LMFDB - Embedded newform 87.3.b.a.59.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,3,Mod(59,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("87.59");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	87.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:	$2.37057829993$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 54 x^{16} + 1187 x^{14} + 13673 x^{12} + 88449 x^{10} + 318861 x^{8} + 593533 x^{6} + \cdots + 15341 $ x^18 + 54x^16 + 1187x^14 + 13673x^12 + 88449x^10 + 318861x^8 + 593533x^6 + 482583x^4 + 152462x^2 + 15341
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.18
Root			$3.74519i$ of defining polynomial
Character	$\chi$	$=$	87.59
Dual form			87.3.b.a.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.74519i q^{2} +(0.905668 + 2.86003i) q^{3} -10.0264 q^{4} -1.22987i q^{5} +(-10.7113 + 3.39190i) q^{6} +5.48015 q^{7} -22.5701i q^{8} +(-7.35953 + 5.18047i) q^{9} +O(q^{10})$	\(q+3.74519i q^{2} +(0.905668 + 2.86003i) q^{3} -10.0264 q^{4} -1.22987i q^{5} +(-10.7113 + 3.39190i) q^{6} +5.48015 q^{7} -22.5701i q^{8} +(-7.35953 + 5.18047i) q^{9} +4.60608 q^{10} +10.2607i q^{11} +(-9.08061 - 28.6759i) q^{12} +18.2828 q^{13} +20.5242i q^{14} +(3.51745 - 1.11385i) q^{15} +44.4235 q^{16} -12.4830i q^{17} +(-19.4018 - 27.5628i) q^{18} -32.3692 q^{19} +12.3312i q^{20} +(4.96320 + 15.6734i) q^{21} -38.4283 q^{22} +20.7040i q^{23} +(64.5511 - 20.4410i) q^{24} +23.4874 q^{25} +68.4727i q^{26} +(-21.4816 - 16.3567i) q^{27} -54.9463 q^{28} -5.38516i q^{29} +(4.17158 + 13.1735i) q^{30} +29.6610 q^{31} +76.0938i q^{32} +(-29.3459 + 9.29280i) q^{33} +46.7513 q^{34} -6.73985i q^{35} +(73.7898 - 51.9416i) q^{36} +24.9732 q^{37} -121.229i q^{38} +(16.5582 + 52.2895i) q^{39} -27.7582 q^{40} +2.23497i q^{41} +(-58.6998 + 18.5881i) q^{42} +59.5864 q^{43} -102.878i q^{44} +(6.37129 + 9.05124i) q^{45} -77.5405 q^{46} +49.3360i q^{47} +(40.2329 + 127.052i) q^{48} -18.9679 q^{49} +87.9648i q^{50} +(35.7018 - 11.3055i) q^{51} -183.312 q^{52} -94.8927i q^{53} +(61.2588 - 80.4526i) q^{54} +12.6193 q^{55} -123.687i q^{56} +(-29.3157 - 92.5767i) q^{57} +20.1684 q^{58} -81.3909i q^{59} +(-35.2675 + 11.1679i) q^{60} -24.8286 q^{61} +111.086i q^{62} +(-40.3314 + 28.3898i) q^{63} -107.292 q^{64} -22.4854i q^{65} +(-34.8033 - 109.906i) q^{66} +43.8938 q^{67} +125.160i q^{68} +(-59.2142 + 18.7510i) q^{69} +25.2420 q^{70} -60.5378i q^{71} +(116.924 + 166.105i) q^{72} -8.77389 q^{73} +93.5294i q^{74} +(21.2718 + 67.1747i) q^{75} +324.547 q^{76} +56.2303i q^{77} +(-195.834 + 62.0135i) q^{78} -15.9288 q^{79} -54.6349i q^{80} +(27.3254 - 76.2517i) q^{81} -8.37037 q^{82} +16.5880i q^{83} +(-49.7631 - 157.148i) q^{84} -15.3525 q^{85} +223.162i q^{86} +(15.4017 - 4.87717i) q^{87} +231.585 q^{88} -18.9952i q^{89} +(-33.8986 + 23.8617i) q^{90} +100.193 q^{91} -207.587i q^{92} +(26.8630 + 84.8312i) q^{93} -184.773 q^{94} +39.8097i q^{95} +(-217.631 + 68.9157i) q^{96} -127.385 q^{97} -71.0384i q^{98} +(-53.1554 - 75.5141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$1$	$-1$

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 $

$2$			3.74519i			1.87259i	0.351210	+	0.936297i	$0.385770\pi$
$2$			3.74519i			1.87259i	−0.351210	+	0.936297i	$0.614230\pi$
$3$	0.905668	+	2.86003i	0.301889	+	0.953343i
$3$	0.905668	+	2.86003i	0.301889	+	0.953343i
$4$	−10.0264			−2.50661
$5$		−	1.22987i		−	0.245973i	−0.992408	−	0.122987i	$-0.960753\pi$
$5$		−	1.22987i		−	0.245973i	0.992408	−	0.122987i	$-0.0392472\pi$
$6$	−10.7113	+	3.39190i	−1.78522	+	0.565316i
$7$	5.48015			0.782879			0.391439	−	0.920204i	$-0.371977\pi$
$7$	5.48015			0.782879			0.391439	+	0.920204i	$0.371977\pi$
$8$		−	22.5701i		−	2.82126i
$9$	−7.35953	+	5.18047i	−0.817726	+	0.575608i
$10$	4.60608			0.460608
$11$			10.2607i			0.932792i	0.884576	+	0.466396i	$0.154448\pi$
$11$			10.2607i			0.932792i	−0.884576	+	0.466396i	$0.845552\pi$
$12$	−9.08061	−	28.6759i	−0.756717	−	2.38965i
$13$	18.2828			1.40637			0.703186	−	0.711006i	$-0.251760\pi$
$13$	18.2828			1.40637			0.703186	+	0.711006i	$0.251760\pi$
$14$			20.5242i			1.46601i
$15$	3.51745	−	1.11385i	0.234497	−	0.0742567i
$16$	44.4235			2.77647
$17$		−	12.4830i		−	0.734296i	−0.930163	−	0.367148i	$-0.880334\pi$
$17$		−	12.4830i		−	0.734296i	0.930163	−	0.367148i	$-0.119666\pi$
$18$	−19.4018	−	27.5628i	−1.07788	−	1.53127i
$19$	−32.3692			−1.70364			−0.851820	−	0.523835i	$-0.824501\pi$
$19$	−32.3692			−1.70364			−0.851820	+	0.523835i	$0.824501\pi$
$20$			12.3312i			0.616558i
$21$	4.96320	+	15.6734i	0.236343	+	0.746352i
$22$	−38.4283			−1.74674
$23$			20.7040i			0.900176i	0.892984	+	0.450088i	$0.148607\pi$
$23$			20.7040i			0.900176i	−0.892984	+	0.450088i	$0.851393\pi$
$24$	64.5511	−	20.4410i	2.68963	−	0.851708i
$25$	23.4874			0.939497
$26$			68.4727i			2.63356i
$27$	−21.4816	−	16.3567i	−0.795615	−	0.605803i
$28$	−54.9463			−1.96237
$29$		−	5.38516i		−	0.185695i
$29$		−	5.38516i		−	0.185695i
$30$	4.17158	+	13.1735i	0.139053	+	0.439117i
$31$	29.6610			0.956805			0.478403	−	0.878141i	$-0.341216\pi$
$31$	29.6610			0.956805			0.478403	+	0.878141i	$0.341216\pi$
$32$			76.0938i			2.37793i
$33$	−29.3459	+	9.29280i	−0.889271	+	0.281600i
$34$	46.7513			1.37504
$35$		−	6.73985i		−	0.192567i
$36$	73.7898	−	51.9416i	2.04972	−	1.44282i
$37$	24.9732			0.674952			0.337476	−	0.941334i	$-0.390427\pi$
$37$	24.9732			0.674952			0.337476	+	0.941334i	$0.390427\pi$
$38$		−	121.229i		−	3.19022i
$39$	16.5582	+	52.2895i	0.424569	+	1.34076i
$40$	−27.7582			−0.693954
$41$			2.23497i			0.0545114i	0.999628	+	0.0272557i	$0.00867683\pi$
$41$			2.23497i			0.0545114i	−0.999628	+	0.0272557i	$0.991323\pi$
$42$	−58.6998	+	18.5881i	−1.39761	+	0.442574i
$43$	59.5864			1.38573			0.692865	−	0.721067i	$-0.256348\pi$
$43$	59.5864			1.38573			0.692865	+	0.721067i	$0.256348\pi$
$44$		−	102.878i		−	2.33814i
$45$	6.37129	+	9.05124i	0.141584	+	0.201139i
$46$	−77.5405			−1.68566
$47$			49.3360i			1.04970i	0.851194	+	0.524851i	$0.175879\pi$
$47$			49.3360i			1.04970i	−0.851194	+	0.524851i	$0.824121\pi$
$48$	40.2329	+	127.052i	0.838185	+	2.64692i
$49$	−18.9679			−0.387101
$50$			87.9648i			1.75930i
$51$	35.7018	−	11.3055i	0.700036	−	0.221676i
$52$	−183.312			−3.52522
$53$		−	94.8927i		−	1.79043i	−0.445637	−	0.895214i	$-0.647023\pi$
$53$		−	94.8927i		−	1.79043i	0.445637	−	0.895214i	$-0.352977\pi$
$54$	61.2588	−	80.4526i	1.13442	−	1.48986i
$55$	12.6193			0.229442
$56$		−	123.687i		−	2.20870i
$57$	−29.3157	−	92.5767i	−0.514311	−	1.62415i
$58$	20.1684			0.347732
$59$		−	81.3909i		−	1.37951i	−0.724044	−	0.689753i	$-0.757719\pi$
$59$		−	81.3909i		−	1.37951i	0.724044	−	0.689753i	$-0.242281\pi$
$60$	−35.2675	+	11.1679i	−0.587791	+	0.186132i
$61$	−24.8286			−0.407026			−0.203513	−	0.979072i	$-0.565236\pi$
$61$	−24.8286			−0.407026			−0.203513	+	0.979072i	$0.565236\pi$
$62$			111.086i			1.79171i
$63$	−40.3314	+	28.3898i	−0.640180	+	0.450631i
$64$	−107.292			−1.67643
$65$		−	22.4854i		−	0.345930i
$66$	−34.8033	−	109.906i	−0.527322	−	1.66524i
$67$	43.8938			0.655132			0.327566	−	0.944828i	$-0.393772\pi$
$67$	43.8938			0.655132			0.327566	+	0.944828i	$0.393772\pi$
$68$			125.160i			1.84059i
$69$	−59.2142	+	18.7510i	−0.858176	+	0.271753i
$70$	25.2420			0.360600
$71$		−	60.5378i		−	0.852645i	−0.904571	−	0.426322i	$-0.859809\pi$
$71$		−	60.5378i		−	0.852645i	0.904571	−	0.426322i	$-0.140191\pi$
$72$	116.924	+	166.105i	1.62394	+	2.30702i
$73$	−8.77389			−0.120190			−0.0600951	−	0.998193i	$-0.519140\pi$
$73$	−8.77389			−0.120190			−0.0600951	+	0.998193i	$0.519140\pi$
$74$			93.5294i			1.26391i
$75$	21.2718	+	67.1747i	0.283624	+	0.895663i
$76$	324.547			4.27035
$77$			56.2303i			0.730264i
$78$	−195.834	+	62.0135i	−2.51069	+	0.795045i
$79$	−15.9288			−0.201631			−0.100815	−	0.994905i	$-0.532145\pi$
$79$	−15.9288			−0.201631			−0.100815	+	0.994905i	$0.532145\pi$
$80$		−	54.6349i		−	0.682936i
$81$	27.3254	−	76.2517i	0.337351	−	0.941379i
$82$	−8.37037			−0.102078
$83$			16.5880i			0.199855i	0.994995	+	0.0999274i	$0.0318611\pi$
$83$			16.5880i			0.199855i	−0.994995	+	0.0999274i	$0.968139\pi$
$84$	−49.7631	−	157.148i	−0.592418	−	1.87081i
$85$	−15.3525			−0.180617
$86$			223.162i			2.59491i
$87$	15.4017	−	4.87717i	0.177031	−	0.0560594i
$88$	231.585			2.63165
$89$		−	18.9952i		−	0.213429i	−0.994290	−	0.106715i	$-0.965967\pi$
$89$		−	18.9952i		−	0.213429i	0.994290	−	0.106715i	$-0.0340332\pi$
$90$	−33.8986	+	23.8617i	−0.376651	+	0.265130i
$91$	100.193			1.10102
$92$		−	207.587i		−	2.25639i
$93$	26.8630	+	84.8312i	0.288849	+	0.912164i
$94$	−184.773			−1.96567
$95$			39.8097i			0.419050i
$96$	−217.631	+	68.9157i	−2.26698	+	0.717872i
$97$	−127.385			−1.31325			−0.656626	−	0.754216i	$-0.728017\pi$
$97$	−127.385			−1.31325			−0.656626	+	0.754216i	$0.728017\pi$
$98$		−	71.0384i		−	0.724882i
$99$	−53.1554	−	75.5141i	−0.536923	−	0.762768i
$100$	−235.495			−2.35495
$101$		−	11.0340i		−	0.109248i	−0.998507	−	0.0546239i	$-0.982604\pi$
$101$		−	11.0340i		−	0.109248i	0.998507	−	0.0546239i	$-0.0173960\pi$
$102$	42.3411	+	133.710i	0.415109	+	1.31088i
$103$	−24.4068			−0.236960			−0.118480	−	0.992956i	$-0.537802\pi$
$103$	−24.4068			−0.236960			−0.118480	+	0.992956i	$0.537802\pi$
$104$		−	412.645i		−	3.96774i
$105$	19.2762	−	6.10407i	0.183583	−	0.0581340i
$106$	355.391			3.35274
$107$			11.9062i			0.111273i	0.998451	+	0.0556364i	$0.0177187\pi$
$107$			11.9062i			0.111273i	−0.998451	+	0.0556364i	$0.982281\pi$
$108$	215.384	+	163.999i	1.99429	+	1.51851i
$109$	−74.4419			−0.682954			−0.341477	−	0.939890i	$-0.610927\pi$
$109$	−74.4419			−0.682954			−0.341477	+	0.939890i	$0.610927\pi$
$110$			47.2616i			0.429651i
$111$	22.6175	+	71.4242i	0.203761	+	0.643461i
$112$	243.447			2.17364
$113$			75.6653i			0.669605i	0.942288	+	0.334802i	$0.108670\pi$
$113$			75.6653i			0.669605i	−0.942288	+	0.334802i	$0.891330\pi$
$114$	346.717	−	109.793i	3.04138	−	0.963095i
$115$	25.4632			0.221419
$116$			53.9939i			0.465465i
$117$	−134.553	+	94.7138i	−1.15003	+	0.809520i
$118$	304.824			2.58326
$119$		−	68.4089i		−	0.574865i
$120$	−25.1397	−	79.3892i	−0.209497	−	0.661576i
$121$	15.7177			0.129898
$122$		−	92.9877i		−	0.762194i
$123$	−6.39207	+	2.02414i	−0.0519680	+	0.0164564i
$124$	−297.393			−2.39833
$125$		−	59.6330i		−	0.477064i
$126$	−106.325	−	151.048i	−0.843850	−	1.19880i
$127$	−23.5788			−0.185660			−0.0928299	−	0.995682i	$-0.529591\pi$
$127$	−23.5788			−0.185660			−0.0928299	+	0.995682i	$0.529591\pi$
$128$		−	97.4523i		−	0.761346i
$129$	53.9655	+	170.419i	0.418337	+	1.32108i
$130$	84.2122			0.647786
$131$		−	24.5075i		−	0.187080i	−0.995616	−	0.0935399i	$-0.970182\pi$
$131$		−	24.5075i		−	0.187080i	0.995616	−	0.0935399i	$-0.0298183\pi$
$132$	294.235	−	93.1736i	2.22905	−	0.705860i
$133$	−177.388			−1.33374
$134$			164.391i			1.22680i
$135$	−20.1165	+	26.4195i	−0.149011	+	0.195700i
$136$	−281.743			−2.07164
$137$		−	20.5935i		−	0.150318i	−0.997172	−	0.0751588i	$-0.976054\pi$
$137$		−	20.5935i		−	0.150318i	0.997172	−	0.0751588i	$-0.0239464\pi$
$138$	−70.2260	−	221.768i	−0.508884	−	1.60702i
$139$	−111.065			−0.799031			−0.399515	−	0.916727i	$-0.630822\pi$
$139$	−111.065			−0.799031			−0.399515	+	0.916727i	$0.630822\pi$
$140$			67.5766i			0.482690i
$141$	−141.102	+	44.6820i	−1.00073	+	0.316894i
$142$	226.725			1.59666
$143$			187.595i			1.31185i
$144$	−326.936	+	230.135i	−2.27039	+	1.59816i
$145$	−6.62303			−0.0456761
$146$		−	32.8599i		−	0.225068i
$147$	−17.1786	−	54.2488i	−0.116862	−	0.369040i
$148$	−250.392			−1.69184
$149$		−	77.4875i		−	0.520050i	−0.965602	−	0.260025i	$-0.916269\pi$
$149$		−	77.4875i		−	0.520050i	0.965602	−	0.260025i	$-0.0837308\pi$
$150$	−251.582	+	79.6669i	−1.67721	+	0.531113i
$151$	−116.616			−0.772290			−0.386145	−	0.922438i	$-0.626194\pi$
$151$	−116.616			−0.772290			−0.386145	+	0.922438i	$0.626194\pi$
$152$			730.574i			4.80641i
$153$	64.6680	+	91.8693i	0.422667	+	0.600453i
$154$	−210.593			−1.36749
$155$		−	36.4790i		−	0.235348i
$156$	−166.019	−	524.276i	−1.06423	−	3.36075i
$157$	−125.378			−0.798585			−0.399293	−	0.916823i	$-0.630744\pi$
$157$	−125.378			−0.798585			−0.399293	+	0.916823i	$0.630744\pi$
$158$		−	59.6564i		−	0.377572i
$159$	271.396	−	85.9412i	1.70689	−	0.540511i
$160$	93.5852			0.584907
$161$			113.461i			0.704729i
$162$	285.577	+	102.339i	1.76282	+	0.631720i
$163$	10.3609			0.0635640			0.0317820	−	0.999495i	$-0.489882\pi$
$163$	10.3609			0.0635640			0.0317820	+	0.999495i	$0.489882\pi$
$164$		−	22.4087i		−	0.136639i
$165$	11.4289	+	36.0916i	0.0692661	+	0.218737i
$166$	−62.1250			−0.374247
$167$		−	200.084i		−	1.19811i	−0.800709	−	0.599054i	$-0.795543\pi$
$167$		−	200.084i		−	1.19811i	0.800709	−	0.599054i	$-0.204457\pi$
$168$	353.750	−	112.020i	2.10565	−	0.666784i
$169$	165.262			0.977884
$170$		−	57.4978i		−	0.338222i
$171$	238.222	−	167.688i	1.39311	−	0.980629i
$172$	−597.438			−3.47348
$173$		−	232.774i		−	1.34551i	−0.739863	−	0.672757i	$-0.765110\pi$
$173$		−	232.774i		−	1.34551i	0.739863	−	0.672757i	$-0.234890\pi$
$174$	18.2659	+	57.6823i	0.104977	+	0.331508i
$175$	128.715			0.735513
$176$			455.816i			2.58987i
$177$	232.780	−	73.7131i	1.31514	−	0.416458i
$178$	71.1406			0.399667
$179$			299.434i			1.67281i	0.548109	+	0.836407i	$0.315348\pi$
$179$			299.434i			1.67281i	−0.548109	+	0.836407i	$0.684652\pi$
$180$	−63.8812	−	90.7515i	−0.354896	−	0.504175i
$181$	−167.414			−0.924939			−0.462470	−	0.886635i	$-0.653037\pi$
$181$	−167.414			−0.924939			−0.462470	+	0.886635i	$0.653037\pi$
$182$			375.241i			2.06176i
$183$	−22.4865	−	71.0105i	−0.122877	−	0.388035i
$184$	467.292			2.53963
$185$		−	30.7137i		−	0.166020i
$186$	−317.709	+	100.607i	−1.70811	+	0.540897i
$187$	128.085			0.684946
$188$		−	494.664i		−	2.63119i
$189$	−117.722	−	89.6371i	−0.622870	−	0.474270i
$190$	−149.095			−0.784710
$191$			253.251i			1.32592i	0.748655	+	0.662960i	$0.230700\pi$
$191$			253.251i			1.32592i	−0.748655	+	0.662960i	$0.769300\pi$
$192$	−97.1707	−	306.858i	−0.506097	−	1.59822i
$193$	−357.232			−1.85094			−0.925471	−	0.378818i	$-0.876331\pi$
$193$	−357.232			−1.85094			−0.925471	+	0.378818i	$0.876331\pi$
$194$		−	477.082i		−	2.45919i
$195$	64.3090	−	20.3643i	0.329790	−	0.104433i
$196$	190.180			0.970308
$197$		−	127.042i		−	0.644883i	−0.946589	−	0.322442i	$-0.895496\pi$
$197$		−	127.042i		−	0.644883i	0.946589	−	0.322442i	$-0.104504\pi$
$198$	282.814	−	199.077i	1.42835	−	1.00544i
$199$	195.144			0.980624			0.490312	−	0.871547i	$-0.336883\pi$
$199$	195.144			0.980624			0.490312	+	0.871547i	$0.336883\pi$
$200$		−	530.113i		−	2.65057i
$201$	39.7532	+	125.538i	0.197777	+	0.624565i
$202$	41.3245			0.204577
$203$		−	29.5115i		−	0.145377i
$204$	−357.962	+	113.354i	−1.75471	+	0.555655i
$205$	2.74871			0.0134083
$206$		−	91.4082i		−	0.443729i
$207$	−107.257	−	152.372i	−0.518149	−	0.736097i
$208$	812.187			3.90475
$209$		−	332.131i		−	1.58914i
$210$	22.8609	+	72.1929i	0.108861	+	0.343776i
$211$	101.802			0.482473			0.241236	−	0.970466i	$-0.422447\pi$
$211$	101.802			0.482473			0.241236	+	0.970466i	$0.422447\pi$
$212$			951.434i			4.48790i
$213$	173.140	−	54.8271i	0.812863	−	0.257404i
$214$	−44.5909			−0.208369
$215$		−	73.2833i		−	0.340852i
$216$	−369.172	+	484.841i	−1.70913	+	2.24464i
$217$	162.547			0.749063
$218$		−	278.799i		−	1.27889i
$219$	−7.94623	−	25.0936i	−0.0362842	−	0.114583i
$220$	−126.526			−0.575120
$221$		−	228.225i		−	1.03269i
$222$	−267.497	+	84.7066i	−1.20494	+	0.381561i
$223$	286.980			1.28690			0.643452	−	0.765486i	$-0.277502\pi$
$223$	286.980			1.28690			0.643452	+	0.765486i	$0.277502\pi$
$224$			417.006i			1.86163i
$225$	−172.856	+	121.676i	−0.768251	+	0.540782i
$226$	−283.381			−1.25390
$227$			14.6184i			0.0643984i	0.999481	+	0.0321992i	$0.0102511\pi$
$227$			14.6184i			0.0643984i	−0.999481	+	0.0321992i	$0.989749\pi$
$228$	293.932	+	928.213i	1.28917	+	4.07111i
$229$	18.9453			0.0827307			0.0413653	−	0.999144i	$-0.486829\pi$
$229$	18.9453			0.0827307			0.0413653	+	0.999144i	$0.486829\pi$
$230$			95.3644i			0.414628i
$231$	−160.820	+	50.9260i	−0.696192	+	0.220459i
$232$	−121.544			−0.523895
$233$			302.178i			1.29690i	0.761257	+	0.648451i	$0.224583\pi$
$233$			302.178i			1.29690i	−0.761257	+	0.648451i	$0.775417\pi$
$234$	−354.721	−	503.927i	−1.51590	−	2.15353i
$235$	60.6767			0.258199
$236$			816.060i			3.45788i
$237$	−14.4262	−	45.5569i	−0.0608701	−	0.192223i
$238$	256.204			1.07649
$239$			167.286i			0.699942i	0.936761	+	0.349971i	$0.113809\pi$
$239$			167.286i			0.699942i	−0.936761	+	0.349971i	$0.886191\pi$
$240$	156.257	−	49.4811i	0.651072	−	0.206171i
$241$	448.934			1.86280			0.931399	−	0.364001i	$-0.118589\pi$
$241$	448.934			1.86280			0.931399	+	0.364001i	$0.118589\pi$
$242$			58.8657i			0.243247i
$243$	242.830	+	9.09269i	0.999300	+	0.0374185i
$244$	248.942			1.02025
$245$			23.3280i			0.0952163i
$246$	−7.58077	−	23.9395i	−0.0308161	−	0.0973150i
$247$	−591.800			−2.39595
$248$		−	669.450i		−	2.69940i
$249$	−47.4420	+	15.0232i	−0.190530	+	0.0603341i
$250$	223.337			0.893347
$251$		−	398.377i		−	1.58716i	−0.608466	−	0.793580i	$-0.708215\pi$
$251$		−	398.377i		−	1.58716i	0.608466	−	0.793580i	$-0.291785\pi$
$252$	404.379	−	284.648i	1.60468	−	1.12956i
$253$	−212.438			−0.839677
$254$		−	88.3070i		−	0.347665i
$255$	−13.9042	−	43.9085i	−0.0545264	−	0.172190i
$256$	−64.1899			−0.250742
$257$		−	231.515i		−	0.900835i	−0.892818	−	0.450417i	$-0.851275\pi$
$257$		−	231.515i		−	0.900835i	0.892818	−	0.450417i	$-0.148725\pi$
$258$	−638.250	+	202.111i	−2.47384	+	0.783375i
$259$	136.857			0.528406
$260$			225.449i			0.867110i
$261$	27.8977	+	39.6323i	0.106888	+	0.151848i
$262$	91.7850			0.350324
$263$			380.593i			1.44712i	0.690261	+	0.723560i	$0.257496\pi$
$263$			380.593i			1.44712i	−0.690261	+	0.723560i	$0.742504\pi$
$264$	209.739	+	662.340i	0.794467	+	2.50886i
$265$	−116.705			−0.440397
$266$		−	664.351i		−	2.49756i
$267$	54.3269	−	17.2034i	0.203471	−	0.0644321i
$268$	−440.098			−1.64216
$269$			21.0680i			0.0783198i	0.999233	+	0.0391599i	$0.0124682\pi$
$269$			21.0680i			0.0783198i	−0.999233	+	0.0391599i	$0.987532\pi$
$270$	−98.9459	−	75.3401i	−0.366466	−	0.279038i
$271$	162.063			0.598017			0.299009	−	0.954250i	$-0.403344\pi$
$271$	162.063			0.598017			0.299009	+	0.954250i	$0.403344\pi$
$272$		−	554.540i		−	2.03875i
$273$	90.7414	+	286.554i	0.332386	+	1.04965i
$274$	77.1266			0.281484
$275$			240.998i			0.876356i
$276$	593.706	−	188.005i	2.15111	−	0.681179i
$277$	313.920			1.13328			0.566642	−	0.823964i	$-0.308242\pi$
$277$	313.920			1.13328			0.566642	+	0.823964i	$0.308242\pi$
$278$		−	415.960i		−	1.49626i
$279$	−218.291	+	153.658i	−0.782404	+	0.550745i
$280$	−152.119			−0.543282
$281$			123.542i			0.439651i	0.975539	+	0.219825i	$0.0705488\pi$
$281$			123.542i			0.439651i	−0.975539	+	0.219825i	$0.929451\pi$
$282$	−167.343	−	528.455i	−0.593414	−	1.87395i
$283$	−489.117			−1.72833			−0.864165	−	0.503209i	$-0.832153\pi$
$283$	−489.117			−1.72833			−0.864165	+	0.503209i	$0.832153\pi$
$284$			606.977i			2.13724i
$285$	−113.857	+	36.0544i	−0.399498	+	0.126507i
$286$	−702.579			−2.45657
$287$			12.2480i			0.0426758i
$288$	−394.202	−	560.015i	−1.36876	−	1.94450i
$289$	133.174			0.460809
$290$		−	24.8045i		−	0.0855327i
$291$	−115.369	−	364.326i	−0.396457	−	1.25198i
$292$	87.9707			0.301270
$293$			272.905i			0.931415i	0.884939	+	0.465708i	$0.154200\pi$
$293$			272.905i			0.931415i	−0.884939	+	0.465708i	$0.845800\pi$
$294$	203.172	−	64.3372i	0.691061	−	0.218834i
$295$	−100.100			−0.339322
$296$		−	563.648i		−	1.90422i
$297$	167.831	−	220.417i	0.565089	−	0.742143i
$298$	290.205			0.973843
$299$			378.529i			1.26598i
$300$	−213.280	−	673.522i	−0.710934	−	2.24507i
$301$	326.543			1.08486
$302$		−	436.748i		−	1.44619i
$303$	31.5576	−	9.99316i	0.104151	−	0.0329807i
$304$	−1437.95			−4.73010
$305$			30.5358i			0.100117i
$306$	−344.068	+	242.194i	−1.12440	+	0.791483i
$307$	275.906			0.898718			0.449359	−	0.893351i	$-0.351652\pi$
$307$	275.906			0.898718			0.449359	+	0.893351i	$0.351652\pi$
$308$		−	563.789i		−	1.83048i
$309$	−22.1045	−	69.8043i	−0.0715356	−	0.225904i
$310$	136.621			0.440712
$311$			189.250i			0.608521i	0.952589	+	0.304261i	$0.0984093\pi$
$311$			189.250i			0.608521i	−0.952589	+	0.304261i	$0.901591\pi$
$312$	1180.18	−	373.720i	3.78262	−	1.19782i
$313$	−193.423			−0.617965			−0.308983	−	0.951068i	$-0.599989\pi$
$313$	−193.423			−0.617965			−0.308983	+	0.951068i	$0.599989\pi$
$314$		−	469.564i		−	1.49543i
$315$	34.9156	+	49.6022i	0.110843	+	0.157467i
$316$	159.709			0.505408
$317$			106.117i			0.334754i	0.985893	+	0.167377i	$0.0535298\pi$
$317$			106.117i			0.334754i	−0.985893	+	0.167377i	$0.946470\pi$
$318$	321.866	+	1016.43i	1.01216	+	3.19631i
$319$	55.2556			0.173215
$320$			131.954i			0.412358i
$321$	−34.0520	+	10.7830i	−0.106081	+	0.0335920i
$322$	−424.934			−1.31967
$323$			404.065i			1.25098i
$324$	−273.976	+	764.532i	−0.845605	+	2.35967i
$325$	429.417			1.32128
$326$			38.8037i			0.119030i
$327$	−67.4197	−	212.906i	−0.206176	−	0.651089i
$328$	50.4434			0.153791
$329$			270.369i			0.821790i
$330$	−135.170	+	42.8034i	−0.409605	+	0.129707i
$331$	−224.448			−0.678092			−0.339046	−	0.940770i	$-0.610104\pi$
$331$	−224.448			−0.678092			−0.339046	+	0.940770i	$0.610104\pi$
$332$		−	166.318i		−	0.500957i
$333$	−183.791	+	129.373i	−0.551926	+	0.388508i
$334$	749.352			2.24357
$335$		−	53.9835i		−	0.161145i
$336$	220.482	+	696.266i	0.656198	+	2.07222i
$337$	185.836			0.551442			0.275721	−	0.961238i	$-0.411083\pi$
$337$	185.836			0.551442			0.275721	+	0.961238i	$0.411083\pi$
$338$			618.939i			1.83118i
$339$	−216.405	+	68.5277i	−0.638363	+	0.202147i
$340$	153.930			0.452736
$341$			304.343i			0.892501i
$342$	628.021	+	892.185i	1.83632	+	2.60873i
$343$	−372.475			−1.08593
$344$		−	1344.87i		−	3.90950i
$345$	23.0612	+	72.8255i	0.0668441	+	0.211088i
$346$	871.782			2.51960
$347$		−	532.449i		−	1.53444i	−0.641387	−	0.767218i	$-0.721640\pi$
$347$		−	532.449i		−	1.53444i	0.641387	−	0.767218i	$-0.278360\pi$
$348$	−154.424	+	48.9006i	−0.443748	+	0.140519i
$349$	−581.307			−1.66564			−0.832818	−	0.553547i	$-0.813274\pi$
$349$	−581.307			−1.66564			−0.832818	+	0.553547i	$0.813274\pi$
$350$			482.061i			1.37732i
$351$	−392.745	−	299.047i	−1.11893	−	0.851985i
$352$	−780.777			−2.21812
$353$		−	362.745i		−	1.02761i	−0.857908	−	0.513804i	$-0.828236\pi$
$353$		−	362.745i		−	1.02761i	0.857908	−	0.513804i	$-0.171764\pi$
$354$	276.069	+	871.806i	0.779857	+	2.46273i
$355$	−74.4533			−0.209728
$356$			190.454i			0.534983i
$357$	195.652	−	61.9558i	0.548044	−	0.173546i
$358$	−1121.44			−3.13250
$359$			254.842i			0.709866i	0.934892	+	0.354933i	$0.115496\pi$
$359$			254.842i			0.709866i	−0.934892	+	0.354933i	$0.884504\pi$
$360$	204.287	−	143.800i	0.567464	−	0.399446i
$361$	686.762			1.90239
$362$		−	626.997i		−	1.73203i
$363$	14.2350	+	44.9531i	0.0392149	+	0.123838i
$364$	−1004.58			−2.75982
$365$			10.7907i			0.0295636i
$366$	265.948	−	84.2160i	0.726633	−	0.230098i
$367$	−223.346			−0.608572			−0.304286	−	0.952581i	$-0.598418\pi$
$367$	−223.346			−0.608572			−0.304286	+	0.952581i	$0.598418\pi$
$368$			919.745i			2.49931i
$369$	−11.5782	−	16.4483i	−0.0313772	−	0.0445754i
$370$	115.029			0.310888
$371$		−	520.026i		−	1.40169i
$372$	−269.340	−	850.554i	−0.724031	−	2.28643i
$373$	−463.259			−1.24198			−0.620990	−	0.783819i	$-0.713269\pi$
$373$	−463.259			−1.24198			−0.620990	+	0.783819i	$0.713269\pi$
$374$			479.702i			1.28263i
$375$	170.552	−	54.0077i	0.454806	−	0.144021i
$376$	1113.52			2.96148
$377$		−	98.4561i		−	0.261157i
$378$	335.708	−	440.892i	0.888116	−	1.16638i
$379$	−3.44678			−0.00909441			−0.00454720	−	0.999990i	$-0.501447\pi$
$379$	−3.44678			−0.00909441			−0.00454720	+	0.999990i	$0.501447\pi$
$380$		−	399.149i		−	1.05039i
$381$	−21.3546	−	67.4360i	−0.0560487	−	0.176997i
$382$	−948.471			−2.48291
$383$			629.757i			1.64427i	0.569290	+	0.822136i	$0.307218\pi$
$383$			629.757i			1.64427i	−0.569290	+	0.822136i	$0.692782\pi$
$384$	278.716	−	88.2595i	0.725824	−	0.229842i
$385$	69.1557			0.179625
$386$		−	1337.90i		−	3.46606i
$387$	−438.528	+	308.686i	−1.13315	+	0.797638i
$388$	1277.22			3.29181
$389$		−	288.386i		−	0.741353i	−0.928762	−	0.370676i	$-0.879126\pi$
$389$		−	288.386i		−	0.741353i	0.928762	−	0.370676i	$-0.120874\pi$
$390$	76.2683	+	240.849i	0.195560	+	0.617562i
$391$	258.449			0.660996
$392$			428.108i			1.09211i
$393$	70.0920	−	22.1956i	0.178351	−	0.0564774i
$394$	475.796			1.20760
$395$			19.5903i			0.0495957i
$396$	532.958	+	757.136i	1.34585	+	1.91196i
$397$	51.5262			0.129789			0.0648945	−	0.997892i	$-0.479329\pi$
$397$	51.5262			0.129789			0.0648945	+	0.997892i	$0.479329\pi$
$398$			730.851i			1.83631i
$399$	−160.655	−	507.335i	−0.402643	−	1.27152i
$400$	1043.39			2.60848
$401$		−	118.454i		−	0.295396i	−0.989033	−	0.147698i	$-0.952814\pi$
$401$		−	118.454i		−	0.295396i	0.989033	−	0.147698i	$-0.0471863\pi$
$402$	−470.162	+	148.883i	−1.16956	+	0.370356i
$403$	542.287			1.34563
$404$			110.632i			0.273841i
$405$	−93.7794	−	33.6066i	−0.231554	−	0.0829792i
$406$	110.526			0.272232
$407$			256.243i			0.629590i
$408$	−255.166	−	805.793i	−0.625406	−	1.97498i
$409$	−129.354			−0.316270			−0.158135	−	0.987418i	$-0.550548\pi$
$409$	−129.354			−0.316270			−0.158135	+	0.987418i	$0.550548\pi$
$410$			10.2944i			0.0251084i
$411$	58.8980	−	18.6509i	0.143304	−	0.0453793i
$412$	244.713			0.593964
$413$		−	446.035i		−	1.07999i
$414$	570.662	−	401.697i	1.37841	−	0.970281i
$415$	20.4010			0.0491589
$416$			1391.21i			3.34426i
$417$	−100.588	−	317.650i	−0.241219	−	0.761750i
$418$	1243.89			2.97582
$419$		−	14.1150i		−	0.0336875i	−0.999858	−	0.0168437i	$-0.994638\pi$
$419$		−	14.1150i		−	0.0336875i	0.999858	−	0.0168437i	$-0.00536178\pi$
$420$	−193.271	+	61.2020i	−0.460169	+	0.145719i
$421$	−226.136			−0.537141			−0.268571	−	0.963260i	$-0.586551\pi$
$421$	−226.136			−0.537141			−0.268571	+	0.963260i	$0.586551\pi$
$422$			381.267i			0.903475i
$423$	−255.584	−	363.090i	−0.604217	−	0.858369i
$424$	−2141.73			−5.05126
$425$		−	293.194i		−	0.689869i
$426$	205.338	+	648.441i	0.482014	+	1.52216i
$427$	−136.064			−0.318652
$428$		−	119.376i		−	0.278917i
$429$	−536.527	+	169.899i	−1.25065	+	0.396035i
$430$	274.460			0.638278
$431$		−	771.927i		−	1.79101i	−0.445048	−	0.895507i	$-0.646814\pi$
$431$		−	771.927i		−	1.79101i	0.445048	−	0.895507i	$-0.353186\pi$
$432$	−954.287	−	726.620i	−2.20900	−	1.68199i
$433$	672.537			1.55320			0.776602	−	0.629991i	$-0.216942\pi$
$433$	672.537			1.55320			0.776602	+	0.629991i	$0.216942\pi$
$434$			608.767i			1.40269i
$435$	−5.99827	−	18.9421i	−0.0137891	−	0.0435450i
$436$	746.386			1.71190
$437$		−	670.172i		−	1.53358i
$438$	93.9801	−	29.7601i	0.214567	−	0.0679455i
$439$	244.404			0.556729			0.278364	−	0.960476i	$-0.410208\pi$
$439$	244.404			0.556729			0.278364	+	0.960476i	$0.410208\pi$
$440$		−	284.819i		−	0.647315i
$441$	139.595	−	98.2628i	0.316542	−	0.222818i
$442$	854.747			1.93382
$443$			107.986i			0.243761i	0.992545	+	0.121880i	$0.0388924\pi$
$443$			107.986i			0.243761i	−0.992545	+	0.121880i	$0.961108\pi$
$444$	−226.772	−	716.129i	−0.510748	−	1.61290i
$445$	−23.3616			−0.0524979
$446$			1074.79i			2.40985i
$447$	221.616	−	70.1779i	0.495786	−	0.156998i
$448$	−587.975			−1.31244
$449$			598.901i			1.33385i	0.745123	+	0.666927i	$0.232391\pi$
$449$			598.901i			1.33385i	−0.745123	+	0.666927i	$0.767609\pi$
$450$	−455.699	−	647.380i	−1.01267	−	1.43862i
$451$	−22.9324			−0.0508478
$452$		−	758.653i		−	1.67844i
$453$	−105.615	−	333.525i	−0.233146	−	0.736257i
$454$	−54.7487			−0.120592
$455$		−	123.224i		−	0.270821i
$456$	−2089.46	+	661.658i	−4.58216	+	1.45100i
$457$	384.587			0.841547			0.420773	−	0.907166i	$-0.361759\pi$
$457$	384.587			0.841547			0.420773	+	0.907166i	$0.361759\pi$
$458$			70.9538i			0.154921i
$459$	−204.181	+	268.155i	−0.444839	+	0.584217i
$460$	−255.305			−0.555010
$461$			185.859i			0.403166i	0.979471	+	0.201583i	$0.0646085\pi$
$461$			185.859i			0.403166i	−0.979471	+	0.201583i	$0.935391\pi$
$462$	−190.727	−	602.302i	−0.412830	−	1.30368i
$463$	−434.531			−0.938512			−0.469256	−	0.883062i	$-0.655478\pi$
$463$	−434.531			−0.938512			−0.469256	+	0.883062i	$0.655478\pi$
$464$		−	239.228i		−	0.515577i
$465$	104.331	−	33.0379i	0.224368	−	0.0710492i
$466$	−1131.71			−2.42857
$467$			287.301i			0.615206i	0.951515	+	0.307603i	$0.0995269\pi$
$467$			287.301i			0.615206i	−0.951515	+	0.307603i	$0.900473\pi$
$468$	1349.09	−	949.641i	2.88266	−	2.02915i
$469$	240.545			0.512889
$470$			227.245i			0.483501i
$471$	−113.551	−	358.584i	−0.241084	−	0.761326i
$472$	−1837.00			−3.89195
$473$			611.399i			1.29260i
$474$	170.619	−	54.0289i	0.359956	−	0.113985i
$475$	−760.268			−1.60056
$476$			685.897i			1.44096i
$477$	491.589	+	698.365i	1.03058	+	1.46408i
$478$	−626.518			−1.31071
$479$			371.229i			0.775007i	0.921868	+	0.387504i	$0.126663\pi$
$479$			371.229i			0.775007i	−0.921868	+	0.387504i	$0.873337\pi$
$480$	84.7571	+	267.656i	0.176577	+	0.557617i
$481$	456.582			0.949234
$482$			1681.34i			3.48826i
$483$	−324.503	+	102.758i	−0.671848	+	0.212750i
$484$	−157.592			−0.325604
$485$			156.667i			0.323025i
$486$	−34.0538	+	909.443i	−0.0700696	+	1.87128i
$487$	139.202			0.285835			0.142917	−	0.989735i	$-0.454352\pi$
$487$	139.202			0.285835			0.142917	+	0.989735i	$0.454352\pi$
$488$			560.383i			1.14833i
$489$	9.38357	+	29.6326i	0.0191893	+	0.0605983i
$490$	−87.3677			−0.178301
$491$		−	809.943i		−	1.64958i	−0.565440	−	0.824789i	$-0.691294\pi$
$491$		−	809.943i		−	1.64958i	0.565440	−	0.824789i	$-0.308706\pi$
$492$	64.0896	−	20.2949i	0.130263	−	0.0412497i
$493$	−67.2232			−0.136355
$494$		−	2216.40i		−	4.48665i
$495$	−92.8722	+	65.3740i	−0.187621	+	0.132069i
$496$	1317.64			2.65654
$497$		−	331.756i		−	0.667517i
$498$	−56.2646	−	177.679i	−0.112981	−	0.356786i
$499$	−337.418			−0.676188			−0.338094	−	0.941112i	$-0.609782\pi$
$499$	−337.418			−0.676188			−0.338094	+	0.941112i	$0.609782\pi$
$500$			597.906i			1.19581i
$501$	572.246	−	181.210i	1.14221	−	0.361696i
$502$	1492.00			2.97210
$503$		−	182.431i		−	0.362685i	−0.983420	−	0.181343i	$-0.941956\pi$
$503$		−	182.431i		−	0.362685i	0.983420	−	0.181343i	$-0.0580443\pi$
$504$	640.760	+	910.282i	1.27135	+	1.80611i
$505$	−13.5704			−0.0268720
$506$		−	795.621i		−	1.57237i
$507$	149.673	+	472.655i	0.295213	+	0.932259i
$508$	236.411			0.465376
$509$		−	393.438i		−	0.772963i	−0.922297	−	0.386481i	$-0.873690\pi$
$509$		−	393.438i		−	0.772963i	0.922297	−	0.386481i	$-0.126310\pi$
$510$	164.445	−	52.0739i	0.322442	−	0.102106i
$511$	−48.0823			−0.0940944
$512$		−	630.212i		−	1.23088i
$513$	695.341	+	529.452i	1.35544	+	1.03207i
$514$	867.065			1.68690
$515$			30.0171i			0.0582857i
$516$	−541.081	−	1708.69i	−1.04861	−	3.31142i
$517$	−506.223			−0.979154
$518$			512.555i			0.989489i
$519$	665.740	−	210.816i	1.28274	−	0.406196i
$520$	−507.498			−0.975958
$521$			812.843i			1.56016i	0.625681	+	0.780079i	$0.284821\pi$
$521$			812.843i			1.56016i	−0.625681	+	0.780079i	$0.715179\pi$
$522$	−148.430	+	104.482i	−0.284349	+	0.200157i
$523$	−909.231			−1.73849			−0.869246	−	0.494380i	$-0.835395\pi$
$523$	−909.231			−1.73849			−0.869246	+	0.494380i	$0.835395\pi$
$524$			245.722i			0.468935i
$525$	116.573	+	368.128i	0.222043	+	0.701196i
$526$	−1425.39			−2.70987
$527$		−	370.259i		−	0.702579i
$528$	−1303.65	+	412.818i	−2.46903	+	0.781853i
$529$	100.343			0.189684
$530$		−	437.083i		−	0.824685i
$531$	421.643	+	598.999i	0.794055	+	1.12806i
$532$	1778.57			3.34317
$533$			40.8615i			0.0766633i
$534$	64.4298	+	203.464i	0.120655	+	0.381019i
$535$	14.6430			0.0273701
$536$		−	990.687i		−	1.84830i
$537$	−856.389	+	271.188i	−1.59477	+	0.505005i
$538$	−78.9037			−0.146661
$539$		−	194.625i		−	0.361084i
$540$	201.697	−	264.893i	0.373513	−	0.490542i
$541$	−840.267			−1.55317			−0.776587	−	0.630010i	$-0.783051\pi$
$541$	−840.267			−1.55317			−0.776587	+	0.630010i	$0.783051\pi$
$542$			606.955i			1.11984i
$543$	−151.621	−	478.809i	−0.279229	−	0.881784i
$544$	949.882			1.74611
$545$			91.5536i			0.167988i
$546$	−1073.20	+	339.843i	−1.96557	+	0.622424i
$547$	−181.177			−0.331219			−0.165609	−	0.986191i	$-0.552959\pi$
$547$	−181.177			−0.331219			−0.165609	+	0.986191i	$0.552959\pi$
$548$			206.479i			0.376787i
$549$	182.727	−	128.624i	0.332836	−	0.234288i
$550$	−902.582			−1.64106
$551$			174.313i			0.316358i
$552$	423.211	+	1336.47i	0.766687	+	2.42114i
$553$	−87.2923			−0.157852
$554$			1175.69i			2.12218i
$555$	87.8421	−	27.8164i	0.158274	−	0.0501197i
$556$	1113.59			2.00285
$557$			464.682i			0.834259i	0.908847	+	0.417130i	$0.136964\pi$
$557$			464.682i			0.834259i	−0.908847	+	0.417130i	$0.863036\pi$
$558$	−575.477	−	817.540i	−1.03132	−	1.46513i
$559$	1089.41			1.94885
$560$		−	299.408i		−	0.534656i
$561$	116.002	+	366.326i	0.206778	+	0.652988i
$562$	−462.687			−0.823287
$563$		−	610.362i		−	1.08412i	−0.840338	−	0.542062i	$-0.817644\pi$
$563$		−	610.362i		−	1.08412i	0.840338	−	0.542062i	$-0.182356\pi$
$564$	1414.75	−	448.001i	2.50843	−	0.794328i
$565$	93.0582			0.164705
$566$		−	1831.84i		−	3.23646i
$567$	149.747	−	417.871i	0.264105	−	0.736986i
$568$	−1366.34			−2.40553
$569$		−	554.320i		−	0.974200i	−0.873346	−	0.487100i	$-0.838055\pi$
$569$		−	554.320i		−	0.974200i	0.873346	−	0.487100i	$-0.161945\pi$
$570$	−135.030	−	426.416i	−0.236895	−	0.748097i
$571$	−85.4935			−0.149726			−0.0748630	−	0.997194i	$-0.523852\pi$
$571$	−85.4935			−0.149726			−0.0748630	+	0.997194i	$0.523852\pi$
$572$		−	1880.91i		−	3.28830i
$573$	−724.305	+	229.361i	−1.26406	+	0.400281i
$574$	−45.8709			−0.0799144
$575$			486.285i			0.845713i
$576$	789.617	−	555.822i	1.37086	−	0.964969i
$577$	−98.0550			−0.169939			−0.0849697	−	0.996384i	$-0.527079\pi$
$577$	−98.0550			−0.169939			−0.0849697	+	0.996384i	$0.527079\pi$
$578$			498.761i			0.862908i
$579$	−323.533	−	1021.69i	−0.558780	−	1.76458i
$580$	66.4053			0.114492
$581$			90.9045i			0.156462i
$582$	1364.47	−	432.078i	2.34445	−	0.742402i
$583$	973.667			1.67010
$584$			198.027i			0.339088i
$585$	116.485	+	165.482i	0.199120	+	0.282876i
$586$	−1022.08			−1.74416
$587$			437.104i			0.744641i	0.928104	+	0.372320i	$0.121438\pi$
$587$			437.104i			0.744641i	−0.928104	+	0.372320i	$0.878562\pi$
$588$	172.240	+	543.922i	0.292926	+	0.925037i
$589$	−960.101			−1.63005
$590$		−	374.893i		−	0.635411i
$591$	363.344	−	115.058i	0.614795	−	0.194683i
$592$	1109.40			1.87398
$593$		−	75.3583i		−	0.127080i	−0.997979	−	0.0635399i	$-0.979761\pi$
$593$		−	75.3583i		−	0.127080i	0.997979	−	0.0635399i	$-0.0202390\pi$
$594$	825.501	+	628.559i	1.38973	+	1.05818i
$595$	−84.1338			−0.141401
$596$			776.922i			1.30356i
$597$	176.736	+	558.118i	0.296040	+	0.934871i
$598$	−1417.66			−2.37067
$599$			775.904i			1.29533i	0.761924	+	0.647666i	$0.224255\pi$
$599$			775.904i			1.29533i	−0.761924	+	0.647666i	$0.775745\pi$
$600$	1516.14	−	480.106i	2.52690	−	0.800177i
$601$	−155.251			−0.258321			−0.129160	−	0.991624i	$-0.541228\pi$
$601$	−155.251			−0.258321			−0.129160	+	0.991624i	$0.541228\pi$
$602$			1222.96i			2.03150i
$603$	−323.038	+	227.391i	−0.535718	+	0.377099i
$604$	1169.24			1.93583
$605$		−	19.3307i		−	0.0319515i
$606$	37.4263	+	118.189i	0.0617595	+	0.195032i
$607$	−34.7585			−0.0572628			−0.0286314	−	0.999590i	$-0.509115\pi$
$607$	−34.7585			−0.0572628			−0.0286314	+	0.999590i	$0.509115\pi$
$608$		−	2463.09i		−	4.05114i
$609$	84.4038	−	26.7276i	0.138594	−	0.0438878i
$610$	−114.362			−0.187479
$611$			902.003i			1.47627i
$612$	−648.389	−	921.120i	−1.05946	−	1.50510i
$613$	237.912			0.388111			0.194055	−	0.980991i	$-0.437836\pi$
$613$	237.912			0.388111			0.194055	+	0.980991i	$0.437836\pi$
$614$			1033.32i			1.68293i
$615$	2.48942	+	7.86139i	0.00404783	+	0.0127827i
$616$	1269.12			2.06026
$617$			712.814i			1.15529i	0.816288	+	0.577645i	$0.196028\pi$
$617$			712.814i			1.15529i	−0.816288	+	0.577645i	$0.803972\pi$
$618$	261.430	−	82.7854i	0.423026	−	0.133957i
$619$	60.3708			0.0975296			0.0487648	−	0.998810i	$-0.484472\pi$
$619$	60.3708			0.0975296			0.0487648	+	0.998810i	$0.484472\pi$
$620$			365.754i			0.589926i
$621$	338.649	−	444.756i	0.545329	−	0.716193i
$622$	−708.777			−1.13951
$623$		−	104.097i		−	0.167089i
$624$	735.572	+	2322.88i	1.17880	+	3.72256i
$625$	513.845			0.822152
$626$		−	724.406i		−	1.15720i
$627$	949.904	−	300.800i	1.51500	−	0.479745i
$628$	1257.09			2.00174
$629$		−	311.742i		−	0.495615i
$630$	−185.769	+	130.766i	−0.294872	+	0.207564i
$631$	−699.344			−1.10831			−0.554156	−	0.832413i	$-0.686959\pi$
$631$	−699.344			−1.10831			−0.554156	+	0.832413i	$0.686959\pi$
$632$			359.514i			0.568852i
$633$	92.1986	+	291.156i	0.145653	+	0.459962i
$634$	−397.428			−0.626859
$635$			28.9987i			0.0456673i
$636$	−2721.13	+	861.683i	−4.27850	+	1.35485i
$637$	−346.788			−0.544408
$638$			206.943i			0.324362i
$639$	313.614	+	445.530i	0.490789	+	0.697229i
$640$	−119.853			−0.187271
$641$		−	742.351i		−	1.15811i	−0.815287	−	0.579057i	$-0.803421\pi$
$641$		−	742.351i		−	1.15811i	0.815287	−	0.579057i	$-0.196579\pi$
$642$	−40.3845	−	127.531i	−0.0629042	−	0.198647i
$643$	−71.5118			−0.111216			−0.0556079	−	0.998453i	$-0.517710\pi$
$643$	−71.5118			−0.111216			−0.0556079	+	0.998453i	$0.517710\pi$
$644$		−	1137.61i		−	1.76648i
$645$	209.592	−	66.3703i	0.324949	−	0.102900i
$646$	−1513.30			−2.34257
$647$		−	93.6010i		−	0.144669i	−0.997380	−	0.0723346i	$-0.976955\pi$
$647$		−	93.6010i		−	0.144669i	0.997380	−	0.0723346i	$-0.0230450\pi$
$648$	−1721.01	−	616.736i	−2.65587	−	0.951753i
$649$	835.129			1.28679
$650$			1608.25i			2.47423i
$651$	147.213	+	464.888i	0.226134	+	0.714114i
$652$	−103.883			−0.159330
$653$			400.402i			0.613173i	0.951843	+	0.306587i	$0.0991869\pi$
$653$			400.402i			0.613173i	−0.951843	+	0.306587i	$0.900813\pi$
$654$	797.373	−	252.499i	1.21922	−	0.386084i
$655$	−30.1409			−0.0460166
$656$			99.2849i			0.151349i
$657$	64.5717	−	45.4529i	0.0982827	−	0.0691825i
$658$	−1012.58			−1.53888
$659$		−	112.245i		−	0.170326i	−0.996367	−	0.0851631i	$-0.972859\pi$
$659$		−	112.245i		−	0.170326i	0.996367	−	0.0851631i	$-0.0271411\pi$
$660$	−114.591	−	361.869i	−0.173623	−	0.548287i
$661$	382.154			0.578146			0.289073	−	0.957307i	$-0.406653\pi$
$661$	382.154			0.578146			0.289073	+	0.957307i	$0.406653\pi$
$662$		−	840.601i		−	1.26979i
$663$	652.731	−	206.696i	0.984512	−	0.311759i
$664$	374.391			0.563842
$665$			218.163i			0.328065i
$666$	−484.527	−	688.333i	−0.727517	−	1.03353i
$667$	111.495			0.167158
$668$			2006.13i			3.00318i
$669$	259.908	+	820.770i	0.388503	+	1.22686i
$670$	202.178			0.301759
$671$		−	254.759i		−	0.379671i
$672$	−1192.65	+	377.669i	−1.77477	+	0.562007i
$673$	1212.70			1.80194			0.900968	−	0.433885i	$-0.142858\pi$
$673$	1212.70			1.80194			0.900968	+	0.433885i	$0.142858\pi$
$674$			695.990i			1.03263i
$675$	−504.547	−	384.176i	−0.747478	−	0.569150i
$676$	−1656.99			−2.45117
$677$		−	1042.37i		−	1.53969i	−0.638233	−	0.769843i	$-0.720334\pi$
$677$		−	1042.37i		−	1.53969i	0.638233	−	0.769843i	$-0.279666\pi$
$678$	−256.649	−	810.477i	−0.378538	−	1.19539i
$679$	−698.092			−1.02812
$680$			346.506i			0.509568i
$681$	−41.8091	+	13.2394i	−0.0613937	+	0.0194412i
$682$	−1139.82			−1.67129
$683$			1137.51i			1.66546i	0.553680	+	0.832729i	$0.313223\pi$
$683$			1137.51i			1.66546i	−0.553680	+	0.832729i	$0.686777\pi$
$684$	−2388.51	+	1681.31i	−3.49198	+	2.45805i
$685$	−25.3273			−0.0369741
$686$		−	1394.99i		−	2.03351i
$687$	17.1582	+	54.1842i	0.0249755	+	0.0788707i
$688$	2647.03			3.84743
$689$		−	1734.91i		−	2.51801i
$690$	−272.745	+	86.3685i	−0.395283	+	0.125172i
$691$	−75.9173			−0.109866			−0.0549329	−	0.998490i	$-0.517494\pi$
$691$	−75.9173			−0.109866			−0.0549329	+	0.998490i	$0.517494\pi$
$692$			2333.89i			3.37267i
$693$	−291.300	−	413.829i	−0.420346	−	0.597155i
$694$	1994.12			2.87337
$695$			136.595i			0.196540i
$696$	−110.078	−	347.618i	−0.158158	−	0.499451i
$697$	27.8992			0.0400275
$698$		−	2177.10i		−	3.11906i
$699$	−864.238	+	273.673i	−1.23639	+	0.391521i
$700$	−1290.55			−1.84364
$701$		−	382.716i		−	0.545958i	−0.962020	−	0.272979i	$-0.911991\pi$
$701$		−	382.716i		−	0.545958i	0.962020	−	0.272979i	$-0.0880089\pi$
$702$	1119.99	−	1470.90i	1.59542	−	2.09530i
$703$	−808.362			−1.14988
$704$		−	1100.89i		−	1.56376i
$705$	54.9529	+	173.537i	0.0779474	+	0.246152i
$706$	1358.55			1.92429
$707$		−	60.4681i		−	0.0855278i
$708$	−2333.95	+	739.079i	−3.29655	+	1.04390i
$709$	−48.9954			−0.0691050			−0.0345525	−	0.999403i	$-0.511001\pi$
$709$	−48.9954			−0.0691050			−0.0345525	+	0.999403i	$0.511001\pi$
$710$		−	278.842i		−	0.392735i
$711$	117.229	−	82.5188i	0.164878	−	0.116060i
$712$	−428.724			−0.602140
$713$			614.102i			0.861293i
$714$	232.036	+	732.751i	0.324980	+	1.02626i
$715$	230.717			0.322681
$716$		−	3002.25i		−	4.19309i
$717$	−478.443	+	151.506i	−0.667285	+	0.211305i
$718$	−954.430			−1.32929
$719$		−	985.783i		−	1.37105i	−0.728051	−	0.685523i	$-0.759573\pi$
$719$		−	985.783i		−	1.37105i	0.728051	−	0.685523i	$-0.240427\pi$
$720$	283.035	+	402.087i	0.393104	+	0.558454i
$721$	−133.753			−0.185511
$722$			2572.05i			3.56240i
$723$	406.585	+	1283.96i	0.562359	+	1.77588i
$724$	1678.56			2.31846
$725$		−	126.484i		−	0.174460i
$726$	−168.358	+	53.3128i	−0.231898	+	0.0734336i
$727$	−32.2452			−0.0443538			−0.0221769	−	0.999754i	$-0.507060\pi$
$727$	−32.2452			−0.0443538			−0.0221769	+	0.999754i	$0.507060\pi$
$728$		−	2261.36i		−	3.10626i
$729$	193.918	+	702.735i	0.266005	+	0.963972i
$730$	−40.4132			−0.0553606
$731$		−	743.819i		−	1.01754i
$732$	225.459	+	711.981i	0.308004	+	0.972652i
$733$	546.891			0.746100			0.373050	−	0.927811i	$-0.378312\pi$
$733$	546.891			0.746100			0.373050	+	0.927811i	$0.378312\pi$
$734$		−	836.472i		−	1.13961i
$735$	−66.7188	+	21.1274i	−0.0907738	+	0.0287448i
$736$	−1575.45			−2.14056
$737$			450.382i			0.611102i
$738$	61.6020	−	43.3625i	0.0834715	−	0.0587567i
$739$	985.913			1.33412			0.667059	−	0.745005i	$-0.267553\pi$
$739$	985.913			1.33412			0.667059	+	0.745005i	$0.267553\pi$
$740$			307.949i			0.416147i
$741$	−535.975	−	1692.57i	−0.723313	−	2.28416i
$742$	1947.60			2.62479
$743$		−	197.757i		−	0.266160i	−0.991105	−	0.133080i	$-0.957513\pi$
$743$		−	197.757i		−	0.266160i	0.991105	−	0.133080i	$-0.0424868\pi$
$744$	1914.65	−	606.300i	2.57345	−	0.814919i
$745$	−95.2992			−0.127918
$746$		−	1734.99i		−	2.32572i
$747$	−85.9335	−	122.080i	−0.115038	−	0.163426i
$748$	−1284.23			−1.71689
$749$			65.2477i			0.0871131i
$750$	202.269	+	638.750i	0.269692	+	0.851666i
$751$	−119.393			−0.158979			−0.0794896	−	0.996836i	$-0.525329\pi$
$751$	−119.393			−0.158979			−0.0794896	+	0.996836i	$0.525329\pi$
$752$			2191.68i			2.91446i
$753$	1139.37	−	360.797i	1.51311	−	0.479147i
$754$	368.737			0.489041
$755$			143.422i			0.189963i
$756$	1180.33	+	898.740i	1.56129	+	1.18881i
$757$	−1173.55			−1.55026			−0.775130	−	0.631802i	$-0.782316\pi$
$757$	−1173.55			−1.55026			−0.775130	+	0.631802i	$0.782316\pi$
$758$		−	12.9088i		−	0.0170301i
$759$	−192.399	−	607.580i	−0.253490	−	0.800500i
$760$	898.508			1.18225
$761$		−	118.347i		−	0.155516i	−0.996972	−	0.0777578i	$-0.975224\pi$
$761$		−	118.347i		−	0.155516i	0.996972	−	0.0777578i	$-0.0247761\pi$
$762$	252.560	−	79.9768i	0.331444	−	0.104956i
$763$	−407.953			−0.534670
$764$		−	2539.20i		−	3.32356i
$765$	112.987	−	79.5330i	0.147695	−	0.103965i
$766$	−2358.56			−3.07905
$767$		−	1488.06i		−	1.94010i
$768$	−58.1347	−	183.585i	−0.0756962	−	0.239043i
$769$	−223.427			−0.290542			−0.145271	−	0.989392i	$-0.546405\pi$
$769$	−223.427			−0.290542			−0.145271	+	0.989392i	$0.546405\pi$
$770$			259.001i			0.336365i
$771$	662.138	−	209.675i	0.858805	−	0.271952i
$772$	3581.76			4.63958
$773$		−	474.194i		−	0.613446i	−0.951799	−	0.306723i	$-0.900767\pi$
$773$		−	474.194i		−	0.613446i	0.951799	−	0.306723i	$-0.0992326\pi$
$774$	−1156.09	−	1642.37i	−1.49365	−	2.12192i
$775$	696.660			0.898916
$776$			2875.10i			3.70503i
$777$	123.947	+	391.415i	0.159520	+	0.503752i
$778$	1080.06			1.38825
$779$		−	72.3440i		−	0.0928678i
$780$	−644.789	+	204.182i	−0.826653	+	0.261771i
$781$	621.161			0.795340
$782$			967.941i			1.23778i
$783$	−88.0834	+	115.682i	−0.112495	+	0.147742i
$784$	−842.621			−1.07477
$785$			154.198i			0.196431i
$786$	83.1267	+	262.508i	0.105759	+	0.333979i
$787$	−260.006			−0.330376			−0.165188	−	0.986262i	$-0.552823\pi$
$787$	−260.006			−0.330376			−0.165188	+	0.986262i	$0.552823\pi$
$788$			1273.78i			1.61647i
$789$	−1088.51	+	344.691i	−1.37960	+	0.436870i
$790$	−73.3693			−0.0928726
$791$			414.658i			0.524220i
$792$	−1704.36	+	1199.72i	−2.15197	+	1.51480i
$793$	−453.937			−0.572430
$794$			192.975i			0.243042i
$795$	−105.696	−	333.780i	−0.132951	−	0.419849i
$796$	−1956.60			−2.45804
$797$			459.055i			0.575979i	0.957634	+	0.287989i	$0.0929868\pi$
$797$			459.055i			0.575979i	−0.957634	+	0.287989i	$0.907013\pi$
$798$	1900.06	−	601.681i	2.38103	−	0.753987i
$799$	615.863			0.770792
$800$			1787.25i			2.23406i
$801$	98.4042	+	139.796i	0.122852	+	0.174527i
$802$	443.631			0.553156
$803$		−	90.0264i		−	0.112113i
$804$	−398.583	−	1258.69i	−0.495750	−	1.56554i
$805$	139.542			0.173344
$806$			2030.97i			2.51981i
$807$	−60.2552	+	19.0806i	−0.0746656	+	0.0236439i
$808$	−249.039			−0.308216
$809$		−	1308.34i		−	1.61723i	−0.588338	−	0.808615i	$-0.700218\pi$
$809$		−	1308.34i		−	1.61723i	0.588338	−	0.808615i	$-0.299782\pi$
$810$	125.863	−	351.221i	0.155386	−	0.433606i
$811$	625.052			0.770718			0.385359	−	0.922767i	$-0.374078\pi$
$811$	625.052			0.770718			0.385359	+	0.922767i	$0.374078\pi$
$812$			295.895i			0.364403i
$813$	146.775	+	463.504i	0.180535	+	0.570116i
$814$	−959.679			−1.17897
$815$		−	12.7426i		−	0.0156350i
$816$	1586.00	−	502.229i	1.94363	−	0.615476i
$817$	−1928.76			−2.36079
$818$		−	484.456i		−	0.592245i
$819$	−737.372	+	519.046i	−0.900332	+	0.633756i
$820$	−27.5597			−0.0336094
$821$			1403.51i			1.70951i	0.519030	+	0.854756i	$0.326293\pi$
$821$			1403.51i			1.70951i	−0.519030	+	0.854756i	$0.673707\pi$
$822$	69.8510	+	220.584i	0.0849769	+	0.268351i
$823$	−1217.22			−1.47901			−0.739505	−	0.673151i	$-0.764940\pi$
$823$	−1217.22			−1.47901			−0.739505	+	0.673151i	$0.764940\pi$
$824$			550.864i			0.668525i
$825$	−689.261	+	218.264i	−0.835468	+	0.264562i
$826$	1670.48			2.02238
$827$		−	38.6306i		−	0.0467117i	−0.999727	−	0.0233558i	$-0.992565\pi$
$827$		−	38.6306i		−	0.0467117i	0.999727	−	0.0233558i	$-0.00743507\pi$
$828$	1075.40	+	1527.75i	1.29879	+	1.84510i
$829$	−887.799			−1.07093			−0.535464	−	0.844558i	$-0.679863\pi$
$829$	−887.799			−1.07093			−0.535464	+	0.844558i	$0.679863\pi$
$830$			76.4054i			0.0920547i
$831$	284.307	+	897.819i	0.342126	+	1.08041i
$832$	−1961.60			−2.35769
$833$			236.777i			0.284246i
$834$	1189.66	−	376.722i	1.42645	−	0.451705i
$835$	−246.077			−0.294702
$836$			3330.08i			3.98335i
$837$	−637.165	−	485.155i	−0.761248	−	0.579636i
$838$	52.8635			0.0630829
$839$			616.144i			0.734379i	0.930146	+	0.367189i	$0.119680\pi$
$839$			616.144i			0.734379i	−0.930146	+	0.367189i	$0.880320\pi$
$840$	−137.769	−	435.065i	−0.164011	−	0.517934i
$841$	−29.0000			−0.0344828
$842$		−	846.923i		−	1.00585i
$843$	−353.333	+	111.888i	−0.419138	+	0.132726i
$844$	−1020.71			−1.20937
$845$		−	203.251i		−	0.240533i
$846$	1359.84	−	957.209i	1.60738	−	1.13145i
$847$	86.1354			0.101695
$848$		−	4215.46i		−	4.97106i
$849$	−442.978	−	1398.89i	−0.521764	−	1.64769i
$850$	1098.07			1.29184
$851$			517.047i			0.607576i
$852$	−1735.97	+	549.720i	−2.03753	+	0.645211i
$853$	1497.88			1.75601			0.878005	−	0.478651i	$-0.158874\pi$
$853$	1497.88			1.75601			0.878005	+	0.478651i	$0.158874\pi$
$854$		−	509.587i		−	0.596706i
$855$	−206.233	−	292.981i	−0.241208	−	0.342668i
$856$	268.723			0.313929
$857$		−	422.279i		−	0.492741i	−0.969176	−	0.246370i	$-0.920762\pi$
$857$		−	422.279i		−	0.492741i	0.969176	−	0.246370i	$-0.0792380\pi$
$858$	−636.303	−	2009.40i	−0.741612	−	2.34195i
$859$	1535.87			1.78798			0.893989	−	0.448090i	$-0.147895\pi$
$859$	1535.87			1.78798			0.893989	+	0.448090i	$0.147895\pi$
$860$			734.769i			0.854383i
$861$	−35.0295	+	11.0926i	−0.0406847	+	0.0128834i
$862$	2891.01			3.35384
$863$			1160.30i			1.34450i	0.740324	+	0.672251i	$0.234672\pi$
$863$			1160.30i			1.34450i	−0.740324	+	0.672251i	$0.765328\pi$
$864$	1244.64	−	1634.62i	1.44056	−	1.89192i
$865$	−286.281			−0.330960
$866$			2518.78i			2.90852i
$867$	120.611	+	380.881i	0.139113	+	0.439309i
$868$	−1629.76			−1.87761
$869$		−	163.441i		−	0.188079i
$870$	70.9415	−	22.4646i	0.0815420	−	0.0258214i
$871$	802.504			0.921359
$872$			1680.16i			1.92679i
$873$	937.497	−	659.917i	1.07388	−	0.755919i
$874$	2509.92			2.87176
$875$		−	326.798i		−	0.373484i
$876$	79.6723	+	251.599i	0.0909501	+	0.287213i
$877$	57.2895			0.0653244			0.0326622	−	0.999466i	$-0.489601\pi$
$877$	57.2895			0.0653244			0.0326622	+	0.999466i	$0.489601\pi$
$878$			915.338i			1.04253i
$879$	−780.515	+	247.161i	−0.887958	+	0.281184i
$880$	560.593			0.637038
$881$		−	135.167i		−	0.153424i	−0.997053	−	0.0767120i	$-0.975558\pi$
$881$		−	135.167i		−	0.153424i	0.997053	−	0.0767120i	$-0.0244422\pi$
$882$	368.013	+	522.809i	0.417248	+	0.592754i
$883$	899.660			1.01887			0.509434	−	0.860510i	$-0.329855\pi$
$883$	899.660			1.01887			0.509434	+	0.860510i	$0.329855\pi$
$884$			2288.28i			2.58856i
$885$	−90.6573	−	286.289i	−0.102438	−	0.323490i
$886$	−404.427			−0.456464
$887$			280.501i			0.316236i	0.987420	+	0.158118i	$0.0505426\pi$
$887$			280.501i			0.316236i	−0.987420	+	0.158118i	$0.949457\pi$
$888$	1612.05	−	510.478i	1.81537	−	0.574862i
$889$	−129.215			−0.145349
$890$		−	87.4934i		−	0.0983072i
$891$	782.397	+	280.378i	0.878111	+	0.314678i
$892$	−2877.38			−3.22576
$893$		−	1596.97i		−	1.78832i
$894$	262.829	+	829.995i	0.293993	+	0.928406i
$895$	368.263			0.411467
$896$		−	534.054i		−	0.596042i
$897$	−1082.60	+	342.821i	−1.20692	+	0.382187i
$898$	−2243.00			−2.49777
$899$		−	159.729i		−	0.177674i
$900$	1733.13	−	1219.97i	1.92570	−	1.35553i
$901$	−1184.55			−1.31470
$902$		−	85.8860i		−	0.0952172i
$903$	295.739	+	933.921i	0.327507	+	1.03424i
$904$	1707.77			1.88913
$905$			205.897i			0.227510i
$906$	1249.11	−	395.549i	1.37871	−	0.436588i
$907$	−755.609			−0.833086			−0.416543	−	0.909116i	$-0.636758\pi$
$907$	−755.609			−0.833086			−0.416543	+	0.909116i	$0.636758\pi$
$908$		−	146.571i		−	0.161421i
$909$	57.1615	+	81.2052i	0.0628839	+	0.0893347i
$910$	461.496			0.507138
$911$		−	476.645i		−	0.523211i	−0.965175	−	0.261605i	$-0.915748\pi$
$911$		−	476.645i		−	0.523211i	0.965175	−	0.261605i	$-0.0842519\pi$
$912$	−1302.31	−	4112.58i	−1.42797	−	4.50941i
$913$	−170.204			−0.186423
$914$			1440.35i			1.57588i
$915$	−87.3334	+	27.6553i	−0.0954463	+	0.0302244i
$916$	−189.954			−0.207373
$917$		−	134.305i		−	0.146461i
$918$	−1004.29	−	764.696i	−1.09400	−	0.833002i
$919$	−1058.49			−1.15179			−0.575895	−	0.817524i	$-0.695346\pi$
$919$	−1058.49			−1.15179			−0.575895	+	0.817524i	$0.695346\pi$
$920$		−	574.706i		−	0.624681i
$921$	249.879	+	789.100i	0.271313	+	0.856786i
$922$	−696.078			−0.754966
$923$		−	1106.80i		−	1.19914i
$924$	1612.45	−	510.605i	1.74508	−	0.552603i
$925$	586.557			0.634116
$926$		−	1627.40i		−	1.75745i
$927$	179.623	−	126.439i	0.193768	−	0.136396i
$928$	409.778			0.441571
$929$		−	237.035i		−	0.255150i	−0.991829	−	0.127575i	$-0.959281\pi$
$929$		−	237.035i		−	0.255150i	0.991829	−	0.127575i	$-0.0407194\pi$
$930$	123.733	+	390.739i	0.133046	+	0.420150i
$931$	613.976			0.659480
$932$		−	3029.76i		−	3.25082i
$933$	−541.261	+	171.398i	−0.580129	+	0.183706i
$934$	−1076.00			−1.15203
$935$		−	157.527i		−	0.168478i
$936$	2137.70	+	3036.88i	2.28386	+	3.24453i
$937$	1070.50			1.14248			0.571240	−	0.820783i	$-0.306463\pi$
$937$	1070.50			1.14248			0.571240	+	0.820783i	$0.306463\pi$
$938$			900.885i			0.960432i
$939$	−175.177	−	553.196i	−0.186557	−	0.589133i
$940$	−608.370			−0.647202
$941$			1154.60i			1.22699i	0.789698	+	0.613496i	$0.210237\pi$
$941$			1154.60i			1.22699i	−0.789698	+	0.613496i	$0.789763\pi$
$942$	1342.97	−	425.269i	1.42565	−	0.451453i
$943$	−46.2728			−0.0490698
$944$		−	3615.67i		−	3.83015i
$945$	−110.242	+	144.783i	−0.116658	+	0.153209i
$946$	−2289.80			−2.42051
$947$		−	118.147i		−	0.124759i	−0.998053	−	0.0623795i	$-0.980131\pi$
$947$		−	118.147i		−	0.124759i	0.998053	−	0.0623795i	$-0.0198689\pi$
$948$	144.643	+	456.772i	0.152577	+	0.481827i
$949$	−160.412			−0.169032
$950$		−	2847.35i		−	2.99721i
$951$	−303.498	+	96.1069i	−0.319136	+	0.101059i
$952$	−1543.99			−1.62184
$953$		−	1280.68i		−	1.34384i	−0.740626	−	0.671918i	$-0.765471\pi$
$953$		−	1280.68i		−	1.34384i	0.740626	−	0.671918i	$-0.234529\pi$
$954$	−2615.51	+	1841.09i	−2.74162	+	1.92987i
$955$	311.464			0.326141
$956$		−	1677.28i		−	1.75448i
$957$	50.0433	+	158.033i	0.0522918	+	0.165133i
$958$	−1390.32			−1.45127
$959$		−	112.856i		−	0.117681i
$960$	−377.394	+	119.507i	−0.393118	+	0.124486i
$961$	−81.2270			−0.0845234
$962$			1709.98i			1.77753i
$963$	−61.6796	−	87.6239i	−0.0640495	−	0.0909905i
$964$	−4501.20			−4.66930
$965$			439.347i			0.455282i
$966$	−384.849	−	1215.32i	−0.398394	−	1.25810i
$967$	−1131.93			−1.17055			−0.585277	−	0.810833i	$-0.699014\pi$
$967$	−1131.93			−1.17055			−0.585277	+	0.810833i	$0.699014\pi$
$968$		−	354.750i		−	0.366477i
$969$	−1155.64	+	365.949i	−1.19261	+	0.377656i
$970$	−586.747			−0.604894
$971$			614.448i			0.632799i	0.948626	+	0.316400i	$0.102474\pi$
$971$			614.448i			0.632799i	−0.948626	+	0.316400i	$0.897526\pi$
$972$	−2434.71	−	91.1672i	−2.50485	−	0.0937934i
$973$	−608.655			−0.625544
$974$			521.336i			0.535253i
$975$	388.909	+	1228.15i	0.398881	+	1.25964i
$976$	−1102.97			−1.13009
$977$			617.401i			0.631935i	0.948770	+	0.315968i	$0.102329\pi$
$977$			617.401i			0.631935i	−0.948770	+	0.315968i	$0.897671\pi$
$978$	−110.980	+	35.1432i	−0.113476	+	0.0359338i
$979$	194.905			0.199085
$980$		−	233.896i		−	0.238670i
$981$	547.858	−	385.644i	0.558469	−	0.393114i
$982$	3033.39			3.08899
$983$		−	1266.03i		−	1.28793i	−0.765057	−	0.643963i	$-0.777289\pi$
$983$		−	1266.03i		−	1.28793i	0.765057	−	0.643963i	$-0.222711\pi$
$984$	45.6849	+	144.269i	0.0464278	+	0.146615i
$985$	−156.245			−0.158624
$986$		−	251.763i		−	0.255338i
$987$	−773.263	+	244.864i	−0.783448	+	0.248090i
$988$	5933.64			6.00571
$989$			1233.68i			1.24740i
$990$	−244.838	−	347.824i	−0.247311	−	0.351337i
$991$	1794.64			1.81093			0.905467	−	0.424416i	$-0.139521\pi$
$991$	1794.64			1.81093			0.905467	+	0.424416i	$0.139521\pi$
$992$			2257.02i			2.27522i
$993$	−203.276	−	641.929i	−0.204709	−	0.646454i
$994$	1242.49			1.24999
$995$		−	240.001i		−	0.241207i
$996$	475.674	−	150.629i	0.477584	−	0.151234i
$997$	−321.969			−0.322938			−0.161469	−	0.986878i	$-0.551623\pi$
$997$	−321.969			−0.322938			−0.161469	+	0.986878i	$0.551623\pi$
$998$		−	1263.69i		−	1.26622i
$999$	−536.465	−	408.479i	−0.537002	−	0.408888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.3.b.a.59.18	yes	18
3.2	odd	2	inner	87.3.b.a.59.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.3.b.a.59.1	✓	18	3.2	odd	2	inner
87.3.b.a.59.18	yes	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	87.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.74519i q^{2} +(0.905668 + 2.86003i) q^{3} -10.0264 q^{4} -1.22987i q^{5} +(-10.7113 + 3.39190i) q^{6} +5.48015 q^{7} -22.5701i q^{8} +(-7.35953 + 5.18047i) q^{9} +O(q^{10})\)	\(q+3.74519i q^{2} +(0.905668 + 2.86003i) q^{3} -10.0264 q^{4} -1.22987i q^{5} +(-10.7113 + 3.39190i) q^{6} +5.48015 q^{7} -22.5701i q^{8} +(-7.35953 + 5.18047i) q^{9} +4.60608 q^{10} +10.2607i q^{11} +(-9.08061 - 28.6759i) q^{12} +18.2828 q^{13} +20.5242i q^{14} +(3.51745 - 1.11385i) q^{15} +44.4235 q^{16} -12.4830i q^{17} +(-19.4018 - 27.5628i) q^{18} -32.3692 q^{19} +12.3312i q^{20} +(4.96320 + 15.6734i) q^{21} -38.4283 q^{22} +20.7040i q^{23} +(64.5511 - 20.4410i) q^{24} +23.4874 q^{25} +68.4727i q^{26} +(-21.4816 - 16.3567i) q^{27} -54.9463 q^{28} -5.38516i q^{29} +(4.17158 + 13.1735i) q^{30} +29.6610 q^{31} +76.0938i q^{32} +(-29.3459 + 9.29280i) q^{33} +46.7513 q^{34} -6.73985i q^{35} +(73.7898 - 51.9416i) q^{36} +24.9732 q^{37} -121.229i q^{38} +(16.5582 + 52.2895i) q^{39} -27.7582 q^{40} +2.23497i q^{41} +(-58.6998 + 18.5881i) q^{42} +59.5864 q^{43} -102.878i q^{44} +(6.37129 + 9.05124i) q^{45} -77.5405 q^{46} +49.3360i q^{47} +(40.2329 + 127.052i) q^{48} -18.9679 q^{49} +87.9648i q^{50} +(35.7018 - 11.3055i) q^{51} -183.312 q^{52} -94.8927i q^{53} +(61.2588 - 80.4526i) q^{54} +12.6193 q^{55} -123.687i q^{56} +(-29.3157 - 92.5767i) q^{57} +20.1684 q^{58} -81.3909i q^{59} +(-35.2675 + 11.1679i) q^{60} -24.8286 q^{61} +111.086i q^{62} +(-40.3314 + 28.3898i) q^{63} -107.292 q^{64} -22.4854i q^{65} +(-34.8033 - 109.906i) q^{66} +43.8938 q^{67} +125.160i q^{68} +(-59.2142 + 18.7510i) q^{69} +25.2420 q^{70} -60.5378i q^{71} +(116.924 + 166.105i) q^{72} -8.77389 q^{73} +93.5294i q^{74} +(21.2718 + 67.1747i) q^{75} +324.547 q^{76} +56.2303i q^{77} +(-195.834 + 62.0135i) q^{78} -15.9288 q^{79} -54.6349i q^{80} +(27.3254 - 76.2517i) q^{81} -8.37037 q^{82} +16.5880i q^{83} +(-49.7631 - 157.148i) q^{84} -15.3525 q^{85} +223.162i q^{86} +(15.4017 - 4.87717i) q^{87} +231.585 q^{88} -18.9952i q^{89} +(-33.8986 + 23.8617i) q^{90} +100.193 q^{91} -207.587i q^{92} +(26.8630 + 84.8312i) q^{93} -184.773 q^{94} +39.8097i q^{95} +(-217.631 + 68.9157i) q^{96} -127.385 q^{97} -71.0384i q^{98} +(-53.1554 - 75.5141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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