LMFDB - Embedded newform 819.2.et.c.514.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			514.7
Character	$\chi$	$=$	819.514
Dual form			819.2.et.c.145.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.926196 + 0.926196i) q^{2} -0.284323i q^{4} +(-0.409991 - 0.109857i) q^{5} +(-2.25606 - 1.38209i) q^{7} +(2.11573 - 2.11573i) q^{8} +O(q^{10})$	\(q+(0.926196 + 0.926196i) q^{2} -0.284323i q^{4} +(-0.409991 - 0.109857i) q^{5} +(-2.25606 - 1.38209i) q^{7} +(2.11573 - 2.11573i) q^{8} +(-0.277983 - 0.481481i) q^{10} +(-1.35455 - 0.362951i) q^{11} +(-3.54669 - 0.648849i) q^{13} +(-0.809468 - 3.36964i) q^{14} +3.35051 q^{16} +6.94638 q^{17} +(-0.143382 - 0.535108i) q^{19} +(-0.0312348 + 0.116570i) q^{20} +(-0.918416 - 1.59074i) q^{22} -7.84271i q^{23} +(-4.17410 - 2.40992i) q^{25} +(-2.68397 - 3.88589i) q^{26} +(-0.392961 + 0.641450i) q^{28} +(3.01567 - 5.22330i) q^{29} +(-2.17020 - 8.09928i) q^{31} +(-1.12823 - 1.12823i) q^{32} +(6.43371 + 6.43371i) q^{34} +(0.773134 + 0.814490i) q^{35} +(-4.24059 + 4.24059i) q^{37} +(0.362815 - 0.628415i) q^{38} +(-1.09986 + 0.635004i) q^{40} +(0.434817 + 1.62276i) q^{41} +(6.49491 - 3.74984i) q^{43} +(-0.103195 + 0.385130i) q^{44} +(7.26389 - 7.26389i) q^{46} +(-2.62582 + 9.79969i) q^{47} +(3.17964 + 6.23618i) q^{49} +(-1.63398 - 6.09809i) q^{50} +(-0.184483 + 1.00840i) q^{52} +(-3.77860 + 6.54472i) q^{53} +(0.515482 + 0.297614i) q^{55} +(-7.69736 + 1.84909i) q^{56} +(7.63090 - 2.04469i) q^{58} +(4.83450 + 4.83450i) q^{59} +(2.38809 + 1.37876i) q^{61} +(5.49149 - 9.51155i) q^{62} -8.79095i q^{64} +(1.38283 + 0.655650i) q^{65} +(3.70163 - 13.8147i) q^{67} -1.97502i q^{68} +(-0.0383037 + 1.47045i) q^{70} +(-1.00255 + 3.74157i) q^{71} +(-11.0713 + 2.96655i) q^{73} -7.85524 q^{74} +(-0.152144 + 0.0407667i) q^{76} +(2.55432 + 2.69096i) q^{77} +(4.32696 + 7.49452i) q^{79} +(-1.37368 - 0.368077i) q^{80} +(-1.10027 + 1.90572i) q^{82} +(2.26360 - 2.26360i) q^{83} +(-2.84796 - 0.763108i) q^{85} +(9.48864 + 2.54247i) q^{86} +(-3.63377 + 2.09796i) q^{88} +(8.19285 + 8.19285i) q^{89} +(7.10478 + 6.36569i) q^{91} -2.22986 q^{92} +(-11.5085 + 6.64441i) q^{94} +0.235141i q^{95} +(15.5709 + 4.17221i) q^{97} +(-2.83095 + 8.72089i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.926196	+	0.926196i	0.654919	+	0.654919i	0.954173	−	0.299254i	$-0.0967378\pi$
$2$	0.926196	+	0.926196i	0.654919	+	0.654919i	−0.299254	+	0.954173i	$0.596738\pi$
$3$		0			0
$3$		0			0
$4$		−	0.284323i		−	0.142161i
$5$	−0.409991	−	0.109857i	−0.183354	−	0.0491295i	0.165974	−	0.986130i	$-0.446923\pi$
$5$	−0.409991	−	0.109857i	−0.183354	−	0.0491295i	−0.349328	+	0.937001i	$0.613590\pi$
$6$		0			0
$7$	−2.25606	−	1.38209i	−0.852712	−	0.522382i
$7$	−2.25606	−	1.38209i	−0.852712	−	0.522382i
$8$	2.11573	−	2.11573i	0.748024	−	0.748024i
$9$		0			0
$10$	−0.277983	−	0.481481i	−0.0879060	−	0.152258i
$11$	−1.35455	−	0.362951i	−0.408413	−	0.109434i	0.0487628	−	0.998810i	$-0.484472\pi$
$11$	−1.35455	−	0.362951i	−0.408413	−	0.109434i	−0.457175	+	0.889377i	$0.651139\pi$
$12$		0			0
$13$	−3.54669	−	0.648849i	−0.983674	−	0.179958i
$13$	−3.54669	−	0.648849i	−0.983674	−	0.179958i
$14$	−0.809468	−	3.36964i	−0.216339	−	0.900575i
$15$		0			0
$16$	3.35051			0.837629
$17$	6.94638			1.68475			0.842373	−	0.538895i	$-0.181158\pi$
$17$	6.94638			1.68475			0.842373	+	0.538895i	$0.181158\pi$
$18$		0			0
$19$	−0.143382	−	0.535108i	−0.0328941	−	0.122762i	0.947527	−	0.319677i	$-0.103574\pi$
$19$	−0.143382	−	0.535108i	−0.0328941	−	0.122762i	−0.980421	+	0.196915i	$0.936908\pi$
$20$	−0.0312348	+	0.116570i	−0.00698432	+	0.0260658i
$21$		0			0
$22$	−0.918416	−	1.59074i	−0.195807	−	0.339148i
$23$		−	7.84271i		−	1.63532i	−0.575702	−	0.817659i	$-0.695271\pi$
$23$		−	7.84271i		−	1.63532i	0.575702	−	0.817659i	$-0.304729\pi$
$24$		0			0
$25$	−4.17410	−	2.40992i	−0.834821	−	0.481984i
$26$	−2.68397	−	3.88589i	−0.526369	−	0.762085i
$27$		0			0
$28$	−0.392961	+	0.641450i	−0.0742626	+	0.121223i
$29$	3.01567	−	5.22330i	0.559997	−	0.969943i	−0.437499	−	0.899219i	$-0.644136\pi$
$29$	3.01567	−	5.22330i	0.559997	−	0.969943i	0.997496	−	0.0707238i	$-0.0225309\pi$
$30$		0			0
$31$	−2.17020	−	8.09928i	−0.389779	−	1.45467i	−0.830494	−	0.557027i	$-0.811942\pi$
$31$	−2.17020	−	8.09928i	−0.389779	−	1.45467i	0.440715	−	0.897647i	$-0.354725\pi$
$32$	−1.12823	−	1.12823i	−0.199444	−	0.199444i
$33$		0			0
$34$	6.43371	+	6.43371i	1.10337	+	1.10337i
$35$	0.773134	+	0.814490i	0.130684	+	0.137674i
$36$		0			0
$37$	−4.24059	+	4.24059i	−0.697149	+	0.697149i	−0.963795	−	0.266646i	$-0.914085\pi$
$37$	−4.24059	+	4.24059i	−0.697149	+	0.697149i	0.266646	+	0.963795i	$0.414085\pi$
$38$	0.362815	−	0.628415i	0.0588564	−	0.101942i
$39$		0			0
$40$	−1.09986	+	0.635004i	−0.173903	+	0.100403i
$41$	0.434817	+	1.62276i	0.0679070	+	0.253433i	0.991532	−	0.129866i	$-0.0414547\pi$
$41$	0.434817	+	1.62276i	0.0679070	+	0.253433i	−0.923625	+	0.383299i	$0.874788\pi$
$42$		0			0
$43$	6.49491	−	3.74984i	0.990464	−	0.571845i	0.0850513	−	0.996377i	$-0.472895\pi$
$43$	6.49491	−	3.74984i	0.990464	−	0.571845i	0.905413	+	0.424532i	$0.139561\pi$
$44$	−0.103195	+	0.385130i	−0.0155573	+	0.0580605i
$45$		0			0
$46$	7.26389	−	7.26389i	1.07100	−	1.07100i
$47$	−2.62582	+	9.79969i	−0.383015	+	1.42943i	0.458257	+	0.888820i	$0.348474\pi$
$47$	−2.62582	+	9.79969i	−0.383015	+	1.42943i	−0.841272	+	0.540612i	$0.818193\pi$
$48$		0			0
$49$	3.17964	+	6.23618i	0.454234	+	0.890882i
$50$	−1.63398	−	6.09809i	−0.231080	−	0.862401i
$51$		0			0
$52$	−0.184483	+	1.00840i	−0.0255831	+	0.139841i
$53$	−3.77860	+	6.54472i	−0.519030	+	0.898986i	0.480725	+	0.876871i	$0.340373\pi$
$53$	−3.77860	+	6.54472i	−0.519030	+	0.898986i	−0.999755	+	0.0221152i	$0.992960\pi$
$54$		0			0
$55$	0.515482	+	0.297614i	0.0695076	+	0.0401302i
$56$	−7.69736	+	1.84909i	−1.02860	+	0.247094i
$57$		0			0
$58$	7.63090	−	2.04469i	1.00199	−	0.268482i
$59$	4.83450	+	4.83450i	0.629398	+	0.629398i	0.947917	−	0.318519i	$-0.103185\pi$
$59$	4.83450	+	4.83450i	0.629398	+	0.629398i	−0.318519	+	0.947917i	$0.603185\pi$
$60$		0			0
$61$	2.38809	+	1.37876i	0.305763	+	0.176533i	0.645029	−	0.764158i	$-0.276845\pi$
$61$	2.38809	+	1.37876i	0.305763	+	0.176533i	−0.339266	+	0.940691i	$0.610179\pi$
$62$	5.49149	−	9.51155i	0.697421	−	1.20797i
$63$		0			0
$64$		−	8.79095i		−	1.09887i
$65$	1.38283	+	0.655650i	0.171519	+	0.0813234i
$66$		0			0
$67$	3.70163	−	13.8147i	0.452226	−	1.68773i	−0.243893	−	0.969802i	$-0.578424\pi$
$67$	3.70163	−	13.8147i	0.452226	−	1.68773i	0.696118	−	0.717927i	$-0.254909\pi$
$68$		−	1.97502i		−	0.239506i
$69$		0			0
$70$	−0.0383037	+	1.47045i	−0.00457817	+	0.175752i
$71$	−1.00255	+	3.74157i	−0.118981	+	0.444042i	−0.999554	−	0.0298681i	$-0.990491\pi$
$71$	−1.00255	+	3.74157i	−0.118981	+	0.444042i	0.880573	+	0.473910i	$0.157158\pi$
$72$		0			0
$73$	−11.0713	+	2.96655i	−1.29580	+	0.347209i	−0.839861	−	0.542802i	$-0.817363\pi$
$73$	−11.0713	+	2.96655i	−1.29580	+	0.347209i	−0.455940	+	0.890011i	$0.650697\pi$
$74$	−7.85524			−0.913153
$75$		0			0
$76$	−0.152144	+	0.0407667i	−0.0174521	+	0.00467627i
$77$	2.55432	+	2.69096i	0.291092	+	0.306663i
$78$		0			0
$79$	4.32696	+	7.49452i	0.486821	+	0.843199i	0.999885	−	0.0151513i	$-0.00482300\pi$
$79$	4.32696	+	7.49452i	0.486821	+	0.843199i	−0.513064	+	0.858350i	$0.671490\pi$
$80$	−1.37368	−	0.368077i	−0.153582	−	0.0411523i
$81$		0			0
$82$	−1.10027	+	1.90572i	−0.121504	+	0.210452i
$83$	2.26360	−	2.26360i	0.248462	−	0.248462i	−0.571877	−	0.820339i	$-0.693785\pi$
$83$	2.26360	−	2.26360i	0.248462	−	0.248462i	0.820339	+	0.571877i	$0.193785\pi$
$84$		0			0
$85$	−2.84796	−	0.763108i	−0.308904	−	0.0827707i
$86$	9.48864	+	2.54247i	1.02319	+	0.274162i
$87$		0			0
$88$	−3.63377	+	2.09796i	−0.387361	+	0.223643i
$89$	8.19285	+	8.19285i	0.868441	+	0.868441i	0.992300	−	0.123859i	$-0.0395271\pi$
$89$	8.19285	+	8.19285i	0.868441	+	0.868441i	−0.123859	+	0.992300i	$0.539527\pi$
$90$		0			0
$91$	7.10478	+	6.36569i	0.744784	+	0.667306i
$92$	−2.22986			−0.232479
$93$		0			0
$94$	−11.5085	+	6.64441i	−1.18701	+	0.685318i
$95$			0.235141i			0.0241250i
$96$		0			0
$97$	15.5709	+	4.17221i	1.58099	+	0.423624i	0.939231	−	0.343286i	$-0.111540\pi$
$97$	15.5709	+	4.17221i	1.58099	+	0.423624i	0.641755	+	0.766910i	$0.278207\pi$
$98$	−2.83095	+	8.72089i	−0.285969	+	0.880943i
$99$		0			0
$100$	−0.685195	+	1.18679i	−0.0685195	+	0.118679i
$101$	−3.55466	−	6.15686i	−0.353702	−	0.612630i	0.633193	−	0.773994i	$-0.281744\pi$
$101$	−3.55466	−	6.15686i	−0.353702	−	0.612630i	−0.986895	+	0.161364i	$0.948411\pi$
$102$		0			0
$103$	5.13973	+	8.90227i	0.506432	+	0.877167i	0.999972	+	0.00744360i	$0.00236939\pi$
$103$	5.13973	+	8.90227i	0.506432	+	0.877167i	−0.493540	+	0.869723i	$0.664297\pi$
$104$	−8.87662	+	6.13105i	−0.870425	+	0.601198i
$105$		0			0
$106$	−9.56141	+	2.56197i	−0.928686	+	0.248841i
$107$	−4.49430			−0.434480			−0.217240	−	0.976118i	$-0.569705\pi$
$107$	−4.49430			−0.434480			−0.217240	+	0.976118i	$0.569705\pi$
$108$		0			0
$109$	−4.38513	+	1.17499i	−0.420019	+	0.112544i	−0.462637	−	0.886548i	$-0.653097\pi$
$109$	−4.38513	+	1.17499i	−0.420019	+	0.112544i	0.0426183	+	0.999091i	$0.486430\pi$
$110$	0.201789	+	0.753085i	0.0192398	+	0.0718039i
$111$		0			0
$112$	−7.55897	−	4.63072i	−0.714256	−	0.437562i
$113$	3.41572	+	5.91619i	0.321324	+	0.556549i	0.980761	−	0.195210i	$-0.0625390\pi$
$113$	3.41572	+	5.91619i	0.321324	+	0.556549i	−0.659438	+	0.751759i	$0.729206\pi$
$114$		0			0
$115$	−0.861576	+	3.21544i	−0.0803424	+	0.299842i
$116$	−1.48510	−	0.857425i	−0.137888	−	0.0796099i
$117$		0			0
$118$			8.95538i			0.824410i
$119$	−15.6715	−	9.60054i	−1.43660	−	0.880080i
$120$		0			0
$121$	−7.82320	−	4.51673i	−0.711200	−	0.410612i
$122$	0.934832	+	3.48884i	0.0846357	+	0.315865i
$123$		0			0
$124$	−2.30281	+	0.617036i	−0.206799	+	0.0554115i
$125$	2.94727	+	2.94727i	0.263612	+	0.263612i
$126$		0			0
$127$	0.727835	+	0.420216i	0.0645850	+	0.0372881i	0.531945	−	0.846779i	$-0.321461\pi$
$127$	0.727835	+	0.420216i	0.0645850	+	0.0372881i	−0.467360	+	0.884067i	$0.654795\pi$
$128$	5.88568	−	5.88568i	0.520226	−	0.520226i
$129$		0			0
$130$	0.673512	+	1.88803i	0.0590709	+	0.165591i
$131$	15.6642	−	9.04371i	1.36858	−	0.790152i	0.377837	−	0.925872i	$-0.376668\pi$
$131$	15.6642	−	9.04371i	1.36858	−	0.790152i	0.990747	+	0.135720i	$0.0433347\pi$
$132$		0			0
$133$	−0.416091	+	1.40541i	−0.0360796	+	0.121864i
$134$	16.2235	−	9.36665i	1.40150	−	0.809155i
$135$		0			0
$136$	14.6967	−	14.6967i	1.26023	−	1.26023i
$137$	10.2762	−	10.2762i	0.877957	−	0.877957i	−0.115366	−	0.993323i	$-0.536804\pi$
$137$	10.2762	−	10.2762i	0.877957	−	0.877957i	0.993323	+	0.115366i	$0.0368040\pi$
$138$		0			0
$139$	−10.1485	+	5.85922i	−0.860782	+	0.496973i	−0.864274	−	0.503021i	$-0.832222\pi$
$139$	−10.1485	+	5.85922i	−0.860782	+	0.496973i	0.00349232	+	0.999994i	$0.498888\pi$
$140$	0.231578	−	0.219820i	0.0195719	−	0.0185782i
$141$		0			0
$142$	−4.39398	+	2.53687i	−0.368735	+	0.212889i
$143$	4.56867	+	2.16617i	0.382051	+	0.181144i
$144$		0			0
$145$	−1.81022	+	1.81022i	−0.150330	+	0.150330i
$146$	−13.0018	−	7.50661i	−1.07604	−	0.621251i
$147$		0			0
$148$	1.20570	+	1.20570i	0.0991077	+	0.0991077i
$149$	−6.09666	+	1.63360i	−0.499458	+	0.133829i	−0.499748	−	0.866171i	$-0.666574\pi$
$149$	−6.09666	+	1.63360i	−0.499458	+	0.133829i	0.000290536		1.00000i	$0.499908\pi$
$150$		0			0
$151$	1.46708	+	5.47520i	0.119389	+	0.445565i	0.999578	−	0.0290583i	$-0.00925084\pi$
$151$	1.46708	+	5.47520i	0.119389	+	0.445565i	−0.880189	+	0.474624i	$0.842584\pi$
$152$	−1.43550	−	0.828788i	−0.116435	−	0.0672235i
$153$		0			0
$154$	−0.126550	+	4.85815i	−0.0101977	+	0.391481i
$155$			3.55905i			0.285870i
$156$		0			0
$157$	−4.05121	−	2.33897i	−0.323322	−	0.186670i	0.329550	−	0.944138i	$-0.393103\pi$
$157$	−4.05121	−	2.33897i	−0.323322	−	0.186670i	−0.652872	+	0.757468i	$0.726436\pi$
$158$	−2.93378	+	10.9490i	−0.233399	+	0.871056i
$159$		0			0
$160$	0.338620	+	0.586507i	0.0267703	+	0.0463675i
$161$	−10.8394	+	17.6937i	−0.854261	+	1.39446i
$162$		0			0
$163$	−3.11598	−	11.6290i	−0.244063	−	0.910855i	−0.973852	−	0.227183i	$-0.927049\pi$
$163$	−3.11598	−	11.6290i	−0.244063	−	0.910855i	0.729789	−	0.683672i	$-0.239618\pi$
$164$	0.461388	−	0.123629i	0.0360283	−	0.00965376i
$165$		0			0
$166$	4.19307			0.325445
$167$	−2.16916	+	0.581223i	−0.167854	+	0.0449764i	−0.341767	−	0.939785i	$-0.611025\pi$
$167$	−2.16916	+	0.581223i	−0.167854	+	0.0449764i	0.173913	+	0.984761i	$0.444359\pi$
$168$		0			0
$169$	12.1580	+	4.60253i	0.935230	+	0.354041i
$170$	−1.93098	−	3.34455i	−0.148099	−	0.256516i
$171$		0			0
$172$	−1.06616	−	1.84665i	−0.0812943	−	0.140806i
$173$	−5.82086	+	10.0820i	−0.442552	+	0.766523i	−0.997878	−	0.0651101i	$-0.979260\pi$
$173$	−5.82086	+	10.0820i	−0.442552	+	0.766523i	0.555326	+	0.831633i	$0.312593\pi$
$174$		0			0
$175$	6.08631	+	11.2059i	0.460082	+	0.847088i
$176$	−4.53844	−	1.21607i	−0.342098	−	0.0916649i
$177$		0			0
$178$			15.1764i			1.13752i
$179$	16.3721	−	9.45241i	1.22370	−	0.706506i	0.257999	−	0.966145i	$-0.416937\pi$
$179$	16.3721	−	9.45241i	1.22370	−	0.706506i	0.965706	+	0.259639i	$0.0836035\pi$
$180$		0			0
$181$	0.400647			0.0297799			0.0148899	−	0.999889i	$-0.495260\pi$
$181$	0.400647			0.0297799			0.0148899	+	0.999889i	$0.495260\pi$
$182$	0.684540	+	12.4763i	0.0507415	+	0.924805i
$183$		0			0
$184$	−16.5931	−	16.5931i	−1.22326	−	1.22326i
$185$	2.20446	−	1.27275i	0.162075	−	0.0935743i
$186$		0			0
$187$	−9.40923	−	2.52120i	−0.688071	−	0.184368i
$188$	2.78628	+	0.746580i	0.203210	+	0.0544500i
$189$		0			0
$190$	−0.217787	+	0.217787i	−0.0157999	+	0.0157999i
$191$	−5.12611	+	8.87869i	−0.370912	+	0.642439i	−0.989706	−	0.143114i	$-0.954288\pi$
$191$	−5.12611	+	8.87869i	−0.370912	+	0.642439i	0.618794	+	0.785554i	$0.287622\pi$
$192$		0			0
$193$	−8.65734	−	2.31973i	−0.623169	−	0.166978i	−0.0666009	−	0.997780i	$-0.521215\pi$
$193$	−8.65734	−	2.31973i	−0.623169	−	0.166978i	−0.556568	+	0.830802i	$0.687882\pi$
$194$	10.5574	+	18.2860i	0.757979	+	1.31286i
$195$		0			0
$196$	1.77309	−	0.904045i	0.126649	−	0.0645746i
$197$	4.04286	−	1.08328i	0.288042	−	0.0771806i	−0.111905	−	0.993719i	$-0.535695\pi$
$197$	4.04286	−	1.08328i	0.288042	−	0.0771806i	0.399947	+	0.916538i	$0.369029\pi$
$198$		0			0
$199$	0.0731516			0.00518558			0.00259279	−	0.999997i	$-0.499175\pi$
$199$	0.0731516			0.00518558			0.00259279	+	0.999997i	$0.499175\pi$
$200$	−13.9300	+	3.73254i	−0.985001	+	0.263930i
$201$		0			0
$202$	2.41014	−	8.99477i	0.169577	−	0.632870i
$203$	−14.0226	+	7.61615i	−0.984196	+	0.534549i
$204$		0			0
$205$		−	0.713085i		−	0.0498040i
$206$	−3.48485	+	13.0056i	−0.242801	+	0.906146i
$207$		0			0
$208$	−11.8832	−	2.17398i	−0.823954	−	0.150738i
$209$			0.776872i			0.0537374i
$210$		0			0
$211$	10.3736	−	17.9676i	0.714148	−	1.23694i	−0.249140	−	0.968468i	$-0.580148\pi$
$211$	10.3736	−	17.9676i	0.714148	−	1.23694i	0.963287	−	0.268472i	$-0.0865188\pi$
$212$	1.86081	+	1.07434i	0.127801	+	0.0737861i
$213$		0			0
$214$	−4.16260	−	4.16260i	−0.284549	−	0.284549i
$215$	−3.07480	+	0.823891i	−0.209700	+	0.0561889i
$216$		0			0
$217$	−6.29786	+	21.2719i	−0.427526	+	1.44403i
$218$	−5.14976	−	2.97321i	−0.348785	−	0.201371i
$219$		0			0
$220$	0.0846184	−	0.146563i	0.00570497	−	0.00988129i
$221$	−24.6367	−	4.50715i	−1.65724	−	0.303184i
$222$		0			0
$223$	−0.0283672	−	0.105868i	−0.00189961	−	0.00708942i	0.964970	−	0.262362i	$-0.0845015\pi$
$223$	−0.0283672	−	0.105868i	−0.00189961	−	0.00708942i	−0.966869	+	0.255273i	$0.917835\pi$
$224$	0.986038	+	4.10467i	0.0658824	+	0.274255i
$225$		0			0
$226$	−2.31593	+	8.64317i	−0.154053	+	0.574935i
$227$	−2.22859	+	2.22859i	−0.147917	+	0.147917i	−0.777187	−	0.629270i	$-0.783354\pi$
$227$	−2.22859	+	2.22859i	−0.147917	+	0.147917i	0.629270	+	0.777187i	$0.283354\pi$
$228$		0			0
$229$	4.14901	−	15.4843i	0.274174	−	1.02323i	−0.682218	−	0.731148i	$-0.738985\pi$
$229$	4.14901	−	15.4843i	0.274174	−	1.02323i	0.956393	−	0.292084i	$-0.0943486\pi$
$230$	−3.77612	+	2.18014i	−0.248990	+	0.143754i
$231$		0			0
$232$	−4.67074	−	17.4314i	−0.306649	−	1.14443i
$233$	21.8559	−	12.6185i	1.43183	−	0.826668i	0.434570	−	0.900638i	$-0.356900\pi$
$233$	21.8559	−	12.6185i	1.43183	−	0.826668i	0.997260	+	0.0739699i	$0.0235669\pi$
$234$		0			0
$235$	2.15313	−	3.72932i	0.140454	−	0.243274i
$236$	1.37456	−	1.37456i	0.0894761	−	0.0894761i
$237$		0			0
$238$	−5.62287	−	23.4068i	−0.364477	−	1.51724i
$239$	−3.59516	−	3.59516i	−0.232552	−	0.232552i	0.581205	−	0.813757i	$-0.302581\pi$
$239$	−3.59516	−	3.59516i	−0.232552	−	0.232552i	−0.813757	+	0.581205i	$0.802581\pi$
$240$		0			0
$241$	2.15492	+	2.15492i	0.138811	+	0.138811i	0.773098	−	0.634287i	$-0.218706\pi$
$241$	2.15492	+	2.15492i	0.138811	+	0.138811i	−0.634287	+	0.773098i	$0.718706\pi$
$242$	−3.06244	−	11.4292i	−0.196861	−	0.734696i
$243$		0			0
$244$	0.392014	−	0.678988i	0.0250961	−	0.0434678i
$245$	−0.618539	−	2.90608i	−0.0395170	−	0.185663i
$246$		0			0
$247$	0.161326	+	1.99090i	0.0102649	+	0.126678i
$248$	−21.7274	−	12.5443i	−1.37969	−	0.796567i
$249$		0			0
$250$			5.45950i			0.345289i
$251$	−3.62476	−	6.27826i	−0.228793	−	0.396280i	0.728658	−	0.684878i	$-0.240144\pi$
$251$	−3.62476	−	6.27826i	−0.228793	−	0.396280i	−0.957451	+	0.288597i	$0.906811\pi$
$252$		0			0
$253$	−2.84652	+	10.6234i	−0.178959	+	0.667885i
$254$	0.284916	+	1.06332i	0.0178772	+	0.0667187i
$255$		0			0
$256$	−6.67931			−0.417457
$257$	11.4669			0.715289			0.357644	−	0.933858i	$-0.383580\pi$
$257$	11.4669			0.715289			0.357644	+	0.933858i	$0.383580\pi$
$258$		0			0
$259$	15.4279	−	3.70615i	0.958645	−	0.230289i
$260$	0.186416	−	0.393171i	0.0115611	−	0.0243834i
$261$		0			0
$262$	22.8843	+	6.13184i	1.41380	+	0.378826i
$263$	−8.29386	−	14.3654i	−0.511421	−	0.885808i	−0.999912	−	0.0132387i	$-0.995786\pi$
$263$	−8.29386	−	14.3654i	−0.511421	−	0.885808i	0.488491	−	0.872569i	$-0.337547\pi$
$264$		0			0
$265$	2.26817	−	2.26817i	0.139333	−	0.139333i
$266$	−1.68706	+	0.916299i	−0.103440	+	0.0561819i
$267$		0			0
$268$	−3.92782	−	1.05246i	−0.239930	−	0.0642891i
$269$			9.39879i			0.573055i	0.958072	+	0.286527i	$0.0925009\pi$
$269$			9.39879i			0.573055i	−0.958072	+	0.286527i	$0.907499\pi$
$270$		0			0
$271$	16.6976	+	16.6976i	1.01431	+	1.01431i	0.999896	+	0.0144118i	$0.00458758\pi$
$271$	16.6976	+	16.6976i	1.01431	+	1.01431i	0.0144118	+	0.999896i	$0.495412\pi$
$272$	23.2740			1.41119
$273$		0			0
$274$	19.0356			1.14998
$275$	4.77935	+	4.77935i	0.288206	+	0.288206i
$276$		0			0
$277$		−	7.83005i		−	0.470462i	−0.971940	−	0.235231i	$-0.924415\pi$
$277$		−	7.83005i		−	0.470462i	0.971940	−	0.235231i	$-0.0755846\pi$
$278$	−14.8263	−	3.97268i	−0.889219	−	0.238266i
$279$		0			0
$280$	3.35898	+	0.0874981i	0.200738	+	0.00522901i
$281$	−7.60467	+	7.60467i	−0.453656	+	0.453656i	−0.896566	−	0.442910i	$-0.853946\pi$
$281$	−7.60467	+	7.60467i	−0.453656	+	0.453656i	0.442910	+	0.896566i	$0.353946\pi$
$282$		0			0
$283$	−6.54596	−	11.3379i	−0.389117	−	0.673971i	0.603214	−	0.797580i	$-0.293887\pi$
$283$	−6.54596	−	11.3379i	−0.389117	−	0.673971i	−0.992331	+	0.123609i	$0.960553\pi$
$284$	1.06381	+	0.285048i	0.0631257	+	0.0169145i
$285$		0			0
$286$	2.22518	+	6.23778i	0.131578	+	0.368848i
$287$	1.26183	−	4.26201i	0.0744834	−	0.251578i
$288$		0			0
$289$	31.2522			1.83837
$290$	−3.35323			−0.196908
$291$		0			0
$292$	0.843459	+	3.14783i	0.0493597	+	0.184213i
$293$	−1.63802	+	6.11317i	−0.0956941	+	0.357135i	−0.997124	−	0.0757902i	$-0.975852\pi$
$293$	−1.63802	+	6.11317i	−0.0956941	+	0.357135i	0.901430	+	0.432926i	$0.142519\pi$
$294$		0			0
$295$	−1.45100	−	2.51321i	−0.0844805	−	0.146324i
$296$			17.9439i			1.04297i
$297$		0			0
$298$	−7.15973	−	4.13367i	−0.414752	−	0.239457i
$299$	−5.08873	+	27.8157i	−0.294289	+	1.60862i
$300$		0			0
$301$	−19.8355	−	0.516695i	−1.14330	−	0.0297818i
$302$	−3.71231	+	6.42991i	−0.213619	+	0.369999i
$303$		0			0
$304$	−0.480403	−	1.79289i	−0.0275530	−	0.102829i
$305$	−0.827629	−	0.827629i	−0.0473899	−	0.0473899i
$306$		0			0
$307$	−0.930901	−	0.930901i	−0.0531293	−	0.0531293i	0.680043	−	0.733172i	$-0.261961\pi$
$307$	−0.930901	−	0.930901i	−0.0531293	−	0.0531293i	−0.733172	+	0.680043i	$0.761961\pi$
$308$	0.765100	−	0.726252i	0.0435956	−	0.0413821i
$309$		0			0
$310$	−3.29637	+	3.29637i	−0.187221	+	0.187221i
$311$	15.2632	−	26.4366i	0.865495	−	1.49908i	−0.00106060	−	0.999999i	$-0.500338\pi$
$311$	15.2632	−	26.4366i	0.865495	−	1.49908i	0.866555	−	0.499081i	$-0.166329\pi$
$312$		0			0
$313$	−15.9124	+	9.18705i	−0.899425	+	0.519283i	−0.877013	−	0.480466i	$-0.840468\pi$
$313$	−15.9124	+	9.18705i	−0.899425	+	0.519283i	−0.0224111	+	0.999749i	$0.507134\pi$
$314$	−1.58587	−	5.91856i	−0.0894960	−	0.334004i
$315$		0			0
$316$	2.13086	−	1.23025i	0.119870	−	0.0692072i
$317$	4.00188	−	14.9352i	0.224768	−	0.838845i	−0.757730	−	0.652569i	$-0.773691\pi$
$317$	4.00188	−	14.9352i	0.224768	−	0.838845i	0.982497	−	0.186276i	$-0.0596420\pi$
$318$		0			0
$319$	−5.98069	+	5.98069i	−0.334854	+	0.334854i
$320$	−0.965746	+	3.60421i	−0.0539868	+	0.201482i
$321$		0			0
$322$	−26.4272	+	6.34842i	−1.47273	+	0.353784i
$323$	−0.995985	−	3.71707i	−0.0554181	−	0.206823i
$324$		0			0
$325$	13.2406	+	11.2556i	0.734454	+	0.624348i
$326$	7.88473	−	13.6568i	0.436695	−	0.756378i
$327$		0			0
$328$	4.35328	+	2.51337i	0.240370	+	0.138777i
$329$	19.4681	−	18.4796i	1.07331	−	1.01881i
$330$		0			0
$331$	25.7839	−	6.90877i	1.41721	−	0.379740i	0.532717	−	0.846293i	$-0.321171\pi$
$331$	25.7839	−	6.90877i	1.41721	−	0.379740i	0.884493	+	0.466553i	$0.154504\pi$
$332$	−0.643592	−	0.643592i	−0.0353217	−	0.0353217i
$333$		0			0
$334$	−2.54739	−	1.47074i	−0.139387	−	0.0804751i
$335$	−3.03527	+	5.25724i	−0.165835	+	0.287234i
$336$		0			0
$337$			25.3802i			1.38255i	0.722592	+	0.691275i	$0.242951\pi$
$337$			25.3802i			1.38255i	−0.722592	+	0.691275i	$0.757049\pi$
$338$	6.99784	+	15.5235i	0.380632	+	0.844368i
$339$		0			0
$340$	−0.216969	+	0.809740i	−0.0117668	+	0.0439143i
$341$			11.7586i			0.636762i
$342$		0			0
$343$	1.44550	−	18.4638i	0.0780498	−	0.996949i
$344$	5.80783	−	21.6751i	0.313137	−	1.16864i
$345$		0			0
$346$	−14.7292	+	3.94668i	−0.791846	+	0.212175i
$347$	2.33363			0.125276			0.0626380	−	0.998036i	$-0.480049\pi$
$347$	2.33363			0.125276			0.0626380	+	0.998036i	$0.480049\pi$
$348$		0			0
$349$	−28.6493	+	7.67654i	−1.53356	+	0.410916i	−0.924178	−	0.381962i	$-0.875249\pi$
$349$	−28.6493	+	7.67654i	−1.53356	+	0.410916i	−0.609381	+	0.792878i	$0.708582\pi$
$350$	−4.74177	+	16.0160i	−0.253458	+	0.856091i
$351$		0			0
$352$	1.11875	+	1.93773i	0.0596296	+	0.103282i
$353$	−4.21930	−	1.13056i	−0.224571	−	0.0601736i	0.144779	−	0.989464i	$-0.453753\pi$
$353$	−4.21930	−	1.13056i	−0.224571	−	0.0601736i	−0.369350	+	0.929290i	$0.620420\pi$
$354$		0			0
$355$	0.822073	−	1.42387i	0.0436311	−	0.0755713i
$356$	2.32942	−	2.32942i	0.123459	−	0.123459i
$357$		0			0
$358$	23.9185	+	6.40895i	1.26413	+	0.338723i
$359$	20.7047	+	5.54780i	1.09275	+	0.292802i	0.759809	−	0.650146i	$-0.225292\pi$
$359$	20.7047	+	5.54780i	1.09275	+	0.292802i	0.332941	+	0.942948i	$0.391959\pi$
$360$		0			0
$361$	16.1887	−	9.34655i	0.852037	−	0.491924i
$362$	0.371078	+	0.371078i	0.0195034	+	0.0195034i
$363$		0			0
$364$	1.80991	−	2.02005i	0.0948652	−	0.105880i
$365$	4.86505			0.254648
$366$		0			0
$367$	10.9156	−	6.30214i	0.569791	−	0.328969i	−0.187275	−	0.982308i	$-0.559965\pi$
$367$	10.9156	−	6.30214i	0.569791	−	0.328969i	0.757066	+	0.653338i	$0.226632\pi$
$368$		−	26.2771i		−	1.36979i
$369$		0			0
$370$	3.22058	+	0.862952i	0.167430	+	0.0448627i
$371$	17.5702	−	9.54293i	0.912197	−	0.495444i
$372$		0			0
$373$	7.97476	−	13.8127i	0.412917	−	0.715194i	−0.582290	−	0.812981i	$-0.697843\pi$
$373$	7.97476	−	13.8127i	0.412917	−	0.715194i	0.995207	+	0.0977873i	$0.0311765\pi$
$374$	−6.37967	−	11.0499i	−0.329885	−	0.571377i
$375$		0			0
$376$	15.1780	+	26.2890i	0.782744	+	1.35575i
$377$	−14.0848	+	16.5687i	−0.725403	+	0.853331i
$378$		0			0
$379$	−33.0651	+	8.85976i	−1.69844	+	0.455095i	−0.972545	−	0.232713i	$-0.925240\pi$
$379$	−33.0651	+	8.85976i	−1.69844	+	0.455095i	−0.725893	+	0.687808i	$0.758573\pi$
$380$	0.0668561			0.00342964
$381$		0			0
$382$	−12.9712	+	3.47562i	−0.663664	+	0.177828i
$383$	3.37726	+	12.6041i	0.172570	+	0.644039i	0.996953	+	0.0780068i	$0.0248556\pi$
$383$	3.37726	+	12.6041i	0.172570	+	0.644039i	−0.824383	+	0.566032i	$0.808478\pi$
$384$		0			0
$385$	−0.751630	−	1.38388i	−0.0383066	−	0.0705290i
$386$	−5.86987	−	10.1669i	−0.298768	−	0.517482i
$387$		0			0
$388$	1.18626	−	4.42717i	0.0602230	−	0.224755i
$389$	14.8252	+	8.55933i	0.751667	+	0.433975i	0.826296	−	0.563236i	$-0.190444\pi$
$389$	14.8252	+	8.55933i	0.751667	+	0.433975i	−0.0746290	+	0.997211i	$0.523777\pi$
$390$		0			0
$391$		−	54.4785i		−	2.75510i
$392$	19.9213	+	6.46680i	1.00618	+	0.326623i
$393$		0			0
$394$	4.74781	+	2.74115i	0.239191	+	0.138097i
$395$	−0.950693	−	3.54803i	−0.0478345	−	0.178521i
$396$		0			0
$397$	−9.36386	+	2.50904i	−0.469959	+	0.125925i	−0.486023	−	0.873946i	$-0.661553\pi$
$397$	−9.36386	+	2.50904i	−0.469959	+	0.125925i	0.0160646	+	0.999871i	$0.494886\pi$
$398$	0.0677527	+	0.0677527i	0.00339613	+	0.00339613i
$399$		0			0
$400$	−13.9854	−	8.07447i	−0.699270	−	0.403723i
$401$	5.44277	−	5.44277i	0.271799	−	0.271799i	−0.558025	−	0.829824i	$-0.688441\pi$
$401$	5.44277	−	5.44277i	0.271799	−	0.271799i	0.829824	+	0.558025i	$0.188441\pi$
$402$		0			0
$403$	2.44180	+	30.1338i	0.121635	+	1.50107i
$404$	−1.75054	+	1.01067i	−0.0870924	+	0.0502828i
$405$		0			0
$406$	−20.0418	−	5.93365i	−0.994656	−	0.294482i
$407$	7.28323	−	4.20497i	0.361016	−	0.208433i
$408$		0			0
$409$	−2.18322	+	2.18322i	−0.107954	+	0.107954i	−0.759020	−	0.651067i	$-0.774322\pi$
$409$	−2.18322	+	2.18322i	−0.107954	+	0.107954i	0.651067	+	0.759020i	$0.274322\pi$
$410$	0.660457	−	0.660457i	0.0326176	−	0.0326176i
$411$		0			0
$412$	2.53112	−	1.46134i	0.124699	−	0.0719952i
$413$	−4.22521	−	17.5887i	−0.207909	−	0.865481i
$414$		0			0
$415$	−1.17673	+	0.679384i	−0.0577633	+	0.0333496i
$416$	3.26942	+	4.73352i	0.160297	+	0.232080i
$417$		0			0
$418$	−0.719536	+	0.719536i	−0.0351937	+	0.0351937i
$419$	2.29397	+	1.32442i	0.112068	+	0.0647023i	0.554986	−	0.831860i	$-0.312724\pi$
$419$	2.29397	+	1.32442i	0.112068	+	0.0647023i	−0.442918	+	0.896562i	$0.646057\pi$
$420$		0			0
$421$	8.96466	+	8.96466i	0.436911	+	0.436911i	0.890971	−	0.454060i	$-0.150025\pi$
$421$	8.96466	+	8.96466i	0.436911	+	0.436911i	−0.454060	+	0.890971i	$0.650025\pi$
$422$	26.2495	−	7.03353i	1.27780	−	0.342387i
$423$		0			0
$424$	5.85237	+	21.8414i	0.284216	+	1.06071i
$425$	−28.9949	−	16.7402i	−1.40646	−	0.812020i
$426$		0			0
$427$	−3.48210	−	6.41114i	−0.168511	−	0.310257i
$428$			1.27783i			0.0617663i
$429$		0			0
$430$	−3.61095	−	2.08478i	−0.174136	−	0.100537i
$431$	3.00230	−	11.2048i	0.144616	−	0.539714i	−0.855156	−	0.518370i	$-0.826539\pi$
$431$	3.00230	−	11.2048i	0.144616	−	0.539714i	0.999772	−	0.0213436i	$-0.00679441\pi$
$432$		0			0
$433$	−1.08503	−	1.87932i	−0.0521430	−	0.0903143i	0.838776	−	0.544477i	$-0.183272\pi$
$433$	−1.08503	−	1.87932i	−0.0521430	−	0.0903143i	−0.890919	+	0.454163i	$0.849938\pi$
$434$	−25.5350	+	13.8689i	−1.22572	+	0.665728i
$435$		0			0
$436$	0.334077	+	1.24679i	0.0159994	+	0.0597105i
$437$	−4.19670	+	1.12450i	−0.200755	+	0.0537923i
$438$		0			0
$439$	20.7361			0.989680			0.494840	−	0.868984i	$-0.335227\pi$
$439$	20.7361			0.989680			0.494840	+	0.868984i	$0.335227\pi$
$440$	1.72029	−	0.460950i	0.0820116	−	0.0219749i
$441$		0			0
$442$	−18.6439	−	26.9929i	−0.886798	−	1.28392i
$443$	9.36776	+	16.2254i	0.445075	+	0.770893i	0.998057	−	0.0622999i	$-0.0198435\pi$
$443$	9.36776	+	16.2254i	0.445075	+	0.770893i	−0.552982	+	0.833193i	$0.686510\pi$
$444$		0			0
$445$	−2.45896	−	4.25904i	−0.116566	−	0.201898i
$446$	0.0717806	−	0.124328i	0.00339891	−	0.00588709i
$447$		0			0
$448$	−12.1499	+	19.8329i	−0.574029	+	0.937018i
$449$	−14.2069	−	3.80673i	−0.670465	−	0.179651i	−0.0925007	−	0.995713i	$-0.529486\pi$
$449$	−14.2069	−	3.80673i	−0.670465	−	0.179651i	−0.577964	+	0.816062i	$0.696153\pi$
$450$		0			0
$451$		−	2.35593i		−	0.110936i
$452$	1.68211	−	0.971166i	0.0791198	−	0.0456798i
$453$		0			0
$454$	−4.12822			−0.193747
$455$	−2.21358	−	3.39039i	−0.103774	−	0.158944i
$456$		0			0
$457$	17.1891	+	17.1891i	0.804074	+	0.804074i	0.983730	−	0.179655i	$-0.0574982\pi$
$457$	17.1891	+	17.1891i	0.804074	+	0.804074i	−0.179655	+	0.983730i	$0.557498\pi$
$458$	18.1843	−	10.4987i	0.849697	−	0.490573i
$459$		0			0
$460$	0.914225	+	0.244966i	0.0426259	+	0.0114216i
$461$	3.71656	+	0.995848i	0.173097	+	0.0463813i	0.344327	−	0.938850i	$-0.388107\pi$
$461$	3.71656	+	0.995848i	0.173097	+	0.0463813i	−0.171229	+	0.985231i	$0.554774\pi$
$462$		0			0
$463$	−4.99628	+	4.99628i	−0.232197	+	0.232197i	−0.813609	−	0.581412i	$-0.802500\pi$
$463$	−4.99628	+	4.99628i	−0.232197	+	0.232197i	0.581412	+	0.813609i	$0.302500\pi$
$464$	10.1041	−	17.5007i	0.469069	−	0.812452i
$465$		0			0
$466$	31.9301	+	8.55565i	1.47913	+	0.396333i
$467$	−4.32120	−	7.48453i	−0.199961	−	0.346343i	0.748554	−	0.663073i	$-0.230748\pi$
$467$	−4.32120	−	7.48453i	−0.199961	−	0.346343i	−0.948516	+	0.316731i	$0.897415\pi$
$468$		0			0
$469$	−27.4442	+	26.0507i	−1.26726	+	1.20291i
$470$	5.44830	−	1.45987i	0.251311	−	0.0673387i
$471$		0			0
$472$	20.4570			0.941609
$473$	−10.1587	+	2.72201i	−0.467097	+	0.125158i
$474$		0			0
$475$	−0.691077	+	2.57914i	−0.0317088	+	0.118339i
$476$	−2.72965	+	4.45576i	−0.125114	+	0.204229i
$477$		0			0
$478$		−	6.65964i		−	0.304605i
$479$	6.58134	−	24.5619i	0.300709	−	1.12226i	−0.635867	−	0.771799i	$-0.719357\pi$
$479$	6.58134	−	24.5619i	0.300709	−	1.12226i	0.936576	−	0.350464i	$-0.113976\pi$
$480$		0			0
$481$	17.7916	−	12.2886i	0.811225	−	0.560310i
$482$			3.99176i			0.181820i
$483$		0			0
$484$	−1.28421	+	2.22432i	−0.0583732	+	0.101105i
$485$	−5.92559	−	3.42114i	−0.269067	−	0.155346i
$486$		0			0
$487$	−13.1080	−	13.1080i	−0.593981	−	0.593981i	0.344723	−	0.938704i	$-0.387973\pi$
$487$	−13.1080	−	13.1080i	−0.593981	−	0.593981i	−0.938704	+	0.344723i	$0.887973\pi$
$488$	7.96964	−	2.13546i	0.360769	−	0.0966677i
$489$		0			0
$490$	2.11871	−	3.26449i	0.0957138	−	0.147475i
$491$	25.0489	+	14.4620i	1.13044	+	0.652661i	0.944046	−	0.329814i	$-0.106986\pi$
$491$	25.0489	+	14.4620i	1.13044	+	0.652661i	0.186396	+	0.982475i	$0.440319\pi$
$492$		0			0
$493$	20.9480	−	36.2830i	0.943452	−	1.63411i
$494$	−1.69454	+	1.99338i	−0.0762409	+	0.0896863i
$495$		0			0
$496$	−7.27127	−	27.1368i	−0.326490	−	1.21848i
$497$	7.43301	−	7.05559i	0.333416	−	0.316487i
$498$		0			0
$499$	−7.48822	+	27.9464i	−0.335219	+	1.25105i	0.568413	+	0.822743i	$0.307557\pi$
$499$	−7.48822	+	27.9464i	−0.335219	+	1.25105i	−0.903632	+	0.428310i	$0.859109\pi$
$500$	0.837977	−	0.837977i	0.0374755	−	0.0374755i
$501$		0			0
$502$	2.45767	−	9.17213i	0.109691	−	0.409372i
$503$	−4.27955	+	2.47080i	−0.190816	+	0.110168i	−0.592364	−	0.805670i	$-0.701805\pi$
$503$	−4.27955	+	2.47080i	−0.190816	+	0.110168i	0.401549	+	0.915838i	$0.368472\pi$
$504$		0			0
$505$	0.781009	+	2.91476i	0.0347544	+	0.129705i
$506$	−12.4757	+	7.20287i	−0.554614	+	0.320207i
$507$		0			0
$508$	0.119477	−	0.206940i	0.00530094	−	0.00918149i
$509$	0.555629	−	0.555629i	0.0246278	−	0.0246278i	−0.694686	−	0.719313i	$-0.744457\pi$
$509$	0.555629	−	0.555629i	0.0246278	−	0.0246278i	0.719313	+	0.694686i	$0.244457\pi$
$510$		0			0
$511$	29.0777	+	8.60887i	1.28632	+	0.380834i
$512$	−17.9577	−	17.9577i	−0.793626	−	0.793626i
$513$		0			0
$514$	10.6206	+	10.6206i	0.468456	+	0.468456i
$515$	−1.12927	−	4.21449i	−0.0497615	−	0.185713i
$516$		0			0
$517$	7.11361	−	12.3211i	0.312856	−	0.541883i
$518$	17.7219	+	10.8567i	0.778656	+	0.477014i
$519$		0			0
$520$	4.31288	−	1.53852i	0.189132	−	0.0674685i
$521$	19.1469	+	11.0545i	0.838840	+	0.484304i	0.856870	−	0.515533i	$-0.172406\pi$
$521$	19.1469	+	11.0545i	0.838840	+	0.484304i	−0.0180299	+	0.999837i	$0.505739\pi$
$522$		0			0
$523$		−	28.2350i		−	1.23463i	−0.786716	−	0.617316i	$-0.788220\pi$
$523$		−	28.2350i		−	1.23463i	0.786716	−	0.617316i	$-0.211780\pi$
$524$	−2.57133	−	4.45368i	−0.112329	−	0.194560i
$525$		0			0
$526$	5.62342	−	20.9869i	0.245193	−	0.915072i
$527$	−15.0750	−	56.2607i	−0.656678	−	2.45076i
$528$		0			0
$529$	−38.5081			−1.67427
$530$	4.20155			0.182504
$531$		0			0
$532$	0.399589	+	0.118304i	0.0173244	+	0.00512913i
$533$	−0.489235	−	6.03755i	−0.0211911	−	0.261516i
$534$		0			0
$535$	1.84262	+	0.493729i	0.0796636	+	0.0213458i
$536$	−21.3964	−	37.0597i	−0.924186	−	1.60074i
$537$		0			0
$538$	−8.70512	+	8.70512i	−0.375305	+	0.375305i
$539$	−2.04356	−	9.60127i	−0.0880224	−	0.413556i
$540$		0			0
$541$	1.19554	+	0.320344i	0.0514003	+	0.0137727i	0.284428	−	0.958698i	$-0.408196\pi$
$541$	1.19554	+	0.320344i	0.0514003	+	0.0137727i	−0.233027	+	0.972470i	$0.574863\pi$
$542$			30.9305i			1.32858i
$543$		0			0
$544$	−7.83710	−	7.83710i	−0.336013	−	0.336013i
$545$	1.92694			0.0825412
$546$		0			0
$547$	1.83004			0.0782468			0.0391234	−	0.999234i	$-0.487543\pi$
$547$	1.83004			0.0782468			0.0391234	+	0.999234i	$0.487543\pi$
$548$	−2.92177	−	2.92177i	−0.124812	−	0.124812i
$549$		0			0
$550$			8.85324i			0.377503i
$551$	−3.22742	−	0.864786i	−0.137493	−	0.0368411i
$552$		0			0
$553$	0.596218	−	22.8884i	0.0253538	−	0.973312i
$554$	7.25216	−	7.25216i	0.308115	−	0.308115i
$555$		0			0
$556$	1.66591	+	2.88544i	0.0706503	+	0.122370i
$557$	12.7054	+	3.40440i	0.538345	+	0.144249i	0.517739	−	0.855539i	$-0.326774\pi$
$557$	12.7054	+	3.40440i	0.538345	+	0.144249i	0.0206059	+	0.999788i	$0.493440\pi$
$558$		0			0
$559$	−25.4685	+	9.08529i	−1.07720	+	0.384267i
$560$	2.59040	+	2.72896i	0.109464	+	0.115320i
$561$		0			0
$562$	−14.0868			−0.594217
$563$	−10.6635			−0.449413			−0.224706	−	0.974427i	$-0.572142\pi$
$563$	−10.6635			−0.449413			−0.224706	+	0.974427i	$0.572142\pi$
$564$		0			0
$565$	−0.750480	−	2.80083i	−0.0315729	−	0.117832i
$566$	4.43831	−	16.5640i	0.186556	−	0.696237i
$567$		0			0
$568$	5.79502	+	10.0373i	0.243154	+	0.421154i
$569$			33.3642i			1.39870i	0.714780	+	0.699349i	$0.246527\pi$
$569$			33.3642i			1.39870i	−0.714780	+	0.699349i	$0.753473\pi$
$570$		0			0
$571$	15.3066	+	8.83728i	0.640562	+	0.369829i	0.784831	−	0.619710i	$-0.212750\pi$
$571$	15.3066	+	8.83728i	0.640562	+	0.369829i	−0.144269	+	0.989539i	$0.546083\pi$
$572$	0.615893	−	1.29898i	0.0257518	−	0.0543130i
$573$		0			0
$574$	5.11615	−	2.77875i	0.213544	−	0.115983i
$575$	−18.9003	+	32.7363i	−0.788197	+	1.36520i
$576$		0			0
$577$	0.423680	+	1.58119i	0.0176380	+	0.0658260i	0.974184	−	0.225756i	$-0.0724851\pi$
$577$	0.423680	+	1.58119i	0.0176380	+	0.0658260i	−0.956546	+	0.291582i	$0.905818\pi$
$578$	28.9457	+	28.9457i	1.20398	+	1.20398i
$579$		0			0
$580$	0.514686	+	0.514686i	0.0213712	+	0.0213712i
$581$	−8.23532	+	1.97832i	−0.341659	+	0.0820744i
$582$		0			0
$583$	7.49372	−	7.49372i	0.310358	−	0.310358i
$584$	−17.1475	+	29.7004i	−0.709569	+	1.22901i
$585$		0			0
$586$	−7.17912	+	4.14487i	−0.296567	+	0.171223i
$587$	−0.520017	−	1.94073i	−0.0214634	−	0.0801025i	0.954363	−	0.298648i	$-0.0965355\pi$
$587$	−0.520017	−	1.94073i	−0.0214634	−	0.0801025i	−0.975827	+	0.218545i	$0.929869\pi$
$588$		0			0
$589$	−4.02283	+	2.32258i	−0.165758	+	0.0957003i
$590$	0.983810	−	3.67163i	0.0405028	−	0.151159i
$591$		0			0
$592$	−14.2082	+	14.2082i	−0.583952	+	0.583952i
$593$	−11.7799	+	43.9632i	−0.483743	+	1.80535i	0.101912	+	0.994793i	$0.467504\pi$
$593$	−11.7799	+	43.9632i	−0.483743	+	1.80535i	−0.585655	+	0.810561i	$0.699163\pi$
$594$		0			0
$595$	5.37049	+	5.65776i	0.220168	+	0.231946i
$596$	0.464468	+	1.73342i	0.0190254	+	0.0710037i
$597$		0			0
$598$	−30.4759	+	21.0496i	−1.24625	+	0.860781i
$599$	−19.7690	+	34.2408i	−0.807738	+	1.39904i	0.106689	+	0.994292i	$0.465975\pi$
$599$	−19.7690	+	34.2408i	−0.807738	+	1.39904i	−0.914427	+	0.404751i	$0.867358\pi$
$600$		0			0
$601$	−0.950504	−	0.548773i	−0.0387718	−	0.0223849i	0.480489	−	0.877001i	$-0.340459\pi$
$601$	−0.950504	−	0.548773i	−0.0387718	−	0.0223849i	−0.519261	+	0.854616i	$0.673793\pi$
$602$	−17.8930	−	18.8502i	−0.729266	−	0.768275i
$603$		0			0
$604$	1.55672	−	0.417123i	0.0633422	−	0.0169725i
$605$	2.71125	+	2.71125i	0.110228	+	0.110228i
$606$		0			0
$607$	13.5220	+	7.80692i	0.548840	+	0.316873i	0.748654	−	0.662961i	$-0.230700\pi$
$607$	13.5220	+	7.80692i	0.548840	+	0.316873i	−0.199814	+	0.979834i	$0.564034\pi$
$608$	−0.441957	+	0.765492i	−0.0179237	+	0.0310448i
$609$		0			0
$610$		−	1.53309i		−	0.0620731i
$611$	15.6715	−	33.0527i	0.634000	−	1.33717i
$612$		0			0
$613$	6.90744	−	25.7789i	0.278989	−	1.04120i	−0.674132	−	0.738611i	$-0.735482\pi$
$613$	6.90744	−	25.7789i	0.278989	−	1.04120i	0.953121	−	0.302590i	$-0.0978513\pi$
$614$		−	1.72439i		−	0.0695908i
$615$		0			0
$616$	11.0976	+	0.289081i	0.447135	+	0.0116474i
$617$	2.13161	−	7.95529i	0.0858155	−	0.320268i	−0.909652	−	0.415372i	$-0.863652\pi$
$617$	2.13161	−	7.95529i	0.0858155	−	0.320268i	0.995467	+	0.0951036i	$0.0303182\pi$
$618$		0			0
$619$	21.9027	−	5.86882i	0.880346	−	0.235888i	0.209789	−	0.977747i	$-0.432722\pi$
$619$	21.9027	−	5.86882i	0.880346	−	0.235888i	0.670556	+	0.741859i	$0.266055\pi$
$620$	1.01192			0.0406396
$621$		0			0
$622$	38.6221	−	10.3488i	1.54861	−	0.414948i
$623$	−7.16031	−	29.8069i	−0.286872	−	1.19419i
$624$		0			0
$625$	11.1650	+	19.3384i	0.446601	+	0.773535i
$626$	−23.2471	−	6.22903i	−0.929139	−	0.248962i
$627$		0			0
$628$	−0.665023	+	1.15185i	−0.0265373	+	0.0459639i
$629$	−29.4568	+	29.4568i	−1.17452	+	1.17452i
$630$		0			0
$631$	17.2097	+	4.61132i	0.685106	+	0.183574i	0.584550	−	0.811358i	$-0.301271\pi$
$631$	17.2097	+	4.61132i	0.685106	+	0.183574i	0.100556	+	0.994931i	$0.467938\pi$
$632$	25.0111	+	6.70169i	0.994886	+	0.266579i
$633$		0			0
$634$	17.5395	−	10.1264i	0.696581	−	0.402171i
$635$	−0.252243	−	0.252243i	−0.0100099	−	0.0100099i
$636$		0			0
$637$	−7.23086	−	24.1809i	−0.286497	−	0.958081i
$638$	−11.0786			−0.438605
$639$		0			0
$640$	−3.05966	+	1.76650i	−0.120944	+	0.0698269i
$641$		−	23.0810i		−	0.911645i	−0.890071	−	0.455822i	$-0.849345\pi$
$641$		−	23.0810i		−	0.911645i	0.890071	−	0.455822i	$-0.150655\pi$
$642$		0			0
$643$	−39.1565	−	10.4920i	−1.54418	−	0.413763i	−0.616569	−	0.787301i	$-0.711478\pi$
$643$	−39.1565	−	10.4920i	−1.54418	−	0.413763i	−0.927615	+	0.373538i	$0.878144\pi$
$644$	5.03071	+	3.08188i	0.198238	+	0.121443i
$645$		0			0
$646$	2.52025	−	4.36521i	0.0991581	−	0.171747i
$647$	−16.1610	−	27.9916i	−0.635353	−	1.10046i	−0.986440	−	0.164121i	$-0.947521\pi$
$647$	−16.1610	−	27.9916i	−0.635353	−	1.10046i	0.351087	−	0.936343i	$-0.385812\pi$
$648$		0			0
$649$	−4.79389	−	8.30326i	−0.188177	−	0.325932i
$650$	1.83847	+	22.6882i	0.0721109	+	0.889906i
$651$		0			0
$652$	−3.30639	+	0.885946i	−0.129488	+	0.0346963i
$653$	−36.5732			−1.43122			−0.715610	−	0.698500i	$-0.753851\pi$
$653$	−36.5732			−1.43122			−0.715610	+	0.698500i	$0.753851\pi$
$654$		0			0
$655$	−7.41569	+	1.98703i	−0.289755	+	0.0776396i
$656$	1.45686	+	5.43708i	0.0568809	+	0.212282i
$657$		0			0
$658$	35.1470	+	0.915542i	1.37017	+	0.0356916i
$659$	21.1206	+	36.5820i	0.822742	+	1.42503i	0.903633	+	0.428308i	$0.140890\pi$
$659$	21.1206	+	36.5820i	0.822742	+	1.42503i	−0.0808906	+	0.996723i	$0.525776\pi$
$660$		0			0
$661$	−1.49909	+	5.59468i	−0.0583078	+	0.217608i	−0.988932	−	0.148368i	$-0.952598\pi$
$661$	−1.49909	+	5.59468i	−0.0583078	+	0.217608i	0.930624	+	0.365976i	$0.119265\pi$
$662$	30.2798	+	17.4821i	1.17686	+	0.679459i
$663$		0			0
$664$		−	9.57832i		−	0.371711i
$665$	0.324987	−	0.530494i	0.0126025	−	0.0205717i
$666$		0			0
$667$	−40.9648	−	23.6511i	−1.58617	−	0.915773i
$668$	0.165255	+	0.616740i	0.00639391	+	0.0238624i
$669$		0			0
$670$	−7.68049	+	2.05798i	−0.296723	+	0.0795067i
$671$	−2.73436	−	2.73436i	−0.105559	−	0.105559i
$672$		0			0
$673$	−36.4698	−	21.0558i	−1.40581	−	0.811642i	−0.410826	−	0.911714i	$-0.634760\pi$
$673$	−36.4698	−	21.0558i	−1.40581	−	0.811642i	−0.994980	+	0.100071i	$0.968093\pi$
$674$	−23.5071	+	23.5071i	−0.905459	+	0.905459i
$675$		0			0
$676$	1.30860	−	3.45680i	0.0503309	−	0.132954i
$677$	−0.771810	+	0.445605i	−0.0296631	+	0.0171260i	−0.514758	−	0.857335i	$-0.672118\pi$
$677$	−0.771810	+	0.445605i	−0.0296631	+	0.0171260i	0.485095	+	0.874461i	$0.338785\pi$
$678$		0			0
$679$	−29.3626	−	30.9332i	−1.12683	−	1.18711i
$680$	−7.64004	+	4.41098i	−0.292982	+	0.169153i
$681$		0			0
$682$	−10.8907	+	10.8907i	−0.417028	+	0.417028i
$683$	−9.01592	+	9.01592i	−0.344985	+	0.344985i	−0.858238	−	0.513253i	$-0.828440\pi$
$683$	−9.01592	+	9.01592i	−0.344985	+	0.344985i	0.513253	+	0.858238i	$0.328440\pi$
$684$		0			0
$685$	−5.34208	+	3.08425i	−0.204110	+	0.117843i
$686$	18.4399	−	15.7622i	0.704038	−	0.601805i
$687$		0			0
$688$	21.7613	−	12.5639i	0.829641	−	0.478994i
$689$	17.6480	−	20.7603i	0.672337	−	0.790906i
$690$		0			0
$691$	18.7650	−	18.7650i	0.713855	−	0.713855i	−0.253484	−	0.967340i	$-0.581577\pi$
$691$	18.7650	−	18.7650i	0.713855	−	0.713855i	0.967340	+	0.253484i	$0.0815766\pi$
$692$	2.86655	+	1.65500i	0.108970	+	0.0629138i
$693$		0			0
$694$	2.16140	+	2.16140i	0.0820457	+	0.0820457i
$695$	4.80446	−	1.28735i	0.182244	−	0.0488320i
$696$		0			0
$697$	3.02041	+	11.2723i	0.114406	+	0.426969i
$698$	−33.6448	−	19.4248i	−1.27347	−	0.735241i
$699$		0			0
$700$	3.18610	−	1.73048i	0.120423	−	0.0654059i
$701$		−	0.589627i		−	0.0222699i	−0.999938	−	0.0111350i	$-0.996456\pi$
$701$		−	0.589627i		−	0.0222699i	0.999938	−	0.0111350i	$-0.00354444\pi$
$702$		0			0
$703$	2.87720	+	1.66115i	0.108516	+	0.0626515i
$704$	−3.19068	+	11.9078i	−0.120253	+	0.448792i
$705$		0			0
$706$	−2.86078	−	4.95502i	−0.107667	−	0.186485i
$707$	−0.489802	+	18.8031i	−0.0184209	+	0.707165i
$708$		0			0
$709$	0.917349	+	3.42359i	0.0344518	+	0.128576i	0.981010	−	0.193957i	$-0.0621323\pi$
$709$	0.917349	+	3.42359i	0.0344518	+	0.128576i	−0.946558	+	0.322533i	$0.895466\pi$
$710$	2.08019	−	0.557384i	0.0780680	−	0.0209183i
$711$		0			0
$712$	34.6677			1.29923
$713$	−63.5203	+	17.0202i	−2.37886	+	0.637412i
$714$		0			0
$715$	−1.63515	−	1.39001i	−0.0611510	−	0.0519835i
$716$	−2.68754	−	4.65495i	−0.100438	−	0.173964i
$717$		0			0
$718$	14.0382	+	24.3149i	0.523902	+	0.907425i
$719$	−3.90389	+	6.76173i	−0.145590	+	0.252170i	−0.929593	−	0.368587i	$-0.879842\pi$
$719$	−3.90389	+	6.76173i	−0.145590	+	0.252170i	0.784003	+	0.620757i	$0.213175\pi$
$720$		0			0
$721$	0.708210	−	27.1877i	0.0263751	−	1.01252i
$722$	23.6506	+	6.33717i	0.880186	+	0.235845i
$723$		0			0
$724$		−	0.113913i		−	0.00423355i
$725$	−25.1755	+	14.5351i	−0.934993	+	0.539819i
$726$		0			0
$727$	−7.63181			−0.283048			−0.141524	−	0.989935i	$-0.545200\pi$
$727$	−7.63181			−0.283048			−0.141524	+	0.989935i	$0.545200\pi$
$728$	28.4999	−	1.56371i	1.05628	−	0.0579550i
$729$		0			0
$730$	4.50598	+	4.50598i	0.166774	+	0.166774i
$731$	45.1161	−	26.0478i	1.66868	−	0.963413i
$732$		0			0
$733$	−12.0644	−	3.23266i	−0.445610	−	0.119401i	0.0290344	−	0.999578i	$-0.490757\pi$
$733$	−12.0644	−	3.23266i	−0.445610	−	0.119401i	−0.474645	+	0.880178i	$0.657423\pi$
$734$	15.9470	+	4.27299i	0.588615	+	0.157719i
$735$		0			0
$736$	−8.84837	+	8.84837i	−0.326155	+	0.326155i
$737$	−10.0281	+	17.3692i	−0.369389	+	0.639801i
$738$		0			0
$739$	−18.0770	−	4.84371i	−0.664972	−	0.178179i	−0.0894831	−	0.995988i	$-0.528522\pi$
$739$	−18.0770	−	4.84371i	−0.664972	−	0.178179i	−0.575489	+	0.817810i	$0.695188\pi$
$740$	−0.361871	−	0.626780i	−0.0133027	−	0.0230409i
$741$		0			0
$742$	25.1120	+	7.43478i	0.921892	+	0.272939i
$743$	−15.7645	+	4.22409i	−0.578343	+	0.154967i	−0.536120	−	0.844142i	$-0.680111\pi$
$743$	−15.7645	+	4.22409i	−0.578343	+	0.154967i	−0.0422231	+	0.999108i	$0.513444\pi$
$744$		0			0
$745$	2.67904			0.0981524
$746$	20.1794	−	5.40706i	0.738822	−	0.197967i
$747$		0			0
$748$	−0.716834	+	2.67526i	−0.0262100	+	0.0978172i
$749$	10.1394	+	6.21154i	0.370486	+	0.226965i
$750$		0			0
$751$		−	1.91061i		−	0.0697190i	−0.999392	−	0.0348595i	$-0.988902\pi$
$751$		−	1.91061i		−	0.0697190i	0.999392	−	0.0348595i	$-0.0110984\pi$
$752$	−8.79784	+	32.8340i	−0.320824	+	1.19733i
$753$		0			0
$754$	−28.3911	+	2.30059i	−1.03394	+	0.0837826i
$755$		−	2.40595i		−	0.0875616i
$756$		0			0
$757$	−25.6580	+	44.4410i	−0.932556	+	1.61523i	−0.153622	+	0.988130i	$0.549094\pi$
$757$	−25.6580	+	44.4410i	−0.932556	+	1.61523i	−0.778935	+	0.627105i	$0.784240\pi$
$758$	−38.8306	−	22.4189i	−1.41039	−	0.814289i
$759$		0			0
$760$	0.497496	+	0.497496i	0.0180461	+	0.0180461i
$761$	24.1952	−	6.48309i	0.877076	−	0.235012i	0.207931	−	0.978143i	$-0.433327\pi$
$761$	24.1952	−	6.48309i	0.877076	−	0.235012i	0.669145	+	0.743132i	$0.266660\pi$
$762$		0			0
$763$	11.5171	+	3.40980i	0.416946	+	0.123443i
$764$	2.52441	+	1.45747i	0.0913301	+	0.0527295i
$765$		0			0
$766$	−8.54586	+	14.8019i	−0.308774	+	0.534813i
$767$	−14.0096	−	20.2833i	−0.505857	−	0.732388i
$768$		0			0
$769$	10.9969	+	41.0409i	0.396558	+	1.47997i	0.819111	+	0.573635i	$0.194467\pi$
$769$	10.9969	+	41.0409i	0.396558	+	1.47997i	−0.422553	+	0.906338i	$0.638866\pi$
$770$	0.585586	−	1.97790i	0.0211031	−	0.0712785i
$771$		0			0
$772$	−0.659552	+	2.46148i	−0.0237378	+	0.0885906i
$773$	−18.6449	+	18.6449i	−0.670609	+	0.670609i	−0.957856	−	0.287248i	$-0.907260\pi$
$773$	−18.6449	+	18.6449i	−0.670609	+	0.670609i	0.287248	+	0.957856i	$0.407260\pi$
$774$		0			0
$775$	−10.4600	+	39.0372i	−0.375734	+	1.40226i
$776$	41.7711	−	24.1166i	1.49950	−	0.865734i
$777$		0			0
$778$	5.80341	+	21.6586i	0.208062	+	0.776500i
$779$	0.806008	−	0.465349i	0.0288782	−	0.0166728i
$780$		0			0
$781$	2.71601	−	4.70427i	0.0971865	−	0.168332i
$782$	50.4577	−	50.4577i	1.80437	−	1.80437i
$783$		0			0
$784$	10.6534	+	20.8944i	0.380480	+	0.746228i
$785$	1.40401	+	1.40401i	0.0501113	+	0.0501113i
$786$		0			0
$787$	−37.4963	−	37.4963i	−1.33660	−	1.33660i	−0.899330	−	0.437270i	$-0.855945\pi$
$787$	−37.4963	−	37.4963i	−1.33660	−	1.33660i	−0.437270	−	0.899330i	$-0.644055\pi$
$788$	−0.308002	−	1.14948i	−0.0109721	−	0.0409485i
$789$		0			0
$790$	2.40565	−	4.16670i	0.0855891	−	0.148245i
$791$	0.470656	−	18.0681i	0.0167346	−	0.642429i
$792$		0			0
$793$	−7.57519	−	6.43955i	−0.269003	−	0.228675i
$794$	−10.9966	−	6.34890i	−0.390256	−	0.225314i
$795$		0			0
$796$		−	0.0207987i		−	0.000737189i
$797$	−23.6844	−	41.0227i	−0.838946	−	1.45310i	−0.890777	−	0.454441i	$-0.849839\pi$
$797$	−23.6844	−	41.0227i	−0.838946	−	1.45310i	0.0518307	−	0.998656i	$-0.483494\pi$
$798$		0			0
$799$	−18.2399	+	68.0724i	−0.645283	+	2.40823i
$800$	1.99040	+	7.42828i	0.0703713	+	0.262629i
$801$		0			0
$802$	10.0821			0.356013
$803$	16.0734			0.567218
$804$		0			0
$805$	6.38781	−	6.06347i	0.225141	−	0.213709i
$806$	−25.6482	+	30.1713i	−0.903418	+	1.06274i
$807$		0			0
$808$	−20.5470	−	5.50554i	−0.722840	−	0.193684i
$809$	5.86227	+	10.1538i	0.206107	+	0.356987i	0.950485	−	0.310771i	$-0.100587\pi$
$809$	5.86227	+	10.1538i	0.206107	+	0.356987i	−0.744378	+	0.667758i	$0.767254\pi$
$810$		0			0
$811$	−9.09842	+	9.09842i	−0.319489	+	0.319489i	−0.848571	−	0.529082i	$-0.822536\pi$
$811$	−9.09842	+	9.09842i	−0.319489	+	0.319489i	0.529082	+	0.848571i	$0.322536\pi$
$812$	2.16545	+	3.98696i	0.0759923	+	0.139915i
$813$		0			0
$814$	10.6403	+	2.85107i	0.372943	+	0.0999298i
$815$			5.11011i			0.178999i
$816$		0			0
$817$	−2.93782	−	2.93782i	−0.102781	−	0.102781i
$818$	−4.04419			−0.141402
$819$		0			0
$820$	−0.202747			−0.00708022
$821$	34.0250	+	34.0250i	1.18748	+	1.18748i	0.977762	+	0.209718i	$0.0672546\pi$
$821$	34.0250	+	34.0250i	1.18748	+	1.18748i	0.209718	+	0.977762i	$0.432745\pi$
$822$		0			0
$823$			16.4408i			0.573091i	0.958067	+	0.286545i	$0.0925069\pi$
$823$			16.4408i			0.573091i	−0.958067	+	0.286545i	$0.907493\pi$
$824$	29.7091	+	7.96052i	1.03496	+	0.277318i
$825$		0			0
$826$	12.3772	−	20.2039i	0.430657	−	0.702984i
$827$	−17.6849	+	17.6849i	−0.614966	+	0.614966i	−0.944236	−	0.329270i	$-0.893197\pi$
$827$	−17.6849	+	17.6849i	−0.614966	+	0.614966i	0.329270	+	0.944236i	$0.393197\pi$
$828$		0			0
$829$	17.4550	+	30.2330i	0.606239	+	1.05004i	0.991854	+	0.127377i	$0.0406558\pi$
$829$	17.4550	+	30.2330i	0.606239	+	1.05004i	−0.385616	+	0.922660i	$0.626011\pi$
$830$	−1.71912	−	0.460637i	−0.0596716	−	0.0159890i
$831$		0			0
$832$	−5.70400	+	31.1788i	−0.197750	+	1.08093i
$833$	22.0870	+	43.3189i	0.765269	+	1.50091i
$834$		0			0
$835$	0.953186			0.0329864
$836$	0.220883			0.00763939
$837$		0			0
$838$	0.897988	+	3.35134i	0.0310205	+	0.115770i
$839$	11.7730	−	43.9373i	0.406448	−	1.51689i	−0.394921	−	0.918715i	$-0.629228\pi$
$839$	11.7730	−	43.9373i	0.406448	−	1.51689i	0.801369	−	0.598170i	$-0.204105\pi$
$840$		0			0
$841$	−3.68858	−	6.38881i	−0.127192	−	0.220304i
$842$			16.6061i			0.572283i
$843$		0			0
$844$	−5.10860	−	2.94945i	−0.175845	−	0.101524i
$845$	−4.47905	−	3.22264i	−0.154084	−	0.110862i
$846$		0			0
$847$	11.4071	+	21.0024i	0.391953	+	0.721651i
$848$	−12.6602	+	21.9282i	−0.434754	+	0.753017i
$849$		0			0
$850$	−11.3502	−	42.3597i	−0.389310	−	1.45293i
$851$	33.2577	+	33.2577i	1.14006	+	1.14006i
$852$		0			0
$853$	21.3746	+	21.3746i	0.731852	+	0.731852i	0.970987	−	0.239134i	$-0.0768636\pi$
$853$	21.3746	+	21.3746i	0.731852	+	0.731852i	−0.239134	+	0.970987i	$0.576864\pi$
$854$	2.71286	−	9.16307i	0.0928322	−	0.313554i
$855$		0			0
$856$	−9.50872	+	9.50872i	−0.325001	+	0.325001i
$857$	−25.9528	+	44.9515i	−0.886530	+	1.53552i	−0.0425805	+	0.999093i	$0.513558\pi$
$857$	−25.9528	+	44.9515i	−0.886530	+	1.53552i	−0.843950	+	0.536422i	$0.819775\pi$
$858$		0			0
$859$	−38.6675	+	22.3247i	−1.31932	+	0.761708i	−0.983619	−	0.180261i	$-0.942306\pi$
$859$	−38.6675	+	22.3247i	−1.31932	+	0.761708i	−0.335699	+	0.941969i	$0.608972\pi$
$860$	0.234251	+	0.874237i	0.00798789	+	0.0298112i
$861$		0			0
$862$	13.1585	−	7.59707i	0.448181	−	0.258757i
$863$	−9.68381	+	36.1405i	−0.329641	+	1.23024i	0.579923	+	0.814671i	$0.303083\pi$
$863$	−9.68381	+	36.1405i	−0.329641	+	1.23024i	−0.909564	+	0.415565i	$0.863584\pi$
$864$		0			0
$865$	3.49408	−	3.49408i	0.118802	−	0.118802i
$866$	0.735671	−	2.74556i	0.0249991	−	0.0932980i
$867$		0			0
$868$	6.04809	+	1.79063i	0.205286	+	0.0607778i
$869$	−3.14095	−	11.7222i	−0.106549	−	0.397648i
$870$		0			0
$871$	−22.0921	+	46.5945i	−0.748564	+	1.57879i
$872$	−6.79178	+	11.7637i	−0.229999	+	0.398369i
$873$		0			0
$874$	−4.92848	−	2.84546i	−0.166708	−	0.0962490i
$875$	−2.57583	−	10.7226i	−0.0870789	−	0.362491i
$876$		0			0
$877$	−30.5935	+	8.19750i	−1.03307	+	0.276810i	−0.735238	−	0.677809i	$-0.762930\pi$
$877$	−30.5935	+	8.19750i	−1.03307	+	0.276810i	−0.297830	+	0.954619i	$0.596263\pi$
$878$	19.2057	+	19.2057i	0.648161	+	0.648161i
$879$		0			0
$880$	1.72713	+	0.997159i	0.0582215	+	0.0336142i
$881$	19.0003	−	32.9095i	0.640138	−	1.10875i	−0.345264	−	0.938506i	$-0.612211\pi$
$881$	19.0003	−	32.9095i	0.640138	−	1.10875i	0.985402	−	0.170245i	$-0.0544560\pi$
$882$		0			0
$883$		−	17.8135i		−	0.599473i	−0.954022	−	0.299736i	$-0.903101\pi$
$883$		−	17.8135i		−	0.599473i	0.954022	−	0.299736i	$-0.0968987\pi$
$884$	−1.28149	+	7.00477i	−0.0431011	+	0.235596i
$885$		0			0
$886$	−6.35155	+	23.7043i	−0.213384	+	0.796361i
$887$		−	52.8690i		−	1.77517i	−0.460648	−	0.887583i	$-0.652383\pi$
$887$		−	52.8690i		−	1.77517i	0.460648	−	0.887583i	$-0.347617\pi$
$888$		0			0
$889$	−1.06127	−	1.95397i	−0.0355937	−	0.0655340i
$890$	1.66723	−	6.22218i	0.0558856	−	0.208568i
$891$		0			0
$892$	−0.0301006	+	0.00806543i	−0.00100784	+	0.000270051i
$893$	5.62039			0.188079
$894$		0			0
$895$	−7.75081	+	2.07682i	−0.259081	+	0.0694206i
$896$	−21.4130	+	5.14391i	−0.715359	+	0.171846i
$897$		0			0
$898$	−9.63260	−	16.6841i	−0.321444	−	0.556757i
$899$	−48.8496	−	13.0892i	−1.62923	−	0.436550i
$900$		0			0
$901$	−26.2476	+	45.4621i	−0.874434	+	1.51456i
$902$	2.18205	−	2.18205i	0.0726544	−	0.0726544i
$903$		0			0
$904$	19.7438	+	5.29034i	0.656669	+	0.175954i
$905$	−0.164262	−	0.0440139i	−0.00546025	−	0.00146307i
$906$		0			0
$907$	33.3744	−	19.2687i	1.10818	−	0.639808i	0.169823	−	0.985475i	$-0.445680\pi$
$907$	33.3744	−	19.2687i	1.10818	−	0.639808i	0.938357	+	0.345666i	$0.112347\pi$
$908$	0.633640	+	0.633640i	0.0210281	+	0.0210281i
$909$		0			0
$910$	1.08995	−	5.19038i	0.0361315	−	0.172059i
$911$	11.2153			0.371581			0.185790	−	0.982589i	$-0.440515\pi$
$911$	11.2153			0.371581			0.185790	+	0.982589i	$0.440515\pi$
$912$		0			0
$913$	−3.88773	+	2.24458i	−0.128665	+	0.0742849i
$914$			31.8410i			1.05321i
$915$		0			0
$916$	−4.40255	−	1.17966i	−0.145464	−	0.0389770i
$917$	−47.8386	−	1.24615i	−1.57977	−	0.0411513i
$918$		0			0
$919$	23.0555	−	39.9334i	0.760532	−	1.31728i	−0.182045	−	0.983290i	$-0.558272\pi$
$919$	23.0555	−	39.9334i	0.760532	−	1.31728i	0.942577	−	0.333990i	$-0.108395\pi$
$920$	4.98015	+	8.62588i	0.164191	+	0.284387i
$921$		0			0
$922$	2.51991	+	4.36461i	0.0829888	+	0.143741i
$923$	5.98344	−	12.6197i	0.196947	−	0.415381i
$924$		0			0
$925$	27.9202	−	7.48118i	0.918009	−	0.245980i
$926$	−9.25506			−0.304140
$927$		0			0
$928$	−9.29544	+	2.49071i	−0.305138	+	0.0817614i
$929$	−0.331311	−	1.23647i	−0.0108700	−	0.0405673i	0.960278	−	0.279046i	$-0.0900181\pi$
$929$	−0.331311	−	1.23647i	−0.0108700	−	0.0405673i	−0.971148	+	0.238478i	$0.923351\pi$
$930$		0			0
$931$	2.88113	−	2.59561i	0.0944251	−	0.0850676i
$932$	−3.58774	−	6.21415i	−0.117520	−	0.203551i
$933$		0			0
$934$	2.92987	−	10.9344i	0.0958682	−	0.357785i
$935$	3.58073	+	2.06734i	0.117103	+	0.0676092i
$936$		0			0
$937$		−	33.7512i		−	1.10261i	−0.834305	−	0.551303i	$-0.814131\pi$
$937$		−	33.7512i		−	1.10261i	0.834305	−	0.551303i	$-0.185869\pi$
$938$	−49.5468	−	1.29064i	−1.61776	−	0.0421410i
$939$		0			0
$940$	−1.06033	−	0.612183i	−0.0345842	−	0.0199672i
$941$	9.79130	+	36.5416i	0.319187	+	1.19122i	0.920027	+	0.391854i	$0.128166\pi$
$941$	9.79130	+	36.5416i	0.319187	+	1.19122i	−0.600840	+	0.799369i	$0.705167\pi$
$942$		0			0
$943$	12.7268	−	3.41015i	0.414443	−	0.111050i
$944$	16.1981	+	16.1981i	0.527202	+	0.527202i
$945$		0			0
$946$	−11.9301	−	6.88782i	−0.387880	−	0.223942i
$947$	8.67668	−	8.67668i	0.281954	−	0.281954i	−0.551934	−	0.833888i	$-0.686110\pi$
$947$	8.67668	−	8.67668i	0.281954	−	0.281954i	0.833888	+	0.551934i	$0.186110\pi$
$948$		0			0
$949$	41.1914	−	3.33782i	1.33713	−	0.108350i
$950$	−3.02886	+	1.74871i	−0.0982691	+	0.0567357i
$951$		0			0
$952$	−53.4688	+	12.8445i	−1.73293	+	0.416291i
$953$	22.7640	−	13.1428i	0.737399	−	0.425738i	−0.0837238	−	0.996489i	$-0.526681\pi$
$953$	22.7640	−	13.1428i	0.737399	−	0.425738i	0.821123	+	0.570751i	$0.193348\pi$
$954$		0			0
$955$	3.07705	−	3.07705i	0.0995709	−	0.0995709i
$956$	−1.02219	+	1.02219i	−0.0330599	+	0.0330599i
$957$		0			0
$958$	28.8448	−	16.6535i	0.931932	−	0.538051i
$959$	−37.3865	+	8.98112i	−1.20727	+	0.290015i
$960$		0			0
$961$	−34.0418	+	19.6541i	−1.09812	+	0.634002i
$962$	27.8601	+	5.09686i	0.898245	+	0.164329i
$963$		0			0
$964$	0.612693	−	0.612693i	0.0197335	−	0.0197335i
$965$	3.29460	+	1.90214i	0.106057	+	0.0612319i
$966$		0			0
$967$	18.8266	+	18.8266i	0.605423	+	0.605423i	0.941747	−	0.336323i	$-0.109184\pi$
$967$	18.8266	+	18.8266i	0.605423	+	0.605423i	−0.336323	+	0.941747i	$0.609184\pi$
$968$	−26.1080	+	6.99561i	−0.839142	+	0.224847i
$969$		0			0
$970$	−2.31961	−	8.65690i	−0.0744782	−	0.277956i
$971$	−15.1611	−	8.75326i	−0.486542	−	0.280905i	0.236597	−	0.971608i	$-0.423968\pi$
$971$	−15.1611	−	8.75326i	−0.486542	−	0.280905i	−0.723139	+	0.690703i	$0.757301\pi$
$972$		0			0
$973$	30.9936	+	0.807350i	0.993608	+	0.0258825i
$974$		−	24.2812i		−	0.778019i
$975$		0			0
$976$	8.00132	+	4.61957i	0.256116	+	0.147869i
$977$	−4.51447	+	16.8482i	−0.144431	+	0.539023i	0.855349	+	0.518052i	$0.173343\pi$
$977$	−4.51447	+	16.8482i	−0.144431	+	0.539023i	−0.999780	+	0.0209713i	$0.993324\pi$
$978$		0			0
$979$	−8.12404	−	14.0712i	−0.259645	−	0.449719i
$980$	−0.826266	+	0.175865i	−0.0263941	+	0.00561779i
$981$		0			0
$982$	9.80556	+	36.5949i	0.312908	+	1.16779i
$983$	36.1248	−	9.67960i	1.15220	−	0.308731i	0.368354	−	0.929685i	$-0.379921\pi$
$983$	36.1248	−	9.67960i	1.15220	−	0.308731i	0.783847	+	0.620954i	$0.213255\pi$
$984$		0			0
$985$	−1.77655			−0.0566054
$986$	53.0072	−	14.2032i	1.68809	−	0.452323i
$987$		0			0
$988$	0.566057	−	0.0458688i	0.0180087	−	0.00145928i
$989$	−29.4089	−	50.9377i	−0.935149	−	1.61972i
$990$		0			0
$991$	−7.56709	−	13.1066i	−0.240377	−	0.416344i	0.720445	−	0.693512i	$-0.243938\pi$
$991$	−7.56709	−	13.1066i	−0.240377	−	0.416344i	−0.960822	+	0.277168i	$0.910604\pi$
$992$	−6.68936	+	11.5863i	−0.212387	+	0.367866i
$993$		0			0
$994$	13.4193	+	0.349558i	0.425634	+	0.0110873i
$995$	−0.0299915	−	0.00803620i	−0.000950795	−	0.000254765i
$996$		0			0
$997$		−	43.0361i		−	1.36297i	−0.731834	−	0.681483i	$-0.761335\pi$
$997$		−	43.0361i		−	1.36297i	0.731834	−	0.681483i	$-0.238665\pi$
$998$	−32.8194	+	18.9483i	−1.03888	+	0.599798i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.514.7		36
3.2	odd	2		273.2.bt.a.241.3	yes	36
7.5	odd	6		819.2.gh.c.397.7		36
13.2	odd	12		819.2.gh.c.262.7		36
21.5	even	6		273.2.cg.a.124.3	yes	36
39.2	even	12		273.2.cg.a.262.3	yes	36
91.54	even	12	inner	819.2.et.c.145.7		36
273.236	odd	12		273.2.bt.a.145.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.3	✓	36	273.236	odd	12
273.2.bt.a.241.3	yes	36	3.2	odd	2
273.2.cg.a.124.3	yes	36	21.5	even	6
273.2.cg.a.262.3	yes	36	39.2	even	12
819.2.et.c.145.7		36	91.54	even	12	inner
819.2.et.c.514.7		36	1.1	even	1	trivial
819.2.gh.c.262.7		36	13.2	odd	12
819.2.gh.c.397.7		36	7.5	odd	6

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.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.926196 + 0.926196i) q^{2} -0.284323i q^{4} +(-0.409991 - 0.109857i) q^{5} +(-2.25606 - 1.38209i) q^{7} +(2.11573 - 2.11573i) q^{8} +O(q^{10})\)	\(q+(0.926196 + 0.926196i) q^{2} -0.284323i q^{4} +(-0.409991 - 0.109857i) q^{5} +(-2.25606 - 1.38209i) q^{7} +(2.11573 - 2.11573i) q^{8} +(-0.277983 - 0.481481i) q^{10} +(-1.35455 - 0.362951i) q^{11} +(-3.54669 - 0.648849i) q^{13} +(-0.809468 - 3.36964i) q^{14} +3.35051 q^{16} +6.94638 q^{17} +(-0.143382 - 0.535108i) q^{19} +(-0.0312348 + 0.116570i) q^{20} +(-0.918416 - 1.59074i) q^{22} -7.84271i q^{23} +(-4.17410 - 2.40992i) q^{25} +(-2.68397 - 3.88589i) q^{26} +(-0.392961 + 0.641450i) q^{28} +(3.01567 - 5.22330i) q^{29} +(-2.17020 - 8.09928i) q^{31} +(-1.12823 - 1.12823i) q^{32} +(6.43371 + 6.43371i) q^{34} +(0.773134 + 0.814490i) q^{35} +(-4.24059 + 4.24059i) q^{37} +(0.362815 - 0.628415i) q^{38} +(-1.09986 + 0.635004i) q^{40} +(0.434817 + 1.62276i) q^{41} +(6.49491 - 3.74984i) q^{43} +(-0.103195 + 0.385130i) q^{44} +(7.26389 - 7.26389i) q^{46} +(-2.62582 + 9.79969i) q^{47} +(3.17964 + 6.23618i) q^{49} +(-1.63398 - 6.09809i) q^{50} +(-0.184483 + 1.00840i) q^{52} +(-3.77860 + 6.54472i) q^{53} +(0.515482 + 0.297614i) q^{55} +(-7.69736 + 1.84909i) q^{56} +(7.63090 - 2.04469i) q^{58} +(4.83450 + 4.83450i) q^{59} +(2.38809 + 1.37876i) q^{61} +(5.49149 - 9.51155i) q^{62} -8.79095i q^{64} +(1.38283 + 0.655650i) q^{65} +(3.70163 - 13.8147i) q^{67} -1.97502i q^{68} +(-0.0383037 + 1.47045i) q^{70} +(-1.00255 + 3.74157i) q^{71} +(-11.0713 + 2.96655i) q^{73} -7.85524 q^{74} +(-0.152144 + 0.0407667i) q^{76} +(2.55432 + 2.69096i) q^{77} +(4.32696 + 7.49452i) q^{79} +(-1.37368 - 0.368077i) q^{80} +(-1.10027 + 1.90572i) q^{82} +(2.26360 - 2.26360i) q^{83} +(-2.84796 - 0.763108i) q^{85} +(9.48864 + 2.54247i) q^{86} +(-3.63377 + 2.09796i) q^{88} +(8.19285 + 8.19285i) q^{89} +(7.10478 + 6.36569i) q^{91} -2.22986 q^{92} +(-11.5085 + 6.64441i) q^{94} +0.235141i q^{95} +(15.5709 + 4.17221i) q^{97} +(-2.83095 + 8.72089i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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