LMFDB - Embedded newform 810.2.s.a.557.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.3
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.82201 - 1.29626i) q^{5} +(0.960666 + 2.06015i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.82201 - 1.29626i) q^{5} +(0.960666 + 2.06015i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.749001 + 2.10689i) q^{10} +(0.117436 + 0.139955i) q^{11} +(-0.983160 - 1.40410i) q^{13} +(0.394725 - 2.23860i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.952636 + 3.55528i) q^{17} +(0.0524828 - 0.0303010i) q^{19} +(0.594918 - 2.15548i) q^{20} +(-0.0159232 - 0.182002i) q^{22} +(-0.314181 - 0.146505i) q^{23} +(1.63944 + 4.72358i) q^{25} +1.71409i q^{26} +(-1.60735 + 1.60735i) q^{28} +(1.26508 + 7.17461i) q^{29} +(2.54000 - 0.924483i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.25887 - 3.45873i) q^{34} +(0.920145 - 4.99889i) q^{35} +(-3.48926 + 0.934944i) q^{37} +(-0.0603714 - 0.00528181i) q^{38} +(-1.72366 + 1.42443i) q^{40} +(11.0821 + 1.95407i) q^{41} +(-0.788032 + 9.00724i) q^{43} +(-0.0913488 + 0.158221i) q^{44} +(0.173330 + 0.300216i) q^{46} +(5.68160 - 2.64937i) q^{47} +(1.17815 - 1.40407i) q^{49} +(1.36638 - 4.80968i) q^{50} +(0.983160 - 1.40410i) q^{52} +(6.90204 + 6.90204i) q^{53} +(-0.0325523 - 0.407225i) q^{55} +(2.23860 - 0.394725i) q^{56} +(3.07890 - 6.60271i) q^{58} +(-8.74898 - 7.34127i) q^{59} +(12.0127 + 4.37226i) q^{61} +(-2.61091 - 0.699590i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-0.0287430 + 3.83271i) q^{65} +(-10.2421 + 7.17156i) q^{67} +(-3.01505 + 2.11116i) q^{68} +(-3.62099 + 3.56708i) q^{70} +(7.52652 + 4.34544i) q^{71} +(-5.44870 - 1.45997i) q^{73} +(3.39450 + 1.23550i) q^{74} +(0.0464238 + 0.0389542i) q^{76} +(-0.175511 + 0.376386i) q^{77} +(15.5249 - 2.73746i) q^{79} +(2.22896 - 0.178176i) q^{80} +(-7.95711 - 7.95711i) q^{82} +(-7.83255 + 11.1860i) q^{83} +(2.87285 - 7.71262i) q^{85} +(5.81186 - 6.92631i) q^{86} +(0.165580 - 0.0772114i) q^{88} +(-5.06451 - 8.77199i) q^{89} +(1.94817 - 3.37433i) q^{91} +(0.0302134 - 0.345341i) q^{92} +(-6.17371 - 1.08859i) q^{94} +(-0.134902 - 0.0128225i) q^{95} +(6.26559 + 0.548168i) q^{97} +(-1.77043 + 0.474385i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−1.82201	−	1.29626i	−0.814828	−	0.579703i
$5$	−1.82201	−	1.29626i	−0.814828	−	0.579703i
$6$		0			0
$7$	0.960666	+	2.06015i	0.363098	+	0.778665i	0.999970	+	0.00769641i	$0.00244987\pi$
$7$	0.960666	+	2.06015i	0.363098	+	0.778665i	−0.636873	+	0.770969i	$0.719772\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$		0			0
$10$	0.749001	+	2.10689i	0.236855	+	0.666258i
$11$	0.117436	+	0.139955i	0.0354082	+	0.0421979i	0.783458	−	0.621445i	$-0.213454\pi$
$11$	0.117436	+	0.139955i	0.0354082	+	0.0421979i	−0.748050	+	0.663643i	$0.769010\pi$
$12$		0			0
$13$	−0.983160	−	1.40410i	−0.272680	−	0.389427i	0.659334	−	0.751850i	$-0.270838\pi$
$13$	−0.983160	−	1.40410i	−0.272680	−	0.389427i	−0.932014	+	0.362423i	$0.881949\pi$
$14$	0.394725	−	2.23860i	0.105495	−	0.598290i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	0.952636	+	3.55528i	0.231048	+	0.862283i	0.979891	+	0.199535i	$0.0639432\pi$
$17$	0.952636	+	3.55528i	0.231048	+	0.862283i	−0.748843	+	0.662748i	$0.769390\pi$
$18$		0			0
$19$	0.0524828	−	0.0303010i	0.0120404	−	0.00695152i	−0.493968	−	0.869480i	$-0.664454\pi$
$19$	0.0524828	−	0.0303010i	0.0120404	−	0.00695152i	0.506008	+	0.862529i	$0.331121\pi$
$20$	0.594918	−	2.15548i	0.133028	−	0.481979i
$21$		0			0
$22$	−0.0159232	−	0.182002i	−0.00339483	−	0.0388031i
$23$	−0.314181	−	0.146505i	−0.0655112	−	0.0305484i	0.389587	−	0.920990i	$-0.372618\pi$
$23$	−0.314181	−	0.146505i	−0.0655112	−	0.0305484i	−0.455098	+	0.890441i	$0.650396\pi$
$24$		0			0
$25$	1.63944	+	4.72358i	0.327888	+	0.944717i
$26$			1.71409i			0.336160i
$27$		0			0
$28$	−1.60735	+	1.60735i	−0.303760	+	0.303760i
$29$	1.26508	+	7.17461i	0.234919	+	1.33229i	0.842784	+	0.538251i	$0.180915\pi$
$29$	1.26508	+	7.17461i	0.234919	+	1.33229i	−0.607865	+	0.794040i	$0.707974\pi$
$30$		0			0
$31$	2.54000	−	0.924483i	0.456197	−	0.166042i	−0.103693	−	0.994609i	$-0.533066\pi$
$31$	2.54000	−	0.924483i	0.456197	−	0.166042i	0.559889	+	0.828567i	$0.310844\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$		0			0
$34$	1.25887	−	3.45873i	0.215895	−	0.593167i
$35$	0.920145	−	4.99889i	0.155533	−	0.844967i
$36$		0			0
$37$	−3.48926	+	0.934944i	−0.573631	+	0.153704i	−0.533961	−	0.845509i	$-0.679297\pi$
$37$	−3.48926	+	0.934944i	−0.573631	+	0.153704i	−0.0396695	+	0.999213i	$0.512630\pi$
$38$	−0.0603714	−	0.00528181i	−0.00979353	−	0.000856823i
$39$		0			0
$40$	−1.72366	+	1.42443i	−0.272534	+	0.225222i
$41$	11.0821	+	1.95407i	1.73073	+	0.305175i	0.948256	−	0.317507i	$-0.102846\pi$
$41$	11.0821	+	1.95407i	1.73073	+	0.305175i	0.782476	+	0.622681i	$0.213957\pi$
$42$		0			0
$43$	−0.788032	+	9.00724i	−0.120174	+	1.37359i	0.661519	+	0.749928i	$0.269912\pi$
$43$	−0.788032	+	9.00724i	−0.120174	+	1.37359i	−0.781693	+	0.623664i	$0.785644\pi$
$44$	−0.0913488	+	0.158221i	−0.0137714	+	0.0238527i
$45$		0			0
$46$	0.173330	+	0.300216i	0.0255561	+	0.0442645i
$47$	5.68160	−	2.64937i	0.828747	−	0.386451i	0.0385141	−	0.999258i	$-0.487738\pi$
$47$	5.68160	−	2.64937i	0.828747	−	0.386451i	0.790232	+	0.612807i	$0.209960\pi$
$48$		0			0
$49$	1.17815	−	1.40407i	0.168308	−	0.200581i
$50$	1.36638	−	4.80968i	0.193236	−	0.680191i
$51$		0			0
$52$	0.983160	−	1.40410i	0.136340	−	0.194713i
$53$	6.90204	+	6.90204i	0.948069	+	0.948069i	0.998717	−	0.0506478i	$-0.0161286\pi$
$53$	6.90204	+	6.90204i	0.948069	+	0.948069i	−0.0506478	+	0.998717i	$0.516129\pi$
$54$		0			0
$55$	−0.0325523	−	0.407225i	−0.00438935	−	0.0549103i
$56$	2.23860	−	0.394725i	0.299145	−	0.0527473i
$57$		0			0
$58$	3.07890	−	6.60271i	0.404279	−	0.866979i
$59$	−8.74898	−	7.34127i	−1.13902	−	0.955752i	−0.139615	−	0.990206i	$-0.544586\pi$
$59$	−8.74898	−	7.34127i	−1.13902	−	0.955752i	−0.999406	+	0.0344540i	$0.989031\pi$
$60$		0			0
$61$	12.0127	+	4.37226i	1.53807	+	0.559810i	0.965580	−	0.260105i	$-0.0837570\pi$
$61$	12.0127	+	4.37226i	1.53807	+	0.559810i	0.572486	+	0.819915i	$0.305979\pi$
$62$	−2.61091	−	0.699590i	−0.331585	−	0.0888480i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−0.0287430	+	3.83271i	−0.00356513	+	0.475389i
$66$		0			0
$67$	−10.2421	+	7.17156i	−1.25127	+	0.876146i	−0.995879	−	0.0906930i	$-0.971092\pi$
$67$	−10.2421	+	7.17156i	−1.25127	+	0.876146i	−0.255387	+	0.966839i	$0.582203\pi$
$68$	−3.01505	+	2.11116i	−0.365629	+	0.256016i
$69$		0			0
$70$	−3.62099	+	3.56708i	−0.432790	+	0.426347i
$71$	7.52652	+	4.34544i	0.893233	+	0.515708i	0.874999	−	0.484125i	$-0.160862\pi$
$71$	7.52652	+	4.34544i	0.893233	+	0.515708i	0.0182346	+	0.999834i	$0.494195\pi$
$72$		0			0
$73$	−5.44870	−	1.45997i	−0.637722	−	0.170877i	−0.0745505	−	0.997217i	$-0.523752\pi$
$73$	−5.44870	−	1.45997i	−0.637722	−	0.170877i	−0.563171	+	0.826340i	$0.690419\pi$
$74$	3.39450	+	1.23550i	0.394602	+	0.143623i
$75$		0			0
$76$	0.0464238	+	0.0389542i	0.00532518	+	0.00446835i
$77$	−0.175511	+	0.376386i	−0.0200014	+	0.0428931i
$78$		0			0
$79$	15.5249	−	2.73746i	1.74669	−	0.307988i	0.793098	−	0.609093i	$-0.208467\pi$
$79$	15.5249	−	2.73746i	1.74669	−	0.307988i	0.953591	+	0.301105i	$0.0973554\pi$
$80$	2.22896	−	0.178176i	0.249205	−	0.0199207i
$81$		0			0
$82$	−7.95711	−	7.95711i	−0.878715	−	0.878715i
$83$	−7.83255	+	11.1860i	−0.859734	+	1.22783i	0.112461	+	0.993656i	$0.464127\pi$
$83$	−7.83255	+	11.1860i	−0.859734	+	1.22783i	−0.972195	+	0.234171i	$0.924762\pi$
$84$		0			0
$85$	2.87285	−	7.71262i	0.311604	−	0.836551i
$86$	5.81186	−	6.92631i	0.626709	−	0.746883i
$87$		0			0
$88$	0.165580	−	0.0772114i	0.0176509	−	0.00823076i
$89$	−5.06451	−	8.77199i	−0.536837	−	0.929829i	−0.999072	−	0.0430716i	$-0.986286\pi$
$89$	−5.06451	−	8.77199i	−0.536837	−	0.929829i	0.462235	−	0.886758i	$-0.347048\pi$
$90$		0			0
$91$	1.94817	−	3.37433i	0.204224	−	0.353726i
$92$	0.0302134	−	0.345341i	0.00314997	−	0.0360043i
$93$		0			0
$94$	−6.17371	−	1.08859i	−0.636770	−	0.112280i
$95$	−0.134902	−	0.0128225i	−0.0138407	−	0.00131556i
$96$		0			0
$97$	6.26559	+	0.548168i	0.636175	+	0.0556581i	0.400681	−	0.916218i	$-0.368774\pi$
$97$	6.26559	+	0.548168i	0.636175	+	0.0556581i	0.235494	+	0.971876i	$0.424329\pi$
$98$	−1.77043	+	0.474385i	−0.178840	+	0.0479201i
$99$		0			0
$100$	−3.87799	+	3.15613i	−0.387799	+	0.315613i
$101$	−3.52837	+	9.69412i	−0.351086	+	0.964601i	0.630936	+	0.775835i	$0.282671\pi$
$101$	−3.52837	+	9.69412i	−0.351086	+	0.964601i	−0.982022	+	0.188766i	$0.939551\pi$
$102$		0			0
$103$	−1.57703	+	0.137973i	−0.155390	+	0.0135948i	−0.164585	−	0.986363i	$-0.552629\pi$
$103$	−1.57703	+	0.137973i	−0.155390	+	0.0135948i	0.00919536	+	0.999958i	$0.497073\pi$
$104$	−1.61072	+	0.586252i	−0.157944	+	0.0574868i
$105$		0			0
$106$	−1.69497	−	9.61267i	−0.164630	−	0.933665i
$107$	5.87254	−	5.87254i	0.567720	−	0.567720i	−0.363769	−	0.931489i	$-0.618510\pi$
$107$	5.87254	−	5.87254i	0.567720	−	0.567720i	0.931489	+	0.363769i	$0.118510\pi$
$108$		0			0
$109$			10.1610i			0.973249i	0.873611	+	0.486624i	$0.161772\pi$
$109$			10.1610i			0.973249i	−0.873611	+	0.486624i	$0.838228\pi$
$110$	−0.206910	+	0.352251i	−0.0197281	+	0.0335858i
$111$		0			0
$112$	−2.06015	−	0.960666i	−0.194666	−	0.0907744i
$113$	0.503761	+	5.75802i	0.0473899	+	0.541669i	0.982367	+	0.186961i	$0.0598640\pi$
$113$	0.503761	+	5.75802i	0.0473899	+	0.541669i	−0.934977	+	0.354707i	$0.884580\pi$
$114$		0			0
$115$	0.382533	+	0.674192i	0.0356714	+	0.0628687i
$116$	−6.30924	+	3.64264i	−0.585799	+	0.338211i
$117$		0			0
$118$	2.95597	+	11.0318i	0.272119	+	1.01556i
$119$	−6.40927	+	5.37802i	−0.587537	+	0.493002i
$120$		0			0
$121$	1.90433	−	10.8000i	0.173121	−	0.981819i
$122$	−7.33239	−	10.4717i	−0.663843	−	0.948066i
$123$		0			0
$124$	1.73746	+	2.07062i	0.156029	+	0.185948i
$125$	3.13589	−	10.7316i	0.280483	−	0.959859i
$126$		0			0
$127$	0.377183	−	1.40767i	0.0334696	−	0.124910i	−0.947170	−	0.320733i	$-0.896071\pi$
$127$	0.377183	−	1.40767i	0.0334696	−	0.124910i	0.980639	+	0.195822i	$0.0627376\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$		0			0
$130$	2.22190	−	3.12308i	0.194873	−	0.273913i
$131$	−1.33948	−	3.68020i	−0.117031	−	0.321541i	0.867322	−	0.497748i	$-0.165839\pi$
$131$	−1.33948	−	3.68020i	−0.117031	−	0.321541i	−0.984353	+	0.176207i	$0.943617\pi$
$132$		0			0
$133$	0.112843	+	0.0790137i	0.00978475	+	0.00685135i
$134$	12.5032			1.08012
$135$		0			0
$136$	3.68070			0.315618
$137$	−10.6010	−	7.42293i	−0.905708	−	0.634183i	0.0251030	−	0.999685i	$-0.492009\pi$
$137$	−10.6010	−	7.42293i	−0.905708	−	0.634183i	−0.930811	+	0.365501i	$0.880898\pi$
$138$		0			0
$139$	4.32708	+	11.8886i	0.367018	+	1.00837i	0.976489	+	0.215566i	$0.0691596\pi$
$139$	4.32708	+	11.8886i	0.367018	+	1.00837i	−0.609471	+	0.792808i	$0.708618\pi$
$140$	5.01213	−	0.845068i	0.423602	−	0.0714213i
$141$		0			0
$142$	−3.67292	−	7.87661i	−0.308225	−	0.660990i
$143$	0.0810517	−	0.302489i	0.00677789	−	0.0252954i
$144$		0			0
$145$	6.99515	−	14.7121i	0.580915	−	1.22177i
$146$	3.62590	+	4.32118i	0.300082	+	0.357624i
$147$		0			0
$148$	−2.07196	−	2.95906i	−0.170314	−	0.243233i
$149$	1.45973	−	8.27853i	0.119586	−	0.678204i	−0.864792	−	0.502131i	$-0.832550\pi$
$149$	1.45973	−	8.27853i	0.119586	−	0.678204i	0.984377	−	0.176073i	$-0.0563393\pi$
$150$		0			0
$151$	3.27104	−	2.74473i	0.266193	−	0.223363i	−0.499915	−	0.866075i	$-0.666635\pi$
$151$	3.27104	−	2.74473i	0.266193	−	0.223363i	0.766108	+	0.642712i	$0.222191\pi$
$152$	−0.0156849	−	0.0585370i	−0.00127222	−	0.00474798i
$153$		0			0
$154$	0.359656	−	0.207648i	0.0289819	−	0.0167327i
$155$	−5.82627	−	1.60807i	−0.467977	−	0.129163i
$156$		0			0
$157$	−0.226813	−	2.59249i	−0.0181017	−	0.206903i	−0.999859	−	0.0167670i	$-0.994663\pi$
$157$	−0.226813	−	2.59249i	−0.0181017	−	0.206903i	0.981758	−	0.190136i	$-0.0608929\pi$
$158$	−14.2874	−	6.66233i	−1.13665	−	0.530026i
$159$		0			0
$160$	−1.92805	−	1.13252i	−0.152426	−	0.0895339i
$161$		−	0.788003i		−	0.0621034i
$162$		0			0
$163$	−11.8927	+	11.8927i	−0.931505	+	0.931505i	−0.997800	−	0.0662955i	$-0.978882\pi$
$163$	−11.8927	+	11.8927i	−0.931505	+	0.931505i	0.0662955	+	0.997800i	$0.478882\pi$
$164$	1.95407	+	11.0821i	0.152587	+	0.865366i
$165$		0			0
$166$	12.8321	−	4.67050i	0.995964	−	0.362501i
$167$	−3.94924	+	0.345514i	−0.305602	+	0.0267367i	−0.238925	−	0.971038i	$-0.576795\pi$
$167$	−3.94924	+	0.345514i	−0.305602	+	0.0267367i	−0.0666764	+	0.997775i	$0.521240\pi$
$168$		0			0
$169$	3.44137	−	9.45510i	0.264721	−	0.727315i
$170$	−6.77708	+	4.67001i	−0.519778	+	0.358174i
$171$		0			0
$172$	−8.73356	+	2.34015i	−0.665928	+	0.178435i
$173$	−20.2246	−	1.76942i	−1.53765	−	0.134527i	−0.713401	−	0.700757i	$-0.752846\pi$
$173$	−20.2246	−	1.76942i	−1.53765	−	0.134527i	−0.824247	+	0.566230i	$0.808401\pi$
$174$		0			0
$175$	−8.15636	+	7.91529i	−0.616563	+	0.598339i
$176$	−0.179922	−	0.0317251i	−0.0135621	−	0.00239137i
$177$		0			0
$178$	−0.882802	+	10.0905i	−0.0661688	+	0.756313i
$179$	−12.9196	+	22.3774i	−0.965657	+	1.67257i	−0.257819	+	0.966193i	$0.583004\pi$
$179$	−12.9196	+	22.3774i	−0.965657	+	1.67257i	−0.707838	+	0.706374i	$0.750329\pi$
$180$		0			0
$181$	−6.85431	−	11.8720i	−0.509477	−	0.882440i	−0.999940	−	0.0109777i	$-0.996506\pi$
$181$	−6.85431	−	11.8720i	−0.509477	−	0.882440i	0.490463	−	0.871462i	$-0.336828\pi$
$182$	−3.53129	+	1.64667i	−0.261756	+	0.122059i
$183$		0			0
$184$	−0.222829	+	0.265557i	−0.0164272	+	0.0195771i
$185$	7.56939	+	2.81950i	0.556513	+	0.207293i
$186$		0			0
$187$	−0.385705	+	0.550843i	−0.0282055	+	0.0402817i
$188$	4.43282	+	4.43282i	0.323297	+	0.323297i
$189$		0			0
$190$	0.103151	+	0.0878802i	0.00748333	+	0.00637550i
$191$	−9.16934	+	1.61680i	−0.663470	+	0.116988i	−0.495235	−	0.868759i	$-0.664918\pi$
$191$	−9.16934	+	1.61680i	−0.663470	+	0.116988i	−0.168236	+	0.985747i	$0.553807\pi$
$192$		0			0
$193$	2.40696	−	5.16173i	0.173256	−	0.371550i	−0.800435	−	0.599419i	$-0.795398\pi$
$193$	2.40696	−	5.16173i	0.173256	−	0.371550i	0.973692	+	0.227870i	$0.0731760\pi$
$194$	−4.81806	−	4.04283i	−0.345916	−	0.290258i
$195$		0			0
$196$	1.72235	+	0.626883i	0.123025	+	0.0447774i
$197$	−4.24946	−	1.13864i	−0.302761	−	0.0811246i	0.104240	−	0.994552i	$-0.466759\pi$
$197$	−4.24946	−	1.13864i	−0.302761	−	0.0811246i	−0.407001	+	0.913428i	$0.633426\pi$
$198$		0			0
$199$	3.30768	+	1.90969i	0.234475	+	0.135374i	0.612635	−	0.790366i	$-0.290110\pi$
$199$	3.30768	+	1.90969i	0.234475	+	0.135374i	−0.378160	+	0.925740i	$0.623443\pi$
$200$	4.98695	−	0.361025i	0.352631	−	0.0255283i
$201$		0			0
$202$	8.45059	−	5.91717i	0.594581	−	0.416330i
$203$	−13.5655	+	9.49866i	−0.952111	+	0.666675i
$204$		0			0
$205$	−17.6587	−	17.9256i	−1.23334	−	1.25198i
$206$	1.37097	+	0.791529i	0.0955199	+	0.0551485i
$207$		0			0
$208$	1.65568	+	0.443638i	0.114801	+	0.0307608i
$209$	0.0104041	+	0.00378679i	0.000719668	+	0.000261938i
$210$		0			0
$211$	−18.9313	−	15.8853i	−1.30329	−	1.09359i	−0.989567	−	0.144071i	$-0.953981\pi$
$211$	−18.9313	−	15.8853i	−1.30329	−	1.09359i	−0.313718	−	0.949516i	$-0.601575\pi$
$212$	−4.12516	+	8.84644i	−0.283317	+	0.607576i
$213$		0			0
$214$	−8.17885	+	1.44215i	−0.559095	+	0.0985835i
$215$	13.1115	−	15.3898i	0.894197	−	1.04958i
$216$		0			0
$217$	4.34467	+	4.34467i	0.294935	+	0.294935i
$218$	5.82812	−	8.32341i	0.394730	−	0.563733i
$219$		0			0
$220$	0.371533	−	0.169868i	0.0250488	−	0.0114525i
$221$	4.05538	−	4.83301i	0.272794	−	0.325103i
$222$		0			0
$223$	−20.3789	+	9.50284i	−1.36467	+	0.636357i	−0.960488	−	0.278320i	$-0.910222\pi$
$223$	−20.3789	+	9.50284i	−1.36467	+	0.636357i	−0.404184	+	0.914678i	$0.632445\pi$
$224$	1.13656	+	1.96859i	0.0759399	+	0.131532i
$225$		0			0
$226$	2.89001	−	5.00564i	0.192240	−	0.332970i
$227$	1.97227	−	22.5431i	0.130904	−	1.49624i	−0.592363	−	0.805671i	$-0.701805\pi$
$227$	1.97227	−	22.5431i	0.130904	−	1.49624i	0.723267	−	0.690569i	$-0.242640\pi$
$228$		0			0
$229$	−9.80853	−	1.72951i	−0.648166	−	0.114289i	−0.160107	−	0.987100i	$-0.551184\pi$
$229$	−9.80853	−	1.72951i	−0.648166	−	0.114289i	−0.488059	+	0.872811i	$0.662295\pi$
$230$	0.0733483	−	0.771678i	0.00483644	−	0.0508829i
$231$		0			0
$232$	7.25757	+	0.634955i	0.476483	+	0.0416868i
$233$	−2.66111	+	0.713042i	−0.174335	+	0.0467129i	−0.344930	−	0.938628i	$-0.612098\pi$
$233$	−2.66111	+	0.713042i	−0.174335	+	0.0467129i	0.170596	+	0.985341i	$0.445431\pi$
$234$		0			0
$235$	−13.7862	−	2.53762i	−0.899312	−	0.165536i
$236$	3.90621	−	10.7322i	0.254272	−	0.698608i
$237$		0			0
$238$	8.33487	−	0.729207i	0.540269	−	0.0472675i
$239$	−18.9197	+	6.88620i	−1.22381	+	0.445431i	−0.871474	−	0.490442i	$-0.836835\pi$
$239$	−18.9197	+	6.88620i	−1.22381	+	0.445431i	−0.352338	+	0.935873i	$0.614613\pi$
$240$		0			0
$241$	3.97916	+	22.5669i	0.256320	+	1.45366i	0.792661	+	0.609663i	$0.208695\pi$
$241$	3.97916	+	22.5669i	0.256320	+	1.45366i	−0.536341	+	0.844001i	$0.680194\pi$
$242$	−7.75457	+	7.75457i	−0.498483	+	0.498483i
$243$		0			0
$244$			12.7836i			0.818388i
$245$	−3.96664	+	1.03104i	−0.253420	+	0.0658707i
$246$		0			0
$247$	−0.0941446	−	0.0439004i	−0.00599028	−	0.00279331i
$248$	−0.235583	−	2.69272i	−0.0149595	−	0.170988i
$249$		0			0
$250$	−8.72414	+	6.99210i	−0.551763	+	0.442219i
$251$	7.41389	−	4.28041i	0.467961	−	0.270177i	−0.247425	−	0.968907i	$-0.579584\pi$
$251$	7.41389	−	4.28041i	0.467961	−	0.270177i	0.715386	+	0.698730i	$0.246251\pi$
$252$		0			0
$253$	−0.0163920	−	0.0611760i	−0.00103056	−	0.00384610i
$254$	−1.11638	+	0.936750i	−0.0700476	+	0.0587769i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.60465	+	3.71983i	0.162474	+	0.232036i	0.892131	−	0.451776i	$-0.149209\pi$
$257$	2.60465	+	3.71983i	0.162474	+	0.232036i	−0.729658	+	0.683813i	$0.760321\pi$
$258$		0			0
$259$	−5.27814	−	6.29024i	−0.327968	−	0.390857i
$260$	−3.61140	+	1.28385i	−0.223969	+	0.0796212i
$261$		0			0
$262$	−1.01364	+	3.78294i	−0.0626227	+	0.233711i
$263$	−3.27861	−	7.03100i	−0.202168	−	0.433550i	0.778917	−	0.627126i	$-0.215769\pi$
$263$	−3.27861	−	7.03100i	−0.202168	−	0.433550i	−0.981085	+	0.193576i	$0.937991\pi$
$264$		0			0
$265$	−3.62878	−	21.5224i	−0.222914	−	1.32211i
$266$	−0.0471154	−	0.129448i	−0.00288883	−	0.00793699i
$267$		0			0
$268$	−10.2421	−	7.17156i	−0.625633	−	0.438073i
$269$	29.4585			1.79611			0.898057	−	0.439879i	$-0.144979\pi$
$269$	29.4585			1.79611			0.898057	+	0.439879i	$0.144979\pi$
$270$		0			0
$271$	8.25703			0.501579			0.250789	−	0.968042i	$-0.419310\pi$
$271$	8.25703			0.501579			0.250789	+	0.968042i	$0.419310\pi$
$272$	−3.01505	−	2.11116i	−0.182814	−	0.128008i
$273$		0			0
$274$	4.42625	+	12.1610i	0.267399	+	0.734674i
$275$	−0.468558	+	0.784165i	−0.0282551	+	0.0472869i
$276$		0			0
$277$	−4.78269	−	10.2565i	−0.287364	−	0.616255i	0.708639	−	0.705571i	$-0.249309\pi$
$277$	−4.78269	−	10.2565i	−0.287364	−	0.616255i	−0.996003	+	0.0893166i	$0.971532\pi$
$278$	3.27446	−	12.2204i	0.196389	−	0.732934i
$279$		0			0
$280$	−4.59041	−	2.18260i	−0.274329	−	0.130435i
$281$	−4.14728	−	4.94254i	−0.247406	−	0.294847i	0.628022	−	0.778196i	$-0.283865\pi$
$281$	−4.14728	−	4.94254i	−0.247406	−	0.294847i	−0.875428	+	0.483349i	$0.839420\pi$
$282$		0			0
$283$	13.3303	+	19.0376i	0.792402	+	1.13167i	0.988520	+	0.151087i	$0.0482774\pi$
$283$	13.3303	+	19.0376i	0.792402	+	1.13167i	−0.196118	+	0.980580i	$0.562834\pi$
$284$	−1.50915	+	8.55884i	−0.0895518	+	0.507874i
$285$		0			0
$286$	−0.239894	+	0.201295i	−0.0141853	+	0.0119028i
$287$	6.62050	+	24.7080i	0.390796	+	1.45847i
$288$		0			0
$289$	2.98990	−	1.72622i	0.175876	−	0.101542i
$290$	−14.1686	+	8.03917i	−0.832008	+	0.472077i
$291$		0			0
$292$	−0.491637	−	5.61944i	−0.0287709	−	0.328853i
$293$	20.1435	+	9.39305i	1.17679	+	0.548748i	0.909839	−	0.414961i	$-0.136205\pi$
$293$	20.1435	+	9.39305i	1.17679	+	0.548748i	0.266954	+	0.963709i	$0.413983\pi$
$294$		0			0
$295$	6.42457	+	24.7168i	0.374053	+	1.43907i
$296$			3.61235i			0.209963i
$297$		0			0
$298$	−5.94411	+	5.94411i	−0.344333	+	0.344333i
$299$	0.103183	+	0.585178i	0.00596721	+	0.0338417i
$300$		0			0
$301$	−19.3134	+	7.02949i	−1.11320	+	0.405173i
$302$	−4.25379	+	0.372158i	−0.244778	+	0.0214153i
$303$		0			0
$304$	−0.0207271	+	0.0569472i	−0.00118878	+	0.00326615i
$305$	−16.2197	−	23.5378i	−0.928735	−	1.34777i
$306$		0			0
$307$	−3.05184	+	0.817737i	−0.174178	+	0.0466707i	−0.344854	−	0.938656i	$-0.612071\pi$
$307$	−3.05184	+	0.817737i	−0.174178	+	0.0466707i	0.170676	+	0.985327i	$0.445405\pi$
$308$	−0.413715	−	0.0361954i	−0.0235736	−	0.00206242i
$309$		0			0
$310$	3.85025	+	4.65906i	0.218679	+	0.264617i
$311$	5.58916	+	0.985519i	0.316932	+	0.0558837i	0.329851	−	0.944033i	$-0.393001\pi$
$311$	5.58916	+	0.985519i	0.316932	+	0.0558837i	−0.0129193	+	0.999917i	$0.504112\pi$
$312$		0			0
$313$	1.78450	−	20.3969i	0.100866	−	1.15290i	−0.762038	−	0.647532i	$-0.775801\pi$
$313$	1.78450	−	20.3969i	0.100866	−	1.15290i	0.862904	−	0.505368i	$-0.168643\pi$
$314$	−1.30120	+	2.25374i	−0.0734307	+	0.127186i
$315$		0			0
$316$	7.88221	+	13.6524i	0.443409	+	0.768006i
$317$	23.4856	−	10.9515i	1.31908	−	0.615098i	0.369679	−	0.929160i	$-0.379468\pi$
$317$	23.4856	−	10.9515i	1.31908	−	0.615098i	0.949402	+	0.314062i	$0.101690\pi$
$318$		0			0
$319$	−0.855554	+	1.01961i	−0.0479018	+	0.0570872i
$320$	0.929779	+	2.03360i	0.0519762	+	0.113681i
$321$		0			0
$322$	−0.451980	+	0.645495i	−0.0251879	+	0.0359720i
$323$	0.157726	+	0.157726i	0.00877609	+	0.00877609i
$324$		0			0
$325$	5.02054	−	6.94597i	0.278490	−	0.385293i
$326$	16.5632	−	2.92055i	0.917353	−	0.161754i
$327$		0			0
$328$	4.75574	−	10.1987i	0.262592	−	0.563130i
$329$	10.9162	+	9.15981i	0.601832	+	0.504997i
$330$		0			0
$331$	−2.04963	−	0.746004i	−0.112658	−	0.0410041i	0.285076	−	0.958505i	$-0.407981\pi$
$331$	−2.04963	−	0.746004i	−0.112658	−	0.0410041i	−0.397734	+	0.917501i	$0.630203\pi$
$332$	−13.1903	−	3.53434i	−0.723913	−	0.193972i
$333$		0			0
$334$	3.43321	+	1.98216i	0.187857	+	0.108459i
$335$	27.9573	+	0.209663i	1.52747	+	0.0114551i
$336$		0			0
$337$	16.6523	−	11.6600i	0.907107	−	0.635163i	−0.0240779	−	0.999710i	$-0.507665\pi$
$337$	16.6523	−	11.6600i	0.907107	−	0.635163i	0.931185	+	0.364547i	$0.118776\pi$
$338$	−8.24223	+	5.77127i	−0.448318	+	0.313916i
$339$		0			0
$340$	8.23007	+	0.0617206i	0.446338	+	0.00334727i
$341$	0.427672	+	0.246917i	0.0231597	+	0.0133713i
$342$		0			0
$343$	19.3941	+	5.19664i	1.04718	+	0.280592i
$344$	8.49637	+	3.09243i	0.458094	+	0.166732i
$345$		0			0
$346$	15.5521	+	13.0498i	0.836087	+	0.701561i
$347$	−0.595344	+	1.27672i	−0.0319597	+	0.0685379i	−0.921640	−	0.388047i	$-0.873150\pi$
$347$	−0.595344	+	1.27672i	−0.0319597	+	0.0685379i	0.889680	+	0.456585i	$0.150928\pi$
$348$		0			0
$349$	5.30411	−	0.935258i	0.283923	−	0.0500632i	−0.0298732	−	0.999554i	$-0.509510\pi$
$349$	5.30411	−	0.935258i	0.283923	−	0.0500632i	0.313796	+	0.949490i	$0.398399\pi$
$350$	11.2213	−	1.80553i	0.599805	−	0.0965096i
$351$		0			0
$352$	0.129187	+	0.129187i	0.00688568	+	0.00688568i
$353$	18.0126	−	25.7247i	0.958714	−	1.36919i	0.0295316	−	0.999564i	$-0.490598\pi$
$353$	18.0126	−	25.7247i	0.958714	−	1.36919i	0.929182	−	0.369622i	$-0.120513\pi$
$354$		0			0
$355$	−8.08059	−	17.6737i	−0.428873	−	0.938024i
$356$	6.51081	−	7.75928i	0.345072	−	0.411241i
$357$		0			0
$358$	23.4183	−	10.9201i	1.23770	−	0.577147i
$359$	2.67831	+	4.63896i	0.141356	+	0.244835i	0.928007	−	0.372562i	$-0.121521\pi$
$359$	2.67831	+	4.63896i	0.141356	+	0.244835i	−0.786652	+	0.617397i	$0.788187\pi$
$360$		0			0
$361$	−9.49816	+	16.4513i	−0.499903	+	0.865858i
$362$	−1.19478	+	13.6565i	−0.0627965	+	0.717767i
$363$		0			0
$364$	3.83715	+	0.676593i	0.201121	+	0.0354631i
$365$	8.03508	+	9.72299i	0.420575	+	0.508925i
$366$		0			0
$367$	17.2267	+	1.50714i	0.899225	+	0.0786720i	0.527387	−	0.849625i	$-0.323172\pi$
$367$	17.2267	+	1.50714i	0.899225	+	0.0786720i	0.371838	+	0.928297i	$0.378728\pi$
$368$	0.334848	−	0.0897222i	0.0174552	−	0.00467710i
$369$		0			0
$370$	−4.58329	−	6.65122i	−0.238274	−	0.345780i
$371$	−7.58872	+	20.8498i	−0.393987	+	1.08247i
$372$		0			0
$373$	22.0209	−	1.92658i	1.14020	−	0.0997544i	0.498626	−	0.866817i	$-0.333838\pi$
$373$	22.0209	−	1.92658i	1.14020	−	0.0997544i	0.641572	+	0.767063i	$0.278283\pi$
$374$	0.631902	−	0.229993i	0.0326749	−	0.0118927i
$375$		0			0
$376$	−1.08859	−	6.17371i	−0.0561399	−	0.318385i
$377$	8.83008	−	8.83008i	0.454772	−	0.454772i
$378$		0			0
$379$		−	37.8395i		−	1.94368i	−0.235632	−	0.971842i	$-0.575716\pi$
$379$		−	37.8395i		−	1.94368i	0.235632	−	0.971842i	$-0.424284\pi$
$380$	−0.0340900	−	0.131152i	−0.00174878	−	0.00672796i
$381$		0			0
$382$	8.43845	+	3.93491i	0.431749	+	0.201328i
$383$	1.53470	+	17.5417i	0.0784195	+	0.896339i	0.928899	+	0.370332i	$0.120756\pi$
$383$	1.53470	+	17.5417i	0.0784195	+	0.896339i	−0.850480	+	0.526008i	$0.823688\pi$
$384$		0			0
$385$	0.807676	−	0.458270i	0.0411630	−	0.0233556i
$386$	−4.93231	+	2.84767i	−0.251048	+	0.144943i
$387$		0			0
$388$	1.62785	+	6.07522i	0.0826415	+	0.308422i
$389$	11.4580	−	9.61437i	0.580942	−	0.487468i	−0.304315	−	0.952572i	$-0.598427\pi$
$389$	11.4580	−	9.61437i	0.580942	−	0.487468i	0.885256	+	0.465104i	$0.153983\pi$
$390$		0			0
$391$	0.221567	−	1.25657i	0.0112051	−	0.0635474i
$392$	−1.05130	−	1.50141i	−0.0530986	−	0.0758327i
$393$		0			0
$394$	2.82785	+	3.37011i	0.142465	+	0.169783i
$395$	−31.8350	−	15.1366i	−1.60179	−	0.761604i
$396$		0			0
$397$	−7.35300	+	27.4418i	−0.369037	+	1.37726i	0.492829	+	0.870126i	$0.335963\pi$
$397$	−7.35300	+	27.4418i	−0.369037	+	1.37726i	−0.861866	+	0.507137i	$0.830704\pi$
$398$	−1.61414	−	3.46154i	−0.0809096	−	0.173511i
$399$		0			0
$400$	−4.29215	−	2.56466i	−0.214607	−	0.128233i
$401$	0.0598940	+	0.164557i	0.00299096	+	0.00821761i	0.941179	−	0.337908i	$-0.109719\pi$
$401$	0.0598940	+	0.164557i	0.00299096	+	0.00821761i	−0.938188	+	0.346126i	$0.887497\pi$
$402$		0			0
$403$	−3.79529	−	2.65749i	−0.189057	−	0.132379i
$404$	−10.3163			−0.513253
$405$		0			0
$406$	16.5604			0.821879
$407$	−0.540614	−	0.378542i	−0.0267972	−	0.0187636i
$408$		0			0
$409$	11.7278	+	32.2219i	0.579903	+	1.59327i	0.788343	+	0.615235i	$0.210939\pi$
$409$	11.7278	+	32.2219i	0.579903	+	1.59327i	−0.208441	+	0.978035i	$0.566839\pi$
$410$	4.18348	+	24.8124i	0.206607	+	1.22540i
$411$		0			0
$412$	−0.669029	−	1.43474i	−0.0329607	−	0.0706845i
$413$	6.71930	−	25.0768i	0.330635	−	1.23395i
$414$		0			0
$415$	28.7710	−	10.2281i	1.41231	−	0.502077i
$416$	−1.10179	−	1.31307i	−0.0540199	−	0.0643784i
$417$		0			0
$418$	−0.00635055	−	0.00906952i	−0.000310615	−	0.000443605i
$419$	3.93483	−	22.3156i	0.192229	−	1.09019i	−0.724080	−	0.689716i	$-0.757736\pi$
$419$	3.93483	−	22.3156i	0.192229	−	1.09019i	0.916310	−	0.400471i	$-0.131153\pi$
$420$		0			0
$421$	1.61536	−	1.35545i	0.0787278	−	0.0660605i	−0.602574	−	0.798063i	$-0.705858\pi$
$421$	1.61536	−	1.35545i	0.0787278	−	0.0660605i	0.681302	+	0.732002i	$0.261414\pi$
$422$	6.39622	+	23.8710i	0.311363	+	1.16202i
$423$		0			0
$424$	8.45324	−	4.88048i	0.410526	−	0.237017i
$425$	−15.2319	+	10.3285i	−0.738855	+	0.501007i
$426$		0			0
$427$	2.53264	+	28.9483i	0.122563	+	1.40090i
$428$	7.52691	+	3.50985i	0.363827	+	0.169655i
$429$		0			0
$430$	−19.5675	+	5.08614i	−0.943630	+	0.245275i
$431$		−	0.390386i		−	0.0188042i	−0.999956	−	0.00940211i	$-0.997007\pi$
$431$		−	0.390386i		−	0.0188042i	0.999956	−	0.00940211i	$-0.00299283\pi$
$432$		0			0
$433$	6.27555	−	6.27555i	0.301584	−	0.301584i	−0.540050	−	0.841633i	$-0.681595\pi$
$433$	6.27555	−	6.27555i	0.301584	−	0.301584i	0.841633	+	0.540050i	$0.181595\pi$
$434$	−1.06694	−	6.05094i	−0.0512150	−	0.290454i
$435$		0			0
$436$	−9.54823	+	3.47527i	−0.457277	+	0.166435i
$437$	−0.0209283	+	0.00183099i	−0.00100114	+	8.75883e-5i
$438$		0			0
$439$	−9.09299	+	24.9828i	−0.433985	+	1.19236i	0.509362	+	0.860553i	$0.329882\pi$
$439$	−9.09299	+	24.9828i	−0.433985	+	1.19236i	−0.943346	+	0.331810i	$0.892341\pi$
$440$	−0.401775	−	0.0739546i	−0.0191539	−	0.00352565i
$441$		0			0
$442$	−6.09407	+	1.63290i	−0.289865	+	0.0776692i
$443$	−10.6874	−	0.935026i	−0.507773	−	0.0444244i	−0.169609	−	0.985511i	$-0.554250\pi$
$443$	−10.6874	−	0.935026i	−0.507773	−	0.0444244i	−0.338164	+	0.941087i	$0.609806\pi$
$444$		0			0
$445$	−2.14315	+	22.5476i	−0.101595	+	1.06886i
$446$	22.1440	+	3.90459i	1.04855	+	0.184888i
$447$		0			0
$448$	0.198116	−	2.26448i	0.00936011	−	0.106987i
$449$	−7.47104	+	12.9402i	−0.352580	+	0.610687i	−0.986701	−	0.162547i	$-0.948029\pi$
$449$	−7.47104	+	12.9402i	−0.352580	+	0.610687i	0.634121	+	0.773234i	$0.281362\pi$
$450$		0			0
$451$	1.02795	+	1.78047i	0.0484044	+	0.0838389i
$452$	−5.23847	+	2.44274i	−0.246397	+	0.114897i
$453$		0			0
$454$	−14.5458	+	17.3350i	−0.682668	+	0.813572i
$455$	−7.92359	+	3.62274i	−0.371463	+	0.169837i
$456$		0			0
$457$	−0.492756	+	0.703729i	−0.0230502	+	0.0329190i	−0.830512	−	0.557001i	$-0.811952\pi$
$457$	−0.492756	+	0.703729i	−0.0230502	+	0.0329190i	0.807462	+	0.589920i	$0.200841\pi$
$458$	7.04267	+	7.04267i	0.329082	+	0.329082i
$459$		0			0
$460$	−0.502699	+	0.590050i	−0.0234385	+	0.0275112i
$461$	20.0692	−	3.53874i	0.934714	−	0.164815i	0.314509	−	0.949255i	$-0.398160\pi$
$461$	20.0692	−	3.53874i	0.934714	−	0.164815i	0.620206	+	0.784439i	$0.287049\pi$
$462$		0			0
$463$	−2.21441	+	4.74881i	−0.102912	+	0.220696i	−0.951021	−	0.309126i	$-0.899964\pi$
$463$	−2.21441	+	4.74881i	−0.102912	+	0.220696i	0.848109	+	0.529822i	$0.177741\pi$
$464$	−5.58085	−	4.68289i	−0.259085	−	0.217398i
$465$		0			0
$466$	2.58884	+	0.942259i	0.119925	+	0.0436493i
$467$	−13.8766	−	3.71823i	−0.642133	−	0.172059i	−0.0769636	−	0.997034i	$-0.524523\pi$
$467$	−13.8766	−	3.71823i	−0.642133	−	0.172059i	−0.565169	+	0.824975i	$0.691189\pi$
$468$		0			0
$469$	−24.6137	−	14.2107i	−1.13656	−	0.656191i
$470$	9.83747	+	9.98614i	0.453769	+	0.460626i
$471$		0			0
$472$	−9.35553	+	6.55081i	−0.430623	+	0.301525i
$473$	−1.35315	+	0.947484i	−0.0622178	+	0.0435654i
$474$		0			0
$475$	0.229172	+	0.198230i	0.0105151	+	0.00909543i
$476$	−7.24578	−	4.18335i	−0.332110	−	0.191744i
$477$		0			0
$478$	19.4478	+	5.21103i	0.889524	+	0.238347i
$479$	−10.5919	−	3.85514i	−0.483957	−	0.176146i	0.0885076	−	0.996076i	$-0.471790\pi$
$479$	−10.5919	−	3.85514i	−0.483957	−	0.176146i	−0.572464	+	0.819930i	$0.694012\pi$
$480$		0			0
$481$	4.74325	+	3.98006i	0.216274	+	0.181475i
$482$	9.68433	−	20.7681i	0.441109	−	0.945961i
$483$		0			0
$484$	10.8000	−	1.90433i	0.490910	−	0.0865606i
$485$	−10.7054	−	9.12058i	−0.486108	−	0.414144i
$486$		0			0
$487$	−17.0688	−	17.0688i	−0.773463	−	0.773463i	0.205247	−	0.978710i	$-0.434200\pi$
$487$	−17.0688	−	17.0688i	−0.773463	−	0.773463i	−0.978710	+	0.205247i	$0.934200\pi$
$488$	7.33239	−	10.4717i	0.331922	−	0.474033i
$489$		0			0
$490$	3.84066	+	1.43060i	0.173504	+	0.0646277i
$491$	−1.62435	+	1.93583i	−0.0733059	+	0.0873626i	−0.801451	−	0.598060i	$-0.795938\pi$
$491$	−1.62435	+	1.93583i	−0.0733059	+	0.0873626i	0.728145	+	0.685423i	$0.240383\pi$
$492$		0			0
$493$	−24.3026	+	11.3325i	−1.09453	+	0.510390i
$494$	0.0519385	+	0.0899602i	0.00233683	+	0.00404750i
$495$		0			0
$496$	−1.35150	+	2.34087i	−0.0606843	+	0.105108i
$497$	−1.72180	+	19.6803i	−0.0772334	+	0.882782i
$498$		0			0
$499$	−20.1431	−	3.55178i	−0.901730	−	0.158999i	−0.296484	−	0.955038i	$-0.595814\pi$
$499$	−20.1431	−	3.55178i	−0.901730	−	0.158999i	−0.605246	+	0.796038i	$0.706925\pi$
$500$	11.1569	−	0.723630i	0.498952	−	0.0323617i
$501$		0			0
$502$	−8.52825	−	0.746125i	−0.380634	−	0.0333012i
$503$	−3.68639	+	0.987766i	−0.164368	+	0.0440423i	−0.340065	−	0.940402i	$-0.610449\pi$
$503$	−3.68639	+	0.987766i	−0.164368	+	0.0440423i	0.175697	+	0.984444i	$0.443782\pi$
$504$		0			0
$505$	18.9948	−	13.0891i	0.845257	−	0.582458i
$506$	−0.0216615	+	0.0595145i	−0.000962971	+	0.00264574i
$507$		0			0
$508$	1.45178	−	0.127014i	0.0644123	−	0.00563534i
$509$	23.6994	−	8.62589i	1.05046	−	0.382336i	0.241623	−	0.970370i	$-0.422320\pi$
$509$	23.6994	−	8.62589i	1.05046	−	0.382336i	0.808836	+	0.588034i	$0.200098\pi$
$510$		0			0
$511$	−2.22661	−	12.6277i	−0.0984992	−	0.558617i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	4.54107i		−	0.200298i
$515$	3.05222	+	1.79285i	0.134497	+	0.0790025i
$516$		0			0
$517$	1.03802	+	0.484034i	0.0456519	+	0.0212878i
$518$	0.715665	+	8.18008i	0.0314445	+	0.359412i
$519$		0			0
$520$	3.69467	+	1.01974i	0.162022	+	0.0447186i
$521$	−1.53429	+	0.885826i	−0.0672187	+	0.0388087i	−0.533233	−	0.845969i	$-0.679023\pi$
$521$	−1.53429	+	0.885826i	−0.0672187	+	0.0388087i	0.466014	+	0.884777i	$0.345690\pi$
$522$		0			0
$523$	3.63521	+	13.5668i	0.158957	+	0.593235i	0.998734	+	0.0503036i	$0.0160189\pi$
$523$	3.63521	+	13.5668i	0.158957	+	0.593235i	−0.839777	+	0.542931i	$0.817314\pi$
$524$	3.00013	−	2.51741i	0.131061	−	0.109973i
$525$		0			0
$526$	−1.34714	+	7.63999i	−0.0587380	+	0.333119i
$527$	5.70649	+	8.14971i	0.248579	+	0.355007i
$528$		0			0
$529$	−14.7069	−	17.5270i	−0.639429	−	0.762042i
$530$	−9.37223	+	19.7115i	−0.407104	+	0.856213i
$531$		0			0
$532$	−0.0356539	+	0.133062i	−0.00154579	+	0.00576898i
$533$	−8.15176	−	17.4815i	−0.353092	−	0.757208i
$534$		0			0
$535$	−18.3121	+	3.08751i	−0.791703	+	0.133485i
$536$	4.27636	+	11.7492i	0.184711	+	0.507488i
$537$		0			0
$538$	−24.1310	−	16.8967i	−1.04036	−	0.728467i
$539$	0.334864			0.0144236
$540$		0			0
$541$	7.05754			0.303427			0.151714	−	0.988424i	$-0.451521\pi$
$541$	7.05754			0.303427			0.151714	+	0.988424i	$0.451521\pi$
$542$	−6.76376	−	4.73604i	−0.290529	−	0.203430i
$543$		0			0
$544$	1.25887	+	3.45873i	0.0539738	+	0.148292i
$545$	13.1713	−	18.5135i	0.564195	−	0.793030i
$546$		0			0
$547$	2.98392	+	6.39903i	0.127583	+	0.273603i	0.959715	−	0.280975i	$-0.0906577\pi$
$547$	2.98392	+	6.39903i	0.127583	+	0.273603i	−0.832132	+	0.554577i	$0.812880\pi$
$548$	3.34950	−	12.5005i	0.143084	−	0.533995i
$549$		0			0
$550$	0.833599	−	0.373597i	0.0355448	−	0.0159302i
$551$	0.283793	+	0.338211i	0.0120900	+	0.0144083i
$552$		0			0
$553$	20.5539	+	29.3539i	0.874039	+	1.24826i
$554$	−1.96514	+	11.1449i	−0.0834910	+	0.473501i
$555$		0			0
$556$	−9.69164	+	8.13225i	−0.411017	+	0.344884i
$557$	6.82754	+	25.4807i	0.289292	+	1.07965i	0.945646	+	0.325199i	$0.105431\pi$
$557$	6.82754	+	25.4807i	0.289292	+	1.07965i	−0.656354	+	0.754453i	$0.727902\pi$
$558$		0			0
$559$	13.4218	−	7.74909i	0.567682	−	0.327752i
$560$	2.50835	+	4.42083i	0.105997	+	0.186814i
$561$		0			0
$562$	0.562331	+	6.42747i	0.0237205	+	0.271127i
$563$	12.1511	+	5.66613i	0.512106	+	0.238799i	0.661454	−	0.749986i	$-0.269940\pi$
$563$	12.1511	+	5.66613i	0.512106	+	0.238799i	−0.149348	+	0.988785i	$0.547717\pi$
$564$		0			0
$565$	6.54601	−	11.1442i	0.275393	−	0.468839i
$566$		−	23.2406i		−	0.976876i
$567$		0			0
$568$	6.14538	−	6.14538i	0.257854	−	0.257854i
$569$	1.13543	+	6.43935i	0.0475998	+	0.269952i	0.999314	−	0.0370336i	$-0.0117909\pi$
$569$	1.13543	+	6.43935i	0.0475998	+	0.269952i	−0.951714	+	0.306985i	$0.900680\pi$
$570$		0			0
$571$	−26.1068	+	9.50211i	−1.09254	+	0.397651i	−0.824560	−	0.565775i	$-0.808577\pi$
$571$	−26.1068	+	9.50211i	−1.09254	+	0.397651i	−0.267977	+	0.963425i	$0.586355\pi$
$572$	0.311968	−	0.0272937i	0.0130440	−	0.00114121i
$573$		0			0
$574$	8.74875	−	24.0370i	0.365166	−	1.00328i
$575$	0.176947	−	1.72425i	0.00737921	−	0.0719060i
$576$		0			0
$577$	−4.53587	+	1.21538i	−0.188831	+	0.0505970i	−0.351995	−	0.936002i	$-0.614497\pi$
$577$	−4.53587	+	1.21538i	−0.188831	+	0.0505970i	0.163164	+	0.986599i	$0.447830\pi$
$578$	−3.43930	−	0.300900i	−0.143056	−	0.0125158i
$579$		0			0
$580$	16.2173	+	1.54146i	0.673387	+	0.0640057i
$581$	−30.5694	−	5.39022i	−1.26823	−	0.223624i
$582$		0			0
$583$	−0.155425	+	1.77652i	−0.00643706	+	0.0735759i
$584$	−2.82045	+	4.88517i	−0.116711	+	0.202150i
$585$		0			0
$586$	−11.1129	−	19.2481i	−0.459071	−	0.795134i
$587$	29.6956	−	13.8473i	1.22567	−	0.571539i	0.301480	−	0.953473i	$-0.402519\pi$
$587$	29.6956	−	13.8473i	1.22567	−	0.571539i	0.924190	+	0.381934i	$0.124742\pi$
$588$		0			0
$589$	0.105293	−	0.125484i	0.00433854	−	0.00517047i
$590$	8.91427	−	23.9318i	0.366995	−	0.985256i
$591$		0			0
$592$	2.07196	−	2.95906i	0.0851569	−	0.121617i
$593$	−14.9025	−	14.9025i	−0.611974	−	0.611974i	0.331486	−	0.943460i	$-0.392450\pi$
$593$	−14.9025	−	14.9025i	−0.611974	−	0.611974i	−0.943460	+	0.331486i	$0.892450\pi$
$594$		0			0
$595$	18.6490	−	1.49075i	0.764536	−	0.0611146i
$596$	8.27853	−	1.45973i	0.339102	−	0.0597928i
$597$		0			0
$598$	0.251122	−	0.538533i	0.0102692	−	0.0220223i
$599$	−10.5345	−	8.83950i	−0.430428	−	0.361172i	0.401685	−	0.915778i	$-0.368425\pi$
$599$	−10.5345	−	8.83950i	−0.430428	−	0.361172i	−0.832113	+	0.554606i	$0.812869\pi$
$600$		0			0
$601$	−4.08936	−	1.48841i	−0.166808	−	0.0607133i	0.257266	−	0.966341i	$-0.417178\pi$
$601$	−4.08936	−	1.48841i	−0.166808	−	0.0607133i	−0.424075	+	0.905627i	$0.639401\pi$
$602$	19.8525	+	5.31947i	0.809128	+	0.216805i
$603$		0			0
$604$	3.69796	+	2.13502i	0.150468	+	0.0868726i
$605$	−17.4693	+	17.2092i	−0.710228	+	0.699655i
$606$		0			0
$607$	19.2240	−	13.4608i	0.780278	−	0.546357i	−0.114206	−	0.993457i	$-0.536432\pi$
$607$	19.2240	−	13.4608i	0.780278	−	0.546357i	0.894484	+	0.447101i	$0.147543\pi$
$608$	0.0496422	−	0.0347599i	0.00201326	−	0.00140970i
$609$		0			0
$610$	−0.214365	+	28.5843i	−0.00867937	+	1.15734i
$611$	−9.30590	−	5.37277i	−0.376477	−	0.217359i
$612$		0			0
$613$	−7.51980	−	2.01493i	−0.303722	−	0.0813821i	0.103739	−	0.994605i	$-0.466919\pi$
$613$	−7.51980	−	2.01493i	−0.303722	−	0.0813821i	−0.407461	+	0.913222i	$0.633586\pi$
$614$	2.96895	+	1.08061i	0.119817	+	0.0436099i
$615$		0			0
$616$	0.318135	+	0.266947i	0.0128180	+	0.0107556i
$617$	11.4156	−	24.4808i	0.459573	−	0.985558i	−0.530846	−	0.847468i	$-0.678126\pi$
$617$	11.4156	−	24.4808i	0.459573	−	0.985558i	0.990420	−	0.138090i	$-0.0440964\pi$
$618$		0			0
$619$	5.43890	−	0.959025i	0.218608	−	0.0385465i	−0.0632713	−	0.997996i	$-0.520153\pi$
$619$	5.43890	−	0.959025i	0.218608	−	0.0385465i	0.281879	+	0.959450i	$0.409042\pi$
$620$	−0.481611	−	6.02489i	−0.0193419	−	0.241965i
$621$		0			0
$622$	−4.01310	−	4.01310i	−0.160911	−	0.160911i
$623$	13.2064	−	18.8606i	0.529101	−	0.755635i
$624$		0			0
$625$	−19.6245	+	15.4881i	−0.784979	+	0.619523i
$626$	−13.1609	+	15.6846i	−0.526017	+	0.626883i
$627$		0			0
$628$	2.35857	−	1.09982i	0.0941170	−	0.0438875i
$629$	−6.64798	−	11.5146i	−0.265073	−	0.459119i
$630$		0			0
$631$	7.45143	−	12.9062i	0.296637	−	0.513790i	−0.678728	−	0.734390i	$-0.737468\pi$
$631$	7.45143	−	12.9062i	0.296637	−	0.513790i	0.975364	+	0.220600i	$0.0708017\pi$
$632$	1.37396	−	15.7044i	0.0546532	−	0.624688i
$633$		0			0
$634$	−25.5198	−	4.49983i	−1.01352	−	0.178711i
$635$	−2.51193	+	2.07586i	−0.0996828	+	0.0823779i
$636$		0			0
$637$	−3.12977	−	0.273819i	−0.124006	−	0.0108491i
$638$	1.28565	−	0.344490i	0.0508995	−	0.0136385i
$639$		0			0
$640$	0.404792	−	2.19912i	0.0160008	−	0.0869280i
$641$	−13.0636	+	35.8920i	−0.515982	+	1.41765i	0.358928	+	0.933365i	$0.383142\pi$
$641$	−13.0636	+	35.8920i	−0.515982	+	1.41765i	−0.874910	+	0.484285i	$0.839080\pi$
$642$		0			0
$643$	−3.66403	+	0.320561i	−0.144495	+	0.0126417i	−0.159174	−	0.987251i	$-0.550883\pi$
$643$	−3.66403	+	0.320561i	−0.144495	+	0.0126417i	0.0146787	+	0.999892i	$0.495327\pi$
$644$	0.740481	−	0.269513i	0.0291790	−	0.0106203i
$645$		0			0
$646$	−0.0387336	−	0.219669i	−0.00152395	−	0.00864276i
$647$	−4.49591	+	4.49591i	−0.176752	+	0.176752i	−0.789939	−	0.613186i	$-0.789888\pi$
$647$	−4.49591	+	4.49591i	−0.176752	+	0.176752i	0.613186	+	0.789939i	$0.289888\pi$
$648$		0			0
$649$		−	2.08659i		−	0.0819058i
$650$	−8.09663	+	2.81015i	−0.317576	+	0.110223i
$651$		0			0
$652$	−15.2430	−	7.10791i	−0.596961	−	0.278367i
$653$	4.16340	+	47.5879i	0.162926	+	1.86226i	0.435586	+	0.900147i	$0.356541\pi$
$653$	4.16340	+	47.5879i	0.162926	+	1.86226i	−0.272659	+	0.962111i	$0.587903\pi$
$654$		0			0
$655$	−2.32993	+	8.44169i	−0.0910380	+	0.329844i
$656$	−9.74543	+	5.62652i	−0.380495	+	0.219679i
$657$		0			0
$658$	−3.68821	−	13.7646i	−0.143781	−	0.536599i
$659$	28.3506	−	23.7890i	1.10438	−	0.926687i	0.106670	−	0.994294i	$-0.465981\pi$
$659$	28.3506	−	23.7890i	1.10438	−	0.926687i	0.997712	+	0.0676076i	$0.0215366\pi$
$660$		0			0
$661$	6.60714	−	37.4710i	0.256988	−	1.45745i	−0.533930	−	0.845529i	$-0.679285\pi$
$661$	6.60714	−	37.4710i	0.256988	−	1.45745i	0.790918	−	0.611922i	$-0.209604\pi$
$662$	1.25107	+	1.78671i	0.0486241	+	0.0694425i
$663$		0			0
$664$	8.77767	+	10.4608i	0.340640	+	0.405959i
$665$	−0.103180	−	0.290237i	−0.00400113	−	0.0112549i
$666$		0			0
$667$	0.653652	−	2.43946i	0.0253095	−	0.0944564i
$668$	−1.67540	−	3.59290i	−0.0648231	−	0.139014i
$669$		0			0
$670$	−22.7810	−	16.2074i	−0.880108	−	0.626146i
$671$	0.798801	+	2.19469i	0.0308374	+	0.0847250i
$672$		0			0
$673$	−27.9768	−	19.5895i	−1.07843	−	0.755122i	−0.107428	−	0.994213i	$-0.534262\pi$
$673$	−27.9768	−	19.5895i	−1.07843	−	0.755122i	−0.970997	+	0.239091i	$0.923151\pi$
$674$	−20.3287			−0.783031
$675$		0			0
$676$	10.0619			0.386996
$677$	16.4004	+	11.4837i	0.630320	+	0.441355i	0.844585	−	0.535421i	$-0.179847\pi$
$677$	16.4004	+	11.4837i	0.630320	+	0.441355i	−0.214266	+	0.976775i	$0.568736\pi$
$678$		0			0
$679$	4.88983	+	13.4347i	0.187654	+	0.515576i
$680$	−6.70627	−	4.77113i	−0.257174	−	0.182965i
$681$		0			0
$682$	−0.208703	−	0.447565i	−0.00799165	−	0.0171381i
$683$	−5.20041	+	19.4082i	−0.198988	+	0.742634i	0.792210	+	0.610248i	$0.208930\pi$
$683$	−5.20041	+	19.4082i	−0.198988	+	0.742634i	−0.991198	+	0.132385i	$0.957736\pi$
$684$		0			0
$685$	9.69318	+	27.2663i	0.370358	+	1.04179i
$686$	−12.9061	−	15.3809i	−0.492756	−	0.587244i
$687$		0			0
$688$	−5.18608	−	7.40649i	−0.197717	−	0.282370i
$689$	2.90533	−	16.4770i	0.110684	−	0.627722i
$690$		0			0
$691$	22.3755	−	18.7753i	0.851205	−	0.714246i	−0.108849	−	0.994058i	$-0.534717\pi$
$691$	22.3755	−	18.7753i	0.851205	−	0.714246i	0.960055	+	0.279812i	$0.0902722\pi$
$692$	−5.25451	−	19.6101i	−0.199746	−	0.745464i
$693$		0			0
$694$	1.21997	−	0.704352i	0.0463096	−	0.0267368i
$695$	7.52663	−	27.2701i	0.285501	−	1.03441i
$696$		0			0
$697$	3.60991	+	41.2615i	0.136735	+	1.56289i
$698$	−4.88132	−	2.27620i	−0.184761	−	0.0861553i
$699$		0			0
$700$	−10.2276	−	4.95728i	−0.386566	−	0.187368i
$701$			7.24059i			0.273473i	0.990607	+	0.136737i	$0.0436614\pi$
$701$			7.24059i			0.273473i	−0.990607	+	0.136737i	$0.956339\pi$
$702$		0			0
$703$	−0.154797	+	0.154797i	−0.00583826	+	0.00583826i
$704$	−0.0317251	−	0.179922i	−0.00119569	−	0.00678107i
$705$		0			0
$706$	−29.5101	+	10.7408i	−1.11063	+	0.404235i
$707$	−23.3610	+	2.04382i	−0.878579	+	0.0768657i
$708$		0			0
$709$	−1.65091	+	4.53583i	−0.0620012	+	0.170347i	−0.966825	−	0.255439i	$-0.917780\pi$
$709$	−1.65091	+	4.53583i	−0.0620012	+	0.170347i	0.904824	+	0.425786i	$0.140002\pi$
$710$	−3.51800	+	19.1123i	−0.132028	+	0.717272i
$711$		0			0
$712$	−9.78388	+	2.62158i	−0.366667	+	0.0982480i
$713$	−0.933459	−	0.0816671i	−0.0349583	−	0.00305846i
$714$		0			0
$715$	−0.539780	+	0.446075i	−0.0201866	+	0.0166822i
$716$	−25.4467	−	4.48694i	−0.950987	−	0.167685i
$717$		0			0
$718$	0.466860	−	5.33623i	0.0174230	−	0.199146i
$719$	−22.3094	+	38.6410i	−0.832000	+	1.44107i	0.0644498	+	0.997921i	$0.479471\pi$
$719$	−22.3094	+	38.6410i	−0.832000	+	1.44107i	−0.896450	+	0.443145i	$0.853863\pi$
$720$		0			0
$721$	−1.79925	−	3.11639i	−0.0670075	−	0.116060i
$722$	17.2165	−	8.02819i	0.640733	−	0.298778i
$723$		0			0
$724$	8.81173	−	10.5014i	0.327485	−	0.390282i
$725$	−31.8158	+	17.7380i	−1.18161	+	0.658774i
$726$		0			0
$727$	12.2628	−	17.5131i	0.454802	−	0.649525i	−0.524623	−	0.851335i	$-0.675794\pi$
$727$	12.2628	−	17.5131i	0.454802	−	0.649525i	0.979425	+	0.201810i	$0.0646824\pi$
$728$	−2.75513	−	2.75513i	−0.102112	−	0.102112i
$729$		0			0
$730$	−1.00507	−	12.5733i	−0.0371994	−	0.465360i
$731$	−32.7740	+	5.77894i	−1.21219	+	0.213742i
$732$		0			0
$733$	20.7640	−	44.5285i	0.766935	−	1.64470i	0.00249956	−	0.999997i	$-0.499204\pi$
$733$	20.7640	−	44.5285i	0.766935	−	1.64470i	0.764435	−	0.644700i	$-0.223018\pi$
$734$	−13.2468	−	11.1154i	−0.488948	−	0.410276i
$735$		0			0
$736$	−0.325754	−	0.118565i	−0.0120075	−	0.00437035i
$737$	−2.20648	−	0.591224i	−0.0812766	−	0.0217780i
$738$		0			0
$739$	−22.8570	−	13.1965i	−0.840809	−	0.485441i	0.0167301	−	0.999860i	$-0.494674\pi$
$739$	−22.8570	−	13.1965i	−0.840809	−	0.485441i	−0.857539	+	0.514419i	$0.828008\pi$
$740$	−0.0605743	+	8.07723i	−0.00222676	+	0.296925i
$741$		0			0
$742$	18.1753	−	12.7265i	0.667236	−	0.467204i
$743$	−16.9596	+	11.8753i	−0.622188	+	0.435661i	−0.841697	−	0.539950i	$-0.818443\pi$
$743$	−16.9596	+	11.8753i	−0.622188	+	0.435661i	0.219509	+	0.975610i	$0.429554\pi$
$744$		0			0
$745$	−13.3907	+	13.1914i	−0.490598	+	0.483295i
$746$	−19.1435	−	11.0525i	−0.700893	−	0.404661i
$747$		0			0
$748$	−0.649542	−	0.174044i	−0.0237496	−	0.00636369i
$749$	17.7399	+	6.45679i	0.648201	+	0.235926i
$750$		0			0
$751$	−0.157694	−	0.132321i	−0.00575432	−	0.00482845i	0.639906	−	0.768453i	$-0.278973\pi$
$751$	−0.157694	−	0.132321i	−0.00575432	−	0.00482845i	−0.645660	+	0.763625i	$0.723418\pi$
$752$	−2.64937	+	5.68160i	−0.0966127	+	0.207187i
$753$		0			0
$754$	−12.2979	+	2.16845i	−0.447863	+	0.0789704i
$755$	−9.51773	+	0.760817i	−0.346386	+	0.0276890i
$756$		0			0
$757$	20.6464	+	20.6464i	0.750405	+	0.750405i	0.974555	−	0.224150i	$-0.0719605\pi$
$757$	20.6464	+	20.6464i	0.750405	+	0.750405i	−0.224150	+	0.974555i	$0.571961\pi$
$758$	−21.7038	+	30.9963i	−0.788319	+	1.12584i
$759$		0			0
$760$	−0.0473008	+	0.126987i	−0.00171578	+	0.00460629i
$761$	−9.90544	+	11.8048i	−0.359072	+	0.427925i	−0.915093	−	0.403243i	$-0.867883\pi$
$761$	−9.90544	+	11.8048i	−0.359072	+	0.427925i	0.556021	+	0.831168i	$0.312327\pi$
$762$		0			0
$763$	−20.9333	+	9.76134i	−0.757835	+	0.353384i
$764$	−4.65540	−	8.06339i	−0.168426	−	0.291723i
$765$		0			0
$766$	8.80436	−	15.2496i	0.318114	−	0.550990i
$767$	−1.70621	+	19.5021i	−0.0616077	+	0.704179i
$768$		0			0
$769$	15.4364	+	2.72186i	0.556651	+	0.0981526i	0.444895	−	0.895583i	$-0.353241\pi$
$769$	15.4364	+	2.72186i	0.556651	+	0.0981526i	0.111757	+	0.993736i	$0.464352\pi$
$770$	−0.924462	−	0.0878705i	−0.0333153	−	0.00316663i
$771$		0			0
$772$	5.67367	+	0.496382i	0.204200	+	0.0178652i
$773$	44.6136	−	11.9542i	1.60464	−	0.429962i	0.658199	−	0.752844i	$-0.271318\pi$
$773$	44.6136	−	11.9542i	1.60464	−	0.429962i	0.946439	+	0.322882i	$0.104652\pi$
$774$		0			0
$775$	8.53105	+	10.4822i	0.306444	+	0.376533i
$776$	2.15115	−	5.91022i	0.0772216	−	0.212165i
$777$		0			0
$778$	−14.9004	+	1.30362i	−0.534205	+	0.0467369i
$779$	0.640830	−	0.233243i	0.0229601	−	0.00835680i
$780$		0			0
$781$	0.275719	+	1.56368i	0.00986600	+	0.0559529i
$782$	−0.902235	+	0.902235i	−0.0322638	+	0.0322638i
$783$		0			0
$784$			1.83288i			0.0654601i
$785$	−2.94727	+	5.01755i	−0.105193	+	0.179084i
$786$		0			0
$787$	−12.6990	−	5.92162i	−0.452669	−	0.211083i	0.182893	−	0.983133i	$-0.441454\pi$
$787$	−12.6990	−	5.92162i	−0.452669	−	0.211083i	−0.635562	+	0.772050i	$0.719232\pi$
$788$	−0.383430	−	4.38262i	−0.0136591	−	0.156124i
$789$		0			0
$790$	17.3957	+	30.6590i	0.618912	+	1.09080i
$791$	−11.3785	+	6.56936i	−0.404572	+	0.233580i
$792$		0			0
$793$	−5.67131	−	21.1656i	−0.201394	−	0.751613i
$794$	21.7632	−	18.2615i	0.772346	−	0.648075i
$795$		0			0
$796$	−0.663229	+	3.76136i	−0.0235075	+	0.133318i
$797$	−11.7907	−	16.8389i	−0.417649	−	0.596465i	0.554109	−	0.832444i	$-0.313059\pi$
$797$	−11.7907	−	16.8389i	−0.417649	−	0.596465i	−0.971758	+	0.235979i	$0.924170\pi$
$798$		0			0
$799$	14.8318	+	17.6758i	0.524710	+	0.625325i
$800$	2.04489	+	4.56272i	0.0722978	+	0.161317i
$801$		0			0
$802$	0.0453240	−	0.169151i	0.00160044	−	0.00597294i
$803$	−0.435542	−	0.934023i	−0.0153699	−	0.0329610i
$804$		0			0
$805$	−1.02145	+	1.43575i	−0.0360015	+	0.0506035i
$806$	1.58465	+	4.35378i	0.0558167	+	0.153355i
$807$		0			0
$808$	8.45059	+	5.91717i	0.297291	+	0.208165i
$809$	−40.1953			−1.41319			−0.706597	−	0.707617i	$-0.749770\pi$
$809$	−40.1953			−1.41319			−0.706597	+	0.707617i	$0.749770\pi$
$810$		0			0
$811$	−45.5327			−1.59887			−0.799434	−	0.600754i	$-0.794867\pi$
$811$	−45.5327			−1.59887			−0.799434	+	0.600754i	$0.794867\pi$
$812$	−13.5655	−	9.49866i	−0.476055	−	0.333337i
$813$		0			0
$814$	0.225722	+	0.620167i	0.00791156	+	0.0217368i
$815$	37.0845	−	6.25261i	1.29901	−	0.219019i
$816$		0			0
$817$	0.231570	+	0.496604i	0.00810162	+	0.0173740i
$818$	8.87486	−	33.1214i	0.310302	−	1.15806i
$819$		0			0
$820$	10.8049	−	22.7247i	0.377323	−	0.793579i
$821$	−2.70382	−	3.22229i	−0.0943641	−	0.112459i	0.716796	−	0.697283i	$-0.245608\pi$
$821$	−2.70382	−	3.22229i	−0.0943641	−	0.112459i	−0.811160	+	0.584824i	$0.801163\pi$
$822$		0			0
$823$	−26.8470	−	38.3414i	−0.935826	−	1.33650i	−0.941678	−	0.336515i	$-0.890752\pi$
$823$	−26.8470	−	38.3414i	−0.935826	−	1.33650i	0.00585204	−	0.999983i	$-0.498137\pi$
$824$	−0.274895	+	1.55901i	−0.00957643	+	0.0543106i
$825$		0			0
$826$	−19.8876	+	16.6877i	−0.691977	+	0.580638i
$827$	−2.16768	−	8.08990i	−0.0753777	−	0.281313i	0.917941	−	0.396717i	$-0.129851\pi$
$827$	−2.16768	−	8.08990i	−0.0753777	−	0.281313i	−0.993319	+	0.115404i	$0.963184\pi$
$828$		0			0
$829$	−24.2386	+	13.9942i	−0.841842	+	0.486038i	−0.857890	−	0.513833i	$-0.828225\pi$
$829$	−24.2386	+	13.9942i	−0.841842	+	0.486038i	0.0160476	+	0.999871i	$0.494892\pi$
$830$	−29.4344	−	8.12398i	−1.02168	−	0.281988i
$831$		0			0
$832$	0.149393	+	1.70756i	0.00517926	+	0.0591992i
$833$	6.11422	+	2.85111i	0.211845	+	0.0987850i
$834$		0			0
$835$	7.64343	+	4.48970i	0.264512	+	0.155372i
$836$			0.0110718i			0.000382928i
$837$		0			0
$838$	−16.0229	+	16.0229i	−0.553502	+	0.553502i
$839$	−1.65417	−	9.38128i	−0.0571084	−	0.323878i	0.942848	−	0.333223i	$-0.108136\pi$
$839$	−1.65417	−	9.38128i	−0.0571084	−	0.323878i	−0.999956	+	0.00934551i	$0.997025\pi$
$840$		0			0
$841$	−22.6235	+	8.23428i	−0.780121	+	0.283941i
$842$	−2.10068	+	0.183786i	−0.0723942	+	0.00633367i
$843$		0			0
$844$	8.45237	−	23.2227i	0.290943	−	0.799358i
$845$	−18.5264	+	12.7664i	−0.637329	+	0.439177i
$846$		0			0
$847$	24.0791	−	6.45198i	0.827369	−	0.221693i
$848$	−9.72382	−	0.850724i	−0.333917	−	0.0292140i
$849$		0			0
$850$	18.4014	+	0.276015i	0.631164	+	0.00946723i
$851$	1.23323	+	0.217452i	0.0422746	+	0.00745416i
$852$		0			0
$853$	4.58175	−	52.3696i	0.156876	−	1.79310i	−0.355845	−	0.934545i	$-0.615807\pi$
$853$	4.58175	−	52.3696i	0.156876	−	1.79310i	0.512721	−	0.858556i	$-0.328638\pi$
$854$	14.5294	−	25.1657i	0.497186	−	0.861152i
$855$		0			0
$856$	−4.15251	−	7.19236i	−0.141930	−	0.245830i
$857$	−0.942121	+	0.439318i	−0.0321822	+	0.0150068i	−0.438643	−	0.898662i	$-0.644541\pi$
$857$	−0.942121	+	0.439318i	−0.0321822	+	0.0150068i	0.406461	+	0.913668i	$0.366763\pi$
$858$		0			0
$859$	17.3437	−	20.6694i	0.591759	−	0.705231i	−0.384184	−	0.923257i	$-0.625517\pi$
$859$	17.3437	−	20.6694i	0.591759	−	0.705231i	0.975943	+	0.218025i	$0.0699616\pi$
$860$	18.9461	+	7.05715i	0.646056	+	0.240647i
$861$		0			0
$862$	−0.223916	+	0.319785i	−0.00762661	+	0.0108919i
$863$	21.4264	+	21.4264i	0.729364	+	0.729364i	0.970493	−	0.241129i	$-0.0775178\pi$
$863$	21.4264	+	21.4264i	0.729364	+	0.729364i	−0.241129	+	0.970493i	$0.577518\pi$
$864$		0			0
$865$	34.5558	+	29.4402i	1.17493	+	1.00100i
$866$	−8.74014	+	1.54112i	−0.297002	+	0.0523695i
$867$		0			0
$868$	−2.59669	+	5.56861i	−0.0881373	+	0.189011i
$869$	2.20630	+	1.85131i	0.0748436	+	0.0628013i
$870$		0			0
$871$	20.1392	+	7.33005i	0.682389	+	0.248369i
$872$	9.81478	+	2.62986i	0.332371	+	0.0890584i
$873$		0			0
$874$	0.0181937	+	0.0105041i	0.000615411	+	0.000355308i
$875$	25.1212	−	3.84901i	0.849252	−	0.130120i
$876$		0			0
$877$	21.5503	−	15.0897i	0.727701	−	0.509541i	−0.150039	−	0.988680i	$-0.547940\pi$
$877$	21.5503	−	15.0897i	0.727701	−	0.509541i	0.877739	+	0.479139i	$0.159051\pi$
$878$	21.7781	−	15.2492i	0.734974	−	0.514635i
$879$		0			0
$880$	0.286696	+	0.291029i	0.00966452	+	0.00981057i
$881$	−33.0323	−	19.0712i	−1.11289	−	0.642526i	−0.173311	−	0.984867i	$-0.555447\pi$
$881$	−33.0323	−	19.0712i	−1.11289	−	0.642526i	−0.939576	+	0.342342i	$0.888780\pi$
$882$		0			0
$883$	16.1538	+	4.32839i	0.543618	+	0.145662i	0.520170	−	0.854063i	$-0.325869\pi$
$883$	16.1538	+	4.32839i	0.543618	+	0.145662i	0.0234486	+	0.999725i	$0.492535\pi$
$884$	5.92856	+	2.15782i	0.199399	+	0.0725753i
$885$		0			0
$886$	8.21829	+	6.89597i	0.276099	+	0.231674i
$887$	−19.4263	+	41.6598i	−0.652271	+	1.39880i	0.250261	+	0.968178i	$0.419484\pi$
$887$	−19.4263	+	41.6598i	−0.652271	+	1.39880i	−0.902532	+	0.430622i	$0.858294\pi$
$888$		0			0
$889$	3.26236	−	0.575242i	0.109416	−	0.0192930i
$890$	14.6883	−	17.2406i	0.492353	−	0.577907i
$891$		0			0
$892$	−15.8997	−	15.8997i	−0.532363	−	0.532363i
$893$	0.217908	−	0.311205i	0.00729201	−	0.0104141i
$894$		0			0
$895$	52.5465	−	24.0248i	1.75644	−	0.803060i
$896$	−1.46114	+	1.74132i	−0.0488132	+	0.0581734i
$897$		0			0
$898$	13.5421	−	6.31480i	0.451906	−	0.210727i
$899$	9.84610	+	17.0539i	0.328386	+	0.568781i
$900$		0			0
$901$	−17.9636	+	31.1139i	−0.598454	+	1.03655i
$902$	0.179184	−	2.04808i	0.00596618	−	0.0681937i
$903$		0			0
$904$	5.69220	+	1.00369i	0.189320	+	0.0333822i
$905$	−2.90055	+	30.5159i	−0.0964174	+	1.01438i
$906$		0			0
$907$	−41.1671	−	3.60165i	−1.36693	−	0.119591i	−0.620057	−	0.784557i	$-0.712891\pi$
$907$	−41.1671	−	3.60165i	−1.36693	−	0.119591i	−0.746874	+	0.664966i	$0.768446\pi$
$908$	21.8582	−	5.85688i	0.725389	−	0.194367i
$909$		0			0
$910$	8.56854	+	1.57721i	0.284044	+	0.0522840i
$911$	3.62100	−	9.94863i	0.119969	−	0.329613i	−0.865143	−	0.501525i	$-0.832772\pi$
$911$	3.62100	−	9.94863i	0.119969	−	0.329613i	0.985112	+	0.171913i	$0.0549946\pi$
$912$		0			0
$913$	−2.48536	+	0.217441i	−0.0822534	+	0.00719624i
$914$	0.807284	−	0.293827i	0.0267026	−	0.00971895i
$915$		0			0
$916$	−1.72951	−	9.80853i	−0.0571445	−	0.324083i
$917$	6.29499	−	6.29499i	0.207879	−	0.207879i
$918$		0			0
$919$		−	33.3158i		−	1.09899i	−0.835498	−	0.549493i	$-0.814821\pi$
$919$		−	33.3158i		−	1.09899i	0.835498	−	0.549493i	$-0.185179\pi$
$920$	0.750226	−	0.195004i	0.0247342	−	0.00642911i
$921$		0			0
$922$	−18.4694	−	8.61244i	−0.608258	−	0.283636i
$923$	−1.29835	−	14.8402i	−0.0427358	−	0.488472i
$924$		0			0
$925$	−10.1367	−	14.9490i	−0.333293	−	0.491521i
$926$	4.53775	−	2.61987i	0.149120	−	0.0860942i
$927$		0			0
$928$	1.88557	+	7.03705i	0.0618969	+	0.231002i
$929$	−7.79186	+	6.53815i	−0.255643	+	0.214510i	−0.761598	−	0.648050i	$-0.775585\pi$
$929$	−7.79186	+	6.53815i	−0.255643	+	0.214510i	0.505955	+	0.862560i	$0.331140\pi$
$930$		0			0
$931$	0.0192882	−	0.109389i	0.000632145	−	0.00358507i
$932$	−1.58019	−	2.25675i	−0.0517609	−	0.0739223i
$933$		0			0
$934$	9.23437	+	11.0051i	0.302158	+	0.360098i
$935$	1.41679	−	0.503670i	0.0463340	−	0.0164718i
$936$		0			0
$937$	6.14513	−	22.9339i	0.200753	−	0.749219i	−0.789950	−	0.613172i	$-0.789893\pi$
$937$	6.14513	−	22.9339i	0.200753	−	0.749219i	0.990702	−	0.136047i	$-0.0434399\pi$
$938$	12.0114	+	25.7586i	0.392187	+	0.841048i
$939$		0			0
$940$	−2.33057	−	13.8227i	−0.0760149	−	0.450847i
$941$	−13.3332	−	36.6328i	−0.434651	−	1.19419i	−0.942927	−	0.332999i	$-0.891939\pi$
$941$	−13.3332	−	36.6328i	−0.434651	−	1.19419i	0.508276	−	0.861194i	$-0.330283\pi$
$942$		0			0
$943$	−3.19550	−	2.23751i	−0.104060	−	0.0728634i
$944$	11.4210			0.371722
$945$		0			0
$946$	1.65189			0.0537075
$947$	−17.7996	−	12.4634i	−0.578409	−	0.405006i	0.247435	−	0.968904i	$-0.420412\pi$
$947$	−17.7996	−	12.4634i	−0.578409	−	0.405006i	−0.825844	+	0.563898i	$0.809301\pi$
$948$		0			0
$949$	3.30699	+	9.08589i	0.107350	+	0.294941i
$950$	−0.0740262	−	0.293828i	−0.00240173	−	0.00953305i
$951$		0			0
$952$	3.53592	+	7.58281i	0.114600	+	0.245760i
$953$	−11.2586	+	42.0178i	−0.364703	+	1.36109i	0.503121	+	0.864216i	$0.332185\pi$
$953$	−11.2586	+	42.0178i	−0.364703	+	1.36109i	−0.867823	+	0.496873i	$0.834482\pi$
$954$		0			0
$955$	18.8024	+	8.93999i	0.608432	+	0.289291i
$956$	−12.9418	−	15.4235i	−0.418568	−	0.498830i
$957$		0			0
$958$	6.46517	+	9.23321i	0.208880	+	0.298312i
$959$	5.10832	−	28.9707i	0.164956	−	0.935514i
$960$		0			0
$961$	−18.1505	+	15.2300i	−0.585499	+	0.491292i
$962$	−1.60258	−	5.98090i	−0.0516691	−	0.192832i
$963$		0			0
$964$	−19.8450	+	11.4575i	−0.639165	+	0.369022i
$965$	−11.0764	+	6.28470i	−0.356563	+	0.202312i
$966$		0			0
$967$	3.82521	+	43.7224i	0.123011	+	1.40602i	0.767326	+	0.641257i	$0.221587\pi$
$967$	3.82521	+	43.7224i	0.123011	+	1.40602i	−0.644315	+	0.764760i	$0.722858\pi$
$968$	−9.93913	−	4.63469i	−0.319456	−	0.148965i
$969$		0			0
$970$	3.53801	+	13.6115i	0.113599	+	0.437039i
$971$			17.6250i			0.565613i	0.959177	+	0.282806i	$0.0912654\pi$
$971$			17.6250i			0.565613i	−0.959177	+	0.282806i	$0.908735\pi$
$972$		0			0
$973$	−20.3354	+	20.3354i	−0.651922	+	0.651922i
$974$	4.19169	+	23.7723i	0.134310	+	0.761712i
$975$		0			0
$976$	−12.0127	+	4.37226i	−0.384517	+	0.139953i
$977$	46.1789	−	4.04013i	1.47739	−	0.129255i	0.680222	−	0.733006i	$-0.261883\pi$
$977$	46.1789	−	4.04013i	1.47739	−	0.129255i	0.797173	+	0.603751i	$0.206328\pi$
$978$		0			0
$979$	0.632925	−	1.73895i	0.0202284	−	0.0555770i
$980$	−2.32553	−	3.37479i	−0.0742864	−	0.107804i
$981$		0			0
$982$	2.44093	−	0.654046i	0.0778933	−	0.0208715i
$983$	14.8728	+	1.30120i	0.474367	+	0.0415018i	0.321833	−	0.946796i	$-0.395701\pi$
$983$	14.8728	+	1.30120i	0.474367	+	0.0415018i	0.152534	+	0.988298i	$0.451257\pi$
$984$		0			0
$985$	6.26658	+	7.58299i	0.199670	+	0.241614i
$986$	26.4076	+	4.65637i	0.840989	+	0.148289i
$987$		0			0
$988$	0.00905348	−	0.103482i	0.000288030	−	0.00329219i
$989$	1.56719	−	2.71445i	0.0498337	−	0.0863146i
$990$		0			0
$991$	8.28007	+	14.3415i	0.263025	+	0.455573i	0.967044	−	0.254608i	$-0.0819465\pi$
$991$	8.28007	+	14.3415i	0.263025	+	0.455573i	−0.704019	+	0.710181i	$0.748613\pi$
$992$	2.44976	−	1.14234i	0.0777799	−	0.0362693i
$993$		0			0
$994$	12.6986	−	15.1336i	0.402774	−	0.480008i
$995$	−3.55118	−	7.76708i	−0.112580	−	0.246233i
$996$		0			0
$997$	27.8019	−	39.7053i	0.880496	−	1.25748i	−0.0848204	−	0.996396i	$-0.527032\pi$
$997$	27.8019	−	39.7053i	0.880496	−	1.25748i	0.965317	−	0.261082i	$-0.0840794\pi$
$998$	14.4631	+	14.4631i	0.457820	+	0.457820i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.3		216
3.2	odd	2		270.2.r.a.257.15	yes	216
5.3	odd	4	inner	810.2.s.a.233.7		216
15.8	even	4		270.2.r.a.203.18	yes	216
27.2	odd	18	inner	810.2.s.a.737.7		216
27.25	even	9		270.2.r.a.137.18	yes	216
135.83	even	36	inner	810.2.s.a.413.3		216
135.133	odd	36		270.2.r.a.83.15	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.15	✓	216	135.133	odd	36
270.2.r.a.137.18	yes	216	27.25	even	9
270.2.r.a.203.18	yes	216	15.8	even	4
270.2.r.a.257.15	yes	216	3.2	odd	2
810.2.s.a.233.7		216	5.3	odd	4	inner
810.2.s.a.413.3		216	135.83	even	36	inner
810.2.s.a.557.3		216	1.1	even	1	trivial
810.2.s.a.737.7		216	27.2	odd	18	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.82201 - 1.29626i) q^{5} +(0.960666 + 2.06015i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.82201 - 1.29626i) q^{5} +(0.960666 + 2.06015i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.749001 + 2.10689i) q^{10} +(0.117436 + 0.139955i) q^{11} +(-0.983160 - 1.40410i) q^{13} +(0.394725 - 2.23860i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.952636 + 3.55528i) q^{17} +(0.0524828 - 0.0303010i) q^{19} +(0.594918 - 2.15548i) q^{20} +(-0.0159232 - 0.182002i) q^{22} +(-0.314181 - 0.146505i) q^{23} +(1.63944 + 4.72358i) q^{25} +1.71409i q^{26} +(-1.60735 + 1.60735i) q^{28} +(1.26508 + 7.17461i) q^{29} +(2.54000 - 0.924483i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.25887 - 3.45873i) q^{34} +(0.920145 - 4.99889i) q^{35} +(-3.48926 + 0.934944i) q^{37} +(-0.0603714 - 0.00528181i) q^{38} +(-1.72366 + 1.42443i) q^{40} +(11.0821 + 1.95407i) q^{41} +(-0.788032 + 9.00724i) q^{43} +(-0.0913488 + 0.158221i) q^{44} +(0.173330 + 0.300216i) q^{46} +(5.68160 - 2.64937i) q^{47} +(1.17815 - 1.40407i) q^{49} +(1.36638 - 4.80968i) q^{50} +(0.983160 - 1.40410i) q^{52} +(6.90204 + 6.90204i) q^{53} +(-0.0325523 - 0.407225i) q^{55} +(2.23860 - 0.394725i) q^{56} +(3.07890 - 6.60271i) q^{58} +(-8.74898 - 7.34127i) q^{59} +(12.0127 + 4.37226i) q^{61} +(-2.61091 - 0.699590i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-0.0287430 + 3.83271i) q^{65} +(-10.2421 + 7.17156i) q^{67} +(-3.01505 + 2.11116i) q^{68} +(-3.62099 + 3.56708i) q^{70} +(7.52652 + 4.34544i) q^{71} +(-5.44870 - 1.45997i) q^{73} +(3.39450 + 1.23550i) q^{74} +(0.0464238 + 0.0389542i) q^{76} +(-0.175511 + 0.376386i) q^{77} +(15.5249 - 2.73746i) q^{79} +(2.22896 - 0.178176i) q^{80} +(-7.95711 - 7.95711i) q^{82} +(-7.83255 + 11.1860i) q^{83} +(2.87285 - 7.71262i) q^{85} +(5.81186 - 6.92631i) q^{86} +(0.165580 - 0.0772114i) q^{88} +(-5.06451 - 8.77199i) q^{89} +(1.94817 - 3.37433i) q^{91} +(0.0302134 - 0.345341i) q^{92} +(-6.17371 - 1.08859i) q^{94} +(-0.134902 - 0.0128225i) q^{95} +(6.26559 + 0.548168i) q^{97} +(-1.77043 + 0.474385i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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