LMFDB - Embedded newform 819.2.fm.f.370.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			370.3
Character	$\chi$	$=$	819.370
Dual form			819.2.fm.f.622.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0578232 - 0.215799i) q^{2} +(1.68883 - 0.975044i) q^{4} +(1.08760 + 1.08760i) q^{5} +(-0.643420 + 2.56632i) q^{7} +(-0.624019 - 0.624019i) q^{8} +O(q^{10})$	\(q+(-0.0578232 - 0.215799i) q^{2} +(1.68883 - 0.975044i) q^{4} +(1.08760 + 1.08760i) q^{5} +(-0.643420 + 2.56632i) q^{7} +(-0.624019 - 0.624019i) q^{8} +(0.171815 - 0.297592i) q^{10} +(-4.17464 + 1.11859i) q^{11} +(3.01096 + 1.98346i) q^{13} +(0.591015 - 0.00954346i) q^{14} +(1.85151 - 3.20690i) q^{16} +(3.78401 + 6.55410i) q^{17} +(-1.31714 + 4.91565i) q^{19} +(2.89722 + 0.776309i) q^{20} +(0.482783 + 0.836204i) q^{22} +(1.85976 + 1.07373i) q^{23} -2.63425i q^{25} +(0.253926 - 0.764453i) q^{26} +(1.41565 + 4.96143i) q^{28} +(2.66646 - 4.61844i) q^{29} +(-1.09410 - 1.09410i) q^{31} +(-2.50396 - 0.670934i) q^{32} +(1.19557 - 1.19557i) q^{34} +(-3.49092 + 2.09135i) q^{35} +(-2.82556 + 0.757106i) q^{37} +1.13695 q^{38} -1.35737i q^{40} +(1.37894 - 0.369486i) q^{41} +(-6.58558 + 3.80219i) q^{43} +(-5.95956 + 5.95956i) q^{44} +(0.124173 - 0.463422i) q^{46} +(5.26364 - 5.26364i) q^{47} +(-6.17202 - 3.30245i) q^{49} +(-0.568470 + 0.152321i) q^{50} +(7.01895 + 0.413900i) q^{52} +13.1808 q^{53} +(-5.75692 - 3.32376i) q^{55} +(2.00294 - 1.19993i) q^{56} +(-1.15084 - 0.308366i) q^{58} +(-8.73809 - 2.34136i) q^{59} +(10.1891 - 5.88266i) q^{61} +(-0.172842 + 0.299371i) q^{62} -6.82688i q^{64} +(1.11751 + 5.43193i) q^{65} +(-1.28138 - 4.78216i) q^{67} +(12.7811 + 7.37915i) q^{68} +(0.653167 + 0.632408i) q^{70} +(5.25942 + 1.40926i) q^{71} +(-8.04396 + 8.04396i) q^{73} +(0.326766 + 0.565975i) q^{74} +(2.56854 + 9.58594i) q^{76} +(-0.184619 - 11.4332i) q^{77} +9.06635 q^{79} +(5.50153 - 1.47413i) q^{80} +(-0.159469 - 0.276209i) q^{82} +(1.13072 + 1.13072i) q^{83} +(-3.01275 + 11.2437i) q^{85} +(1.20131 + 1.20131i) q^{86} +(3.30308 + 1.90703i) q^{88} +(-0.217351 - 0.811166i) q^{89} +(-7.02751 + 6.45090i) q^{91} +4.18775 q^{92} +(-1.44025 - 0.831529i) q^{94} +(-6.77878 + 3.91373i) q^{95} +(4.35890 - 16.2676i) q^{97} +(-0.355779 + 1.52288i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.0578232	−	0.215799i	−0.0408872	−	0.152593i	0.942464	−	0.334307i	$-0.108502\pi$
$2$	−0.0578232	−	0.215799i	−0.0408872	−	0.152593i	−0.983351	+	0.181714i	$0.941836\pi$
$3$		0			0
$3$		0			0
$4$	1.68883	−	0.975044i	0.844413	−	0.487522i
$5$	1.08760	+	1.08760i	0.486390	+	0.486390i	0.907165	−	0.420775i	$-0.138242\pi$
$5$	1.08760	+	1.08760i	0.486390	+	0.486390i	−0.420775	+	0.907165i	$0.638242\pi$
$6$		0			0
$7$	−0.643420	+	2.56632i	−0.243190	+	0.969979i
$7$	−0.643420	+	2.56632i	−0.243190	+	0.969979i
$8$	−0.624019	−	0.624019i	−0.220624	−	0.220624i
$9$		0			0
$10$	0.171815	−	0.297592i	0.0543326	−	0.0941068i
$11$	−4.17464	+	1.11859i	−1.25870	+	0.337268i	−0.825692	−	0.564121i	$-0.809215\pi$
$11$	−4.17464	+	1.11859i	−1.25870	+	0.337268i	−0.433010	+	0.901389i	$0.642548\pi$
$12$		0			0
$13$	3.01096	+	1.98346i	0.835090	+	0.550113i
$13$	3.01096	+	1.98346i	0.835090	+	0.550113i
$14$	0.591015	−	0.00954346i	0.157955	−	0.00255060i
$15$		0			0
$16$	1.85151	−	3.20690i	0.462877	−	0.801726i
$17$	3.78401	+	6.55410i	0.917757	+	1.58960i	0.802813	+	0.596231i	$0.203336\pi$
$17$	3.78401	+	6.55410i	0.917757	+	1.58960i	0.114944	+	0.993372i	$0.463331\pi$
$18$		0			0
$19$	−1.31714	+	4.91565i	−0.302173	+	1.12773i	0.633178	+	0.774006i	$0.281750\pi$
$19$	−1.31714	+	4.91565i	−0.302173	+	1.12773i	−0.935351	+	0.353720i	$0.884916\pi$
$20$	2.89722	+	0.776309i	0.647839	+	0.173588i
$21$		0			0
$22$	0.482783	+	0.836204i	0.102930	+	0.178279i
$23$	1.85976	+	1.07373i	0.387787	+	0.223889i	0.681201	−	0.732097i	$-0.261458\pi$
$23$	1.85976	+	1.07373i	0.387787	+	0.223889i	−0.293414	+	0.955985i	$0.594791\pi$
$24$		0			0
$25$		−	2.63425i		−	0.526850i
$26$	0.253926	−	0.764453i	0.0497989	−	0.149922i
$27$		0			0
$28$	1.41565	+	4.96143i	0.267533	+	0.937623i
$29$	2.66646	−	4.61844i	0.495148	−	0.857622i	−0.504836	−	0.863215i	$-0.668447\pi$
$29$	2.66646	−	4.61844i	0.495148	−	0.857622i	0.999984	+	0.00559304i	$0.00178033\pi$
$30$		0			0
$31$	−1.09410	−	1.09410i	−0.196507	−	0.196507i	0.601994	−	0.798501i	$-0.294373\pi$
$31$	−1.09410	−	1.09410i	−0.196507	−	0.196507i	−0.798501	+	0.601994i	$0.794373\pi$
$32$	−2.50396	−	0.670934i	−0.442642	−	0.118605i
$33$		0			0
$34$	1.19557	−	1.19557i	0.205038	−	0.205038i
$35$	−3.49092	+	2.09135i	−0.590073	+	0.353502i
$36$		0			0
$37$	−2.82556	+	0.757106i	−0.464519	+	0.124467i	−0.483485	−	0.875353i	$-0.660629\pi$
$37$	−2.82556	+	0.757106i	−0.464519	+	0.124467i	0.0189661	+	0.999820i	$0.493963\pi$
$38$	1.13695			0.184438
$39$		0			0
$40$		−	1.35737i		−	0.214618i
$41$	1.37894	−	0.369486i	0.215354	−	0.0577039i	−0.149529	−	0.988757i	$-0.547776\pi$
$41$	1.37894	−	0.369486i	0.215354	−	0.0577039i	0.364883	+	0.931053i	$0.381109\pi$
$42$		0			0
$43$	−6.58558	+	3.80219i	−1.00429	+	0.579828i	−0.909515	−	0.415671i	$-0.863547\pi$
$43$	−6.58558	+	3.80219i	−1.00429	+	0.579828i	−0.0947764	+	0.995499i	$0.530214\pi$
$44$	−5.95956	+	5.95956i	−0.898438	+	0.898438i
$45$		0			0
$46$	0.124173	−	0.463422i	0.0183084	−	0.0683278i
$47$	5.26364	−	5.26364i	0.767781	−	0.767781i	−0.209934	−	0.977716i	$-0.567325\pi$
$47$	5.26364	−	5.26364i	0.767781	−	0.767781i	0.977716	+	0.209934i	$0.0673250\pi$
$48$		0			0
$49$	−6.17202	−	3.30245i	−0.881717	−	0.471778i
$50$	−0.568470	+	0.152321i	−0.0803937	+	0.0215414i
$51$		0			0
$52$	7.01895	+	0.413900i	0.973353	+	0.0573976i
$53$	13.1808			1.81053			0.905263	−	0.424851i	$-0.139673\pi$
$53$	13.1808			1.81053			0.905263	+	0.424851i	$0.139673\pi$
$54$		0			0
$55$	−5.75692	−	3.32376i	−0.776263	−	0.448176i
$56$	2.00294	−	1.19993i	0.267654	−	0.160347i
$57$		0			0
$58$	−1.15084	−	0.308366i	−0.151112	−	0.0404905i
$59$	−8.73809	−	2.34136i	−1.13760	−	0.304820i	−0.359616	−	0.933101i	$-0.617092\pi$
$59$	−8.73809	−	2.34136i	−1.13760	−	0.304820i	−0.777987	+	0.628281i	$0.783759\pi$
$60$		0			0
$61$	10.1891	−	5.88266i	1.30458	−	0.753197i	0.323391	−	0.946266i	$-0.395177\pi$
$61$	10.1891	−	5.88266i	1.30458	−	0.753197i	0.981185	+	0.193068i	$0.0618439\pi$
$62$	−0.172842	+	0.299371i	−0.0219510	+	0.0380202i
$63$		0			0
$64$		−	6.82688i		−	0.853360i
$65$	1.11751	+	5.43193i	0.138610	+	0.673748i
$66$		0			0
$67$	−1.28138	−	4.78216i	−0.156545	−	0.584234i	−0.998968	−	0.0454175i	$-0.985538\pi$
$67$	−1.28138	−	4.78216i	−0.156545	−	0.584234i	0.842423	−	0.538817i	$-0.181128\pi$
$68$	12.7811	+	7.37915i	1.54993	+	0.894854i
$69$		0			0
$70$	0.653167	+	0.632408i	0.0780684	+	0.0755873i
$71$	5.25942	+	1.40926i	0.624179	+	0.167248i	0.557027	−	0.830495i	$-0.311942\pi$
$71$	5.25942	+	1.40926i	0.624179	+	0.167248i	0.0671520	+	0.997743i	$0.478609\pi$
$72$		0			0
$73$	−8.04396	+	8.04396i	−0.941474	+	0.941474i	−0.998380	−	0.0569055i	$-0.981877\pi$
$73$	−8.04396	+	8.04396i	−0.941474	+	0.941474i	0.0569055	+	0.998380i	$0.481877\pi$
$74$	0.326766	+	0.565975i	0.0379857	+	0.0657932i
$75$		0			0
$76$	2.56854	+	9.58594i	0.294632	+	1.09958i
$77$	−0.184619	−	11.4332i	−0.0210392	−	1.30293i
$78$		0			0
$79$	9.06635			1.02004			0.510022	−	0.860161i	$-0.329637\pi$
$79$	9.06635			1.02004			0.510022	+	0.860161i	$0.329637\pi$
$80$	5.50153	−	1.47413i	0.615090	−	0.164813i
$81$		0			0
$82$	−0.159469	−	0.276209i	−0.0176104	−	0.0305022i
$83$	1.13072	+	1.13072i	0.124113	+	0.124113i	0.766435	−	0.642322i	$-0.222029\pi$
$83$	1.13072	+	1.13072i	0.124113	+	0.124113i	−0.642322	+	0.766435i	$0.722029\pi$
$84$		0			0
$85$	−3.01275	+	11.2437i	−0.326778	+	1.21955i
$86$	1.20131	+	1.20131i	0.129540	+	0.129540i
$87$		0			0
$88$	3.30308	+	1.90703i	0.352109	+	0.203290i
$89$	−0.217351	−	0.811166i	−0.0230392	−	0.0859834i	0.953449	−	0.301554i	$-0.0975054\pi$
$89$	−0.217351	−	0.811166i	−0.0230392	−	0.0859834i	−0.976488	+	0.215571i	$0.930839\pi$
$90$		0			0
$91$	−7.02751	+	6.45090i	−0.736683	+	0.676238i
$92$	4.18775			0.436603
$93$		0			0
$94$	−1.44025	−	0.831529i	−0.148551	−	0.0857657i
$95$	−6.77878	+	3.91373i	−0.695488	+	0.401540i
$96$		0			0
$97$	4.35890	−	16.2676i	0.442579	−	1.65173i	−0.279672	−	0.960096i	$-0.590226\pi$
$97$	4.35890	−	16.2676i	0.442579	−	1.65173i	0.722251	−	0.691631i	$-0.243108\pi$
$98$	−0.355779	+	1.52288i	−0.0359391	+	0.153834i
$99$		0			0
$100$	−2.56851	−	4.44879i	−0.256851	−	0.444879i
$101$	−5.48585	+	9.50177i	−0.545863	+	0.945462i	0.452690	+	0.891668i	$0.350465\pi$
$101$	−5.48585	+	9.50177i	−0.545863	+	0.945462i	−0.998552	+	0.0537934i	$0.982869\pi$
$102$		0			0
$103$	4.70231			0.463332			0.231666	−	0.972795i	$-0.425582\pi$
$103$	4.70231			0.463332			0.231666	+	0.972795i	$0.425582\pi$
$104$	−0.641180	−	3.11661i	−0.0628728	−	0.305609i
$105$		0			0
$106$	−0.762158	−	2.84441i	−0.0740274	−	0.276274i
$107$	−6.55307	+	11.3502i	−0.633509	+	1.09727i	0.353320	+	0.935503i	$0.385053\pi$
$107$	−6.55307	+	11.3502i	−0.633509	+	1.09727i	−0.986829	+	0.161767i	$0.948281\pi$
$108$		0			0
$109$	−0.872057	+	0.872057i	−0.0835279	+	0.0835279i	−0.747636	−	0.664108i	$-0.768811\pi$
$109$	−0.872057	+	0.872057i	−0.0835279	+	0.0835279i	0.664108	+	0.747636i	$0.268811\pi$
$110$	−0.384381	+	1.43453i	−0.0366493	+	0.136777i
$111$		0			0
$112$	7.03865	+	6.81495i	0.665090	+	0.643952i
$113$	−6.21370	−	10.7625i	−0.584536	−	1.01245i	−0.994933	−	0.100539i	$-0.967943\pi$
$113$	−6.21370	−	10.7625i	−0.584536	−	1.01245i	0.410397	−	0.911907i	$-0.365390\pi$
$114$		0			0
$115$	0.854883	+	3.19047i	0.0797183	+	0.297513i
$116$		−	10.3996i		−	0.965583i
$117$		0			0
$118$			2.02106i			0.186053i
$119$	−19.2546	+	5.49395i	−1.76507	+	0.503630i
$120$		0			0
$121$	6.65011	−	3.83944i	0.604556	−	0.349040i
$122$	−1.85864	−	1.85864i	−0.168273	−	0.168273i
$123$		0			0
$124$	−2.91455	−	0.780950i	−0.261734	−	0.0701314i
$125$	8.30301	−	8.30301i	0.742644	−	0.742644i
$126$		0			0
$127$	5.51334	+	3.18313i	0.489230	+	0.282457i	0.724255	−	0.689532i	$-0.242184\pi$
$127$	5.51334	+	3.18313i	0.489230	+	0.282457i	−0.235025	+	0.971989i	$0.575517\pi$
$128$	−6.48115	+	1.73662i	−0.572858	+	0.153497i
$129$		0			0
$130$	1.10759	−	0.555250i	0.0971420	−	0.0486986i
$131$		−	3.73498i		−	0.326327i	−0.986599	−	0.163163i	$-0.947830\pi$
$131$		−	3.73498i		−	0.326327i	0.986599	−	0.163163i	$-0.0521698\pi$
$132$		0			0
$133$	−11.7677	−	6.54304i	−1.02039	−	0.567354i
$134$	−0.957894	+	0.553040i	−0.0827494	+	0.0477754i
$135$		0			0
$136$	1.72859	−	6.45118i	0.148225	−	0.553184i
$137$	−0.00793713	+	0.0296218i	−0.000678115	+	0.00253076i	−0.966264	−	0.257553i	$-0.917084\pi$
$137$	−0.00793713	+	0.0296218i	−0.000678115	+	0.00253076i	0.965586	+	0.260084i	$0.0837503\pi$
$138$		0			0
$139$	−2.85559	+	1.64867i	−0.242208	+	0.139839i	−0.616191	−	0.787597i	$-0.711325\pi$
$139$	−2.85559	+	1.64867i	−0.242208	+	0.139839i	0.373983	+	0.927435i	$0.377992\pi$
$140$	−3.85639	+	6.93572i	−0.325924	+	0.586175i
$141$		0			0
$142$		−	1.21647i		−	0.102084i
$143$	−14.7884	−	4.91220i	−1.23667	−	0.410779i
$144$		0			0
$145$	7.92305	−	2.12297i	0.657974	−	0.176303i
$146$	2.20101	+	1.27075i	0.182157	+	0.105168i
$147$		0			0
$148$	−4.03366	+	4.03366i	−0.331565	+	0.331565i
$149$	−4.52646	−	1.21286i	−0.370822	−	0.0993615i	0.0685950	−	0.997645i	$-0.478148\pi$
$149$	−4.52646	−	1.21286i	−0.370822	−	0.0993615i	−0.439417	+	0.898283i	$0.644815\pi$
$150$		0			0
$151$	−4.74970	−	4.74970i	−0.386525	−	0.386525i	0.486921	−	0.873446i	$-0.338120\pi$
$151$	−4.74970	−	4.74970i	−0.386525	−	0.386525i	−0.873446	+	0.486921i	$0.838120\pi$
$152$	3.88938	−	2.24553i	0.315470	−	0.182137i
$153$		0			0
$154$	−2.45660	+	0.700945i	−0.197959	+	0.0564838i
$155$		−	2.37989i		−	0.191158i
$156$		0			0
$157$			17.1115i			1.36565i	0.730584	+	0.682823i	$0.239248\pi$
$157$			17.1115i			1.36565i	−0.730584	+	0.682823i	$0.760752\pi$
$158$	−0.524246	−	1.95651i	−0.0417068	−	0.155652i
$159$		0			0
$160$	−1.99360	−	3.45301i	−0.157608	−	0.272985i
$161$	−3.95215	+	4.08188i	−0.311473	+	0.321697i
$162$		0			0
$163$	5.05271	−	18.8570i	0.395759	−	1.47699i	−0.424726	−	0.905322i	$-0.639630\pi$
$163$	5.05271	−	18.8570i	0.395759	−	1.47699i	0.820484	−	0.571669i	$-0.193704\pi$
$164$	1.96852	−	1.96852i	0.153716	−	0.153716i
$165$		0			0
$166$	0.178627	−	0.309390i	0.0138641	−	0.0240134i
$167$	−3.66374	−	13.6733i	−0.283508	−	1.05807i	−0.949922	−	0.312486i	$-0.898838\pi$
$167$	−3.66374	−	13.6733i	−0.283508	−	1.05807i	0.666414	−	0.745582i	$-0.267828\pi$
$168$		0			0
$169$	5.13177	+	11.9442i	0.394751	+	0.918788i
$170$	2.60060			0.199457
$171$		0			0
$172$	−7.41460	+	12.8425i	−0.565358	+	0.979228i
$173$	−9.66072	−	16.7329i	−0.734491	−	1.27218i	−0.954946	−	0.296778i	$-0.904088\pi$
$173$	−9.66072	−	16.7329i	−0.734491	−	1.27218i	0.220456	−	0.975397i	$-0.429246\pi$
$174$		0			0
$175$	6.76034	+	1.69493i	0.511034	+	0.128125i
$176$	−4.14216	+	15.4588i	−0.312227	+	1.16525i
$177$		0			0
$178$	−0.162481	+	0.0938085i	−0.0121785	+	0.00703124i
$179$	−3.56116	−	2.05604i	−0.266173	−	0.153675i	0.360974	−	0.932576i	$-0.382444\pi$
$179$	−3.56116	−	2.05604i	−0.266173	−	0.153675i	−0.627147	+	0.778901i	$0.715778\pi$
$180$		0			0
$181$	−2.09652			−0.155833			−0.0779165	−	0.996960i	$-0.524827\pi$
$181$	−2.09652			−0.155833			−0.0779165	+	0.996960i	$0.524827\pi$
$182$	1.79845	+	1.14352i	0.133310	+	0.0847633i
$183$		0			0
$184$	−0.490496	−	1.83056i	−0.0361598	−	0.134950i
$185$	−3.89650	−	2.24965i	−0.286477	−	0.165397i
$186$		0			0
$187$	−23.1283	−	23.1283i	−1.69131	−	1.69131i
$188$	3.75709	−	14.0217i	0.274014	−	1.02263i
$189$		0			0
$190$	1.23655	+	1.23655i	0.0897089	+	0.0897089i
$191$	−4.22074	−	7.31054i	−0.305402	−	0.528972i	0.671949	−	0.740598i	$-0.265458\pi$
$191$	−4.22074	−	7.31054i	−0.305402	−	0.528972i	−0.977351	+	0.211626i	$0.932124\pi$
$192$		0			0
$193$	1.96647	−	0.526915i	0.141550	−	0.0379282i	−0.187348	−	0.982294i	$-0.559989\pi$
$193$	1.96647	−	0.526915i	0.141550	−	0.0379282i	0.328898	+	0.944365i	$0.393323\pi$
$194$	−3.76259			−0.270138
$195$		0			0
$196$	−13.6435	+	0.440734i	−0.974535	+	0.0314810i
$197$	−3.46988	−	12.9498i	−0.247219	−	0.922632i	−0.972255	−	0.233922i	$-0.924844\pi$
$197$	−3.46988	−	12.9498i	−0.247219	−	0.922632i	0.725037	−	0.688710i	$-0.241823\pi$
$198$		0			0
$199$	−3.76822	−	6.52675i	−0.267122	−	0.462669i	0.700995	−	0.713166i	$-0.252739\pi$
$199$	−3.76822	−	6.52675i	−0.267122	−	0.462669i	−0.968117	+	0.250497i	$0.919406\pi$
$200$	−1.64382	+	1.64382i	−0.116236	+	0.116236i
$201$		0			0
$202$	2.36768	+	0.634419i	0.166590	+	0.0446376i
$203$	10.1367	+	9.81458i	0.711460	+	0.688849i
$204$		0			0
$205$	1.90159	+	1.09788i	0.132813	+	0.0766794i
$206$	−0.271903	−	1.01475i	−0.0189444	−	0.0707013i
$207$		0			0
$208$	11.9356	−	5.98347i	0.827584	−	0.414879i
$209$		−	21.9944i		−	1.52139i
$210$		0			0
$211$	8.48310	−	14.6932i	0.584001	−	1.01152i	−0.410998	−	0.911636i	$-0.634820\pi$
$211$	8.48310	−	14.6932i	0.584001	−	1.01152i	0.994999	−	0.0998830i	$-0.0318469\pi$
$212$	22.2601	−	12.8519i	1.52883	−	0.882671i
$213$		0			0
$214$	2.82829	+	0.757839i	0.193338	+	0.0518048i
$215$	−11.2977	−	3.02722i	−0.770499	−	0.206455i
$216$		0			0
$217$	3.51179	−	2.10385i	0.238396	−	0.142819i
$218$	0.238614	+	0.137764i	0.0161610	+	0.00933056i
$219$		0			0
$220$	−12.9632			−0.873982
$221$	−1.60629	+	27.2396i	−0.108051	+	1.83233i
$222$		0			0
$223$	12.1895	−	3.26617i	0.816269	−	0.218719i	0.173555	−	0.984824i	$-0.444475\pi$
$223$	12.1895	−	3.26617i	0.816269	−	0.218719i	0.642715	+	0.766106i	$0.277808\pi$
$224$	3.33293	−	5.99427i	0.222691	−	0.400509i
$225$		0			0
$226$	−1.96323	+	1.96323i	−0.130592	+	0.130592i
$227$	−5.09212	+	19.0040i	−0.337976	+	1.26134i	0.562631	+	0.826708i	$0.309789\pi$
$227$	−5.09212	+	19.0040i	−0.337976	+	1.26134i	−0.900607	+	0.434635i	$0.856878\pi$
$228$		0			0
$229$	−19.8246	+	19.8246i	−1.31004	+	1.31004i	−0.388666	+	0.921379i	$0.627064\pi$
$229$	−19.8246	+	19.8246i	−1.31004	+	1.31004i	−0.921379	+	0.388666i	$0.872936\pi$
$230$	0.639068	−	0.368966i	0.0421389	−	0.0243289i
$231$		0			0
$232$	−4.54591	+	1.21807i	−0.298454	+	0.0799704i
$233$		−	10.8900i		−	0.713427i	−0.934214	−	0.356714i	$-0.883897\pi$
$233$		−	10.8900i		−	0.713427i	0.934214	−	0.356714i	$-0.116103\pi$
$234$		0			0
$235$	11.4495			0.746882
$236$	−17.0400	+	4.56586i	−1.10921	+	0.297212i
$237$		0			0
$238$	2.29896	+	3.83746i	0.149019	+	0.248745i
$239$	10.0403	−	10.0403i	0.649451	−	0.649451i	−0.303409	−	0.952860i	$-0.598125\pi$
$239$	10.0403	−	10.0403i	0.649451	−	0.649451i	0.952860	+	0.303409i	$0.0981250\pi$
$240$		0			0
$241$	−15.1305	−	4.05421i	−0.974642	−	0.261155i	−0.263856	−	0.964562i	$-0.584994\pi$
$241$	−15.1305	−	4.05421i	−0.974642	−	0.261155i	−0.710787	+	0.703408i	$0.751661\pi$
$242$	−1.21308	−	1.21308i	−0.0779797	−	0.0779797i
$243$		0			0
$244$	11.4717	−	19.8696i	0.734400	−	1.27202i
$245$	−3.12095	−	10.3044i	−0.199390	−	0.658326i
$246$		0			0
$247$	−13.7159	+	12.1883i	−0.872719	+	0.775524i
$248$			1.36548i			0.0867082i
$249$		0			0
$250$	−2.27189	−	1.31168i	−0.143687	−	0.0829577i
$251$	10.7847	+	18.6797i	0.680727	+	1.17905i	0.974759	+	0.223258i	$0.0716692\pi$
$251$	10.7847	+	18.6797i	0.680727	+	1.17905i	−0.294033	+	0.955795i	$0.594997\pi$
$252$		0			0
$253$	−8.96490	−	2.40214i	−0.563619	−	0.151021i
$254$	0.368118	−	1.37383i	0.0230977	−	0.0862020i
$255$		0			0
$256$	−6.07736	−	10.5263i	−0.379835	−	0.657893i
$257$	−1.05953	+	1.83517i	−0.0660920	+	0.114475i	−0.897178	−	0.441669i	$-0.854386\pi$
$257$	−1.05953	+	1.83517i	−0.0660920	+	0.114475i	0.831086	+	0.556144i	$0.187720\pi$
$258$		0			0
$259$	−0.124957	−	7.73843i	−0.00776444	−	0.480843i
$260$	7.18365	+	8.08396i	0.445511	+	0.501346i
$261$		0			0
$262$	−0.806006	+	0.215969i	−0.0497952	+	0.0133426i
$263$	−5.53188	+	9.58150i	−0.341111	+	0.590821i	−0.984639	−	0.174601i	$-0.944136\pi$
$263$	−5.53188	+	9.58150i	−0.341111	+	0.590821i	0.643529	+	0.765422i	$0.277470\pi$
$264$		0			0
$265$	14.3355	+	14.3355i	0.880621	+	0.880621i
$266$	−0.731539	+	2.91779i	−0.0448536	+	0.178901i
$267$		0			0
$268$	−6.82684	−	6.82684i	−0.417016	−	0.417016i
$269$	−23.8459	+	13.7675i	−1.45391	+	0.839416i	−0.998700	−	0.0509670i	$-0.983770\pi$
$269$	−23.8459	+	13.7675i	−1.45391	+	0.839416i	−0.455211	+	0.890383i	$0.650436\pi$
$270$		0			0
$271$	3.80218	+	14.1899i	0.230966	+	0.861978i	0.979926	+	0.199362i	$0.0638870\pi$
$271$	3.80218	+	14.1899i	0.230966	+	0.861978i	−0.748960	+	0.662616i	$0.769446\pi$
$272$	28.0245			1.69923
$273$		0			0
$274$	0.00685131			0.000413903
$275$	2.94665	+	10.9971i	0.177690	+	0.663148i
$276$		0			0
$277$	4.50623	−	2.60167i	0.270753	−	0.156319i	−0.358477	−	0.933539i	$-0.616704\pi$
$277$	4.50623	−	2.60167i	0.270753	−	0.156319i	0.629230	+	0.777219i	$0.283370\pi$
$278$	0.520902	+	0.520902i	0.0312416	+	0.0312416i
$279$		0			0
$280$	3.48344	+	0.873357i	0.208175	+	0.0521931i
$281$	10.7634	+	10.7634i	0.642088	+	0.642088i	0.951068	−	0.308980i	$-0.0999877\pi$
$281$	10.7634	+	10.7634i	0.642088	+	0.642088i	−0.308980	+	0.951068i	$0.599988\pi$
$282$		0			0
$283$	−2.03356	+	3.52223i	−0.120882	+	0.209375i	−0.920116	−	0.391646i	$-0.871906\pi$
$283$	−2.03356	+	3.52223i	−0.120882	+	0.209375i	0.799233	+	0.601021i	$0.205239\pi$
$284$	10.2563	−	2.74818i	0.608601	−	0.163074i
$285$		0			0
$286$	−0.204938	+	3.47536i	−0.0121183	+	0.205502i
$287$	0.0609819	+	3.77654i	0.00359965	+	0.222922i
$288$		0			0
$289$	−20.1375	+	34.8791i	−1.18456	+	2.05171i
$290$	−0.916273	−	1.58703i	−0.0538054	−	0.0931937i
$291$		0			0
$292$	−5.74163	+	21.4280i	−0.336003	+	1.25398i
$293$	21.3183	+	5.71221i	1.24543	+	0.333711i	0.820568	−	0.571549i	$-0.193657\pi$
$293$	21.3183	+	5.71221i	1.24543	+	0.333711i	0.424858	+	0.905260i	$0.360324\pi$
$294$		0			0
$295$	−6.95708	−	12.0500i	−0.405057	−	0.701579i
$296$	2.23565	+	1.29075i	0.129944	+	0.0750235i
$297$		0			0
$298$			1.04694i			0.0606475i
$299$	3.46996	+	6.92173i	0.200673	+	0.400294i
$300$		0			0
$301$	−5.52034	−	19.3471i	−0.318187	−	1.11515i
$302$	−0.750339	+	1.29962i	−0.0431771	+	0.0747850i
$303$		0			0
$304$	13.3253	+	13.3253i	0.764259	+	0.764259i
$305$	17.4796	+	4.68365i	1.00088	+	0.268185i
$306$		0			0
$307$	9.60326	−	9.60326i	0.548087	−	0.548087i	−0.377800	−	0.925887i	$-0.623319\pi$
$307$	9.60326	−	9.60326i	0.548087	−	0.548087i	0.925887	+	0.377800i	$0.123319\pi$
$308$	−11.4597	−	19.1287i	−0.652975	−	1.08996i
$309$		0			0
$310$	−0.513579	+	0.137613i	−0.0291693	+	0.00781590i
$311$	−16.2194			−0.919715			−0.459858	−	0.887993i	$-0.652100\pi$
$311$	−16.2194			−0.919715			−0.459858	+	0.887993i	$0.652100\pi$
$312$		0			0
$313$		−	24.2234i		−	1.36919i	−0.728926	−	0.684593i	$-0.759980\pi$
$313$		−	24.2234i		−	1.36919i	0.728926	−	0.684593i	$-0.240020\pi$
$314$	3.69265	−	0.989442i	0.208388	−	0.0558375i
$315$		0			0
$316$	15.3115	−	8.84009i	0.861338	−	0.497294i
$317$	18.9182	−	18.9182i	1.06255	−	1.06255i	0.0646418	−	0.997909i	$-0.479410\pi$
$317$	18.9182	−	18.9182i	1.06255	−	1.06255i	0.997909	−	0.0646418i	$-0.0205905\pi$
$318$		0			0
$319$	−5.96535	+	22.2630i	−0.333996	+	1.24649i
$320$	7.42492	−	7.42492i	0.415065	−	0.415065i
$321$		0			0
$322$	1.10939	+	0.616844i	0.0618241	+	0.0343754i
$323$	−37.2017	+	9.96817i	−2.06996	+	0.554644i
$324$		0			0
$325$	5.22494	−	7.93163i	0.289827	−	0.439968i
$326$	−4.36148			−0.241560
$327$		0			0
$328$	−1.09105	−	0.629918i	−0.0602432	−	0.0347814i
$329$	10.1215	+	16.8949i	0.558015	+	0.931448i
$330$		0			0
$331$	13.9589	+	3.74029i	0.767253	+	0.205585i	0.621157	−	0.783686i	$-0.286663\pi$
$331$	13.9589	+	3.74029i	0.767253	+	0.205585i	0.146095	+	0.989271i	$0.453329\pi$
$332$	3.01209	+	0.807087i	0.165310	+	0.0442947i
$333$		0			0
$334$	−2.73883	+	1.58126i	−0.149862	+	0.0865229i
$335$	3.80746	−	6.59471i	0.208024	−	0.360307i
$336$		0			0
$337$		−	5.15524i		−	0.280824i	−0.990093	−	0.140412i	$-0.955157\pi$
$337$		−	5.15524i		−	0.280824i	0.990093	−	0.140412i	$-0.0448426\pi$
$338$	2.28082	−	1.79809i	0.124060	−	0.0978030i
$339$		0			0
$340$	5.87512	+	21.9263i	0.318623	+	1.18912i
$341$	5.79134	+	3.34363i	0.313619	+	0.181068i
$342$		0			0
$343$	12.4463	−	13.7145i	0.672040	−	0.740515i
$344$	6.48216	+	1.73689i	0.349495	+	0.0936469i
$345$		0			0
$346$	−3.05232	+	3.05232i	−0.164094	+	0.164094i
$347$	−11.9012	−	20.6134i	−0.638888	−	1.10659i	−0.985677	−	0.168643i	$-0.946062\pi$
$347$	−11.9012	−	20.6134i	−0.638888	−	1.10659i	0.346789	−	0.937943i	$-0.387272\pi$
$348$		0			0
$349$	−3.16538	−	11.8134i	−0.169439	−	0.632355i	−0.997432	−	0.0716166i	$-0.977184\pi$
$349$	−3.16538	−	11.8134i	−0.169439	−	0.632355i	0.827993	−	0.560738i	$-0.189482\pi$
$350$	−0.0251399	−	1.55688i	−0.00134378	−	0.0832189i
$351$		0			0
$352$	11.2036			0.597156
$353$	16.5186	−	4.42614i	0.879196	−	0.235580i	0.209136	−	0.977887i	$-0.432935\pi$
$353$	16.5186	−	4.42614i	0.879196	−	0.235580i	0.670060	+	0.742307i	$0.266268\pi$
$354$		0			0
$355$	4.18744	+	7.25286i	0.222246	+	0.384942i
$356$	−1.15799	−	1.15799i	−0.0613734	−	0.0613734i
$357$		0			0
$358$	−0.237773	+	0.887382i	−0.0125667	+	0.0468996i
$359$	−14.6210	−	14.6210i	−0.771665	−	0.771665i	0.206733	−	0.978397i	$-0.433717\pi$
$359$	−14.6210	−	14.6210i	−0.771665	−	0.771665i	−0.978397	+	0.206733i	$0.933717\pi$
$360$		0			0
$361$	−5.97423	−	3.44922i	−0.314433	−	0.181538i
$362$	0.121228	+	0.452427i	0.00637158	+	0.0237790i
$363$		0			0
$364$	−5.57833	+	17.7466i	−0.292384	+	0.930173i
$365$	−17.4972			−0.915846
$366$		0			0
$367$	0.401157	+	0.231608i	0.0209402	+	0.0120898i	0.510434	−	0.859917i	$-0.329485\pi$
$367$	0.401157	+	0.231608i	0.0209402	+	0.0120898i	−0.489493	+	0.872007i	$0.662818\pi$
$368$	6.88672	−	3.97605i	0.358995	−	0.207266i
$369$		0			0
$370$	−0.260164	+	0.970945i	−0.0135253	+	0.0504770i
$371$	−8.48081	+	33.8263i	−0.440302	+	1.75617i
$372$		0			0
$373$	−0.348917	−	0.604342i	−0.0180662	−	0.0312916i	0.856851	−	0.515564i	$-0.172418\pi$
$373$	−0.348917	−	0.604342i	−0.0180662	−	0.0312916i	−0.874917	+	0.484273i	$0.839084\pi$
$374$	−3.65371	+	6.32841i	−0.188929	+	0.327234i
$375$		0			0
$376$	−6.56923			−0.338782
$377$	17.1891	−	8.61712i	0.885283	−	0.443804i
$378$		0			0
$379$	1.85118	+	6.90871i	0.0950889	+	0.354877i	0.997033	−	0.0769763i	$-0.0245266\pi$
$379$	1.85118	+	6.90871i	0.0950889	+	0.354877i	−0.901944	+	0.431853i	$0.857860\pi$
$380$	−7.63212	+	13.2192i	−0.391519	+	0.678132i
$381$		0			0
$382$	−1.33355	+	1.33355i	−0.0682305	+	0.0682305i
$383$	−0.496583	+	1.85327i	−0.0253742	+	0.0946979i	−0.977452	−	0.211159i	$-0.932276\pi$
$383$	−0.496583	+	1.85327i	−0.0253742	+	0.0946979i	0.952078	+	0.305857i	$0.0989429\pi$
$384$		0			0
$385$	12.2340	−	12.6355i	0.623500	−	0.643967i
$386$	−0.227416	−	0.393895i	−0.0115751	−	0.0200487i
$387$		0			0
$388$	−8.50023	−	31.7233i	−0.431534	−	1.61051i
$389$		−	6.17075i		−	0.312870i	−0.987688	−	0.156435i	$-0.950000\pi$
$389$		−	6.17075i		−	0.312870i	0.987688	−	0.156435i	$-0.0500001\pi$
$390$		0			0
$391$			16.2521i			0.821903i
$392$	1.79067	+	5.91225i	0.0904424	+	0.298614i
$393$		0			0
$394$	−2.59391	+	1.49759i	−0.130679	+	0.0754477i
$395$	9.86057	+	9.86057i	0.496139	+	0.496139i
$396$		0			0
$397$	30.1243	+	8.07177i	1.51189	+	0.405111i	0.917063	−	0.398741i	$-0.130553\pi$
$397$	30.1243	+	8.07177i	1.51189	+	0.405111i	0.594830	+	0.803852i	$0.297220\pi$
$398$	−1.19058	+	1.19058i	−0.0596782	+	0.0596782i
$399$		0			0
$400$	−8.44780	−	4.87734i	−0.422390	−	0.243867i
$401$	−24.2526	+	6.49846i	−1.21112	+	0.324517i	−0.807199	−	0.590279i	$-0.799018\pi$
$401$	−24.2526	+	6.49846i	−1.21112	+	0.324517i	−0.403916	+	0.914796i	$0.632351\pi$
$402$		0			0
$403$	−1.12419	−	5.46441i	−0.0559999	−	0.272202i
$404$			21.3958i			1.06448i
$405$		0			0
$406$	1.53184	−	2.75501i	0.0760239	−	0.136729i
$407$	10.9488	−	6.32129i	0.542712	−	0.313335i
$408$		0			0
$409$	−3.92450	+	14.6464i	−0.194054	+	0.724219i	0.798456	+	0.602053i	$0.205651\pi$
$409$	−3.92450	+	14.6464i	−0.194054	+	0.724219i	−0.992510	+	0.122165i	$0.961016\pi$
$410$	0.126966	−	0.473844i	0.00627041	−	0.0234015i
$411$		0			0
$412$	7.94138	−	4.58496i	0.391244	−	0.225885i
$413$	11.6310	−	20.9183i	0.572322	−	1.02932i
$414$		0			0
$415$			2.45954i			0.120734i
$416$	−6.20855	−	6.98666i	−0.304399	−	0.342549i
$417$		0			0
$418$	−4.74638	+	1.27179i	−0.232153	+	0.0622052i
$419$	3.99149	+	2.30449i	0.194997	+	0.112582i	0.594320	−	0.804229i	$-0.297421\pi$
$419$	3.99149	+	2.30449i	0.194997	+	0.112582i	−0.399323	+	0.916810i	$0.630755\pi$
$420$		0			0
$421$	12.6437	−	12.6437i	0.616216	−	0.616216i	−0.328342	−	0.944559i	$-0.606490\pi$
$421$	12.6437	−	12.6437i	0.616216	−	0.616216i	0.944559	+	0.328342i	$0.106490\pi$
$422$	−3.66129	−	0.981041i	−0.178229	−	0.0477563i
$423$		0			0
$424$	−8.22509	−	8.22509i	−0.399446	−	0.399446i
$425$	17.2652	−	9.96804i	0.837483	−	0.483521i
$426$		0			0
$427$	8.54095	+	29.9334i	0.413325	+	1.44858i
$428$			25.5581i			1.23540i
$429$		0			0
$430$			2.61309i			0.126014i
$431$	−2.12448	−	7.92867i	−0.102333	−	0.381911i	0.895696	−	0.444666i	$-0.146678\pi$
$431$	−2.12448	−	7.92867i	−0.102333	−	0.381911i	−0.998029	+	0.0627557i	$0.980011\pi$
$432$		0			0
$433$	−8.67779	−	15.0304i	−0.417028	−	0.722314i	0.578611	−	0.815604i	$-0.303595\pi$
$433$	−8.67779	−	15.0304i	−0.417028	−	0.722314i	−0.995639	+	0.0932901i	$0.970262\pi$
$434$	−0.657073	−	0.636190i	−0.0315405	−	0.0305381i
$435$		0			0
$436$	−0.622458	+	2.32305i	−0.0298103	+	0.111254i
$437$	−7.72766	+	7.72766i	−0.369664	+	0.369664i
$438$		0			0
$439$	7.78946	−	13.4917i	0.371771	−	0.643926i	−0.618067	−	0.786125i	$-0.712084\pi$
$439$	7.78946	−	13.4917i	0.371771	−	0.643926i	0.989838	+	0.142199i	$0.0454174\pi$
$440$	1.51834	+	5.66652i	0.0723840	+	0.270141i
$441$		0			0
$442$	5.97116	−	1.22844i	0.284019	−	0.0584311i
$443$	30.0278			1.42667			0.713333	−	0.700825i	$-0.247185\pi$
$443$	30.0278			1.42667			0.713333	+	0.700825i	$0.247185\pi$
$444$		0			0
$445$	0.645833	−	1.11862i	0.0306154	−	0.0530274i
$446$	−1.40967	−	2.44162i	−0.0667499	−	0.115614i
$447$		0			0
$448$	17.5200	+	4.39255i	0.827741	+	0.207529i
$449$	−1.79908	+	6.71427i	−0.0849040	+	0.316866i	−0.995296	−	0.0968807i	$-0.969113\pi$
$449$	−1.79908	+	6.71427i	−0.0849040	+	0.316866i	0.910392	+	0.413747i	$0.135780\pi$
$450$		0			0
$451$	−5.34327	+	3.08494i	−0.251605	+	0.145264i
$452$	−20.9877	−	12.1173i	−0.987179	−	0.569948i
$453$		0			0
$454$	4.39550			0.206291
$455$	−14.6591	−	0.627126i	−0.687230	−	0.0294001i
$456$		0			0
$457$	5.76514	+	21.5158i	0.269682	+	1.00647i	0.959322	+	0.282314i	$0.0911020\pi$
$457$	5.76514	+	21.5158i	0.269682	+	1.00647i	−0.689640	+	0.724152i	$0.742231\pi$
$458$	5.42445	+	3.13181i	0.253468	+	0.146340i
$459$		0			0
$460$	4.55459	+	4.55459i	0.212359	+	0.212359i
$461$	−3.01705	+	11.2598i	−0.140518	+	0.524420i	0.859396	+	0.511311i	$0.170840\pi$
$461$	−3.01705	+	11.2598i	−0.140518	+	0.524420i	−0.999914	+	0.0131099i	$0.995827\pi$
$462$		0			0
$463$	16.6774	+	16.6774i	0.775063	+	0.775063i	0.978987	−	0.203924i	$-0.0653694\pi$
$463$	16.6774	+	16.6774i	0.775063	+	0.775063i	−0.203924	+	0.978987i	$0.565369\pi$
$464$	−9.87392	−	17.1021i	−0.458385	−	0.793947i
$465$		0			0
$466$	−2.35005	+	0.629695i	−0.108864	+	0.0291700i
$467$	−17.0336			−0.788223			−0.394111	−	0.919063i	$-0.628948\pi$
$467$	−17.0336			−0.788223			−0.394111	+	0.919063i	$0.628948\pi$
$468$		0			0
$469$	13.0970	−	0.211485i	0.604765	−	0.00976549i
$470$	−0.662046	−	2.47079i	−0.0305379	−	0.113969i
$471$		0			0
$472$	3.99168	+	6.91379i	0.183732	+	0.318233i
$473$	23.2393	−	23.2393i	1.06855	−	1.06855i
$474$		0			0
$475$	12.9491	+	3.46969i	0.594143	+	0.159200i
$476$	−27.1609	+	28.0524i	−1.24492	+	1.28578i
$477$		0			0
$478$	−2.74724	−	1.58612i	−0.125656	−	0.0725475i
$479$	8.69175	+	32.4380i	0.397136	+	1.48213i	0.818111	+	0.575060i	$0.195021\pi$
$479$	8.69175	+	32.4380i	0.397136	+	1.48213i	−0.420976	+	0.907072i	$0.638312\pi$
$480$		0			0
$481$	−10.0093	−	3.32477i	−0.456386	−	0.151596i
$482$			3.49958i			0.159402i
$483$		0			0
$484$	7.48725	−	12.9683i	0.340330	−	0.589468i
$485$	22.4334	−	12.9519i	1.01865	−	0.588117i
$486$		0			0
$487$	−3.78357	−	1.01381i	−0.171450	−	0.0459399i	0.172073	−	0.985084i	$-0.444954\pi$
$487$	−3.78357	−	1.01381i	−0.171450	−	0.0459399i	−0.343523	+	0.939144i	$0.611620\pi$
$488$	−10.0291	−	2.68728i	−0.453994	−	0.121647i
$489$		0			0
$490$	−2.04323	+	1.26933i	−0.0923035	+	0.0573427i
$491$	6.15458	+	3.55335i	0.277752	+	0.160360i	0.632405	−	0.774638i	$-0.282068\pi$
$491$	6.15458	+	3.55335i	0.277752	+	0.160360i	−0.354653	+	0.934998i	$0.615401\pi$
$492$		0			0
$493$	40.3596			1.81770
$494$	3.42332	+	2.25510i	0.154023	+	0.101462i
$495$		0			0
$496$	−5.53442	+	1.48294i	−0.248503	+	0.0665861i
$497$	−7.00063	+	12.5906i	−0.314021	+	0.564767i
$498$		0			0
$499$	5.42530	−	5.42530i	0.242870	−	0.242870i	−0.575167	−	0.818036i	$-0.695063\pi$
$499$	5.42530	−	5.42530i	0.242870	−	0.242870i	0.818036	+	0.575167i	$0.195063\pi$
$500$	5.92654	−	22.1181i	0.265043	−	0.989153i
$501$		0			0
$502$	3.40746	−	3.40746i	0.152082	−	0.152082i
$503$	11.4527	−	6.61222i	0.510651	−	0.294824i	−0.222450	−	0.974944i	$-0.571406\pi$
$503$	11.4527	−	6.61222i	0.510651	−	0.294824i	0.733101	+	0.680120i	$0.238072\pi$
$504$		0			0
$505$	−16.3005	+	4.36772i	−0.725364	+	0.194361i
$506$			2.07352i			0.0921792i
$507$		0			0
$508$	12.4148			0.550816
$509$	38.3913	−	10.2869i	1.70167	−	0.455960i	0.728308	−	0.685250i	$-0.240307\pi$
$509$	38.3913	−	10.2869i	1.70167	−	0.455960i	0.973358	+	0.229290i	$0.0736405\pi$
$510$		0			0
$511$	−15.4677	−	25.8190i	−0.684253	−	1.14217i
$512$	−11.4092	+	11.4092i	−0.504221	+	0.504221i
$513$		0			0
$514$	0.457294	+	0.122531i	0.0201704	+	0.00540463i
$515$	5.11423	+	5.11423i	0.225360	+	0.225360i
$516$		0			0
$517$	−16.0860	+	27.8617i	−0.707460	+	1.22536i
$518$	−1.66272	+	0.474426i	−0.0730558	+	0.0208451i
$519$		0			0
$520$	2.69228	−	4.08698i	0.118064	−	0.179226i
$521$		−	9.34550i		−	0.409434i	−0.978821	−	0.204717i	$-0.934373\pi$
$521$		−	9.34550i		−	0.409434i	0.978821	−	0.204717i	$-0.0656274\pi$
$522$		0			0
$523$	16.9149	+	9.76580i	0.739635	+	0.427028i	0.821937	−	0.569579i	$-0.192894\pi$
$523$	16.9149	+	9.76580i	0.739635	+	0.427028i	−0.0823016	+	0.996607i	$0.526227\pi$
$524$	−3.64177	−	6.30773i	−0.159091	−	0.275554i
$525$		0			0
$526$	2.38755	+	0.639743i	0.104102	+	0.0278941i
$527$	3.03076	−	11.3110i	0.132022	−	0.492713i
$528$		0			0
$529$	−9.19419	−	15.9248i	−0.399748	−	0.692383i
$530$	2.26466	−	3.92251i	0.0983706	−	0.170383i
$531$		0			0
$532$	−26.2533	+	0.423927i	−1.13822	+	0.0183796i
$533$	4.88479	+	1.62256i	0.211584	+	0.0702811i
$534$		0			0
$535$	−19.4716	+	5.21741i	−0.841833	+	0.225568i
$536$	−2.18456	+	3.78376i	−0.0943585	+	0.163434i
$537$		0			0
$538$	4.34985	+	4.34985i	0.187536	+	0.187536i
$539$	29.4601	+	6.88256i	1.26894	+	0.296453i
$540$		0			0
$541$	−0.184083	−	0.184083i	−0.00791436	−	0.00791436i	0.703139	−	0.711053i	$-0.251781\pi$
$541$	−0.184083	−	0.184083i	−0.00791436	−	0.00791436i	−0.711053	+	0.703139i	$0.751781\pi$
$542$	2.84232	−	1.64102i	0.122088	−	0.0704877i
$543$		0			0
$544$	−5.07764	−	18.9500i	−0.217702	−	0.812475i
$545$	−1.89690			−0.0812542
$546$		0			0
$547$	−26.9425			−1.15198			−0.575990	−	0.817457i	$-0.695383\pi$
$547$	−26.9425			−1.15198			−0.575990	+	0.817457i	$0.695383\pi$
$548$	0.0154781	+	0.0577651i	0.000661192	+	0.00246760i
$549$		0			0
$550$	2.20277	−	1.27177i	0.0939265	−	0.0542285i
$551$	19.1905	+	19.1905i	0.817543	+	0.817543i
$552$		0			0
$553$	−5.83347	+	23.2672i	−0.248065	+	0.989421i
$554$	−0.822003	−	0.822003i	−0.0349236	−	0.0349236i
$555$		0			0
$556$	−3.21506	+	5.56864i	−0.136349	+	0.236163i
$557$	−29.5799	+	7.92591i	−1.25334	+	0.335832i	−0.823626	−	0.567133i	$-0.808052\pi$
$557$	−29.5799	+	7.92591i	−1.25334	+	0.335832i	−0.429715	+	0.902965i	$0.641386\pi$
$558$		0			0
$559$	−27.3704	−	1.61400i	−1.15765	−	0.0682651i
$560$	0.243299	+	15.0672i	0.0102812	+	0.636705i
$561$		0			0
$562$	1.70035	−	2.94510i	0.0717250	−	0.124231i
$563$	−7.49329	−	12.9788i	−0.315804	−	0.546989i	0.663804	−	0.747907i	$-0.268941\pi$
$563$	−7.49329	−	12.9788i	−0.315804	−	0.546989i	−0.979608	+	0.200917i	$0.935608\pi$
$564$		0			0
$565$	4.94722	−	18.4633i	0.208131	−	0.776756i
$566$	0.877680	+	0.235174i	0.0368917	+	0.00988509i
$567$		0			0
$568$	−2.40258	−	4.16138i	−0.100810	−	0.174608i
$569$	−6.07156	−	3.50542i	−0.254533	−	0.146955i	0.367305	−	0.930101i	$-0.380280\pi$
$569$	−6.07156	−	3.50542i	−0.254533	−	0.146955i	−0.621838	+	0.783146i	$0.713614\pi$
$570$		0			0
$571$		−	0.237494i		−	0.00993882i	−0.999988	−	0.00496941i	$-0.998418\pi$
$571$		−	0.237494i		−	0.00993882i	0.999988	−	0.00496941i	$-0.00158182\pi$
$572$	−29.7646	+	6.12345i	−1.24452	+	0.256034i
$573$		0			0
$574$	0.811447	−	0.231531i	0.0338692	−	0.00966393i
$575$	2.82848	−	4.89908i	0.117956	−	0.204306i
$576$		0			0
$577$	3.41695	+	3.41695i	0.142250	+	0.142250i	0.774645	−	0.632396i	$-0.217928\pi$
$577$	3.41695	+	3.41695i	0.142250	+	0.142250i	−0.632396	+	0.774645i	$0.717928\pi$
$578$	8.69131	+	2.32883i	0.361511	+	0.0968665i
$579$		0			0
$580$	11.3107	−	11.3107i	0.469649	−	0.469649i
$581$	−3.62932	+	2.17426i	−0.150570	+	0.0902037i
$582$		0			0
$583$	−55.0253	+	14.7440i	−2.27891	+	0.610633i
$584$	10.0392			0.415424
$585$		0			0
$586$		−	4.93076i		−	0.203688i
$587$	−7.16064	+	1.91869i	−0.295551	+	0.0791927i	−0.403548	−	0.914959i	$-0.632223\pi$
$587$	−7.16064	+	1.91869i	−0.295551	+	0.0791927i	0.107997	+	0.994151i	$0.465556\pi$
$588$		0			0
$589$	6.81931	−	3.93713i	0.280985	−	0.162227i
$590$	−2.19810	+	2.19810i	−0.0904945	+	0.0904945i
$591$		0			0
$592$	−2.80357	+	10.4631i	−0.115226	+	0.430030i
$593$	20.9219	−	20.9219i	0.859161	−	0.859161i	−0.132078	−	0.991239i	$-0.542165\pi$
$593$	20.9219	−	20.9219i	0.859161	−	0.859161i	0.991239	+	0.132078i	$0.0421649\pi$
$594$		0			0
$595$	−26.9166	−	14.9661i	−1.10347	−	0.613551i
$596$	−8.82700	+	2.36519i	−0.361568	+	0.0968818i
$597$		0			0
$598$	1.29306	−	1.14905i	0.0528771	−	0.0469882i
$599$	35.0083			1.43040			0.715199	−	0.698920i	$-0.246336\pi$
$599$	35.0083			1.43040			0.715199	+	0.698920i	$0.246336\pi$
$600$		0			0
$601$	25.0031	+	14.4355i	1.01990	+	0.588838i	0.914074	−	0.405547i	$-0.132919\pi$
$601$	25.0031	+	14.4355i	1.01990	+	0.588838i	0.105823	+	0.994385i	$0.466252\pi$
$602$	−3.85589	+	2.31000i	−0.157154	+	0.0941485i
$603$		0			0
$604$	−12.6526	−	3.39025i	−0.514826	−	0.137947i
$605$	11.4084	+	3.05688i	0.463819	+	0.124280i
$606$		0			0
$607$	−22.1458	+	12.7859i	−0.898871	+	0.518964i	−0.876834	−	0.480793i	$-0.840349\pi$
$607$	−22.1458	+	12.7859i	−0.898871	+	0.518964i	−0.0220376	+	0.999757i	$0.507015\pi$
$608$	6.59615	−	11.4249i	0.267509	−	0.463339i
$609$		0			0
$610$		−	4.04291i		−	0.163693i
$611$	26.2889	−	5.40839i	1.06353	−	0.218800i
$612$		0			0
$613$	−6.84627	−	25.5506i	−0.276518	−	1.03198i	−0.954817	−	0.297194i	$-0.903949\pi$
$613$	−6.84627	−	25.5506i	−0.276518	−	1.03198i	0.678299	−	0.734786i	$-0.262718\pi$
$614$	−2.62767	−	1.51708i	−0.106044	−	0.0612245i
$615$		0			0
$616$	−7.01933	+	7.24974i	−0.282817	+	0.292100i
$617$	41.2766	+	11.0600i	1.66173	+	0.445260i	0.962864	−	0.269988i	$-0.0870199\pi$
$617$	41.2766	+	11.0600i	1.66173	+	0.445260i	0.698870	+	0.715249i	$0.253687\pi$
$618$		0			0
$619$	−7.36404	+	7.36404i	−0.295986	+	0.295986i	−0.839439	−	0.543453i	$-0.817116\pi$
$619$	−7.36404	+	7.36404i	−0.295986	+	0.295986i	0.543453	+	0.839439i	$0.317116\pi$
$620$	−2.32050	−	4.01922i	−0.0931935	−	0.161416i
$621$		0			0
$622$	0.937855	+	3.50012i	0.0376046	+	0.140342i
$623$	2.22156	−	0.0358728i	0.0890050	−	0.00143722i
$624$		0			0
$625$	4.88945			0.195578
$626$	−5.22738	+	1.40067i	−0.208928	+	0.0559822i
$627$		0			0
$628$	16.6845	+	28.8983i	0.665782	+	1.15317i
$629$	−15.6541	−	15.6541i	−0.624169	−	0.624169i
$630$		0			0
$631$	−3.47681	+	12.9756i	−0.138410	+	0.516552i	0.861551	+	0.507671i	$0.169494\pi$
$631$	−3.47681	+	12.9756i	−0.138410	+	0.516552i	−0.999961	+	0.00888079i	$0.997173\pi$
$632$	−5.65758	−	5.65758i	−0.225046	−	0.225046i
$633$		0			0
$634$	−5.17644	−	2.98862i	−0.205583	−	0.118693i
$635$	2.53434	+	9.45828i	0.100572	+	0.375340i
$636$		0			0
$637$	−12.0334	−	22.1855i	−0.476782	−	0.879021i
$638$	5.14927			0.203862
$639$		0			0
$640$	−8.93765	−	5.16016i	−0.353292	−	0.203973i
$641$	9.03607	−	5.21698i	0.356903	−	0.206058i	−0.310818	−	0.950469i	$-0.600603\pi$
$641$	9.03607	−	5.21698i	0.356903	−	0.206058i	0.667722	+	0.744411i	$0.267270\pi$
$642$		0			0
$643$	2.33827	−	8.72656i	0.0922125	−	0.344142i	−0.904370	−	0.426750i	$-0.859658\pi$
$643$	2.33827	−	8.72656i	0.0922125	−	0.344142i	0.996582	+	0.0826083i	$0.0263251\pi$
$644$	−2.69448	+	10.7471i	−0.106177	+	0.423495i
$645$		0			0
$646$	4.30225	+	7.45171i	0.169270	+	0.293184i
$647$	−4.86550	+	8.42729i	−0.191283	+	0.331311i	−0.945676	−	0.325112i	$-0.894598\pi$
$647$	−4.86550	+	8.42729i	−0.191283	+	0.331311i	0.754393	+	0.656423i	$0.227931\pi$
$648$		0			0
$649$	39.0974			1.53471
$650$	−2.01376	−	0.668905i	−0.0789863	−	0.0262366i
$651$		0			0
$652$	−9.85322	−	36.7727i	−0.385882	−	1.44013i
$653$	−19.3917	+	33.5874i	−0.758855	+	1.31437i	0.184580	+	0.982817i	$0.440907\pi$
$653$	−19.3917	+	33.5874i	−0.758855	+	1.31437i	−0.943435	+	0.331557i	$0.892426\pi$
$654$		0			0
$655$	4.06217	−	4.06217i	0.158722	−	0.158722i
$656$	1.36821	−	5.10623i	0.0534196	−	0.199365i
$657$		0			0
$658$	3.06066	−	3.16113i	0.119317	−	0.123233i
$659$	−16.5452	−	28.6571i	−0.644509	−	1.11632i	−0.984415	−	0.175863i	$-0.943728\pi$
$659$	−16.5452	−	28.6571i	−0.644509	−	1.11632i	0.339905	−	0.940460i	$-0.389605\pi$
$660$		0			0
$661$	−3.34087	−	12.4683i	−0.129945	−	0.484960i	0.870023	−	0.493011i	$-0.164104\pi$
$661$	−3.34087	−	12.4683i	−0.129945	−	0.484960i	−0.999968	+	0.00805129i	$0.997437\pi$
$662$		−	3.22860i		−	0.125483i
$663$		0			0
$664$		−	1.41118i		−	0.0547645i
$665$	−5.68229	−	19.9147i	−0.220350	−	0.772260i
$666$		0			0
$667$	9.91794	−	5.72612i	0.384024	−	0.221716i
$668$	−19.5194	−	19.5194i	−0.755229	−	0.755229i
$669$		0			0
$670$	−1.64329	−	0.440319i	−0.0634859	−	0.0170110i
$671$	−35.9554	+	35.9554i	−1.38804	+	1.38804i
$672$		0			0
$673$	22.5255	+	13.0051i	0.868295	+	0.501310i	0.866781	−	0.498689i	$-0.166185\pi$
$673$	22.5255	+	13.0051i	0.868295	+	0.501310i	0.00151340	+	0.999999i	$0.499518\pi$
$674$	−1.11250	+	0.298092i	−0.0428517	+	0.0114821i
$675$		0			0
$676$	20.3128	+	15.1680i	0.781262	+	0.583386i
$677$			41.0161i			1.57638i	0.615434	+	0.788188i	$0.288981\pi$
$677$			41.0161i			1.57638i	−0.615434	+	0.788188i	$0.711019\pi$
$678$		0			0
$679$	38.9434	+	21.6533i	1.49451	+	0.830976i
$680$	8.89631	−	5.13629i	0.341158	−	0.196968i
$681$		0			0
$682$	0.386679	−	1.44311i	0.0148067	−	0.0552594i
$683$	−8.69145	+	32.4369i	−0.332569	+	1.24116i	0.573912	+	0.818917i	$0.305425\pi$
$683$	−8.69145	+	32.4369i	−0.332569	+	1.24116i	−0.906481	+	0.422247i	$0.861241\pi$
$684$		0			0
$685$	−0.0408491	+	0.0235842i	−0.00156076	+	0.000901107i
$686$	−3.67927	−	1.89289i	−0.140475	−	0.0722710i
$687$		0			0
$688$			28.1591i			1.07356i
$689$	39.6870	+	26.1437i	1.51195	+	0.995994i
$690$		0			0
$691$	−33.3878	+	8.94624i	−1.27013	+	0.340331i	−0.830082	−	0.557642i	$-0.811706\pi$
$691$	−33.3878	+	8.94624i	−1.27013	+	0.340331i	−0.440051	+	0.897973i	$0.645040\pi$
$692$	−32.6305	−	18.8392i	−1.24043	−	0.716160i
$693$		0			0
$694$	−3.76020	+	3.76020i	−0.142735	+	0.142735i
$695$	−4.89884	−	1.31264i	−0.185823	−	0.0497912i
$696$		0			0
$697$	7.63956	+	7.63956i	0.289369	+	0.289369i
$698$	−2.36628	+	1.36617i	−0.0895651	+	0.0517104i
$699$		0			0
$700$	13.0697	−	3.72918i	0.493987	−	0.140950i
$701$		−	4.79362i		−	0.181053i	−0.995894	−	0.0905263i	$-0.971145\pi$
$701$		−	4.79362i		−	0.181053i	0.995894	−	0.0905263i	$-0.0288549\pi$
$702$		0			0
$703$		−	14.8867i		−	0.561461i
$704$	7.63649	+	28.4998i	0.287811	+	1.07413i
$705$		0			0
$706$	−1.91032	−	3.30876i	−0.0718957	−	0.124527i
$707$	−20.8549	−	20.1921i	−0.784329	−	0.759402i
$708$		0			0
$709$	2.76549	−	10.3209i	0.103860	−	0.387611i	−0.894353	−	0.447361i	$-0.852364\pi$
$709$	2.76549	−	10.3209i	0.103860	−	0.387611i	0.998213	+	0.0597505i	$0.0190305\pi$
$710$	1.32303	−	1.32303i	0.0496524	−	0.0496524i
$711$		0			0
$712$	−0.370552	+	0.641814i	−0.0138870	+	0.0240530i
$713$	−0.859994	−	3.20954i	−0.0322070	−	0.120198i
$714$		0			0
$715$	−10.7413	−	21.4263i	−0.401703	−	0.801300i
$716$	−8.01890			−0.299680
$717$		0			0
$718$	−2.30976	+	4.00062i	−0.0861995	+	0.149302i
$719$	−14.9272	−	25.8547i	−0.556690	−	0.964216i	−0.997770	−	0.0667479i	$-0.978738\pi$
$719$	−14.9272	−	25.8547i	−0.556690	−	0.964216i	0.441080	−	0.897468i	$-0.354596\pi$
$720$		0			0
$721$	−3.02556	+	12.0676i	−0.112678	+	0.449423i
$722$	−0.398890	+	1.48868i	−0.0148452	+	0.0554029i
$723$		0			0
$724$	−3.54065	+	2.04420i	−0.131587	+	0.0759720i
$725$	−12.1661	−	7.02412i	−0.451839	−	0.260869i
$726$		0			0
$727$	−41.2241			−1.52892			−0.764459	−	0.644672i	$-0.776994\pi$
$727$	−41.2241			−1.52892			−0.764459	+	0.644672i	$0.776994\pi$
$728$	8.41078	+	0.359819i	0.311724	+	0.0133358i
$729$		0			0
$730$	1.01175	+	3.77589i	0.0374464	+	0.139752i
$731$	−49.8398	−	28.7750i	−1.84339	−	1.06428i
$732$		0			0
$733$	−14.3345	−	14.3345i	−0.529456	−	0.529456i	0.390954	−	0.920410i	$-0.372145\pi$
$733$	−14.3345	−	14.3345i	−0.529456	−	0.529456i	−0.920410	+	0.390954i	$0.872145\pi$
$734$	0.0267847	−	0.0999617i	0.000988640	−	0.00368965i
$735$		0			0
$736$	−3.93636	−	3.93636i	−0.145096	−	0.145096i
$737$	10.6986	+	18.5305i	0.394087	+	0.682579i
$738$		0			0
$739$	24.4381	−	6.54818i	0.898972	−	0.240879i	0.220397	−	0.975410i	$-0.429265\pi$
$739$	24.4381	−	6.54818i	0.898972	−	0.240879i	0.678575	+	0.734532i	$0.262598\pi$
$740$	−8.77402			−0.322539
$741$		0			0
$742$	7.79007	−	0.125791i	0.285982	−	0.00461793i
$743$	−10.9162	−	40.7397i	−0.400476	−	1.49460i	−0.812250	−	0.583310i	$-0.801757\pi$
$743$	−10.9162	−	40.7397i	−0.400476	−	1.49460i	0.411774	−	0.911286i	$-0.364909\pi$
$744$		0			0
$745$	−3.60387	−	6.24209i	−0.132036	−	0.228693i
$746$	−0.110241	+	0.110241i	−0.00403621	+	0.00403621i
$747$		0			0
$748$	−61.6106	−	16.5085i	−2.25271	−	0.603611i
$749$	−24.9120	−	24.1203i	−0.910265	−	0.881335i
$750$		0			0
$751$	−6.23654	−	3.60067i	−0.227574	−	0.131390i	0.381878	−	0.924213i	$-0.375277\pi$
$751$	−6.23654	−	3.60067i	−0.227574	−	0.131390i	−0.609453	+	0.792823i	$0.708611\pi$
$752$	−7.13433	−	26.6257i	−0.260162	−	0.970938i
$753$		0			0
$754$	−2.85350	−	3.21112i	−0.103918	−	0.116942i
$755$		−	10.3315i		−	0.376004i
$756$		0			0
$757$	−11.5449	+	19.9964i	−0.419607	+	0.726780i	−0.995900	−	0.0904628i	$-0.971165\pi$
$757$	−11.5449	+	19.9964i	−0.419607	+	0.726780i	0.576293	+	0.817243i	$0.304499\pi$
$758$	1.38385	−	0.798968i	0.0502638	−	0.0290198i
$759$		0			0
$760$	6.67233	+	1.78785i	0.242031	+	0.0648520i
$761$	5.76843	+	1.54565i	0.209105	+	0.0560296i	0.361851	−	0.932236i	$-0.382145\pi$
$761$	5.76843	+	1.54565i	0.209105	+	0.0560296i	−0.152746	+	0.988266i	$0.548812\pi$
$762$		0			0
$763$	−1.67688	−	2.79908i	−0.0607071	−	0.101333i
$764$	−14.2562	−	8.23082i	−0.515771	−	0.297780i
$765$		0			0
$766$	0.428649			0.0154877
$767$	−21.6660	−	24.3814i	−0.782315	−	0.880362i
$768$		0			0
$769$	32.9326	−	8.82426i	1.18758	−	0.318211i	0.389650	−	0.920963i	$-0.372596\pi$
$769$	32.9326	−	8.82426i	1.18758	−	0.318211i	0.797929	+	0.602752i	$0.205929\pi$
$770$	−3.43415	−	1.90945i	−0.123758	−	0.0688119i
$771$		0			0
$772$	2.80726	−	2.80726i	0.101036	−	0.101036i
$773$	−0.0200118	+	0.0746850i	−0.000719774	+	0.00268623i	−0.966285	−	0.257476i	$-0.917109\pi$
$773$	−0.0200118	+	0.0746850i	−0.000719774	+	0.00268623i	0.965565	+	0.260162i	$0.0837759\pi$
$774$		0			0
$775$	−2.88214	+	2.88214i	−0.103530	+	0.103530i
$776$	−12.8713	+	7.43127i	−0.462054	+	0.266767i
$777$		0			0
$778$	−1.33164	+	0.356813i	−0.0477417	+	0.0127924i
$779$			7.26504i			0.260297i
$780$		0			0
$781$	−23.5326			−0.842063
$782$	3.50718	−	0.939747i	0.125417	−	0.0336053i
$783$		0			0
$784$	−22.0182	+	13.6786i	−0.786363	+	0.488521i
$785$	−18.6105	+	18.6105i	−0.664236	+	0.664236i
$786$		0			0
$787$	13.7109	+	3.67383i	0.488742	+	0.130958i	0.494770	−	0.869024i	$-0.335252\pi$
$787$	13.7109	+	3.67383i	0.488742	+	0.130958i	−0.00602847	+	0.999982i	$0.501919\pi$
$788$	−18.4866	−	18.4866i	−0.658558	−	0.658558i
$789$		0			0
$790$	1.55773	−	2.69807i	0.0554216	−	0.0959931i
$791$	31.6179	−	9.02159i	1.12420	−	0.320771i
$792$		0			0
$793$	42.3469	+	2.49715i	1.50378	+	0.0886765i
$794$		−	6.96753i		−	0.247268i
$795$		0			0
$796$	−12.7277	−	7.34835i	−0.451122	−	0.260455i
$797$	−4.85453	−	8.40830i	−0.171956	−	0.297837i	0.767147	−	0.641471i	$-0.221676\pi$
$797$	−4.85453	−	8.40830i	−0.171956	−	0.297837i	−0.939104	+	0.343634i	$0.888342\pi$
$798$		0			0
$799$	54.4161	+	14.5808i	1.92510	+	0.515830i
$800$	−1.76741	+	6.59606i	−0.0624873	+	0.233206i
$801$		0			0
$802$	2.80472	+	4.85792i	0.0990382	+	0.171539i
$803$	24.5827	−	42.5786i	0.867506	−	1.50256i
$804$		0			0
$805$	−8.73782	+	0.141095i	−0.307968	+	0.00497293i
$806$	−1.11421	+	0.558569i	−0.0392464	+	0.0196748i
$807$		0			0
$808$	9.35256	−	2.50601i	0.329022	−	0.0881612i
$809$	−22.8046	+	39.4988i	−0.801768	+	1.38870i	0.116683	+	0.993169i	$0.462774\pi$
$809$	−22.8046	+	39.4988i	−0.801768	+	1.38870i	−0.918451	+	0.395534i	$0.870559\pi$
$810$		0			0
$811$	−6.90491	−	6.90491i	−0.242464	−	0.242464i	0.575405	−	0.817869i	$-0.304845\pi$
$811$	−6.90491	−	6.90491i	−0.242464	−	0.242464i	−0.817869	+	0.575405i	$0.804845\pi$
$812$	26.6888	+	6.69134i	0.936595	+	0.234820i
$813$		0			0
$814$	−1.99722	−	1.99722i	−0.0700027	−	0.0700027i
$815$	26.0042	−	15.0135i	0.910886	−	0.525900i
$816$		0			0
$817$	−10.0161	−	37.3804i	−0.350417	−	1.30778i
$818$	3.38761			0.118445
$819$		0			0
$820$	4.28193			0.149531
$821$	−4.30181	−	16.0546i	−0.150134	−	0.560308i	−0.999473	−	0.0324603i	$-0.989666\pi$
$821$	−4.30181	−	16.0546i	−0.150134	−	0.560308i	0.849339	−	0.527848i	$-0.177001\pi$
$822$		0			0
$823$	8.40900	−	4.85494i	0.293119	−	0.169233i	−0.346228	−	0.938150i	$-0.612538\pi$
$823$	8.40900	−	4.85494i	0.293119	−	0.169233i	0.639348	+	0.768918i	$0.279204\pi$
$824$	−2.93433	−	2.93433i	−0.102222	−	0.102222i
$825$		0			0
$826$	−5.18669	−	1.30039i	−0.180468	−	0.0452463i
$827$	23.2961	+	23.2961i	0.810086	+	0.810086i	0.984647	−	0.174560i	$-0.0558503\pi$
$827$	23.2961	+	23.2961i	0.810086	+	0.810086i	−0.174560	+	0.984647i	$0.555850\pi$
$828$		0			0
$829$	−14.7204	+	25.4965i	−0.511261	+	0.885531i	0.488653	+	0.872478i	$0.337488\pi$
$829$	−14.7204	+	25.4965i	−0.511261	+	0.885531i	−0.999915	+	0.0130527i	$0.995845\pi$
$830$	0.530767	−	0.142219i	0.0184232	−	0.00493648i
$831$		0			0
$832$	13.5408	−	20.5555i	0.469444	−	0.712633i
$833$	−1.71043	−	52.9485i	−0.0592628	−	1.83456i
$834$		0			0
$835$	10.8863	−	18.8557i	0.376738	−	0.652529i
$836$	−21.4455	−	37.1447i	−0.741708	−	1.28468i
$837$		0			0
$838$	0.266506	−	0.994613i	0.00920629	−	0.0343583i
$839$	−18.5876	−	4.98054i	−0.641716	−	0.171947i	−0.0767354	−	0.997051i	$-0.524450\pi$
$839$	−18.5876	−	4.98054i	−0.641716	−	0.171947i	−0.564981	+	0.825104i	$0.691116\pi$
$840$		0			0
$841$	0.280024	+	0.485016i	0.00965600	+	0.0167247i
$842$	−3.45960	−	1.99740i	−0.119226	−	0.0688350i
$843$		0			0
$844$		−	33.0856i		−	1.13885i
$845$	−7.40925	+	18.5719i	−0.254886	+	0.638892i
$846$		0			0
$847$	5.57443	+	19.5367i	0.191540	+	0.671289i
$848$	24.4044	−	42.2697i	0.838051	−	1.45155i
$849$		0			0
$850$	−3.14942	−	3.14942i	−0.108024	−	0.108024i
$851$	−6.06779	−	1.62586i	−0.208001	−	0.0557337i
$852$		0			0
$853$	14.9327	−	14.9327i	0.511287	−	0.511287i	−0.403634	−	0.914921i	$-0.632253\pi$
$853$	14.9327	−	14.9327i	0.511287	−	0.511287i	0.914921	+	0.403634i	$0.132253\pi$
$854$	5.96575	−	3.57398i	0.204144	−	0.122299i
$855$		0			0
$856$	11.1720	−	2.99353i	0.381851	−	0.102317i
$857$	5.36310			0.183200			0.0916001	−	0.995796i	$-0.470802\pi$
$857$	5.36310			0.183200			0.0916001	+	0.995796i	$0.470802\pi$
$858$		0			0
$859$		−	21.1000i		−	0.719923i	−0.932967	−	0.359962i	$-0.882790\pi$
$859$		−	21.1000i		−	0.719923i	0.932967	−	0.359962i	$-0.117210\pi$
$860$	−22.0316	+	5.90334i	−0.751270	+	0.201302i
$861$		0			0
$862$	−1.58816	+	0.916923i	−0.0540929	+	0.0312305i
$863$	−0.437792	+	0.437792i	−0.0149026	+	0.0149026i	−0.714519	−	0.699616i	$-0.753354\pi$
$863$	−0.437792	+	0.437792i	−0.0149026	+	0.0149026i	0.699616	+	0.714519i	$0.253354\pi$
$864$		0			0
$865$	7.69166	−	28.7056i	0.261524	−	0.976021i
$866$	−2.74176	+	2.74176i	−0.0931690	+	0.0931690i
$867$		0			0
$868$	3.87945	−	6.97718i	0.131677	−	0.236821i
$869$	−37.8488	+	10.1416i	−1.28393	+	0.344029i
$870$		0			0
$871$	5.62706	−	16.9405i	0.190666	−	0.574006i
$872$	1.08836			0.0368565
$873$		0			0
$874$	2.11446	+	1.22079i	0.0715228	+	0.0412937i
$875$	15.9659	+	26.6505i	0.539745	+	0.900953i
$876$		0			0
$877$	−0.601435	−	0.161154i	−0.0203090	−	0.00544178i	0.248650	−	0.968593i	$-0.420013\pi$
$877$	−0.601435	−	0.161154i	−0.0203090	−	0.00544178i	−0.268959	+	0.963152i	$0.586680\pi$
$878$	−3.36192	−	0.900824i	−0.113459	−	0.0304013i
$879$		0			0
$880$	−21.3180	+	12.3079i	−0.718628	+	0.414900i
$881$	−9.21121	+	15.9543i	−0.310333	+	0.537513i	−0.978435	−	0.206557i	$-0.933774\pi$
$881$	−9.21121	+	15.9543i	−0.310333	+	0.537513i	0.668101	+	0.744070i	$0.267107\pi$
$882$		0			0
$883$			15.8935i			0.534859i	0.963577	+	0.267429i	$0.0861742\pi$
$883$			15.8935i			0.534859i	−0.963577	+	0.267429i	$0.913826\pi$
$884$	23.8470	+	47.5691i	0.802062	+	1.59992i
$885$		0			0
$886$	−1.73631	−	6.47998i	−0.0583324	−	0.217699i
$887$	−29.3404	−	16.9397i	−0.985154	−	0.568779i	−0.0813318	−	0.996687i	$-0.525917\pi$
$887$	−29.3404	−	16.9397i	−0.985154	−	0.568779i	−0.903822	+	0.427908i	$0.859251\pi$
$888$		0			0
$889$	−11.7163	+	12.1009i	−0.392953	+	0.405852i
$890$	−0.278740	−	0.0746883i	−0.00934340	−	0.00250356i
$891$		0			0
$892$	17.4013	−	17.4013i	0.582638	−	0.582638i
$893$	18.9412	+	32.8072i	0.633844	+	1.09785i
$894$		0			0
$895$	−1.63697	−	6.10926i	−0.0547179	−	0.204210i
$896$	−0.286621	−	17.7501i	−0.00957535	−	0.592989i
$897$		0			0
$898$	1.55296			0.0518231
$899$	−7.97042	+	2.13567i	−0.265828	+	0.0712285i
$900$		0			0
$901$	49.8764	+	86.3885i	1.66162	+	2.87802i
$902$	0.974693	+	0.974693i	0.0324537	+	0.0324537i
$903$		0			0
$904$	−2.83850	+	10.5934i	−0.0944073	+	0.352333i
$905$	−2.28017	−	2.28017i	−0.0757956	−	0.0757956i
$906$		0			0
$907$	37.0978	+	21.4184i	1.23181	+	0.711187i	0.967407	−	0.253225i	$-0.0814914\pi$
$907$	37.0978	+	21.4184i	1.23181	+	0.711187i	0.264404	+	0.964412i	$0.414825\pi$
$908$	9.93007	+	37.0595i	0.329541	+	1.22986i
$909$		0			0
$910$	0.712304	+	3.19969i	0.0236127	+	0.106069i
$911$	9.59124			0.317772			0.158886	−	0.987297i	$-0.449210\pi$
$911$	9.59124			0.317772			0.158886	+	0.987297i	$0.449210\pi$
$912$		0			0
$913$	−5.98517	−	3.45554i	−0.198080	−	0.114362i
$914$	4.30973	−	2.48822i	0.142553	−	0.0823032i
$915$		0			0
$916$	−14.1504	+	52.8101i	−0.467543	+	1.74489i
$917$	9.58517	+	2.40316i	0.316530	+	0.0793594i
$918$		0			0
$919$	−3.74479	−	6.48617i	−0.123529	−	0.213959i	0.797628	−	0.603150i	$-0.206088\pi$
$919$	−3.74479	−	6.48617i	−0.123529	−	0.213959i	−0.921157	+	0.389191i	$0.872755\pi$
$920$	1.45745	−	2.52438i	0.0480507	−	0.0832262i
$921$		0			0
$922$	2.60431			0.0857683
$923$	13.0407	+	14.6751i	0.429240	+	0.483036i
$924$		0			0
$925$	1.99441	+	7.44323i	0.0655757	+	0.244732i
$926$	2.63462	−	4.56330i	0.0865791	−	0.149959i
$927$		0			0
$928$	−9.77536	+	9.77536i	−0.320892	+	0.320892i
$929$	9.80192	−	36.5812i	0.321590	−	1.20019i	−0.596105	−	0.802907i	$-0.703286\pi$
$929$	9.80192	−	36.5812i	0.321590	−	1.20019i	0.917695	−	0.397285i	$-0.130048\pi$
$930$		0			0
$931$	24.3631	−	25.9897i	0.798468	−	0.851777i
$932$	−10.6182	−	18.3913i	−0.347811	−	0.602427i
$933$		0			0
$934$	0.984940	+	3.67585i	0.0322282	+	0.120277i
$935$		−	50.3086i		−	1.64527i
$936$		0			0
$937$			9.27559i			0.303020i	0.988456	+	0.151510i	$0.0484136\pi$
$937$			9.27559i			0.303020i	−0.988456	+	0.151510i	$0.951586\pi$
$938$	−0.802951	−	2.81410i	−0.0262173	−	0.0918837i
$939$		0			0
$940$	19.3362	−	11.1637i	0.630676	−	0.364121i
$941$	38.7691	+	38.7691i	1.26384	+	1.26384i	0.949219	+	0.314617i	$0.101876\pi$
$941$	38.7691	+	38.7691i	1.26384	+	1.26384i	0.314617	+	0.949219i	$0.398124\pi$
$942$		0			0
$943$	2.96122	+	0.793458i	0.0964307	+	0.0258385i
$944$	−23.6872	+	23.6872i	−0.770951	+	0.770951i
$945$		0			0
$946$	−6.35881	−	3.67126i	−0.206743	−	0.119363i
$947$	−50.1290	+	13.4320i	−1.62898	+	0.436483i	−0.953621	−	0.301011i	$-0.902676\pi$
$947$	−50.1290	+	13.4320i	−1.62898	+	0.436483i	−0.675354	+	0.737493i	$0.736009\pi$
$948$		0			0
$949$	−40.1749	+	8.26517i	−1.30413	+	0.268299i
$950$		−	2.99502i		−	0.0971714i
$951$		0			0
$952$	15.4436	+	8.58693i	0.500530	+	0.278304i
$953$	−12.2620	+	7.07949i	−0.397206	+	0.229327i	−0.685278	−	0.728282i	$-0.740319\pi$
$953$	−12.2620	+	7.07949i	−0.397206	+	0.229327i	0.288072	+	0.957609i	$0.406986\pi$
$954$		0			0
$955$	3.36046	−	12.5414i	0.108742	−	0.405831i
$956$	7.16655	−	26.7459i	0.231783	−	0.865026i
$957$		0			0
$958$	6.49752	−	3.75134i	0.209925	−	0.121200i
$959$	−0.0709121	−	0.0394285i	−0.00228987	−	0.00127321i
$960$		0			0
$961$		−	28.6059i		−	0.922770i
$962$	−0.138710	+	2.35225i	−0.00447219	+	0.0758397i
$963$		0			0
$964$	−29.5058	+	7.90606i	−0.950319	+	0.254637i
$965$	2.71181	+	1.56566i	0.0872962	+	0.0504005i
$966$		0			0
$967$	−24.4554	+	24.4554i	−0.786433	+	0.786433i	−0.980908	−	0.194474i	$-0.937700\pi$
$967$	−24.4554	+	24.4554i	−0.786433	+	0.786433i	0.194474	+	0.980908i	$0.437700\pi$
$968$	−6.54568	−	1.75391i	−0.210386	−	0.0563728i
$969$		0			0
$970$	−4.09219	−	4.09219i	−0.131392	−	0.131392i
$971$	4.45063	−	2.56957i	0.142828	−	0.0824615i	−0.426883	−	0.904307i	$-0.640389\pi$
$971$	4.45063	−	2.56957i	0.142828	−	0.0824615i	0.569711	+	0.821845i	$0.307055\pi$
$972$		0			0
$973$	−2.39369	−	8.38915i	−0.0767381	−	0.268944i
$974$			0.875113i			0.0280404i
$975$		0			0
$976$		−	43.5671i		−	1.39455i
$977$	4.45430	+	16.6237i	0.142506	+	0.531839i	0.999854	+	0.0171015i	$0.00544385\pi$
$977$	4.45430	+	16.6237i	0.142506	+	0.531839i	−0.857348	+	0.514737i	$0.827889\pi$
$978$		0			0
$979$	1.81473	+	3.14320i	0.0579989	+	0.100457i
$980$	−15.3180	−	14.3593i	−0.489316	−	0.458692i
$981$		0			0
$982$	0.410932	−	1.53362i	0.0131134	−	0.0489398i
$983$	13.7631	−	13.7631i	0.438975	−	0.438975i	−0.452692	−	0.891667i	$-0.649536\pi$
$983$	13.7631	−	13.7631i	0.438975	−	0.438975i	0.891667	+	0.452692i	$0.149536\pi$
$984$		0			0
$985$	10.3103	−	17.8580i	0.328514	−	0.569003i
$986$	−2.33372	−	8.70957i	−0.0743209	−	0.277369i
$987$		0			0
$988$	−11.2795	+	33.9575i	−0.358850	+	1.08033i
$989$	−16.3301			−0.519268
$990$		0			0
$991$	−22.9230	+	39.7039i	−0.728174	+	1.26124i	0.229480	+	0.973313i	$0.426298\pi$
$991$	−22.9230	+	39.7039i	−0.728174	+	1.26124i	−0.957654	+	0.287922i	$0.907036\pi$
$992$	2.00552	+	3.47366i	0.0636753	+	0.110289i
$993$		0			0
$994$	3.12185	+	0.782700i	0.0990190	+	0.0248257i
$995$	3.00017	−	11.1968i	0.0951119	−	0.354963i
$996$		0			0
$997$	−26.8851	+	15.5221i	−0.851461	+	0.491591i	−0.861143	−	0.508362i	$-0.830251\pi$
$997$	−26.8851	+	15.5221i	−0.851461	+	0.491591i	0.00968271	+	0.999953i	$0.496918\pi$
$998$	−1.48448	−	0.857066i	−0.0469905	−	0.0271300i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.370.3		32
3.2	odd	2		273.2.by.c.97.6	yes	32
7.6	odd	2		819.2.fm.e.370.3		32
13.11	odd	12		819.2.fm.e.622.3		32
21.20	even	2		273.2.by.d.97.6	yes	32
39.11	even	12		273.2.by.d.76.6	yes	32
91.76	even	12	inner	819.2.fm.f.622.3		32
273.167	odd	12		273.2.by.c.76.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.6	✓	32	273.167	odd	12
273.2.by.c.97.6	yes	32	3.2	odd	2
273.2.by.d.76.6	yes	32	39.11	even	12
273.2.by.d.97.6	yes	32	21.20	even	2
819.2.fm.e.370.3		32	7.6	odd	2
819.2.fm.e.622.3		32	13.11	odd	12
819.2.fm.f.370.3		32	1.1	even	1	trivial
819.2.fm.f.622.3		32	91.76	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.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0578232 - 0.215799i) q^{2} +(1.68883 - 0.975044i) q^{4} +(1.08760 + 1.08760i) q^{5} +(-0.643420 + 2.56632i) q^{7} +(-0.624019 - 0.624019i) q^{8} +O(q^{10})\)	\(q+(-0.0578232 - 0.215799i) q^{2} +(1.68883 - 0.975044i) q^{4} +(1.08760 + 1.08760i) q^{5} +(-0.643420 + 2.56632i) q^{7} +(-0.624019 - 0.624019i) q^{8} +(0.171815 - 0.297592i) q^{10} +(-4.17464 + 1.11859i) q^{11} +(3.01096 + 1.98346i) q^{13} +(0.591015 - 0.00954346i) q^{14} +(1.85151 - 3.20690i) q^{16} +(3.78401 + 6.55410i) q^{17} +(-1.31714 + 4.91565i) q^{19} +(2.89722 + 0.776309i) q^{20} +(0.482783 + 0.836204i) q^{22} +(1.85976 + 1.07373i) q^{23} -2.63425i q^{25} +(0.253926 - 0.764453i) q^{26} +(1.41565 + 4.96143i) q^{28} +(2.66646 - 4.61844i) q^{29} +(-1.09410 - 1.09410i) q^{31} +(-2.50396 - 0.670934i) q^{32} +(1.19557 - 1.19557i) q^{34} +(-3.49092 + 2.09135i) q^{35} +(-2.82556 + 0.757106i) q^{37} +1.13695 q^{38} -1.35737i q^{40} +(1.37894 - 0.369486i) q^{41} +(-6.58558 + 3.80219i) q^{43} +(-5.95956 + 5.95956i) q^{44} +(0.124173 - 0.463422i) q^{46} +(5.26364 - 5.26364i) q^{47} +(-6.17202 - 3.30245i) q^{49} +(-0.568470 + 0.152321i) q^{50} +(7.01895 + 0.413900i) q^{52} +13.1808 q^{53} +(-5.75692 - 3.32376i) q^{55} +(2.00294 - 1.19993i) q^{56} +(-1.15084 - 0.308366i) q^{58} +(-8.73809 - 2.34136i) q^{59} +(10.1891 - 5.88266i) q^{61} +(-0.172842 + 0.299371i) q^{62} -6.82688i q^{64} +(1.11751 + 5.43193i) q^{65} +(-1.28138 - 4.78216i) q^{67} +(12.7811 + 7.37915i) q^{68} +(0.653167 + 0.632408i) q^{70} +(5.25942 + 1.40926i) q^{71} +(-8.04396 + 8.04396i) q^{73} +(0.326766 + 0.565975i) q^{74} +(2.56854 + 9.58594i) q^{76} +(-0.184619 - 11.4332i) q^{77} +9.06635 q^{79} +(5.50153 - 1.47413i) q^{80} +(-0.159469 - 0.276209i) q^{82} +(1.13072 + 1.13072i) q^{83} +(-3.01275 + 11.2437i) q^{85} +(1.20131 + 1.20131i) q^{86} +(3.30308 + 1.90703i) q^{88} +(-0.217351 - 0.811166i) q^{89} +(-7.02751 + 6.45090i) q^{91} +4.18775 q^{92} +(-1.44025 - 0.831529i) q^{94} +(-6.77878 + 3.91373i) q^{95} +(4.35890 - 16.2676i) q^{97} +(-0.355779 + 1.52288i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more