LMFDB - Embedded newform 1166.2.c.b.529.9

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			529.9
Character	$\chi$	$=$	1166.529
Dual form			1166.2.c.b.529.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +1.49995i q^{3} -1.00000 q^{4} -4.12793i q^{5} +1.49995 q^{6} -0.327299 q^{7} +1.00000i q^{8} +0.750159 q^{9} -4.12793 q^{10} -1.00000 q^{11} -1.49995i q^{12} -6.53814 q^{13} +0.327299i q^{14} +6.19168 q^{15} +1.00000 q^{16} -2.35430 q^{17} -0.750159i q^{18} -2.67844i q^{19} +4.12793i q^{20} -0.490931i q^{21} +1.00000i q^{22} -3.59400i q^{23} -1.49995 q^{24} -12.0398 q^{25} +6.53814i q^{26} +5.62504i q^{27} +0.327299 q^{28} +6.50589 q^{29} -6.19168i q^{30} +8.56689i q^{31} -1.00000i q^{32} -1.49995i q^{33} +2.35430i q^{34} +1.35107i q^{35} -0.750159 q^{36} -7.12241 q^{37} -2.67844 q^{38} -9.80686i q^{39} +4.12793 q^{40} -2.13251i q^{41} -0.490931 q^{42} +2.21010 q^{43} +1.00000 q^{44} -3.09660i q^{45} -3.59400 q^{46} -4.65172 q^{47} +1.49995i q^{48} -6.89288 q^{49} +12.0398i q^{50} -3.53133i q^{51} +6.53814 q^{52} +(-2.68277 + 6.76777i) q^{53} +5.62504 q^{54} +4.12793i q^{55} -0.327299i q^{56} +4.01751 q^{57} -6.50589i q^{58} -3.31481 q^{59} -6.19168 q^{60} -6.96964i q^{61} +8.56689 q^{62} -0.245526 q^{63} -1.00000 q^{64} +26.9890i q^{65} -1.49995 q^{66} +13.5065i q^{67} +2.35430 q^{68} +5.39080 q^{69} +1.35107 q^{70} -10.4988i q^{71} +0.750159i q^{72} -7.18906i q^{73} +7.12241i q^{74} -18.0591i q^{75} +2.67844i q^{76} +0.327299 q^{77} -9.80686 q^{78} -12.3156i q^{79} -4.12793i q^{80} -6.18679 q^{81} -2.13251 q^{82} -5.55901i q^{83} +0.490931i q^{84} +9.71841i q^{85} -2.21010i q^{86} +9.75849i q^{87} -1.00000i q^{88} -4.36174 q^{89} -3.09660 q^{90} +2.13992 q^{91} +3.59400i q^{92} -12.8499 q^{93} +4.65172i q^{94} -11.0564 q^{95} +1.49995 q^{96} -15.3507 q^{97} +6.89288i q^{98} -0.750159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			1.49995i			0.865995i	0.901395	+	0.432997i	$0.142544\pi$
$3$			1.49995i			0.865995i	−0.901395	+	0.432997i	$0.857456\pi$
$4$	−1.00000			−0.500000
$5$		−	4.12793i		−	1.84607i	−0.384719	−	0.923034i	$-0.625702\pi$
$5$		−	4.12793i		−	1.84607i	0.384719	−	0.923034i	$-0.374298\pi$
$6$	1.49995			0.612351
$7$	−0.327299			−0.123707			−0.0618536	−	0.998085i	$-0.519701\pi$
$7$	−0.327299			−0.123707			−0.0618536	+	0.998085i	$0.519701\pi$
$8$			1.00000i			0.353553i
$9$	0.750159			0.250053
$10$	−4.12793			−1.30537
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	1.49995i		−	0.432997i
$13$	−6.53814			−1.81335			−0.906677	−	0.421827i	$-0.861389\pi$
$13$	−6.53814			−1.81335			−0.906677	+	0.421827i	$0.861389\pi$
$14$			0.327299i			0.0874742i
$15$	6.19168			1.59868
$16$	1.00000			0.250000
$17$	−2.35430			−0.571003			−0.285501	−	0.958378i	$-0.592160\pi$
$17$	−2.35430			−0.571003			−0.285501	+	0.958378i	$0.592160\pi$
$18$		−	0.750159i		−	0.176814i
$19$		−	2.67844i		−	0.614475i	−0.951633	−	0.307238i	$-0.900595\pi$
$19$		−	2.67844i		−	0.614475i	0.951633	−	0.307238i	$-0.0994047\pi$
$20$			4.12793i			0.923034i
$21$		−	0.490931i		−	0.107130i
$22$			1.00000i			0.213201i
$23$		−	3.59400i		−	0.749400i	−0.927146	−	0.374700i	$-0.877746\pi$
$23$		−	3.59400i		−	0.749400i	0.927146	−	0.374700i	$-0.122254\pi$
$24$	−1.49995			−0.306175
$25$	−12.0398			−2.40796
$26$			6.53814i			1.28223i
$27$			5.62504i			1.08254i
$28$	0.327299			0.0618536
$29$	6.50589			1.20811			0.604057	−	0.796941i	$-0.293550\pi$
$29$	6.50589			1.20811			0.604057	+	0.796941i	$0.293550\pi$
$30$		−	6.19168i		−	1.13044i
$31$			8.56689i			1.53866i	0.638852	+	0.769329i	$0.279409\pi$
$31$			8.56689i			1.53866i	−0.638852	+	0.769329i	$0.720591\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	1.49995i		−	0.261107i
$34$			2.35430i			0.403760i
$35$			1.35107i			0.228372i
$36$	−0.750159			−0.125026
$37$	−7.12241			−1.17092			−0.585458	−	0.810702i	$-0.699085\pi$
$37$	−7.12241			−1.17092			−0.585458	+	0.810702i	$0.699085\pi$
$38$	−2.67844			−0.434500
$39$		−	9.80686i		−	1.57035i
$40$	4.12793			0.652683
$41$		−	2.13251i		−	0.333042i	−0.986038	−	0.166521i	$-0.946747\pi$
$41$		−	2.13251i		−	0.333042i	0.986038	−	0.166521i	$-0.0532534\pi$
$42$	−0.490931			−0.0757522
$43$	2.21010			0.337037			0.168519	−	0.985698i	$-0.446102\pi$
$43$	2.21010			0.337037			0.168519	+	0.985698i	$0.446102\pi$
$44$	1.00000			0.150756
$45$		−	3.09660i		−	0.461614i
$46$	−3.59400			−0.529906
$47$	−4.65172			−0.678523			−0.339261	−	0.940692i	$-0.610177\pi$
$47$	−4.65172			−0.678523			−0.339261	+	0.940692i	$0.610177\pi$
$48$			1.49995i			0.216499i
$49$	−6.89288			−0.984697
$50$			12.0398i			1.70269i
$51$		−	3.53133i		−	0.494485i
$52$	6.53814			0.906677
$53$	−2.68277	+	6.76777i	−0.368507	+	0.929625i
$53$	−2.68277	+	6.76777i	−0.368507	+	0.929625i
$54$	5.62504			0.765471
$55$			4.12793i			0.556610i
$56$		−	0.327299i		−	0.0437371i
$57$	4.01751			0.532133
$58$		−	6.50589i		−	0.854265i
$59$	−3.31481			−0.431552			−0.215776	−	0.976443i	$-0.569228\pi$
$59$	−3.31481			−0.431552			−0.215776	+	0.976443i	$0.569228\pi$
$60$	−6.19168			−0.799342
$61$		−	6.96964i		−	0.892371i	−0.894940	−	0.446186i	$-0.852782\pi$
$61$		−	6.96964i		−	0.892371i	0.894940	−	0.446186i	$-0.147218\pi$
$62$	8.56689			1.08800
$63$	−0.245526			−0.0309333
$64$	−1.00000			−0.125000
$65$			26.9890i			3.34757i
$66$	−1.49995			−0.184631
$67$			13.5065i			1.65009i	0.565070	+	0.825043i	$0.308849\pi$
$67$			13.5065i			1.65009i	−0.565070	+	0.825043i	$0.691151\pi$
$68$	2.35430			0.285501
$69$	5.39080			0.648976
$70$	1.35107			0.161483
$71$		−	10.4988i		−	1.24598i	−0.782231	−	0.622989i	$-0.785918\pi$
$71$		−	10.4988i		−	1.24598i	0.782231	−	0.622989i	$-0.214082\pi$
$72$			0.750159i			0.0884070i
$73$		−	7.18906i		−	0.841415i	−0.907196	−	0.420708i	$-0.861782\pi$
$73$		−	7.18906i		−	0.841415i	0.907196	−	0.420708i	$-0.138218\pi$
$74$			7.12241i			0.827963i
$75$		−	18.0591i		−	2.08528i
$76$			2.67844i			0.307238i
$77$	0.327299			0.0372991
$78$	−9.80686			−1.11041
$79$		−	12.3156i		−	1.38562i	−0.721122	−	0.692808i	$-0.756373\pi$
$79$		−	12.3156i		−	1.38562i	0.721122	−	0.692808i	$-0.243627\pi$
$80$		−	4.12793i		−	0.461517i
$81$	−6.18679			−0.687421
$82$	−2.13251			−0.235496
$83$		−	5.55901i		−	0.610181i	−0.952323	−	0.305091i	$-0.901313\pi$
$83$		−	5.55901i		−	0.610181i	0.952323	−	0.305091i	$-0.0986867\pi$
$84$			0.490931i			0.0535649i
$85$			9.71841i			1.05411i
$86$		−	2.21010i		−	0.238321i
$87$			9.75849i			1.04622i
$88$		−	1.00000i		−	0.106600i
$89$	−4.36174			−0.462344			−0.231172	−	0.972913i	$-0.574256\pi$
$89$	−4.36174			−0.462344			−0.231172	+	0.972913i	$0.574256\pi$
$90$	−3.09660			−0.326411
$91$	2.13992			0.224325
$92$			3.59400i			0.374700i
$93$	−12.8499			−1.33247
$94$			4.65172i			0.479788i
$95$	−11.0564			−1.13436
$96$	1.49995			0.153088
$97$	−15.3507			−1.55863			−0.779313	−	0.626635i	$-0.784432\pi$
$97$	−15.3507			−1.55863			−0.779313	+	0.626635i	$0.784432\pi$
$98$			6.89288i			0.696286i
$99$	−0.750159			−0.0753938
$100$	12.0398			1.20398
$101$		−	7.71192i		−	0.767365i	−0.923465	−	0.383682i	$-0.874656\pi$
$101$		−	7.71192i		−	0.767365i	0.923465	−	0.383682i	$-0.125344\pi$
$102$	−3.53133			−0.349654
$103$		−	7.76894i		−	0.765497i	−0.923853	−	0.382748i	$-0.874978\pi$
$103$		−	7.76894i		−	0.765497i	0.923853	−	0.382748i	$-0.125022\pi$
$104$		−	6.53814i		−	0.641117i
$105$	−2.02653			−0.197769
$106$	6.76777	+	2.68277i	0.657344	+	0.260574i
$107$	−7.06621			−0.683116			−0.341558	−	0.939861i	$-0.610955\pi$
$107$	−7.06621			−0.683116			−0.341558	+	0.939861i	$0.610955\pi$
$108$		−	5.62504i		−	0.541270i
$109$			12.6393i			1.21063i	0.795986	+	0.605315i	$0.206953\pi$
$109$			12.6393i			1.21063i	−0.795986	+	0.605315i	$0.793047\pi$
$110$	4.12793			0.393583
$111$		−	10.6832i		−	1.01401i
$112$	−0.327299			−0.0309268
$113$	−6.27797			−0.590581			−0.295291	−	0.955407i	$-0.595416\pi$
$113$	−6.27797			−0.590581			−0.295291	+	0.955407i	$0.595416\pi$
$114$		−	4.01751i		−	0.376275i
$115$	−14.8358			−1.38344
$116$	−6.50589			−0.604057
$117$	−4.90464			−0.453434
$118$			3.31481i			0.305153i
$119$	0.770560			0.0706371
$120$			6.19168i			0.565220i
$121$	1.00000			0.0909091
$122$	−6.96964			−0.631002
$123$	3.19865			0.288413
$124$		−	8.56689i		−	0.769329i
$125$			29.0599i			2.59920i
$126$			0.245526i			0.0218732i
$127$		−	17.7193i		−	1.57234i	−0.618012	−	0.786169i	$-0.712062\pi$
$127$		−	17.7193i		−	1.57234i	0.618012	−	0.786169i	$-0.287938\pi$
$128$			1.00000i			0.0883883i
$129$			3.31504i			0.291873i
$130$	26.9890			2.36709
$131$	3.64825			0.318749			0.159374	−	0.987218i	$-0.449052\pi$
$131$	3.64825			0.318749			0.159374	+	0.987218i	$0.449052\pi$
$132$			1.49995i			0.130554i
$133$			0.876648i			0.0760150i
$134$	13.5065			1.16679
$135$	23.2198			1.99844
$136$		−	2.35430i		−	0.201880i
$137$			10.6768i			0.912178i	0.889934	+	0.456089i	$0.150750\pi$
$137$			10.6768i			0.912178i	−0.889934	+	0.456089i	$0.849250\pi$
$138$		−	5.39080i		−	0.458896i
$139$		−	0.488252i		−	0.0414130i	−0.999786	−	0.0207065i	$-0.993408\pi$
$139$		−	0.488252i		−	0.0414130i	0.999786	−	0.0207065i	$-0.00659155\pi$
$140$		−	1.35107i		−	0.114186i
$141$		−	6.97733i		−	0.587597i
$142$	−10.4988			−0.881039
$143$	6.53814			0.546747
$144$	0.750159			0.0625132
$145$		−	26.8559i		−	2.23026i
$146$	−7.18906			−0.594970
$147$		−	10.3389i		−	0.852742i
$148$	7.12241			0.585458
$149$	18.6351			1.52664			0.763322	−	0.646018i	$-0.223567\pi$
$149$	18.6351			1.52664			0.763322	+	0.646018i	$0.223567\pi$
$150$	−18.0591			−1.47452
$151$		−	20.3460i		−	1.65573i	−0.560924	−	0.827867i	$-0.689554\pi$
$151$		−	20.3460i		−	1.65573i	0.560924	−	0.827867i	$-0.310446\pi$
$152$	2.67844			0.217250
$153$	−1.76610			−0.142781
$154$		−	0.327299i		−	0.0263745i
$155$	35.3635			2.84047
$156$			9.80686i			0.785177i
$157$		−	6.51469i		−	0.519929i	−0.965618	−	0.259964i	$-0.916289\pi$
$157$		−	6.51469i		−	0.519929i	0.965618	−	0.259964i	$-0.0837108\pi$
$158$	−12.3156			−0.979779
$159$	−10.1513	−	4.02402i	−0.805050	−	0.319125i
$160$	−4.12793			−0.326342
$161$			1.17631i			0.0927062i
$162$			6.18679i			0.486080i
$163$	21.8674			1.71278			0.856392	−	0.516326i	$-0.172701\pi$
$163$	21.8674			1.71278			0.856392	+	0.516326i	$0.172701\pi$
$164$			2.13251i			0.166521i
$165$	−6.19168			−0.482022
$166$	−5.55901			−0.431463
$167$			8.00140i			0.619167i	0.950872	+	0.309584i	$0.100190\pi$
$167$			8.00140i			0.619167i	−0.950872	+	0.309584i	$0.899810\pi$
$168$	0.490931			0.0378761
$169$	29.7472			2.28825
$170$	9.71841			0.745368
$171$		−	2.00925i		−	0.153651i
$172$	−2.21010			−0.168519
$173$			11.3962i			0.866434i	0.901290	+	0.433217i	$0.142622\pi$
$173$			11.3962i			0.866434i	−0.901290	+	0.433217i	$0.857378\pi$
$174$	9.75849			0.739789
$175$	3.94062			0.297883
$176$	−1.00000			−0.0753778
$177$		−	4.97204i		−	0.373721i
$178$			4.36174i			0.326927i
$179$			4.06672i			0.303961i	0.988383	+	0.151981i	$0.0485651\pi$
$179$			4.06672i			0.303961i	−0.988383	+	0.151981i	$0.951435\pi$
$180$			3.09660i			0.230807i
$181$			6.07048i			0.451215i	0.974218	+	0.225608i	$0.0724368\pi$
$181$			6.07048i			0.451215i	−0.974218	+	0.225608i	$0.927563\pi$
$182$		−	2.13992i		−	0.158622i
$183$	10.4541			0.772789
$184$	3.59400			0.264953
$185$			29.4008i			2.16159i
$186$			12.8499i			0.942199i
$187$	2.35430			0.172164
$188$	4.65172			0.339261
$189$		−	1.84107i		−	0.133918i
$190$			11.0564i			0.802116i
$191$		−	0.0645017i		−	0.00466718i	−0.999997	−	0.00233359i	$-0.999257\pi$
$191$		−	0.0645017i		−	0.00466718i	0.999997	−	0.00233359i	$-0.000742806\pi$
$192$		−	1.49995i		−	0.108249i
$193$		−	7.53924i		−	0.542687i	−0.962483	−	0.271343i	$-0.912532\pi$
$193$		−	7.53924i		−	0.542687i	0.962483	−	0.271343i	$-0.0874679\pi$
$194$			15.3507i			1.10211i
$195$	−40.4820			−2.89898
$196$	6.89288			0.492348
$197$	23.4862			1.67332			0.836660	−	0.547722i	$-0.184505\pi$
$197$	23.4862			1.67332			0.836660	+	0.547722i	$0.184505\pi$
$198$			0.750159i			0.0533115i
$199$	7.74218			0.548829			0.274414	−	0.961612i	$-0.411516\pi$
$199$	7.74218			0.548829			0.274414	+	0.961612i	$0.411516\pi$
$200$		−	12.0398i		−	0.851344i
$201$	−20.2591			−1.42897
$202$	−7.71192			−0.542609
$203$	−2.12937			−0.149452
$204$			3.53133i			0.247243i
$205$	−8.80286			−0.614818
$206$	−7.76894			−0.541288
$207$		−	2.69607i		−	0.187390i
$208$	−6.53814			−0.453338
$209$			2.67844i			0.185271i
$210$			2.02653i			0.139844i
$211$	8.17360			0.562694			0.281347	−	0.959606i	$-0.409219\pi$
$211$	8.17360			0.562694			0.281347	+	0.959606i	$0.409219\pi$
$212$	2.68277	−	6.76777i	0.184254	−	0.464812i
$213$	15.7476			1.07901
$214$			7.06621i			0.483036i
$215$		−	9.12315i		−	0.622194i
$216$	−5.62504			−0.382735
$217$		−	2.80393i		−	0.190343i
$218$	12.6393			0.856045
$219$	10.7832			0.728661
$220$		−	4.12793i		−	0.278305i
$221$	15.3928			1.03543
$222$	−10.6832			−0.717012
$223$	8.11044			0.543115			0.271558	−	0.962422i	$-0.412461\pi$
$223$	8.11044			0.543115			0.271558	+	0.962422i	$0.412461\pi$
$224$			0.327299i			0.0218686i
$225$	−9.03177			−0.602118
$226$			6.27797i			0.417604i
$227$	−6.42422			−0.426391			−0.213195	−	0.977010i	$-0.568387\pi$
$227$	−6.42422			−0.426391			−0.213195	+	0.977010i	$0.568387\pi$
$228$	−4.01751			−0.266066
$229$	17.1107			1.13070			0.565352	−	0.824850i	$-0.308740\pi$
$229$	17.1107			1.13070			0.565352	+	0.824850i	$0.308740\pi$
$230$			14.8358i			0.978242i
$231$			0.490931i			0.0323009i
$232$			6.50589i			0.427133i
$233$		−	6.88848i		−	0.451280i	−0.974211	−	0.225640i	$-0.927553\pi$
$233$		−	6.88848i		−	0.451280i	0.974211	−	0.225640i	$-0.0724472\pi$
$234$			4.90464i			0.320626i
$235$			19.2020i			1.25260i
$236$	3.31481			0.215776
$237$	18.4728			1.19994
$238$		−	0.770560i		−	0.0499480i
$239$			6.49626i			0.420208i	0.977679	+	0.210104i	$0.0673802\pi$
$239$			6.49626i			0.420208i	−0.977679	+	0.210104i	$0.932620\pi$
$240$	6.19168			0.399671
$241$	−8.48537			−0.546591			−0.273295	−	0.961930i	$-0.588114\pi$
$241$	−8.48537			−0.546591			−0.273295	+	0.961930i	$0.588114\pi$
$242$		−	1.00000i		−	0.0642824i
$243$			7.59527i			0.487237i
$244$			6.96964i			0.446186i
$245$			28.4533i			1.81782i
$246$		−	3.19865i		−	0.203939i
$247$			17.5120i			1.11426i
$248$	−8.56689			−0.543998
$249$	8.33823			0.528414
$250$	29.0599			1.83791
$251$		−	17.0955i		−	1.07906i	−0.841966	−	0.539531i	$-0.818602\pi$
$251$		−	17.0955i		−	1.07906i	0.841966	−	0.539531i	$-0.181398\pi$
$252$	0.245526			0.0154667
$253$			3.59400i			0.225953i
$254$	−17.7193			−1.11181
$255$	−14.5771			−0.912853
$256$	1.00000			0.0625000
$257$		−	20.6923i		−	1.29075i	−0.763865	−	0.645376i	$-0.776701\pi$
$257$		−	20.6923i		−	1.29075i	0.763865	−	0.645376i	$-0.223299\pi$
$258$	3.31504			0.206385
$259$	2.33115			0.144851
$260$		−	26.9890i		−	1.67379i
$261$	4.88045			0.302092
$262$		−	3.64825i		−	0.225390i
$263$		−	21.1472i		−	1.30399i	−0.758221	−	0.651997i	$-0.773931\pi$
$263$		−	21.1472i		−	1.30399i	0.758221	−	0.651997i	$-0.226069\pi$
$264$	1.49995			0.0923154
$265$	27.9369	+	11.0743i	1.71615	+	0.680289i
$266$	0.876648			0.0537508
$267$		−	6.54239i		−	0.400388i
$268$		−	13.5065i		−	0.825043i
$269$	−0.717681			−0.0437578			−0.0218789	−	0.999761i	$-0.506965\pi$
$269$	−0.717681			−0.0437578			−0.0218789	+	0.999761i	$0.506965\pi$
$270$		−	23.2198i		−	1.41311i
$271$	−17.6289			−1.07088			−0.535439	−	0.844574i	$-0.679854\pi$
$271$	−17.6289			−1.07088			−0.535439	+	0.844574i	$0.679854\pi$
$272$	−2.35430			−0.142751
$273$			3.20977i			0.194264i
$274$	10.6768			0.645008
$275$	12.0398			0.726028
$276$	−5.39080			−0.324488
$277$		−	23.6890i		−	1.42334i	−0.702516	−	0.711668i	$-0.747940\pi$
$277$		−	23.6890i		−	1.42334i	0.702516	−	0.711668i	$-0.252060\pi$
$278$	−0.488252			−0.0292834
$279$			6.42653i			0.384746i
$280$	−1.35107			−0.0807416
$281$	−28.6005			−1.70616			−0.853081	−	0.521778i	$-0.825269\pi$
$281$	−28.6005			−1.70616			−0.853081	+	0.521778i	$0.825269\pi$
$282$	−6.97733			−0.415494
$283$			3.01087i			0.178978i	0.995988	+	0.0894889i	$0.0285234\pi$
$283$			3.01087i			0.178978i	−0.995988	+	0.0894889i	$0.971477\pi$
$284$			10.4988i			0.622989i
$285$		−	16.5840i		−	0.982352i
$286$		−	6.53814i		−	0.386608i
$287$			0.697968i			0.0411997i
$288$		−	0.750159i		−	0.0442035i
$289$	−11.4573			−0.673956
$290$	−26.8559			−1.57703
$291$		−	23.0252i		−	1.34976i
$292$			7.18906i			0.420708i
$293$	−3.57590			−0.208906			−0.104453	−	0.994530i	$-0.533309\pi$
$293$	−3.57590			−0.208906			−0.104453	+	0.994530i	$0.533309\pi$
$294$	−10.3389			−0.602980
$295$			13.6833i			0.796673i
$296$		−	7.12241i		−	0.413982i
$297$		−	5.62504i		−	0.326398i
$298$		−	18.6351i		−	1.07950i
$299$			23.4980i			1.35893i
$300$			18.0591i			1.04264i
$301$	−0.723363			−0.0416940
$302$	−20.3460			−1.17078
$303$	11.5675			0.664534
$304$		−	2.67844i		−	0.153619i
$305$	−28.7702			−1.64738
$306$			1.76610i			0.100961i
$307$	18.8480			1.07571			0.537856	−	0.843037i	$-0.319234\pi$
$307$	18.8480			1.07571			0.537856	+	0.843037i	$0.319234\pi$
$308$	−0.327299			−0.0186496
$309$	11.6530			0.662916
$310$		−	35.3635i		−	2.00851i
$311$	9.22585			0.523150			0.261575	−	0.965183i	$-0.415758\pi$
$311$	9.22585			0.523150			0.261575	+	0.965183i	$0.415758\pi$
$312$	9.80686			0.555204
$313$		−	24.2936i		−	1.37316i	−0.727056	−	0.686578i	$-0.759112\pi$
$313$		−	24.2936i		−	1.37316i	0.727056	−	0.686578i	$-0.240888\pi$
$314$	−6.51469			−0.367645
$315$			1.01351i			0.0571050i
$316$			12.3156i			0.692808i
$317$	9.06290			0.509023			0.254512	−	0.967070i	$-0.418085\pi$
$317$	9.06290			0.509023			0.254512	+	0.967070i	$0.418085\pi$
$318$	−4.02402	+	10.1513i	−0.225656	+	0.569257i
$319$	−6.50589			−0.364260
$320$			4.12793i			0.230758i
$321$		−	10.5989i		−	0.591575i
$322$	1.17631			0.0655532
$323$			6.30585i			0.350867i
$324$	6.18679			0.343710
$325$	78.7180			4.36649
$326$		−	21.8674i		−	1.21112i
$327$	−18.9584			−1.04840
$328$	2.13251			0.117748
$329$	1.52250			0.0839382
$330$			6.19168i			0.340841i
$331$	−29.1632			−1.60296			−0.801478	−	0.598024i	$-0.795953\pi$
$331$	−29.1632			−1.60296			−0.801478	+	0.598024i	$0.795953\pi$
$332$			5.55901i			0.305091i
$333$	−5.34294			−0.292791
$334$	8.00140			0.437817
$335$	55.7541			3.04617
$336$		−	0.490931i		−	0.0267825i
$337$			2.91211i			0.158633i	0.996850	+	0.0793163i	$0.0252737\pi$
$337$			2.91211i			0.158633i	−0.996850	+	0.0793163i	$0.974726\pi$
$338$		−	29.7472i		−	1.61804i
$339$		−	9.41662i		−	0.511440i
$340$		−	9.71841i		−	0.527055i
$341$		−	8.56689i		−	0.463923i
$342$	−2.00925			−0.108648
$343$	4.54712			0.245521
$344$			2.21010i			0.119161i
$345$		−	22.2529i		−	1.19805i
$346$	11.3962			0.612661
$347$	−17.7070			−0.950564			−0.475282	−	0.879834i	$-0.657654\pi$
$347$	−17.7070			−0.950564			−0.475282	+	0.879834i	$0.657654\pi$
$348$		−	9.75849i		−	0.523110i
$349$		−	10.0981i		−	0.540537i	−0.962785	−	0.270268i	$-0.912888\pi$
$349$		−	10.0981i		−	0.540537i	0.962785	−	0.270268i	$-0.0871125\pi$
$350$		−	3.94062i		−	0.210635i
$351$		−	36.7773i		−	1.96303i
$352$			1.00000i			0.0533002i
$353$		−	31.5684i		−	1.68022i	−0.542419	−	0.840108i	$-0.682492\pi$
$353$		−	31.5684i		−	1.68022i	0.542419	−	0.840108i	$-0.317508\pi$
$354$	−4.97204			−0.264261
$355$	−43.3383			−2.30016
$356$	4.36174			0.231172
$357$			1.15580i			0.0611714i
$358$	4.06672			0.214933
$359$			29.6441i			1.56456i	0.622930	+	0.782278i	$0.285942\pi$
$359$			29.6441i			1.56456i	−0.622930	+	0.782278i	$0.714058\pi$
$360$	3.09660			0.163205
$361$	11.8260			0.622420
$362$	6.07048			0.319057
$363$			1.49995i			0.0787268i
$364$	−2.13992			−0.112162
$365$	−29.6759			−1.55331
$366$		−	10.4541i		−	0.546444i
$367$	−31.6279			−1.65096			−0.825482	−	0.564428i	$-0.809097\pi$
$367$	−31.6279			−1.65096			−0.825482	+	0.564428i	$0.809097\pi$
$368$		−	3.59400i		−	0.187350i
$369$		−	1.59972i		−	0.0832782i
$370$	29.4008			1.52848
$371$	0.878068	−	2.21508i	0.0455870	−	0.115001i
$372$	12.8499			0.666235
$373$			31.3261i			1.62200i	0.585044	+	0.811001i	$0.301077\pi$
$373$			31.3261i			1.62200i	−0.585044	+	0.811001i	$0.698923\pi$
$374$		−	2.35430i		−	0.121738i
$375$	−43.5883			−2.25089
$376$		−	4.65172i		−	0.239894i
$377$	−42.5364			−2.19074
$378$	−1.84107			−0.0946943
$379$		−	6.75558i		−	0.347011i	−0.984833	−	0.173505i	$-0.944491\pi$
$379$		−	6.75558i		−	0.347011i	0.984833	−	0.173505i	$-0.0555094\pi$
$380$	11.0564			0.567181
$381$	26.5781			1.36164
$382$	−0.0645017			−0.00330020
$383$			2.47507i			0.126470i	0.997999	+	0.0632351i	$0.0201418\pi$
$383$			2.47507i			0.126470i	−0.997999	+	0.0632351i	$0.979858\pi$
$384$	−1.49995			−0.0765439
$385$		−	1.35107i		−	0.0688567i
$386$	−7.53924			−0.383737
$387$	1.65793			0.0842772
$388$	15.3507			0.779313
$389$		−	15.6222i		−	0.792076i	−0.918234	−	0.396038i	$-0.870385\pi$
$389$		−	15.6222i		−	0.792076i	0.918234	−	0.396038i	$-0.129615\pi$
$390$			40.4820i			2.04989i
$391$			8.46136i			0.427909i
$392$		−	6.89288i		−	0.348143i
$393$			5.47218i			0.276035i
$394$		−	23.4862i		−	1.18322i
$395$	−50.8381			−2.55794
$396$	0.750159			0.0376969
$397$			30.9334i			1.55250i	0.630423	+	0.776252i	$0.282882\pi$
$397$			30.9334i			1.55250i	−0.630423	+	0.776252i	$0.717118\pi$
$398$		−	7.74218i		−	0.388080i
$399$	−1.31493			−0.0658286
$400$	−12.0398			−0.601991
$401$			8.74483i			0.436696i	0.975871	+	0.218348i	$0.0700668\pi$
$401$			8.74483i			0.436696i	−0.975871	+	0.218348i	$0.929933\pi$
$402$			20.2591i			1.01043i
$403$		−	56.0115i		−	2.79013i
$404$			7.71192i			0.383682i
$405$			25.5386i			1.26902i
$406$			2.12937i			0.105679i
$407$	7.12241			0.353045
$408$	3.53133			0.174827
$409$	7.46974			0.369355			0.184677	−	0.982799i	$-0.440876\pi$
$409$	7.46974			0.369355			0.184677	+	0.982799i	$0.440876\pi$
$410$			8.80286i			0.434742i
$411$	−16.0146			−0.789942
$412$			7.76894i			0.382748i
$413$	1.08493			0.0533861
$414$	−2.69607			−0.132504
$415$	−22.9472			−1.12644
$416$			6.53814i			0.320559i
$417$	0.732352			0.0358634
$418$	2.67844			0.131007
$419$			0.228861i			0.0111806i	0.999984	+	0.00559029i	$0.00177945\pi$
$419$			0.228861i			0.0111806i	−0.999984	+	0.00559029i	$0.998221\pi$
$420$	2.02653			0.0988844
$421$		−	24.3628i		−	1.18737i	−0.804698	−	0.593685i	$-0.797673\pi$
$421$		−	24.3628i		−	1.18737i	0.804698	−	0.593685i	$-0.202327\pi$
$422$		−	8.17360i		−	0.397884i
$423$	−3.48953			−0.169667
$424$	−6.76777	−	2.68277i	−0.328672	−	0.130287i
$425$	28.3454			1.37495
$426$		−	15.7476i		−	0.762975i
$427$			2.28115i			0.110393i
$428$	7.06621			0.341558
$429$			9.80686i			0.473480i
$430$	−9.12315			−0.439957
$431$	32.1564			1.54892			0.774461	−	0.632622i	$-0.218021\pi$
$431$	32.1564			1.54892			0.774461	+	0.632622i	$0.218021\pi$
$432$			5.62504i			0.270635i
$433$	−13.6044			−0.653787			−0.326894	−	0.945061i	$-0.606002\pi$
$433$	−13.6044			−0.653787			−0.326894	+	0.945061i	$0.606002\pi$
$434$	−2.80393			−0.134593
$435$	40.2824			1.93139
$436$		−	12.6393i		−	0.605315i
$437$	−9.62629			−0.460488
$438$		−	10.7832i		−	0.515241i
$439$	28.1537			1.34370			0.671851	−	0.740687i	$-0.265500\pi$
$439$	28.1537			1.34370			0.671851	+	0.740687i	$0.265500\pi$
$440$	−4.12793			−0.196791
$441$	−5.17075			−0.246226
$442$		−	15.3928i		−	0.732159i
$443$			13.4538i			0.639211i	0.947551	+	0.319606i	$0.103550\pi$
$443$			13.4538i			0.639211i	−0.947551	+	0.319606i	$0.896450\pi$
$444$			10.6832i			0.507004i
$445$			18.0050i			0.853518i
$446$		−	8.11044i		−	0.384041i
$447$			27.9516i			1.32207i
$448$	0.327299			0.0154634
$449$	−27.5238			−1.29893			−0.649463	−	0.760393i	$-0.725006\pi$
$449$	−27.5238			−1.29893			−0.649463	+	0.760393i	$0.725006\pi$
$450$			9.03177i			0.425762i
$451$			2.13251i			0.100416i
$452$	6.27797			0.295291
$453$	30.5179			1.43386
$454$			6.42422i			0.301504i
$455$		−	8.83346i		−	0.414119i
$456$			4.01751i			0.188137i
$457$		−	0.628748i		−	0.0294116i	−0.999892	−	0.0147058i	$-0.995319\pi$
$457$		−	0.628748i		−	0.0294116i	0.999892	−	0.0147058i	$-0.00468117\pi$
$458$		−	17.1107i		−	0.799529i
$459$		−	13.2431i		−	0.618133i
$460$	14.8358			0.691721
$461$	−13.5706			−0.632046			−0.316023	−	0.948752i	$-0.602348\pi$
$461$	−13.5706			−0.632046			−0.316023	+	0.948752i	$0.602348\pi$
$462$	0.490931			0.0228402
$463$			19.2750i			0.895785i	0.894087	+	0.447892i	$0.147825\pi$
$463$			19.2750i			0.895785i	−0.894087	+	0.447892i	$0.852175\pi$
$464$	6.50589			0.302028
$465$			53.0434i			2.45983i
$466$	−6.88848			−0.319103
$467$	−4.54645			−0.210385			−0.105192	−	0.994452i	$-0.533546\pi$
$467$	−4.54645			−0.210385			−0.105192	+	0.994452i	$0.533546\pi$
$468$	4.90464			0.226717
$469$		−	4.42067i		−	0.204128i
$470$	19.2020			0.885721
$471$	9.77169			0.450256
$472$		−	3.31481i		−	0.152577i
$473$	−2.21010			−0.101621
$474$		−	18.4728i		−	0.848484i
$475$			32.2479i			1.47963i
$476$	−0.770560			−0.0353186
$477$	−2.01251	+	5.07690i	−0.0921463	+	0.232455i
$478$	6.49626			0.297132
$479$		−	22.3517i		−	1.02128i	−0.859796	−	0.510638i	$-0.829409\pi$
$479$		−	22.3517i		−	1.02128i	0.859796	−	0.510638i	$-0.170591\pi$
$480$		−	6.19168i		−	0.282610i
$481$	46.5673			2.12329
$482$			8.48537i			0.386498i
$483$	−1.76440			−0.0802831
$484$	−1.00000			−0.0454545
$485$			63.3666i			2.87733i
$486$	7.59527			0.344528
$487$	20.1753			0.914231			0.457115	−	0.889407i	$-0.348883\pi$
$487$	20.1753			0.914231			0.457115	+	0.889407i	$0.348883\pi$
$488$	6.96964			0.315501
$489$			32.7999i			1.48326i
$490$	28.4533			1.28539
$491$			31.2607i			1.41078i	0.708821	+	0.705389i	$0.249228\pi$
$491$			31.2607i			1.41078i	−0.708821	+	0.705389i	$0.750772\pi$
$492$	−3.19865			−0.144206
$493$	−15.3168			−0.689836
$494$	17.5120			0.787901
$495$			3.09660i			0.139182i
$496$			8.56689i			0.384665i
$497$			3.43624i			0.154136i
$498$		−	8.33823i		−	0.373645i
$499$		−	38.7213i		−	1.73340i	−0.498828	−	0.866701i	$-0.666236\pi$
$499$		−	38.7213i		−	1.73340i	0.498828	−	0.866701i	$-0.333764\pi$
$500$		−	29.0599i		−	1.29960i
$501$	−12.0017			−0.536196
$502$	−17.0955			−0.763011
$503$		−	18.2717i		−	0.814697i	−0.913273	−	0.407348i	$-0.866453\pi$
$503$		−	18.2717i		−	0.814697i	0.913273	−	0.407348i	$-0.133547\pi$
$504$		−	0.245526i		−	0.0109366i
$505$	−31.8343			−1.41661
$506$	3.59400			0.159773
$507$			44.6193i			1.98161i
$508$			17.7193i			0.786169i
$509$		−	2.43867i		−	0.108092i	−0.998538	−	0.0540460i	$-0.982788\pi$
$509$		−	2.43867i		−	0.108092i	0.998538	−	0.0540460i	$-0.0172118\pi$
$510$			14.5771i			0.645485i
$511$			2.35297i			0.104089i
$512$		−	1.00000i		−	0.0441942i
$513$	15.0663			0.665194
$514$	−20.6923			−0.912699
$515$	−32.0697			−1.41316
$516$		−	3.31504i		−	0.145936i
$517$	4.65172			0.204582
$518$		−	2.33115i		−	0.102425i
$519$	−17.0936			−0.750328
$520$	−26.9890			−1.18355
$521$	25.8682			1.13331			0.566654	−	0.823956i	$-0.308238\pi$
$521$	25.8682			1.13331			0.566654	+	0.823956i	$0.308238\pi$
$522$		−	4.88045i		−	0.213611i
$523$	−26.0150			−1.13756			−0.568778	−	0.822491i	$-0.692584\pi$
$523$	−26.0150			−1.13756			−0.568778	+	0.822491i	$0.692584\pi$
$524$	−3.64825			−0.159374
$525$			5.91071i			0.257965i
$526$	−21.1472			−0.922063
$527$		−	20.1691i		−	0.878578i
$528$		−	1.49995i		−	0.0652768i
$529$	10.0832			0.438400
$530$	11.0743	−	27.9369i	0.481037	−	1.21350i
$531$	−2.48663			−0.107911
$532$		−	0.876648i		−	0.0380075i
$533$			13.9426i			0.603923i
$534$	−6.54239			−0.283117
$535$			29.1688i			1.26108i
$536$	−13.5065			−0.583394
$537$	−6.09987			−0.263229
$538$			0.717681i			0.0309414i
$539$	6.89288			0.296897
$540$	−23.2198			−0.999220
$541$	−26.3403			−1.13246			−0.566228	−	0.824249i	$-0.691598\pi$
$541$	−26.3403			−1.13246			−0.566228	+	0.824249i	$0.691598\pi$
$542$			17.6289i			0.757226i
$543$	−9.10540			−0.390750
$544$			2.35430i			0.100940i
$545$	52.1744			2.23490
$546$	3.20977			0.137366
$547$	37.1942			1.59031			0.795155	−	0.606407i	$-0.207390\pi$
$547$	37.1942			1.59031			0.795155	+	0.606407i	$0.207390\pi$
$548$		−	10.6768i		−	0.456089i
$549$		−	5.22834i		−	0.223140i
$550$		−	12.0398i		−	0.513380i
$551$		−	17.4256i		−	0.742356i
$552$			5.39080i			0.229448i
$553$			4.03089i			0.171411i
$554$	−23.6890			−1.00645
$555$	−44.0997			−1.87193
$556$			0.488252i			0.0207065i
$557$		−	23.4133i		−	0.992055i	−0.868307	−	0.496028i	$-0.834791\pi$
$557$		−	23.4133i		−	0.992055i	0.868307	−	0.496028i	$-0.165209\pi$
$558$	6.42653			0.272057
$559$	−14.4500			−0.611168
$560$			1.35107i			0.0570930i
$561$			3.53133i			0.149093i
$562$			28.6005i			1.20644i
$563$			16.4928i			0.695087i	0.937664	+	0.347543i	$0.112984\pi$
$563$			16.4928i			0.695087i	−0.937664	+	0.347543i	$0.887016\pi$
$564$			6.97733i			0.293799i
$565$			25.9150i			1.09025i
$566$	3.01087			0.126556
$567$	2.02493			0.0850389
$568$	10.4988			0.440520
$569$			25.3592i			1.06311i	0.847023	+	0.531556i	$0.178392\pi$
$569$			25.3592i			1.06311i	−0.847023	+	0.531556i	$0.821608\pi$
$570$	−16.5840			−0.694628
$571$			7.98061i			0.333978i	0.985959	+	0.166989i	$0.0534045\pi$
$571$			7.98061i			0.333978i	−0.985959	+	0.166989i	$0.946596\pi$
$572$	−6.53814			−0.273373
$573$	0.0967492			0.00404175
$574$	0.697968			0.0291326
$575$			43.2711i			1.80453i
$576$	−0.750159			−0.0312566
$577$	−22.5794			−0.939994			−0.469997	−	0.882668i	$-0.655745\pi$
$577$	−22.5794			−0.939994			−0.469997	+	0.882668i	$0.655745\pi$
$578$			11.4573i			0.476559i
$579$	11.3085			0.469964
$580$			26.8559i			1.11513i
$581$			1.81946i			0.0754838i
$582$	−23.0252			−0.954426
$583$	2.68277	−	6.76777i	0.111109	−	0.280292i
$584$	7.18906			0.297485
$585$			20.2460i			0.837070i
$586$			3.57590i			0.147719i
$587$	−37.5884			−1.55144			−0.775720	−	0.631077i	$-0.782613\pi$
$587$	−37.5884			−1.55144			−0.775720	+	0.631077i	$0.782613\pi$
$588$			10.3389i			0.426371i
$589$	22.9459			0.945468
$590$	13.6833			0.563333
$591$			35.2280i			1.44909i
$592$	−7.12241			−0.292729
$593$	−46.7780			−1.92094			−0.960471	−	0.278381i	$-0.910202\pi$
$593$	−46.7780			−1.92094			−0.960471	+	0.278381i	$0.910202\pi$
$594$	−5.62504			−0.230798
$595$		−	3.18082i		−	0.130401i
$596$	−18.6351			−0.763322
$597$			11.6129i			0.475283i
$598$	23.4980			0.960906
$599$	−26.5999			−1.08684			−0.543422	−	0.839460i	$-0.682871\pi$
$599$	−26.5999			−1.08684			−0.543422	+	0.839460i	$0.682871\pi$
$600$	18.0591			0.737259
$601$			44.1865i			1.80240i	0.433398	+	0.901202i	$0.357314\pi$
$601$			44.1865i			1.80240i	−0.433398	+	0.901202i	$0.642686\pi$
$602$			0.723363i			0.0294821i
$603$			10.1320i			0.412609i
$604$			20.3460i			0.827867i
$605$		−	4.12793i		−	0.167824i
$606$		−	11.5675i		−	0.469896i
$607$	−30.5009			−1.23799			−0.618996	−	0.785394i	$-0.712460\pi$
$607$	−30.5009			−1.23799			−0.618996	+	0.785394i	$0.712460\pi$
$608$	−2.67844			−0.108625
$609$		−	3.19394i		−	0.129425i
$610$			28.7702i			1.16487i
$611$	30.4136			1.23040
$612$	1.76610			0.0713904
$613$		−	24.0632i		−	0.971902i	−0.873986	−	0.485951i	$-0.838473\pi$
$613$		−	24.0632i		−	0.971902i	0.873986	−	0.485951i	$-0.161527\pi$
$614$		−	18.8480i		−	0.760644i
$615$		−	13.2038i		−	0.532430i
$616$			0.327299i			0.0131872i
$617$			4.27933i			0.172279i	0.996283	+	0.0861397i	$0.0274531\pi$
$617$			4.27933i			0.172279i	−0.996283	+	0.0861397i	$0.972547\pi$
$618$		−	11.6530i		−	0.468753i
$619$	−28.7991			−1.15753			−0.578767	−	0.815493i	$-0.696466\pi$
$619$	−28.7991			−1.15753			−0.578767	+	0.815493i	$0.696466\pi$
$620$	−35.3635			−1.42023
$621$	20.2164			0.811255
$622$		−	9.22585i		−	0.369923i
$623$	1.42759			0.0571953
$624$		−	9.80686i		−	0.392589i
$625$	59.7582			2.39033
$626$	−24.2936			−0.970968
$627$	−4.01751			−0.160444
$628$			6.51469i			0.259964i
$629$	16.7683			0.668597
$630$	1.01351			0.0403794
$631$		−	9.38214i		−	0.373497i	−0.982408	−	0.186749i	$-0.940205\pi$
$631$		−	9.38214i		−	0.373497i	0.982408	−	0.186749i	$-0.0597950\pi$
$632$	12.3156			0.489889
$633$			12.2600i			0.487290i
$634$		−	9.06290i		−	0.359934i
$635$	−73.1442			−2.90264
$636$	10.1513	+	4.02402i	0.402525	+	0.159563i
$637$	45.0666			1.78560
$638$			6.50589i			0.257571i
$639$		−	7.87576i		−	0.311560i
$640$	4.12793			0.163171
$641$			22.5970i			0.892527i	0.894902	+	0.446263i	$0.147246\pi$
$641$			22.5970i			0.892527i	−0.894902	+	0.446263i	$0.852754\pi$
$642$	−10.5989			−0.418307
$643$	−5.04232			−0.198850			−0.0994249	−	0.995045i	$-0.531700\pi$
$643$	−5.04232			−0.198850			−0.0994249	+	0.995045i	$0.531700\pi$
$644$		−	1.17631i		−	0.0463531i
$645$	13.6842			0.538817
$646$	6.30585			0.248100
$647$	45.0278			1.77022			0.885112	−	0.465377i	$-0.154081\pi$
$647$	45.0278			1.77022			0.885112	+	0.465377i	$0.154081\pi$
$648$		−	6.18679i		−	0.243040i
$649$	3.31481			0.130118
$650$		−	78.7180i		−	3.08757i
$651$	4.20575			0.164836
$652$	−21.8674			−0.856392
$653$	3.69208			0.144482			0.0722412	−	0.997387i	$-0.476985\pi$
$653$	3.69208			0.144482			0.0722412	+	0.997387i	$0.476985\pi$
$654$			18.9584i			0.741330i
$655$		−	15.0597i		−	0.588432i
$656$		−	2.13251i		−	0.0832606i
$657$		−	5.39293i		−	0.210398i
$658$		−	1.52250i		−	0.0593532i
$659$		−	26.7564i		−	1.04228i	−0.853471	−	0.521140i	$-0.825507\pi$
$659$		−	26.7564i		−	1.04228i	0.853471	−	0.521140i	$-0.174493\pi$
$660$	6.19168			0.241011
$661$	−31.2379			−1.21501			−0.607506	−	0.794315i	$-0.707830\pi$
$661$	−31.2379			−1.21501			−0.607506	+	0.794315i	$0.707830\pi$
$662$			29.1632i			1.13346i
$663$			23.0883i			0.896676i
$664$	5.55901			0.215732
$665$	3.61874			0.140329
$666$			5.34294i			0.207035i
$667$		−	23.3821i		−	0.905360i
$668$		−	8.00140i		−	0.309584i
$669$			12.1652i			0.470335i
$670$		−	55.7541i		−	2.15397i
$671$			6.96964i			0.269060i
$672$	−0.490931			−0.0189381
$673$	−6.25173			−0.240986			−0.120493	−	0.992714i	$-0.538448\pi$
$673$	−6.25173			−0.240986			−0.120493	+	0.992714i	$0.538448\pi$
$674$	2.91211			0.112170
$675$		−	67.7245i		−	2.60672i
$676$	−29.7472			−1.14412
$677$		−	0.840985i		−	0.0323217i	−0.999869	−	0.0161608i	$-0.994856\pi$
$677$		−	0.840985i		−	0.0323217i	0.999869	−	0.0161608i	$-0.00514438\pi$
$678$	−9.41662			−0.361643
$679$	5.02426			0.192813
$680$	−9.71841			−0.372684
$681$		−	9.63600i		−	0.369252i
$682$	−8.56689			−0.328043
$683$	51.4675			1.96935			0.984675	−	0.174400i	$-0.0557986\pi$
$683$	51.4675			1.96935			0.984675	+	0.174400i	$0.0557986\pi$
$684$			2.00925i			0.0768257i
$685$	44.0730			1.68394
$686$		−	4.54712i		−	0.173610i
$687$			25.6651i			0.979184i
$688$	2.21010			0.0842594
$689$	17.5403	−	44.2486i	0.668234	−	1.68574i
$690$	−22.2529			−0.847152
$691$		−	21.6185i		−	0.822405i	−0.911544	−	0.411203i	$-0.865109\pi$
$691$		−	21.6185i		−	0.822405i	0.911544	−	0.411203i	$-0.134891\pi$
$692$		−	11.3962i		−	0.433217i
$693$	0.245526			0.00932675
$694$			17.7070i			0.672150i
$695$	−2.01547			−0.0764512
$696$	−9.75849			−0.369895
$697$			5.02058i			0.190168i
$698$	−10.0981			−0.382217
$699$	10.3324			0.390806
$700$	−3.94062			−0.148941
$701$		−	40.9312i		−	1.54595i	−0.634436	−	0.772976i	$-0.718767\pi$
$701$		−	40.9312i		−	1.54595i	0.634436	−	0.772976i	$-0.281233\pi$
$702$	−36.7773			−1.38807
$703$			19.0769i			0.719500i
$704$	1.00000			0.0376889
$705$	−28.8019			−1.08474
$706$	−31.5684			−1.18809
$707$			2.52410i			0.0949285i
$708$			4.97204i			0.186861i
$709$			8.89920i			0.334217i	0.985939	+	0.167108i	$0.0534429\pi$
$709$			8.89920i			0.334217i	−0.985939	+	0.167108i	$0.946557\pi$
$710$			43.3383i			1.62646i
$711$		−	9.23868i		−	0.346477i
$712$		−	4.36174i		−	0.163463i
$713$	30.7894			1.15307
$714$	1.15580			0.0432547
$715$		−	26.9890i		−	1.00933i
$716$		−	4.06672i		−	0.151981i
$717$	−9.74404			−0.363898
$718$	29.6441			1.10631
$719$			27.9729i			1.04321i	0.853186	+	0.521607i	$0.174667\pi$
$719$			27.9729i			1.04321i	−0.853186	+	0.521607i	$0.825333\pi$
$720$		−	3.09660i		−	0.115404i
$721$			2.54276i			0.0946975i
$722$		−	11.8260i		−	0.440117i
$723$		−	12.7276i		−	0.473345i
$724$		−	6.07048i		−	0.225608i
$725$	−78.3297			−2.90909
$726$	1.49995			0.0556683
$727$	26.9718			1.00033			0.500164	−	0.865931i	$-0.333273\pi$
$727$	26.9718			1.00033			0.500164	+	0.865931i	$0.333273\pi$
$728$			2.13992i			0.0793108i
$729$	−29.9529			−1.10937
$730$			29.6759i			1.09836i
$731$	−5.20325			−0.192449
$732$	−10.4541			−0.386395
$733$	9.88846			0.365239			0.182619	−	0.983184i	$-0.441542\pi$
$733$	9.88846			0.365239			0.182619	+	0.983184i	$0.441542\pi$
$734$			31.6279i			1.16741i
$735$	−42.6785			−1.57422
$736$	−3.59400			−0.132476
$737$		−	13.5065i		−	0.497520i
$738$	−1.59972			−0.0588866
$739$		−	23.5372i		−	0.865831i	−0.901435	−	0.432915i	$-0.857485\pi$
$739$		−	23.5372i		−	0.865831i	0.901435	−	0.432915i	$-0.142515\pi$
$740$		−	29.4008i		−	1.08080i
$741$	−26.2671			−0.964944
$742$	−2.21508	−	0.878068i	−0.0813182	−	0.0322349i
$743$	−14.7080			−0.539584			−0.269792	−	0.962919i	$-0.586955\pi$
$743$	−14.7080			−0.539584			−0.269792	+	0.962919i	$0.586955\pi$
$744$		−	12.8499i		−	0.471099i
$745$		−	76.9243i		−	2.81829i
$746$	31.3261			1.14693
$747$		−	4.17014i		−	0.152578i
$748$	−2.35430			−0.0860819
$749$	2.31276			0.0845064
$750$			43.5883i			1.59162i
$751$	−9.23743			−0.337079			−0.168539	−	0.985695i	$-0.553905\pi$
$751$	−9.23743			−0.337079			−0.168539	+	0.985695i	$0.553905\pi$
$752$	−4.65172			−0.169631
$753$	25.6424			0.934461
$754$			42.5364i			1.54908i
$755$	−83.9869			−3.05660
$756$			1.84107i			0.0669590i
$757$	12.9708			0.471434			0.235717	−	0.971822i	$-0.424256\pi$
$757$	12.9708			0.471434			0.235717	+	0.971822i	$0.424256\pi$
$758$	−6.75558			−0.245374
$759$	−5.39080			−0.195674
$760$		−	11.0564i		−	0.401058i
$761$			46.7301i			1.69396i	0.531622	+	0.846982i	$0.321583\pi$
$761$			46.7301i			1.69396i	−0.531622	+	0.846982i	$0.678417\pi$
$762$		−	26.5781i		−	0.962822i
$763$		−	4.13684i		−	0.149764i
$764$			0.0645017i			0.00233359i
$765$			7.29035i			0.263583i
$766$	2.47507			0.0894279
$767$	21.6727			0.782555
$768$			1.49995i			0.0541247i
$769$		−	4.98067i		−	0.179607i	−0.995959	−	0.0898037i	$-0.971376\pi$
$769$		−	4.98067i		−	0.179607i	0.995959	−	0.0898037i	$-0.0286240\pi$
$770$	−1.35107			−0.0486890
$771$	31.0374			1.11778
$772$			7.53924i			0.271343i
$773$		−	35.8831i		−	1.29063i	−0.763919	−	0.645313i	$-0.776727\pi$
$773$		−	35.8831i		−	1.29063i	0.763919	−	0.645313i	$-0.223273\pi$
$774$		−	1.65793i		−	0.0595930i
$775$		−	103.144i		−	3.70503i
$776$		−	15.3507i		−	0.551057i
$777$			3.49661i			0.125440i
$778$	−15.6222			−0.560083
$779$	−5.71179			−0.204646
$780$	40.4820			1.44949
$781$			10.4988i			0.375676i
$782$	8.46136			0.302578
$783$			36.5959i			1.30783i
$784$	−6.89288			−0.246174
$785$	−26.8922			−0.959823
$786$	5.47218			0.195186
$787$			33.0797i			1.17916i	0.807708	+	0.589582i	$0.200708\pi$
$787$			33.0797i			1.17916i	−0.807708	+	0.589582i	$0.799292\pi$
$788$	−23.4862			−0.836660
$789$	31.7197			1.12925
$790$			50.8381i			1.80874i
$791$	2.05477			0.0730592
$792$		−	0.750159i		−	0.0266557i
$793$			45.5685i			1.61818i
$794$	30.9334			1.09779
$795$	−16.6109	+	41.9039i	−0.589127	+	1.48618i
$796$	−7.74218			−0.274414
$797$			20.6330i			0.730860i	0.930839	+	0.365430i	$0.119078\pi$
$797$			20.6330i			0.730860i	−0.930839	+	0.365430i	$0.880922\pi$
$798$			1.31493i			0.0465479i
$799$	10.9516			0.387438
$800$			12.0398i			0.425672i
$801$	−3.27200			−0.115610
$802$	8.74483			0.308791
$803$			7.18906i			0.253696i
$804$	20.2591			0.714483
$805$	4.85573			0.171142
$806$	−56.0115			−1.97292
$807$		−	1.07648i		−	0.0378940i
$808$	7.71192			0.271304
$809$			4.98970i			0.175428i	0.996146	+	0.0877142i	$0.0279562\pi$
$809$			4.98970i			0.175428i	−0.996146	+	0.0877142i	$0.972044\pi$
$810$	25.5386			0.897336
$811$	−24.9825			−0.877256			−0.438628	−	0.898669i	$-0.644535\pi$
$811$	−24.9825			−0.877256			−0.438628	+	0.898669i	$0.644535\pi$
$812$	2.12937			0.0747262
$813$		−	26.4424i		−	0.927376i
$814$		−	7.12241i		−	0.249640i
$815$		−	90.2670i		−	3.16191i
$816$		−	3.53133i		−	0.123621i
$817$		−	5.91962i		−	0.207101i
$818$		−	7.46974i		−	0.261173i
$819$	1.60528			0.0560931
$820$	8.80286			0.307409
$821$		−	9.72052i		−	0.339249i	−0.985509	−	0.169624i	$-0.945745\pi$
$821$		−	9.72052i		−	0.339249i	0.985509	−	0.169624i	$-0.0542554\pi$
$822$			16.0146i			0.558573i
$823$	54.5879			1.90281			0.951407	−	0.307935i	$-0.0996379\pi$
$823$	54.5879			1.90281			0.951407	+	0.307935i	$0.0996379\pi$
$824$	7.76894			0.270644
$825$			18.0591i			0.628737i
$826$		−	1.08493i		−	0.0377496i
$827$			53.1941i			1.84974i	0.380282	+	0.924871i	$0.375827\pi$
$827$			53.1941i			1.84974i	−0.380282	+	0.924871i	$0.624173\pi$
$828$			2.69607i			0.0936948i
$829$			19.4302i			0.674840i	0.941354	+	0.337420i	$0.109554\pi$
$829$			19.4302i			0.674840i	−0.941354	+	0.337420i	$0.890446\pi$
$830$			22.9472i			0.796510i
$831$	35.5323			1.23260
$832$	6.53814			0.226669
$833$	16.2279			0.562264
$834$		−	0.732352i		−	0.0253593i
$835$	33.0292			1.14302
$836$		−	2.67844i		−	0.0926357i
$837$	−48.1891			−1.66566
$838$	0.228861			0.00790586
$839$	22.0061			0.759735			0.379868	−	0.925041i	$-0.375970\pi$
$839$	22.0061			0.759735			0.379868	+	0.925041i	$0.375970\pi$
$840$		−	2.02653i		−	0.0699218i
$841$	13.3266			0.459538
$842$	−24.3628			−0.839597
$843$		−	42.8992i		−	1.47753i
$844$	−8.17360			−0.281347
$845$		−	122.795i		−	4.22426i
$846$			3.48953i			0.119972i
$847$	−0.327299			−0.0112461
$848$	−2.68277	+	6.76777i	−0.0921268	+	0.232406i
$849$	−4.51615			−0.154994
$850$		−	28.3454i		−	0.972239i
$851$			25.5979i			0.877485i
$852$	−15.7476			−0.539505
$853$		−	22.4325i		−	0.768073i	−0.923318	−	0.384036i	$-0.874534\pi$
$853$		−	22.4325i		−	0.768073i	0.923318	−	0.384036i	$-0.125466\pi$
$854$	2.28115			0.0780595
$855$	−8.29405			−0.283651
$856$		−	7.06621i		−	0.241518i
$857$	4.73573			0.161769			0.0808847	−	0.996723i	$-0.474225\pi$
$857$	4.73573			0.161769			0.0808847	+	0.996723i	$0.474225\pi$
$858$	9.80686			0.334801
$859$	52.6047			1.79485			0.897424	−	0.441169i	$-0.145436\pi$
$859$	52.6047			1.79485			0.897424	+	0.441169i	$0.145436\pi$
$860$			9.12315i			0.311097i
$861$	−1.04691			−0.0356788
$862$		−	32.1564i		−	1.09525i
$863$	−32.9783			−1.12260			−0.561298	−	0.827614i	$-0.689698\pi$
$863$	−32.9783			−1.12260			−0.561298	+	0.827614i	$0.689698\pi$
$864$	5.62504			0.191368
$865$	47.0426			1.59950
$866$			13.6044i			0.462297i
$867$		−	17.1853i		−	0.583643i
$868$			2.80393i			0.0951716i
$869$			12.3156i			0.417779i
$870$		−	40.2824i		−	1.36570i
$871$		−	88.3076i		−	2.99219i
$872$	−12.6393			−0.428022
$873$	−11.5154			−0.389739
$874$			9.62629i			0.325614i
$875$		−	9.51126i		−	0.321539i
$876$	−10.7832			−0.364331
$877$	−17.3228			−0.584948			−0.292474	−	0.956273i	$-0.594479\pi$
$877$	−17.3228			−0.584948			−0.292474	+	0.956273i	$0.594479\pi$
$878$		−	28.1537i		−	0.950140i
$879$		−	5.36366i		−	0.180912i
$880$			4.12793i			0.139153i
$881$			40.2478i			1.35598i	0.735070	+	0.677991i	$0.237149\pi$
$881$			40.2478i			1.35598i	−0.735070	+	0.677991i	$0.762851\pi$
$882$			5.17075i			0.174108i
$883$		−	10.9614i		−	0.368879i	−0.982844	−	0.184440i	$-0.940953\pi$
$883$		−	10.9614i		−	0.368879i	0.982844	−	0.184440i	$-0.0590471\pi$
$884$	−15.3928			−0.517715
$885$	−20.5242			−0.689915
$886$	13.4538			0.451991
$887$			16.6197i			0.558036i	0.960286	+	0.279018i	$0.0900089\pi$
$887$			16.6197i			0.558036i	−0.960286	+	0.279018i	$0.909991\pi$
$888$	10.6832			0.358506
$889$			5.79951i			0.194509i
$890$	18.0050			0.603528
$891$	6.18679			0.207265
$892$	−8.11044			−0.271558
$893$			12.4593i			0.416936i
$894$	27.9516			0.934842
$895$	16.7872			0.561133
$896$		−	0.327299i		−	0.0109343i
$897$	−35.2458			−1.17682
$898$			27.5238i			0.918480i
$899$			55.7352i			1.85887i
$900$	9.03177			0.301059
$901$	6.31606	−	15.9334i	0.210419	−	0.530818i
$902$	2.13251			0.0710048
$903$		−	1.08501i		−	0.0361068i
$904$		−	6.27797i		−	0.208802i
$905$	25.0585			0.832974
$906$		−	30.5179i		−	1.01389i
$907$	14.0523			0.466599			0.233300	−	0.972405i	$-0.425048\pi$
$907$	14.0523			0.466599			0.233300	+	0.972405i	$0.425048\pi$
$908$	6.42422			0.213195
$909$		−	5.78516i		−	0.191882i
$910$	−8.83346			−0.292826
$911$	21.0827			0.698501			0.349250	−	0.937029i	$-0.386436\pi$
$911$	21.0827			0.698501			0.349250	+	0.937029i	$0.386436\pi$
$912$	4.01751			0.133033
$913$			5.55901i			0.183977i
$914$	−0.628748			−0.0207971
$915$		−	43.1538i		−	1.42662i
$916$	−17.1107			−0.565352
$917$	−1.19407			−0.0394315
$918$	−13.2431			−0.437086
$919$		−	14.8147i		−	0.488693i	−0.969688	−	0.244347i	$-0.921427\pi$
$919$		−	14.8147i		−	0.488693i	0.969688	−	0.244347i	$-0.0785735\pi$
$920$		−	14.8358i		−	0.489121i
$921$			28.2710i			0.931562i
$922$			13.5706i			0.446924i
$923$			68.6425i			2.25940i
$924$		−	0.490931i		−	0.0161504i
$925$	85.7525			2.81953
$926$	19.2750			0.633416
$927$		−	5.82794i		−	0.191415i
$928$		−	6.50589i		−	0.213566i
$929$	−45.0565			−1.47826			−0.739128	−	0.673565i	$-0.764762\pi$
$929$	−45.0565			−1.47826			−0.739128	+	0.673565i	$0.764762\pi$
$930$	53.0434			1.73936
$931$			18.4621i			0.605072i
$932$			6.88848i			0.225640i
$933$			13.8383i			0.453045i
$934$			4.54645i			0.148764i
$935$		−	9.71841i		−	0.317826i
$936$		−	4.90464i		−	0.160313i
$937$	−43.5334			−1.42217			−0.711087	−	0.703104i	$-0.751797\pi$
$937$	−43.5334			−1.42217			−0.711087	+	0.703104i	$0.751797\pi$
$938$	−4.42067			−0.144340
$939$	36.4391			1.18915
$940$		−	19.2020i		−	0.626299i
$941$	−10.6298			−0.346521			−0.173261	−	0.984876i	$-0.555430\pi$
$941$	−10.6298			−0.346521			−0.173261	+	0.984876i	$0.555430\pi$
$942$		−	9.77169i		−	0.318379i
$943$	−7.66424			−0.249582
$944$	−3.31481			−0.107888
$945$	−7.59980			−0.247222
$946$			2.21010i			0.0718566i
$947$	−6.42018			−0.208628			−0.104314	−	0.994544i	$-0.533265\pi$
$947$	−6.42018			−0.208628			−0.104314	+	0.994544i	$0.533265\pi$
$948$	−18.4728			−0.599968
$949$			47.0030i			1.52578i
$950$	32.2479			1.04626
$951$			13.5939i			0.440812i
$952$			0.770560i			0.0249740i
$953$	15.0930			0.488910			0.244455	−	0.969661i	$-0.421391\pi$
$953$	15.0930			0.488910			0.244455	+	0.969661i	$0.421391\pi$
$954$	5.07690	+	2.01251i	0.164371	+	0.0651573i
$955$	−0.266259			−0.00861593
$956$		−	6.49626i		−	0.210104i
$957$		−	9.75849i		−	0.315447i
$958$	−22.3517			−0.722151
$959$		−	3.49449i		−	0.112843i
$960$	−6.19168			−0.199836
$961$	−42.3916			−1.36747
$962$		−	46.5673i		−	1.50139i
$963$	−5.30078			−0.170815
$964$	8.48537			0.273295
$965$	−31.1215			−1.00184
$966$			1.76440i			0.0567687i
$967$	3.55566			0.114342			0.0571712	−	0.998364i	$-0.481792\pi$
$967$	3.55566			0.114342			0.0571712	+	0.998364i	$0.481792\pi$
$968$			1.00000i			0.0321412i
$969$	−9.45845			−0.303849
$970$	63.3666			2.03458
$971$	47.8958			1.53705			0.768524	−	0.639821i	$-0.220992\pi$
$971$	47.8958			1.53705			0.768524	+	0.639821i	$0.220992\pi$
$972$		−	7.59527i		−	0.243618i
$973$			0.159804i			0.00512309i
$974$		−	20.1753i		−	0.646459i
$975$			118.073i			3.78136i
$976$		−	6.96964i		−	0.223093i
$977$		−	0.228779i		−	0.00731929i	−0.999993	−	0.00365964i	$-0.998835\pi$
$977$		−	0.228779i		−	0.00731929i	0.999993	−	0.00365964i	$-0.00116490\pi$
$978$	32.7999			1.04882
$979$	4.36174			0.139402
$980$		−	28.4533i		−	0.908908i
$981$			9.48152i			0.302722i
$982$	31.2607			0.997570
$983$	6.22212			0.198455			0.0992274	−	0.995065i	$-0.468363\pi$
$983$	6.22212			0.198455			0.0992274	+	0.995065i	$0.468363\pi$
$984$			3.19865i			0.101969i
$985$		−	96.9493i		−	3.08906i
$986$			15.3168i			0.487788i
$987$			2.28367i			0.0726900i
$988$		−	17.5120i		−	0.557130i
$989$		−	7.94310i		−	0.252576i
$990$	3.09660			0.0984165
$991$	−51.0918			−1.62298			−0.811492	−	0.584363i	$-0.801344\pi$
$991$	−51.0918			−1.62298			−0.811492	+	0.584363i	$0.801344\pi$
$992$	8.56689			0.271999
$993$		−	43.7433i		−	1.38815i
$994$	3.43624			0.108991
$995$		−	31.9592i		−	1.01317i
$996$	−8.33823			−0.264207
$997$	−29.2437			−0.926157			−0.463078	−	0.886317i	$-0.653255\pi$
$997$	−29.2437			−0.926157			−0.463078	+	0.886317i	$0.653255\pi$
$998$	−38.7213			−1.22570
$999$		−	40.0638i		−	1.26756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1166.2.c.b.529.9	✓	22
53.52	even	2	inner	1166.2.c.b.529.14	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1166.2.c.b.529.9	✓	22	1.1	even	1	trivial
1166.2.c.b.529.14	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.49995i q^{3} -1.00000 q^{4} -4.12793i q^{5} +1.49995 q^{6} -0.327299 q^{7} +1.00000i q^{8} +0.750159 q^{9} -4.12793 q^{10} -1.00000 q^{11} -1.49995i q^{12} -6.53814 q^{13} +0.327299i q^{14} +6.19168 q^{15} +1.00000 q^{16} -2.35430 q^{17} -0.750159i q^{18} -2.67844i q^{19} +4.12793i q^{20} -0.490931i q^{21} +1.00000i q^{22} -3.59400i q^{23} -1.49995 q^{24} -12.0398 q^{25} +6.53814i q^{26} +5.62504i q^{27} +0.327299 q^{28} +6.50589 q^{29} -6.19168i q^{30} +8.56689i q^{31} -1.00000i q^{32} -1.49995i q^{33} +2.35430i q^{34} +1.35107i q^{35} -0.750159 q^{36} -7.12241 q^{37} -2.67844 q^{38} -9.80686i q^{39} +4.12793 q^{40} -2.13251i q^{41} -0.490931 q^{42} +2.21010 q^{43} +1.00000 q^{44} -3.09660i q^{45} -3.59400 q^{46} -4.65172 q^{47} +1.49995i q^{48} -6.89288 q^{49} +12.0398i q^{50} -3.53133i q^{51} +6.53814 q^{52} +(-2.68277 + 6.76777i) q^{53} +5.62504 q^{54} +4.12793i q^{55} -0.327299i q^{56} +4.01751 q^{57} -6.50589i q^{58} -3.31481 q^{59} -6.19168 q^{60} -6.96964i q^{61} +8.56689 q^{62} -0.245526 q^{63} -1.00000 q^{64} +26.9890i q^{65} -1.49995 q^{66} +13.5065i q^{67} +2.35430 q^{68} +5.39080 q^{69} +1.35107 q^{70} -10.4988i q^{71} +0.750159i q^{72} -7.18906i q^{73} +7.12241i q^{74} -18.0591i q^{75} +2.67844i q^{76} +0.327299 q^{77} -9.80686 q^{78} -12.3156i q^{79} -4.12793i q^{80} -6.18679 q^{81} -2.13251 q^{82} -5.55901i q^{83} +0.490931i q^{84} +9.71841i q^{85} -2.21010i q^{86} +9.75849i q^{87} -1.00000i q^{88} -4.36174 q^{89} -3.09660 q^{90} +2.13992 q^{91} +3.59400i q^{92} -12.8499 q^{93} +4.65172i q^{94} -11.0564 q^{95} +1.49995 q^{96} -15.3507 q^{97} +6.89288i q^{98} -0.750159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 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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