LMFDB - Embedded newform 58.2.b.a.57.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,2,Mod(57,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	58.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.463132331723$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			57.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	58.57
Dual form			58.2.b.a.57.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000i q^{8} +2.00000 q^{9} -1.00000i q^{10} +5.00000i q^{11} +1.00000i q^{12} -1.00000 q^{13} +2.00000i q^{14} -1.00000i q^{15} +1.00000 q^{16} +2.00000i q^{17} -2.00000i q^{18} -4.00000i q^{19} -1.00000 q^{20} +2.00000i q^{21} +5.00000 q^{22} -6.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +1.00000i q^{26} -5.00000i q^{27} +2.00000 q^{28} +(5.00000 - 2.00000i) q^{29} -1.00000 q^{30} -5.00000i q^{31} -1.00000i q^{32} +5.00000 q^{33} +2.00000 q^{34} -2.00000 q^{35} -2.00000 q^{36} -8.00000i q^{37} -4.00000 q^{38} +1.00000i q^{39} +1.00000i q^{40} +10.0000i q^{41} +2.00000 q^{42} +9.00000i q^{43} -5.00000i q^{44} +2.00000 q^{45} +6.00000i q^{46} -3.00000i q^{47} -1.00000i q^{48} -3.00000 q^{49} +4.00000i q^{50} +2.00000 q^{51} +1.00000 q^{52} -1.00000 q^{53} -5.00000 q^{54} +5.00000i q^{55} -2.00000i q^{56} -4.00000 q^{57} +(-2.00000 - 5.00000i) q^{58} +10.0000 q^{59} +1.00000i q^{60} +10.0000i q^{61} -5.00000 q^{62} -4.00000 q^{63} -1.00000 q^{64} -1.00000 q^{65} -5.00000i q^{66} +8.00000 q^{67} -2.00000i q^{68} +6.00000i q^{69} +2.00000i q^{70} -8.00000 q^{71} +2.00000i q^{72} -16.0000i q^{73} -8.00000 q^{74} +4.00000i q^{75} +4.00000i q^{76} -10.0000i q^{77} +1.00000 q^{78} +1.00000i q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +14.0000 q^{83} -2.00000i q^{84} +2.00000i q^{85} +9.00000 q^{86} +(-2.00000 - 5.00000i) q^{87} -5.00000 q^{88} -14.0000i q^{89} -2.00000i q^{90} +2.00000 q^{91} +6.00000 q^{92} -5.00000 q^{93} -3.00000 q^{94} -4.00000i q^{95} -1.00000 q^{96} +2.00000i q^{97} +3.00000i q^{98} +10.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{9} - 2 q^{13} + 2 q^{16} - 2 q^{20} + 10 q^{22} - 12 q^{23} + 2 q^{24} - 8 q^{25} + 4 q^{28} + 10 q^{29} - 2 q^{30} + 10 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36}+ \cdots - 2 q^{96}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^9 - 2 * q^13 + 2 * q^16 - 2 * q^20 + 10 * q^22 - 12 * q^23 + 2 * q^24 - 8 * q^25 + 4 * q^28 + 10 * q^29 - 2 * q^30 + 10 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 8 * q^38 + 4 * q^42 + 4 * q^45 - 6 * q^49 + 4 * q^51 + 2 * q^52 - 2 * q^53 - 10 * q^54 - 8 * q^57 - 4 * q^58 + 20 * q^59 - 10 * q^62 - 8 * q^63 - 2 * q^64 - 2 * q^65 + 16 * q^67 - 16 * q^71 - 16 * q^74 + 2 * q^78 + 2 * q^80 + 2 * q^81 + 20 * q^82 + 28 * q^83 + 18 * q^86 - 4 * q^87 - 10 * q^88 + 4 * q^91 + 12 * q^92 - 10 * q^93 - 6 * q^94 - 2 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i	−0.957427	−	0.288675i	$-0.906785\pi$
$3$		−	1.00000i		−	0.577350i	0.957427	−	0.288675i	$-0.0932147\pi$
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−1.00000			−0.408248
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$			1.00000i			0.353553i
$9$	2.00000			0.666667
$10$		−	1.00000i		−	0.316228i
$11$			5.00000i			1.50756i	0.657129	+	0.753778i	$0.271771\pi$
$11$			5.00000i			1.50756i	−0.657129	+	0.753778i	$0.728229\pi$
$12$			1.00000i			0.288675i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$			2.00000i			0.534522i
$15$		−	1.00000i		−	0.258199i
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	2.00000i		−	0.471405i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−1.00000			−0.223607
$21$			2.00000i			0.436436i
$22$	5.00000			1.06600
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	1.00000			0.204124
$25$	−4.00000			−0.800000
$26$			1.00000i			0.196116i
$27$		−	5.00000i		−	0.962250i
$28$	2.00000			0.377964
$29$	5.00000	−	2.00000i	0.928477	−	0.371391i
$29$	5.00000	−	2.00000i	0.928477	−	0.371391i
$30$	−1.00000			−0.182574
$31$		−	5.00000i		−	0.898027i	−0.893525	−	0.449013i	$-0.851776\pi$
$31$		−	5.00000i		−	0.898027i	0.893525	−	0.449013i	$-0.148224\pi$
$32$		−	1.00000i		−	0.176777i
$33$	5.00000			0.870388
$34$	2.00000			0.342997
$35$	−2.00000			−0.338062
$36$	−2.00000			−0.333333
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	−4.00000			−0.648886
$39$			1.00000i			0.160128i
$40$			1.00000i			0.158114i
$41$			10.0000i			1.56174i	0.624695	+	0.780869i	$0.285223\pi$
$41$			10.0000i			1.56174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$	2.00000			0.308607
$43$			9.00000i			1.37249i	0.727372	+	0.686244i	$0.240742\pi$
$43$			9.00000i			1.37249i	−0.727372	+	0.686244i	$0.759258\pi$
$44$		−	5.00000i		−	0.753778i
$45$	2.00000			0.298142
$46$			6.00000i			0.884652i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.00000			−0.428571
$50$			4.00000i			0.565685i
$51$	2.00000			0.280056
$52$	1.00000			0.138675
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$	−5.00000			−0.680414
$55$			5.00000i			0.674200i
$56$		−	2.00000i		−	0.267261i
$57$	−4.00000			−0.529813
$58$	−2.00000	−	5.00000i	−0.262613	−	0.656532i
$59$	10.0000			1.30189			0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000			1.30189			0.650945	+	0.759125i	$0.274373\pi$
$60$			1.00000i			0.129099i
$61$			10.0000i			1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$61$			10.0000i			1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$	−5.00000			−0.635001
$63$	−4.00000			−0.503953
$64$	−1.00000			−0.125000
$65$	−1.00000			−0.124035
$66$		−	5.00000i		−	0.615457i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$		−	2.00000i		−	0.242536i
$69$			6.00000i			0.722315i
$70$			2.00000i			0.239046i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$			2.00000i			0.235702i
$73$		−	16.0000i		−	1.87266i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$		−	16.0000i		−	1.87266i	0.351123	−	0.936329i	$-0.385800\pi$
$74$	−8.00000			−0.929981
$75$			4.00000i			0.461880i
$76$			4.00000i			0.458831i
$77$		−	10.0000i		−	1.13961i
$78$	1.00000			0.113228
$79$			1.00000i			0.112509i	0.998416	+	0.0562544i	$0.0179158\pi$
$79$			1.00000i			0.112509i	−0.998416	+	0.0562544i	$0.982084\pi$
$80$	1.00000			0.111803
$81$	1.00000			0.111111
$82$	10.0000			1.10432
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$		−	2.00000i		−	0.218218i
$85$			2.00000i			0.216930i
$86$	9.00000			0.970495
$87$	−2.00000	−	5.00000i	−0.214423	−	0.536056i
$88$	−5.00000			−0.533002
$89$		−	14.0000i		−	1.48400i	−0.670402	−	0.741999i	$-0.733878\pi$
$89$		−	14.0000i		−	1.48400i	0.670402	−	0.741999i	$-0.266122\pi$
$90$		−	2.00000i		−	0.210819i
$91$	2.00000			0.209657
$92$	6.00000			0.625543
$93$	−5.00000			−0.518476
$94$	−3.00000			−0.309426
$95$		−	4.00000i		−	0.410391i
$96$	−1.00000			−0.102062
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$			3.00000i			0.303046i
$99$			10.0000i			1.00504i
$100$	4.00000			0.400000
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		−	2.00000i		−	0.198030i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		−	1.00000i		−	0.0980581i
$105$			2.00000i			0.195180i
$106$			1.00000i			0.0971286i
$107$	−2.00000			−0.193347			−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000			−0.193347			−0.0966736	+	0.995316i	$0.530820\pi$
$108$			5.00000i			0.481125i
$109$	−15.0000			−1.43674			−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000			−1.43674			−0.718370	+	0.695662i	$0.755111\pi$
$110$	5.00000			0.476731
$111$	−8.00000			−0.759326
$112$	−2.00000			−0.188982
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$			4.00000i			0.374634i
$115$	−6.00000			−0.559503
$116$	−5.00000	+	2.00000i	−0.464238	+	0.185695i
$117$	−2.00000			−0.184900
$118$		−	10.0000i		−	0.920575i
$119$		−	4.00000i		−	0.366679i
$120$	1.00000			0.0912871
$121$	−14.0000			−1.27273
$122$	10.0000			0.905357
$123$	10.0000			0.901670
$124$			5.00000i			0.449013i
$125$	−9.00000			−0.804984
$126$			4.00000i			0.356348i
$127$			12.0000i			1.06483i	0.846484	+	0.532414i	$0.178715\pi$
$127$			12.0000i			1.06483i	−0.846484	+	0.532414i	$0.821285\pi$
$128$			1.00000i			0.0883883i
$129$	9.00000			0.792406
$130$			1.00000i			0.0877058i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	−5.00000			−0.435194
$133$			8.00000i			0.693688i
$134$		−	8.00000i		−	0.691095i
$135$		−	5.00000i		−	0.430331i
$136$	−2.00000			−0.171499
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$	6.00000			0.510754
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$	2.00000			0.169031
$141$	−3.00000			−0.252646
$142$			8.00000i			0.671345i
$143$		−	5.00000i		−	0.418121i
$144$	2.00000			0.166667
$145$	5.00000	−	2.00000i	0.415227	−	0.166091i
$146$	−16.0000			−1.32417
$147$			3.00000i			0.247436i
$148$			8.00000i			0.657596i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$	4.00000			0.326599
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	4.00000			0.324443
$153$			4.00000i			0.323381i
$154$	−10.0000			−0.805823
$155$		−	5.00000i		−	0.401610i
$156$		−	1.00000i		−	0.0800641i
$157$		−	18.0000i		−	1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$		−	18.0000i		−	1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$	1.00000			0.0795557
$159$			1.00000i			0.0793052i
$160$		−	1.00000i		−	0.0790569i
$161$	12.0000			0.945732
$162$		−	1.00000i		−	0.0785674i
$163$		−	1.00000i		−	0.0783260i	−0.999233	−	0.0391630i	$-0.987531\pi$
$163$		−	1.00000i		−	0.0783260i	0.999233	−	0.0391630i	$-0.0124692\pi$
$164$		−	10.0000i		−	0.780869i
$165$	5.00000			0.389249
$166$		−	14.0000i		−	1.08661i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$	−2.00000			−0.154303
$169$	−12.0000			−0.923077
$170$	2.00000			0.153393
$171$		−	8.00000i		−	0.611775i
$172$		−	9.00000i		−	0.686244i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	−5.00000	+	2.00000i	−0.379049	+	0.151620i
$175$	8.00000			0.604743
$176$			5.00000i			0.376889i
$177$		−	10.0000i		−	0.751646i
$178$	−14.0000			−1.04934
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−2.00000			−0.149071
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$		−	2.00000i		−	0.148250i
$183$	10.0000			0.739221
$184$		−	6.00000i		−	0.442326i
$185$		−	8.00000i		−	0.588172i
$186$			5.00000i			0.366618i
$187$	−10.0000			−0.731272
$188$			3.00000i			0.218797i
$189$			10.0000i			0.727393i
$190$	−4.00000			−0.290191
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$			1.00000i			0.0721688i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	2.00000			0.143592
$195$			1.00000i			0.0716115i
$196$	3.00000			0.214286
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	10.0000			0.710669
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		−	4.00000i		−	0.282843i
$201$		−	8.00000i		−	0.564276i
$202$		0			0
$203$	−10.0000	+	4.00000i	−0.701862	+	0.280745i
$204$	−2.00000			−0.140028
$205$			10.0000i			0.698430i
$206$		−	4.00000i		−	0.278693i
$207$	−12.0000			−0.834058
$208$	−1.00000			−0.0693375
$209$	20.0000			1.38343
$210$	2.00000			0.138013
$211$		−	5.00000i		−	0.344214i	−0.985078	−	0.172107i	$-0.944942\pi$
$211$		−	5.00000i		−	0.344214i	0.985078	−	0.172107i	$-0.0550575\pi$
$212$	1.00000			0.0686803
$213$			8.00000i			0.548151i
$214$			2.00000i			0.136717i
$215$			9.00000i			0.613795i
$216$	5.00000			0.340207
$217$			10.0000i			0.678844i
$218$			15.0000i			1.01593i
$219$	−16.0000			−1.08118
$220$		−	5.00000i		−	0.337100i
$221$		−	2.00000i		−	0.134535i
$222$			8.00000i			0.536925i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$			2.00000i			0.133631i
$225$	−8.00000			−0.533333
$226$	4.00000			0.266076
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$	4.00000			0.264906
$229$			6.00000i			0.396491i	0.980152	+	0.198246i	$0.0635244\pi$
$229$			6.00000i			0.396491i	−0.980152	+	0.198246i	$0.936476\pi$
$230$			6.00000i			0.395628i
$231$	−10.0000			−0.657952
$232$	2.00000	+	5.00000i	0.131306	+	0.328266i
$233$	−1.00000			−0.0655122			−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000			−0.0655122			−0.0327561	+	0.999463i	$0.510428\pi$
$234$			2.00000i			0.130744i
$235$		−	3.00000i		−	0.195698i
$236$	−10.0000			−0.650945
$237$	1.00000			0.0649570
$238$	−4.00000			−0.259281
$239$	−30.0000			−1.94054			−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−30.0000			−1.94054			−0.970269	+	0.242028i	$0.922188\pi$
$240$		−	1.00000i		−	0.0645497i
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$			14.0000i			0.899954i
$243$		−	16.0000i		−	1.02640i
$244$		−	10.0000i		−	0.640184i
$245$	−3.00000			−0.191663
$246$		−	10.0000i		−	0.637577i
$247$			4.00000i			0.254514i
$248$	5.00000			0.317500
$249$		−	14.0000i		−	0.887214i
$250$			9.00000i			0.569210i
$251$			15.0000i			0.946792i	0.880850	+	0.473396i	$0.156972\pi$
$251$			15.0000i			0.946792i	−0.880850	+	0.473396i	$0.843028\pi$
$252$	4.00000			0.251976
$253$		−	30.0000i		−	1.88608i
$254$	12.0000			0.752947
$255$	2.00000			0.125245
$256$	1.00000			0.0625000
$257$	−7.00000			−0.436648			−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000			−0.436648			−0.218324	+	0.975876i	$0.570059\pi$
$258$		−	9.00000i		−	0.560316i
$259$			16.0000i			0.994192i
$260$	1.00000			0.0620174
$261$	10.0000	−	4.00000i	0.618984	−	0.247594i
$262$		0			0
$263$			19.0000i			1.17159i	0.810459	+	0.585795i	$0.199218\pi$
$263$			19.0000i			1.17159i	−0.810459	+	0.585795i	$0.800782\pi$
$264$			5.00000i			0.307729i
$265$	−1.00000			−0.0614295
$266$	8.00000			0.490511
$267$	−14.0000			−0.856786
$268$	−8.00000			−0.488678
$269$			26.0000i			1.58525i	0.609711	+	0.792624i	$0.291286\pi$
$269$			26.0000i			1.58525i	−0.609711	+	0.792624i	$0.708714\pi$
$270$	−5.00000			−0.304290
$271$		−	25.0000i		−	1.51864i	−0.650716	−	0.759321i	$-0.725531\pi$
$271$		−	25.0000i		−	1.51864i	0.650716	−	0.759321i	$-0.274469\pi$
$272$			2.00000i			0.121268i
$273$		−	2.00000i		−	0.121046i
$274$	12.0000			0.724947
$275$		−	20.0000i		−	1.20605i
$276$		−	6.00000i		−	0.361158i
$277$	18.0000			1.08152			0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000			1.08152			0.540758	+	0.841178i	$0.318138\pi$
$278$		−	10.0000i		−	0.599760i
$279$		−	10.0000i		−	0.598684i
$280$		−	2.00000i		−	0.119523i
$281$	−13.0000			−0.775515			−0.387757	−	0.921761i	$-0.626750\pi$
$281$	−13.0000			−0.775515			−0.387757	+	0.921761i	$0.626750\pi$
$282$			3.00000i			0.178647i
$283$	−6.00000			−0.356663			−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000			−0.356663			−0.178331	+	0.983970i	$0.557070\pi$
$284$	8.00000			0.474713
$285$	−4.00000			−0.236940
$286$	−5.00000			−0.295656
$287$		−	20.0000i		−	1.18056i
$288$		−	2.00000i		−	0.117851i
$289$	13.0000			0.764706
$290$	−2.00000	−	5.00000i	−0.117444	−	0.293610i
$291$	2.00000			0.117242
$292$			16.0000i			0.936329i
$293$			4.00000i			0.233682i	0.993151	+	0.116841i	$0.0372769\pi$
$293$			4.00000i			0.233682i	−0.993151	+	0.116841i	$0.962723\pi$
$294$	3.00000			0.174964
$295$	10.0000			0.582223
$296$	8.00000			0.464991
$297$	25.0000			1.45065
$298$		−	15.0000i		−	0.868927i
$299$	6.00000			0.346989
$300$		−	4.00000i		−	0.230940i
$301$		−	18.0000i		−	1.03750i
$302$		−	2.00000i		−	0.115087i
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$			10.0000i			0.572598i
$306$	4.00000			0.228665
$307$		−	3.00000i		−	0.171219i	−0.996329	−	0.0856095i	$-0.972716\pi$
$307$		−	3.00000i		−	0.171219i	0.996329	−	0.0856095i	$-0.0272838\pi$
$308$			10.0000i			0.569803i
$309$		−	4.00000i		−	0.227552i
$310$	−5.00000			−0.283981
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	−1.00000			−0.0566139
$313$	−31.0000			−1.75222			−0.876112	−	0.482108i	$-0.839871\pi$
$313$	−31.0000			−1.75222			−0.876112	+	0.482108i	$0.839871\pi$
$314$	−18.0000			−1.01580
$315$	−4.00000			−0.225374
$316$		−	1.00000i		−	0.0562544i
$317$			22.0000i			1.23564i	0.786318	+	0.617822i	$0.211985\pi$
$317$			22.0000i			1.23564i	−0.786318	+	0.617822i	$0.788015\pi$
$318$	1.00000			0.0560772
$319$	10.0000	+	25.0000i	0.559893	+	1.39973i
$320$	−1.00000			−0.0559017
$321$			2.00000i			0.111629i
$322$		−	12.0000i		−	0.668734i
$323$	8.00000			0.445132
$324$	−1.00000			−0.0555556
$325$	4.00000			0.221880
$326$	−1.00000			−0.0553849
$327$			15.0000i			0.829502i
$328$	−10.0000			−0.552158
$329$			6.00000i			0.330791i
$330$		−	5.00000i		−	0.275241i
$331$		−	25.0000i		−	1.37412i	−0.726599	−	0.687062i	$-0.758900\pi$
$331$		−	25.0000i		−	1.37412i	0.726599	−	0.687062i	$-0.241100\pi$
$332$	−14.0000			−0.768350
$333$		−	16.0000i		−	0.876795i
$334$			12.0000i			0.656611i
$335$	8.00000			0.437087
$336$			2.00000i			0.109109i
$337$			22.0000i			1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$			22.0000i			1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$			12.0000i			0.652714i
$339$	4.00000			0.217250
$340$		−	2.00000i		−	0.108465i
$341$	25.0000			1.35383
$342$	−8.00000			−0.432590
$343$	20.0000			1.07990
$344$	−9.00000			−0.485247
$345$			6.00000i			0.323029i
$346$			6.00000i			0.322562i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$	2.00000	+	5.00000i	0.107211	+	0.268028i
$349$	−25.0000			−1.33822			−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000			−1.33822			−0.669110	+	0.743164i	$0.733324\pi$
$350$		−	8.00000i		−	0.427618i
$351$			5.00000i			0.266880i
$352$	5.00000			0.266501
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$	−10.0000			−0.531494
$355$	−8.00000			−0.424596
$356$			14.0000i			0.741999i
$357$	−4.00000			−0.211702
$358$		0			0
$359$		−	19.0000i		−	1.00278i	−0.865221	−	0.501391i	$-0.832822\pi$
$359$		−	19.0000i		−	1.00278i	0.865221	−	0.501391i	$-0.167178\pi$
$360$			2.00000i			0.105409i
$361$	3.00000			0.157895
$362$		−	17.0000i		−	0.893500i
$363$			14.0000i			0.734809i
$364$	−2.00000			−0.104828
$365$		−	16.0000i		−	0.837478i
$366$		−	10.0000i		−	0.522708i
$367$			32.0000i			1.67039i	0.549957	+	0.835193i	$0.314644\pi$
$367$			32.0000i			1.67039i	−0.549957	+	0.835193i	$0.685356\pi$
$368$	−6.00000			−0.312772
$369$			20.0000i			1.04116i
$370$	−8.00000			−0.415900
$371$	2.00000			0.103835
$372$	5.00000			0.259238
$373$	−11.0000			−0.569558			−0.284779	−	0.958593i	$-0.591920\pi$
$373$	−11.0000			−0.569558			−0.284779	+	0.958593i	$0.591920\pi$
$374$			10.0000i			0.517088i
$375$			9.00000i			0.464758i
$376$	3.00000			0.154713
$377$	−5.00000	+	2.00000i	−0.257513	+	0.103005i
$378$	10.0000			0.514344
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$			4.00000i			0.205196i
$381$	12.0000			0.614779
$382$		0			0
$383$	−6.00000			−0.306586			−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000			−0.306586			−0.153293	+	0.988181i	$0.548988\pi$
$384$	1.00000			0.0510310
$385$		−	10.0000i		−	0.509647i
$386$	14.0000			0.712581
$387$			18.0000i			0.914991i
$388$		−	2.00000i		−	0.101535i
$389$		−	24.0000i		−	1.21685i	−0.793612	−	0.608424i	$-0.791802\pi$
$389$		−	24.0000i		−	1.21685i	0.793612	−	0.608424i	$-0.208198\pi$
$390$	1.00000			0.0506370
$391$		−	12.0000i		−	0.606866i
$392$		−	3.00000i		−	0.151523i
$393$		0			0
$394$			2.00000i			0.100759i
$395$			1.00000i			0.0503155i
$396$		−	10.0000i		−	0.502519i
$397$	−27.0000			−1.35509			−0.677546	−	0.735481i	$-0.736956\pi$
$397$	−27.0000			−1.35509			−0.677546	+	0.735481i	$0.736956\pi$
$398$		−	10.0000i		−	0.501255i
$399$	8.00000			0.400501
$400$	−4.00000			−0.200000
$401$	7.00000			0.349563			0.174782	−	0.984607i	$-0.444078\pi$
$401$	7.00000			0.349563			0.174782	+	0.984607i	$0.444078\pi$
$402$	−8.00000			−0.399004
$403$			5.00000i			0.249068i
$404$		0			0
$405$	1.00000			0.0496904
$406$	4.00000	+	10.0000i	0.198517	+	0.496292i
$407$	40.0000			1.98273
$408$			2.00000i			0.0990148i
$409$		−	4.00000i		−	0.197787i	−0.995098	−	0.0988936i	$-0.968470\pi$
$409$		−	4.00000i		−	0.197787i	0.995098	−	0.0988936i	$-0.0315304\pi$
$410$	10.0000			0.493865
$411$	12.0000			0.591916
$412$	−4.00000			−0.197066
$413$	−20.0000			−0.984136
$414$			12.0000i			0.589768i
$415$	14.0000			0.687233
$416$			1.00000i			0.0490290i
$417$		−	10.0000i		−	0.489702i
$418$		−	20.0000i		−	0.978232i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		−	2.00000i		−	0.0975900i
$421$			10.0000i			0.487370i	0.969854	+	0.243685i	$0.0783563\pi$
$421$			10.0000i			0.487370i	−0.969854	+	0.243685i	$0.921644\pi$
$422$	−5.00000			−0.243396
$423$		−	6.00000i		−	0.291730i
$424$		−	1.00000i		−	0.0485643i
$425$		−	8.00000i		−	0.388057i
$426$	8.00000			0.387601
$427$		−	20.0000i		−	0.967868i
$428$	2.00000			0.0966736
$429$	−5.00000			−0.241402
$430$	9.00000			0.434019
$431$	22.0000			1.05970			0.529851	−	0.848091i	$-0.322248\pi$
$431$	22.0000			1.05970			0.529851	+	0.848091i	$0.322248\pi$
$432$		−	5.00000i		−	0.240563i
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	10.0000			0.480015
$435$	−2.00000	−	5.00000i	−0.0958927	−	0.239732i
$436$	15.0000			0.718370
$437$			24.0000i			1.14808i
$438$			16.0000i			0.764510i
$439$	−30.0000			−1.43182			−0.715911	−	0.698192i	$-0.753988\pi$
$439$	−30.0000			−1.43182			−0.715911	+	0.698192i	$0.753988\pi$
$440$	−5.00000			−0.238366
$441$	−6.00000			−0.285714
$442$	−2.00000			−0.0951303
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$	8.00000			0.379663
$445$		−	14.0000i		−	0.663664i
$446$		−	24.0000i		−	1.13643i
$447$		−	15.0000i		−	0.709476i
$448$	2.00000			0.0944911
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$			8.00000i			0.377124i
$451$	−50.0000			−2.35441
$452$		−	4.00000i		−	0.188144i
$453$		−	2.00000i		−	0.0939682i
$454$			12.0000i			0.563188i
$455$	2.00000			0.0937614
$456$		−	4.00000i		−	0.187317i
$457$	18.0000			0.842004			0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000			0.842004			0.421002	+	0.907060i	$0.361678\pi$
$458$	6.00000			0.280362
$459$	10.0000			0.466760
$460$	6.00000			0.279751
$461$		−	20.0000i		−	0.931493i	−0.884918	−	0.465746i	$-0.845786\pi$
$461$		−	20.0000i		−	0.931493i	0.884918	−	0.465746i	$-0.154214\pi$
$462$			10.0000i			0.465242i
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	5.00000	−	2.00000i	0.232119	−	0.0928477i
$465$	−5.00000			−0.231869
$466$			1.00000i			0.0463241i
$467$		−	3.00000i		−	0.138823i	−0.997588	−	0.0694117i	$-0.977888\pi$
$467$		−	3.00000i		−	0.138823i	0.997588	−	0.0694117i	$-0.0221122\pi$
$468$	2.00000			0.0924500
$469$	−16.0000			−0.738811
$470$	−3.00000			−0.138380
$471$	−18.0000			−0.829396
$472$			10.0000i			0.460287i
$473$	−45.0000			−2.06910
$474$		−	1.00000i		−	0.0459315i
$475$			16.0000i			0.734130i
$476$			4.00000i			0.183340i
$477$	−2.00000			−0.0915737
$478$			30.0000i			1.37217i
$479$			11.0000i			0.502603i	0.967909	+	0.251301i	$0.0808585\pi$
$479$			11.0000i			0.502603i	−0.967909	+	0.251301i	$0.919141\pi$
$480$	−1.00000			−0.0456435
$481$			8.00000i			0.364769i
$482$		−	7.00000i		−	0.318841i
$483$		−	12.0000i		−	0.546019i
$484$	14.0000			0.636364
$485$			2.00000i			0.0908153i
$486$	−16.0000			−0.725775
$487$	38.0000			1.72194			0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000			1.72194			0.860972	+	0.508652i	$0.169856\pi$
$488$	−10.0000			−0.452679
$489$	−1.00000			−0.0452216
$490$			3.00000i			0.135526i
$491$		−	15.0000i		−	0.676941i	−0.940977	−	0.338470i	$-0.890091\pi$
$491$		−	15.0000i		−	0.676941i	0.940977	−	0.338470i	$-0.109909\pi$
$492$	−10.0000			−0.450835
$493$	4.00000	+	10.0000i	0.180151	+	0.450377i
$494$	4.00000			0.179969
$495$			10.0000i			0.449467i
$496$		−	5.00000i		−	0.224507i
$497$	16.0000			0.717698
$498$	−14.0000			−0.627355
$499$	−30.0000			−1.34298			−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000			−1.34298			−0.671492	+	0.741012i	$0.734346\pi$
$500$	9.00000			0.402492
$501$			12.0000i			0.536120i
$502$	15.0000			0.669483
$503$			39.0000i			1.73892i	0.494000	+	0.869462i	$0.335534\pi$
$503$			39.0000i			1.73892i	−0.494000	+	0.869462i	$0.664466\pi$
$504$		−	4.00000i		−	0.178174i
$505$		0			0
$506$	−30.0000			−1.33366
$507$			12.0000i			0.532939i
$508$		−	12.0000i		−	0.532414i
$509$	15.0000			0.664863			0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000			0.664863			0.332432	+	0.943127i	$0.392131\pi$
$510$		−	2.00000i		−	0.0885615i
$511$			32.0000i			1.41560i
$512$		−	1.00000i		−	0.0441942i
$513$	−20.0000			−0.883022
$514$			7.00000i			0.308757i
$515$	4.00000			0.176261
$516$	−9.00000			−0.396203
$517$	15.0000			0.659699
$518$	16.0000			0.703000
$519$			6.00000i			0.263371i
$520$		−	1.00000i		−	0.0438529i
$521$	17.0000			0.744784			0.372392	−	0.928076i	$-0.378538\pi$
$521$	17.0000			0.744784			0.372392	+	0.928076i	$0.378538\pi$
$522$	−4.00000	−	10.0000i	−0.175075	−	0.437688i
$523$	4.00000			0.174908			0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000			0.174908			0.0874539	+	0.996169i	$0.472127\pi$
$524$		0			0
$525$		−	8.00000i		−	0.349149i
$526$	19.0000			0.828439
$527$	10.0000			0.435607
$528$	5.00000			0.217597
$529$	13.0000			0.565217
$530$			1.00000i			0.0434372i
$531$	20.0000			0.867926
$532$		−	8.00000i		−	0.346844i
$533$		−	10.0000i		−	0.433148i
$534$			14.0000i			0.605839i
$535$	−2.00000			−0.0864675
$536$			8.00000i			0.345547i
$537$		0			0
$538$	26.0000			1.12094
$539$		−	15.0000i		−	0.646096i
$540$			5.00000i			0.215166i
$541$			40.0000i			1.71973i	0.510518	+	0.859867i	$0.329454\pi$
$541$			40.0000i			1.71973i	−0.510518	+	0.859867i	$0.670546\pi$
$542$	−25.0000			−1.07384
$543$		−	17.0000i		−	0.729540i
$544$	2.00000			0.0857493
$545$	−15.0000			−0.642529
$546$	−2.00000			−0.0855921
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$		−	12.0000i		−	0.512615i
$549$			20.0000i			0.853579i
$550$	−20.0000			−0.852803
$551$	−8.00000	−	20.0000i	−0.340811	−	0.852029i
$552$	−6.00000			−0.255377
$553$		−	2.00000i		−	0.0850487i
$554$		−	18.0000i		−	0.764747i
$555$	−8.00000			−0.339581
$556$	−10.0000			−0.424094
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$	−10.0000			−0.423334
$559$		−	9.00000i		−	0.380659i
$560$	−2.00000			−0.0845154
$561$			10.0000i			0.422200i
$562$			13.0000i			0.548372i
$563$			19.0000i			0.800755i	0.916350	+	0.400377i	$0.131121\pi$
$563$			19.0000i			0.800755i	−0.916350	+	0.400377i	$0.868879\pi$
$564$	3.00000			0.126323
$565$			4.00000i			0.168281i
$566$			6.00000i			0.252199i
$567$	−2.00000			−0.0839921
$568$		−	8.00000i		−	0.335673i
$569$		−	24.0000i		−	1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$569$		−	24.0000i		−	1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$570$			4.00000i			0.167542i
$571$	−8.00000			−0.334790			−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000			−0.334790			−0.167395	+	0.985890i	$0.553535\pi$
$572$			5.00000i			0.209061i
$573$		0			0
$574$	−20.0000			−0.834784
$575$	24.0000			1.00087
$576$	−2.00000			−0.0833333
$577$			2.00000i			0.0832611i	0.999133	+	0.0416305i	$0.0132552\pi$
$577$			2.00000i			0.0832611i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$		−	13.0000i		−	0.540729i
$579$	14.0000			0.581820
$580$	−5.00000	+	2.00000i	−0.207614	+	0.0830455i
$581$	−28.0000			−1.16164
$582$		−	2.00000i		−	0.0829027i
$583$		−	5.00000i		−	0.207079i
$584$	16.0000			0.662085
$585$	−2.00000			−0.0826898
$586$	4.00000			0.165238
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		−	3.00000i		−	0.123718i
$589$	−20.0000			−0.824086
$590$		−	10.0000i		−	0.411693i
$591$			2.00000i			0.0822690i
$592$		−	8.00000i		−	0.328798i
$593$	29.0000			1.19089			0.595444	−	0.803397i	$-0.296976\pi$
$593$	29.0000			1.19089			0.595444	+	0.803397i	$0.296976\pi$
$594$		−	25.0000i		−	1.02576i
$595$		−	4.00000i		−	0.163984i
$596$	−15.0000			−0.614424
$597$		−	10.0000i		−	0.409273i
$598$		−	6.00000i		−	0.245358i
$599$		−	39.0000i		−	1.59350i	−0.604311	−	0.796748i	$-0.706552\pi$
$599$		−	39.0000i		−	1.59350i	0.604311	−	0.796748i	$-0.293448\pi$
$600$	−4.00000			−0.163299
$601$		−	30.0000i		−	1.22373i	−0.790964	−	0.611863i	$-0.790420\pi$
$601$		−	30.0000i		−	1.22373i	0.790964	−	0.611863i	$-0.209580\pi$
$602$	−18.0000			−0.733625
$603$	16.0000			0.651570
$604$	−2.00000			−0.0813788
$605$	−14.0000			−0.569181
$606$		0			0
$607$		−	13.0000i		−	0.527654i	−0.964570	−	0.263827i	$-0.915015\pi$
$607$		−	13.0000i		−	0.527654i	0.964570	−	0.263827i	$-0.0849848\pi$
$608$	−4.00000			−0.162221
$609$	4.00000	+	10.0000i	0.162088	+	0.405220i
$610$	10.0000			0.404888
$611$			3.00000i			0.121367i
$612$		−	4.00000i		−	0.161690i
$613$	29.0000			1.17130			0.585649	−	0.810564i	$-0.300840\pi$
$613$	29.0000			1.17130			0.585649	+	0.810564i	$0.300840\pi$
$614$	−3.00000			−0.121070
$615$	10.0000			0.403239
$616$	10.0000			0.402911
$617$		−	28.0000i		−	1.12724i	−0.826035	−	0.563619i	$-0.809409\pi$
$617$		−	28.0000i		−	1.12724i	0.826035	−	0.563619i	$-0.190591\pi$
$618$	−4.00000			−0.160904
$619$		−	49.0000i		−	1.96948i	−0.174042	−	0.984738i	$-0.555683\pi$
$619$		−	49.0000i		−	1.96948i	0.174042	−	0.984738i	$-0.444317\pi$
$620$			5.00000i			0.200805i
$621$			30.0000i			1.20386i
$622$		0			0
$623$			28.0000i			1.12180i
$624$			1.00000i			0.0400320i
$625$	11.0000			0.440000
$626$			31.0000i			1.23901i
$627$		−	20.0000i		−	0.798723i
$628$			18.0000i			0.718278i
$629$	16.0000			0.637962
$630$			4.00000i			0.159364i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−1.00000			−0.0397779
$633$	−5.00000			−0.198732
$634$	22.0000			0.873732
$635$			12.0000i			0.476205i
$636$		−	1.00000i		−	0.0396526i
$637$	3.00000			0.118864
$638$	25.0000	−	10.0000i	0.989759	−	0.395904i
$639$	−16.0000			−0.632950
$640$			1.00000i			0.0395285i
$641$			30.0000i			1.18493i	0.805597	+	0.592464i	$0.201845\pi$
$641$			30.0000i			1.18493i	−0.805597	+	0.592464i	$0.798155\pi$
$642$	2.00000			0.0789337
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$	−12.0000			−0.472866
$645$	9.00000			0.354375
$646$		−	8.00000i		−	0.314756i
$647$	−22.0000			−0.864909			−0.432455	−	0.901656i	$-0.642352\pi$
$647$	−22.0000			−0.864909			−0.432455	+	0.901656i	$0.642352\pi$
$648$			1.00000i			0.0392837i
$649$			50.0000i			1.96267i
$650$		−	4.00000i		−	0.156893i
$651$	10.0000			0.391931
$652$			1.00000i			0.0391630i
$653$		−	6.00000i		−	0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$		−	6.00000i		−	0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$	15.0000			0.586546
$655$		0			0
$656$			10.0000i			0.390434i
$657$		−	32.0000i		−	1.24844i
$658$	6.00000			0.233904
$659$			31.0000i			1.20759i	0.797140	+	0.603794i	$0.206345\pi$
$659$			31.0000i			1.20759i	−0.797140	+	0.603794i	$0.793655\pi$
$660$	−5.00000			−0.194625
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$	−25.0000			−0.971653
$663$	−2.00000			−0.0776736
$664$			14.0000i			0.543305i
$665$			8.00000i			0.310227i
$666$	−16.0000			−0.619987
$667$	−30.0000	+	12.0000i	−1.16160	+	0.464642i
$668$	12.0000			0.464294
$669$		−	24.0000i		−	0.927894i
$670$		−	8.00000i		−	0.309067i
$671$	−50.0000			−1.93023
$672$	2.00000			0.0771517
$673$	19.0000			0.732396			0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000			0.732396			0.366198	+	0.930537i	$0.380659\pi$
$674$	22.0000			0.847408
$675$			20.0000i			0.769800i
$676$	12.0000			0.461538
$677$		−	8.00000i		−	0.307465i	−0.988113	−	0.153732i	$-0.950871\pi$
$677$		−	8.00000i		−	0.307465i	0.988113	−	0.153732i	$-0.0491294\pi$
$678$		−	4.00000i		−	0.153619i
$679$		−	4.00000i		−	0.153506i
$680$	−2.00000			−0.0766965
$681$			12.0000i			0.459841i
$682$		−	25.0000i		−	0.957299i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$			8.00000i			0.305888i
$685$			12.0000i			0.458496i
$686$		−	20.0000i		−	0.763604i
$687$	6.00000			0.228914
$688$			9.00000i			0.343122i
$689$	1.00000			0.0380970
$690$	6.00000			0.228416
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	6.00000			0.228086
$693$		−	20.0000i		−	0.759737i
$694$			12.0000i			0.455514i
$695$	10.0000			0.379322
$696$	5.00000	−	2.00000i	0.189525	−	0.0758098i
$697$	−20.0000			−0.757554
$698$			25.0000i			0.946264i
$699$			1.00000i			0.0378235i
$700$	−8.00000			−0.302372
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$	5.00000			0.188713
$703$	−32.0000			−1.20690
$704$		−	5.00000i		−	0.188445i
$705$	−3.00000			−0.112987
$706$			6.00000i			0.225813i
$707$		0			0
$708$			10.0000i			0.375823i
$709$	−5.00000			−0.187779			−0.0938895	−	0.995583i	$-0.529930\pi$
$709$	−5.00000			−0.187779			−0.0938895	+	0.995583i	$0.529930\pi$
$710$			8.00000i			0.300235i
$711$			2.00000i			0.0750059i
$712$	14.0000			0.524672
$713$			30.0000i			1.12351i
$714$			4.00000i			0.149696i
$715$		−	5.00000i		−	0.186989i
$716$		0			0
$717$			30.0000i			1.12037i
$718$	−19.0000			−0.709074
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$	2.00000			0.0745356
$721$	−8.00000			−0.297936
$722$		−	3.00000i		−	0.111648i
$723$		−	7.00000i		−	0.260333i
$724$	−17.0000			−0.631800
$725$	−20.0000	+	8.00000i	−0.742781	+	0.297113i
$726$	14.0000			0.519589
$727$		−	48.0000i		−	1.78022i	−0.455744	−	0.890111i	$-0.650627\pi$
$727$		−	48.0000i		−	1.78022i	0.455744	−	0.890111i	$-0.349373\pi$
$728$			2.00000i			0.0741249i
$729$	−13.0000			−0.481481
$730$	−16.0000			−0.592187
$731$	−18.0000			−0.665754
$732$	−10.0000			−0.369611
$733$		−	36.0000i		−	1.32969i	−0.746981	−	0.664845i	$-0.768498\pi$
$733$		−	36.0000i		−	1.32969i	0.746981	−	0.664845i	$-0.231502\pi$
$734$	32.0000			1.18114
$735$			3.00000i			0.110657i
$736$			6.00000i			0.221163i
$737$			40.0000i			1.47342i
$738$	20.0000			0.736210
$739$		−	9.00000i		−	0.331070i	−0.986204	−	0.165535i	$-0.947065\pi$
$739$		−	9.00000i		−	0.331070i	0.986204	−	0.165535i	$-0.0529351\pi$
$740$			8.00000i			0.294086i
$741$	4.00000			0.146944
$742$		−	2.00000i		−	0.0734223i
$743$		−	16.0000i		−	0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$		−	16.0000i		−	0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$		−	5.00000i		−	0.183309i
$745$	15.0000			0.549557
$746$			11.0000i			0.402739i
$747$	28.0000			1.02447
$748$	10.0000			0.365636
$749$	4.00000			0.146157
$750$	9.00000			0.328634
$751$			40.0000i			1.45962i	0.683650	+	0.729810i	$0.260392\pi$
$751$			40.0000i			1.45962i	−0.683650	+	0.729810i	$0.739608\pi$
$752$		−	3.00000i		−	0.109399i
$753$	15.0000			0.546630
$754$	2.00000	+	5.00000i	0.0728357	+	0.182089i
$755$	2.00000			0.0727875
$756$		−	10.0000i		−	0.363696i
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	−4.00000			−0.145287
$759$	−30.0000			−1.08893
$760$	4.00000			0.145095
$761$	2.00000			0.0724999			0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000			0.0724999			0.0362500	+	0.999343i	$0.488459\pi$
$762$		−	12.0000i		−	0.434714i
$763$	30.0000			1.08607
$764$		0			0
$765$			4.00000i			0.144620i
$766$			6.00000i			0.216789i
$767$	−10.0000			−0.361079
$768$		−	1.00000i		−	0.0360844i
$769$		−	34.0000i		−	1.22607i	−0.790055	−	0.613036i	$-0.789948\pi$
$769$		−	34.0000i		−	1.22607i	0.790055	−	0.613036i	$-0.210052\pi$
$770$	−10.0000			−0.360375
$771$			7.00000i			0.252099i
$772$		−	14.0000i		−	0.503871i
$773$			14.0000i			0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$			14.0000i			0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$	18.0000			0.646997
$775$			20.0000i			0.718421i
$776$	−2.00000			−0.0717958
$777$	16.0000			0.573997
$778$	−24.0000			−0.860442
$779$	40.0000			1.43315
$780$		−	1.00000i		−	0.0358057i
$781$		−	40.0000i		−	1.43131i
$782$	−12.0000			−0.429119
$783$	−10.0000	−	25.0000i	−0.357371	−	0.893427i
$784$	−3.00000			−0.107143
$785$		−	18.0000i		−	0.642448i
$786$		0			0
$787$	−32.0000			−1.14068			−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000			−1.14068			−0.570338	+	0.821410i	$0.693188\pi$
$788$	2.00000			0.0712470
$789$	19.0000			0.676418
$790$	1.00000			0.0355784
$791$		−	8.00000i		−	0.284447i
$792$	−10.0000			−0.355335
$793$		−	10.0000i		−	0.355110i
$794$			27.0000i			0.958194i
$795$			1.00000i			0.0354663i
$796$	−10.0000			−0.354441
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		−	8.00000i		−	0.283197i
$799$	6.00000			0.212265
$800$			4.00000i			0.141421i
$801$		−	28.0000i		−	0.989331i
$802$		−	7.00000i		−	0.247179i
$803$	80.0000			2.82314
$804$			8.00000i			0.282138i
$805$	12.0000			0.422944
$806$	5.00000			0.176117
$807$	26.0000			0.915243
$808$		0			0
$809$		−	4.00000i		−	0.140633i	−0.997525	−	0.0703163i	$-0.977599\pi$
$809$		−	4.00000i		−	0.140633i	0.997525	−	0.0703163i	$-0.0224008\pi$
$810$		−	1.00000i		−	0.0351364i
$811$	−18.0000			−0.632065			−0.316033	−	0.948748i	$-0.602351\pi$
$811$	−18.0000			−0.632065			−0.316033	+	0.948748i	$0.602351\pi$
$812$	10.0000	−	4.00000i	0.350931	−	0.140372i
$813$	−25.0000			−0.876788
$814$		−	40.0000i		−	1.40200i
$815$		−	1.00000i		−	0.0350285i
$816$	2.00000			0.0700140
$817$	36.0000			1.25948
$818$	−4.00000			−0.139857
$819$	4.00000			0.139771
$820$		−	10.0000i		−	0.349215i
$821$	−33.0000			−1.15171			−0.575854	−	0.817553i	$-0.695330\pi$
$821$	−33.0000			−1.15171			−0.575854	+	0.817553i	$0.695330\pi$
$822$		−	12.0000i		−	0.418548i
$823$			4.00000i			0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$			4.00000i			0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$			4.00000i			0.139347i
$825$	−20.0000			−0.696311
$826$			20.0000i			0.695889i
$827$		−	33.0000i		−	1.14752i	−0.819023	−	0.573761i	$-0.805484\pi$
$827$		−	33.0000i		−	1.14752i	0.819023	−	0.573761i	$-0.194516\pi$
$828$	12.0000			0.417029
$829$			26.0000i			0.903017i	0.892267	+	0.451509i	$0.149114\pi$
$829$			26.0000i			0.903017i	−0.892267	+	0.451509i	$0.850886\pi$
$830$		−	14.0000i		−	0.485947i
$831$		−	18.0000i		−	0.624413i
$832$	1.00000			0.0346688
$833$		−	6.00000i		−	0.207888i
$834$	−10.0000			−0.346272
$835$	−12.0000			−0.415277
$836$	−20.0000			−0.691714
$837$	−25.0000			−0.864126
$838$		0			0
$839$			21.0000i			0.725001i	0.931984	+	0.362500i	$0.118077\pi$
$839$			21.0000i			0.725001i	−0.931984	+	0.362500i	$0.881923\pi$
$840$	−2.00000			−0.0690066
$841$	21.0000	−	20.0000i	0.724138	−	0.689655i
$842$	10.0000			0.344623
$843$			13.0000i			0.447744i
$844$			5.00000i			0.172107i
$845$	−12.0000			−0.412813
$846$	−6.00000			−0.206284
$847$	28.0000			0.962091
$848$	−1.00000			−0.0343401
$849$			6.00000i			0.205919i
$850$	−8.00000			−0.274398
$851$			48.0000i			1.64542i
$852$		−	8.00000i		−	0.274075i
$853$			4.00000i			0.136957i	0.997653	+	0.0684787i	$0.0218145\pi$
$853$			4.00000i			0.136957i	−0.997653	+	0.0684787i	$0.978185\pi$
$854$	−20.0000			−0.684386
$855$		−	8.00000i		−	0.273594i
$856$		−	2.00000i		−	0.0683586i
$857$	13.0000			0.444072			0.222036	−	0.975039i	$-0.428730\pi$
$857$	13.0000			0.444072			0.222036	+	0.975039i	$0.428730\pi$
$858$			5.00000i			0.170697i
$859$			41.0000i			1.39890i	0.714681	+	0.699451i	$0.246572\pi$
$859$			41.0000i			1.39890i	−0.714681	+	0.699451i	$0.753428\pi$
$860$		−	9.00000i		−	0.306897i
$861$	−20.0000			−0.681598
$862$		−	22.0000i		−	0.749323i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	−5.00000			−0.170103
$865$	−6.00000			−0.204006
$866$	−16.0000			−0.543702
$867$		−	13.0000i		−	0.441503i
$868$		−	10.0000i		−	0.339422i
$869$	−5.00000			−0.169613
$870$	−5.00000	+	2.00000i	−0.169516	+	0.0678064i
$871$	−8.00000			−0.271070
$872$		−	15.0000i		−	0.507964i
$873$			4.00000i			0.135379i
$874$	24.0000			0.811812
$875$	18.0000			0.608511
$876$	16.0000			0.540590
$877$	43.0000			1.45201			0.726003	−	0.687691i	$-0.241376\pi$
$877$	43.0000			1.45201			0.726003	+	0.687691i	$0.241376\pi$
$878$			30.0000i			1.01245i
$879$	4.00000			0.134917
$880$			5.00000i			0.168550i
$881$			40.0000i			1.34763i	0.738898	+	0.673817i	$0.235346\pi$
$881$			40.0000i			1.34763i	−0.738898	+	0.673817i	$0.764654\pi$
$882$			6.00000i			0.202031i
$883$	34.0000			1.14419			0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000			1.14419			0.572096	+	0.820187i	$0.306131\pi$
$884$			2.00000i			0.0672673i
$885$		−	10.0000i		−	0.336146i
$886$	4.00000			0.134383
$887$			27.0000i			0.906571i	0.891365	+	0.453286i	$0.149748\pi$
$887$			27.0000i			0.906571i	−0.891365	+	0.453286i	$0.850252\pi$
$888$		−	8.00000i		−	0.268462i
$889$		−	24.0000i		−	0.804934i
$890$	−14.0000			−0.469281
$891$			5.00000i			0.167506i
$892$	−24.0000			−0.803579
$893$	−12.0000			−0.401565
$894$	−15.0000			−0.501675
$895$		0			0
$896$		−	2.00000i		−	0.0668153i
$897$		−	6.00000i		−	0.200334i
$898$	−24.0000			−0.800890
$899$	−10.0000	−	25.0000i	−0.333519	−	0.833797i
$900$	8.00000			0.266667
$901$		−	2.00000i		−	0.0666297i
$902$			50.0000i			1.66482i
$903$	−18.0000			−0.599002
$904$	−4.00000			−0.133038
$905$	17.0000			0.565099
$906$	−2.00000			−0.0664455
$907$		−	28.0000i		−	0.929725i	−0.885383	−	0.464862i	$-0.846104\pi$
$907$		−	28.0000i		−	0.929725i	0.885383	−	0.464862i	$-0.153896\pi$
$908$	12.0000			0.398234
$909$		0			0
$910$		−	2.00000i		−	0.0662994i
$911$			15.0000i			0.496972i	0.968635	+	0.248486i	$0.0799330\pi$
$911$			15.0000i			0.496972i	−0.968635	+	0.248486i	$0.920067\pi$
$912$	−4.00000			−0.132453
$913$			70.0000i			2.31666i
$914$		−	18.0000i		−	0.595387i
$915$	10.0000			0.330590
$916$		−	6.00000i		−	0.198246i
$917$		0			0
$918$		−	10.0000i		−	0.330049i
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$		−	6.00000i		−	0.197814i
$921$	−3.00000			−0.0988534
$922$	−20.0000			−0.658665
$923$	8.00000			0.263323
$924$	10.0000			0.328976
$925$			32.0000i			1.05215i
$926$		−	14.0000i		−	0.460069i
$927$	8.00000			0.262754
$928$	−2.00000	−	5.00000i	−0.0656532	−	0.164133i
$929$	−50.0000			−1.64045			−0.820223	−	0.572043i	$-0.806151\pi$
$929$	−50.0000			−1.64045			−0.820223	+	0.572043i	$0.806151\pi$
$930$			5.00000i			0.163956i
$931$			12.0000i			0.393284i
$932$	1.00000			0.0327561
$933$		0			0
$934$	−3.00000			−0.0981630
$935$	−10.0000			−0.327035
$936$		−	2.00000i		−	0.0653720i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$			16.0000i			0.522419i
$939$			31.0000i			1.01165i
$940$			3.00000i			0.0978492i
$941$	57.0000			1.85815			0.929073	−	0.369895i	$-0.120606\pi$
$941$	57.0000			1.85815			0.929073	+	0.369895i	$0.120606\pi$
$942$			18.0000i			0.586472i
$943$		−	60.0000i		−	1.95387i
$944$	10.0000			0.325472
$945$			10.0000i			0.325300i
$946$			45.0000i			1.46308i
$947$		−	3.00000i		−	0.0974869i	−0.998811	−	0.0487435i	$-0.984478\pi$
$947$		−	3.00000i		−	0.0974869i	0.998811	−	0.0487435i	$-0.0155217\pi$
$948$	−1.00000			−0.0324785
$949$			16.0000i			0.519382i
$950$	16.0000			0.519109
$951$	22.0000			0.713399
$952$	4.00000			0.129641
$953$	−41.0000			−1.32812			−0.664060	−	0.747679i	$-0.731168\pi$
$953$	−41.0000			−1.32812			−0.664060	+	0.747679i	$0.731168\pi$
$954$			2.00000i			0.0647524i
$955$		0			0
$956$	30.0000			0.970269
$957$	25.0000	−	10.0000i	0.808135	−	0.323254i
$958$	11.0000			0.355394
$959$		−	24.0000i		−	0.775000i
$960$			1.00000i			0.0322749i
$961$	6.00000			0.193548
$962$	8.00000			0.257930
$963$	−4.00000			−0.128898
$964$	−7.00000			−0.225455
$965$			14.0000i			0.450676i
$966$	−12.0000			−0.386094
$967$			17.0000i			0.546683i	0.961917	+	0.273342i	$0.0881289\pi$
$967$			17.0000i			0.546683i	−0.961917	+	0.273342i	$0.911871\pi$
$968$		−	14.0000i		−	0.449977i
$969$		−	8.00000i		−	0.256997i
$970$	2.00000			0.0642161
$971$			20.0000i			0.641831i	0.947108	+	0.320915i	$0.103990\pi$
$971$			20.0000i			0.641831i	−0.947108	+	0.320915i	$0.896010\pi$
$972$			16.0000i			0.513200i
$973$	−20.0000			−0.641171
$974$		−	38.0000i		−	1.21760i
$975$		−	4.00000i		−	0.128103i
$976$			10.0000i			0.320092i
$977$	−27.0000			−0.863807			−0.431903	−	0.901920i	$-0.642158\pi$
$977$	−27.0000			−0.863807			−0.431903	+	0.901920i	$0.642158\pi$
$978$			1.00000i			0.0319765i
$979$	70.0000			2.23721
$980$	3.00000			0.0958315
$981$	−30.0000			−0.957826
$982$	−15.0000			−0.478669
$983$		−	31.0000i		−	0.988746i	−0.869250	−	0.494373i	$-0.835398\pi$
$983$		−	31.0000i		−	0.988746i	0.869250	−	0.494373i	$-0.164602\pi$
$984$			10.0000i			0.318788i
$985$	−2.00000			−0.0637253
$986$	10.0000	−	4.00000i	0.318465	−	0.127386i
$987$	6.00000			0.190982
$988$		−	4.00000i		−	0.127257i
$989$		−	54.0000i		−	1.71710i
$990$	10.0000			0.317821
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−5.00000			−0.158750
$993$	−25.0000			−0.793351
$994$		−	16.0000i		−	0.507489i
$995$	10.0000			0.317021
$996$			14.0000i			0.443607i
$997$		−	28.0000i		−	0.886769i	−0.896332	−	0.443384i	$-0.853778\pi$
$997$		−	28.0000i		−	0.886769i	0.896332	−	0.443384i	$-0.146222\pi$
$998$			30.0000i			0.949633i
$999$	−40.0000			−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.2.b.a.57.1	✓	2
3.2	odd	2		522.2.d.a.289.2		2
4.3	odd	2		464.2.e.c.289.2		2
5.2	odd	4		1450.2.d.c.1449.1		2
5.3	odd	4		1450.2.d.b.1449.2		2
5.4	even	2		1450.2.c.a.1101.2		2
8.3	odd	2		1856.2.e.d.1217.1		2
8.5	even	2		1856.2.e.b.1217.2		2
12.11	even	2		4176.2.o.d.289.2		2
29.12	odd	4		1682.2.a.g.1.1		1
29.17	odd	4		1682.2.a.c.1.1		1
29.28	even	2	inner	58.2.b.a.57.2	yes	2
87.86	odd	2		522.2.d.a.289.1		2
116.115	odd	2		464.2.e.c.289.1		2
145.28	odd	4		1450.2.d.c.1449.2		2
145.57	odd	4		1450.2.d.b.1449.1		2
145.144	even	2		1450.2.c.a.1101.1		2
232.115	odd	2		1856.2.e.d.1217.2		2
232.173	even	2		1856.2.e.b.1217.1		2
348.347	even	2		4176.2.o.d.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.b.a.57.1	✓	2	1.1	even	1	trivial
58.2.b.a.57.2	yes	2	29.28	even	2	inner
464.2.e.c.289.1		2	116.115	odd	2
464.2.e.c.289.2		2	4.3	odd	2
522.2.d.a.289.1		2	87.86	odd	2
522.2.d.a.289.2		2	3.2	odd	2
1450.2.c.a.1101.1		2	145.144	even	2
1450.2.c.a.1101.2		2	5.4	even	2
1450.2.d.b.1449.1		2	145.57	odd	4
1450.2.d.b.1449.2		2	5.3	odd	4
1450.2.d.c.1449.1		2	5.2	odd	4
1450.2.d.c.1449.2		2	145.28	odd	4
1682.2.a.c.1.1		1	29.17	odd	4
1682.2.a.g.1.1		1	29.12	odd	4
1856.2.e.b.1217.1		2	232.173	even	2
1856.2.e.b.1217.2		2	8.5	even	2
1856.2.e.d.1217.1		2	8.3	odd	2
1856.2.e.d.1217.2		2	232.115	odd	2
4176.2.o.d.289.1		2	348.347	even	2
4176.2.o.d.289.2		2	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000i q^{8} +2.00000 q^{9} -1.00000i q^{10} +5.00000i q^{11} +1.00000i q^{12} -1.00000 q^{13} +2.00000i q^{14} -1.00000i q^{15} +1.00000 q^{16} +2.00000i q^{17} -2.00000i q^{18} -4.00000i q^{19} -1.00000 q^{20} +2.00000i q^{21} +5.00000 q^{22} -6.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +1.00000i q^{26} -5.00000i q^{27} +2.00000 q^{28} +(5.00000 - 2.00000i) q^{29} -1.00000 q^{30} -5.00000i q^{31} -1.00000i q^{32} +5.00000 q^{33} +2.00000 q^{34} -2.00000 q^{35} -2.00000 q^{36} -8.00000i q^{37} -4.00000 q^{38} +1.00000i q^{39} +1.00000i q^{40} +10.0000i q^{41} +2.00000 q^{42} +9.00000i q^{43} -5.00000i q^{44} +2.00000 q^{45} +6.00000i q^{46} -3.00000i q^{47} -1.00000i q^{48} -3.00000 q^{49} +4.00000i q^{50} +2.00000 q^{51} +1.00000 q^{52} -1.00000 q^{53} -5.00000 q^{54} +5.00000i q^{55} -2.00000i q^{56} -4.00000 q^{57} +(-2.00000 - 5.00000i) q^{58} +10.0000 q^{59} +1.00000i q^{60} +10.0000i q^{61} -5.00000 q^{62} -4.00000 q^{63} -1.00000 q^{64} -1.00000 q^{65} -5.00000i q^{66} +8.00000 q^{67} -2.00000i q^{68} +6.00000i q^{69} +2.00000i q^{70} -8.00000 q^{71} +2.00000i q^{72} -16.0000i q^{73} -8.00000 q^{74} +4.00000i q^{75} +4.00000i q^{76} -10.0000i q^{77} +1.00000 q^{78} +1.00000i q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +14.0000 q^{83} -2.00000i q^{84} +2.00000i q^{85} +9.00000 q^{86} +(-2.00000 - 5.00000i) q^{87} -5.00000 q^{88} -14.0000i q^{89} -2.00000i q^{90} +2.00000 q^{91} +6.00000 q^{92} -5.00000 q^{93} -3.00000 q^{94} -4.00000i q^{95} -1.00000 q^{96} +2.00000i q^{97} +3.00000i q^{98} +10.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{9} - 2 q^{13} + 2 q^{16} - 2 q^{20} + 10 q^{22} - 12 q^{23} + 2 q^{24} - 8 q^{25} + 4 q^{28} + 10 q^{29} - 2 q^{30} + 10 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36}+ \cdots - 2 q^{96}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^9 - 2 * q^13 + 2 * q^16 - 2 * q^20 + 10 * q^22 - 12 * q^23 + 2 * q^24 - 8 * q^25 + 4 * q^28 + 10 * q^29 - 2 * q^30 + 10 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 8 * q^38 + 4 * q^42 + 4 * q^45 - 6 * q^49 + 4 * q^51 + 2 * q^52 - 2 * q^53 - 10 * q^54 - 8 * q^57 - 4 * q^58 + 20 * q^59 - 10 * q^62 - 8 * q^63 - 2 * q^64 - 2 * q^65 + 16 * q^67 - 16 * q^71 - 16 * q^74 + 2 * q^78 + 2 * q^80 + 2 * q^81 + 20 * q^82 + 28 * q^83 + 18 * q^86 - 4 * q^87 - 10 * q^88 + 4 * q^91 + 12 * q^92 - 10 * q^93 - 6 * q^94 - 2 * q^96

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