LMFDB - Embedded newform 380.3.b.a.191.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(191,380)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.15
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65600 - 1.12146i) q^{2} +5.88343i q^{3} +(1.48464 + 3.71428i) q^{4} +2.23607 q^{5} +(6.59806 - 9.74294i) q^{6} -1.76155i q^{7} +(1.70687 - 7.81579i) q^{8} -25.6148 q^{9} +O(q^{10})$	\(q+(-1.65600 - 1.12146i) q^{2} +5.88343i q^{3} +(1.48464 + 3.71428i) q^{4} +2.23607 q^{5} +(6.59806 - 9.74294i) q^{6} -1.76155i q^{7} +(1.70687 - 7.81579i) q^{8} -25.6148 q^{9} +(-3.70292 - 2.50767i) q^{10} +8.04800i q^{11} +(-21.8527 + 8.73478i) q^{12} +1.13027 q^{13} +(-1.97551 + 2.91712i) q^{14} +13.1558i q^{15} +(-11.5917 + 11.0287i) q^{16} -22.4610 q^{17} +(42.4180 + 28.7261i) q^{18} +4.35890i q^{19} +(3.31975 + 8.30537i) q^{20} +10.3640 q^{21} +(9.02554 - 13.3274i) q^{22} +13.9910i q^{23} +(45.9837 + 10.0423i) q^{24} +5.00000 q^{25} +(-1.87173 - 1.26756i) q^{26} -97.7521i q^{27} +(6.54288 - 2.61527i) q^{28} -29.0420 q^{29} +(14.7537 - 21.7859i) q^{30} -0.247372i q^{31} +(31.5641 - 5.26384i) q^{32} -47.3499 q^{33} +(37.1953 + 25.1892i) q^{34} -3.93894i q^{35} +(-38.0287 - 95.1404i) q^{36} -64.5666 q^{37} +(4.88835 - 7.21831i) q^{38} +6.64989i q^{39} +(3.81668 - 17.4766i) q^{40} +51.2202 q^{41} +(-17.1627 - 11.6228i) q^{42} -65.1853i q^{43} +(-29.8925 + 11.9484i) q^{44} -57.2764 q^{45} +(15.6903 - 23.1689i) q^{46} +9.79817i q^{47} +(-64.8867 - 68.1990i) q^{48} +45.8969 q^{49} +(-8.27998 - 5.60732i) q^{50} -132.148i q^{51} +(1.67805 + 4.19815i) q^{52} -57.3993 q^{53} +(-109.625 + 161.877i) q^{54} +17.9959i q^{55} +(-13.7679 - 3.00674i) q^{56} -25.6453 q^{57} +(48.0933 + 32.5695i) q^{58} +69.7899i q^{59} +(-48.8641 + 19.5316i) q^{60} +54.2218 q^{61} +(-0.277418 + 0.409646i) q^{62} +45.1217i q^{63} +(-58.1732 - 26.6811i) q^{64} +2.52737 q^{65} +(78.4112 + 53.1012i) q^{66} -2.79637i q^{67} +(-33.3465 - 83.4264i) q^{68} -82.3148 q^{69} +(-4.41738 + 6.52287i) q^{70} +74.3304i q^{71} +(-43.7211 + 200.200i) q^{72} -6.33184 q^{73} +(106.922 + 72.4091i) q^{74} +29.4172i q^{75} +(-16.1902 + 6.47139i) q^{76} +14.1769 q^{77} +(7.45760 - 11.0122i) q^{78} +26.1944i q^{79} +(-25.9198 + 24.6610i) q^{80} +344.585 q^{81} +(-84.8204 - 57.4416i) q^{82} -38.5097i q^{83} +(15.3867 + 38.4946i) q^{84} -50.2244 q^{85} +(-73.1030 + 107.947i) q^{86} -170.866i q^{87} +(62.9015 + 13.7369i) q^{88} -110.737 q^{89} +(94.8495 + 64.2334i) q^{90} -1.99103i q^{91} +(-51.9663 + 20.7715i) q^{92} +1.45540 q^{93} +(10.9883 - 16.2257i) q^{94} +9.74679i q^{95} +(30.9695 + 185.705i) q^{96} +81.9963 q^{97} +(-76.0051 - 51.4717i) q^{98} -206.148i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	−1.65600	−	1.12146i	−0.827998	−	0.560732i
$2$	−1.65600	−	1.12146i	−0.827998	−	0.560732i
$3$			5.88343i			1.96114i	0.196158	+	0.980572i	$0.437154\pi$
$3$			5.88343i			1.96114i	−0.196158	+	0.980572i	$0.562846\pi$
$4$	1.48464	+	3.71428i	0.371160	+	0.928569i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$	6.59806	−	9.74294i	1.09968	−	1.62382i
$7$		−	1.76155i		−	0.251650i	−0.992052	−	0.125825i	$-0.959842\pi$
$7$		−	1.76155i		−	0.251650i	0.992052	−	0.125825i	$-0.0401578\pi$
$8$	1.70687	−	7.81579i	0.213359	−	0.976974i
$9$	−25.6148			−2.84609
$10$	−3.70292	−	2.50767i	−0.370292	−	0.250767i
$11$			8.04800i			0.731636i	0.930686	+	0.365818i	$0.119211\pi$
$11$			8.04800i			0.731636i	−0.930686	+	0.365818i	$0.880789\pi$
$12$	−21.8527	+	8.73478i	−1.82106	+	0.727898i
$13$	1.13027			0.0869441			0.0434720	−	0.999055i	$-0.486158\pi$
$13$	1.13027			0.0869441			0.0434720	+	0.999055i	$0.486158\pi$
$14$	−1.97551	+	2.91712i	−0.141108	+	0.208366i
$15$			13.1558i			0.877051i
$16$	−11.5917	+	11.0287i	−0.724481	+	0.689295i
$17$	−22.4610			−1.32124			−0.660618	−	0.750722i	$-0.729706\pi$
$17$	−22.4610			−1.32124			−0.660618	+	0.750722i	$0.729706\pi$
$18$	42.4180	+	28.7261i	2.35655	+	1.59589i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	3.31975	+	8.30537i	0.165988	+	0.415269i
$21$	10.3640			0.493522
$22$	9.02554	−	13.3274i	0.410252	−	0.605793i
$23$			13.9910i			0.608302i	0.952624	+	0.304151i	$0.0983728\pi$
$23$			13.9910i			0.608302i	−0.952624	+	0.304151i	$0.901627\pi$
$24$	45.9837	+	10.0423i	1.91599	+	0.418428i
$25$	5.00000			0.200000
$26$	−1.87173	−	1.26756i	−0.0719895	−	0.0487523i
$27$		−	97.7521i		−	3.62045i
$28$	6.54288	−	2.61527i	0.233674	−	0.0934023i
$29$	−29.0420			−1.00145			−0.500723	−	0.865607i	$-0.666933\pi$
$29$	−29.0420			−1.00145			−0.500723	+	0.865607i	$0.666933\pi$
$30$	14.7537	−	21.7859i	0.491790	−	0.726196i
$31$		−	0.247372i		−	0.00797973i	−0.999992	−	0.00398987i	$-0.998730\pi$
$31$		−	0.247372i		−	0.00797973i	0.999992	−	0.00398987i	$-0.00127002\pi$
$32$	31.5641	−	5.26384i	0.986378	−	0.164495i
$33$	−47.3499			−1.43484
$34$	37.1953	+	25.1892i	1.09398	+	0.740859i
$35$		−	3.93894i		−	0.112541i
$36$	−38.0287	−	95.1404i	−1.05635	−	2.64279i
$37$	−64.5666			−1.74504			−0.872522	−	0.488575i	$-0.837517\pi$
$37$	−64.5666			−1.74504			−0.872522	+	0.488575i	$0.837517\pi$
$38$	4.88835	−	7.21831i	0.128641	−	0.189956i
$39$			6.64989i			0.170510i
$40$	3.81668	−	17.4766i	0.0954170	−	0.436916i
$41$	51.2202			1.24927			0.624637	−	0.780915i	$-0.285247\pi$
$41$	51.2202			1.24927			0.624637	+	0.780915i	$0.285247\pi$
$42$	−17.1627	−	11.6228i	−0.408635	−	0.276733i
$43$		−	65.1853i		−	1.51594i	−0.652291	−	0.757969i	$-0.726192\pi$
$43$		−	65.1853i		−	1.51594i	0.652291	−	0.757969i	$-0.273808\pi$
$44$	−29.8925	+	11.9484i	−0.679375	+	0.271554i
$45$	−57.2764			−1.27281
$46$	15.6903	−	23.1689i	0.341094	−	0.503673i
$47$			9.79817i			0.208472i	0.994553	+	0.104236i	$0.0332397\pi$
$47$			9.79817i			0.208472i	−0.994553	+	0.104236i	$0.966760\pi$
$48$	−64.8867	−	68.1990i	−1.35181	−	1.42081i
$49$	45.8969			0.936672
$50$	−8.27998	−	5.60732i	−0.165600	−	0.112146i
$51$		−	132.148i		−	2.59114i
$52$	1.67805	+	4.19815i	0.0322701	+	0.0807336i
$53$	−57.3993			−1.08301			−0.541503	−	0.840699i	$-0.682145\pi$
$53$	−57.3993			−1.08301			−0.541503	+	0.840699i	$0.682145\pi$
$54$	−109.625	+	161.877i	−2.03010	+	2.99772i
$55$			17.9959i			0.327198i
$56$	−13.7679	−	3.00674i	−0.245855	−	0.0536917i
$57$	−25.6453			−0.449917
$58$	48.0933	+	32.5695i	0.829195	+	0.561543i
$59$			69.7899i			1.18288i	0.806349	+	0.591439i	$0.201440\pi$
$59$			69.7899i			1.18288i	−0.806349	+	0.591439i	$0.798560\pi$
$60$	−48.8641	+	19.5316i	−0.814402	+	0.325526i
$61$	54.2218			0.888882			0.444441	−	0.895808i	$-0.353402\pi$
$61$	54.2218			0.888882			0.444441	+	0.895808i	$0.353402\pi$
$62$	−0.277418	+	0.409646i	−0.00447449	+	0.00660720i
$63$			45.1217i			0.716218i
$64$	−58.1732	−	26.6811i	−0.908956	−	0.416892i
$65$	2.52737			0.0388826
$66$	78.4112	+	53.1012i	1.18805	+	0.804563i
$67$		−	2.79637i		−	0.0417369i	−0.999782	−	0.0208684i	$-0.993357\pi$
$67$		−	2.79637i		−	0.0417369i	0.999782	−	0.0208684i	$-0.00664311\pi$
$68$	−33.3465	−	83.4264i	−0.490390	−	1.22686i
$69$	−82.3148			−1.19297
$70$	−4.41738	+	6.52287i	−0.0631055	+	0.0931839i
$71$			74.3304i			1.04691i	0.852054	+	0.523454i	$0.175357\pi$
$71$			74.3304i			1.04691i	−0.852054	+	0.523454i	$0.824643\pi$
$72$	−43.7211	+	200.200i	−0.607238	+	2.78055i
$73$	−6.33184			−0.0867375			−0.0433688	−	0.999059i	$-0.513809\pi$
$73$	−6.33184			−0.0867375			−0.0433688	+	0.999059i	$0.513809\pi$
$74$	106.922	+	72.4091i	1.44489	+	0.978501i
$75$			29.4172i			0.392229i
$76$	−16.1902	+	6.47139i	−0.213028	+	0.0851499i
$77$	14.1769			0.184116
$78$	7.45760	−	11.0122i	0.0956103	−	0.141182i
$79$			26.1944i			0.331574i	0.986162	+	0.165787i	$0.0530164\pi$
$79$			26.1944i			0.331574i	−0.986162	+	0.165787i	$0.946984\pi$
$80$	−25.9198	+	24.6610i	−0.323998	+	0.308262i
$81$	344.585			4.25413
$82$	−84.8204	−	57.4416i	−1.03440	−	0.700507i
$83$		−	38.5097i		−	0.463973i	−0.972719	−	0.231986i	$-0.925478\pi$
$83$		−	38.5097i		−	0.463973i	0.972719	−	0.231986i	$-0.0745225\pi$
$84$	15.3867	+	38.4946i	0.183175	+	0.458269i
$85$	−50.2244			−0.590875
$86$	−73.1030	+	107.947i	−0.850035	+	1.25519i
$87$		−	170.866i		−	1.96398i
$88$	62.9015	+	13.7369i	0.714790	+	0.156101i
$89$	−110.737			−1.24424			−0.622120	−	0.782922i	$-0.713729\pi$
$89$	−110.737			−1.24424			−0.622120	+	0.782922i	$0.713729\pi$
$90$	94.8495	+	64.2334i	1.05388	+	0.713705i
$91$		−	1.99103i		−	0.0218795i
$92$	−51.9663	+	20.7715i	−0.564851	+	0.225777i
$93$	1.45540			0.0156494
$94$	10.9883	−	16.2257i	0.116897	−	0.172614i
$95$			9.74679i			0.102598i
$96$	30.9695	+	185.705i	0.322598	+	1.93443i
$97$	81.9963			0.845323			0.422661	−	0.906288i	$-0.361096\pi$
$97$	81.9963			0.845323			0.422661	+	0.906288i	$0.361096\pi$
$98$	−76.0051	−	51.4717i	−0.775562	−	0.525222i
$99$		−	206.148i		−	2.08230i
$100$	7.42319	+	18.5714i	0.0742319	+	0.185714i
$101$	−143.160			−1.41743			−0.708715	−	0.705495i	$-0.750725\pi$
$101$	−143.160			−1.41743			−0.708715	+	0.705495i	$0.750725\pi$
$102$	−148.199	+	218.836i	−1.45293	+	2.14545i
$103$		−	23.4795i		−	0.227957i	−0.993483	−	0.113978i	$-0.963641\pi$
$103$		−	23.4795i		−	0.227957i	0.993483	−	0.113978i	$-0.0363594\pi$
$104$	1.92923	−	8.83398i	0.0185503	−	0.0849421i
$105$	23.1745			0.220710
$106$	95.0530	+	64.3713i	0.896727	+	0.607276i
$107$		−	25.3635i		−	0.237042i	−0.992952	−	0.118521i	$-0.962185\pi$
$107$		−	25.3635i		−	0.237042i	0.992952	−	0.118521i	$-0.0378152\pi$
$108$	363.078	−	145.127i	3.36184	−	1.34376i
$109$	92.6287			0.849805			0.424903	−	0.905239i	$-0.360308\pi$
$109$	92.6287			0.849805			0.424903	+	0.905239i	$0.360308\pi$
$110$	20.1817	−	29.8011i	0.183470	−	0.270919i
$111$		−	379.873i		−	3.42228i
$112$	19.4276	+	20.4193i	0.173461	+	0.182316i
$113$	−198.982			−1.76090			−0.880452	−	0.474136i	$-0.842761\pi$
$113$	−198.982			−1.76090			−0.880452	+	0.474136i	$0.842761\pi$
$114$	42.4685	+	28.7603i	0.372531	+	0.252283i
$115$			31.2847i			0.272041i
$116$	−43.1168	−	107.870i	−0.371697	−	0.929912i
$117$	−28.9517			−0.247451
$118$	78.2668	−	115.572i	0.663278	−	0.979421i
$119$			39.5662i			0.332489i
$120$	102.823	+	22.4552i	0.856856	+	0.187126i
$121$	56.2297			0.464708
$122$	−89.7911	−	60.8078i	−0.735992	−	0.498425i
$123$			301.351i			2.45001i
$124$	0.918807	−	0.367258i	0.00740973	−	0.00296176i
$125$	11.1803			0.0894427
$126$	50.6024	−	74.7214i	0.401606	−	0.593027i
$127$			230.167i			1.81234i	0.422917	+	0.906168i	$0.361006\pi$
$127$			230.167i			1.81234i	−0.422917	+	0.906168i	$0.638994\pi$
$128$	66.4126	+	109.423i	0.518849	+	0.854866i
$129$	383.514			2.97297
$130$	−4.18531	−	2.83435i	−0.0321947	−	0.0218027i
$131$		−	41.1020i		−	0.313756i	−0.987618	−	0.156878i	$-0.949857\pi$
$131$		−	41.1020i		−	0.313756i	0.987618	−	0.156878i	$-0.0501429\pi$
$132$	−70.2975	−	175.871i	−0.532557	−	1.33235i
$133$	7.67842			0.0577325
$134$	−3.13603	+	4.63077i	−0.0234032	+	0.0345580i
$135$		−	218.580i		−	1.61911i
$136$	−38.3381	+	175.551i	−0.281897	+	1.29081i
$137$	−102.801			−0.750369			−0.375185	−	0.926950i	$-0.622421\pi$
$137$	−102.801			−0.750369			−0.375185	+	0.926950i	$0.622421\pi$
$138$	136.313	+	92.3131i	0.987775	+	0.668936i
$139$		−	74.5720i		−	0.536489i	−0.963351	−	0.268245i	$-0.913556\pi$
$139$		−	74.5720i		−	0.536489i	0.963351	−	0.268245i	$-0.0864435\pi$
$140$	14.6303	−	5.84791i	0.104502	−	0.0417708i
$141$	−57.6469			−0.408843
$142$	83.3588	−	123.091i	0.587034	−	0.866836i
$143$			9.09643i			0.0636114i
$144$	296.919	−	282.498i	2.06194	−	1.96179i
$145$	−64.9398			−0.447861
$146$	10.4855	+	7.10093i	0.0718185	+	0.0486365i
$147$			270.032i			1.83695i
$148$	−95.8581	−	239.818i	−0.647690	−	1.62039i
$149$	137.541			0.923092			0.461546	−	0.887116i	$-0.347295\pi$
$149$	137.541			0.923092			0.461546	+	0.887116i	$0.347295\pi$
$150$	32.9903	−	48.7147i	0.219935	−	0.324765i
$151$			275.295i			1.82315i	0.411135	+	0.911574i	$0.365132\pi$
$151$			275.295i			1.82315i	−0.411135	+	0.911574i	$0.634868\pi$
$152$	34.0682	+	7.44008i	0.224133	+	0.0489479i
$153$	575.335			3.76036
$154$	−23.4770	−	15.8989i	−0.152448	−	0.103240i
$155$		−	0.553140i		−	0.00356865i
$156$	−24.6995	+	9.87268i	−0.158330	+	0.0632864i
$157$	205.161			1.30676			0.653378	−	0.757031i	$-0.273351\pi$
$157$	205.161			1.30676			0.653378	+	0.757031i	$0.273351\pi$
$158$	29.3760	−	43.3777i	0.185924	−	0.274543i
$159$		−	337.705i		−	2.12393i
$160$	70.5795	−	11.7703i	0.441122	−	0.0735644i
$161$	24.6458			0.153079
$162$	−570.631	−	386.439i	−3.52241	−	2.38543i
$163$			309.735i			1.90021i	0.311926	+	0.950106i	$0.399026\pi$
$163$			309.735i			1.90021i	−0.311926	+	0.950106i	$0.600974\pi$
$164$	76.0435	+	190.246i	0.463680	+	1.16004i
$165$	−105.878			−0.641682
$166$	−43.1873	+	63.7719i	−0.260164	+	0.384168i
$167$			281.208i			1.68388i	0.539573	+	0.841939i	$0.318586\pi$
$167$			281.208i			1.68388i	−0.539573	+	0.841939i	$0.681414\pi$
$168$	17.6899	−	81.0026i	0.105297	−	0.482158i
$169$	−167.722			−0.992441
$170$	83.1713	+	56.3248i	0.489243	+	0.331322i
$171$		−	111.652i		−	0.652938i
$172$	242.116	−	96.7767i	1.40765	−	0.562655i
$173$	−168.513			−0.974062			−0.487031	−	0.873385i	$-0.661920\pi$
$173$	−168.513			−0.974062			−0.487031	+	0.873385i	$0.661920\pi$
$174$	−191.620	+	282.954i	−1.10127	+	1.62617i
$175$		−	8.80775i		−	0.0503300i
$176$	−88.7591	−	93.2899i	−0.504313	−	0.530057i
$177$	−410.604			−2.31980
$178$	183.381	+	124.188i	1.03023	+	0.697685i
$179$			213.687i			1.19378i	0.802322	+	0.596892i	$0.203598\pi$
$179$			213.687i			1.19378i	−0.802322	+	0.596892i	$0.796402\pi$
$180$	−85.0348	−	212.740i	−0.472416	−	1.18189i
$181$	−194.746			−1.07594			−0.537972	−	0.842963i	$-0.680809\pi$
$181$	−194.746			−1.07594			−0.537972	+	0.842963i	$0.680809\pi$
$182$	−2.23287	+	3.29714i	−0.0122685	+	0.0181161i
$183$			319.011i			1.74323i
$184$	109.350	+	23.8807i	0.594295	+	0.129787i
$185$	−144.375			−0.780407
$186$	−2.41013	−	1.63217i	−0.0129577	−	0.00877512i
$187$		−	180.766i		−	0.966665i
$188$	−36.3931	+	14.5467i	−0.193580	+	0.0773763i
$189$	−172.195			−0.911085
$190$	10.9307	−	16.1406i	0.0575299	−	0.0849508i
$191$			130.576i			0.683643i	0.939765	+	0.341821i	$0.111044\pi$
$191$			130.576i			0.683643i	−0.939765	+	0.341821i	$0.888956\pi$
$192$	156.976	−	342.258i	0.817586	−	1.78259i
$193$	92.0503			0.476945			0.238472	−	0.971149i	$-0.423353\pi$
$193$	92.0503			0.476945			0.238472	+	0.971149i	$0.423353\pi$
$194$	−135.786	−	91.9559i	−0.699925	−	0.473999i
$195$			14.8696i			0.0762543i
$196$	68.1404	+	170.474i	0.347655	+	0.869765i
$197$	26.4924			0.134479			0.0672396	−	0.997737i	$-0.478581\pi$
$197$	26.4924			0.134479			0.0672396	+	0.997737i	$0.478581\pi$
$198$	−231.187	+	341.380i	−1.16761	+	1.72414i
$199$		−	7.89892i		−	0.0396931i	−0.999803	−	0.0198465i	$-0.993682\pi$
$199$		−	7.89892i		−	0.0396931i	0.999803	−	0.0198465i	$-0.00631776\pi$
$200$	8.53435	−	39.0790i	0.0426718	−	0.195395i
$201$	16.4523			0.0818520
$202$	237.073	+	160.549i	1.17363	+	0.794798i
$203$			51.1588i			0.252014i
$204$	490.834	−	196.192i	2.40605	−	0.961725i
$205$	114.532			0.558692
$206$	−26.3314	+	38.8820i	−0.127822	+	0.188747i
$207$		−	358.375i		−	1.73128i
$208$	−13.1018	+	12.4655i	−0.0629893	+	0.0599301i
$209$	−35.0804			−0.167849
$210$	−38.3769	−	25.9894i	−0.182747	−	0.123759i
$211$			142.264i			0.674236i	0.941462	+	0.337118i	$0.109452\pi$
$211$			142.264i			0.674236i	−0.941462	+	0.337118i	$0.890548\pi$
$212$	−85.2173	−	213.197i	−0.401968	−	1.00565i
$213$	−437.318			−2.05314
$214$	−28.4442	+	42.0018i	−0.132917	+	0.196270i
$215$		−	145.759i		−	0.677948i
$216$	−764.010	−	166.850i	−3.53708	−	0.772454i
$217$	−0.435758			−0.00200810
$218$	−153.393	−	103.880i	−0.703636	−	0.476513i
$219$		−	37.2530i		−	0.170105i
$220$	−66.8416	+	26.7174i	−0.303826	+	0.121443i
$221$	−25.3871			−0.114874
$222$	−426.014	+	629.068i	−1.91898	+	2.83364i
$223$		−	373.881i		−	1.67660i	−0.545212	−	0.838298i	$-0.683551\pi$
$223$		−	373.881i		−	1.67660i	0.545212	−	0.838298i	$-0.316449\pi$
$224$	−9.27251	−	55.6017i	−0.0413952	−	0.248222i
$225$	−128.074			−0.569218
$226$	329.513	+	223.151i	1.45802	+	0.987395i
$227$			3.64840i			0.0160722i	0.999968	+	0.00803611i	$0.00255800\pi$
$227$			3.64840i			0.0160722i	−0.999968	+	0.00803611i	$0.997442\pi$
$228$	−38.0740	−	95.2537i	−0.166991	−	0.417779i
$229$	51.6225			0.225426			0.112713	−	0.993628i	$-0.464046\pi$
$229$	51.6225			0.225426			0.112713	+	0.993628i	$0.464046\pi$
$230$	35.0847	−	51.8073i	0.152542	−	0.225249i
$231$			83.4092i			0.361079i
$232$	−49.5709	+	226.986i	−0.213668	+	0.978387i
$233$	202.831			0.870520			0.435260	−	0.900305i	$-0.356657\pi$
$233$	202.831			0.870520			0.435260	+	0.900305i	$0.356657\pi$
$234$	47.9439	+	32.4683i	0.204888	+	0.138753i
$235$			21.9094i			0.0932314i
$236$	−259.219	+	103.613i	−1.09838	+	0.439037i
$237$	−154.113			−0.650265
$238$	44.3721	−	65.5214i	0.186437	−	0.275300i
$239$		−	138.431i		−	0.579209i	−0.957146	−	0.289604i	$-0.906476\pi$
$239$		−	138.431i		−	0.579209i	0.957146	−	0.289604i	$-0.0935238\pi$
$240$	−145.091	−	152.498i	−0.604546	−	0.635406i
$241$	−18.2591			−0.0757639			−0.0378819	−	0.999282i	$-0.512061\pi$
$241$	−18.2591			−0.0757639			−0.0378819	+	0.999282i	$0.512061\pi$
$242$	−93.1161	−	63.0596i	−0.384777	−	0.260577i
$243$			1147.57i			4.72252i
$244$	80.4998	+	201.395i	0.329917	+	0.825389i
$245$	102.629			0.418893
$246$	337.954	−	499.035i	1.37380	−	2.02860i
$247$			4.92674i			0.0199463i
$248$	−1.93341	−	0.422232i	−0.00779599	−	0.00170255i
$249$	226.569			0.909917
$250$	−18.5146	−	12.5383i	−0.0740583	−	0.0501534i
$251$			339.167i			1.35126i	0.737239	+	0.675632i	$0.236129\pi$
$251$			339.167i			1.35126i	−0.737239	+	0.675632i	$0.763871\pi$
$252$	−167.595	+	66.9895i	−0.665058	+	0.265831i
$253$	−112.599			−0.445056
$254$	258.124	−	381.155i	1.01623	−	1.50061i
$255$		−	295.492i		−	1.15879i
$256$	12.7348	−	255.683i	0.0497451	−	0.998762i
$257$	167.240			0.650738			0.325369	−	0.945587i	$-0.394511\pi$
$257$	167.240			0.650738			0.325369	+	0.945587i	$0.394511\pi$
$258$	−635.097	−	430.097i	−2.46161	−	1.66704i
$259$			113.737i			0.439140i
$260$	3.75223	+	9.38734i	0.0144316	+	0.0361051i
$261$	743.904			2.85021
$262$	−46.0944	+	68.0648i	−0.175933	+	0.259789i
$263$		−	201.068i		−	0.764517i	−0.924055	−	0.382258i	$-0.875146\pi$
$263$		−	201.068i		−	0.764517i	0.924055	−	0.382258i	$-0.124854\pi$
$264$	−80.8201	+	370.077i	−0.306137	+	1.40181i
$265$	−128.349			−0.484335
$266$	−12.7154	−	8.61106i	−0.0478023	−	0.0323724i
$267$		−	651.516i		−	2.44014i
$268$	10.3865	−	4.15160i	0.0387556	−	0.0154910i
$269$	−315.593			−1.17321			−0.586603	−	0.809874i	$-0.699535\pi$
$269$	−315.593			−1.17321			−0.586603	+	0.809874i	$0.699535\pi$
$270$	−245.130	+	361.968i	−0.907888	+	1.34062i
$271$			506.702i			1.86975i	0.354977	+	0.934875i	$0.384489\pi$
$271$			506.702i			1.86975i	−0.354977	+	0.934875i	$0.615511\pi$
$272$	260.361	−	247.716i	0.957211	−	0.910722i
$273$	11.7141			0.0429088
$274$	170.237	+	115.287i	0.621304	+	0.420756i
$275$			40.2400i			0.146327i
$276$	−122.208	−	305.740i	−0.442782	−	1.10775i
$277$	−476.759			−1.72115			−0.860577	−	0.509321i	$-0.829897\pi$
$277$	−476.759			−1.72115			−0.860577	+	0.509321i	$0.829897\pi$
$278$	−83.6298	+	123.491i	−0.300826	+	0.444212i
$279$			6.33638i			0.0227110i
$280$	−30.7860	−	6.72327i	−0.109950	−	0.0240117i
$281$	−23.9703			−0.0853037			−0.0426519	−	0.999090i	$-0.513581\pi$
$281$	−23.9703			−0.0853037			−0.0426519	+	0.999090i	$0.513581\pi$
$282$	95.4630	+	64.6489i	0.338521	+	0.229251i
$283$			102.171i			0.361030i	0.983572	+	0.180515i	$0.0577764\pi$
$283$			102.171i			0.361030i	−0.983572	+	0.180515i	$0.942224\pi$
$284$	−276.084	+	110.354i	−0.972126	+	0.388570i
$285$	−57.3446			−0.201209
$286$	10.2013	−	15.0637i	0.0356690	−	0.0526701i
$287$		−	90.2270i		−	0.314380i
$288$	−808.508	+	134.832i	−2.80732	+	0.468167i
$289$	215.498			0.745666
$290$	107.540	+	72.8276i	0.370827	+	0.251130i
$291$			482.420i			1.65780i
$292$	−9.40050	−	23.5182i	−0.0321935	−	0.0805418i
$293$	−217.756			−0.743196			−0.371598	−	0.928394i	$-0.621190\pi$
$293$	−217.756			−0.743196			−0.371598	+	0.928394i	$0.621190\pi$
$294$	302.831	−	447.171i	1.03004	−	1.52099i
$295$			156.055i			0.529000i
$296$	−110.207	+	504.639i	−0.372320	+	1.70486i
$297$	786.709			2.64885
$298$	−227.767	−	154.247i	−0.764318	−	0.517607i
$299$			15.8136i			0.0528883i
$300$	−109.263	+	43.6739i	−0.364212	+	0.145580i
$301$	−114.827			−0.381486
$302$	308.734	−	455.888i	1.02230	−	1.50956i
$303$		−	842.275i		−	2.77978i
$304$	−48.0731	−	50.5270i	−0.158135	−	0.166207i
$305$	121.244			0.397520
$306$	−952.751	−	645.217i	−3.11357	−	2.10855i
$307$		−	491.015i		−	1.59940i	−0.600402	−	0.799698i	$-0.704993\pi$
$307$		−	491.015i		−	1.59940i	0.600402	−	0.799698i	$-0.295007\pi$
$308$	21.0477	+	52.6571i	0.0683365	+	0.170965i
$309$	138.140			0.447056
$310$	−0.620326	+	0.915997i	−0.00200105	+	0.00295483i
$311$		−	95.4478i		−	0.306906i	−0.988156	−	0.153453i	$-0.950961\pi$
$311$		−	95.4478i		−	0.306906i	0.988156	−	0.153453i	$-0.0490394\pi$
$312$	51.9741	+	11.3505i	0.166584	+	0.0363798i
$313$	264.306			0.844428			0.422214	−	0.906496i	$-0.361253\pi$
$313$	264.306			0.844428			0.422214	+	0.906496i	$0.361253\pi$
$314$	−339.745	−	230.080i	−1.08199	−	0.732740i
$315$			100.895i			0.320302i
$316$	−97.2931	+	38.8892i	−0.307889	+	0.123067i
$317$	−225.215			−0.710457			−0.355229	−	0.934779i	$-0.615597\pi$
$317$	−225.215			−0.710457			−0.355229	+	0.934779i	$0.615597\pi$
$318$	−378.724	+	559.238i	−1.19096	+	1.75861i
$319$		−	233.730i		−	0.732695i
$320$	−130.079	−	59.6607i	−0.406497	−	0.186440i
$321$	149.224			0.464873
$322$	−40.8132	−	27.6393i	−0.126749	−	0.0858364i
$323$		−	97.9053i		−	0.303112i
$324$	511.584	+	1279.88i	1.57896	+	3.95026i
$325$	5.65136			0.0173888
$326$	347.356	−	512.919i	1.06551	−	1.57337i
$327$			544.975i			1.66659i
$328$	87.4263	−	400.327i	0.266544	−	1.22051i
$329$	17.2600			0.0524619
$330$	175.333	+	118.738i	0.531311	+	0.359812i
$331$		−	117.922i		−	0.356259i	−0.984007	−	0.178129i	$-0.942995\pi$
$331$		−	117.922i		−	0.356259i	0.984007	−	0.178129i	$-0.0570046\pi$
$332$	143.036	−	57.1730i	0.430831	−	0.172208i
$333$	1653.86			4.96655
$334$	315.364	−	465.678i	0.944204	−	1.39425i
$335$		−	6.25287i		−	0.0186653i
$336$	−120.136	+	114.301i	−0.357547	+	0.340182i
$337$	218.426			0.648147			0.324074	−	0.946032i	$-0.394947\pi$
$337$	218.426			0.648147			0.324074	+	0.946032i	$0.394947\pi$
$338$	277.748	+	188.095i	0.821738	+	0.556493i
$339$		−	1170.70i		−	3.45339i
$340$	−74.5651	−	186.547i	−0.219309	−	0.548668i
$341$	1.99085			0.00583826
$342$	−125.214	+	184.896i	−0.366123	+	0.540631i
$343$		−	167.166i		−	0.487363i
$344$	−509.475	−	111.263i	−1.48103	−	0.323439i
$345$	−184.062			−0.533512
$346$	279.056	+	188.981i	0.806521	+	0.546188i
$347$			189.111i			0.544989i	0.962157	+	0.272495i	$0.0878487\pi$
$347$			189.111i			0.544989i	−0.962157	+	0.272495i	$0.912151\pi$
$348$	634.645	−	253.675i	1.82369	−	0.728951i
$349$	207.977			0.595922			0.297961	−	0.954578i	$-0.403693\pi$
$349$	207.977			0.595922			0.297961	+	0.954578i	$0.403693\pi$
$350$	−9.87757	+	14.5856i	−0.0282216	+	0.0416731i
$351$		−	110.487i		−	0.314776i
$352$	42.3634	+	254.028i	0.120351	+	0.721670i
$353$	533.523			1.51140			0.755698	−	0.654920i	$-0.227298\pi$
$353$	533.523			1.51140			0.755698	+	0.654920i	$0.227298\pi$
$354$	679.958	+	460.477i	1.92079	+	1.30078i
$355$			166.208i			0.468191i
$356$	−164.405	−	411.309i	−0.461812	−	1.15536i
$357$	−232.785			−0.652059
$358$	239.642	−	353.865i	0.669392	−	0.988449i
$359$		−	52.8610i		−	0.147245i	−0.997286	−	0.0736226i	$-0.976544\pi$
$359$		−	52.8610i		−	0.147245i	0.997286	−	0.0736226i	$-0.0234560\pi$
$360$	−97.7635	+	447.661i	−0.271565	+	1.24350i
$361$	−19.0000			−0.0526316
$362$	322.498	+	218.400i	0.890878	+	0.603316i
$363$			330.824i			0.911360i
$364$	7.39524	−	2.95596i	0.0203166	−	0.00812078i
$365$	−14.1584			−0.0387902
$366$	357.759	−	528.280i	0.977483	−	1.44339i
$367$		−	44.8938i		−	0.122326i	−0.998128	−	0.0611632i	$-0.980519\pi$
$367$		−	44.8938i		−	0.122326i	0.998128	−	0.0611632i	$-0.0194810\pi$
$368$	−154.302	−	162.179i	−0.419300	−	0.440703i
$369$	−1312.00			−3.55554
$370$	239.085	+	161.912i	0.646175	+	0.437599i
$371$			101.112i			0.272539i
$372$	2.16074	+	5.40574i	0.00580843	+	0.0145316i
$373$	−19.7572			−0.0529684			−0.0264842	−	0.999649i	$-0.508431\pi$
$373$	−19.7572			−0.0529684			−0.0264842	+	0.999649i	$0.508431\pi$
$374$	−202.723	+	299.348i	−0.542040	+	0.800396i
$375$			65.7788i			0.175410i
$376$	76.5805	+	16.7242i	0.203671	+	0.0444793i
$377$	−32.8253			−0.0870698
$378$	285.154	+	193.111i	0.754376	+	0.510874i
$379$		−	704.326i		−	1.85838i	−0.369602	−	0.929190i	$-0.620506\pi$
$379$		−	704.326i		−	1.85838i	0.369602	−	0.929190i	$-0.379494\pi$
$380$	−36.2023	+	14.4705i	−0.0952692	+	0.0380802i
$381$	−1354.17			−3.55425
$382$	146.436	−	216.233i	0.383340	−	0.566055i
$383$			205.995i			0.537846i	0.963162	+	0.268923i	$0.0866677\pi$
$383$			205.995i			0.537846i	−0.963162	+	0.268923i	$0.913332\pi$
$384$	−643.782	+	390.734i	−1.67652	+	1.01754i
$385$	31.7006			0.0823393
$386$	−152.435	−	103.231i	−0.394909	−	0.267438i
$387$			1669.71i			4.31449i
$388$	121.735	+	304.557i	0.313750	+	0.784941i
$389$	252.421			0.648898			0.324449	−	0.945903i	$-0.394821\pi$
$389$	252.421			0.648898			0.324449	+	0.945903i	$0.394821\pi$
$390$	16.6757	−	24.6240i	0.0427582	−	0.0631384i
$391$		−	314.251i		−	0.803711i
$392$	78.3401	−	358.721i	0.199847	−	0.915104i
$393$	241.821			0.615321
$394$	−43.8713	−	29.7103i	−0.111348	−	0.0754067i
$395$			58.5724i			0.148284i
$396$	765.690	−	306.055i	1.93356	−	0.772867i
$397$	−143.596			−0.361702			−0.180851	−	0.983510i	$-0.557885\pi$
$397$	−143.596			−0.361702			−0.180851	+	0.983510i	$0.557885\pi$
$398$	−8.85835	+	13.0806i	−0.0222572	+	0.0328658i
$399$			45.1755i			0.113222i
$400$	−57.9585	+	55.1436i	−0.144896	+	0.137859i
$401$	−617.139			−1.53900			−0.769499	−	0.638647i	$-0.779494\pi$
$401$	−617.139			−1.53900			−0.769499	+	0.638647i	$0.779494\pi$
$402$	−27.2449	−	18.4506i	−0.0677733	−	0.0458970i
$403$		−	0.279598i		−	0.000693790i
$404$	−212.541	−	531.737i	−0.526093	−	1.31618i
$405$	770.515			1.90251
$406$	57.3728	−	84.7188i	0.141312	−	0.208667i
$407$		−	519.632i		−	1.27674i
$408$	−1032.84	−	225.559i	−2.53147	−	0.552842i
$409$	−578.155			−1.41358			−0.706791	−	0.707422i	$-0.749858\pi$
$409$	−578.155			−1.41358			−0.706791	+	0.707422i	$0.749858\pi$
$410$	−189.664	−	128.443i	−0.462596	−	0.313276i
$411$		−	604.820i		−	1.47158i
$412$	87.2094	−	34.8586i	0.211673	−	0.0846083i
$413$	122.938			0.297671
$414$	−401.905	+	593.468i	−0.970785	+	1.43350i
$415$		−	86.1104i		−	0.207495i
$416$	35.6760	−	5.94957i	0.0857597	−	0.0143019i
$417$	438.739			1.05213
$418$	58.0930	+	39.3414i	0.138978	+	0.0941182i
$419$			479.447i			1.14426i	0.820162	+	0.572132i	$0.193883\pi$
$419$			479.447i			1.14426i	−0.820162	+	0.572132i	$0.806117\pi$
$420$	34.4058	+	86.0766i	0.0819186	+	0.204944i
$421$	620.126			1.47298			0.736491	−	0.676447i	$-0.236481\pi$
$421$	620.126			1.47298			0.736491	+	0.676447i	$0.236481\pi$
$422$	159.544	−	235.588i	0.378065	−	0.558265i
$423$		−	250.978i		−	0.593329i
$424$	−97.9733	+	448.621i	−0.231069	+	1.05807i
$425$	−112.305			−0.264247
$426$	724.196	+	490.436i	1.69999	+	1.15126i
$427$		−	95.5144i		−	0.223687i
$428$	94.2069	−	37.6556i	0.220110	−	0.0879803i
$429$	−53.5183			−0.124751
$430$	−163.463	+	241.376i	−0.380147	+	0.561339i
$431$			174.363i			0.404556i	0.979328	+	0.202278i	$0.0648344\pi$
$431$			174.363i			0.404556i	−0.979328	+	0.202278i	$0.935166\pi$
$432$	1078.08	+	1133.11i	2.49556	+	2.62294i
$433$	38.8589			0.0897433			0.0448717	−	0.998993i	$-0.485712\pi$
$433$	38.8589			0.0897433			0.0448717	+	0.998993i	$0.485712\pi$
$434$	0.721612	+	0.488686i	0.00166270	+	0.00112601i
$435$		−	382.069i		−	0.878320i
$436$	137.520	+	344.049i	0.315413	+	0.789103i
$437$	−60.9851			−0.139554
$438$	−41.7778	+	61.6907i	−0.0953832	+	0.140846i
$439$			540.084i			1.23026i	0.788426	+	0.615130i	$0.210896\pi$
$439$			540.084i			1.23026i	−0.788426	+	0.615130i	$0.789104\pi$
$440$	140.652	+	30.7166i	0.319664	+	0.0698105i
$441$	−1175.64			−2.66585
$442$	42.0409	+	28.4707i	0.0951151	+	0.0644133i
$443$			58.1362i			0.131233i	0.997845	+	0.0656165i	$0.0209014\pi$
$443$			58.1362i			0.131233i	−0.997845	+	0.0656165i	$0.979099\pi$
$444$	1410.95	−	563.975i	3.17783	−	1.27021i
$445$	−247.616			−0.556441
$446$	−419.294	+	619.145i	−0.940121	+	1.38822i
$447$			809.212i			1.81032i
$448$	−47.0001	+	102.475i	−0.104911	+	0.228739i
$449$	720.386			1.60442			0.802212	−	0.597040i	$-0.203657\pi$
$449$	720.386			1.60442			0.802212	+	0.597040i	$0.203657\pi$
$450$	212.090	+	143.630i	0.471311	+	0.319178i
$451$			412.220i			0.914014i
$452$	−295.417	−	739.074i	−0.653577	−	1.63512i
$453$	−1619.68			−3.57546
$454$	4.09154	−	6.04172i	0.00901221	−	0.0133078i
$455$		−	4.45208i		−	0.00978480i
$456$	−43.7732	+	200.438i	−0.0959939	+	0.439558i
$457$	−191.938			−0.419996			−0.209998	−	0.977702i	$-0.567346\pi$
$457$	−191.938			−0.419996			−0.209998	+	0.977702i	$0.567346\pi$
$458$	−85.4866	−	57.8927i	−0.186652	−	0.126403i
$459$			2195.61i			4.78347i
$460$	−116.200	+	46.4465i	−0.252609	+	0.100971i
$461$	781.991			1.69629			0.848146	−	0.529762i	$-0.177719\pi$
$461$	781.991			1.69629			0.848146	+	0.529762i	$0.177719\pi$
$462$	93.5403	−	138.125i	0.202468	−	0.298972i
$463$		−	667.295i		−	1.44124i	−0.693330	−	0.720620i	$-0.743857\pi$
$463$		−	667.295i		−	1.44124i	0.693330	−	0.720620i	$-0.256143\pi$
$464$	336.645	−	320.296i	0.725529	−	0.690292i
$465$	3.25436			0.00699863
$466$	−335.887	−	227.468i	−0.720788	−	0.488128i
$467$			195.230i			0.418051i	0.977910	+	0.209026i	$0.0670292\pi$
$467$			195.230i			0.418051i	−0.977910	+	0.209026i	$0.932971\pi$
$468$	−42.9828	−	107.535i	−0.0918437	−	0.229775i
$469$	−4.92594			−0.0105031
$470$	24.5706	−	36.2818i	0.0522778	−	0.0771954i
$471$			1207.05i			2.56274i
$472$	545.463	+	119.122i	1.15564	+	0.252378i
$473$	524.611			1.10912
$474$	255.210	+	172.832i	0.538418	+	0.364624i
$475$			21.7945i			0.0458831i
$476$	−146.960	+	58.7415i	−0.308739	+	0.123407i
$477$	1470.27			3.08233
$478$	−155.245	+	229.241i	−0.324781	+	0.479584i
$479$		−	488.518i		−	1.01987i	−0.860213	−	0.509935i	$-0.829670\pi$
$479$		−	488.518i		−	1.01987i	0.860213	−	0.509935i	$-0.170330\pi$
$480$	69.2498	+	415.250i	0.144270	+	0.865103i
$481$	−72.9779			−0.151721
$482$	30.2370	+	20.4769i	0.0627323	+	0.0424832i
$483$			145.002i			0.300211i
$484$	83.4808	+	208.853i	0.172481	+	0.431514i
$485$	183.349			0.378040
$486$	1286.96	−	1900.37i	2.64807	−	3.91024i
$487$			89.0019i			0.182755i	0.995816	+	0.0913777i	$0.0291271\pi$
$487$			89.0019i			0.182755i	−0.995816	+	0.0913777i	$0.970873\pi$
$488$	92.5496	−	423.786i	0.189651	−	0.868415i
$489$	−1822.30			−3.72659
$490$	−169.953	−	115.094i	−0.346842	−	0.234886i
$491$		−	0.930138i		−	0.00189437i	−1.00000		0.000947187i	$-0.999699\pi$
$491$		−	0.930138i		−	0.00189437i	1.00000		0.000947187i	$-0.000301499\pi$
$492$	−1119.30	+	447.397i	−2.27500	+	0.909344i
$493$	652.312			1.32315
$494$	5.52516	−	8.15866i	0.0111845	−	0.0165155i
$495$		−	460.961i		−	0.931234i
$496$	2.72819	+	2.86746i	0.00550039	+	0.00578116i
$497$	130.937			0.263454
$498$	−375.198	−	254.089i	−0.753409	−	0.510220i
$499$		−	634.634i		−	1.27181i	−0.771767	−	0.635906i	$-0.780627\pi$
$499$		−	634.634i		−	1.27181i	0.771767	−	0.635906i	$-0.219373\pi$
$500$	16.5988	+	41.5269i	0.0331975	+	0.0830537i
$501$	−1654.47			−3.30233
$502$	380.364	−	561.659i	0.757697	−	1.11884i
$503$			532.444i			1.05854i	0.848454	+	0.529269i	$0.177534\pi$
$503$			532.444i			1.05854i	−0.848454	+	0.529269i	$0.822466\pi$
$504$	352.662	+	77.0170i	0.699726	+	0.152811i
$505$	−320.116			−0.633894
$506$	186.464	+	126.276i	0.368505	+	0.249557i
$507$		−	986.784i		−	1.94632i
$508$	−854.903	+	341.714i	−1.68288	+	0.672666i
$509$	99.3964			0.195278			0.0976389	−	0.995222i	$-0.468871\pi$
$509$	99.3964			0.195278			0.0976389	+	0.995222i	$0.468871\pi$
$510$	−331.383	+	489.333i	−0.649771	+	0.959476i
$511$			11.1539i			0.0218275i
$512$	−307.828	+	409.128i	−0.601226	+	0.799079i
$513$	426.091			0.830588
$514$	−276.948	−	187.553i	−0.538810	−	0.364890i
$515$		−	52.5018i		−	0.101945i
$516$	569.379	+	1424.48i	1.10345	+	2.76061i
$517$	−78.8557			−0.152525
$518$	127.552	−	188.348i	0.246240	−	0.363607i
$519$		−	991.434i		−	1.91028i
$520$	4.31389	−	19.7534i	0.00829594	−	0.0379873i
$521$	−159.278			−0.305716			−0.152858	−	0.988248i	$-0.548848\pi$
$521$	−159.278			−0.305716			−0.152858	+	0.988248i	$0.548848\pi$
$522$	−1231.90	−	834.261i	−2.35996	−	1.59820i
$523$		−	340.189i		−	0.650456i	−0.945636	−	0.325228i	$-0.894559\pi$
$523$		−	340.189i		−	0.650456i	0.945636	−	0.325228i	$-0.105441\pi$
$524$	152.664	−	61.0217i	0.291344	−	0.116454i
$525$	51.8198			0.0987044
$526$	−225.490	+	332.968i	−0.428689	+	0.633018i
$527$			5.55622i			0.0105431i
$528$	548.865	−	522.208i	1.03952	−	0.989031i
$529$	333.253			0.629968
$530$	212.545	+	143.939i	0.401028	+	0.271582i
$531$		−	1787.65i		−	3.36658i
$532$	11.3997	+	28.5198i	0.0214280	+	0.0536086i
$533$	57.8928			0.108617
$534$	−730.652	+	1078.91i	−1.36826	+	2.02043i
$535$		−	56.7144i		−	0.106008i
$536$	−21.8558	−	4.77304i	−0.0407758	−	0.00890493i
$537$	−1257.21			−2.34118
$538$	522.620	+	353.926i	0.971412	+	0.657854i
$539$			369.379i			0.685303i
$540$	811.868	−	324.513i	1.50346	−	0.600950i
$541$	757.112			1.39947			0.699734	−	0.714404i	$-0.253302\pi$
$541$	757.112			1.39947			0.699734	+	0.714404i	$0.253302\pi$
$542$	568.248	−	839.097i	1.04843	−	1.54815i
$543$		−	1145.77i		−	2.11008i
$544$	−708.962	+	118.231i	−1.30324	+	0.217337i
$545$	207.124			0.380044
$546$	−19.3985	−	13.1369i	−0.0355284	−	0.0240603i
$547$			530.960i			0.970677i	0.874326	+	0.485338i	$0.161304\pi$
$547$			530.960i			0.970677i	−0.874326	+	0.485338i	$0.838696\pi$
$548$	−152.622	−	381.830i	−0.278507	−	0.696770i
$549$	−1388.88			−2.52984
$550$	45.1277	−	66.6372i	0.0820503	−	0.121159i
$551$		−	126.591i		−	0.229748i
$552$	−140.501	+	643.356i	−0.254530	+	1.16550i
$553$	46.1427			0.0834406
$554$	789.511	+	534.668i	1.42511	+	0.965105i
$555$		−	849.423i		−	1.53049i
$556$	276.981	−	110.712i	0.498167	−	0.199123i
$557$	−648.534			−1.16433			−0.582167	−	0.813069i	$-0.697795\pi$
$557$	−648.534			−1.16433			−0.582167	+	0.813069i	$0.697795\pi$
$558$	7.10602	−	10.4930i	0.0127348	−	0.0188047i
$559$		−	73.6772i		−	0.131802i
$560$	43.4415	+	45.6590i	0.0775741	+	0.0815340i
$561$	1063.53			1.89577
$562$	39.6948	+	26.8819i	0.0706313	+	0.0478325i
$563$		−	601.133i		−	1.06773i	−0.845569	−	0.533866i	$-0.820739\pi$
$563$		−	601.133i		−	1.06773i	0.845569	−	0.533866i	$-0.179261\pi$
$564$	−85.5848	−	214.117i	−0.151746	−	0.379639i
$565$	−444.937			−0.787500
$566$	114.581	−	169.195i	0.202441	−	0.298932i
$567$		−	607.003i		−	1.07055i
$568$	580.951	+	126.872i	1.02280	+	0.223367i
$569$	−99.1099			−0.174183			−0.0870913	−	0.996200i	$-0.527757\pi$
$569$	−99.1099			−0.174183			−0.0870913	+	0.996200i	$0.527757\pi$
$570$	94.9624	+	64.3099i	0.166601	+	0.112824i
$571$		−	467.315i		−	0.818415i	−0.912441	−	0.409207i	$-0.865805\pi$
$571$		−	467.315i		−	0.818415i	0.912441	−	0.409207i	$-0.134195\pi$
$572$	−33.7867	+	13.5049i	−0.0590676	+	0.0236100i
$573$	−768.234			−1.34072
$574$	−101.186	+	149.415i	−0.176283	+	0.260306i
$575$			69.9548i			0.121660i
$576$	1490.09	+	683.431i	2.58697	+	1.18651i
$577$	356.617			0.618053			0.309027	−	0.951053i	$-0.399997\pi$
$577$	356.617			0.618053			0.309027	+	0.951053i	$0.399997\pi$
$578$	−356.863	−	241.673i	−0.617410	−	0.418119i
$579$			541.572i			0.935358i
$580$	−96.4121	−	241.204i	−0.166228	−	0.415870i
$581$	−67.8368			−0.116759
$582$	541.016	−	798.885i	0.929582	−	1.37265i
$583$		−	461.950i		−	0.792367i
$584$	−10.8076	+	49.4883i	−0.0185062	+	0.0847403i
$585$	−64.7380			−0.110663
$586$	360.603	+	244.206i	0.615364	+	0.416733i
$587$		−	535.079i		−	0.911549i	−0.890095	−	0.455774i	$-0.849362\pi$
$587$		−	535.079i		−	0.911549i	0.890095	−	0.455774i	$-0.150638\pi$
$588$	−1002.97	+	400.900i	−1.70573	+	0.681802i
$589$	1.07827			0.00183068
$590$	175.010	−	258.426i	0.296627	−	0.438010i
$591$			155.866i			0.263733i
$592$	748.436	−	712.087i	1.26425	−	1.20285i
$593$	469.429			0.791617			0.395809	−	0.918333i	$-0.370464\pi$
$593$	469.429			0.791617			0.395809	+	0.918333i	$0.370464\pi$
$594$	−1302.79	−	882.265i	−2.19324	−	1.48529i
$595$			88.4727i			0.148694i
$596$	204.198	+	510.864i	0.342615	+	0.857155i
$597$	46.4728			0.0778439
$598$	17.7344	−	26.1872i	0.0296561	−	0.0437914i
$599$			149.813i			0.250106i	0.992150	+	0.125053i	$0.0399101\pi$
$599$			149.813i			0.250106i	−0.992150	+	0.125053i	$0.960090\pi$
$600$	229.918	+	50.2113i	0.383197	+	0.0836855i
$601$	841.554			1.40026			0.700129	−	0.714017i	$-0.253126\pi$
$601$	841.554			1.40026			0.700129	+	0.714017i	$0.253126\pi$
$602$	190.153	+	128.775i	0.315869	+	0.213911i
$603$			71.6284i			0.118787i
$604$	−1022.52	+	408.714i	−1.69292	+	0.676679i
$605$	125.733			0.207824
$606$	−944.580	+	1394.80i	−1.55871	+	2.30165i
$607$			731.706i			1.20545i	0.797950	+	0.602723i	$0.205918\pi$
$607$			731.706i			1.20545i	−0.797950	+	0.602723i	$0.794082\pi$
$608$	22.9445	+	137.585i	0.0377377	+	0.226291i
$609$	−300.990			−0.494236
$610$	−200.779	−	135.970i	−0.329146	−	0.222902i
$611$			11.0746i			0.0181254i
$612$	854.164	+	2136.95i	1.39569	+	3.49175i
$613$	−227.734			−0.371507			−0.185754	−	0.982596i	$-0.559473\pi$
$613$	−227.734			−0.371507			−0.185754	+	0.982596i	$0.559473\pi$
$614$	−550.655	+	813.118i	−0.896832	+	1.32430i
$615$			673.841i			1.09568i
$616$	24.1982	−	110.804i	0.0392828	−	0.179877i
$617$	321.186			0.520561			0.260280	−	0.965533i	$-0.416185\pi$
$617$	321.186			0.520561			0.260280	+	0.965533i	$0.416185\pi$
$618$	−228.760	−	154.919i	−0.370161	−	0.250678i
$619$		−	168.858i		−	0.272792i	−0.990654	−	0.136396i	$-0.956448\pi$
$619$		−	168.858i		−	0.272792i	0.990654	−	0.136396i	$-0.0435519\pi$
$620$	2.05451	−	0.821213i	0.00331373	−	0.00132454i
$621$	1367.64			2.20233
$622$	−107.041	+	158.061i	−0.172092	+	0.254117i
$623$			195.069i			0.313113i
$624$	−73.3397	−	77.0834i	−0.117532	−	0.123531i
$625$	25.0000			0.0400000
$626$	−437.689	−	296.409i	−0.699184	−	0.473497i
$627$		−	206.393i		−	0.329176i
$628$	304.590	+	762.024i	0.485016	+	1.21341i
$629$	1450.23			2.30562
$630$	113.150	−	167.082i	0.179604	−	0.265210i
$631$		−	220.418i		−	0.349316i	−0.984629	−	0.174658i	$-0.944118\pi$
$631$		−	220.418i		−	0.349316i	0.984629	−	0.174658i	$-0.0558819\pi$
$632$	204.730	+	44.7104i	0.323939	+	0.0707443i
$633$	−836.999			−1.32227
$634$	372.955	+	252.570i	0.588257	+	0.398376i
$635$			514.668i			0.810502i
$636$	1254.33	−	501.370i	1.97222	−	0.788318i
$637$	51.8761			0.0814381
$638$	−262.119	+	387.055i	−0.410845	+	0.606670i
$639$		−	1903.96i		−	2.97959i
$640$	148.503	+	244.677i	0.232036	+	0.382308i
$641$	−736.161			−1.14846			−0.574229	−	0.818695i	$-0.694698\pi$
$641$	−736.161			−1.14846			−0.574229	+	0.818695i	$0.694698\pi$
$642$	−247.115	−	167.350i	−0.384914	−	0.260669i
$643$			823.619i			1.28090i	0.768000	+	0.640450i	$0.221252\pi$
$643$			823.619i			1.28090i	−0.768000	+	0.640450i	$0.778748\pi$
$644$	36.5900	+	91.5411i	0.0568168	+	0.142145i
$645$	857.562			1.32955
$646$	−109.797	+	162.131i	−0.169965	+	0.250976i
$647$			137.351i			0.212289i	0.994351	+	0.106145i	$0.0338506\pi$
$647$			137.351i			0.212289i	−0.994351	+	0.106145i	$0.966149\pi$
$648$	588.161	−	2693.20i	0.907657	−	4.15618i
$649$	−561.669			−0.865437
$650$	−9.35863	−	6.33780i	−0.0143979	−	0.00975046i
$651$		−	2.56375i		−	0.00393817i
$652$	−1150.44	+	459.844i	−1.76448	+	0.705282i
$653$	1220.60			1.86922			0.934608	−	0.355680i	$-0.115751\pi$
$653$	1220.60			1.86922			0.934608	+	0.355680i	$0.115751\pi$
$654$	611.170	−	902.476i	0.934510	−	1.37993i
$655$		−	91.9069i		−	0.140316i
$656$	−593.729	+	564.893i	−0.905075	+	0.861118i
$657$	162.189			0.246863
$658$	−28.5824	−	19.3564i	−0.0434383	−	0.0294171i
$659$		−	586.759i		−	0.890377i	−0.895437	−	0.445189i	$-0.853137\pi$
$659$		−	586.759i		−	0.890377i	0.895437	−	0.445189i	$-0.146863\pi$
$660$	−157.190	−	393.258i	−0.238167	−	0.595846i
$661$	−280.889			−0.424946			−0.212473	−	0.977167i	$-0.568152\pi$
$661$	−280.889			−0.424946			−0.212473	+	0.977167i	$0.568152\pi$
$662$	−132.245	+	195.278i	−0.199766	+	0.294982i
$663$		−	149.363i		−	0.225284i
$664$	−300.984	−	65.7311i	−0.453289	−	0.0989927i
$665$	17.1695			0.0258187
$666$	−2738.78	−	1854.74i	−4.11229	−	2.78490i
$667$		−	406.325i		−	0.609182i
$668$	−1044.48	+	417.492i	−1.56360	+	0.624988i
$669$	2199.70			3.28805
$670$	−7.01237	+	10.3547i	−0.0104662	+	0.0154548i
$671$			436.377i			0.650339i
$672$	327.129	−	54.5542i	0.486799	−	0.0811819i
$673$	901.867			1.34007			0.670035	−	0.742330i	$-0.266279\pi$
$673$	901.867			1.34007			0.670035	+	0.742330i	$0.266279\pi$
$674$	−361.712	−	244.956i	−0.536664	−	0.363437i
$675$		−	488.760i		−	0.724089i
$676$	−249.007	−	622.968i	−0.368354	−	0.921550i
$677$	365.860			0.540414			0.270207	−	0.962802i	$-0.412908\pi$
$677$	365.860			0.540414			0.270207	+	0.962802i	$0.412908\pi$
$678$	−1312.90	+	1938.67i	−1.93642	+	2.85940i
$679$		−	144.441i		−	0.212725i
$680$	−85.7265	+	392.543i	−0.126068	+	0.577269i
$681$	−21.4651			−0.0315200
$682$	−3.29683	−	2.23266i	−0.00483407	−	0.00327370i
$683$			1159.51i			1.69767i	0.528661	+	0.848833i	$0.322694\pi$
$683$			1159.51i			1.69767i	−0.528661	+	0.848833i	$0.677306\pi$
$684$	414.708	−	165.763i	0.606298	−	0.242344i
$685$	−229.869			−0.335575
$686$	−187.470	+	276.826i	−0.273280	+	0.403536i
$687$			303.717i			0.442092i
$688$	718.911	+	755.608i	1.04493	+	1.09827i
$689$	−64.8769			−0.0941610
$690$	304.805	+	206.418i	0.441746	+	0.299157i
$691$			607.193i			0.878717i	0.898312	+	0.439358i	$0.144794\pi$
$691$			607.193i			0.878717i	−0.898312	+	0.439358i	$0.855206\pi$
$692$	−250.181	−	625.903i	−0.361533	−	0.904484i
$693$	−363.140			−0.524011
$694$	212.081	−	313.167i	0.305593	−	0.451250i
$695$		−	166.748i		−	0.239925i
$696$	−1335.46	−	291.647i	−1.91876	−	0.419033i
$697$	−1150.46			−1.65059
$698$	−344.409	−	233.238i	−0.493422	−	0.334153i
$699$			1193.34i			1.70722i
$700$	32.7144	−	13.0763i	0.0467349	−	0.0186805i
$701$	−219.331			−0.312883			−0.156442	−	0.987687i	$-0.550002\pi$
$701$	−219.331			−0.312883			−0.156442	+	0.987687i	$0.550002\pi$
$702$	−123.907	+	182.965i	−0.176505	+	0.260634i
$703$		−	281.439i		−	0.400340i
$704$	214.729	−	468.178i	0.305013	−	0.665025i
$705$	−128.902			−0.182840
$706$	−883.511	−	598.326i	−1.25143	−	0.847488i
$707$			252.184i			0.356696i
$708$	−609.599	−	1525.10i	−0.861015	−	2.15409i
$709$	−83.3555			−0.117568			−0.0587839	−	0.998271i	$-0.518722\pi$
$709$	−83.3555			−0.117568			−0.0587839	+	0.998271i	$0.518722\pi$
$710$	186.396	−	275.239i	0.262530	−	0.387661i
$711$		−	670.963i		−	0.943689i
$712$	−189.014	+	865.501i	−0.265470	+	1.21559i
$713$	3.46097			0.00485409
$714$	385.491	+	261.060i	0.539903	+	0.365630i
$715$			20.3402i			0.0284479i
$716$	−793.693	+	317.248i	−1.10851	+	0.443084i
$717$	814.449			1.13591
$718$	−59.2817	+	87.5375i	−0.0825650	+	0.121919i
$719$		−	969.586i		−	1.34852i	−0.738494	−	0.674260i	$-0.764463\pi$
$719$		−	969.586i		−	1.34852i	0.738494	−	0.674260i	$-0.235537\pi$
$720$	663.931	−	631.686i	0.922126	−	0.877341i
$721$	−41.3603			−0.0573652
$722$	31.4639	+	21.3078i	0.0435788	+	0.0295122i
$723$		−	107.426i		−	0.148584i
$724$	−289.127	−	723.339i	−0.399347	−	0.999088i
$725$	−145.210			−0.200289
$726$	371.007	−	547.843i	0.511029	−	0.754604i
$727$		−	1135.95i		−	1.56251i	−0.624211	−	0.781256i	$-0.714579\pi$
$727$		−	1135.95i		−	1.56251i	0.624211	−	0.781256i	$-0.285421\pi$
$728$	−15.5615	−	3.39843i	−0.0213757	−	0.00466818i
$729$	−3650.41			−5.00742
$730$	23.4463	+	15.8782i	0.0321182	+	0.0217509i
$731$			1464.13i			2.00291i
$732$	−1184.89	+	473.616i	−1.61871	+	0.647016i
$733$	−910.594			−1.24228			−0.621142	−	0.783698i	$-0.713331\pi$
$733$	−910.594			−1.24228			−0.621142	+	0.783698i	$0.713331\pi$
$734$	−50.3468	+	74.3439i	−0.0685923	+	0.101286i
$735$			603.809i			0.821509i
$736$	73.6461	+	441.612i	0.100063	+	0.600016i
$737$	22.5052			0.0305362
$738$	2172.66	+	1471.36i	2.94398	+	1.99371i
$739$		−	946.424i		−	1.28068i	−0.768091	−	0.640341i	$-0.778793\pi$
$739$		−	946.424i		−	1.28068i	0.768091	−	0.640341i	$-0.221207\pi$
$740$	−214.345	−	536.250i	−0.289656	−	0.724662i
$741$	−28.9862			−0.0391176
$742$	113.393	−	167.441i	0.152821	−	0.225661i
$743$			878.156i			1.18191i	0.806706	+	0.590953i	$0.201248\pi$
$743$			878.156i			1.18191i	−0.806706	+	0.590953i	$0.798752\pi$
$744$	2.48417	−	11.3751i	0.00333894	−	0.0152891i
$745$	307.551			0.412819
$746$	32.7179	+	22.1570i	0.0438577	+	0.0297011i
$747$			986.419i			1.32051i
$748$	671.416	−	268.373i	0.897615	−	0.358787i
$749$	−44.6790			−0.0596515
$750$	73.7685	−	108.929i	0.0983580	−	0.145239i
$751$		−	439.458i		−	0.585163i	−0.956241	−	0.292582i	$-0.905486\pi$
$751$		−	439.458i		−	0.585163i	0.956241	−	0.292582i	$-0.0945144\pi$
$752$	−108.061	−	113.577i	−0.143699	−	0.151034i
$753$	−1995.47			−2.65002
$754$	54.3586	+	36.8124i	0.0720936	+	0.0488228i
$755$			615.579i			0.815337i
$756$	−255.648	−	639.580i	−0.338158	−	0.846006i
$757$	−28.8784			−0.0381485			−0.0190742	−	0.999818i	$-0.506072\pi$
$757$	−28.8784			−0.0381485			−0.0190742	+	0.999818i	$0.506072\pi$
$758$	−789.876	+	1166.36i	−1.04205	+	1.53873i
$759$		−	662.470i		−	0.872819i
$760$	76.1789	+	16.6365i	0.100235	+	0.0218902i
$761$	−283.601			−0.372668			−0.186334	−	0.982486i	$-0.559661\pi$
$761$	−283.601			−0.372668			−0.186334	+	0.982486i	$0.559661\pi$
$762$	2242.50	+	1518.65i	2.94291	+	1.99298i
$763$		−	163.170i		−	0.213853i
$764$	−484.994	+	193.858i	−0.634810	+	0.253741i
$765$	1286.49			1.68168
$766$	231.016	−	341.127i	0.301587	−	0.445335i
$767$			78.8816i			0.102844i
$768$	1504.29	+	74.9241i	1.95872	+	0.0975574i
$769$	−523.314			−0.680512			−0.340256	−	0.940333i	$-0.610514\pi$
$769$	−523.314			−0.680512			−0.340256	+	0.940333i	$0.610514\pi$
$770$	−52.4961	−	35.5511i	−0.0681767	−	0.0461703i
$771$			983.944i			1.27619i
$772$	136.661	+	341.900i	0.177023	+	0.442876i
$773$	417.361			0.539924			0.269962	−	0.962871i	$-0.412989\pi$
$773$	417.361			0.539924			0.269962	+	0.962871i	$0.412989\pi$
$774$	1872.52	−	2765.03i	2.41927	−	3.57239i
$775$		−	1.23686i		−	0.00159595i
$776$	139.957	−	640.866i	0.180357	−	0.825859i
$777$	−669.166			−0.861217
$778$	−418.009	−	283.081i	−0.537286	−	0.363858i
$779$			223.264i			0.286603i
$780$	−55.2298	+	22.0760i	−0.0708074	+	0.0283025i
$781$	−598.211			−0.765955
$782$	−352.421	+	520.398i	−0.450666	+	0.665471i
$783$			2838.91i			3.62569i
$784$	−532.023	+	506.184i	−0.678601	+	0.645643i
$785$	458.754			0.584399
$786$	−400.455	−	271.194i	−0.509484	−	0.345030i
$787$			117.028i			0.148702i	0.997232	+	0.0743509i	$0.0236885\pi$
$787$			117.028i			0.148702i	−0.997232	+	0.0743509i	$0.976312\pi$
$788$	39.3316	+	98.4001i	0.0499132	+	0.124873i
$789$	1182.97			1.49933
$790$	65.6868	−	96.9955i	0.0831478	−	0.122779i
$791$			350.517i			0.443131i
$792$	−1611.21	−	351.868i	−2.03435	−	0.444277i
$793$	61.2855			0.0772830
$794$	237.794	+	161.037i	0.299488	+	0.202818i
$795$		−	755.132i		−	0.949852i
$796$	29.3388	−	11.7270i	0.0368578	−	0.0147325i
$797$	1056.67			1.32580			0.662902	−	0.748706i	$-0.269325\pi$
$797$	1056.67			1.32580			0.662902	+	0.748706i	$0.269325\pi$
$798$	50.6626	−	74.8103i	0.0634870	−	0.0937473i
$799$		−	220.077i		−	0.275441i
$800$	157.820	−	26.3192i	0.197276	−	0.0328990i
$801$	2836.52			3.54122
$802$	1021.98	+	692.098i	1.27429	+	0.862966i
$803$		−	50.9586i		−	0.0634603i
$804$	24.4257	+	61.1082i	0.0303802	+	0.0760053i
$805$	55.1096			0.0684591
$806$	−0.313558	+	0.463012i	−0.000389030	+	0.000574457i
$807$		−	1856.77i		−	2.30083i
$808$	−244.356	+	1118.91i	−0.302421	+	1.38479i
$809$	226.866			0.280428			0.140214	−	0.990121i	$-0.455221\pi$
$809$	226.866			0.280428			0.140214	+	0.990121i	$0.455221\pi$
$810$	−1275.97	−	864.104i	−1.57527	−	1.06680i
$811$			805.832i			0.993628i	0.867857	+	0.496814i	$0.165497\pi$
$811$			805.832i			0.993628i	−0.867857	+	0.496814i	$0.834503\pi$
$812$	−190.018	+	75.9524i	−0.234012	+	0.0935375i
$813$	−2981.15			−3.66685
$814$	−582.748	+	860.508i	−0.715907	+	1.05714i
$815$			692.588i			0.849801i
$816$	1457.42	+	1531.82i	1.78606	+	1.87723i
$817$	284.136			0.347780
$818$	957.422	+	648.380i	1.17044	+	0.792641i
$819$			50.9999i			0.0622709i
$820$	170.039	+	425.403i	0.207364	+	0.518784i
$821$	−30.6435			−0.0373247			−0.0186623	−	0.999826i	$-0.505941\pi$
$821$	−30.6435			−0.0373247			−0.0186623	+	0.999826i	$0.505941\pi$
$822$	−678.284	+	1001.58i	−0.825163	+	1.21847i
$823$			376.392i			0.457341i	0.973504	+	0.228671i	$0.0734379\pi$
$823$			376.392i			0.457341i	−0.973504	+	0.228671i	$0.926562\pi$
$824$	−183.511	−	40.0765i	−0.222708	−	0.0486365i
$825$	−236.749			−0.286969
$826$	−203.585	−	137.871i	−0.246471	−	0.166914i
$827$			1104.81i			1.33593i	0.744193	+	0.667965i	$0.232834\pi$
$827$			1104.81i			1.33593i	−0.744193	+	0.667965i	$0.767166\pi$
$828$	1331.11	−	532.058i	1.60762	−	0.642582i
$829$	−588.939			−0.710421			−0.355210	−	0.934786i	$-0.615591\pi$
$829$	−588.939			−0.710421			−0.355210	+	0.934786i	$0.615591\pi$
$830$	−96.5696	+	142.598i	−0.116349	+	0.171805i
$831$		−	2804.98i		−	3.37543i
$832$	−65.7516	−	30.1569i	−0.0790283	−	0.0362463i
$833$	−1030.89			−1.23757
$834$	−726.550	−	492.030i	−0.871163	−	0.589964i
$835$			628.799i			0.753053i
$836$	−52.0818	−	130.298i	−0.0622987	−	0.155859i
$837$	−24.1811			−0.0288902
$838$	537.682	−	793.961i	0.641625	−	0.947448i
$839$		−	539.748i		−	0.643323i	−0.946855	−	0.321662i	$-0.895759\pi$
$839$		−	539.748i		−	0.643323i	0.946855	−	0.321662i	$-0.104241\pi$
$840$	39.5559	−	181.127i	0.0470904	−	0.215628i
$841$	2.43528			0.00289570
$842$	−1026.92	−	695.448i	−1.21963	−	0.825948i
$843$		−	141.028i		−	0.167293i
$844$	−528.407	+	211.210i	−0.626074	+	0.250249i
$845$	−375.039			−0.443833
$846$	−281.463	+	415.619i	−0.332698	+	0.491275i
$847$		−	99.0514i		−	0.116944i
$848$	665.356	−	633.041i	0.784618	−	0.746511i
$849$	−601.118			−0.708031
$850$	185.977	+	125.946i	0.218796	+	0.148172i
$851$		−	903.348i		−	1.06151i
$852$	−649.259	−	1624.32i	−0.762042	−	1.90648i
$853$	−1017.22			−1.19252			−0.596261	−	0.802791i	$-0.703348\pi$
$853$	−1017.22			−1.19252			−0.596261	+	0.802791i	$0.703348\pi$
$854$	−107.116	+	158.171i	−0.125429	+	0.185212i
$855$		−	249.662i		−	0.292003i
$856$	−198.236	−	43.2921i	−0.231584	−	0.0505749i
$857$	169.929			0.198283			0.0991416	−	0.995073i	$-0.468390\pi$
$857$	169.929			0.198283			0.0991416	+	0.995073i	$0.468390\pi$
$858$	88.6260	+	60.0188i	0.103294	+	0.0699520i
$859$			118.503i			0.137954i	0.997618	+	0.0689770i	$0.0219735\pi$
$859$			118.503i			0.137954i	−0.997618	+	0.0689770i	$0.978026\pi$
$860$	541.389	−	216.399i	0.629522	−	0.251627i
$861$	530.844			0.616544
$862$	195.542	−	288.745i	0.226847	−	0.334971i
$863$			379.908i			0.440218i	0.975475	+	0.220109i	$0.0706413\pi$
$863$			379.908i			0.440218i	−0.975475	+	0.220109i	$0.929359\pi$
$864$	−514.551	−	3085.46i	−0.595545	−	3.57113i
$865$	−376.806			−0.435614
$866$	−64.3501	−	43.5788i	−0.0743072	−	0.0503219i
$867$			1267.87i			1.46236i
$868$	−0.646943	−	1.61852i	−0.000745326	−	0.00186466i
$869$	−210.812			−0.242592
$870$	−428.476	+	632.704i	−0.492502	+	0.727246i
$871$		−	3.16066i		−	0.00362877i
$872$	158.105	−	723.967i	0.181313	−	0.830237i
$873$	−2100.32			−2.40586
$874$	100.991	+	68.3926i	0.115550	+	0.0782524i
$875$		−	19.6947i		−	0.0225083i
$876$	138.368	−	55.3072i	0.157954	−	0.0631361i
$877$	922.245			1.05159			0.525795	−	0.850611i	$-0.323768\pi$
$877$	922.245			1.05159			0.525795	+	0.850611i	$0.323768\pi$
$878$	605.684	−	894.376i	0.689845	−	1.01865i
$879$		−	1281.15i		−	1.45751i
$880$	−198.471	−	208.603i	−0.225536	−	0.237048i
$881$	611.091			0.693634			0.346817	−	0.937933i	$-0.387263\pi$
$881$	611.091			0.693634			0.346817	+	0.937933i	$0.387263\pi$
$882$	1946.86	+	1318.44i	2.20732	+	1.49483i
$883$		−	683.353i		−	0.773899i	−0.922101	−	0.386950i	$-0.873529\pi$
$883$		−	683.353i		−	0.773899i	0.922101	−	0.386950i	$-0.126471\pi$
$884$	−37.6907	−	94.2946i	−0.0426365	−	0.106668i
$885$	−918.139			−1.03744
$886$	65.1976	−	96.2733i	0.0735865	−	0.108661i
$887$		−	9.51379i		−	0.0107258i	−0.999986	−	0.00536290i	$-0.998293\pi$
$887$		−	9.51379i		−	0.0107258i	0.999986	−	0.00536290i	$-0.00170707\pi$
$888$	−2969.01	−	648.395i	−3.34348	−	0.730174i
$889$	405.450			0.456074
$890$	410.052	+	277.693i	0.460732	+	0.312014i
$891$			2773.22i			3.11248i
$892$	1388.70	−	555.078i	1.55684	−	0.622285i
$893$	−42.7092			−0.0478267
$894$	907.502	−	1340.05i	1.01510	−	1.49894i
$895$			477.819i			0.533876i
$896$	192.754	−	116.989i	0.215127	−	0.130568i
$897$	−93.0382			−0.103722
$898$	−1192.96	−	807.887i	−1.32846	−	0.899651i
$899$			7.18416i			0.00799128i
$900$	−190.144	−	475.702i	−0.211271	−	0.528558i
$901$	1289.25			1.43091
$902$	462.290	−	682.635i	0.512517	−	0.756801i
$903$		−	675.578i		−	0.748149i
$904$	−339.637	+	1555.20i	−0.375704	+	1.72036i
$905$	−435.465			−0.481177
$906$	2682.19	+	1816.42i	2.96047	+	2.00487i
$907$		−	474.399i		−	0.523042i	−0.965198	−	0.261521i	$-0.915776\pi$
$907$		−	474.399i		−	0.523042i	0.965198	−	0.261521i	$-0.0842240\pi$
$908$	−13.5511	+	5.41655i	−0.0149242	+	0.00596536i
$909$	3667.02			4.03413
$910$	−4.99285	+	7.37263i	−0.00548665	+	0.00810179i
$911$		−	268.493i		−	0.294723i	−0.989083	−	0.147362i	$-0.952922\pi$
$911$		−	268.493i		−	0.294723i	0.989083	−	0.147362i	$-0.0470781\pi$
$912$	297.272	−	282.835i	0.325957	−	0.310126i
$913$	309.926			0.339459
$914$	317.849	+	215.252i	0.347756	+	0.235505i
$915$			713.329i			0.779595i
$916$	76.6407	+	191.740i	0.0836689	+	0.209323i
$917$	−72.4033			−0.0789567
$918$	2462.30	−	3635.92i	2.68224	−	3.96070i
$919$			1191.69i			1.29672i	0.761333	+	0.648361i	$0.224545\pi$
$919$			1191.69i			1.29672i	−0.761333	+	0.648361i	$0.775455\pi$
$920$	244.515	+	53.3990i	0.265777	+	0.0580424i
$921$	2888.85			3.13665
$922$	−1294.97	−	876.974i	−1.40453	−	0.951165i
$923$			84.0136i			0.0910224i
$924$	−309.805	+	123.832i	−0.335286	+	0.134018i
$925$	−322.833			−0.349009
$926$	−748.347	+	1105.04i	−0.808150	+	1.19334i
$927$			601.423i			0.648784i
$928$	−916.683	+	152.872i	−0.987805	+	0.164733i
$929$	900.005			0.968789			0.484395	−	0.874850i	$-0.339040\pi$
$929$	900.005			0.968789			0.484395	+	0.874850i	$0.339040\pi$
$930$	−5.38921	−	3.64965i	−0.00579485	−	0.00392435i
$931$			200.060i			0.214887i
$932$	301.131	+	753.371i	0.323102	+	0.808338i
$933$	561.561			0.601887
$934$	218.943	−	323.300i	0.234415	−	0.346145i
$935$		−	404.206i		−	0.432306i
$936$	−49.4168	+	226.281i	−0.0527957	+	0.241753i
$937$	−807.977			−0.862302			−0.431151	−	0.902280i	$-0.641892\pi$
$937$	−807.977			−0.862302			−0.431151	+	0.902280i	$0.641892\pi$
$938$	8.15734	+	5.52427i	0.00869652	+	0.00588941i
$939$			1555.03i			1.65604i
$940$	−81.3775	+	32.5275i	−0.0865718	+	0.0346037i
$941$	−1188.52			−1.26304			−0.631520	−	0.775359i	$-0.717569\pi$
$941$	−1188.52			−1.26304			−0.631520	+	0.775359i	$0.717569\pi$
$942$	1353.66	−	1998.87i	1.43701	−	2.12194i
$943$			716.620i			0.759936i
$944$	−769.693	−	808.983i	−0.815352	−	0.856973i
$945$	−385.040			−0.407450
$946$	−868.754	−	588.333i	−0.918345	−	0.621916i
$947$		−	117.004i		−	0.123552i	−0.998090	−	0.0617762i	$-0.980323\pi$
$947$		−	117.004i		−	0.123552i	0.998090	−	0.0617762i	$-0.0196765\pi$
$948$	−228.802	−	572.417i	−0.241352	−	0.603816i
$949$	−7.15671			−0.00754131
$950$	24.4417	−	36.0916i	0.0257281	−	0.0379911i
$951$		−	1325.04i		−	1.39331i
$952$	309.241	+	67.5344i	0.324833	+	0.0709395i
$953$	1355.08			1.42191			0.710953	−	0.703239i	$-0.248264\pi$
$953$	1355.08			1.42191			0.710953	+	0.703239i	$0.248264\pi$
$954$	−2434.76	−	1648.86i	−2.55216	−	1.72836i
$955$			291.976i			0.305734i
$956$	514.171	−	205.520i	0.537835	−	0.214979i
$957$	1375.13			1.43692
$958$	−547.855	+	808.983i	−0.571873	+	0.844449i
$959$			181.088i			0.188830i
$960$	351.010	−	765.312i	0.365635	−	0.797200i
$961$	960.939			0.999936
$962$	120.851	+	81.8420i	0.125625	+	0.0850749i
$963$			649.680i			0.674642i
$964$	−27.1082	−	67.8193i	−0.0281205	−	0.0703520i
$965$	205.831			0.213296
$966$	162.614	−	240.122i	0.168338	−	0.248574i
$967$			415.646i			0.429830i	0.976633	+	0.214915i	$0.0689474\pi$
$967$			415.646i			0.429830i	−0.976633	+	0.214915i	$0.931053\pi$
$968$	95.9768	−	439.480i	0.0991496	−	0.454008i
$969$	576.020			0.594447
$970$	−303.626	−	205.620i	−0.313016	−	0.211979i
$971$		−	1657.41i		−	1.70691i	−0.521165	−	0.853456i	$-0.674503\pi$
$971$		−	1657.41i		−	1.70691i	0.521165	−	0.853456i	$-0.325497\pi$
$972$	−4262.40	+	1703.73i	−4.38519	+	1.75281i
$973$	−131.362			−0.135007
$974$	99.8124	−	147.387i	0.102477	−	0.151321i
$975$			33.2494i			0.0341020i
$976$	−628.523	+	597.997i	−0.643978	+	0.612702i
$977$	−1106.49			−1.13254			−0.566269	−	0.824221i	$-0.691614\pi$
$977$	−1106.49			−1.13254			−0.566269	+	0.824221i	$0.691614\pi$
$978$	3017.73	+	2043.65i	3.08561	+	2.08962i
$979$		−	891.215i		−	0.910332i
$980$	152.367	+	381.191i	0.155476	+	0.388971i
$981$	−2372.67			−2.41862
$982$	−1.04312	+	1.54030i	−0.00106224	+	0.00156854i
$983$			1217.89i			1.23895i	0.785017	+	0.619474i	$0.212654\pi$
$983$			1217.89i			1.23895i	−0.785017	+	0.619474i	$0.787346\pi$
$984$	2355.29	+	514.367i	2.39359	+	0.522730i
$985$	59.2388			0.0601409
$986$	−1080.23	−	731.544i	−1.09556	−	0.741931i
$987$			101.548i			0.102885i
$988$	−18.2993	+	7.31444i	−0.0185215	+	0.00740328i
$989$	912.005			0.922148
$990$	−516.951	+	763.349i	−0.522172	+	0.771059i
$991$			493.603i			0.498086i	0.968492	+	0.249043i	$0.0801160\pi$
$991$			493.603i			0.498086i	−0.968492	+	0.249043i	$0.919884\pi$
$992$	−1.30213	−	7.80806i	−0.00131263	−	0.00787103i
$993$	693.785			0.698675
$994$	−216.831	−	146.841i	−0.218139	−	0.147727i
$995$		−	17.6625i		−	0.0177513i
$996$	336.374	+	841.542i	0.337725	+	0.844921i
$997$	−1424.98			−1.42927			−0.714633	−	0.699499i	$-0.753406\pi$
$997$	−1424.98			−1.42927			−0.714633	+	0.699499i	$0.753406\pi$
$998$	−711.719	+	1050.95i	−0.713145	+	1.05306i
$999$			6311.52i			6.31784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.15	✓	72
4.3	odd	2	inner	380.3.b.a.191.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.15	✓	72	1.1	even	1	trivial
380.3.b.a.191.16	yes	72	4.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65600 - 1.12146i) q^{2} +5.88343i q^{3} +(1.48464 + 3.71428i) q^{4} +2.23607 q^{5} +(6.59806 - 9.74294i) q^{6} -1.76155i q^{7} +(1.70687 - 7.81579i) q^{8} -25.6148 q^{9} +O(q^{10})\)	\(q+(-1.65600 - 1.12146i) q^{2} +5.88343i q^{3} +(1.48464 + 3.71428i) q^{4} +2.23607 q^{5} +(6.59806 - 9.74294i) q^{6} -1.76155i q^{7} +(1.70687 - 7.81579i) q^{8} -25.6148 q^{9} +(-3.70292 - 2.50767i) q^{10} +8.04800i q^{11} +(-21.8527 + 8.73478i) q^{12} +1.13027 q^{13} +(-1.97551 + 2.91712i) q^{14} +13.1558i q^{15} +(-11.5917 + 11.0287i) q^{16} -22.4610 q^{17} +(42.4180 + 28.7261i) q^{18} +4.35890i q^{19} +(3.31975 + 8.30537i) q^{20} +10.3640 q^{21} +(9.02554 - 13.3274i) q^{22} +13.9910i q^{23} +(45.9837 + 10.0423i) q^{24} +5.00000 q^{25} +(-1.87173 - 1.26756i) q^{26} -97.7521i q^{27} +(6.54288 - 2.61527i) q^{28} -29.0420 q^{29} +(14.7537 - 21.7859i) q^{30} -0.247372i q^{31} +(31.5641 - 5.26384i) q^{32} -47.3499 q^{33} +(37.1953 + 25.1892i) q^{34} -3.93894i q^{35} +(-38.0287 - 95.1404i) q^{36} -64.5666 q^{37} +(4.88835 - 7.21831i) q^{38} +6.64989i q^{39} +(3.81668 - 17.4766i) q^{40} +51.2202 q^{41} +(-17.1627 - 11.6228i) q^{42} -65.1853i q^{43} +(-29.8925 + 11.9484i) q^{44} -57.2764 q^{45} +(15.6903 - 23.1689i) q^{46} +9.79817i q^{47} +(-64.8867 - 68.1990i) q^{48} +45.8969 q^{49} +(-8.27998 - 5.60732i) q^{50} -132.148i q^{51} +(1.67805 + 4.19815i) q^{52} -57.3993 q^{53} +(-109.625 + 161.877i) q^{54} +17.9959i q^{55} +(-13.7679 - 3.00674i) q^{56} -25.6453 q^{57} +(48.0933 + 32.5695i) q^{58} +69.7899i q^{59} +(-48.8641 + 19.5316i) q^{60} +54.2218 q^{61} +(-0.277418 + 0.409646i) q^{62} +45.1217i q^{63} +(-58.1732 - 26.6811i) q^{64} +2.52737 q^{65} +(78.4112 + 53.1012i) q^{66} -2.79637i q^{67} +(-33.3465 - 83.4264i) q^{68} -82.3148 q^{69} +(-4.41738 + 6.52287i) q^{70} +74.3304i q^{71} +(-43.7211 + 200.200i) q^{72} -6.33184 q^{73} +(106.922 + 72.4091i) q^{74} +29.4172i q^{75} +(-16.1902 + 6.47139i) q^{76} +14.1769 q^{77} +(7.45760 - 11.0122i) q^{78} +26.1944i q^{79} +(-25.9198 + 24.6610i) q^{80} +344.585 q^{81} +(-84.8204 - 57.4416i) q^{82} -38.5097i q^{83} +(15.3867 + 38.4946i) q^{84} -50.2244 q^{85} +(-73.1030 + 107.947i) q^{86} -170.866i q^{87} +(62.9015 + 13.7369i) q^{88} -110.737 q^{89} +(94.8495 + 64.2334i) q^{90} -1.99103i q^{91} +(-51.9663 + 20.7715i) q^{92} +1.45540 q^{93} +(10.9883 - 16.2257i) q^{94} +9.74679i q^{95} +(30.9695 + 185.705i) q^{96} +81.9963 q^{97} +(-76.0051 - 51.4717i) q^{98} -206.148i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more