LMFDB - Embedded newform 1166.2.c.b.529.13

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			529.13
Character	$\chi$	$=$	1166.529
Dual form			1166.2.c.b.529.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -2.09046i q^{3} -1.00000 q^{4} -2.97150i q^{5} +2.09046 q^{6} +2.18061 q^{7} -1.00000i q^{8} -1.37003 q^{9} +2.97150 q^{10} -1.00000 q^{11} +2.09046i q^{12} +4.61763 q^{13} +2.18061i q^{14} -6.21181 q^{15} +1.00000 q^{16} +8.09440 q^{17} -1.37003i q^{18} -1.69881i q^{19} +2.97150i q^{20} -4.55848i q^{21} -1.00000i q^{22} +2.72722i q^{23} -2.09046 q^{24} -3.82981 q^{25} +4.61763i q^{26} -3.40739i q^{27} -2.18061 q^{28} +2.19291 q^{29} -6.21181i q^{30} +1.47980i q^{31} +1.00000i q^{32} +2.09046i q^{33} +8.09440i q^{34} -6.47968i q^{35} +1.37003 q^{36} -3.94126 q^{37} +1.69881 q^{38} -9.65298i q^{39} -2.97150 q^{40} -4.33225i q^{41} +4.55848 q^{42} -6.81756 q^{43} +1.00000 q^{44} +4.07105i q^{45} -2.72722 q^{46} -3.68770 q^{47} -2.09046i q^{48} -2.24495 q^{49} -3.82981i q^{50} -16.9210i q^{51} -4.61763 q^{52} +(-7.06251 + 1.76662i) q^{53} +3.40739 q^{54} +2.97150i q^{55} -2.18061i q^{56} -3.55129 q^{57} +2.19291i q^{58} -2.80552 q^{59} +6.21181 q^{60} +6.67241i q^{61} -1.47980 q^{62} -2.98750 q^{63} -1.00000 q^{64} -13.7213i q^{65} -2.09046 q^{66} -2.96227i q^{67} -8.09440 q^{68} +5.70115 q^{69} +6.47968 q^{70} -9.69546i q^{71} +1.37003i q^{72} +5.69259i q^{73} -3.94126i q^{74} +8.00607i q^{75} +1.69881i q^{76} -2.18061 q^{77} +9.65298 q^{78} +9.23645i q^{79} -2.97150i q^{80} -11.2331 q^{81} +4.33225 q^{82} +3.96253i q^{83} +4.55848i q^{84} -24.0525i q^{85} -6.81756i q^{86} -4.58419i q^{87} +1.00000i q^{88} +15.5276 q^{89} -4.07105 q^{90} +10.0692 q^{91} -2.72722i q^{92} +3.09347 q^{93} -3.68770i q^{94} -5.04800 q^{95} +2.09046 q^{96} +2.25689 q^{97} -2.24495i q^{98} +1.37003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	2.09046i		−	1.20693i	−0.797390	−	0.603464i	$-0.793787\pi$
$3$		−	2.09046i		−	1.20693i	0.797390	−	0.603464i	$-0.206213\pi$
$4$	−1.00000			−0.500000
$5$		−	2.97150i		−	1.32889i	−0.747335	−	0.664447i	$-0.768667\pi$
$5$		−	2.97150i		−	1.32889i	0.747335	−	0.664447i	$-0.231333\pi$
$6$	2.09046			0.853427
$7$	2.18061			0.824193			0.412096	−	0.911140i	$-0.364797\pi$
$7$	2.18061			0.824193			0.412096	+	0.911140i	$0.364797\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.37003			−0.456677
$10$	2.97150			0.939671
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			2.09046i			0.603464i
$13$	4.61763			1.28070			0.640350	−	0.768083i	$-0.278789\pi$
$13$	4.61763			1.28070			0.640350	+	0.768083i	$0.278789\pi$
$14$			2.18061i			0.582792i
$15$	−6.21181			−1.60388
$16$	1.00000			0.250000
$17$	8.09440			1.96318			0.981591	−	0.190997i	$-0.0611722\pi$
$17$	8.09440			1.96318			0.981591	+	0.190997i	$0.0611722\pi$
$18$		−	1.37003i		−	0.322919i
$19$		−	1.69881i		−	0.389733i	−0.980830	−	0.194866i	$-0.937573\pi$
$19$		−	1.69881i		−	0.389733i	0.980830	−	0.194866i	$-0.0624273\pi$
$20$			2.97150i			0.664447i
$21$		−	4.55848i		−	0.994742i
$22$		−	1.00000i		−	0.213201i
$23$			2.72722i			0.568664i	0.958726	+	0.284332i	$0.0917719\pi$
$23$			2.72722i			0.568664i	−0.958726	+	0.284332i	$0.908228\pi$
$24$	−2.09046			−0.426714
$25$	−3.82981			−0.765962
$26$			4.61763i			0.905592i
$27$		−	3.40739i		−	0.655752i
$28$	−2.18061			−0.412096
$29$	2.19291			0.407213			0.203606	−	0.979053i	$-0.434734\pi$
$29$	2.19291			0.407213			0.203606	+	0.979053i	$0.434734\pi$
$30$		−	6.21181i		−	1.13412i
$31$			1.47980i			0.265781i	0.991131	+	0.132890i	$0.0424258\pi$
$31$			1.47980i			0.265781i	−0.991131	+	0.132890i	$0.957574\pi$
$32$			1.00000i			0.176777i
$33$			2.09046i			0.363903i
$34$			8.09440i			1.38818i
$35$		−	6.47968i		−	1.09527i
$36$	1.37003			0.228338
$37$	−3.94126			−0.647939			−0.323969	−	0.946068i	$-0.605017\pi$
$37$	−3.94126			−0.647939			−0.323969	+	0.946068i	$0.605017\pi$
$38$	1.69881			0.275583
$39$		−	9.65298i		−	1.54571i
$40$	−2.97150			−0.469835
$41$		−	4.33225i		−	0.676583i	−0.941041	−	0.338292i	$-0.890151\pi$
$41$		−	4.33225i		−	0.676583i	0.941041	−	0.338292i	$-0.109849\pi$
$42$	4.55848			0.703389
$43$	−6.81756			−1.03967			−0.519834	−	0.854267i	$-0.674006\pi$
$43$	−6.81756			−1.03967			−0.519834	+	0.854267i	$0.674006\pi$
$44$	1.00000			0.150756
$45$			4.07105i			0.606876i
$46$	−2.72722			−0.402107
$47$	−3.68770			−0.537906			−0.268953	−	0.963153i	$-0.586678\pi$
$47$	−3.68770			−0.537906			−0.268953	+	0.963153i	$0.586678\pi$
$48$		−	2.09046i		−	0.301732i
$49$	−2.24495			−0.320707
$50$		−	3.82981i		−	0.541617i
$51$		−	16.9210i		−	2.36942i
$52$	−4.61763			−0.640350
$53$	−7.06251	+	1.76662i	−0.970110	+	0.242665i
$53$	−7.06251	+	1.76662i	−0.970110	+	0.242665i
$54$	3.40739			0.463687
$55$			2.97150i			0.400677i
$56$		−	2.18061i		−	0.291396i
$57$	−3.55129			−0.470380
$58$			2.19291i			0.287943i
$59$	−2.80552			−0.365248			−0.182624	−	0.983183i	$-0.558459\pi$
$59$	−2.80552			−0.365248			−0.182624	+	0.983183i	$0.558459\pi$
$60$	6.21181			0.801941
$61$			6.67241i			0.854315i	0.904177	+	0.427157i	$0.140485\pi$
$61$			6.67241i			0.854315i	−0.904177	+	0.427157i	$0.859515\pi$
$62$	−1.47980			−0.187935
$63$	−2.98750			−0.376390
$64$	−1.00000			−0.125000
$65$		−	13.7213i		−	1.70192i
$66$	−2.09046			−0.257318
$67$		−	2.96227i		−	0.361899i	−0.983492	−	0.180949i	$-0.942083\pi$
$67$		−	2.96227i		−	0.361899i	0.983492	−	0.180949i	$-0.0579170\pi$
$68$	−8.09440			−0.981591
$69$	5.70115			0.686337
$70$	6.47968			0.774469
$71$		−	9.69546i		−	1.15064i	−0.817929	−	0.575319i	$-0.804878\pi$
$71$		−	9.69546i		−	1.15064i	0.817929	−	0.575319i	$-0.195122\pi$
$72$			1.37003i			0.161460i
$73$			5.69259i			0.666267i	0.942880	+	0.333134i	$0.108106\pi$
$73$			5.69259i			0.666267i	−0.942880	+	0.333134i	$0.891894\pi$
$74$		−	3.94126i		−	0.458162i
$75$			8.00607i			0.924461i
$76$			1.69881i			0.194866i
$77$	−2.18061			−0.248503
$78$	9.65298			1.09298
$79$			9.23645i			1.03918i	0.854415	+	0.519591i	$0.173916\pi$
$79$			9.23645i			1.03918i	−0.854415	+	0.519591i	$0.826084\pi$
$80$		−	2.97150i		−	0.332224i
$81$	−11.2331			−1.24812
$82$	4.33225			0.478417
$83$			3.96253i			0.434944i	0.976067	+	0.217472i	$0.0697811\pi$
$83$			3.96253i			0.434944i	−0.976067	+	0.217472i	$0.930219\pi$
$84$			4.55848i			0.497371i
$85$		−	24.0525i		−	2.60886i
$86$		−	6.81756i		−	0.735157i
$87$		−	4.58419i		−	0.491477i
$88$			1.00000i			0.106600i
$89$	15.5276			1.64592			0.822961	−	0.568098i	$-0.192321\pi$
$89$	15.5276			1.64592			0.822961	+	0.568098i	$0.192321\pi$
$90$	−4.07105			−0.429126
$91$	10.0692			1.05554
$92$		−	2.72722i		−	0.284332i
$93$	3.09347			0.320778
$94$		−	3.68770i		−	0.380357i
$95$	−5.04800			−0.517914
$96$	2.09046			0.213357
$97$	2.25689			0.229152			0.114576	−	0.993414i	$-0.463449\pi$
$97$	2.25689			0.229152			0.114576	+	0.993414i	$0.463449\pi$
$98$		−	2.24495i		−	0.226774i
$99$	1.37003			0.137693
$100$	3.82981			0.382981
$101$		−	13.4471i		−	1.33804i	−0.743246	−	0.669018i	$-0.766715\pi$
$101$		−	13.4471i		−	1.33804i	0.743246	−	0.669018i	$-0.233285\pi$
$102$	16.9210			1.67543
$103$			16.5709i			1.63278i	0.577502	+	0.816389i	$0.304028\pi$
$103$			16.5709i			1.63278i	−0.577502	+	0.816389i	$0.695972\pi$
$104$		−	4.61763i		−	0.452796i
$105$	−13.5455			−1.32191
$106$	−1.76662	−	7.06251i	−0.171590	−	0.685972i
$107$	−3.52801			−0.341065			−0.170533	−	0.985352i	$-0.554549\pi$
$107$	−3.52801			−0.341065			−0.170533	+	0.985352i	$0.554549\pi$
$108$			3.40739i			0.327876i
$109$			2.20263i			0.210973i	0.994421	+	0.105487i	$0.0336400\pi$
$109$			2.20263i			0.210973i	−0.994421	+	0.105487i	$0.966360\pi$
$110$	−2.97150			−0.283321
$111$			8.23905i			0.782016i
$112$	2.18061			0.206048
$113$	−3.81030			−0.358443			−0.179222	−	0.983809i	$-0.557358\pi$
$113$	−3.81030			−0.358443			−0.179222	+	0.983809i	$0.557358\pi$
$114$		−	3.55129i		−	0.332609i
$115$	8.10393			0.755695
$116$	−2.19291			−0.203606
$117$	−6.32629			−0.584866
$118$		−	2.80552i		−	0.258269i
$119$	17.6507			1.61804
$120$			6.21181i			0.567058i
$121$	1.00000			0.0909091
$122$	−6.67241			−0.604092
$123$	−9.05640			−0.816588
$124$		−	1.47980i		−	0.132890i
$125$		−	3.47722i		−	0.311012i
$126$		−	2.98750i		−	0.266148i
$127$			4.61021i			0.409090i	0.978857	+	0.204545i	$0.0655715\pi$
$127$			4.61021i			0.409090i	−0.978857	+	0.204545i	$0.934429\pi$
$128$		−	1.00000i		−	0.0883883i
$129$			14.2519i			1.25481i
$130$	13.7213			1.20344
$131$	10.1879			0.890119			0.445060	−	0.895501i	$-0.353182\pi$
$131$	10.1879			0.890119			0.445060	+	0.895501i	$0.353182\pi$
$132$		−	2.09046i		−	0.181951i
$133$		−	3.70443i		−	0.321215i
$134$	2.96227			0.255901
$135$	−10.1251			−0.871426
$136$		−	8.09440i		−	0.694089i
$137$			19.5375i			1.66920i	0.550855	+	0.834601i	$0.314302\pi$
$137$			19.5375i			1.66920i	−0.550855	+	0.834601i	$0.685698\pi$
$138$			5.70115i			0.485314i
$139$			9.98558i			0.846966i	0.905904	+	0.423483i	$0.139193\pi$
$139$			9.98558i			0.846966i	−0.905904	+	0.423483i	$0.860807\pi$
$140$			6.47968i			0.547633i
$141$			7.70899i			0.649214i
$142$	9.69546			0.813625
$143$	−4.61763			−0.386146
$144$	−1.37003			−0.114169
$145$		−	6.51623i		−	0.541143i
$146$	−5.69259			−0.471122
$147$			4.69298i			0.387070i
$148$	3.94126			0.323969
$149$	−0.111768			−0.00915637			−0.00457818	−	0.999990i	$-0.501457\pi$
$149$	−0.111768			−0.00915637			−0.00457818	+	0.999990i	$0.501457\pi$
$150$	−8.00607			−0.653693
$151$			4.40211i			0.358239i	0.983827	+	0.179119i	$0.0573249\pi$
$151$			4.40211i			0.358239i	−0.983827	+	0.179119i	$0.942675\pi$
$152$	−1.69881			−0.137791
$153$	−11.0896			−0.896539
$154$		−	2.18061i		−	0.175718i
$155$	4.39724			0.353195
$156$			9.65298i			0.772857i
$157$		−	7.35304i		−	0.586836i	−0.955984	−	0.293418i	$-0.905207\pi$
$157$		−	7.35304i		−	0.586836i	0.955984	−	0.293418i	$-0.0947928\pi$
$158$	−9.23645			−0.734812
$159$	3.69306	+	14.7639i	0.292879	+	1.17085i
$160$	2.97150			0.234918
$161$			5.94700i			0.468689i
$162$		−	11.2331i		−	0.882556i
$163$	3.90417			0.305798			0.152899	−	0.988242i	$-0.451139\pi$
$163$	3.90417			0.305798			0.152899	+	0.988242i	$0.451139\pi$
$164$			4.33225i			0.338292i
$165$	6.21181			0.483588
$166$	−3.96253			−0.307552
$167$		−	0.280131i		−	0.0216772i	−0.999941	−	0.0108386i	$-0.996550\pi$
$167$		−	0.280131i		−	0.0216772i	0.999941	−	0.0108386i	$-0.00345010\pi$
$168$	−4.55848			−0.351694
$169$	8.32250			0.640192
$170$	24.0525			1.84474
$171$			2.32742i			0.177982i
$172$	6.81756			0.519834
$173$			14.0444i			1.06778i	0.845555	+	0.533888i	$0.179270\pi$
$173$			14.0444i			1.06778i	−0.845555	+	0.533888i	$0.820730\pi$
$174$	4.58419			0.347527
$175$	−8.35131			−0.631300
$176$	−1.00000			−0.0753778
$177$			5.86484i			0.440828i
$178$			15.5276i			1.16384i
$179$		−	10.9758i		−	0.820372i	−0.912002	−	0.410186i	$-0.865464\pi$
$179$		−	10.9758i		−	0.820372i	0.912002	−	0.410186i	$-0.134536\pi$
$180$		−	4.07105i		−	0.303438i
$181$		−	12.3420i		−	0.917373i	−0.888598	−	0.458686i	$-0.848320\pi$
$181$		−	12.3420i		−	0.917373i	0.888598	−	0.458686i	$-0.151680\pi$
$182$			10.0692i			0.746382i
$183$	13.9484			1.03110
$184$	2.72722			0.201053
$185$			11.7114i			0.861042i
$186$			3.09347i			0.226824i
$187$	−8.09440			−0.591921
$188$	3.68770			0.268953
$189$		−	7.43018i		−	0.540466i
$190$		−	5.04800i		−	0.366220i
$191$		−	15.6388i		−	1.13159i	−0.824547	−	0.565794i	$-0.808570\pi$
$191$		−	15.6388i		−	1.13159i	0.824547	−	0.565794i	$-0.191430\pi$
$192$			2.09046i			0.150866i
$193$			20.0467i			1.44299i	0.692420	+	0.721495i	$0.256545\pi$
$193$			20.0467i			1.44299i	−0.692420	+	0.721495i	$0.743455\pi$
$194$			2.25689i			0.162035i
$195$	−28.6838			−2.05409
$196$	2.24495			0.160353
$197$	19.6508			1.40006			0.700031	−	0.714112i	$-0.253169\pi$
$197$	19.6508			1.40006			0.700031	+	0.714112i	$0.253169\pi$
$198$			1.37003i			0.0973638i
$199$	7.31092			0.518257			0.259129	−	0.965843i	$-0.416565\pi$
$199$	7.31092			0.518257			0.259129	+	0.965843i	$0.416565\pi$
$200$			3.82981i			0.270808i
$201$	−6.19251			−0.436786
$202$	13.4471			0.946134
$203$	4.78187			0.335622
$204$			16.9210i			1.18471i
$205$	−12.8733			−0.899108
$206$	−16.5709			−1.15455
$207$		−	3.73637i		−	0.259696i
$208$	4.61763			0.320175
$209$			1.69881i			0.117509i
$210$		−	13.5455i		−	0.934729i
$211$	−14.1838			−0.976454			−0.488227	−	0.872717i	$-0.662356\pi$
$211$	−14.1838			−0.976454			−0.488227	+	0.872717i	$0.662356\pi$
$212$	7.06251	−	1.76662i	0.485055	−	0.121332i
$213$	−20.2680			−1.38874
$214$		−	3.52801i		−	0.241170i
$215$			20.2584i			1.38161i
$216$	−3.40739			−0.231843
$217$			3.22687i			0.219054i
$218$	−2.20263			−0.149181
$219$	11.9001			0.804137
$220$		−	2.97150i		−	0.200338i
$221$	37.3769			2.51425
$222$	−8.23905			−0.552969
$223$	−2.98063			−0.199598			−0.0997990	−	0.995008i	$-0.531820\pi$
$223$	−2.98063			−0.199598			−0.0997990	+	0.995008i	$0.531820\pi$
$224$			2.18061i			0.145698i
$225$	5.24696			0.349797
$226$		−	3.81030i		−	0.253458i
$227$	−13.9981			−0.929085			−0.464542	−	0.885551i	$-0.653781\pi$
$227$	−13.9981			−0.929085			−0.464542	+	0.885551i	$0.653781\pi$
$228$	3.55129			0.235190
$229$	−23.5756			−1.55792			−0.778960	−	0.627074i	$-0.784253\pi$
$229$	−23.5756			−1.55792			−0.778960	+	0.627074i	$0.784253\pi$
$230$			8.10393i			0.534357i
$231$			4.55848i			0.299926i
$232$		−	2.19291i		−	0.143971i
$233$		−	14.8095i		−	0.970200i	−0.874459	−	0.485100i	$-0.838783\pi$
$233$		−	14.8095i		−	0.970200i	0.874459	−	0.485100i	$-0.161217\pi$
$234$		−	6.32629i		−	0.413563i
$235$			10.9580i			0.714820i
$236$	2.80552			0.182624
$237$	19.3084			1.25422
$238$			17.6507i			1.14413i
$239$			15.0125i			0.971080i	0.874214	+	0.485540i	$0.161377\pi$
$239$			15.0125i			0.971080i	−0.874214	+	0.485540i	$0.838623\pi$
$240$	−6.21181			−0.400970
$241$	−0.519115			−0.0334391			−0.0167196	−	0.999860i	$-0.505322\pi$
$241$	−0.519115			−0.0334391			−0.0167196	+	0.999860i	$0.505322\pi$
$242$			1.00000i			0.0642824i
$243$			13.2602i			0.850643i
$244$		−	6.67241i		−	0.427157i
$245$			6.67086i			0.426185i
$246$		−	9.05640i		−	0.577415i
$247$		−	7.84445i		−	0.499131i
$248$	1.47980			0.0939676
$249$	8.28352			0.524947
$250$	3.47722			0.219919
$251$			20.2151i			1.27596i	0.770052	+	0.637982i	$0.220230\pi$
$251$			20.2151i			1.27596i	−0.770052	+	0.637982i	$0.779770\pi$
$252$	2.98750			0.188195
$253$		−	2.72722i		−	0.171459i
$254$	−4.61021			−0.289270
$255$	−50.2809			−3.14871
$256$	1.00000			0.0625000
$257$		−	10.4298i		−	0.650594i	−0.945612	−	0.325297i	$-0.894536\pi$
$257$		−	10.4298i		−	0.650594i	0.945612	−	0.325297i	$-0.105464\pi$
$258$	−14.2519			−0.887282
$259$	−8.59434			−0.534026
$260$			13.7213i			0.850958i
$261$	−3.00435			−0.185965
$262$			10.1879i			0.629409i
$263$		−	28.8298i		−	1.77772i	−0.458179	−	0.888860i	$-0.651498\pi$
$263$		−	28.8298i		−	1.77772i	0.458179	−	0.888860i	$-0.348502\pi$
$264$	2.09046			0.128659
$265$	5.24952	+	20.9862i	0.322476	+	1.28917i
$266$	3.70443			0.227133
$267$		−	32.4598i		−	1.98651i
$268$			2.96227i			0.180949i
$269$	3.60039			0.219520			0.109760	−	0.993958i	$-0.464992\pi$
$269$	3.60039			0.219520			0.109760	+	0.993958i	$0.464992\pi$
$270$		−	10.1251i		−	0.616191i
$271$	−29.8102			−1.81084			−0.905420	−	0.424518i	$-0.860444\pi$
$271$	−29.8102			−1.81084			−0.905420	+	0.424518i	$0.860444\pi$
$272$	8.09440			0.490795
$273$		−	21.0494i		−	1.27397i
$274$	−19.5375			−1.18030
$275$	3.82981			0.230946
$276$	−5.70115			−0.343169
$277$		−	7.27912i		−	0.437360i	−0.975797	−	0.218680i	$-0.929825\pi$
$277$		−	7.27912i		−	0.437360i	0.975797	−	0.218680i	$-0.0701751\pi$
$278$	−9.98558			−0.598895
$279$		−	2.02738i		−	0.121376i
$280$	−6.47968			−0.387235
$281$	−19.5468			−1.16607			−0.583033	−	0.812449i	$-0.698134\pi$
$281$	−19.5468			−1.16607			−0.583033	+	0.812449i	$0.698134\pi$
$282$	−7.70899			−0.459063
$283$		−	20.4074i		−	1.21309i	−0.795048	−	0.606546i	$-0.792555\pi$
$283$		−	20.4074i		−	1.21309i	0.795048	−	0.606546i	$-0.207445\pi$
$284$			9.69546i			0.575319i
$285$			10.5527i			0.625085i
$286$		−	4.61763i		−	0.273046i
$287$		−	9.44693i		−	0.557635i
$288$		−	1.37003i		−	0.0807298i
$289$	48.5194			2.85408
$290$	6.51623			0.382646
$291$		−	4.71794i		−	0.276571i
$292$		−	5.69259i		−	0.333134i
$293$	26.6856			1.55899			0.779494	−	0.626410i	$-0.215476\pi$
$293$	26.6856			1.55899			0.779494	+	0.626410i	$0.215476\pi$
$294$	−4.69298			−0.273700
$295$			8.33661i			0.485376i
$296$			3.94126i			0.229081i
$297$			3.40739i			0.197717i
$298$		−	0.111768i		−	0.00647453i
$299$			12.5933i			0.728288i
$300$		−	8.00607i		−	0.462231i
$301$	−14.8664			−0.856887
$302$	−4.40211			−0.253313
$303$	−28.1106			−1.61491
$304$		−	1.69881i		−	0.0974332i
$305$	19.8271			1.13529
$306$		−	11.0896i		−	0.633949i
$307$	26.9561			1.53846			0.769232	−	0.638970i	$-0.220639\pi$
$307$	26.9561			1.53846			0.769232	+	0.638970i	$0.220639\pi$
$308$	2.18061			0.124252
$309$	34.6408			1.97065
$310$			4.39724i			0.249746i
$311$	19.8853			1.12759			0.563795	−	0.825915i	$-0.309341\pi$
$311$	19.8853			1.12759			0.563795	+	0.825915i	$0.309341\pi$
$312$	−9.65298			−0.546492
$313$			8.44322i			0.477239i	0.971113	+	0.238620i	$0.0766949\pi$
$313$			8.44322i			0.477239i	−0.971113	+	0.238620i	$0.923305\pi$
$314$	7.35304			0.414956
$315$			8.87736i			0.500182i
$316$		−	9.23645i		−	0.519591i
$317$	23.3810			1.31321			0.656603	−	0.754236i	$-0.271993\pi$
$317$	23.3810			1.31321			0.656603	+	0.754236i	$0.271993\pi$
$318$	−14.7639	+	3.69306i	−0.827919	+	0.207097i
$319$	−2.19291			−0.122779
$320$			2.97150i			0.166112i
$321$			7.37516i			0.411641i
$322$	−5.94700			−0.331413
$323$		−	13.7508i		−	0.765116i
$324$	11.2331			0.624062
$325$	−17.6846			−0.980967
$326$			3.90417i			0.216232i
$327$	4.60451			0.254630
$328$	−4.33225			−0.239208
$329$	−8.04142			−0.443338
$330$			6.21181i			0.341949i
$331$	−24.5436			−1.34904			−0.674519	−	0.738257i	$-0.735649\pi$
$331$	−24.5436			−1.34904			−0.674519	+	0.738257i	$0.735649\pi$
$332$		−	3.96253i		−	0.217472i
$333$	5.39964			0.295899
$334$	0.280131			0.0153281
$335$	−8.80238			−0.480925
$336$		−	4.55848i		−	0.248685i
$337$		−	21.7740i		−	1.18610i	−0.805165	−	0.593051i	$-0.797923\pi$
$337$		−	21.7740i		−	1.18610i	0.805165	−	0.593051i	$-0.202077\pi$
$338$			8.32250i			0.452684i
$339$			7.96529i			0.432615i
$340$			24.0525i			1.30443i
$341$		−	1.47980i		−	0.0801359i
$342$	−2.32742			−0.125852
$343$	−20.1596			−1.08852
$344$			6.81756i			0.367578i
$345$		−	16.9410i		−	0.912070i
$346$	−14.0444			−0.755032
$347$	−25.3463			−1.36066			−0.680331	−	0.732905i	$-0.738164\pi$
$347$	−25.3463			−1.36066			−0.680331	+	0.732905i	$0.738164\pi$
$348$			4.58419i			0.245738i
$349$			16.7038i			0.894136i	0.894500	+	0.447068i	$0.147532\pi$
$349$			16.7038i			0.894136i	−0.894500	+	0.447068i	$0.852468\pi$
$350$		−	8.35131i		−	0.446396i
$351$		−	15.7341i		−	0.839822i
$352$		−	1.00000i		−	0.0533002i
$353$			7.74252i			0.412093i	0.978542	+	0.206047i	$0.0660598\pi$
$353$			7.74252i			0.412093i	−0.978542	+	0.206047i	$0.933940\pi$
$354$	−5.86484			−0.311713
$355$	−28.8100			−1.52908
$356$	−15.5276			−0.822961
$357$		−	36.8982i		−	1.95286i
$358$	10.9758			0.580091
$359$			28.7106i			1.51529i	0.652668	+	0.757644i	$0.273650\pi$
$359$			28.7106i			1.51529i	−0.652668	+	0.757644i	$0.726350\pi$
$360$	4.07105			0.214563
$361$	16.1141			0.848108
$362$	12.3420			0.648681
$363$		−	2.09046i		−	0.109721i
$364$	−10.0692			−0.527772
$365$	16.9155			0.885399
$366$			13.9484i			0.729096i
$367$	−28.7385			−1.50014			−0.750070	−	0.661359i	$-0.769980\pi$
$367$	−28.7385			−1.50014			−0.750070	+	0.661359i	$0.769980\pi$
$368$			2.72722i			0.142166i
$369$			5.93531i			0.308980i
$370$	−11.7114			−0.608849
$371$	−15.4006	+	3.85232i	−0.799558	+	0.200002i
$372$	−3.09347			−0.160389
$373$			10.5039i			0.543869i	0.962316	+	0.271934i	$0.0876634\pi$
$373$			10.5039i			0.543869i	−0.962316	+	0.271934i	$0.912337\pi$
$374$		−	8.09440i		−	0.418552i
$375$	−7.26900			−0.375370
$376$			3.68770i			0.190178i
$377$	10.1260			0.521517
$378$	7.43018			0.382167
$379$			12.4284i			0.638406i	0.947686	+	0.319203i	$0.103415\pi$
$379$			12.4284i			0.638406i	−0.947686	+	0.319203i	$0.896585\pi$
$380$	5.04800			0.258957
$381$	9.63747			0.493742
$382$	15.6388			0.800153
$383$			24.3727i			1.24539i	0.782467	+	0.622693i	$0.213961\pi$
$383$			24.3727i			1.24539i	−0.782467	+	0.622693i	$0.786039\pi$
$384$	−2.09046			−0.106678
$385$			6.47968i			0.330235i
$386$	−20.0467			−1.02035
$387$	9.34027			0.474793
$388$	−2.25689			−0.114576
$389$			11.2239i			0.569072i	0.958665	+	0.284536i	$0.0918396\pi$
$389$			11.2239i			0.569072i	−0.958665	+	0.284536i	$0.908160\pi$
$390$		−	28.6838i		−	1.45246i
$391$			22.0752i			1.11639i
$392$			2.24495i			0.113387i
$393$		−	21.2974i		−	1.07431i
$394$			19.6508i			0.989994i
$395$	27.4461			1.38096
$396$	−1.37003			−0.0688466
$397$			4.80277i			0.241044i	0.992711	+	0.120522i	$0.0384568\pi$
$397$			4.80277i			0.241044i	−0.992711	+	0.120522i	$0.961543\pi$
$398$			7.31092i			0.366463i
$399$	−7.74397			−0.387683
$400$	−3.82981			−0.191490
$401$			1.51978i			0.0758941i	0.999280	+	0.0379471i	$0.0120818\pi$
$401$			1.51978i			0.0758941i	−0.999280	+	0.0379471i	$0.987918\pi$
$402$		−	6.19251i		−	0.308854i
$403$			6.83318i			0.340385i
$404$			13.4471i			0.669018i
$405$			33.3792i			1.65862i
$406$			4.78187i			0.237320i
$407$	3.94126			0.195361
$408$	−16.9210			−0.837716
$409$	−6.29925			−0.311478			−0.155739	−	0.987798i	$-0.549776\pi$
$409$	−6.29925			−0.311478			−0.155739	+	0.987798i	$0.549776\pi$
$410$		−	12.8733i		−	0.635765i
$411$	40.8424			2.01461
$412$		−	16.5709i		−	0.816389i
$413$	−6.11775			−0.301035
$414$	3.73637			0.183633
$415$	11.7747			0.577995
$416$			4.61763i			0.226398i
$417$	20.8745			1.02223
$418$	−1.69881			−0.0830913
$419$		−	20.2458i		−	0.989074i	−0.869157	−	0.494537i	$-0.835338\pi$
$419$		−	20.2458i		−	0.989074i	0.869157	−	0.494537i	$-0.164662\pi$
$420$	13.5455			0.660954
$421$			32.9704i			1.60688i	0.595385	+	0.803441i	$0.297000\pi$
$421$			32.9704i			1.60688i	−0.595385	+	0.803441i	$0.703000\pi$
$422$		−	14.1838i		−	0.690457i
$423$	5.05226			0.245649
$424$	1.76662	+	7.06251i	0.0857949	+	0.342986i
$425$	−31.0000			−1.50372
$426$		−	20.2680i		−	0.981987i
$427$			14.5499i			0.704120i
$428$	3.52801			0.170533
$429$			9.65298i			0.466050i
$430$	−20.2584			−0.976946
$431$	−15.8484			−0.763391			−0.381696	−	0.924288i	$-0.624660\pi$
$431$	−15.8484			−0.763391			−0.381696	+	0.924288i	$0.624660\pi$
$432$		−	3.40739i		−	0.163938i
$433$	21.0688			1.01250			0.506251	−	0.862386i	$-0.331031\pi$
$433$	21.0688			1.01250			0.506251	+	0.862386i	$0.331031\pi$
$434$	−3.22687			−0.154895
$435$	−13.6219			−0.653121
$436$		−	2.20263i		−	0.105487i
$437$	4.63302			0.221627
$438$			11.9001i			0.568611i
$439$	12.2922			0.586677			0.293338	−	0.956009i	$-0.405234\pi$
$439$	12.2922			0.586677			0.293338	+	0.956009i	$0.405234\pi$
$440$	2.97150			0.141661
$441$	3.07565			0.146459
$442$			37.3769i			1.77784i
$443$		−	14.7934i		−	0.702857i	−0.936215	−	0.351429i	$-0.885696\pi$
$443$		−	14.7934i		−	0.702857i	0.936215	−	0.351429i	$-0.114304\pi$
$444$		−	8.23905i		−	0.391008i
$445$		−	46.1402i		−	2.18726i
$446$		−	2.98063i		−	0.141137i
$447$			0.233646i			0.0110511i
$448$	−2.18061			−0.103024
$449$	−21.1485			−0.998060			−0.499030	−	0.866585i	$-0.666310\pi$
$449$	−21.1485			−0.998060			−0.499030	+	0.866585i	$0.666310\pi$
$450$			5.24696i			0.247344i
$451$			4.33225i			0.203998i
$452$	3.81030			0.179222
$453$	9.20245			0.432369
$454$		−	13.9981i		−	0.656962i
$455$		−	29.9207i		−	1.40271i
$456$			3.55129i			0.166304i
$457$			1.95093i			0.0912608i	0.998958	+	0.0456304i	$0.0145296\pi$
$457$			1.95093i			0.0912608i	−0.998958	+	0.0456304i	$0.985470\pi$
$458$		−	23.5756i		−	1.10162i
$459$		−	27.5808i		−	1.28736i
$460$	−8.10393			−0.377848
$461$	2.03290			0.0946818			0.0473409	−	0.998879i	$-0.484925\pi$
$461$	2.03290			0.0946818			0.0473409	+	0.998879i	$0.484925\pi$
$462$	−4.55848			−0.212080
$463$			20.8861i			0.970659i	0.874331	+	0.485329i	$0.161300\pi$
$463$			20.8861i			0.970659i	−0.874331	+	0.485329i	$0.838700\pi$
$464$	2.19291			0.101803
$465$		−	9.19225i		−	0.426281i
$466$	14.8095			0.686035
$467$	−26.1018			−1.20785			−0.603925	−	0.797041i	$-0.706397\pi$
$467$	−26.1018			−1.20785			−0.603925	+	0.797041i	$0.706397\pi$
$468$	6.32629			0.292433
$469$		−	6.45955i		−	0.298274i
$470$	−10.9580			−0.505454
$471$	−15.3712			−0.708269
$472$			2.80552i			0.129135i
$473$	6.81756			0.313472
$474$			19.3084i			0.886866i
$475$			6.50610i			0.298520i
$476$	−17.6507			−0.809020
$477$	9.67585	−	2.42033i	0.443027	−	0.110819i
$478$	−15.0125			−0.686657
$479$			4.97176i			0.227166i	0.993529	+	0.113583i	$0.0362327\pi$
$479$			4.97176i			0.227166i	−0.993529	+	0.113583i	$0.963767\pi$
$480$		−	6.21181i		−	0.283529i
$481$	−18.1993			−0.829815
$482$		−	0.519115i		−	0.0236450i
$483$	12.4320			0.565674
$484$	−1.00000			−0.0454545
$485$		−	6.70634i		−	0.304519i
$486$	−13.2602			−0.601496
$487$	16.8100			0.761734			0.380867	−	0.924630i	$-0.375626\pi$
$487$	16.8100			0.761734			0.380867	+	0.924630i	$0.375626\pi$
$488$	6.67241			0.302046
$489$		−	8.16152i		−	0.369077i
$490$	−6.67086			−0.301359
$491$		−	35.4330i		−	1.59907i	−0.600620	−	0.799534i	$-0.705080\pi$
$491$		−	35.4330i		−	1.59907i	0.600620	−	0.799534i	$-0.294920\pi$
$492$	9.05640			0.408294
$493$	17.7503			0.799433
$494$	7.84445			0.352939
$495$		−	4.07105i		−	0.182980i
$496$			1.47980i			0.0664452i
$497$		−	21.1420i		−	0.948348i
$498$			8.28352i			0.371193i
$499$			22.7739i			1.01950i	0.860322	+	0.509750i	$0.170262\pi$
$499$			22.7739i			1.01950i	−0.860322	+	0.509750i	$0.829738\pi$
$500$			3.47722i			0.155506i
$501$	−0.585603			−0.0261628
$502$	−20.2151			−0.902242
$503$		−	16.5270i		−	0.736902i	−0.929647	−	0.368451i	$-0.879888\pi$
$503$		−	16.5270i		−	0.736902i	0.929647	−	0.368451i	$-0.120112\pi$
$504$			2.98750i			0.133074i
$505$	−39.9580			−1.77811
$506$	2.72722			0.121240
$507$		−	17.3979i		−	0.772666i
$508$		−	4.61021i		−	0.204545i
$509$		−	21.3048i		−	0.944319i	−0.881513	−	0.472159i	$-0.843475\pi$
$509$		−	21.3048i		−	0.944319i	0.881513	−	0.472159i	$-0.156525\pi$
$510$		−	50.2809i		−	2.22647i
$511$			12.4133i			0.549133i
$512$			1.00000i			0.0441942i
$513$	−5.78849			−0.255568
$514$	10.4298			0.460040
$515$	49.2404			2.16979
$516$		−	14.2519i		−	0.627403i
$517$	3.68770			0.162185
$518$		−	8.59434i		−	0.377613i
$519$	29.3593			1.28873
$520$	−13.7213			−0.601718
$521$	39.6735			1.73813			0.869064	−	0.494700i	$-0.164722\pi$
$521$	39.6735			1.73813			0.869064	+	0.494700i	$0.164722\pi$
$522$		−	3.00435i		−	0.131497i
$523$	34.1734			1.49430			0.747149	−	0.664656i	$-0.231422\pi$
$523$	34.1734			1.49430			0.747149	+	0.664656i	$0.231422\pi$
$524$	−10.1879			−0.445060
$525$			17.4581i			0.761934i
$526$	28.8298			1.25704
$527$			11.9781i			0.521775i
$528$			2.09046i			0.0909757i
$529$	15.5623			0.676621
$530$	−20.9862	+	5.24952i	−0.911584	+	0.228025i
$531$	3.84365			0.166800
$532$			3.70443i			0.160607i
$533$		−	20.0047i		−	0.866500i
$534$	32.4598			1.40467
$535$			10.4835i			0.453240i
$536$	−2.96227			−0.127951
$537$	−22.9446			−0.990131
$538$			3.60039i			0.155224i
$539$	2.24495			0.0966967
$540$	10.1251			0.435713
$541$	21.5603			0.926948			0.463474	−	0.886111i	$-0.346603\pi$
$541$	21.5603			0.926948			0.463474	+	0.886111i	$0.346603\pi$
$542$		−	29.8102i		−	1.28046i
$543$	−25.8005			−1.10720
$544$			8.09440i			0.347045i
$545$	6.54510			0.280361
$546$	21.0494			0.900830
$547$	10.9124			0.466580			0.233290	−	0.972407i	$-0.425051\pi$
$547$	10.9124			0.466580			0.233290	+	0.972407i	$0.425051\pi$
$548$		−	19.5375i		−	0.834601i
$549$		−	9.14141i		−	0.390146i
$550$			3.82981i			0.163304i
$551$		−	3.72533i		−	0.158704i
$552$		−	5.70115i		−	0.242657i
$553$			20.1411i			0.856486i
$554$	7.27912			0.309260
$555$	24.4823			1.03922
$556$		−	9.98558i		−	0.423483i
$557$		−	18.9885i		−	0.804570i	−0.915515	−	0.402285i	$-0.868216\pi$
$557$		−	18.9885i		−	0.804570i	0.915515	−	0.402285i	$-0.131784\pi$
$558$	2.02738			0.0858257
$559$	−31.4810			−1.33150
$560$		−	6.47968i		−	0.273816i
$561$			16.9210i			0.714407i
$562$		−	19.5468i		−	0.824533i
$563$		−	25.0830i		−	1.05712i	−0.848895	−	0.528561i	$-0.822732\pi$
$563$		−	25.0830i		−	1.05712i	0.848895	−	0.528561i	$-0.177268\pi$
$564$		−	7.70899i		−	0.324607i
$565$			11.3223i			0.476333i
$566$	20.4074			0.857785
$567$	−24.4950			−1.02869
$568$	−9.69546			−0.406812
$569$			40.1190i			1.68188i	0.541131	+	0.840938i	$0.317996\pi$
$569$			40.1190i			1.68188i	−0.541131	+	0.840938i	$0.682004\pi$
$570$	−10.5527			−0.442002
$571$			21.4344i			0.897003i	0.893782	+	0.448501i	$0.148042\pi$
$571$			21.4344i			0.897003i	−0.893782	+	0.448501i	$0.851958\pi$
$572$	4.61763			0.193073
$573$	−32.6924			−1.36575
$574$	9.44693			0.394307
$575$		−	10.4447i		−	0.435575i
$576$	1.37003			0.0570846
$577$	−46.3264			−1.92860			−0.964298	−	0.264821i	$-0.914687\pi$
$577$	−46.3264			−1.92860			−0.964298	+	0.264821i	$0.914687\pi$
$578$			48.5194i			2.01814i
$579$	41.9068			1.74159
$580$			6.51623i			0.270572i
$581$			8.64073i			0.358478i
$582$	4.71794			0.195565
$583$	7.06251	−	1.76662i	0.292499	−	0.0731661i
$584$	5.69259			0.235561
$585$			18.7986i			0.777225i
$586$			26.6856i			1.10237i
$587$	37.7710			1.55898			0.779488	−	0.626417i	$-0.215479\pi$
$587$	37.7710			1.55898			0.779488	+	0.626417i	$0.215479\pi$
$588$		−	4.69298i		−	0.193535i
$589$	2.51390			0.103583
$590$	−8.33661			−0.343213
$591$		−	41.0793i		−	1.68978i
$592$	−3.94126			−0.161985
$593$	14.7029			0.603774			0.301887	−	0.953344i	$-0.402383\pi$
$593$	14.7029			0.603774			0.301887	+	0.953344i	$0.402383\pi$
$594$	−3.40739			−0.139807
$595$		−	52.4491i		−	2.15020i
$596$	0.111768			0.00457818
$597$		−	15.2832i		−	0.625500i
$598$	−12.5933			−0.514978
$599$	29.9578			1.22404			0.612020	−	0.790842i	$-0.290357\pi$
$599$	29.9578			1.22404			0.612020	+	0.790842i	$0.290357\pi$
$600$	8.00607			0.326846
$601$		−	10.3892i		−	0.423783i	−0.977293	−	0.211892i	$-0.932038\pi$
$601$		−	10.3892i		−	0.423783i	0.977293	−	0.211892i	$-0.0679624\pi$
$602$		−	14.8664i		−	0.605911i
$603$			4.05840i			0.165271i
$604$		−	4.40211i		−	0.179119i
$605$		−	2.97150i		−	0.120809i
$606$		−	28.1106i		−	1.14192i
$607$	30.2655			1.22844			0.614219	−	0.789136i	$-0.289471\pi$
$607$	30.2655			1.22844			0.614219	+	0.789136i	$0.289471\pi$
$608$	1.69881			0.0688957
$609$		−	9.99633i		−	0.405072i
$610$			19.8271i			0.802775i
$611$	−17.0284			−0.688896
$612$	11.0896			0.448270
$613$		−	47.7048i		−	1.92678i	−0.268110	−	0.963388i	$-0.586399\pi$
$613$		−	47.7048i		−	1.92678i	0.268110	−	0.963388i	$-0.413601\pi$
$614$			26.9561i			1.08786i
$615$			26.9111i			1.08516i
$616$			2.18061i			0.0878592i
$617$		−	34.1216i		−	1.37368i	−0.726808	−	0.686841i	$-0.758997\pi$
$617$		−	34.1216i		−	1.37368i	0.726808	−	0.686841i	$-0.241003\pi$
$618$			34.6408i			1.39346i
$619$	15.9001			0.639080			0.319540	−	0.947573i	$-0.396472\pi$
$619$	15.9001			0.639080			0.319540	+	0.947573i	$0.396472\pi$
$620$	−4.39724			−0.176597
$621$	9.29270			0.372903
$622$			19.8853i			0.797326i
$623$	33.8596			1.35656
$624$		−	9.65298i		−	0.386428i
$625$	−29.4816			−1.17926
$626$	−8.44322			−0.337459
$627$	3.55129			0.141825
$628$			7.35304i			0.293418i
$629$	−31.9021			−1.27202
$630$	−8.87736			−0.353682
$631$			13.1376i			0.523000i	0.965204	+	0.261500i	$0.0842171\pi$
$631$			13.1376i			0.523000i	−0.965204	+	0.261500i	$0.915783\pi$
$632$	9.23645			0.367406
$633$			29.6507i			1.17851i
$634$			23.3810i			0.928577i
$635$	13.6992			0.543638
$636$	−3.69306	−	14.7639i	−0.146439	−	0.585427i
$637$	−10.3663			−0.410729
$638$		−	2.19291i		−	0.0868181i
$639$			13.2831i			0.525470i
$640$	−2.97150			−0.117459
$641$			25.8353i			1.02043i	0.860046	+	0.510216i	$0.170435\pi$
$641$			25.8353i			1.02043i	−0.860046	+	0.510216i	$0.829565\pi$
$642$	−7.37516			−0.291074
$643$	−47.5078			−1.87353			−0.936763	−	0.349965i	$-0.886194\pi$
$643$	−47.5078			−1.87353			−0.936763	+	0.349965i	$0.886194\pi$
$644$		−	5.94700i		−	0.234345i
$645$	42.3494			1.66751
$646$	13.7508			0.541019
$647$	32.7958			1.28934			0.644668	−	0.764463i	$-0.276996\pi$
$647$	32.7958			1.28934			0.644668	+	0.764463i	$0.276996\pi$
$648$			11.2331i			0.441278i
$649$	2.80552			0.110126
$650$		−	17.6846i		−	0.693648i
$651$	6.74565			0.264383
$652$	−3.90417			−0.152899
$653$	43.4149			1.69896			0.849479	−	0.527622i	$-0.176916\pi$
$653$	43.4149			1.69896			0.849479	+	0.527622i	$0.176916\pi$
$654$			4.60451i			0.180050i
$655$		−	30.2733i		−	1.18287i
$656$		−	4.33225i		−	0.169146i
$657$		−	7.79902i		−	0.304269i
$658$		−	8.04142i		−	0.313487i
$659$		−	24.4657i		−	0.953047i	−0.879162	−	0.476523i	$-0.841897\pi$
$659$		−	24.4657i		−	0.953047i	0.879162	−	0.476523i	$-0.158103\pi$
$660$	−6.21181			−0.241794
$661$	−13.6853			−0.532296			−0.266148	−	0.963932i	$-0.585751\pi$
$661$	−13.6853			−0.532296			−0.266148	+	0.963932i	$0.585751\pi$
$662$		−	24.5436i		−	0.953914i
$663$		−	78.1351i		−	3.03452i
$664$	3.96253			0.153776
$665$	−11.0077			−0.426861
$666$			5.39964i			0.209232i
$667$			5.98054i			0.231567i
$668$			0.280131i			0.0108386i
$669$			6.23090i			0.240901i
$670$		−	8.80238i		−	0.340066i
$671$		−	6.67241i		−	0.257586i
$672$	4.55848			0.175847
$673$	21.7204			0.837261			0.418631	−	0.908157i	$-0.362510\pi$
$673$	21.7204			0.837261			0.418631	+	0.908157i	$0.362510\pi$
$674$	21.7740			0.838701
$675$			13.0496i			0.502281i
$676$	−8.32250			−0.320096
$677$			39.6496i			1.52386i	0.647660	+	0.761930i	$0.275748\pi$
$677$			39.6496i			1.52386i	−0.647660	+	0.761930i	$0.724252\pi$
$678$	−7.96529			−0.305905
$679$	4.92139			0.188866
$680$	−24.0525			−0.922372
$681$			29.2624i			1.12134i
$682$	1.47980			0.0566646
$683$	0.348258			0.0133257			0.00666286	−	0.999978i	$-0.497879\pi$
$683$	0.348258			0.0133257			0.00666286	+	0.999978i	$0.497879\pi$
$684$		−	2.32742i		−	0.0889910i
$685$	58.0557			2.21819
$686$		−	20.1596i		−	0.769697i
$687$			49.2839i			1.88030i
$688$	−6.81756			−0.259917
$689$	−32.6120	+	8.15762i	−1.24242	+	0.310780i
$690$	16.9410			0.644931
$691$		−	33.8600i		−	1.28809i	−0.764986	−	0.644047i	$-0.777254\pi$
$691$		−	33.8600i		−	1.28809i	0.764986	−	0.644047i	$-0.222746\pi$
$692$		−	14.0444i		−	0.533888i
$693$	2.98750			0.113486
$694$		−	25.3463i		−	0.962134i
$695$	29.6721			1.12553
$696$	−4.58419			−0.173763
$697$		−	35.0670i		−	1.32826i
$698$	−16.7038			−0.632250
$699$	−30.9586			−1.17096
$700$	8.35131			0.315650
$701$		−	18.8917i		−	0.713531i	−0.934194	−	0.356765i	$-0.883880\pi$
$701$		−	18.8917i		−	0.713531i	0.934194	−	0.356765i	$-0.116120\pi$
$702$	15.7341			0.593844
$703$			6.69543i			0.252523i
$704$	1.00000			0.0376889
$705$	22.9072			0.862737
$706$	−7.74252			−0.291394
$707$		−	29.3228i		−	1.10280i
$708$		−	5.86484i		−	0.220414i
$709$			29.1472i			1.09465i	0.836922	+	0.547323i	$0.184353\pi$
$709$			29.1472i			1.09465i	−0.836922	+	0.547323i	$0.815647\pi$
$710$		−	28.8100i		−	1.08122i
$711$		−	12.6542i		−	0.474570i
$712$		−	15.5276i		−	0.581921i
$713$	−4.03575			−0.151140
$714$	36.8982			1.38088
$715$			13.7213i			0.513147i
$716$			10.9758i			0.410186i
$717$	31.3831			1.17202
$718$	−28.7106			−1.07147
$719$			45.1874i			1.68521i	0.538535	+	0.842603i	$0.318978\pi$
$719$			45.1874i			1.68521i	−0.538535	+	0.842603i	$0.681022\pi$
$720$			4.07105i			0.151719i
$721$			36.1346i			1.34572i
$722$			16.1141i			0.599703i
$723$			1.08519i			0.0403586i
$724$			12.3420i			0.458686i
$725$	−8.39842			−0.311909
$726$	2.09046			0.0775843
$727$	5.06598			0.187887			0.0939434	−	0.995578i	$-0.470053\pi$
$727$	5.06598			0.187887			0.0939434	+	0.995578i	$0.470053\pi$
$728$		−	10.0692i		−	0.373191i
$729$	−5.97935			−0.221457
$730$			16.9155i			0.626072i
$731$	−55.1841			−2.04106
$732$	−13.9484			−0.515549
$733$	12.0701			0.445820			0.222910	−	0.974839i	$-0.428444\pi$
$733$	12.0701			0.445820			0.222910	+	0.974839i	$0.428444\pi$
$734$		−	28.7385i		−	1.06076i
$735$	13.9452			0.514375
$736$	−2.72722			−0.100527
$737$			2.96227i			0.109117i
$738$	−5.93531			−0.218482
$739$			2.17096i			0.0798600i	0.999202	+	0.0399300i	$0.0127135\pi$
$739$			2.17096i			0.0798600i	−0.999202	+	0.0399300i	$0.987287\pi$
$740$		−	11.7114i		−	0.430521i
$741$	−16.3985			−0.602415
$742$	−3.85232	−	15.4006i	−0.141423	−	0.565373i
$743$	5.82815			0.213814			0.106907	−	0.994269i	$-0.465905\pi$
$743$	5.82815			0.213814			0.106907	+	0.994269i	$0.465905\pi$
$744$		−	3.09347i		−	0.113412i
$745$			0.332118i			0.0121679i
$746$	−10.5039			−0.384573
$747$		−	5.42879i		−	0.198629i
$748$	8.09440			0.295961
$749$	−7.69320			−0.281103
$750$		−	7.26900i		−	0.265426i
$751$	28.9849			1.05767			0.528837	−	0.848723i	$-0.322628\pi$
$751$	28.9849			1.05767			0.528837	+	0.848723i	$0.322628\pi$
$752$	−3.68770			−0.134476
$753$	42.2588			1.54000
$754$			10.1260i			0.368769i
$755$	13.0809			0.476062
$756$			7.43018i			0.270233i
$757$	9.18980			0.334009			0.167004	−	0.985956i	$-0.446591\pi$
$757$	9.18980			0.334009			0.167004	+	0.985956i	$0.446591\pi$
$758$	−12.4284			−0.451421
$759$	−5.70115			−0.206939
$760$			5.04800i			0.183110i
$761$		−	23.9981i		−	0.869929i	−0.900448	−	0.434965i	$-0.856761\pi$
$761$		−	23.9981i		−	0.869929i	0.900448	−	0.434965i	$-0.143239\pi$
$762$			9.63747i			0.349129i
$763$			4.80307i			0.173883i
$764$			15.6388i			0.565794i
$765$			32.9527i			1.19141i
$766$	−24.3727			−0.880620
$767$	−12.9549			−0.467773
$768$		−	2.09046i		−	0.0754330i
$769$		−	33.4261i		−	1.20538i	−0.797976	−	0.602689i	$-0.794096\pi$
$769$		−	33.4261i		−	1.20538i	0.797976	−	0.602689i	$-0.205904\pi$
$770$	−6.47968			−0.233511
$771$	−21.8031			−0.785221
$772$		−	20.0467i		−	0.721495i
$773$		−	29.9311i		−	1.07655i	−0.842770	−	0.538274i	$-0.819077\pi$
$773$		−	29.9311i		−	1.07655i	0.842770	−	0.538274i	$-0.180923\pi$
$774$			9.34027i			0.335729i
$775$		−	5.66737i		−	0.203578i
$776$		−	2.25689i		−	0.0810176i
$777$			17.9661i			0.644531i
$778$	−11.2239			−0.402395
$779$	−7.35965			−0.263687
$780$	28.6838			1.02705
$781$			9.69546i			0.346931i
$782$	−22.0752			−0.789408
$783$		−	7.47209i		−	0.267031i
$784$	−2.24495			−0.0801767
$785$	−21.8495			−0.779844
$786$	21.2974			0.759652
$787$			1.54889i			0.0552121i	0.999619	+	0.0276060i	$0.00878839\pi$
$787$			1.54889i			0.0552121i	−0.999619	+	0.0276060i	$0.991212\pi$
$788$	−19.6508			−0.700031
$789$	−60.2675			−2.14558
$790$			27.4461i			0.976488i
$791$	−8.30878			−0.295426
$792$		−	1.37003i		−	0.0486819i
$793$			30.8107i			1.09412i
$794$	−4.80277			−0.170444
$795$	43.8709	−	10.9739i	1.55594	−	0.389205i
$796$	−7.31092			−0.259129
$797$			9.60741i			0.340312i	0.985417	+	0.170156i	$0.0544271\pi$
$797$			9.60741i			0.340312i	−0.985417	+	0.170156i	$0.945573\pi$
$798$		−	7.74397i		−	0.274134i
$799$	−29.8497			−1.05601
$800$		−	3.82981i		−	0.135404i
$801$	−21.2733			−0.751654
$802$	−1.51978			−0.0536653
$803$		−	5.69259i		−	0.200887i
$804$	6.19251			0.218393
$805$	17.6715			0.622838
$806$	−6.83318			−0.240689
$807$		−	7.52648i		−	0.264945i
$808$	−13.4471			−0.473067
$809$			22.6301i			0.795632i	0.917465	+	0.397816i	$0.130232\pi$
$809$			22.6301i			0.795632i	−0.917465	+	0.397816i	$0.869768\pi$
$810$	−33.3792			−1.17282
$811$	5.19001			0.182246			0.0911230	−	0.995840i	$-0.470954\pi$
$811$	5.19001			0.182246			0.0911230	+	0.995840i	$0.470954\pi$
$812$	−4.78187			−0.167811
$813$			62.3170i			2.18555i
$814$			3.94126i			0.138141i
$815$		−	11.6012i		−	0.406374i
$816$		−	16.9210i		−	0.592355i
$817$			11.5817i			0.405193i
$818$		−	6.29925i		−	0.220248i
$819$	−13.7952			−0.482042
$820$	12.8733			0.449554
$821$			36.5452i			1.27544i	0.770269	+	0.637719i	$0.220122\pi$
$821$			36.5452i			1.27544i	−0.770269	+	0.637719i	$0.779878\pi$
$822$			40.8424i			1.42454i
$823$	−44.1692			−1.53964			−0.769822	−	0.638259i	$-0.779655\pi$
$823$	−44.1692			−1.53964			−0.769822	+	0.638259i	$0.779655\pi$
$824$	16.5709			0.577275
$825$		−	8.00607i		−	0.278736i
$826$		−	6.11775i		−	0.212864i
$827$			55.2958i			1.92282i	0.275115	+	0.961411i	$0.411284\pi$
$827$			55.2958i			1.92282i	−0.275115	+	0.961411i	$0.588716\pi$
$828$			3.73637i			0.129848i
$829$		−	47.6204i		−	1.65392i	−0.562258	−	0.826962i	$-0.690067\pi$
$829$		−	47.6204i		−	1.65392i	0.562258	−	0.826962i	$-0.309933\pi$
$830$			11.7747i			0.408704i
$831$	−15.2167			−0.527862
$832$	−4.61763			−0.160087
$833$	−18.1715			−0.629605
$834$			20.8745i			0.722824i
$835$	−0.832409			−0.0288067
$836$		−	1.69881i		−	0.0587544i
$837$	5.04227			0.174286
$838$	20.2458			0.699381
$839$	−8.85568			−0.305732			−0.152866	−	0.988247i	$-0.548850\pi$
$839$	−8.85568			−0.305732			−0.152866	+	0.988247i	$0.548850\pi$
$840$			13.5455i			0.467365i
$841$	−24.1912			−0.834178
$842$	−32.9704			−1.13624
$843$			40.8619i			1.40736i
$844$	14.1838			0.488227
$845$		−	24.7303i		−	0.850748i
$846$			5.05226i			0.173700i
$847$	2.18061			0.0749266
$848$	−7.06251	+	1.76662i	−0.242528	+	0.0606661i
$849$	−42.6608			−1.46412
$850$		−	31.0000i		−	1.06329i
$851$		−	10.7487i		−	0.368460i
$852$	20.2680			0.694370
$853$			6.47478i			0.221692i	0.993838	+	0.110846i	$0.0353560\pi$
$853$			6.47478i			0.221692i	−0.993838	+	0.110846i	$0.964644\pi$
$854$	−14.5499			−0.497888
$855$	6.91591			0.236519
$856$			3.52801i			0.120585i
$857$	−53.8722			−1.84024			−0.920119	−	0.391638i	$-0.871908\pi$
$857$	−53.8722			−1.84024			−0.920119	+	0.391638i	$0.871908\pi$
$858$	−9.65298			−0.329547
$859$	−35.7026			−1.21816			−0.609078	−	0.793110i	$-0.708460\pi$
$859$	−35.7026			−1.21816			−0.609078	+	0.793110i	$0.708460\pi$
$860$		−	20.2584i		−	0.690805i
$861$	−19.7485			−0.673026
$862$		−	15.8484i		−	0.539799i
$863$	−35.0799			−1.19413			−0.597066	−	0.802192i	$-0.703667\pi$
$863$	−35.0799			−1.19413			−0.597066	+	0.802192i	$0.703667\pi$
$864$	3.40739			0.115922
$865$	41.7329			1.41896
$866$			21.0688i			0.715947i
$867$		−	101.428i		−	3.44467i
$868$		−	3.22687i		−	0.109527i
$869$		−	9.23645i		−	0.313325i
$870$		−	13.6219i		−	0.461826i
$871$		−	13.6787i		−	0.463484i
$872$	2.20263			0.0745904
$873$	−3.09201			−0.104649
$874$			4.63302i			0.156714i
$875$		−	7.58246i		−	0.256334i
$876$	−11.9001			−0.402069
$877$	17.6294			0.595304			0.297652	−	0.954674i	$-0.403796\pi$
$877$	17.6294			0.595304			0.297652	+	0.954674i	$0.403796\pi$
$878$			12.2922i			0.414843i
$879$		−	55.7852i		−	1.88159i
$880$			2.97150i			0.100169i
$881$		−	12.5325i		−	0.422232i	−0.977461	−	0.211116i	$-0.932290\pi$
$881$		−	12.5325i		−	0.422232i	0.977461	−	0.211116i	$-0.0677098\pi$
$882$			3.07565i			0.103562i
$883$		−	4.93061i		−	0.165928i	−0.996553	−	0.0829641i	$-0.973561\pi$
$883$		−	4.93061i		−	0.165928i	0.996553	−	0.0829641i	$-0.0264387\pi$
$884$	−37.3769			−1.25712
$885$	17.4274			0.585814
$886$	14.7934			0.496995
$887$			46.7626i			1.57013i	0.619410	+	0.785067i	$0.287372\pi$
$887$			46.7626i			1.57013i	−0.619410	+	0.785067i	$0.712628\pi$
$888$	8.23905			0.276484
$889$			10.0531i			0.337169i
$890$	46.1402			1.54662
$891$	11.2331			0.376323
$892$	2.98063			0.0997990
$893$			6.26468i			0.209639i
$894$	−0.233646			−0.00781430
$895$	−32.6147			−1.09019
$896$		−	2.18061i		−	0.0728490i
$897$	26.3258			0.878992
$898$		−	21.1485i		−	0.705735i
$899$			3.24507i			0.108229i
$900$	−5.24696			−0.174899
$901$	−57.1668	+	14.2998i	−1.90450	+	0.476394i
$902$	−4.33225			−0.144248
$903$			31.0777i			1.03420i
$904$			3.81030i			0.126729i
$905$	−36.6742			−1.21909
$906$			9.20245i			0.305731i
$907$	−39.8615			−1.32358			−0.661790	−	0.749689i	$-0.730203\pi$
$907$	−39.8615			−1.32358			−0.661790	+	0.749689i	$0.730203\pi$
$908$	13.9981			0.464542
$909$			18.4229i			0.611050i
$910$	29.9207			0.991863
$911$	−2.97911			−0.0987023			−0.0493511	−	0.998781i	$-0.515715\pi$
$911$	−2.97911			−0.0987023			−0.0493511	+	0.998781i	$0.515715\pi$
$912$	−3.55129			−0.117595
$913$		−	3.96253i		−	0.131141i
$914$	−1.95093			−0.0645311
$915$		−	41.4477i		−	1.37022i
$916$	23.5756			0.778960
$917$	22.2158			0.733630
$918$	27.5808			0.910301
$919$			40.9986i			1.35242i	0.736709	+	0.676210i	$0.236379\pi$
$919$			40.9986i			1.35242i	−0.736709	+	0.676210i	$0.763621\pi$
$920$		−	8.10393i		−	0.267179i
$921$		−	56.3506i		−	1.85682i
$922$			2.03290i			0.0669501i
$923$		−	44.7700i		−	1.47362i
$924$		−	4.55848i		−	0.149963i
$925$	15.0943			0.496296
$926$	−20.8861			−0.686359
$927$		−	22.7026i		−	0.745652i
$928$			2.19291i			0.0719857i
$929$	−4.75451			−0.155991			−0.0779953	−	0.996954i	$-0.524852\pi$
$929$	−4.75451			−0.155991			−0.0779953	+	0.996954i	$0.524852\pi$
$930$	9.19225			0.301426
$931$			3.81373i			0.124990i
$932$			14.8095i			0.485100i
$933$		−	41.5694i		−	1.36092i
$934$		−	26.1018i		−	0.854078i
$935$			24.0525i			0.786601i
$936$			6.32629i			0.206781i
$937$	28.7004			0.937603			0.468801	−	0.883304i	$-0.344686\pi$
$937$	28.7004			0.937603			0.468801	+	0.883304i	$0.344686\pi$
$938$	6.45955			0.210912
$939$	17.6502			0.575993
$940$		−	10.9580i		−	0.357410i
$941$	−14.5228			−0.473431			−0.236715	−	0.971579i	$-0.576071\pi$
$941$	−14.5228			−0.473431			−0.236715	+	0.971579i	$0.576071\pi$
$942$		−	15.3712i		−	0.500822i
$943$	11.8150			0.384749
$944$	−2.80552			−0.0913120
$945$	−22.0788			−0.718223
$946$			6.81756i			0.221658i
$947$	−2.52723			−0.0821241			−0.0410620	−	0.999157i	$-0.513074\pi$
$947$	−2.52723			−0.0821241			−0.0410620	+	0.999157i	$0.513074\pi$
$948$	−19.3084			−0.627109
$949$			26.2863i			0.853288i
$950$	−6.50610			−0.211086
$951$		−	48.8770i		−	1.58495i
$952$		−	17.6507i		−	0.572063i
$953$	−52.7796			−1.70970			−0.854849	−	0.518877i	$-0.826350\pi$
$953$	−52.7796			−1.70970			−0.854849	+	0.518877i	$0.826350\pi$
$954$	2.42033	+	9.67585i	0.0783611	+	0.313267i
$955$	−46.4708			−1.50376
$956$		−	15.0125i		−	0.485540i
$957$			4.58419i			0.148186i
$958$	−4.97176			−0.160630
$959$			42.6037i			1.37574i
$960$	6.21181			0.200485
$961$	28.8102			0.929361
$962$		−	18.1993i		−	0.586768i
$963$	4.83348			0.155757
$964$	0.519115			0.0167196
$965$	59.5686			1.91758
$966$			12.4320i			0.399992i
$967$	−53.5446			−1.72188			−0.860939	−	0.508708i	$-0.830123\pi$
$967$	−53.5446			−1.72188			−0.860939	+	0.508708i	$0.830123\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	−28.7456			−0.923440
$970$	6.70634			0.215328
$971$	−50.5617			−1.62260			−0.811302	−	0.584628i	$-0.801241\pi$
$971$	−50.5617			−1.62260			−0.811302	+	0.584628i	$0.801241\pi$
$972$		−	13.2602i		−	0.425322i
$973$			21.7746i			0.698063i
$974$			16.8100i			0.538627i
$975$			36.9691i			1.18396i
$976$			6.67241i			0.213579i
$977$		−	20.3181i		−	0.650032i	−0.945708	−	0.325016i	$-0.894630\pi$
$977$		−	20.3181i		−	0.650032i	0.945708	−	0.325016i	$-0.105370\pi$
$978$	8.16152			0.260977
$979$	−15.5276			−0.496264
$980$		−	6.67086i		−	0.213093i
$981$		−	3.01767i		−	0.0963467i
$982$	35.4330			1.13071
$983$	−29.8383			−0.951695			−0.475848	−	0.879528i	$-0.657859\pi$
$983$	−29.8383			−0.951695			−0.475848	+	0.879528i	$0.657859\pi$
$984$			9.05640i			0.288707i
$985$		−	58.3924i		−	1.86054i
$986$			17.7503i			0.565284i
$987$			16.8103i			0.535077i
$988$			7.84445i			0.249565i
$989$		−	18.5930i		−	0.591223i
$990$	4.07105			0.129386
$991$	−21.2041			−0.673572			−0.336786	−	0.941581i	$-0.609340\pi$
$991$	−21.2041			−0.673572			−0.336786	+	0.941581i	$0.609340\pi$
$992$	−1.47980			−0.0469838
$993$			51.3075i			1.62819i
$994$	21.1420			0.670583
$995$		−	21.7244i		−	0.688709i
$996$	−8.28352			−0.262473
$997$	45.2147			1.43196			0.715982	−	0.698119i	$-0.245979\pi$
$997$	45.2147			1.43196			0.715982	+	0.698119i	$0.245979\pi$
$998$	−22.7739			−0.720896
$999$			13.4294i			0.424887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1166.2.c.b.529.13	yes	22
53.52	even	2	inner	1166.2.c.b.529.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1166.2.c.b.529.10	✓	22	53.52	even	2	inner
1166.2.c.b.529.13	yes	22	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.09046i q^{3} -1.00000 q^{4} -2.97150i q^{5} +2.09046 q^{6} +2.18061 q^{7} -1.00000i q^{8} -1.37003 q^{9} +2.97150 q^{10} -1.00000 q^{11} +2.09046i q^{12} +4.61763 q^{13} +2.18061i q^{14} -6.21181 q^{15} +1.00000 q^{16} +8.09440 q^{17} -1.37003i q^{18} -1.69881i q^{19} +2.97150i q^{20} -4.55848i q^{21} -1.00000i q^{22} +2.72722i q^{23} -2.09046 q^{24} -3.82981 q^{25} +4.61763i q^{26} -3.40739i q^{27} -2.18061 q^{28} +2.19291 q^{29} -6.21181i q^{30} +1.47980i q^{31} +1.00000i q^{32} +2.09046i q^{33} +8.09440i q^{34} -6.47968i q^{35} +1.37003 q^{36} -3.94126 q^{37} +1.69881 q^{38} -9.65298i q^{39} -2.97150 q^{40} -4.33225i q^{41} +4.55848 q^{42} -6.81756 q^{43} +1.00000 q^{44} +4.07105i q^{45} -2.72722 q^{46} -3.68770 q^{47} -2.09046i q^{48} -2.24495 q^{49} -3.82981i q^{50} -16.9210i q^{51} -4.61763 q^{52} +(-7.06251 + 1.76662i) q^{53} +3.40739 q^{54} +2.97150i q^{55} -2.18061i q^{56} -3.55129 q^{57} +2.19291i q^{58} -2.80552 q^{59} +6.21181 q^{60} +6.67241i q^{61} -1.47980 q^{62} -2.98750 q^{63} -1.00000 q^{64} -13.7213i q^{65} -2.09046 q^{66} -2.96227i q^{67} -8.09440 q^{68} +5.70115 q^{69} +6.47968 q^{70} -9.69546i q^{71} +1.37003i q^{72} +5.69259i q^{73} -3.94126i q^{74} +8.00607i q^{75} +1.69881i q^{76} -2.18061 q^{77} +9.65298 q^{78} +9.23645i q^{79} -2.97150i q^{80} -11.2331 q^{81} +4.33225 q^{82} +3.96253i q^{83} +4.55848i q^{84} -24.0525i q^{85} -6.81756i q^{86} -4.58419i q^{87} +1.00000i q^{88} +15.5276 q^{89} -4.07105 q^{90} +10.0692 q^{91} -2.72722i q^{92} +3.09347 q^{93} -3.68770i q^{94} -5.04800 q^{95} +2.09046 q^{96} +2.25689 q^{97} -2.24495i q^{98} +1.37003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 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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