LMFDB - Embedded newform 731.2.m.b.87.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.2
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81709 - 1.81709i) q^{2} +(-2.81259 + 1.16501i) q^{3} +4.60365i q^{4} +(-1.37650 - 3.32317i) q^{5} +(7.22768 + 2.99380i) q^{6} +(0.758828 - 1.83197i) q^{7} +(4.73108 - 4.73108i) q^{8} +(4.43209 - 4.43209i) q^{9} +O(q^{10})$	\(q+(-1.81709 - 1.81709i) q^{2} +(-2.81259 + 1.16501i) q^{3} +4.60365i q^{4} +(-1.37650 - 3.32317i) q^{5} +(7.22768 + 2.99380i) q^{6} +(0.758828 - 1.83197i) q^{7} +(4.73108 - 4.73108i) q^{8} +(4.43209 - 4.43209i) q^{9} +(-3.53728 + 8.53975i) q^{10} +(-2.57277 - 1.06568i) q^{11} +(-5.36332 - 12.9482i) q^{12} +5.45581i q^{13} +(-4.70773 + 1.95000i) q^{14} +(7.74308 + 7.74308i) q^{15} -7.98632 q^{16} +(-0.724303 + 4.05899i) q^{17} -16.1070 q^{18} +(1.62346 + 1.62346i) q^{19} +(15.2987 - 6.33694i) q^{20} +6.03664i q^{21} +(2.73853 + 6.61140i) q^{22} +(4.15195 + 1.71979i) q^{23} +(-7.79482 + 18.8184i) q^{24} +(-5.61318 + 5.61318i) q^{25} +(9.91372 - 9.91372i) q^{26} +(-3.80718 + 9.19134i) q^{27} +(8.43377 + 3.49338i) q^{28} +(-0.682963 - 1.64882i) q^{29} -28.1398i q^{30} +(6.63701 - 2.74914i) q^{31} +(5.04972 + 5.04972i) q^{32} +8.47769 q^{33} +(8.69168 - 6.05943i) q^{34} -7.13249 q^{35} +(20.4038 + 20.4038i) q^{36} +(-9.17450 + 3.80020i) q^{37} -5.89997i q^{38} +(-6.35609 - 15.3450i) q^{39} +(-22.2345 - 9.20985i) q^{40} +(0.204615 - 0.493985i) q^{41} +(10.9691 - 10.9691i) q^{42} +(0.707107 - 0.707107i) q^{43} +(4.90601 - 11.8442i) q^{44} +(-20.8294 - 8.62782i) q^{45} +(-4.41945 - 10.6695i) q^{46} +0.510297i q^{47} +(22.4622 - 9.30417i) q^{48} +(2.16944 + 2.16944i) q^{49} +20.3993 q^{50} +(-2.69161 - 12.2601i) q^{51} -25.1167 q^{52} +(3.09108 + 3.09108i) q^{53} +(23.6195 - 9.78352i) q^{54} +10.0167i q^{55} +(-5.07714 - 12.2573i) q^{56} +(-6.45750 - 2.67478i) q^{57} +(-1.75505 + 4.23706i) q^{58} +(5.23979 - 5.23979i) q^{59} +(-35.6465 + 35.6465i) q^{60} +(4.26296 - 10.2917i) q^{61} +(-17.0555 - 7.06462i) q^{62} +(-4.75628 - 11.4827i) q^{63} -2.37899i q^{64} +(18.1306 - 7.50994i) q^{65} +(-15.4047 - 15.4047i) q^{66} +6.43282 q^{67} +(-18.6862 - 3.33444i) q^{68} -13.6813 q^{69} +(12.9604 + 12.9604i) q^{70} +(14.8600 - 6.15522i) q^{71} -41.9372i q^{72} +(3.55175 + 8.57469i) q^{73} +(23.5762 + 9.76560i) q^{74} +(9.24815 - 22.3270i) q^{75} +(-7.47387 + 7.47387i) q^{76} +(-3.90459 + 3.90459i) q^{77} +(-16.3336 + 39.4328i) q^{78} +(-9.94665 - 4.12004i) q^{79} +(10.9932 + 26.5399i) q^{80} -11.4831i q^{81} +(-1.26942 + 0.525812i) q^{82} +(-10.8951 - 10.8951i) q^{83} -27.7906 q^{84} +(14.4857 - 3.18023i) q^{85} -2.56976 q^{86} +(3.84179 + 3.84179i) q^{87} +(-17.2138 + 7.13019i) q^{88} +13.2051i q^{89} +(22.1714 + 53.5265i) q^{90} +(9.99490 + 4.14002i) q^{91} +(-7.91734 + 19.1141i) q^{92} +(-15.4644 + 15.4644i) q^{93} +(0.927257 - 0.927257i) q^{94} +(3.16035 - 7.62975i) q^{95} +(-20.0858 - 8.31981i) q^{96} +(-2.52472 - 6.09520i) q^{97} -7.88415i q^{98} +(-16.1259 + 6.67959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−1.81709	−	1.81709i	−1.28488	−	1.28488i	−0.937857	−	0.347022i	$-0.887193\pi$
$2$	−1.81709	−	1.81709i	−1.28488	−	1.28488i	−0.347022	−	0.937857i	$-0.612807\pi$
$3$	−2.81259	+	1.16501i	−1.62385	+	0.672621i	−0.994523	−	0.104519i	$-0.966670\pi$
$3$	−2.81259	+	1.16501i	−1.62385	+	0.672621i	−0.629327	+	0.777140i	$0.716670\pi$
$4$			4.60365i			2.30183i
$5$	−1.37650	−	3.32317i	−0.615591	−	1.48617i	−0.856776	−	0.515689i	$-0.827536\pi$
$5$	−1.37650	−	3.32317i	−0.615591	−	1.48617i	0.241185	−	0.970479i	$-0.422464\pi$
$6$	7.22768	+	2.99380i	2.95069	+	1.22221i
$7$	0.758828	−	1.83197i	0.286810	−	0.692421i	−0.713153	−	0.701008i	$-0.752734\pi$
$7$	0.758828	−	1.83197i	0.286810	−	0.692421i	0.999963	+	0.00858751i	$0.00273352\pi$
$8$	4.73108	−	4.73108i	1.67269	−	1.67269i
$9$	4.43209	−	4.43209i	1.47736	−	1.47736i
$10$	−3.53728	+	8.53975i	−1.11859	+	2.70050i
$11$	−2.57277	−	1.06568i	−0.775720	−	0.321314i	−0.0405332	−	0.999178i	$-0.512906\pi$
$11$	−2.57277	−	1.06568i	−0.775720	−	0.321314i	−0.735187	+	0.677864i	$0.762906\pi$
$12$	−5.36332	−	12.9482i	−1.54826	−	3.73782i
$13$			5.45581i			1.51317i	0.653896	+	0.756585i	$0.273134\pi$
$13$			5.45581i			1.51317i	−0.653896	+	0.756585i	$0.726866\pi$
$14$	−4.70773	+	1.95000i	−1.25819	+	0.521161i
$15$	7.74308	+	7.74308i	1.99925	+	1.99925i
$16$	−7.98632			−1.99658
$17$	−0.724303	+	4.05899i	−0.175669	+	0.984449i
$17$	−0.724303	+	4.05899i	−0.175669	+	0.984449i
$18$	−16.1070			−3.79647
$19$	1.62346	+	1.62346i	0.372448	+	0.372448i	0.868368	−	0.495920i	$-0.165169\pi$
$19$	1.62346	+	1.62346i	0.372448	+	0.372448i	−0.495920	+	0.868368i	$0.665169\pi$
$20$	15.2987	−	6.33694i	3.42090	−	1.41698i
$21$			6.03664i			1.31730i
$22$	2.73853	+	6.61140i	0.583857	+	1.40956i
$23$	4.15195	+	1.71979i	0.865742	+	0.358602i	0.770950	−	0.636895i	$-0.219782\pi$
$23$	4.15195	+	1.71979i	0.865742	+	0.358602i	0.0947912	+	0.995497i	$0.469782\pi$
$24$	−7.79482	+	18.8184i	−1.59111	+	3.84128i
$25$	−5.61318	+	5.61318i	−1.12264	+	1.12264i
$26$	9.91372	−	9.91372i	1.94424	−	1.94424i
$27$	−3.80718	+	9.19134i	−0.732692	+	1.76887i
$28$	8.43377	+	3.49338i	1.59383	+	0.660187i
$29$	−0.682963	−	1.64882i	−0.126823	−	0.306178i	0.847696	−	0.530482i	$-0.177989\pi$
$29$	−0.682963	−	1.64882i	−0.126823	−	0.306178i	−0.974519	+	0.224304i	$0.927989\pi$
$30$		−	28.1398i		−	5.13760i
$31$	6.63701	−	2.74914i	1.19204	−	0.493760i	0.303622	−	0.952792i	$-0.401804\pi$
$31$	6.63701	−	2.74914i	1.19204	−	0.493760i	0.888419	+	0.459033i	$0.151804\pi$
$32$	5.04972	+	5.04972i	0.892673	+	0.892673i
$33$	8.47769			1.47578
$34$	8.69168	−	6.05943i	1.49061	−	1.03918i
$35$	−7.13249			−1.20561
$36$	20.4038	+	20.4038i	3.40064	+	3.40064i
$37$	−9.17450	+	3.80020i	−1.50828	+	0.624750i	−0.975202	−	0.221317i	$-0.928964\pi$
$37$	−9.17450	+	3.80020i	−1.50828	+	0.624750i	−0.533077	+	0.846067i	$0.678964\pi$
$38$		−	5.89997i		−	0.957102i
$39$	−6.35609	−	15.3450i	−1.01779	−	2.45716i
$40$	−22.2345	−	9.20985i	−3.51559	−	1.45620i
$41$	0.204615	−	0.493985i	0.0319555	−	0.0771475i	−0.907096	−	0.420923i	$-0.861706\pi$
$41$	0.204615	−	0.493985i	0.0319555	−	0.0771475i	0.939052	+	0.343776i	$0.111706\pi$
$42$	10.9691	−	10.9691i	1.69257	−	1.69257i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	4.90601	−	11.8442i	0.739609	−	1.78557i
$45$	−20.8294	−	8.62782i	−3.10506	−	1.28616i
$46$	−4.41945	−	10.6695i	−0.651613	−	1.57313i
$47$			0.510297i			0.0744344i	0.999307	+	0.0372172i	$0.0118493\pi$
$47$			0.510297i			0.0744344i	−0.999307	+	0.0372172i	$0.988151\pi$
$48$	22.4622	−	9.30417i	3.24215	−	1.34294i
$49$	2.16944	+	2.16944i	0.309920	+	0.309920i
$50$	20.3993			2.88490
$51$	−2.69161	−	12.2601i	−0.376900	−	1.71676i
$52$	−25.1167			−3.48305
$53$	3.09108	+	3.09108i	0.424593	+	0.424593i	0.886782	−	0.462189i	$-0.152936\pi$
$53$	3.09108	+	3.09108i	0.424593	+	0.424593i	−0.462189	+	0.886782i	$0.652936\pi$
$54$	23.6195	−	9.78352i	3.21421	−	1.33137i
$55$			10.0167i			1.35065i
$56$	−5.07714	−	12.2573i	−0.678461	−	1.63795i
$57$	−6.45750	−	2.67478i	−0.855317	−	0.354284i
$58$	−1.75505	+	4.23706i	−0.230449	+	0.556353i
$59$	5.23979	−	5.23979i	0.682162	−	0.682162i	−0.278325	−	0.960487i	$-0.589779\pi$
$59$	5.23979	−	5.23979i	0.682162	−	0.682162i	0.960487	+	0.278325i	$0.0897791\pi$
$60$	−35.6465	+	35.6465i	−4.60194	+	4.60194i
$61$	4.26296	−	10.2917i	0.545817	−	1.31772i	−0.374748	−	0.927127i	$-0.622271\pi$
$61$	4.26296	−	10.2917i	0.545817	−	1.31772i	0.920564	−	0.390591i	$-0.127729\pi$
$62$	−17.0555	−	7.06462i	−2.16605	−	0.897208i
$63$	−4.75628	−	11.4827i	−0.599235	−	1.44668i
$64$		−	2.37899i		−	0.297374i
$65$	18.1306	−	7.50994i	2.24882	−	0.931493i
$66$	−15.4047	−	15.4047i	−1.89619	−	1.89619i
$67$	6.43282			0.785894			0.392947	−	0.919561i	$-0.371456\pi$
$67$	6.43282			0.785894			0.392947	+	0.919561i	$0.371456\pi$
$68$	−18.6862	−	3.33444i	−2.26603	−	0.404360i
$69$	−13.6813			−1.64704
$70$	12.9604	+	12.9604i	1.54906	+	1.54906i
$71$	14.8600	−	6.15522i	1.76356	−	0.730490i	0.767576	−	0.640958i	$-0.221463\pi$
$71$	14.8600	−	6.15522i	1.76356	−	0.730490i	0.995984	−	0.0895323i	$-0.0285372\pi$
$72$		−	41.9372i		−	4.94234i
$73$	3.55175	+	8.57469i	0.415701	+	1.00359i	0.983579	+	0.180479i	$0.0577646\pi$
$73$	3.55175	+	8.57469i	0.415701	+	1.00359i	−0.567878	+	0.823113i	$0.692235\pi$
$74$	23.5762	+	9.76560i	2.74068	+	1.13523i
$75$	9.24815	−	22.3270i	1.06788	−	2.57810i
$76$	−7.47387	+	7.47387i	−0.857311	+	0.857311i
$77$	−3.90459	+	3.90459i	−0.444969	+	0.444969i
$78$	−16.3336	+	39.4328i	−1.84942	+	4.46489i
$79$	−9.94665	−	4.12004i	−1.11909	−	0.463541i	−0.255028	−	0.966934i	$-0.582085\pi$
$79$	−9.94665	−	4.12004i	−1.11909	−	0.463541i	−0.864058	+	0.503393i	$0.832085\pi$
$80$	10.9932	+	26.5399i	1.22908	+	2.96725i
$81$		−	11.4831i		−	1.27590i
$82$	−1.26942	+	0.525812i	−0.140184	+	0.0580662i
$83$	−10.8951	−	10.8951i	−1.19589	−	1.19589i	−0.975386	−	0.220506i	$-0.929229\pi$
$83$	−10.8951	−	10.8951i	−1.19589	−	1.19589i	−0.220506	−	0.975386i	$-0.570771\pi$
$84$	−27.7906			−3.03220
$85$	14.4857	−	3.18023i	1.57120	−	0.344944i
$86$	−2.56976			−0.277104
$87$	3.84179	+	3.84179i	0.411883	+	0.411883i
$88$	−17.2138	+	7.13019i	−1.83500	+	0.760081i
$89$			13.2051i			1.39973i	0.714273	+	0.699867i	$0.246758\pi$
$89$			13.2051i			1.39973i	−0.714273	+	0.699867i	$0.753242\pi$
$90$	22.1714	+	53.5265i	2.33707	+	5.64219i
$91$	9.99490	+	4.14002i	1.04775	+	0.433992i
$92$	−7.91734	+	19.1141i	−0.825439	+	1.99279i
$93$	−15.4644	+	15.4644i	−1.60358	+	1.60358i
$94$	0.927257	−	0.927257i	0.0956392	−	0.0956392i
$95$	3.16035	−	7.62975i	0.324245	−	0.782796i
$96$	−20.0858	−	8.31981i	−2.05000	−	0.849137i
$97$	−2.52472	−	6.09520i	−0.256346	−	0.618874i	0.742345	−	0.670018i	$-0.233713\pi$
$97$	−2.52472	−	6.09520i	−0.256346	−	0.618874i	−0.998691	+	0.0511433i	$0.983713\pi$
$98$		−	7.88415i		−	0.796420i
$99$	−16.1259	+	6.67959i	−1.62072	+	0.671324i
$100$	−25.8411	−	25.8411i	−2.58411	−	2.58411i
$101$	−7.78120			−0.774258			−0.387129	−	0.922026i	$-0.626533\pi$
$101$	−7.78120			−0.774258			−0.387129	+	0.922026i	$0.626533\pi$
$102$	−17.3868	+	27.1686i	−1.72155	+	2.69010i
$103$	7.16493			0.705982			0.352991	−	0.935627i	$-0.385165\pi$
$103$	7.16493			0.705982			0.352991	+	0.935627i	$0.385165\pi$
$104$	25.8119	+	25.8119i	2.53106	+	2.53106i
$105$	20.0608	−	8.30945i	1.95773	−	0.810919i
$106$		−	11.2336i		−	1.09110i
$107$	0.339303	+	0.819151i	0.0328017	+	0.0791903i	0.939432	−	0.342737i	$-0.111354\pi$
$107$	0.339303	+	0.819151i	0.0328017	+	0.0791903i	−0.906630	+	0.421927i	$0.861354\pi$
$108$	−42.3137	−	17.5269i	−4.07164	−	1.68653i
$109$	3.35210	−	8.09268i	0.321073	−	0.775138i	−0.678120	−	0.734952i	$-0.737205\pi$
$109$	3.35210	−	8.09268i	0.321073	−	0.775138i	0.999192	−	0.0401864i	$-0.0127952\pi$
$110$	18.2012	−	18.2012i	1.73542	−	1.73542i
$111$	21.3768	−	21.3768i	2.02900	−	2.02900i
$112$	−6.06024	+	14.6307i	−0.572639	+	1.38247i
$113$	−13.3317	−	5.52215i	−1.25414	−	0.519480i	−0.346032	−	0.938223i	$-0.612471\pi$
$113$	−13.3317	−	5.52215i	−1.25414	−	0.519480i	−0.908105	+	0.418742i	$0.862471\pi$
$114$	6.87354	+	16.5942i	0.643766	+	1.55419i
$115$		−	16.1649i		−	1.50739i
$116$	7.59058	−	3.14412i	0.704768	−	0.291925i
$117$	24.1807	+	24.1807i	2.23550	+	2.23550i
$118$	−19.0424			−1.75299
$119$	6.88634	+	4.40698i	0.631270	+	0.403987i
$120$	73.2663			6.68826
$121$	−2.29468	−	2.29468i	−0.208608	−	0.208608i
$122$	−26.4472	+	10.9548i	−2.39442	+	0.991799i
$123$			1.62776i			0.146770i
$124$	12.6561	+	30.5545i	1.13655	+	2.74387i
$125$	9.76425	+	4.04449i	0.873341	+	0.361750i
$126$	−12.2225	+	29.5077i	−1.08887	+	2.62875i
$127$	9.28481	−	9.28481i	0.823893	−	0.823893i	−0.162771	−	0.986664i	$-0.552043\pi$
$127$	9.28481	−	9.28481i	0.823893	−	0.823893i	0.986664	+	0.162771i	$0.0520430\pi$
$128$	5.77660	−	5.77660i	0.510584	−	0.510584i
$129$	−1.16501	+	2.81259i	−0.102574	+	0.247635i
$130$	−46.5912	−	19.2987i	−4.08632	−	1.69261i
$131$	3.89502	+	9.40340i	0.340309	+	0.821579i	0.997684	+	0.0680156i	$0.0216668\pi$
$131$	3.89502	+	9.40340i	0.340309	+	0.821579i	−0.657375	+	0.753564i	$0.728333\pi$
$132$			39.0283i			3.39698i
$133$	4.20607	−	1.74221i	0.364713	−	0.151069i
$134$	−11.6890	−	11.6890i	−1.00978	−	1.00978i
$135$	35.7850			3.07988
$136$	15.7767	+	22.6301i	1.35284	+	1.94052i
$137$	−4.94793			−0.422730			−0.211365	−	0.977407i	$-0.567791\pi$
$137$	−4.94793			−0.422730			−0.211365	+	0.977407i	$0.567791\pi$
$138$	24.8602	+	24.8602i	2.11624	+	2.11624i
$139$	−9.95594	+	4.12389i	−0.844452	+	0.349783i	−0.762607	−	0.646862i	$-0.776081\pi$
$139$	−9.95594	+	4.12389i	−0.844452	+	0.349783i	−0.0818445	+	0.996645i	$0.526081\pi$
$140$		−	32.8355i		−	2.77511i
$141$	−0.594503	−	1.43526i	−0.0500662	−	0.120870i
$142$	−38.1866	−	15.8174i	−3.20455	−	1.32737i
$143$	5.81413	−	14.0366i	0.486202	−	1.17380i
$144$	−35.3961	+	35.3961i	−2.94968	+	2.94968i
$145$	−4.53920	+	4.53920i	−0.376960	+	0.376960i
$146$	9.12714	−	22.0349i	0.755368	−	1.82362i
$147$	−8.62918	−	3.57432i	−0.711723	−	0.294805i
$148$	−17.4948	−	42.2362i	−1.43807	−	3.47180i
$149$			14.8380i			1.21557i	0.794100	+	0.607787i	$0.207943\pi$
$149$			14.8380i			1.21557i	−0.794100	+	0.607787i	$0.792057\pi$
$150$	−57.3750	+	23.7655i	−4.68465	+	1.94044i
$151$	−3.21516	−	3.21516i	−0.261646	−	0.261646i	0.564077	−	0.825722i	$-0.309232\pi$
$151$	−3.21516	−	3.21516i	−0.261646	−	0.261646i	−0.825722	+	0.564077i	$0.809232\pi$
$152$	15.3615			1.24598
$153$	14.7796	+	21.2000i	1.19486	+	1.71392i
$154$	14.1900			1.14346
$155$	−18.2717	−	18.2717i	−1.46762	−	1.46762i
$156$	70.6429	−	29.2612i	5.65596	−	2.34277i
$157$		−	11.8128i		−	0.942762i	−0.881930	−	0.471381i	$-0.843756\pi$
$157$		−	11.8128i		−	0.942762i	0.881930	−	0.471381i	$-0.156244\pi$
$158$	10.5875	+	25.5605i	0.842296	+	2.03348i
$159$	−12.2951	−	5.09280i	−0.975065	−	0.403885i
$160$	9.83014	−	23.7320i	0.777140	−	1.87618i
$161$	6.30124	−	6.30124i	0.496607	−	0.496607i
$162$	−20.8659	+	20.8659i	−1.63938	+	1.63938i
$163$	−0.724825	+	1.74988i	−0.0567727	+	0.137061i	−0.949721	−	0.313098i	$-0.898633\pi$
$163$	−0.724825	+	1.74988i	−0.0567727	+	0.137061i	0.892948	+	0.450160i	$0.148633\pi$
$164$	2.27414	+	0.941978i	0.177580	+	0.0735561i
$165$	−11.6696	−	28.1728i	−0.908474	−	2.19325i
$166$			39.5948i			3.07315i
$167$	12.6547	−	5.24176i	0.979252	−	0.405620i	0.165104	−	0.986276i	$-0.447204\pi$
$167$	12.6547	−	5.24176i	0.979252	−	0.405620i	0.814149	+	0.580657i	$0.197204\pi$
$168$	28.5598	+	28.5598i	2.20344	+	2.20344i
$169$	−16.7659			−1.28968
$170$	−32.1007	−	20.5431i	−2.46201	−	1.57559i
$171$	14.3907			1.10048
$172$	3.25527	+	3.25527i	0.248212	+	0.248212i
$173$	5.68420	−	2.35447i	0.432162	−	0.179007i	−0.155989	−	0.987759i	$-0.549856\pi$
$173$	5.68420	−	2.35447i	0.432162	−	0.179007i	0.588150	+	0.808752i	$0.299856\pi$
$174$		−	13.9618i		−	1.05844i
$175$	6.02376	+	14.5426i	0.455353	+	1.09932i
$176$	20.5470	+	8.51084i	1.54879	+	0.641529i
$177$	−8.63296	+	20.8418i	−0.648893	+	1.56657i
$178$	23.9948	−	23.9948i	1.79849	−	1.79849i
$179$	7.02629	−	7.02629i	0.525170	−	0.525170i	−0.393958	−	0.919128i	$-0.628895\pi$
$179$	7.02629	−	7.02629i	0.525170	−	0.525170i	0.919128	+	0.393958i	$0.128895\pi$
$180$	39.7195	−	95.8913i	2.96052	−	7.14732i
$181$	16.5187	+	6.84229i	1.22783	+	0.508583i	0.899891	−	0.436116i	$-0.143646\pi$
$181$	16.5187	+	6.84229i	1.22783	+	0.508583i	0.327938	+	0.944699i	$0.393646\pi$
$182$	−10.6389	−	25.6845i	−0.788604	−	1.90386i
$183$			33.9128i			2.50690i
$184$	27.7797	−	11.5067i	2.04795	−	0.848287i
$185$	25.2575	+	25.2575i	1.85697	+	1.85697i
$186$	56.2005			4.12082
$187$	6.18904	−	9.67098i	0.452587	−	0.707212i
$188$	−2.34923			−0.171335
$189$	13.9493	+	13.9493i	1.01466	+	1.01466i
$190$	−19.6066	+	8.12133i	−1.42241	+	0.589183i
$191$		−	20.9598i		−	1.51660i	−0.651908	−	0.758298i	$-0.726031\pi$
$191$		−	20.9598i		−	1.51660i	0.651908	−	0.758298i	$-0.273969\pi$
$192$	2.77155	+	6.69112i	0.200020	+	0.482890i
$193$	5.96101	+	2.46913i	0.429083	+	0.177732i	0.586764	−	0.809758i	$-0.300402\pi$
$193$	5.96101	+	2.46913i	0.429083	+	0.177732i	−0.157681	+	0.987490i	$0.550402\pi$
$194$	−6.48791	+	15.6632i	−0.465805	+	1.12455i
$195$	−42.2448	+	42.2448i	−3.02521	+	3.02521i
$196$	−9.98735	+	9.98735i	−0.713382	+	0.713382i
$197$	−2.80706	+	6.77684i	−0.199995	+	0.482830i	−0.991778	−	0.127973i	$-0.959153\pi$
$197$	−2.80706	+	6.77684i	−0.199995	+	0.482830i	0.791783	+	0.610802i	$0.209153\pi$
$198$	41.4398	+	17.1649i	2.94500	+	1.21986i
$199$	5.64679	+	13.6325i	0.400290	+	0.966386i	0.987595	+	0.157020i	$0.0501888\pi$
$199$	5.64679	+	13.6325i	0.400290	+	0.966386i	−0.587305	+	0.809365i	$0.699811\pi$
$200$			53.1128i			3.75564i
$201$	−18.0929	+	7.49433i	−1.27617	+	0.528609i
$202$	14.1392	+	14.1392i	0.994828	+	0.994828i
$203$	−3.53884			−0.248378
$204$	56.4412	−	12.3912i	3.95168	−	0.867559i
$205$	−1.92325			−0.134326
$206$	−13.0193	−	13.0193i	−0.907101	−	0.907101i
$207$	26.0241	−	10.7795i	1.80880	−	0.749230i
$208$		−	43.5718i		−	3.02116i
$209$	−2.44672	−	5.90689i	−0.169243	−	0.408588i
$210$	−51.5514	−	21.3533i	−3.55738	−	1.47352i
$211$	3.42595	−	8.27097i	0.235852	−	0.569397i	−0.760994	−	0.648759i	$-0.775288\pi$
$211$	3.42595	−	8.27097i	0.235852	−	0.569397i	0.996846	+	0.0793621i	$0.0252883\pi$
$212$	−14.2303	+	14.2303i	−0.977339	+	0.977339i
$213$	−34.6242	+	34.6242i	−2.37241	+	2.37241i
$214$	0.871927	−	2.10502i	0.0596037	−	0.143896i
$215$	−3.32317	−	1.37650i	−0.226638	−	0.0938767i
$216$	25.4729	+	61.4970i	1.73321	+	4.18434i
$217$		−	14.2449i		−	0.967010i
$218$	−20.7962	+	8.61408i	−1.40850	+	0.583419i
$219$	−19.9793	−	19.9793i	−1.35007	−	1.35007i
$220$	−46.1133			−3.10896
$221$	−22.1451	−	3.95166i	−1.48964	−	0.265817i
$222$	−77.6874			−5.21404
$223$	14.2247	+	14.2247i	0.952554	+	0.952554i	0.998924	−	0.0463706i	$-0.0147655\pi$
$223$	14.2247	+	14.2247i	0.952554	+	0.952554i	−0.0463706	+	0.998924i	$0.514765\pi$
$224$	13.0828	−	5.41908i	0.874133	−	0.362078i
$225$			49.7563i			3.31708i
$226$	14.1906	+	34.2591i	0.943944	+	2.27888i
$227$	11.3030	+	4.68187i	0.750208	+	0.310746i	0.724827	−	0.688931i	$-0.241920\pi$
$227$	11.3030	+	4.68187i	0.750208	+	0.310746i	0.0253818	+	0.999678i	$0.491920\pi$
$228$	12.3138	−	29.7281i	0.815500	−	1.96879i
$229$	19.1379	−	19.1379i	1.26467	−	1.26467i	0.315861	−	0.948806i	$-0.397707\pi$
$229$	19.1379	−	19.1379i	1.26467	−	1.26467i	0.948806	−	0.315861i	$-0.102293\pi$
$230$	−29.3732	+	29.3732i	−1.93681	+	1.93681i
$231$	6.43311	−	15.5309i	0.423267	−	1.02186i
$232$	−11.0318	−	4.56954i	−0.724276	−	0.300005i
$233$	6.13202	+	14.8040i	0.401722	+	0.969842i	0.987248	+	0.159189i	$0.0508878\pi$
$233$	6.13202	+	14.8040i	0.401722	+	0.969842i	−0.585526	+	0.810653i	$0.699112\pi$
$234$		−	87.8770i		−	5.74470i
$235$	1.69580	−	0.702425i	0.110622	−	0.0458212i
$236$	24.1222	+	24.1222i	1.57022	+	1.57022i
$237$	32.7758			2.12902
$238$	−4.50522	−	20.5210i	−0.292030	−	1.33018i
$239$	−1.98675			−0.128512			−0.0642560	−	0.997933i	$-0.520467\pi$
$239$	−1.98675			−0.128512			−0.0642560	+	0.997933i	$0.520467\pi$
$240$	−61.8387	−	61.8387i	−3.99167	−	3.99167i
$241$	−5.09048	+	2.10855i	−0.327907	+	0.135823i	−0.540563	−	0.841304i	$-0.681789\pi$
$241$	−5.09048	+	2.10855i	−0.327907	+	0.135823i	0.212656	+	0.977127i	$0.431789\pi$
$242$			8.33931i			0.536071i
$243$	1.95645	+	4.72329i	0.125506	+	0.302999i
$244$	47.3794	+	19.6252i	3.03316	+	1.25638i
$245$	4.22318	−	10.1957i	0.269809	−	0.651377i
$246$	2.95779	−	2.95779i	0.188582	−	0.188582i
$247$	−8.85731	+	8.85731i	−0.563577	+	0.563577i
$248$	18.3938	−	44.4066i	1.16801	−	2.81982i
$249$	43.3364	+	17.9505i	2.74633	+	1.13757i
$250$	−10.3933	−	25.0918i	−0.657333	−	1.58694i
$251$			20.5472i			1.29693i	0.761246	+	0.648463i	$0.224588\pi$
$251$			20.5472i			1.29693i	−0.761246	+	0.648463i	$0.775412\pi$
$252$	52.8623	−	21.8963i	3.33001	−	1.37933i
$253$	−8.84928	−	8.84928i	−0.556349	−	0.556349i
$254$	−33.7427			−2.11721
$255$	−37.0374	+	25.8207i	−2.31937	+	1.61696i
$256$	−25.7512			−1.60945
$257$	−9.16672	−	9.16672i	−0.571805	−	0.571805i	0.360828	−	0.932632i	$-0.382494\pi$
$257$	−9.16672	−	9.16672i	−0.571805	−	0.571805i	−0.932632	+	0.360828i	$0.882494\pi$
$258$	7.22768	−	2.99380i	0.449976	−	0.186386i
$259$			19.6911i			1.22355i
$260$	34.5732	+	83.4670i	2.14414	+	5.17640i
$261$	−10.3347	−	4.28076i	−0.639700	−	0.264972i
$262$	10.0093	−	24.1645i	0.618374	−	1.49289i
$263$	−4.77664	+	4.77664i	−0.294540	+	0.294540i	−0.838871	−	0.544331i	$-0.816784\pi$
$263$	−4.77664	+	4.77664i	−0.294540	+	0.294540i	0.544331	+	0.838871i	$0.316784\pi$
$264$	40.1086	−	40.1086i	2.46851	−	2.46851i
$265$	6.01732	−	14.5271i	0.369641	−	0.892392i
$266$	−10.8086	−	4.47706i	−0.662717	−	0.274506i
$267$	−15.3841	−	37.1405i	−0.941491	−	2.27296i
$268$			29.6145i			1.80899i
$269$	1.92844	−	0.798788i	0.117579	−	0.0487029i	−0.323118	−	0.946359i	$-0.604731\pi$
$269$	1.92844	−	0.798788i	0.117579	−	0.0487029i	0.440698	+	0.897656i	$0.354731\pi$
$270$	−65.0247	−	65.0247i	−3.95727	−	3.95727i
$271$	13.1030			0.795949			0.397975	−	0.917396i	$-0.369713\pi$
$271$	13.1030			0.795949			0.397975	+	0.917396i	$0.369713\pi$
$272$	5.78451	−	32.4164i	0.350738	−	1.96553i
$273$	−32.9348			−1.99330
$274$	8.99084	+	8.99084i	0.543157	+	0.543157i
$275$	20.4233	−	8.45959i	1.23157	−	0.510133i
$276$		−	62.9841i		−	3.79120i
$277$	−9.34206	−	22.5537i	−0.561310	−	1.35512i	−0.908719	−	0.417409i	$-0.862938\pi$
$277$	−9.34206	−	22.5537i	−0.561310	−	1.35512i	0.347409	−	0.937714i	$-0.387062\pi$
$278$	25.5844	+	10.5974i	1.53445	+	0.635589i
$279$	17.2314	−	41.6003i	1.03162	−	2.49054i
$280$	−33.7444	+	33.7444i	−2.01661	+	2.01661i
$281$	16.3322	−	16.3322i	0.974300	−	0.974300i	−0.0253778	−	0.999678i	$-0.508079\pi$
$281$	16.3322	−	16.3322i	0.974300	−	0.974300i	0.999678	+	0.0253778i	$0.00807889\pi$
$282$	−1.52773	+	3.68826i	−0.0909749	+	0.219633i
$283$	−14.7319	−	6.10214i	−0.875718	−	0.362734i	−0.100884	−	0.994898i	$-0.532167\pi$
$283$	−14.7319	−	6.10214i	−0.875718	−	0.362734i	−0.774835	+	0.632164i	$0.782167\pi$
$284$	28.3365	+	68.4104i	1.68146	+	4.05941i
$285$			25.1412i			1.48924i
$286$	−36.0706	+	14.9409i	−2.13290	+	0.883475i
$287$	−0.749700	−	0.749700i	−0.0442534	−	0.0442534i
$288$	44.7617			2.63761
$289$	−15.9508	−	5.87987i	−0.938281	−	0.345875i
$290$	16.4963			0.968697
$291$	14.2020	+	14.2020i	0.832535	+	0.832535i
$292$	−39.4749	+	16.3510i	−2.31009	+	0.956872i
$293$		−	2.58806i		−	0.151196i	−0.997138	−	0.0755981i	$-0.975913\pi$
$293$		−	2.58806i		−	0.151196i	0.997138	−	0.0755981i	$-0.0240866\pi$
$294$	9.18514	+	22.1749i	0.535688	+	1.29327i
$295$	−24.6253	−	10.2001i	−1.43374	−	0.593875i
$296$	−25.4262	+	61.3844i	−1.47787	+	3.56789i
$297$	19.5900	−	19.5900i	1.13673	−	1.13673i
$298$	26.9620	−	26.9620i	1.56187	−	1.56187i
$299$	−9.38287	+	22.6523i	−0.542626	+	1.31001i
$300$	102.786	+	42.5753i	5.93434	+	2.45808i
$301$	−0.758828	−	1.83197i	−0.0437381	−	0.105593i
$302$			11.6845i			0.672366i
$303$	21.8853	−	9.06520i	1.25728	−	0.520782i
$304$	−12.9655	−	12.9655i	−0.743622	−	0.743622i
$305$	−40.0691			−2.29435
$306$	11.6664	−	65.3783i	0.666923	−	3.73743i
$307$	12.7556			0.728001			0.364000	−	0.931399i	$-0.381411\pi$
$307$	12.7556			0.728001			0.364000	+	0.931399i	$0.381411\pi$
$308$	−17.9754	−	17.9754i	−1.02424	−	1.02424i
$309$	−20.1520	+	8.34724i	−1.14641	+	0.474858i
$310$			66.4028i			3.77143i
$311$	−4.95968	−	11.9737i	−0.281238	−	0.678968i	0.718627	−	0.695395i	$-0.244771\pi$
$311$	−4.95968	−	11.9737i	−0.281238	−	0.678968i	−0.999865	+	0.0164277i	$0.994771\pi$
$312$	−102.669	−	42.5271i	−5.81251	−	2.40762i
$313$	2.60268	−	6.28343i	0.147112	−	0.355161i	−0.833096	−	0.553128i	$-0.813434\pi$
$313$	2.60268	−	6.28343i	0.147112	−	0.355161i	0.980209	+	0.197967i	$0.0634340\pi$
$314$	−21.4649	+	21.4649i	−1.21133	+	1.21133i
$315$	−31.6119	+	31.6119i	−1.78113	+	1.78113i
$316$	18.9672	−	45.7910i	1.06699	−	2.57594i
$317$	7.04074	+	2.91637i	0.395448	+	0.163800i	0.571541	−	0.820574i	$-0.306346\pi$
$317$	7.04074	+	2.91637i	0.395448	+	0.163800i	−0.176093	+	0.984374i	$0.556346\pi$
$318$	13.0873	+	31.5954i	0.733897	+	1.77178i
$319$			4.96985i			0.278258i
$320$	−7.90579	+	3.27468i	−0.441947	+	0.183060i
$321$	−1.90864	−	1.90864i	−0.106530	−	0.106530i
$322$	−22.8999			−1.27616
$323$	−7.76550	+	5.41374i	−0.432084	+	0.301229i
$324$	52.8643			2.93690
$325$	−30.6244	−	30.6244i	−1.69874	−	1.69874i
$326$	4.49677	−	1.86263i	0.249053	−	0.103161i
$327$			26.6666i			1.47467i
$328$	−1.36903	−	3.30513i	−0.0755921	−	0.182495i
$329$	0.934850	+	0.387228i	0.0515400	+	0.0213486i
$330$	−29.9879	+	72.3973i	−1.65078	+	3.98534i
$331$	1.46018	−	1.46018i	0.0802589	−	0.0802589i	−0.665838	−	0.746097i	$-0.731926\pi$
$331$	1.46018	−	1.46018i	0.0802589	−	0.0802589i	0.746097	+	0.665838i	$0.231926\pi$
$332$	50.1572	−	50.1572i	2.75274	−	2.75274i
$333$	−23.8194	+	57.5051i	−1.30529	+	3.15126i
$334$	−32.5196	−	13.4701i	−1.77939	−	0.737048i
$335$	−8.85480	−	21.3774i	−0.483789	−	1.16797i
$336$		−	48.2105i		−	2.63010i
$337$	20.2507	−	8.38811i	1.10313	−	0.456930i	0.244560	−	0.969634i	$-0.421356\pi$
$337$	20.2507	−	8.38811i	1.10313	−	0.456930i	0.858565	+	0.512705i	$0.171356\pi$
$338$	30.4651	+	30.4651i	1.65709	+	1.65709i
$339$	43.9299			2.38594
$340$	14.6407	+	66.6872i	0.794001	+	3.61662i
$341$	−20.0052			−1.08334
$342$	−26.1492	−	26.1492i	−1.41399	−	1.41399i
$343$	18.4444	−	7.63992i	0.995904	−	0.412517i
$344$		−	6.69076i		−	0.360741i
$345$	18.8324	+	45.4654i	1.01390	+	2.44777i
$346$	−14.6070	−	6.05042i	−0.785278	−	0.325273i
$347$	−5.21335	+	12.5861i	−0.279867	+	0.675659i	−0.999832	−	0.0183519i	$-0.994158\pi$
$347$	−5.21335	+	12.5861i	−0.279867	+	0.675659i	0.719964	+	0.694011i	$0.244158\pi$
$348$	−17.6863	+	17.6863i	−0.948083	+	0.948083i
$349$	−6.59366	+	6.59366i	−0.352950	+	0.352950i	−0.861206	−	0.508256i	$-0.830290\pi$
$349$	−6.59366	+	6.59366i	−0.352950	+	0.352950i	0.508256	+	0.861206i	$0.330290\pi$
$350$	15.4796	−	37.3710i	0.827419	−	1.99757i
$351$	−50.1462	−	20.7712i	−2.67661	−	1.10869i
$352$	−7.61041	−	18.3732i	−0.405636	−	0.979293i
$353$			8.69853i			0.462976i	0.972838	+	0.231488i	$0.0743594\pi$
$353$			8.69853i			0.462976i	−0.972838	+	0.231488i	$0.925641\pi$
$354$	53.5584	−	22.1846i	2.84660	−	1.17910i
$355$	−40.9097	−	40.9097i	−2.17126	−	2.17126i
$356$	−60.7916			−3.22195
$357$	−24.5026	−	4.37236i	−1.29682	−	0.231410i
$358$	−25.5349			−1.34956
$359$	−16.2889	−	16.2889i	−0.859695	−	0.859695i	0.131607	−	0.991302i	$-0.457986\pi$
$359$	−16.2889	−	16.2889i	−0.859695	−	0.859695i	−0.991302	+	0.131607i	$0.957986\pi$
$360$	−139.364	+	57.7266i	−7.34515	+	3.04246i
$361$		−	13.7287i		−	0.722565i
$362$	−17.5830	−	42.4492i	−0.924143	−	2.23108i
$363$	9.12734	+	3.78067i	0.479061	+	0.198434i
$364$	−19.0592	+	46.0131i	−0.998975	+	2.41174i
$365$	23.6062	−	23.6062i	1.23560	−	1.23560i
$366$	61.6226	−	61.6226i	3.22107	−	3.22107i
$367$	−5.40253	+	13.0429i	−0.282010	+	0.680831i	−0.999882	−	0.0153430i	$-0.995116\pi$
$367$	−5.40253	+	13.0429i	−0.282010	+	0.680831i	0.717873	+	0.696174i	$0.245116\pi$
$368$	−33.1588	−	13.7348i	−1.72852	−	0.715977i
$369$	−1.28251	−	3.09626i	−0.0667650	−	0.161185i
$370$		−	91.7903i		−	4.77195i
$371$	8.00838	−	3.31718i	0.415775	−	0.172219i
$372$	−71.1928	−	71.1928i	−3.69117	−	3.69117i
$373$	13.0913			0.677842			0.338921	−	0.940815i	$-0.389938\pi$
$373$	13.0913			0.677842			0.338921	+	0.940815i	$0.389938\pi$
$374$	−28.8191	+	6.32701i	−1.49020	+	0.327162i
$375$	−32.1747			−1.66150
$376$	2.41426	+	2.41426i	0.124506	+	0.124506i
$377$	8.99564	−	3.72611i	0.463299	−	0.191905i
$378$		−	50.6943i		−	2.60744i
$379$	3.76616	+	9.09231i	0.193455	+	0.467041i	0.990607	−	0.136737i	$-0.0436615\pi$
$379$	3.76616	+	9.09231i	0.193455	+	0.467041i	−0.797153	+	0.603778i	$0.793662\pi$
$380$	35.1247	+	14.5491i	1.80186	+	0.746355i
$381$	−15.2974	+	36.9313i	−0.783712	+	1.89205i
$382$	−38.0858	+	38.0858i	−1.94864	+	1.94864i
$383$	−16.9801	+	16.9801i	−0.867641	+	0.867641i	−0.992211	−	0.124569i	$-0.960245\pi$
$383$	−16.9801	+	16.9801i	−0.867641	+	0.867641i	0.124569	+	0.992211i	$0.460245\pi$
$384$	−9.51739	+	22.9770i	−0.485683	+	1.17254i
$385$	18.3503	+	7.60094i	0.935217	+	0.387380i
$386$	−6.34507	−	15.3184i	−0.322956	−	0.779684i
$387$		−	6.26793i		−	0.318617i
$388$	28.0602	−	11.6229i	1.42454	−	0.590064i
$389$	−1.44045	−	1.44045i	−0.0730335	−	0.0730335i	0.669646	−	0.742680i	$-0.266446\pi$
$389$	−1.44045	−	1.44045i	−0.0730335	−	0.0730335i	−0.742680	+	0.669646i	$0.766446\pi$
$390$	153.525			7.77406
$391$	−9.98790	+	15.6071i	−0.505110	+	0.789283i
$392$	20.5276			1.03680
$393$	−21.9102	−	21.9102i	−1.10522	−	1.10522i
$394$	17.4148	−	7.21346i	0.877347	−	0.363409i
$395$			38.7257i			1.94850i
$396$	−30.7505	−	74.2383i	−1.54527	−	3.73061i
$397$	18.7237	+	7.75561i	0.939716	+	0.389243i	0.799356	−	0.600858i	$-0.205174\pi$
$397$	18.7237	+	7.75561i	0.939716	+	0.389243i	0.140360	+	0.990101i	$0.455174\pi$
$398$	14.5109	−	35.0323i	0.727364	−	1.75601i
$399$	−9.80027	+	9.80027i	−0.490627	+	0.490627i
$400$	44.8286	−	44.8286i	2.24143	−	2.24143i
$401$	3.25908	−	7.86811i	0.162751	−	0.392915i	−0.821375	−	0.570389i	$-0.806793\pi$
$401$	3.25908	−	7.86811i	0.162751	−	0.392915i	0.984125	+	0.177474i	$0.0567926\pi$
$402$	46.4944	+	19.2586i	2.31893	+	0.960532i
$403$	14.9988	+	36.2103i	0.747142	+	1.80376i
$404$		−	35.8219i		−	1.78221i
$405$	−38.1604	+	15.8065i	−1.89620	+	0.785433i
$406$	6.43040	+	6.43040i	0.319136	+	0.319136i
$407$	27.6537			1.37074
$408$	−70.7377	−	45.2693i	−3.50204	−	2.24116i
$409$	16.6052			0.821075			0.410537	−	0.911844i	$-0.365341\pi$
$409$	16.6052			0.821075			0.410537	+	0.911844i	$0.365341\pi$
$410$	3.49473	+	3.49473i	0.172592	+	0.172592i
$411$	13.9165	−	5.76440i	0.686450	−	0.284337i
$412$			32.9849i			1.62505i
$413$	−5.62305	−	13.5753i	−0.276692	−	0.667995i
$414$	−66.8757	−	27.7008i	−3.28676	−	1.36142i
$415$	−21.2091	+	51.2034i	−1.04112	+	2.51348i
$416$	−27.5503	+	27.5503i	−1.35077	+	1.35077i
$417$	23.1976	−	23.1976i	1.13599	−	1.13599i
$418$	−6.28746	+	15.1793i	−0.307530	+	0.742443i
$419$	8.07625	+	3.34529i	0.394550	+	0.163428i	0.571133	−	0.820858i	$-0.306504\pi$
$419$	8.07625	+	3.34529i	0.394550	+	0.163428i	−0.176582	+	0.984286i	$0.556504\pi$
$420$	38.2538	+	92.3529i	1.86660	+	4.50636i
$421$			18.8599i			0.919176i	0.888132	+	0.459588i	$0.152003\pi$
$421$			18.8599i			0.919176i	−0.888132	+	0.459588i	$0.847997\pi$
$422$	−21.2544	+	8.80385i	−1.03465	+	0.428565i
$423$	2.26168	+	2.26168i	0.109967	+	0.109967i
$424$	29.2483			1.42042
$425$	−18.7182	−	26.8495i	−0.907965	−	1.30239i
$426$	125.831			6.09653
$427$	−15.6193	−	15.6193i	−0.755870	−	0.755870i
$428$	−3.77109	+	1.56203i	−0.182282	+	0.0755038i
$429$			46.2527i			2.23310i
$430$	3.53728	+	8.53975i	0.170583	+	0.411823i
$431$	−6.30965	−	2.61354i	−0.303925	−	0.125890i	0.225509	−	0.974241i	$-0.427596\pi$
$431$	−6.30965	−	2.61354i	−0.303925	−	0.125890i	−0.529434	+	0.848351i	$0.677596\pi$
$432$	30.4053	−	73.4050i	1.46288	−	3.53170i
$433$	16.9323	−	16.9323i	0.813715	−	0.813715i	−0.171474	−	0.985189i	$-0.554853\pi$
$433$	16.9323	−	16.9323i	0.813715	−	0.813715i	0.985189	+	0.171474i	$0.0548530\pi$
$434$	−25.8844	+	25.8844i	−1.24249	+	1.24249i
$435$	7.47869	−	18.0552i	0.358576	−	0.865679i
$436$	37.2559	+	15.4319i	1.78423	+	0.739054i
$437$	3.94852	+	9.53257i	0.188883	+	0.456005i
$438$			72.6083i			3.46936i
$439$	23.3684	−	9.67953i	1.11532	−	0.461979i	0.252550	−	0.967584i	$-0.418731\pi$
$439$	23.3684	−	9.67953i	1.11532	−	0.461979i	0.862765	+	0.505605i	$0.168731\pi$
$440$	47.3897	+	47.3897i	2.25921	+	2.25921i
$441$	19.2303			0.915730
$442$	33.0591	+	47.4202i	1.57246	+	2.25555i
$443$	−22.7883			−1.08270			−0.541352	−	0.840796i	$-0.682088\pi$
$443$	−22.7883			−1.08270			−0.541352	+	0.840796i	$0.682088\pi$
$444$	98.4115	+	98.4115i	4.67041	+	4.67041i
$445$	43.8827	−	18.1768i	2.08024	−	0.861664i
$446$		−	51.6951i		−	2.44783i
$447$	−17.2864	−	41.7332i	−0.817621	−	1.97391i
$448$	−4.35824	−	1.80524i	−0.205908	−	0.0852898i
$449$	−0.980330	+	2.36672i	−0.0462646	+	0.111693i	−0.945322	−	0.326137i	$-0.894253\pi$
$449$	−0.980330	+	2.36672i	−0.0462646	+	0.111693i	0.899058	+	0.437830i	$0.144253\pi$
$450$	90.4117	−	90.4117i	4.26205	−	4.26205i
$451$	−1.05286	+	1.05286i	−0.0495771	+	0.0495771i
$452$	25.4221	−	61.3743i	1.19575	−	2.88681i
$453$	12.7886	+	5.29722i	0.600862	+	0.248885i
$454$	−12.0313	−	29.0460i	−0.564655	−	1.36320i
$455$		−	38.9135i		−	1.82429i
$456$	−43.2056	+	17.8963i	−2.02329	+	0.838072i
$457$	26.6188	+	26.6188i	1.24517	+	1.24517i	0.957826	+	0.287349i	$0.0927739\pi$
$457$	26.6188	+	26.6188i	1.24517	+	1.24517i	0.287349	+	0.957826i	$0.407226\pi$
$458$	−69.5506			−3.24989
$459$	−34.5500	−	22.1106i	−1.61266	−	1.03203i
$460$	74.4178			3.46975
$461$	17.9651	+	17.9651i	0.836719	+	0.836719i	0.988426	−	0.151706i	$-0.0484768\pi$
$461$	17.9651	+	17.9651i	0.836719	+	0.836719i	−0.151706	+	0.988426i	$0.548477\pi$
$462$	−39.9106	+	16.5315i	−1.85681	+	0.769116i
$463$			0.220808i			0.0102618i	0.999987	+	0.00513091i	$0.00163323\pi$
$463$			0.220808i			0.0102618i	−0.999987	+	0.00513091i	$0.998367\pi$
$464$	5.45436	+	13.1680i	0.253212	+	0.611308i
$465$	72.6777	+	30.1041i	3.37035	+	1.39604i
$466$	15.7578	−	38.0427i	0.729966	−	1.76229i
$467$	23.9748	−	23.9748i	1.10942	−	1.10942i	0.116193	−	0.993227i	$-0.462931\pi$
$467$	23.9748	−	23.9748i	1.10942	−	1.10942i	0.993227	−	0.116193i	$-0.0370692\pi$
$468$	−111.319	+	111.319i	−5.14574	+	5.14574i
$469$	4.88141	−	11.7848i	0.225402	−	0.544170i
$470$	−4.35781	−	1.80506i	−0.201011	−	0.0832613i
$471$	13.7620	+	33.2245i	0.634121	+	1.53090i
$472$		−	49.5797i		−	2.28209i
$473$	−2.57277	+	1.06568i	−0.118296	+	0.0489999i
$474$	−59.5566	−	59.5566i	−2.73553	−	2.73553i
$475$	−18.2256			−0.836247
$476$	−20.2882	+	31.7023i	−0.929908	+	1.45307i
$477$	27.3999			1.25456
$478$	3.61010	+	3.61010i	0.165122	+	0.165122i
$479$	36.8042	−	15.2448i	1.68163	−	0.696553i	0.682226	−	0.731142i	$-0.261012\pi$
$479$	36.8042	−	15.2448i	1.68163	−	0.696553i	0.999402	+	0.0345888i	$0.0110122\pi$
$480$			78.2008i			3.56936i
$481$	−20.7332	−	50.0543i	−0.945352	−	2.28228i
$482$	13.0813	+	5.41845i	0.595837	+	0.246804i
$483$	−10.3818	+	25.0638i	−0.472387	+	1.14044i
$484$	10.5639	−	10.5639i	0.480179	−	0.480179i
$485$	−16.7801	+	16.7801i	−0.761947	+	0.761947i
$486$	5.02761	−	12.1377i	0.228057	−	0.550578i
$487$	−32.3696	−	13.4079i	−1.46681	−	0.607572i	−0.500680	−	0.865633i	$-0.666917\pi$
$487$	−32.3696	−	13.4079i	−1.46681	−	0.607572i	−0.966129	+	0.258061i	$0.916917\pi$
$488$	−28.5225	−	68.8593i	−1.29115	−	3.11711i
$489$		−	5.76614i		−	0.260754i
$490$	−26.2004	+	10.8526i	−1.18361	+	0.490269i
$491$	−10.7164	−	10.7164i	−0.483623	−	0.483623i	0.422664	−	0.906287i	$-0.361095\pi$
$491$	−10.7164	−	10.7164i	−0.483623	−	0.483623i	−0.906287	+	0.422664i	$0.861095\pi$
$492$	−7.49363			−0.337839
$493$	7.18720	−	1.57789i	0.323695	−	0.0710648i
$494$	32.1891			1.44826
$495$	44.3948	+	44.3948i	1.99540	+	1.99540i
$496$	−53.0052	+	21.9555i	−2.38001	+	0.985831i
$497$		−	31.8939i		−	1.43064i
$498$	−46.1285	−	111.364i	−2.06707	−	4.99034i
$499$	5.28346	+	2.18848i	0.236520	+	0.0979699i	0.497796	−	0.867294i	$-0.334143\pi$
$499$	5.28346	+	2.18848i	0.236520	+	0.0979699i	−0.261275	+	0.965264i	$0.584143\pi$
$500$	−18.6194	+	44.9512i	−0.832685	+	2.01028i
$501$	−29.4859	+	29.4859i	−1.31733	+	1.31733i
$502$	37.3361	−	37.3361i	1.66639	−	1.66639i
$503$	14.5466	−	35.1185i	0.648600	−	1.56586i	−0.166185	−	0.986095i	$-0.553145\pi$
$503$	14.5466	−	35.1185i	0.648600	−	1.56586i	0.814785	−	0.579764i	$-0.196855\pi$
$504$	−76.8278	−	31.8231i	−3.42218	−	1.41751i
$505$	10.7108	+	25.8583i	0.476626	+	1.15068i
$506$			32.1599i			1.42968i
$507$	47.1555	−	19.5325i	2.09425	−	0.867467i
$508$	42.7440	+	42.7440i	1.89646	+	1.89646i
$509$	18.5981			0.824347			0.412173	−	0.911105i	$-0.364770\pi$
$509$	18.5981			0.824347			0.412173	+	0.911105i	$0.364770\pi$
$510$	114.219	+	20.3817i	5.05771	+	0.902518i
$511$	18.4038			0.814135
$512$	35.2391	+	35.2391i	1.55736	+	1.55736i
$513$	−21.1026	+	8.74099i	−0.931704	+	0.385924i
$514$			33.3136i			1.46940i
$515$	−9.86255	−	23.8103i	−0.434596	−	1.04921i
$516$	−12.9482	−	5.36332i	−0.570013	−	0.236107i
$517$	0.543812	−	1.31288i	0.0239168	−	0.0577403i
$518$	35.7806	−	35.7806i	1.57211	−	1.57211i
$519$	−13.2443	+	13.2443i	−0.581362	+	0.581362i
$520$	50.2472	−	121.307i	2.20348	−	5.31968i
$521$	17.8820	+	7.40699i	0.783427	+	0.324506i	0.738297	−	0.674475i	$-0.235630\pi$
$521$	17.8820	+	7.40699i	0.783427	+	0.324506i	0.0451291	+	0.998981i	$0.485630\pi$
$522$	11.0005	+	26.5576i	0.481479	+	1.16239i
$523$		−	8.01370i		−	0.350415i	−0.984532	−	0.175207i	$-0.943940\pi$
$523$		−	8.01370i		−	0.350415i	0.984532	−	0.175207i	$-0.0560596\pi$
$524$	−43.2900	+	17.9313i	−1.89113	+	0.783333i
$525$	−33.8847	−	33.8847i	−1.47885	−	1.47885i
$526$	17.3592			0.756897
$527$	6.35152	+	28.9307i	0.276676	+	1.26024i
$528$	−67.7055			−2.94650
$529$	−1.98245	−	1.98245i	−0.0861936	−	0.0861936i
$530$	−37.3311	+	15.4630i	−1.62156	+	0.671672i
$531$		−	46.4465i		−	2.01560i
$532$	8.02054	+	19.3633i	0.347735	+	0.839506i
$533$	2.69509	+	1.11634i	0.116737	+	0.0483542i
$534$	−39.5334	+	95.4420i	−1.71078	+	4.13018i
$535$	2.25513	−	2.25513i	0.0974976	−	0.0974976i
$536$	30.4342	−	30.4342i	1.31456	−	1.31456i
$537$	−11.5764	+	27.9478i	−0.499557	+	1.20604i
$538$	−4.95563	−	2.05269i	−0.213653	−	0.0884978i
$539$	−3.26955	−	7.89340i	−0.140830	−	0.339993i
$540$			164.742i			7.08935i
$541$	−8.71939	+	3.61169i	−0.374876	+	0.155279i	−0.562163	−	0.827027i	$-0.690031\pi$
$541$	−8.71939	+	3.61169i	−0.374876	+	0.155279i	0.187287	+	0.982305i	$0.440031\pi$
$542$	−23.8093	−	23.8093i	−1.02270	−	1.02270i
$543$	−54.4318			−2.33589
$544$	−24.1543	+	16.8392i	−1.03561	+	0.721976i
$545$	−31.5075			−1.34963
$546$	59.8455	+	59.8455i	2.56115	+	2.56115i
$547$	−17.0245	+	7.05176i	−0.727913	+	0.301512i	−0.715694	−	0.698414i	$-0.753890\pi$
$547$	−17.0245	+	7.05176i	−0.727913	+	0.301512i	−0.0122191	+	0.999925i	$0.503890\pi$
$548$		−	22.7785i		−	0.973051i
$549$	−26.7199	−	64.5076i	−1.14038	−	2.75312i
$550$	−52.4828	−	21.7391i	−2.23788	−	0.926959i
$551$	1.56803	−	3.78556i	0.0668004	−	0.161270i
$552$	−64.7274	+	64.7274i	−2.75498	+	2.75498i
$553$	−15.0956	+	15.0956i	−0.641930	+	0.641930i
$554$	−24.0068	+	57.9576i	−1.01995	+	2.46238i
$555$	−100.464	−	41.6136i	−4.26447	−	1.76640i
$556$	−18.9849	−	45.8337i	−0.805141	−	1.94378i
$557$			4.05701i			0.171901i	0.996299	+	0.0859506i	$0.0273927\pi$
$557$			4.05701i			0.171901i	−0.996299	+	0.0859506i	$0.972607\pi$
$558$	−106.903	+	44.2805i	−4.52555	+	1.87454i
$559$	3.85784	+	3.85784i	0.163169	+	0.163169i
$560$	56.9623			2.40710
$561$	−6.14041	+	34.4108i	−0.259248	+	1.45283i
$562$	−59.3544			−2.50371
$563$	6.61437	+	6.61437i	0.278763	+	0.278763i	0.832615	−	0.553852i	$-0.186843\pi$
$563$	6.61437	+	6.61437i	0.278763	+	0.278763i	−0.553852	+	0.832615i	$0.686843\pi$
$564$	6.60742	−	2.73688i	0.278223	−	0.115244i
$565$			51.9046i			2.18364i
$566$	15.6810	+	37.8573i	0.659122	+	1.59126i
$567$	−21.0368	−	8.71371i	−0.883461	−	0.365942i
$568$	41.1831	−	99.4248i	1.72800	−	4.17177i
$569$	−23.3461	+	23.3461i	−0.978720	+	0.978720i	−0.999778	−	0.0210579i	$-0.993297\pi$
$569$	−23.3461	+	23.3461i	−0.978720	+	0.978720i	0.0210579	+	0.999778i	$0.493297\pi$
$570$	45.6839	−	45.6839i	1.91349	−	1.91349i
$571$	−2.23487	+	5.39546i	−0.0935265	+	0.225793i	−0.963719	−	0.266919i	$-0.913994\pi$
$571$	−2.23487	+	5.39546i	−0.0935265	+	0.225793i	0.870192	+	0.492712i	$0.163994\pi$
$572$	64.6195	+	26.7663i	2.70188	+	1.11915i
$573$	24.4184	+	58.9513i	1.02009	+	2.46272i
$574$			2.72455i			0.113720i
$575$	−32.9591	+	13.6521i	−1.37449	+	0.569333i
$576$	−10.5439	−	10.5439i	−0.439329	−	0.439329i
$577$	6.09606			0.253782			0.126891	−	0.991917i	$-0.459500\pi$
$577$	6.09606			0.253782			0.126891	+	0.991917i	$0.459500\pi$
$578$	18.2998	+	39.6683i	0.761169	+	1.64998i
$579$	−19.6425			−0.816313
$580$	−20.8969	−	20.8969i	−0.867698	−	0.867698i
$581$	−28.2270	+	11.6920i	−1.17105	+	0.485067i
$582$		−	51.6127i		−	2.13941i
$583$	−4.65856	−	11.2468i	−0.192938	−	0.465793i
$584$	57.3712	+	23.7639i	2.37404	+	0.983358i
$585$	47.0717	−	113.641i	1.94618	−	4.69849i
$586$	−4.70275	+	4.70275i	−0.194269	+	0.194269i
$587$	9.04567	−	9.04567i	0.373355	−	0.373355i	−0.495343	−	0.868698i	$-0.664958\pi$
$587$	9.04567	−	9.04567i	0.373355	−	0.373355i	0.868698	+	0.495343i	$0.164958\pi$
$588$	16.4549	−	39.7257i	0.678590	−	1.63826i
$589$	15.2381	+	6.31182i	0.627874	+	0.260074i
$590$	26.2119	+	63.2811i	1.07913	+	2.60524i
$591$		−	22.3307i		−	0.918564i
$592$	73.2705	−	30.3496i	3.01140	−	1.24736i
$593$	5.01614	+	5.01614i	0.205988	+	0.205988i	0.802560	−	0.596572i	$-0.203471\pi$
$593$	5.01614	+	5.01614i	0.205988	+	0.205988i	−0.596572	+	0.802560i	$0.703471\pi$
$594$	−71.1937			−2.92111
$595$	5.16609	−	28.9507i	0.211789	−	1.18686i
$596$	−68.3089			−2.79804
$597$	−31.7642	−	31.7642i	−1.30002	−	1.30002i
$598$	58.2108	−	24.1117i	2.38042	−	0.986001i
$599$			26.9304i			1.10035i	0.835051	+	0.550173i	$0.185438\pi$
$599$			26.9304i			1.10035i	−0.835051	+	0.550173i	$0.814562\pi$
$600$	−61.8771	−	149.385i	−2.52612	−	6.09860i
$601$	16.0487	+	6.64759i	0.654640	+	0.271161i	0.685181	−	0.728373i	$-0.259723\pi$
$601$	16.0487	+	6.64759i	0.654640	+	0.271161i	−0.0305409	+	0.999534i	$0.509723\pi$
$602$	−1.95000	+	4.70773i	−0.0794763	+	0.191873i
$603$	28.5109	−	28.5109i	1.16105	−	1.16105i
$604$	14.8015	−	14.8015i	0.602263	−	0.602263i
$605$	−4.46699	+	10.7843i	−0.181609	+	0.438443i
$606$	−56.2400	−	23.2954i	−2.28459	−	0.946310i
$607$	7.56242	+	18.2573i	0.306949	+	0.741041i	0.999801	+	0.0199607i	$0.00635411\pi$
$607$	7.56242	+	18.2573i	0.306949	+	0.741041i	−0.692852	+	0.721080i	$0.743646\pi$
$608$			16.3961i			0.664949i
$609$	9.95332	−	4.12280i	0.403329	−	0.167064i
$610$	72.8092	+	72.8092i	2.94796	+	2.94796i
$611$	−2.78408			−0.112632
$612$	−97.5974	+	68.0403i	−3.94514	+	2.75037i
$613$	3.16567			0.127860			0.0639300	−	0.997954i	$-0.479637\pi$
$613$	3.16567			0.127860			0.0639300	+	0.997954i	$0.479637\pi$
$614$	−23.1781	−	23.1781i	−0.935392	−	0.935392i
$615$	5.40932	−	2.24061i	0.218125	−	0.0903502i
$616$			36.9458i			1.48859i
$617$	1.59059	+	3.84003i	0.0640349	+	0.154594i	0.952658	−	0.304045i	$-0.0983372\pi$
$617$	1.59059	+	3.84003i	0.0640349	+	0.154594i	−0.888623	+	0.458639i	$0.848337\pi$
$618$	51.7858	+	21.4504i	2.08313	+	0.862861i
$619$	10.5828	−	25.5490i	0.425357	−	1.02690i	−0.555385	−	0.831593i	$-0.687429\pi$
$619$	10.5828	−	25.5490i	0.425357	−	1.02690i	0.980742	−	0.195309i	$-0.0625709\pi$
$620$	84.1167	−	84.1167i	3.37821	−	3.37821i
$621$	−31.6144	+	31.6144i	−1.26864	+	1.26864i
$622$	−12.7452	+	30.7696i	−0.511035	+	1.23375i
$623$	24.1913	+	10.0204i	0.969205	+	0.401458i
$624$	50.7618	+	122.550i	2.03210	+	4.90592i
$625$			1.67563i			0.0670252i
$626$	−16.1469	+	6.68826i	−0.645360	+	0.267317i
$627$	13.7632	+	13.7632i	0.549650	+	0.549650i
$628$	54.3819			2.17007
$629$	−8.77986	−	39.9917i	−0.350076	−	1.59457i
$630$	114.883			4.57706
$631$	12.3478	+	12.3478i	0.491557	+	0.491557i	0.908797	−	0.417239i	$-0.137002\pi$
$631$	12.3478	+	12.3478i	0.491557	+	0.491557i	−0.417239	+	0.908797i	$0.637002\pi$
$632$	−66.5507	+	27.5662i	−2.64724	+	1.09652i
$633$			27.2541i			1.08325i
$634$	−7.49437	−	18.0930i	−0.297639	−	0.718565i
$635$	−43.6356	−	18.0744i	−1.73162	−	0.717263i
$636$	23.4455	−	56.6024i	0.929674	−	2.24443i
$637$	−11.8361	+	11.8361i	−0.468962	+	0.468962i
$638$	9.03068	−	9.03068i	0.357528	−	0.357528i
$639$	38.5805	−	93.1415i	1.52622	−	3.68462i
$640$	−27.1481	−	11.2451i	−1.07312	−	0.444503i
$641$	−17.6068	−	42.5065i	−0.695426	−	1.67891i	−0.733551	−	0.679634i	$-0.762139\pi$
$641$	−17.6068	−	42.5065i	−0.695426	−	1.67891i	0.0381252	−	0.999273i	$-0.487861\pi$
$642$			6.93636i			0.273756i
$643$	−12.6218	+	5.22811i	−0.497754	+	0.206177i	−0.617414	−	0.786638i	$-0.711820\pi$
$643$	−12.6218	+	5.22811i	−0.497754	+	0.206177i	0.119660	+	0.992815i	$0.461820\pi$
$644$	29.0087	+	29.0087i	1.14310	+	1.14310i
$645$	10.9504			0.431170
$646$	23.9479	+	4.27337i	0.942218	+	0.168133i
$647$	25.3293			0.995796			0.497898	−	0.867236i	$-0.334105\pi$
$647$	25.3293			0.995796			0.497898	+	0.867236i	$0.334105\pi$
$648$	−54.3275	−	54.3275i	−2.13419	−	2.13419i
$649$	−19.0647	+	7.89686i	−0.748355	+	0.309979i
$650$			111.295i			4.36534i
$651$	16.5956	+	40.0652i	0.650431	+	1.57028i
$652$	−8.05585	−	3.33684i	−0.315492	−	0.130681i
$653$	−1.26362	+	3.05066i	−0.0494494	+	0.119381i	−0.946674	−	0.322193i	$-0.895580\pi$
$653$	−1.26362	+	3.05066i	−0.0494494	+	0.119381i	0.897225	+	0.441575i	$0.145580\pi$
$654$	48.4558	−	48.4558i	1.89477	−	1.89477i
$655$	25.8876	−	25.8876i	1.01151	−	1.01151i
$656$	−1.63412	+	3.94512i	−0.0638018	+	0.154031i
$657$	53.7455	+	22.2621i	2.09681	+	0.868528i
$658$	−0.995081	−	2.40234i	−0.0387923	−	0.0936529i
$659$		−	23.2310i		−	0.904950i	−0.891777	−	0.452475i	$-0.850541\pi$
$659$		−	23.2310i		−	0.904950i	0.891777	−	0.452475i	$-0.149459\pi$
$660$	129.698	−	53.7226i	5.04848	−	2.09115i
$661$	23.7368	+	23.7368i	0.923253	+	0.923253i	0.997258	−	0.0740050i	$-0.0235781\pi$
$661$	23.7368	+	23.7368i	0.923253	+	0.923253i	−0.0740050	+	0.997258i	$0.523578\pi$
$662$	−5.30657			−0.206246
$663$	66.8888	−	14.6849i	2.59774	−	0.570314i
$664$	−103.091			−4.00071
$665$	−11.5793	−	11.5793i	−0.449028	−	0.449028i
$666$	147.774	−	61.2101i	5.72613	−	2.37184i
$667$		−	8.02037i		−	0.310550i
$668$	24.1312	+	58.2580i	0.933666	+	2.25407i
$669$	−56.5801	−	23.4362i	−2.18751	−	0.906097i
$670$	−22.7547	+	54.9347i	−0.879090	+	2.12231i
$671$	−21.9353	+	21.9353i	−0.846802	+	0.846802i
$672$	−30.4833	+	30.4833i	−1.17592	+	1.17592i
$673$	11.6867	−	28.2142i	0.450489	−	1.08758i	−0.521647	−	0.853161i	$-0.674682\pi$
$673$	11.6867	−	28.2142i	0.450489	−	1.08758i	0.972136	−	0.234416i	$-0.0753177\pi$
$674$	−52.0394	−	21.5554i	−2.00448	−	0.830283i
$675$	−30.2223	−	72.9630i	−1.16326	−	2.80835i
$676$		−	77.1843i		−	2.96863i
$677$	8.38010	−	3.47115i	0.322073	−	0.133407i	−0.215789	−	0.976440i	$-0.569232\pi$
$677$	8.38010	−	3.47115i	0.322073	−	0.133407i	0.537862	+	0.843033i	$0.319232\pi$
$678$	−79.8247	−	79.8247i	−3.06565	−	3.06565i
$679$	−13.0821			−0.502044
$680$	53.4872	−	83.5790i	2.05114	−	3.20511i
$681$	−37.2452			−1.42724
$682$	36.3513	+	36.3513i	1.39196	+	1.39196i
$683$	33.1423	−	13.7280i	1.26815	−	0.525287i	0.355751	−	0.934581i	$-0.384225\pi$
$683$	33.1423	−	13.7280i	1.26815	−	0.525287i	0.912403	+	0.409294i	$0.134225\pi$
$684$			66.2497i			2.53312i
$685$	6.81084	+	16.4428i	0.260229	+	0.628248i
$686$	−47.3976	−	19.6327i	−1.80965	−	0.749582i
$687$	−31.5311	+	76.1229i	−1.20299	+	2.90427i
$688$	−5.64718	+	5.64718i	−0.215297	+	0.215297i
$689$	−16.8644	+	16.8644i	−0.642481	+	0.642481i
$690$	48.3947	−	116.835i	1.84235	−	4.44783i
$691$	6.42132	+	2.65980i	0.244278	+	0.101183i	0.501464	−	0.865179i	$-0.332795\pi$
$691$	6.42132	+	2.65980i	0.244278	+	0.101183i	−0.257185	+	0.966362i	$0.582795\pi$
$692$	10.8392	+	26.1681i	0.412044	+	0.994761i
$693$			34.6110i			1.31476i
$694$	32.3433	−	13.3970i	1.22774	−	0.508545i
$695$	27.4088	+	27.4088i	1.03967	+	1.03967i
$696$	36.3516			1.37790
$697$	1.85688	+	1.18833i	0.0703342	+	0.0450111i
$698$	23.9626			0.906997
$699$	−34.4937	−	34.4937i	−1.30467	−	1.30467i
$700$	−66.9492	+	27.7313i	−2.53044	+	1.04814i
$701$		−	19.3431i		−	0.730579i	−0.930894	−	0.365289i	$-0.880970\pi$
$701$		−	19.3431i		−	0.730579i	0.930894	−	0.365289i	$-0.119030\pi$
$702$	53.3770	+	128.864i	2.01459	+	4.86364i
$703$	−21.0640	−	8.72498i	−0.794443	−	0.329069i
$704$	−2.53523	+	6.12060i	−0.0955502	+	0.230679i
$705$	−3.95127	+	3.95127i	−0.148813	+	0.148813i
$706$	15.8060	−	15.8060i	0.594868	−	0.594868i
$707$	−5.90459	+	14.2550i	−0.222065	+	0.536113i
$708$	−95.9485	−	39.7432i	−3.60596	−	1.49364i
$709$	13.1227	+	31.6810i	0.492833	+	1.18980i	0.953272	+	0.302113i	$0.0976919\pi$
$709$	13.1227	+	31.6810i	0.492833	+	1.18980i	−0.460439	+	0.887691i	$0.652308\pi$
$710$			148.674i			5.57962i
$711$	−62.3449	+	25.8241i	−2.33812	+	0.968479i
$712$	62.4742	+	62.4742i	2.34132	+	2.34132i
$713$	32.2845			1.20906
$714$	36.5786	+	52.4686i	1.36892	+	1.96359i
$715$	−54.6491			−2.04376
$716$	32.3466	+	32.3466i	1.20885	+	1.20885i
$717$	5.58790	−	2.31459i	0.208684	−	0.0864398i
$718$			59.1969i			2.20921i
$719$	14.1309	+	34.1149i	0.526992	+	1.27227i	0.933485	+	0.358618i	$0.116752\pi$
$719$	14.1309	+	34.1149i	0.526992	+	1.27227i	−0.406492	+	0.913654i	$0.633248\pi$
$720$	166.350	+	68.9045i	6.19950	+	2.56792i
$721$	5.43695	−	13.1260i	0.202483	−	0.488836i
$722$	−24.9464	+	24.9464i	−0.928408	+	0.928408i
$723$	11.8610	−	11.8610i	0.441114	−	0.441114i
$724$	−31.4995	+	76.0466i	−1.17067	+	2.82625i
$725$	13.0887	+	5.42152i	0.486102	+	0.201350i
$726$	−9.71540	−	23.4551i	−0.360572	−	0.870499i
$727$		−	27.2898i		−	1.01212i	−0.862498	−	0.506061i	$-0.831101\pi$
$727$		−	27.2898i		−	1.01212i	0.862498	−	0.506061i	$-0.168899\pi$
$728$	66.8735	−	27.6999i	2.47850	−	1.02663i
$729$	13.3540	+	13.3540i	0.494591	+	0.494591i
$730$	−85.7892			−3.17520
$731$	2.35798	+	3.38230i	0.0872130	+	0.125099i
$732$	−156.123			−5.77046
$733$	−28.6166	−	28.6166i	−1.05698	−	1.05698i	−0.998275	−	0.0587035i	$-0.981303\pi$
$733$	−28.6166	−	28.6166i	−1.05698	−	1.05698i	−0.0587035	−	0.998275i	$-0.518697\pi$
$734$	33.5170	−	13.8832i	1.23713	−	0.512438i
$735$			33.5963i			1.23922i
$736$	12.2817	+	29.6507i	0.452710	+	1.09294i
$737$	−16.5502	−	6.85531i	−0.609634	−	0.252519i
$738$	−3.29575	+	7.95664i	−0.121318	+	0.292888i
$739$	−20.3835	+	20.3835i	−0.749820	+	0.749820i	−0.974445	−	0.224625i	$-0.927884\pi$
$739$	−20.3835	+	20.3835i	−0.749820	+	0.749820i	0.224625	+	0.974445i	$0.427884\pi$
$740$	−116.277	+	116.277i	−4.27441	+	4.27441i
$741$	14.5931	−	35.2309i	0.536091	−	1.29424i
$742$	−20.5796	−	8.52435i	−0.755501	−	0.312939i
$743$	−15.7217	−	37.9556i	−0.576774	−	1.39246i	−0.895693	−	0.444674i	$-0.853320\pi$
$743$	−15.7217	−	37.9556i	−0.576774	−	1.39246i	0.318918	−	0.947782i	$-0.396680\pi$
$744$			146.327i			5.36460i
$745$	49.3092	−	20.4245i	1.80655	−	0.748297i
$746$	−23.7881	−	23.7881i	−0.870944	−	0.870944i
$747$	−96.5761			−3.53354
$748$	44.5218	+	28.4922i	1.62788	+	1.04178i
$749$	1.75814			0.0642409
$750$	58.4645	+	58.4645i	2.13482	+	2.13482i
$751$	10.1503	−	4.20440i	0.370390	−	0.153421i	−0.189721	−	0.981838i	$-0.560758\pi$
$751$	10.1503	−	4.20440i	0.370390	−	0.153421i	0.560111	+	0.828417i	$0.310758\pi$
$752$		−	4.07539i		−	0.148614i
$753$	−23.9377	−	57.7908i	−0.872340	−	2.10601i
$754$	−23.1166	−	9.57521i	−0.841857	−	0.348709i
$755$	−6.25885	+	15.1102i	−0.227783	+	0.549916i
$756$	−64.2177	+	64.2177i	−2.33558	+	2.33558i
$757$	−36.3141	+	36.3141i	−1.31986	+	1.31986i	−0.405972	+	0.913885i	$0.633067\pi$
$757$	−36.3141	+	36.3141i	−1.31986	+	1.31986i	−0.913885	+	0.405972i	$0.866933\pi$
$758$	9.67811	−	23.3650i	0.351525	−	0.848656i
$759$	35.1989	+	14.5799i	1.27764	+	0.529216i
$760$	−21.1451	−	51.0488i	−0.767014	−	1.85174i
$761$		−	35.3058i		−	1.27983i	−0.768445	−	0.639916i	$-0.778969\pi$
$761$		−	35.3058i		−	1.27983i	0.768445	−	0.639916i	$-0.221031\pi$
$762$	94.9045	−	39.3107i	3.43803	−	1.42408i
$763$	−12.2819	−	12.2819i	−0.444635	−	0.444635i
$764$	96.4915			3.49094
$765$	50.1070	−	78.2971i	1.81162	−	2.83084i
$766$	61.7088			2.22963
$767$	28.5873	+	28.5873i	1.03223	+	1.03223i
$768$	72.4276	−	30.0005i	2.61351	−	1.08255i
$769$			15.0755i			0.543637i	0.962349	+	0.271819i	$0.0876251\pi$
$769$			15.0755i			0.543637i	−0.962349	+	0.271819i	$0.912375\pi$
$770$	−19.5326	−	47.1558i	−0.703905	−	1.69938i
$771$	36.4616	+	15.1029i	1.31313	+	0.543917i
$772$	−11.3670	+	27.4424i	−0.409108	+	0.987675i
$773$	−1.17392	+	1.17392i	−0.0422230	+	0.0422230i	−0.727903	−	0.685680i	$-0.759505\pi$
$773$	−1.17392	+	1.17392i	−0.0422230	+	0.0422230i	0.685680	+	0.727903i	$0.259505\pi$
$774$	−11.3894	+	11.3894i	−0.409384	+	0.409384i
$775$	−21.8233	+	52.6861i	−0.783916	+	1.89254i
$776$	−40.7815	−	16.8923i	−1.46397	−	0.606397i
$777$	−22.9405	−	55.3831i	−0.822984	−	1.98686i
$778$			5.23485i			0.187678i
$779$	1.13415	−	0.469781i	0.0406352	−	0.0168317i
$780$	−194.480	−	194.480i	−6.96351	−	6.96351i
$781$	−44.7909			−1.60275
$782$	46.5084	−	10.2106i	1.66314	−	0.365129i
$783$	17.7550			0.634512
$784$	−17.3258	−	17.3258i	−0.618780	−	0.618780i
$785$	−39.2559	+	16.2603i	−1.40110	+	0.580355i
$786$			79.6257i			2.84015i
$787$	−11.3134	−	27.3129i	−0.403279	−	0.973600i	−0.986865	−	0.161549i	$-0.948351\pi$
$787$	−11.3134	−	27.3129i	−0.403279	−	0.973600i	0.583586	−	0.812051i	$-0.301649\pi$
$788$	−31.1982	−	12.9227i	−1.11139	−	0.460353i
$789$	7.86988	−	18.9996i	0.280175	−	0.676403i
$790$	70.3682	−	70.3682i	2.50359	−	2.50359i
$791$	−20.2329	+	20.2329i	−0.719398	+	0.719398i
$792$	−44.6915	+	107.895i	−1.58804	+	3.83388i
$793$	56.1496	+	23.2579i	1.99393	+	0.825913i
$794$	−19.9300	−	48.1154i	−0.707291	−	1.70755i
$795$			47.8690i			1.69774i
$796$	−62.7595	+	25.9958i	−2.22445	+	0.921398i
$797$	28.4091	+	28.4091i	1.00630	+	1.00630i	0.999980	+	0.00632300i	$0.00201269\pi$
$797$	28.4091	+	28.4091i	1.00630	+	1.00630i	0.00632300	+	0.999980i	$0.497987\pi$
$798$	35.6160			1.26079
$799$	−2.07129	−	0.369610i	−0.0732769	−	0.0130758i
$800$	−56.6900			−2.00429
$801$	58.5261	+	58.5261i	2.06792	+	2.06792i
$802$	−20.2191	+	8.37504i	−0.713962	+	0.295733i
$803$		−	25.8457i		−	0.912077i
$804$	−34.5013	−	83.2935i	−1.21677	−	2.93753i
$805$	−29.6138	−	12.2664i	−1.04375	−	0.432334i
$806$	38.5432	−	93.0516i	1.35763	−	3.27760i
$807$	−4.49333	+	4.49333i	−0.158173	+	0.158173i
$808$	−36.8135	+	36.8135i	−1.29509	+	1.29509i
$809$	1.36949	−	3.30625i	0.0481488	−	0.116242i	−0.897975	−	0.440046i	$-0.854962\pi$
$809$	1.36949	−	3.30625i	0.0481488	−	0.116242i	0.946124	+	0.323805i	$0.104962\pi$
$810$	98.0629	+	40.6190i	3.44558	+	1.42721i
$811$	3.28034	+	7.91944i	0.115188	+	0.278089i	0.970951	−	0.239280i	$-0.0769114\pi$
$811$	3.28034	+	7.91944i	0.115188	+	0.278089i	−0.855762	+	0.517369i	$0.826911\pi$
$812$		−	16.2916i		−	0.571723i
$813$	−36.8533	+	15.2651i	−1.29250	+	0.535372i
$814$	−50.2493	−	50.2493i	−1.76124	−	1.76124i
$815$	6.81289			0.238645
$816$	21.4960	+	97.9130i	0.752512	+	3.42764i
$817$	2.29593			0.0803243
$818$	−30.1732	−	30.1732i	−1.05498	−	1.05498i
$819$	62.6473	−	25.9494i	2.18907	−	0.906744i
$820$		−	8.85398i		−	0.309194i
$821$	−10.0403	−	24.2394i	−0.350408	−	0.845960i	−0.996570	−	0.0827593i	$-0.973627\pi$
$821$	−10.0403	−	24.2394i	−0.350408	−	0.845960i	0.646161	−	0.763201i	$-0.276373\pi$
$822$	−35.7620	−	14.8131i	−1.24734	−	0.516667i
$823$	1.74913	−	4.22278i	0.0609709	−	0.147197i	−0.890458	−	0.455066i	$-0.849616\pi$
$823$	1.74913	−	4.22278i	0.0609709	−	0.147197i	0.951429	+	0.307869i	$0.0996158\pi$
$824$	33.8979	−	33.8979i	1.18089	−	1.18089i
$825$	−47.5868	+	47.5868i	−1.65676	+	1.65676i
$826$	−14.4499	+	34.8851i	−0.502776	+	1.21381i
$827$	−5.13366	−	2.12643i	−0.178515	−	0.0739432i	0.291636	−	0.956529i	$-0.405800\pi$
$827$	−5.13366	−	2.12643i	−0.178515	−	0.0739432i	−0.470151	+	0.882586i	$0.655800\pi$
$828$	49.6253	+	119.806i	1.72460	+	4.16355i
$829$			20.8782i			0.725130i	0.931958	+	0.362565i	$0.118099\pi$
$829$			20.8782i			0.725130i	−0.931958	+	0.362565i	$0.881901\pi$
$830$	131.580	−	54.5023i	4.56722	−	1.89180i
$831$	52.5508	+	52.5508i	1.82297	+	1.82297i
$832$	12.9793			0.449977
$833$	−10.3771	+	7.23440i	−0.359544	+	0.250657i
$834$	−84.3044			−2.91922
$835$	−34.8385	−	34.8385i	−1.20564	−	1.20564i
$836$	27.1933	−	11.2638i	0.940500	−	0.389568i
$837$			71.4694i			2.47035i
$838$	−8.59658	−	20.7540i	−0.296964	−	0.716935i
$839$	−34.4218	−	14.2580i	−1.18837	−	0.492240i	−0.301147	−	0.953578i	$-0.597369\pi$
$839$	−34.4218	−	14.2580i	−1.18837	−	0.492240i	−0.887224	+	0.461338i	$0.847369\pi$
$840$	55.5965	−	134.222i	1.91826	−	4.63109i
$841$	18.2539	−	18.2539i	0.629446	−	0.629446i
$842$	34.2702	−	34.2702i	1.18103	−	1.18103i
$843$	−26.9086	+	64.9632i	−0.926783	+	2.23745i
$844$	38.0767	+	15.7719i	1.31065	+	0.542890i
$845$	23.0783	+	55.7159i	0.793917	+	1.91668i
$846$		−	8.21938i		−	0.282588i
$847$	−5.94507	+	2.46253i	−0.204275	+	0.0846135i
$848$	−24.6864	−	24.6864i	−0.847733	−	0.847733i
$849$	48.5438			1.66602
$850$	−14.7753	+	82.8006i	−0.506789	+	2.84004i
$851$	−44.6276			−1.52982
$852$	−159.398	−	159.398i	−5.46089	−	5.46089i
$853$	5.47266	−	2.26685i	0.187380	−	0.0776155i	−0.287020	−	0.957924i	$-0.592665\pi$
$853$	5.47266	−	2.26685i	0.187380	−	0.0776155i	0.474401	+	0.880309i	$0.342665\pi$
$854$			56.7633i			1.94240i
$855$	−19.8088	−	47.8227i	−0.677447	−	1.63550i
$856$	5.48074	+	2.27020i	0.187328	+	0.0775937i
$857$	3.62060	−	8.74090i	0.123677	−	0.298584i	−0.849899	−	0.526946i	$-0.823337\pi$
$857$	3.62060	−	8.74090i	0.123677	−	0.298584i	0.973576	+	0.228362i	$0.0733371\pi$
$858$	84.0454	−	84.0454i	2.86926	−	2.86926i
$859$	3.85121	−	3.85121i	0.131402	−	0.131402i	−0.638347	−	0.769749i	$-0.720382\pi$
$859$	3.85121	−	3.85121i	0.131402	−	0.131402i	0.769749	+	0.638347i	$0.220382\pi$
$860$	6.33694	−	15.2987i	0.216088	−	0.521682i
$861$	2.98201	+	1.23519i	0.101627	+	0.0420951i
$862$	6.71617	+	16.2143i	0.228754	+	0.552260i
$863$			1.34049i			0.0456309i	0.999740	+	0.0228154i	$0.00726301\pi$
$863$			1.34049i			0.0456309i	−0.999740	+	0.0228154i	$0.992737\pi$
$864$	−65.6389	+	27.1885i	−2.23308	+	0.924972i
$865$	−15.6486	−	15.6486i	−0.532070	−	0.532070i
$866$	−61.5351			−2.09105
$867$	51.7131	−	2.04518i	1.75627	−	0.0694579i
$868$	65.5788			2.22589
$869$	21.1998	+	21.1998i	0.719156	+	0.719156i
$870$	−46.3974	+	19.2184i	−1.57302	+	0.651566i
$871$			35.0963i			1.18919i
$872$	−22.4281	−	54.1461i	−0.759510	−	1.83362i
$873$	−38.2043	−	15.8247i	−1.29302	−	0.535586i
$874$	10.1467	−	24.4964i	0.343218	−	0.828603i
$875$	14.8188	−	14.8188i	0.500966	−	0.500966i
$876$	91.9776	−	91.9776i	3.10763	−	3.10763i
$877$	11.6622	−	28.1551i	0.393805	−	0.950729i	−0.595298	−	0.803505i	$-0.702966\pi$
$877$	11.6622	−	28.1551i	0.393805	−	0.950729i	0.989103	−	0.147224i	$-0.0470339\pi$
$878$	−60.0512	−	24.8740i	−2.02663	−	0.839458i
$879$	3.01513	+	7.27916i	0.101698	+	0.245520i
$880$		−	79.9963i		−	2.69668i
$881$	−21.9412	+	9.08835i	−0.739218	+	0.306194i	−0.720334	−	0.693627i	$-0.756011\pi$
$881$	−21.9412	+	9.08835i	−0.739218	+	0.306194i	−0.0188844	+	0.999822i	$0.506011\pi$
$882$	−34.9433	−	34.9433i	−1.17660	−	1.17660i
$883$	9.43274			0.317437			0.158719	−	0.987324i	$-0.449264\pi$
$883$	9.43274			0.317437			0.158719	+	0.987324i	$0.449264\pi$
$884$	18.1921	−	101.948i	0.611866	−	3.42889i
$885$	81.1442			2.72763
$886$	41.4085	+	41.4085i	1.39114	+	1.39114i
$887$	−29.5965	+	12.2593i	−0.993752	+	0.411626i	−0.819502	−	0.573076i	$-0.805750\pi$
$887$	−29.5965	+	12.2593i	−0.993752	+	0.411626i	−0.174250	+	0.984701i	$0.555750\pi$
$888$		−	202.271i		−	6.78777i
$889$	−9.96395	−	24.0551i	−0.334180	−	0.806782i
$890$	−112.768	−	46.7100i	−3.77999	−	1.56572i
$891$	−12.2373	+	29.5434i	−0.409965	+	0.989743i
$892$	−65.4854	+	65.4854i	−2.19261	+	2.19261i
$893$	−0.828449	+	0.828449i	−0.0277230	+	0.0277230i
$894$	−44.4220	+	107.244i	−1.48569	+	3.58678i
$895$	−33.0213	−	13.6779i	−1.10378	−	0.457201i
$896$	−6.19913	−	14.9660i	−0.207098	−	0.499980i
$897$		−	74.6427i		−	2.49225i
$898$	6.08191	−	2.51921i	0.202956	−	0.0840671i
$899$	−9.06566	−	9.06566i	−0.302357	−	0.302357i
$900$	−229.061			−7.63535
$901$	−14.7855	+	10.3078i	−0.492578	+	0.343402i
$902$	3.82628			0.127401
$903$	4.26855	+	4.26855i	0.142048	+	0.142048i
$904$	−89.1989	+	36.9474i	−2.96671	+	1.22885i
$905$		−	64.3131i		−	2.13784i
$906$	−13.6126	−	32.8637i	−0.452247	−	1.09182i
$907$	51.4594	+	21.3152i	1.70868	+	0.707760i	0.999998	+	0.00223504i	$0.000711435\pi$
$907$	51.4594	+	21.3152i	1.70868	+	0.707760i	0.708685	+	0.705525i	$0.249289\pi$
$908$	−21.5537	+	52.0352i	−0.715285	+	1.72685i
$909$	−34.4870	+	34.4870i	−1.14386	+	1.14386i
$910$	−70.7095	+	70.7095i	−2.34400	+	2.34400i
$911$	−12.3759	+	29.8781i	−0.410032	+	0.989904i	0.575097	+	0.818085i	$0.304964\pi$
$911$	−12.3759	+	29.8781i	−0.410032	+	0.989904i	−0.985129	+	0.171819i	$0.945036\pi$
$912$	51.5716	+	21.3617i	1.70771	+	0.707356i
$913$	16.4199	+	39.6412i	0.543421	+	1.31193i
$914$		−	96.7377i		−	3.19980i
$915$	112.698	−	46.6810i	3.72568	−	1.54323i
$916$	88.1041	+	88.1041i	2.91104	+	2.91104i
$917$	20.1824			0.666483
$918$	22.6035	+	102.958i	0.746027	+	3.39811i
$919$	4.80684			0.158563			0.0792815	−	0.996852i	$-0.474737\pi$
$919$	4.80684			0.158563			0.0792815	+	0.996852i	$0.474737\pi$
$920$	−76.4777	−	76.4777i	−2.52139	−	2.52139i
$921$	−35.8763	+	14.8604i	−1.18216	+	0.489668i
$922$		−	65.2886i		−	2.15017i
$923$	33.5817	+	81.0735i	1.10536	+	2.66857i
$924$	71.4989	+	29.6158i	2.35214	+	0.974288i
$925$	30.1669	−	72.8293i	0.991881	−	2.39461i
$926$	0.401228	−	0.401228i	0.0131852	−	0.0131852i
$927$	31.7556	−	31.7556i	1.04299	−	1.04299i
$928$	4.87730	−	11.7748i	0.160105	−	0.386528i
$929$	−17.8497	−	7.39360i	−0.585630	−	0.242576i	0.0701392	−	0.997537i	$-0.477656\pi$
$929$	−17.8497	−	7.39360i	−0.585630	−	0.242576i	−0.655769	+	0.754961i	$0.727656\pi$
$930$	−77.3602	−	186.764i	−2.53674	−	6.12423i
$931$			7.04402i			0.230858i
$932$	−68.1525	+	28.2297i	−2.23241	+	0.924694i
$933$	27.8991	+	27.8991i	0.913375	+	0.913375i
$934$	−87.1287			−2.85094
$935$	−40.6576	−	7.25511i	−1.32964	−	0.237267i
$936$	228.801			7.47860
$937$	−2.97889	−	2.97889i	−0.0973162	−	0.0973162i	0.656773	−	0.754089i	$-0.271921\pi$
$937$	−2.97889	−	2.97889i	−0.0973162	−	0.0973162i	−0.754089	+	0.656773i	$0.771921\pi$
$938$	−30.2840	+	12.5440i	−0.988807	+	0.409577i
$939$			20.7049i			0.675678i
$940$	3.23372	+	7.80689i	0.105472	+	0.254633i
$941$	15.5390	+	6.43648i	0.506558	+	0.209823i	0.621301	−	0.783572i	$-0.286604\pi$
$941$	15.5390	+	6.43648i	0.506558	+	0.209823i	−0.114743	+	0.993395i	$0.536604\pi$
$942$	35.3651	−	85.3789i	1.15226	−	2.78179i
$943$	1.69911	−	1.69911i	0.0553305	−	0.0553305i
$944$	−41.8466	+	41.8466i	−1.36199	+	1.36199i
$945$	27.1547	−	65.5572i	0.883341	−	2.13257i
$946$	6.61140	+	2.73853i	0.214955	+	0.0890374i
$947$	2.58017	+	6.22909i	0.0838444	+	0.202418i	0.960241	−	0.279171i	$-0.0900597\pi$
$947$	2.58017	+	6.22909i	0.0838444	+	0.202418i	−0.876397	+	0.481589i	$0.840060\pi$
$948$			150.888i			4.90062i
$949$	−46.7819	+	19.3777i	−1.51860	+	0.629026i
$950$	33.1176	+	33.1176i	1.07448	+	1.07448i
$951$	−23.2003			−0.752323
$952$	53.4296	−	11.7300i	1.73166	−	0.380173i
$953$	26.9022			0.871449			0.435724	−	0.900080i	$-0.356492\pi$
$953$	26.9022			0.871449			0.435724	+	0.900080i	$0.356492\pi$
$954$	−49.7882	−	49.7882i	−1.61195	−	1.61195i
$955$	−69.6529	+	28.8512i	−2.25392	+	0.933602i
$956$		−	9.14629i		−	0.295812i
$957$	−5.78994	−	13.9782i	−0.187162	−	0.451850i
$958$	−94.5779	−	39.1754i	−3.05567	−	1.26570i
$959$	−3.75463	+	9.06447i	−0.121243	+	0.292707i
$960$	18.4207	−	18.4207i	0.594526	−	0.594526i
$961$	14.5718	−	14.5718i	0.470058	−	0.470058i
$962$	−53.2793	+	128.628i	−1.71779	+	4.14712i
$963$	5.13438	+	2.12673i	0.165453	+	0.0685329i
$964$	−9.70701	−	23.4348i	−0.312642	−	0.754784i
$965$		−	23.2082i		−	0.747100i
$966$	64.4079	−	26.6786i	2.07229	−	0.858371i
$967$	−5.23547	−	5.23547i	−0.168361	−	0.168361i	0.617897	−	0.786259i	$-0.287985\pi$
$967$	−5.23547	−	5.23547i	−0.168361	−	0.168361i	−0.786259	+	0.617897i	$0.787985\pi$
$968$	−21.7127			−0.697871
$969$	15.5341	−	24.2736i	0.499027	−	0.779779i
$970$	60.9821			1.95802
$971$	−15.7256	−	15.7256i	−0.504660	−	0.504660i	0.408223	−	0.912882i	$-0.366149\pi$
$971$	−15.7256	−	15.7256i	−0.504660	−	0.504660i	−0.912882	+	0.408223i	$0.866149\pi$
$972$	−21.7444	+	9.00683i	−0.697452	+	0.288894i
$973$			21.3683i			0.685038i
$974$	34.4552	+	83.1821i	1.10401	+	2.66533i
$975$	121.812	+	50.4561i	3.90110	+	1.61589i
$976$	−34.0454	+	82.1928i	−1.08977	+	2.63093i
$977$	13.3033	−	13.3033i	0.425611	−	0.425611i	−0.461519	−	0.887130i	$-0.652695\pi$
$977$	13.3033	−	13.3033i	0.425611	−	0.425611i	0.887130	+	0.461519i	$0.152695\pi$
$978$	−10.4776	+	10.4776i	−0.335037	+	0.335037i
$979$	14.0723	−	33.9736i	0.449754	−	1.08580i
$980$	46.9373	+	19.4421i	1.49936	+	0.621054i
$981$	−21.0107	−	50.7243i	−0.670820	−	1.61950i
$982$			38.9453i			1.24279i
$983$	4.80309	−	1.98951i	0.153195	−	0.0634554i	−0.304768	−	0.952426i	$-0.598579\pi$
$983$	4.80309	−	1.98951i	0.153195	−	0.0634554i	0.457963	+	0.888971i	$0.348579\pi$
$984$	7.70105	+	7.70105i	0.245501	+	0.245501i
$985$	26.3845			0.840681
$986$	−15.9270	−	10.1926i	−0.507219	−	0.324600i
$987$	−3.08048			−0.0980527
$988$	−40.7760	−	40.7760i	−1.29726	−	1.29726i
$989$	4.15195	−	1.71979i	0.132024	−	0.0546863i
$990$		−	161.339i		−	5.12769i
$991$	16.1209	+	38.9192i	0.512096	+	1.23631i	0.942662	+	0.333750i	$0.108314\pi$
$991$	16.1209	+	38.9192i	0.512096	+	1.23631i	−0.430565	+	0.902559i	$0.641686\pi$
$992$	47.3974	+	19.6327i	1.50487	+	0.623337i
$993$	−2.40576	+	5.80803i	−0.0763446	+	0.184312i
$994$	−57.9542	+	57.9542i	−1.83820	+	1.83820i
$995$	37.5305	−	37.5305i	1.18980	−	1.18980i
$996$	−82.6379	+	199.506i	−2.61848	+	6.32158i
$997$	18.9169	+	7.83565i	0.599105	+	0.248158i	0.661562	−	0.749890i	$-0.269894\pi$
$997$	18.9169	+	7.83565i	0.599105	+	0.248158i	−0.0624571	+	0.998048i	$0.519894\pi$
$998$	−5.62387	−	13.5772i	−0.178020	−	0.429779i
$999$		−	98.7940i		−	3.12570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.2	✓	116
17.9	even	8	inner	731.2.m.b.689.2	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.2	✓	116	1.1	even	1	trivial
731.2.m.b.689.2	yes	116	17.9	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.81709 - 1.81709i) q^{2} +(-2.81259 + 1.16501i) q^{3} +4.60365i q^{4} +(-1.37650 - 3.32317i) q^{5} +(7.22768 + 2.99380i) q^{6} +(0.758828 - 1.83197i) q^{7} +(4.73108 - 4.73108i) q^{8} +(4.43209 - 4.43209i) q^{9} +O(q^{10})\)	\(q+(-1.81709 - 1.81709i) q^{2} +(-2.81259 + 1.16501i) q^{3} +4.60365i q^{4} +(-1.37650 - 3.32317i) q^{5} +(7.22768 + 2.99380i) q^{6} +(0.758828 - 1.83197i) q^{7} +(4.73108 - 4.73108i) q^{8} +(4.43209 - 4.43209i) q^{9} +(-3.53728 + 8.53975i) q^{10} +(-2.57277 - 1.06568i) q^{11} +(-5.36332 - 12.9482i) q^{12} +5.45581i q^{13} +(-4.70773 + 1.95000i) q^{14} +(7.74308 + 7.74308i) q^{15} -7.98632 q^{16} +(-0.724303 + 4.05899i) q^{17} -16.1070 q^{18} +(1.62346 + 1.62346i) q^{19} +(15.2987 - 6.33694i) q^{20} +6.03664i q^{21} +(2.73853 + 6.61140i) q^{22} +(4.15195 + 1.71979i) q^{23} +(-7.79482 + 18.8184i) q^{24} +(-5.61318 + 5.61318i) q^{25} +(9.91372 - 9.91372i) q^{26} +(-3.80718 + 9.19134i) q^{27} +(8.43377 + 3.49338i) q^{28} +(-0.682963 - 1.64882i) q^{29} -28.1398i q^{30} +(6.63701 - 2.74914i) q^{31} +(5.04972 + 5.04972i) q^{32} +8.47769 q^{33} +(8.69168 - 6.05943i) q^{34} -7.13249 q^{35} +(20.4038 + 20.4038i) q^{36} +(-9.17450 + 3.80020i) q^{37} -5.89997i q^{38} +(-6.35609 - 15.3450i) q^{39} +(-22.2345 - 9.20985i) q^{40} +(0.204615 - 0.493985i) q^{41} +(10.9691 - 10.9691i) q^{42} +(0.707107 - 0.707107i) q^{43} +(4.90601 - 11.8442i) q^{44} +(-20.8294 - 8.62782i) q^{45} +(-4.41945 - 10.6695i) q^{46} +0.510297i q^{47} +(22.4622 - 9.30417i) q^{48} +(2.16944 + 2.16944i) q^{49} +20.3993 q^{50} +(-2.69161 - 12.2601i) q^{51} -25.1167 q^{52} +(3.09108 + 3.09108i) q^{53} +(23.6195 - 9.78352i) q^{54} +10.0167i q^{55} +(-5.07714 - 12.2573i) q^{56} +(-6.45750 - 2.67478i) q^{57} +(-1.75505 + 4.23706i) q^{58} +(5.23979 - 5.23979i) q^{59} +(-35.6465 + 35.6465i) q^{60} +(4.26296 - 10.2917i) q^{61} +(-17.0555 - 7.06462i) q^{62} +(-4.75628 - 11.4827i) q^{63} -2.37899i q^{64} +(18.1306 - 7.50994i) q^{65} +(-15.4047 - 15.4047i) q^{66} +6.43282 q^{67} +(-18.6862 - 3.33444i) q^{68} -13.6813 q^{69} +(12.9604 + 12.9604i) q^{70} +(14.8600 - 6.15522i) q^{71} -41.9372i q^{72} +(3.55175 + 8.57469i) q^{73} +(23.5762 + 9.76560i) q^{74} +(9.24815 - 22.3270i) q^{75} +(-7.47387 + 7.47387i) q^{76} +(-3.90459 + 3.90459i) q^{77} +(-16.3336 + 39.4328i) q^{78} +(-9.94665 - 4.12004i) q^{79} +(10.9932 + 26.5399i) q^{80} -11.4831i q^{81} +(-1.26942 + 0.525812i) q^{82} +(-10.8951 - 10.8951i) q^{83} -27.7906 q^{84} +(14.4857 - 3.18023i) q^{85} -2.56976 q^{86} +(3.84179 + 3.84179i) q^{87} +(-17.2138 + 7.13019i) q^{88} +13.2051i q^{89} +(22.1714 + 53.5265i) q^{90} +(9.99490 + 4.14002i) q^{91} +(-7.91734 + 19.1141i) q^{92} +(-15.4644 + 15.4644i) q^{93} +(0.927257 - 0.927257i) q^{94} +(3.16035 - 7.62975i) q^{95} +(-20.0858 - 8.31981i) q^{96} +(-2.52472 - 6.09520i) q^{97} -7.88415i q^{98} +(-16.1259 + 6.67959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

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