LMFDB - Embedded newform 95.2.b.a.39.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,2,Mod(39,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.39"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.758578819202$
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			39.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	95.39
Dual form			95.2.b.a.39.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -2.00000i q^{7} +3.00000i q^{8} +3.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -4.00000 q^{11} -2.00000i q^{13} +2.00000 q^{14} -1.00000 q^{16} -4.00000i q^{17} +3.00000i q^{18} -1.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -4.00000i q^{22} -6.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -2.00000i q^{28} +6.00000 q^{29} -4.00000 q^{31} +5.00000i q^{32} +4.00000 q^{34} +(4.00000 + 2.00000i) q^{35} +3.00000 q^{36} +10.0000i q^{37} -1.00000i q^{38} +(-6.00000 - 3.00000i) q^{40} -10.0000 q^{41} +2.00000i q^{43} -4.00000 q^{44} +(-3.00000 + 6.00000i) q^{45} +6.00000 q^{46} +6.00000i q^{47} +3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -2.00000i q^{52} +10.0000i q^{53} +(4.00000 - 8.00000i) q^{55} +6.00000 q^{56} +6.00000i q^{58} +2.00000 q^{61} -4.00000i q^{62} -6.00000i q^{63} -7.00000 q^{64} +(4.00000 + 2.00000i) q^{65} -8.00000i q^{67} -4.00000i q^{68} +(-2.00000 + 4.00000i) q^{70} +4.00000 q^{71} +9.00000i q^{72} +4.00000i q^{73} -10.0000 q^{74} -1.00000 q^{76} +8.00000i q^{77} -4.00000 q^{79} +(1.00000 - 2.00000i) q^{80} +9.00000 q^{81} -10.0000i q^{82} -18.0000i q^{83} +(8.00000 + 4.00000i) q^{85} -2.00000 q^{86} -12.0000i q^{88} +2.00000 q^{89} +(-6.00000 - 3.00000i) q^{90} -4.00000 q^{91} -6.00000i q^{92} -6.00000 q^{94} +(1.00000 - 2.00000i) q^{95} -6.00000i q^{97} +3.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 2 q^{5} + 6 q^{9} - 4 q^{10} - 8 q^{11} + 4 q^{14} - 2 q^{16} - 2 q^{19} - 2 q^{20} - 6 q^{25} + 4 q^{26} + 12 q^{29} - 8 q^{31} + 8 q^{34} + 8 q^{35} + 6 q^{36} - 12 q^{40} - 20 q^{41}+ \cdots - 24 q^{99}+O(q^{100}) $ 2 * q + 2 * q^4 - 2 * q^5 + 6 * q^9 - 4 * q^10 - 8 * q^11 + 4 * q^14 - 2 * q^16 - 2 * q^19 - 2 * q^20 - 6 * q^25 + 4 * q^26 + 12 * q^29 - 8 * q^31 + 8 * q^34 + 8 * q^35 + 6 * q^36 - 12 * q^40 - 20 * q^41 - 8 * q^44 - 6 * q^45 + 12 * q^46 + 6 * q^49 + 8 * q^50 + 8 * q^55 + 12 * q^56 + 4 * q^61 - 14 * q^64 + 8 * q^65 - 4 * q^70 + 8 * q^71 - 20 * q^74 - 2 * q^76 - 8 * q^79 + 2 * q^80 + 18 * q^81 + 16 * q^85 - 4 * q^86 + 4 * q^89 - 12 * q^90 - 8 * q^91 - 12 * q^94 + 2 * q^95 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$	1.00000			0.500000
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$			3.00000i			1.06066i
$9$	3.00000			1.00000
$10$	−2.00000	−	1.00000i	−0.632456	−	0.316228i
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	2.00000			0.534522
$15$		0			0
$16$	−1.00000			−0.250000
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$			3.00000i			0.707107i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$		0			0
$22$		−	4.00000i		−	0.852803i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	2.00000			0.392232
$27$		0			0
$28$		−	2.00000i		−	0.377964i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$			5.00000i			0.883883i
$33$		0			0
$34$	4.00000			0.685994
$35$	4.00000	+	2.00000i	0.676123	+	0.338062i
$36$	3.00000			0.500000
$37$			10.0000i			1.64399i	0.569495	+	0.821995i	$0.307139\pi$
$37$			10.0000i			1.64399i	−0.569495	+	0.821995i	$0.692861\pi$
$38$		−	1.00000i		−	0.162221i
$39$		0			0
$40$	−6.00000	−	3.00000i	−0.948683	−	0.474342i
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−4.00000			−0.603023
$45$	−3.00000	+	6.00000i	−0.447214	+	0.894427i
$46$	6.00000			0.884652
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$		0			0
$52$		−	2.00000i		−	0.277350i
$53$			10.0000i			1.37361i	0.726844	+	0.686803i	$0.240986\pi$
$53$			10.0000i			1.37361i	−0.726844	+	0.686803i	$0.759014\pi$
$54$		0			0
$55$	4.00000	−	8.00000i	0.539360	−	1.07872i
$56$	6.00000			0.801784
$57$		0			0
$58$			6.00000i			0.787839i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		−	4.00000i		−	0.508001i
$63$		−	6.00000i		−	0.755929i
$64$	−7.00000			−0.875000
$65$	4.00000	+	2.00000i	0.496139	+	0.248069i
$66$		0			0
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$		−	4.00000i		−	0.485071i
$69$		0			0
$70$	−2.00000	+	4.00000i	−0.239046	+	0.478091i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$			9.00000i			1.06066i
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−10.0000			−1.16248
$75$		0			0
$76$	−1.00000			−0.114708
$77$			8.00000i			0.911685i
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.00000	−	2.00000i	0.111803	−	0.223607i
$81$	9.00000			1.00000
$82$		−	10.0000i		−	1.10432i
$83$		−	18.0000i		−	1.97576i	−0.155230	−	0.987878i	$-0.549612\pi$
$83$		−	18.0000i		−	1.97576i	0.155230	−	0.987878i	$-0.450388\pi$
$84$		0			0
$85$	8.00000	+	4.00000i	0.867722	+	0.433861i
$86$	−2.00000			−0.215666
$87$		0			0
$88$		−	12.0000i		−	1.27920i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	−6.00000	−	3.00000i	−0.632456	−	0.316228i
$91$	−4.00000			−0.419314
$92$		−	6.00000i		−	0.625543i
$93$		0			0
$94$	−6.00000			−0.618853
$95$	1.00000	−	2.00000i	0.102598	−	0.205196i
$96$		0			0
$97$		−	6.00000i		−	0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$97$		−	6.00000i		−	0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$98$			3.00000i			0.303046i
$99$	−12.0000			−1.20605
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$			16.0000i			1.57653i	0.615338	+	0.788263i	$0.289020\pi$
$103$			16.0000i			1.57653i	−0.615338	+	0.788263i	$0.710980\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$	−10.0000			−0.971286
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$		0			0
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	8.00000	+	4.00000i	0.762770	+	0.381385i
$111$		0			0
$112$			2.00000i			0.188982i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	12.0000	+	6.00000i	1.11901	+	0.559503i
$116$	6.00000			0.557086
$117$		−	6.00000i		−	0.554700i
$118$		0			0
$119$	−8.00000			−0.733359
$120$		0			0
$121$	5.00000			0.454545
$122$			2.00000i			0.181071i
$123$		0			0
$124$	−4.00000			−0.359211
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	6.00000			0.534522
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$			3.00000i			0.265165i
$129$		0			0
$130$	−2.00000	+	4.00000i	−0.175412	+	0.350823i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$			2.00000i			0.173422i
$134$	8.00000			0.691095
$135$		0			0
$136$	12.0000			1.02899
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	4.00000	+	2.00000i	0.338062	+	0.169031i
$141$		0			0
$142$			4.00000i			0.335673i
$143$			8.00000i			0.668994i
$144$	−3.00000			−0.250000
$145$	−6.00000	+	12.0000i	−0.498273	+	0.996546i
$146$	−4.00000			−0.331042
$147$		0			0
$148$			10.0000i			0.821995i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$	24.0000			1.95309			0.976546	−	0.215308i	$-0.0690756\pi$
$151$	24.0000			1.95309			0.976546	+	0.215308i	$0.0690756\pi$
$152$		−	3.00000i		−	0.243332i
$153$		−	12.0000i		−	0.970143i
$154$	−8.00000			−0.644658
$155$	4.00000	−	8.00000i	0.321288	−	0.642575i
$156$		0			0
$157$			8.00000i			0.638470i	0.947676	+	0.319235i	$0.103426\pi$
$157$			8.00000i			0.638470i	−0.947676	+	0.319235i	$0.896574\pi$
$158$		−	4.00000i		−	0.318223i
$159$		0			0
$160$	−10.0000	−	5.00000i	−0.790569	−	0.395285i
$161$	−12.0000			−0.945732
$162$			9.00000i			0.707107i
$163$			10.0000i			0.783260i	0.920123	+	0.391630i	$0.128089\pi$
$163$			10.0000i			0.783260i	−0.920123	+	0.391630i	$0.871911\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$	18.0000			1.39707
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−4.00000	+	8.00000i	−0.306786	+	0.613572i
$171$	−3.00000			−0.229416
$172$			2.00000i			0.152499i
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$		0			0
$175$	−8.00000	+	6.00000i	−0.604743	+	0.453557i
$176$	4.00000			0.301511
$177$		0			0
$178$			2.00000i			0.149906i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−3.00000	+	6.00000i	−0.223607	+	0.447214i
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		−	4.00000i		−	0.296500i
$183$		0			0
$184$	18.0000			1.32698
$185$	−20.0000	−	10.0000i	−1.47043	−	0.735215i
$186$		0			0
$187$			16.0000i			1.17004i
$188$			6.00000i			0.437595i
$189$		0			0
$190$	2.00000	+	1.00000i	0.145095	+	0.0725476i
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$		0			0
$193$		−	26.0000i		−	1.87152i	−0.352636	−	0.935760i	$-0.614715\pi$
$193$		−	26.0000i		−	1.87152i	0.352636	−	0.935760i	$-0.385285\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	3.00000			0.214286
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		−	12.0000i		−	0.852803i
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	12.0000	−	9.00000i	0.848528	−	0.636396i
$201$		0			0
$202$		−	6.00000i		−	0.422159i
$203$		−	12.0000i		−	0.842235i
$204$		0			0
$205$	10.0000	−	20.0000i	0.698430	−	1.39686i
$206$	−16.0000			−1.11477
$207$		−	18.0000i		−	1.25109i
$208$			2.00000i			0.138675i
$209$	4.00000			0.276686
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$			10.0000i			0.686803i
$213$		0			0
$214$	−4.00000			−0.273434
$215$	−4.00000	−	2.00000i	−0.272798	−	0.136399i
$216$		0			0
$217$			8.00000i			0.543075i
$218$		−	6.00000i		−	0.406371i
$219$		0			0
$220$	4.00000	−	8.00000i	0.269680	−	0.539360i
$221$	−8.00000			−0.538138
$222$		0			0
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$	10.0000			0.668153
$225$	−9.00000	−	12.0000i	−0.600000	−	0.800000i
$226$	−6.00000			−0.399114
$227$		−	20.0000i		−	1.32745i	−0.747978	−	0.663723i	$-0.768975\pi$
$227$		−	20.0000i		−	1.32745i	0.747978	−	0.663723i	$-0.231025\pi$
$228$		0			0
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	−6.00000	+	12.0000i	−0.395628	+	0.791257i
$231$		0			0
$232$			18.0000i			1.18176i
$233$			16.0000i			1.04819i	0.851658	+	0.524097i	$0.175597\pi$
$233$			16.0000i			1.04819i	−0.851658	+	0.524097i	$0.824403\pi$
$234$	6.00000			0.392232
$235$	−12.0000	−	6.00000i	−0.782794	−	0.391397i
$236$		0			0
$237$		0			0
$238$		−	8.00000i		−	0.518563i
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−2.00000			−0.128831			−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000			−0.128831			−0.0644157	+	0.997923i	$0.520518\pi$
$242$			5.00000i			0.321412i
$243$		0			0
$244$	2.00000			0.128037
$245$	−3.00000	+	6.00000i	−0.191663	+	0.383326i
$246$		0			0
$247$			2.00000i			0.127257i
$248$		−	12.0000i		−	0.762001i
$249$		0			0
$250$	2.00000	+	11.0000i	0.126491	+	0.695701i
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		−	6.00000i		−	0.377964i
$253$			24.0000i			1.50887i
$254$		0			0
$255$		0			0
$256$	−17.0000			−1.06250
$257$			6.00000i			0.374270i	0.982334	+	0.187135i	$0.0599201\pi$
$257$			6.00000i			0.374270i	−0.982334	+	0.187135i	$0.940080\pi$
$258$		0			0
$259$	20.0000			1.24274
$260$	4.00000	+	2.00000i	0.248069	+	0.124035i
$261$	18.0000			1.11417
$262$		−	12.0000i		−	0.741362i
$263$		−	6.00000i		−	0.369976i	−0.982741	−	0.184988i	$-0.940775\pi$
$263$		−	6.00000i		−	0.369976i	0.982741	−	0.184988i	$-0.0592246\pi$
$264$		0			0
$265$	−20.0000	−	10.0000i	−1.22859	−	0.614295i
$266$	−2.00000			−0.122628
$267$		0			0
$268$		−	8.00000i		−	0.488678i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$	24.0000			1.45790			0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000			1.45790			0.728948	+	0.684569i	$0.240010\pi$
$272$			4.00000i			0.242536i
$273$		0			0
$274$	12.0000			0.724947
$275$	12.0000	+	16.0000i	0.723627	+	0.964836i
$276$		0			0
$277$		−	8.00000i		−	0.480673i	−0.970690	−	0.240337i	$-0.922742\pi$
$277$		−	8.00000i		−	0.480673i	0.970690	−	0.240337i	$-0.0772579\pi$
$278$			4.00000i			0.239904i
$279$	−12.0000			−0.718421
$280$	−6.00000	+	12.0000i	−0.358569	+	0.717137i
$281$	−26.0000			−1.55103			−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000			−1.55103			−0.775515	+	0.631329i	$0.782510\pi$
$282$		0			0
$283$			14.0000i			0.832214i	0.909316	+	0.416107i	$0.136606\pi$
$283$			14.0000i			0.832214i	−0.909316	+	0.416107i	$0.863394\pi$
$284$	4.00000			0.237356
$285$		0			0
$286$	−8.00000			−0.473050
$287$			20.0000i			1.18056i
$288$			15.0000i			0.883883i
$289$	1.00000			0.0588235
$290$	−12.0000	−	6.00000i	−0.704664	−	0.352332i
$291$		0			0
$292$			4.00000i			0.234082i
$293$		−	14.0000i		−	0.817889i	−0.912559	−	0.408944i	$-0.865897\pi$
$293$		−	14.0000i		−	0.817889i	0.912559	−	0.408944i	$-0.134103\pi$
$294$		0			0
$295$		0			0
$296$	−30.0000			−1.74371
$297$		0			0
$298$			10.0000i			0.579284i
$299$	−12.0000			−0.693978
$300$		0			0
$301$	4.00000			0.230556
$302$			24.0000i			1.38104i
$303$		0			0
$304$	1.00000			0.0573539
$305$	−2.00000	+	4.00000i	−0.114520	+	0.229039i
$306$	12.0000			0.685994
$307$			20.0000i			1.14146i	0.821138	+	0.570730i	$0.193340\pi$
$307$			20.0000i			1.14146i	−0.821138	+	0.570730i	$0.806660\pi$
$308$			8.00000i			0.455842i
$309$		0			0
$310$	8.00000	+	4.00000i	0.454369	+	0.227185i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$		−	24.0000i		−	1.35656i	−0.734803	−	0.678280i	$-0.762726\pi$
$313$		−	24.0000i		−	1.35656i	0.734803	−	0.678280i	$-0.237274\pi$
$314$	−8.00000			−0.451466
$315$	12.0000	+	6.00000i	0.676123	+	0.338062i
$316$	−4.00000			−0.225018
$317$		−	22.0000i		−	1.23564i	−0.786318	−	0.617822i	$-0.788015\pi$
$317$		−	22.0000i		−	1.23564i	0.786318	−	0.617822i	$-0.211985\pi$
$318$		0			0
$319$	−24.0000			−1.34374
$320$	7.00000	−	14.0000i	0.391312	−	0.782624i
$321$		0			0
$322$		−	12.0000i		−	0.668734i
$323$			4.00000i			0.222566i
$324$	9.00000			0.500000
$325$	−8.00000	+	6.00000i	−0.443760	+	0.332820i
$326$	−10.0000			−0.553849
$327$		0			0
$328$		−	30.0000i		−	1.65647i
$329$	12.0000			0.661581
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$		−	18.0000i		−	0.987878i
$333$			30.0000i			1.64399i
$334$	12.0000			0.656611
$335$	16.0000	+	8.00000i	0.874173	+	0.437087i
$336$		0			0
$337$		−	22.0000i		−	1.19842i	−0.800593	−	0.599208i	$-0.795482\pi$
$337$		−	22.0000i		−	1.19842i	0.800593	−	0.599208i	$-0.204518\pi$
$338$			9.00000i			0.489535i
$339$		0			0
$340$	8.00000	+	4.00000i	0.433861	+	0.216930i
$341$	16.0000			0.866449
$342$		−	3.00000i		−	0.162221i
$343$		−	20.0000i		−	1.07990i
$344$	−6.00000			−0.323498
$345$		0			0
$346$	6.00000			0.322562
$347$			6.00000i			0.322097i	0.986947	+	0.161048i	$0.0514875\pi$
$347$			6.00000i			0.322097i	−0.986947	+	0.161048i	$0.948512\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−6.00000	−	8.00000i	−0.320713	−	0.427618i
$351$		0			0
$352$		−	20.0000i		−	1.06600i
$353$			4.00000i			0.212899i	0.994318	+	0.106449i	$0.0339482\pi$
$353$			4.00000i			0.212899i	−0.994318	+	0.106449i	$0.966052\pi$
$354$		0			0
$355$	−4.00000	+	8.00000i	−0.212298	+	0.424596i
$356$	2.00000			0.106000
$357$		0			0
$358$		0			0
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$	−18.0000	−	9.00000i	−0.948683	−	0.474342i
$361$	1.00000			0.0526316
$362$		−	18.0000i		−	0.946059i
$363$		0			0
$364$	−4.00000			−0.209657
$365$	−8.00000	−	4.00000i	−0.418739	−	0.209370i
$366$		0			0
$367$			22.0000i			1.14839i	0.818718	+	0.574195i	$0.194685\pi$
$367$			22.0000i			1.14839i	−0.818718	+	0.574195i	$0.805315\pi$
$368$			6.00000i			0.312772i
$369$	−30.0000			−1.56174
$370$	10.0000	−	20.0000i	0.519875	−	1.03975i
$371$	20.0000			1.03835
$372$		0			0
$373$		−	6.00000i		−	0.310668i	−0.987862	−	0.155334i	$-0.950355\pi$
$373$		−	6.00000i		−	0.310668i	0.987862	−	0.155334i	$-0.0496454\pi$
$374$	−16.0000			−0.827340
$375$		0			0
$376$	−18.0000			−0.928279
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	1.00000	−	2.00000i	0.0512989	−	0.102598i
$381$		0			0
$382$		−	24.0000i		−	1.22795i
$383$			12.0000i			0.613171i	0.951843	+	0.306586i	$0.0991866\pi$
$383$			12.0000i			0.613171i	−0.951843	+	0.306586i	$0.900813\pi$
$384$		0			0
$385$	−16.0000	−	8.00000i	−0.815436	−	0.407718i
$386$	26.0000			1.32337
$387$			6.00000i			0.304997i
$388$		−	6.00000i		−	0.304604i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$			9.00000i			0.454569i
$393$		0			0
$394$	−12.0000			−0.604551
$395$	4.00000	−	8.00000i	0.201262	−	0.402524i
$396$	−12.0000			−0.603023
$397$			8.00000i			0.401508i	0.979642	+	0.200754i	$0.0643393\pi$
$397$			8.00000i			0.401508i	−0.979642	+	0.200754i	$0.935661\pi$
$398$		−	16.0000i		−	0.802008i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$		0			0
$403$			8.00000i			0.398508i
$404$	−6.00000			−0.298511
$405$	−9.00000	+	18.0000i	−0.447214	+	0.894427i
$406$	12.0000			0.595550
$407$		−	40.0000i		−	1.98273i
$408$		0			0
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	20.0000	+	10.0000i	0.987730	+	0.493865i
$411$		0			0
$412$			16.0000i			0.788263i
$413$		0			0
$414$	18.0000			0.884652
$415$	36.0000	+	18.0000i	1.76717	+	0.883585i
$416$	10.0000			0.490290
$417$		0			0
$418$			4.00000i			0.195646i
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$		0			0
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$			20.0000i			0.973585i
$423$			18.0000i			0.875190i
$424$	−30.0000			−1.45693
$425$	−16.0000	+	12.0000i	−0.776114	+	0.582086i
$426$		0			0
$427$		−	4.00000i		−	0.193574i
$428$			4.00000i			0.193347i
$429$		0			0
$430$	2.00000	−	4.00000i	0.0964486	−	0.192897i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	−6.00000			−0.287348
$437$			6.00000i			0.287019i
$438$		0			0
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$	24.0000	+	12.0000i	1.14416	+	0.572078i
$441$	9.00000			0.428571
$442$		−	8.00000i		−	0.380521i
$443$		−	2.00000i		−	0.0950229i	−0.998871	−	0.0475114i	$-0.984871\pi$
$443$		−	2.00000i		−	0.0950229i	0.998871	−	0.0475114i	$-0.0151291\pi$
$444$		0			0
$445$	−2.00000	+	4.00000i	−0.0948091	+	0.189618i
$446$	−16.0000			−0.757622
$447$		0			0
$448$			14.0000i			0.661438i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	12.0000	−	9.00000i	0.565685	−	0.424264i
$451$	40.0000			1.88353
$452$			6.00000i			0.282216i
$453$		0			0
$454$	20.0000			0.938647
$455$	4.00000	−	8.00000i	0.187523	−	0.375046i
$456$		0			0
$457$			8.00000i			0.374224i	0.982339	+	0.187112i	$0.0599128\pi$
$457$			8.00000i			0.374224i	−0.982339	+	0.187112i	$0.940087\pi$
$458$			10.0000i			0.467269i
$459$		0			0
$460$	12.0000	+	6.00000i	0.559503	+	0.279751i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$			2.00000i			0.0929479i	0.998920	+	0.0464739i	$0.0147984\pi$
$463$			2.00000i			0.0929479i	−0.998920	+	0.0464739i	$0.985202\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	−16.0000			−0.741186
$467$			38.0000i			1.75843i	0.476425	+	0.879215i	$0.341932\pi$
$467$			38.0000i			1.75843i	−0.476425	+	0.879215i	$0.658068\pi$
$468$		−	6.00000i		−	0.277350i
$469$	−16.0000			−0.738811
$470$	6.00000	−	12.0000i	0.276759	−	0.553519i
$471$		0			0
$472$		0			0
$473$		−	8.00000i		−	0.367840i
$474$		0			0
$475$	3.00000	+	4.00000i	0.137649	+	0.183533i
$476$	−8.00000			−0.366679
$477$			30.0000i			1.37361i
$478$			16.0000i			0.731823i
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		0			0
$481$	20.0000			0.911922
$482$		−	2.00000i		−	0.0910975i
$483$		0			0
$484$	5.00000			0.227273
$485$	12.0000	+	6.00000i	0.544892	+	0.272446i
$486$		0			0
$487$			20.0000i			0.906287i	0.891438	+	0.453143i	$0.149697\pi$
$487$			20.0000i			0.906287i	−0.891438	+	0.453143i	$0.850303\pi$
$488$			6.00000i			0.271607i
$489$		0			0
$490$	−6.00000	−	3.00000i	−0.271052	−	0.135526i
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$		0			0
$493$		−	24.0000i		−	1.08091i
$494$	−2.00000			−0.0899843
$495$	12.0000	−	24.0000i	0.539360	−	1.07872i
$496$	4.00000			0.179605
$497$		−	8.00000i		−	0.358849i
$498$		0			0
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$		0			0
$502$			4.00000i			0.178529i
$503$			10.0000i			0.445878i	0.974832	+	0.222939i	$0.0715651\pi$
$503$			10.0000i			0.445878i	−0.974832	+	0.222939i	$0.928435\pi$
$504$	18.0000			0.801784
$505$	6.00000	−	12.0000i	0.266996	−	0.533993i
$506$	−24.0000			−1.06693
$507$		0			0
$508$		0			0
$509$	6.00000			0.265945			0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000			0.265945			0.132973	+	0.991120i	$0.457548\pi$
$510$		0			0
$511$	8.00000			0.353899
$512$		−	11.0000i		−	0.486136i
$513$		0			0
$514$	−6.00000			−0.264649
$515$	−32.0000	−	16.0000i	−1.41009	−	0.705044i
$516$		0			0
$517$		−	24.0000i		−	1.05552i
$518$			20.0000i			0.878750i
$519$		0			0
$520$	−6.00000	+	12.0000i	−0.263117	+	0.526235i
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$			18.0000i			0.787839i
$523$		−	44.0000i		−	1.92399i	−0.273075	−	0.961993i	$-0.588041\pi$
$523$		−	44.0000i		−	1.92399i	0.273075	−	0.961993i	$-0.411959\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	6.00000			0.261612
$527$			16.0000i			0.696971i
$528$		0			0
$529$	−13.0000			−0.565217
$530$	10.0000	−	20.0000i	0.434372	−	0.868744i
$531$		0			0
$532$			2.00000i			0.0867110i
$533$			20.0000i			0.866296i
$534$		0			0
$535$	−8.00000	−	4.00000i	−0.345870	−	0.172935i
$536$	24.0000			1.03664
$537$		0			0
$538$			18.0000i			0.776035i
$539$	−12.0000			−0.516877
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$			24.0000i			1.03089i
$543$		0			0
$544$	20.0000			0.857493
$545$	6.00000	−	12.0000i	0.257012	−	0.514024i
$546$		0			0
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$		−	12.0000i		−	0.512615i
$549$	6.00000			0.256074
$550$	−16.0000	+	12.0000i	−0.682242	+	0.511682i
$551$	−6.00000			−0.255609
$552$		0			0
$553$			8.00000i			0.340195i
$554$	8.00000			0.339887
$555$		0			0
$556$	4.00000			0.169638
$557$			16.0000i			0.677942i	0.940797	+	0.338971i	$0.110079\pi$
$557$			16.0000i			0.677942i	−0.940797	+	0.338971i	$0.889921\pi$
$558$		−	12.0000i		−	0.508001i
$559$	4.00000			0.169182
$560$	−4.00000	−	2.00000i	−0.169031	−	0.0845154i
$561$		0			0
$562$		−	26.0000i		−	1.09674i
$563$			12.0000i			0.505740i	0.967500	+	0.252870i	$0.0813744\pi$
$563$			12.0000i			0.505740i	−0.967500	+	0.252870i	$0.918626\pi$
$564$		0			0
$565$	−12.0000	−	6.00000i	−0.504844	−	0.252422i
$566$	−14.0000			−0.588464
$567$		−	18.0000i		−	0.755929i
$568$			12.0000i			0.503509i
$569$	−42.0000			−1.76073			−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000			−1.76073			−0.880366	+	0.474295i	$0.842703\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$			8.00000i			0.334497i
$573$		0			0
$574$	−20.0000			−0.834784
$575$	−24.0000	+	18.0000i	−1.00087	+	0.750652i
$576$	−21.0000			−0.875000
$577$		−	24.0000i		−	0.999133i	−0.866276	−	0.499567i	$-0.833493\pi$
$577$		−	24.0000i		−	0.999133i	0.866276	−	0.499567i	$-0.166507\pi$
$578$			1.00000i			0.0415945i
$579$		0			0
$580$	−6.00000	+	12.0000i	−0.249136	+	0.498273i
$581$	−36.0000			−1.49353
$582$		0			0
$583$		−	40.0000i		−	1.65663i
$584$	−12.0000			−0.496564
$585$	12.0000	+	6.00000i	0.496139	+	0.248069i
$586$	14.0000			0.578335
$587$		−	18.0000i		−	0.742940i	−0.928445	−	0.371470i	$-0.878854\pi$
$587$		−	18.0000i		−	0.742940i	0.928445	−	0.371470i	$-0.121146\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$		0			0
$591$		0			0
$592$		−	10.0000i		−	0.410997i
$593$		−	8.00000i		−	0.328521i	−0.986417	−	0.164260i	$-0.947476\pi$
$593$		−	8.00000i		−	0.328521i	0.986417	−	0.164260i	$-0.0525237\pi$
$594$		0			0
$595$	8.00000	−	16.0000i	0.327968	−	0.655936i
$596$	10.0000			0.409616
$597$		0			0
$598$		−	12.0000i		−	0.490716i
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$			4.00000i			0.163028i
$603$		−	24.0000i		−	0.977356i
$604$	24.0000			0.976546
$605$	−5.00000	+	10.0000i	−0.203279	+	0.406558i
$606$		0			0
$607$			44.0000i			1.78590i	0.450151	+	0.892952i	$0.351370\pi$
$607$			44.0000i			1.78590i	−0.450151	+	0.892952i	$0.648630\pi$
$608$		−	5.00000i		−	0.202777i
$609$		0			0
$610$	−4.00000	−	2.00000i	−0.161955	−	0.0809776i
$611$	12.0000			0.485468
$612$		−	12.0000i		−	0.485071i
$613$		−	24.0000i		−	0.969351i	−0.874694	−	0.484675i	$-0.838938\pi$
$613$		−	24.0000i		−	0.969351i	0.874694	−	0.484675i	$-0.161062\pi$
$614$	−20.0000			−0.807134
$615$		0			0
$616$	−24.0000			−0.966988
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$		0			0
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$	4.00000	−	8.00000i	0.160644	−	0.321288i
$621$		0			0
$622$			24.0000i			0.962312i
$623$		−	4.00000i		−	0.160257i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	24.0000			0.959233
$627$		0			0
$628$			8.00000i			0.319235i
$629$	40.0000			1.59490
$630$	−6.00000	+	12.0000i	−0.239046	+	0.478091i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		−	12.0000i		−	0.477334i
$633$		0			0
$634$	22.0000			0.873732
$635$		0			0
$636$		0			0
$637$		−	6.00000i		−	0.237729i
$638$		−	24.0000i		−	0.950169i
$639$	12.0000			0.474713
$640$	−6.00000	−	3.00000i	−0.237171	−	0.118585i
$641$	6.00000			0.236986			0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000			0.236986			0.118493	+	0.992955i	$0.462194\pi$
$642$		0			0
$643$			38.0000i			1.49857i	0.662246	+	0.749287i	$0.269604\pi$
$643$			38.0000i			1.49857i	−0.662246	+	0.749287i	$0.730396\pi$
$644$	−12.0000			−0.472866
$645$		0			0
$646$	−4.00000			−0.157378
$647$		−	30.0000i		−	1.17942i	−0.807614	−	0.589711i	$-0.799242\pi$
$647$		−	30.0000i		−	1.17942i	0.807614	−	0.589711i	$-0.200758\pi$
$648$			27.0000i			1.06066i
$649$		0			0
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$		0			0
$652$			10.0000i			0.391630i
$653$			16.0000i			0.626128i	0.949732	+	0.313064i	$0.101356\pi$
$653$			16.0000i			0.626128i	−0.949732	+	0.313064i	$0.898644\pi$
$654$		0			0
$655$	12.0000	−	24.0000i	0.468879	−	0.937758i
$656$	10.0000			0.390434
$657$			12.0000i			0.468165i
$658$			12.0000i			0.467809i
$659$	16.0000			0.623272			0.311636	−	0.950202i	$-0.399123\pi$
$659$	16.0000			0.623272			0.311636	+	0.950202i	$0.399123\pi$
$660$		0			0
$661$	−30.0000			−1.16686			−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000			−1.16686			−0.583432	+	0.812162i	$0.698291\pi$
$662$		−	4.00000i		−	0.155464i
$663$		0			0
$664$	54.0000			2.09561
$665$	−4.00000	−	2.00000i	−0.155113	−	0.0775567i
$666$	−30.0000			−1.16248
$667$		−	36.0000i		−	1.39393i
$668$		−	12.0000i		−	0.464294i
$669$		0			0
$670$	−8.00000	+	16.0000i	−0.309067	+	0.618134i
$671$	−8.00000			−0.308837
$672$		0			0
$673$			34.0000i			1.31060i	0.755367	+	0.655302i	$0.227459\pi$
$673$			34.0000i			1.31060i	−0.755367	+	0.655302i	$0.772541\pi$
$674$	22.0000			0.847408
$675$		0			0
$676$	9.00000			0.346154
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$		0			0
$679$	−12.0000			−0.460518
$680$	−12.0000	+	24.0000i	−0.460179	+	0.920358i
$681$		0			0
$682$			16.0000i			0.612672i
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$	−3.00000			−0.114708
$685$	24.0000	+	12.0000i	0.916993	+	0.458496i
$686$	20.0000			0.763604
$687$		0			0
$688$		−	2.00000i		−	0.0762493i
$689$	20.0000			0.761939
$690$		0			0
$691$	−12.0000			−0.456502			−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000			−0.456502			−0.228251	+	0.973602i	$0.573301\pi$
$692$		−	6.00000i		−	0.228086i
$693$			24.0000i			0.911685i
$694$	−6.00000			−0.227757
$695$	−4.00000	+	8.00000i	−0.151729	+	0.303457i
$696$		0			0
$697$			40.0000i			1.51511i
$698$		−	2.00000i		−	0.0757011i
$699$		0			0
$700$	−8.00000	+	6.00000i	−0.302372	+	0.226779i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$		−	10.0000i		−	0.377157i
$704$	28.0000			1.05529
$705$		0			0
$706$	−4.00000			−0.150542
$707$			12.0000i			0.451306i
$708$		0			0
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$	−8.00000	−	4.00000i	−0.300235	−	0.150117i
$711$	−12.0000			−0.450035
$712$			6.00000i			0.224860i
$713$			24.0000i			0.898807i
$714$		0			0
$715$	−16.0000	−	8.00000i	−0.598366	−	0.299183i
$716$		0			0
$717$		0			0
$718$			8.00000i			0.298557i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	3.00000	−	6.00000i	0.111803	−	0.223607i
$721$	32.0000			1.19174
$722$			1.00000i			0.0372161i
$723$		0			0
$724$	−18.0000			−0.668965
$725$	−18.0000	−	24.0000i	−0.668503	−	0.891338i
$726$		0			0
$727$		−	2.00000i		−	0.0741759i	−0.999312	−	0.0370879i	$-0.988192\pi$
$727$		−	2.00000i		−	0.0741759i	0.999312	−	0.0370879i	$-0.0118082\pi$
$728$		−	12.0000i		−	0.444750i
$729$	27.0000			1.00000
$730$	4.00000	−	8.00000i	0.148047	−	0.296093i
$731$	8.00000			0.295891
$732$		0			0
$733$		−	12.0000i		−	0.443230i	−0.975134	−	0.221615i	$-0.928867\pi$
$733$		−	12.0000i		−	0.443230i	0.975134	−	0.221615i	$-0.0711328\pi$
$734$	−22.0000			−0.812035
$735$		0			0
$736$	30.0000			1.10581
$737$			32.0000i			1.17874i
$738$		−	30.0000i		−	1.10432i
$739$	−4.00000			−0.147142			−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000			−0.147142			−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−20.0000	−	10.0000i	−0.735215	−	0.367607i
$741$		0			0
$742$			20.0000i			0.734223i
$743$		−	4.00000i		−	0.146746i	−0.997305	−	0.0733729i	$-0.976624\pi$
$743$		−	4.00000i		−	0.146746i	0.997305	−	0.0733729i	$-0.0233763\pi$
$744$		0			0
$745$	−10.0000	+	20.0000i	−0.366372	+	0.732743i
$746$	6.00000			0.219676
$747$		−	54.0000i		−	1.97576i
$748$			16.0000i			0.585018i
$749$	8.00000			0.292314
$750$		0			0
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$		−	6.00000i		−	0.218797i
$753$		0			0
$754$	12.0000			0.437014
$755$	−24.0000	+	48.0000i	−0.873449	+	1.74690i
$756$		0			0
$757$			4.00000i			0.145382i	0.997354	+	0.0726912i	$0.0231588\pi$
$757$			4.00000i			0.145382i	−0.997354	+	0.0726912i	$0.976841\pi$
$758$		−	28.0000i		−	1.01701i
$759$		0			0
$760$	6.00000	+	3.00000i	0.217643	+	0.108821i
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$		0			0
$763$			12.0000i			0.434429i
$764$	−24.0000			−0.868290
$765$	24.0000	+	12.0000i	0.867722	+	0.433861i
$766$	−12.0000			−0.433578
$767$		0			0
$768$		0			0
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$	8.00000	−	16.0000i	0.288300	−	0.576600i
$771$		0			0
$772$		−	26.0000i		−	0.935760i
$773$			46.0000i			1.65451i	0.561830	+	0.827253i	$0.310097\pi$
$773$			46.0000i			1.65451i	−0.561830	+	0.827253i	$0.689903\pi$
$774$	−6.00000			−0.215666
$775$	12.0000	+	16.0000i	0.431053	+	0.574737i
$776$	18.0000			0.646162
$777$		0			0
$778$			30.0000i			1.07555i
$779$	10.0000			0.358287
$780$		0			0
$781$	−16.0000			−0.572525
$782$		−	24.0000i		−	0.858238i
$783$		0			0
$784$	−3.00000			−0.107143
$785$	−16.0000	−	8.00000i	−0.571064	−	0.285532i
$786$		0			0
$787$			44.0000i			1.56843i	0.620489	+	0.784215i	$0.286934\pi$
$787$			44.0000i			1.56843i	−0.620489	+	0.784215i	$0.713066\pi$
$788$			12.0000i			0.427482i
$789$		0			0
$790$	8.00000	+	4.00000i	0.284627	+	0.142314i
$791$	12.0000			0.426671
$792$		−	36.0000i		−	1.27920i
$793$		−	4.00000i		−	0.142044i
$794$	−8.00000			−0.283909
$795$		0			0
$796$	−16.0000			−0.567105
$797$			6.00000i			0.212531i	0.994338	+	0.106265i	$0.0338893\pi$
$797$			6.00000i			0.212531i	−0.994338	+	0.106265i	$0.966111\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	20.0000	−	15.0000i	0.707107	−	0.530330i
$801$	6.00000			0.212000
$802$			18.0000i			0.635602i
$803$		−	16.0000i		−	0.564628i
$804$		0			0
$805$	12.0000	−	24.0000i	0.422944	−	0.845889i
$806$	−8.00000			−0.281788
$807$		0			0
$808$		−	18.0000i		−	0.633238i
$809$	10.0000			0.351581			0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000			0.351581			0.175791	+	0.984428i	$0.443752\pi$
$810$	−18.0000	−	9.00000i	−0.632456	−	0.316228i
$811$	−24.0000			−0.842754			−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000			−0.842754			−0.421377	+	0.906886i	$0.638453\pi$
$812$		−	12.0000i		−	0.421117i
$813$		0			0
$814$	40.0000			1.40200
$815$	−20.0000	−	10.0000i	−0.700569	−	0.350285i
$816$		0			0
$817$		−	2.00000i		−	0.0699711i
$818$			14.0000i			0.489499i
$819$	−12.0000			−0.419314
$820$	10.0000	−	20.0000i	0.349215	−	0.698430i
$821$	−42.0000			−1.46581			−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000			−1.46581			−0.732905	+	0.680331i	$0.761836\pi$
$822$		0			0
$823$		−	42.0000i		−	1.46403i	−0.681290	−	0.732014i	$-0.738581\pi$
$823$		−	42.0000i		−	1.46403i	0.681290	−	0.732014i	$-0.261419\pi$
$824$	−48.0000			−1.67216
$825$		0			0
$826$		0			0
$827$		−	24.0000i		−	0.834562i	−0.908778	−	0.417281i	$-0.862983\pi$
$827$		−	24.0000i		−	0.834562i	0.908778	−	0.417281i	$-0.137017\pi$
$828$		−	18.0000i		−	0.625543i
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$	−18.0000	+	36.0000i	−0.624789	+	1.24958i
$831$		0			0
$832$			14.0000i			0.485363i
$833$		−	12.0000i		−	0.415775i
$834$		0			0
$835$	24.0000	+	12.0000i	0.830554	+	0.415277i
$836$	4.00000			0.138343
$837$		0			0
$838$		−	36.0000i		−	1.24360i
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		−	30.0000i		−	1.03387i
$843$		0			0
$844$	20.0000			0.688428
$845$	−9.00000	+	18.0000i	−0.309609	+	0.619219i
$846$	−18.0000			−0.618853
$847$		−	10.0000i		−	0.343604i
$848$		−	10.0000i		−	0.343401i
$849$		0			0
$850$	−12.0000	−	16.0000i	−0.411597	−	0.548795i
$851$	60.0000			2.05677
$852$		0			0
$853$		−	4.00000i		−	0.136957i	−0.997653	−	0.0684787i	$-0.978185\pi$
$853$		−	4.00000i		−	0.136957i	0.997653	−	0.0684787i	$-0.0218145\pi$
$854$	4.00000			0.136877
$855$	3.00000	−	6.00000i	0.102598	−	0.205196i
$856$	−12.0000			−0.410152
$857$			6.00000i			0.204956i	0.994735	+	0.102478i	$0.0326771\pi$
$857$			6.00000i			0.204956i	−0.994735	+	0.102478i	$0.967323\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$	−4.00000	−	2.00000i	−0.136399	−	0.0681994i
$861$		0			0
$862$		0			0
$863$		−	28.0000i		−	0.953131i	−0.879139	−	0.476566i	$-0.841881\pi$
$863$		−	28.0000i		−	0.953131i	0.879139	−	0.476566i	$-0.158119\pi$
$864$		0			0
$865$	12.0000	+	6.00000i	0.408012	+	0.204006i
$866$	34.0000			1.15537
$867$		0			0
$868$			8.00000i			0.271538i
$869$	16.0000			0.542763
$870$		0			0
$871$	−16.0000			−0.542139
$872$		−	18.0000i		−	0.609557i
$873$		−	18.0000i		−	0.609208i
$874$	−6.00000			−0.202953
$875$	−4.00000	−	22.0000i	−0.135225	−	0.743736i
$876$		0			0
$877$		−	2.00000i		−	0.0675352i	−0.999430	−	0.0337676i	$-0.989249\pi$
$877$		−	2.00000i		−	0.0675352i	0.999430	−	0.0337676i	$-0.0107506\pi$
$878$		−	20.0000i		−	0.674967i
$879$		0			0
$880$	−4.00000	+	8.00000i	−0.134840	+	0.269680i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$			9.00000i			0.303046i
$883$			34.0000i			1.14419i	0.820187	+	0.572096i	$0.193869\pi$
$883$			34.0000i			1.14419i	−0.820187	+	0.572096i	$0.806131\pi$
$884$	−8.00000			−0.269069
$885$		0			0
$886$	2.00000			0.0671913
$887$		−	8.00000i		−	0.268614i	−0.990940	−	0.134307i	$-0.957119\pi$
$887$		−	8.00000i		−	0.268614i	0.990940	−	0.134307i	$-0.0428808\pi$
$888$		0			0
$889$		0			0
$890$	−4.00000	−	2.00000i	−0.134080	−	0.0670402i
$891$	−36.0000			−1.20605
$892$			16.0000i			0.535720i
$893$		−	6.00000i		−	0.200782i
$894$		0			0
$895$		0			0
$896$	6.00000			0.200446
$897$		0			0
$898$		−	10.0000i		−	0.333704i
$899$	−24.0000			−0.800445
$900$	−9.00000	−	12.0000i	−0.300000	−	0.400000i
$901$	40.0000			1.33259
$902$			40.0000i			1.33185i
$903$		0			0
$904$	−18.0000			−0.598671
$905$	18.0000	−	36.0000i	0.598340	−	1.19668i
$906$		0			0
$907$		−	12.0000i		−	0.398453i	−0.979953	−	0.199227i	$-0.936157\pi$
$907$		−	12.0000i		−	0.398453i	0.979953	−	0.199227i	$-0.0638430\pi$
$908$		−	20.0000i		−	0.663723i
$909$	−18.0000			−0.597022
$910$	8.00000	+	4.00000i	0.265197	+	0.132599i
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$			72.0000i			2.38285i
$914$	−8.00000			−0.264616
$915$		0			0
$916$	10.0000			0.330409
$917$			24.0000i			0.792550i
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	−18.0000	+	36.0000i	−0.593442	+	1.18688i
$921$		0			0
$922$			14.0000i			0.461065i
$923$		−	8.00000i		−	0.263323i
$924$		0			0
$925$	40.0000	−	30.0000i	1.31519	−	0.986394i
$926$	−2.00000			−0.0657241
$927$			48.0000i			1.57653i
$928$			30.0000i			0.984798i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$	−3.00000			−0.0983210
$932$			16.0000i			0.524097i
$933$		0			0
$934$	−38.0000			−1.24340
$935$	−32.0000	−	16.0000i	−1.04651	−	0.523256i
$936$	18.0000			0.588348
$937$			20.0000i			0.653372i	0.945133	+	0.326686i	$0.105932\pi$
$937$			20.0000i			0.653372i	−0.945133	+	0.326686i	$0.894068\pi$
$938$		−	16.0000i		−	0.522419i
$939$		0			0
$940$	−12.0000	−	6.00000i	−0.391397	−	0.195698i
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$		0			0
$943$			60.0000i			1.95387i
$944$		0			0
$945$		0			0
$946$	8.00000			0.260102
$947$			30.0000i			0.974869i	0.873160	+	0.487435i	$0.162067\pi$
$947$			30.0000i			0.974869i	−0.873160	+	0.487435i	$0.837933\pi$
$948$		0			0
$949$	8.00000			0.259691
$950$	−4.00000	+	3.00000i	−0.129777	+	0.0973329i
$951$		0			0
$952$		−	24.0000i		−	0.777844i
$953$		−	30.0000i		−	0.971795i	−0.874016	−	0.485898i	$-0.838493\pi$
$953$		−	30.0000i		−	0.971795i	0.874016	−	0.485898i	$-0.161507\pi$
$954$	−30.0000			−0.971286
$955$	24.0000	−	48.0000i	0.776622	−	1.55324i
$956$	16.0000			0.517477
$957$		0			0
$958$			24.0000i			0.775405i
$959$	−24.0000			−0.775000
$960$		0			0
$961$	−15.0000			−0.483871
$962$			20.0000i			0.644826i
$963$			12.0000i			0.386695i
$964$	−2.00000			−0.0644157
$965$	52.0000	+	26.0000i	1.67394	+	0.836970i
$966$		0			0
$967$			2.00000i			0.0643157i	0.999483	+	0.0321578i	$0.0102379\pi$
$967$			2.00000i			0.0643157i	−0.999483	+	0.0321578i	$0.989762\pi$
$968$			15.0000i			0.482118i
$969$		0			0
$970$	−6.00000	+	12.0000i	−0.192648	+	0.385297i
$971$	24.0000			0.770197			0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000			0.770197			0.385098	+	0.922876i	$0.374168\pi$
$972$		0			0
$973$		−	8.00000i		−	0.256468i
$974$	−20.0000			−0.640841
$975$		0			0
$976$	−2.00000			−0.0640184
$977$			14.0000i			0.447900i	0.974601	+	0.223950i	$0.0718952\pi$
$977$			14.0000i			0.447900i	−0.974601	+	0.223950i	$0.928105\pi$
$978$		0			0
$979$	−8.00000			−0.255681
$980$	−3.00000	+	6.00000i	−0.0958315	+	0.191663i
$981$	−18.0000			−0.574696
$982$		−	20.0000i		−	0.638226i
$983$		−	12.0000i		−	0.382741i	−0.981518	−	0.191370i	$-0.938707\pi$
$983$		−	12.0000i		−	0.382741i	0.981518	−	0.191370i	$-0.0612931\pi$
$984$		0			0
$985$	−24.0000	−	12.0000i	−0.764704	−	0.382352i
$986$	24.0000			0.764316
$987$		0			0
$988$			2.00000i			0.0636285i
$989$	12.0000			0.381578
$990$	24.0000	+	12.0000i	0.762770	+	0.381385i
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$		−	20.0000i		−	0.635001i
$993$		0			0
$994$	8.00000			0.253745
$995$	16.0000	−	32.0000i	0.507234	−	1.01447i
$996$		0			0
$997$		−	32.0000i		−	1.01345i	−0.862108	−	0.506725i	$-0.830856\pi$
$997$		−	32.0000i		−	1.01345i	0.862108	−	0.506725i	$-0.169144\pi$
$998$		−	4.00000i		−	0.126618i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.b.a.39.2	yes	2
3.2	odd	2		855.2.c.b.514.1		2
4.3	odd	2		1520.2.d.b.609.2		2
5.2	odd	4		475.2.a.a.1.1		1
5.3	odd	4		475.2.a.c.1.1		1
5.4	even	2	inner	95.2.b.a.39.1	✓	2
15.2	even	4		4275.2.a.p.1.1		1
15.8	even	4		4275.2.a.e.1.1		1
15.14	odd	2		855.2.c.b.514.2		2
19.18	odd	2		1805.2.b.c.1084.1		2
20.3	even	4		7600.2.a.l.1.1		1
20.7	even	4		7600.2.a.i.1.1		1
20.19	odd	2		1520.2.d.b.609.1		2
95.18	even	4		9025.2.a.c.1.1		1
95.37	even	4		9025.2.a.h.1.1		1
95.94	odd	2		1805.2.b.c.1084.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.b.a.39.1	✓	2	5.4	even	2	inner
95.2.b.a.39.2	yes	2	1.1	even	1	trivial
475.2.a.a.1.1		1	5.2	odd	4
475.2.a.c.1.1		1	5.3	odd	4
855.2.c.b.514.1		2	3.2	odd	2
855.2.c.b.514.2		2	15.14	odd	2
1520.2.d.b.609.1		2	20.19	odd	2
1520.2.d.b.609.2		2	4.3	odd	2
1805.2.b.c.1084.1		2	19.18	odd	2
1805.2.b.c.1084.2		2	95.94	odd	2
4275.2.a.e.1.1		1	15.8	even	4
4275.2.a.p.1.1		1	15.2	even	4
7600.2.a.i.1.1		1	20.7	even	4
7600.2.a.l.1.1		1	20.3	even	4
9025.2.a.c.1.1		1	95.18	even	4
9025.2.a.h.1.1		1	95.37	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -2.00000i q^{7} +3.00000i q^{8} +3.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -4.00000 q^{11} -2.00000i q^{13} +2.00000 q^{14} -1.00000 q^{16} -4.00000i q^{17} +3.00000i q^{18} -1.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -4.00000i q^{22} -6.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -2.00000i q^{28} +6.00000 q^{29} -4.00000 q^{31} +5.00000i q^{32} +4.00000 q^{34} +(4.00000 + 2.00000i) q^{35} +3.00000 q^{36} +10.0000i q^{37} -1.00000i q^{38} +(-6.00000 - 3.00000i) q^{40} -10.0000 q^{41} +2.00000i q^{43} -4.00000 q^{44} +(-3.00000 + 6.00000i) q^{45} +6.00000 q^{46} +6.00000i q^{47} +3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -2.00000i q^{52} +10.0000i q^{53} +(4.00000 - 8.00000i) q^{55} +6.00000 q^{56} +6.00000i q^{58} +2.00000 q^{61} -4.00000i q^{62} -6.00000i q^{63} -7.00000 q^{64} +(4.00000 + 2.00000i) q^{65} -8.00000i q^{67} -4.00000i q^{68} +(-2.00000 + 4.00000i) q^{70} +4.00000 q^{71} +9.00000i q^{72} +4.00000i q^{73} -10.0000 q^{74} -1.00000 q^{76} +8.00000i q^{77} -4.00000 q^{79} +(1.00000 - 2.00000i) q^{80} +9.00000 q^{81} -10.0000i q^{82} -18.0000i q^{83} +(8.00000 + 4.00000i) q^{85} -2.00000 q^{86} -12.0000i q^{88} +2.00000 q^{89} +(-6.00000 - 3.00000i) q^{90} -4.00000 q^{91} -6.00000i q^{92} -6.00000 q^{94} +(1.00000 - 2.00000i) q^{95} -6.00000i q^{97} +3.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 2 q^{5} + 6 q^{9} - 4 q^{10} - 8 q^{11} + 4 q^{14} - 2 q^{16} - 2 q^{19} - 2 q^{20} - 6 q^{25} + 4 q^{26} + 12 q^{29} - 8 q^{31} + 8 q^{34} + 8 q^{35} + 6 q^{36} - 12 q^{40} - 20 q^{41}+ \cdots - 24 q^{99}+O(q^{100}) \) 2 * q + 2 * q^4 - 2 * q^5 + 6 * q^9 - 4 * q^10 - 8 * q^11 + 4 * q^14 - 2 * q^16 - 2 * q^19 - 2 * q^20 - 6 * q^25 + 4 * q^26 + 12 * q^29 - 8 * q^31 + 8 * q^34 + 8 * q^35 + 6 * q^36 - 12 * q^40 - 20 * q^41 - 8 * q^44 - 6 * q^45 + 12 * q^46 + 6 * q^49 + 8 * q^50 + 8 * q^55 + 12 * q^56 + 4 * q^61 - 14 * q^64 + 8 * q^65 - 4 * q^70 + 8 * q^71 - 20 * q^74 - 2 * q^76 - 8 * q^79 + 2 * q^80 + 18 * q^81 + 16 * q^85 - 4 * q^86 + 4 * q^89 - 12 * q^90 - 8 * q^91 - 12 * q^94 + 2 * q^95 - 24 * q^99

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