LMFDB - Embedded newform 845.2.c.g.506.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(506,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("845.506");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.c (of order $2$, degree $1$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			506.5
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	845.506
Dual form			845.2.c.g.506.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.219687i q^{2} -1.60020 q^{3} +1.95174 q^{4} +1.00000i q^{5} -0.351542i q^{6} -0.332247i q^{7} +0.868145i q^{8} -0.439374 q^{9} +O(q^{10})$	\(q+0.219687i q^{2} -1.60020 q^{3} +1.95174 q^{4} +1.00000i q^{5} -0.351542i q^{6} -0.332247i q^{7} +0.868145i q^{8} -0.439374 q^{9} -0.219687 q^{10} -5.37182i q^{11} -3.12316 q^{12} +0.0729902 q^{14} -1.60020i q^{15} +3.71276 q^{16} +5.06430 q^{17} -0.0965246i q^{18} -2.26795i q^{19} +1.95174i q^{20} +0.531659i q^{21} +1.18012 q^{22} +2.83918 q^{23} -1.38920i q^{24} -1.00000 q^{25} +5.50367 q^{27} -0.648458i q^{28} -2.90348 q^{29} +0.351542 q^{30} -5.46410i q^{31} +2.55193i q^{32} +8.59596i q^{33} +1.11256i q^{34} +0.332247 q^{35} -0.857542 q^{36} +5.97201i q^{37} +0.498239 q^{38} -0.868145 q^{40} -3.73205i q^{41} -0.116799 q^{42} +5.06430 q^{43} -10.4844i q^{44} -0.439374i q^{45} +0.623730i q^{46} +8.34285i q^{47} -5.94114 q^{48} +6.88961 q^{49} -0.219687i q^{50} -8.10387 q^{51} -1.56063 q^{53} +1.20908i q^{54} +5.37182 q^{55} +0.288438 q^{56} +3.62916i q^{57} -0.637855i q^{58} +2.70732i q^{59} -3.12316i q^{60} +14.1039 q^{61} +1.20039 q^{62} +0.145980i q^{63} +6.86488 q^{64} -1.88842 q^{66} -10.3322i q^{67} +9.88418 q^{68} -4.54324 q^{69} +0.0729902i q^{70} -12.7973i q^{71} -0.381440i q^{72} -9.68922i q^{73} -1.31197 q^{74} +1.60020 q^{75} -4.42644i q^{76} -1.78477 q^{77} +4.51851 q^{79} +3.71276i q^{80} -7.48883 q^{81} +0.819883 q^{82} +4.26371i q^{83} +1.03766i q^{84} +5.06430i q^{85} +1.11256i q^{86} +4.64613 q^{87} +4.66351 q^{88} +3.22584i q^{89} +0.0965246 q^{90} +5.54133 q^{92} +8.74363i q^{93} -1.83281 q^{94} +2.26795 q^{95} -4.08359i q^{96} +2.50791i q^{97} +1.51356i q^{98} +2.36023i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{4} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 4 * q^4 + 8 * q^9	$ 8 q - 4 q^{3} - 4 q^{4} + 8 q^{9} + 4 q^{10} + 20 q^{12} + 4 q^{14} + 4 q^{16} + 4 q^{17} + 24 q^{22} + 20 q^{23} - 8 q^{25} - 4 q^{27} + 16 q^{29} - 8 q^{30} - 20 q^{35} - 40 q^{36} - 16 q^{38} - 12 q^{40} - 8 q^{42} + 4 q^{43} - 56 q^{48} - 24 q^{49} - 8 q^{51} - 24 q^{53} - 24 q^{56} + 56 q^{61} - 8 q^{62} - 8 q^{64} + 12 q^{66} + 28 q^{68} + 32 q^{69} - 20 q^{74} + 4 q^{75} - 36 q^{77} - 16 q^{79} - 16 q^{81} - 8 q^{82} - 44 q^{87} + 36 q^{88} + 40 q^{90} + 44 q^{92} - 64 q^{94} + 32 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^4 + 8 * q^9 + 4 * q^10 + 20 * q^12 + 4 * q^14 + 4 * q^16 + 4 * q^17 + 24 * q^22 + 20 * q^23 - 8 * q^25 - 4 * q^27 + 16 * q^29 - 8 * q^30 - 20 * q^35 - 40 * q^36 - 16 * q^38 - 12 * q^40 - 8 * q^42 + 4 * q^43 - 56 * q^48 - 24 * q^49 - 8 * q^51 - 24 * q^53 - 24 * q^56 + 56 * q^61 - 8 * q^62 - 8 * q^64 + 12 * q^66 + 28 * q^68 + 32 * q^69 - 20 * q^74 + 4 * q^75 - 36 * q^77 - 16 * q^79 - 16 * q^81 - 8 * q^82 - 44 * q^87 + 36 * q^88 + 40 * q^90 + 44 * q^92 - 64 * q^94 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.219687i	0.155342i	0.996979	+	0.0776710i	$0.0247484\pi$
$2$	0.219687i	0.155342i	−0.996979	+	0.0776710i	$0.975252\pi$
$3$	−1.60020	−0.923873	−0.461937	−	0.886913i	$-0.652845\pi$
$3$	−1.60020	−0.923873	−0.461937	+	0.886913i	$0.652845\pi$
$4$	1.95174	0.975869
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	− 0.351542i	− 0.143516i
$7$	− 0.332247i	− 0.125577i	−0.998027	−	0.0627887i	$-0.980001\pi$
$7$	− 0.332247i	− 0.125577i	0.998027	−	0.0627887i	$-0.0199994\pi$
$8$	0.868145i	0.306936i
$9$	−0.439374	−0.146458
$10$	−0.219687	−0.0694711
$11$	− 5.37182i	− 1.61966i	−0.586662	−	0.809832i	$-0.699558\pi$
$11$	− 5.37182i	− 1.61966i	0.586662	−	0.809832i	$-0.300442\pi$
$12$	−3.12316	−0.901579
$13$	0	0
$13$	0	0
$14$	0.0729902	0.0195074
$15$	− 1.60020i	− 0.413169i
$16$	3.71276	0.928189
$17$	5.06430	1.22827	0.614136	−	0.789200i	$-0.289505\pi$
$17$	5.06430	1.22827	0.614136	+	0.789200i	$0.289505\pi$
$18$	− 0.0965246i	− 0.0227511i
$19$	− 2.26795i	− 0.520303i	−0.965568	−	0.260152i	$-0.916227\pi$
$19$	− 2.26795i	− 0.520303i	0.965568	−	0.260152i	$-0.0837725\pi$
$20$	1.95174i	0.436422i
$21$	0.531659i	0.116018i
$22$	1.18012	0.251602
$23$	2.83918	0.592010	0.296005	−	0.955186i	$-0.404346\pi$
$23$	2.83918	0.592010	0.296005	+	0.955186i	$0.404346\pi$
$24$	− 1.38920i	− 0.283570i
$25$	−1.00000	−0.200000
$26$	0	0
$27$	5.50367	1.05918
$28$	− 0.648458i	− 0.122547i
$29$	−2.90348	−0.539162	−0.269581	−	0.962978i	$-0.586885\pi$
$29$	−2.90348	−0.539162	−0.269581	+	0.962978i	$0.586885\pi$
$30$	0.351542	0.0641825
$31$	− 5.46410i	− 0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$	− 5.46410i	− 0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	2.55193i	0.451122i
$33$	8.59596i	1.49636i
$34$	1.11256i	0.190802i
$35$	0.332247	0.0561599
$36$	−0.857542	−0.142924
$37$	5.97201i	0.981793i	0.871218	+	0.490896i	$0.163331\pi$
$37$	5.97201i	0.981793i	−0.871218	+	0.490896i	$0.836669\pi$
$38$	0.498239	0.0808250
$39$	0	0
$40$	−0.868145	−0.137266
$41$	− 3.73205i	− 0.582848i	−0.956594	−	0.291424i	$-0.905871\pi$
$41$	− 3.73205i	− 0.582848i	0.956594	−	0.291424i	$-0.0941291\pi$
$42$	−0.116799	−0.0180224
$43$	5.06430	0.772298	0.386149	−	0.922436i	$-0.373805\pi$
$43$	5.06430	0.772298	0.386149	+	0.922436i	$0.373805\pi$
$44$	− 10.4844i	− 1.58058i
$45$	− 0.439374i	− 0.0654980i
$46$	0.623730i	0.0919640i
$47$	8.34285i	1.21693i	0.793581	+	0.608465i	$0.208214\pi$
$47$	8.34285i	1.21693i	−0.793581	+	0.608465i	$0.791786\pi$
$48$	−5.94114	−0.857529
$49$	6.88961	0.984230
$50$	− 0.219687i	− 0.0310684i
$51$	−8.10387	−1.13477
$52$	0	0
$53$	−1.56063	−0.214369	−0.107184	−	0.994239i	$-0.534183\pi$
$53$	−1.56063	−0.214369	−0.107184	+	0.994239i	$0.534183\pi$
$54$	1.20908i	0.164536i
$55$	5.37182	0.724336
$56$	0.288438	0.0385442
$57$	3.62916i	0.480694i
$58$	− 0.637855i	− 0.0837545i
$59$	2.70732i	0.352463i	0.984349	+	0.176232i	$0.0563908\pi$
$59$	2.70732i	0.352463i	−0.984349	+	0.176232i	$0.943609\pi$
$60$	− 3.12316i	− 0.403199i
$61$	14.1039	1.80582	0.902908	−	0.429835i	$-0.141428\pi$
$61$	14.1039	1.80582	0.902908	+	0.429835i	$0.141428\pi$
$62$	1.20039	0.152450
$63$	0.145980i	0.0183918i
$64$	6.86488	0.858111
$65$	0	0
$66$	−1.88842	−0.232448
$67$	− 10.3322i	− 1.26228i	−0.775667	−	0.631142i	$-0.782586\pi$
$67$	− 10.3322i	− 1.26228i	0.775667	−	0.631142i	$-0.217414\pi$
$68$	9.88418	1.19863
$69$	−4.54324	−0.546942
$70$	0.0729902i	0.00872400i
$71$	− 12.7973i	− 1.51876i	−0.650645	−	0.759382i	$-0.725502\pi$
$71$	− 12.7973i	− 1.51876i	0.650645	−	0.759382i	$-0.274498\pi$
$72$	− 0.381440i	− 0.0449531i
$73$	− 9.68922i	− 1.13404i	−0.823705	−	0.567019i	$-0.808097\pi$
$73$	− 9.68922i	− 1.13404i	0.823705	−	0.567019i	$-0.191903\pi$
$74$	−1.31197	−0.152514
$75$	1.60020	0.184775
$76$	− 4.42644i	− 0.507748i
$77$	−1.78477	−0.203393
$78$	0	0
$79$	4.51851	0.508372	0.254186	−	0.967155i	$-0.418192\pi$
$79$	4.51851	0.508372	0.254186	+	0.967155i	$0.418192\pi$
$80$	3.71276i	0.415099i
$81$	−7.48883	−0.832092
$82$	0.819883	0.0905409
$83$	4.26371i	0.468003i	0.972236	+	0.234001i	$0.0751821\pi$
$83$	4.26371i	0.468003i	−0.972236	+	0.234001i	$0.924818\pi$
$84$	1.03766i	0.113218i
$85$	5.06430i	0.549300i
$86$	1.11256i	0.119970i
$87$	4.64613	0.498117
$88$	4.66351	0.497132
$89$	3.22584i	0.341938i	0.985276	+	0.170969i	$0.0546898\pi$
$89$	3.22584i	0.341938i	−0.985276	+	0.170969i	$0.945310\pi$
$90$	0.0965246	0.0101746
$91$	0	0
$92$	5.54133	0.577724
$93$	8.74363i	0.906672i
$94$	−1.83281	−0.189040
$95$	2.26795	0.232687
$96$	− 4.08359i	− 0.416780i
$97$	2.50791i	0.254640i	0.991862	+	0.127320i	$0.0406375\pi$
$97$	2.50791i	0.254640i	−0.991862	+	0.127320i	$0.959363\pi$
$98$	1.51356i	0.152892i
$99$	2.36023i	0.237213i
$100$	−1.95174	−0.195174
$101$	−12.4467	−1.23849	−0.619247	−	0.785196i	$-0.712562\pi$
$101$	−12.4467	−1.23849	−0.619247	+	0.785196i	$0.712562\pi$
$102$	− 1.78031i	− 0.176277i
$103$	15.0247	1.48043	0.740215	−	0.672370i	$-0.234724\pi$
$103$	15.0247	1.48043	0.740215	+	0.672370i	$0.234724\pi$
$104$	0	0
$105$	−0.531659	−0.0518846
$106$	− 0.342849i	− 0.0333004i
$107$	−13.0643	−1.26297	−0.631487	−	0.775387i	$-0.717555\pi$
$107$	−13.0643	−1.26297	−0.631487	+	0.775387i	$0.717555\pi$
$108$	10.7417	1.03362
$109$	11.2325i	1.07587i	0.842985	+	0.537937i	$0.180796\pi$
$109$	11.2325i	1.07587i	−0.842985	+	0.537937i	$0.819204\pi$
$110$	1.18012i	0.112520i
$111$	− 9.55639i	− 0.907052i
$112$	− 1.23355i	− 0.116560i
$113$	−18.3438	−1.72564	−0.862821	−	0.505509i	$-0.831305\pi$
$113$	−18.3438	−1.72564	−0.862821	+	0.505509i	$0.831305\pi$
$114$	−0.797279	−0.0746721
$115$	2.83918i	0.264755i
$116$	−5.66682	−0.526151
$117$	0	0
$118$	−0.594763	−0.0547524
$119$	− 1.68260i	− 0.154243i
$120$	1.38920	0.126816
$121$	−17.8564	−1.62331
$122$	3.09843i	0.280519i
$123$	5.97201i	0.538478i
$124$	− 10.6645i	− 0.957700i
$125$	− 1.00000i	− 0.0894427i
$126$	−0.0320700	−0.00285702
$127$	−3.23996	−0.287500	−0.143750	−	0.989614i	$-0.545916\pi$
$127$	−3.23996	−0.287500	−0.143750	+	0.989614i	$0.545916\pi$
$128$	6.61199i	0.584423i
$129$	−8.10387	−0.713506
$130$	0	0
$131$	0.175664	0.0153478	0.00767390	−	0.999971i	$-0.497557\pi$
$131$	0.175664	0.0153478	0.00767390	+	0.999971i	$0.497557\pi$
$132$	16.7771i	1.46025i
$133$	−0.753518	−0.0653383
$134$	2.26986	0.196086
$135$	5.50367i	0.473681i
$136$	4.39654i	0.377001i
$137$	− 17.9829i	− 1.53638i	−0.640221	−	0.768190i	$-0.721157\pi$
$137$	− 17.9829i	− 1.53638i	0.640221	−	0.768190i	$-0.278843\pi$
$138$	− 0.998090i	− 0.0849631i
$139$	11.9861	1.01665	0.508325	−	0.861165i	$-0.330265\pi$
$139$	11.9861	1.01665	0.508325	+	0.861165i	$0.330265\pi$
$140$	0.648458	0.0548047
$141$	− 13.3502i	− 1.12429i
$142$	2.81140	0.235928
$143$	0	0
$144$	−1.63129	−0.135941
$145$	− 2.90348i	− 0.241121i
$146$	2.12859	0.176164
$147$	−11.0247	−0.909304
$148$	11.6558i	0.958101i
$149$	3.41041i	0.279391i	0.990194	+	0.139696i	$0.0446124\pi$
$149$	3.41041i	0.279391i	−0.990194	+	0.139696i	$0.955388\pi$
$150$	0.351542i	0.0287033i
$151$	7.96141i	0.647890i	0.946076	+	0.323945i	$0.105009\pi$
$151$	7.96141i	0.647890i	−0.946076	+	0.323945i	$0.894991\pi$
$152$	1.96891	0.159700
$153$	−2.22512	−0.179890
$154$	− 0.392090i	− 0.0315955i
$155$	5.46410	0.438887
$156$	0	0
$157$	−16.4329	−1.31148	−0.655742	−	0.754985i	$-0.727644\pi$
$157$	−16.4329	−1.31148	−0.655742	+	0.754985i	$0.727644\pi$
$158$	0.992658i	0.0789716i
$159$	2.49731	0.198049
$160$	−2.55193	−0.201748
$161$	− 0.943307i	− 0.0743430i
$162$	− 1.64520i	− 0.129259i
$163$	17.8072i	1.39477i	0.716697	+	0.697384i	$0.245653\pi$
$163$	17.8072i	1.39477i	−0.716697	+	0.697384i	$0.754347\pi$
$164$	− 7.28398i	− 0.568784i
$165$	−8.59596	−0.669194
$166$	−0.936681	−0.0727006
$167$	− 6.29366i	− 0.487018i	−0.969899	−	0.243509i	$-0.921702\pi$
$167$	− 6.29366i	− 0.487018i	0.969899	−	0.243509i	$-0.0782985\pi$
$168$	−0.461557	−0.0356099
$169$	0	0
$170$	−1.11256	−0.0853294
$171$	0.996477i	0.0762025i
$172$	9.88418	0.753662
$173$	−15.9751	−1.21457	−0.607283	−	0.794486i	$-0.707740\pi$
$173$	−15.9751	−1.21457	−0.607283	+	0.794486i	$0.707740\pi$
$174$	1.02069i	0.0773786i
$175$	0.332247i	0.0251155i
$176$	− 19.9442i	− 1.50335i
$177$	− 4.33225i	− 0.325632i
$178$	−0.708674	−0.0531173
$179$	−23.6174	−1.76525	−0.882625	−	0.470079i	$-0.844226\pi$
$179$	−23.6174	−1.76525	−0.882625	+	0.470079i	$0.844226\pi$
$180$	− 0.857542i	− 0.0639174i
$181$	2.62590	0.195182	0.0975909	−	0.995227i	$-0.468886\pi$
$181$	2.62590	0.195182	0.0975909	+	0.995227i	$0.468886\pi$
$182$	0	0
$183$	−22.5689	−1.66834
$184$	2.46482i	0.181709i
$185$	−5.97201	−0.439071
$186$	−1.92086	−0.140844
$187$	− 27.2045i	− 1.98939i
$188$	16.2831i	1.18756i
$189$	− 1.82858i	− 0.133009i
$190$	0.498239i	0.0361460i
$191$	−2.01582	−0.145860	−0.0729298	−	0.997337i	$-0.523235\pi$
$191$	−2.01582	−0.145860	−0.0729298	+	0.997337i	$0.523235\pi$
$192$	−10.9852	−0.792786
$193$	22.8211i	1.64270i	0.570427	+	0.821348i	$0.306778\pi$
$193$	22.8211i	1.64270i	−0.570427	+	0.821348i	$0.693222\pi$
$194$	−0.550955	−0.0395563
$195$	0	0
$196$	13.4467	0.960480
$197$	0.643026i	0.0458137i	0.999738	+	0.0229068i	$0.00729211\pi$
$197$	0.643026i	0.0458137i	−0.999738	+	0.0229068i	$0.992708\pi$
$198$	−0.518513	−0.0368491
$199$	−3.06684	−0.217403	−0.108701	−	0.994074i	$-0.534669\pi$
$199$	−3.06684	−0.217403	−0.108701	+	0.994074i	$0.534669\pi$
$200$	− 0.868145i	− 0.0613871i
$201$	16.5336i	1.16619i
$202$	− 2.73438i	− 0.192390i
$203$	0.964670i	0.0677065i
$204$	−15.8166	−1.10739
$205$	3.73205	0.260658
$206$	3.30074i	0.229973i
$207$	−1.24746	−0.0867045
$208$	0	0
$209$	−12.1830	−0.842716
$210$	− 0.116799i	− 0.00805987i
$211$	−8.20039	−0.564538	−0.282269	−	0.959335i	$-0.591087\pi$
$211$	−8.20039	−0.564538	−0.282269	+	0.959335i	$0.591087\pi$
$212$	−3.04593	−0.209196
$213$	20.4782i	1.40314i
$214$	− 2.87005i	− 0.196193i
$215$	5.06430i	0.345382i
$216$	4.77798i	0.325101i
$217$	−1.81543	−0.123239
$218$	−2.46762	−0.167129
$219$	15.5046i	1.04771i
$220$	10.4844	0.706856
$221$	0	0
$222$	2.09941	0.140903
$223$	− 10.2442i	− 0.686002i	−0.939335	−	0.343001i	$-0.888557\pi$
$223$	− 10.2442i	− 0.686002i	0.939335	−	0.343001i	$-0.111443\pi$
$224$	0.847871	0.0566508
$225$	0.439374	0.0292916
$226$	− 4.02990i	− 0.268065i
$227$	− 7.04381i	− 0.467514i	−0.972295	−	0.233757i	$-0.924898\pi$
$227$	− 7.04381i	− 0.467514i	0.972295	−	0.233757i	$-0.0751020\pi$
$228$	7.08317i	0.469095i
$229$	1.32899i	0.0878219i	0.999035	+	0.0439109i	$0.0139818\pi$
$229$	1.32899i	0.0878219i	−0.999035	+	0.0439109i	$0.986018\pi$
$230$	−0.623730	−0.0411275
$231$	2.85598	0.187909
$232$	− 2.52064i	− 0.165488i
$233$	1.24746	0.0817238	0.0408619	−	0.999165i	$-0.486990\pi$
$233$	1.24746	0.0817238	0.0408619	+	0.999165i	$0.486990\pi$
$234$	0	0
$235$	−8.34285	−0.544227
$236$	5.28398i	0.343958i
$237$	−7.23050	−0.469672
$238$	0.369644	0.0239605
$239$	9.94207i	0.643099i	0.946893	+	0.321549i	$0.104204\pi$
$239$	9.94207i	0.643099i	−0.946893	+	0.321549i	$0.895796\pi$
$240$	− 5.94114i	− 0.383499i
$241$	− 22.5869i	− 1.45495i	−0.686134	−	0.727475i	$-0.740694\pi$
$241$	− 22.5869i	− 1.45495i	0.686134	−	0.727475i	$-0.259306\pi$
$242$	− 3.92282i	− 0.252168i
$243$	−4.52742	−0.290434
$244$	27.5270	1.76224
$245$	6.88961i	0.440161i
$246$	−1.31197	−0.0836483
$247$	0	0
$248$	4.74363	0.301221
$249$	− 6.82277i	− 0.432376i
$250$	0.219687	0.0138942
$251$	6.76836	0.427215	0.213608	−	0.976920i	$-0.431479\pi$
$251$	6.76836	0.427215	0.213608	+	0.976920i	$0.431479\pi$
$252$	0.284915i	0.0179480i
$253$	− 15.2515i	− 0.958856i
$254$	− 0.711777i	− 0.0446609i
$255$	− 8.10387i	− 0.507484i
$256$	12.2772	0.767325
$257$	10.2538	0.639616	0.319808	−	0.947482i	$-0.396382\pi$
$257$	10.2538	0.639616	0.319808	+	0.947482i	$0.396382\pi$
$258$	− 1.78031i	− 0.110837i
$259$	1.98418	0.123291
$260$	0	0
$261$	1.27571	0.0789645
$262$	0.0385910i	0.00238416i
$263$	18.6570	1.15044	0.575220	−	0.817999i	$-0.304917\pi$
$263$	18.6570	1.15044	0.575220	+	0.817999i	$0.304917\pi$
$264$	−7.46254	−0.459287
$265$	− 1.56063i	− 0.0958685i
$266$	− 0.165538i	− 0.0101498i
$267$	− 5.16197i	− 0.315907i
$268$	− 20.1658i	− 1.23182i
$269$	17.9579	1.09491	0.547456	−	0.836835i	$-0.315596\pi$
$269$	17.9579	1.09491	0.547456	+	0.836835i	$0.315596\pi$
$270$	−1.20908	−0.0735825
$271$	30.8977i	1.87690i	0.345415	+	0.938450i	$0.387738\pi$
$271$	30.8977i	1.87690i	−0.345415	+	0.938450i	$0.612262\pi$
$272$	18.8025	1.14007
$273$	0	0
$274$	3.95060	0.238665
$275$	5.37182i	0.323933i
$276$	−8.86721	−0.533744
$277$	−26.5045	−1.59250	−0.796250	−	0.604967i	$-0.793186\pi$
$277$	−26.5045	−1.59250	−0.796250	+	0.604967i	$0.793186\pi$
$278$	2.63320i	0.157929i
$279$	2.40078i	0.143731i
$280$	0.288438i	0.0172375i
$281$	4.97766i	0.296942i	0.988917	+	0.148471i	$0.0474352\pi$
$281$	4.97766i	0.296942i	−0.988917	+	0.148471i	$0.952565\pi$
$282$	2.93286	0.174649
$283$	12.5863	0.748180	0.374090	−	0.927392i	$-0.377955\pi$
$283$	12.5863	0.748180	0.374090	+	0.927392i	$0.377955\pi$
$284$	− 24.9770i	− 1.48211i
$285$	−3.62916	−0.214973
$286$	0	0
$287$	−1.23996	−0.0731926
$288$	− 1.12125i	− 0.0660704i
$289$	8.64711	0.508653
$290$	0.637855	0.0374562
$291$	− 4.01315i	− 0.235255i
$292$	− 18.9108i	− 1.10667i
$293$	16.9176i	0.988337i	0.869366	+	0.494168i	$0.164527\pi$
$293$	16.9176i	0.988337i	−0.869366	+	0.494168i	$0.835473\pi$
$294$	− 2.42199i	− 0.141253i
$295$	−2.70732	−0.157626
$296$	−5.18457	−0.301347
$297$	− 29.5647i	− 1.71552i
$298$	−0.749222	−0.0434012
$299$	0	0
$300$	3.12316	0.180316
$301$	− 1.68260i	− 0.0969832i
$302$	−1.74902	−0.100645
$303$	19.9172	1.14421
$304$	− 8.42034i	− 0.482940i
$305$	14.1039i	0.807585i
$306$	− 0.488829i	− 0.0279445i
$307$	− 4.30426i	− 0.245657i	−0.992428	−	0.122828i	$-0.960803\pi$
$307$	− 4.30426i	− 0.245657i	0.992428	−	0.122828i	$-0.0391965\pi$
$308$	−3.48340	−0.198485
$309$	−24.0425	−1.36773
$310$	1.20039i	0.0681776i
$311$	2.22512	0.126175	0.0630875	−	0.998008i	$-0.479905\pi$
$311$	2.22512	0.126175	0.0630875	+	0.998008i	$0.479905\pi$
$312$	0	0
$313$	7.20887	0.407469	0.203735	−	0.979026i	$-0.434692\pi$
$313$	7.20887	0.407469	0.203735	+	0.979026i	$0.434692\pi$
$314$	− 3.61008i	− 0.203729i
$315$	−0.145980	−0.00822506
$316$	8.81895	0.496105
$317$	0.321644i	0.0180653i	0.999959	+	0.00903266i	$0.00287522\pi$
$317$	0.321644i	0.0180653i	−0.999959	+	0.00903266i	$0.997125\pi$
$318$	0.548626i	0.0307654i
$319$	15.5969i	0.873261i
$320$	6.86488i	0.383759i
$321$	20.9054	1.16683
$322$	0.207232	0.0115486
$323$	− 11.4856i	− 0.639074i
$324$	−14.6162	−0.812013
$325$	0	0
$326$	−3.91201	−0.216666
$327$	− 17.9741i	− 0.993972i
$328$	3.23996	0.178897
$329$	2.77188	0.152819
$330$	− 1.88842i	− 0.103954i
$331$	− 16.6320i	− 0.914178i	−0.889421	−	0.457089i	$-0.848892\pi$
$331$	− 16.6320i	− 0.914178i	0.889421	−	0.457089i	$-0.151108\pi$
$332$	8.32164i	0.456710i
$333$	− 2.62395i	− 0.143791i
$334$	1.38263	0.0756543
$335$	10.3322	0.564511
$336$	1.97392i	0.107686i
$337$	−24.2186	−1.31927	−0.659636	−	0.751586i	$-0.729289\pi$
$337$	−24.2186	−1.31927	−0.659636	+	0.751586i	$0.729289\pi$
$338$	0	0
$339$	29.3537	1.59427
$340$	9.88418i	0.536045i
$341$	−29.3521	−1.58951
$342$	−0.218913	−0.0118375
$343$	− 4.61478i	− 0.249174i
$344$	4.39654i	0.237046i
$345$	− 4.54324i	− 0.244600i
$346$	− 3.50952i	− 0.188673i
$347$	−6.27360	−0.336784	−0.168392	−	0.985720i	$-0.553857\pi$
$347$	−6.27360	−0.336784	−0.168392	+	0.985720i	$0.553857\pi$
$348$	9.06802	0.486097
$349$	7.06994i	0.378445i	0.981934	+	0.189223i	$0.0605968\pi$
$349$	7.06994i	0.378445i	−0.981934	+	0.189223i	$0.939403\pi$
$350$	−0.0729902	−0.00390149
$351$	0	0
$352$	13.7085	0.730666
$353$	21.7898i	1.15976i	0.814704	+	0.579878i	$0.196900\pi$
$353$	21.7898i	1.15976i	−0.814704	+	0.579878i	$0.803100\pi$
$354$	0.951738	0.0505843
$355$	12.7973	0.679212
$356$	6.29598i	0.333687i
$357$	2.69248i	0.142501i
$358$	− 5.18844i	− 0.274217i
$359$	23.9737i	1.26528i	0.774444	+	0.632642i	$0.218029\pi$
$359$	23.9737i	1.26528i	−0.774444	+	0.632642i	$0.781971\pi$
$360$	0.381440	0.0201037
$361$	13.8564	0.729285
$362$	0.576876i	0.0303199i
$363$	28.5737	1.49973
$364$	0	0
$365$	9.68922	0.507157
$366$	− 4.95810i	− 0.259164i
$367$	6.39133	0.333625	0.166812	−	0.985989i	$-0.446653\pi$
$367$	6.39133	0.333625	0.166812	+	0.985989i	$0.446653\pi$
$368$	10.5412	0.549497
$369$	1.63977i	0.0853628i
$370$	− 1.31197i	− 0.0682062i
$371$	0.518513i	0.0269198i
$372$	17.0653i	0.884793i
$373$	−20.0801	−1.03971	−0.519855	−	0.854255i	$-0.674014\pi$
$373$	−20.0801	−1.03971	−0.519855	+	0.854255i	$0.674014\pi$
$374$	5.97647	0.309036
$375$	1.60020i	0.0826338i
$376$	−7.24280	−0.373519
$377$	0	0
$378$	0.401714	0.0206619
$379$	5.46182i	0.280555i	0.990112	+	0.140277i	$0.0447994\pi$
$379$	5.46182i	0.280555i	−0.990112	+	0.140277i	$0.955201\pi$
$380$	4.42644	0.227072
$381$	5.18457	0.265614
$382$	− 0.442849i	− 0.0226581i
$383$	5.66775i	0.289609i	0.989460	+	0.144804i	$0.0462553\pi$
$383$	5.66775i	0.289609i	−0.989460	+	0.144804i	$0.953745\pi$
$384$	− 10.5805i	− 0.539933i
$385$	− 1.78477i	− 0.0909602i
$386$	−5.01349	−0.255180
$387$	−2.22512	−0.113109
$388$	4.89478i	0.248495i
$389$	−10.6174	−0.538325	−0.269162	−	0.963095i	$-0.586747\pi$
$389$	−10.6174	−0.538325	−0.269162	+	0.963095i	$0.586747\pi$
$390$	0	0
$391$	14.3784	0.727149
$392$	5.98118i	0.302095i
$393$	−0.281096	−0.0141794
$394$	−0.141264	−0.00711679
$395$	4.51851i	0.227351i
$396$	4.60656i	0.231488i
$397$	28.0338i	1.40697i	0.710708	+	0.703487i	$0.248375\pi$
$397$	28.0338i	1.40697i	−0.710708	+	0.703487i	$0.751625\pi$
$398$	− 0.673745i	− 0.0337718i
$399$	1.20578	0.0603643
$400$	−3.71276	−0.185638
$401$	− 22.5143i	− 1.12431i	−0.827032	−	0.562155i	$-0.809973\pi$
$401$	− 22.5143i	− 1.12431i	0.827032	−	0.562155i	$-0.190027\pi$
$402$	−3.63222	−0.181159
$403$	0	0
$404$	−24.2927	−1.20861
$405$	− 7.48883i	− 0.372123i
$406$	−0.211925	−0.0105177
$407$	32.0805	1.59017
$408$	− 7.03533i	− 0.348301i
$409$	− 4.28772i	− 0.212014i	−0.994365	−	0.106007i	$-0.966193\pi$
$409$	− 4.28772i	− 0.212014i	0.994365	−	0.106007i	$-0.0338066\pi$
$410$	0.819883i	0.0404911i
$411$	28.7761i	1.41942i
$412$	29.3243	1.44471
$413$	0.899499	0.0442614
$414$	− 0.274051i	− 0.0134689i
$415$	−4.26371	−0.209297
$416$	0	0
$417$	−19.1802	−0.939257
$418$	− 2.67645i	− 0.130909i
$419$	17.7116	0.865266	0.432633	−	0.901570i	$-0.357585\pi$
$419$	17.7116	0.865266	0.432633	+	0.901570i	$0.357585\pi$
$420$	−1.03766	−0.0506326
$421$	− 12.8787i	− 0.627672i	−0.949477	−	0.313836i	$-0.898386\pi$
$421$	− 12.8787i	− 0.627672i	0.949477	−	0.313836i	$-0.101614\pi$
$422$	− 1.80152i	− 0.0876965i
$423$	− 3.66563i	− 0.178229i
$424$	− 1.35485i	− 0.0657973i
$425$	−5.06430	−0.245655
$426$	−4.49880	−0.217967
$427$	− 4.68596i	− 0.226770i
$428$	−25.4981	−1.23250
$429$	0	0
$430$	−1.11256	−0.0536524
$431$	− 9.49845i	− 0.457524i	−0.973482	−	0.228762i	$-0.926532\pi$
$431$	− 9.49845i	− 0.457524i	0.973482	−	0.228762i	$-0.0734678\pi$
$432$	20.4338	0.983121
$433$	1.39628	0.0671010	0.0335505	−	0.999437i	$-0.489319\pi$
$433$	1.39628	0.0671010	0.0335505	+	0.999437i	$0.489319\pi$
$434$	− 0.398826i	− 0.0191443i
$435$	4.64613i	0.222765i
$436$	21.9228i	1.04991i
$437$	− 6.43911i	− 0.308024i
$438$	−3.40617	−0.162753
$439$	−4.16180	−0.198632	−0.0993159	−	0.995056i	$-0.531665\pi$
$439$	−4.16180	−0.198632	−0.0993159	+	0.995056i	$0.531665\pi$
$440$	4.66351i	0.222324i
$441$	−3.02711	−0.144148
$442$	0	0
$443$	9.54563	0.453526	0.226763	−	0.973950i	$-0.427186\pi$
$443$	9.54563	0.453526	0.226763	+	0.973950i	$0.427186\pi$
$444$	− 18.6516i	− 0.885164i
$445$	−3.22584	−0.152919
$446$	2.25052	0.106565
$447$	− 5.45732i	− 0.258122i
$448$	− 2.28083i	− 0.107759i
$449$	21.7171i	1.02489i	0.858720	+	0.512446i	$0.171260\pi$
$449$	21.7171i	1.02489i	−0.858720	+	0.512446i	$0.828740\pi$
$450$	0.0965246i	0.00455022i
$451$	−20.0479	−0.944018
$452$	−35.8023	−1.68400
$453$	− 12.7398i	− 0.598569i
$454$	1.54743	0.0726246
$455$	0	0
$456$	−3.15064	−0.147542
$457$	− 4.72259i	− 0.220914i	−0.993881	−	0.110457i	$-0.964769\pi$
$457$	− 4.72259i	− 0.220914i	0.993881	−	0.110457i	$-0.0352314\pi$
$458$	−0.291961	−0.0136424
$459$	27.8722	1.30096
$460$	5.54133i	0.258366i
$461$	1.78151i	0.0829730i	0.999139	+	0.0414865i	$0.0132094\pi$
$461$	1.78151i	0.0829730i	−0.999139	+	0.0414865i	$0.986791\pi$
$462$	0.627421i	0.0291902i
$463$	6.80200i	0.316116i	0.987430	+	0.158058i	$0.0505232\pi$
$463$	6.80200i	0.316116i	−0.987430	+	0.158058i	$0.949477\pi$
$464$	−10.7799	−0.500444
$465$	−8.74363	−0.405476
$466$	0.274051i	0.0126952i
$467$	−18.2374	−0.843927	−0.421963	−	0.906613i	$-0.638659\pi$
$467$	−18.2374	−0.843927	−0.421963	+	0.906613i	$0.638659\pi$
$468$	0	0
$469$	−3.43285	−0.158514
$470$	− 1.83281i	− 0.0845414i
$471$	26.2958	1.21165
$472$	−2.35035	−0.108184
$473$	− 27.2045i	− 1.25086i
$474$	− 1.58845i	− 0.0729598i
$475$	2.26795i	0.104061i
$476$	− 3.28398i	− 0.150521i
$477$	0.685698	0.0313960
$478$	−2.18414	−0.0999003
$479$	− 35.1807i	− 1.60745i	−0.595002	−	0.803724i	$-0.702849\pi$
$479$	− 35.1807i	− 1.60745i	0.595002	−	0.803724i	$-0.297151\pi$
$480$	4.08359	0.186390
$481$	0	0
$482$	4.96204	0.226015
$483$	1.50948i	0.0686835i
$484$	−34.8510	−1.58414
$485$	−2.50791	−0.113878
$486$	− 0.994615i	− 0.0451166i
$487$	10.3040i	0.466919i	0.972367	+	0.233459i	$0.0750046\pi$
$487$	10.3040i	0.466919i	−0.972367	+	0.233459i	$0.924995\pi$
$488$	12.2442i	0.554269i
$489$	− 28.4950i	− 1.28859i
$490$	−1.51356	−0.0683756
$491$	−9.33198	−0.421147	−0.210573	−	0.977578i	$-0.567533\pi$
$491$	−9.33198	−0.421147	−0.210573	+	0.977578i	$0.567533\pi$
$492$	11.6558i	0.525484i
$493$	−14.7041	−0.662238
$494$	0	0
$495$	−2.36023	−0.106085
$496$	− 20.2869i	− 0.910907i
$497$	−4.25187	−0.190722
$498$	1.49887	0.0671661
$499$	− 23.9421i	− 1.07179i	−0.844283	−	0.535897i	$-0.819974\pi$
$499$	− 23.9421i	− 1.07179i	0.844283	−	0.535897i	$-0.180026\pi$
$500$	− 1.95174i	− 0.0872844i
$501$	10.0711i	0.449943i
$502$	1.48692i	0.0663645i
$503$	42.1443	1.87912	0.939560	−	0.342385i	$-0.111235\pi$
$503$	42.1443	1.87912	0.939560	+	0.342385i	$0.111235\pi$
$504$	−0.126732	−0.00564510
$505$	− 12.4467i	− 0.553872i
$506$	3.35056	0.148951
$507$	0	0
$508$	−6.32355	−0.280562
$509$	33.5602i	1.48753i	0.668441	+	0.743765i	$0.266962\pi$
$509$	33.5602i	1.48753i	−0.668441	+	0.743765i	$0.733038\pi$
$510$	1.78031	0.0788336
$511$	−3.21921	−0.142409
$512$	15.9211i	0.703621i
$513$	− 12.4820i	− 0.551096i
$514$	2.25263i	0.0993593i
$515$	15.0247i	0.662069i
$516$	−15.8166	−0.696288
$517$	44.8162	1.97102
$518$	0.435898i	0.0191523i
$519$	25.5633	1.12210
$520$	0	0
$521$	12.4649	0.546098	0.273049	−	0.962000i	$-0.411968\pi$
$521$	12.4649	0.546098	0.273049	+	0.962000i	$0.411968\pi$
$522$	0.280257i	0.0122665i
$523$	−5.65956	−0.247475	−0.123738	−	0.992315i	$-0.539488\pi$
$523$	−5.65956	−0.247475	−0.123738	+	0.992315i	$0.539488\pi$
$524$	0.342849	0.0149774
$525$	− 0.531659i	− 0.0232035i
$526$	4.09870i	0.178712i
$527$	− 27.6718i	− 1.20540i
$528$	31.9147i	1.38891i
$529$	−14.9391	−0.649525
$530$	0.342849	0.0148924
$531$	− 1.18953i	− 0.0516211i
$532$	−1.47067	−0.0637616
$533$	0	0
$534$	1.13402	0.0490737
$535$	− 13.0643i	− 0.564819i
$536$	8.96989	0.387440
$537$	37.7925	1.63087
$538$	3.94511i	0.170086i
$539$	− 37.0097i	− 1.59412i
$540$	10.7417i	0.462250i
$541$	− 15.4750i	− 0.665321i	−0.943047	−	0.332660i	$-0.892054\pi$
$541$	− 15.4750i	− 0.665321i	0.943047	−	0.332660i	$-0.107946\pi$
$542$	−6.78781	−0.291562
$543$	−4.20196	−0.180323
$544$	12.9237i	0.554101i
$545$	−11.2325	−0.481146
$546$	0	0
$547$	25.1765	1.07647	0.538234	−	0.842795i	$-0.319092\pi$
$547$	25.1765	1.07647	0.538234	+	0.842795i	$0.319092\pi$
$548$	− 35.0979i	− 1.49931i
$549$	−6.19687	−0.264476
$550$	−1.18012	−0.0503204
$551$	6.58493i	0.280528i
$552$	− 3.94419i	− 0.167876i
$553$	− 1.50126i	− 0.0638401i
$554$	− 5.82269i	− 0.247382i
$555$	9.55639	0.405646
$556$	23.3938	0.992118
$557$	42.3489i	1.79438i	0.441645	+	0.897190i	$0.354395\pi$
$557$	42.3489i	1.79438i	−0.441645	+	0.897190i	$0.645605\pi$
$558$	−0.527420	−0.0223275
$559$	0	0
$560$	1.23355	0.0521270
$561$	43.5325i	1.83794i
$562$	−1.09353	−0.0461276
$563$	−23.7905	−1.00265	−0.501326	−	0.865259i	$-0.667154\pi$
$563$	−23.7905	−1.00265	−0.501326	+	0.865259i	$0.667154\pi$
$564$	− 26.0561i	− 1.09716i
$565$	− 18.3438i	− 0.771731i
$566$	2.76505i	0.116224i
$567$	2.48814i	0.104492i
$568$	11.1099	0.466162
$569$	26.7421	1.12109	0.560543	−	0.828125i	$-0.310593\pi$
$569$	26.7421	1.12109	0.560543	+	0.828125i	$0.310593\pi$
$570$	− 0.797279i	− 0.0333944i
$571$	16.7159	0.699539	0.349769	−	0.936836i	$-0.386260\pi$
$571$	16.7159	0.699539	0.349769	+	0.936836i	$0.386260\pi$
$572$	0	0
$573$	3.22571	0.134756
$574$	− 0.272403i	− 0.0113699i
$575$	−2.83918	−0.118402
$576$	−3.01625	−0.125677
$577$	20.6768i	0.860786i	0.902642	+	0.430393i	$0.141625\pi$
$577$	20.6768i	0.860786i	−0.902642	+	0.430393i	$0.858375\pi$
$578$	1.89966i	0.0790153i
$579$	− 36.5182i	− 1.51764i
$580$	− 5.66682i	− 0.235302i
$581$	1.41660	0.0587706
$582$	0.881636	0.0365450
$583$	8.38340i	0.347205i
$584$	8.41165	0.348076
$585$	0	0
$586$	−3.71657	−0.153530
$587$	− 20.7972i	− 0.858391i	−0.903212	−	0.429196i	$-0.858797\pi$
$587$	− 20.7972i	− 0.858391i	0.903212	−	0.429196i	$-0.141203\pi$
$588$	−21.5174	−0.887362
$589$	−12.3923	−0.510616
$590$	− 0.594763i	− 0.0244860i
$591$	− 1.02897i	− 0.0423260i
$592$	22.1726i	0.911289i
$593$	− 21.8475i	− 0.897169i	−0.893740	−	0.448585i	$-0.851928\pi$
$593$	− 21.8475i	− 0.897169i	0.893740	−	0.448585i	$-0.148072\pi$
$594$	6.49498	0.266492
$595$	1.68260	0.0689797
$596$	6.65622i	0.272649i
$597$	4.90755	0.200853
$598$	0	0
$599$	−3.58040	−0.146291	−0.0731456	−	0.997321i	$-0.523304\pi$
$599$	−3.58040	−0.146291	−0.0731456	+	0.997321i	$0.523304\pi$
$600$	1.38920i	0.0567139i
$601$	21.3486	0.870829	0.435414	−	0.900230i	$-0.356602\pi$
$601$	21.3486	0.870829	0.435414	+	0.900230i	$0.356602\pi$
$602$	0.369644	0.0150656
$603$	4.53972i	0.184872i
$604$	15.5386i	0.632256i
$605$	− 17.8564i	− 0.725966i
$606$	4.37554i	0.177744i
$607$	−3.29976	−0.133933	−0.0669665	−	0.997755i	$-0.521332\pi$
$607$	−3.29976	−0.133933	−0.0669665	+	0.997755i	$0.521332\pi$
$608$	5.78766	0.234720
$609$	− 1.54366i	− 0.0625523i
$610$	−3.09843	−0.125452
$611$	0	0
$612$	−4.34285	−0.175549
$613$	− 9.88635i	− 0.399306i	−0.979867	−	0.199653i	$-0.936019\pi$
$613$	− 9.88635i	− 0.399306i	0.979867	−	0.199653i	$-0.0639815\pi$
$614$	0.945589	0.0381609
$615$	−5.97201	−0.240815
$616$	− 1.54944i	− 0.0624286i
$617$	45.7169i	1.84049i	0.391339	+	0.920246i	$0.372012\pi$
$617$	45.7169i	1.84049i	−0.391339	+	0.920246i	$0.627988\pi$
$618$	− 5.28182i	− 0.212466i
$619$	19.9143i	0.800425i	0.916422	+	0.400212i	$0.131064\pi$
$619$	19.9143i	0.800425i	−0.916422	+	0.400212i	$0.868936\pi$
$620$	10.6645	0.428296
$621$	15.6259	0.627046
$622$	0.488829i	0.0196003i
$623$	1.07177	0.0429397
$624$	0	0
$625$	1.00000	0.0400000
$626$	1.58369i	0.0632971i
$627$	19.4952	0.778563
$628$	−32.0726	−1.27984
$629$	30.2440i	1.20591i
$630$	− 0.0320700i	− 0.00127770i
$631$	14.5958i	0.581050i	0.956867	+	0.290525i	$0.0938299\pi$
$631$	14.5958i	0.581050i	−0.956867	+	0.290525i	$0.906170\pi$
$632$	3.92272i	0.156038i
$633$	13.1222	0.521562
$634$	−0.0706609	−0.00280630
$635$	− 3.23996i	− 0.128574i
$636$	4.87409	0.193270
$637$	0	0
$638$	−3.42644	−0.135654
$639$	5.62281i	0.222435i
$640$	−6.61199	−0.261362
$641$	14.1637	0.559431	0.279716	−	0.960083i	$-0.409760\pi$
$641$	14.1637	0.559431	0.279716	+	0.960083i	$0.409760\pi$
$642$	4.59265i	0.181257i
$643$	− 16.7716i	− 0.661408i	−0.943735	−	0.330704i	$-0.892714\pi$
$643$	− 16.7716i	− 0.661408i	0.943735	−	0.330704i	$-0.107286\pi$
$644$	− 1.84109i	− 0.0725490i
$645$	− 8.10387i	− 0.319089i
$646$	2.52323	0.0992751
$647$	2.99168	0.117615	0.0588075	−	0.998269i	$-0.481270\pi$
$647$	2.99168	0.117615	0.0588075	+	0.998269i	$0.481270\pi$
$648$	− 6.50139i	− 0.255399i
$649$	14.5432	0.570872
$650$	0	0
$651$	2.90504	0.113858
$652$	34.7550i	1.36111i
$653$	−11.6643	−0.456461	−0.228230	−	0.973607i	$-0.573294\pi$
$653$	−11.6643	−0.456461	−0.228230	+	0.973607i	$0.573294\pi$
$654$	3.94868	0.154406
$655$	0.175664i	0.00686374i
$656$	− 13.8562i	− 0.540993i
$657$	4.25719i	0.166089i
$658$	0.608946i	0.0237392i
$659$	−1.81047	−0.0705260	−0.0352630	−	0.999378i	$-0.511227\pi$
$659$	−1.81047	−0.0705260	−0.0352630	+	0.999378i	$0.511227\pi$
$660$	−16.7771	−0.653046
$661$	− 12.3406i	− 0.479992i	−0.970774	−	0.239996i	$-0.922854\pi$
$661$	− 12.3406i	− 0.479992i	0.970774	−	0.239996i	$-0.0771462\pi$
$662$	3.65383	0.142010
$663$	0	0
$664$	−3.70152	−0.143647
$665$	− 0.753518i	− 0.0292202i
$666$	0.576446	0.0223368
$667$	−8.24348	−0.319189
$668$	− 12.2836i	− 0.475265i
$669$	16.3927i	0.633779i
$670$	2.26986i	0.0876923i
$671$	− 75.7634i	− 2.92481i
$672$	−1.35676	−0.0523381
$673$	−9.26625	−0.357188	−0.178594	−	0.983923i	$-0.557155\pi$
$673$	−9.26625	−0.357188	−0.178594	+	0.983923i	$0.557155\pi$
$674$	− 5.32051i	− 0.204938i
$675$	−5.50367	−0.211836
$676$	0	0
$677$	13.8984	0.534158	0.267079	−	0.963675i	$-0.413941\pi$
$677$	13.8984	0.534158	0.267079	+	0.963675i	$0.413941\pi$
$678$	6.44863i	0.247658i
$679$	0.833244	0.0319770
$680$	−4.39654	−0.168600
$681$	11.2715i	0.431924i
$682$	− 6.44828i	− 0.246917i
$683$	− 37.7512i	− 1.44451i	−0.691626	−	0.722255i	$-0.743105\pi$
$683$	− 37.7512i	− 1.44451i	0.691626	−	0.722255i	$-0.256895\pi$
$684$	1.94486i	0.0743637i
$685$	17.9829	0.687090
$686$	1.01381	0.0387073
$687$	− 2.12664i	− 0.0811363i
$688$	18.8025	0.716838
$689$	0	0
$690$	0.998090	0.0379966
$691$	1.65291i	0.0628797i	0.999506	+	0.0314399i	$0.0100093\pi$
$691$	1.65291i	0.0628797i	−0.999506	+	0.0314399i	$0.989991\pi$
$692$	−31.1792	−1.18526
$693$	0.784180	0.0297885
$694$	− 1.37823i	− 0.0523168i
$695$	11.9861i	0.454660i
$696$	4.03351i	0.152890i
$697$	− 18.9002i	− 0.715897i
$698$	−1.55317	−0.0587885
$699$	−1.99618	−0.0755025
$700$	0.648458i	0.0245094i
$701$	−20.4819	−0.773590	−0.386795	−	0.922166i	$-0.626418\pi$
$701$	−20.4819	−0.773590	−0.386795	+	0.922166i	$0.626418\pi$
$702$	0	0
$703$	13.5442	0.510830
$704$	− 36.8769i	− 1.38985i
$705$	13.3502	0.502797
$706$	−4.78694	−0.180159
$707$	4.13538i	0.155527i
$708$	− 8.45541i	− 0.317774i
$709$	21.9417i	0.824039i	0.911175	+	0.412020i	$0.135177\pi$
$709$	21.9417i	0.824039i	−0.911175	+	0.412020i	$0.864823\pi$
$710$	2.81140i	0.105510i
$711$	−1.98532	−0.0744552
$712$	−2.80049	−0.104953
$713$	− 15.5136i	− 0.580987i
$714$	−0.591503	−0.0221364
$715$	0	0
$716$	−46.0950	−1.72265
$717$	− 15.9093i	− 0.594142i
$718$	−5.26671	−0.196552
$719$	−38.8475	−1.44877	−0.724384	−	0.689397i	$-0.757876\pi$
$719$	−38.8475	−1.44877	−0.724384	+	0.689397i	$0.757876\pi$
$720$	− 1.63129i	− 0.0607945i
$721$	− 4.99191i	− 0.185909i
$722$	3.04407i	0.113289i
$723$	36.1434i	1.34419i
$724$	5.12507	0.190472
$725$	2.90348	0.107832
$726$	6.27728i	0.232972i
$727$	30.6598	1.13711	0.568555	−	0.822645i	$-0.307503\pi$
$727$	30.6598	1.13711	0.568555	+	0.822645i	$0.307503\pi$
$728$	0	0
$729$	29.7112	1.10042
$730$	2.12859i	0.0787828i
$731$	25.6471	0.948593
$732$	−44.0487	−1.62809
$733$	− 24.3858i	− 0.900709i	−0.892850	−	0.450355i	$-0.851298\pi$
$733$	− 24.3858i	− 0.900709i	0.892850	−	0.450355i	$-0.148702\pi$
$734$	1.40409i	0.0518259i
$735$	− 11.0247i	− 0.406653i
$736$	7.24539i	0.267069i
$737$	−55.5029	−2.04448
$738$	−0.360235	−0.0132604
$739$	38.2788i	1.40811i	0.710146	+	0.704054i	$0.248629\pi$
$739$	38.2788i	1.40811i	−0.710146	+	0.704054i	$0.751371\pi$
$740$	−11.6558	−0.428476
$741$	0	0
$742$	−0.113910	−0.00418178
$743$	40.0079i	1.46775i	0.679286	+	0.733874i	$0.262290\pi$
$743$	40.0079i	1.46775i	−0.679286	+	0.733874i	$0.737710\pi$
$744$	−7.59074	−0.278290
$745$	−3.41041	−0.124948
$746$	− 4.41134i	− 0.161511i
$747$	− 1.87336i	− 0.0685427i
$748$	− 53.0960i	− 1.94138i
$749$	4.34057i	0.158601i
$750$	−0.351542	−0.0128365
$751$	−25.6020	−0.934230	−0.467115	−	0.884197i	$-0.654707\pi$
$751$	−25.6020	−0.934230	−0.467115	+	0.884197i	$0.654707\pi$
$752$	30.9750i	1.12954i
$753$	−10.8307	−0.394693
$754$	0	0
$755$	−7.96141	−0.289745
$756$	− 3.56890i	− 0.129800i
$757$	−1.84848	−0.0671840	−0.0335920	−	0.999436i	$-0.510695\pi$
$757$	−1.84848	−0.0671840	−0.0335920	+	0.999436i	$0.510695\pi$
$758$	−1.19989	−0.0435820
$759$	24.4055i	0.885862i
$760$	1.96891i	0.0714198i
$761$	26.2124i	0.950199i	0.879932	+	0.475099i	$0.157588\pi$
$761$	26.2124i	0.950199i	−0.879932	+	0.475099i	$0.842412\pi$
$762$	1.13898i	0.0412610i
$763$	3.73195	0.135106
$764$	−3.93435	−0.142340
$765$	− 2.22512i	− 0.0804494i
$766$	−1.24513	−0.0449884
$767$	0	0
$768$	−19.6459	−0.708911
$769$	44.3495i	1.59928i	0.600478	+	0.799641i	$0.294977\pi$
$769$	44.3495i	1.59928i	−0.600478	+	0.799641i	$0.705023\pi$
$770$	0.392090	0.0141299
$771$	−16.4081	−0.590924
$772$	44.5408i	1.60306i
$773$	23.2638i	0.836742i	0.908276	+	0.418371i	$0.137399\pi$
$773$	23.2638i	0.836742i	−0.908276	+	0.418371i	$0.862601\pi$
$774$	− 0.488829i	− 0.0175706i
$775$	5.46410i	0.196276i
$776$	−2.17723	−0.0781580
$777$	−3.17508	−0.113905
$778$	− 2.33251i	− 0.0836245i
$779$	−8.46410	−0.303258
$780$	0	0
$781$	−68.7449	−2.45989
$782$	3.15875i	0.112957i
$783$	−15.9798	−0.571071
$784$	25.5794	0.913552
$785$	− 16.4329i	− 0.586514i
$786$	− 0.0617531i	− 0.00220266i
$787$	− 47.9133i	− 1.70793i	−0.520334	−	0.853963i	$-0.674192\pi$
$787$	− 47.9133i	− 1.70793i	0.520334	−	0.853963i	$-0.325808\pi$
$788$	1.25502i	0.0447081i
$789$	−29.8548	−1.06286
$790$	−0.992658	−0.0353172
$791$	6.09467i	0.216702i
$792$	−2.04903	−0.0728090
$793$	0	0
$794$	−6.15865	−0.218562
$795$	2.49731i	0.0885704i
$796$	−5.98567	−0.212156
$797$	20.6952	0.733060	0.366530	−	0.930406i	$-0.380546\pi$
$797$	20.6952	0.733060	0.366530	+	0.930406i	$0.380546\pi$
$798$	0.264893i	0.00937712i
$799$	42.2507i	1.49472i
$800$	− 2.55193i	− 0.0902245i
$801$	− 1.41735i	− 0.0500795i
$802$	4.94609	0.174653
$803$	−52.0487	−1.83676
$804$	32.2693i	1.13805i
$805$	0.943307	0.0332472
$806$	0	0
$807$	−28.7361	−1.01156
$808$	− 10.8056i	− 0.380138i
$809$	15.8915	0.558714	0.279357	−	0.960187i	$-0.409879\pi$
$809$	15.8915	0.558714	0.279357	+	0.960187i	$0.409879\pi$
$810$	1.64520	0.0578063
$811$	23.8796i	0.838525i	0.907865	+	0.419263i	$0.137711\pi$
$811$	23.8796i	0.838525i	−0.907865	+	0.419263i	$0.862289\pi$
$812$	1.88278i	0.0660727i
$813$	− 49.4423i	− 1.73402i
$814$	7.04768i	0.247021i
$815$	−17.8072	−0.623759
$816$	−30.0877	−1.05328
$817$	− 11.4856i	− 0.401829i
$818$	0.941956	0.0329347
$819$	0	0
$820$	7.28398	0.254368
$821$	− 15.9097i	− 0.555251i	−0.960689	−	0.277626i	$-0.910453\pi$
$821$	− 15.9097i	− 0.555251i	0.960689	−	0.277626i	$-0.0895475\pi$
$822$	−6.32174	−0.220496
$823$	14.8115	0.516295	0.258147	−	0.966106i	$-0.416888\pi$
$823$	14.8115	0.516295	0.258147	+	0.966106i	$0.416888\pi$
$824$	13.0436i	0.454397i
$825$	− 8.59596i	− 0.299273i
$826$	0.197608i	0.00687566i
$827$	33.9498i	1.18055i	0.807202	+	0.590275i	$0.200981\pi$
$827$	33.9498i	1.18055i	−0.807202	+	0.590275i	$0.799019\pi$
$828$	−2.43472	−0.0846122
$829$	−23.3146	−0.809749	−0.404875	−	0.914372i	$-0.632685\pi$
$829$	−23.3146	−0.809749	−0.404875	+	0.914372i	$0.632685\pi$
$830$	− 0.936681i	− 0.0325127i
$831$	42.4124	1.47127
$832$	0	0
$833$	34.8910	1.20890
$834$	− 4.21363i	− 0.145906i
$835$	6.29366	0.217801
$836$	−23.7780	−0.822380
$837$	− 30.0726i	− 1.03946i
$838$	3.89100i	0.134412i
$839$	− 14.7930i	− 0.510710i	−0.966847	−	0.255355i	$-0.917808\pi$
$839$	− 14.7930i	− 0.510710i	0.966847	−	0.255355i	$-0.0821924\pi$
$840$	− 0.461557i	− 0.0159252i
$841$	−20.5698	−0.709305
$842$	2.82929	0.0975038
$843$	− 7.96523i	− 0.274337i
$844$	−16.0050	−0.550915
$845$	0	0
$846$	0.805291	0.0276865
$847$	5.93273i	0.203851i
$848$	−5.79422	−0.198974
$849$	−20.1406	−0.691223
$850$	− 1.11256i	− 0.0381605i
$851$	16.9556i	0.581231i
$852$	39.9681i	1.36929i
$853$	− 16.3452i	− 0.559650i	−0.960051	−	0.279825i	$-0.909724\pi$
$853$	− 16.3452i	− 0.559650i	0.960051	−	0.279825i	$-0.0902765\pi$
$854$	1.02944	0.0352268
$855$	−0.996477	−0.0340788
$856$	− 11.3417i	− 0.387651i
$857$	34.1418	1.16626	0.583132	−	0.812378i	$-0.301827\pi$
$857$	34.1418	1.16626	0.583132	+	0.812378i	$0.301827\pi$
$858$	0	0
$859$	−45.1996	−1.54219	−0.771096	−	0.636719i	$-0.780291\pi$
$859$	−45.1996	−1.54219	−0.771096	+	0.636719i	$0.780291\pi$
$860$	9.88418i	0.337048i
$861$	1.98418	0.0676207
$862$	2.08669	0.0710728
$863$	− 4.75058i	− 0.161712i	−0.996726	−	0.0808559i	$-0.974235\pi$
$863$	− 4.75058i	− 0.161712i	0.996726	−	0.0808559i	$-0.0257653\pi$
$864$	14.0450i	0.477821i
$865$	− 15.9751i	− 0.543170i
$866$	0.306745i	0.0104236i
$867$	−13.8371	−0.469931
$868$	−3.54324	−0.120265
$869$	− 24.2726i	− 0.823392i
$870$	−1.02069	−0.0346048
$871$	0	0
$872$	−9.75140	−0.330224
$873$	− 1.10191i	− 0.0372940i
$874$	1.41459	0.0478492
$875$	−0.332247	−0.0112320
$876$	30.2610i	1.02242i
$877$	− 2.25506i	− 0.0761481i	−0.999275	−	0.0380741i	$-0.987878\pi$
$877$	− 2.25506i	− 0.0761481i	0.999275	−	0.0380741i	$-0.0121223\pi$
$878$	− 0.914293i	− 0.0308559i
$879$	− 27.0715i	− 0.913098i
$880$	19.9442	0.672320
$881$	2.98304	0.100501	0.0502507	−	0.998737i	$-0.483998\pi$
$881$	2.98304	0.100501	0.0502507	+	0.998737i	$0.483998\pi$
$882$	− 0.665017i	− 0.0223923i
$883$	−28.2874	−0.951947	−0.475973	−	0.879460i	$-0.657904\pi$
$883$	−28.2874	−0.951947	−0.475973	+	0.879460i	$0.657904\pi$
$884$	0	0
$885$	4.33225	0.145627
$886$	2.09705i	0.0704517i
$887$	−27.9816	−0.939531	−0.469766	−	0.882791i	$-0.655662\pi$
$887$	−27.9816	−0.939531	−0.469766	+	0.882791i	$0.655662\pi$
$888$	8.29633	0.278407
$889$	1.07647i	0.0361035i
$890$	− 0.708674i	− 0.0237548i
$891$	40.2286i	1.34771i
$892$	− 19.9940i	− 0.669448i
$893$	18.9212	0.633172
$894$	1.19890	0.0400973
$895$	− 23.6174i	− 0.789443i
$896$	2.19681	0.0733903
$897$	0	0
$898$	−4.77095	−0.159209
$899$	15.8649i	0.529124i
$900$	0.857542	0.0285847
$901$	−7.90348	−0.263303
$902$	− 4.40426i	− 0.146646i
$903$	2.69248i	0.0896002i
$904$	− 15.9251i	− 0.529661i
$905$	2.62590i	0.0872879i
$906$	2.79877	0.0929829
$907$	−16.5520	−0.549600	−0.274800	−	0.961501i	$-0.588612\pi$
$907$	−16.5520	−0.549600	−0.274800	+	0.961501i	$0.588612\pi$
$908$	− 13.7477i	− 0.456232i
$909$	5.46876	0.181387
$910$	0	0
$911$	7.04863	0.233532	0.116766	−	0.993159i	$-0.462747\pi$
$911$	7.04863	0.233532	0.116766	+	0.993159i	$0.462747\pi$
$912$	13.4742i	0.446175i
$913$	22.9039	0.758007
$914$	1.03749	0.0343172
$915$	− 22.5689i	− 0.746106i
$916$	2.59383i	0.0857026i
$917$	− 0.0583636i	− 0.00192734i
$918$	6.12316i	0.202094i
$919$	16.5438	0.545728	0.272864	−	0.962053i	$-0.412029\pi$
$919$	16.5438	0.545728	0.272864	+	0.962053i	$0.412029\pi$
$920$	−2.46482	−0.0812626
$921$	6.88766i	0.226956i
$922$	−0.391374	−0.0128892
$923$	0	0
$924$	5.57412	0.183375
$925$	− 5.97201i	− 0.196359i
$926$	−1.49431	−0.0491060
$927$	−6.60147	−0.216821
$928$	− 7.40948i	− 0.243228i
$929$	− 33.8367i	− 1.11015i	−0.831801	−	0.555074i	$-0.812690\pi$
$929$	− 33.8367i	− 1.11015i	0.831801	−	0.555074i	$-0.187310\pi$
$930$	− 1.92086i	− 0.0629875i
$931$	− 15.6253i	− 0.512098i
$932$	2.43472	0.0797517
$933$	−3.56063	−0.116570
$934$	− 4.00652i	− 0.131097i
$935$	27.2045	0.889681
$936$	0	0
$937$	−30.4606	−0.995104	−0.497552	−	0.867434i	$-0.665768\pi$
$937$	−30.4606	−0.995104	−0.497552	+	0.867434i	$0.665768\pi$
$938$	− 0.754153i	− 0.0246240i
$939$	−11.5356	−0.376450
$940$	−16.2831	−0.531095
$941$	38.2101i	1.24561i	0.782375	+	0.622807i	$0.214008\pi$
$941$	38.2101i	1.24561i	−0.782375	+	0.622807i	$0.785992\pi$
$942$	5.77684i	0.188220i
$943$	− 10.5960i	− 0.345052i
$944$	10.0516i	0.327153i
$945$	1.82858	0.0594836
$946$	5.97647	0.194312
$947$	52.4482i	1.70434i	0.523266	+	0.852169i	$0.324713\pi$
$947$	52.4482i	1.70434i	−0.523266	+	0.852169i	$0.675287\pi$
$948$	−14.1120	−0.458338
$949$	0	0
$950$	−0.498239	−0.0161650
$951$	− 0.514693i	− 0.0166901i
$952$	1.46074	0.0473427
$953$	−39.7500	−1.28763	−0.643814	−	0.765182i	$-0.722649\pi$
$953$	−39.7500	−1.28763	−0.643814	+	0.765182i	$0.722649\pi$
$954$	0.150639i	0.00487711i
$955$	− 2.01582i	− 0.0652304i
$956$	19.4043i	0.627580i
$957$	− 24.9581i	− 0.806782i
$958$	7.72874	0.249704
$959$	−5.97475	−0.192935
$960$	− 10.9852i	− 0.354544i
$961$	1.14359	0.0368901
$962$	0	0
$963$	5.74011	0.184972
$964$	− 44.0837i	− 1.41984i
$965$	−22.8211	−0.734636
$966$	−0.331612	−0.0106694
$967$	− 25.7857i	− 0.829214i	−0.910001	−	0.414607i	$-0.863919\pi$
$967$	− 25.7857i	− 0.829214i	0.910001	−	0.414607i	$-0.136081\pi$
$968$	− 15.5019i	− 0.498251i
$969$	18.3792i	0.590424i
$970$	− 0.550955i	− 0.0176901i
$971$	−55.5252	−1.78189	−0.890945	−	0.454111i	$-0.849957\pi$
$971$	−55.5252	−1.78189	−0.890945	+	0.454111i	$0.849957\pi$
$972$	−8.83634	−0.283426
$973$	− 3.98235i	− 0.127668i
$974$	−2.26365	−0.0725321
$975$	0	0
$976$	52.3642	1.67614
$977$	40.5161i	1.29622i	0.761545	+	0.648112i	$0.224441\pi$
$977$	40.5161i	1.29622i	−0.761545	+	0.648112i	$0.775559\pi$
$978$	6.25998	0.200172
$979$	17.3286	0.553824
$980$	13.4467i	0.429540i
$981$	− 4.93525i	− 0.157570i
$982$	− 2.05011i	− 0.0654218i
$983$	34.8059i	1.11014i	0.831805	+	0.555068i	$0.187308\pi$
$983$	34.8059i	1.11014i	−0.831805	+	0.555068i	$0.812692\pi$
$984$	−5.18457	−0.165278
$985$	−0.643026	−0.0204885
$986$	− 3.23029i	− 0.102873i
$987$	−4.43555	−0.141185
$988$	0	0
$989$	14.3784	0.457208
$990$	− 0.518513i	− 0.0164794i
$991$	43.8855	1.39407	0.697034	−	0.717038i	$-0.254503\pi$
$991$	43.8855	1.39407	0.697034	+	0.717038i	$0.254503\pi$
$992$	13.9440	0.442723
$993$	26.6145i	0.844584i
$994$	− 0.934079i	− 0.0296272i
$995$	− 3.06684i	− 0.0972254i
$996$	− 13.3163i	− 0.421942i
$997$	−5.49137	−0.173914	−0.0869568	−	0.996212i	$-0.527714\pi$
$997$	−5.49137	−0.173914	−0.0869568	+	0.996212i	$0.527714\pi$
$998$	5.25976	0.166495
$999$	32.8680i	1.03990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.c.g.506.5		8
13.2	odd	12		845.2.e.n.191.2		8
13.3	even	3		65.2.m.a.56.2	yes	8
13.4	even	6		65.2.m.a.36.2	✓	8
13.5	odd	4		845.2.a.l.1.3		4
13.6	odd	12		845.2.e.n.146.2		8
13.7	odd	12		845.2.e.m.146.3		8
13.8	odd	4		845.2.a.m.1.2		4
13.9	even	3		845.2.m.g.361.3		8
13.10	even	6		845.2.m.g.316.3		8
13.11	odd	12		845.2.e.m.191.3		8
13.12	even	2	inner	845.2.c.g.506.4		8
39.5	even	4		7605.2.a.cj.1.2		4
39.8	even	4		7605.2.a.cf.1.3		4
39.17	odd	6		585.2.bu.c.361.3		8
39.29	odd	6		585.2.bu.c.316.3		8
52.3	odd	6		1040.2.da.b.641.2		8
52.43	odd	6		1040.2.da.b.881.2		8
65.3	odd	12		325.2.m.c.199.2		8
65.4	even	6		325.2.n.d.101.3		8
65.17	odd	12		325.2.m.c.49.2		8
65.29	even	6		325.2.n.d.251.3		8
65.34	odd	4		4225.2.a.bi.1.3		4
65.42	odd	12		325.2.m.b.199.3		8
65.43	odd	12		325.2.m.b.49.3		8
65.44	odd	4		4225.2.a.bl.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.2	✓	8	13.4	even	6
65.2.m.a.56.2	yes	8	13.3	even	3
325.2.m.b.49.3		8	65.43	odd	12
325.2.m.b.199.3		8	65.42	odd	12
325.2.m.c.49.2		8	65.17	odd	12
325.2.m.c.199.2		8	65.3	odd	12
325.2.n.d.101.3		8	65.4	even	6
325.2.n.d.251.3		8	65.29	even	6
585.2.bu.c.316.3		8	39.29	odd	6
585.2.bu.c.361.3		8	39.17	odd	6
845.2.a.l.1.3		4	13.5	odd	4
845.2.a.m.1.2		4	13.8	odd	4
845.2.c.g.506.4		8	13.12	even	2	inner
845.2.c.g.506.5		8	1.1	even	1	trivial
845.2.e.m.146.3		8	13.7	odd	12
845.2.e.m.191.3		8	13.11	odd	12
845.2.e.n.146.2		8	13.6	odd	12
845.2.e.n.191.2		8	13.2	odd	12
845.2.m.g.316.3		8	13.10	even	6
845.2.m.g.361.3		8	13.9	even	3
1040.2.da.b.641.2		8	52.3	odd	6
1040.2.da.b.881.2		8	52.43	odd	6
4225.2.a.bi.1.3		4	65.34	odd	4
4225.2.a.bl.1.2		4	65.44	odd	4
7605.2.a.cf.1.3		4	39.8	even	4
7605.2.a.cj.1.2		4	39.5	even	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.219687i q^{2} -1.60020 q^{3} +1.95174 q^{4} +1.00000i q^{5} -0.351542i q^{6} -0.332247i q^{7} +0.868145i q^{8} -0.439374 q^{9} +O(q^{10})\)	\(q+0.219687i q^{2} -1.60020 q^{3} +1.95174 q^{4} +1.00000i q^{5} -0.351542i q^{6} -0.332247i q^{7} +0.868145i q^{8} -0.439374 q^{9} -0.219687 q^{10} -5.37182i q^{11} -3.12316 q^{12} +0.0729902 q^{14} -1.60020i q^{15} +3.71276 q^{16} +5.06430 q^{17} -0.0965246i q^{18} -2.26795i q^{19} +1.95174i q^{20} +0.531659i q^{21} +1.18012 q^{22} +2.83918 q^{23} -1.38920i q^{24} -1.00000 q^{25} +5.50367 q^{27} -0.648458i q^{28} -2.90348 q^{29} +0.351542 q^{30} -5.46410i q^{31} +2.55193i q^{32} +8.59596i q^{33} +1.11256i q^{34} +0.332247 q^{35} -0.857542 q^{36} +5.97201i q^{37} +0.498239 q^{38} -0.868145 q^{40} -3.73205i q^{41} -0.116799 q^{42} +5.06430 q^{43} -10.4844i q^{44} -0.439374i q^{45} +0.623730i q^{46} +8.34285i q^{47} -5.94114 q^{48} +6.88961 q^{49} -0.219687i q^{50} -8.10387 q^{51} -1.56063 q^{53} +1.20908i q^{54} +5.37182 q^{55} +0.288438 q^{56} +3.62916i q^{57} -0.637855i q^{58} +2.70732i q^{59} -3.12316i q^{60} +14.1039 q^{61} +1.20039 q^{62} +0.145980i q^{63} +6.86488 q^{64} -1.88842 q^{66} -10.3322i q^{67} +9.88418 q^{68} -4.54324 q^{69} +0.0729902i q^{70} -12.7973i q^{71} -0.381440i q^{72} -9.68922i q^{73} -1.31197 q^{74} +1.60020 q^{75} -4.42644i q^{76} -1.78477 q^{77} +4.51851 q^{79} +3.71276i q^{80} -7.48883 q^{81} +0.819883 q^{82} +4.26371i q^{83} +1.03766i q^{84} +5.06430i q^{85} +1.11256i q^{86} +4.64613 q^{87} +4.66351 q^{88} +3.22584i q^{89} +0.0965246 q^{90} +5.54133 q^{92} +8.74363i q^{93} -1.83281 q^{94} +2.26795 q^{95} -4.08359i q^{96} +2.50791i q^{97} +1.51356i q^{98} +2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{4} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 4 * q^4 + 8 * q^9	\( 8 q - 4 q^{3} - 4 q^{4} + 8 q^{9} + 4 q^{10} + 20 q^{12} + 4 q^{14} + 4 q^{16} + 4 q^{17} + 24 q^{22} + 20 q^{23} - 8 q^{25} - 4 q^{27} + 16 q^{29} - 8 q^{30} - 20 q^{35} - 40 q^{36} - 16 q^{38} - 12 q^{40} - 8 q^{42} + 4 q^{43} - 56 q^{48} - 24 q^{49} - 8 q^{51} - 24 q^{53} - 24 q^{56} + 56 q^{61} - 8 q^{62} - 8 q^{64} + 12 q^{66} + 28 q^{68} + 32 q^{69} - 20 q^{74} + 4 q^{75} - 36 q^{77} - 16 q^{79} - 16 q^{81} - 8 q^{82} - 44 q^{87} + 36 q^{88} + 40 q^{90} + 44 q^{92} - 64 q^{94} + 32 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^4 + 8 * q^9 + 4 * q^10 + 20 * q^12 + 4 * q^14 + 4 * q^16 + 4 * q^17 + 24 * q^22 + 20 * q^23 - 8 * q^25 - 4 * q^27 + 16 * q^29 - 8 * q^30 - 20 * q^35 - 40 * q^36 - 16 * q^38 - 12 * q^40 - 8 * q^42 + 4 * q^43 - 56 * q^48 - 24 * q^49 - 8 * q^51 - 24 * q^53 - 24 * q^56 + 56 * q^61 - 8 * q^62 - 8 * q^64 + 12 * q^66 + 28 * q^68 + 32 * q^69 - 20 * q^74 + 4 * q^75 - 36 * q^77 - 16 * q^79 - 16 * q^81 - 8 * q^82 - 44 * q^87 + 36 * q^88 + 40 * q^90 + 44 * q^92 - 64 * q^94 + 32 * q^95

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