	0.374251	+	0.216074i
$231$		0			0
$232$	−5.37243	+	20.0502i	−0.352718	+	1.31636i
$233$	2.20932	−	1.27555i	0.144737	−	0.0835641i	−0.425883	−	0.904778i	$-0.640036\pi$
$233$	2.20932	−	1.27555i	0.144737	−	0.0835641i	0.570620	+	0.821214i	$0.306703\pi$
$234$		0			0
$235$	0.0216512	−	0.0375009i	0.00141237	−	0.00244629i
$236$	−26.2463	+	7.03269i	−1.70849	+	0.457789i
$237$		0			0
$238$	30.4409	−	18.1171i	1.97319	−	1.17436i
$239$	−7.35563	+	7.35563i	−0.475796	+	0.475796i	−0.903784	−	0.427988i	$-0.859222\pi$
$239$	−7.35563	+	7.35563i	−0.475796	+	0.475796i	0.427988	+	0.903784i	$0.359222\pi$
$240$		0			0
$241$	−3.49299	−	0.935943i	−0.225003	−	0.0602894i	0.144556	−	0.989497i	$-0.453825\pi$
$241$	−3.49299	−	0.935943i	−0.225003	−	0.0602894i	−0.369559	+	0.929207i	$0.620491\pi$
$242$	−17.7781	+	4.76362i	−1.14282	+	0.306217i
$243$		0			0
$244$	−1.85066	−	3.20543i	−0.118476	−	0.205207i
$245$	−2.50830	+	2.64491i	−0.160249	+	0.168977i
$246$		0			0
$247$	−25.9499	+	1.41853i	−1.65115	+	0.0902587i
$248$	22.2293	+	12.8341i	1.41156	+	0.814967i
$249$		0			0
$250$	11.5351	+	6.65979i	0.729544	+	0.421202i
$251$	−0.0388167	+	0.0672326i	−0.00245009	+	0.00424368i	−0.867248	−	0.497877i	$-0.834113\pi$
$251$	−0.0388167	+	0.0672326i	−0.00245009	+	0.00424368i	0.864798	+	0.502120i	$0.167447\pi$
$252$		0			0
$253$	−2.47780	−	9.24728i	−0.155778	−	0.581371i
$254$	12.4138	+	12.4138i	0.778913	+	0.778913i
$255$		0			0
$256$	5.51751	+	9.55660i	0.344844	+	0.597288i
$257$	−1.14492	+	1.98305i	−0.0714179	+	0.123699i	−0.899523	−	0.436874i	$-0.856086\pi$
$257$	−1.14492	+	1.98305i	−0.0714179	+	0.123699i	0.828105	+	0.560573i	$0.189419\pi$
$258$		0			0
$259$	−19.6581	+	0.260526i	−1.22149	+	0.0161883i
$260$	8.22725	+	4.16871i	0.510233	+	0.258532i
$261$		0			0
$262$	−0.577463	−	0.577463i	−0.0356758	−	0.0356758i
$263$	5.04181			0.310891			0.155446	−	0.987844i	$-0.450319\pi$
$263$	5.04181			0.310891			0.155446	+	0.987844i	$0.450319\pi$
$264$		0			0
$265$	−5.04886	−	5.04886i	−0.310149	−	0.310149i
$266$	−34.9805	+	35.9201i	−2.14479	+	2.20240i
$267$		0			0
$268$	13.8173	−	51.5670i	0.844029	−	3.14996i
$269$	−14.1938	+	8.19481i	−0.865413	+	0.499646i	−0.865821	−	0.500353i	$-0.833203\pi$
$269$	−14.1938	+	8.19481i	−0.865413	+	0.499646i	0.000408161		1.00000i	$0.499870\pi$
$270$		0			0
$271$	1.70008	+	6.34477i	0.103272	+	0.385418i	0.998143	−	0.0609071i	$-0.0193993\pi$
$271$	1.70008	+	6.34477i	0.103272	+	0.385418i	−0.894871	+	0.446325i	$0.852733\pi$
$272$	−52.4865			−3.18246
$273$		0			0
$274$	−12.7345			−0.769320
$275$	−2.44767	−	9.13484i	−0.147600	−	0.550852i
$276$		0			0
$277$	1.35080	−	0.779884i	0.0811616	−	0.0468587i	−0.458870	−	0.888503i	$-0.651746\pi$
$277$	1.35080	−	0.779884i	0.0811616	−	0.0468587i	0.540032	+	0.841645i	$0.318412\pi$
$278$	7.28364	−	27.1829i	0.436844	−	1.63032i
$279$		0			0
$280$	10.1527	−	2.86514i	0.606740	−	0.171225i
$281$	−0.519129	−	0.519129i	−0.0309687	−	0.0309687i	0.691453	−	0.722422i	$-0.256971\pi$
$281$	−0.519129	−	0.519129i	−0.0309687	−	0.0309687i	−0.722422	+	0.691453i	$0.756971\pi$
$282$		0			0
$283$	−27.5291			−1.63644			−0.818218	−	0.574908i	$-0.805038\pi$
$283$	−27.5291			−1.63644			−0.818218	+	0.574908i	$0.805038\pi$
$284$	−17.9838	−	17.9838i	−1.06714	−	1.06714i
$285$		0			0
$286$	−5.89883	−	18.0167i	−0.348805	−	1.06535i
$287$	−4.68797	+	8.37416i	−0.276722	+	0.494311i
$288$		0			0
$289$	−4.46730	+	7.73758i	−0.262782	+	0.455152i
$290$	1.85575	+	3.21425i	0.108973	+	0.188748i
$291$		0			0
$292$	−7.39685	−	7.39685i	−0.432868	−	0.432868i
$293$	−2.78349	−	10.3881i	−0.162613	−	0.606881i	−0.998333	−	0.0577244i	$-0.981616\pi$
$293$	−2.78349	−	10.3881i	−0.162613	−	0.606881i	0.835719	−	0.549157i	$-0.185051\pi$
$294$		0			0
$295$	−1.44020	+	2.49450i	−0.0838518	+	0.145236i
$296$	49.2738	+	28.4482i	2.86398	+	1.65352i
$297$		0			0
$298$	−38.7624	−	22.3795i	−2.24545	−	1.29641i
$299$	−16.4031	+	5.37052i	−0.948616	+	0.310585i
$300$		0			0
$301$	7.92957	+	7.72214i	0.457053	+	0.445097i
$302$	−24.0141	−	41.5937i	−1.38186	−	2.39345i
$303$		0			0
$304$	71.7568	−	19.2272i	4.11554	−	1.10275i
$305$	−0.378991	−	0.101550i	−0.0217009	−	0.00581475i
$306$		0			0
$307$	2.62443	−	2.62443i	0.149784	−	0.149784i	−0.628237	−	0.778022i	$-0.716223\pi$
$307$	2.62443	−	2.62443i	0.149784	−	0.149784i	0.778022	+	0.628237i	$0.216223\pi$
$308$	−22.6800	−	12.6966i	−1.29232	−	0.723456i
$309$		0			0
$310$	4.43317	−	1.18786i	0.251787	−	0.0674662i
$311$	−2.68970	+	4.65870i	−0.152519	+	0.264171i	−0.932153	−	0.362065i	$-0.882072\pi$
$311$	−2.68970	+	4.65870i	−0.152519	+	0.264171i	0.779634	+	0.626236i	$0.215405\pi$
$312$		0			0
$313$	27.3358	−	15.7824i	1.54511	−	0.892072i	0.546610	−	0.837387i	$-0.315918\pi$
$313$	27.3358	−	15.7824i	1.54511	−	0.892072i	0.998504	−	0.0546842i	$-0.0174152\pi$
$314$	−3.34506	+	12.4839i	−0.188773	+	0.704510i
$315$		0			0
$316$	−52.5150	−	30.3196i	−2.95420	−	1.70561i
$317$	−10.9296	−	2.92857i	−0.613866	−	0.164485i	−0.0615283	−	0.998105i	$-0.519597\pi$
$317$	−10.9296	−	2.92857i	−0.613866	−	0.164485i	−0.552338	+	0.833620i	$0.686264\pi$
$318$		0			0
$319$	1.40320	−	5.23681i	0.0785641	−	0.293205i
$320$	−5.21424	−	1.39715i	−0.291485	−	0.0781032i
$321$		0			0
$322$	−16.2658	+	29.0557i	−0.906457	+	1.61921i
$323$	9.50052	−	35.4564i	0.528623	−	1.97285i
$324$		0			0
$325$	−16.2037	+	5.30523i	−0.898818	+	0.294281i
$326$	3.98909	−	6.90931i	0.220935	−	0.382672i
$327$		0			0
$328$	24.0533	−	13.8872i	1.32812	−	0.766792i
$329$	0.191976	+	0.107471i	0.0105840	+	0.00592505i
$330$		0			0
$331$	−12.8446	+	12.8446i	−0.706004	+	0.706004i	−0.965692	−	0.259688i	$-0.916380\pi$
$331$	−12.8446	+	12.8446i	−0.706004	+	0.706004i	0.259688	+	0.965692i	$0.416380\pi$
$332$	−47.6233	−	12.7606i	−2.61367	−	0.700331i
$333$		0			0
$334$		−	24.8250i		−	1.35836i
$335$	−2.82961	−	4.90103i	−0.154598	−	0.267772i
$336$		0			0
$337$		−	20.1380i		−	1.09698i	−0.836156	−	0.548492i	$-0.815202\pi$
$337$		−	20.1380i		−	1.09698i	0.836156	−	0.548492i	$-0.184798\pi$
$338$	−31.8532	+	12.3920i	−1.73258	+	0.674037i
$339$		0			0
$340$	−9.21150	+	9.21150i	−0.499564	+	0.499564i
$341$	−5.80597	−	3.35208i	−0.314411	−	0.181525i
$342$		0			0
$343$	−13.6060	−	12.5650i	−0.734653	−	0.678444i
$344$	−8.29062	−	30.9410i	−0.447000	−	1.66823i
$345$		0			0
$346$	14.9560	+	55.8166i	0.804041	+	3.00072i
$347$	−4.81207	−	8.33476i	−0.258326	−	0.447433i	0.707468	−	0.706746i	$-0.249837\pi$
$347$	−4.81207	−	8.33476i	−0.258326	−	0.447433i	−0.965794	+	0.259312i	$0.916504\pi$
$348$		0			0
$349$	−24.0092	−	6.43324i	−1.28518	−	0.344364i	−0.449354	−	0.893354i	$-0.648346\pi$
$349$	−24.0092	−	6.43324i	−1.28518	−	0.344364i	−0.835829	+	0.548990i	$0.815012\pi$
$350$	−16.0680	+	28.7024i	−0.858872	+	1.53421i
$351$		0			0
$352$	11.7824	+	20.4076i	0.628002	+	1.08773i
$353$	−6.44715	−	6.44715i	−0.343147	−	0.343147i	0.514402	−	0.857549i	$-0.328014\pi$
$353$	−6.44715	−	6.44715i	−0.343147	−	0.343147i	−0.857549	+	0.514402i	$0.828014\pi$
$354$		0			0
$355$	−2.69603			−0.143090
$356$	47.4040	+	47.4040i	2.51241	+	2.51241i
$357$		0			0
$358$	43.3712	−	11.6213i	2.29224	−	0.614204i
$359$	−0.911092	+	3.40024i	−0.0480856	+	0.179458i	−0.985792	−	0.167971i	$-0.946278\pi$
$359$	−0.911092	+	3.40024i	−0.0480856	+	0.179458i	0.937706	+	0.347429i	$0.112945\pi$
$360$		0			0
$361$			32.9545i			1.73445i
$362$	12.2602	+	45.7558i	0.644384	+	2.40487i
$363$		0			0
$364$	−20.6246	+	42.0780i	−1.08102	+	2.20549i
$365$	−1.10890			−0.0580422
$366$		0			0
$367$		−	1.44234i		−	0.0752895i	−0.999291	−	0.0376448i	$-0.988014\pi$
$367$		−	1.44234i		−	0.0752895i	0.999291	−	0.0376448i	$-0.0119855\pi$
$368$	42.7273	−	24.6686i	2.22731	−	1.28594i
$369$		0			0
$370$	9.82662	−	2.63304i	0.510862	−	0.136885i
$371$	25.3101	−	25.9899i	1.31403	−	1.34933i
$372$		0			0
$373$	7.38975			0.382627			0.191313	−	0.981529i	$-0.438725\pi$
$373$	7.38975			0.382627			0.191313	+	0.981529i	$0.438725\pi$
$374$	26.7766			1.38459
$375$		0			0
$376$	−0.318361	−	0.551417i	−0.0164182	−	0.0284371i
$377$	−9.56538	−	2.01070i	−0.492642	−	0.103556i
$378$		0			0
$379$	−12.7292	−	3.41078i	−0.653855	−	0.175200i	−0.0833836	−	0.996518i	$-0.526573\pi$
$379$	−12.7292	−	3.41078i	−0.653855	−	0.175200i	−0.570471	+	0.821318i	$0.693239\pi$
$380$	9.21908	−	15.9679i	0.472929	−	0.819136i
$381$		0			0
$382$	−15.0178	−	56.0474i	−0.768380	−	2.86763i
$383$	14.5825	+	14.5825i	0.745133	+	0.745133i	0.973561	−	0.228427i	$-0.0733584\pi$
$383$	14.5825	+	14.5825i	0.745133	+	0.745133i	−0.228427	+	0.973561i	$0.573358\pi$
$384$		0			0
$385$	−2.65174	+	0.748331i	−0.135145	+	0.0381385i
$386$	9.60509	−	16.6365i	0.488886	−	0.846776i
$387$		0			0
$388$	−11.8201	+	11.8201i	−0.600072	+	0.600072i
$389$	31.3755	+	18.1147i	1.59080	+	0.918449i	0.993170	+	0.116678i	$0.0372247\pi$
$389$	31.3755	+	18.1147i	1.59080	+	0.918449i	0.597631	+	0.801771i	$0.296109\pi$
$390$		0			0
$391$		−	24.3785i		−	1.23287i
$392$	15.2395	+	51.3864i	0.769710	+	2.59541i
$393$		0			0
$394$		−	61.2935i		−	3.08792i
$395$	−6.20905	+	1.66371i	−0.312411	+	0.0837104i
$396$		0			0
$397$	−19.3303	+	19.3303i	−0.970161	+	0.970161i	−0.999568	−	0.0294069i	$-0.990638\pi$
$397$	−19.3303	+	19.3303i	−0.970161	+	0.970161i	0.0294069	+	0.999568i	$0.490638\pi$
$398$	33.0139	−	33.0139i	1.65484	−	1.65484i
$399$		0			0
$400$	42.2078	−	24.3687i	2.11039	−	1.21843i
$401$	13.2850	−	3.55970i	0.663421	−	0.177763i	0.0886316	−	0.996064i	$-0.471751\pi$
$401$	13.2850	−	3.55970i	0.663421	−	0.177763i	0.574789	+	0.818301i	$0.305084\pi$
$402$		0			0
$403$	−5.46306	+	10.7818i	−0.272135	+	0.537078i
$404$	51.4557	−	29.7080i	2.56002	−	1.47803i
$405$		0			0
$406$	−16.2046	+	9.64428i	−0.804220	+	0.478637i
$407$	−12.8696	−	7.43026i	−0.637922	−	0.368304i
$408$		0			0
$409$	4.02721	−	15.0297i	0.199133	−	0.743173i	−0.792026	−	0.610488i	$-0.790973\pi$
$409$	4.02721	−	15.0297i	0.199133	−	0.743173i	0.991158	−	0.132685i	$-0.0423599\pi$
$410$	1.28533	−	4.79693i	0.0634781	−	0.236903i
$411$		0			0
$412$	34.4096	+	19.8664i	1.69524	+	0.978748i
$413$	−12.7699	−	7.14878i	−0.628367	−	0.351768i
$414$		0			0
$415$	−4.52622	+	2.61321i	−0.222183	+	0.128278i
$416$	35.5784	−	23.2188i	1.74437	−	1.13840i
$417$		0			0
$418$	−36.6076	+	9.80897i	−1.79054	+	0.479773i
$419$	−17.5367	+	10.1248i	−0.856726	+	0.494631i	−0.862914	−	0.505350i	$-0.831363\pi$
$419$	−17.5367	+	10.1248i	−0.856726	+	0.494631i	0.00618874	+	0.999981i	$0.498030\pi$
$420$		0			0
$421$	14.0732	−	14.0732i	0.685887	−	0.685887i	−0.275433	−	0.961320i	$-0.588821\pi$
$421$	14.0732	−	14.0732i	0.685887	−	0.685887i	0.961320	+	0.275433i	$0.0888213\pi$
$422$	−10.0210	+	10.0210i	−0.487817	+	0.487817i
$423$		0			0
$424$	−101.412	+	27.1733i	−4.92501	+	1.31965i
$425$		−	24.0821i		−	1.16815i
$426$		0			0
$427$	0.490394	−	1.93224i	0.0237318	−	0.0935078i
$428$		−	27.7412i		−	1.34092i
$429$		0			0
$430$	−4.96017	−	2.86375i	−0.239200	−	0.138102i
$431$	−9.14707	+	9.14707i	−0.440599	+	0.440599i	−0.892213	−	0.451614i	$-0.850848\pi$
$431$	−9.14707	+	9.14707i	−0.440599	+	0.440599i	0.451614	+	0.892213i	$0.350848\pi$
$432$		0			0
$433$	10.1407	−	17.5642i	0.487331	−	0.844082i	−0.512563	−	0.858650i	$-0.671304\pi$
$433$	10.1407	−	17.5642i	0.487331	−	0.844082i	0.999894	+	0.0145673i	$0.00463709\pi$
$434$	6.33325	+	22.4421i	0.304006	+	1.07725i
$435$		0			0
$436$	−33.6383	−	33.6383i	−1.61098	−	1.61098i
$437$	8.93047	+	33.3290i	0.427202	+	1.59434i
$438$		0			0
$439$	10.7585	−	18.6343i	0.513475	−	0.889365i	−0.486403	−	0.873735i	$-0.661691\pi$
$439$	10.7585	−	18.6343i	0.513475	−	0.889365i	0.999878	−	0.0156304i	$-0.00497550\pi$
$440$	7.70228	+	2.06382i	0.367192	+	0.0983888i
$441$		0			0
$442$	−2.63499	−	48.2032i	−0.125333	−	2.29279i
$443$	12.3515	+	21.3934i	0.586836	+	1.01643i	0.994644	+	0.103362i	$0.0329599\pi$
$443$	12.3515	+	21.3934i	0.586836	+	1.01643i	−0.407808	+	0.913068i	$0.633707\pi$
$444$		0			0
$445$	7.10655			0.336883
$446$	37.6480			1.78268
$447$		0			0
$448$	6.74695	−	26.5843i	0.318764	−	1.25599i
$449$	−36.3730	+	9.74613i	−1.71655	+	0.459948i	−0.977015	−	0.213170i	$-0.931621\pi$
$449$	−36.3730	+	9.74613i	−1.71655	+	0.459948i	−0.739535	+	0.673118i	$0.764955\pi$
$450$		0			0
$451$	−6.28237	+	3.62713i	−0.295825	+	0.170795i
$452$		−	94.4076i		−	4.44056i
$453$		0			0
$454$	−15.5604			−0.730284
$455$	1.60809	+	4.70001i	0.0753885	+	0.220340i
$456$		0			0
$457$	−6.91179	−	25.7951i	−0.323320	−	1.20665i	−0.915990	−	0.401201i	$-0.868593\pi$
$457$	−6.91179	−	25.7951i	−0.323320	−	1.20665i	0.592670	−	0.805445i	$-0.298074\pi$
$458$		−	77.7181i		−	3.63153i
$459$		0			0
$460$	3.16934	−	11.8281i	0.147771	−	0.551490i
$461$	4.97413	−	1.33281i	0.231668	−	0.0620754i	−0.141117	−	0.989993i	$-0.545069\pi$
$461$	4.97413	−	1.33281i	0.231668	−	0.0620754i	0.372785	+	0.927918i	$0.378403\pi$
$462$		0			0
$463$	13.3125	+	13.3125i	0.618683	+	0.618683i	0.945193	−	0.326511i	$-0.105873\pi$
$463$	13.3125	+	13.3125i	0.618683	+	0.618683i	−0.326511	+	0.945193i	$0.605873\pi$
$464$	27.9401			1.29709
$465$		0			0
$466$	−4.74270	−	4.74270i	−0.219701	−	0.219701i
$467$	−9.27178	−	16.0592i	−0.429047	−	0.743131i	0.567742	−	0.823207i	$-0.307817\pi$
$467$	−9.27178	−	16.0592i	−0.429047	−	0.743131i	−0.996789	+	0.0800755i	$0.974484\pi$
$468$		0			0
$469$	24.7084	−	14.7054i	1.14093	−	0.679032i
$470$	−0.109968	−	0.0294659i	−0.00507246	−	0.00135916i
$471$		0			0
$472$	21.1768	+	36.6794i	0.974744	+	1.68831i
$473$	2.16539	+	8.08133i	0.0995645	+	0.371580i
$474$		0			0
$475$	8.82189	+	32.9238i	0.404776	+	1.51065i
$476$	−47.4179	−	46.1775i	−2.17339	−	2.11654i
$477$		0			0
$478$	23.6853	+	13.6747i	1.08334	+	0.625466i
$479$	−15.9594	+	15.9594i	−0.729202	+	0.729202i	−0.970461	−	0.241259i	$-0.922440\pi$
$479$	−15.9594	+	15.9594i	−0.729202	+	0.729202i	0.241259	+	0.970461i	$0.422440\pi$
$480$		0			0
$481$	−12.1095	+	23.8990i	−0.552145	+	1.08970i
$482$			9.50748i			0.433054i
$483$		0			0
$484$	17.1944	+	29.7816i	0.781564	+	1.35371i
$485$			1.77200i			0.0804623i
$486$		0			0
$487$	14.4863	+	3.88160i	0.656439	+	0.175892i	0.571638	−	0.820506i	$-0.306308\pi$
$487$	14.4863	+	3.88160i	0.656439	+	0.175892i	0.0848003	+	0.996398i	$0.472975\pi$
$488$	−4.07951	+	4.07951i	−0.184671	+	0.184671i
$489$		0			0
$490$	8.42370	+	4.57016i	0.380544	+	0.206459i
$491$	−0.576104	+	0.332614i	−0.0259992	+	0.0150106i	−0.512943	−	0.858423i	$-0.671445\pi$
$491$	−0.576104	+	0.332614i	−0.0259992	+	0.0150106i	0.486944	+	0.873433i	$0.338112\pi$
$492$		0			0
$493$	6.90287	−	11.9561i	0.310889	−	0.538476i
$494$	21.2605	+	64.9357i	0.956556	+	2.92159i
$495$		0			0
$496$	8.94221	−	33.3728i	0.401517	−	1.49848i
$497$	−0.181521	−	13.6968i	−0.00814234	−	0.614384i
$498$		0			0
$499$	18.9600	+	5.08032i	0.848767	+	0.227426i	0.656884	−	0.753992i	$-0.271874\pi$
$499$	18.9600	+	5.08032i	0.848767	+	0.227426i	0.191883	+	0.981418i	$0.438541\pi$
$500$	6.44114	−	24.0387i	0.288057	−	1.07504i
$501$		0			0
$502$	0.197154	+	0.0528272i	0.00879941	+	0.00235779i
$503$	−18.5259	−	10.6959i	−0.826028	−	0.476907i	0.0264628	−	0.999650i	$-0.491576\pi$
$503$	−18.5259	−	10.6959i	−0.826028	−	0.476907i	−0.852491	+	0.522742i	$0.824909\pi$
$504$		0			0
$505$	1.63015	−	6.08380i	0.0725407	−	0.270726i
$506$	−21.7978	+	12.5850i	−0.969032	+	0.559471i
$507$		0			0
$508$	16.4009	−	28.4071i	0.727671	−	1.26036i
$509$	32.7976	−	8.78810i	1.45373	−	0.389526i	0.556410	−	0.830908i	$-0.312178\pi$
$509$	32.7976	−	8.78810i	1.45373	−	0.389526i	0.897319	+	0.441382i	$0.145512\pi$
$510$		0			0
$511$	−0.0746609	−	5.63358i	−0.00330281	−	0.249215i
$512$	25.7315	−	25.7315i	1.13718	−	1.13718i
$513$		0			0
$514$	5.81514	+	1.55816i	0.256495	+	0.0687275i
$515$	4.06838	−	1.09012i	0.179274	−	0.0480364i
$516$		0			0
$517$	0.0831510	+	0.144022i	0.00365698	+	0.00633407i
$518$	14.0384	+	49.7454i	0.616810	+	2.18569i
$519$		0			0
$520$	2.95733	−	14.0687i	0.129688	−	0.616955i
$521$	−3.73842	−	2.15838i	−0.163783	−	0.0945602i	0.415868	−	0.909425i	$-0.363478\pi$
$521$	−3.73842	−	2.15838i	−0.163783	−	0.0945602i	−0.579651	+	0.814865i	$0.696811\pi$
$522$		0			0
$523$	−30.6798	−	17.7130i	−1.34154	−	0.774536i	−0.354503	−	0.935055i	$-0.615350\pi$
$523$	−30.6798	−	17.7130i	−1.34154	−	0.774536i	−0.987033	+	0.160519i	$0.948683\pi$
$524$	−0.762931	+	1.32144i	−0.0333288	+	0.0577272i
$525$		0			0
$526$	−3.43080	−	12.8039i	−0.149590	−	0.558277i
$527$	−12.0716	−	12.0716i	−0.525848	−	0.525848i
$528$		0			0
$529$	−0.0421417	−	0.0729916i	−0.00183225	−	0.00317355i
$530$	−9.38623	+	16.2574i	−0.407712	+	0.706177i
$531$		0			0
$532$	81.7433	+	45.7610i	3.54402	+	1.98399i
$533$	7.14778	+	10.9526i	0.309605	+	0.474409i
$534$		0			0
$535$	−2.07941	−	2.07941i	−0.0899006	−	0.0899006i
$536$	−83.2137			−3.59428
$537$		0			0
$538$	30.4696	+	30.4696i	1.31364	+	1.31364i
$539$	−3.98032	−	13.4214i	−0.171445	−	0.578099i
$540$		0			0
$541$	−0.765699	+	2.85763i	−0.0329200	+	0.122859i	−0.980430	−	0.196866i	$-0.936924\pi$
$541$	−0.765699	+	2.85763i	−0.0329200	+	0.122859i	0.947511	+	0.319725i	$0.103590\pi$
$542$	14.9560	−	8.63485i	0.642416	−	0.370899i
$543$		0			0
$544$	15.5308	+	57.9619i	0.665879	+	2.48509i
$545$	−5.04287			−0.216013
$546$		0			0
$547$	14.0808			0.602052			0.301026	−	0.953616i	$-0.402671\pi$
$547$	14.0808			0.602052			0.301026	+	0.953616i	$0.402671\pi$
$548$	6.15821	+	22.9828i	0.263066	+	0.981775i
$549$		0			0
$550$	−21.5328	+	12.4320i	−0.918162	+	0.530101i
$551$	−5.05740	+	18.8745i	−0.215453	+	0.804080i
$552$		0			0
$553$	−8.87028	−	31.4321i	−0.377203	−	1.33663i
$554$	−2.89973	−	2.89973i	−0.123198	−	0.123198i
$555$		0			0
$556$	−52.5809			−2.22993
$557$	−26.3249	−	26.3249i	−1.11542	−	1.11542i	−0.992404	−	0.123018i	$-0.960743\pi$
$557$	−26.3249	−	26.3249i	−1.11542	−	1.11542i	−0.123018	−	0.992404i	$-0.539257\pi$
$558$		0			0
$559$	14.3349	−	4.69338i	0.606302	−	0.198509i
$560$	−7.26210	−	12.2020i	−0.306880	−	0.515628i
$561$		0			0
$562$	−0.965102	+	1.67161i	−0.0407104	+	0.0705124i
$563$	22.1262	+	38.3237i	0.932508	+	1.61515i	0.779019	+	0.627001i	$0.215718\pi$
$563$	22.1262	+	38.3237i	0.932508	+	1.61515i	0.153489	+	0.988150i	$0.450949\pi$
$564$		0			0
$565$	−7.07653	−	7.07653i	−0.297712	−	0.297712i
$566$	18.7327	+	69.9115i	0.787395	+	2.93860i
$567$		0			0
$568$	−19.8213	+	34.3315i	−0.831684	+	1.44052i
$569$	−7.20021	−	4.15704i	−0.301848	−	0.174272i	0.341425	−	0.939909i	$-0.389091\pi$
$569$	−7.20021	−	4.15704i	−0.301848	−	0.174272i	−0.643273	+	0.765637i	$0.722424\pi$
$570$		0			0
$571$	21.7326	+	12.5473i	0.909481	+	0.525089i	0.880264	−	0.474484i	$-0.157365\pi$
$571$	21.7326	+	12.5473i	0.909481	+	0.525089i	0.0292166	+	0.999573i	$0.490699\pi$
$572$	−29.6633	+	19.3586i	−1.24028	+	0.809422i
$573$		0			0
$574$	24.4566	+	6.20697i	1.02080	+	0.259074i
$575$	11.3186	+	19.6043i	0.472016	+	0.817556i
$576$		0			0
$577$	−25.5733	+	6.85235i	−1.06463	+	0.285267i	−0.748285	−	0.663377i	$-0.769123\pi$
$577$	−25.5733	+	6.85235i	−1.06463	+	0.285267i	−0.316346	+	0.948644i	$0.602456\pi$
$578$	22.6898	+	6.07972i	0.943772	+	0.252883i
$579$		0			0
$580$	4.90355	−	4.90355i	0.203609	−	0.203609i
$581$	−13.5808	−	22.8188i	−0.563426	−	0.946684i
$582$		0			0
$583$	26.4873	−	7.09726i	1.09699	−	0.293939i
$584$	−8.15264	+	14.1208i	−0.337359	+	0.584322i
$585$		0			0
$586$	−24.4871	+	14.1376i	−1.01155	+	0.584020i
$587$	−0.317942	+	1.18658i	−0.0131229	+	0.0489752i	−0.972177	−	0.234248i	$-0.924737\pi$
$587$	−0.317942	+	1.18658i	−0.0131229	+	0.0489752i	0.959054	+	0.283223i	$0.0914038\pi$
$588$		0			0
$589$	20.9258	+	12.0815i	0.862234	+	0.497811i
$590$	7.31493	+	1.96003i	0.301151	+	0.0806931i
$591$		0			0
$592$	19.8214	−	73.9745i	0.814655	−	3.04033i
$593$	−22.0301	−	5.90295i	−0.904669	−	0.242405i	−0.223648	−	0.974670i	$-0.571797\pi$
$593$	−22.0301	−	5.90295i	−0.904669	−	0.242405i	−0.681020	+	0.732265i	$0.738463\pi$
$594$		0			0
$595$	−7.01565	+	0.0929774i	−0.287614	+	0.00381170i
$596$	−21.6447	+	80.7793i	−0.886603	+	3.30885i
$597$		0			0
$598$	24.8005	+	38.0020i	1.01417	+	1.55402i
$599$	−4.86660	+	8.42920i	−0.198844	+	0.344408i	−0.948154	−	0.317812i	$-0.897052\pi$
$599$	−4.86660	+	8.42920i	−0.198844	+	0.344408i	0.749310	+	0.662220i	$0.230385\pi$
$600$		0			0
$601$	7.28411	−	4.20549i	0.297125	−	0.171545i	−0.344025	−	0.938960i	$-0.611791\pi$
$601$	7.28411	−	4.20549i	0.297125	−	0.171545i	0.641151	+	0.767415i	$0.278457\pi$
$602$	14.2149	−	25.3922i	0.579356	−	1.03491i
$603$		0			0
$604$	−63.4538	+	63.4538i	−2.58190	+	2.58190i
$605$	3.52119	+	0.943500i	0.143157	+	0.0383587i
$606$		0			0
$607$		−	26.6604i		−	1.08211i	−0.840987	−	0.541056i	$-0.818025\pi$
$607$		−	26.6604i		−	1.08211i	0.840987	−	0.541056i	$-0.181975\pi$
$608$	−42.4659	−	73.5531i	−1.72222	−	2.98297i
$609$		0			0
$610$			1.03157i			0.0417669i
$611$	0.251085	−	0.163861i	0.0101578	−	0.00662911i
$612$		0			0
$613$	6.71483	−	6.71483i	0.271209	−	0.271209i	−0.558378	−	0.829587i	$-0.688576\pi$
$613$	6.71483	−	6.71483i	0.271209	−	0.271209i	0.829587	+	0.558378i	$0.188576\pi$
$614$	−8.45072	−	4.87902i	−0.341043	−	0.196901i
$615$		0			0
$616$	−9.96634	+	39.2692i	−0.401555	+	1.58220i
$617$	2.76556	+	10.3212i	0.111337	+	0.415516i	0.998987	−	0.0450034i	$-0.0143299\pi$
$617$	2.76556	+	10.3212i	0.111337	+	0.415516i	−0.887650	+	0.460519i	$0.847663\pi$
$618$		0			0
$619$	−4.64947	−	17.3520i	−0.186878	−	0.697438i	−0.994221	−	0.107355i	$-0.965762\pi$
$619$	−4.64947	−	17.3520i	−0.186878	−	0.697438i	0.807343	−	0.590083i	$-0.200905\pi$
$620$	−4.28762	−	7.42638i	−0.172195	−	0.298251i
$621$		0			0
$622$	13.6613	+	3.66052i	0.547767	+	0.146774i
$623$	0.478478	+	36.1038i	0.0191698	+	1.44647i
$624$		0			0
$625$	10.5030	+	18.1918i	0.420121	+	0.727671i
$626$	−58.6813	−	58.6813i	−2.34538	−	2.34538i
$627$		0			0
$628$	24.1482			0.963616
$629$	−26.7581	−	26.7581i	−1.06692	−	1.06692i
$630$		0			0
$631$	17.3537	−	4.64990i	0.690838	−	0.185110i	0.103715	−	0.994607i	$-0.466927\pi$
$631$	17.3537	−	4.64990i	0.690838	−	0.185110i	0.587123	+	0.809497i	$0.300260\pi$
$632$	−24.4633	+	91.2984i	−0.973099	+	3.63165i
$633$		0			0
$634$			29.7490i			1.18148i
$635$	−0.899957	−	3.35869i	−0.0357137	−	0.133285i
$636$		0			0
$637$	−23.7694	+	8.48612i	−0.941779	+	0.336232i
$638$	−14.2540			−0.564320
$639$		0			0
$640$			1.92080i			0.0759263i
$641$	−6.20731	+	3.58379i	−0.245174	+	0.141551i	−0.617552	−	0.786530i	$-0.711876\pi$
$641$	−6.20731	+	3.58379i	−0.245174	+	0.141551i	0.372378	+	0.928081i	$0.378542\pi$
$642$		0			0
$643$	41.0624	−	11.0026i	1.61934	−	0.433902i	0.668535	−	0.743681i	$-0.266922\pi$
$643$	41.0624	−	11.0026i	1.61934	−	0.433902i	0.950809	+	0.309779i	$0.100255\pi$
$644$	60.3045	+	15.3050i	2.37633	+	0.603101i
$645$		0			0
$646$	−96.5081			−3.79706
$647$	4.72974			0.185945			0.0929726	−	0.995669i	$-0.470363\pi$
$647$	4.72974			0.185945			0.0929726	+	0.995669i	$0.470363\pi$
$648$		0			0
$649$	−5.53108	−	9.58010i	−0.217114	−	0.376052i
$650$	24.4990	+	37.5400i	0.960929	+	1.47244i
$651$		0			0
$652$	−14.3987	−	3.85813i	−0.563898	−	0.151096i
$653$	0.0818691	−	0.141801i	0.00320379	−	0.00554912i	−0.864419	−	0.502772i	$-0.832314\pi$
$653$	0.0818691	−	0.141801i	0.00320379	−	0.00554912i	0.867623	+	0.497223i	$0.165647\pi$
$654$		0			0
$655$	0.0418640	+	0.156238i	0.00163576	+	0.00610474i
$656$	−26.4352	−	26.4352i	−1.03212	−	1.03212i
$657$		0			0
$658$	0.142293	−	0.560662i	0.00554717	−	0.0218569i
$659$	11.4177	−	19.7761i	0.444772	−	0.770367i	−0.553265	−	0.833006i	$-0.686618\pi$
$659$	11.4177	−	19.7761i	0.444772	−	0.770367i	0.998036	+	0.0626385i	$0.0199515\pi$
$660$		0			0
$661$	−22.4488	+	22.4488i	−0.873158	+	0.873158i	−0.992815	−	0.119657i	$-0.961821\pi$
$661$	−22.4488	+	22.4488i	−0.873158	+	0.873158i	0.119657	+	0.992815i	$0.461821\pi$
$662$	41.3599	+	23.8791i	1.60750	+	0.928089i
$663$		0			0
$664$			76.8497i			2.98235i
$665$	9.55737	−	2.69713i	0.370619	−	0.104590i
$666$		0			0
$667$			12.9774i			0.502486i
$668$	−44.8032	+	12.0050i	−1.73349	+	0.464486i
$669$		0			0
$670$	−10.5209	+	10.5209i	−0.406459	+	0.406459i
$671$	1.06551	−	1.06551i	0.0411334	−	0.0411334i
$672$		0			0
$673$	−31.2839	+	18.0618i	−1.20591	+	0.696231i	−0.961862	−	0.273534i	$-0.911808\pi$
$673$	−31.2839	+	18.0618i	−1.20591	+	0.696231i	−0.244044	+	0.969764i	$0.578474\pi$
$674$	−51.1413	+	13.7033i	−1.96989	+	0.527830i
$675$		0			0
$676$	37.7683	+	51.4948i	1.45263	+	1.98057i
$677$	34.8720	−	20.1334i	1.34024	−	0.773788i	0.353398	−	0.935473i	$-0.385026\pi$
$677$	34.8720	−	20.1334i	1.34024	−	0.773788i	0.986842	+	0.161685i	$0.0516928\pi$
$678$		0			0
$679$	−9.00237	+	0.119307i	−0.345479	+	0.00457858i
$680$	17.5850	+	10.1527i	0.674354	+	0.389339i
$681$		0			0
$682$	−4.56197	+	17.0255i	−0.174687	+	0.651941i
$683$	8.55543	−	31.9293i	0.327364	−	1.22174i	−0.584549	−	0.811358i	$-0.698729\pi$
$683$	8.55543	−	31.9293i	0.327364	−	1.22174i	0.911914	−	0.410382i	$-0.134605\pi$
$684$		0			0
$685$	2.18433	+	1.26112i	0.0834589	+	0.0481850i
$686$	−22.6509	+	43.1030i	−0.864813	+	1.64568i
$687$		0			0
$688$	−37.3400	+	21.5583i	−1.42357	+	0.821901i
$689$	−15.3830	−	46.9841i	−0.586046	−	1.78995i
$690$		0			0
$691$	−13.4764	+	3.61100i	−0.512668	+	0.137369i	−0.505873	−	0.862608i	$-0.668830\pi$
$691$	−13.4764	+	3.61100i	−0.512668	+	0.137369i	−0.00679506	+	0.999977i	$0.502163\pi$
$692$	93.5032	−	53.9841i	3.55446	−	2.05217i
$693$		0			0
$694$	−17.8920	+	17.8920i	−0.679173	+	0.679173i
$695$	−3.94132	+	3.94132i	−0.149503	+	0.149503i
$696$		0			0
$697$	−17.8432	+	4.78107i	−0.675860	+	0.181096i
$698$			65.3501i			2.47354i
$699$		0			0
$700$	59.5713	+	15.1189i	2.25158	+	0.571441i
$701$		−	26.0431i		−	0.983633i	−0.870699	−	0.491817i	$-0.836333\pi$
$701$		−	26.0431i		−	0.983633i	0.870699	−	0.491817i	$-0.163667\pi$
$702$		0			0
$703$	46.3845	+	26.7801i	1.74942	+	1.01003i
$704$	14.6595	−	14.6595i	0.552500	−	0.552500i
$705$		0			0
$706$	−11.9857	+	20.7599i	−0.451090	+	0.781310i
$707$	31.0176	+	7.87212i	1.16654	+	0.296061i
$708$		0			0
$709$	−3.04089	−	3.04089i	−0.114203	−	0.114203i	0.647696	−	0.761899i	$-0.275733\pi$
$709$	−3.04089	−	3.04089i	−0.114203	−	0.114203i	−0.761899	+	0.647696i	$0.775733\pi$
$710$	1.83457	+	6.84669i	0.0688500	+	0.256952i
$711$		0			0
$712$	52.2476	−	90.4955i	1.95806	−	3.39146i
$713$	15.5007	+	4.15340i	0.580506	+	0.155546i
$714$		0			0
$715$	−0.772411	+	3.67454i	−0.0288865	+	0.137420i
$716$	−41.9473	−	72.6548i	−1.56764	−	2.71524i
$717$		0			0
$718$	9.25504			0.345395
$719$	−4.51154			−0.168252			−0.0841260	−	0.996455i	$-0.526810\pi$
$719$	−4.51154			−0.168252			−0.0841260	+	0.996455i	$0.526810\pi$
$720$		0			0
$721$	5.81211	+	20.5954i	0.216454	+	0.767013i
$722$	83.6895	−	22.4245i	3.11460	−	0.834554i
$723$		0			0
$724$	76.6495	−	44.2536i	2.84866	−	1.64467i
$725$			12.8196i			0.476107i
$726$		0			0
$727$	6.85388			0.254196			0.127098	−	0.991890i	$-0.459434\pi$
$727$	6.85388			0.254196			0.127098	+	0.991890i	$0.459434\pi$
$728$	71.6732	+	14.0771i	2.65638	+	0.521730i
$729$		0			0
$730$	0.754570	+	2.81609i	0.0279279	+	0.104228i
$731$			21.3047i			0.787983i
$732$		0			0
$733$	−5.06911	+	18.9182i	−0.187232	+	0.698758i	0.806910	+	0.590674i	$0.201138\pi$
$733$	−5.06911	+	18.9182i	−0.187232	+	0.698758i	−0.994142	+	0.108084i	$0.965528\pi$
$734$	−3.66289	+	0.981468i	−0.135200	+	0.0362267i
$735$		0			0
$736$	−39.8851	−	39.8851i	−1.47018	−	1.47018i
$737$	21.7342			0.800588
$738$		0			0
$739$	−6.73165	−	6.73165i	−0.247628	−	0.247628i	0.572369	−	0.819996i	$-0.306025\pi$
$739$	−6.73165	−	6.73165i	−0.247628	−	0.247628i	−0.819996	+	0.572369i	$0.806025\pi$
$740$	−9.50400	−	16.4614i	−0.349374	−	0.605133i
$741$		0			0
$742$	−83.2254	−	46.5907i	−3.05530	−	1.71040i
$743$	−33.4189	−	8.95458i	−1.22602	−	0.328512i	−0.412993	−	0.910734i	$-0.635516\pi$
$743$	−33.4189	−	8.95458i	−1.22602	−	0.328512i	−0.813029	+	0.582223i	$0.802183\pi$
$744$		0			0
$745$	4.43256	+	7.67742i	0.162397	+	0.281279i
$746$	−5.02850	−	18.7666i	−0.184106	−	0.687095i
$747$		0			0
$748$	−12.9487	−	48.3254i	−0.473453	−	1.76695i
$749$	10.4241	−	10.7041i	0.380889	−	0.391120i
$750$		0			0
$751$	37.0313	+	21.3801i	1.35129	+	0.780169i	0.988431	−	0.151674i	$-0.0484662\pi$
$751$	37.0313	+	21.3801i	1.35129	+	0.780169i	0.362862	+	0.931843i	$0.381800\pi$
$752$	−0.606020	+	0.606020i	−0.0220993	+	0.0220993i
$753$		0			0
$754$	1.40268	+	25.6600i	0.0510826	+	0.934481i
$755$			9.51265i			0.346201i
$756$		0			0
$757$	0.327683	+	0.567563i	0.0119098	+	0.0206284i	0.871919	−	0.489650i	$-0.162876\pi$
$757$	0.327683	+	0.567563i	0.0119098	+	0.0206284i	−0.860009	+	0.510279i	$0.829542\pi$
$758$			34.6473i			1.25845i
$759$		0			0
$760$	−27.7605	−	7.43841i	−1.00698	−	0.269819i
$761$	−8.57390	+	8.57390i	−0.310803	+	0.310803i	−0.845221	−	0.534417i	$-0.820531\pi$
$761$	−8.57390	+	8.57390i	−0.310803	+	0.310803i	0.534417	+	0.845221i	$0.320531\pi$
$762$		0			0
$763$	−0.339532	−	25.6195i	−0.0122919	−	0.927489i
$764$	−93.8897	+	54.2073i	−3.39681	+	1.96115i
$765$		0			0
$766$	27.1101	−	46.9561i	0.979528	−	1.69659i
$767$	−16.7018	+	10.8998i	−0.603067	+	0.393568i
$768$		0			0
$769$	1.93954	−	7.23846i	0.0699416	−	0.261025i	−0.922097	−	0.386958i	$-0.873526\pi$
$769$	1.93954	−	7.23846i	0.0699416	−	0.261025i	0.992039	+	0.125933i	$0.0401924\pi$
$770$	3.70485	+	6.22499i	0.133513	+	0.224333i
$771$		0			0
$772$	−34.6698	−	9.28974i	−1.24779	−	0.334345i
$773$	7.93706	−	29.6215i	0.285476	−	1.06541i	−0.663015	−	0.748606i	$-0.730723\pi$
$773$	7.93706	−	29.6215i	0.285476	−	1.06541i	0.948491	−	0.316805i	$-0.102610\pi$
$774$		0			0
$775$	15.3122	+	4.10290i	0.550032	+	0.147381i
$776$	22.5648	+	13.0278i	0.810029	+	0.467671i
$777$		0			0
$778$	24.6529	−	92.0061i	0.883851	−	3.29858i
$779$	22.6429	−	13.0729i	0.811265	−	0.468384i
$780$		0			0
$781$	5.17703	−	8.96688i	0.185249	−	0.320860i
$782$	−61.9103	+	16.5888i	−2.21391	+	0.593215i
$783$		0			0
$784$	61.5015	−	37.7156i	2.19648	−	1.34698i
$785$	1.81008	−	1.81008i	0.0646045	−	0.0646045i
$786$		0			0
$787$	4.40030	+	1.17906i	0.156854	+	0.0420289i	0.336391	−	0.941722i	$-0.390793\pi$
$787$	4.40030	+	1.17906i	0.156854	+	0.0420289i	−0.179538	+	0.983751i	$0.557460\pi$
$788$	−110.620	+	29.6406i	−3.94068	+	1.05590i
$789$		0			0
$790$	8.45015	+	14.6361i	0.300643	+	0.520728i
$791$	35.4748	−	36.4277i	1.26134	−	1.29522i
$792$		0			0
$793$	−2.02297	−	1.81327i	−0.0718379	−	0.0643911i
$794$	62.2440	+	35.9366i	2.20896	+	1.27534i
$795$		0			0
$796$	−75.5472	−	43.6172i	−2.67770	−	1.54597i
$797$	16.9732	−	29.3985i	0.601222	−	1.04135i	−0.391414	−	0.920215i	$-0.628014\pi$
$797$	16.9732	−	29.3985i	0.601222	−	1.04135i	0.992636	−	0.121133i	$-0.0386528\pi$
$798$		0			0
$799$	0.109605	+	0.409051i	0.00387754	+	0.0144712i
$800$	−39.4002	−	39.4002i	−1.39301	−	1.39301i
$801$		0			0
$802$	−18.0801	−	31.3156i	−0.638430	−	1.10579i
$803$	2.12935	−	3.68814i	0.0751430	−	0.130152i
$804$		0			0
$805$	5.66748	−	3.37304i	0.199752	−	0.118884i
$806$	31.0983	+	6.53704i	1.09539	+	0.230258i
$807$		0			0
$808$	−65.4869	−	65.4869i	−2.30382	−	2.30382i
$809$	−28.6673			−1.00789			−0.503945	−	0.863736i	$-0.668119\pi$
$809$	−28.6673			−1.00789			−0.503945	+	0.863736i	$0.668119\pi$
$810$		0			0
$811$	3.29098	+	3.29098i	0.115562	+	0.115562i	0.762523	−	0.646961i	$-0.223960\pi$
$811$	3.29098	+	3.29098i	0.115562	+	0.115562i	−0.646961	+	0.762523i	$0.723960\pi$
$812$	25.2419	+	24.5816i	0.885817	+	0.862645i
$813$		0			0
$814$	−10.1121	+	37.7390i	−0.354430	+	1.32275i
$815$	−1.36848	+	0.790094i	−0.0479359	+	0.0276758i
$816$		0			0
$817$	−7.80447	−	29.1267i	−0.273044	−	1.01901i
$818$	−40.9091			−1.43035
$819$		0			0
$820$	−9.27888			−0.324032
$821$	7.71032	+	28.7753i	0.269092	+	1.00426i	0.959698	+	0.281034i	$0.0906772\pi$
$821$	7.71032	+	28.7753i	0.269092	+	1.00426i	−0.690606	+	0.723231i	$0.742656\pi$
$822$		0			0
$823$	−28.7199	+	16.5814i	−1.00111	+	0.577993i	−0.908577	−	0.417716i	$-0.862831\pi$
$823$	−28.7199	+	16.5814i	−1.00111	+	0.577993i	−0.0925357	+	0.995709i	$0.529497\pi$
$824$	16.0292	−	59.8218i	0.558404	−	2.08399i
$825$		0			0
$826$	−9.46512	+	37.2944i	−0.329334	+	1.29764i
$827$	13.0460	+	13.0460i	0.453653	+	0.453653i	0.896565	−	0.442912i	$-0.146055\pi$
$827$	13.0460	+	13.0460i	0.453653	+	0.453653i	−0.442912	+	0.896565i	$0.646055\pi$
$828$		0			0
$829$	−25.1378			−0.873070			−0.436535	−	0.899687i	$-0.643795\pi$
$829$	−25.1378			−0.873070			−0.436535	+	0.899687i	$0.643795\pi$
$830$	9.71633	+	9.71633i	0.337259	+	0.337259i
$831$		0			0
$832$	−27.8326	−	24.9474i	−0.964921	−	0.864895i
$833$	−0.944715	−	35.6357i	−0.0327324	−	1.23470i
$834$		0			0
$835$	−2.45846	+	4.25818i	−0.0850786	+	0.147360i
$836$	35.4057	+	61.3245i	1.22453	+	2.12095i
$837$		0			0
$838$	37.6457	+	37.6457i	1.30045	+	1.30045i
$839$	−1.98291	−	7.40032i	−0.0684577	−	0.255488i	0.923213	−	0.384289i	$-0.125554\pi$
$839$	−1.98291	−	7.40032i	−0.0684577	−	0.255488i	−0.991670	+	0.128802i	$0.958887\pi$
$840$		0			0
$841$	10.8254	−	18.7502i	0.373290	−	0.646557i
$842$	−45.3160	−	26.1632i	−1.56169	−	0.901644i
$843$		0			0
$844$	22.9316	+	13.2396i	0.789339	+	0.455725i
$845$	6.69092	+	1.02890i	0.230175	+	0.0353951i
$846$		0			0
$847$	−4.55623	+	17.9524i	−0.156554	+	0.616852i
$848$	70.6593	+	122.385i	2.42645	+	4.20273i
$849$		0			0
$850$	−61.1576	+	16.3871i	−2.09769	+	0.562074i
$851$	34.3590	+	9.20648i	1.17781	+	0.315594i
$852$		0			0
$853$	18.8489	−	18.8489i	0.645373	−	0.645373i	−0.306498	−	0.951871i	$-0.599157\pi$
$853$	18.8489	−	18.8489i	0.645373	−	0.645373i	0.951871	+	0.306498i	$0.0991574\pi$
$854$	−5.24072	+	0.0694545i	−0.179334	+	0.00237668i
$855$		0			0
$856$	−41.7672	+	11.1915i	−1.42758	+	0.382518i
$857$	9.97165	−	17.2714i	0.340625	−	0.589980i	−0.643924	−	0.765090i	$-0.722695\pi$
$857$	9.97165	−	17.2714i	0.340625	−	0.589980i	0.984549	+	0.175110i	$0.0560280\pi$
$858$		0			0
$859$	0.354309	−	0.204560i	0.0120889	−	0.00697950i	−0.493943	−	0.869494i	$-0.664445\pi$
$859$	0.354309	−	0.204560i	0.0120889	−	0.00697950i	0.506032	+	0.862515i	$0.331112\pi$
$860$	−2.76973	+	10.3368i	−0.0944471	+	0.352481i
$861$		0			0
$862$	29.4537	+	17.0051i	1.00320	+	0.579196i
$863$	10.6641	+	2.85743i	0.363010	+	0.0972682i	0.435714	−	0.900085i	$-0.356496\pi$
$863$	10.6641	+	2.85743i	0.363010	+	0.0972682i	−0.0727037	+	0.997354i	$0.523163\pi$
$864$		0			0
$865$	2.96224	−	11.0552i	0.100719	−	0.375890i
$866$	−51.5056	−	13.8009i	−1.75023	−	0.468973i
$867$		0			0
$868$	37.4399	−	22.2826i	1.27079	−	0.756322i
$869$	6.38945	−	23.8458i	0.216747	−	0.808912i
$870$		0			0
$871$	−2.13878	−	39.1258i	−0.0724697	−	1.32573i
$872$	−37.0754	+	64.2164i	−1.25553	+	2.17464i
$873$		0			0
$874$	78.5636	−	45.3587i	2.65745	−	1.53428i
$875$	11.5182	−	6.85512i	0.389386	−	0.231746i
$876$		0			0
$877$	−19.3771	+	19.3771i	−0.654318	+	0.654318i	−0.954030	−	0.299712i	$-0.903110\pi$
$877$	−19.3771	+	19.3771i	−0.654318	+	0.654318i	0.299712	+	0.954030i	$0.403110\pi$
$878$	−54.6435	−	14.6417i	−1.84413	−	0.494132i
$879$		0			0
$880$		−	10.7332i		−	0.361815i
$881$	15.9556	+	27.6359i	0.537557	+	0.931077i	0.999035	+	0.0439247i	$0.0139862\pi$
$881$	15.9556	+	27.6359i	0.537557	+	0.931077i	−0.461478	+	0.887152i	$0.652681\pi$
$882$		0			0
$883$			32.9852i			1.11004i	0.831837	+	0.555019i	$0.187289\pi$
$883$			32.9852i			1.11004i	−0.831837	+	0.555019i	$0.812711\pi$
$884$	−85.7211	+	28.0658i	−2.88311	+	0.943956i
$885$		0			0
$886$	45.9247	−	45.9247i	1.54287	−	1.54287i
$887$	19.5103	+	11.2643i	0.655091	+	0.378217i	0.790404	−	0.612586i	$-0.209871\pi$
$887$	19.5103	+	11.2643i	0.655091	+	0.378217i	−0.135313	+	0.990803i	$0.543204\pi$
$888$		0			0
$889$	17.0027	−	4.79823i	0.570252	−	0.160928i
$890$	−4.83579	−	18.0474i	−0.162096	−	0.604951i
$891$		0			0
$892$	−18.2060	−	67.9456i	−0.609581	−	2.27499i
$893$	−0.299692	−	0.519082i	−0.0100288	−	0.0173704i
$894$		0			0
$895$	−8.59026	−	2.30175i	−0.287141	−	0.0769391i
$896$	−9.75834	+	0.129326i	−0.326003	+	0.00432047i
$897$		0			0
$898$	49.5015	+	85.7392i	1.65189	+	2.86115i
$899$	6.42607	+	6.42607i	0.214321	+	0.214321i
$900$		0			0
$901$	69.8282			2.32632
$902$	13.4862	+	13.4862i	0.449042	+	0.449042i
$903$		0			0
$904$	−142.140	+	38.0864i	−4.72752	+	1.26673i
$905$	2.42831	−	9.06256i	0.0807197	−	0.301250i
$906$		0			0
$907$			26.2585i			0.871900i	0.899971	+	0.435950i	$0.143587\pi$
$907$			26.2585i			0.871900i	−0.899971	+	0.435950i	$0.856413\pi$
$908$	7.52474	+	28.0827i	0.249717	+	0.931958i
$909$		0			0
$910$	10.8416	−	7.28204i	0.359397	−	0.241397i
$911$	6.71393			0.222442			0.111221	−	0.993796i	$-0.464524\pi$
$911$	6.71393			0.222442			0.111221	+	0.993796i	$0.464524\pi$
$912$		0			0
$913$		−	20.0720i		−	0.664286i
$914$	−60.8047	+	35.1056i	−2.01124	+	1.16119i
$915$		0			0
$916$	−140.263	+	37.5832i	−4.63441	+	1.24179i
$917$	−0.790927	+	0.223203i	−0.0261187	+	0.00737081i
$918$		0			0
$919$	47.9672			1.58229			0.791146	−	0.611627i	$-0.209485\pi$
$919$	47.9672			1.58229			0.791146	+	0.611627i	$0.209485\pi$
$920$	−19.0871			−0.629282
$921$		0			0
$922$	−6.76949	−	11.7251i	−0.222941	−	0.386146i
$923$	−16.6516	−	8.43728i	−0.548094	−	0.277717i
$924$		0			0
$925$	33.9413	+	9.09454i	1.11598	+	0.299027i
$926$	24.7489	−	42.8664i	0.813300	−	1.40868i
$927$		0			0
$928$	−8.26751	−	30.8548i	−0.271394	−	1.01286i
$929$	7.96550	+	7.96550i	0.261339	+	0.261339i	0.825598	−	0.564259i	$-0.190838\pi$
$929$	7.96550	+	7.96550i	0.261339	+	0.261339i	−0.564259	+	0.825598i	$0.690838\pi$
$930$		0			0
$931$	14.3459	+	48.3732i	0.470166	+	1.58537i
$932$	−6.26594	+	10.8529i	−0.205248	+	0.355500i
$933$		0			0
$934$	−34.4739	+	34.4739i	−1.12802	+	1.12802i
$935$	−4.59294	−	2.65174i	−0.150205	−	0.0867210i
$936$		0			0
$937$			15.4167i			0.503641i	0.967774	+	0.251820i	$0.0810292\pi$
$937$			15.4167i			0.503641i	−0.967774	+	0.251820i	$0.918971\pi$
$938$	−54.1584	−	52.7417i	−1.76834	−	1.72208i
$939$		0			0
$940$			0.212716i			0.00693803i
$941$	7.84684	−	2.10255i	0.255800	−	0.0685413i	−0.128640	−	0.991691i	$-0.541061\pi$
$941$	7.84684	−	2.10255i	0.255800	−	0.0685413i	0.384440	+	0.923150i	$0.374395\pi$
$942$		0			0
$943$	12.2784	−	12.2784i	0.399839	−	0.399839i
$944$	40.3115	−	40.3115i	1.31203	−	1.31203i
$945$		0			0
$946$	19.0494	−	10.9982i	0.619351	−	0.357582i
$947$	−1.40726	+	0.377073i	−0.0457297	+	0.0122532i	−0.281611	−	0.959529i	$-0.590869\pi$
$947$	−1.40726	+	0.377073i	−0.0457297	+	0.0122532i	0.235882	+	0.971782i	$0.424202\pi$
$948$		0			0
$949$	−6.84892	−	3.47031i	−0.222325	−	0.112651i
$950$	77.6084	−	44.8072i	2.51795	−	1.45374i
$951$		0			0
$952$	−50.3953	+	90.0216i	−1.63332	+	2.91762i
$953$	−21.4785	−	12.4006i	−0.695756	−	0.401695i	0.110009	−	0.993931i	$-0.464912\pi$
$953$	−21.4785	−	12.4006i	−0.695756	−	0.401695i	−0.805765	+	0.592236i	$0.798245\pi$
$954$		0			0
$955$	−2.97449	+	11.1009i	−0.0962522	+	0.359218i
$956$	13.2257	−	49.3591i	0.427751	−	1.59639i
$957$		0			0
$958$	51.3895	+	29.6697i	1.66032	+	0.958585i
$959$	−6.25987	+	11.1821i	−0.202142	+	0.361088i
$960$		0			0
$961$	−17.1146	+	9.88110i	−0.552083	+	0.318745i
$962$	68.9328	+	14.4901i	2.22248	+	0.467179i
$963$		0			0
$964$	17.1587	−	4.59767i	0.552646	−	0.148081i
$965$	−3.29508	+	1.90242i	−0.106073	+	0.0612410i
$966$		0			0
$967$	−4.62828	+	4.62828i	−0.148835	+	0.148835i	−0.777598	−	0.628762i	$-0.783562\pi$
$967$	−4.62828	+	4.62828i	−0.148835	+	0.148835i	0.628762	+	0.777598i	$0.283562\pi$
$968$	37.9026	−	37.9026i	1.21823	−	1.21823i
$969$		0			0
$970$	4.50007	−	1.20579i	0.144489	−	0.0387156i
$971$			16.7974i			0.539054i	0.962993	+	0.269527i	$0.0868674\pi$
$971$			16.7974i			0.539054i	−0.962993	+	0.269527i	$0.913133\pi$
$972$		0			0
$973$	−20.2887	−	19.7579i	−0.650424	−	0.633410i
$974$		−	39.4301i		−	1.26342i
$975$		0			0
$976$	6.72521	+	3.88280i	0.215269	+	0.124285i
$977$	17.3829	−	17.3829i	0.556127	−	0.556127i	−0.372076	−	0.928202i	$-0.621354\pi$
$977$	17.3829	−	17.3829i	0.556127	−	0.556127i	0.928202	+	0.372076i	$0.121354\pi$
$978$		0			0
$979$	−13.6463	+	23.6361i	−0.436138	+	0.755412i
$980$	4.17448	−	17.4128i	0.133349	−	0.556232i
$981$		0			0
$982$	1.23671	+	1.23671i	0.0394650	+	0.0394650i
$983$	6.01359	+	22.4430i	0.191804	+	0.715822i	0.993071	+	0.117515i	$0.0374928\pi$
$983$	6.01359	+	22.4430i	0.191804	+	0.715822i	−0.801267	+	0.598307i	$0.795840\pi$
$984$		0			0
$985$	−6.07001	+	10.5136i	−0.193407	+	0.334990i
$986$	−35.0603	−	9.39438i	−1.11655	−	0.299178i
$987$		0			0
$988$	106.912	−	69.7720i	3.40133	−	2.21974i
$989$	−10.0132	−	17.3434i	−0.318401	−	0.551487i
$990$		0			0
$991$	−49.7853			−1.58148			−0.790741	−	0.612151i	$-0.790304\pi$
$991$	−49.7853			−1.58148			−0.790741	+	0.612151i	$0.790304\pi$
$992$	−39.5002			−1.25413
$993$		0			0
$994$	−34.6601	+	9.78122i	−1.09935	+	0.310241i
$995$	−8.93224	+	2.39339i	−0.283171	+	0.0758754i
$996$		0			0
$997$	2.73713	−	1.58028i	0.0866856	−	0.0500480i	−0.456031	−	0.889964i	$-0.650729\pi$
$997$	2.73713	−	1.58028i	0.0866856	−	0.0500480i	0.542716	+	0.839916i	$0.317396\pi$
$998$		−	51.6069i		−	1.63359i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.262.1		40
3.2	odd	2		273.2.cg.b.262.10	yes	40
7.5	odd	6		819.2.et.d.145.1		40
13.7	odd	12		819.2.et.d.514.1		40
21.5	even	6		273.2.bt.b.145.10	✓	40
39.20	even	12		273.2.bt.b.241.10	yes	40
91.33	even	12	inner	819.2.gh.d.397.1		40
273.215	odd	12		273.2.cg.b.124.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.10	✓	40	21.5	even	6
273.2.bt.b.241.10	yes	40	39.20	even	12
273.2.cg.b.124.10	yes	40	273.215	odd	12
273.2.cg.b.262.10	yes	40	3.2	odd	2
819.2.et.d.145.1		40	7.5	odd	6
819.2.et.d.514.1		40	13.7	odd	12
819.2.gh.d.262.1		40	1.1	even	1	trivial
819.2.gh.d.397.1		40	91.33	even	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.gh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.680470 - 2.53955i) q^{2} +(-4.25421 + 2.45617i) q^{4} +(-0.134776 + 0.502992i) q^{5} +(-2.56445 - 0.650845i) q^{7} +(5.41427 + 5.41427i) q^{8} +O(q^{10})\)	\(q+(-0.680470 - 2.53955i) q^{2} +(-4.25421 + 2.45617i) q^{4} +(-0.134776 + 0.502992i) q^{5} +(-2.56445 - 0.650845i) q^{7} +(5.41427 + 5.41427i) q^{8} +1.36908 q^{10} +(-1.41413 - 1.41413i) q^{11} +(-2.40655 + 2.68487i) q^{13} +(0.0921792 + 6.95542i) q^{14} +(5.15321 - 8.92562i) q^{16} +(-2.54630 - 4.41032i) q^{17} +(5.09679 + 5.09679i) q^{19} +(-0.662067 - 2.47087i) q^{20} +(-2.62897 + 4.55351i) q^{22} +(4.14570 + 2.39352i) q^{23} +(4.09529 + 2.36442i) q^{25} +(8.45594 + 4.28458i) q^{26} +(12.5083 - 3.52989i) q^{28} +(1.35547 + 2.34774i) q^{29} +(3.23806 - 0.867635i) q^{31} +(-11.3816 - 3.04969i) q^{32} +(-9.46754 + 9.46754i) q^{34} +(0.672997 - 1.20218i) q^{35} +(7.17752 - 1.92321i) q^{37} +(9.47532 - 16.4117i) q^{38} +(-3.45305 + 1.99362i) q^{40} +(0.938828 - 3.50375i) q^{41} +(-3.62298 - 2.09173i) q^{43} +(9.48933 + 2.54266i) q^{44} +(3.25743 - 12.1569i) q^{46} +(-0.0803226 - 0.0215224i) q^{47} +(6.15280 + 3.33812i) q^{49} +(3.21783 - 12.0091i) q^{50} +(3.64348 - 17.3329i) q^{52} +(-6.85585 + 11.8747i) q^{53} +(0.901885 - 0.520704i) q^{55} +(-10.3608 - 17.4085i) q^{56} +(5.03985 - 5.03985i) q^{58} +(5.34294 + 1.43164i) q^{59} +0.753473i q^{61} +(-4.40680 - 7.63280i) q^{62} +10.3665i q^{64} +(-1.02612 - 1.57233i) q^{65} +(-7.68466 + 7.68466i) q^{67} +(21.6650 + 12.5083i) q^{68} +(-3.51095 - 0.891061i) q^{70} +(1.34000 + 5.00093i) q^{71} +(0.551150 + 2.05692i) q^{73} +(-9.76817 - 16.9190i) q^{74} +(-34.2014 - 9.16424i) q^{76} +(2.70608 + 4.54683i) q^{77} +(6.17212 + 10.6904i) q^{79} +(3.79499 + 3.79499i) q^{80} -9.53679 q^{82} +(7.09696 + 7.09696i) q^{83} +(2.56154 - 0.686362i) q^{85} +(-2.84672 + 10.6241i) q^{86} -15.3129i q^{88} +(-3.53214 - 13.1821i) q^{89} +(7.91891 - 5.31892i) q^{91} -23.5156 q^{92} +0.218629i q^{94} +(-3.25057 + 1.87672i) q^{95} +(3.28692 - 0.880729i) q^{97} +(4.29051 - 17.8968i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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