LMFDB - Embedded newform 333.2.br.a.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,2,Mod(17,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("333.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	333.br (of order $36$, degree $12$, 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:	$2.65901838731$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	333.35
Dual form			333.2.br.a.314.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.740607 - 0.0647947i) q^{2} +(-1.42532 - 0.251322i) q^{4} +(0.605949 - 1.29946i) q^{5} +(-3.90763 + 1.42226i) q^{7} +(2.47552 + 0.663314i) q^{8} +O(q^{10})$	\(q+(-0.740607 - 0.0647947i) q^{2} +(-1.42532 - 0.251322i) q^{4} +(0.605949 - 1.29946i) q^{5} +(-3.90763 + 1.42226i) q^{7} +(2.47552 + 0.663314i) q^{8} +(-0.532968 + 0.923127i) q^{10} +(2.84195 + 4.92241i) q^{11} +(0.416077 - 0.291340i) q^{13} +(2.98617 - 0.800143i) q^{14} +(0.929631 + 0.338358i) q^{16} +(2.60709 + 1.82551i) q^{17} +(0.357603 + 4.08742i) q^{19} +(-1.19025 + 1.69985i) q^{20} +(-1.78582 - 3.82971i) q^{22} +(-0.532251 - 1.98639i) q^{23} +(1.89251 + 2.25541i) q^{25} +(-0.327027 + 0.188809i) q^{26} +(5.92705 - 1.04510i) q^{28} +(0.711102 - 2.65387i) q^{29} +(-6.49451 + 6.49451i) q^{31} +(-5.31203 - 2.47704i) q^{32} +(-1.81255 - 1.52091i) q^{34} +(-0.519651 + 5.93963i) q^{35} +(3.89907 + 4.66875i) q^{37} -3.05034i q^{38} +(2.36199 - 2.81491i) q^{40} +(-1.92858 + 10.9375i) q^{41} +(-6.05082 - 6.05082i) q^{43} +(-2.81357 - 7.73023i) q^{44} +(0.265482 + 1.50562i) q^{46} +(4.29458 + 2.47948i) q^{47} +(7.88445 - 6.61584i) q^{49} +(-1.25547 - 1.79300i) q^{50} +(-0.666261 + 0.310682i) q^{52} +(2.11669 - 5.81557i) q^{53} +(8.11855 - 0.710281i) q^{55} +(-10.6168 + 0.928853i) q^{56} +(-0.698604 + 1.91940i) q^{58} +(-1.45301 + 0.677550i) q^{59} +(-6.21024 - 8.86914i) q^{61} +(5.23069 - 4.38907i) q^{62} +(2.06012 + 1.18941i) q^{64} +(-0.126464 - 0.717213i) q^{65} +(3.03401 + 8.33588i) q^{67} +(-3.25714 - 3.25714i) q^{68} +(0.769714 - 4.36526i) q^{70} +(-4.15729 + 4.95447i) q^{71} -2.61493i q^{73} +(-2.58517 - 3.71035i) q^{74} +(0.517560 - 5.91573i) q^{76} +(-18.1063 - 15.1930i) q^{77} +(-10.2794 - 4.79336i) q^{79} +(1.00299 - 1.00299i) q^{80} +(2.13701 - 7.97542i) q^{82} +(17.1994 - 3.03272i) q^{83} +(3.95194 - 2.28165i) q^{85} +(4.08922 + 4.87334i) q^{86} +(3.77021 + 14.0706i) q^{88} +(0.634129 + 1.35989i) q^{89} +(-1.21151 + 1.73022i) q^{91} +(0.259404 + 2.96500i) q^{92} +(-3.01994 - 2.11458i) q^{94} +(5.52813 + 2.01207i) q^{95} +(-0.468762 + 0.125604i) q^{97} +(-6.26795 + 4.38887i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q+O(q^{10}) $ 144 * q	$ 144 q + 24 q^{16} - 48 q^{28} - 48 q^{31} - 144 q^{34} - 12 q^{37} - 72 q^{40} - 48 q^{43} - 216 q^{46} + 108 q^{49} - 120 q^{52} + 132 q^{58} - 48 q^{67} + 48 q^{70} + 72 q^{82} + 144 q^{88} - 108 q^{91} + 144 q^{94} + 144 q^{97}+O(q^{100}) $ 144 * q + 24 * q^16 - 48 * q^28 - 48 * q^31 - 144 * q^34 - 12 * q^37 - 72 * q^40 - 48 * q^43 - 216 * q^46 + 108 * q^49 - 120 * q^52 + 132 * q^58 - 48 * q^67 + 48 * q^70 + 72 * q^82 + 144 * q^88 - 108 * q^91 + 144 * q^94 + 144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$-1$	$e\left(\frac{19}{36}\right)$

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 $

$2$	−0.740607	−	0.0647947i	−0.523688	−	0.0458168i	−0.177753	−	0.984075i	$-0.556883\pi$
$2$	−0.740607	−	0.0647947i	−0.523688	−	0.0458168i	−0.345935	+	0.938258i	$0.612438\pi$
$3$		0			0
$3$		0			0
$4$	−1.42532	−	0.251322i	−0.712658	−	0.125661i
$5$	0.605949	−	1.29946i	0.270988	−	0.581137i	−0.722972	−	0.690878i	$-0.757224\pi$
$5$	0.605949	−	1.29946i	0.270988	−	0.581137i	0.993960	+	0.109741i	$0.0350021\pi$
$6$		0			0
$7$	−3.90763	+	1.42226i	−1.47695	+	0.537565i	−0.949977	−	0.312320i	$-0.898894\pi$
$7$	−3.90763	+	1.42226i	−1.47695	+	0.537565i	−0.526969	+	0.849884i	$0.676672\pi$
$8$	2.47552	+	0.663314i	0.875229	+	0.234517i
$9$		0			0
$10$	−0.532968	+	0.923127i	−0.168539	+	0.291919i
$11$	2.84195	+	4.92241i	0.856881	+	1.48416i	0.874889	+	0.484324i	$0.160934\pi$
$11$	2.84195	+	4.92241i	0.856881	+	1.48416i	−0.0180077	+	0.999838i	$0.505732\pi$
$12$		0			0
$13$	0.416077	−	0.291340i	0.115399	−	0.0808032i	−0.514452	−	0.857519i	$-0.672005\pi$
$13$	0.416077	−	0.291340i	0.115399	−	0.0808032i	0.629851	+	0.776716i	$0.283116\pi$
$14$	2.98617	−	0.800143i	0.798089	−	0.213847i
$15$		0			0
$16$	0.929631	+	0.338358i	0.232408	+	0.0845895i
$17$	2.60709	+	1.82551i	0.632313	+	0.442750i	0.845291	−	0.534307i	$-0.179427\pi$
$17$	2.60709	+	1.82551i	0.632313	+	0.442750i	−0.212978	+	0.977057i	$0.568316\pi$
$18$		0			0
$19$	0.357603	+	4.08742i	0.0820397	+	0.937718i	0.919982	+	0.391960i	$0.128203\pi$
$19$	0.357603	+	4.08742i	0.0820397	+	0.937718i	−0.837943	+	0.545758i	$0.816242\pi$
$20$	−1.19025	+	1.69985i	−0.266148	+	0.380099i
$21$		0			0
$22$	−1.78582	−	3.82971i	−0.380739	−	0.816497i
$23$	−0.532251	−	1.98639i	−0.110982	−	0.414191i	0.887973	−	0.459896i	$-0.152113\pi$
$23$	−0.532251	−	1.98639i	−0.110982	−	0.414191i	−0.998955	+	0.0457050i	$0.985447\pi$
$24$		0			0
$25$	1.89251	+	2.25541i	0.378503	+	0.451082i
$26$	−0.327027	+	0.188809i	−0.0641352	+	0.0370285i
$27$		0			0
$28$	5.92705	−	1.04510i	1.12011	−	0.197505i
$29$	0.711102	−	2.65387i	0.132048	−	0.492811i	−0.867944	−	0.496662i	$-0.834559\pi$
$29$	0.711102	−	2.65387i	0.132048	−	0.492811i	0.999993	+	0.00385050i	$0.00122566\pi$
$30$		0			0
$31$	−6.49451	+	6.49451i	−1.16645	+	1.16645i	−0.183413	+	0.983036i	$0.558715\pi$
$31$	−6.49451	+	6.49451i	−1.16645	+	1.16645i	−0.983036	+	0.183413i	$0.941285\pi$
$32$	−5.31203	−	2.47704i	−0.939043	−	0.437883i
$33$		0			0
$34$	−1.81255	−	1.52091i	−0.310849	−	0.260834i
$35$	−0.519651	+	5.93963i	−0.0878370	+	1.00398i
$36$		0			0
$37$	3.89907	+	4.66875i	0.641003	+	0.767539i
$37$	3.89907	+	4.66875i	0.641003	+	0.767539i
$38$		−	3.05034i		−	0.494831i
$39$		0			0
$40$	2.36199	−	2.81491i	0.373463	−	0.445076i
$41$	−1.92858	+	10.9375i	−0.301193	+	1.70815i	0.339712	+	0.940530i	$0.389671\pi$
$41$	−1.92858	+	10.9375i	−0.301193	+	1.70815i	−0.640905	+	0.767621i	$0.721441\pi$
$42$		0			0
$43$	−6.05082	−	6.05082i	−0.922742	−	0.922742i	0.0744805	−	0.997222i	$-0.476270\pi$
$43$	−6.05082	−	6.05082i	−0.922742	−	0.922742i	−0.997222	+	0.0744805i	$0.976270\pi$
$44$	−2.81357	−	7.73023i	−0.424162	−	1.16538i
$45$		0			0
$46$	0.265482	+	1.50562i	0.0391431	+	0.221992i
$47$	4.29458	+	2.47948i	0.626429	+	0.361669i	0.779368	−	0.626567i	$-0.215540\pi$
$47$	4.29458	+	2.47948i	0.626429	+	0.361669i	−0.152939	+	0.988236i	$0.548874\pi$
$48$		0			0
$49$	7.88445	−	6.61584i	1.12635	−	0.945120i
$50$	−1.25547	−	1.79300i	−0.177550	−	0.253568i
$51$		0			0
$52$	−0.666261	+	0.310682i	−0.0923937	+	0.0430839i
$53$	2.11669	−	5.81557i	0.290750	−	0.798830i	−0.705207	−	0.709002i	$-0.749146\pi$
$53$	2.11669	−	5.81557i	0.290750	−	0.798830i	0.995957	−	0.0898285i	$-0.0286319\pi$
$54$		0			0
$55$	8.11855	−	0.710281i	1.09471	−	0.0957743i
$56$	−10.6168	+	0.928853i	−1.41873	+	0.124123i
$57$		0			0
$58$	−0.698604	+	1.91940i	−0.0917312	+	0.252029i
$59$	−1.45301	+	0.677550i	−0.189166	+	0.0882095i	−0.514893	−	0.857254i	$-0.672169\pi$
$59$	−1.45301	+	0.677550i	−0.189166	+	0.0882095i	0.325728	+	0.945464i	$0.394391\pi$
$60$		0			0
$61$	−6.21024	−	8.86914i	−0.795140	−	1.13558i	−0.988016	−	0.154354i	$-0.950670\pi$
$61$	−6.21024	−	8.86914i	−0.795140	−	1.13558i	0.192876	−	0.981223i	$-0.438219\pi$
$62$	5.23069	−	4.38907i	0.664298	−	0.557413i
$63$		0			0
$64$	2.06012	+	1.18941i	0.257515	+	0.148676i
$65$	−0.126464	−	0.717213i	−0.0156859	−	0.0889593i
$66$		0			0
$67$	3.03401	+	8.33588i	0.370664	+	1.01839i	0.975106	+	0.221741i	$0.0711739\pi$
$67$	3.03401	+	8.33588i	0.370664	+	1.01839i	−0.604442	+	0.796649i	$0.706604\pi$
$68$	−3.25714	−	3.25714i	−0.394986	−	0.394986i
$69$		0			0
$70$	0.769714	−	4.36526i	0.0919984	−	0.521749i
$71$	−4.15729	+	4.95447i	−0.493380	+	0.587987i	−0.954074	−	0.299572i	$-0.903156\pi$
$71$	−4.15729	+	4.95447i	−0.493380	+	0.587987i	0.460694	+	0.887559i	$0.347601\pi$
$72$		0			0
$73$		−	2.61493i		−	0.306055i	−0.988222	−	0.153027i	$-0.951098\pi$
$73$		−	2.61493i		−	0.306055i	0.988222	−	0.153027i	$-0.0489023\pi$
$74$	−2.58517	−	3.71035i	−0.300519	−	0.431319i
$75$		0			0
$76$	0.517560	−	5.91573i	0.0593682	−	0.678581i
$77$	−18.1063	−	15.1930i	−2.06340	−	1.73140i
$78$		0			0
$79$	−10.2794	−	4.79336i	−1.15652	−	0.539295i	−0.252843	−	0.967507i	$-0.581366\pi$
$79$	−10.2794	−	4.79336i	−1.15652	−	0.539295i	−0.903678	+	0.428213i	$0.859143\pi$
$80$	1.00299	−	1.00299i	0.112138	−	0.112138i
$81$		0			0
$82$	2.13701	−	7.97542i	0.235993	−	0.880738i
$83$	17.1994	−	3.03272i	1.88788	−	0.332884i	0.894435	−	0.447197i	$-0.147578\pi$
$83$	17.1994	−	3.03272i	1.88788	−	0.332884i	0.993445	+	0.114313i	$0.0364667\pi$
$84$		0			0
$85$	3.95194	−	2.28165i	0.428648	−	0.247480i
$86$	4.08922	+	4.87334i	0.440952	+	0.525506i
$87$		0			0
$88$	3.77021	+	14.0706i	0.401906	+	1.49993i
$89$	0.634129	+	1.35989i	0.0672175	+	0.144148i	0.937046	−	0.349206i	$-0.113549\pi$
$89$	0.634129	+	1.35989i	0.0672175	+	0.144148i	−0.869829	+	0.493354i	$0.835771\pi$
$90$		0			0
$91$	−1.21151	+	1.73022i	−0.127001	+	0.181376i
$92$	0.259404	+	2.96500i	0.0270447	+	0.309122i
$93$		0			0
$94$	−3.01994	−	2.11458i	−0.311483	−	0.218103i
$95$	5.52813	+	2.01207i	0.567174	+	0.206434i
$96$		0			0
$97$	−0.468762	+	0.125604i	−0.0475956	+	0.0127532i	−0.282538	−	0.959256i	$-0.591176\pi$
$97$	−0.468762	+	0.125604i	−0.0475956	+	0.0127532i	0.234943	+	0.972009i	$0.424510\pi$
$98$	−6.26795	+	4.38887i	−0.633159	+	0.443343i
$99$		0			0
$100$	−2.13059	−	3.69030i	−0.213059	−	0.369030i
$101$	3.72199	−	6.44668i	0.370352	−	0.641468i	−0.619268	−	0.785180i	$-0.712570\pi$
$101$	3.72199	−	6.44668i	0.370352	−	0.641468i	0.989620	+	0.143712i	$0.0459038\pi$
$102$		0			0
$103$	−1.78970	−	0.479547i	−0.176344	−	0.0472512i	0.169567	−	0.985519i	$-0.445763\pi$
$103$	−1.78970	−	0.479547i	−0.176344	−	0.0472512i	−0.345910	+	0.938268i	$0.612430\pi$
$104$	1.22326	−	0.445229i	0.119950	−	0.0436583i
$105$		0			0
$106$	−1.94446	+	4.16990i	−0.188862	+	0.405017i
$107$	−9.44205	−	1.66489i	−0.912798	−	0.160951i	−0.302524	−	0.953142i	$-0.597829\pi$
$107$	−9.44205	−	1.66489i	−0.912798	−	0.160951i	−0.610273	+	0.792191i	$0.708940\pi$
$108$		0			0
$109$	−0.485235	−	0.0424525i	−0.0464771	−	0.00406622i	0.0638935	−	0.997957i	$-0.479648\pi$
$109$	−0.485235	−	0.0424525i	−0.0464771	−	0.00406622i	−0.110371	+	0.993891i	$0.535204\pi$
$110$	−6.05868			−0.577672
$111$		0			0
$112$	−4.11389			−0.388726
$113$	0.371267	+	0.0324817i	0.0349259	+	0.00305562i	0.104605	−	0.994514i	$-0.466642\pi$
$113$	0.371267	+	0.0324817i	0.0349259	+	0.00305562i	−0.0696794	+	0.997569i	$0.522198\pi$
$114$		0			0
$115$	−2.90375	−	0.512010i	−0.270776	−	0.0477452i
$116$	−1.68052	+	3.60389i	−0.156032	+	0.334612i
$117$		0			0
$118$	1.12001	−	0.407651i	0.103105	−	0.0375273i
$119$	−12.7839	−	3.42544i	−1.17190	−	0.314009i
$120$		0			0
$121$	−10.6534	+	18.4522i	−0.968491	+	1.67747i
$122$	4.02467	+	6.97094i	0.364377	+	0.631119i
$123$		0			0
$124$	10.8889	−	7.62452i	0.977856	−	0.684702i
$125$	11.0023	−	2.94805i	0.984075	−	0.263682i
$126$		0			0
$127$	12.7388	+	4.63655i	1.13039	+	0.411427i	0.838433	−	0.545005i	$-0.183472\pi$
$127$	12.7388	+	4.63655i	1.13039	+	0.411427i	0.291955	+	0.956432i	$0.405694\pi$
$128$	8.15371	+	5.70929i	0.720693	+	0.504635i
$129$		0			0
$130$	0.0471885	+	0.539367i	0.00413870	+	0.0473056i
$131$	−3.35015	+	4.78451i	−0.292704	+	0.418025i	−0.938390	−	0.345579i	$-0.887683\pi$
$131$	−3.35015	+	4.78451i	−0.292704	+	0.418025i	0.645686	+	0.763603i	$0.276572\pi$
$132$		0			0
$133$	−7.21076	−	15.4635i	−0.625252	−	1.34086i
$134$	−1.70689	−	6.37020i	−0.147453	−	0.550301i
$135$		0			0
$136$	5.24303	+	6.24840i	0.449586	+	0.535796i
$137$	−0.230909	+	0.133315i	−0.0197279	+	0.0113899i	−0.509832	−	0.860274i	$-0.670292\pi$
$137$	−0.230909	+	0.133315i	−0.0197279	+	0.0113899i	0.490104	+	0.871664i	$0.336959\pi$
$138$		0			0
$139$	11.9633	−	2.10945i	1.01471	−	0.178921i	0.358526	−	0.933520i	$-0.383279\pi$
$139$	11.9633	−	2.10945i	1.01471	−	0.178921i	0.656187	+	0.754598i	$0.272168\pi$
$140$	2.23342	−	8.33525i	0.188759	−	0.704457i
$141$		0			0
$142$	3.39994	−	3.39994i	0.285317	−	0.285317i
$143$	2.61657	+	1.22012i	0.218808	+	0.102032i
$144$		0			0
$145$	−3.01771	−	2.53216i	−0.250607	−	0.210284i
$146$	−0.169434	+	1.93664i	−0.0140224	+	0.160277i
$147$		0			0
$148$	−4.38404	−	7.63437i	−0.360366	−	0.627541i
$149$		−	0.779996i		−	0.0638997i	−0.999489	−	0.0319499i	$-0.989828\pi$
$149$		−	0.779996i		−	0.0638997i	0.999489	−	0.0319499i	$-0.0101717\pi$
$150$		0			0
$151$	3.13011	−	3.73032i	0.254725	−	0.303570i	−0.623494	−	0.781828i	$-0.714287\pi$
$151$	3.13011	−	3.73032i	0.254725	−	0.303570i	0.878219	+	0.478259i	$0.158732\pi$
$152$	−1.82599	+	10.3557i	−0.148107	+	0.839958i
$153$		0			0
$154$	12.4252	+	12.4252i	1.00125	+	1.00125i
$155$	4.50403	+	12.3747i	0.361772	+	0.993961i
$156$		0			0
$157$	0.174343	+	0.988747i	0.0139141	+	0.0789106i	0.990974	−	0.134053i	$-0.0427994\pi$
$157$	0.174343	+	0.988747i	0.0139141	+	0.0789106i	−0.977060	+	0.212964i	$0.931688\pi$
$158$	7.30240	+	4.21604i	0.580948	+	0.335410i
$159$		0			0
$160$	−6.43763	+	5.40181i	−0.508939	+	0.427051i
$161$	4.90501	+	7.00508i	0.386569	+	0.552078i
$162$		0			0
$163$	−8.87645	+	4.13916i	−0.695257	+	0.324204i	−0.737922	−	0.674886i	$-0.764193\pi$
$163$	−8.87645	+	4.13916i	−0.695257	+	0.324204i	0.0426651	+	0.999089i	$0.486415\pi$
$164$	5.49766	−	15.1047i	0.429295	−	1.17948i
$165$		0			0
$166$	−12.9345	+	1.13162i	−1.00391	+	0.0878309i
$167$	16.8769	−	1.47654i	1.30598	−	0.114258i	0.587167	−	0.809465i	$-0.300243\pi$
$167$	16.8769	−	1.47654i	1.30598	−	0.114258i	0.718809	+	0.695207i	$0.244687\pi$
$168$		0			0
$169$	−4.35802	+	11.9736i	−0.335232	+	0.921043i
$170$	−3.07467	+	1.43374i	−0.235816	+	0.109963i
$171$		0			0
$172$	7.10363	+	10.1450i	0.541647	+	0.773552i
$173$	−11.7481	+	9.85782i	−0.893191	+	0.749476i	−0.968848	−	0.247658i	$-0.920339\pi$
$173$	−11.7481	+	9.85782i	−0.893191	+	0.749476i	0.0756565	+	0.997134i	$0.475895\pi$
$174$		0			0
$175$	−10.6030	−	6.12166i	−0.801514	−	0.462754i
$176$	0.976432	+	5.53762i	0.0736013	+	0.417414i
$177$		0			0
$178$	−0.381526	−	1.04823i	−0.0285966	−	0.0785685i
$179$	18.2031	+	18.2031i	1.36056	+	1.36056i	0.873202	+	0.487358i	$0.162039\pi$
$179$	18.2031	+	18.2031i	1.36056	+	1.36056i	0.487358	+	0.873202i	$0.337961\pi$
$180$		0			0
$181$	−2.20095	+	12.4822i	−0.163595	+	0.927794i	0.786906	+	0.617073i	$0.211682\pi$
$181$	−2.20095	+	12.4822i	−0.163595	+	0.927794i	−0.950501	+	0.310721i	$0.899429\pi$
$182$	1.00936	−	1.20291i	0.0748191	−	0.0891659i
$183$		0			0
$184$		−	5.27040i		−	0.388539i
$185$	8.42950	−	2.23766i	0.619749	−	0.164516i
$186$		0			0
$187$	−1.57665	+	18.0212i	−0.115296	+	1.31784i
$188$	−5.49798	−	4.61336i	−0.400982	−	0.336464i
$189$		0			0
$190$	−3.96380	−	1.84835i	−0.287564	−	0.134093i
$191$	10.6881	−	10.6881i	0.773362	−	0.773362i	−0.205330	−	0.978693i	$-0.565827\pi$
$191$	10.6881	−	10.6881i	0.773362	−	0.773362i	0.978693	+	0.205330i	$0.0658269\pi$
$192$		0			0
$193$	−1.69327	+	6.31936i	−0.121884	+	0.454877i	−0.999709	−	0.0241034i	$-0.992327\pi$
$193$	−1.69327	+	6.31936i	−0.121884	+	0.454877i	0.877825	+	0.478981i	$0.158994\pi$
$194$	0.355307	−	0.0626502i	0.0255095	−	0.00449802i
$195$		0			0
$196$	−12.9005	+	7.44813i	−0.921467	+	0.532009i
$197$	−1.20580	−	1.43701i	−0.0859095	−	0.102383i	0.721377	−	0.692542i	$-0.243509\pi$
$197$	−1.20580	−	1.43701i	−0.0859095	−	0.102383i	−0.807287	+	0.590159i	$0.799065\pi$
$198$		0			0
$199$	3.87323	+	14.4551i	0.274566	+	1.02469i	0.956132	+	0.292937i	$0.0946327\pi$
$199$	3.87323	+	14.4551i	0.274566	+	1.02469i	−0.681566	+	0.731757i	$0.738701\pi$
$200$	3.18891	+	6.83864i	0.225490	+	0.483565i
$201$		0			0
$202$	−3.17424	+	4.53329i	−0.223339	+	0.318961i
$203$	0.995772	+	11.3817i	0.0698895	+	0.798840i
$204$		0			0
$205$	13.0442	+	9.13367i	0.911049	+	0.637923i
$206$	1.29439	+	0.471119i	0.0901843	+	0.0328244i
$207$		0			0
$208$	0.485375	−	0.130056i	0.0336547	−	0.00901776i
$209$	−19.1036	+	13.3765i	−1.32143	+	0.925273i
$210$		0			0
$211$	−13.1823	−	22.8325i	−0.907508	−	1.57185i	−0.817514	−	0.575908i	$-0.804648\pi$
$211$	−13.1823	−	22.8325i	−0.907508	−	1.57185i	−0.0899943	−	0.995942i	$-0.528685\pi$
$212$	−4.47854	+	7.75705i	−0.307587	+	0.532756i
$213$		0			0
$214$	6.88497	+	1.84482i	0.470647	+	0.126110i
$215$	−11.5293	+	4.19632i	−0.786292	+	0.286187i
$216$		0			0
$217$	16.1413	−	34.6151i	1.09574	−	2.34982i
$218$	0.356617	+	0.0628813i	0.0241532	+	0.00425886i
$219$		0			0
$220$	−11.7500	−	1.02799i	−0.792185	−	0.0693072i
$221$	1.61659			0.108744
$222$		0			0
$223$	4.61643			0.309139			0.154570	−	0.987982i	$-0.450601\pi$
$223$	4.61643			0.309139			0.154570	+	0.987982i	$0.450601\pi$
$224$	24.2804	+	2.12426i	1.62231	+	0.141933i
$225$		0			0
$226$	−0.272858	−	0.0481123i	−0.0181503	−	0.00320038i
$227$	10.6446	−	22.8275i	0.706508	−	1.51511i	−0.144243	−	0.989542i	$-0.546075\pi$
$227$	10.6446	−	22.8275i	0.706508	−	1.51511i	0.850751	−	0.525569i	$-0.176147\pi$
$228$		0			0
$229$	2.60058	−	0.946535i	0.171851	−	0.0625488i	−0.254662	−	0.967030i	$-0.581964\pi$
$229$	2.60058	−	0.946535i	0.171851	−	0.0625488i	0.426513	+	0.904481i	$0.359742\pi$
$230$	2.11736	+	0.567346i	0.139615	+	0.0374097i
$231$		0			0
$232$	3.52070	−	6.09803i	0.231145	−	0.400355i
$233$	−10.3590	−	17.9422i	−0.678638	−	1.17543i	−0.975391	−	0.220481i	$-0.929237\pi$
$233$	−10.3590	−	17.9422i	−0.678638	−	1.17543i	0.296754	−	0.954954i	$-0.404096\pi$
$234$		0			0
$235$	5.82428	−	4.07820i	0.379934	−	0.266033i
$236$	2.24128	−	0.600549i	0.145895	−	0.0390924i
$237$		0			0
$238$	9.24590	+	3.36523i	0.599323	+	0.218136i
$239$	−24.2948	−	17.0114i	−1.57150	−	1.10038i	−0.947870	−	0.318657i	$-0.896768\pi$
$239$	−24.2948	−	17.0114i	−1.57150	−	1.10038i	−0.623630	−	0.781720i	$-0.714343\pi$
$240$		0			0
$241$	−1.05085	−	12.0112i	−0.0676911	−	0.773712i	−0.951858	−	0.306540i	$-0.900829\pi$
$241$	−1.05085	−	12.0112i	−0.0676911	−	0.773712i	0.884167	−	0.467172i	$-0.154727\pi$
$242$	9.08558	−	12.9756i	0.584043	−	0.834101i
$243$		0			0
$244$	6.62254	+	14.2021i	0.423965	+	0.909196i
$245$	−3.81946	−	14.2544i	−0.244016	−	0.910680i
$246$		0			0
$247$	1.33962	+	1.59650i	0.0852379	+	0.101583i
$248$	−20.3852	+	11.7694i	−1.29446	+	0.747358i
$249$		0			0
$250$	−8.33939	+	1.47046i	−0.527429	+	0.0930000i
$251$	2.39432	−	8.93572i	0.151128	−	0.564018i	−0.848278	−	0.529552i	$-0.822360\pi$
$251$	2.39432	−	8.93572i	0.151128	−	0.564018i	0.999406	−	0.0344663i	$-0.0109731\pi$
$252$		0			0
$253$	8.26518	−	8.26518i	0.519628	−	0.519628i
$254$	−9.13403	−	4.25927i	−0.573120	−	0.267250i
$255$		0			0
$256$	−9.31333	−	7.81481i	−0.582083	−	0.488426i
$257$	2.16390	−	24.7335i	0.134980	−	1.54283i	−0.562845	−	0.826562i	$-0.690293\pi$
$257$	2.16390	−	24.7335i	0.134980	−	1.54283i	0.697825	−	0.716268i	$-0.254151\pi$
$258$		0			0
$259$	−21.8763	−	12.6983i	−1.35933	−	0.789033i
$260$			1.05404i			0.0653686i
$261$		0			0
$262$	2.79115	−	3.32637i	0.172438	−	0.205504i
$263$	−2.86899	+	16.2708i	−0.176909	+	1.00330i	0.759008	+	0.651082i	$0.225685\pi$
$263$	−2.86899	+	16.2708i	−0.176909	+	1.00330i	−0.935917	+	0.352221i	$0.885427\pi$
$264$		0			0
$265$	−6.27450	−	6.27450i	−0.385439	−	0.385439i
$266$	4.33838	+	11.9196i	0.266003	+	0.730838i
$267$		0			0
$268$	−2.22944	−	12.6438i	−0.136185	−	0.772341i
$269$	12.9664	+	7.48616i	0.790576	+	0.456439i	0.840165	−	0.542330i	$-0.182458\pi$
$269$	12.9664	+	7.48616i	0.790576	+	0.456439i	−0.0495890	+	0.998770i	$0.515791\pi$
$270$		0			0
$271$	−9.38872	+	7.87807i	−0.570324	+	0.478559i	−0.881753	−	0.471710i	$-0.843637\pi$
$271$	−9.38872	+	7.87807i	−0.570324	+	0.478559i	0.311429	+	0.950269i	$0.399192\pi$
$272$	1.80596	+	2.57918i	0.109502	+	0.156386i
$273$		0			0
$274$	0.179651	−	0.0837726i	0.0108531	−	0.00506089i
$275$	−5.72361	+	15.7255i	−0.345147	+	0.948282i
$276$		0			0
$277$	13.0060	−	1.13787i	0.781453	−	0.0683683i	0.310554	−	0.950556i	$-0.399485\pi$
$277$	13.0060	−	1.13787i	0.781453	−	0.0683683i	0.470899	+	0.882187i	$0.343930\pi$
$278$	−8.99677	+	0.787116i	−0.539591	+	0.0472081i
$279$		0			0
$280$	−5.22625	+	14.3590i	−0.312328	+	0.858115i
$281$	−20.5346	+	9.57543i	−1.22499	+	0.571223i	−0.923996	−	0.382403i	$-0.875097\pi$
$281$	−20.5346	+	9.57543i	−1.22499	+	0.571223i	−0.300995	+	0.953626i	$0.597319\pi$
$282$		0			0
$283$	−9.14106	−	13.0548i	−0.543379	−	0.776026i	0.449737	−	0.893161i	$-0.351518\pi$
$283$	−9.14106	−	13.0548i	−0.543379	−	0.776026i	−0.993116	+	0.117135i	$0.962629\pi$
$284$	7.17062	−	6.01686i	0.425498	−	0.357035i
$285$		0			0
$286$	−1.85879	−	1.07317i	−0.109912	−	0.0634580i
$287$	−8.01982	−	45.4827i	−0.473395	−	2.68476i
$288$		0			0
$289$	−2.34988	−	6.45625i	−0.138228	−	0.379779i
$290$	2.07086	+	2.07086i	0.121605	+	0.121605i
$291$		0			0
$292$	−0.657189	+	3.72711i	−0.0384591	+	0.218112i
$293$	15.0876	−	17.9807i	0.881426	−	1.05044i	−0.116931	−	0.993140i	$-0.537305\pi$
$293$	15.0876	−	17.9807i	0.881426	−	1.05044i	0.998357	−	0.0573028i	$-0.0182501\pi$
$294$		0			0
$295$			2.29869i			0.133835i
$296$	6.55538	+	14.1439i	0.381024	+	0.822098i
$297$		0			0
$298$	−0.0505396	+	0.577670i	−0.00292768	+	0.0334635i
$299$	−0.800172	−	0.671424i	−0.0462752	−	0.0388295i
$300$		0			0
$301$	32.2503	+	15.0385i	1.85887	+	0.866807i
$302$	−2.55989	+	2.55989i	−0.147305	+	0.147305i
$303$		0			0
$304$	−1.05057	+	3.92079i	−0.0602545	+	0.224873i
$305$	−15.2882	+	2.69572i	−0.875399	+	0.154357i
$306$		0			0
$307$	2.92068	−	1.68626i	0.166692	−	0.0962397i	−0.414333	−	0.910125i	$-0.635985\pi$
$307$	2.92068	−	1.68626i	0.166692	−	0.0962397i	0.581025	+	0.813886i	$0.302652\pi$
$308$	21.9888	+	26.2053i	1.25293	+	1.49318i
$309$		0			0
$310$	−2.53390	−	9.45663i	−0.143916	−	0.537101i
$311$	8.32258	+	17.8478i	0.471930	+	1.01206i	0.987848	+	0.155420i	$0.0496731\pi$
$311$	8.32258	+	17.8478i	0.471930	+	1.01206i	−0.515918	+	0.856638i	$0.672549\pi$
$312$		0			0
$313$	10.2872	−	14.6917i	0.581469	−	0.830423i	−0.415388	−	0.909644i	$-0.636354\pi$
$313$	10.2872	−	14.6917i	0.581469	−	0.830423i	0.996857	+	0.0792208i	$0.0252432\pi$
$314$	−0.0650539	−	0.743569i	−0.00367120	−	0.0419620i
$315$		0			0
$316$	13.4467	+	9.41547i	0.756435	+	0.529662i
$317$	−17.9537	−	6.53461i	−1.00838	−	0.367020i	−0.215570	−	0.976488i	$-0.569161\pi$
$317$	−17.9537	−	6.53461i	−1.00838	−	0.367020i	−0.792811	+	0.609468i	$0.791383\pi$
$318$		0			0
$319$	15.0843	−	4.04184i	0.844561	−	0.226299i
$320$	2.79392	−	1.95632i	0.156185	−	0.109362i
$321$		0			0
$322$	−3.17879	−	5.50583i	−0.177147	−	0.306828i
$323$	−6.52930	+	11.3091i	−0.363300	+	0.629254i
$324$		0			0
$325$	1.44452	+	0.387058i	0.0801277	+	0.0214701i
$326$	6.84216	−	2.49034i	0.378952	−	0.137927i
$327$		0			0
$328$	−12.0292	+	25.7968i	−0.664203	+	1.42439i
$329$	−20.3081	−	3.58087i	−1.11962	−	0.197420i
$330$		0			0
$331$	13.3176	+	1.16514i	0.731999	+	0.0640417i	0.447060	−	0.894504i	$-0.352471\pi$
$331$	13.3176	+	1.16514i	0.731999	+	0.0640417i	0.284939	+	0.958546i	$0.408027\pi$
$332$	−25.2768			−1.38724
$333$		0			0
$334$	−12.5948			−0.689159
$335$	12.6706	+	1.10853i	0.692269	+	0.0605657i
$336$		0			0
$337$	20.9151	+	3.68790i	1.13932	+	0.200893i	0.711307	−	0.702881i	$-0.248103\pi$
$337$	20.9151	+	3.68790i	1.13932	+	0.200893i	0.428011	+	0.903774i	$0.359215\pi$
$338$	4.00340	−	8.58533i	0.217756	−	0.466980i
$339$		0			0
$340$	−6.20619	+	2.25887i	−0.336578	+	0.122504i
$341$	−50.4257	−	13.5115i	−2.73071	−	0.731691i
$342$		0			0
$343$	−6.84563	+	11.8570i	−0.369630	+	0.640217i
$344$	−10.9653	−	18.9925i	−0.591212	−	1.02401i
$345$		0			0
$346$	9.33945	−	6.53956i	0.502092	−	0.351569i
$347$	6.75570	−	1.81018i	0.362665	−	0.0971757i	−0.0728851	−	0.997340i	$-0.523221\pi$
$347$	6.75570	−	1.81018i	0.362665	−	0.0971757i	0.435550	+	0.900165i	$0.356554\pi$
$348$		0			0
$349$	8.21780	+	2.99103i	0.439889	+	0.160106i	0.552464	−	0.833537i	$-0.313688\pi$
$349$	8.21780	+	2.99103i	0.439889	+	0.160106i	−0.112575	+	0.993643i	$0.535910\pi$
$350$	7.45602	+	5.22076i	0.398541	+	0.279062i
$351$		0			0
$352$	−2.90354	−	33.1876i	−0.154759	−	1.76890i
$353$	12.8513	−	18.3536i	0.684008	−	0.976864i	−0.315601	−	0.948892i	$-0.602206\pi$
$353$	12.8513	−	18.3536i	0.684008	−	0.976864i	0.999609	−	0.0279722i	$-0.00890499\pi$
$354$		0			0
$355$	3.91903	+	8.40440i	0.208001	+	0.446059i
$356$	−0.562063	−	2.09765i	−0.0297893	−	0.111175i
$357$		0			0
$358$	−12.3018	−	14.6608i	−0.650173	−	0.774846i
$359$	−1.97334	+	1.13931i	−0.104149	+	0.0601304i	−0.551170	−	0.834393i	$-0.685818\pi$
$359$	−1.97334	+	1.13931i	−0.104149	+	0.0601304i	0.447021	+	0.894524i	$0.352485\pi$
$360$		0			0
$361$	2.13224	−	0.375972i	0.112223	−	0.0197880i
$362$	2.43882	−	9.10179i	0.128181	−	0.478379i
$363$		0			0
$364$	2.16163	−	2.16163i	0.113300	−	0.113300i
$365$	−3.39801	−	1.58452i	−0.177860	−	0.0829374i
$366$		0			0
$367$	2.36313	+	1.98290i	0.123354	+	0.103507i	0.702378	−	0.711804i	$-0.252122\pi$
$367$	2.36313	+	1.98290i	0.123354	+	0.103507i	−0.579024	+	0.815311i	$0.696566\pi$
$368$	0.177313	−	2.02670i	0.00924310	−	0.105649i
$369$		0			0
$370$	−6.38793	+	1.11104i	−0.332093	+	0.0577602i
$371$			25.7356i			1.33613i
$372$		0			0
$373$	14.7767	−	17.6102i	0.765108	−	0.911820i	−0.233051	−	0.972464i	$-0.574871\pi$
$373$	14.7767	−	17.6102i	0.765108	−	0.911820i	0.998159	+	0.0606441i	$0.0193155\pi$
$374$	2.33535	−	13.2444i	0.120758	−	0.684854i
$375$		0			0
$376$	8.98665	+	8.98665i	0.463451	+	0.463451i
$377$	−0.477305	−	1.31139i	−0.0245825	−	0.0675398i
$378$		0			0
$379$	0.265018	+	1.50299i	0.0136131	+	0.0772036i	0.990857	−	0.134913i	$-0.0430755\pi$
$379$	0.265018	+	1.50299i	0.0136131	+	0.0772036i	−0.977244	+	0.212117i	$0.931964\pi$
$380$	−7.37365	−	4.25718i	−0.378260	−	0.218389i
$381$		0			0
$382$	−8.60820	+	7.22313i	−0.440434	+	0.369568i
$383$	−0.269672	−	0.385131i	−0.0137796	−	0.0196793i	0.812203	−	0.583375i	$-0.198268\pi$
$383$	−0.269672	−	0.385131i	−0.0137796	−	0.0196793i	−0.825983	+	0.563695i	$0.809379\pi$
$384$		0			0
$385$	−30.7141	+	14.3222i	−1.56534	+	0.729928i
$386$	1.66351	−	4.57044i	0.0846702	−	0.232629i
$387$		0			0
$388$	0.699701	−	0.0612159i	0.0355219	−	0.00310777i
$389$	8.06302	−	0.705423i	0.408811	−	0.0357664i	0.119104	−	0.992882i	$-0.461998\pi$
$389$	8.06302	−	0.705423i	0.408811	−	0.0357664i	0.289707	+	0.957115i	$0.406442\pi$
$390$		0			0
$391$	2.23854	−	6.15033i	0.113208	−	0.311035i
$392$	23.9065	−	11.1478i	1.20746	−	0.563049i
$393$		0			0
$394$	0.799911	+	1.14239i	0.0402989	+	0.0575529i
$395$	−12.4576	+	10.4531i	−0.626808	+	0.525954i
$396$		0			0
$397$	−17.2063	−	9.93409i	−0.863562	−	0.498578i	0.00164165	−	0.999999i	$-0.499477\pi$
$397$	−17.2063	−	9.93409i	−0.863562	−	0.498578i	−0.865203	+	0.501421i	$0.832811\pi$
$398$	−1.93193	−	10.9565i	−0.0968388	−	0.549200i
$399$		0			0
$400$	0.996203	+	2.73705i	0.0498102	+	0.136852i
$401$	9.51370	+	9.51370i	0.475091	+	0.475091i	0.903558	−	0.428466i	$-0.140946\pi$
$401$	9.51370	+	9.51370i	0.475091	+	0.475091i	−0.428466	+	0.903558i	$0.640946\pi$
$402$		0			0
$403$	−0.810104	+	4.59433i	−0.0403542	+	0.228860i
$404$	−6.92520	+	8.25313i	−0.344542	+	0.410609i
$405$		0			0
$406$		−	8.49390i		−	0.421545i
$407$	−11.9005	+	32.4612i	−0.589888	+	1.60904i
$408$		0			0
$409$	−1.35051	+	15.4364i	−0.0667784	+	0.763280i	0.886804	+	0.462147i	$0.152921\pi$
$409$	−1.35051	+	15.4364i	−0.0667784	+	0.763280i	−0.953582	+	0.301134i	$0.902635\pi$
$410$	−9.06884	−	7.60966i	−0.447878	−	0.375814i
$411$		0			0
$412$	2.43036	+	1.13330i	0.119735	+	0.0558335i
$413$	4.71418	−	4.71418i	0.231970	−	0.231970i
$414$		0			0
$415$	6.48106	−	24.1876i	0.318143	−	1.18732i
$416$	−2.93187	+	0.516968i	−0.143747	+	0.0253464i
$417$		0			0
$418$	15.0150	−	8.66892i	0.734409	−	0.424011i
$419$	19.2784	+	22.9751i	0.941812	+	1.12241i	0.992322	+	0.123684i	$0.0394710\pi$
$419$	19.2784	+	22.9751i	0.941812	+	1.12241i	−0.0505098	+	0.998724i	$0.516085\pi$
$420$		0			0
$421$	1.21557	+	4.53658i	0.0592433	+	0.221099i	0.989200	−	0.146569i	$-0.0468230\pi$
$421$	1.21557	+	4.53658i	0.0592433	+	0.221099i	−0.929957	+	0.367668i	$0.880156\pi$
$422$	8.28350	+	17.7640i	0.403234	+	0.864739i
$423$		0			0
$424$	9.09747	−	12.9925i	0.441812	−	0.630973i
$425$	0.816694	+	9.33485i	0.0396155	+	0.452807i
$426$		0			0
$427$	36.8816	+	25.8248i	1.78482	+	1.24975i
$428$	13.0395	+	4.74598i	0.630287	+	0.229406i
$429$		0			0
$430$	8.81058	−	2.36079i	0.424884	−	0.113847i
$431$	0.417892	−	0.292611i	0.0201292	−	0.0140946i	−0.563469	−	0.826138i	$-0.690533\pi$
$431$	0.417892	−	0.292611i	0.0201292	−	0.0140946i	0.583598	+	0.812043i	$0.301645\pi$
$432$		0			0
$433$	0.261703	+	0.453284i	0.0125767	+	0.0217834i	0.872245	−	0.489069i	$-0.162663\pi$
$433$	0.261703	+	0.453284i	0.0125767	+	0.0217834i	−0.859669	+	0.510852i	$0.829330\pi$
$434$	−14.1972	+	24.5903i	−0.681488	+	1.18037i
$435$		0			0
$436$	0.680943	+	0.182458i	0.0326113	+	0.00873816i
$437$	7.92887	−	2.88587i	0.379289	−	0.138050i
$438$		0			0
$439$	5.87135	−	12.5911i	0.280224	−	0.600943i	−0.714938	−	0.699188i	$-0.753545\pi$
$439$	5.87135	−	12.5911i	0.280224	−	0.600943i	0.995162	+	0.0982451i	$0.0313229\pi$
$440$	20.5688	+	3.62683i	0.980579	+	0.172903i
$441$		0			0
$442$	−1.19726	−	0.104747i	−0.0569479	−	0.00498229i
$443$	0.245627			0.0116701			0.00583504	−	0.999983i	$-0.498143\pi$
$443$	0.245627			0.0116701			0.00583504	+	0.999983i	$0.498143\pi$
$444$		0			0
$445$	2.15138			0.101985
$446$	−3.41896	−	0.299121i	−0.161893	−	0.0141638i
$447$		0			0
$448$	−9.74184	−	1.71775i	−0.460259	−	0.0811560i
$449$	5.01393	−	10.7524i	0.236622	−	0.507437i	−0.751758	−	0.659439i	$-0.770794\pi$
$449$	5.01393	−	10.7524i	0.236622	−	0.507437i	0.988380	+	0.152001i	$0.0485718\pi$
$450$		0			0
$451$	−59.3197	+	21.5906i	−2.79326	+	1.01666i
$452$	−0.521009	−	0.139604i	−0.0245062	−	0.00656642i
$453$		0			0
$454$	−9.36257	+	16.2165i	−0.439407	+	0.761076i
$455$	1.51424	+	2.62274i	0.0709886	+	0.122956i
$456$		0			0
$457$	−28.3528	+	19.8529i	−1.32629	+	0.928678i	−0.999863	−	0.0165453i	$-0.994733\pi$
$457$	−28.3528	+	19.8529i	−1.32629	+	0.928678i	−0.326426	+	0.945223i	$0.605844\pi$
$458$	−1.98734	+	0.532506i	−0.0928623	+	0.0248824i
$459$		0			0
$460$	4.01008	+	1.45955i	0.186971	+	0.0680519i
$461$	12.4350	+	8.70706i	0.579154	+	0.405528i	0.826118	−	0.563497i	$-0.190544\pi$
$461$	12.4350	+	8.70706i	0.579154	+	0.405528i	−0.246964	+	0.969025i	$0.579433\pi$
$462$		0			0
$463$	1.30766	+	14.9466i	0.0607720	+	0.694628i	0.964076	+	0.265626i	$0.0855788\pi$
$463$	1.30766	+	14.9466i	0.0607720	+	0.694628i	−0.903304	+	0.429001i	$0.858866\pi$
$464$	1.55902	−	2.22651i	0.0723757	−	0.103363i
$465$		0			0
$466$	6.50935	+	13.9593i	0.301540	+	0.646654i
$467$	−0.602930	−	2.25017i	−0.0279003	−	0.104125i	0.950572	−	0.310505i	$-0.100498\pi$
$467$	−0.602930	−	2.25017i	−0.0279003	−	0.104125i	−0.978472	+	0.206380i	$0.933832\pi$
$468$		0			0
$469$	−23.7116	−	28.2584i	−1.09490	−	1.30485i
$470$	−4.57775	+	2.64296i	−0.211156	+	0.121911i
$471$		0			0
$472$	−4.04639	+	0.713487i	−0.186250	+	0.0328409i
$473$	12.5885	−	46.9808i	0.578818	−	2.16018i
$474$		0			0
$475$	−8.54203	+	8.54203i	−0.391935	+	0.391935i
$476$	17.3602	+	8.09520i	0.795704	+	0.371043i
$477$		0			0
$478$	16.8906	+	14.1729i	0.772560	+	0.648255i
$479$	3.38213	−	38.6579i	0.154533	−	1.76632i	−0.383634	−	0.923485i	$-0.625327\pi$
$479$	3.38213	−	38.6579i	0.154533	−	1.76632i	0.538167	−	0.842838i	$-0.319117\pi$
$480$		0			0
$481$	2.98251	+	0.806606i	0.135991	+	0.0367781i
$482$			8.96370i			0.408285i
$483$		0			0
$484$	19.8219	−	23.6228i	0.900995	−	1.07376i
$485$	−0.120828	+	0.685248i	−0.00548650	+	0.0311155i
$486$		0			0
$487$	−13.2288	−	13.2288i	−0.599456	−	0.599456i	0.340712	−	0.940168i	$-0.389332\pi$
$487$	−13.2288	−	13.2288i	−0.599456	−	0.599456i	−0.940168	+	0.340712i	$0.889332\pi$
$488$	−9.49056	−	26.0751i	−0.429617	−	1.18036i
$489$		0			0
$490$	1.90511	+	10.8044i	0.0860639	+	0.488092i
$491$	24.0835	+	13.9046i	1.08687	+	0.627507i	0.932742	−	0.360543i	$-0.117409\pi$
$491$	24.0835	+	13.9046i	1.08687	+	0.627507i	0.154131	+	0.988050i	$0.450742\pi$
$492$		0			0
$493$	6.69856	−	5.62076i	0.301688	−	0.253146i
$494$	−0.888687	−	1.26918i	−0.0399839	−	0.0571029i
$495$		0			0
$496$	−8.23497	+	3.84003i	−0.369761	+	0.172422i
$497$	9.19862	−	25.2730i	0.412615	−	1.13365i
$498$		0			0
$499$	−40.9286	+	3.58079i	−1.83222	+	0.160298i	−0.950347	−	0.311192i	$-0.899272\pi$
$499$	−40.9286	+	3.58079i	−1.83222	+	0.160298i	−0.881871	+	0.471491i	$0.843716\pi$
$500$	−16.4226	+	1.43679i	−0.734443	+	0.0642554i
$501$		0			0
$502$	−2.35224	+	6.46272i	−0.104985	+	0.288445i
$503$	−11.2071	+	5.22596i	−0.499700	+	0.233014i	−0.656092	−	0.754681i	$-0.727792\pi$
$503$	−11.2071	+	5.22596i	−0.499700	+	0.233014i	0.156392	+	0.987695i	$0.450014\pi$
$504$		0			0
$505$	−6.12187	−	8.74294i	−0.272420	−	0.389056i
$506$	−6.65679	+	5.58571i	−0.295931	+	0.248315i
$507$		0			0
$508$	−16.9916	−	9.81009i	−0.753879	−	0.435252i
$509$	6.01732	+	34.1259i	0.266713	+	1.51261i	0.764112	+	0.645083i	$0.223177\pi$
$509$	6.01732	+	34.1259i	0.266713	+	1.51261i	−0.497399	+	0.867522i	$0.665712\pi$
$510$		0			0
$511$	3.71912	+	10.2182i	0.164524	+	0.452027i
$512$	−7.68571	−	7.68571i	−0.339664	−	0.339664i
$513$		0			0
$514$	−3.20519	+	18.1776i	−0.141375	+	0.801777i
$515$	−1.70762	+	2.03506i	−0.0752466	+	0.0896754i
$516$		0			0
$517$			28.1862i			1.23963i
$518$	15.3790	+	10.8219i	0.675713	+	0.475487i
$519$		0			0
$520$	0.162673	−	1.85936i	0.00713368	−	0.0815384i
$521$	17.2282	+	14.4561i	0.754779	+	0.633335i	0.936762	−	0.349967i	$-0.113807\pi$
$521$	17.2282	+	14.4561i	0.754779	+	0.633335i	−0.181983	+	0.983302i	$0.558252\pi$
$522$		0			0
$523$	7.66990	+	3.57653i	0.335381	+	0.156391i	0.583012	−	0.812464i	$-0.301874\pi$
$523$	7.66990	+	3.57653i	0.335381	+	0.156391i	−0.247630	+	0.968855i	$0.579652\pi$
$524$	5.97747	−	5.97747i	0.261127	−	0.261127i
$525$		0			0
$526$	3.17906	−	11.8644i	0.138613	−	0.517312i
$527$	−28.7876	+	5.07602i	−1.25401	+	0.221115i
$528$		0			0
$529$	16.2561	−	9.38548i	0.706788	−	0.408064i
$530$	4.24038	+	5.05349i	0.184190	+	0.219510i
$531$		0			0
$532$	6.39129	+	23.8526i	0.277098	+	1.03414i
$533$	2.38410	+	5.11271i	0.103267	+	0.221456i
$534$		0			0
$535$	−7.88486	+	11.2607i	−0.340892	+	0.486844i
$536$	1.98146	+	22.6482i	0.0855859	+	0.978251i
$537$		0			0
$538$	−9.11795	−	6.38446i	−0.393103	−	0.275254i
$539$	54.9731	+	20.0086i	2.36786	+	0.861831i
$540$		0			0
$541$	0.787272	−	0.210949i	0.0338475	−	0.00906941i	−0.241856	−	0.970312i	$-0.577756\pi$
$541$	0.787272	−	0.210949i	0.0338475	−	0.00906941i	0.275703	+	0.961243i	$0.411089\pi$
$542$	7.46381	−	5.22622i	0.320598	−	0.224485i
$543$		0			0
$544$	−9.32710	−	16.1550i	−0.399896	−	0.692640i
$545$	−0.349193	+	0.604820i	−0.0149578	+	0.0259076i
$546$		0			0
$547$	14.0165	+	3.75570i	0.599301	+	0.160582i	0.545701	−	0.837980i	$-0.316264\pi$
$547$	14.0165	+	3.75570i	0.599301	+	0.160582i	0.0536006	+	0.998562i	$0.482930\pi$
$548$	0.362623	−	0.131984i	0.0154905	−	0.00563808i
$549$		0			0
$550$	5.25787	−	11.2755i	0.224196	−	0.480791i
$551$	11.1018	+	1.95754i	0.472951	+	0.0833940i
$552$		0			0
$553$	46.9855	+	4.11070i	1.99803	+	0.174805i
$554$	−9.70604			−0.412370
$555$		0			0
$556$	−17.5816			−0.745626
$557$	38.2419	+	3.34573i	1.62036	+	0.141763i	0.860894	−	0.508785i	$-0.169905\pi$
$557$	38.2419	+	3.34573i	1.62036	+	0.141763i	0.759465	+	0.650548i	$0.225461\pi$
$558$		0			0
$559$	−4.28046	−	0.754760i	−0.181044	−	0.0319229i
$560$	−2.49281	+	5.34584i	−0.105340	+	0.225903i
$561$		0			0
$562$	15.8285	−	5.76110i	0.667685	−	0.243017i
$563$	−23.2335	−	6.22539i	−0.979173	−	0.262369i	−0.266477	−	0.963841i	$-0.585860\pi$
$563$	−23.2335	−	6.22539i	−0.979173	−	0.262369i	−0.712696	+	0.701473i	$0.752526\pi$
$564$		0			0
$565$	0.267177	−	0.462765i	0.0112402	−	0.0194687i
$566$	5.92405	+	10.2608i	0.249006	+	0.431292i
$567$		0			0
$568$	−13.5778	+	9.50731i	−0.569714	+	0.398918i
$569$	26.7850	−	7.17701i	1.12288	−	0.300876i	0.350834	−	0.936438i	$-0.385898\pi$
$569$	26.7850	−	7.17701i	1.12288	−	0.300876i	0.772050	+	0.635562i	$0.219232\pi$
$570$		0			0
$571$	−25.7668	−	9.37833i	−1.07831	−	0.392471i	−0.259029	−	0.965870i	$-0.583402\pi$
$571$	−25.7668	−	9.37833i	−1.07831	−	0.392471i	−0.819277	+	0.573399i	$0.805625\pi$
$572$	−3.42279	−	2.39666i	−0.143114	−	0.100209i
$573$		0			0
$574$	2.99250	+	34.2044i	0.124904	+	1.42766i
$575$	3.47283	−	4.95971i	0.144827	−	0.206834i
$576$		0			0
$577$	−16.1390	−	34.6103i	−0.671877	−	1.44085i	−0.885834	−	0.464002i	$-0.846413\pi$
$577$	−16.1390	−	34.6103i	−0.671877	−	1.44085i	0.213957	−	0.976843i	$-0.431365\pi$
$578$	1.32201	+	4.93380i	0.0549883	+	0.205219i
$579$		0			0
$580$	3.66480	+	4.36754i	0.152173	+	0.181352i
$581$	−62.8956	+	36.3128i	−2.60935	+	1.50651i
$582$		0			0
$583$	34.6422	−	6.10835i	1.43473	−	0.252982i
$584$	1.73452	−	6.47333i	0.0717751	−	0.267868i
$585$		0			0
$586$	−12.3390	+	12.3390i	−0.509720	+	0.509720i
$587$	−3.98060	−	1.85618i	−0.164297	−	0.0766129i	0.338730	−	0.940884i	$-0.390003\pi$
$587$	−3.98060	−	1.85618i	−0.164297	−	0.0766129i	−0.503027	+	0.864271i	$0.667780\pi$
$588$		0			0
$589$	−28.8682	−	24.2233i	−1.18950	−	0.998105i
$590$	0.148943	−	1.70243i	0.00613189	−	0.0700878i
$591$		0			0
$592$	2.04498	+	5.65950i	0.0840483	+	0.232604i
$593$		−	27.8480i		−	1.14358i	−0.820400	−	0.571790i	$-0.806249\pi$
$593$		−	27.8480i		−	1.14358i	0.820400	−	0.571790i	$-0.193751\pi$
$594$		0			0
$595$	−12.1976	+	14.5366i	−0.500053	+	0.595940i
$596$	−0.196030	+	1.11174i	−0.00802969	+	0.0455386i
$597$		0			0
$598$	0.549108	+	0.549108i	0.0224547	+	0.0224547i
$599$	0.905037	+	2.48657i	0.0369788	+	0.101598i	0.956808	−	0.290721i	$-0.0938951\pi$
$599$	0.905037	+	2.48657i	0.0369788	+	0.101598i	−0.919829	+	0.392319i	$0.871673\pi$
$600$		0			0
$601$	3.24089	+	18.3800i	0.132199	+	0.749735i	0.976770	+	0.214292i	$0.0687443\pi$
$601$	3.24089	+	18.3800i	0.132199	+	0.749735i	−0.844571	+	0.535443i	$0.820145\pi$
$602$	−22.9103	−	13.2273i	−0.933756	−	0.539104i
$603$		0			0
$604$	−5.39891	+	4.53022i	−0.219679	+	0.184332i
$605$	17.5225	+	25.0248i	0.712392	+	1.01740i
$606$		0			0
$607$	41.4758	−	19.3405i	1.68345	−	0.785006i	0.685048	−	0.728498i	$-0.259781\pi$
$607$	41.4758	−	19.3405i	1.68345	−	0.785006i	0.998402	−	0.0565074i	$-0.0179965\pi$
$608$	8.22510	−	22.5983i	0.333572	−	0.916481i
$609$		0			0
$610$	11.4972	−	1.00588i	0.465508	−	0.0407267i
$611$	2.50925	−	0.219531i	0.101513	−	0.00888126i
$612$		0			0
$613$	−14.5124	+	39.8725i	−0.586151	+	1.61044i	0.191327	+	0.981526i	$0.438721\pi$
$613$	−14.5124	+	39.8725i	−0.586151	+	1.61044i	−0.777478	+	0.628910i	$0.783501\pi$
$614$	−2.27234	+	1.05961i	−0.0917040	+	0.0427623i
$615$		0			0
$616$	−34.7447	−	49.6206i	−1.39991	−	1.99927i
$617$	−2.75165	+	2.30891i	−0.110777	+	0.0929533i	−0.696494	−	0.717563i	$-0.745258\pi$
$617$	−2.75165	+	2.30891i	−0.110777	+	0.0929533i	0.585716	+	0.810516i	$0.300813\pi$
$618$		0			0
$619$	31.6537	+	18.2753i	1.27227	+	0.734545i	0.975415	−	0.220378i	$-0.0707290\pi$
$619$	31.6537	+	18.2753i	1.27227	+	0.734545i	0.296855	+	0.954923i	$0.404062\pi$
$620$	−3.30963	−	18.7698i	−0.132918	−	0.753814i
$621$		0			0
$622$	−5.00732	−	13.7575i	−0.200775	−	0.551625i
$623$	−4.41207	−	4.41207i	−0.176766	−	0.176766i
$624$		0			0
$625$	0.279641	−	1.58592i	0.0111856	−	0.0634369i
$626$	−8.57074	+	10.2142i	−0.342556	+	0.408242i
$627$		0			0
$628$		−	1.45309i		−	0.0579847i
$629$	1.64239	+	19.2896i	0.0654864	+	0.769129i
$630$		0			0
$631$	3.59645	−	41.1076i	0.143172	−	1.63647i	−0.496655	−	0.867948i	$-0.665439\pi$
$631$	3.59645	−	41.1076i	0.143172	−	1.63647i	0.639828	−	0.768518i	$-0.279006\pi$
$632$	−22.2673	−	18.6845i	−0.885747	−	0.743230i
$633$		0			0
$634$	12.8732	+	6.00288i	0.511261	+	0.238405i
$635$	13.7441	−	13.7441i	0.545417	−	0.545417i
$636$		0			0
$637$	1.35308	−	5.04976i	0.0536109	−	0.200079i
$638$	−11.4335	+	2.01603i	−0.452655	+	0.0798153i
$639$		0			0
$640$	12.3597	−	7.13590i	0.488561	−	0.282071i
$641$	−8.48184	−	10.1083i	−0.335012	−	0.399252i	0.572070	−	0.820205i	$-0.306140\pi$
$641$	−8.48184	−	10.1083i	−0.335012	−	0.399252i	−0.907083	+	0.420952i	$0.861696\pi$
$642$		0			0
$643$	2.62704	+	9.80424i	0.103600	+	0.386641i	0.998183	−	0.0602617i	$-0.0191935\pi$
$643$	2.62704	+	9.80424i	0.103600	+	0.386641i	−0.894582	+	0.446903i	$0.852527\pi$
$644$	−5.23066	−	11.2172i	−0.206117	−	0.442019i
$645$		0			0
$646$	5.56841	−	7.95252i	0.219086	−	0.312888i
$647$	−2.58561	−	29.5536i	−0.101651	−	1.16187i	−0.860095	−	0.510134i	$-0.829596\pi$
$647$	−2.58561	−	29.5536i	−0.101651	−	1.16187i	0.758444	−	0.651738i	$-0.225960\pi$
$648$		0			0
$649$	−7.46456	−	5.22674i	−0.293010	−	0.205168i
$650$	−1.04474	−	0.380255i	−0.0409782	−	0.0149148i
$651$		0			0
$652$	13.6920	−	3.66876i	0.536220	−	0.143680i
$653$	−34.4759	+	24.1403i	−1.34914	+	0.944681i	−0.349174	+	0.937058i	$0.613538\pi$
$653$	−34.4759	+	24.1403i	−1.34914	+	0.944681i	−0.999971	+	0.00762349i	$0.997573\pi$
$654$		0			0
$655$	4.18727	+	7.25256i	0.163610	+	0.283381i
$656$	−5.49366	+	9.51529i	−0.214491	+	0.371510i
$657$		0			0
$658$	14.8083	+	3.96787i	0.577288	+	0.154684i
$659$	−31.7871	+	11.5695i	−1.23825	+	0.450685i	−0.876415	−	0.481557i	$-0.840071\pi$
$659$	−31.7871	+	11.5695i	−1.23825	+	0.450685i	−0.361833	+	0.932243i	$0.617849\pi$
$660$		0			0
$661$	1.97087	−	4.22654i	0.0766578	−	0.164393i	−0.864244	−	0.503073i	$-0.832203\pi$
$661$	1.97087	−	4.22654i	0.0766578	−	0.164393i	0.940902	+	0.338680i	$0.109980\pi$
$662$	−9.78758	−	1.72581i	−0.380405	−	0.0670757i
$663$		0			0
$664$	44.5891	+	3.90104i	1.73039	+	0.151390i
$665$	−24.4636			−0.948658
$666$		0			0
$667$	−5.65010			−0.218773
$668$	−24.4260	−	2.13700i	−0.945072	−	0.0826831i
$669$		0			0
$670$	−9.31211	−	1.64198i	−0.359758	−	0.0634351i
$671$	26.0083	−	55.7750i	1.00404	−	2.15317i
$672$		0			0
$673$	16.0394	−	5.83786i	0.618273	−	0.225033i	−0.0138464	−	0.999904i	$-0.504408\pi$
$673$	16.0394	−	5.83786i	0.618273	−	0.225033i	0.632119	+	0.774871i	$0.282185\pi$
$674$	−15.2509	−	4.08647i	−0.587443	−	0.157405i
$675$		0			0
$676$	9.22077	−	15.9708i	0.354645	−	0.614263i
$677$	14.8741	+	25.7627i	0.571658	+	0.990141i	0.996396	+	0.0848249i	$0.0270331\pi$
$677$	14.8741	+	25.7627i	0.571658	+	0.990141i	−0.424737	+	0.905317i	$0.639634\pi$
$678$		0			0
$679$	1.65311	−	1.15752i	0.0634405	−	0.0444215i
$680$	11.2966	−	3.02690i	0.433203	−	0.116076i
$681$		0			0
$682$	36.4702	+	13.2741i	1.39652	+	0.508290i
$683$	3.13736	+	2.19680i	0.120048	+	0.0840583i	0.632058	−	0.774921i	$-0.282210\pi$
$683$	3.13736	+	2.19680i	0.120048	+	0.0840583i	−0.512011	+	0.858979i	$0.671099\pi$
$684$		0			0
$685$	0.0333192	+	0.380840i	0.00127306	+	0.0145511i
$686$	5.83819	−	8.33780i	0.222903	−	0.318339i
$687$		0			0
$688$	−3.57769	−	7.67238i	−0.136398	−	0.292507i
$689$	−0.813602	−	3.03640i	−0.0309957	−	0.115678i
$690$		0			0
$691$	−29.5318	−	35.1946i	−1.12344	−	1.33887i	−0.934124	−	0.356949i	$-0.883817\pi$
$691$	−29.5318	−	35.1946i	−1.12344	−	1.33887i	−0.189318	−	0.981916i	$-0.560628\pi$
$692$	19.2222	−	11.0980i	0.730719	−	0.421881i
$693$		0			0
$694$	−5.12060	+	0.902901i	−0.194375	+	0.0342736i
$695$	4.50799	−	16.8240i	0.170998	−	0.638172i
$696$		0			0
$697$	−24.9944	+	24.9944i	−0.946732	+	0.946732i
$698$	−5.89236	−	2.74765i	−0.223029	−	0.104000i
$699$		0			0
$700$	13.5742	+	11.3901i	0.513055	+	0.430504i
$701$	−3.27298	+	37.4104i	−0.123619	+	1.41297i	0.640532	+	0.767932i	$0.278714\pi$
$701$	−3.27298	+	37.4104i	−0.123619	+	1.41297i	−0.764151	+	0.645038i	$0.776842\pi$
$702$		0			0
$703$	−17.6888	+	17.6067i	−0.667147	+	0.664048i
$704$			13.5210i			0.509592i
$705$		0			0
$706$	−10.7070	+	12.7601i	−0.402963	+	0.480233i
$707$	−5.37531	+	30.4849i	−0.202159	+	1.14650i
$708$		0			0
$709$	−16.8941	−	16.8941i	−0.634469	−	0.634469i	0.314716	−	0.949186i	$-0.398091\pi$
$709$	−16.8941	−	16.8941i	−0.634469	−	0.634469i	−0.949186	+	0.314716i	$0.898091\pi$
$710$	−2.35790	−	6.47829i	−0.0884905	−	0.243126i
$711$		0			0
$712$	0.667763	+	3.78707i	0.0250255	+	0.141927i
$713$	16.3573	+	9.44392i	0.612587	+	0.353678i
$714$		0			0
$715$	3.17101	−	2.66079i	0.118589	−	0.0995080i
$716$	−21.3703	−	30.5199i	−0.798645	−	1.14058i
$717$		0			0
$718$	1.53529	−	0.715918i	0.0572966	−	0.0267178i
$719$	7.49026	−	20.5793i	0.279340	−	0.767479i	−0.718098	−	0.695942i	$-0.754987\pi$
$719$	7.49026	−	20.5793i	0.279340	−	0.767479i	0.997438	−	0.0715376i	$-0.0227906\pi$
$720$		0			0
$721$	7.67552	−	0.671521i	0.285851	−	0.0250087i
$722$	−1.60351	+	0.140289i	−0.0596766	+	0.00522103i
$723$		0			0
$724$	6.27409	−	17.2379i	0.233175	−	0.640642i
$725$	7.33133	−	3.41866i	0.272279	−	0.126966i
$726$		0			0
$727$	15.5356	+	22.1871i	0.576183	+	0.822874i	0.996420	−	0.0845401i	$-0.0269421\pi$
$727$	15.5356	+	22.1871i	0.576183	+	0.822874i	−0.420237	+	0.907414i	$0.638053\pi$
$728$	−4.14681	+	3.47958i	−0.153691	+	0.128962i
$729$		0			0
$730$	2.41392	+	1.39368i	0.0893431	+	0.0515823i
$731$	−4.72924	−	26.8209i	−0.174917	−	0.992006i
$732$		0			0
$733$	2.65079	+	7.28298i	0.0979090	+	0.269003i	0.978972	−	0.203997i	$-0.0653933\pi$
$733$	2.65079	+	7.28298i	0.0979090	+	0.269003i	−0.881062	+	0.473000i	$0.843171\pi$
$734$	−1.62167	−	1.62167i	−0.0598569	−	0.0598569i
$735$		0			0
$736$	−2.09303	+	11.8702i	−0.0771501	+	0.437540i
$737$	−32.4101	+	38.6248i	−1.19384	+	1.42276i
$738$		0			0
$739$		−	19.3069i		−	0.710214i	−0.934826	−	0.355107i	$-0.884444\pi$
$739$		−	19.3069i		−	0.710214i	0.934826	−	0.355107i	$-0.115556\pi$
$740$	−12.5771	+	1.07086i	−0.462342	+	0.0393655i
$741$		0			0
$742$	1.66753	−	19.0600i	0.0612170	−	0.699713i
$743$	−33.7112	−	28.2871i	−1.23675	−	1.03775i	−0.997771	−	0.0667264i	$-0.978745\pi$
$743$	−33.7112	−	28.2871i	−1.23675	−	1.03775i	−0.238974	−	0.971026i	$-0.576811\pi$
$744$		0			0
$745$	−1.01357	−	0.472637i	−0.0371345	−	0.0173161i
$746$	−12.0848	+	12.0848i	−0.442455	+	0.442455i
$747$		0			0
$748$	6.77633	−	25.2896i	0.247767	−	0.924680i
$749$	39.2640	−	6.92330i	1.43467	−	0.252972i
$750$		0			0
$751$	−27.6585	+	15.9687i	−1.00927	+	0.582704i	−0.910979	−	0.412453i	$-0.864672\pi$
$751$	−27.6585	+	15.9687i	−1.00927	+	0.582704i	−0.0982948	+	0.995157i	$0.531339\pi$
$752$	3.15342	+	3.75810i	0.114994	+	0.137044i
$753$		0			0
$754$	0.268525	+	1.00215i	0.00977910	+	0.0364961i
$755$	−2.95072	−	6.32785i	−0.107388	−	0.230294i
$756$		0			0
$757$	−12.4614	+	17.7968i	−0.452919	+	0.646835i	−0.979062	−	0.203561i	$-0.934749\pi$
$757$	−12.4614	+	17.7968i	−0.452919	+	0.646835i	0.526144	+	0.850396i	$0.323637\pi$
$758$	−0.0988884	−	1.13030i	−0.00359179	−	0.0410543i
$759$		0			0
$760$	12.3504	+	8.64782i	0.447995	+	0.313689i
$761$	50.0802	+	18.2277i	1.81540	+	0.660753i	0.996184	+	0.0872744i	$0.0278157\pi$
$761$	50.0802	+	18.2277i	1.81540	+	0.660753i	0.819220	+	0.573479i	$0.194407\pi$
$762$		0			0
$763$	1.95650	−	0.524242i	0.0708300	−	0.0189788i
$764$	−17.9200	+	12.5477i	−0.648324	+	0.453961i
$765$		0			0
$766$	0.174766	+	0.302704i	0.00631456	+	0.0109371i
$767$	−0.407167	+	0.705233i	−0.0147019	+	0.0254645i
$768$		0			0
$769$	29.4229	+	7.88385i	1.06102	+	0.284299i	0.746798	−	0.665051i	$-0.231590\pi$
$769$	29.4229	+	7.88385i	1.06102	+	0.284299i	0.314220	+	0.949350i	$0.398257\pi$
$770$	23.6751	−	8.61703i	0.853191	−	0.310536i
$771$		0			0
$772$	4.00163	−	8.58152i	0.144022	−	0.308856i
$773$	33.6496	+	5.93333i	1.21029	+	0.213407i	0.742142	−	0.670242i	$-0.233810\pi$
$773$	33.6496	+	5.93333i	1.21029	+	0.213407i	0.468149	+	0.883649i	$0.344921\pi$
$774$		0			0
$775$	−26.9387	−	2.35683i	−0.967668	−	0.0846600i
$776$	−1.24375			−0.0446479
$777$		0			0
$778$	−6.01724			−0.215728
$779$	−45.3958	−	3.97162i	−1.62647	−	0.142298i
$780$		0			0
$781$	−36.2028	−	6.38352i	−1.29544	−	0.228420i
$782$	−2.05638	+	4.40993i	−0.0735361	+	0.157699i
$783$		0			0
$784$	9.56816	−	3.48253i	0.341720	−	0.124376i
$785$	1.39048	+	0.372578i	0.0496284	+	0.0132979i
$786$		0			0
$787$	−15.6702	+	27.1416i	−0.558583	+	0.967495i	0.439032	+	0.898472i	$0.355322\pi$
$787$	−15.6702	+	27.1416i	−0.558583	+	0.967495i	−0.997615	+	0.0690232i	$0.978012\pi$
$788$	1.35749	+	2.35124i	0.0483586	+	0.0837595i
$789$		0			0
$790$	9.90346	−	6.93448i	0.352349	−	0.246718i
$791$	−1.49697	+	0.401113i	−0.0532262	+	0.0142619i
$792$		0			0
$793$	−5.16787	−	1.88095i	−0.183517	−	0.0667946i
$794$	12.0995	+	8.47213i	0.429394	+	0.300665i
$795$		0			0
$796$	−1.88770	−	21.5765i	−0.0669077	−	0.764758i
$797$	2.01996	−	2.88480i	0.0715507	−	0.102185i	−0.781782	−	0.623552i	$-0.785689\pi$
$797$	2.01996	−	2.88480i	0.0715507	−	0.102185i	0.853332	+	0.521367i	$0.174578\pi$
$798$		0			0
$799$	6.67007	+	14.3040i	0.235970	+	0.506039i
$800$	−4.46634	−	16.6686i	−0.157909	−	0.589325i
$801$		0			0
$802$	−6.42947	−	7.66235i	−0.227033	−	0.270567i
$803$	12.8718	−	7.43152i	0.454235	−	0.262253i
$804$		0			0
$805$	12.0750	−	2.12915i	0.425588	−	0.0750427i
$806$	0.897657	−	3.35010i	0.0316186	−	0.118002i
$807$		0			0
$808$	13.4900	−	13.4900i	0.474578	−	0.474578i
$809$	−35.0094	−	16.3252i	−1.23087	−	0.573962i	−0.305194	−	0.952290i	$-0.598721\pi$
$809$	−35.0094	−	16.3252i	−1.23087	−	0.573962i	−0.925672	+	0.378328i	$0.876499\pi$
$810$		0			0
$811$	11.7444	+	9.85474i	0.412402	+	0.346047i	0.825264	−	0.564747i	$-0.191026\pi$
$811$	11.7444	+	9.85474i	0.412402	+	0.346047i	−0.412862	+	0.910794i	$0.635471\pi$
$812$	1.44118	−	16.4728i	0.0505756	−	0.578082i
$813$		0			0
$814$	10.9169	−	23.2699i	0.382638	−	0.815609i
$815$			14.0427i			0.491895i
$816$		0			0
$817$	22.5685	−	26.8960i	0.789570	−	0.940973i
$818$	2.00039	−	11.3448i	0.0699421	−	0.396661i
$819$		0			0
$820$	−16.2967	−	16.2967i	−0.569104	−	0.569104i
$821$	−7.79087	−	21.4052i	−0.271903	−	0.747048i	−0.998217	−	0.0596850i	$-0.980990\pi$
$821$	−7.79087	−	21.4052i	−0.271903	−	0.747048i	0.726314	−	0.687363i	$-0.241232\pi$
$822$		0			0
$823$	−5.80971	−	32.9485i	−0.202514	−	1.14851i	−0.901304	−	0.433187i	$-0.857389\pi$
$823$	−5.80971	−	32.9485i	−0.202514	−	1.14851i	0.698790	−	0.715326i	$-0.253722\pi$
$824$	−4.11234	−	2.37426i	−0.143260	−	0.0827113i
$825$		0			0
$826$	−3.79681	+	3.18590i	−0.132108	+	0.110852i
$827$	−3.20438	−	4.57632i	−0.111427	−	0.159134i	0.759565	−	0.650431i	$-0.225412\pi$
$827$	−3.20438	−	4.57632i	−0.111427	−	0.159134i	−0.870992	+	0.491297i	$0.836523\pi$
$828$		0			0
$829$	−22.8980	+	10.6775i	−0.795282	+	0.370846i	−0.777410	−	0.628994i	$-0.783467\pi$
$829$	−22.8980	+	10.6775i	−0.795282	+	0.370846i	−0.0178718	+	0.999840i	$0.505689\pi$
$830$	−6.36714	+	17.4936i	−0.221007	+	0.607211i
$831$		0			0
$832$	1.20369	−	0.105309i	0.0417305	−	0.00365094i
$833$	32.6328	−	2.85500i	1.13066	−	0.0989198i
$834$		0			0
$835$	8.30785	−	22.8256i	0.287505	−	0.789914i
$836$	30.5905	−	14.2646i	1.05800	−	0.493351i
$837$		0			0
$838$	−12.7891	−	18.2647i	−0.441791	−	0.630942i
$839$	−11.6530	+	9.77802i	−0.402306	+	0.337575i	−0.821384	−	0.570375i	$-0.806798\pi$
$839$	−11.6530	+	9.77802i	−0.402306	+	0.337575i	0.419078	+	0.907950i	$0.362353\pi$
$840$		0			0
$841$	18.5774	+	10.7257i	0.640599	+	0.369850i
$842$	−0.606315	−	3.43858i	−0.0208950	−	0.118501i
$843$		0			0
$844$	13.0507	+	35.8564i	0.449223	+	1.23423i
$845$	12.9184	+	12.9184i	0.444408	+	0.444408i
$846$		0			0
$847$	15.3857	−	87.2564i	0.528658	−	2.99817i
$848$	3.93549	−	4.69014i	0.135145	−	0.161060i
$849$		0			0
$850$		−	6.96637i		−	0.238945i
$851$	7.19868	−	10.2300i	0.246768	−	0.350681i
$852$		0			0
$853$	−2.25715	+	25.7994i	−0.0772835	+	0.883354i	0.854289	+	0.519799i	$0.173993\pi$
$853$	−2.25715	+	25.7994i	−0.0772835	+	0.883354i	−0.931572	+	0.363556i	$0.881563\pi$
$854$	−25.6414	−	21.5157i	−0.877432	−	0.736253i
$855$		0			0
$856$	−22.2697	−	10.3845i	−0.761161	−	0.354935i
$857$	−32.6975	+	32.6975i	−1.11693	+	1.11693i	−0.124736	+	0.992190i	$0.539808\pi$
$857$	−32.6975	+	32.6975i	−1.11693	+	1.11693i	−0.992190	+	0.124736i	$0.960192\pi$
$858$		0			0
$859$	−3.34117	+	12.4694i	−0.113999	+	0.425451i	−0.999210	−	0.0397388i	$-0.987347\pi$
$859$	−3.34117	+	12.4694i	−0.113999	+	0.425451i	0.885211	+	0.465190i	$0.154014\pi$
$860$	17.4875	−	3.08352i	0.596319	−	0.105147i
$861$		0			0
$862$	−0.328454	+	0.189633i	−0.0111872	+	0.00645892i
$863$	−6.74752	−	8.04138i	−0.229688	−	0.273732i	0.638875	−	0.769311i	$-0.279400\pi$
$863$	−6.74752	−	8.04138i	−0.229688	−	0.273732i	−0.868563	+	0.495579i	$0.834956\pi$
$864$		0			0
$865$	5.69111	+	21.2395i	0.193504	+	0.722166i
$866$	−0.164449	−	0.352662i	−0.00558820	−	0.0119839i
$867$		0			0
$868$	−31.7059	+	45.2807i	−1.07617	+	1.53693i
$869$	−5.61868	−	64.2218i	−0.190601	−	2.17858i
$870$		0			0
$871$	3.69096	+	2.58444i	0.125063	+	0.0875703i
$872$	−1.17305	−	0.426955i	−0.0397245	−	0.0144585i
$873$		0			0
$874$	−6.05916	+	1.62355i	−0.204954	+	0.0549173i
$875$	−38.8000	+	27.1680i	−1.31168	+	0.918448i
$876$		0			0
$877$	−14.1303	−	24.4744i	−0.477147	−	0.826442i	0.522510	−	0.852633i	$-0.324996\pi$
$877$	−14.1303	−	24.4744i	−0.477147	−	0.826442i	−0.999657	+	0.0261907i	$0.991662\pi$
$878$	−5.16420	+	8.94466i	−0.174283	+	0.301868i
$879$		0			0
$880$	7.78759	+	2.08668i	0.262520	+	0.0703419i
$881$	26.5235	−	9.65377i	0.893600	−	0.325244i	0.145915	−	0.989297i	$-0.453388\pi$
$881$	26.5235	−	9.65377i	0.893600	−	0.325244i	0.747685	+	0.664054i	$0.231165\pi$
$882$		0			0
$883$	3.50619	−	7.51905i	0.117993	−	0.253036i	−0.838437	−	0.544998i	$-0.816530\pi$
$883$	3.50619	−	7.51905i	0.117993	−	0.253036i	0.956430	+	0.291962i	$0.0943081\pi$
$884$	−2.30416	−	0.406285i	−0.0774972	−	0.0136648i
$885$		0			0
$886$	−0.181913	−	0.0159153i	−0.00611148	−	0.000534685i
$887$	3.09848			0.104037			0.0520184	−	0.998646i	$-0.483435\pi$
$887$	3.09848			0.104037			0.0520184	+	0.998646i	$0.483435\pi$
$888$		0			0
$889$	−56.3730			−1.89069
$890$	−1.59333	−	0.139398i	−0.0534084	−	0.00467263i
$891$		0			0
$892$	−6.57988	−	1.16021i	−0.220311	−	0.0388467i
$893$	−8.59890	+	18.4404i	−0.287751	+	0.617085i
$894$		0			0
$895$	34.6843	−	12.6240i	1.15937	−	0.421975i
$896$	−39.9818	−	10.7131i	−1.33570	−	0.357899i
$897$		0			0
$898$	−4.41005	+	7.63843i	−0.147165	+	0.254898i
$899$	12.6173	+	21.8539i	0.420811	+	0.728867i
$900$		0			0
$901$	16.1348	−	11.2977i	0.537527	−	0.376381i
$902$	45.3316	−	12.1466i	1.50938	−	0.404436i
$903$		0			0
$904$	0.897534	+	0.326676i	0.0298515	+	0.0108651i
$905$	14.8865	+	10.4236i	0.494843	+	0.346493i
$906$		0			0
$907$	1.39854	+	15.9854i	0.0464377	+	0.530786i	0.983412	+	0.181387i	$0.0580586\pi$
$907$	1.39854	+	15.9854i	0.0464377	+	0.530786i	−0.936974	+	0.349399i	$0.886386\pi$
$908$	−20.9090	+	29.8611i	−0.693888	+	0.990975i
$909$		0			0
$910$	−0.951516	−	2.04053i	−0.0315425	−	0.0676430i
$911$	−0.589538	−	2.20019i	−0.0195323	−	0.0728955i	0.955472	−	0.295082i	$-0.0953471\pi$
$911$	−0.589538	−	2.20019i	−0.0195323	−	0.0728955i	−0.975004	+	0.222187i	$0.928680\pi$
$912$		0			0
$913$	63.8082	+	76.0436i	2.11174	+	2.51668i
$914$	22.2847	−	12.8660i	0.737111	−	0.425571i
$915$		0			0
$916$	−3.94454	+	0.695528i	−0.130331	+	0.0229809i
$917$	6.28633	−	23.4609i	0.207593	−	0.774747i
$918$		0			0
$919$	−19.8949	+	19.8949i	−0.656271	+	0.656271i	−0.954496	−	0.298225i	$-0.903606\pi$
$919$	−19.8949	+	19.8949i	−0.656271	+	0.656271i	0.298225	+	0.954496i	$0.403606\pi$
$920$	−6.84868	−	3.19359i	−0.225794	−	0.105290i
$921$		0			0
$922$	−8.64525	−	7.25423i	−0.284716	−	0.238905i
$923$	−0.286318	+	3.27263i	−0.00942426	+	0.107720i
$924$		0			0
$925$	−3.15092	+	17.6297i	−0.103601	+	0.579660i
$926$		−	11.1543i		−	0.366553i
$927$		0			0
$928$	−10.3511	+	12.3360i	−0.339793	+	0.404949i
$929$	−2.56262	+	14.5333i	−0.0840767	+	0.476823i	0.913475	+	0.406894i	$0.133388\pi$
$929$	−2.56262	+	14.5333i	−0.0840767	+	0.476823i	−0.997552	+	0.0699285i	$0.977723\pi$
$930$		0			0
$931$	29.8612	+	29.8612i	0.978662	+	0.978662i
$932$	10.2555	+	28.1768i	0.335930	+	0.922961i
$933$		0			0
$934$	0.300735	+	1.70555i	0.00984036	+	0.0558074i
$935$	22.4624	+	12.9687i	0.734600	+	0.424122i
$936$		0			0
$937$	−40.5059	+	33.9885i	−1.32327	+	1.11035i	−0.337669	+	0.941265i	$0.609638\pi$
$937$	−40.5059	+	33.9885i	−1.32327	+	1.11035i	−0.985601	+	0.169090i	$0.945917\pi$
$938$	15.7300	+	22.4648i	0.513602	+	0.733500i
$939$		0			0
$940$	−9.32637	+	4.34896i	−0.304193	+	0.141847i
$941$	−6.50201	+	17.8641i	−0.211960	+	0.582354i	−0.999422	−	0.0340092i	$-0.989172\pi$
$941$	−6.50201	+	17.8641i	−0.211960	+	0.582354i	0.787462	+	0.616363i	$0.211395\pi$
$942$		0			0
$943$	22.7526	−	1.99060i	0.740927	−	0.0648227i
$944$	−1.58002	+	0.138234i	−0.0514252	+	0.00449912i
$945$		0			0
$946$	−12.3672	+	33.9786i	−0.402093	+	1.10474i
$947$	7.67088	−	3.57699i	0.249270	−	0.116237i	−0.293968	−	0.955815i	$-0.594976\pi$
$947$	7.67088	−	3.57699i	0.249270	−	0.116237i	0.543238	+	0.839579i	$0.317198\pi$
$948$		0			0
$949$	−0.761835	−	1.08801i	−0.0247302	−	0.0353184i
$950$	6.87976	−	5.77281i	0.223209	−	0.187295i
$951$		0			0
$952$	−29.3747	−	16.9595i	−0.952039	−	0.549660i
$953$	2.81603	+	15.9705i	0.0912201	+	0.517335i	0.995840	+	0.0911163i	$0.0290435\pi$
$953$	2.81603	+	15.9705i	0.0912201	+	0.517335i	−0.904620	+	0.426219i	$0.859845\pi$
$954$		0			0
$955$	−7.41232	−	20.3652i	−0.239857	−	0.659002i
$956$	30.3524	+	30.3524i	0.981668	+	0.981668i
$957$		0			0
$958$	−5.00965	+	28.4111i	−0.161854	+	0.917922i
$959$	0.712699	−	0.849361i	0.0230142	−	0.0274273i
$960$		0			0
$961$		−	53.3574i		−	1.72121i
$962$	−2.15660	−	0.790628i	−0.0695316	−	0.0254909i
$963$		0			0
$964$	−1.52090	+	17.3839i	−0.0489847	+	0.559898i
$965$	7.18572	+	6.02954i	0.231317	+	0.194098i
$966$		0			0
$967$	32.7940	+	15.2921i	1.05459	+	0.491761i	0.871021	−	0.491246i	$-0.163459\pi$
$967$	32.7940	+	15.2921i	1.05459	+	0.491761i	0.183565	+	0.983008i	$0.441236\pi$
$968$	−38.6123	+	38.6123i	−1.24105	+	1.24105i
$969$		0			0
$970$	0.133886	−	0.499670i	0.00429883	−	0.0160434i
$971$	28.1561	−	4.96468i	0.903573	−	0.159324i	0.297489	−	0.954725i	$-0.403851\pi$
$971$	28.1561	−	4.96468i	0.903573	−	0.159324i	0.606084	+	0.795401i	$0.292740\pi$
$972$		0			0
$973$	−43.7479	+	25.2579i	−1.40249	+	0.809731i
$974$	8.94021	+	10.6545i	0.286463	+	0.341393i
$975$		0			0
$976$	−2.77229	−	10.3463i	−0.0887388	−	0.331178i
$977$	7.19344	+	15.4264i	0.230138	+	0.493533i	0.987136	−	0.159885i	$-0.0511122\pi$
$977$	7.19344	+	15.4264i	0.230138	+	0.493533i	−0.756997	+	0.653418i	$0.773334\pi$
$978$		0			0
$979$	−4.89179	+	6.98619i	−0.156342	+	0.223280i
$980$	1.86149	+	21.2769i	0.0594631	+	0.679667i
$981$		0			0
$982$	−16.9355	−	11.8583i	−0.540433	−	0.378415i
$983$	−2.65624	−	0.966793i	−0.0847210	−	0.0308359i	0.299312	−	0.954155i	$-0.403243\pi$
$983$	−2.65624	−	0.966793i	−0.0847210	−	0.0308359i	−0.384033	+	0.923319i	$0.625465\pi$
$984$		0			0
$985$	−2.59800	+	0.696131i	−0.0827790	+	0.0221806i
$986$	−5.32520	+	3.72874i	−0.169589	+	0.118747i
$987$		0			0
$988$	−1.50815	−	2.61219i	−0.0479805	−	0.0831047i
$989$	−8.79873	+	15.2399i	−0.279783	+	0.484599i
$990$		0			0
$991$	46.4993	+	12.4595i	1.47710	+	0.395788i	0.905359	−	0.424646i	$-0.139602\pi$
$991$	46.4993	+	12.4595i	1.47710	+	0.395788i	0.571741	+	0.820434i	$0.306268\pi$
$992$	50.5862	−	18.4119i	1.60611	−	0.584577i
$993$		0			0
$994$	−8.45012	+	18.1213i	−0.268022	+	0.574774i
$995$	21.1308	+	3.72593i	0.669892	+	0.118120i
$996$		0			0
$997$	−33.9870	−	2.97348i	−1.07638	−	0.0941710i	−0.464847	−	0.885391i	$-0.653891\pi$
$997$	−33.9870	−	2.97348i	−1.07638	−	0.0941710i	−0.611532	+	0.791220i	$0.709446\pi$
$998$	30.5441			0.966855
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.2.br.a.35.5	✓	144
3.2	odd	2	inner	333.2.br.a.35.8	yes	144
37.18	odd	36	inner	333.2.br.a.314.8	yes	144
111.92	even	36	inner	333.2.br.a.314.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
333.2.br.a.35.5	✓	144	1.1	even	1	trivial
333.2.br.a.35.8	yes	144	3.2	odd	2	inner
333.2.br.a.314.5	yes	144	111.92	even	36	inner
333.2.br.a.314.8	yes	144	37.18	odd	36	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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.br (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.740607 - 0.0647947i) q^{2} +(-1.42532 - 0.251322i) q^{4} +(0.605949 - 1.29946i) q^{5} +(-3.90763 + 1.42226i) q^{7} +(2.47552 + 0.663314i) q^{8} +O(q^{10})\)	\(q+(-0.740607 - 0.0647947i) q^{2} +(-1.42532 - 0.251322i) q^{4} +(0.605949 - 1.29946i) q^{5} +(-3.90763 + 1.42226i) q^{7} +(2.47552 + 0.663314i) q^{8} +(-0.532968 + 0.923127i) q^{10} +(2.84195 + 4.92241i) q^{11} +(0.416077 - 0.291340i) q^{13} +(2.98617 - 0.800143i) q^{14} +(0.929631 + 0.338358i) q^{16} +(2.60709 + 1.82551i) q^{17} +(0.357603 + 4.08742i) q^{19} +(-1.19025 + 1.69985i) q^{20} +(-1.78582 - 3.82971i) q^{22} +(-0.532251 - 1.98639i) q^{23} +(1.89251 + 2.25541i) q^{25} +(-0.327027 + 0.188809i) q^{26} +(5.92705 - 1.04510i) q^{28} +(0.711102 - 2.65387i) q^{29} +(-6.49451 + 6.49451i) q^{31} +(-5.31203 - 2.47704i) q^{32} +(-1.81255 - 1.52091i) q^{34} +(-0.519651 + 5.93963i) q^{35} +(3.89907 + 4.66875i) q^{37} -3.05034i q^{38} +(2.36199 - 2.81491i) q^{40} +(-1.92858 + 10.9375i) q^{41} +(-6.05082 - 6.05082i) q^{43} +(-2.81357 - 7.73023i) q^{44} +(0.265482 + 1.50562i) q^{46} +(4.29458 + 2.47948i) q^{47} +(7.88445 - 6.61584i) q^{49} +(-1.25547 - 1.79300i) q^{50} +(-0.666261 + 0.310682i) q^{52} +(2.11669 - 5.81557i) q^{53} +(8.11855 - 0.710281i) q^{55} +(-10.6168 + 0.928853i) q^{56} +(-0.698604 + 1.91940i) q^{58} +(-1.45301 + 0.677550i) q^{59} +(-6.21024 - 8.86914i) q^{61} +(5.23069 - 4.38907i) q^{62} +(2.06012 + 1.18941i) q^{64} +(-0.126464 - 0.717213i) q^{65} +(3.03401 + 8.33588i) q^{67} +(-3.25714 - 3.25714i) q^{68} +(0.769714 - 4.36526i) q^{70} +(-4.15729 + 4.95447i) q^{71} -2.61493i q^{73} +(-2.58517 - 3.71035i) q^{74} +(0.517560 - 5.91573i) q^{76} +(-18.1063 - 15.1930i) q^{77} +(-10.2794 - 4.79336i) q^{79} +(1.00299 - 1.00299i) q^{80} +(2.13701 - 7.97542i) q^{82} +(17.1994 - 3.03272i) q^{83} +(3.95194 - 2.28165i) q^{85} +(4.08922 + 4.87334i) q^{86} +(3.77021 + 14.0706i) q^{88} +(0.634129 + 1.35989i) q^{89} +(-1.21151 + 1.73022i) q^{91} +(0.259404 + 2.96500i) q^{92} +(-3.01994 - 2.11458i) q^{94} +(5.52813 + 2.01207i) q^{95} +(-0.468762 + 0.125604i) q^{97} +(-6.26795 + 4.38887i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q+O(q^{10}) \) 144 * q	\( 144 q + 24 q^{16} - 48 q^{28} - 48 q^{31} - 144 q^{34} - 12 q^{37} - 72 q^{40} - 48 q^{43} - 216 q^{46} + 108 q^{49} - 120 q^{52} + 132 q^{58} - 48 q^{67} + 48 q^{70} + 72 q^{82} + 144 q^{88} - 108 q^{91} + 144 q^{94} + 144 q^{97}+O(q^{100}) \) 144 * q + 24 * q^16 - 48 * q^28 - 48 * q^31 - 144 * q^34 - 12 * q^37 - 72 * q^40 - 48 * q^43 - 216 * q^46 + 108 * q^49 - 120 * q^52 + 132 * q^58 - 48 * q^67 + 48 * q^70 + 72 * q^82 + 144 * q^88 - 108 * q^91 + 144 * q^94 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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