LMFDB - Embedded newform 1166.2.c.b.529.15

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			529.15
Character	$\chi$	$=$	1166.529
Dual form			1166.2.c.b.529.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -0.796611i q^{3} -1.00000 q^{4} +3.27208i q^{5} +0.796611 q^{6} +4.51075 q^{7} -1.00000i q^{8} +2.36541 q^{9} -3.27208 q^{10} -1.00000 q^{11} +0.796611i q^{12} +5.02256 q^{13} +4.51075i q^{14} +2.60658 q^{15} +1.00000 q^{16} +0.174521 q^{17} +2.36541i q^{18} -3.00609i q^{19} -3.27208i q^{20} -3.59331i q^{21} -1.00000i q^{22} -7.64818i q^{23} -0.796611 q^{24} -5.70652 q^{25} +5.02256i q^{26} -4.27415i q^{27} -4.51075 q^{28} -4.10897 q^{29} +2.60658i q^{30} +4.85096i q^{31} +1.00000i q^{32} +0.796611i q^{33} +0.174521i q^{34} +14.7595i q^{35} -2.36541 q^{36} +6.35354 q^{37} +3.00609 q^{38} -4.00103i q^{39} +3.27208 q^{40} +1.44458i q^{41} +3.59331 q^{42} -8.59687 q^{43} +1.00000 q^{44} +7.73982i q^{45} +7.64818 q^{46} +4.57519 q^{47} -0.796611i q^{48} +13.3468 q^{49} -5.70652i q^{50} -0.139025i q^{51} -5.02256 q^{52} +(6.74996 + 2.72727i) q^{53} +4.27415 q^{54} -3.27208i q^{55} -4.51075i q^{56} -2.39468 q^{57} -4.10897i q^{58} -15.0224 q^{59} -2.60658 q^{60} +1.30931i q^{61} -4.85096 q^{62} +10.6698 q^{63} -1.00000 q^{64} +16.4342i q^{65} -0.796611 q^{66} -9.56581i q^{67} -0.174521 q^{68} -6.09263 q^{69} -14.7595 q^{70} +13.6555i q^{71} -2.36541i q^{72} +11.2956i q^{73} +6.35354i q^{74} +4.54587i q^{75} +3.00609i q^{76} -4.51075 q^{77} +4.00103 q^{78} -2.87745i q^{79} +3.27208i q^{80} +3.69140 q^{81} -1.44458 q^{82} -5.00269i q^{83} +3.59331i q^{84} +0.571046i q^{85} -8.59687i q^{86} +3.27325i q^{87} +1.00000i q^{88} -9.69150 q^{89} -7.73982 q^{90} +22.6555 q^{91} +7.64818i q^{92} +3.86433 q^{93} +4.57519i q^{94} +9.83617 q^{95} +0.796611 q^{96} -12.4981 q^{97} +13.3468i q^{98} -2.36541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	0.796611i		−	0.459924i	−0.973200	−	0.229962i	$-0.926140\pi$
$3$		−	0.796611i		−	0.459924i	0.973200	−	0.229962i	$-0.0738601\pi$
$4$	−1.00000			−0.500000
$5$			3.27208i			1.46332i	0.681670	+	0.731660i	$0.261254\pi$
$5$			3.27208i			1.46332i	−0.681670	+	0.731660i	$0.738746\pi$
$6$	0.796611			0.325215
$7$	4.51075			1.70490			0.852451	−	0.522807i	$-0.175115\pi$
$7$	4.51075			1.70490			0.852451	+	0.522807i	$0.175115\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.36541			0.788470
$10$	−3.27208			−1.03472
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			0.796611i			0.229962i
$13$	5.02256			1.39301			0.696504	−	0.717553i	$-0.254738\pi$
$13$	5.02256			1.39301			0.696504	+	0.717553i	$0.254738\pi$
$14$			4.51075i			1.20555i
$15$	2.60658			0.673015
$16$	1.00000			0.250000
$17$	0.174521			0.0423275			0.0211637	−	0.999776i	$-0.493263\pi$
$17$	0.174521			0.0423275			0.0211637	+	0.999776i	$0.493263\pi$
$18$			2.36541i			0.557533i
$19$		−	3.00609i		−	0.689644i	−0.938668	−	0.344822i	$-0.887939\pi$
$19$		−	3.00609i		−	0.689644i	0.938668	−	0.344822i	$-0.112061\pi$
$20$		−	3.27208i		−	0.731660i
$21$		−	3.59331i		−	0.784124i
$22$		−	1.00000i		−	0.213201i
$23$		−	7.64818i		−	1.59476i	−0.603480	−	0.797378i	$-0.706220\pi$
$23$		−	7.64818i		−	1.59476i	0.603480	−	0.797378i	$-0.293780\pi$
$24$	−0.796611			−0.162608
$25$	−5.70652			−1.14130
$26$			5.02256i			0.985005i
$27$		−	4.27415i		−	0.822560i
$28$	−4.51075			−0.852451
$29$	−4.10897			−0.763017			−0.381508	−	0.924365i	$-0.624595\pi$
$29$	−4.10897			−0.763017			−0.381508	+	0.924365i	$0.624595\pi$
$30$			2.60658i			0.475894i
$31$			4.85096i			0.871259i	0.900126	+	0.435629i	$0.143474\pi$
$31$			4.85096i			0.871259i	−0.900126	+	0.435629i	$0.856526\pi$
$32$			1.00000i			0.176777i
$33$			0.796611i			0.138672i
$34$			0.174521i			0.0299300i
$35$			14.7595i			2.49482i
$36$	−2.36541			−0.394235
$37$	6.35354			1.04452			0.522258	−	0.852788i	$-0.325090\pi$
$37$	6.35354			1.04452			0.522258	+	0.852788i	$0.325090\pi$
$38$	3.00609			0.487652
$39$		−	4.00103i		−	0.640677i
$40$	3.27208			0.517362
$41$			1.44458i			0.225606i	0.993617	+	0.112803i	$0.0359829\pi$
$41$			1.44458i			0.225606i	−0.993617	+	0.112803i	$0.964017\pi$
$42$	3.59331			0.554460
$43$	−8.59687			−1.31101			−0.655505	−	0.755191i	$-0.727544\pi$
$43$	−8.59687			−1.31101			−0.655505	+	0.755191i	$0.727544\pi$
$44$	1.00000			0.150756
$45$			7.73982i			1.15378i
$46$	7.64818			1.12766
$47$	4.57519			0.667361			0.333680	−	0.942686i	$-0.391709\pi$
$47$	4.57519			0.667361			0.333680	+	0.942686i	$0.391709\pi$
$48$		−	0.796611i		−	0.114981i
$49$	13.3468			1.90669
$50$		−	5.70652i		−	0.807024i
$51$		−	0.139025i		−	0.0194674i
$52$	−5.02256			−0.696504
$53$	6.74996	+	2.72727i	0.927179	+	0.374619i
$53$	6.74996	+	2.72727i	0.927179	+	0.374619i
$54$	4.27415			0.581638
$55$		−	3.27208i		−	0.441207i
$56$		−	4.51075i		−	0.602774i
$57$	−2.39468			−0.317184
$58$		−	4.10897i		−	0.539534i
$59$	−15.0224			−1.95575			−0.977877	−	0.209180i	$-0.932921\pi$
$59$	−15.0224			−1.95575			−0.977877	+	0.209180i	$0.932921\pi$
$60$	−2.60658			−0.336508
$61$			1.30931i			0.167639i	0.996481	+	0.0838197i	$0.0267120\pi$
$61$			1.30931i			0.167639i	−0.996481	+	0.0838197i	$0.973288\pi$
$62$	−4.85096			−0.616073
$63$	10.6698			1.34426
$64$	−1.00000			−0.125000
$65$			16.4342i			2.03842i
$66$	−0.796611			−0.0980560
$67$		−	9.56581i		−	1.16865i	−0.811520	−	0.584325i	$-0.801359\pi$
$67$		−	9.56581i		−	1.16865i	0.811520	−	0.584325i	$-0.198641\pi$
$68$	−0.174521			−0.0211637
$69$	−6.09263			−0.733466
$70$	−14.7595			−1.76410
$71$			13.6555i			1.62061i	0.586008	+	0.810306i	$0.300699\pi$
$71$			13.6555i			1.62061i	−0.586008	+	0.810306i	$0.699301\pi$
$72$		−	2.36541i		−	0.278766i
$73$			11.2956i			1.32205i	0.750363	+	0.661026i	$0.229879\pi$
$73$			11.2956i			1.32205i	−0.750363	+	0.661026i	$0.770121\pi$
$74$			6.35354i			0.738584i
$75$			4.54587i			0.524912i
$76$			3.00609i			0.344822i
$77$	−4.51075			−0.514047
$78$	4.00103			0.453027
$79$		−	2.87745i		−	0.323739i	−0.986812	−	0.161869i	$-0.948248\pi$
$79$		−	2.87745i		−	0.323739i	0.986812	−	0.161869i	$-0.0517523\pi$
$80$			3.27208i			0.365830i
$81$	3.69140			0.410156
$82$	−1.44458			−0.159527
$83$		−	5.00269i		−	0.549116i	−0.961570	−	0.274558i	$-0.911468\pi$
$83$		−	5.00269i		−	0.549116i	0.961570	−	0.274558i	$-0.0885316\pi$
$84$			3.59331i			0.392062i
$85$			0.571046i			0.0619386i
$86$		−	8.59687i		−	0.927024i
$87$			3.27325i			0.350929i
$88$			1.00000i			0.106600i
$89$	−9.69150			−1.02730			−0.513649	−	0.858001i	$-0.671707\pi$
$89$	−9.69150			−1.02730			−0.513649	+	0.858001i	$0.671707\pi$
$90$	−7.73982			−0.815848
$91$	22.6555			2.37494
$92$			7.64818i			0.797378i
$93$	3.86433			0.400712
$94$			4.57519i			0.471895i
$95$	9.83617			1.00917
$96$	0.796611			0.0813038
$97$	−12.4981			−1.26899			−0.634495	−	0.772927i	$-0.718792\pi$
$97$	−12.4981			−1.26899			−0.634495	+	0.772927i	$0.718792\pi$
$98$			13.3468i			1.34823i
$99$	−2.36541			−0.237733
$100$	5.70652			0.570652
$101$			4.00312i			0.398326i	0.979966	+	0.199163i	$0.0638223\pi$
$101$			4.00312i			0.398326i	−0.979966	+	0.199163i	$0.936178\pi$
$102$	0.139025			0.0137655
$103$		−	3.79197i		−	0.373633i	−0.982395	−	0.186817i	$-0.940183\pi$
$103$		−	3.79197i		−	0.373633i	0.982395	−	0.186817i	$-0.0598171\pi$
$104$		−	5.02256i		−	0.492503i
$105$	11.7576			1.14742
$106$	−2.72727	+	6.74996i	−0.264896	+	0.655614i
$107$	−7.10878			−0.687232			−0.343616	−	0.939110i	$-0.611652\pi$
$107$	−7.10878			−0.687232			−0.343616	+	0.939110i	$0.611652\pi$
$108$			4.27415i			0.411280i
$109$			3.31959i			0.317959i	0.987282	+	0.158979i	$0.0508203\pi$
$109$			3.31959i			0.317959i	−0.987282	+	0.158979i	$0.949180\pi$
$110$	3.27208			0.311981
$111$		−	5.06130i		−	0.480397i
$112$	4.51075			0.426225
$113$	8.12574			0.764406			0.382203	−	0.924078i	$-0.375166\pi$
$113$	8.12574			0.764406			0.382203	+	0.924078i	$0.375166\pi$
$114$		−	2.39468i		−	0.224283i
$115$	25.0255			2.33364
$116$	4.10897			0.381508
$117$	11.8804			1.09835
$118$		−	15.0224i		−	1.38293i
$119$	0.787218			0.0721642
$120$		−	2.60658i		−	0.237947i
$121$	1.00000			0.0909091
$122$	−1.30931			−0.118539
$123$	1.15077			0.103761
$124$		−	4.85096i		−	0.435629i
$125$		−	2.31178i		−	0.206772i
$126$			10.6698i			0.950538i
$127$		−	20.2531i		−	1.79717i	−0.438798	−	0.898586i	$-0.644596\pi$
$127$		−	20.2531i		−	1.79717i	0.438798	−	0.898586i	$-0.355404\pi$
$128$		−	1.00000i		−	0.0883883i
$129$			6.84836i			0.602964i
$130$	−16.4342			−1.44138
$131$	−16.7787			−1.46596			−0.732981	−	0.680249i	$-0.761872\pi$
$131$	−16.7787			−1.46596			−0.732981	+	0.680249i	$0.761872\pi$
$132$		−	0.796611i		−	0.0693361i
$133$		−	13.5597i		−	1.17578i
$134$	9.56581			0.826360
$135$	13.9854			1.20367
$136$		−	0.174521i		−	0.0149650i
$137$			11.9209i			1.01847i	0.860627	+	0.509236i	$0.170072\pi$
$137$			11.9209i			1.01847i	−0.860627	+	0.509236i	$0.829928\pi$
$138$		−	6.09263i		−	0.518639i
$139$			9.80914i			0.832000i	0.909365	+	0.416000i	$0.136568\pi$
$139$			9.80914i			0.832000i	−0.909365	+	0.416000i	$0.863432\pi$
$140$		−	14.7595i		−	1.24741i
$141$		−	3.64465i		−	0.306935i
$142$	−13.6555			−1.14595
$143$	−5.02256			−0.420008
$144$	2.36541			0.197118
$145$		−	13.4449i		−	1.11654i
$146$	−11.2956			−0.934832
$147$		−	10.6322i		−	0.876932i
$148$	−6.35354			−0.522258
$149$	−15.4675			−1.26714			−0.633572	−	0.773684i	$-0.718412\pi$
$149$	−15.4675			−1.26714			−0.633572	+	0.773684i	$0.718412\pi$
$150$	−4.54587			−0.371169
$151$			17.9704i			1.46241i	0.682160	+	0.731203i	$0.261041\pi$
$151$			17.9704i			1.46241i	−0.682160	+	0.731203i	$0.738959\pi$
$152$	−3.00609			−0.243826
$153$	0.412813			0.0333739
$154$		−	4.51075i		−	0.363486i
$155$	−15.8727			−1.27493
$156$			4.00103i			0.320339i
$157$			3.70167i			0.295426i	0.989030	+	0.147713i	$0.0471911\pi$
$157$			3.70167i			0.295426i	−0.989030	+	0.147713i	$0.952809\pi$
$158$	2.87745			0.228918
$159$	2.17257	−	5.37709i	0.172296	−	0.426431i
$160$	−3.27208			−0.258681
$161$		−	34.4990i		−	2.71890i
$162$			3.69140i			0.290024i
$163$	−9.70825			−0.760409			−0.380204	−	0.924902i	$-0.624146\pi$
$163$	−9.70825			−0.760409			−0.380204	+	0.924902i	$0.624146\pi$
$164$		−	1.44458i		−	0.112803i
$165$	−2.60658			−0.202922
$166$	5.00269			0.388284
$167$			1.95611i			0.151368i	0.997132	+	0.0756841i	$0.0241140\pi$
$167$			1.95611i			0.151368i	−0.997132	+	0.0756841i	$0.975886\pi$
$168$	−3.59331			−0.277230
$169$	12.2261			0.940471
$170$	−0.571046			−0.0437972
$171$		−	7.11064i		−	0.543764i
$172$	8.59687			0.655505
$173$		−	14.2962i		−	1.08692i	−0.839434	−	0.543461i	$-0.817114\pi$
$173$		−	14.2962i		−	1.08692i	0.839434	−	0.543461i	$-0.182886\pi$
$174$	−3.27325			−0.248145
$175$	−25.7407			−1.94581
$176$	−1.00000			−0.0753778
$177$			11.9670i			0.899498i
$178$		−	9.69150i		−	0.726409i
$179$			3.88510i			0.290386i	0.989403	+	0.145193i	$0.0463803\pi$
$179$			3.88510i			0.290386i	−0.989403	+	0.145193i	$0.953620\pi$
$180$		−	7.73982i		−	0.576892i
$181$		−	2.10077i		−	0.156149i	−0.996948	−	0.0780746i	$-0.975123\pi$
$181$		−	2.10077i		−	0.156149i	0.996948	−	0.0780746i	$-0.0248772\pi$
$182$			22.6555i			1.67934i
$183$	1.04301			0.0771013
$184$	−7.64818			−0.563831
$185$			20.7893i			1.52846i
$186$			3.86433i			0.283346i
$187$	−0.174521			−0.0127622
$188$	−4.57519			−0.333680
$189$		−	19.2796i		−	1.40238i
$190$			9.83617i			0.713591i
$191$		−	18.8194i		−	1.36172i	−0.732413	−	0.680860i	$-0.761606\pi$
$191$		−	18.8194i		−	1.36172i	0.732413	−	0.680860i	$-0.238394\pi$
$192$			0.796611i			0.0574904i
$193$		−	19.3942i		−	1.39602i	−0.716087	−	0.698011i	$-0.754068\pi$
$193$		−	19.3942i		−	1.39602i	0.716087	−	0.698011i	$-0.245932\pi$
$194$		−	12.4981i		−	0.897311i
$195$	13.0917			0.937515
$196$	−13.3468			−0.953345
$197$	−6.05246			−0.431220			−0.215610	−	0.976480i	$-0.569174\pi$
$197$	−6.05246			−0.431220			−0.215610	+	0.976480i	$0.569174\pi$
$198$		−	2.36541i		−	0.168102i
$199$	−14.5332			−1.03023			−0.515115	−	0.857121i	$-0.672251\pi$
$199$	−14.5332			−1.03023			−0.515115	+	0.857121i	$0.672251\pi$
$200$			5.70652i			0.403512i
$201$	−7.62023			−0.537489
$202$	−4.00312			−0.281659
$203$	−18.5345			−1.30087
$204$			0.139025i			0.00973370i
$205$	−4.72679			−0.330133
$206$	3.79197			0.264199
$207$		−	18.0911i		−	1.25742i
$208$	5.02256			0.348252
$209$			3.00609i			0.207936i
$210$			11.7576i			0.811352i
$211$	11.8758			0.817561			0.408780	−	0.912633i	$-0.365954\pi$
$211$	11.8758			0.817561			0.408780	+	0.912633i	$0.365954\pi$
$212$	−6.74996	−	2.72727i	−0.463589	−	0.187310i
$213$	10.8781			0.745357
$214$		−	7.10878i		−	0.485946i
$215$		−	28.1296i		−	1.91843i
$216$	−4.27415			−0.290819
$217$			21.8815i			1.48541i
$218$	−3.31959			−0.224831
$219$	8.99822			0.608043
$220$			3.27208i			0.220604i
$221$	0.876540			0.0589625
$222$	5.06130			0.339692
$223$	8.02612			0.537469			0.268735	−	0.963214i	$-0.413395\pi$
$223$	8.02612			0.537469			0.268735	+	0.963214i	$0.413395\pi$
$224$			4.51075i			0.301387i
$225$	−13.4983			−0.899884
$226$			8.12574i			0.540516i
$227$	−14.8744			−0.987250			−0.493625	−	0.869675i	$-0.664328\pi$
$227$	−14.8744			−0.987250			−0.493625	+	0.869675i	$0.664328\pi$
$228$	2.39468			0.158592
$229$	−1.66073			−0.109744			−0.0548721	−	0.998493i	$-0.517475\pi$
$229$	−1.66073			−0.109744			−0.0548721	+	0.998493i	$0.517475\pi$
$230$			25.0255i			1.65013i
$231$			3.59331i			0.236422i
$232$			4.10897i			0.269767i
$233$		−	5.88768i		−	0.385714i	−0.981227	−	0.192857i	$-0.938225\pi$
$233$		−	5.88768i		−	0.385714i	0.981227	−	0.192857i	$-0.0617754\pi$
$234$			11.8804i			0.776648i
$235$			14.9704i			0.976562i
$236$	15.0224			0.977877
$237$	−2.29221			−0.148895
$238$			0.787218i			0.0510278i
$239$			2.00963i			0.129992i	0.997886	+	0.0649961i	$0.0207035\pi$
$239$			2.00963i			0.129992i	−0.997886	+	0.0649961i	$0.979297\pi$
$240$	2.60658			0.168254
$241$	14.3687			0.925572			0.462786	−	0.886470i	$-0.346850\pi$
$241$	14.3687			0.925572			0.462786	+	0.886470i	$0.346850\pi$
$242$			1.00000i			0.0642824i
$243$		−	15.7630i		−	1.01120i
$244$		−	1.30931i		−	0.0838197i
$245$			43.6719i			2.79010i
$246$			1.15077i			0.0733704i
$247$		−	15.0983i		−	0.960680i
$248$	4.85096			0.308036
$249$	−3.98520			−0.252552
$250$	2.31178			0.146210
$251$		−	6.57278i		−	0.414870i	−0.978249	−	0.207435i	$-0.933488\pi$
$251$		−	6.57278i		−	0.414870i	0.978249	−	0.207435i	$-0.0665116\pi$
$252$	−10.6698			−0.672132
$253$			7.64818i			0.480837i
$254$	20.2531			1.27079
$255$	0.454901			0.0284870
$256$	1.00000			0.0625000
$257$			0.238304i			0.0148650i	0.999972	+	0.00743251i	$0.00236586\pi$
$257$			0.238304i			0.0148650i	−0.999972	+	0.00743251i	$0.997634\pi$
$258$	−6.84836			−0.426360
$259$	28.6592			1.78080
$260$		−	16.4342i		−	1.01921i
$261$	−9.71940			−0.601616
$262$		−	16.7787i		−	1.03659i
$263$			6.61625i			0.407976i	0.978973	+	0.203988i	$0.0653903\pi$
$263$			6.61625i			0.407976i	−0.978973	+	0.203988i	$0.934610\pi$
$264$	0.796611			0.0490280
$265$	−8.92385	+	22.0864i	−0.548188	+	1.35676i
$266$	13.5597			0.831399
$267$			7.72036i			0.472478i
$268$			9.56581i			0.584325i
$269$	−31.4776			−1.91922			−0.959612	−	0.281326i	$-0.909226\pi$
$269$	−31.4776			−1.91922			−0.959612	+	0.281326i	$0.909226\pi$
$270$			13.9854i			0.851121i
$271$	24.4876			1.48752			0.743758	−	0.668449i	$-0.233042\pi$
$271$	24.4876			1.48752			0.743758	+	0.668449i	$0.233042\pi$
$272$	0.174521			0.0105819
$273$		−	18.0476i		−	1.09229i
$274$	−11.9209			−0.720169
$275$	5.70652			0.344116
$276$	6.09263			0.366733
$277$		−	20.3192i		−	1.22086i	−0.792069	−	0.610431i	$-0.790996\pi$
$277$		−	20.3192i		−	1.22086i	0.792069	−	0.610431i	$-0.209004\pi$
$278$	−9.80914			−0.588313
$279$			11.4745i			0.686962i
$280$	14.7595			0.882051
$281$	14.2468			0.849893			0.424947	−	0.905218i	$-0.360293\pi$
$281$	14.2468			0.849893			0.424947	+	0.905218i	$0.360293\pi$
$282$	3.64465			0.217036
$283$			25.3971i			1.50970i	0.655896	+	0.754851i	$0.272291\pi$
$283$			25.3971i			1.50970i	−0.655896	+	0.754851i	$0.727709\pi$
$284$		−	13.6555i		−	0.810306i
$285$		−	7.83560i		−	0.464141i
$286$		−	5.02256i		−	0.296990i
$287$			6.51614i			0.384636i
$288$			2.36541i			0.139383i
$289$	−16.9695			−0.998208
$290$	13.4449			0.789511
$291$			9.95612i			0.583638i
$292$		−	11.2956i		−	0.661026i
$293$	4.58909			0.268098			0.134049	−	0.990975i	$-0.457202\pi$
$293$	4.58909			0.268098			0.134049	+	0.990975i	$0.457202\pi$
$294$	10.6322			0.620084
$295$		−	49.1546i		−	2.86189i
$296$		−	6.35354i		−	0.369292i
$297$			4.27415i			0.248011i
$298$		−	15.4675i		−	0.896006i
$299$		−	38.4135i		−	2.22151i
$300$		−	4.54587i		−	0.262456i
$301$	−38.7783			−2.23514
$302$	−17.9704			−1.03408
$303$	3.18893			0.183199
$304$		−	3.00609i		−	0.172411i
$305$	−4.28415			−0.245310
$306$			0.412813i			0.0235989i
$307$	−7.68204			−0.438437			−0.219219	−	0.975676i	$-0.570351\pi$
$307$	−7.68204			−0.438437			−0.219219	+	0.975676i	$0.570351\pi$
$308$	4.51075			0.257024
$309$	−3.02072			−0.171843
$310$		−	15.8727i		−	0.901511i
$311$	12.9605			0.734922			0.367461	−	0.930039i	$-0.380227\pi$
$311$	12.9605			0.734922			0.367461	+	0.930039i	$0.380227\pi$
$312$	−4.00103			−0.226514
$313$			4.14770i			0.234442i	0.993106	+	0.117221i	$0.0373986\pi$
$313$			4.14770i			0.234442i	−0.993106	+	0.117221i	$0.962601\pi$
$314$	−3.70167			−0.208898
$315$			34.9124i			1.96709i
$316$			2.87745i			0.161869i
$317$	2.17359			0.122081			0.0610405	−	0.998135i	$-0.480558\pi$
$317$	2.17359			0.122081			0.0610405	+	0.998135i	$0.480558\pi$
$318$	5.37709	+	2.17257i	0.301533	+	0.121832i
$319$	4.10897			0.230058
$320$		−	3.27208i		−	0.182915i
$321$			5.66293i			0.316074i
$322$	34.4990			1.92255
$323$		−	0.524625i		−	0.0291909i
$324$	−3.69140			−0.205078
$325$	−28.6613			−1.58985
$326$		−	9.70825i		−	0.537690i
$327$	2.64442			0.146237
$328$	1.44458			0.0797637
$329$	20.6375			1.13778
$330$		−	2.60658i		−	0.143487i
$331$	−12.1821			−0.669588			−0.334794	−	0.942291i	$-0.608667\pi$
$331$	−12.1821			−0.669588			−0.334794	+	0.942291i	$0.608667\pi$
$332$			5.00269i			0.274558i
$333$	15.0287			0.823570
$334$	−1.95611			−0.107033
$335$	31.3001			1.71011
$336$		−	3.59331i		−	0.196031i
$337$		−	27.1911i		−	1.48120i	−0.671949	−	0.740598i	$-0.734543\pi$
$337$		−	27.1911i		−	1.48120i	0.671949	−	0.740598i	$-0.265457\pi$
$338$			12.2261i			0.665014i
$339$		−	6.47306i		−	0.351568i
$340$		−	0.571046i		−	0.0309693i
$341$		−	4.85096i		−	0.262694i
$342$	7.11064			0.384499
$343$	28.6289			1.54582
$344$			8.59687i			0.463512i
$345$		−	19.9356i		−	1.07329i
$346$	14.2962			0.768570
$347$	36.4903			1.95890			0.979452	−	0.201678i	$-0.0646393\pi$
$347$	36.4903			1.95890			0.979452	+	0.201678i	$0.0646393\pi$
$348$		−	3.27325i		−	0.175465i
$349$		−	32.7622i		−	1.75372i	−0.480746	−	0.876860i	$-0.659634\pi$
$349$		−	32.7622i		−	1.75372i	0.480746	−	0.876860i	$-0.340366\pi$
$350$		−	25.7407i		−	1.37590i
$351$		−	21.4672i		−	1.14583i
$352$		−	1.00000i		−	0.0533002i
$353$		−	6.62203i		−	0.352455i	−0.984349	−	0.176228i	$-0.943611\pi$
$353$		−	6.62203i		−	0.352455i	0.984349	−	0.176228i	$-0.0563895\pi$
$354$	−11.9670			−0.636041
$355$	−44.6819			−2.37147
$356$	9.69150			0.513649
$357$		−	0.627107i		−	0.0331900i
$358$	−3.88510			−0.205334
$359$		−	26.5473i		−	1.40111i	−0.713597	−	0.700557i	$-0.752935\pi$
$359$		−	26.5473i		−	1.40111i	0.713597	−	0.700557i	$-0.247065\pi$
$360$	7.73982			0.407924
$361$	9.96342			0.524391
$362$	2.10077			0.110414
$363$		−	0.796611i		−	0.0418112i
$364$	−22.6555			−1.18747
$365$	−36.9602			−1.93459
$366$			1.04301i			0.0545188i
$367$	34.0860			1.77928			0.889638	−	0.456666i	$-0.150956\pi$
$367$	34.0860			1.77928			0.889638	+	0.456666i	$0.150956\pi$
$368$		−	7.64818i		−	0.398689i
$369$			3.41703i			0.177883i
$370$	−20.7893			−1.08078
$371$	30.4474	+	12.3020i	1.58075	+	0.638689i
$372$	−3.86433			−0.200356
$373$		−	29.3821i		−	1.52135i	−0.649134	−	0.760674i	$-0.724869\pi$
$373$		−	29.3821i		−	1.52135i	0.649134	−	0.760674i	$-0.275131\pi$
$374$		−	0.174521i		−	0.00902424i
$375$	−1.84159			−0.0950994
$376$		−	4.57519i		−	0.235948i
$377$	−20.6376			−1.06289
$378$	19.2796			0.991635
$379$		−	1.30743i		−	0.0671584i	−0.999436	−	0.0335792i	$-0.989309\pi$
$379$		−	1.30743i		−	0.0671584i	0.999436	−	0.0335792i	$-0.0106906\pi$
$380$	−9.83617			−0.504585
$381$	−16.1338			−0.826562
$382$	18.8194			0.962882
$383$			32.1921i			1.64494i	0.568810	+	0.822469i	$0.307404\pi$
$383$			32.1921i			1.64494i	−0.568810	+	0.822469i	$0.692596\pi$
$384$	−0.796611			−0.0406519
$385$		−	14.7595i		−	0.752215i
$386$	19.3942			0.987137
$387$	−20.3351			−1.03369
$388$	12.4981			0.634495
$389$			6.05959i			0.307234i	0.988131	+	0.153617i	$0.0490921\pi$
$389$			6.05959i			0.307234i	−0.988131	+	0.153617i	$0.950908\pi$
$390$			13.0917i			0.662923i
$391$		−	1.33477i		−	0.0675020i
$392$		−	13.3468i		−	0.674117i
$393$			13.3661i			0.674231i
$394$		−	6.05246i		−	0.304919i
$395$	9.41525			0.473733
$396$	2.36541			0.118866
$397$			30.3069i			1.52106i	0.649302	+	0.760531i	$0.275061\pi$
$397$			30.3069i			1.52106i	−0.649302	+	0.760531i	$0.724939\pi$
$398$		−	14.5332i		−	0.728483i
$399$	−10.8018			−0.540767
$400$	−5.70652			−0.285326
$401$			33.9699i			1.69638i	0.529695	+	0.848188i	$0.322306\pi$
$401$			33.9699i			1.69638i	−0.529695	+	0.848188i	$0.677694\pi$
$402$		−	7.62023i		−	0.380062i
$403$			24.3643i			1.21367i
$404$		−	4.00312i		−	0.199163i
$405$			12.0786i			0.600189i
$406$		−	18.5345i		−	0.919853i
$407$	−6.35354			−0.314933
$408$	−0.139025			−0.00688276
$409$	5.65474			0.279609			0.139805	−	0.990179i	$-0.455353\pi$
$409$	5.65474			0.279609			0.139805	+	0.990179i	$0.455353\pi$
$410$		−	4.72679i		−	0.233440i
$411$	9.49633			0.468420
$412$			3.79197i			0.186817i
$413$	−67.7624			−3.33437
$414$	18.0911			0.889129
$415$	16.3692			0.803533
$416$			5.02256i			0.246251i
$417$	7.81407			0.382657
$418$	−3.00609			−0.147033
$419$			29.3873i			1.43567i	0.696216	+	0.717833i	$0.254866\pi$
$419$			29.3873i			1.43567i	−0.696216	+	0.717833i	$0.745134\pi$
$420$	−11.7576			−0.573712
$421$			21.3104i			1.03861i	0.854590	+	0.519304i	$0.173809\pi$
$421$			21.3104i			1.03861i	−0.854590	+	0.519304i	$0.826191\pi$
$422$			11.8758i			0.578103i
$423$	10.8222			0.526194
$424$	2.72727	−	6.74996i	0.132448	−	0.327807i
$425$	−0.995905			−0.0483085
$426$			10.8781i			0.527047i
$427$			5.90594i			0.285809i
$428$	7.10878			0.343616
$429$			4.00103i			0.193171i
$430$	28.1296			1.35653
$431$	24.1342			1.16250			0.581251	−	0.813724i	$-0.302563\pi$
$431$	24.1342			1.16250			0.581251	+	0.813724i	$0.302563\pi$
$432$		−	4.27415i		−	0.205640i
$433$	−5.60335			−0.269280			−0.134640	−	0.990895i	$-0.542988\pi$
$433$	−5.60335			−0.269280			−0.134640	+	0.990895i	$0.542988\pi$
$434$	−21.8815			−1.05034
$435$	−10.7103			−0.513522
$436$		−	3.31959i		−	0.158979i
$437$	−22.9911			−1.09981
$438$			8.99822i			0.429951i
$439$	−1.65837			−0.0791498			−0.0395749	−	0.999217i	$-0.512600\pi$
$439$	−1.65837			−0.0791498			−0.0395749	+	0.999217i	$0.512600\pi$
$440$	−3.27208			−0.155990
$441$	31.5707			1.50337
$442$			0.876540i			0.0416928i
$443$		−	29.6521i		−	1.40882i	−0.709795	−	0.704408i	$-0.751213\pi$
$443$		−	29.6521i		−	1.40882i	0.709795	−	0.704408i	$-0.248787\pi$
$444$			5.06130i			0.240199i
$445$		−	31.7114i		−	1.50326i
$446$			8.02612i			0.380048i
$447$			12.3215i			0.582789i
$448$	−4.51075			−0.213113
$449$	−28.4016			−1.34035			−0.670177	−	0.742201i	$-0.733782\pi$
$449$	−28.4016			−1.34035			−0.670177	+	0.742201i	$0.733782\pi$
$450$		−	13.4983i		−	0.636314i
$451$		−	1.44458i		−	0.0680227i
$452$	−8.12574			−0.382203
$453$	14.3154			0.672595
$454$		−	14.8744i		−	0.698091i
$455$			74.1306i			3.47530i
$456$			2.39468i			0.112141i
$457$			4.62908i			0.216539i	0.994122	+	0.108270i	$0.0345310\pi$
$457$			4.62908i			0.216539i	−0.994122	+	0.108270i	$0.965469\pi$
$458$		−	1.66073i		−	0.0776009i
$459$		−	0.745926i		−	0.0348169i
$460$	−25.0255			−1.16682
$461$	4.27370			0.199046			0.0995231	−	0.995035i	$-0.468268\pi$
$461$	4.27370			0.199046			0.0995231	+	0.995035i	$0.468268\pi$
$462$	−3.59331			−0.167176
$463$			19.9497i			0.927140i	0.886060	+	0.463570i	$0.153432\pi$
$463$			19.9497i			0.927140i	−0.886060	+	0.463570i	$0.846568\pi$
$464$	−4.10897			−0.190754
$465$			12.6444i			0.586370i
$466$	5.88768			0.272741
$467$	37.7361			1.74622			0.873110	−	0.487524i	$-0.162100\pi$
$467$	37.7361			1.74622			0.873110	+	0.487524i	$0.162100\pi$
$468$	−11.8804			−0.549173
$469$		−	43.1489i		−	1.99243i
$470$	−14.9704			−0.690534
$471$	2.94879			0.135873
$472$			15.0224i			0.691464i
$473$	8.59687			0.395284
$474$		−	2.29221i		−	0.105285i
$475$			17.1543i			0.787094i
$476$	−0.787218			−0.0360821
$477$	15.9664	+	6.45111i	0.731053	+	0.295376i
$478$	−2.00963			−0.0919184
$479$		−	7.61371i		−	0.347879i	−0.984756	−	0.173940i	$-0.944350\pi$
$479$		−	7.61371i		−	0.347879i	0.984756	−	0.173940i	$-0.0556498\pi$
$480$			2.60658i			0.118973i
$481$	31.9111			1.45502
$482$			14.3687i			0.654478i
$483$	−27.4823			−1.25049
$484$	−1.00000			−0.0454545
$485$		−	40.8948i		−	1.85694i
$486$	15.7630			0.715026
$487$	−22.0930			−1.00113			−0.500565	−	0.865699i	$-0.666874\pi$
$487$	−22.0930			−1.00113			−0.500565	+	0.865699i	$0.666874\pi$
$488$	1.30931			0.0592695
$489$			7.73370i			0.349730i
$490$	−43.6719			−1.97290
$491$		−	14.1397i		−	0.638116i	−0.947735	−	0.319058i	$-0.896634\pi$
$491$		−	14.1397i		−	0.638116i	0.947735	−	0.319058i	$-0.103366\pi$
$492$	−1.15077			−0.0518807
$493$	−0.717100			−0.0322966
$494$	15.0983			0.679303
$495$		−	7.73982i		−	0.347879i
$496$			4.85096i			0.217815i
$497$			61.5965i			2.76298i
$498$		−	3.98520i		−	0.178581i
$499$		−	6.96383i		−	0.311744i	−0.987777	−	0.155872i	$-0.950181\pi$
$499$		−	6.96383i		−	0.311744i	0.987777	−	0.155872i	$-0.0498187\pi$
$500$			2.31178i			0.103386i
$501$	1.55826			0.0696178
$502$	6.57278			0.293357
$503$			5.84542i			0.260634i	0.991472	+	0.130317i	$0.0415996\pi$
$503$			5.84542i			0.260634i	−0.991472	+	0.130317i	$0.958400\pi$
$504$		−	10.6698i		−	0.475269i
$505$	−13.0985			−0.582878
$506$	−7.64818			−0.340003
$507$		−	9.73947i		−	0.432545i
$508$			20.2531i			0.898586i
$509$			11.2865i			0.500264i	0.968212	+	0.250132i	$0.0804740\pi$
$509$			11.2865i			0.500264i	−0.968212	+	0.250132i	$0.919526\pi$
$510$			0.454901i			0.0201434i
$511$			50.9517i			2.25397i
$512$			1.00000i			0.0441942i
$513$	−12.8485			−0.567274
$514$	−0.238304			−0.0105112
$515$	12.4076			0.546745
$516$		−	6.84836i		−	0.301482i
$517$	−4.57519			−0.201217
$518$			28.6592i			1.25921i
$519$	−11.3885			−0.499901
$520$	16.4342			0.720689
$521$	20.9967			0.919882			0.459941	−	0.887950i	$-0.347871\pi$
$521$	20.9967			0.919882			0.459941	+	0.887950i	$0.347871\pi$
$522$		−	9.71940i		−	0.425407i
$523$	−3.85329			−0.168493			−0.0842463	−	0.996445i	$-0.526848\pi$
$523$	−3.85329			−0.168493			−0.0842463	+	0.996445i	$0.526848\pi$
$524$	16.7787			0.732981
$525$			20.5053i			0.894924i
$526$	−6.61625			−0.288482
$527$			0.846593i			0.0368782i
$528$			0.796611i			0.0346680i
$529$	−35.4947			−1.54325
$530$	−22.0864	−	8.92385i	−0.959373	−	0.387627i
$531$	−35.5342			−1.54205
$532$			13.5597i			0.587888i
$533$			7.25550i			0.314271i
$534$	−7.72036			−0.334093
$535$		−	23.2605i		−	1.00564i
$536$	−9.56581			−0.413180
$537$	3.09491			0.133555
$538$		−	31.4776i		−	1.35710i
$539$	−13.3468			−0.574889
$540$	−13.9854			−0.601834
$541$	−40.9597			−1.76100			−0.880498	−	0.474050i	$-0.842792\pi$
$541$	−40.9597			−1.76100			−0.880498	+	0.474050i	$0.842792\pi$
$542$			24.4876i			1.05183i
$543$	−1.67350			−0.0718167
$544$			0.174521i			0.00748251i
$545$	−10.8620			−0.465275
$546$	18.0476			0.772367
$547$	18.3046			0.782649			0.391324	−	0.920253i	$-0.372017\pi$
$547$	18.3046			0.782649			0.391324	+	0.920253i	$0.372017\pi$
$548$		−	11.9209i		−	0.509236i
$549$			3.09704i			0.132179i
$550$			5.70652i			0.243327i
$551$			12.3519i			0.526210i
$552$			6.09263i			0.259319i
$553$		−	12.9794i		−	0.551942i
$554$	20.3192			0.863280
$555$	16.5610			0.702975
$556$		−	9.80914i		−	0.416000i
$557$			32.7523i			1.38776i	0.720091	+	0.693880i	$0.244100\pi$
$557$			32.7523i			1.38776i	−0.720091	+	0.693880i	$0.755900\pi$
$558$	−11.4745			−0.485755
$559$	−43.1783			−1.82625
$560$			14.7595i			0.623704i
$561$			0.139025i			0.00586964i
$562$			14.2468i			0.600965i
$563$		−	38.0682i		−	1.60438i	−0.597067	−	0.802191i	$-0.703667\pi$
$563$		−	38.0682i		−	1.60438i	0.597067	−	0.802191i	$-0.296333\pi$
$564$			3.64465i			0.153467i
$565$			26.5881i			1.11857i
$566$	−25.3971			−1.06752
$567$	16.6510			0.699275
$568$	13.6555			0.572973
$569$		−	9.63290i		−	0.403832i	−0.979403	−	0.201916i	$-0.935283\pi$
$569$		−	9.63290i		−	0.403832i	0.979403	−	0.201916i	$-0.0647169\pi$
$570$	7.83560			0.328197
$571$			18.0561i			0.755626i	0.925882	+	0.377813i	$0.123324\pi$
$571$			18.0561i			0.755626i	−0.925882	+	0.377813i	$0.876676\pi$
$572$	5.02256			0.210004
$573$	−14.9917			−0.626287
$574$	−6.51614			−0.271979
$575$			43.6445i			1.82010i
$576$	−2.36541			−0.0985588
$577$	−13.2376			−0.551087			−0.275543	−	0.961289i	$-0.588858\pi$
$577$	−13.2376			−0.551087			−0.275543	+	0.961289i	$0.588858\pi$
$578$		−	16.9695i		−	0.705840i
$579$	−15.4496			−0.642064
$580$			13.4449i			0.558269i
$581$		−	22.5659i		−	0.936190i
$582$	−9.95612			−0.412694
$583$	−6.74996	−	2.72727i	−0.279555	−	0.112952i
$584$	11.2956			0.467416
$585$			38.8737i			1.60723i
$586$			4.58909i			0.189574i
$587$	10.4098			0.429657			0.214829	−	0.976652i	$-0.431081\pi$
$587$	10.4098			0.429657			0.214829	+	0.976652i	$0.431081\pi$
$588$			10.6322i			0.438466i
$589$	14.5824			0.600859
$590$	49.1546			2.02366
$591$			4.82146i			0.198328i
$592$	6.35354			0.261129
$593$	22.2149			0.912257			0.456128	−	0.889914i	$-0.349236\pi$
$593$	22.2149			0.912257			0.456128	+	0.889914i	$0.349236\pi$
$594$	−4.27415			−0.175370
$595$			2.57584i			0.105599i
$596$	15.4675			0.633572
$597$			11.5773i			0.473827i
$598$	38.4135			1.57084
$599$	−23.9417			−0.978230			−0.489115	−	0.872219i	$-0.662680\pi$
$599$	−23.9417			−0.978230			−0.489115	+	0.872219i	$0.662680\pi$
$600$	4.54587			0.185585
$601$		−	27.2624i		−	1.11206i	−0.831163	−	0.556028i	$-0.812325\pi$
$601$		−	27.2624i		−	1.11206i	0.831163	−	0.556028i	$-0.187675\pi$
$602$		−	38.7783i		−	1.58048i
$603$		−	22.6271i		−	0.921445i
$604$		−	17.9704i		−	0.731203i
$605$			3.27208i			0.133029i
$606$			3.18893i			0.129542i
$607$	0.841343			0.0341491			0.0170745	−	0.999854i	$-0.494565\pi$
$607$	0.841343			0.0341491			0.0170745	+	0.999854i	$0.494565\pi$
$608$	3.00609			0.121913
$609$			14.7648i			0.598300i
$610$		−	4.28415i		−	0.173460i
$611$	22.9792			0.929639
$612$	−0.412813			−0.0166870
$613$			24.2340i			0.978801i	0.872059	+	0.489400i	$0.162784\pi$
$613$			24.2340i			0.978801i	−0.872059	+	0.489400i	$0.837216\pi$
$614$		−	7.68204i		−	0.310022i
$615$			3.76541i			0.151836i
$616$			4.51075i			0.181743i
$617$		−	29.6900i		−	1.19528i	−0.801766	−	0.597638i	$-0.796106\pi$
$617$		−	29.6900i		−	1.19528i	0.801766	−	0.597638i	$-0.203894\pi$
$618$		−	3.02072i		−	0.121511i
$619$	20.9984			0.843998			0.421999	−	0.906596i	$-0.361329\pi$
$619$	20.9984			0.843998			0.421999	+	0.906596i	$0.361329\pi$
$620$	15.8727			0.637465
$621$	−32.6894			−1.31178
$622$			12.9605i			0.519668i
$623$	−43.7159			−1.75144
$624$		−	4.00103i		−	0.160169i
$625$	−20.9682			−0.838730
$626$	−4.14770			−0.165776
$627$	2.39468			0.0956345
$628$		−	3.70167i		−	0.147713i
$629$	1.10882			0.0442117
$630$	−34.9124			−1.39094
$631$		−	26.5709i		−	1.05777i	−0.848694	−	0.528885i	$-0.822610\pi$
$631$		−	26.5709i		−	1.05777i	0.848694	−	0.528885i	$-0.177390\pi$
$632$	−2.87745			−0.114459
$633$		−	9.46036i		−	0.376015i
$634$			2.17359i			0.0863242i
$635$	66.2698			2.62984
$636$	−2.17257	+	5.37709i	−0.0861481	+	0.213216i
$637$	67.0353			2.65603
$638$			4.10897i			0.162676i
$639$			32.3009i			1.27780i
$640$	3.27208			0.129340
$641$			15.3070i			0.604592i	0.953214	+	0.302296i	$0.0977531\pi$
$641$			15.3070i			0.604592i	−0.953214	+	0.302296i	$0.902247\pi$
$642$	−5.66293			−0.223498
$643$	−46.5575			−1.83605			−0.918024	−	0.396526i	$-0.870216\pi$
$643$	−46.5575			−1.83605			−0.918024	+	0.396526i	$0.870216\pi$
$644$			34.4990i			1.35945i
$645$	−22.4084			−0.882329
$646$	0.524625			0.0206411
$647$	−6.36078			−0.250068			−0.125034	−	0.992152i	$-0.539904\pi$
$647$	−6.36078			−0.250068			−0.125034	+	0.992152i	$0.539904\pi$
$648$		−	3.69140i		−	0.145012i
$649$	15.0224			0.589682
$650$		−	28.6613i		−	1.12419i
$651$	17.4310			0.683175
$652$	9.70825			0.380204
$653$	47.1086			1.84350			0.921751	−	0.387783i	$-0.126759\pi$
$653$	47.1086			1.84350			0.921751	+	0.387783i	$0.126759\pi$
$654$			2.64442i			0.103405i
$655$		−	54.9013i		−	2.14517i
$656$			1.44458i			0.0564015i
$657$			26.7188i			1.04240i
$658$			20.6375i			0.804535i
$659$		−	3.80570i		−	0.148249i	−0.997249	−	0.0741245i	$-0.976384\pi$
$659$		−	3.80570i		−	0.148249i	0.997249	−	0.0741245i	$-0.0236162\pi$
$660$	2.60658			0.101461
$661$	−35.2225			−1.37000			−0.684999	−	0.728544i	$-0.740197\pi$
$661$	−35.2225			−1.37000			−0.684999	+	0.728544i	$0.740197\pi$
$662$		−	12.1821i		−	0.473470i
$663$		−	0.698262i		−	0.0271182i
$664$	−5.00269			−0.194142
$665$	44.3685			1.72054
$666$			15.0287i			0.582352i
$667$			31.4262i			1.21683i
$668$		−	1.95611i		−	0.0756841i
$669$		−	6.39370i		−	0.247195i
$670$			31.3001i			1.20923i
$671$		−	1.30931i		−	0.0505452i
$672$	3.59331			0.138615
$673$	−19.5702			−0.754375			−0.377187	−	0.926137i	$-0.623109\pi$
$673$	−19.5702			−0.754375			−0.377187	+	0.926137i	$0.623109\pi$
$674$	27.1911			1.04736
$675$			24.3905i			0.938790i
$676$	−12.2261			−0.470236
$677$		−	8.23197i		−	0.316380i	−0.987409	−	0.158190i	$-0.949434\pi$
$677$		−	8.23197i		−	0.316380i	0.987409	−	0.158190i	$-0.0505659\pi$
$678$	6.47306			0.248596
$679$	−56.3757			−2.16350
$680$	0.571046			0.0218986
$681$			11.8491i			0.454059i
$682$	4.85096			0.185753
$683$	9.92169			0.379643			0.189821	−	0.981819i	$-0.439209\pi$
$683$	9.92169			0.379643			0.189821	+	0.981819i	$0.439209\pi$
$684$			7.11064i			0.271882i
$685$	−39.0062			−1.49035
$686$			28.6289i			1.09306i
$687$			1.32296i			0.0504740i
$688$	−8.59687			−0.327752
$689$	33.9021	+	13.6979i	1.29157	+	0.521848i
$690$	19.9356			0.758934
$691$		−	4.14952i		−	0.157855i	−0.996880	−	0.0789276i	$-0.974850\pi$
$691$		−	4.14952i		−	0.157855i	0.996880	−	0.0789276i	$-0.0251496\pi$
$692$			14.2962i			0.543461i
$693$	−10.6698			−0.405311
$694$			36.4903i			1.38515i
$695$	−32.0963			−1.21748
$696$	3.27325			0.124072
$697$			0.252109i			0.00954932i
$698$	32.7622			1.24007
$699$	−4.69019			−0.177399
$700$	25.7407			0.972905
$701$		−	40.5716i		−	1.53237i	−0.642621	−	0.766184i	$-0.722153\pi$
$701$		−	40.5716i		−	1.53237i	0.642621	−	0.766184i	$-0.277847\pi$
$702$	21.4672			0.810226
$703$		−	19.0993i		−	0.720344i
$704$	1.00000			0.0376889
$705$	11.9256			0.449144
$706$	6.62203			0.249223
$707$			18.0571i			0.679106i
$708$		−	11.9670i		−	0.449749i
$709$			30.9456i			1.16219i	0.813837	+	0.581093i	$0.197375\pi$
$709$			30.9456i			1.16219i	−0.813837	+	0.581093i	$0.802625\pi$
$710$		−	44.6819i		−	1.67688i
$711$		−	6.80635i		−	0.255258i
$712$			9.69150i			0.363204i
$713$	37.1010			1.38944
$714$	0.627107			0.0234689
$715$		−	16.4342i		−	0.614605i
$716$		−	3.88510i		−	0.145193i
$717$	1.60089			0.0597865
$718$	26.5473			0.990737
$719$		−	3.99630i		−	0.149037i	−0.997220	−	0.0745185i	$-0.976258\pi$
$719$		−	3.99630i		−	0.149037i	0.997220	−	0.0745185i	$-0.0237420\pi$
$720$			7.73982i			0.288446i
$721$		−	17.1046i		−	0.637008i
$722$			9.96342i			0.370800i
$723$		−	11.4463i		−	0.425692i
$724$			2.10077i			0.0780746i
$725$	23.4479			0.870834
$726$	0.796611			0.0295650
$727$	33.3401			1.23651			0.618257	−	0.785976i	$-0.287839\pi$
$727$	33.3401			1.23651			0.618257	+	0.785976i	$0.287839\pi$
$728$		−	22.6555i		−	0.839669i
$729$	−1.48281			−0.0549190
$730$		−	36.9602i		−	1.36796i
$731$	−1.50033			−0.0554917
$732$	−1.04301			−0.0385506
$733$	−20.6818			−0.763898			−0.381949	−	0.924183i	$-0.624747\pi$
$733$	−20.6818			−0.763898			−0.381949	+	0.924183i	$0.624747\pi$
$734$			34.0860i			1.25814i
$735$	34.7895			1.28323
$736$	7.64818			0.281916
$737$			9.56581i			0.352361i
$738$	−3.41703			−0.125783
$739$			19.4792i			0.716553i	0.933616	+	0.358276i	$0.116635\pi$
$739$			19.4792i			0.716553i	−0.933616	+	0.358276i	$0.883365\pi$
$740$		−	20.7893i		−	0.764230i
$741$	−12.0275			−0.441839
$742$	−12.3020	+	30.4474i	−0.451621	+	1.11776i
$743$	−44.3204			−1.62596			−0.812979	−	0.582293i	$-0.802156\pi$
$743$	−44.3204			−1.62596			−0.812979	+	0.582293i	$0.802156\pi$
$744$		−	3.86433i		−	0.141673i
$745$		−	50.6108i		−	1.85424i
$746$	29.3821			1.07576
$747$		−	11.8334i		−	0.432962i
$748$	0.174521			0.00638110
$749$	−32.0659			−1.17166
$750$		−	1.84159i		−	0.0672455i
$751$	32.5216			1.18673			0.593365	−	0.804933i	$-0.297799\pi$
$751$	32.5216			1.18673			0.593365	+	0.804933i	$0.297799\pi$
$752$	4.57519			0.166840
$753$	−5.23595			−0.190809
$754$		−	20.6376i		−	0.751576i
$755$	−58.8005			−2.13997
$756$			19.2796i			0.701192i
$757$	0.375859			0.0136608			0.00683042	−	0.999977i	$-0.497826\pi$
$757$	0.375859			0.0136608			0.00683042	+	0.999977i	$0.497826\pi$
$758$	1.30743			0.0474881
$759$	6.09263			0.221148
$760$		−	9.83617i		−	0.356795i
$761$		−	34.2962i		−	1.24324i	−0.783320	−	0.621618i	$-0.786475\pi$
$761$		−	34.2962i		−	1.24324i	0.783320	−	0.621618i	$-0.213525\pi$
$762$		−	16.1338i		−	0.584467i
$763$			14.9738i			0.542088i
$764$			18.8194i			0.680860i
$765$			1.35076i			0.0488367i
$766$	−32.1921			−1.16315
$767$	−75.4511			−2.72438
$768$		−	0.796611i		−	0.0287452i
$769$		−	19.3731i		−	0.698612i	−0.937009	−	0.349306i	$-0.886417\pi$
$769$		−	19.3731i		−	0.698612i	0.937009	−	0.349306i	$-0.113583\pi$
$770$	14.7595			0.531897
$771$	0.189836			0.00683677
$772$			19.3942i			0.698011i
$773$			54.5901i			1.96347i	0.190256	+	0.981735i	$0.439068\pi$
$773$			54.5901i			1.96347i	−0.190256	+	0.981735i	$0.560932\pi$
$774$		−	20.3351i		−	0.730931i
$775$		−	27.6821i		−	0.994371i
$776$			12.4981i			0.448655i
$777$		−	22.8302i		−	0.819030i
$778$	−6.05959			−0.217247
$779$	4.34254			0.155588
$780$	−13.0917			−0.468758
$781$		−	13.6555i		−	0.488633i
$782$	1.33477			0.0477311
$783$			17.5623i			0.627627i
$784$	13.3468			0.476672
$785$	−12.1122			−0.432302
$786$	−13.3661			−0.476753
$787$			43.6996i			1.55772i	0.627195	+	0.778862i	$0.284203\pi$
$787$			43.6996i			1.55772i	−0.627195	+	0.778862i	$0.715797\pi$
$788$	6.05246			0.215610
$789$	5.27058			0.187638
$790$			9.41525i			0.334980i
$791$	36.6532			1.30324
$792$			2.36541i			0.0840512i
$793$			6.57607i			0.233523i
$794$	−30.3069			−1.07555
$795$	17.5943	+	7.10883i	0.624005	+	0.252124i
$796$	14.5332			0.515115
$797$		−	7.88840i		−	0.279421i	−0.990192	−	0.139711i	$-0.955383\pi$
$797$		−	7.88840i		−	0.279421i	0.990192	−	0.139711i	$-0.0446173\pi$
$798$		−	10.8018i		−	0.382380i
$799$	0.798466			0.0282477
$800$		−	5.70652i		−	0.201756i
$801$	−22.9244			−0.809994
$802$	−33.9699			−1.19952
$803$		−	11.2956i		−	0.398614i
$804$	7.62023			0.268745
$805$	112.884			3.97862
$806$	−24.3643			−0.858194
$807$			25.0754i			0.882697i
$808$	4.00312			0.140829
$809$		−	37.5640i		−	1.32068i	−0.750967	−	0.660340i	$-0.770412\pi$
$809$		−	37.5640i		−	1.32068i	0.750967	−	0.660340i	$-0.229588\pi$
$810$	−12.0786			−0.424398
$811$	37.0173			1.29985			0.649926	−	0.759997i	$-0.274800\pi$
$811$	37.0173			1.29985			0.649926	+	0.759997i	$0.274800\pi$
$812$	18.5345			0.650434
$813$		−	19.5071i		−	0.684143i
$814$		−	6.35354i		−	0.222692i
$815$		−	31.7662i		−	1.11272i
$816$		−	0.139025i		−	0.00486685i
$817$			25.8430i			0.904131i
$818$			5.65474i			0.197713i
$819$	53.5896			1.87257
$820$	4.72679			0.165067
$821$			39.9133i			1.39298i	0.717564	+	0.696492i	$0.245257\pi$
$821$			39.9133i			1.39298i	−0.717564	+	0.696492i	$0.754743\pi$
$822$			9.49633i			0.331223i
$823$	−21.6020			−0.752998			−0.376499	−	0.926417i	$-0.622872\pi$
$823$	−21.6020			−0.752998			−0.376499	+	0.926417i	$0.622872\pi$
$824$	−3.79197			−0.132099
$825$		−	4.54587i		−	0.158267i
$826$		−	67.7624i		−	2.35776i
$827$			47.1672i			1.64017i	0.572245	+	0.820083i	$0.306073\pi$
$827$			47.1672i			1.64017i	−0.572245	+	0.820083i	$0.693927\pi$
$828$			18.0911i			0.628709i
$829$		−	17.3200i		−	0.601548i	−0.953695	−	0.300774i	$-0.902755\pi$
$829$		−	17.3200i		−	0.601548i	0.953695	−	0.300774i	$-0.0972449\pi$
$830$			16.3692i			0.568183i
$831$	−16.1865			−0.561503
$832$	−5.02256			−0.174126
$833$	2.32930			0.0807053
$834$			7.81407i			0.270579i
$835$	−6.40054			−0.221500
$836$		−	3.00609i		−	0.103968i
$837$	20.7337			0.716662
$838$	−29.3873			−1.01517
$839$	27.7513			0.958081			0.479040	−	0.877793i	$-0.340985\pi$
$839$	27.7513			0.958081			0.479040	+	0.877793i	$0.340985\pi$
$840$		−	11.7576i		−	0.405676i
$841$	−12.1164			−0.417805
$842$	−21.3104			−0.734406
$843$		−	11.3492i		−	0.390886i
$844$	−11.8758			−0.408780
$845$			40.0049i			1.37621i
$846$			10.8222i			0.372075i
$847$	4.51075			0.154991
$848$	6.74996	+	2.72727i	0.231795	+	0.0936548i
$849$	20.2316			0.694348
$850$		−	0.995905i		−	0.0341593i
$851$		−	48.5930i		−	1.66575i
$852$	−10.8781			−0.372679
$853$		−	33.2720i		−	1.13921i	−0.821918	−	0.569605i	$-0.807096\pi$
$853$		−	33.2720i		−	1.13921i	0.821918	−	0.569605i	$-0.192904\pi$
$854$	−5.90594			−0.202097
$855$	23.2666			0.795701
$856$			7.10878i			0.242973i
$857$	−5.75736			−0.196668			−0.0983339	−	0.995153i	$-0.531351\pi$
$857$	−5.75736			−0.196668			−0.0983339	+	0.995153i	$0.531351\pi$
$858$	−4.00103			−0.136593
$859$	−18.2582			−0.622962			−0.311481	−	0.950252i	$-0.600825\pi$
$859$	−18.2582			−0.622962			−0.311481	+	0.950252i	$0.600825\pi$
$860$			28.1296i			0.959213i
$861$	5.19083			0.176903
$862$			24.1342i			0.822013i
$863$	51.9820			1.76949			0.884744	−	0.466077i	$-0.154333\pi$
$863$	51.9820			1.76949			0.884744	+	0.466077i	$0.154333\pi$
$864$	4.27415			0.145409
$865$	46.7784			1.59051
$866$		−	5.60335i		−	0.190409i
$867$			13.5181i			0.459100i
$868$		−	21.8815i		−	0.742705i
$869$			2.87745i			0.0976108i
$870$		−	10.7103i		−	0.363115i
$871$		−	48.0449i		−	1.62794i
$872$	3.31959			0.112415
$873$	−29.5631			−1.00056
$874$		−	22.9911i		−	0.777686i
$875$		−	10.4279i		−	0.352526i
$876$	−8.99822			−0.304022
$877$	11.1878			0.377786			0.188893	−	0.981998i	$-0.439510\pi$
$877$	11.1878			0.377786			0.188893	+	0.981998i	$0.439510\pi$
$878$		−	1.65837i		−	0.0559674i
$879$		−	3.65572i		−	0.123304i
$880$		−	3.27208i		−	0.110302i
$881$		−	30.9296i		−	1.04205i	−0.853543	−	0.521023i	$-0.825551\pi$
$881$		−	30.9296i		−	1.04205i	0.853543	−	0.521023i	$-0.174449\pi$
$882$			31.5707i			1.06304i
$883$		−	26.1207i		−	0.879032i	−0.898235	−	0.439516i	$-0.855150\pi$
$883$		−	26.1207i		−	0.879032i	0.898235	−	0.439516i	$-0.144850\pi$
$884$	−0.876540			−0.0294812
$885$	−39.1571			−1.31625
$886$	29.6521			0.996183
$887$			28.2694i			0.949192i	0.880204	+	0.474596i	$0.157406\pi$
$887$			28.2694i			0.949192i	−0.880204	+	0.474596i	$0.842594\pi$
$888$	−5.06130			−0.169846
$889$		−	91.3566i		−	3.06400i
$890$	31.7114			1.06297
$891$	−3.69140			−0.123667
$892$	−8.02612			−0.268735
$893$		−	13.7534i		−	0.460242i
$894$	−12.3215			−0.412094
$895$	−12.7124			−0.424927
$896$		−	4.51075i		−	0.150693i
$897$	−30.6006			−1.02172
$898$		−	28.4016i		−	0.947774i
$899$		−	19.9325i		−	0.664785i
$900$	13.4983			0.449942
$901$	1.17801	+	0.475965i	0.0392451	+	0.0158567i
$902$	1.44458			0.0480993
$903$			30.8912i			1.02799i
$904$		−	8.12574i		−	0.270258i
$905$	6.87390			0.228496
$906$			14.3154i			0.475597i
$907$	−8.24411			−0.273741			−0.136871	−	0.990589i	$-0.543704\pi$
$907$	−8.24411			−0.273741			−0.136871	+	0.990589i	$0.543704\pi$
$908$	14.8744			0.493625
$909$			9.46903i			0.314068i
$910$	−74.1306			−2.45741
$911$	8.31503			0.275489			0.137745	−	0.990468i	$-0.456015\pi$
$911$	8.31503			0.275489			0.137745	+	0.990468i	$0.456015\pi$
$912$	−2.39468			−0.0792959
$913$			5.00269i			0.165565i
$914$	−4.62908			−0.153116
$915$			3.41280i			0.112824i
$916$	1.66073			0.0548721
$917$	−75.6845			−2.49932
$918$	0.745926			0.0246192
$919$		−	15.3888i		−	0.507630i	−0.967253	−	0.253815i	$-0.918315\pi$
$919$		−	15.3888i		−	0.507630i	0.967253	−	0.253815i	$-0.0816854\pi$
$920$		−	25.0255i		−	0.825065i
$921$			6.11960i			0.201648i
$922$			4.27370i			0.140747i
$923$			68.5856i			2.25752i
$924$		−	3.59331i		−	0.118211i
$925$	−36.2566			−1.19211
$926$	−19.9497			−0.655587
$927$		−	8.96956i		−	0.294599i
$928$		−	4.10897i		−	0.134884i
$929$	39.4274			1.29357			0.646786	−	0.762672i	$-0.276113\pi$
$929$	39.4274			1.29357			0.646786	+	0.762672i	$0.276113\pi$
$930$	−12.6444			−0.414626
$931$		−	40.1218i		−	1.31494i
$932$			5.88768i			0.192857i
$933$		−	10.3245i		−	0.338008i
$934$			37.7361i			1.23476i
$935$		−	0.571046i		−	0.0186752i
$936$		−	11.8804i		−	0.388324i
$937$	−18.9409			−0.618771			−0.309385	−	0.950937i	$-0.600123\pi$
$937$	−18.9409			−0.618771			−0.309385	+	0.950937i	$0.600123\pi$
$938$	43.1489			1.40886
$939$	3.30411			0.107825
$940$		−	14.9704i		−	0.488281i
$941$	37.8160			1.23277			0.616384	−	0.787446i	$-0.288597\pi$
$941$	37.8160			1.23277			0.616384	+	0.787446i	$0.288597\pi$
$942$			2.94879i			0.0960769i
$943$	11.0484			0.359786
$944$	−15.0224			−0.488939
$945$	63.0844			2.05213
$946$			8.59687i			0.279508i
$947$	8.93343			0.290297			0.145149	−	0.989410i	$-0.453634\pi$
$947$	8.93343			0.290297			0.145149	+	0.989410i	$0.453634\pi$
$948$	2.29221			0.0744475
$949$			56.7330i			1.84163i
$950$	−17.1543			−0.556559
$951$		−	1.73150i		−	0.0561479i
$952$		−	0.787218i		−	0.0255139i
$953$	−22.6755			−0.734531			−0.367265	−	0.930116i	$-0.619706\pi$
$953$	−22.6755			−0.734531			−0.367265	+	0.930116i	$0.619706\pi$
$954$	−6.45111	+	15.9664i	−0.208862	+	0.516932i
$955$	61.5785			1.99263
$956$		−	2.00963i		−	0.0649961i
$957$		−	3.27325i		−	0.105809i
$958$	7.61371			0.245988
$959$			53.7722i			1.73640i
$960$	−2.60658			−0.0841269
$961$	7.46816			0.240908
$962$			31.9111i			1.02885i
$963$	−16.8152			−0.541862
$964$	−14.3687			−0.462786
$965$	63.4593			2.04283
$966$		−	27.4823i		−	0.884228i
$967$	−28.4943			−0.916315			−0.458157	−	0.888871i	$-0.651490\pi$
$967$	−28.4943			−0.916315			−0.458157	+	0.888871i	$0.651490\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	−0.417922			−0.0134256
$970$	40.8948			1.31305
$971$	−54.1978			−1.73929			−0.869645	−	0.493677i	$-0.835652\pi$
$971$	−54.1978			−1.73929			−0.869645	+	0.493677i	$0.835652\pi$
$972$			15.7630i			0.505600i
$973$			44.2465i			1.41848i
$974$		−	22.0930i		−	0.707906i
$975$			22.8319i			0.731207i
$976$			1.30931i			0.0419098i
$977$			44.7287i			1.43100i	0.698614	+	0.715499i	$0.253800\pi$
$977$			44.7287i			1.43100i	−0.698614	+	0.715499i	$0.746200\pi$
$978$	−7.73370			−0.247296
$979$	9.69150			0.309742
$980$		−	43.6719i		−	1.39505i
$981$			7.85218i			0.250701i
$982$	14.1397			0.451216
$983$	−39.5761			−1.26228			−0.631141	−	0.775668i	$-0.717413\pi$
$983$	−39.5761			−1.26228			−0.631141	+	0.775668i	$0.717413\pi$
$984$		−	1.15077i		−	0.0366852i
$985$		−	19.8041i		−	0.631013i
$986$		−	0.717100i		−	0.0228371i
$987$		−	16.4401i		−	0.523294i
$988$			15.0983i			0.480340i
$989$			65.7504i			2.09074i
$990$	7.73982			0.245988
$991$	−38.5406			−1.22428			−0.612140	−	0.790749i	$-0.709691\pi$
$991$	−38.5406			−1.22428			−0.612140	+	0.790749i	$0.709691\pi$
$992$	−4.85096			−0.154018
$993$			9.70439i			0.307959i
$994$	−61.5965			−1.95372
$995$		−	47.5538i		−	1.50756i
$996$	3.98520			0.126276
$997$	13.6761			0.433128			0.216564	−	0.976268i	$-0.430515\pi$
$997$	13.6761			0.433128			0.216564	+	0.976268i	$0.430515\pi$
$998$	6.96383			0.220436
$999$		−	27.1560i		−	0.859177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1166.2.c.b.529.15	yes	22
53.52	even	2	inner	1166.2.c.b.529.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1166.2.c.b.529.8	✓	22	53.52	even	2	inner
1166.2.c.b.529.15	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.796611i q^{3} -1.00000 q^{4} +3.27208i q^{5} +0.796611 q^{6} +4.51075 q^{7} -1.00000i q^{8} +2.36541 q^{9} -3.27208 q^{10} -1.00000 q^{11} +0.796611i q^{12} +5.02256 q^{13} +4.51075i q^{14} +2.60658 q^{15} +1.00000 q^{16} +0.174521 q^{17} +2.36541i q^{18} -3.00609i q^{19} -3.27208i q^{20} -3.59331i q^{21} -1.00000i q^{22} -7.64818i q^{23} -0.796611 q^{24} -5.70652 q^{25} +5.02256i q^{26} -4.27415i q^{27} -4.51075 q^{28} -4.10897 q^{29} +2.60658i q^{30} +4.85096i q^{31} +1.00000i q^{32} +0.796611i q^{33} +0.174521i q^{34} +14.7595i q^{35} -2.36541 q^{36} +6.35354 q^{37} +3.00609 q^{38} -4.00103i q^{39} +3.27208 q^{40} +1.44458i q^{41} +3.59331 q^{42} -8.59687 q^{43} +1.00000 q^{44} +7.73982i q^{45} +7.64818 q^{46} +4.57519 q^{47} -0.796611i q^{48} +13.3468 q^{49} -5.70652i q^{50} -0.139025i q^{51} -5.02256 q^{52} +(6.74996 + 2.72727i) q^{53} +4.27415 q^{54} -3.27208i q^{55} -4.51075i q^{56} -2.39468 q^{57} -4.10897i q^{58} -15.0224 q^{59} -2.60658 q^{60} +1.30931i q^{61} -4.85096 q^{62} +10.6698 q^{63} -1.00000 q^{64} +16.4342i q^{65} -0.796611 q^{66} -9.56581i q^{67} -0.174521 q^{68} -6.09263 q^{69} -14.7595 q^{70} +13.6555i q^{71} -2.36541i q^{72} +11.2956i q^{73} +6.35354i q^{74} +4.54587i q^{75} +3.00609i q^{76} -4.51075 q^{77} +4.00103 q^{78} -2.87745i q^{79} +3.27208i q^{80} +3.69140 q^{81} -1.44458 q^{82} -5.00269i q^{83} +3.59331i q^{84} +0.571046i q^{85} -8.59687i q^{86} +3.27325i q^{87} +1.00000i q^{88} -9.69150 q^{89} -7.73982 q^{90} +22.6555 q^{91} +7.64818i q^{92} +3.86433 q^{93} +4.57519i q^{94} +9.83617 q^{95} +0.796611 q^{96} -12.4981 q^{97} +13.3468i q^{98} -2.36541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 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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