LMFDB - Embedded newform 1166.2.c.b.529.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1166,2,Mod(529,1166)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1166, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("1166.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1166 = 2 \cdot 11 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1166.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,0,-22,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.31055687568$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			529.11
Character	$\chi$	$=$	1166.529
Dual form			1166.2.c.b.529.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +3.24977i q^{3} -1.00000 q^{4} -1.22090i q^{5} +3.24977 q^{6} -3.83413 q^{7} +1.00000i q^{8} -7.56098 q^{9} -1.22090 q^{10} -1.00000 q^{11} -3.24977i q^{12} -1.39676 q^{13} +3.83413i q^{14} +3.96764 q^{15} +1.00000 q^{16} +7.82216 q^{17} +7.56098i q^{18} -6.90056i q^{19} +1.22090i q^{20} -12.4600i q^{21} +1.00000i q^{22} +5.07535i q^{23} -3.24977 q^{24} +3.50940 q^{25} +1.39676i q^{26} -14.8221i q^{27} +3.83413 q^{28} +0.736034 q^{29} -3.96764i q^{30} -5.86712i q^{31} -1.00000i q^{32} -3.24977i q^{33} -7.82216i q^{34} +4.68108i q^{35} +7.56098 q^{36} -7.76696 q^{37} -6.90056 q^{38} -4.53914i q^{39} +1.22090 q^{40} -11.4479i q^{41} -12.4600 q^{42} -2.75352 q^{43} +1.00000 q^{44} +9.23120i q^{45} +5.07535 q^{46} +9.74856 q^{47} +3.24977i q^{48} +7.70052 q^{49} -3.50940i q^{50} +25.4202i q^{51} +1.39676 q^{52} +(6.94700 - 2.17698i) q^{53} -14.8221 q^{54} +1.22090i q^{55} -3.83413i q^{56} +22.4252 q^{57} -0.736034i q^{58} -8.71833 q^{59} -3.96764 q^{60} +1.83687i q^{61} -5.86712 q^{62} +28.9897 q^{63} -1.00000 q^{64} +1.70530i q^{65} -3.24977 q^{66} -6.72228i q^{67} -7.82216 q^{68} -16.4937 q^{69} +4.68108 q^{70} +7.31463i q^{71} -7.56098i q^{72} -8.08412i q^{73} +7.76696i q^{74} +11.4047i q^{75} +6.90056i q^{76} +3.83413 q^{77} -4.53914 q^{78} +10.5961i q^{79} -1.22090i q^{80} +25.4855 q^{81} -11.4479 q^{82} -4.35919i q^{83} +12.4600i q^{84} -9.55007i q^{85} +2.75352i q^{86} +2.39194i q^{87} -1.00000i q^{88} -18.7159 q^{89} +9.23120 q^{90} +5.35536 q^{91} -5.07535i q^{92} +19.0668 q^{93} -9.74856i q^{94} -8.42490 q^{95} +3.24977 q^{96} +7.53326 q^{97} -7.70052i q^{98} +7.56098 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) $ 22 * q - 22 * q^4 - 6 * q^6 - 24 * q^9 + 4 * q^10 - 22 * q^11 + 6 * q^13 + 30 * q^15 + 22 * q^16 + 18 * q^17 + 6 * q^24 - 30 * q^25 + 28 * q^29 + 24 * q^36 - 34 * q^37 - 18 * q^38 - 4 * q^40 + 4 * q^42 - 34 * q^43 + 22 * q^44 + 6 * q^46 + 8 * q^47 + 6 * q^49 - 6 * q^52 + 16 * q^53 + 12 * q^54 + 14 * q^57 - 60 * q^59 - 30 * q^60 - 8 * q^62 + 116 * q^63 - 22 * q^64 + 6 * q^66 - 18 * q^68 - 26 * q^69 - 32 * q^70 - 4 * q^78 + 62 * q^81 - 44 * q^82 - 34 * q^89 - 6 * q^90 + 12 * q^91 + 4 * q^93 - 6 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1166\mathbb{Z}\right)^\times$.

$n$	$849$	$903$
$\chi(n)$	$1$	$-1$

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
$2$		−	1.00000i		−	0.707107i
$3$			3.24977i			1.87625i	0.346292	+	0.938127i	$0.387440\pi$
$3$			3.24977i			1.87625i	−0.346292	+	0.938127i	$0.612560\pi$
$4$	−1.00000			−0.500000
$5$		−	1.22090i		−	0.546003i	−0.962014	−	0.273001i	$-0.911984\pi$
$5$		−	1.22090i		−	0.546003i	0.962014	−	0.273001i	$-0.0880164\pi$
$6$	3.24977			1.32671
$7$	−3.83413			−1.44916			−0.724582	−	0.689189i	$-0.757967\pi$
$7$	−3.83413			−1.44916			−0.724582	+	0.689189i	$0.757967\pi$
$8$			1.00000i			0.353553i
$9$	−7.56098			−2.52033
$10$	−1.22090			−0.386082
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	3.24977i		−	0.938127i
$13$	−1.39676			−0.387392			−0.193696	−	0.981062i	$-0.562047\pi$
$13$	−1.39676			−0.387392			−0.193696	+	0.981062i	$0.562047\pi$
$14$			3.83413i			1.02471i
$15$	3.96764			1.02444
$16$	1.00000			0.250000
$17$	7.82216			1.89715			0.948576	−	0.316550i	$-0.102524\pi$
$17$	7.82216			1.89715			0.948576	+	0.316550i	$0.102524\pi$
$18$			7.56098i			1.78214i
$19$		−	6.90056i		−	1.58310i	−0.611106	−	0.791549i	$-0.709275\pi$
$19$		−	6.90056i		−	1.58310i	0.611106	−	0.791549i	$-0.290725\pi$
$20$			1.22090i			0.273001i
$21$		−	12.4600i		−	2.71900i
$22$			1.00000i			0.213201i
$23$			5.07535i			1.05828i	0.848534	+	0.529141i	$0.177486\pi$
$23$			5.07535i			1.05828i	−0.848534	+	0.529141i	$0.822514\pi$
$24$	−3.24977			−0.663356
$25$	3.50940			0.701881
$26$			1.39676i			0.273927i
$27$		−	14.8221i		−	2.85252i
$28$	3.83413			0.724582
$29$	0.736034			0.136678			0.0683390	−	0.997662i	$-0.478230\pi$
$29$	0.736034			0.136678			0.0683390	+	0.997662i	$0.478230\pi$
$30$		−	3.96764i		−	0.724388i
$31$		−	5.86712i		−	1.05377i	−0.849938	−	0.526883i	$-0.823361\pi$
$31$		−	5.86712i		−	1.05377i	0.849938	−	0.526883i	$-0.176639\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	3.24977i		−	0.565712i
$34$		−	7.82216i		−	1.34149i
$35$			4.68108i			0.791247i
$36$	7.56098			1.26016
$37$	−7.76696			−1.27688			−0.638440	−	0.769672i	$-0.720420\pi$
$37$	−7.76696			−1.27688			−0.638440	+	0.769672i	$0.720420\pi$
$38$	−6.90056			−1.11942
$39$		−	4.53914i		−	0.726845i
$40$	1.22090			0.193041
$41$		−	11.4479i		−	1.78786i	−0.448207	−	0.893930i	$-0.647937\pi$
$41$		−	11.4479i		−	1.78786i	0.448207	−	0.893930i	$-0.352063\pi$
$42$	−12.4600			−1.92262
$43$	−2.75352			−0.419909			−0.209954	−	0.977711i	$-0.567332\pi$
$43$	−2.75352			−0.419909			−0.209954	+	0.977711i	$0.567332\pi$
$44$	1.00000			0.150756
$45$			9.23120i			1.37611i
$46$	5.07535			0.748319
$47$	9.74856			1.42197			0.710987	−	0.703205i	$-0.248248\pi$
$47$	9.74856			1.42197			0.710987	+	0.703205i	$0.248248\pi$
$48$			3.24977i			0.469063i
$49$	7.70052			1.10007
$50$		−	3.50940i		−	0.496305i
$51$			25.4202i			3.55954i
$52$	1.39676			0.193696
$53$	6.94700	−	2.17698i	0.954243	−	0.299031i
$53$	6.94700	−	2.17698i	0.954243	−	0.299031i
$54$	−14.8221			−2.01703
$55$			1.22090i			0.164626i
$56$		−	3.83413i		−	0.512357i
$57$	22.4252			2.97029
$58$		−	0.736034i		−	0.0966460i
$59$	−8.71833			−1.13503			−0.567515	−	0.823363i	$-0.692095\pi$
$59$	−8.71833			−1.13503			−0.567515	+	0.823363i	$0.692095\pi$
$60$	−3.96764			−0.512220
$61$			1.83687i			0.235187i	0.993062	+	0.117593i	$0.0375179\pi$
$61$			1.83687i			0.235187i	−0.993062	+	0.117593i	$0.962482\pi$
$62$	−5.86712			−0.745125
$63$	28.9897			3.65236
$64$	−1.00000			−0.125000
$65$			1.70530i			0.211517i
$66$	−3.24977			−0.400019
$67$		−	6.72228i		−	0.821257i	−0.911803	−	0.410629i	$-0.865309\pi$
$67$		−	6.72228i		−	0.821257i	0.911803	−	0.410629i	$-0.134691\pi$
$68$	−7.82216			−0.948576
$69$	−16.4937			−1.98561
$70$	4.68108			0.559496
$71$			7.31463i			0.868087i	0.900892	+	0.434043i	$0.142914\pi$
$71$			7.31463i			0.868087i	−0.900892	+	0.434043i	$0.857086\pi$
$72$		−	7.56098i		−	0.891070i
$73$		−	8.08412i		−	0.946175i	−0.881015	−	0.473088i	$-0.843139\pi$
$73$		−	8.08412i		−	0.946175i	0.881015	−	0.473088i	$-0.156861\pi$
$74$			7.76696i			0.902890i
$75$			11.4047i			1.31691i
$76$			6.90056i			0.791549i
$77$	3.83413			0.436939
$78$	−4.53914			−0.513957
$79$			10.5961i			1.19215i	0.802927	+	0.596077i	$0.203275\pi$
$79$			10.5961i			1.19215i	−0.802927	+	0.596077i	$0.796725\pi$
$80$		−	1.22090i		−	0.136501i
$81$	25.4855			2.83172
$82$	−11.4479			−1.26421
$83$		−	4.35919i		−	0.478483i	−0.970960	−	0.239242i	$-0.923101\pi$
$83$		−	4.35919i		−	0.478483i	0.970960	−	0.239242i	$-0.0768988\pi$
$84$			12.4600i			1.35950i
$85$		−	9.55007i		−	1.03585i
$86$			2.75352i			0.296920i
$87$			2.39194i			0.256443i
$88$		−	1.00000i		−	0.106600i
$89$	−18.7159			−1.98388			−0.991942	−	0.126689i	$-0.959565\pi$
$89$	−18.7159			−1.98388			−0.991942	+	0.126689i	$0.959565\pi$
$90$	9.23120			0.973053
$91$	5.35536			0.561394
$92$		−	5.07535i		−	0.529141i
$93$	19.0668			1.97713
$94$		−	9.74856i		−	1.00549i
$95$	−8.42490			−0.864376
$96$	3.24977			0.331678
$97$	7.53326			0.764886			0.382443	−	0.923979i	$-0.375083\pi$
$97$	7.53326			0.764886			0.382443	+	0.923979i	$0.375083\pi$
$98$		−	7.70052i		−	0.777870i
$99$	7.56098			0.759907
$100$	−3.50940			−0.350940
$101$		−	17.8368i		−	1.77483i	−0.460972	−	0.887415i	$-0.652499\pi$
$101$		−	17.8368i		−	1.77483i	0.460972	−	0.887415i	$-0.347501\pi$
$102$	25.4202			2.51697
$103$			4.13594i			0.407527i	0.979020	+	0.203763i	$0.0653173\pi$
$103$			4.13594i			0.407527i	−0.979020	+	0.203763i	$0.934683\pi$
$104$		−	1.39676i		−	0.136964i
$105$	−15.2124			−1.48458
$106$	−2.17698	−	6.94700i	−0.211447	−	0.674752i
$107$	−10.4395			−1.00923			−0.504614	−	0.863345i	$-0.668365\pi$
$107$	−10.4395			−1.00923			−0.504614	+	0.863345i	$0.668365\pi$
$108$			14.8221i			1.42626i
$109$		−	14.0315i		−	1.34397i	−0.740564	−	0.671985i	$-0.765442\pi$
$109$		−	14.0315i		−	1.34397i	0.740564	−	0.671985i	$-0.234558\pi$
$110$	1.22090			0.116408
$111$		−	25.2408i		−	2.39575i
$112$	−3.83413			−0.362291
$113$	−14.8275			−1.39485			−0.697427	−	0.716656i	$-0.745672\pi$
$113$	−14.8275			−1.39485			−0.697427	+	0.716656i	$0.745672\pi$
$114$		−	22.4252i		−	2.10031i
$115$	6.19649			0.577825
$116$	−0.736034			−0.0683390
$117$	10.5609			0.976353
$118$			8.71833i			0.802588i
$119$	−29.9911			−2.74928
$120$			3.96764i			0.362194i
$121$	1.00000			0.0909091
$122$	1.83687			0.166302
$123$	37.2030			3.35448
$124$			5.86712i			0.526883i
$125$		−	10.3891i		−	0.929232i
$126$		−	28.9897i		−	2.58261i
$127$		−	4.51350i		−	0.400509i	−0.979744	−	0.200254i	$-0.935823\pi$
$127$		−	4.51350i		−	0.400509i	0.979744	−	0.200254i	$-0.0641769\pi$
$128$			1.00000i			0.0883883i
$129$		−	8.94831i		−	0.787855i
$130$	1.70530			0.149565
$131$	13.3203			1.16380			0.581901	−	0.813260i	$-0.302309\pi$
$131$	13.3203			1.16380			0.581901	+	0.813260i	$0.302309\pi$
$132$			3.24977i			0.282856i
$133$			26.4576i			2.29417i
$134$	−6.72228			−0.580716
$135$	−18.0963			−1.55748
$136$			7.82216i			0.670744i
$137$		−	13.2256i		−	1.12994i	−0.825112	−	0.564970i	$-0.808888\pi$
$137$		−	13.2256i		−	1.12994i	0.825112	−	0.564970i	$-0.191112\pi$
$138$			16.4937i			1.40404i
$139$		−	7.75109i		−	0.657439i	−0.944428	−	0.328719i	$-0.893383\pi$
$139$		−	7.75109i		−	0.657439i	0.944428	−	0.328719i	$-0.106617\pi$
$140$		−	4.68108i		−	0.395624i
$141$			31.6806i			2.66798i
$142$	7.31463			0.613830
$143$	1.39676			0.116803
$144$	−7.56098			−0.630082
$145$		−	0.898624i		−	0.0746266i
$146$	−8.08412			−0.669047
$147$			25.0249i			2.06402i
$148$	7.76696			0.638440
$149$	4.95598			0.406010			0.203005	−	0.979178i	$-0.434929\pi$
$149$	4.95598			0.406010			0.203005	+	0.979178i	$0.434929\pi$
$150$	11.4047			0.931193
$151$			3.92758i			0.319622i	0.987148	+	0.159811i	$0.0510884\pi$
$151$			3.92758i			0.319622i	−0.987148	+	0.159811i	$0.948912\pi$
$152$	6.90056			0.559710
$153$	−59.1432			−4.78144
$154$		−	3.83413i		−	0.308963i
$155$	−7.16316			−0.575359
$156$			4.53914i			0.363422i
$157$			5.73996i			0.458099i	0.973415	+	0.229049i	$0.0735617\pi$
$157$			5.73996i			0.458099i	−0.973415	+	0.229049i	$0.926438\pi$
$158$	10.5961			0.842980
$159$	7.07466	+	22.5761i	0.561057	+	1.79040i
$160$	−1.22090			−0.0965206
$161$		−	19.4595i		−	1.53362i
$162$		−	25.4855i		−	2.00233i
$163$	−5.29170			−0.414478			−0.207239	−	0.978290i	$-0.566448\pi$
$163$	−5.29170			−0.414478			−0.207239	+	0.978290i	$0.566448\pi$
$164$			11.4479i			0.893930i
$165$	−3.96764			−0.308880
$166$	−4.35919			−0.338339
$167$			11.1589i			0.863499i	0.901993	+	0.431750i	$0.142104\pi$
$167$			11.1589i			0.863499i	−0.901993	+	0.431750i	$0.857896\pi$
$168$	12.4600			0.961311
$169$	−11.0491			−0.849928
$170$	−9.55007			−0.732457
$171$			52.1750i			3.98992i
$172$	2.75352			0.209954
$173$			5.33490i			0.405605i	0.979220	+	0.202803i	$0.0650050\pi$
$173$			5.33490i			0.405605i	−0.979220	+	0.202803i	$0.934995\pi$
$174$	2.39194			0.181332
$175$	−13.4555			−1.01714
$176$	−1.00000			−0.0753778
$177$		−	28.3325i		−	2.12960i
$178$			18.7159i			1.40282i
$179$		−	8.89259i		−	0.664663i	−0.943163	−	0.332332i	$-0.892165\pi$
$179$		−	8.89259i		−	0.664663i	0.943163	−	0.332332i	$-0.107835\pi$
$180$		−	9.23120i		−	0.688053i
$181$		−	17.1667i		−	1.27599i	−0.770039	−	0.637997i	$-0.779763\pi$
$181$		−	17.1667i		−	1.27599i	0.770039	−	0.637997i	$-0.220237\pi$
$182$		−	5.35536i		−	0.396965i
$183$	−5.96939			−0.441270
$184$	−5.07535			−0.374159
$185$			9.48267i			0.697180i
$186$		−	19.0668i		−	1.39804i
$187$	−7.82216			−0.572013
$188$	−9.74856			−0.710987
$189$			56.8298i			4.13376i
$190$			8.42490i			0.611206i
$191$			15.4673i			1.11918i	0.828770	+	0.559589i	$0.189041\pi$
$191$			15.4673i			1.11918i	−0.828770	+	0.559589i	$0.810959\pi$
$192$		−	3.24977i		−	0.234532i
$193$			5.39018i			0.387993i	0.981002	+	0.193997i	$0.0621451\pi$
$193$			5.39018i			0.387993i	−0.981002	+	0.193997i	$0.937855\pi$
$194$		−	7.53326i		−	0.540856i
$195$	−5.54184			−0.396859
$196$	−7.70052			−0.550037
$197$	12.5461			0.893874			0.446937	−	0.894565i	$-0.352515\pi$
$197$	12.5461			0.893874			0.446937	+	0.894565i	$0.352515\pi$
$198$		−	7.56098i		−	0.537335i
$199$	−6.05360			−0.429128			−0.214564	−	0.976710i	$-0.568833\pi$
$199$	−6.05360			−0.429128			−0.214564	+	0.976710i	$0.568833\pi$
$200$			3.50940i			0.248152i
$201$	21.8458			1.54089
$202$	−17.8368			−1.25499
$203$	−2.82205			−0.198069
$204$		−	25.4202i		−	1.77977i
$205$	−13.9767			−0.976177
$206$	4.13594			0.288165
$207$		−	38.3746i		−	2.66722i
$208$	−1.39676			−0.0968479
$209$			6.90056i			0.477322i
$210$			15.2124i			1.04976i
$211$	9.82786			0.676578			0.338289	−	0.941042i	$-0.390152\pi$
$211$	9.82786			0.676578			0.338289	+	0.941042i	$0.390152\pi$
$212$	−6.94700	+	2.17698i	−0.477122	+	0.149515i
$213$	−23.7708			−1.62875
$214$			10.4395i			0.713631i
$215$			3.36178i			0.229271i
$216$	14.8221			1.00852
$217$			22.4953i			1.52708i
$218$	−14.0315			−0.950331
$219$	26.2715			1.77526
$220$		−	1.22090i		−	0.0823130i
$221$	−10.9257			−0.734941
$222$	−25.2408			−1.69405
$223$	0.250033			0.0167434			0.00837172	−	0.999965i	$-0.497335\pi$
$223$	0.250033			0.0167434			0.00837172	+	0.999965i	$0.497335\pi$
$224$			3.83413i			0.256178i
$225$	−26.5345			−1.76897
$226$			14.8275i			0.986310i
$227$	−0.820688			−0.0544710			−0.0272355	−	0.999629i	$-0.508670\pi$
$227$	−0.820688			−0.0544710			−0.0272355	+	0.999629i	$0.508670\pi$
$228$	−22.4252			−1.48515
$229$	4.63516			0.306300			0.153150	−	0.988203i	$-0.451058\pi$
$229$	4.63516			0.306300			0.153150	+	0.988203i	$0.451058\pi$
$230$		−	6.19649i		−	0.408584i
$231$			12.4600i			0.819809i
$232$			0.736034i			0.0483230i
$233$		−	24.1256i		−	1.58052i	−0.612770	−	0.790261i	$-0.709945\pi$
$233$		−	24.1256i		−	1.58052i	0.612770	−	0.790261i	$-0.290055\pi$
$234$		−	10.5609i		−	0.690386i
$235$		−	11.9020i		−	0.776402i
$236$	8.71833			0.567515
$237$	−34.4348			−2.23678
$238$			29.9911i			1.94404i
$239$			10.1487i			0.656466i	0.944597	+	0.328233i	$0.106453\pi$
$239$			10.1487i			0.656466i	−0.944597	+	0.328233i	$0.893547\pi$
$240$	3.96764			0.256110
$241$	−9.00975			−0.580369			−0.290184	−	0.956971i	$-0.593717\pi$
$241$	−9.00975			−0.580369			−0.290184	+	0.956971i	$0.593717\pi$
$242$		−	1.00000i		−	0.0642824i
$243$			38.3554i			2.46050i
$244$		−	1.83687i		−	0.117593i
$245$		−	9.40156i		−	0.600644i
$246$		−	37.2030i		−	2.37197i
$247$			9.63843i			0.613279i
$248$	5.86712			0.372562
$249$	14.1663			0.897755
$250$	−10.3891			−0.657066
$251$		−	3.07003i		−	0.193779i	−0.995295	−	0.0968893i	$-0.969111\pi$
$251$		−	3.07003i		−	0.193779i	0.995295	−	0.0968893i	$-0.0308893\pi$
$252$	−28.9897			−1.82618
$253$		−	5.07535i		−	0.319084i
$254$	−4.51350			−0.283202
$255$	31.0355			1.94352
$256$	1.00000			0.0625000
$257$		−	31.3518i		−	1.95567i	−0.209373	−	0.977836i	$-0.567142\pi$
$257$		−	31.3518i		−	1.95567i	0.209373	−	0.977836i	$-0.432858\pi$
$258$	−8.94831			−0.557097
$259$	29.7795			1.85041
$260$		−	1.70530i		−	0.105758i
$261$	−5.56514			−0.344473
$262$		−	13.3203i		−	0.822932i
$263$			8.77352i			0.540998i	0.962720	+	0.270499i	$0.0871888\pi$
$263$			8.77352i			0.540998i	−0.962720	+	0.270499i	$0.912811\pi$
$264$	3.24977			0.200009
$265$	−2.65787	−	8.48159i	−0.163272	−	0.521020i
$266$	26.4576			1.62222
$267$		−	60.8224i		−	3.72227i
$268$			6.72228i			0.410629i
$269$	9.26887			0.565133			0.282566	−	0.959248i	$-0.408814\pi$
$269$	9.26887			0.565133			0.282566	+	0.959248i	$0.408814\pi$
$270$			18.0963i			1.10131i
$271$	−16.9647			−1.03053			−0.515265	−	0.857031i	$-0.672307\pi$
$271$	−16.9647			−1.03053			−0.515265	+	0.857031i	$0.672307\pi$
$272$	7.82216			0.474288
$273$			17.4037i			1.05332i
$274$	−13.2256			−0.798988
$275$	−3.50940			−0.211625
$276$	16.4937			0.992803
$277$			2.44388i			0.146839i	0.997301	+	0.0734194i	$0.0233912\pi$
$277$			2.44388i			0.146839i	−0.997301	+	0.0734194i	$0.976609\pi$
$278$	−7.75109			−0.464879
$279$			44.3612i			2.65583i
$280$	−4.68108			−0.279748
$281$	12.1898			0.727184			0.363592	−	0.931558i	$-0.381550\pi$
$281$	12.1898			0.727184			0.363592	+	0.931558i	$0.381550\pi$
$282$	31.6806			1.88655
$283$			19.2995i			1.14724i	0.819122	+	0.573619i	$0.194461\pi$
$283$			19.2995i			1.14724i	−0.819122	+	0.573619i	$0.805539\pi$
$284$		−	7.31463i		−	0.434043i
$285$		−	27.3789i		−	1.62179i
$286$		−	1.39676i		−	0.0825922i
$287$			43.8926i			2.59090i
$288$			7.56098i			0.445535i
$289$	44.1861			2.59918
$290$	−0.898624			−0.0527690
$291$			24.4813i			1.43512i
$292$			8.08412i			0.473088i
$293$	19.4434			1.13590			0.567949	−	0.823064i	$-0.307737\pi$
$293$	19.4434			1.13590			0.567949	+	0.823064i	$0.307737\pi$
$294$	25.0249			1.45948
$295$			10.6442i			0.619730i
$296$		−	7.76696i		−	0.451445i
$297$			14.8221i			0.860066i
$298$		−	4.95598i		−	0.287092i
$299$		−	7.08904i		−	0.409970i
$300$		−	11.4047i		−	0.658453i
$301$	10.5574			0.608516
$302$	3.92758			0.226007
$303$	57.9655			3.33003
$304$		−	6.90056i		−	0.395774i
$305$	2.24263			0.128413
$306$			59.1432i			3.38099i
$307$	4.72499			0.269669			0.134835	−	0.990868i	$-0.456950\pi$
$307$	4.72499			0.269669			0.134835	+	0.990868i	$0.456950\pi$
$308$	−3.83413			−0.218470
$309$	−13.4408			−0.764623
$310$			7.16316i			0.406840i
$311$	−16.2390			−0.920831			−0.460415	−	0.887704i	$-0.652300\pi$
$311$	−16.2390			−0.920831			−0.460415	+	0.887704i	$0.652300\pi$
$312$	4.53914			0.256978
$313$			1.59242i			0.0900090i	0.998987	+	0.0450045i	$0.0143302\pi$
$313$			1.59242i			0.0900090i	−0.998987	+	0.0450045i	$0.985670\pi$
$314$	5.73996			0.323925
$315$		−	35.3936i		−	1.99420i
$316$		−	10.5961i		−	0.596077i
$317$	−21.7876			−1.22372			−0.611858	−	0.790968i	$-0.709578\pi$
$317$	−21.7876			−1.22372			−0.611858	+	0.790968i	$0.709578\pi$
$318$	22.5761	−	7.07466i	1.26601	−	0.396727i
$319$	−0.736034			−0.0412100
$320$			1.22090i			0.0682504i
$321$		−	33.9260i		−	1.89357i
$322$	−19.4595			−1.08444
$323$		−	53.9773i		−	3.00338i
$324$	−25.4855			−1.41586
$325$	−4.90180			−0.271903
$326$			5.29170i			0.293080i
$327$	45.5990			2.52163
$328$	11.4479			0.632104
$329$	−37.3772			−2.06067
$330$			3.96764i			0.218411i
$331$	−28.7611			−1.58085			−0.790427	−	0.612556i	$-0.790141\pi$
$331$	−28.7611			−1.58085			−0.790427	+	0.612556i	$0.790141\pi$
$332$			4.35919i			0.239242i
$333$	58.7258			3.21815
$334$	11.1589			0.610586
$335$	−8.20723			−0.448409
$336$		−	12.4600i		−	0.679749i
$337$			14.1276i			0.769579i	0.923004	+	0.384790i	$0.125726\pi$
$337$			14.1276i			0.769579i	−0.923004	+	0.384790i	$0.874274\pi$
$338$			11.0491i			0.600990i
$339$		−	48.1859i		−	2.61710i
$340$			9.55007i			0.517925i
$341$			5.86712i			0.317722i
$342$	52.1750			2.82130
$343$	−2.68589			−0.145024
$344$		−	2.75352i		−	0.148460i
$345$			20.1371i			1.08415i
$346$	5.33490			0.286806
$347$	−13.5977			−0.729960			−0.364980	−	0.931015i	$-0.618924\pi$
$347$	−13.5977			−0.729960			−0.364980	+	0.931015i	$0.618924\pi$
$348$		−	2.39194i		−	0.128221i
$349$			7.01389i			0.375445i	0.982222	+	0.187722i	$0.0601106\pi$
$349$			7.01389i			0.375445i	−0.982222	+	0.187722i	$0.939889\pi$
$350$			13.4555i			0.719227i
$351$			20.7029i			1.10504i
$352$			1.00000i			0.0533002i
$353$			2.25186i			0.119854i	0.998203	+	0.0599271i	$0.0190868\pi$
$353$			2.25186i			0.119854i	−0.998203	+	0.0599271i	$0.980913\pi$
$354$	−28.3325			−1.50586
$355$	8.93043			0.473978
$356$	18.7159			0.991942
$357$		−	97.4642i		−	5.15835i
$358$	−8.89259			−0.469988
$359$		−	12.9911i		−	0.685645i	−0.939400	−	0.342823i	$-0.888617\pi$
$359$		−	12.9911i		−	0.685645i	0.939400	−	0.342823i	$-0.111383\pi$
$360$	−9.23120			−0.486527
$361$	−28.6178			−1.50620
$362$	−17.1667			−0.902264
$363$			3.24977i			0.170568i
$364$	−5.35536			−0.280697
$365$	−9.86990			−0.516614
$366$			5.96939i			0.312025i
$367$	−3.61151			−0.188519			−0.0942596	−	0.995548i	$-0.530048\pi$
$367$	−3.61151			−0.188519			−0.0942596	+	0.995548i	$0.530048\pi$
$368$			5.07535i			0.264571i
$369$			86.5572i			4.50599i
$370$	9.48267			0.492981
$371$	−26.6357	+	8.34680i	−1.38285	+	0.433344i
$372$	−19.0668			−0.988566
$373$			20.6459i			1.06901i	0.845167	+	0.534503i	$0.179501\pi$
$373$			20.6459i			1.06901i	−0.845167	+	0.534503i	$0.820499\pi$
$374$			7.82216i			0.404474i
$375$	33.7622			1.74347
$376$			9.74856i			0.502744i
$377$	−1.02806			−0.0529479
$378$	56.8298			2.92301
$379$		−	17.0098i		−	0.873732i	−0.899526	−	0.436866i	$-0.856088\pi$
$379$		−	17.0098i		−	0.873732i	0.899526	−	0.436866i	$-0.143912\pi$
$380$	8.42490			0.432188
$381$	14.6678			0.751456
$382$	15.4673			0.791378
$383$		−	13.2034i		−	0.674661i	−0.941386	−	0.337330i	$-0.890476\pi$
$383$		−	13.2034i		−	0.674661i	0.941386	−	0.337330i	$-0.109524\pi$
$384$	−3.24977			−0.165839
$385$		−	4.68108i		−	0.238570i
$386$	5.39018			0.274353
$387$	20.8193			1.05831
$388$	−7.53326			−0.382443
$389$			26.3757i			1.33730i	0.743578	+	0.668650i	$0.233127\pi$
$389$			26.3757i			1.33730i	−0.743578	+	0.668650i	$0.766873\pi$
$390$			5.54184i			0.280622i
$391$			39.7002i			2.00772i
$392$			7.70052i			0.388935i
$393$			43.2879i			2.18359i
$394$		−	12.5461i		−	0.632064i
$395$	12.9368			0.650919
$396$	−7.56098			−0.379953
$397$			0.560584i			0.0281349i	0.999901	+	0.0140675i	$0.00447796\pi$
$397$			0.560584i			0.0281349i	−0.999901	+	0.0140675i	$0.995522\pi$
$398$			6.05360i			0.303439i
$399$	−85.9811			−4.30444
$400$	3.50940			0.175470
$401$			19.1575i			0.956679i	0.878175	+	0.478339i	$0.158761\pi$
$401$			19.1575i			0.956679i	−0.878175	+	0.478339i	$0.841239\pi$
$402$		−	21.8458i		−	1.08957i
$403$			8.19496i			0.408220i
$404$			17.8368i			0.887415i
$405$		−	31.1152i		−	1.54613i
$406$			2.82205i			0.140056i
$407$	7.76696			0.384994
$408$	−25.4202			−1.25849
$409$	23.1556			1.14497			0.572485	−	0.819915i	$-0.305979\pi$
$409$	23.1556			1.14497			0.572485	+	0.819915i	$0.305979\pi$
$410$			13.9767i			0.690261i
$411$	42.9801			2.12005
$412$		−	4.13594i		−	0.203763i
$413$	33.4272			1.64484
$414$	−38.3746			−1.88601
$415$	−5.32213			−0.261253
$416$			1.39676i			0.0684818i
$417$	25.1892			1.23352
$418$	6.90056			0.337518
$419$		−	15.7794i		−	0.770874i	−0.922734	−	0.385437i	$-0.874051\pi$
$419$		−	15.7794i		−	0.770874i	0.922734	−	0.385437i	$-0.125949\pi$
$420$	15.2124			0.742290
$421$		−	12.1231i		−	0.590845i	−0.955367	−	0.295422i	$-0.904540\pi$
$421$		−	12.1231i		−	0.590845i	0.955367	−	0.295422i	$-0.0954604\pi$
$422$		−	9.82786i		−	0.478413i
$423$	−73.7087			−3.58384
$424$	2.17698	+	6.94700i	0.105723	+	0.337376i
$425$	27.4511			1.33157
$426$			23.7708i			1.15170i
$427$		−	7.04278i		−	0.340824i
$428$	10.4395			0.504614
$429$			4.53914i			0.219152i
$430$	3.36178			0.162119
$431$	−23.0942			−1.11241			−0.556204	−	0.831046i	$-0.687743\pi$
$431$	−23.0942			−1.11241			−0.556204	+	0.831046i	$0.687743\pi$
$432$		−	14.8221i		−	0.713129i
$433$	0.295719			0.0142113			0.00710567	−	0.999975i	$-0.497738\pi$
$433$	0.295719			0.0142113			0.00710567	+	0.999975i	$0.497738\pi$
$434$	22.4953			1.07981
$435$	2.92032			0.140018
$436$			14.0315i			0.671985i
$437$	35.0228			1.67537
$438$		−	26.2715i		−	1.25530i
$439$	16.1019			0.768501			0.384251	−	0.923229i	$-0.374460\pi$
$439$	16.1019			0.768501			0.384251	+	0.923229i	$0.374460\pi$
$440$	−1.22090			−0.0582041
$441$	−58.2235			−2.77255
$442$			10.9257i			0.519682i
$443$		−	17.8170i		−	0.846511i	−0.906010	−	0.423255i	$-0.860887\pi$
$443$		−	17.8170i		−	0.846511i	0.906010	−	0.423255i	$-0.139113\pi$
$444$			25.2408i			1.19787i
$445$			22.8503i			1.08321i
$446$		−	0.250033i		−	0.0118394i
$447$			16.1058i			0.761777i
$448$	3.83413			0.181145
$449$	−3.69734			−0.174488			−0.0872440	−	0.996187i	$-0.527806\pi$
$449$	−3.69734			−0.174488			−0.0872440	+	0.996187i	$0.527806\pi$
$450$			26.5345i			1.25085i
$451$			11.4479i			0.539060i
$452$	14.8275			0.697427
$453$	−12.7637			−0.599691
$454$			0.820688i			0.0385168i
$455$		−	6.53835i		−	0.306523i
$456$			22.4252i			1.05016i
$457$			17.9502i			0.839677i	0.907599	+	0.419838i	$0.137913\pi$
$457$			17.9502i			0.839677i	−0.907599	+	0.419838i	$0.862087\pi$
$458$		−	4.63516i		−	0.216587i
$459$		−	115.941i		−	5.41166i
$460$	−6.19649			−0.288913
$461$	−27.9701			−1.30270			−0.651348	−	0.758779i	$-0.725796\pi$
$461$	−27.9701			−1.30270			−0.651348	+	0.758779i	$0.725796\pi$
$462$	12.4600			0.579692
$463$		−	12.5739i		−	0.584359i	−0.956364	−	0.292179i	$-0.905620\pi$
$463$		−	12.5739i		−	0.584359i	0.956364	−	0.292179i	$-0.0943804\pi$
$464$	0.736034			0.0341695
$465$		−	23.2786i		−	1.07952i
$466$	−24.1256			−1.11760
$467$	25.3693			1.17395			0.586975	−	0.809605i	$-0.300319\pi$
$467$	25.3693			1.17395			0.586975	+	0.809605i	$0.300319\pi$
$468$	−10.5609			−0.488177
$469$			25.7741i			1.19014i
$470$	−11.9020			−0.548999
$471$	−18.6535			−0.859509
$472$		−	8.71833i		−	0.401294i
$473$	2.75352			0.126607
$474$			34.4348i			1.58164i
$475$		−	24.2169i		−	1.11115i
$476$	29.9911			1.37464
$477$	−52.5261	+	16.4601i	−2.40500	+	0.753655i
$478$	10.1487			0.464191
$479$			16.4541i			0.751806i	0.926659	+	0.375903i	$0.122667\pi$
$479$			16.4541i			0.751806i	−0.926659	+	0.375903i	$0.877333\pi$
$480$		−	3.96764i		−	0.181097i
$481$	10.8486			0.494653
$482$			9.00975i			0.410383i
$483$	63.2389			2.87747
$484$	−1.00000			−0.0454545
$485$		−	9.19735i		−	0.417630i
$486$	38.3554			1.73984
$487$	−27.0440			−1.22548			−0.612740	−	0.790284i	$-0.709933\pi$
$487$	−27.0440			−1.22548			−0.612740	+	0.790284i	$0.709933\pi$
$488$	−1.83687			−0.0831511
$489$		−	17.1968i		−	0.777665i
$490$	−9.40156			−0.424719
$491$		−	38.8353i		−	1.75261i	−0.481756	−	0.876306i	$-0.660001\pi$
$491$		−	38.8353i		−	1.75261i	0.481756	−	0.876306i	$-0.339999\pi$
$492$	−37.2030			−1.67724
$493$	5.75737			0.259299
$494$	9.63843			0.433654
$495$		−	9.23120i		−	0.414911i
$496$		−	5.86712i		−	0.263441i
$497$		−	28.0452i		−	1.25800i
$498$		−	14.1663i		−	0.634809i
$499$			14.3490i			0.642348i	0.947020	+	0.321174i	$0.104077\pi$
$499$			14.3490i			0.642348i	−0.947020	+	0.321174i	$0.895923\pi$
$500$			10.3891i			0.464616i
$501$	−36.2637			−1.62014
$502$	−3.07003			−0.137022
$503$		−	28.0960i		−	1.25274i	−0.779526	−	0.626370i	$-0.784540\pi$
$503$		−	28.0960i		−	1.25274i	0.779526	−	0.626370i	$-0.215460\pi$
$504$			28.9897i			1.29131i
$505$	−21.7770			−0.969062
$506$	−5.07535			−0.225627
$507$		−	35.9069i		−	1.59468i
$508$			4.51350i			0.200254i
$509$			5.66864i			0.251258i	0.992077	+	0.125629i	$0.0400949\pi$
$509$			5.66864i			0.251258i	−0.992077	+	0.125629i	$0.959905\pi$
$510$		−	31.0355i		−	1.37427i
$511$			30.9955i			1.37116i
$512$		−	1.00000i		−	0.0441942i
$513$	−102.281			−4.51581
$514$	−31.3518			−1.38287
$515$	5.04957			0.222511
$516$			8.94831i			0.393927i
$517$	−9.74856			−0.428741
$518$		−	29.7795i		−	1.30844i
$519$	−17.3372			−0.761018
$520$	−1.70530			−0.0747825
$521$	14.6382			0.641313			0.320656	−	0.947196i	$-0.396097\pi$
$521$	14.6382			0.641313			0.320656	+	0.947196i	$0.396097\pi$
$522$			5.56514i			0.243579i
$523$	−30.4325			−1.33072			−0.665361	−	0.746522i	$-0.731722\pi$
$523$	−30.4325			−1.33072			−0.665361	+	0.746522i	$0.731722\pi$
$524$	−13.3203			−0.581901
$525$		−	43.7272i		−	1.90841i
$526$	8.77352			0.382544
$527$		−	45.8935i		−	1.99915i
$528$		−	3.24977i		−	0.141428i
$529$	−2.75914			−0.119963
$530$	−8.48159	+	2.65787i	−0.368417	+	0.115450i
$531$	65.9191			2.86065
$532$		−	26.4576i		−	1.14708i
$533$			15.9900i			0.692602i
$534$	−60.8224			−2.63204
$535$			12.7456i			0.551041i
$536$	6.72228			0.290358
$537$	28.8988			1.24708
$538$		−	9.26887i		−	0.399609i
$539$	−7.70052			−0.331685
$540$	18.0963			0.778741
$541$	32.1645			1.38286			0.691429	−	0.722444i	$-0.256981\pi$
$541$	32.1645			1.38286			0.691429	+	0.722444i	$0.256981\pi$
$542$			16.9647i			0.728695i
$543$	55.7879			2.39409
$544$		−	7.82216i		−	0.335372i
$545$	−17.1310			−0.733812
$546$	17.4037			0.744808
$547$	39.6552			1.69553			0.847767	−	0.530369i	$-0.177947\pi$
$547$	39.6552			1.69553			0.847767	+	0.530369i	$0.177947\pi$
$548$			13.2256i			0.564970i
$549$		−	13.8885i		−	0.592747i
$550$			3.50940i			0.149641i
$551$		−	5.07905i		−	0.216375i
$552$		−	16.4937i		−	0.702018i
$553$		−	40.6268i		−	1.72763i
$554$	2.44388			0.103831
$555$	−30.8165			−1.30809
$556$			7.75109i			0.328719i
$557$		−	22.2356i		−	0.942152i	−0.882093	−	0.471076i	$-0.843866\pi$
$557$		−	22.2356i		−	0.942152i	0.882093	−	0.471076i	$-0.156134\pi$
$558$	44.3612			1.87796
$559$	3.84601			0.162669
$560$			4.68108i			0.197812i
$561$		−	25.4202i		−	1.07324i
$562$		−	12.1898i		−	0.514197i
$563$		−	21.9261i		−	0.924073i	−0.886861	−	0.462037i	$-0.847119\pi$
$563$		−	21.9261i		−	0.924073i	0.886861	−	0.462037i	$-0.152881\pi$
$564$		−	31.6806i		−	1.33399i
$565$			18.1029i			0.761594i
$566$	19.2995			0.811219
$567$	−97.7145			−4.10362
$568$	−7.31463			−0.306915
$569$		−	5.93260i		−	0.248707i	−0.992238	−	0.124354i	$-0.960314\pi$
$569$		−	5.93260i		−	0.248707i	0.992238	−	0.124354i	$-0.0396857\pi$
$570$	−27.3789			−1.14678
$571$			8.08531i			0.338360i	0.985585	+	0.169180i	$0.0541119\pi$
$571$			8.08531i			0.338360i	−0.985585	+	0.169180i	$0.945888\pi$
$572$	−1.39676			−0.0584015
$573$	−50.2652			−2.09986
$574$	43.8926			1.83204
$575$			17.8114i			0.742788i
$576$	7.56098			0.315041
$577$	3.06176			0.127463			0.0637313	−	0.997967i	$-0.479700\pi$
$577$	3.06176			0.127463			0.0637313	+	0.997967i	$0.479700\pi$
$578$		−	44.1861i		−	1.83790i
$579$	−17.5168			−0.727974
$580$			0.898624i			0.0373133i
$581$			16.7137i			0.693400i
$582$	24.4813			1.01478
$583$	−6.94700	+	2.17698i	−0.287715	+	0.0901612i
$584$	8.08412			0.334523
$585$		−	12.8938i		−	0.533092i
$586$		−	19.4434i		−	0.803201i
$587$	−29.7494			−1.22789			−0.613945	−	0.789349i	$-0.710418\pi$
$587$	−29.7494			−1.22789			−0.613945	+	0.789349i	$0.710418\pi$
$588$		−	25.0249i		−	1.03201i
$589$	−40.4864			−1.66821
$590$	10.6442			0.438215
$591$			40.7719i			1.67713i
$592$	−7.76696			−0.319220
$593$	−7.51588			−0.308640			−0.154320	−	0.988021i	$-0.549319\pi$
$593$	−7.51588			−0.308640			−0.154320	+	0.988021i	$0.549319\pi$
$594$	14.8221			0.608159
$595$			36.6162i			1.50112i
$596$	−4.95598			−0.203005
$597$		−	19.6728i		−	0.805153i
$598$	−7.08904			−0.289893
$599$	−9.76420			−0.398954			−0.199477	−	0.979902i	$-0.563924\pi$
$599$	−9.76420			−0.398954			−0.199477	+	0.979902i	$0.563924\pi$
$600$	−11.4047			−0.465597
$601$			9.09763i			0.371100i	0.982635	+	0.185550i	$0.0594067\pi$
$601$			9.09763i			0.371100i	−0.982635	+	0.185550i	$0.940593\pi$
$602$		−	10.5574i		−	0.430286i
$603$			50.8270i			2.06984i
$604$		−	3.92758i		−	0.159811i
$605$		−	1.22090i		−	0.0496366i
$606$		−	57.9655i		−	2.35469i
$607$	22.9170			0.930170			0.465085	−	0.885266i	$-0.346024\pi$
$607$	22.9170			0.930170			0.465085	+	0.885266i	$0.346024\pi$
$608$	−6.90056			−0.279855
$609$		−	9.17099i		−	0.371627i
$610$		−	2.24263i		−	0.0908014i
$611$	−13.6164			−0.550861
$612$	59.1432			2.39072
$613$			7.50411i			0.303088i	0.988451	+	0.151544i	$0.0484245\pi$
$613$			7.50411i			0.303088i	−0.988451	+	0.151544i	$0.951575\pi$
$614$		−	4.72499i		−	0.190685i
$615$		−	45.4211i		−	1.83155i
$616$			3.83413i			0.154481i
$617$		−	14.0679i		−	0.566351i	−0.959068	−	0.283175i	$-0.908612\pi$
$617$		−	14.0679i		−	0.566351i	0.959068	−	0.283175i	$-0.0913878\pi$
$618$			13.4408i			0.540670i
$619$	14.7916			0.594524			0.297262	−	0.954796i	$-0.403926\pi$
$619$	14.7916			0.594524			0.297262	+	0.954796i	$0.403926\pi$
$620$	7.16316			0.287680
$621$	75.2274			3.01877
$622$			16.2390i			0.651126i
$623$	71.7592			2.87497
$624$		−	4.53914i		−	0.181711i
$625$	4.86294			0.194518
$626$	1.59242			0.0636460
$627$	−22.4252			−0.895577
$628$		−	5.73996i		−	0.229049i
$629$	−60.7544			−2.42243
$630$	−35.3936			−1.41011
$631$			16.6338i			0.662182i	0.943599	+	0.331091i	$0.107417\pi$
$631$			16.6338i			0.662182i	−0.943599	+	0.331091i	$0.892583\pi$
$632$	−10.5961			−0.421490
$633$			31.9383i			1.26943i
$634$			21.7876i			0.865298i
$635$	−5.51054			−0.218679
$636$	−7.07466	−	22.5761i	−0.280529	−	0.895201i
$637$	−10.7558			−0.426160
$638$			0.736034i			0.0291399i
$639$		−	55.3058i		−	2.18786i
$640$	1.22090			0.0482603
$641$			38.0492i			1.50285i	0.659817	+	0.751427i	$0.270634\pi$
$641$			38.0492i			1.50285i	−0.659817	+	0.751427i	$0.729366\pi$
$642$	−33.9260			−1.33895
$643$	44.7335			1.76412			0.882059	−	0.471138i	$-0.156157\pi$
$643$	44.7335			1.76412			0.882059	+	0.471138i	$0.156157\pi$
$644$			19.4595i			0.766812i
$645$	−10.9250			−0.430171
$646$	−53.9773			−2.12371
$647$	−9.09773			−0.357668			−0.178834	−	0.983879i	$-0.557233\pi$
$647$	−9.09773			−0.357668			−0.178834	+	0.983879i	$0.557233\pi$
$648$			25.4855i			1.00116i
$649$	8.71833			0.342224
$650$			4.90180i			0.192264i
$651$	−73.1044			−2.86519
$652$	5.29170			0.207239
$653$	14.4818			0.566717			0.283358	−	0.959014i	$-0.408551\pi$
$653$	14.4818			0.566717			0.283358	+	0.959014i	$0.408551\pi$
$654$		−	45.5990i		−	1.78306i
$655$		−	16.2628i		−	0.635439i
$656$		−	11.4479i		−	0.446965i
$657$			61.1239i			2.38467i
$658$			37.3772i			1.45712i
$659$		−	8.61282i		−	0.335508i	−0.985829	−	0.167754i	$-0.946349\pi$
$659$		−	8.61282i		−	0.335508i	0.985829	−	0.167754i	$-0.0536514\pi$
$660$	3.96764			0.154440
$661$	18.7707			0.730094			0.365047	−	0.930989i	$-0.381053\pi$
$661$	18.7707			0.730094			0.365047	+	0.930989i	$0.381053\pi$
$662$			28.7611i			1.11783i
$663$		−	35.5059i		−	1.37893i
$664$	4.35919			0.169169
$665$	32.3021			1.25262
$666$		−	58.7258i		−	2.27558i
$667$			3.73563i			0.144644i
$668$		−	11.1589i		−	0.431750i
$669$			0.812548i			0.0314149i
$670$			8.20723i			0.317073i
$671$		−	1.83687i		−	0.0709115i
$672$	−12.4600			−0.480655
$673$	6.56774			0.253168			0.126584	−	0.991956i	$-0.459599\pi$
$673$	6.56774			0.253168			0.126584	+	0.991956i	$0.459599\pi$
$674$	14.1276			0.544175
$675$		−	52.0168i		−	2.00213i
$676$	11.0491			0.424964
$677$			37.7402i			1.45047i	0.688500	+	0.725236i	$0.258270\pi$
$677$			37.7402i			1.45047i	−0.688500	+	0.725236i	$0.741730\pi$
$678$	−48.1859			−1.85057
$679$	−28.8835			−1.10845
$680$	9.55007			0.366228
$681$		−	2.66704i		−	0.102201i
$682$	5.86712			0.224664
$683$	−18.5382			−0.709344			−0.354672	−	0.934991i	$-0.615408\pi$
$683$	−18.5382			−0.709344			−0.354672	+	0.934991i	$0.615408\pi$
$684$		−	52.1750i		−	1.99496i
$685$	−16.1471			−0.616950
$686$			2.68589i			0.102548i
$687$			15.0632i			0.574696i
$688$	−2.75352			−0.104977
$689$	−9.70329	+	3.04071i	−0.369666	+	0.115842i
$690$	20.1371			0.766608
$691$			21.1890i			0.806067i	0.915185	+	0.403034i	$0.132044\pi$
$691$			21.1890i			0.806067i	−0.915185	+	0.403034i	$0.867956\pi$
$692$		−	5.33490i		−	0.202803i
$693$	−28.9897			−1.10123
$694$			13.5977i			0.516160i
$695$	−9.46330			−0.358963
$696$	−2.39194			−0.0906662
$697$		−	89.5472i		−	3.39184i
$698$	7.01389			0.265480
$699$	78.4026			2.96546
$700$	13.4555			0.508570
$701$		−	37.8356i		−	1.42903i	−0.699619	−	0.714516i	$-0.746647\pi$
$701$		−	37.8356i		−	1.42903i	0.699619	−	0.714516i	$-0.253353\pi$
$702$	20.7029			0.781382
$703$			53.5964i			2.02143i
$704$	1.00000			0.0376889
$705$	38.6788			1.45673
$706$	2.25186			0.0847498
$707$			68.3886i			2.57202i
$708$			28.3325i			1.06480i
$709$		−	10.2158i		−	0.383661i	−0.981428	−	0.191831i	$-0.938558\pi$
$709$		−	10.2158i		−	0.383661i	0.981428	−	0.191831i	$-0.0614424\pi$
$710$		−	8.93043i		−	0.335153i
$711$		−	80.1168i		−	3.00462i
$712$		−	18.7159i		−	0.701409i
$713$	29.7777			1.11518
$714$	−97.4642			−3.64750
$715$		−	1.70530i		−	0.0637748i
$716$			8.89259i			0.332332i
$717$	−32.9809			−1.23170
$718$	−12.9911			−0.484824
$719$			5.82593i			0.217270i	0.994082	+	0.108635i	$0.0346480\pi$
$719$			5.82593i			0.217270i	−0.994082	+	0.108635i	$0.965352\pi$
$720$			9.23120i			0.344026i
$721$		−	15.8577i		−	0.590573i
$722$			28.6178i			1.06504i
$723$		−	29.2796i		−	1.08892i
$724$			17.1667i			0.637997i
$725$	2.58304			0.0959317
$726$	3.24977			0.120610
$727$	−20.6676			−0.766519			−0.383259	−	0.923641i	$-0.625198\pi$
$727$	−20.6676			−0.766519			−0.383259	+	0.923641i	$0.625198\pi$
$728$			5.35536i			0.198483i
$729$	−48.1898			−1.78481
$730$			9.86990i			0.365302i
$731$	−21.5385			−0.796630
$732$	5.96939			0.220635
$733$	−4.88537			−0.180445			−0.0902226	−	0.995922i	$-0.528758\pi$
$733$	−4.88537			−0.180445			−0.0902226	+	0.995922i	$0.528758\pi$
$734$			3.61151i			0.133303i
$735$	30.5529			1.12696
$736$	5.07535			0.187080
$737$			6.72228i			0.247618i
$738$	86.5572			3.18622
$739$		−	0.378755i		−	0.0139327i	−0.999976	−	0.00696636i	$-0.997783\pi$
$739$		−	0.378755i		−	0.0139327i	0.999976	−	0.00696636i	$-0.00221748\pi$
$740$		−	9.48267i		−	0.348590i
$741$	−31.3227			−1.15067
$742$	8.34680	+	26.6357i	0.306421	+	0.977826i
$743$	43.2980			1.58845			0.794224	−	0.607625i	$-0.207877\pi$
$743$	43.2980			1.58845			0.794224	+	0.607625i	$0.207877\pi$
$744$			19.0668i			0.699022i
$745$		−	6.05075i		−	0.221682i
$746$	20.6459			0.755901
$747$			32.9597i			1.20593i
$748$	7.82216			0.286006
$749$	40.0265			1.46253
$750$		−	33.7622i		−	1.23282i
$751$	12.3249			0.449742			0.224871	−	0.974389i	$-0.427804\pi$
$751$	12.3249			0.449742			0.224871	+	0.974389i	$0.427804\pi$
$752$	9.74856			0.355494
$753$	9.97688			0.363578
$754$			1.02806i			0.0374399i
$755$	4.79518			0.174514
$756$		−	56.8298i		−	2.06688i
$757$	23.8630			0.867314			0.433657	−	0.901078i	$-0.357223\pi$
$757$	23.8630			0.867314			0.433657	+	0.901078i	$0.357223\pi$
$758$	−17.0098			−0.617822
$759$	16.4937			0.598683
$760$		−	8.42490i		−	0.305603i
$761$			3.71404i			0.134634i	0.997732	+	0.0673169i	$0.0214439\pi$
$761$			3.71404i			0.134634i	−0.997732	+	0.0673169i	$0.978556\pi$
$762$		−	14.6678i		−	0.531360i
$763$			53.7984i			1.94763i
$764$		−	15.4673i		−	0.559589i
$765$			72.2079i			2.61068i
$766$	−13.2034			−0.477057
$767$	12.1774			0.439701
$768$			3.24977i			0.117266i
$769$			2.64721i			0.0954607i	0.998860	+	0.0477304i	$0.0151988\pi$
$769$			2.64721i			0.0954607i	−0.998860	+	0.0477304i	$0.984801\pi$
$770$	−4.68108			−0.168695
$771$	101.886			3.66933
$772$		−	5.39018i		−	0.193997i
$773$		−	19.5200i		−	0.702085i	−0.936360	−	0.351042i	$-0.885827\pi$
$773$		−	19.5200i		−	0.702085i	0.936360	−	0.351042i	$-0.114173\pi$
$774$		−	20.8193i		−	0.748336i
$775$		−	20.5901i		−	0.739618i
$776$			7.53326i			0.270428i
$777$			96.7764i			3.47183i
$778$	26.3757			0.945613
$779$	−78.9969			−2.83036
$780$	5.54184			0.198430
$781$		−	7.31463i		−	0.261738i
$782$	39.7002			1.41967
$783$		−	10.9096i		−	0.389877i
$784$	7.70052			0.275019
$785$	7.00791			0.250123
$786$	43.2879			1.54403
$787$		−	15.6371i		−	0.557403i	−0.960378	−	0.278702i	$-0.910096\pi$
$787$		−	15.6371i		−	0.557403i	0.960378	−	0.278702i	$-0.0899040\pi$
$788$	−12.5461			−0.446937
$789$	−28.5119			−1.01505
$790$		−	12.9368i		−	0.460270i
$791$	56.8505			2.02137
$792$			7.56098i			0.268668i
$793$		−	2.56566i		−	0.0911094i
$794$	0.560584			0.0198944
$795$	27.5632	−	8.63745i	0.977565	−	0.306339i
$796$	6.05360			0.214564
$797$			15.3519i			0.543794i	0.962326	+	0.271897i	$0.0876509\pi$
$797$			15.3519i			0.543794i	−0.962326	+	0.271897i	$0.912349\pi$
$798$			85.9811i			3.04370i
$799$	76.2548			2.69770
$800$		−	3.50940i		−	0.124076i
$801$	141.511			5.00004
$802$	19.1575			0.676474
$803$			8.08412i			0.285283i
$804$	−21.8458			−0.770443
$805$	−23.7581			−0.837364
$806$	8.19496			0.288655
$807$			30.1216i			1.06033i
$808$	17.8368			0.627497
$809$		−	4.86408i		−	0.171012i	−0.996338	−	0.0855059i	$-0.972749\pi$
$809$		−	4.86408i		−	0.171012i	0.996338	−	0.0855059i	$-0.0272506\pi$
$810$	−31.1152			−1.09328
$811$	−9.09904			−0.319510			−0.159755	−	0.987157i	$-0.551070\pi$
$811$	−9.09904			−0.319510			−0.159755	+	0.987157i	$0.551070\pi$
$812$	2.82205			0.0990344
$813$		−	55.1312i		−	1.93354i
$814$		−	7.76696i		−	0.272232i
$815$			6.46063i			0.226306i
$816$			25.4202i			0.889884i
$817$			19.0009i			0.664756i
$818$		−	23.1556i		−	0.809616i
$819$	−40.4917			−1.41490
$820$	13.9767			0.488088
$821$			35.5478i			1.24063i	0.784355	+	0.620313i	$0.212994\pi$
$821$			35.5478i			1.24063i	−0.784355	+	0.620313i	$0.787006\pi$
$822$		−	42.9801i		−	1.49910i
$823$	−9.33661			−0.325454			−0.162727	−	0.986671i	$-0.552029\pi$
$823$	−9.33661			−0.325454			−0.162727	+	0.986671i	$0.552029\pi$
$824$	−4.13594			−0.144082
$825$		−	11.4047i		−	0.397062i
$826$		−	33.4272i		−	1.16308i
$827$		−	12.0565i		−	0.419244i	−0.977782	−	0.209622i	$-0.932777\pi$
$827$		−	12.0565i		−	0.419244i	0.977782	−	0.209622i	$-0.0672234\pi$
$828$			38.3746i			1.33361i
$829$			44.7279i			1.55347i	0.629830	+	0.776733i	$0.283124\pi$
$829$			44.7279i			1.55347i	−0.629830	+	0.776733i	$0.716876\pi$
$830$			5.32213i			0.184734i
$831$	−7.94205			−0.275507
$832$	1.39676			0.0484240
$833$	60.2347			2.08701
$834$		−	25.1892i		−	0.872231i
$835$	13.6239			0.471473
$836$		−	6.90056i		−	0.238661i
$837$	−86.9631			−3.00588
$838$	−15.7794			−0.545090
$839$	−34.9434			−1.20638			−0.603191	−	0.797597i	$-0.706104\pi$
$839$	−34.9434			−1.20638			−0.603191	+	0.797597i	$0.706104\pi$
$840$		−	15.2124i		−	0.524878i
$841$	−28.4583			−0.981319
$842$	−12.1231			−0.417790
$843$			39.6141i			1.36438i
$844$	−9.82786			−0.338289
$845$			13.4898i			0.464063i
$846$			73.7087i			2.53416i
$847$	−3.83413			−0.131742
$848$	6.94700	−	2.17698i	0.238561	−	0.0747577i
$849$	−62.7189			−2.15251
$850$		−	27.4511i		−	0.941565i
$851$		−	39.4200i		−	1.35130i
$852$	23.7708			0.814375
$853$		−	38.9810i		−	1.33468i	−0.744752	−	0.667341i	$-0.767432\pi$
$853$		−	38.9810i		−	1.33468i	0.744752	−	0.667341i	$-0.232568\pi$
$854$	−7.04278			−0.240999
$855$	63.7005			2.17851
$856$		−	10.4395i		−	0.356816i
$857$	25.4403			0.869026			0.434513	−	0.900666i	$-0.356921\pi$
$857$	25.4403			0.869026			0.434513	+	0.900666i	$0.356921\pi$
$858$	4.53914			0.154964
$859$	25.7585			0.878869			0.439434	−	0.898275i	$-0.355179\pi$
$859$	25.7585			0.878869			0.439434	+	0.898275i	$0.355179\pi$
$860$		−	3.36178i		−	0.114636i
$861$	−142.641			−4.86119
$862$			23.0942i			0.786591i
$863$	26.0007			0.885073			0.442537	−	0.896750i	$-0.354079\pi$
$863$	26.0007			0.885073			0.442537	+	0.896750i	$0.354079\pi$
$864$	−14.8221			−0.504259
$865$	6.51338			0.221462
$866$		−	0.295719i		−	0.0100489i
$867$			143.595i			4.87673i
$868$		−	22.4953i		−	0.763539i
$869$		−	10.5961i		−	0.359448i
$870$		−	2.92032i		−	0.0990080i
$871$			9.38941i			0.318148i
$872$	14.0315			0.475165
$873$	−56.9588			−1.92776
$874$		−	35.0228i		−	1.18466i
$875$			39.8332i			1.34661i
$876$	−26.2715			−0.887632
$877$	−54.4581			−1.83892			−0.919460	−	0.393183i	$-0.871374\pi$
$877$	−54.4581			−1.83892			−0.919460	+	0.393183i	$0.871374\pi$
$878$		−	16.1019i		−	0.543412i
$879$			63.1866i			2.13123i
$880$			1.22090i			0.0411565i
$881$			3.97885i			0.134051i	0.997751	+	0.0670254i	$0.0213509\pi$
$881$			3.97885i			0.134051i	−0.997751	+	0.0670254i	$0.978649\pi$
$882$			58.2235i			1.96049i
$883$		−	39.4812i		−	1.32865i	−0.747444	−	0.664324i	$-0.768719\pi$
$883$		−	39.4812i		−	1.32865i	0.747444	−	0.664324i	$-0.231281\pi$
$884$	10.9257			0.367470
$885$	−34.5912			−1.16277
$886$	−17.8170			−0.598573
$887$		−	12.2457i		−	0.411170i	−0.978639	−	0.205585i	$-0.934090\pi$
$887$		−	12.2457i		−	0.411170i	0.978639	−	0.205585i	$-0.0659098\pi$
$888$	25.2408			0.847026
$889$			17.3053i			0.580403i
$890$	22.8503			0.765943
$891$	−25.4855			−0.853795
$892$	−0.250033			−0.00837172
$893$		−	67.2706i		−	2.25112i
$894$	16.1058			0.538657
$895$	−10.8570			−0.362908
$896$		−	3.83413i		−	0.128089i
$897$	23.0377			0.769207
$898$			3.69734i			0.123382i
$899$		−	4.31840i		−	0.144027i
$900$	26.5345			0.884484
$901$	54.3405	−	17.0287i	1.81034	−	0.567307i
$902$	11.4479			0.381173
$903$			34.3089i			1.14173i
$904$		−	14.8275i		−	0.493155i
$905$	−20.9589			−0.696696
$906$			12.7637i			0.424046i
$907$	14.6670			0.487011			0.243505	−	0.969900i	$-0.421703\pi$
$907$	14.6670			0.487011			0.243505	+	0.969900i	$0.421703\pi$
$908$	0.820688			0.0272355
$909$			134.864i			4.47315i
$910$	−6.53835			−0.216744
$911$	−49.9797			−1.65590			−0.827951	−	0.560800i	$-0.810494\pi$
$911$	−49.9797			−1.65590			−0.827951	+	0.560800i	$0.810494\pi$
$912$	22.4252			0.742573
$913$			4.35919i			0.144268i
$914$	17.9502			0.593741
$915$			7.28802i			0.240935i
$916$	−4.63516			−0.153150
$917$	−51.0718			−1.68654
$918$	−115.941			−3.82662
$919$		−	50.7824i		−	1.67516i	−0.546316	−	0.837579i	$-0.683970\pi$
$919$		−	50.7824i		−	1.67516i	0.546316	−	0.837579i	$-0.316030\pi$
$920$			6.19649i			0.204292i
$921$			15.3551i			0.505968i
$922$			27.9701i			0.921146i
$923$		−	10.2168i		−	0.336290i
$924$		−	12.4600i		−	0.409904i
$925$	−27.2574			−0.896218
$926$	−12.5739			−0.413204
$927$		−	31.2718i		−	1.02710i
$928$		−	0.736034i		−	0.0241615i
$929$	13.9260			0.456898			0.228449	−	0.973556i	$-0.426635\pi$
$929$	13.9260			0.456898			0.228449	+	0.973556i	$0.426635\pi$
$930$	−23.2786			−0.763336
$931$		−	53.1379i		−	1.74153i
$932$			24.1256i			0.790261i
$933$		−	52.7730i		−	1.72771i
$934$		−	25.3693i		−	0.830107i
$935$			9.55007i			0.312321i
$936$			10.5609i			0.345193i
$937$	−31.3183			−1.02312			−0.511562	−	0.859247i	$-0.670933\pi$
$937$	−31.3183			−1.02312			−0.511562	+	0.859247i	$0.670933\pi$
$938$	25.7741			0.841553
$939$	−5.17500			−0.168880
$940$			11.9020i			0.388201i
$941$	34.8317			1.13548			0.567741	−	0.823207i	$-0.307818\pi$
$941$	34.8317			1.13548			0.567741	+	0.823207i	$0.307818\pi$
$942$			18.6535i			0.607765i
$943$	58.1020			1.89206
$944$	−8.71833			−0.283758
$945$	69.3835			2.25705
$946$		−	2.75352i		−	0.0895248i
$947$	20.1329			0.654232			0.327116	−	0.944984i	$-0.393923\pi$
$947$	20.1329			0.654232			0.327116	+	0.944984i	$0.393923\pi$
$948$	34.4348			1.11839
$949$			11.2916i			0.366540i
$950$	−24.2169			−0.785699
$951$		−	70.8047i		−	2.29600i
$952$		−	29.9911i		−	0.972018i
$953$	24.1486			0.782250			0.391125	−	0.920338i	$-0.372086\pi$
$953$	24.1486			0.782250			0.391125	+	0.920338i	$0.372086\pi$
$954$	16.4601	+	52.5261i	0.532915	+	1.70060i
$955$	18.8841			0.611074
$956$		−	10.1487i		−	0.328233i
$957$		−	2.39194i		−	0.0773204i
$958$	16.4541			0.531607
$959$			50.7086i			1.63747i
$960$	−3.96764			−0.128055
$961$	−3.42310			−0.110423
$962$		−	10.8486i		−	0.349772i
$963$	78.9330			2.54358
$964$	9.00975			0.290184
$965$	6.58087			0.211846
$966$		−	63.2389i		−	2.03468i
$967$	23.2277			0.746951			0.373476	−	0.927640i	$-0.378166\pi$
$967$	23.2277			0.746951			0.373476	+	0.927640i	$0.378166\pi$
$968$			1.00000i			0.0321412i
$969$	175.414			5.63510
$970$	−9.19735			−0.295309
$971$	32.4706			1.04203			0.521016	−	0.853547i	$-0.325553\pi$
$971$	32.4706			1.04203			0.521016	+	0.853547i	$0.325553\pi$
$972$		−	38.3554i		−	1.23025i
$973$			29.7187i			0.952736i
$974$			27.0440i			0.866545i
$975$		−	15.9297i		−	0.510158i
$976$			1.83687i			0.0587967i
$977$			55.1757i			1.76523i	0.470101	+	0.882613i	$0.344218\pi$
$977$			55.1757i			1.76523i	−0.470101	+	0.882613i	$0.655782\pi$
$978$	−17.1968			−0.549892
$979$	18.7159			0.598164
$980$			9.40156i			0.300322i
$981$			106.092i			3.38725i
$982$	−38.8353			−1.23928
$983$	18.7696			0.598658			0.299329	−	0.954150i	$-0.403237\pi$
$983$	18.7696			0.598658			0.299329	+	0.954150i	$0.403237\pi$
$984$			37.2030i			1.18599i
$985$		−	15.3175i		−	0.488058i
$986$		−	5.75737i		−	0.183352i
$987$		−	121.467i		−	3.86634i
$988$		−	9.63843i		−	0.306639i
$989$		−	13.9751i		−	0.444382i
$990$	−9.23120			−0.293387
$991$	−3.24382			−0.103043			−0.0515217	−	0.998672i	$-0.516407\pi$
$991$	−3.24382			−0.103043			−0.0515217	+	0.998672i	$0.516407\pi$
$992$	−5.86712			−0.186281
$993$		−	93.4669i		−	2.96608i
$994$	−28.0452			−0.889540
$995$			7.39083i			0.234305i
$996$	−14.1663			−0.448878
$997$	10.6207			0.336360			0.168180	−	0.985756i	$-0.446211\pi$
$997$	10.6207			0.336360			0.168180	+	0.985756i	$0.446211\pi$
$998$	14.3490			0.454209
$999$			115.123i			3.64232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1166.2.c.b.529.11	✓	22
53.52	even	2	inner	1166.2.c.b.529.12	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1166.2.c.b.529.11	✓	22	1.1	even	1	trivial
1166.2.c.b.529.12	yes	22	53.52	even	2	inner

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:	\( N \)	\(=\)	\( 1166 = 2 \cdot 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1166.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +3.24977i q^{3} -1.00000 q^{4} -1.22090i q^{5} +3.24977 q^{6} -3.83413 q^{7} +1.00000i q^{8} -7.56098 q^{9} -1.22090 q^{10} -1.00000 q^{11} -3.24977i q^{12} -1.39676 q^{13} +3.83413i q^{14} +3.96764 q^{15} +1.00000 q^{16} +7.82216 q^{17} +7.56098i q^{18} -6.90056i q^{19} +1.22090i q^{20} -12.4600i q^{21} +1.00000i q^{22} +5.07535i q^{23} -3.24977 q^{24} +3.50940 q^{25} +1.39676i q^{26} -14.8221i q^{27} +3.83413 q^{28} +0.736034 q^{29} -3.96764i q^{30} -5.86712i q^{31} -1.00000i q^{32} -3.24977i q^{33} -7.82216i q^{34} +4.68108i q^{35} +7.56098 q^{36} -7.76696 q^{37} -6.90056 q^{38} -4.53914i q^{39} +1.22090 q^{40} -11.4479i q^{41} -12.4600 q^{42} -2.75352 q^{43} +1.00000 q^{44} +9.23120i q^{45} +5.07535 q^{46} +9.74856 q^{47} +3.24977i q^{48} +7.70052 q^{49} -3.50940i q^{50} +25.4202i q^{51} +1.39676 q^{52} +(6.94700 - 2.17698i) q^{53} -14.8221 q^{54} +1.22090i q^{55} -3.83413i q^{56} +22.4252 q^{57} -0.736034i q^{58} -8.71833 q^{59} -3.96764 q^{60} +1.83687i q^{61} -5.86712 q^{62} +28.9897 q^{63} -1.00000 q^{64} +1.70530i q^{65} -3.24977 q^{66} -6.72228i q^{67} -7.82216 q^{68} -16.4937 q^{69} +4.68108 q^{70} +7.31463i q^{71} -7.56098i q^{72} -8.08412i q^{73} +7.76696i q^{74} +11.4047i q^{75} +6.90056i q^{76} +3.83413 q^{77} -4.53914 q^{78} +10.5961i q^{79} -1.22090i q^{80} +25.4855 q^{81} -11.4479 q^{82} -4.35919i q^{83} +12.4600i q^{84} -9.55007i q^{85} +2.75352i q^{86} +2.39194i q^{87} -1.00000i q^{88} -18.7159 q^{89} +9.23120 q^{90} +5.35536 q^{91} -5.07535i q^{92} +19.0668 q^{93} -9.74856i q^{94} -8.42490 q^{95} +3.24977 q^{96} +7.53326 q^{97} -7.70052i q^{98} +7.56098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 22 * q - 22 * q^4 - 6 * q^6 - 24 * q^9 + 4 * q^10 - 22 * q^11 + 6 * q^13 + 30 * q^15 + 22 * q^16 + 18 * q^17 + 6 * q^24 - 30 * q^25 + 28 * q^29 + 24 * q^36 - 34 * q^37 - 18 * q^38 - 4 * q^40 + 4 * q^42 - 34 * q^43 + 22 * q^44 + 6 * q^46 + 8 * q^47 + 6 * q^49 - 6 * q^52 + 16 * q^53 + 12 * q^54 + 14 * q^57 - 60 * q^59 - 30 * q^60 - 8 * q^62 + 116 * q^63 - 22 * q^64 + 6 * q^66 - 18 * q^68 - 26 * q^69 - 32 * q^70 - 4 * q^78 + 62 * q^81 - 44 * q^82 - 34 * q^89 - 6 * q^90 + 12 * q^91 + 4 * q^93 - 6 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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