LMFDB - Embedded newform 845.2.c.h.506.8

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 34x^{16} + 407x^{14} + 2175x^{12} + 5555x^{10} + 6664x^{8} + 3544x^{6} + 681x^{4} + 47x^{2} + 1 $ x^18 + 34x^16 + 407x^14 + 2175x^12 + 5555x^10 + 6664x^8 + 3544x^6 + 681x^4 + 47x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			506.8
Root			$2.07331i$ of defining polynomial
Character	$\chi$	$=$	845.506
Dual form			845.2.c.h.506.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.271374i q^{2} -0.319618 q^{3} +1.92636 q^{4} +1.00000i q^{5} +0.0867358i q^{6} +3.38151i q^{7} -1.06551i q^{8} -2.89784 q^{9} +O(q^{10})$	\(q-0.271374i q^{2} -0.319618 q^{3} +1.92636 q^{4} +1.00000i q^{5} +0.0867358i q^{6} +3.38151i q^{7} -1.06551i q^{8} -2.89784 q^{9} +0.271374 q^{10} +1.75204i q^{11} -0.615697 q^{12} +0.917654 q^{14} -0.319618i q^{15} +3.56356 q^{16} -1.95419 q^{17} +0.786399i q^{18} +7.13261i q^{19} +1.92636i q^{20} -1.08079i q^{21} +0.475459 q^{22} -7.61420 q^{23} +0.340556i q^{24} -1.00000 q^{25} +1.88505 q^{27} +6.51400i q^{28} +3.98380 q^{29} -0.0867358 q^{30} -4.86923i q^{31} -3.09808i q^{32} -0.559984i q^{33} +0.530316i q^{34} -3.38151 q^{35} -5.58228 q^{36} +10.5010i q^{37} +1.93560 q^{38} +1.06551 q^{40} -0.911110i q^{41} -0.293298 q^{42} -4.58553 q^{43} +3.37506i q^{44} -2.89784i q^{45} +2.06629i q^{46} -8.58491i q^{47} -1.13898 q^{48} -4.43464 q^{49} +0.271374i q^{50} +0.624593 q^{51} +11.9646 q^{53} -0.511554i q^{54} -1.75204 q^{55} +3.60304 q^{56} -2.27971i q^{57} -1.08110i q^{58} +3.82297i q^{59} -0.615697i q^{60} +7.98476 q^{61} -1.32138 q^{62} -9.79910i q^{63} +6.28638 q^{64} -0.151965 q^{66} -0.472749i q^{67} -3.76446 q^{68} +2.43363 q^{69} +0.917654i q^{70} +5.50312i q^{71} +3.08768i q^{72} +2.93857i q^{73} +2.84969 q^{74} +0.319618 q^{75} +13.7400i q^{76} -5.92456 q^{77} +4.09938 q^{79} +3.56356i q^{80} +8.09104 q^{81} -0.247252 q^{82} +11.7733i q^{83} -2.08199i q^{84} -1.95419i q^{85} +1.24439i q^{86} -1.27329 q^{87} +1.86682 q^{88} -3.85992i q^{89} -0.786399 q^{90} -14.6677 q^{92} +1.55629i q^{93} -2.32972 q^{94} -7.13261 q^{95} +0.990200i q^{96} +6.95775i q^{97} +1.20345i q^{98} -5.07715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9}+O(q^{10}) $ 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9	$ 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40} - 22 q^{42} - 78 q^{43} - 6 q^{48} - 32 q^{49} - 86 q^{51} - 16 q^{53} - 18 q^{55} + 58 q^{56} - 6 q^{61} + 20 q^{62} - 68 q^{64} - 98 q^{66} - 40 q^{68} + 26 q^{69} - 30 q^{74} - 14 q^{75} + 8 q^{77} + 78 q^{79} + 58 q^{81} + 8 q^{82} + 32 q^{87} - 84 q^{88} + 20 q^{90} - 54 q^{92} + 32 q^{94} + 8 q^{95}+O(q^{100}) $ 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * 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 $

$2$	− 0.271374i	− 0.191890i	−0.995387	−	0.0959451i	$-0.969413\pi$
$2$	− 0.271374i	− 0.191890i	0.995387	−	0.0959451i	$-0.0305873\pi$
$3$	−0.319618	−0.184531	−0.0922656	−	0.995734i	$-0.529411\pi$
$3$	−0.319618	−0.184531	−0.0922656	+	0.995734i	$0.529411\pi$
$4$	1.92636	0.963178
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	0.0867358i	0.0354098i
$7$	3.38151i	1.27809i	0.769168	+	0.639046i	$0.220671\pi$
$7$	3.38151i	1.27809i	−0.769168	+	0.639046i	$0.779329\pi$
$8$	− 1.06551i	− 0.376715i
$9$	−2.89784	−0.965948
$10$	0.271374	0.0858159
$11$	1.75204i	0.528261i	0.964487	+	0.264131i	$0.0850850\pi$
$11$	1.75204i	0.528261i	−0.964487	+	0.264131i	$0.914915\pi$
$12$	−0.615697	−0.177736
$13$	0	0
$13$	0	0
$14$	0.917654	0.245253
$15$	− 0.319618i	− 0.0825249i
$16$	3.56356	0.890890
$17$	−1.95419	−0.473960	−0.236980	−	0.971514i	$-0.576158\pi$
$17$	−1.95419	−0.473960	−0.236980	+	0.971514i	$0.576158\pi$
$18$	0.786399i	0.185356i
$19$	7.13261i	1.63633i	0.574981	+	0.818167i	$0.305010\pi$
$19$	7.13261i	1.63633i	−0.574981	+	0.818167i	$0.694990\pi$
$20$	1.92636i	0.430746i
$21$	− 1.08079i	− 0.235848i
$22$	0.475459	0.101368
$23$	−7.61420	−1.58767	−0.793835	−	0.608133i	$-0.791919\pi$
$23$	−7.61420	−1.58767	−0.793835	+	0.608133i	$0.791919\pi$
$24$	0.340556i	0.0695157i
$25$	−1.00000	−0.200000
$26$	0	0
$27$	1.88505	0.362779
$28$	6.51400i	1.23103i
$29$	3.98380	0.739773	0.369886	−	0.929077i	$-0.379397\pi$
$29$	3.98380	0.739773	0.369886	+	0.929077i	$0.379397\pi$
$30$	−0.0867358	−0.0158357
$31$	− 4.86923i	− 0.874540i	−0.899330	−	0.437270i	$-0.855945\pi$
$31$	− 4.86923i	− 0.874540i	0.899330	−	0.437270i	$-0.144055\pi$
$32$	− 3.09808i	− 0.547668i
$33$	− 0.559984i	− 0.0974807i
$34$	0.530316i	0.0909484i
$35$	−3.38151	−0.571580
$36$	−5.58228	−0.930380
$37$	10.5010i	1.72635i	0.504903	+	0.863176i	$0.331528\pi$
$37$	10.5010i	1.72635i	−0.504903	+	0.863176i	$0.668472\pi$
$38$	1.93560	0.313997
$39$	0	0
$40$	1.06551	0.168472
$41$	− 0.911110i	− 0.142292i	−0.997466	−	0.0711458i	$-0.977334\pi$
$41$	− 0.911110i	− 0.142292i	0.997466	−	0.0711458i	$-0.0226656\pi$
$42$	−0.293298	−0.0452569
$43$	−4.58553	−0.699286	−0.349643	−	0.936883i	$-0.613697\pi$
$43$	−4.58553	−0.699286	−0.349643	+	0.936883i	$0.613697\pi$
$44$	3.37506i	0.508810i
$45$	− 2.89784i	− 0.431985i
$46$	2.06629i	0.304658i
$47$	− 8.58491i	− 1.25224i	−0.779728	−	0.626119i	$-0.784643\pi$
$47$	− 8.58491i	− 1.25224i	0.779728	−	0.626119i	$-0.215357\pi$
$48$	−1.13898	−0.164397
$49$	−4.43464	−0.633520
$50$	0.271374i	0.0383781i
$51$	0.624593	0.0874605
$52$	0	0
$53$	11.9646	1.64347	0.821734	−	0.569871i	$-0.193007\pi$
$53$	11.9646	1.64347	0.821734	+	0.569871i	$0.193007\pi$
$54$	− 0.511554i	− 0.0696137i
$55$	−1.75204	−0.236246
$56$	3.60304	0.481476
$57$	− 2.27971i	− 0.301955i
$58$	− 1.08110i	− 0.141955i
$59$	3.82297i	0.497708i	0.968541	+	0.248854i	$0.0800540\pi$
$59$	3.82297i	0.497708i	−0.968541	+	0.248854i	$0.919946\pi$
$60$	− 0.615697i	− 0.0794862i
$61$	7.98476	1.02234	0.511172	−	0.859479i	$-0.329212\pi$
$61$	7.98476	1.02234	0.511172	+	0.859479i	$0.329212\pi$
$62$	−1.32138	−0.167816
$63$	− 9.79910i	− 1.23457i
$64$	6.28638	0.785798
$65$	0	0
$66$	−0.151965	−0.0187056
$67$	− 0.472749i	− 0.0577554i	−0.999583	−	0.0288777i	$-0.990807\pi$
$67$	− 0.472749i	− 0.0577554i	0.999583	−	0.0288777i	$-0.00919334\pi$
$68$	−3.76446	−0.456508
$69$	2.43363	0.292975
$70$	0.917654i	0.109681i
$71$	5.50312i	0.653101i	0.945180	+	0.326550i	$0.105886\pi$
$71$	5.50312i	0.653101i	−0.945180	+	0.326550i	$0.894114\pi$
$72$	3.08768i	0.363887i
$73$	2.93857i	0.343934i	0.985103	+	0.171967i	$0.0550122\pi$
$73$	2.93857i	0.343934i	−0.985103	+	0.171967i	$0.944988\pi$
$74$	2.84969	0.331270
$75$	0.319618	0.0369063
$76$	13.7400i	1.57608i
$77$	−5.92456	−0.675167
$78$	0	0
$79$	4.09938	0.461216	0.230608	−	0.973047i	$-0.425928\pi$
$79$	4.09938	0.461216	0.230608	+	0.973047i	$0.425928\pi$
$80$	3.56356i	0.398418i
$81$	8.09104	0.899004
$82$	−0.247252	−0.0273044
$83$	11.7733i	1.29229i	0.763215	+	0.646144i	$0.223619\pi$
$83$	11.7733i	1.29229i	−0.763215	+	0.646144i	$0.776381\pi$
$84$	− 2.08199i	− 0.227164i
$85$	− 1.95419i	− 0.211961i
$86$	1.24439i	0.134186i
$87$	−1.27329	−0.136511
$88$	1.86682	0.199004
$89$	− 3.85992i	− 0.409151i	−0.978851	−	0.204576i	$-0.934419\pi$
$89$	− 3.85992i	− 0.409151i	0.978851	−	0.204576i	$-0.0655814\pi$
$90$	−0.786399	−0.0828937
$91$	0	0
$92$	−14.6677	−1.52921
$93$	1.55629i	0.161380i
$94$	−2.32972	−0.240292
$95$	−7.13261	−0.731791
$96$	0.990200i	0.101062i
$97$	6.95775i	0.706453i	0.935538	+	0.353226i	$0.114915\pi$
$97$	6.95775i	0.706453i	−0.935538	+	0.353226i	$0.885085\pi$
$98$	1.20345i	0.121566i
$99$	− 5.07715i	− 0.510273i
$100$	−1.92636	−0.192636
$101$	17.8923	1.78035	0.890175	−	0.455619i	$-0.150582\pi$
$101$	17.8923	1.78035	0.890175	+	0.455619i	$0.150582\pi$
$102$	− 0.169498i	− 0.0167828i
$103$	−10.2561	−1.01056	−0.505281	−	0.862955i	$-0.668611\pi$
$103$	−10.2561	−1.01056	−0.505281	+	0.862955i	$0.668611\pi$
$104$	0	0
$105$	1.08079	0.105474
$106$	− 3.24689i	− 0.315366i
$107$	12.8986	1.24696	0.623478	−	0.781841i	$-0.285719\pi$
$107$	12.8986	1.24696	0.623478	+	0.781841i	$0.285719\pi$
$108$	3.63129	0.349421
$109$	− 10.4476i	− 1.00070i	−0.865825	−	0.500348i	$-0.833206\pi$
$109$	− 10.4476i	− 1.00070i	0.865825	−	0.500348i	$-0.166794\pi$
$110$	0.475459i	0.0453332i
$111$	− 3.35630i	− 0.318566i
$112$	12.0502i	1.13864i
$113$	−18.9766	−1.78516	−0.892582	−	0.450884i	$-0.851109\pi$
$113$	−18.9766	−1.78516	−0.892582	+	0.450884i	$0.851109\pi$
$114$	−0.618653	−0.0579422
$115$	− 7.61420i	− 0.710028i
$116$	7.67421	0.712533
$117$	0	0
$118$	1.03745	0.0955054
$119$	− 6.60812i	− 0.605765i
$120$	−0.340556	−0.0310883
$121$	7.93034	0.720940
$122$	− 2.16685i	− 0.196178i
$123$	0.291207i	0.0262572i
$124$	− 9.37987i	− 0.842337i
$125$	− 1.00000i	− 0.0894427i
$126$	−2.65922	−0.236902
$127$	9.88489	0.877142	0.438571	−	0.898697i	$-0.355485\pi$
$127$	9.88489	0.877142	0.438571	+	0.898697i	$0.355485\pi$
$128$	− 7.90212i	− 0.698455i
$129$	1.46561	0.129040
$130$	0	0
$131$	−11.4705	−1.00218	−0.501089	−	0.865396i	$-0.667067\pi$
$131$	−11.4705	−1.00218	−0.501089	+	0.865396i	$0.667067\pi$
$132$	− 1.07873i	− 0.0938913i
$133$	−24.1190	−2.09139
$134$	−0.128292	−0.0110827
$135$	1.88505i	0.162240i
$136$	2.08221i	0.178548i
$137$	− 13.0826i	− 1.11772i	−0.829261	−	0.558861i	$-0.811239\pi$
$137$	− 13.0826i	− 1.11772i	0.829261	−	0.558861i	$-0.188761\pi$
$138$	− 0.660424i	− 0.0562190i
$139$	11.9762	1.01581	0.507904	−	0.861414i	$-0.330421\pi$
$139$	11.9762	1.01581	0.507904	+	0.861414i	$0.330421\pi$
$140$	−6.51400	−0.550534
$141$	2.74389i	0.231077i
$142$	1.49340	0.125324
$143$	0	0
$144$	−10.3266	−0.860554
$145$	3.98380i	0.330836i
$146$	0.797452	0.0659976
$147$	1.41739	0.116904
$148$	20.2287i	1.66278i
$149$	− 16.3052i	− 1.33577i	−0.744262	−	0.667887i	$-0.767199\pi$
$149$	− 16.3052i	− 1.33577i	0.744262	−	0.667887i	$-0.232801\pi$
$150$	− 0.0867358i	− 0.00708195i
$151$	8.75415i	0.712402i	0.934409	+	0.356201i	$0.115928\pi$
$151$	8.75415i	0.712402i	−0.934409	+	0.356201i	$0.884072\pi$
$152$	7.59987	0.616431
$153$	5.66293	0.457821
$154$	1.60777i	0.129558i
$155$	4.86923	0.391106
$156$	0	0
$157$	6.48821	0.517816	0.258908	−	0.965902i	$-0.416637\pi$
$157$	6.48821	0.517816	0.258908	+	0.965902i	$0.416637\pi$
$158$	− 1.11246i	− 0.0885029i
$159$	−3.82411	−0.303271
$160$	3.09808	0.244925
$161$	− 25.7475i	− 2.02919i
$162$	− 2.19570i	− 0.172510i
$163$	− 3.84933i	− 0.301503i	−0.988572	−	0.150751i	$-0.951831\pi$
$163$	− 3.84933i	− 0.301503i	0.988572	−	0.150751i	$-0.0481693\pi$
$164$	− 1.75512i	− 0.137052i
$165$	0.559984	0.0435947
$166$	3.19497	0.247977
$167$	− 6.85894i	− 0.530760i	−0.964144	−	0.265380i	$-0.914503\pi$
$167$	− 6.85894i	− 0.530760i	0.964144	−	0.265380i	$-0.0854975\pi$
$168$	−1.15159	−0.0888474
$169$	0	0
$170$	−0.530316	−0.0406733
$171$	− 20.6692i	− 1.58061i
$172$	−8.83336	−0.673537
$173$	−16.0204	−1.21801	−0.609005	−	0.793166i	$-0.708431\pi$
$173$	−16.0204	−1.21801	−0.609005	+	0.793166i	$0.708431\pi$
$174$	0.345538i	0.0261952i
$175$	− 3.38151i	− 0.255618i
$176$	6.24352i	0.470623i
$177$	− 1.22189i	− 0.0918428i
$178$	−1.04748	−0.0785121
$179$	8.08309	0.604158	0.302079	−	0.953283i	$-0.402319\pi$
$179$	8.08309	0.604158	0.302079	+	0.953283i	$0.402319\pi$
$180$	− 5.58228i	− 0.416079i
$181$	−11.0898	−0.824298	−0.412149	−	0.911117i	$-0.635222\pi$
$181$	−11.0898	−0.824298	−0.412149	+	0.911117i	$0.635222\pi$
$182$	0	0
$183$	−2.55207	−0.188654
$184$	8.11301i	0.598099i
$185$	−10.5010	−0.772048
$186$	0.422337	0.0309672
$187$	− 3.42382i	− 0.250375i
$188$	− 16.5376i	− 1.20613i
$189$	6.37434i	0.463665i
$190$	1.93560i	0.140424i
$191$	21.7532	1.57401	0.787003	−	0.616949i	$-0.211631\pi$
$191$	21.7532	1.57401	0.787003	+	0.616949i	$0.211631\pi$
$192$	−2.00924	−0.145004
$193$	− 22.5285i	− 1.62164i	−0.585296	−	0.810820i	$-0.699022\pi$
$193$	− 22.5285i	− 1.62164i	0.585296	−	0.810820i	$-0.300978\pi$
$194$	1.88815	0.135561
$195$	0	0
$196$	−8.54270	−0.610193
$197$	− 17.2749i	− 1.23078i	−0.788221	−	0.615392i	$-0.788998\pi$
$197$	− 17.2749i	− 1.23078i	0.788221	−	0.615392i	$-0.211002\pi$
$198$	−1.37781	−0.0979164
$199$	−17.4901	−1.23984	−0.619919	−	0.784666i	$-0.712834\pi$
$199$	−17.4901	−1.23984	−0.619919	+	0.784666i	$0.712834\pi$
$200$	1.06551i	0.0753430i
$201$	0.151099i	0.0106577i
$202$	− 4.85550i	− 0.341632i
$203$	13.4713i	0.945498i
$204$	1.20319	0.0842400
$205$	0.911110	0.0636347
$206$	2.78323i	0.193917i
$207$	22.0648	1.53361
$208$	0	0
$209$	−12.4967	−0.864412
$210$	− 0.293298i	− 0.0202395i
$211$	6.33563	0.436163	0.218081	−	0.975931i	$-0.430020\pi$
$211$	6.33563	0.436163	0.218081	+	0.975931i	$0.430020\pi$
$212$	23.0481	1.58295
$213$	− 1.75889i	− 0.120517i
$214$	− 3.50034i	− 0.239279i
$215$	− 4.58553i	− 0.312730i
$216$	− 2.00855i	− 0.136664i
$217$	16.4654	1.11774
$218$	−2.83520	−0.192024
$219$	− 0.939220i	− 0.0634666i
$220$	−3.37506	−0.227547
$221$	0	0
$222$	−0.910812	−0.0611297
$223$	23.4948i	1.57333i	0.617381	+	0.786664i	$0.288194\pi$
$223$	23.4948i	1.57333i	−0.617381	+	0.786664i	$0.711806\pi$
$224$	10.4762	0.699970
$225$	2.89784	0.193190
$226$	5.14974i	0.342556i
$227$	9.59397i	0.636774i	0.947961	+	0.318387i	$0.103141\pi$
$227$	9.59397i	0.636774i	−0.947961	+	0.318387i	$0.896859\pi$
$228$	− 4.39153i	− 0.290836i
$229$	7.23000i	0.477772i	0.971048	+	0.238886i	$0.0767823\pi$
$229$	7.23000i	0.477772i	−0.971048	+	0.238886i	$0.923218\pi$
$230$	−2.06629	−0.136247
$231$	1.89359	0.124589
$232$	− 4.24478i	− 0.278683i
$233$	0.429924	0.0281652	0.0140826	−	0.999901i	$-0.495517\pi$
$233$	0.429924	0.0281652	0.0140826	+	0.999901i	$0.495517\pi$
$234$	0	0
$235$	8.58491	0.560017
$236$	7.36440i	0.479382i
$237$	−1.31023	−0.0851088
$238$	−1.79327	−0.116240
$239$	− 12.7450i	− 0.824405i	−0.911092	−	0.412203i	$-0.864760\pi$
$239$	− 12.7450i	− 0.824405i	0.911092	−	0.412203i	$-0.135240\pi$
$240$	− 1.13898i	− 0.0735206i
$241$	− 19.1338i	− 1.23252i	−0.787545	−	0.616258i	$-0.788648\pi$
$241$	− 19.1338i	− 1.23252i	0.787545	−	0.616258i	$-0.211352\pi$
$242$	− 2.15209i	− 0.138341i
$243$	−8.24120	−0.528673
$244$	15.3815	0.984699
$245$	− 4.43464i	− 0.283319i
$246$	0.0790259	0.00503851
$247$	0	0
$248$	−5.18821	−0.329452
$249$	− 3.76295i	− 0.238468i
$250$	−0.271374	−0.0171632
$251$	−0.411815	−0.0259935	−0.0129968	−	0.999916i	$-0.504137\pi$
$251$	−0.411815	−0.0259935	−0.0129968	+	0.999916i	$0.504137\pi$
$252$	− 18.8766i	− 1.18911i
$253$	− 13.3404i	− 0.838705i
$254$	− 2.68250i	− 0.168315i
$255$	0.624593i	0.0391135i
$256$	10.4283	0.651771
$257$	2.47556	0.154421	0.0772105	−	0.997015i	$-0.475399\pi$
$257$	2.47556	0.154421	0.0772105	+	0.997015i	$0.475399\pi$
$258$	− 0.397729i	− 0.0247616i
$259$	−35.5093	−2.20644
$260$	0	0
$261$	−11.5444	−0.714582
$262$	3.11278i	0.192308i
$263$	−11.3591	−0.700430	−0.350215	−	0.936669i	$-0.613892\pi$
$263$	−11.3591	−0.700430	−0.350215	+	0.936669i	$0.613892\pi$
$264$	−0.596669	−0.0367224
$265$	11.9646i	0.734981i
$266$	6.54527i	0.401317i
$267$	1.23370i	0.0755012i
$268$	− 0.910682i	− 0.0556288i
$269$	−29.6888	−1.81016	−0.905078	−	0.425245i	$-0.860188\pi$
$269$	−29.6888	−1.81016	−0.905078	+	0.425245i	$0.860188\pi$
$270$	0.511554	0.0311322
$271$	14.7761i	0.897583i	0.893636	+	0.448792i	$0.148145\pi$
$271$	14.7761i	0.897583i	−0.893636	+	0.448792i	$0.851855\pi$
$272$	−6.96387	−0.422247
$273$	0	0
$274$	−3.55028	−0.214480
$275$	− 1.75204i	− 0.105652i
$276$	4.68804	0.282187
$277$	1.94652	0.116955	0.0584774	−	0.998289i	$-0.481375\pi$
$277$	1.94652	0.116955	0.0584774	+	0.998289i	$0.481375\pi$
$278$	− 3.25002i	− 0.194924i
$279$	14.1103i	0.844760i
$280$	3.60304i	0.215323i
$281$	− 18.5256i	− 1.10515i	−0.833464	−	0.552573i	$-0.813646\pi$
$281$	− 18.5256i	− 1.10515i	0.833464	−	0.552573i	$-0.186354\pi$
$282$	0.744619	0.0443414
$283$	−13.0952	−0.778427	−0.389214	−	0.921148i	$-0.627253\pi$
$283$	−13.0952	−0.778427	−0.389214	+	0.921148i	$0.627253\pi$
$284$	10.6010i	0.629052i
$285$	2.27971	0.135038
$286$	0	0
$287$	3.08093	0.181862
$288$	8.97775i	0.529019i
$289$	−13.1811	−0.775362
$290$	1.08110	0.0634843
$291$	− 2.22382i	− 0.130363i
$292$	5.66074i	0.331270i
$293$	1.20753i	0.0705445i	0.999378	+	0.0352722i	$0.0112298\pi$
$293$	1.20753i	0.0705445i	−0.999378	+	0.0352722i	$0.988770\pi$
$294$	− 0.384642i	− 0.0224328i
$295$	−3.82297	−0.222582
$296$	11.1889	0.650342
$297$	3.30270i	0.191642i
$298$	−4.42481	−0.256322
$299$	0	0
$300$	0.615697	0.0355473
$301$	− 15.5060i	− 0.893752i
$302$	2.37565	0.136703
$303$	−5.71869	−0.328530
$304$	25.4175i	1.45779i
$305$	7.98476i	0.457206i
$306$	− 1.53677i	− 0.0878514i
$307$	21.9275i	1.25147i	0.780037	+	0.625733i	$0.215200\pi$
$307$	21.9275i	1.25147i	−0.780037	+	0.625733i	$0.784800\pi$
$308$	−11.4128	−0.650306
$309$	3.27802	0.186480
$310$	− 1.32138i	− 0.0750494i
$311$	12.5966	0.714288	0.357144	−	0.934049i	$-0.383751\pi$
$311$	12.5966	0.714288	0.357144	+	0.934049i	$0.383751\pi$
$312$	0	0
$313$	26.8268	1.51634	0.758169	−	0.652058i	$-0.226094\pi$
$313$	26.8268	1.51634	0.758169	+	0.652058i	$0.226094\pi$
$314$	− 1.76073i	− 0.0993638i
$315$	9.79910	0.552117
$316$	7.89687	0.444234
$317$	17.1279i	0.961999i	0.876721	+	0.481000i	$0.159726\pi$
$317$	17.1279i	0.961999i	−0.876721	+	0.481000i	$0.840274\pi$
$318$	1.03776i	0.0581948i
$319$	6.97979i	0.390793i
$320$	6.28638i	0.351420i
$321$	−4.12262	−0.230102
$322$	−6.98720	−0.389382
$323$	− 13.9385i	− 0.775557i
$324$	15.5862	0.865901
$325$	0	0
$326$	−1.04461	−0.0578555
$327$	3.33923i	0.184660i
$328$	−0.970798	−0.0536033
$329$	29.0300	1.60047
$330$	− 0.151965i	− 0.00836540i
$331$	− 1.43062i	− 0.0786338i	−0.999227	−	0.0393169i	$-0.987482\pi$
$331$	− 1.43062i	− 0.0786338i	0.999227	−	0.0393169i	$-0.0125182\pi$
$332$	22.6796i	1.24470i
$333$	− 30.4302i	− 1.66757i
$334$	−1.86134	−0.101848
$335$	0.472749	0.0258290
$336$	− 3.85147i	− 0.210115i
$337$	7.48872	0.407937	0.203968	−	0.978977i	$-0.434616\pi$
$337$	7.48872	0.407937	0.203968	+	0.978977i	$0.434616\pi$
$338$	0	0
$339$	6.06524	0.329419
$340$	− 3.76446i	− 0.204157i
$341$	8.53111	0.461985
$342$	−5.60908	−0.303304
$343$	8.67480i	0.468395i
$344$	4.88593i	0.263431i
$345$	2.43363i	0.131022i
$346$	4.34752i	0.233724i
$347$	6.96813	0.374069	0.187034	−	0.982353i	$-0.440112\pi$
$347$	6.96813	0.374069	0.187034	+	0.982353i	$0.440112\pi$
$348$	−2.45281	−0.131485
$349$	21.9738i	1.17623i	0.808777	+	0.588116i	$0.200130\pi$
$349$	21.9738i	1.17623i	−0.808777	+	0.588116i	$0.799870\pi$
$350$	−0.917654	−0.0490507
$351$	0	0
$352$	5.42797	0.289312
$353$	− 13.0184i	− 0.692899i	−0.938069	−	0.346450i	$-0.887387\pi$
$353$	− 13.0184i	− 0.692899i	0.938069	−	0.346450i	$-0.112613\pi$
$354$	−0.331589	−0.0176237
$355$	−5.50312	−0.292075
$356$	− 7.43559i	− 0.394085i
$357$	2.11207i	0.111783i
$358$	− 2.19354i	− 0.115932i
$359$	9.99211i	0.527363i	0.964610	+	0.263682i	$0.0849369\pi$
$359$	9.99211i	0.527363i	−0.964610	+	0.263682i	$0.915063\pi$
$360$	−3.08768	−0.162735
$361$	−31.8742	−1.67759
$362$	3.00948i	0.158175i
$363$	−2.53468	−0.133036
$364$	0	0
$365$	−2.93857	−0.153812
$366$	0.692564i	0.0362009i
$367$	25.2882	1.32004	0.660018	−	0.751250i	$-0.270549\pi$
$367$	25.2882	1.32004	0.660018	+	0.751250i	$0.270549\pi$
$368$	−27.1337	−1.41444
$369$	2.64026i	0.137446i
$370$	2.84969i	0.148149i
$371$	40.4586i	2.10050i
$372$	2.99797i	0.155438i
$373$	14.2703	0.738887	0.369444	−	0.929253i	$-0.379548\pi$
$373$	14.2703	0.738887	0.369444	+	0.929253i	$0.379548\pi$
$374$	−0.929136	−0.0480445
$375$	0.319618i	0.0165050i
$376$	−9.14730	−0.471736
$377$	0	0
$378$	1.72983	0.0889728
$379$	− 7.01341i	− 0.360255i	−0.983643	−	0.180127i	$-0.942349\pi$
$379$	− 7.01341i	− 0.360255i	0.983643	−	0.180127i	$-0.0576510\pi$
$380$	−13.7400	−0.704845
$381$	−3.15938	−0.161860
$382$	− 5.90325i	− 0.302036i
$383$	− 4.69336i	− 0.239820i	−0.992785	−	0.119910i	$-0.961739\pi$
$383$	− 4.69336i	− 0.239820i	0.992785	−	0.119910i	$-0.0382606\pi$
$384$	2.52565i	0.128887i
$385$	− 5.92456i	− 0.301944i
$386$	−6.11365	−0.311177
$387$	13.2881	0.675474
$388$	13.4031i	0.680440i
$389$	9.34682	0.473902	0.236951	−	0.971522i	$-0.423852\pi$
$389$	9.34682	0.473902	0.236951	+	0.971522i	$0.423852\pi$
$390$	0	0
$391$	14.8796	0.752493
$392$	4.72515i	0.238656i
$393$	3.66616	0.184933
$394$	−4.68795	−0.236176
$395$	4.09938i	0.206262i
$396$	− 9.78041i	− 0.491484i
$397$	− 21.2133i	− 1.06467i	−0.846535	−	0.532334i	$-0.821315\pi$
$397$	− 21.2133i	− 1.06467i	0.846535	−	0.532334i	$-0.178685\pi$
$398$	4.74634i	0.237913i
$399$	7.70887	0.385926
$400$	−3.56356	−0.178178
$401$	18.2172i	0.909725i	0.890562	+	0.454863i	$0.150312\pi$
$401$	18.2172i	0.909725i	−0.890562	+	0.454863i	$0.849688\pi$
$402$	0.0410042	0.00204511
$403$	0	0
$404$	34.4669	1.71479
$405$	8.09104i	0.402047i
$406$	3.65575	0.181432
$407$	−18.3982	−0.911965
$408$	− 0.665510i	− 0.0329477i
$409$	4.36136i	0.215655i	0.994170	+	0.107828i	$0.0343895\pi$
$409$	4.36136i	0.215655i	−0.994170	+	0.107828i	$0.965611\pi$
$410$	− 0.247252i	− 0.0122109i
$411$	4.18143i	0.206255i
$412$	−19.7569	−0.973351
$413$	−12.9274	−0.636117
$414$	− 5.98780i	− 0.294284i
$415$	−11.7733	−0.577929
$416$	0	0
$417$	−3.82780	−0.187448
$418$	3.39127i	0.165872i
$419$	17.0555	0.833214	0.416607	−	0.909087i	$-0.363219\pi$
$419$	17.0555	0.833214	0.416607	+	0.909087i	$0.363219\pi$
$420$	2.08199	0.101591
$421$	− 1.27996i	− 0.0623816i	−0.999513	−	0.0311908i	$-0.990070\pi$
$421$	− 1.27996i	− 0.0623816i	0.999513	−	0.0311908i	$-0.00992995\pi$
$422$	− 1.71932i	− 0.0836954i
$423$	24.8777i	1.20960i
$424$	− 12.7484i	− 0.619119i
$425$	1.95419	0.0947921
$426$	−0.477318	−0.0231261
$427$	27.0006i	1.30665i
$428$	24.8473	1.20104
$429$	0	0
$430$	−1.24439	−0.0600099
$431$	32.8733i	1.58345i	0.610878	+	0.791725i	$0.290817\pi$
$431$	32.8733i	1.58345i	−0.610878	+	0.791725i	$0.709183\pi$
$432$	6.71751	0.323196
$433$	28.2622	1.35819	0.679097	−	0.734048i	$-0.262372\pi$
$433$	28.2622	1.35819	0.679097	+	0.734048i	$0.262372\pi$
$434$	− 4.46827i	− 0.214484i
$435$	− 1.27329i	− 0.0610497i
$436$	− 20.1257i	− 0.963848i
$437$	− 54.3091i	− 2.59796i
$438$	−0.254880	−0.0121786
$439$	−26.2621	−1.25342	−0.626711	−	0.779252i	$-0.715599\pi$
$439$	−26.2621	−1.25342	−0.626711	+	0.779252i	$0.715599\pi$
$440$	1.86682i	0.0889972i
$441$	12.8509	0.611948
$442$	0	0
$443$	−14.0477	−0.667427	−0.333714	−	0.942674i	$-0.608302\pi$
$443$	−14.0477	−0.667427	−0.333714	+	0.942674i	$0.608302\pi$
$444$	− 6.46543i	− 0.306836i
$445$	3.85992	0.182978
$446$	6.37588	0.301906
$447$	5.21143i	0.246492i
$448$	21.2575i	1.00432i
$449$	4.45904i	0.210435i	0.994449	+	0.105218i	$0.0335539\pi$
$449$	4.45904i	0.210435i	−0.994449	+	0.105218i	$0.966446\pi$
$450$	− 0.786399i	− 0.0370712i
$451$	1.59631	0.0751671
$452$	−36.5556	−1.71943
$453$	− 2.79798i	− 0.131461i
$454$	2.60355	0.122191
$455$	0	0
$456$	−2.42905	−0.113751
$457$	16.4149i	0.767855i	0.923363	+	0.383927i	$0.125429\pi$
$457$	16.4149i	0.767855i	−0.923363	+	0.383927i	$0.874571\pi$
$458$	1.96203	0.0916798
$459$	−3.68375	−0.171943
$460$	− 14.6677i	− 0.683883i
$461$	20.5455i	0.956899i	0.878115	+	0.478449i	$0.158801\pi$
$461$	20.5455i	0.956899i	−0.878115	+	0.478449i	$0.841199\pi$
$462$	− 0.513872i	− 0.0239075i
$463$	− 1.58359i	− 0.0735958i	−0.999323	−	0.0367979i	$-0.988284\pi$
$463$	− 1.58359i	− 0.0735958i	0.999323	−	0.0367979i	$-0.0117158\pi$
$464$	14.1965	0.659056
$465$	−1.55629	−0.0721713
$466$	− 0.116670i	− 0.00540463i
$467$	−5.14277	−0.237979	−0.118990	−	0.992896i	$-0.537966\pi$
$467$	−5.14277	−0.237979	−0.118990	+	0.992896i	$0.537966\pi$
$468$	0	0
$469$	1.59861	0.0738168
$470$	− 2.32972i	− 0.107462i
$471$	−2.07375	−0.0955532
$472$	4.07341	0.187494
$473$	− 8.03405i	− 0.369406i
$474$	0.355563i	0.0163316i
$475$	− 7.13261i	− 0.327267i
$476$	− 12.7296i	− 0.583460i
$477$	−34.6716	−1.58751
$478$	−3.45866	−0.158195
$479$	− 22.2914i	− 1.01852i	−0.860613	−	0.509260i	$-0.829919\pi$
$479$	− 22.2914i	− 1.01852i	0.860613	−	0.509260i	$-0.170081\pi$
$480$	−0.990200	−0.0451962
$481$	0	0
$482$	−5.19241	−0.236508
$483$	8.22936i	0.374449i
$484$	15.2767	0.694394
$485$	−6.95775	−0.315935
$486$	2.23645i	0.101447i
$487$	− 23.4185i	− 1.06119i	−0.847624	−	0.530597i	$-0.821968\pi$
$487$	− 23.4185i	− 1.06119i	0.847624	−	0.530597i	$-0.178032\pi$
$488$	− 8.50784i	− 0.385132i
$489$	1.23031i	0.0556367i
$490$	−1.20345	−0.0543661
$491$	−3.39791	−0.153345	−0.0766727	−	0.997056i	$-0.524430\pi$
$491$	−3.39791	−0.153345	−0.0766727	+	0.997056i	$0.524430\pi$
$492$	0.560968i	0.0252904i
$493$	−7.78509	−0.350623
$494$	0	0
$495$	5.07715	0.228201
$496$	− 17.3518i	− 0.779119i
$497$	−18.6089	−0.834723
$498$	−1.02117	−0.0457596
$499$	− 4.87712i	− 0.218330i	−0.994024	−	0.109165i	$-0.965182\pi$
$499$	− 4.87712i	− 0.218330i	0.994024	−	0.109165i	$-0.0348177\pi$
$500$	− 1.92636i	− 0.0861493i
$501$	2.19224i	0.0979419i
$502$	0.111756i	0.00498791i
$503$	−13.9853	−0.623572	−0.311786	−	0.950152i	$-0.600927\pi$
$503$	−13.9853	−0.623572	−0.311786	+	0.950152i	$0.600927\pi$
$504$	−10.4410	−0.465081
$505$	17.8923i	0.796196i
$506$	−3.62024	−0.160939
$507$	0	0
$508$	19.0418	0.844844
$509$	37.0157i	1.64069i	0.571866	+	0.820347i	$0.306220\pi$
$509$	37.0157i	1.64069i	−0.571866	+	0.820347i	$0.693780\pi$
$510$	0.169498	0.00750550
$511$	−9.93683	−0.439579
$512$	− 18.6342i	− 0.823524i
$513$	13.4454i	0.593627i
$514$	− 0.671801i	− 0.0296319i
$515$	− 10.2561i	− 0.451937i
$516$	2.82330	0.124289
$517$	15.0411	0.661508
$518$	9.63628i	0.423394i
$519$	5.12041	0.224761
$520$	0	0
$521$	21.5328	0.943370	0.471685	−	0.881767i	$-0.343646\pi$
$521$	21.5328	0.943370	0.471685	+	0.881767i	$0.343646\pi$
$522$	3.13286i	0.137121i
$523$	36.0055	1.57441	0.787204	−	0.616692i	$-0.211528\pi$
$523$	36.0055	1.57441	0.787204	+	0.616692i	$0.211528\pi$
$524$	−22.0962	−0.965277
$525$	1.08079i	0.0471696i
$526$	3.08255i	0.134406i
$527$	9.51539i	0.414497i
$528$	− 1.99554i	− 0.0868446i
$529$	34.9760	1.52070
$530$	3.24689	0.141036
$531$	− 11.0784i	− 0.480761i
$532$	−46.4619	−2.01438
$533$	0	0
$534$	0.334794	0.0144879
$535$	12.8986i	0.557656i
$536$	−0.503718	−0.0217573
$537$	−2.58350	−0.111486
$538$	8.05676i	0.347351i
$539$	− 7.76969i	− 0.334664i
$540$	3.63129i	0.156266i
$541$	− 0.123280i	− 0.00530020i	−0.999996	−	0.00265010i	$-0.999156\pi$
$541$	− 0.123280i	− 0.00530020i	0.999996	−	0.00265010i	$-0.000843555\pi$
$542$	4.00984	0.172238
$543$	3.54449	0.152109
$544$	6.05423i	0.259573i
$545$	10.4476	0.447525
$546$	0	0
$547$	2.52166	0.107818	0.0539092	−	0.998546i	$-0.482832\pi$
$547$	2.52166	0.107818	0.0539092	+	0.998546i	$0.482832\pi$
$548$	− 25.2018i	− 1.07657i
$549$	−23.1386	−0.987531
$550$	−0.475459	−0.0202736
$551$	28.4149i	1.21052i
$552$	− 2.59306i	− 0.110368i
$553$	13.8621i	0.589477i
$554$	− 0.528233i	− 0.0224425i
$555$	3.35630	0.142467
$556$	23.0704	0.978403
$557$	0.974960i	0.0413104i	0.999787	+	0.0206552i	$0.00657522\pi$
$557$	0.974960i	0.0413104i	−0.999787	+	0.0206552i	$0.993425\pi$
$558$	3.82916	0.162101
$559$	0	0
$560$	−12.0502	−0.509215
$561$	1.09431i	0.0462020i
$562$	−5.02737	−0.212067
$563$	31.5376	1.32915	0.664576	−	0.747220i	$-0.268612\pi$
$563$	31.5376	1.32915	0.664576	+	0.747220i	$0.268612\pi$
$564$	5.28570i	0.222568i
$565$	− 18.9766i	− 0.798350i
$566$	3.55369i	0.149373i
$567$	27.3600i	1.14901i
$568$	5.86363	0.246033
$569$	−24.8762	−1.04287	−0.521433	−	0.853292i	$-0.674602\pi$
$569$	−24.8762	−1.04287	−0.521433	+	0.853292i	$0.674602\pi$
$570$	− 0.618653i	− 0.0259125i
$571$	7.92958	0.331843	0.165921	−	0.986139i	$-0.446940\pi$
$571$	7.92958	0.331843	0.165921	+	0.986139i	$0.446940\pi$
$572$	0	0
$573$	−6.95271	−0.290453
$574$	− 0.836085i	− 0.0348975i
$575$	7.61420	0.317534
$576$	−18.2170	−0.759040
$577$	19.0769i	0.794180i	0.917780	+	0.397090i	$0.129980\pi$
$577$	19.0769i	0.794180i	−0.917780	+	0.397090i	$0.870020\pi$
$578$	3.57702i	0.148784i
$579$	7.20051i	0.299243i
$580$	7.67421i	0.318654i
$581$	−39.8116	−1.65166
$582$	−0.603487	−0.0250153
$583$	20.9626i	0.868181i
$584$	3.13108	0.129565
$585$	0	0
$586$	0.327691	0.0135368
$587$	− 19.1196i	− 0.789149i	−0.918864	−	0.394574i	$-0.870892\pi$
$587$	− 19.1196i	− 0.789149i	0.918864	−	0.394574i	$-0.129108\pi$
$588$	2.73040	0.112600
$589$	34.7303	1.43104
$590$	1.03745i	0.0427113i
$591$	5.52136i	0.227118i
$592$	37.4209i	1.53799i
$593$	36.9354i	1.51676i	0.651814	+	0.758379i	$0.274008\pi$
$593$	36.9354i	1.51676i	−0.651814	+	0.758379i	$0.725992\pi$
$594$	0.896266	0.0367742
$595$	6.60812	0.270906
$596$	− 31.4096i	− 1.28659i
$597$	5.59013	0.228789
$598$	0	0
$599$	−5.19953	−0.212447	−0.106224	−	0.994342i	$-0.533876\pi$
$599$	−5.19953	−0.212447	−0.106224	+	0.994342i	$0.533876\pi$
$600$	− 0.340556i	− 0.0139031i
$601$	−28.3207	−1.15523	−0.577613	−	0.816311i	$-0.696016\pi$
$601$	−28.3207	−1.15523	−0.577613	+	0.816311i	$0.696016\pi$
$602$	−4.20793	−0.171502
$603$	1.36995i	0.0557887i
$604$	16.8636i	0.686170i
$605$	7.93034i	0.322414i
$606$	1.55190i	0.0630417i
$607$	20.1615	0.818332	0.409166	−	0.912460i	$-0.365820\pi$
$607$	20.1615	0.818332	0.409166	+	0.912460i	$0.365820\pi$
$608$	22.0974	0.896168
$609$	− 4.30565i	− 0.174474i
$610$	2.16685	0.0877333
$611$	0	0
$612$	10.9088	0.440963
$613$	− 18.8190i	− 0.760094i	−0.924967	−	0.380047i	$-0.875908\pi$
$613$	− 18.8190i	− 0.760094i	0.924967	−	0.380047i	$-0.124092\pi$
$614$	5.95054	0.240144
$615$	−0.291207	−0.0117426
$616$	6.31268i	0.254345i
$617$	2.82492i	0.113727i	0.998382	+	0.0568634i	$0.0181100\pi$
$617$	2.82492i	0.113727i	−0.998382	+	0.0568634i	$0.981890\pi$
$618$	− 0.889570i	− 0.0357837i
$619$	15.6686i	0.629773i	0.949129	+	0.314886i	$0.101966\pi$
$619$	15.6686i	0.629773i	−0.949129	+	0.314886i	$0.898034\pi$
$620$	9.37987	0.376705
$621$	−14.3532	−0.575973
$622$	− 3.41839i	− 0.137065i
$623$	13.0524	0.522933
$624$	0	0
$625$	1.00000	0.0400000
$626$	− 7.28008i	− 0.290971i
$627$	3.99415	0.159511
$628$	12.4986	0.498749
$629$	− 20.5209i	− 0.818223i
$630$	− 2.65922i	− 0.105946i
$631$	10.1149i	0.402667i	0.979523	+	0.201333i	$0.0645274\pi$
$631$	10.1149i	0.402667i	−0.979523	+	0.201333i	$0.935473\pi$
$632$	− 4.36793i	− 0.173747i
$633$	−2.02498	−0.0804857
$634$	4.64807	0.184598
$635$	9.88489i	0.392270i
$636$	−7.36659	−0.292104
$637$	0	0
$638$	1.89413	0.0749894
$639$	− 15.9472i	− 0.630861i
$640$	7.90212	0.312359
$641$	17.6173	0.695843	0.347922	−	0.937524i	$-0.386888\pi$
$641$	17.6173	0.695843	0.347922	+	0.937524i	$0.386888\pi$
$642$	1.11877i	0.0441544i
$643$	19.0312i	0.750519i	0.926920	+	0.375260i	$0.122446\pi$
$643$	19.0312i	0.750519i	−0.926920	+	0.375260i	$0.877554\pi$
$644$	− 49.5989i	− 1.95447i
$645$	1.46561i	0.0577085i
$646$	−3.78254	−0.148822
$647$	26.6972	1.04957	0.524787	−	0.851233i	$-0.324145\pi$
$647$	26.6972	1.04957	0.524787	+	0.851233i	$0.324145\pi$
$648$	− 8.62108i	− 0.338668i
$649$	−6.69802	−0.262920
$650$	0	0
$651$	−5.26262	−0.206258
$652$	− 7.41518i	− 0.290401i
$653$	−3.16076	−0.123690	−0.0618451	−	0.998086i	$-0.519698\pi$
$653$	−3.16076	−0.123690	−0.0618451	+	0.998086i	$0.519698\pi$
$654$	0.906178	0.0354344
$655$	− 11.4705i	− 0.448188i
$656$	− 3.24680i	− 0.126766i
$657$	− 8.51553i	− 0.332222i
$658$	− 7.87798i	− 0.307116i
$659$	−18.0060	−0.701413	−0.350706	−	0.936486i	$-0.614058\pi$
$659$	−18.0060	−0.701413	−0.350706	+	0.936486i	$0.614058\pi$
$660$	1.07873	0.0419895
$661$	− 3.51786i	− 0.136829i	−0.997657	−	0.0684145i	$-0.978206\pi$
$661$	− 3.51786i	− 0.136829i	0.997657	−	0.0684145i	$-0.0217940\pi$
$662$	−0.388232	−0.0150891
$663$	0	0
$664$	12.5446	0.486824
$665$	− 24.1190i	− 0.935296i
$666$	−8.25797	−0.319990
$667$	−30.3334	−1.17452
$668$	− 13.2128i	− 0.511217i
$669$	− 7.50935i	− 0.290328i
$670$	− 0.128292i	− 0.00495634i
$671$	13.9896i	0.540064i
$672$	−3.34838	−0.129166
$673$	26.0032	1.00235	0.501175	−	0.865346i	$-0.332901\pi$
$673$	26.0032	1.00235	0.501175	+	0.865346i	$0.332901\pi$
$674$	− 2.03224i	− 0.0782791i
$675$	−1.88505	−0.0725558
$676$	0	0
$677$	−28.5157	−1.09595	−0.547975	−	0.836495i	$-0.684601\pi$
$677$	−28.5157	−1.09595	−0.547975	+	0.836495i	$0.684601\pi$
$678$	− 1.64595i	− 0.0632122i
$679$	−23.5277	−0.902912
$680$	−2.08221	−0.0798490
$681$	− 3.06640i	− 0.117505i
$682$	− 2.31512i	− 0.0886505i
$683$	− 28.9493i	− 1.10771i	−0.832612	−	0.553857i	$-0.813155\pi$
$683$	− 28.9493i	− 1.10771i	0.832612	−	0.553857i	$-0.186845\pi$
$684$	− 39.8163i	− 1.52241i
$685$	13.0826	0.499861
$686$	2.35411	0.0898805
$687$	− 2.31084i	− 0.0881639i
$688$	−16.3408	−0.622987
$689$	0	0
$690$	0.660424	0.0251419
$691$	21.6566i	0.823854i	0.911217	+	0.411927i	$0.135144\pi$
$691$	21.6566i	0.823854i	−0.911217	+	0.411927i	$0.864856\pi$
$692$	−30.8611	−1.17316
$693$	17.1685	0.652176
$694$	− 1.89097i	− 0.0717801i
$695$	11.9762i	0.454283i
$696$	1.35671i	0.0514258i
$697$	1.78048i	0.0674405i
$698$	5.96312	0.225707
$699$	−0.137411	−0.00519737
$700$	− 6.51400i	− 0.246206i
$701$	−25.0376	−0.945656	−0.472828	−	0.881155i	$-0.656767\pi$
$701$	−25.0376	−0.945656	−0.472828	+	0.881155i	$0.656767\pi$
$702$	0	0
$703$	−74.8995	−2.82489
$704$	11.0140i	0.415107i
$705$	−2.74389	−0.103341
$706$	−3.53285	−0.132961
$707$	60.5030i	2.27545i
$708$	− 2.35379i	− 0.0884610i
$709$	− 25.6247i	− 0.962355i	−0.876623	−	0.481178i	$-0.840209\pi$
$709$	− 25.6247i	− 0.962355i	0.876623	−	0.481178i	$-0.159791\pi$
$710$	1.49340i	0.0560464i
$711$	−11.8794	−0.445511
$712$	−4.11279	−0.154133
$713$	37.0753i	1.38848i
$714$	0.573160	0.0214500
$715$	0	0
$716$	15.5709	0.581912
$717$	4.07352i	0.152129i
$718$	2.71160	0.101196
$719$	−14.8064	−0.552186	−0.276093	−	0.961131i	$-0.589040\pi$
$719$	−14.8064	−0.552186	−0.276093	+	0.961131i	$0.589040\pi$
$720$	− 10.3266i	− 0.384851i
$721$	− 34.6811i	− 1.29159i
$722$	8.64982i	0.321913i
$723$	6.11549i	0.227438i
$724$	−21.3629	−0.793945
$725$	−3.98380	−0.147955
$726$	0.687845i	0.0255283i
$727$	30.1688	1.11890	0.559449	−	0.828865i	$-0.311013\pi$
$727$	30.1688	1.11890	0.559449	+	0.828865i	$0.311013\pi$
$728$	0	0
$729$	−21.6391	−0.801447
$730$	0.797452i	0.0295150i
$731$	8.96098	0.331434
$732$	−4.91619	−0.181708
$733$	− 49.8997i	− 1.84309i	−0.388275	−	0.921544i	$-0.626929\pi$
$733$	− 49.8997i	− 1.84309i	0.388275	−	0.921544i	$-0.373071\pi$
$734$	− 6.86257i	− 0.253302i
$735$	1.41739i	0.0522812i
$736$	23.5894i	0.869516i
$737$	0.828276	0.0305100
$738$	0.716496	0.0263746
$739$	− 31.5796i	− 1.16167i	−0.814020	−	0.580836i	$-0.802726\pi$
$739$	− 31.5796i	− 1.16167i	0.814020	−	0.580836i	$-0.197274\pi$
$740$	−20.2287	−0.743620
$741$	0	0
$742$	10.9794	0.403066
$743$	− 1.60448i	− 0.0588625i	−0.999567	−	0.0294312i	$-0.990630\pi$
$743$	− 1.60448i	− 0.0588625i	0.999567	−	0.0294312i	$-0.00936961\pi$
$744$	1.65824	0.0607942
$745$	16.3052	0.597377
$746$	− 3.87258i	− 0.141785i
$747$	− 34.1172i	− 1.24828i
$748$	− 6.59551i	− 0.241156i
$749$	43.6168i	1.59372i
$750$	0.0867358	0.00316714
$751$	−10.7873	−0.393634	−0.196817	−	0.980440i	$-0.563060\pi$
$751$	−10.7873	−0.393634	−0.196817	+	0.980440i	$0.563060\pi$
$752$	− 30.5928i	− 1.11561i
$753$	0.131623	0.00479662
$754$	0	0
$755$	−8.75415	−0.318596
$756$	12.2792i	0.446592i
$757$	−6.40389	−0.232753	−0.116377	−	0.993205i	$-0.537128\pi$
$757$	−6.40389	−0.232753	−0.116377	+	0.993205i	$0.537128\pi$
$758$	−1.90326	−0.0691294
$759$	4.26383i	0.154767i
$760$	7.59987i	0.275676i
$761$	− 50.2655i	− 1.82212i	−0.412269	−	0.911062i	$-0.635264\pi$
$761$	− 50.2655i	− 1.82212i	0.412269	−	0.911062i	$-0.364736\pi$
$762$	0.857374i	0.0310594i
$763$	35.3286	1.27898
$764$	41.9044	1.51605
$765$	5.66293i	0.204744i
$766$	−1.27366	−0.0460191
$767$	0	0
$768$	−3.33308	−0.120272
$769$	4.10457i	0.148015i	0.997258	+	0.0740074i	$0.0235788\pi$
$769$	4.10457i	0.148015i	−0.997258	+	0.0740074i	$0.976421\pi$
$770$	−1.60777	−0.0579401
$771$	−0.791232	−0.0284955
$772$	− 43.3980i	− 1.56193i
$773$	− 1.17851i	− 0.0423882i	−0.999775	−	0.0211941i	$-0.993253\pi$
$773$	− 1.17851i	− 0.0423882i	0.999775	−	0.0211941i	$-0.00674680\pi$
$774$	− 3.60605i	− 0.129617i
$775$	4.86923i	0.174908i
$776$	7.41356	0.266131
$777$	11.3494	0.407157
$778$	− 2.53648i	− 0.0909373i
$779$	6.49860	0.232836
$780$	0	0
$781$	−9.64172	−0.345008
$782$	− 4.03793i	− 0.144396i
$783$	7.50968	0.268374
$784$	−15.8031	−0.564397
$785$	6.48821i	0.231574i
$786$	− 0.994900i	− 0.0354869i
$787$	− 33.4916i	− 1.19385i	−0.802298	−	0.596923i	$-0.796390\pi$
$787$	− 33.4916i	− 1.19385i	0.802298	−	0.596923i	$-0.203610\pi$
$788$	− 33.2776i	− 1.18546i
$789$	3.63056	0.129251
$790$	1.11246	0.0395797
$791$	− 64.1695i	− 2.28161i
$792$	−5.40976	−0.192227
$793$	0	0
$794$	−5.75675	−0.204299
$795$	− 3.82411i	− 0.135627i
$796$	−33.6921	−1.19418
$797$	24.9394	0.883400	0.441700	−	0.897163i	$-0.354376\pi$
$797$	24.9394	0.883400	0.441700	+	0.897163i	$0.354376\pi$
$798$	− 2.09198i	− 0.0740555i
$799$	16.7765i	0.593511i
$800$	3.09808i	0.109534i
$801$	11.1855i	0.395219i
$802$	4.94368	0.174567
$803$	−5.14851	−0.181687
$804$	0.291070i	0.0102652i
$805$	25.7475	0.907481
$806$	0	0
$807$	9.48906	0.334031
$808$	− 19.0644i	− 0.670684i
$809$	12.8221	0.450802	0.225401	−	0.974266i	$-0.427631\pi$
$809$	12.8221	0.450802	0.225401	+	0.974266i	$0.427631\pi$
$810$	2.19570	0.0771489
$811$	29.8424i	1.04791i	0.851746	+	0.523954i	$0.175544\pi$
$811$	29.8424i	1.04791i	−0.851746	+	0.523954i	$0.824456\pi$
$812$	25.9505i	0.910683i
$813$	− 4.72270i	− 0.165632i
$814$	4.99279i	0.174997i
$815$	3.84933	0.134836
$816$	2.22577	0.0779177
$817$	− 32.7068i	− 1.14427i
$818$	1.18356	0.0413822
$819$	0	0
$820$	1.75512	0.0612916
$821$	19.6918i	0.687249i	0.939107	+	0.343624i	$0.111655\pi$
$821$	19.6918i	0.687249i	−0.939107	+	0.343624i	$0.888345\pi$
$822$	1.13473	0.0395783
$823$	−41.9069	−1.46078	−0.730390	−	0.683030i	$-0.760662\pi$
$823$	−41.9069	−1.46078	−0.730390	+	0.683030i	$0.760662\pi$
$824$	10.9280i	0.380693i
$825$	0.559984i	0.0194961i
$826$	3.50817i	0.122065i
$827$	− 21.7734i	− 0.757134i	−0.925574	−	0.378567i	$-0.876417\pi$
$827$	− 21.7734i	− 0.757134i	0.925574	−	0.378567i	$-0.123583\pi$
$828$	42.5046	1.47714
$829$	5.87683	0.204111	0.102055	−	0.994779i	$-0.467458\pi$
$829$	5.87683	0.204111	0.102055	+	0.994779i	$0.467458\pi$
$830$	3.19497i	0.110899i
$831$	−0.622141	−0.0215818
$832$	0	0
$833$	8.66612	0.300263
$834$	1.03876i	0.0359695i
$835$	6.85894	0.237363
$836$	−24.0730	−0.832583
$837$	− 9.17876i	− 0.317265i
$838$	− 4.62841i	− 0.159886i
$839$	54.1116i	1.86814i	0.357092	+	0.934069i	$0.383768\pi$
$839$	54.1116i	1.86814i	−0.357092	+	0.934069i	$0.616232\pi$
$840$	− 1.15159i	− 0.0397338i
$841$	−13.1294	−0.452736
$842$	−0.347348	−0.0119704
$843$	5.92112i	0.203934i
$844$	12.2047	0.420103
$845$	0	0
$846$	6.75116	0.232110
$847$	26.8166i	0.921428i
$848$	42.6367	1.46415
$849$	4.18545	0.143644
$850$	− 0.530316i	− 0.0181897i
$851$	− 79.9567i	− 2.74088i
$852$	− 3.38826i	− 0.116080i
$853$	− 10.8001i	− 0.369787i	−0.982759	−	0.184893i	$-0.940806\pi$
$853$	− 10.8001i	− 0.369787i	0.982759	−	0.184893i	$-0.0591940\pi$
$854$	7.32725	0.250733
$855$	20.6692	0.706872
$856$	− 13.7436i	− 0.469747i
$857$	12.0558	0.411817	0.205908	−	0.978571i	$-0.433985\pi$
$857$	12.0558	0.411817	0.205908	+	0.978571i	$0.433985\pi$
$858$	0	0
$859$	−47.6819	−1.62688	−0.813442	−	0.581646i	$-0.802409\pi$
$859$	−47.6819	−1.62688	−0.813442	+	0.581646i	$0.802409\pi$
$860$	− 8.83336i	− 0.301215i
$861$	−0.984720	−0.0335592
$862$	8.92095	0.303849
$863$	− 46.2292i	− 1.57366i	−0.617169	−	0.786831i	$-0.711721\pi$
$863$	− 46.2292i	− 1.57366i	0.617169	−	0.786831i	$-0.288279\pi$
$864$	− 5.84005i	− 0.198682i
$865$	− 16.0204i	− 0.544711i
$866$	− 7.66962i	− 0.260624i
$867$	4.21293	0.143078
$868$	31.7182	1.07658
$869$	7.18230i	0.243643i
$870$	−0.345538	−0.0117148
$871$	0	0
$872$	−11.1320	−0.376977
$873$	− 20.1625i	− 0.682397i
$874$	−14.7381	−0.498523
$875$	3.38151	0.114316
$876$	− 1.80927i	− 0.0611296i
$877$	− 25.2281i	− 0.851893i	−0.904748	−	0.425947i	$-0.859941\pi$
$877$	− 25.2281i	− 0.851893i	0.904748	−	0.425947i	$-0.140059\pi$
$878$	7.12684i	0.240519i
$879$	− 0.385947i	− 0.0130177i
$880$	−6.24352	−0.210469
$881$	12.5086	0.421425	0.210712	−	0.977548i	$-0.432422\pi$
$881$	12.5086	0.421425	0.210712	+	0.977548i	$0.432422\pi$
$882$	− 3.48740i	− 0.117427i
$883$	11.2289	0.377881	0.188941	−	0.981989i	$-0.439495\pi$
$883$	11.2289	0.377881	0.188941	+	0.981989i	$0.439495\pi$
$884$	0	0
$885$	1.22189	0.0410733
$886$	3.81218i	0.128073i
$887$	−54.5383	−1.83122	−0.915609	−	0.402069i	$-0.868291\pi$
$887$	−54.5383	−1.83122	−0.915609	+	0.402069i	$0.868291\pi$
$888$	−3.57617	−0.120009
$889$	33.4259i	1.12107i
$890$	− 1.04748i	− 0.0351117i
$891$	14.1759i	0.474909i
$892$	45.2594i	1.51540i
$893$	61.2328	2.04908
$894$	1.41425	0.0472995
$895$	8.08309i	0.270188i
$896$	26.7211	0.892690
$897$	0	0
$898$	1.21007	0.0403805
$899$	− 19.3980i	− 0.646960i
$900$	5.58228	0.186076
$901$	−23.3811	−0.778939
$902$	− 0.433196i	− 0.0144238i
$903$	4.95600i	0.164925i
$904$	20.2197i	0.672498i
$905$	− 11.0898i	− 0.368637i
$906$	−0.759298	−0.0252260
$907$	−28.9083	−0.959883	−0.479942	−	0.877300i	$-0.659342\pi$
$907$	−28.9083	−0.959883	−0.479942	+	0.877300i	$0.659342\pi$
$908$	18.4814i	0.613327i
$909$	−51.8491	−1.71973
$910$	0	0
$911$	−7.04371	−0.233369	−0.116684	−	0.993169i	$-0.537227\pi$
$911$	−7.04371	−0.233369	−0.116684	+	0.993169i	$0.537227\pi$
$912$	− 8.12388i	− 0.269009i
$913$	−20.6274	−0.682666
$914$	4.45456	0.147344
$915$	− 2.55207i	− 0.0843688i
$916$	13.9276i	0.460180i
$917$	− 38.7875i	− 1.28088i
$918$	0.999674i	0.0329942i
$919$	−17.3638	−0.572780	−0.286390	−	0.958113i	$-0.592455\pi$
$919$	−17.3638	−0.572780	−0.286390	+	0.958113i	$0.592455\pi$
$920$	−8.11301	−0.267478
$921$	− 7.00840i	− 0.230935i
$922$	5.57551	0.183620
$923$	0	0
$924$	3.64774	0.120002
$925$	− 10.5010i	− 0.345271i
$926$	−0.429745	−0.0141223
$927$	29.7205	0.976150
$928$	− 12.3421i	− 0.405150i
$929$	− 30.9381i	− 1.01504i	−0.861639	−	0.507522i	$-0.830561\pi$
$929$	− 30.9381i	− 1.01504i	0.861639	−	0.507522i	$-0.169439\pi$
$930$	0.422337i	0.0138490i
$931$	− 31.6306i	− 1.03665i
$932$	0.828186	0.0271281
$933$	−4.02610	−0.131808
$934$	1.39561i	0.0456659i
$935$	3.42382	0.111971
$936$	0	0
$937$	30.5009	0.996422	0.498211	−	0.867056i	$-0.333990\pi$
$937$	30.5009	0.996422	0.498211	+	0.867056i	$0.333990\pi$
$938$	− 0.433820i	− 0.0141647i
$939$	−8.57431	−0.279812
$940$	16.5376	0.539397
$941$	32.0423i	1.04455i	0.852777	+	0.522275i	$0.174917\pi$
$941$	32.0423i	1.04455i	−0.852777	+	0.522275i	$0.825083\pi$
$942$	0.562761i	0.0183357i
$943$	6.93738i	0.225912i
$944$	13.6234i	0.443404i
$945$	−6.37434	−0.207357
$946$	−2.18023	−0.0708854
$947$	− 8.63395i	− 0.280566i	−0.990111	−	0.140283i	$-0.955199\pi$
$947$	− 8.63395i	− 0.280566i	0.990111	−	0.140283i	$-0.0448012\pi$
$948$	−2.52398	−0.0819750
$949$	0	0
$950$	−1.93560	−0.0627993
$951$	− 5.47438i	− 0.177519i
$952$	−7.04102	−0.228201
$953$	32.4260	1.05038	0.525191	−	0.850984i	$-0.323994\pi$
$953$	32.4260	1.05038	0.525191	+	0.850984i	$0.323994\pi$
$954$	9.40897i	0.304627i
$955$	21.7532i	0.703917i
$956$	− 24.5514i	− 0.794049i
$957$	− 2.23086i	− 0.0721136i
$958$	−6.04930	−0.195444
$959$	44.2390	1.42855
$960$	− 2.00924i	− 0.0648479i
$961$	7.29060	0.235181
$962$	0	0
$963$	−37.3782	−1.20449
$964$	− 36.8585i	− 1.18713i
$965$	22.5285	0.725219
$966$	2.23323	0.0718531
$967$	27.0744i	0.870656i	0.900272	+	0.435328i	$0.143368\pi$
$967$	27.0744i	0.870656i	−0.900272	+	0.435328i	$0.856632\pi$
$968$	− 8.44986i	− 0.271589i
$969$	4.45498i	0.143115i
$970$	1.88815i	0.0606249i
$971$	31.8039	1.02063	0.510317	−	0.859986i	$-0.329528\pi$
$971$	31.8039	1.02063	0.510317	+	0.859986i	$0.329528\pi$
$972$	−15.8755	−0.509207
$973$	40.4977i	1.29830i
$974$	−6.35517	−0.203633
$975$	0	0
$976$	28.4542	0.910796
$977$	31.3672i	1.00353i	0.865005	+	0.501763i	$0.167315\pi$
$977$	31.3672i	1.00353i	−0.865005	+	0.501763i	$0.832685\pi$
$978$	0.333875	0.0106761
$979$	6.76276	0.216139
$980$	− 8.54270i	− 0.272886i
$981$	30.2754i	0.966620i
$982$	0.922103i	0.0294255i
$983$	35.5044i	1.13241i	0.824263	+	0.566207i	$0.191590\pi$
$983$	35.5044i	1.13241i	−0.824263	+	0.566207i	$0.808410\pi$
$984$	0.310284	0.00989149
$985$	17.2749	0.550424
$986$	2.11267i	0.0672811i
$987$	−9.27849	−0.295338
$988$	0	0
$989$	34.9151	1.11024
$990$	− 1.37781i	− 0.0437896i
$991$	−41.0638	−1.30443	−0.652217	−	0.758032i	$-0.726161\pi$
$991$	−41.0638	−1.30443	−0.652217	+	0.758032i	$0.726161\pi$
$992$	−15.0853	−0.478957
$993$	0.457250i	0.0145104i
$994$	5.04997i	0.160175i
$995$	− 17.4901i	− 0.554472i
$996$	− 7.24879i	− 0.229687i
$997$	−44.7904	−1.41853	−0.709264	−	0.704943i	$-0.750972\pi$
$997$	−44.7904	−1.41853	−0.709264	+	0.704943i	$0.750972\pi$
$998$	−1.32352	−0.0418954
$999$	19.7949i	0.626284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.c.h.506.8		18
13.2	odd	12		845.2.e.o.191.6		18
13.3	even	3		845.2.m.j.316.11		36
13.4	even	6		845.2.m.j.361.11		36
13.5	odd	4		845.2.a.o.1.4	yes	9
13.6	odd	12		845.2.e.o.146.6		18
13.7	odd	12		845.2.e.p.146.4		18
13.8	odd	4		845.2.a.n.1.6	✓	9
13.9	even	3		845.2.m.j.361.8		36
13.10	even	6		845.2.m.j.316.8		36
13.11	odd	12		845.2.e.p.191.4		18
13.12	even	2	inner	845.2.c.h.506.11		18
39.5	even	4		7605.2.a.cp.1.6		9
39.8	even	4		7605.2.a.cs.1.4		9
65.34	odd	4		4225.2.a.bt.1.4		9
65.44	odd	4		4225.2.a.bs.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.6	✓	9	13.8	odd	4
845.2.a.o.1.4	yes	9	13.5	odd	4
845.2.c.h.506.8		18	1.1	even	1	trivial
845.2.c.h.506.11		18	13.12	even	2	inner
845.2.e.o.146.6		18	13.6	odd	12
845.2.e.o.191.6		18	13.2	odd	12
845.2.e.p.146.4		18	13.7	odd	12
845.2.e.p.191.4		18	13.11	odd	12
845.2.m.j.316.8		36	13.10	even	6
845.2.m.j.316.11		36	13.3	even	3
845.2.m.j.361.8		36	13.9	even	3
845.2.m.j.361.11		36	13.4	even	6
4225.2.a.bs.1.6		9	65.44	odd	4
4225.2.a.bt.1.4		9	65.34	odd	4
7605.2.a.cp.1.6		9	39.5	even	4
7605.2.a.cs.1.4		9	39.8	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)

\(f(q)\)	\(=\)	\(q-0.271374i q^{2} -0.319618 q^{3} +1.92636 q^{4} +1.00000i q^{5} +0.0867358i q^{6} +3.38151i q^{7} -1.06551i q^{8} -2.89784 q^{9} +O(q^{10})\)	\(q-0.271374i q^{2} -0.319618 q^{3} +1.92636 q^{4} +1.00000i q^{5} +0.0867358i q^{6} +3.38151i q^{7} -1.06551i q^{8} -2.89784 q^{9} +0.271374 q^{10} +1.75204i q^{11} -0.615697 q^{12} +0.917654 q^{14} -0.319618i q^{15} +3.56356 q^{16} -1.95419 q^{17} +0.786399i q^{18} +7.13261i q^{19} +1.92636i q^{20} -1.08079i q^{21} +0.475459 q^{22} -7.61420 q^{23} +0.340556i q^{24} -1.00000 q^{25} +1.88505 q^{27} +6.51400i q^{28} +3.98380 q^{29} -0.0867358 q^{30} -4.86923i q^{31} -3.09808i q^{32} -0.559984i q^{33} +0.530316i q^{34} -3.38151 q^{35} -5.58228 q^{36} +10.5010i q^{37} +1.93560 q^{38} +1.06551 q^{40} -0.911110i q^{41} -0.293298 q^{42} -4.58553 q^{43} +3.37506i q^{44} -2.89784i q^{45} +2.06629i q^{46} -8.58491i q^{47} -1.13898 q^{48} -4.43464 q^{49} +0.271374i q^{50} +0.624593 q^{51} +11.9646 q^{53} -0.511554i q^{54} -1.75204 q^{55} +3.60304 q^{56} -2.27971i q^{57} -1.08110i q^{58} +3.82297i q^{59} -0.615697i q^{60} +7.98476 q^{61} -1.32138 q^{62} -9.79910i q^{63} +6.28638 q^{64} -0.151965 q^{66} -0.472749i q^{67} -3.76446 q^{68} +2.43363 q^{69} +0.917654i q^{70} +5.50312i q^{71} +3.08768i q^{72} +2.93857i q^{73} +2.84969 q^{74} +0.319618 q^{75} +13.7400i q^{76} -5.92456 q^{77} +4.09938 q^{79} +3.56356i q^{80} +8.09104 q^{81} -0.247252 q^{82} +11.7733i q^{83} -2.08199i q^{84} -1.95419i q^{85} +1.24439i q^{86} -1.27329 q^{87} +1.86682 q^{88} -3.85992i q^{89} -0.786399 q^{90} -14.6677 q^{92} +1.55629i q^{93} -2.32972 q^{94} -7.13261 q^{95} +0.990200i q^{96} +6.95775i q^{97} +1.20345i q^{98} -5.07715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9}+O(q^{10}) \) 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40} - 22 q^{42} - 78 q^{43} - 6 q^{48} - 32 q^{49} - 86 q^{51} - 16 q^{53} - 18 q^{55} + 58 q^{56} - 6 q^{61} + 20 q^{62} - 68 q^{64} - 98 q^{66} - 40 q^{68} + 26 q^{69} - 30 q^{74} - 14 q^{75} + 8 q^{77} + 78 q^{79} + 58 q^{81} + 8 q^{82} + 32 q^{87} - 84 q^{88} + 20 q^{90} - 54 q^{92} + 32 q^{94} + 8 q^{95}+O(q^{100}) \) 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * q^95

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