LMFDB - Embedded newform 87.2.c.a.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(28,87)]

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([0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("87.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.c (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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			28.1
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	87.28
Dual form			87.2.c.a.28.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +3.23607 q^{5} +1.61803 q^{6} -4.23607 q^{7} -2.23607i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +3.23607 q^{5} +1.61803 q^{6} -4.23607 q^{7} -2.23607i q^{8} -1.00000 q^{9} -5.23607i q^{10} +2.23607i q^{11} -0.618034i q^{12} -1.00000 q^{13} +6.85410i q^{14} +3.23607i q^{15} -4.85410 q^{16} -3.00000i q^{17} +1.61803i q^{18} +7.70820i q^{19} -2.00000 q^{20} -4.23607i q^{21} +3.61803 q^{22} +1.23607 q^{23} +2.23607 q^{24} +5.47214 q^{25} +1.61803i q^{26} -1.00000i q^{27} +2.61803 q^{28} +(-4.47214 + 3.00000i) q^{29} +5.23607 q^{30} -7.23607i q^{31} +3.38197i q^{32} -2.23607 q^{33} -4.85410 q^{34} -13.7082 q^{35} +0.618034 q^{36} +4.76393i q^{37} +12.4721 q^{38} -1.00000i q^{39} -7.23607i q^{40} -4.47214i q^{41} -6.85410 q^{42} -0.472136i q^{43} -1.38197i q^{44} -3.23607 q^{45} -2.00000i q^{46} -10.2361i q^{47} -4.85410i q^{48} +10.9443 q^{49} -8.85410i q^{50} +3.00000 q^{51} +0.618034 q^{52} +6.76393 q^{53} -1.61803 q^{54} +7.23607i q^{55} +9.47214i q^{56} -7.70820 q^{57} +(4.85410 + 7.23607i) q^{58} +8.94427 q^{59} -2.00000i q^{60} +2.76393i q^{61} -11.7082 q^{62} +4.23607 q^{63} -4.23607 q^{64} -3.23607 q^{65} +3.61803i q^{66} +4.70820 q^{67} +1.85410i q^{68} +1.23607i q^{69} +22.1803i q^{70} +4.76393 q^{71} +2.23607i q^{72} -7.70820i q^{73} +7.70820 q^{74} +5.47214i q^{75} -4.76393i q^{76} -9.47214i q^{77} -1.61803 q^{78} -2.29180i q^{79} -15.7082 q^{80} +1.00000 q^{81} -7.23607 q^{82} -6.00000 q^{83} +2.61803i q^{84} -9.70820i q^{85} -0.763932 q^{86} +(-3.00000 - 4.47214i) q^{87} +5.00000 q^{88} -0.0557281i q^{89} +5.23607i q^{90} +4.23607 q^{91} -0.763932 q^{92} +7.23607 q^{93} -16.5623 q^{94} +24.9443i q^{95} -3.38197 q^{96} +18.1803i q^{97} -17.7082i q^{98} -2.23607i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 - 8 * q^7 - 4 * q^9	$ 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} - 8 q^{7} - 4 q^{9} - 4 q^{13} - 6 q^{16} - 8 q^{20} + 10 q^{22} - 4 q^{23} + 4 q^{25} + 6 q^{28} + 12 q^{30} - 6 q^{34} - 28 q^{35} - 2 q^{36} + 32 q^{38} - 14 q^{42} - 4 q^{45} + 8 q^{49} + 12 q^{51} - 2 q^{52} + 36 q^{53} - 2 q^{54} - 4 q^{57} + 6 q^{58} - 20 q^{62} + 8 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{67} + 28 q^{71} + 4 q^{74} - 2 q^{78} - 36 q^{80} + 4 q^{81} - 20 q^{82} - 24 q^{83} - 12 q^{86} - 12 q^{87} + 20 q^{88} + 8 q^{91} - 12 q^{92} + 20 q^{93} - 26 q^{94} - 18 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 - 8 * q^7 - 4 * q^9 - 4 * q^13 - 6 * q^16 - 8 * q^20 + 10 * q^22 - 4 * q^23 + 4 * q^25 + 6 * q^28 + 12 * q^30 - 6 * q^34 - 28 * q^35 - 2 * q^36 + 32 * q^38 - 14 * q^42 - 4 * q^45 + 8 * q^49 + 12 * q^51 - 2 * q^52 + 36 * q^53 - 2 * q^54 - 4 * q^57 + 6 * q^58 - 20 * q^62 + 8 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^67 + 28 * q^71 + 4 * q^74 - 2 * q^78 - 36 * q^80 + 4 * q^81 - 20 * q^82 - 24 * q^83 - 12 * q^86 - 12 * q^87 + 20 * q^88 + 8 * q^91 - 12 * q^92 + 20 * q^93 - 26 * q^94 - 18 * q^96

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 $

$2$		−	1.61803i		−	1.14412i	−0.820211	−	0.572061i	$-0.806144\pi$
$2$		−	1.61803i		−	1.14412i	0.820211	−	0.572061i	$-0.193856\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.618034			−0.309017
$5$	3.23607			1.44721			0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607			1.44721			0.723607	+	0.690212i	$0.242483\pi$
$6$	1.61803			0.660560
$7$	−4.23607			−1.60108			−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−4.23607			−1.60108			−0.800542	+	0.599277i	$0.795455\pi$
$8$		−	2.23607i		−	0.790569i
$9$	−1.00000			−0.333333
$10$		−	5.23607i		−	1.65579i
$11$			2.23607i			0.674200i	0.941469	+	0.337100i	$0.109446\pi$
$11$			2.23607i			0.674200i	−0.941469	+	0.337100i	$0.890554\pi$
$12$		−	0.618034i		−	0.178411i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$			6.85410i			1.83184i
$15$			3.23607i			0.835549i
$16$	−4.85410			−1.21353
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$			1.61803i			0.381374i
$19$			7.70820i			1.76838i	0.467124	+	0.884192i	$0.345290\pi$
$19$			7.70820i			1.76838i	−0.467124	+	0.884192i	$0.654710\pi$
$20$	−2.00000			−0.447214
$21$		−	4.23607i		−	0.924386i
$22$	3.61803			0.771367
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	2.23607			0.456435
$25$	5.47214			1.09443
$26$			1.61803i			0.317323i
$27$		−	1.00000i		−	0.192450i
$28$	2.61803			0.494762
$29$	−4.47214	+	3.00000i	−0.830455	+	0.557086i
$29$	−4.47214	+	3.00000i	−0.830455	+	0.557086i
$30$	5.23607			0.955971
$31$		−	7.23607i		−	1.29964i	−0.760090	−	0.649818i	$-0.774845\pi$
$31$		−	7.23607i		−	1.29964i	0.760090	−	0.649818i	$-0.225155\pi$
$32$			3.38197i			0.597853i
$33$	−2.23607			−0.389249
$34$	−4.85410			−0.832472
$35$	−13.7082			−2.31711
$36$	0.618034			0.103006
$37$			4.76393i			0.783186i	0.920139	+	0.391593i	$0.128076\pi$
$37$			4.76393i			0.783186i	−0.920139	+	0.391593i	$0.871924\pi$
$38$	12.4721			2.02325
$39$		−	1.00000i		−	0.160128i
$40$		−	7.23607i		−	1.14412i
$41$		−	4.47214i		−	0.698430i	−0.937043	−	0.349215i	$-0.886448\pi$
$41$		−	4.47214i		−	0.698430i	0.937043	−	0.349215i	$-0.113552\pi$
$42$	−6.85410			−1.05761
$43$		−	0.472136i		−	0.0720001i	−0.999352	−	0.0360000i	$-0.988538\pi$
$43$		−	0.472136i		−	0.0720001i	0.999352	−	0.0360000i	$-0.0114616\pi$
$44$		−	1.38197i		−	0.208339i
$45$	−3.23607			−0.482405
$46$		−	2.00000i		−	0.294884i
$47$		−	10.2361i		−	1.49308i	−0.665338	−	0.746542i	$-0.731713\pi$
$47$		−	10.2361i		−	1.49308i	0.665338	−	0.746542i	$-0.268287\pi$
$48$		−	4.85410i		−	0.700629i
$49$	10.9443			1.56347
$50$		−	8.85410i		−	1.25216i
$51$	3.00000			0.420084
$52$	0.618034			0.0857059
$53$	6.76393			0.929098			0.464549	−	0.885548i	$-0.346217\pi$
$53$	6.76393			0.929098			0.464549	+	0.885548i	$0.346217\pi$
$54$	−1.61803			−0.220187
$55$			7.23607i			0.975711i
$56$			9.47214i			1.26577i
$57$	−7.70820			−1.02098
$58$	4.85410	+	7.23607i	0.637375	+	0.950142i
$59$	8.94427			1.16445			0.582223	−	0.813029i	$-0.302183\pi$
$59$	8.94427			1.16445			0.582223	+	0.813029i	$0.302183\pi$
$60$		−	2.00000i		−	0.258199i
$61$			2.76393i			0.353885i	0.984221	+	0.176943i	$0.0566207\pi$
$61$			2.76393i			0.353885i	−0.984221	+	0.176943i	$0.943379\pi$
$62$	−11.7082			−1.48694
$63$	4.23607			0.533694
$64$	−4.23607			−0.529508
$65$	−3.23607			−0.401385
$66$			3.61803i			0.445349i
$67$	4.70820			0.575199			0.287599	−	0.957751i	$-0.407143\pi$
$67$	4.70820			0.575199			0.287599	+	0.957751i	$0.407143\pi$
$68$			1.85410i			0.224843i
$69$			1.23607i			0.148805i
$70$			22.1803i			2.65106i
$71$	4.76393			0.565375			0.282687	−	0.959212i	$-0.408774\pi$
$71$	4.76393			0.565375			0.282687	+	0.959212i	$0.408774\pi$
$72$			2.23607i			0.263523i
$73$		−	7.70820i		−	0.902177i	−0.892479	−	0.451089i	$-0.851036\pi$
$73$		−	7.70820i		−	0.902177i	0.892479	−	0.451089i	$-0.148964\pi$
$74$	7.70820			0.896061
$75$			5.47214i			0.631868i
$76$		−	4.76393i		−	0.546460i
$77$		−	9.47214i		−	1.07945i
$78$	−1.61803			−0.183206
$79$		−	2.29180i		−	0.257847i	−0.991655	−	0.128924i	$-0.958848\pi$
$79$		−	2.29180i		−	0.257847i	0.991655	−	0.128924i	$-0.0411522\pi$
$80$	−15.7082			−1.75623
$81$	1.00000			0.111111
$82$	−7.23607			−0.799090
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$			2.61803i			0.285651i
$85$		−	9.70820i		−	1.05300i
$86$	−0.763932			−0.0823769
$87$	−3.00000	−	4.47214i	−0.321634	−	0.479463i
$88$	5.00000			0.533002
$89$		−	0.0557281i		−	0.00590717i	−0.999996	−	0.00295358i	$-0.999060\pi$
$89$		−	0.0557281i		−	0.00590717i	0.999996	−	0.00295358i	$-0.000940156\pi$
$90$			5.23607i			0.551930i
$91$	4.23607			0.444061
$92$	−0.763932			−0.0796454
$93$	7.23607			0.750345
$94$	−16.5623			−1.70827
$95$			24.9443i			2.55923i
$96$	−3.38197			−0.345170
$97$			18.1803i			1.84593i	0.384879	+	0.922967i	$0.374243\pi$
$97$			18.1803i			1.84593i	−0.384879	+	0.922967i	$0.625757\pi$
$98$		−	17.7082i		−	1.78880i
$99$		−	2.23607i		−	0.224733i
$100$	−3.38197			−0.338197
$101$		−	3.94427i		−	0.392470i	−0.980557	−	0.196235i	$-0.937129\pi$
$101$		−	3.94427i		−	0.392470i	0.980557	−	0.196235i	$-0.0628715\pi$
$102$		−	4.85410i		−	0.480628i
$103$	−19.4164			−1.91316			−0.956578	−	0.291477i	$-0.905853\pi$
$103$	−19.4164			−1.91316			−0.956578	+	0.291477i	$0.905853\pi$
$104$			2.23607i			0.219265i
$105$		−	13.7082i		−	1.33778i
$106$		−	10.9443i		−	1.06300i
$107$	0.763932			0.0738521			0.0369260	−	0.999318i	$-0.488243\pi$
$107$	0.763932			0.0738521			0.0369260	+	0.999318i	$0.488243\pi$
$108$			0.618034i			0.0594703i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$	11.7082			1.11633
$111$	−4.76393			−0.452172
$112$	20.5623			1.94296
$113$			4.52786i			0.425946i	0.977058	+	0.212973i	$0.0683146\pi$
$113$			4.52786i			0.425946i	−0.977058	+	0.212973i	$0.931685\pi$
$114$			12.4721i			1.16812i
$115$	4.00000			0.373002
$116$	2.76393	−	1.85410i	0.256625	−	0.172149i
$117$	1.00000			0.0924500
$118$		−	14.4721i		−	1.33227i
$119$			12.7082i			1.16496i
$120$	7.23607			0.660560
$121$	6.00000			0.545455
$122$	4.47214			0.404888
$123$	4.47214			0.403239
$124$			4.47214i			0.401610i
$125$	1.52786			0.136656
$126$		−	6.85410i		−	0.610612i
$127$		−	12.4721i		−	1.10672i	−0.832941	−	0.553362i	$-0.813345\pi$
$127$		−	12.4721i		−	1.10672i	0.832941	−	0.553362i	$-0.186655\pi$
$128$			13.6180i			1.20368i
$129$	0.472136			0.0415693
$130$			5.23607i			0.459234i
$131$			12.2361i			1.06907i	0.845146	+	0.534535i	$0.179513\pi$
$131$			12.2361i			1.06907i	−0.845146	+	0.534535i	$0.820487\pi$
$132$	1.38197			0.120285
$133$		−	32.6525i		−	2.83133i
$134$		−	7.61803i		−	0.658098i
$135$		−	3.23607i		−	0.278516i
$136$	−6.70820			−0.575224
$137$		−	3.52786i		−	0.301406i	−0.988579	−	0.150703i	$-0.951846\pi$
$137$		−	3.52786i		−	0.301406i	0.988579	−	0.150703i	$-0.0481537\pi$
$138$	2.00000			0.170251
$139$	−6.70820			−0.568982			−0.284491	−	0.958679i	$-0.591825\pi$
$139$	−6.70820			−0.568982			−0.284491	+	0.958679i	$0.591825\pi$
$140$	8.47214			0.716026
$141$	10.2361			0.862032
$142$		−	7.70820i		−	0.646858i
$143$		−	2.23607i		−	0.186989i
$144$	4.85410			0.404508
$145$	−14.4721	+	9.70820i	−1.20185	+	0.806222i
$146$	−12.4721			−1.03220
$147$			10.9443i			0.902668i
$148$		−	2.94427i		−	0.242018i
$149$	−5.52786			−0.452860			−0.226430	−	0.974027i	$-0.572705\pi$
$149$	−5.52786			−0.452860			−0.226430	+	0.974027i	$0.572705\pi$
$150$	8.85410			0.722934
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	17.2361			1.39803
$153$			3.00000i			0.242536i
$154$	−15.3262			−1.23502
$155$		−	23.4164i		−	1.88085i
$156$			0.618034i			0.0494823i
$157$			2.00000i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$157$			2.00000i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$158$	−3.70820			−0.295009
$159$			6.76393i			0.536415i
$160$			10.9443i			0.865221i
$161$	−5.23607			−0.412660
$162$		−	1.61803i		−	0.127125i
$163$			7.41641i			0.580898i	0.956890	+	0.290449i	$0.0938046\pi$
$163$			7.41641i			0.580898i	−0.956890	+	0.290449i	$0.906195\pi$
$164$			2.76393i			0.215827i
$165$	−7.23607			−0.563327
$166$			9.70820i			0.753503i
$167$	15.8885			1.22949			0.614746	−	0.788725i	$-0.289258\pi$
$167$	15.8885			1.22949			0.614746	+	0.788725i	$0.289258\pi$
$168$	−9.47214			−0.730791
$169$	−12.0000			−0.923077
$170$	−15.7082			−1.20476
$171$		−	7.70820i		−	0.589461i
$172$			0.291796i			0.0222492i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	−7.23607	+	4.85410i	−0.548565	+	0.367989i
$175$	−23.1803			−1.75227
$176$		−	10.8541i		−	0.818159i
$177$			8.94427i			0.672293i
$178$	−0.0901699			−0.00675852
$179$	−17.2361			−1.28828			−0.644142	−	0.764906i	$-0.722785\pi$
$179$	−17.2361			−1.28828			−0.644142	+	0.764906i	$0.722785\pi$
$180$	2.00000			0.149071
$181$	20.4164			1.51754			0.758770	−	0.651359i	$-0.225801\pi$
$181$	20.4164			1.51754			0.758770	+	0.651359i	$0.225801\pi$
$182$		−	6.85410i		−	0.508060i
$183$	−2.76393			−0.204316
$184$		−	2.76393i		−	0.203760i
$185$			15.4164i			1.13344i
$186$		−	11.7082i		−	0.858487i
$187$	6.70820			0.490552
$188$			6.32624i			0.461388i
$189$			4.23607i			0.308129i
$190$	40.3607			2.92807
$191$			8.94427i			0.647185i	0.946197	+	0.323592i	$0.104891\pi$
$191$			8.94427i			0.647185i	−0.946197	+	0.323592i	$0.895109\pi$
$192$		−	4.23607i		−	0.305712i
$193$			17.4164i			1.25366i	0.779156	+	0.626830i	$0.215648\pi$
$193$			17.4164i			1.25366i	−0.779156	+	0.626830i	$0.784352\pi$
$194$	29.4164			2.11198
$195$		−	3.23607i		−	0.231740i
$196$	−6.76393			−0.483138
$197$	−3.70820			−0.264199			−0.132099	−	0.991236i	$-0.542172\pi$
$197$	−3.70820			−0.264199			−0.132099	+	0.991236i	$0.542172\pi$
$198$	−3.61803			−0.257122
$199$	−20.1246			−1.42660			−0.713298	−	0.700861i	$-0.752799\pi$
$199$	−20.1246			−1.42660			−0.713298	+	0.700861i	$0.752799\pi$
$200$		−	12.2361i		−	0.865221i
$201$			4.70820i			0.332091i
$202$	−6.38197			−0.449034
$203$	18.9443	−	12.7082i	1.32963	−	0.891941i
$204$	−1.85410			−0.129813
$205$		−	14.4721i		−	1.01078i
$206$			31.4164i			2.18888i
$207$	−1.23607			−0.0859127
$208$	4.85410			0.336571
$209$	−17.2361			−1.19224
$210$	−22.1803			−1.53059
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$	−4.18034			−0.287107
$213$			4.76393i			0.326419i
$214$		−	1.23607i		−	0.0844959i
$215$		−	1.52786i		−	0.104199i
$216$	−2.23607			−0.152145
$217$			30.6525i			2.08083i
$218$		−	8.09017i		−	0.547935i
$219$	7.70820			0.520872
$220$		−	4.47214i		−	0.301511i
$221$			3.00000i			0.201802i
$222$			7.70820i			0.517341i
$223$	−12.7082			−0.851004			−0.425502	−	0.904957i	$-0.639903\pi$
$223$	−12.7082			−0.851004			−0.425502	+	0.904957i	$0.639903\pi$
$224$		−	14.3262i		−	0.957212i
$225$	−5.47214			−0.364809
$226$	7.32624			0.487334
$227$	9.05573			0.601050			0.300525	−	0.953774i	$-0.402838\pi$
$227$	9.05573			0.601050			0.300525	+	0.953774i	$0.402838\pi$
$228$	4.76393			0.315499
$229$			22.1803i			1.46572i	0.680380	+	0.732859i	$0.261815\pi$
$229$			22.1803i			1.46572i	−0.680380	+	0.732859i	$0.738185\pi$
$230$		−	6.47214i		−	0.426760i
$231$	9.47214			0.623221
$232$	6.70820	+	10.0000i	0.440415	+	0.656532i
$233$	−10.4721			−0.686052			−0.343026	−	0.939326i	$-0.611452\pi$
$233$	−10.4721			−0.686052			−0.343026	+	0.939326i	$0.611452\pi$
$234$		−	1.61803i		−	0.105774i
$235$		−	33.1246i		−	2.16081i
$236$	−5.52786			−0.359833
$237$	2.29180			0.148868
$238$	20.5623			1.33286
$239$	26.1803			1.69347			0.846733	−	0.532019i	$-0.178566\pi$
$239$	26.1803			1.69347			0.846733	+	0.532019i	$0.178566\pi$
$240$		−	15.7082i		−	1.01396i
$241$	−3.00000			−0.193247			−0.0966235	−	0.995321i	$-0.530804\pi$
$241$	−3.00000			−0.193247			−0.0966235	+	0.995321i	$0.530804\pi$
$242$		−	9.70820i		−	0.624067i
$243$			1.00000i			0.0641500i
$244$		−	1.70820i		−	0.109357i
$245$	35.4164			2.26267
$246$		−	7.23607i		−	0.461355i
$247$		−	7.70820i		−	0.490461i
$248$	−16.1803			−1.02745
$249$		−	6.00000i		−	0.380235i
$250$		−	2.47214i		−	0.156352i
$251$		−	12.2361i		−	0.772334i	−0.922429	−	0.386167i	$-0.873799\pi$
$251$		−	12.2361i		−	0.772334i	0.922429	−	0.386167i	$-0.126201\pi$
$252$	−2.61803			−0.164921
$253$			2.76393i			0.173767i
$254$	−20.1803			−1.26623
$255$	9.70820			0.607951
$256$	13.5623			0.847644
$257$	−26.4721			−1.65129			−0.825643	−	0.564193i	$-0.809188\pi$
$257$	−26.4721			−1.65129			−0.825643	+	0.564193i	$0.809188\pi$
$258$		−	0.763932i		−	0.0475603i
$259$		−	20.1803i		−	1.25395i
$260$	2.00000			0.124035
$261$	4.47214	−	3.00000i	0.276818	−	0.185695i
$262$	19.7984			1.22315
$263$		−	4.94427i		−	0.304877i	−0.988313	−	0.152438i	$-0.951287\pi$
$263$		−	4.94427i		−	0.304877i	0.988313	−	0.152438i	$-0.0487126\pi$
$264$			5.00000i			0.307729i
$265$	21.8885			1.34460
$266$	−52.8328			−3.23939
$267$	0.0557281			0.00341050
$268$	−2.90983			−0.177746
$269$		−	21.3607i		−	1.30238i	−0.758913	−	0.651192i	$-0.774269\pi$
$269$		−	21.3607i		−	1.30238i	0.758913	−	0.651192i	$-0.225731\pi$
$270$	−5.23607			−0.318657
$271$		−	23.4164i		−	1.42245i	−0.702967	−	0.711223i	$-0.748142\pi$
$271$		−	23.4164i		−	1.42245i	0.702967	−	0.711223i	$-0.251858\pi$
$272$			14.5623i			0.882969i
$273$			4.23607i			0.256378i
$274$	−5.70820			−0.344845
$275$			12.2361i			0.737863i
$276$		−	0.763932i		−	0.0459833i
$277$	6.41641			0.385525			0.192762	−	0.981245i	$-0.438255\pi$
$277$	6.41641			0.385525			0.192762	+	0.981245i	$0.438255\pi$
$278$			10.8541i			0.650986i
$279$			7.23607i			0.433212i
$280$			30.6525i			1.83184i
$281$	−1.41641			−0.0844958			−0.0422479	−	0.999107i	$-0.513452\pi$
$281$	−1.41641			−0.0844958			−0.0422479	+	0.999107i	$0.513452\pi$
$282$		−	16.5623i		−	0.986271i
$283$	−13.8885			−0.825588			−0.412794	−	0.910824i	$-0.635447\pi$
$283$	−13.8885			−0.825588			−0.412794	+	0.910824i	$0.635447\pi$
$284$	−2.94427			−0.174710
$285$	−24.9443			−1.47757
$286$	−3.61803			−0.213939
$287$			18.9443i			1.11825i
$288$		−	3.38197i		−	0.199284i
$289$	8.00000			0.470588
$290$	15.7082	+	23.4164i	0.922417	+	1.37506i
$291$	−18.1803			−1.06575
$292$			4.76393i			0.278788i
$293$		−	29.9443i		−	1.74936i	−0.484698	−	0.874682i	$-0.661071\pi$
$293$		−	29.9443i		−	1.74936i	0.484698	−	0.874682i	$-0.338929\pi$
$294$	17.7082			1.03276
$295$	28.9443			1.68520
$296$	10.6525			0.619163
$297$	2.23607			0.129750
$298$			8.94427i			0.518128i
$299$	−1.23607			−0.0714837
$300$		−	3.38197i		−	0.195258i
$301$			2.00000i			0.115278i
$302$		−	19.4164i		−	1.11729i
$303$	3.94427			0.226593
$304$		−	37.4164i		−	2.14598i
$305$			8.94427i			0.512148i
$306$	4.85410			0.277491
$307$			28.1803i			1.60834i	0.594401	+	0.804168i	$0.297389\pi$
$307$			28.1803i			1.60834i	−0.594401	+	0.804168i	$0.702611\pi$
$308$			5.85410i			0.333568i
$309$		−	19.4164i		−	1.10456i
$310$	−37.8885			−2.15192
$311$		−	15.6525i		−	0.887570i	−0.896133	−	0.443785i	$-0.853635\pi$
$311$		−	15.6525i		−	0.887570i	0.896133	−	0.443785i	$-0.146365\pi$
$312$	−2.23607			−0.126592
$313$	−5.47214			−0.309303			−0.154652	−	0.987969i	$-0.549426\pi$
$313$	−5.47214			−0.309303			−0.154652	+	0.987969i	$0.549426\pi$
$314$	3.23607			0.182622
$315$	13.7082			0.772370
$316$			1.41641i			0.0796792i
$317$			23.8328i			1.33858i	0.742999	+	0.669292i	$0.233403\pi$
$317$			23.8328i			1.33858i	−0.742999	+	0.669292i	$0.766597\pi$
$318$	10.9443			0.613724
$319$	−6.70820	−	10.0000i	−0.375587	−	0.559893i
$320$	−13.7082			−0.766312
$321$			0.763932i			0.0426385i
$322$			8.47214i			0.472134i
$323$	23.1246			1.28669
$324$	−0.618034			−0.0343352
$325$	−5.47214			−0.303539
$326$	12.0000			0.664619
$327$			5.00000i			0.276501i
$328$	−10.0000			−0.552158
$329$			43.3607i			2.39055i
$330$			11.7082i			0.644515i
$331$		−	8.29180i		−	0.455758i	−0.973689	−	0.227879i	$-0.926821\pi$
$331$		−	8.29180i		−	0.455758i	0.973689	−	0.227879i	$-0.0731791\pi$
$332$	3.70820			0.203514
$333$		−	4.76393i		−	0.261062i
$334$		−	25.7082i		−	1.40669i
$335$	15.2361			0.832435
$336$			20.5623i			1.12177i
$337$			19.2361i			1.04786i	0.851763	+	0.523928i	$0.175534\pi$
$337$			19.2361i			1.04786i	−0.851763	+	0.523928i	$0.824466\pi$
$338$			19.4164i			1.05611i
$339$	−4.52786			−0.245920
$340$			6.00000i			0.325396i
$341$	16.1803			0.876215
$342$	−12.4721			−0.674416
$343$	−16.7082			−0.902158
$344$	−1.05573			−0.0569210
$345$			4.00000i			0.215353i
$346$			9.70820i			0.521916i
$347$	−22.6525			−1.21605			−0.608024	−	0.793918i	$-0.708038\pi$
$347$	−22.6525			−1.21605			−0.608024	+	0.793918i	$0.708038\pi$
$348$	1.85410	+	2.76393i	0.0993903	+	0.148162i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$			37.5066i			2.00481i
$351$			1.00000i			0.0533761i
$352$	−7.56231			−0.403072
$353$	4.65248			0.247626			0.123813	−	0.992306i	$-0.460488\pi$
$353$	4.65248			0.247626			0.123813	+	0.992306i	$0.460488\pi$
$354$	14.4721			0.769185
$355$	15.4164			0.818218
$356$			0.0344419i			0.00182541i
$357$	−12.7082			−0.672589
$358$			27.8885i			1.47396i
$359$		−	25.3050i		−	1.33554i	−0.744366	−	0.667772i	$-0.767248\pi$
$359$		−	25.3050i		−	1.33554i	0.744366	−	0.667772i	$-0.232752\pi$
$360$			7.23607i			0.381374i
$361$	−40.4164			−2.12718
$362$		−	33.0344i		−	1.73625i
$363$			6.00000i			0.314918i
$364$	−2.61803			−0.137222
$365$		−	24.9443i		−	1.30564i
$366$			4.47214i			0.233762i
$367$		−	18.0000i		−	0.939592i	−0.882775	−	0.469796i	$-0.844327\pi$
$367$		−	18.0000i		−	0.939592i	0.882775	−	0.469796i	$-0.155673\pi$
$368$	−6.00000			−0.312772
$369$			4.47214i			0.232810i
$370$	24.9443			1.29679
$371$	−28.6525			−1.48756
$372$	−4.47214			−0.231869
$373$	−3.88854			−0.201341			−0.100671	−	0.994920i	$-0.532099\pi$
$373$	−3.88854			−0.201341			−0.100671	+	0.994920i	$0.532099\pi$
$374$		−	10.8541i		−	0.561252i
$375$			1.52786i			0.0788986i
$376$	−22.8885			−1.18039
$377$	4.47214	−	3.00000i	0.230327	−	0.154508i
$378$	6.85410			0.352537
$379$			14.2918i			0.734120i	0.930197	+	0.367060i	$0.119636\pi$
$379$			14.2918i			0.734120i	−0.930197	+	0.367060i	$0.880364\pi$
$380$		−	15.4164i		−	0.790845i
$381$	12.4721			0.638967
$382$	14.4721			0.740459
$383$	−5.34752			−0.273246			−0.136623	−	0.990623i	$-0.543625\pi$
$383$	−5.34752			−0.273246			−0.136623	+	0.990623i	$0.543625\pi$
$384$	−13.6180			−0.694942
$385$		−	30.6525i		−	1.56219i
$386$	28.1803			1.43434
$387$			0.472136i			0.0240000i
$388$		−	11.2361i		−	0.570425i
$389$		−	13.4721i		−	0.683064i	−0.939870	−	0.341532i	$-0.889054\pi$
$389$		−	13.4721i		−	0.683064i	0.939870	−	0.341532i	$-0.110946\pi$
$390$	−5.23607			−0.265139
$391$		−	3.70820i		−	0.187532i
$392$		−	24.4721i		−	1.23603i
$393$	−12.2361			−0.617228
$394$			6.00000i			0.302276i
$395$		−	7.41641i		−	0.373160i
$396$			1.38197i			0.0694464i
$397$	6.94427			0.348523			0.174262	−	0.984699i	$-0.444246\pi$
$397$	6.94427			0.348523			0.174262	+	0.984699i	$0.444246\pi$
$398$			32.5623i			1.63220i
$399$	32.6525			1.63467
$400$	−26.5623			−1.32812
$401$	33.7082			1.68331			0.841654	−	0.540018i	$-0.181582\pi$
$401$	33.7082			1.68331			0.841654	+	0.540018i	$0.181582\pi$
$402$	7.61803			0.379953
$403$			7.23607i			0.360454i
$404$			2.43769i			0.121280i
$405$	3.23607			0.160802
$406$	−20.5623	−	30.6525i	−1.02049	−	1.52126i
$407$	−10.6525			−0.528024
$408$		−	6.70820i		−	0.332106i
$409$		−	10.5836i		−	0.523325i	−0.965159	−	0.261662i	$-0.915729\pi$
$409$		−	10.5836i		−	0.523325i	0.965159	−	0.261662i	$-0.0842707\pi$
$410$	−23.4164			−1.15645
$411$	3.52786			0.174017
$412$	12.0000			0.591198
$413$	−37.8885			−1.86437
$414$			2.00000i			0.0982946i
$415$	−19.4164			−0.953114
$416$		−	3.38197i		−	0.165815i
$417$		−	6.70820i		−	0.328502i
$418$			27.8885i			1.36407i
$419$	3.81966			0.186603			0.0933013	−	0.995638i	$-0.470258\pi$
$419$	3.81966			0.186603			0.0933013	+	0.995638i	$0.470258\pi$
$420$			8.47214i			0.413398i
$421$			20.0000i			0.974740i	0.873195	+	0.487370i	$0.162044\pi$
$421$			20.0000i			0.974740i	−0.873195	+	0.487370i	$0.837956\pi$
$422$	16.1803			0.787647
$423$			10.2361i			0.497695i
$424$		−	15.1246i		−	0.734516i
$425$		−	16.4164i		−	0.796313i
$426$	7.70820			0.373464
$427$		−	11.7082i		−	0.566600i
$428$	−0.472136			−0.0228216
$429$	2.23607			0.107958
$430$	−2.47214			−0.119217
$431$	14.3607			0.691730			0.345865	−	0.938284i	$-0.387586\pi$
$431$	14.3607			0.691730			0.345865	+	0.938284i	$0.387586\pi$
$432$			4.85410i			0.233543i
$433$		−	14.2918i		−	0.686820i	−0.939186	−	0.343410i	$-0.888418\pi$
$433$		−	14.2918i		−	0.686820i	0.939186	−	0.343410i	$-0.111582\pi$
$434$	49.5967			2.38072
$435$	−9.70820	−	14.4721i	−0.465473	−	0.693886i
$436$	−3.09017			−0.147992
$437$			9.52786i			0.455780i
$438$		−	12.4721i		−	0.595942i
$439$	13.2918			0.634383			0.317191	−	0.948362i	$-0.397260\pi$
$439$	13.2918			0.634383			0.317191	+	0.948362i	$0.397260\pi$
$440$	16.1803			0.771367
$441$	−10.9443			−0.521156
$442$	4.85410			0.230886
$443$			9.65248i			0.458603i	0.973355	+	0.229301i	$0.0736442\pi$
$443$			9.65248i			0.458603i	−0.973355	+	0.229301i	$0.926356\pi$
$444$	2.94427			0.139729
$445$		−	0.180340i		−	0.00854893i
$446$			20.5623i			0.973653i
$447$		−	5.52786i		−	0.261459i
$448$	17.9443			0.847787
$449$			18.8885i			0.891405i	0.895181	+	0.445703i	$0.147046\pi$
$449$			18.8885i			0.891405i	−0.895181	+	0.445703i	$0.852954\pi$
$450$			8.85410i			0.417386i
$451$	10.0000			0.470882
$452$		−	2.79837i		−	0.131624i
$453$			12.0000i			0.563809i
$454$		−	14.6525i		−	0.687675i
$455$	13.7082			0.642651
$456$			17.2361i			0.807153i
$457$	6.41641			0.300147			0.150073	−	0.988675i	$-0.452049\pi$
$457$	6.41641			0.300147			0.150073	+	0.988675i	$0.452049\pi$
$458$	35.8885			1.67696
$459$	−3.00000			−0.140028
$460$	−2.47214			−0.115264
$461$		−	18.9443i		−	0.882323i	−0.897428	−	0.441161i	$-0.854567\pi$
$461$		−	18.9443i		−	0.882323i	0.897428	−	0.441161i	$-0.145433\pi$
$462$		−	15.3262i		−	0.713041i
$463$	0.708204			0.0329130			0.0164565	−	0.999865i	$-0.494761\pi$
$463$	0.708204			0.0329130			0.0164565	+	0.999865i	$0.494761\pi$
$464$	21.7082	−	14.5623i	1.00778	−	0.676038i
$465$	23.4164			1.08591
$466$			16.9443i			0.784928i
$467$		−	13.5279i		−	0.625995i	−0.949754	−	0.312997i	$-0.898667\pi$
$467$		−	13.5279i		−	0.625995i	0.949754	−	0.312997i	$-0.101333\pi$
$468$	−0.618034			−0.0285686
$469$	−19.9443			−0.920941
$470$	−53.5967			−2.47223
$471$	−2.00000			−0.0921551
$472$		−	20.0000i		−	0.920575i
$473$	1.05573			0.0485424
$474$		−	3.70820i		−	0.170323i
$475$			42.1803i			1.93537i
$476$		−	7.85410i		−	0.359992i
$477$	−6.76393			−0.309699
$478$		−	42.3607i		−	1.93753i
$479$			10.4721i			0.478484i	0.970960	+	0.239242i	$0.0768989\pi$
$479$			10.4721i			0.478484i	−0.970960	+	0.239242i	$0.923101\pi$
$480$	−10.9443			−0.499535
$481$		−	4.76393i		−	0.217217i
$482$			4.85410i			0.221098i
$483$		−	5.23607i		−	0.238249i
$484$	−3.70820			−0.168555
$485$			58.8328i			2.67146i
$486$	1.61803			0.0733955
$487$	20.3607			0.922630			0.461315	−	0.887236i	$-0.347378\pi$
$487$	20.3607			0.922630			0.461315	+	0.887236i	$0.347378\pi$
$488$	6.18034			0.279771
$489$	−7.41641			−0.335382
$490$		−	57.3050i		−	2.58877i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	−2.76393			−0.124608
$493$	9.00000	+	13.4164i	0.405340	+	0.604245i
$494$	−12.4721			−0.561148
$495$		−	7.23607i		−	0.325237i
$496$			35.1246i			1.57714i
$497$	−20.1803			−0.905212
$498$	−9.70820			−0.435035
$499$	21.1803			0.948162			0.474081	−	0.880481i	$-0.342780\pi$
$499$	21.1803			0.948162			0.474081	+	0.880481i	$0.342780\pi$
$500$	−0.944272			−0.0422291
$501$			15.8885i			0.709848i
$502$	−19.7984			−0.883645
$503$			25.1803i			1.12274i	0.827566	+	0.561368i	$0.189725\pi$
$503$			25.1803i			1.12274i	−0.827566	+	0.561368i	$0.810275\pi$
$504$		−	9.47214i		−	0.421922i
$505$		−	12.7639i		−	0.567988i
$506$	4.47214			0.198811
$507$		−	12.0000i		−	0.532939i
$508$			7.70820i			0.341996i
$509$	−26.8328			−1.18934			−0.594672	−	0.803969i	$-0.702718\pi$
$509$	−26.8328			−1.18934			−0.594672	+	0.803969i	$0.702718\pi$
$510$		−	15.7082i		−	0.695571i
$511$			32.6525i			1.44446i
$512$			5.29180i			0.233867i
$513$	7.70820			0.340326
$514$			42.8328i			1.88927i
$515$	−62.8328			−2.76874
$516$	−0.291796			−0.0128456
$517$	22.8885			1.00664
$518$	−32.6525			−1.43467
$519$		−	6.00000i		−	0.263371i
$520$			7.23607i			0.317323i
$521$	−3.52786			−0.154559			−0.0772793	−	0.997009i	$-0.524623\pi$
$521$	−3.52786			−0.154559			−0.0772793	+	0.997009i	$0.524623\pi$
$522$	−4.85410	−	7.23607i	−0.212458	−	0.316714i
$523$	33.0689			1.44600			0.723001	−	0.690847i	$-0.242762\pi$
$523$	33.0689			1.44600			0.723001	+	0.690847i	$0.242762\pi$
$524$		−	7.56231i		−	0.330361i
$525$		−	23.1803i		−	1.01167i
$526$	−8.00000			−0.348817
$527$	−21.7082			−0.945624
$528$	10.8541			0.472364
$529$	−21.4721			−0.933571
$530$		−	35.4164i		−	1.53839i
$531$	−8.94427			−0.388148
$532$			20.1803i			0.874929i
$533$			4.47214i			0.193710i
$534$		−	0.0901699i		−	0.00390204i
$535$	2.47214			0.106880
$536$		−	10.5279i		−	0.454734i
$537$		−	17.2361i		−	0.743791i
$538$	−34.5623			−1.49009
$539$			24.4721i			1.05409i
$540$			2.00000i			0.0860663i
$541$		−	10.6525i		−	0.457986i	−0.973428	−	0.228993i	$-0.926457\pi$
$541$		−	10.6525i		−	0.457986i	0.973428	−	0.228993i	$-0.0735432\pi$
$542$	−37.8885			−1.62745
$543$			20.4164i			0.876152i
$544$	10.1459			0.435002
$545$	16.1803			0.693090
$546$	6.85410			0.293328
$547$	−6.34752			−0.271401			−0.135700	−	0.990750i	$-0.543328\pi$
$547$	−6.34752			−0.271401			−0.135700	+	0.990750i	$0.543328\pi$
$548$			2.18034i			0.0931395i
$549$		−	2.76393i		−	0.117962i
$550$	19.7984			0.844205
$551$	−23.1246	−	34.4721i	−0.985142	−	1.46856i
$552$	2.76393			0.117641
$553$			9.70820i			0.412835i
$554$		−	10.3820i		−	0.441087i
$555$	−15.4164			−0.654390
$556$	4.14590			0.175825
$557$	−16.4721			−0.697947			−0.348973	−	0.937133i	$-0.613470\pi$
$557$	−16.4721			−0.697947			−0.348973	+	0.937133i	$0.613470\pi$
$558$	11.7082			0.495648
$559$			0.472136i			0.0199692i
$560$	66.5410			2.81187
$561$			6.70820i			0.283221i
$562$			2.29180i			0.0966736i
$563$			13.0689i			0.550788i	0.961331	+	0.275394i	$0.0888083\pi$
$563$			13.0689i			0.550788i	−0.961331	+	0.275394i	$0.911192\pi$
$564$	−6.32624			−0.266383
$565$			14.6525i			0.616434i
$566$			22.4721i			0.944574i
$567$	−4.23607			−0.177898
$568$		−	10.6525i		−	0.446968i
$569$			21.0000i			0.880366i	0.897908	+	0.440183i	$0.145086\pi$
$569$			21.0000i			0.880366i	−0.897908	+	0.440183i	$0.854914\pi$
$570$			40.3607i			1.69052i
$571$	18.8328			0.788129			0.394064	−	0.919083i	$-0.371069\pi$
$571$	18.8328			0.788129			0.394064	+	0.919083i	$0.371069\pi$
$572$			1.38197i			0.0577829i
$573$	−8.94427			−0.373652
$574$	30.6525			1.27941
$575$	6.76393			0.282075
$576$	4.23607			0.176503
$577$		−	24.8328i		−	1.03380i	−0.856045	−	0.516902i	$-0.827085\pi$
$577$		−	24.8328i		−	1.03380i	0.856045	−	0.516902i	$-0.172915\pi$
$578$		−	12.9443i		−	0.538411i
$579$	−17.4164			−0.723801
$580$	8.94427	−	6.00000i	0.371391	−	0.249136i
$581$	25.4164			1.05445
$582$			29.4164i			1.21935i
$583$			15.1246i			0.626397i
$584$	−17.2361			−0.713234
$585$	3.23607			0.133795
$586$	−48.4508			−2.00149
$587$	−0.944272			−0.0389743			−0.0194871	−	0.999810i	$-0.506203\pi$
$587$	−0.944272			−0.0389743			−0.0194871	+	0.999810i	$0.506203\pi$
$588$		−	6.76393i		−	0.278940i
$589$	55.7771			2.29825
$590$		−	46.8328i		−	1.92808i
$591$		−	3.70820i		−	0.152535i
$592$		−	23.1246i		−	0.950416i
$593$	40.1803			1.65001			0.825004	−	0.565126i	$-0.191173\pi$
$593$	40.1803			1.65001			0.825004	+	0.565126i	$0.191173\pi$
$594$		−	3.61803i		−	0.148450i
$595$			41.1246i			1.68594i
$596$	3.41641			0.139942
$597$		−	20.1246i		−	0.823646i
$598$			2.00000i			0.0817861i
$599$		−	1.76393i		−	0.0720723i	−0.999350	−	0.0360362i	$-0.988527\pi$
$599$		−	1.76393i		−	0.0720723i	0.999350	−	0.0360362i	$-0.0114731\pi$
$600$	12.2361			0.499535
$601$		−	18.5410i		−	0.756304i	−0.925744	−	0.378152i	$-0.876560\pi$
$601$		−	18.5410i		−	0.756304i	0.925744	−	0.378152i	$-0.123440\pi$
$602$	3.23607			0.131892
$603$	−4.70820			−0.191733
$604$	−7.41641			−0.301769
$605$	19.4164			0.789389
$606$		−	6.38197i		−	0.259250i
$607$			25.4164i			1.03162i	0.856703	+	0.515810i	$0.172509\pi$
$607$			25.4164i			1.03162i	−0.856703	+	0.515810i	$0.827491\pi$
$608$	−26.0689			−1.05723
$609$	12.7082	+	18.9443i	0.514962	+	0.767661i
$610$	14.4721			0.585960
$611$			10.2361i			0.414107i
$612$		−	1.85410i		−	0.0749476i
$613$	−24.4164			−0.986169			−0.493085	−	0.869981i	$-0.664131\pi$
$613$	−24.4164			−0.986169			−0.493085	+	0.869981i	$0.664131\pi$
$614$	45.5967			1.84013
$615$	14.4721			0.583573
$616$	−21.1803			−0.853380
$617$			19.8885i			0.800683i	0.916366	+	0.400341i	$0.131108\pi$
$617$			19.8885i			0.800683i	−0.916366	+	0.400341i	$0.868892\pi$
$618$	−31.4164			−1.26375
$619$		−	32.5410i		−	1.30793i	−0.756523	−	0.653967i	$-0.773104\pi$
$619$		−	32.5410i		−	1.30793i	0.756523	−	0.653967i	$-0.226896\pi$
$620$			14.4721i			0.581215i
$621$		−	1.23607i		−	0.0496017i
$622$	−25.3262			−1.01549
$623$			0.236068i			0.00945786i
$624$			4.85410i			0.194320i
$625$	−22.4164			−0.896656
$626$			8.85410i			0.353881i
$627$		−	17.2361i		−	0.688342i
$628$		−	1.23607i		−	0.0493245i
$629$	14.2918			0.569851
$630$		−	22.1803i		−	0.883686i
$631$	28.7082			1.14286			0.571428	−	0.820652i	$-0.306390\pi$
$631$	28.7082			1.14286			0.571428	+	0.820652i	$0.306390\pi$
$632$	−5.12461			−0.203846
$633$	−10.0000			−0.397464
$634$	38.5623			1.53150
$635$		−	40.3607i		−	1.60166i
$636$		−	4.18034i		−	0.165761i
$637$	−10.9443			−0.433628
$638$	−16.1803	+	10.8541i	−0.640586	+	0.429718i
$639$	−4.76393			−0.188458
$640$			44.0689i			1.74198i
$641$		−	19.4721i		−	0.769103i	−0.923104	−	0.384552i	$-0.874356\pi$
$641$		−	19.4721i		−	0.769103i	0.923104	−	0.384552i	$-0.125644\pi$
$642$	1.23607			0.0487837
$643$	0.708204			0.0279288			0.0139644	−	0.999902i	$-0.495555\pi$
$643$	0.708204			0.0279288			0.0139644	+	0.999902i	$0.495555\pi$
$644$	3.23607			0.127519
$645$	1.52786			0.0601596
$646$		−	37.4164i		−	1.47213i
$647$	17.5967			0.691800			0.345900	−	0.938271i	$-0.387574\pi$
$647$	17.5967			0.691800			0.345900	+	0.938271i	$0.387574\pi$
$648$		−	2.23607i		−	0.0878410i
$649$			20.0000i			0.785069i
$650$			8.85410i			0.347286i
$651$	−30.6525			−1.20137
$652$		−	4.58359i		−	0.179507i
$653$		−	32.3050i		−	1.26419i	−0.774891	−	0.632095i	$-0.782195\pi$
$653$		−	32.3050i		−	1.26419i	0.774891	−	0.632095i	$-0.217805\pi$
$654$	8.09017			0.316351
$655$			39.5967i			1.54717i
$656$			21.7082i			0.847563i
$657$			7.70820i			0.300726i
$658$	70.1591			2.73508
$659$		−	26.2361i		−	1.02201i	−0.859577	−	0.511006i	$-0.829273\pi$
$659$		−	26.2361i		−	1.02201i	0.859577	−	0.511006i	$-0.170727\pi$
$660$	4.47214			0.174078
$661$	−29.8328			−1.16036			−0.580181	−	0.814488i	$-0.697018\pi$
$661$	−29.8328			−1.16036			−0.580181	+	0.814488i	$0.697018\pi$
$662$	−13.4164			−0.521443
$663$	−3.00000			−0.116510
$664$			13.4164i			0.520658i
$665$		−	105.666i		−	4.09754i
$666$	−7.70820			−0.298687
$667$	−5.52786	+	3.70820i	−0.214040	+	0.143582i
$668$	−9.81966			−0.379934
$669$		−	12.7082i		−	0.491328i
$670$		−	24.6525i		−	0.952408i
$671$	−6.18034			−0.238589
$672$	14.3262			0.552647
$673$	−4.41641			−0.170240			−0.0851200	−	0.996371i	$-0.527127\pi$
$673$	−4.41641			−0.170240			−0.0851200	+	0.996371i	$0.527127\pi$
$674$	31.1246			1.19888
$675$		−	5.47214i		−	0.210623i
$676$	7.41641			0.285246
$677$			18.0557i			0.693938i	0.937877	+	0.346969i	$0.112789\pi$
$677$			18.0557i			0.693938i	−0.937877	+	0.346969i	$0.887211\pi$
$678$			7.32624i			0.281362i
$679$		−	77.0132i		−	2.95549i
$680$	−21.7082			−0.832472
$681$			9.05573i			0.347016i
$682$		−	26.1803i		−	1.00250i
$683$	32.9443			1.26058			0.630289	−	0.776361i	$-0.282936\pi$
$683$	32.9443			1.26058			0.630289	+	0.776361i	$0.282936\pi$
$684$			4.76393i			0.182153i
$685$		−	11.4164i		−	0.436199i
$686$			27.0344i			1.03218i
$687$	−22.1803			−0.846233
$688$			2.29180i			0.0873739i
$689$	−6.76393			−0.257685
$690$	6.47214			0.246390
$691$	−30.2361			−1.15023			−0.575117	−	0.818071i	$-0.695044\pi$
$691$	−30.2361			−1.15023			−0.575117	+	0.818071i	$0.695044\pi$
$692$	3.70820			0.140965
$693$			9.47214i			0.359817i
$694$			36.6525i			1.39131i
$695$	−21.7082			−0.823439
$696$	−10.0000	+	6.70820i	−0.379049	+	0.254274i
$697$	−13.4164			−0.508183
$698$		−	16.1803i		−	0.612435i
$699$		−	10.4721i		−	0.396093i
$700$	14.3262			0.541481
$701$	8.18034			0.308967			0.154484	−	0.987995i	$-0.450629\pi$
$701$	8.18034			0.308967			0.154484	+	0.987995i	$0.450629\pi$
$702$	1.61803			0.0610688
$703$	−36.7214			−1.38497
$704$		−	9.47214i		−	0.356995i
$705$	33.1246			1.24755
$706$		−	7.52786i		−	0.283315i
$707$			16.7082i			0.628377i
$708$		−	5.52786i		−	0.207750i
$709$	−13.4164			−0.503864			−0.251932	−	0.967745i	$-0.581066\pi$
$709$	−13.4164			−0.503864			−0.251932	+	0.967745i	$0.581066\pi$
$710$		−	24.9443i		−	0.936142i
$711$			2.29180i			0.0859491i
$712$	−0.124612			−0.00467002
$713$		−	8.94427i		−	0.334966i
$714$			20.5623i			0.769525i
$715$		−	7.23607i		−	0.270614i
$716$	10.6525			0.398102
$717$			26.1803i			0.977723i
$718$	−40.9443			−1.52803
$719$	−30.0000			−1.11881			−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000			−1.11881			−0.559406	+	0.828894i	$0.688971\pi$
$720$	15.7082			0.585410
$721$	82.2492			3.06312
$722$			65.3951i			2.43375i
$723$		−	3.00000i		−	0.111571i
$724$	−12.6180			−0.468946
$725$	−24.4721	+	16.4164i	−0.908872	+	0.609690i
$726$	9.70820			0.360305
$727$			5.81966i			0.215839i	0.994160	+	0.107920i	$0.0344189\pi$
$727$			5.81966i			0.215839i	−0.994160	+	0.107920i	$0.965581\pi$
$728$		−	9.47214i		−	0.351061i
$729$	−1.00000			−0.0370370
$730$	−40.3607			−1.49382
$731$	−1.41641			−0.0523877
$732$	1.70820			0.0631370
$733$			8.47214i			0.312925i	0.987684	+	0.156463i	$0.0500091\pi$
$733$			8.47214i			0.312925i	−0.987684	+	0.156463i	$0.949991\pi$
$734$	−29.1246			−1.07501
$735$			35.4164i			1.30635i
$736$			4.18034i			0.154089i
$737$			10.5279i			0.387799i
$738$	7.23607			0.266363
$739$			12.1803i			0.448061i	0.974582	+	0.224031i	$0.0719215\pi$
$739$			12.1803i			0.448061i	−0.974582	+	0.224031i	$0.928078\pi$
$740$		−	9.52786i		−	0.350251i
$741$	7.70820			0.283168
$742$			46.3607i			1.70195i
$743$			43.0689i			1.58004i	0.613078	+	0.790022i	$0.289931\pi$
$743$			43.0689i			1.58004i	−0.613078	+	0.790022i	$0.710069\pi$
$744$		−	16.1803i		−	0.593200i
$745$	−17.8885			−0.655386
$746$			6.29180i			0.230359i
$747$	6.00000			0.219529
$748$	−4.14590			−0.151589
$749$	−3.23607			−0.118243
$750$	2.47214			0.0902696
$751$			26.8328i			0.979143i	0.871963	+	0.489572i	$0.162847\pi$
$751$			26.8328i			0.979143i	−0.871963	+	0.489572i	$0.837153\pi$
$752$			49.6869i			1.81190i
$753$	12.2361			0.445907
$754$	−4.85410	−	7.23607i	−0.176776	−	0.263522i
$755$	38.8328			1.41327
$756$		−	2.61803i		−	0.0952170i
$757$		−	38.0000i		−	1.38113i	−0.723269	−	0.690567i	$-0.757361\pi$
$757$		−	38.0000i		−	1.38113i	0.723269	−	0.690567i	$-0.242639\pi$
$758$	23.1246			0.839924
$759$	−2.76393			−0.100324
$760$	55.7771			2.02325
$761$	2.65248			0.0961522			0.0480761	−	0.998844i	$-0.484691\pi$
$761$	2.65248			0.0961522			0.0480761	+	0.998844i	$0.484691\pi$
$762$		−	20.1803i		−	0.731057i
$763$	−21.1803			−0.766780
$764$		−	5.52786i		−	0.199991i
$765$			9.70820i			0.351001i
$766$			8.65248i			0.312627i
$767$	−8.94427			−0.322959
$768$			13.5623i			0.489388i
$769$		−	40.1803i		−	1.44894i	−0.689306	−	0.724470i	$-0.742085\pi$
$769$		−	40.1803i		−	1.44894i	0.689306	−	0.724470i	$-0.257915\pi$
$770$	−49.5967			−1.78734
$771$		−	26.4721i		−	0.953371i
$772$		−	10.7639i		−	0.387402i
$773$			31.8885i			1.14695i	0.819223	+	0.573476i	$0.194405\pi$
$773$			31.8885i			1.14695i	−0.819223	+	0.573476i	$0.805595\pi$
$774$	0.763932			0.0274590
$775$		−	39.5967i		−	1.42236i
$776$	40.6525			1.45934
$777$	20.1803			0.723966
$778$	−21.7984			−0.781510
$779$	34.4721			1.23509
$780$			2.00000i			0.0716115i
$781$			10.6525i			0.381176i
$782$	−6.00000			−0.214560
$783$	3.00000	+	4.47214i	0.107211	+	0.159821i
$784$	−53.1246			−1.89731
$785$			6.47214i			0.231000i
$786$			19.7984i			0.706185i
$787$	−12.0000			−0.427754			−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000			−0.427754			−0.213877	+	0.976861i	$0.568609\pi$
$788$	2.29180			0.0816419
$789$	4.94427			0.176021
$790$	−12.0000			−0.426941
$791$		−	19.1803i		−	0.681974i
$792$	−5.00000			−0.177667
$793$		−	2.76393i		−	0.0981501i
$794$		−	11.2361i		−	0.398753i
$795$			21.8885i			0.776307i
$796$	12.4377			0.440842
$797$		−	44.8328i		−	1.58806i	−0.607879	−	0.794030i	$-0.707979\pi$
$797$		−	44.8328i		−	1.58806i	0.607879	−	0.794030i	$-0.292021\pi$
$798$		−	52.8328i		−	1.87026i
$799$	−30.7082			−1.08638
$800$			18.5066i			0.654306i
$801$			0.0557281i			0.00196906i
$802$		−	54.5410i		−	1.92591i
$803$	17.2361			0.608248
$804$		−	2.90983i		−	0.102622i
$805$	−16.9443			−0.597207
$806$	11.7082			0.412404
$807$	21.3607			0.751932
$808$	−8.81966			−0.310275
$809$			43.3607i			1.52448i	0.647294	+	0.762240i	$0.275900\pi$
$809$			43.3607i			1.52448i	−0.647294	+	0.762240i	$0.724100\pi$
$810$		−	5.23607i		−	0.183977i
$811$	46.5967			1.63623			0.818117	−	0.575052i	$-0.195018\pi$
$811$	46.5967			1.63623			0.818117	+	0.575052i	$0.195018\pi$
$812$	−11.7082	+	7.85410i	−0.410877	+	0.275625i
$813$	23.4164			0.821249
$814$			17.2361i			0.604124i
$815$			24.0000i			0.840683i
$816$	−14.5623			−0.509783
$817$	3.63932			0.127324
$818$	−17.1246			−0.598748
$819$	−4.23607			−0.148020
$820$			8.94427i			0.312348i
$821$	−12.4721			−0.435281			−0.217640	−	0.976029i	$-0.569836\pi$
$821$	−12.4721			−0.435281			−0.217640	+	0.976029i	$0.569836\pi$
$822$		−	5.70820i		−	0.199096i
$823$			26.3607i			0.918876i	0.888210	+	0.459438i	$0.151949\pi$
$823$			26.3607i			0.918876i	−0.888210	+	0.459438i	$0.848051\pi$
$824$			43.4164i			1.51248i
$825$	−12.2361			−0.426005
$826$			61.3050i			2.13307i
$827$			29.8885i			1.03933i	0.854371	+	0.519663i	$0.173943\pi$
$827$			29.8885i			1.03933i	−0.854371	+	0.519663i	$0.826057\pi$
$828$	0.763932			0.0265485
$829$			27.3050i			0.948340i	0.880433	+	0.474170i	$0.157252\pi$
$829$			27.3050i			0.948340i	−0.880433	+	0.474170i	$0.842748\pi$
$830$			31.4164i			1.09048i
$831$			6.41641i			0.222583i
$832$	4.23607			0.146859
$833$		−	32.8328i		−	1.13759i
$834$	−10.8541			−0.375847
$835$	51.4164			1.77934
$836$	10.6525			0.368424
$837$	−7.23607			−0.250115
$838$		−	6.18034i		−	0.213496i
$839$		−	0.708204i		−	0.0244499i	−0.999925	−	0.0122250i	$-0.996109\pi$
$839$		−	0.708204i		−	0.0244499i	0.999925	−	0.0122250i	$-0.00389142\pi$
$840$	−30.6525			−1.05761
$841$	11.0000	−	26.8328i	0.379310	−	0.925270i
$842$	32.3607			1.11522
$843$		−	1.41641i		−	0.0487837i
$844$		−	6.18034i		−	0.212736i
$845$	−38.8328			−1.33589
$846$	16.5623			0.569424
$847$	−25.4164			−0.873318
$848$	−32.8328			−1.12748
$849$		−	13.8885i		−	0.476654i
$850$	−26.5623			−0.911080
$851$			5.88854i			0.201857i
$852$		−	2.94427i		−	0.100869i
$853$		−	45.1935i		−	1.54740i	−0.633555	−	0.773698i	$-0.718405\pi$
$853$		−	45.1935i		−	1.54740i	0.633555	−	0.773698i	$-0.281595\pi$
$854$	−18.9443			−0.648260
$855$		−	24.9443i		−	0.853076i
$856$		−	1.70820i		−	0.0583852i
$857$	37.5967			1.28428			0.642140	−	0.766587i	$-0.278047\pi$
$857$	37.5967			1.28428			0.642140	+	0.766587i	$0.278047\pi$
$858$		−	3.61803i		−	0.123518i
$859$		−	36.3607i		−	1.24061i	−0.784361	−	0.620305i	$-0.787009\pi$
$859$		−	36.3607i		−	1.24061i	0.784361	−	0.620305i	$-0.212991\pi$
$860$			0.944272i			0.0321994i
$861$	−18.9443			−0.645619
$862$		−	23.2361i		−	0.791424i
$863$	−46.6525			−1.58807			−0.794034	−	0.607873i	$-0.792023\pi$
$863$	−46.6525			−1.58807			−0.794034	+	0.607873i	$0.792023\pi$
$864$	3.38197			0.115057
$865$	−19.4164			−0.660178
$866$	−23.1246			−0.785806
$867$			8.00000i			0.271694i
$868$		−	18.9443i		−	0.643010i
$869$	5.12461			0.173841
$870$	−23.4164	+	15.7082i	−0.793891	+	0.532558i
$871$	−4.70820			−0.159531
$872$		−	11.1803i		−	0.378614i
$873$		−	18.1803i		−	0.615311i
$874$	15.4164			0.521468
$875$	−6.47214			−0.218798
$876$	−4.76393			−0.160958
$877$	32.4721			1.09651			0.548253	−	0.836312i	$-0.315293\pi$
$877$	32.4721			1.09651			0.548253	+	0.836312i	$0.315293\pi$
$878$		−	21.5066i		−	0.725812i
$879$	29.9443			1.01000
$880$		−	35.1246i		−	1.18405i
$881$		−	55.2492i		−	1.86139i	−0.365792	−	0.930697i	$-0.619202\pi$
$881$		−	55.2492i		−	1.86139i	0.365792	−	0.930697i	$-0.380798\pi$
$882$			17.7082i			0.596266i
$883$	34.2492			1.15258			0.576289	−	0.817246i	$-0.304500\pi$
$883$	34.2492			1.15258			0.576289	+	0.817246i	$0.304500\pi$
$884$		−	1.85410i		−	0.0623602i
$885$			28.9443i			0.972951i
$886$	15.6180			0.524698
$887$		−	17.0689i		−	0.573117i	−0.958063	−	0.286559i	$-0.907489\pi$
$887$		−	17.0689i		−	0.573117i	0.958063	−	0.286559i	$-0.0925113\pi$
$888$			10.6525i			0.357474i
$889$			52.8328i			1.77196i
$890$	−0.291796			−0.00978103
$891$			2.23607i			0.0749111i
$892$	7.85410			0.262975
$893$	78.9017			2.64034
$894$	−8.94427			−0.299141
$895$	−55.7771			−1.86442
$896$		−	57.6869i		−	1.92718i
$897$		−	1.23607i		−	0.0412711i
$898$	30.5623			1.01988
$899$	21.7082	+	32.3607i	0.724009	+	1.07929i
$900$	3.38197			0.112732
$901$		−	20.2918i		−	0.676018i
$902$		−	16.1803i		−	0.538746i
$903$	−2.00000			−0.0665558
$904$	10.1246			0.336740
$905$	66.0689			2.19620
$906$	19.4164			0.645067
$907$			26.4721i			0.878993i	0.898244	+	0.439496i	$0.144843\pi$
$907$			26.4721i			0.878993i	−0.898244	+	0.439496i	$0.855157\pi$
$908$	−5.59675			−0.185735
$909$			3.94427i			0.130823i
$910$		−	22.1803i		−	0.735271i
$911$		−	51.1803i		−	1.69568i	−0.530252	−	0.847840i	$-0.677903\pi$
$911$		−	51.1803i		−	1.69568i	0.530252	−	0.847840i	$-0.322097\pi$
$912$	37.4164			1.23898
$913$		−	13.4164i		−	0.444018i
$914$		−	10.3820i		−	0.343405i
$915$	−8.94427			−0.295689
$916$		−	13.7082i		−	0.452932i
$917$		−	51.8328i		−	1.71167i
$918$			4.85410i			0.160209i
$919$	−25.6525			−0.846197			−0.423099	−	0.906084i	$-0.639058\pi$
$919$	−25.6525			−0.846197			−0.423099	+	0.906084i	$0.639058\pi$
$920$		−	8.94427i		−	0.294884i
$921$	−28.1803			−0.928574
$922$	−30.6525			−1.00949
$923$	−4.76393			−0.156807
$924$	−5.85410			−0.192586
$925$			26.0689i			0.857140i
$926$		−	1.14590i		−	0.0376565i
$927$	19.4164			0.637719
$928$	−10.1459	−	15.1246i	−0.333055	−	0.496490i
$929$	−32.3607			−1.06172			−0.530860	−	0.847460i	$-0.678131\pi$
$929$	−32.3607			−1.06172			−0.530860	+	0.847460i	$0.678131\pi$
$930$		−	37.8885i		−	1.24241i
$931$			84.3607i			2.76481i
$932$	6.47214			0.212002
$933$	15.6525			0.512439
$934$	−21.8885			−0.716215
$935$	21.7082			0.709934
$936$		−	2.23607i		−	0.0730882i
$937$	33.0000			1.07806			0.539032	−	0.842286i	$-0.318790\pi$
$937$	33.0000			1.07806			0.539032	+	0.842286i	$0.318790\pi$
$938$			32.2705i			1.05367i
$939$		−	5.47214i		−	0.178576i
$940$			20.4721i			0.667727i
$941$	−44.8328			−1.46151			−0.730754	−	0.682641i	$-0.760831\pi$
$941$	−44.8328			−1.46151			−0.730754	+	0.682641i	$0.760831\pi$
$942$			3.23607i			0.105437i
$943$		−	5.52786i		−	0.180012i
$944$	−43.4164			−1.41308
$945$			13.7082i			0.445928i
$946$		−	1.70820i		−	0.0555385i
$947$		−	16.8197i		−	0.546566i	−0.961934	−	0.273283i	$-0.911891\pi$
$947$		−	16.8197i		−	0.546566i	0.961934	−	0.273283i	$-0.0881095\pi$
$948$	−1.41641			−0.0460028
$949$			7.70820i			0.250219i
$950$	68.2492			2.21430
$951$	−23.8328			−0.772832
$952$	28.4164			0.920981
$953$	−59.6656			−1.93276			−0.966380	−	0.257119i	$-0.917227\pi$
$953$	−59.6656			−1.93276			−0.966380	+	0.257119i	$0.917227\pi$
$954$			10.9443i			0.354334i
$955$			28.9443i			0.936615i
$956$	−16.1803			−0.523310
$957$	10.0000	−	6.70820i	0.323254	−	0.216845i
$958$	16.9443			0.547445
$959$			14.9443i			0.482576i
$960$		−	13.7082i		−	0.442430i
$961$	−21.3607			−0.689054
$962$	−7.70820			−0.248522
$963$	−0.763932			−0.0246174
$964$	1.85410			0.0597166
$965$			56.3607i			1.81431i
$966$	−8.47214			−0.272587
$967$			27.1246i			0.872269i	0.899882	+	0.436134i	$0.143653\pi$
$967$			27.1246i			0.872269i	−0.899882	+	0.436134i	$0.856347\pi$
$968$		−	13.4164i		−	0.431220i
$969$			23.1246i			0.742870i
$970$	95.1935			3.05648
$971$			16.5836i			0.532193i	0.963946	+	0.266096i	$0.0857340\pi$
$971$			16.5836i			0.532193i	−0.963946	+	0.266096i	$0.914266\pi$
$972$		−	0.618034i		−	0.0198234i
$973$	28.4164			0.910988
$974$		−	32.9443i		−	1.05560i
$975$		−	5.47214i		−	0.175249i
$976$		−	13.4164i		−	0.429449i
$977$	51.0132			1.63206			0.816028	−	0.578013i	$-0.196172\pi$
$977$	51.0132			1.63206			0.816028	+	0.578013i	$0.196172\pi$
$978$			12.0000i			0.383718i
$979$	0.124612			0.00398261
$980$	−21.8885			−0.699204
$981$	−5.00000			−0.159638
$982$		0			0
$983$		−	13.8885i		−	0.442976i	−0.975163	−	0.221488i	$-0.928909\pi$
$983$		−	13.8885i		−	0.442976i	0.975163	−	0.221488i	$-0.0710913\pi$
$984$		−	10.0000i		−	0.318788i
$985$	−12.0000			−0.382352
$986$	21.7082	−	14.5623i	0.691330	−	0.463758i
$987$	−43.3607			−1.38019
$988$			4.76393i			0.151561i
$989$		−	0.583592i		−	0.0185572i
$990$	−11.7082			−0.372111
$991$	−21.2918			−0.676356			−0.338178	−	0.941082i	$-0.609811\pi$
$991$	−21.2918			−0.676356			−0.338178	+	0.941082i	$0.609811\pi$
$992$	24.4721			0.776991
$993$	8.29180			0.263132
$994$			32.6525i			1.03567i
$995$	−65.1246			−2.06459
$996$			3.70820i			0.117499i
$997$		−	24.5836i		−	0.778570i	−0.921117	−	0.389285i	$-0.872722\pi$
$997$		−	24.5836i		−	0.778570i	0.921117	−	0.389285i	$-0.127278\pi$
$998$		−	34.2705i		−	1.08481i
$999$	4.76393			0.150724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.c.a.28.1	✓	4
3.2	odd	2		261.2.c.b.28.4		4
4.3	odd	2		1392.2.o.i.289.2		4
5.2	odd	4		2175.2.f.b.724.3		4
5.3	odd	4		2175.2.f.a.724.2		4
5.4	even	2		2175.2.d.e.376.4		4
12.11	even	2		4176.2.o.l.289.2		4
29.12	odd	4		2523.2.a.e.1.2		2
29.17	odd	4		2523.2.a.d.1.1		2
29.28	even	2	inner	87.2.c.a.28.4	yes	4
87.17	even	4		7569.2.a.n.1.2		2
87.41	even	4		7569.2.a.f.1.1		2
87.86	odd	2		261.2.c.b.28.1		4
116.115	odd	2		1392.2.o.i.289.4		4
145.28	odd	4		2175.2.f.b.724.4		4
145.57	odd	4		2175.2.f.a.724.1		4
145.144	even	2		2175.2.d.e.376.1		4
348.347	even	2		4176.2.o.l.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.c.a.28.1	✓	4	1.1	even	1	trivial
87.2.c.a.28.4	yes	4	29.28	even	2	inner
261.2.c.b.28.1		4	87.86	odd	2
261.2.c.b.28.4		4	3.2	odd	2
1392.2.o.i.289.2		4	4.3	odd	2
1392.2.o.i.289.4		4	116.115	odd	2
2175.2.d.e.376.1		4	145.144	even	2
2175.2.d.e.376.4		4	5.4	even	2
2175.2.f.a.724.1		4	145.57	odd	4
2175.2.f.a.724.2		4	5.3	odd	4
2175.2.f.b.724.3		4	5.2	odd	4
2175.2.f.b.724.4		4	145.28	odd	4
2523.2.a.d.1.1		2	29.17	odd	4
2523.2.a.e.1.2		2	29.12	odd	4
4176.2.o.l.289.1		4	348.347	even	2
4176.2.o.l.289.2		4	12.11	even	2
7569.2.a.f.1.1		2	87.41	even	4
7569.2.a.n.1.2		2	87.17	even	4

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +3.23607 q^{5} +1.61803 q^{6} -4.23607 q^{7} -2.23607i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +3.23607 q^{5} +1.61803 q^{6} -4.23607 q^{7} -2.23607i q^{8} -1.00000 q^{9} -5.23607i q^{10} +2.23607i q^{11} -0.618034i q^{12} -1.00000 q^{13} +6.85410i q^{14} +3.23607i q^{15} -4.85410 q^{16} -3.00000i q^{17} +1.61803i q^{18} +7.70820i q^{19} -2.00000 q^{20} -4.23607i q^{21} +3.61803 q^{22} +1.23607 q^{23} +2.23607 q^{24} +5.47214 q^{25} +1.61803i q^{26} -1.00000i q^{27} +2.61803 q^{28} +(-4.47214 + 3.00000i) q^{29} +5.23607 q^{30} -7.23607i q^{31} +3.38197i q^{32} -2.23607 q^{33} -4.85410 q^{34} -13.7082 q^{35} +0.618034 q^{36} +4.76393i q^{37} +12.4721 q^{38} -1.00000i q^{39} -7.23607i q^{40} -4.47214i q^{41} -6.85410 q^{42} -0.472136i q^{43} -1.38197i q^{44} -3.23607 q^{45} -2.00000i q^{46} -10.2361i q^{47} -4.85410i q^{48} +10.9443 q^{49} -8.85410i q^{50} +3.00000 q^{51} +0.618034 q^{52} +6.76393 q^{53} -1.61803 q^{54} +7.23607i q^{55} +9.47214i q^{56} -7.70820 q^{57} +(4.85410 + 7.23607i) q^{58} +8.94427 q^{59} -2.00000i q^{60} +2.76393i q^{61} -11.7082 q^{62} +4.23607 q^{63} -4.23607 q^{64} -3.23607 q^{65} +3.61803i q^{66} +4.70820 q^{67} +1.85410i q^{68} +1.23607i q^{69} +22.1803i q^{70} +4.76393 q^{71} +2.23607i q^{72} -7.70820i q^{73} +7.70820 q^{74} +5.47214i q^{75} -4.76393i q^{76} -9.47214i q^{77} -1.61803 q^{78} -2.29180i q^{79} -15.7082 q^{80} +1.00000 q^{81} -7.23607 q^{82} -6.00000 q^{83} +2.61803i q^{84} -9.70820i q^{85} -0.763932 q^{86} +(-3.00000 - 4.47214i) q^{87} +5.00000 q^{88} -0.0557281i q^{89} +5.23607i q^{90} +4.23607 q^{91} -0.763932 q^{92} +7.23607 q^{93} -16.5623 q^{94} +24.9443i q^{95} -3.38197 q^{96} +18.1803i q^{97} -17.7082i q^{98} -2.23607i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 - 8 * q^7 - 4 * q^9	\( 4 q + 2 q^{4} + 4 q^{5} + 2 q^{6} - 8 q^{7} - 4 q^{9} - 4 q^{13} - 6 q^{16} - 8 q^{20} + 10 q^{22} - 4 q^{23} + 4 q^{25} + 6 q^{28} + 12 q^{30} - 6 q^{34} - 28 q^{35} - 2 q^{36} + 32 q^{38} - 14 q^{42} - 4 q^{45} + 8 q^{49} + 12 q^{51} - 2 q^{52} + 36 q^{53} - 2 q^{54} - 4 q^{57} + 6 q^{58} - 20 q^{62} + 8 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{67} + 28 q^{71} + 4 q^{74} - 2 q^{78} - 36 q^{80} + 4 q^{81} - 20 q^{82} - 24 q^{83} - 12 q^{86} - 12 q^{87} + 20 q^{88} + 8 q^{91} - 12 q^{92} + 20 q^{93} - 26 q^{94} - 18 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^6 - 8 * q^7 - 4 * q^9 - 4 * q^13 - 6 * q^16 - 8 * q^20 + 10 * q^22 - 4 * q^23 + 4 * q^25 + 6 * q^28 + 12 * q^30 - 6 * q^34 - 28 * q^35 - 2 * q^36 + 32 * q^38 - 14 * q^42 - 4 * q^45 + 8 * q^49 + 12 * q^51 - 2 * q^52 + 36 * q^53 - 2 * q^54 - 4 * q^57 + 6 * q^58 - 20 * q^62 + 8 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^67 + 28 * q^71 + 4 * q^74 - 2 * q^78 - 36 * q^80 + 4 * q^81 - 20 * q^82 - 24 * q^83 - 12 * q^86 - 12 * q^87 + 20 * q^88 + 8 * q^91 - 12 * q^92 + 20 * q^93 - 26 * q^94 - 18 * q^96

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