LMFDB - Embedded newform 845.2.c.g.506.3

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			506.3
Root			$-1.27597 + 0.609843i$ of defining polynomial
Character	$\chi$	$=$	845.506
Dual form			845.2.c.g.506.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21969i q^{2} +2.33225 q^{3} +0.512364 q^{4} +1.00000i q^{5} -2.84461i q^{6} +3.60020i q^{7} -3.06430i q^{8} +2.43937 q^{9} +O(q^{10})$	\(q-1.21969i q^{2} +2.33225 q^{3} +0.512364 q^{4} +1.00000i q^{5} -2.84461i q^{6} +3.60020i q^{7} -3.06430i q^{8} +2.43937 q^{9} +1.21969 q^{10} +5.37182i q^{11} +1.19496 q^{12} +4.39111 q^{14} +2.33225i q^{15} -2.71276 q^{16} +1.13186 q^{17} -2.97527i q^{18} -2.26795i q^{19} +0.512364i q^{20} +8.39654i q^{21} +6.55193 q^{22} +3.89287 q^{23} -7.14670i q^{24} -1.00000 q^{25} -1.30752 q^{27} +1.84461i q^{28} -0.0247279 q^{29} +2.84461 q^{30} -5.46410i q^{31} -2.81988i q^{32} +12.5284i q^{33} -1.38051i q^{34} -3.60020 q^{35} +1.24985 q^{36} -8.70406i q^{37} -2.76619 q^{38} +3.06430 q^{40} -3.73205i q^{41} +10.2412 q^{42} +1.13186 q^{43} +2.75232i q^{44} +2.43937i q^{45} -4.74809i q^{46} +2.58535i q^{47} -6.32681 q^{48} -5.96141 q^{49} +1.21969i q^{50} +2.63977 q^{51} -4.43937 q^{53} +1.59476i q^{54} -5.37182 q^{55} +11.0321 q^{56} -5.28942i q^{57} +0.0301603i q^{58} -0.171425i q^{59} +1.19496i q^{60} +3.36023 q^{61} -6.66449 q^{62} +8.78222i q^{63} -8.86488 q^{64} +15.2807 q^{66} -6.39980i q^{67} +0.579922 q^{68} +9.07914 q^{69} +4.39111i q^{70} +10.7973i q^{71} -7.47497i q^{72} -4.70308i q^{73} -10.6162 q^{74} -2.33225 q^{75} -1.16202i q^{76} -19.3396 q^{77} -11.9826 q^{79} -2.71276i q^{80} -10.3676 q^{81} -4.55193 q^{82} +12.1286i q^{83} +4.30209i q^{84} +1.13186i q^{85} -1.38051i q^{86} -0.0576715 q^{87} +16.4608 q^{88} -16.1540i q^{89} +2.97527 q^{90} +1.99457 q^{92} -12.7436i q^{93} +3.15332 q^{94} +2.26795 q^{95} -6.57666i q^{96} -12.1682i q^{97} +7.27105i q^{98} +13.1039i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 1.21969i	− 0.862449i	−0.902245	−	0.431224i	$-0.858082\pi$
$2$	− 1.21969i	− 0.862449i	0.902245	−	0.431224i	$-0.141918\pi$
$3$	2.33225	1.34652	0.673262	−	0.739404i	$-0.264893\pi$
$3$	2.33225	1.34652	0.673262	+	0.739404i	$0.264893\pi$
$4$	0.512364	0.256182
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	− 2.84461i	− 1.16131i
$7$	3.60020i	1.36075i	0.732866	+	0.680373i	$0.238182\pi$
$7$	3.60020i	1.36075i	−0.732866	+	0.680373i	$0.761818\pi$
$8$	− 3.06430i	− 1.08339i
$9$	2.43937	0.813125
$10$	1.21969	0.385699
$11$	5.37182i	1.61966i	0.586662	+	0.809832i	$0.300442\pi$
$11$	5.37182i	1.61966i	−0.586662	+	0.809832i	$0.699558\pi$
$12$	1.19496	0.344955
$13$	0	0
$13$	0	0
$14$	4.39111	1.17357
$15$	2.33225i	0.602183i
$16$	−2.71276	−0.678189
$17$	1.13186	0.274515	0.137258	−	0.990535i	$-0.456171\pi$
$17$	1.13186	0.274515	0.137258	+	0.990535i	$0.456171\pi$
$18$	− 2.97527i	− 0.701278i
$19$	− 2.26795i	− 0.520303i	−0.965568	−	0.260152i	$-0.916227\pi$
$19$	− 2.26795i	− 0.520303i	0.965568	−	0.260152i	$-0.0837725\pi$
$20$	0.512364i	0.114568i
$21$	8.39654i	1.83228i
$22$	6.55193	1.39688
$23$	3.89287	0.811720	0.405860	−	0.913935i	$-0.366972\pi$
$23$	3.89287	0.811720	0.405860	+	0.913935i	$0.366972\pi$
$24$	− 7.14670i	− 1.45881i
$25$	−1.00000	−0.200000
$26$	0	0
$27$	−1.30752	−0.251632
$28$	1.84461i	0.348599i
$29$	−0.0247279	−0.00459185	−0.00229593	−	0.999997i	$-0.500731\pi$
$29$	−0.0247279	−0.00459185	−0.00229593	+	0.999997i	$0.500731\pi$
$30$	2.84461	0.519352
$31$	− 5.46410i	− 0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$	− 5.46410i	− 0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	− 2.81988i	− 0.498490i
$33$	12.5284i	2.18091i
$34$	− 1.38051i	− 0.236755i
$35$	−3.60020	−0.608544
$36$	1.24985	0.208308
$37$	− 8.70406i	− 1.43094i	−0.698644	−	0.715470i	$-0.746213\pi$
$37$	− 8.70406i	− 1.43094i	0.698644	−	0.715470i	$-0.253787\pi$
$38$	−2.76619	−0.448735
$39$	0	0
$40$	3.06430	0.484508
$41$	− 3.73205i	− 0.582848i	−0.956594	−	0.291424i	$-0.905871\pi$
$41$	− 3.73205i	− 0.582848i	0.956594	−	0.291424i	$-0.0941291\pi$
$42$	10.2412	1.58024
$43$	1.13186	0.172606	0.0863031	−	0.996269i	$-0.472495\pi$
$43$	1.13186	0.172606	0.0863031	+	0.996269i	$0.472495\pi$
$44$	2.75232i	0.414929i
$45$	2.43937i	0.363640i
$46$	− 4.74809i	− 0.700067i
$47$	2.58535i	0.377113i	0.982062	+	0.188556i	$0.0603808\pi$
$47$	2.58535i	0.377113i	−0.982062	+	0.188556i	$0.939619\pi$
$48$	−6.32681	−0.913197
$49$	−5.96141	−0.851630
$50$	1.21969i	0.172490i
$51$	2.63977	0.369641
$52$	0	0
$53$	−4.43937	−0.609795	−0.304897	−	0.952385i	$-0.598622\pi$
$53$	−4.43937	−0.609795	−0.304897	+	0.952385i	$0.598622\pi$
$54$	1.59476i	0.217020i
$55$	−5.37182	−0.724336
$56$	11.0321	1.47422
$57$	− 5.28942i	− 0.700600i
$58$	0.0301603i	0.00396024i
$59$	− 0.171425i	− 0.0223176i	−0.999938	−	0.0111588i	$-0.996448\pi$
$59$	− 0.171425i	− 0.0223176i	0.999938	−	0.0111588i	$-0.00355203\pi$
$60$	1.19496i	0.154269i
$61$	3.36023	0.430234	0.215117	−	0.976588i	$-0.430987\pi$
$61$	3.36023	0.430234	0.215117	+	0.976588i	$0.430987\pi$
$62$	−6.66449	−0.846391
$63$	8.78222i	1.10646i
$64$	−8.86488	−1.10811
$65$	0	0
$66$	15.2807	1.88093
$67$	− 6.39980i	− 0.781861i	−0.920420	−	0.390930i	$-0.872153\pi$
$67$	− 6.39980i	− 0.781861i	0.920420	−	0.390930i	$-0.127847\pi$
$68$	0.579922	0.0703258
$69$	9.07914	1.09300
$70$	4.39111i	0.524838i
$71$	10.7973i	1.28141i	0.767788	+	0.640703i	$0.221357\pi$
$71$	10.7973i	1.28141i	−0.767788	+	0.640703i	$0.778643\pi$
$72$	− 7.47497i	− 0.880933i
$73$	− 4.70308i	− 0.550454i	−0.961379	−	0.275227i	$-0.911247\pi$
$73$	− 4.70308i	− 0.550454i	0.961379	−	0.275227i	$-0.0887531\pi$
$74$	−10.6162	−1.23411
$75$	−2.33225	−0.269305
$76$	− 1.16202i	− 0.133292i
$77$	−19.3396	−2.20395
$78$	0	0
$79$	−11.9826	−1.34815	−0.674075	−	0.738663i	$-0.735457\pi$
$79$	−11.9826	−1.34815	−0.674075	+	0.738663i	$0.735457\pi$
$80$	− 2.71276i	− 0.303295i
$81$	−10.3676	−1.15195
$82$	−4.55193	−0.502677
$83$	12.1286i	1.33129i	0.746270	+	0.665643i	$0.231843\pi$
$83$	12.1286i	1.33129i	−0.746270	+	0.665643i	$0.768157\pi$
$84$	4.30209i	0.469396i
$85$	1.13186i	0.122767i
$86$	− 1.38051i	− 0.148864i
$87$	−0.0576715	−0.00618303
$88$	16.4608	1.75473
$89$	− 16.1540i	− 1.71232i	−0.516707	−	0.856162i	$-0.672842\pi$
$89$	− 16.1540i	− 1.71232i	0.516707	−	0.856162i	$-0.327158\pi$
$90$	2.97527	0.313621
$91$	0	0
$92$	1.99457	0.207948
$93$	− 12.7436i	− 1.32145i
$94$	3.15332	0.325240
$95$	2.26795	0.232687
$96$	− 6.57666i	− 0.671228i
$97$	− 12.1682i	− 1.23549i	−0.786379	−	0.617745i	$-0.788046\pi$
$97$	− 12.1682i	− 1.23549i	0.786379	−	0.617745i	$-0.211954\pi$
$98$	7.27105i	0.734487i
$99$	13.1039i	1.31699i
$100$	−0.512364	−0.0512364
$101$	4.05441	0.403429	0.201714	−	0.979444i	$-0.435349\pi$
$101$	4.05441	0.403429	0.201714	+	0.979444i	$0.435349\pi$
$102$	− 3.21969i	− 0.318797i
$103$	17.9035	1.76408	0.882041	−	0.471173i	$-0.156169\pi$
$103$	17.9035	1.76408	0.882041	+	0.471173i	$0.156169\pi$
$104$	0	0
$105$	−8.39654	−0.819419
$106$	5.41465i	0.525917i
$107$	−9.13186	−0.882810	−0.441405	−	0.897308i	$-0.645520\pi$
$107$	−9.13186	−0.882810	−0.441405	+	0.897308i	$0.645520\pi$
$108$	−0.669925	−0.0644636
$109$	− 7.37605i	− 0.706498i	−0.935529	−	0.353249i	$-0.885077\pi$
$109$	− 7.37605i	− 0.706498i	0.935529	−	0.353249i	$-0.114923\pi$
$110$	6.55193i	0.624702i
$111$	− 20.3000i	− 1.92679i
$112$	− 9.76645i	− 0.922843i
$113$	7.07588	0.665643	0.332821	−	0.942990i	$-0.391999\pi$
$113$	7.07588	0.665643	0.332821	+	0.942990i	$0.391999\pi$
$114$	−6.45143	−0.604232
$115$	3.89287i	0.363012i
$116$	−0.0126697	−0.00117635
$117$	0	0
$118$	−0.209084	−0.0192478
$119$	4.07490i	0.373545i
$120$	7.14670	0.652401
$121$	−17.8564	−1.62331
$122$	− 4.09843i	− 0.371055i
$123$	− 8.70406i	− 0.784819i
$124$	− 2.79961i	− 0.251412i
$125$	− 1.00000i	− 0.0894427i
$126$	10.7116	0.954262
$127$	11.4361	1.01479	0.507395	−	0.861713i	$-0.330608\pi$
$127$	11.4361	1.01479	0.507395	+	0.861713i	$0.330608\pi$
$128$	5.17262i	0.457199i
$129$	2.63977	0.232418
$130$	0	0
$131$	−10.5680	−0.923328	−0.461664	−	0.887055i	$-0.652747\pi$
$131$	−10.5680	−0.923328	−0.461664	+	0.887055i	$0.652747\pi$
$132$	6.41910i	0.558711i
$133$	8.16506	0.708001
$134$	−7.80576	−0.674315
$135$	− 1.30752i	− 0.112533i
$136$	− 3.46834i	− 0.297408i
$137$	3.78672i	0.323522i	0.986830	+	0.161761i	$0.0517173\pi$
$137$	3.78672i	0.323522i	−0.986830	+	0.161761i	$0.948283\pi$
$138$	− 11.0737i	− 0.942656i
$139$	2.01386	0.170814	0.0854068	−	0.996346i	$-0.472781\pi$
$139$	2.01386	0.170814	0.0854068	+	0.996346i	$0.472781\pi$
$140$	−1.84461	−0.155898
$141$	6.02968i	0.507791i
$142$	13.1694	1.10515
$143$	0	0
$144$	−6.61742	−0.551452
$145$	− 0.0247279i	− 0.00205354i
$146$	−5.73629	−0.474739
$147$	−13.9035	−1.14674
$148$	− 4.45965i	− 0.366581i
$149$	5.51780i	0.452035i	0.974123	+	0.226018i	$0.0725707\pi$
$149$	5.51780i	0.452035i	−0.974123	+	0.226018i	$0.927429\pi$
$150$	2.84461i	0.232261i
$151$	− 4.88961i	− 0.397911i	−0.980009	−	0.198956i	$-0.936245\pi$
$151$	− 4.88961i	− 0.397911i	0.980009	−	0.198956i	$-0.0637549\pi$
$152$	−6.94967	−0.563693
$153$	2.76102	0.223215
$154$	23.5882i	1.90079i
$155$	5.46410	0.438887
$156$	0	0
$157$	10.0405	0.801323	0.400661	−	0.916226i	$-0.368780\pi$
$157$	10.0405	0.801323	0.400661	+	0.916226i	$0.368780\pi$
$158$	14.6150i	1.16271i
$159$	−10.3537	−0.821103
$160$	2.81988	0.222931
$161$	14.0151i	1.10454i
$162$	12.6452i	0.993501i
$163$	6.78124i	0.531148i	0.964090	+	0.265574i	$0.0855615\pi$
$163$	6.78124i	0.531148i	−0.964090	+	0.265574i	$0.914439\pi$
$164$	− 1.91217i	− 0.149315i
$165$	−12.5284	−0.975335
$166$	14.7931	1.14817
$167$	10.4898i	0.811726i	0.913934	+	0.405863i	$0.133029\pi$
$167$	10.4898i	0.811726i	−0.913934	+	0.405863i	$0.866971\pi$
$168$	25.7295	1.98507
$169$	0	0
$170$	1.38051	0.105880
$171$	− 5.53238i	− 0.423071i
$172$	0.579922	0.0442186
$173$	4.45845	0.338970	0.169485	−	0.985533i	$-0.445790\pi$
$173$	4.45845	0.338970	0.169485	+	0.985533i	$0.445790\pi$
$174$	0.0703412i	0.00533255i
$175$	− 3.60020i	− 0.272149i
$176$	− 14.5724i	− 1.09844i
$177$	− 0.399804i	− 0.0300511i
$178$	−19.7029	−1.47679
$179$	−18.6313	−1.39257	−0.696284	−	0.717766i	$-0.745165\pi$
$179$	−18.6313	−1.39257	−0.696284	+	0.717766i	$0.745165\pi$
$180$	1.24985i	0.0931581i
$181$	−18.0900	−1.34462	−0.672310	−	0.740270i	$-0.734698\pi$
$181$	−18.0900	−1.34462	−0.672310	+	0.740270i	$0.734698\pi$
$182$	0	0
$183$	7.83690	0.579320
$184$	− 11.9289i	− 0.879412i
$185$	8.70406	0.639935
$186$	−15.5432	−1.13969
$187$	6.08012i	0.444622i
$188$	1.32464i	0.0966095i
$189$	− 4.70732i	− 0.342407i
$190$	− 2.76619i	− 0.200680i
$191$	27.3363	1.97799	0.988994	−	0.147958i	$-0.0472701\pi$
$191$	27.3363	1.97799	0.988994	+	0.147958i	$0.0472701\pi$
$192$	−20.6751	−1.49210
$193$	21.7674i	1.56685i	0.621486	+	0.783425i	$0.286529\pi$
$193$	21.7674i	1.56685i	−0.621486	+	0.783425i	$0.713471\pi$
$194$	−14.8413	−1.06555
$195$	0	0
$196$	−3.05441	−0.218172
$197$	1.69672i	0.120886i	0.998172	+	0.0604432i	$0.0192514\pi$
$197$	1.69672i	0.120886i	−0.998172	+	0.0604432i	$0.980749\pi$
$198$	15.9826	1.13583
$199$	−25.3255	−1.79527	−0.897637	−	0.440735i	$-0.854718\pi$
$199$	−25.3255	−1.79527	−0.897637	+	0.440735i	$0.854718\pi$
$200$	3.06430i	0.216679i
$201$	− 14.9259i	− 1.05279i
$202$	− 4.94511i	− 0.347937i
$203$	− 0.0890252i	− 0.00624834i
$204$	1.35252	0.0946954
$205$	3.73205	0.260658
$206$	− 21.8366i	− 1.52143i
$207$	9.49617	0.660030
$208$	0	0
$209$	12.1830	0.842716
$210$	10.2412i	0.706707i
$211$	−0.335507	−0.0230973	−0.0115486	−	0.999933i	$-0.503676\pi$
$211$	−0.335507	−0.0230973	−0.0115486	+	0.999933i	$0.503676\pi$
$212$	−2.27458	−0.156218
$213$	25.1820i	1.72544i
$214$	11.1380i	0.761378i
$215$	1.13186i	0.0771919i
$216$	4.00663i	0.272616i
$217$	19.6718	1.33541
$218$	−8.99648	−0.609318
$219$	− 10.9688i	− 0.741200i
$220$	−2.75232	−0.185562
$221$	0	0
$222$	−24.7597	−1.66176
$223$	12.2968i	0.823452i	0.911308	+	0.411726i	$0.135074\pi$
$223$	12.2968i	0.823452i	−0.911308	+	0.411726i	$0.864926\pi$
$224$	10.1521	0.678318
$225$	−2.43937	−0.162625
$226$	− 8.63036i	− 0.574083i
$227$	7.63227i	0.506571i	0.967392	+	0.253286i	$0.0815112\pi$
$227$	7.63227i	0.506571i	−0.967392	+	0.253286i	$0.918489\pi$
$228$	− 2.71011i	− 0.179481i
$229$	− 14.4008i	− 0.951631i	−0.879545	−	0.475815i	$-0.842153\pi$
$229$	− 14.4008i	− 0.951631i	0.879545	−	0.475815i	$-0.157847\pi$
$230$	4.74809	0.313080
$231$	−45.1047	−2.96767
$232$	0.0757736i	0.00497478i
$233$	−9.49617	−0.622115	−0.311057	−	0.950391i	$-0.600683\pi$
$233$	−9.49617	−0.622115	−0.311057	+	0.950391i	$0.600683\pi$
$234$	0	0
$235$	−2.58535	−0.168650
$236$	− 0.0878318i	− 0.00571736i
$237$	−27.9464	−1.81531
$238$	4.97010	0.322164
$239$	19.9143i	1.28815i	0.764962	+	0.644076i	$0.222758\pi$
$239$	19.9143i	1.28815i	−0.764962	+	0.644076i	$0.777242\pi$
$240$	− 6.32681i	− 0.408394i
$241$	23.2664i	1.49872i	0.662163	+	0.749360i	$0.269639\pi$
$241$	23.2664i	1.49872i	−0.662163	+	0.749360i	$0.730361\pi$
$242$	21.7792i	1.40002i
$243$	−20.2572	−1.29950
$244$	1.72166	0.110218
$245$	− 5.96141i	− 0.380860i
$246$	−10.6162	−0.676866
$247$	0	0
$248$	−16.7436	−1.06322
$249$	28.2869i	1.79261i
$250$	−1.21969	−0.0771398
$251$	−11.8402	−0.747344	−0.373672	−	0.927561i	$-0.621901\pi$
$251$	−11.8402	−0.747344	−0.373672	+	0.927561i	$0.621901\pi$
$252$	4.49969i	0.283454i
$253$	20.9118i	1.31471i
$254$	− 13.9485i	− 0.875205i
$255$	2.63977i	0.165309i
$256$	−11.4208	−0.713800
$257$	5.55002	0.346201	0.173100	−	0.984904i	$-0.444621\pi$
$257$	5.55002	0.346201	0.173100	+	0.984904i	$0.444621\pi$
$258$	− 3.21969i	− 0.200449i
$259$	31.3363	1.94714
$260$	0	0
$261$	−0.0603205	−0.00373375
$262$	12.8896i	0.796323i
$263$	6.85967	0.422985	0.211493	−	0.977380i	$-0.432168\pi$
$263$	6.85967	0.422985	0.211493	+	0.977380i	$0.432168\pi$
$264$	38.3907	2.36279
$265$	− 4.43937i	− 0.272709i
$266$	− 9.95882i	− 0.610614i
$267$	− 37.6752i	− 2.30568i
$268$	− 3.27903i	− 0.200299i
$269$	−1.42199	−0.0867001	−0.0433501	−	0.999060i	$-0.513803\pi$
$269$	−1.42199	−0.0867001	−0.0433501	+	0.999060i	$0.513803\pi$
$270$	−1.59476	−0.0970542
$271$	− 9.96947i	− 0.605602i	−0.953054	−	0.302801i	$-0.902078\pi$
$271$	− 9.96947i	− 0.605602i	0.953054	−	0.302801i	$-0.0979218\pi$
$272$	−3.07045	−0.186173
$273$	0	0
$274$	4.61862	0.279021
$275$	− 5.37182i	− 0.323933i
$276$	4.65182	0.280007
$277$	17.5237	1.05290	0.526449	−	0.850206i	$-0.323523\pi$
$277$	17.5237	1.05290	0.526449	+	0.850206i	$0.323523\pi$
$278$	− 2.45628i	− 0.147318i
$279$	− 13.3290i	− 0.797986i
$280$	11.0321i	0.659292i
$281$	10.7352i	0.640406i	0.947349	+	0.320203i	$0.103751\pi$
$281$	10.7352i	0.640406i	−0.947349	+	0.320203i	$0.896249\pi$
$282$	7.35433	0.437944
$283$	−1.31838	−0.0783698	−0.0391849	−	0.999232i	$-0.512476\pi$
$283$	−1.31838	−0.0783698	−0.0391849	+	0.999232i	$0.512476\pi$
$284$	5.53216i	0.328273i
$285$	5.28942	0.313318
$286$	0	0
$287$	13.4361	0.793109
$288$	− 6.87875i	− 0.405334i
$289$	−15.7189	−0.924641
$290$	−0.0301603	−0.00177107
$291$	− 28.3792i	− 1.66362i
$292$	− 2.40969i	− 0.141016i
$293$	18.7427i	1.09496i	0.836820	+	0.547479i	$0.184412\pi$
$293$	18.7427i	1.09496i	−0.836820	+	0.547479i	$0.815588\pi$
$294$	16.9579i	0.989004i
$295$	0.171425	0.00998072
$296$	−26.6718	−1.55027
$297$	− 7.02375i	− 0.407559i
$298$	6.72998	0.389857
$299$	0	0
$300$	−1.19496	−0.0689910
$301$	4.07490i	0.234873i
$302$	−5.96380	−0.343178
$303$	9.45589	0.543226
$304$	6.15239i	0.352864i
$305$	3.36023i	0.192406i
$306$	− 3.36758i	− 0.192512i
$307$	14.3043i	0.816387i	0.912895	+	0.408194i	$0.133841\pi$
$307$	14.3043i	0.816387i	−0.912895	+	0.408194i	$0.866159\pi$
$308$	−9.90891	−0.564612
$309$	41.7553	2.37538
$310$	− 6.66449i	− 0.378518i
$311$	−2.76102	−0.156563	−0.0782815	−	0.996931i	$-0.524943\pi$
$311$	−2.76102	−0.156563	−0.0782815	+	0.996931i	$0.524943\pi$
$312$	0	0
$313$	−16.3858	−0.926179	−0.463090	−	0.886311i	$-0.653259\pi$
$313$	−16.3858	−0.926179	−0.463090	+	0.886311i	$0.653259\pi$
$314$	− 12.2463i	− 0.691100i
$315$	−8.78222	−0.494822
$316$	−6.13946	−0.345372
$317$	− 1.78575i	− 0.100297i	−0.998742	−	0.0501487i	$-0.984030\pi$
$317$	− 1.78575i	− 0.100297i	0.998742	−	0.0501487i	$-0.0159695\pi$
$318$	12.6283i	0.708159i
$319$	− 0.132834i	− 0.00743725i
$320$	− 8.86488i	− 0.495562i
$321$	−21.2977	−1.18872
$322$	17.0940	0.952613
$323$	− 2.56699i	− 0.142831i
$324$	−5.31197	−0.295110
$325$	0	0
$326$	8.27099	0.458088
$327$	− 17.2028i	− 0.951316i
$328$	−11.4361	−0.631454
$329$	−9.30778	−0.513155
$330$	15.2807i	0.841176i
$331$	− 7.22440i	− 0.397089i	−0.980092	−	0.198545i	$-0.936379\pi$
$331$	− 7.22440i	− 0.397089i	0.980092	−	0.198545i	$-0.0636215\pi$
$332$	6.21425i	0.341052i
$333$	− 21.2325i	− 1.16353i
$334$	12.7943	0.700072
$335$	6.39980	0.349659
$336$	− 22.7778i	− 1.24263i
$337$	4.36219	0.237624	0.118812	−	0.992917i	$-0.462091\pi$
$337$	4.36219	0.237624	0.118812	+	0.992917i	$0.462091\pi$
$338$	0	0
$339$	16.5027	0.896303
$340$	0.579922i	0.0314507i
$341$	29.3521	1.58951
$342$	−6.74777	−0.364877
$343$	3.73913i	0.201894i
$344$	− 3.46834i	− 0.187000i
$345$	9.07914i	0.488804i
$346$	− 5.43792i	− 0.292344i
$347$	−26.7072	−1.43372	−0.716858	−	0.697219i	$-0.754420\pi$
$347$	−26.7072	−1.43372	−0.716858	+	0.697219i	$0.754420\pi$
$348$	−0.0295488	−0.00158398
$349$	23.5711i	1.26173i	0.775892	+	0.630865i	$0.217300\pi$
$349$	23.5711i	1.26173i	−0.775892	+	0.630865i	$0.782700\pi$
$350$	−4.39111	−0.234715
$351$	0	0
$352$	15.1479	0.807385
$353$	− 5.73727i	− 0.305364i	−0.988275	−	0.152682i	$-0.951209\pi$
$353$	− 5.73727i	− 0.305364i	0.988275	−	0.152682i	$-0.0487910\pi$
$354$	−0.487636	−0.0259176
$355$	−10.7973	−0.573063
$356$	− 8.27675i	− 0.438667i
$357$	9.50367i	0.502988i
$358$	22.7243i	1.20102i
$359$	− 24.7583i	− 1.30669i	−0.757059	−	0.653347i	$-0.773364\pi$
$359$	− 24.7583i	− 1.30669i	0.757059	−	0.653347i	$-0.226636\pi$
$360$	7.47497	0.393965
$361$	13.8564	0.729285
$362$	22.0641i	1.15967i
$363$	−41.6455	−2.18582
$364$	0	0
$365$	4.70308	0.246171
$366$	− 9.55856i	− 0.499634i
$367$	26.0535	1.35998	0.679992	−	0.733220i	$-0.261983\pi$
$367$	26.0535	1.35998	0.679992	+	0.733220i	$0.261983\pi$
$368$	−10.5604	−0.550499
$369$	− 9.10387i	− 0.473928i
$370$	− 10.6162i	− 0.551912i
$371$	− 15.9826i	− 0.829776i
$372$	− 6.52938i	− 0.338532i
$373$	13.2045	0.683702	0.341851	−	0.939754i	$-0.388946\pi$
$373$	13.2045	0.683702	0.341851	+	0.939754i	$0.388946\pi$
$374$	7.41584	0.383464
$375$	− 2.33225i	− 0.120437i
$376$	7.92229	0.408561
$377$	0	0
$378$	−5.74146	−0.295309
$379$	− 25.9977i	− 1.33541i	−0.744425	−	0.667707i	$-0.767276\pi$
$379$	− 25.9977i	− 1.33541i	0.744425	−	0.667707i	$-0.232724\pi$
$380$	1.16202	0.0596101
$381$	26.6718	1.36644
$382$	− 33.3418i	− 1.70591i
$383$	9.60020i	0.490547i	0.969454	+	0.245274i	$0.0788778\pi$
$383$	9.60020i	0.490547i	−0.969454	+	0.245274i	$0.921122\pi$
$384$	12.0638i	0.615629i
$385$	− 19.3396i	− 0.985637i
$386$	26.5494	1.35133
$387$	2.76102	0.140350
$388$	− 6.23453i	− 0.316510i
$389$	−5.63129	−0.285518	−0.142759	−	0.989758i	$-0.545597\pi$
$389$	−5.63129	−0.285518	−0.142759	+	0.989758i	$0.545597\pi$
$390$	0	0
$391$	4.40617	0.222829
$392$	18.2675i	0.922650i
$393$	−24.6471	−1.24328
$394$	2.06947	0.104258
$395$	− 11.9826i	− 0.602911i
$396$	6.71395i	0.337389i
$397$	− 16.7658i	− 0.841452i	−0.907188	−	0.420726i	$-0.861775\pi$
$397$	− 16.7658i	− 0.841452i	0.907188	−	0.420726i	$-0.138225\pi$
$398$	30.8891i	1.54833i
$399$	19.0429	0.953339
$400$	2.71276	0.135638
$401$	− 13.8780i	− 0.693036i	−0.938043	−	0.346518i	$-0.887364\pi$
$401$	− 13.8780i	− 0.693036i	0.938043	−	0.346518i	$-0.112636\pi$
$402$	−18.2050	−0.907980
$403$	0	0
$404$	2.07733	0.103351
$405$	− 10.3676i	− 0.515169i
$406$	−0.108583	−0.00538888
$407$	46.7566	2.31764
$408$	− 8.08903i	− 0.400466i
$409$	− 29.4251i	− 1.45498i	−0.686120	−	0.727489i	$-0.740687\pi$
$409$	− 29.4251i	− 1.45498i	0.686120	−	0.727489i	$-0.259313\pi$
$410$	− 4.55193i	− 0.224804i
$411$	8.83157i	0.435629i
$412$	9.17310	0.451926
$413$	0.617162	0.0303686
$414$	− 11.5824i	− 0.569242i
$415$	−12.1286	−0.595369
$416$	0	0
$417$	4.69683	0.230005
$418$	− 14.8595i	− 0.726800i
$419$	6.96793	0.340406	0.170203	−	0.985409i	$-0.445558\pi$
$419$	6.96793	0.340406	0.170203	+	0.985409i	$0.445558\pi$
$420$	−4.30209	−0.209920
$421$	− 7.12125i	− 0.347069i	−0.984828	−	0.173534i	$-0.944481\pi$
$421$	− 7.12125i	− 0.347069i	0.984828	−	0.173534i	$-0.0555188\pi$
$422$	0.409213i	0.0199202i
$423$	6.30664i	0.306640i
$424$	13.6036i	0.660647i
$425$	−1.13186	−0.0549030
$426$	30.7142	1.48811
$427$	12.0975i	0.585439i
$428$	−4.67883	−0.226160
$429$	0	0
$430$	1.38051	0.0665740
$431$	− 30.2144i	− 1.45537i	−0.685909	−	0.727687i	$-0.740595\pi$
$431$	− 30.2144i	− 1.45537i	0.685909	−	0.727687i	$-0.259405\pi$
$432$	3.54698	0.170654
$433$	−1.20013	−0.0576745	−0.0288373	−	0.999584i	$-0.509180\pi$
$433$	−1.20013	−0.0576745	−0.0288373	+	0.999584i	$0.509180\pi$
$434$	− 23.9935i	− 1.15172i
$435$	− 0.0576715i	− 0.00276514i
$436$	− 3.77922i	− 0.180992i
$437$	− 8.82884i	− 0.422341i
$438$	−13.3784	−0.639247
$439$	16.5541	0.790084	0.395042	−	0.918663i	$-0.370730\pi$
$439$	16.5541	0.790084	0.395042	+	0.918663i	$0.370730\pi$
$440$	16.4608i	0.784740i
$441$	−14.5421	−0.692481
$442$	0	0
$443$	4.55949	0.216628	0.108314	−	0.994117i	$-0.465455\pi$
$443$	4.55949	0.216628	0.108314	+	0.994117i	$0.465455\pi$
$444$	− 10.4010i	− 0.493610i
$445$	16.1540	0.765775
$446$	14.9982	0.710185
$447$	12.8689i	0.608676i
$448$	− 31.9153i	− 1.50786i
$449$	13.8522i	0.653724i	0.945072	+	0.326862i	$0.105991\pi$
$449$	13.8522i	0.653724i	−0.945072	+	0.326862i	$0.894009\pi$
$450$	2.97527i	0.140256i
$451$	20.0479	0.944018
$452$	3.62542	0.170526
$453$	− 11.4038i	− 0.535796i
$454$	9.30897	0.436892
$455$	0	0
$456$	−16.2083	−0.759025
$457$	− 40.1146i	− 1.87648i	−0.345984	−	0.938240i	$-0.612455\pi$
$457$	− 40.1146i	− 1.87648i	0.345984	−	0.938240i	$-0.387545\pi$
$458$	−17.5644	−0.820733
$459$	−1.47992	−0.0690768
$460$	1.99457i	0.0929972i
$461$	7.53900i	0.351126i	0.984468	+	0.175563i	$0.0561746\pi$
$461$	7.53900i	0.351126i	−0.984468	+	0.175563i	$0.943825\pi$
$462$	55.0136i	2.55946i
$463$	23.3031i	1.08299i	0.840705	+	0.541494i	$0.182141\pi$
$463$	23.3031i	1.08299i	−0.840705	+	0.541494i	$0.817859\pi$
$464$	0.0670807	0.00311414
$465$	12.7436	0.590972
$466$	11.5824i	0.536542i
$467$	22.6297	1.04718	0.523589	−	0.851971i	$-0.324593\pi$
$467$	22.6297	1.04718	0.523589	+	0.851971i	$0.324593\pi$
$468$	0	0
$469$	23.0405	1.06391
$470$	3.15332i	0.145452i
$471$	23.4170	1.07900
$472$	−0.525296	−0.0241787
$473$	6.08012i	0.279564i
$474$	34.0859i	1.56562i
$475$	2.26795i	0.104061i
$476$	2.08783i	0.0956956i
$477$	−10.8293	−0.495839
$478$	24.2893	1.11096
$479$	20.6448i	0.943286i	0.881790	+	0.471643i	$0.156339\pi$
$479$	20.6448i	0.943286i	−0.881790	+	0.471643i	$0.843661\pi$
$480$	6.57666	0.300182
$481$	0	0
$482$	28.3777	1.29257
$483$	32.6867i	1.48730i
$484$	−9.14898	−0.415863
$485$	12.1682	0.552528
$486$	24.7074i	1.12075i
$487$	− 3.03605i	− 0.137576i	−0.997631	−	0.0687882i	$-0.978087\pi$
$487$	− 3.03605i	− 0.137576i	0.997631	−	0.0687882i	$-0.0219133\pi$
$488$	− 10.2968i	− 0.466112i
$489$	15.8155i	0.715203i
$490$	−7.27105	−0.328473
$491$	−10.6680	−0.481441	−0.240720	−	0.970595i	$-0.577384\pi$
$491$	−10.6680	−0.481441	−0.240720	+	0.970595i	$0.577384\pi$
$492$	− 4.45965i	− 0.201056i
$493$	−0.0279884	−0.00126053
$494$	0	0
$495$	−13.1039	−0.588975
$496$	14.8228i	0.665562i
$497$	−38.8725	−1.74367
$498$	34.5011	1.54603
$499$	− 33.9143i	− 1.51821i	−0.650966	−	0.759107i	$-0.725636\pi$
$499$	− 33.9143i	− 1.51821i	0.650966	−	0.759107i	$-0.274364\pi$
$500$	− 0.512364i	− 0.0229136i
$501$	24.4648i	1.09301i
$502$	14.4413i	0.644546i
$503$	−12.6276	−0.563037	−0.281518	−	0.959556i	$-0.590838\pi$
$503$	−12.6276	−0.563037	−0.281518	+	0.959556i	$0.590838\pi$
$504$	26.9113	1.19873
$505$	4.05441i	0.180419i
$506$	25.5058	1.13387
$507$	0	0
$508$	5.85945	0.259971
$509$	24.1526i	1.07055i	0.844679	+	0.535273i	$0.179791\pi$
$509$	24.1526i	1.07055i	−0.844679	+	0.535273i	$0.820209\pi$
$510$	3.21969	0.142570
$511$	16.9320	0.749029
$512$	24.2750i	1.07281i
$513$	2.96539i	0.130925i
$514$	− 6.76929i	− 0.298581i
$515$	17.9035i	0.788921i
$516$	1.35252	0.0595414
$517$	−13.8880	−0.610796
$518$	− 38.2205i	− 1.67931i
$519$	10.3982	0.456431
$520$	0	0
$521$	−24.7521	−1.08441	−0.542205	−	0.840246i	$-0.682410\pi$
$521$	−24.7521	−1.08441	−0.542205	+	0.840246i	$0.682410\pi$
$522$	0.0735722i	0.00322017i
$523$	37.0326	1.61932	0.809662	−	0.586897i	$-0.199650\pi$
$523$	37.0326	1.61932	0.809662	+	0.586897i	$0.199650\pi$
$524$	−5.41465	−0.236540
$525$	− 8.39654i	− 0.366455i
$526$	− 8.36665i	− 0.364803i
$527$	− 6.18457i	− 0.269404i
$528$	− 33.9865i	− 1.47907i
$529$	−7.84554	−0.341111
$530$	−5.41465	−0.235197
$531$	− 0.418169i	− 0.0181470i
$532$	4.18348	0.181377
$533$	0	0
$534$	−45.9519	−1.98854
$535$	− 9.13186i	− 0.394805i
$536$	−19.6109	−0.847062
$537$	−43.4528	−1.87512
$538$	1.73438i	0.0747744i
$539$	− 32.0236i	− 1.37935i
$540$	− 0.669925i	− 0.0288290i
$541$	− 8.38144i	− 0.360346i	−0.983635	−	0.180173i	$-0.942334\pi$
$541$	− 8.38144i	− 0.360346i	0.983635	−	0.180173i	$-0.0576658\pi$
$542$	−12.1596	−0.522301
$543$	−42.1903	−1.81056
$544$	− 3.19170i	− 0.136843i
$545$	7.37605	0.315955
$546$	0	0
$547$	−22.7842	−0.974181	−0.487091	−	0.873351i	$-0.661942\pi$
$547$	−22.7842	−0.974181	−0.487091	+	0.873351i	$0.661942\pi$
$548$	1.94018i	0.0828804i
$549$	8.19687	0.349834
$550$	−6.55193	−0.279375
$551$	0.0560816i	0.00238915i
$552$	− 27.8212i	− 1.18415i
$553$	− 43.1398i	− 1.83449i
$554$	− 21.3735i	− 0.908071i
$555$	20.3000	0.861688
$556$	1.03183	0.0437594
$557$	− 28.1527i	− 1.19287i	−0.802662	−	0.596435i	$-0.796583\pi$
$557$	− 28.1527i	− 1.19287i	0.802662	−	0.596435i	$-0.203417\pi$
$558$	−16.2572	−0.688222
$559$	0	0
$560$	9.76645	0.412708
$561$	14.1803i	0.598694i
$562$	13.0935	0.552317
$563$	18.1303	0.764101	0.382050	−	0.924142i	$-0.375218\pi$
$563$	18.1303	0.764101	0.382050	+	0.924142i	$0.375218\pi$
$564$	3.08939i	0.130087i
$565$	7.07588i	0.297684i
$566$	1.60801i	0.0675899i
$567$	− 37.3253i	− 1.56752i
$568$	33.0862	1.38827
$569$	−40.5985	−1.70198	−0.850988	−	0.525185i	$-0.823996\pi$
$569$	−40.5985	−1.70198	−0.850988	+	0.525185i	$0.823996\pi$
$570$	− 6.45143i	− 0.270221i
$571$	−24.7159	−1.03433	−0.517164	−	0.855886i	$-0.673012\pi$
$571$	−24.7159	−1.03433	−0.517164	+	0.855886i	$0.673012\pi$
$572$	0	0
$573$	63.7551	2.66341
$574$	− 16.3879i	− 0.684016i
$575$	−3.89287	−0.162344
$576$	−21.6248	−0.901032
$577$	− 23.0691i	− 0.960379i	−0.877165	−	0.480189i	$-0.840568\pi$
$577$	− 23.0691i	− 0.960379i	0.877165	−	0.480189i	$-0.159432\pi$
$578$	19.1721i	0.797456i
$579$	50.7669i	2.10980i
$580$	− 0.0126697i	0 0.000526079i
$581$	−43.6653	−1.81154
$582$	−34.6137	−1.43478
$583$	− 23.8475i	− 0.987662i
$584$	−14.4116	−0.596358
$585$	0	0
$586$	22.8602	0.944345
$587$	20.3523i	0.840030i	0.907517	+	0.420015i	$0.137975\pi$
$587$	20.3523i	0.840030i	−0.907517	+	0.420015i	$0.862025\pi$
$588$	−7.12364	−0.293774
$589$	−12.3923	−0.510616
$590$	− 0.209084i	− 0.00860786i
$591$	3.95717i	0.162776i
$592$	23.6120i	0.970447i
$593$	10.3834i	0.426395i	0.977009	+	0.213198i	$0.0683878\pi$
$593$	10.3834i	0.426395i	−0.977009	+	0.213198i	$0.931612\pi$
$594$	−8.56677	−0.351499
$595$	−4.07490	−0.167055
$596$	2.82712i	0.115803i
$597$	−59.0652	−2.41738
$598$	0	0
$599$	−31.5965	−1.29100	−0.645499	−	0.763761i	$-0.723351\pi$
$599$	−31.5965	−1.29100	−0.645499	+	0.763761i	$0.723351\pi$
$600$	7.14670i	0.291763i
$601$	−43.8845	−1.79009	−0.895044	−	0.445979i	$-0.852856\pi$
$601$	−43.8845	−1.79009	−0.895044	+	0.445979i	$0.852856\pi$
$602$	4.97010	0.202566
$603$	− 15.6115i	− 0.635750i
$604$	− 2.50526i	− 0.101938i
$605$	− 17.8564i	− 0.725966i
$606$	− 11.5332i	− 0.468505i
$607$	2.17540	0.0882968	0.0441484	−	0.999025i	$-0.485943\pi$
$607$	2.17540	0.0882968	0.0441484	+	0.999025i	$0.485943\pi$
$608$	−6.39535	−0.259366
$609$	− 0.207629i	− 0.00841354i
$610$	4.09843	0.165941
$611$	0	0
$612$	1.41465	0.0571837
$613$	14.7620i	0.596231i	0.954530	+	0.298116i	$0.0963581\pi$
$613$	14.7620i	0.596231i	−0.954530	+	0.298116i	$0.903642\pi$
$614$	17.4467	0.704092
$615$	8.70406	0.350982
$616$	59.2622i	2.38774i
$617$	20.2972i	0.817134i	0.912728	+	0.408567i	$0.133971\pi$
$617$	20.2972i	0.817134i	−0.912728	+	0.408567i	$0.866029\pi$
$618$	− 50.9284i	− 2.04864i
$619$	9.94207i	0.399605i	0.979836	+	0.199803i	$0.0640301\pi$
$619$	9.94207i	0.399605i	−0.979836	+	0.199803i	$0.935970\pi$
$620$	2.79961	0.112435
$621$	−5.09000	−0.204255
$622$	3.36758i	0.135028i
$623$	58.1577	2.33004
$624$	0	0
$625$	1.00000	0.0400000
$626$	19.9855i	0.798782i
$627$	28.4138	1.13474
$628$	5.14441	0.205284
$629$	− 9.85174i	− 0.392815i
$630$	10.7116i	0.426759i
$631$	0.973420i	0.0387512i	0.999812	+	0.0193756i	$0.00616784\pi$
$631$	0.973420i	0.0387512i	−0.999812	+	0.0193756i	$0.993832\pi$
$632$	36.7183i	1.46058i
$633$	−0.782485	−0.0311010
$634$	−2.17805	−0.0865014
$635$	11.4361i	0.453828i
$636$	−5.30487	−0.210352
$637$	0	0
$638$	−0.162015	−0.00641425
$639$	26.3387i	1.04194i
$640$	−5.17262	−0.204466
$641$	12.6209	0.498497	0.249249	−	0.968440i	$-0.419816\pi$
$641$	12.6209	0.498497	0.249249	+	0.968440i	$0.419816\pi$
$642$	25.9766i	1.02521i
$643$	− 9.96043i	− 0.392801i	−0.980524	−	0.196401i	$-0.937075\pi$
$643$	− 9.96043i	− 0.392801i	0.980524	−	0.196401i	$-0.0629253\pi$
$644$	7.18083i	0.282964i
$645$	2.63977i	0.103941i
$646$	−3.13092	−0.123185
$647$	36.2763	1.42617	0.713084	−	0.701079i	$-0.247298\pi$
$647$	36.2763	1.42617	0.713084	+	0.701079i	$0.247298\pi$
$648$	31.7693i	1.24802i
$649$	0.920861	0.0361470
$650$	0	0
$651$	45.8796	1.79816
$652$	3.47447i	0.136071i
$653$	13.7554	0.538289	0.269145	−	0.963100i	$-0.413259\pi$
$653$	13.7554	0.538289	0.269145	+	0.963100i	$0.413259\pi$
$654$	−20.9820	−0.820461
$655$	− 10.5680i	− 0.412925i
$656$	10.1241i	0.395281i
$657$	− 11.4726i	− 0.447588i
$658$	11.3526i	0.442570i
$659$	−2.58183	−0.100574	−0.0502869	−	0.998735i	$-0.516014\pi$
$659$	−2.58183	−0.100574	−0.0502869	+	0.998735i	$0.516014\pi$
$660$	−6.41910	−0.249863
$661$	24.8765i	0.967582i	0.875183	+	0.483791i	$0.160741\pi$
$661$	24.8765i	0.967582i	−0.875183	+	0.483791i	$0.839259\pi$
$662$	−8.81151	−0.342469
$663$	0	0
$664$	37.1656	1.44231
$665$	8.16506i	0.316627i
$666$	−25.8970	−1.00349
$667$	−0.0962625	−0.00372730
$668$	5.37460i	0.207949i
$669$	28.6791i	1.10880i
$670$	− 7.80576i	− 0.301563i
$671$	18.0506i	0.696834i
$672$	23.6773	0.913370
$673$	−43.3222	−1.66995	−0.834974	−	0.550289i	$-0.814517\pi$
$673$	−43.3222	−1.66995	−0.834974	+	0.550289i	$0.814517\pi$
$674$	− 5.32051i	− 0.204938i
$675$	1.30752	0.0503264
$676$	0	0
$677$	−41.3625	−1.58969	−0.794845	−	0.606813i	$-0.792448\pi$
$677$	−41.3625	−1.58969	−0.794845	+	0.606813i	$0.792448\pi$
$678$	− 20.1281i	− 0.773016i
$679$	43.8078	1.68119
$680$	3.46834	0.133005
$681$	17.8003i	0.682110i
$682$	− 35.8004i	− 1.37087i
$683$	2.62688i	0.100515i	0.998736	+	0.0502574i	$0.0160042\pi$
$683$	2.62688i	0.100515i	−0.998736	+	0.0502574i	$0.983996\pi$
$684$	− 2.83459i	− 0.108383i
$685$	−3.78672	−0.144683
$686$	4.56057	0.174123
$687$	− 33.5862i	− 1.28139i
$688$	−3.07045	−0.117060
$689$	0	0
$690$	11.0737	0.421569
$691$	15.2753i	0.581099i	0.956860	+	0.290550i	$0.0938382\pi$
$691$	15.2753i	0.581099i	−0.956860	+	0.290550i	$0.906162\pi$
$692$	2.28435	0.0868380
$693$	−47.1765	−1.79209
$694$	32.5744i	1.23651i
$695$	2.01386i	0.0763902i
$696$	0.176723i	0.00669865i
$697$	− 4.22414i	− 0.160001i
$698$	28.7493	1.08818
$699$	−22.1474	−0.837692
$700$	− 1.84461i	− 0.0697197i
$701$	48.1947	1.82029	0.910144	−	0.414292i	$-0.135971\pi$
$701$	48.1947	1.82029	0.910144	+	0.414292i	$0.135971\pi$
$702$	0	0
$703$	−19.7404	−0.744522
$704$	− 47.6205i	− 1.79477i
$705$	−6.02968	−0.227091
$706$	−6.99767	−0.263361
$707$	14.5967i	0.548964i
$708$	− 0.204845i	− 0.00769856i
$709$	− 38.8699i	− 1.45979i	−0.683559	−	0.729896i	$-0.739569\pi$
$709$	− 38.8699i	− 1.45979i	0.683559	−	0.729896i	$-0.260431\pi$
$710$	13.1694i	0.494237i
$711$	−29.2301	−1.09621
$712$	−49.5008	−1.85512
$713$	− 21.2711i	− 0.796607i
$714$	11.5915	0.433801
$715$	0	0
$716$	−9.54600	−0.356751
$717$	46.4452i	1.73453i
$718$	−30.1974	−1.12696
$719$	−6.61660	−0.246758	−0.123379	−	0.992360i	$-0.539373\pi$
$719$	−6.61660	−0.246758	−0.123379	+	0.992360i	$0.539373\pi$
$720$	− 6.61742i	− 0.246617i
$721$	64.4560i	2.40047i
$722$	− 16.9005i	− 0.628971i
$723$	54.2629i	2.01806i
$724$	−9.26867	−0.344467
$725$	0.0247279	0.000918370 0
$726$	50.7945i	1.88516i
$727$	18.3735	0.681435	0.340717	−	0.940166i	$-0.389330\pi$
$727$	18.3735	0.681435	0.340717	+	0.940166i	$0.389330\pi$
$728$	0	0
$729$	−16.1420	−0.597853
$730$	− 5.73629i	− 0.212310i
$731$	1.28110	0.0473830
$732$	4.01534	0.148411
$733$	− 0.791131i	− 0.0292211i	−0.999893	−	0.0146105i	$-0.995349\pi$
$733$	− 0.791131i	− 0.0292211i	0.999893	−	0.0146105i	$-0.00465084\pi$
$734$	− 31.7772i	− 1.17292i
$735$	− 13.9035i	− 0.512837i
$736$	− 10.9774i	− 0.404634i
$737$	34.3786	1.26635
$738$	−11.1039	−0.408739
$739$	31.1853i	1.14717i	0.819146	+	0.573585i	$0.194448\pi$
$739$	31.1853i	1.14717i	−0.819146	+	0.573585i	$0.805552\pi$
$740$	4.45965	0.163940
$741$	0	0
$742$	−19.4938	−0.715639
$743$	− 5.56304i	− 0.204088i	−0.994780	−	0.102044i	$-0.967462\pi$
$743$	− 5.56304i	− 0.204088i	0.994780	−	0.102044i	$-0.0325383\pi$
$744$	−39.0503	−1.43165
$745$	−5.51780	−0.202156
$746$	− 16.1053i	− 0.589658i
$747$	29.5862i	1.08250i
$748$	3.11523i	0.113904i
$749$	− 32.8765i	− 1.20128i
$750$	−2.84461	−0.103870
$751$	35.2097	1.28482	0.642410	−	0.766361i	$-0.277935\pi$
$751$	35.2097	1.28482	0.642410	+	0.766361i	$0.277935\pi$
$752$	− 7.01343i	− 0.255754i
$753$	−27.6142	−1.00632
$754$	0	0
$755$	4.88961	0.177951
$756$	− 2.41186i	− 0.0877186i
$757$	50.0446	1.81890	0.909451	−	0.415810i	$-0.136502\pi$
$757$	50.0446	1.81890	0.909451	+	0.415810i	$0.136502\pi$
$758$	−31.7091	−1.15173
$759$	48.7715i	1.77029i
$760$	− 6.94967i	− 0.252091i
$761$	44.8209i	1.62476i	0.583130	+	0.812379i	$0.301828\pi$
$761$	44.8209i	1.62476i	−0.583130	+	0.812379i	$0.698172\pi$
$762$	− 32.5313i	− 1.17848i
$763$	26.5552	0.961364
$764$	14.0061	0.506725
$765$	2.76102i	0.0998248i
$766$	11.7092	0.423072
$767$	0	0
$768$	−26.6361	−0.961148
$769$	39.3633i	1.41948i	0.704465	+	0.709739i	$0.251187\pi$
$769$	39.3633i	1.41948i	−0.704465	+	0.709739i	$0.748813\pi$
$770$	−23.5882	−0.850061
$771$	12.9440	0.466168
$772$	11.1528i	0.401399i
$773$	− 48.7805i	− 1.75451i	−0.480022	−	0.877256i	$-0.659371\pi$
$773$	− 48.7805i	− 1.75451i	0.480022	−	0.877256i	$-0.340629\pi$
$774$	− 3.36758i	− 0.121045i
$775$	5.46410i	0.196276i
$776$	−37.2869	−1.33852
$777$	73.0840	2.62188
$778$	6.86841i	0.246244i
$779$	−8.46410	−0.303258
$780$	0	0
$781$	−58.0013	−2.07545
$782$	− 5.37415i	− 0.192179i
$783$	0.0323322	0.00115546
$784$	16.1718	0.577566
$785$	10.0405i	0.358363i
$786$	30.0618i	1.07227i
$787$	39.8608i	1.42088i	0.703756	+	0.710442i	$0.251505\pi$
$787$	39.8608i	1.42088i	−0.703756	+	0.710442i	$0.748495\pi$
$788$	0.869338i	0.0309689i
$789$	15.9984	0.569559
$790$	−14.6150	−0.519980
$791$	25.4745i	0.905771i
$792$	40.1541	1.42682
$793$	0	0
$794$	−20.4490	−0.725709
$795$	− 10.3537i	− 0.367208i
$796$	−12.9759	−0.459917
$797$	−26.2118	−0.928470	−0.464235	−	0.885712i	$-0.653671\pi$
$797$	−26.2118	−0.928470	−0.464235	+	0.885712i	$0.653671\pi$
$798$	− 23.2264i	− 0.822206i
$799$	2.92625i	0.103523i
$800$	2.81988i	0.0996979i
$801$	− 39.4057i	− 1.39233i
$802$	−16.9269	−0.597708
$803$	25.2641	0.891551
$804$	− 7.64750i	− 0.269707i
$805$	−14.0151	−0.493968
$806$	0	0
$807$	−3.31643	−0.116744
$808$	− 12.4239i	− 0.437072i
$809$	22.2136	0.780990	0.390495	−	0.920605i	$-0.372304\pi$
$809$	22.2136	0.780990	0.390495	+	0.920605i	$0.372304\pi$
$810$	−12.6452	−0.444307
$811$	− 19.0950i	− 0.670515i	−0.942127	−	0.335257i	$-0.891177\pi$
$811$	− 19.0950i	− 0.670515i	0.942127	−	0.335257i	$-0.108823\pi$
$812$	− 0.0456133i	− 0.00160071i
$813$	− 23.2513i	− 0.815457i
$814$	− 57.0284i	− 1.99885i
$815$	−6.78124	−0.237537
$816$	−7.16104	−0.250686
$817$	− 2.56699i	− 0.0898076i
$818$	−35.8894	−1.25484
$819$	0	0
$820$	1.91217	0.0667758
$821$	34.1584i	1.19214i	0.802934	+	0.596068i	$0.203271\pi$
$821$	34.1584i	1.19214i	−0.802934	+	0.596068i	$0.796729\pi$
$822$	10.7718	0.375708
$823$	−4.07940	−0.142199	−0.0710995	−	0.997469i	$-0.522651\pi$
$823$	−4.07940	−0.142199	−0.0710995	+	0.997469i	$0.522651\pi$
$824$	− 54.8616i	− 1.91119i
$825$	− 12.5284i	− 0.436183i
$826$	− 0.752744i	− 0.0261913i
$827$	− 54.8780i	− 1.90830i	−0.299337	−	0.954148i	$-0.596765\pi$
$827$	− 54.8780i	− 1.90830i	0.299337	−	0.954148i	$-0.403235\pi$
$828$	4.86550	0.169088
$829$	−8.14950	−0.283044	−0.141522	−	0.989935i	$-0.545200\pi$
$829$	−8.14950	−0.283044	−0.141522	+	0.989935i	$0.545200\pi$
$830$	14.7931i	0.513476i
$831$	40.8697	1.41775
$832$	0	0
$833$	−6.74745	−0.233785
$834$	− 5.72866i	− 0.198367i
$835$	−10.4898	−0.363015
$836$	6.24213	0.215889
$837$	7.14441i	0.246947i
$838$	− 8.49869i	− 0.293582i
$839$	− 21.8865i	− 0.755606i	−0.925886	−	0.377803i	$-0.876680\pi$
$839$	− 21.8865i	− 0.755606i	0.925886	−	0.377803i	$-0.123320\pi$
$840$	25.7295i	0.887752i
$841$	−28.9994	−0.999979
$842$	−8.68570	−0.299329
$843$	25.0370i	0.862321i
$844$	−0.171902	−0.00591710
$845$	0	0
$846$	7.69213	0.264461
$847$	− 64.2866i	− 2.20891i
$848$	12.0429	0.413556
$849$	−3.07480	−0.105527
$850$	1.38051i	0.0473511i
$851$	− 33.8838i	− 1.16152i
$852$	12.9024i	0.442028i
$853$	− 19.2240i	− 0.658217i	−0.944292	−	0.329108i	$-0.893252\pi$
$853$	− 19.2240i	− 0.658217i	0.944292	−	0.329108i	$-0.106748\pi$
$854$	14.7552	0.504911
$855$	5.53238	0.189203
$856$	27.9827i	0.956430i
$857$	27.8197	0.950302	0.475151	−	0.879904i	$-0.342393\pi$
$857$	27.8197	0.950302	0.475151	+	0.879904i	$0.342393\pi$
$858$	0	0
$859$	45.7355	1.56048	0.780238	−	0.625482i	$-0.215098\pi$
$859$	45.7355	1.56048	0.780238	+	0.625482i	$0.215098\pi$
$860$	0.579922i	0.0197752i
$861$	31.3363	1.06794
$862$	−36.8521	−1.25519
$863$	− 54.8186i	− 1.86605i	−0.359814	−	0.933024i	$-0.617160\pi$
$863$	− 54.8186i	− 1.86605i	0.359814	−	0.933024i	$-0.382840\pi$
$864$	3.68705i	0.125436i
$865$	4.45845i	0.151592i
$866$	1.46378i	0.0497413i
$867$	−36.6604	−1.24505
$868$	10.0791	0.342108
$869$	− 64.3684i	− 2.18355i
$870$	−0.0703412	−0.00238479
$871$	0	0
$872$	−22.6024	−0.765415
$873$	− 29.6827i	− 1.00461i
$874$	−10.7684	−0.364247
$875$	3.60020	0.121709
$876$	− 5.61999i	− 0.189882i
$877$	27.3794i	0.924537i	0.886740	+	0.462269i	$0.152964\pi$
$877$	27.3794i	0.924537i	−0.886740	+	0.462269i	$0.847036\pi$
$878$	− 20.1908i	− 0.681407i
$879$	43.7125i	1.47439i
$880$	14.5724	0.491236
$881$	34.4426	1.16040	0.580200	−	0.814474i	$-0.302974\pi$
$881$	34.4426	1.16040	0.580200	+	0.814474i	$0.302974\pi$
$882$	17.7368i	0.597230i
$883$	17.3592	0.584183	0.292092	−	0.956390i	$-0.405649\pi$
$883$	17.3592	0.584183	0.292092	+	0.956390i	$0.405649\pi$
$884$	0	0
$885$	0.399804	0.0134393
$886$	− 5.56115i	− 0.186831i
$887$	−31.1427	−1.04567	−0.522835	−	0.852434i	$-0.675126\pi$
$887$	−31.1427	−1.04567	−0.522835	+	0.852434i	$0.675126\pi$
$888$	−62.2053	−2.08747
$889$	41.1722i	1.38087i
$890$	− 19.7029i	− 0.660442i
$891$	− 55.6927i	− 1.86578i
$892$	6.30042i	0.210954i
$893$	5.86345	0.196213
$894$	15.6960	0.524952
$895$	− 18.6313i	− 0.622775i
$896$	−18.6224	−0.622132
$897$	0	0
$898$	16.8953	0.563804
$899$	0.135116i	0.00450636i
$900$	−1.24985	−0.0416616
$901$	−5.02473	−0.167398
$902$	− 24.4521i	− 0.814167i
$903$	9.50367i	0.316262i
$904$	− 21.6826i	− 0.721152i
$905$	− 18.0900i	− 0.601332i
$906$	−13.9090	−0.462097
$907$	−17.6057	−0.584587	−0.292294	−	0.956329i	$-0.594418\pi$
$907$	−17.6057	−0.584587	−0.292294	+	0.956329i	$0.594418\pi$
$908$	3.91050i	0.129774i
$909$	9.89022	0.328038
$910$	0	0
$911$	50.0232	1.65734	0.828671	−	0.559737i	$-0.189098\pi$
$911$	50.0232	1.65734	0.828671	+	0.559737i	$0.189098\pi$
$912$	14.3489i	0.475139i
$913$	−65.1526	−2.15624
$914$	−48.9272	−1.61837
$915$	7.83690i	0.259080i
$916$	− 7.37844i	− 0.243791i
$917$	− 38.0468i	− 1.25641i
$918$	1.80504i	0.0595752i
$919$	−7.61556	−0.251214	−0.125607	−	0.992080i	$-0.540088\pi$
$919$	−7.61556	−0.251214	−0.125607	+	0.992080i	$0.540088\pi$
$920$	11.9289	0.393285
$921$	33.3611i	1.09928i
$922$	9.19522	0.302828
$923$	0	0
$924$	−23.1100	−0.760264
$925$	8.70406i	0.286188i
$926$	28.4225	0.934022
$927$	43.6733	1.43442
$928$	0.0697297i	0.00228899i
$929$	14.1239i	0.463391i	0.972788	+	0.231695i	$0.0744273\pi$
$929$	14.1239i	0.463391i	−0.972788	+	0.231695i	$0.925573\pi$
$930$	− 15.5432i	− 0.509683i
$931$	13.5202i	0.443106i
$932$	−4.86550	−0.159375
$933$	−6.43937	−0.210816
$934$	− 27.6012i	− 0.903138i
$935$	−6.08012	−0.198841
$936$	0	0
$937$	−23.9317	−0.781815	−0.390908	−	0.920430i	$-0.627839\pi$
$937$	−23.9317	−0.781815	−0.390908	+	0.920430i	$0.627839\pi$
$938$	− 28.1023i	− 0.917571i
$939$	−38.2157	−1.24712
$940$	−1.32464	−0.0432051
$941$	25.3591i	0.826683i	0.910576	+	0.413342i	$0.135638\pi$
$941$	25.3591i	0.826683i	−0.910576	+	0.413342i	$0.864362\pi$
$942$	− 28.5614i	− 0.930582i
$943$	− 14.5284i	− 0.473110i
$944$	0.465033i	0.0151355i
$945$	4.70732	0.153129
$946$	7.41584	0.241110
$947$	41.4223i	1.34604i	0.739623	+	0.673021i	$0.235004\pi$
$947$	41.4223i	1.34604i	−0.739623	+	0.673021i	$0.764996\pi$
$948$	−14.3187	−0.465051
$949$	0	0
$950$	2.76619	0.0897470
$951$	− 4.16480i	− 0.135053i
$952$	12.4867	0.404696
$953$	−24.3026	−0.787237	−0.393619	−	0.919274i	$-0.628777\pi$
$953$	−24.3026	−0.787237	−0.393619	+	0.919274i	$0.628777\pi$
$954$	13.2083i	0.427636i
$955$	27.3363i	0.884583i
$956$	10.2034i	0.330001i
$957$	− 0.309801i	− 0.0100144i
$958$	25.1802	0.813536
$959$	−13.6329	−0.440231
$960$	− 20.6751i	− 0.667286i
$961$	1.14359	0.0368901
$962$	0	0
$963$	−22.2760	−0.717834
$964$	11.9209i	0.383945i
$965$	−21.7674	−0.700717
$966$	39.8675	1.28272
$967$	− 23.6784i	− 0.761445i	−0.924689	−	0.380722i	$-0.875675\pi$
$967$	− 23.6784i	− 0.761445i	0.924689	−	0.380722i	$-0.124325\pi$
$968$	54.7173i	1.75868i
$969$	− 5.98685i	− 0.192325i
$970$	− 14.8413i	− 0.476527i
$971$	−16.9722	−0.544663	−0.272332	−	0.962203i	$-0.587795\pi$
$971$	−16.9722	−0.544663	−0.272332	+	0.962203i	$0.587795\pi$
$972$	−10.3791	−0.332908
$973$	7.25030i	0.232434i
$974$	−3.70303	−0.118653
$975$	0	0
$976$	−9.11550	−0.291780
$977$	− 24.9994i	− 0.799802i	−0.916558	−	0.399901i	$-0.869044\pi$
$977$	− 24.9994i	− 0.799802i	0.916558	−	0.399901i	$-0.130956\pi$
$978$	19.2900	0.616826
$979$	86.7765	2.77339
$980$	− 3.05441i	− 0.0975696i
$981$	− 17.9930i	− 0.574471i
$982$	13.0116i	0.415218i
$983$	− 27.3418i	− 0.872068i	−0.899930	−	0.436034i	$-0.856383\pi$
$983$	− 27.3418i	− 0.872068i	0.899930	−	0.436034i	$-0.143617\pi$
$984$	−26.6718	−0.850267
$985$	−1.69672	−0.0540620
$986$	0.0341370i	0.00108715i
$987$	−21.7080	−0.690975
$988$	0	0
$989$	4.40617	0.140108
$990$	15.9826i	0.507961i
$991$	16.0760	0.510672	0.255336	−	0.966852i	$-0.417814\pi$
$991$	16.0760	0.510672	0.255336	+	0.966852i	$0.417814\pi$
$992$	−15.4081	−0.489208
$993$	− 16.8491i	− 0.534690i
$994$	47.4123i	1.50383i
$995$	− 25.3255i	− 0.802871i
$996$	14.4932i	0.459234i
$997$	−34.5612	−1.09456	−0.547282	−	0.836948i	$-0.684337\pi$
$997$	−34.5612	−1.09456	−0.547282	+	0.836948i	$0.684337\pi$
$998$	−41.3649	−1.30938
$999$	11.3807i	0.360070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.c.g.506.3		8
13.2	odd	12		845.2.e.n.191.3		8
13.3	even	3		65.2.m.a.56.3	yes	8
13.4	even	6		65.2.m.a.36.3	✓	8
13.5	odd	4		845.2.a.l.1.2		4
13.6	odd	12		845.2.e.n.146.3		8
13.7	odd	12		845.2.e.m.146.2		8
13.8	odd	4		845.2.a.m.1.3		4
13.9	even	3		845.2.m.g.361.2		8
13.10	even	6		845.2.m.g.316.2		8
13.11	odd	12		845.2.e.m.191.2		8
13.12	even	2	inner	845.2.c.g.506.6		8
39.5	even	4		7605.2.a.cj.1.3		4
39.8	even	4		7605.2.a.cf.1.2		4
39.17	odd	6		585.2.bu.c.361.2		8
39.29	odd	6		585.2.bu.c.316.2		8
52.3	odd	6		1040.2.da.b.641.4		8
52.43	odd	6		1040.2.da.b.881.4		8
65.3	odd	12		325.2.m.c.199.3		8
65.4	even	6		325.2.n.d.101.2		8
65.17	odd	12		325.2.m.c.49.3		8
65.29	even	6		325.2.n.d.251.2		8
65.34	odd	4		4225.2.a.bi.1.2		4
65.42	odd	12		325.2.m.b.199.2		8
65.43	odd	12		325.2.m.b.49.2		8
65.44	odd	4		4225.2.a.bl.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	13.4	even	6
65.2.m.a.56.3	yes	8	13.3	even	3
325.2.m.b.49.2		8	65.43	odd	12
325.2.m.b.199.2		8	65.42	odd	12
325.2.m.c.49.3		8	65.17	odd	12
325.2.m.c.199.3		8	65.3	odd	12
325.2.n.d.101.2		8	65.4	even	6
325.2.n.d.251.2		8	65.29	even	6
585.2.bu.c.316.2		8	39.29	odd	6
585.2.bu.c.361.2		8	39.17	odd	6
845.2.a.l.1.2		4	13.5	odd	4
845.2.a.m.1.3		4	13.8	odd	4
845.2.c.g.506.3		8	1.1	even	1	trivial
845.2.c.g.506.6		8	13.12	even	2	inner
845.2.e.m.146.2		8	13.7	odd	12
845.2.e.m.191.2		8	13.11	odd	12
845.2.e.n.146.3		8	13.6	odd	12
845.2.e.n.191.3		8	13.2	odd	12
845.2.m.g.316.2		8	13.10	even	6
845.2.m.g.361.2		8	13.9	even	3
1040.2.da.b.641.4		8	52.3	odd	6
1040.2.da.b.881.4		8	52.43	odd	6
4225.2.a.bi.1.2		4	65.34	odd	4
4225.2.a.bl.1.3		4	65.44	odd	4
7605.2.a.cf.1.2		4	39.8	even	4
7605.2.a.cj.1.3		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)

\(f(q)\)	\(=\)	\(q-1.21969i q^{2} +2.33225 q^{3} +0.512364 q^{4} +1.00000i q^{5} -2.84461i q^{6} +3.60020i q^{7} -3.06430i q^{8} +2.43937 q^{9} +O(q^{10})\)	\(q-1.21969i q^{2} +2.33225 q^{3} +0.512364 q^{4} +1.00000i q^{5} -2.84461i q^{6} +3.60020i q^{7} -3.06430i q^{8} +2.43937 q^{9} +1.21969 q^{10} +5.37182i q^{11} +1.19496 q^{12} +4.39111 q^{14} +2.33225i q^{15} -2.71276 q^{16} +1.13186 q^{17} -2.97527i q^{18} -2.26795i q^{19} +0.512364i q^{20} +8.39654i q^{21} +6.55193 q^{22} +3.89287 q^{23} -7.14670i q^{24} -1.00000 q^{25} -1.30752 q^{27} +1.84461i q^{28} -0.0247279 q^{29} +2.84461 q^{30} -5.46410i q^{31} -2.81988i q^{32} +12.5284i q^{33} -1.38051i q^{34} -3.60020 q^{35} +1.24985 q^{36} -8.70406i q^{37} -2.76619 q^{38} +3.06430 q^{40} -3.73205i q^{41} +10.2412 q^{42} +1.13186 q^{43} +2.75232i q^{44} +2.43937i q^{45} -4.74809i q^{46} +2.58535i q^{47} -6.32681 q^{48} -5.96141 q^{49} +1.21969i q^{50} +2.63977 q^{51} -4.43937 q^{53} +1.59476i q^{54} -5.37182 q^{55} +11.0321 q^{56} -5.28942i q^{57} +0.0301603i q^{58} -0.171425i q^{59} +1.19496i q^{60} +3.36023 q^{61} -6.66449 q^{62} +8.78222i q^{63} -8.86488 q^{64} +15.2807 q^{66} -6.39980i q^{67} +0.579922 q^{68} +9.07914 q^{69} +4.39111i q^{70} +10.7973i q^{71} -7.47497i q^{72} -4.70308i q^{73} -10.6162 q^{74} -2.33225 q^{75} -1.16202i q^{76} -19.3396 q^{77} -11.9826 q^{79} -2.71276i q^{80} -10.3676 q^{81} -4.55193 q^{82} +12.1286i q^{83} +4.30209i q^{84} +1.13186i q^{85} -1.38051i q^{86} -0.0576715 q^{87} +16.4608 q^{88} -16.1540i q^{89} +2.97527 q^{90} +1.99457 q^{92} -12.7436i q^{93} +3.15332 q^{94} +2.26795 q^{95} -6.57666i q^{96} -12.1682i q^{97} +7.27105i q^{98} +13.1039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{4} + 8 q^{9}+O(q^{10}) \) 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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