LMFDB - Embedded newform 315.2.k.b.16.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.10
Character	$\chi$	$=$	315.16
Dual form			315.2.k.b.256.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.805191 + 1.39463i) q^{2} +(1.04104 + 1.38428i) q^{3} +(-0.296664 + 0.513837i) q^{4} -1.00000 q^{5} +(-1.09233 + 2.56648i) q^{6} +(2.48389 + 0.911196i) q^{7} +2.26528 q^{8} +(-0.832482 + 2.88218i) q^{9} +O(q^{10})$	\(q+(0.805191 + 1.39463i) q^{2} +(1.04104 + 1.38428i) q^{3} +(-0.296664 + 0.513837i) q^{4} -1.00000 q^{5} +(-1.09233 + 2.56648i) q^{6} +(2.48389 + 0.911196i) q^{7} +2.26528 q^{8} +(-0.832482 + 2.88218i) q^{9} +(-0.805191 - 1.39463i) q^{10} -2.16786 q^{11} +(-1.02013 + 0.124257i) q^{12} +(-2.21310 - 3.83320i) q^{13} +(0.729225 + 4.19780i) q^{14} +(-1.04104 - 1.38428i) q^{15} +(2.41731 + 4.18690i) q^{16} +(-0.752653 - 1.30363i) q^{17} +(-4.68989 + 1.15970i) q^{18} +(0.165687 - 0.286978i) q^{19} +(0.296664 - 0.513837i) q^{20} +(1.32447 + 4.38700i) q^{21} +(-1.74554 - 3.02336i) q^{22} -1.89944 q^{23} +(2.35824 + 3.13579i) q^{24} +1.00000 q^{25} +(3.56393 - 6.17291i) q^{26} +(-4.85640 + 1.84807i) q^{27} +(-1.20509 + 1.00600i) q^{28} +(-1.99635 + 3.45777i) q^{29} +(1.09233 - 2.56648i) q^{30} +(4.87703 - 8.44726i) q^{31} +(-1.62751 + 2.81893i) q^{32} +(-2.25682 - 3.00093i) q^{33} +(1.21206 - 2.09935i) q^{34} +(-2.48389 - 0.911196i) q^{35} +(-1.23400 - 1.28280i) q^{36} +(-1.09897 + 1.90348i) q^{37} +0.533638 q^{38} +(3.00231 - 7.05406i) q^{39} -2.26528 q^{40} +(-3.44235 - 5.96232i) q^{41} +(-5.05179 + 5.37952i) q^{42} +(6.16406 - 10.6765i) q^{43} +(0.643125 - 1.11392i) q^{44} +(0.832482 - 2.88218i) q^{45} +(-1.52941 - 2.64901i) q^{46} +(0.908467 + 1.57351i) q^{47} +(-3.27935 + 7.70496i) q^{48} +(5.33944 + 4.52663i) q^{49} +(0.805191 + 1.39463i) q^{50} +(1.02106 - 2.39902i) q^{51} +2.62618 q^{52} +(1.32638 + 2.29735i) q^{53} +(-6.48770 - 5.28484i) q^{54} +2.16786 q^{55} +(5.62671 + 2.06411i) q^{56} +(0.569745 - 0.0693974i) q^{57} -6.42975 q^{58} +(-3.78850 + 6.56187i) q^{59} +(1.02013 - 0.124257i) q^{60} +(2.43522 + 4.21792i) q^{61} +15.7077 q^{62} +(-4.69403 + 6.40048i) q^{63} +4.42741 q^{64} +(2.21310 + 3.83320i) q^{65} +(2.36802 - 5.56375i) q^{66} +(-6.61165 + 11.4517i) q^{67} +0.893139 q^{68} +(-1.97739 - 2.62936i) q^{69} +(-0.729225 - 4.19780i) q^{70} +14.9331 q^{71} +(-1.88580 + 6.52895i) q^{72} +(-5.31641 - 9.20829i) q^{73} -3.53953 q^{74} +(1.04104 + 1.38428i) q^{75} +(0.0983066 + 0.170272i) q^{76} +(-5.38473 - 1.97534i) q^{77} +(12.2552 - 1.49274i) q^{78} +(-2.55562 - 4.42647i) q^{79} +(-2.41731 - 4.18690i) q^{80} +(-7.61395 - 4.79873i) q^{81} +(5.54349 - 9.60161i) q^{82} +(2.99740 - 5.19164i) q^{83} +(-2.64712 - 0.620902i) q^{84} +(0.752653 + 1.30363i) q^{85} +19.8530 q^{86} +(-6.86481 + 0.836162i) q^{87} -4.91080 q^{88} +(-2.99220 + 5.18265i) q^{89} +(4.68989 - 1.15970i) q^{90} +(-2.00430 - 11.5378i) q^{91} +(0.563494 - 0.976001i) q^{92} +(16.7706 - 2.04272i) q^{93} +(-1.46298 + 2.53395i) q^{94} +(-0.165687 + 0.286978i) q^{95} +(-5.59649 + 0.681676i) q^{96} +(3.11237 - 5.39079i) q^{97} +(-2.01370 + 11.0913i) q^{98} +(1.80470 - 6.24816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.805191	+	1.39463i	0.569356	+	0.986153i	0.996630	+	0.0820309i	$0.0261406\pi$
$2$	0.805191	+	1.39463i	0.569356	+	0.986153i	−0.427274	+	0.904122i	$0.640526\pi$
$3$	1.04104	+	1.38428i	0.601043	+	0.799216i
$3$	1.04104	+	1.38428i	0.601043	+	0.799216i
$4$	−0.296664	+	0.513837i	−0.148332	+	0.256918i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.09233	+	2.56648i	−0.445942	+	1.04776i
$7$	2.48389	+	0.911196i	0.938823	+	0.344400i
$7$	2.48389	+	0.911196i	0.938823	+	0.344400i
$8$	2.26528			0.800897
$9$	−0.832482	+	2.88218i	−0.277494	+	0.960727i
$10$	−0.805191	−	1.39463i	−0.254624	−	0.441021i
$11$	−2.16786			−0.653634			−0.326817	−	0.945088i	$-0.605976\pi$
$11$	−2.16786			−0.653634			−0.326817	+	0.945088i	$0.605976\pi$
$12$	−1.02013	+	0.124257i	−0.294487	+	0.0358698i
$13$	−2.21310	−	3.83320i	−0.613803	−	1.06314i	−0.990593	−	0.136839i	$-0.956306\pi$
$13$	−2.21310	−	3.83320i	−0.613803	−	1.06314i	0.376790	−	0.926299i	$-0.377028\pi$
$14$	0.729225	+	4.19780i	0.194893	+	1.12191i
$15$	−1.04104	−	1.38428i	−0.268795	−	0.357420i
$16$	2.41731	+	4.18690i	0.604327	+	1.04673i
$17$	−0.752653	−	1.30363i	−0.182545	−	0.316177i	0.760201	−	0.649687i	$-0.225100\pi$
$17$	−0.752653	−	1.30363i	−0.182545	−	0.316177i	−0.942747	+	0.333510i	$0.891767\pi$
$18$	−4.68989	+	1.15970i	−1.10542	+	0.273344i
$19$	0.165687	−	0.286978i	0.0380112	−	0.0658373i	−0.846394	−	0.532557i	$-0.821231\pi$
$19$	0.165687	−	0.286978i	0.0380112	−	0.0658373i	0.884405	+	0.466720i	$0.154564\pi$
$20$	0.296664	−	0.513837i	0.0663360	−	0.114897i
$21$	1.32447	+	4.38700i	0.289023	+	0.957322i
$22$	−1.74554	−	3.02336i	−0.372150	−	0.644583i
$23$	−1.89944			−0.396060			−0.198030	−	0.980196i	$-0.563454\pi$
$23$	−1.89944			−0.396060			−0.198030	+	0.980196i	$0.563454\pi$
$24$	2.35824	+	3.13579i	0.481374	+	0.640090i
$25$	1.00000			0.200000
$26$	3.56393	−	6.17291i	0.698944	−	1.21061i
$27$	−4.85640	+	1.84807i	−0.934615	+	0.355661i
$28$	−1.20509	+	1.00600i	−0.227740	+	0.190115i
$29$	−1.99635	+	3.45777i	−0.370712	+	0.642092i	−0.989675	−	0.143328i	$-0.954220\pi$
$29$	−1.99635	+	3.45777i	−0.370712	+	0.642092i	0.618963	+	0.785420i	$0.287553\pi$
$30$	1.09233	−	2.56648i	0.199431	−	0.468572i
$31$	4.87703	−	8.44726i	0.875940	−	1.51717i	0.0201814	−	0.999796i	$-0.493576\pi$
$31$	4.87703	−	8.44726i	0.875940	−	1.51717i	0.855758	−	0.517376i	$-0.173091\pi$
$32$	−1.62751	+	2.81893i	−0.287706	+	0.498321i
$33$	−2.25682	−	3.00093i	−0.392862	−	0.522395i
$34$	1.21206	−	2.09935i	0.207866	−	0.360035i
$35$	−2.48389	−	0.911196i	−0.419854	−	0.154020i
$36$	−1.23400	−	1.28280i	−0.205667	−	0.213800i
$37$	−1.09897	+	1.90348i	−0.180670	+	0.312930i	−0.942109	−	0.335307i	$-0.891160\pi$
$37$	−1.09897	+	1.90348i	−0.180670	+	0.312930i	0.761439	+	0.648237i	$0.224493\pi$
$38$	0.533638			0.0865676
$39$	3.00231	−	7.05406i	0.480755	−	1.12955i
$40$	−2.26528			−0.358172
$41$	−3.44235	−	5.96232i	−0.537604	−	0.931158i	−0.999032	−	0.0439804i	$-0.985996\pi$
$41$	−3.44235	−	5.96232i	−0.537604	−	0.931158i	0.461428	−	0.887178i	$-0.347337\pi$
$42$	−5.05179	+	5.37952i	−0.779509	+	0.830078i
$43$	6.16406	−	10.6765i	0.940010	−	1.62815i	0.174565	−	0.984646i	$-0.444148\pi$
$43$	6.16406	−	10.6765i	0.940010	−	1.62815i	0.765446	−	0.643500i	$-0.222518\pi$
$44$	0.643125	−	1.11392i	0.0969547	−	0.167930i
$45$	0.832482	−	2.88218i	0.124099	−	0.429650i
$46$	−1.52941	−	2.64901i	−0.225499	−	0.390576i
$47$	0.908467	+	1.57351i	0.132513	+	0.229520i	0.924645	−	0.380831i	$-0.124362\pi$
$47$	0.908467	+	1.57351i	0.132513	+	0.229520i	−0.792131	+	0.610351i	$0.791029\pi$
$48$	−3.27935	+	7.70496i	−0.473333	+	1.11212i
$49$	5.33944	+	4.52663i	0.762778	+	0.646661i
$50$	0.805191	+	1.39463i	0.113871	+	0.197231i
$51$	1.02106	−	2.39902i	0.142977	−	0.335929i
$52$	2.62618			0.364186
$53$	1.32638	+	2.29735i	0.182192	+	0.315566i	0.942627	−	0.333849i	$-0.108347\pi$
$53$	1.32638	+	2.29735i	0.182192	+	0.315566i	−0.760435	+	0.649414i	$0.775014\pi$
$54$	−6.48770	−	5.28484i	−0.882865	−	0.719176i
$55$	2.16786			0.292314
$56$	5.62671	+	2.06411i	0.751901	+	0.275829i
$57$	0.569745	−	0.0693974i	0.0754646	−	0.00919191i
$58$	−6.42975			−0.844268
$59$	−3.78850	+	6.56187i	−0.493220	+	0.854283i	−0.999969	−	0.00781092i	$-0.997514\pi$
$59$	−3.78850	+	6.56187i	−0.493220	+	0.854283i	0.506749	+	0.862094i	$0.330847\pi$
$60$	1.02013	−	0.124257i	0.131699	−	0.0160414i
$61$	2.43522	+	4.21792i	0.311797	+	0.540049i	0.978752	−	0.205050i	$-0.0657356\pi$
$61$	2.43522	+	4.21792i	0.311797	+	0.540049i	−0.666954	+	0.745099i	$0.732402\pi$
$62$	15.7077			1.99489
$63$	−4.69403	+	6.40048i	−0.591392	+	0.806384i
$64$	4.42741			0.553427
$65$	2.21310	+	3.83320i	0.274501	+	0.475450i
$66$	2.36802	−	5.56375i	0.291483	−	0.684851i
$67$	−6.61165	+	11.4517i	−0.807741	+	1.39905i	0.106683	+	0.994293i	$0.465977\pi$
$67$	−6.61165	+	11.4517i	−0.807741	+	1.39905i	−0.914425	+	0.404756i	$0.867356\pi$
$68$	0.893139			0.108309
$69$	−1.97739	−	2.62936i	−0.238049	−	0.316538i
$70$	−0.729225	−	4.19780i	−0.0871590	−	0.501733i
$71$	14.9331			1.77223			0.886115	−	0.463466i	$-0.153394\pi$
$71$	14.9331			1.77223			0.886115	+	0.463466i	$0.153394\pi$
$72$	−1.88580	+	6.52895i	−0.222244	+	0.769444i
$73$	−5.31641	−	9.20829i	−0.622239	−	1.07775i	−0.989068	−	0.147461i	$-0.952890\pi$
$73$	−5.31641	−	9.20829i	−0.622239	−	1.07775i	0.366829	−	0.930288i	$-0.380443\pi$
$74$	−3.53953			−0.411462
$75$	1.04104	+	1.38428i	0.120209	+	0.159843i
$76$	0.0983066	+	0.170272i	0.0112765	+	0.0195315i
$77$	−5.38473	−	1.97534i	−0.613647	−	0.225111i
$78$	12.2552	−	1.49274i	1.38763	−	0.169020i
$79$	−2.55562	−	4.42647i	−0.287530	−	0.498017i	0.685689	−	0.727894i	$-0.259501\pi$
$79$	−2.55562	−	4.42647i	−0.287530	−	0.498017i	−0.973220	+	0.229877i	$0.926168\pi$
$80$	−2.41731	−	4.18690i	−0.270263	−	0.468110i
$81$	−7.61395	−	4.79873i	−0.845994	−	0.533192i
$82$	5.54349	−	9.60161i	0.612176	−	1.06032i
$83$	2.99740	−	5.19164i	0.329007	−	0.569857i	−0.653308	−	0.757092i	$-0.726619\pi$
$83$	2.99740	−	5.19164i	0.329007	−	0.569857i	0.982315	+	0.187235i	$0.0599527\pi$
$84$	−2.64712	−	0.620902i	−0.288825	−	0.0677459i
$85$	0.752653	+	1.30363i	0.0816367	+	0.141399i
$86$	19.8530			2.14080
$87$	−6.86481	+	0.836162i	−0.735984	+	0.0896460i
$88$	−4.91080			−0.523493
$89$	−2.99220	+	5.18265i	−0.317173	+	0.549360i	−0.979897	−	0.199504i	$-0.936067\pi$
$89$	−2.99220	+	5.18265i	−0.317173	+	0.549360i	0.662724	+	0.748864i	$0.269400\pi$
$90$	4.68989	−	1.15970i	0.494357	−	0.122243i
$91$	−2.00430	−	11.5378i	−0.210108	−	1.20949i
$92$	0.563494	−	0.976001i	0.0587483	−	0.101755i
$93$	16.7706	−	2.04272i	1.73903	−	0.211821i
$94$	−1.46298	+	2.53395i	−0.150895	+	0.261357i
$95$	−0.165687	+	0.286978i	−0.0169991	+	0.0294433i
$96$	−5.59649	+	0.681676i	−0.571190	+	0.0695733i
$97$	3.11237	−	5.39079i	0.316014	−	0.547352i	−0.663639	−	0.748053i	$-0.730989\pi$
$97$	3.11237	−	5.39079i	0.316014	−	0.547352i	0.979652	+	0.200702i	$0.0643222\pi$
$98$	−2.01370	+	11.0913i	−0.203415	+	1.12040i
$99$	1.80470	−	6.24816i	0.181379	−	0.627964i
$100$	−0.296664	+	0.513837i	−0.0296664	+	0.0513837i
$101$	−7.75721			−0.771871			−0.385935	−	0.922526i	$-0.626121\pi$
$101$	−7.75721			−0.771871			−0.385935	+	0.922526i	$0.626121\pi$
$102$	4.16789	−	0.507666i	0.412682	−	0.0502664i
$103$	−12.5677			−1.23833			−0.619164	−	0.785262i	$-0.712528\pi$
$103$	−12.5677			−1.23833			−0.619164	+	0.785262i	$0.712528\pi$
$104$	−5.01328	−	8.68326i	−0.491593	−	0.851464i
$105$	−1.32447	−	4.38700i	−0.129255	−	0.428127i
$106$	−2.13597	+	3.69961i	−0.207464	+	0.359338i
$107$	−0.758514	+	1.31378i	−0.0733283	+	0.127008i	−0.900358	−	0.435150i	$-0.856695\pi$
$107$	−0.758514	+	1.31378i	−0.0733283	+	0.127008i	0.827030	+	0.562158i	$0.190029\pi$
$108$	0.491112	−	3.04365i	0.0472573	−	0.292876i
$109$	7.96403	+	13.7941i	0.762816	+	1.32124i	0.941393	+	0.337311i	$0.109517\pi$
$109$	7.96403	+	13.7941i	0.762816	+	1.32124i	−0.178577	+	0.983926i	$0.557149\pi$
$110$	1.74554	+	3.02336i	0.166431	+	0.288266i
$111$	−3.77903	+	0.460301i	−0.358689	+	0.0436899i
$112$	2.18925	+	12.6025i	0.206864	+	1.19082i
$113$	0.570145	+	0.987520i	0.0536347	+	0.0928980i	0.891596	−	0.452831i	$-0.149586\pi$
$113$	0.570145	+	0.987520i	0.0536347	+	0.0928980i	−0.837962	+	0.545729i	$0.816253\pi$
$114$	0.555537	+	0.738707i	0.0520308	+	0.0691862i
$115$	1.89944			0.177124
$116$	−1.18449	−	2.05159i	−0.109977	−	0.190485i
$117$	12.8903	−	3.18748i	1.19171	−	0.294683i
$118$	−12.2018			−1.12327
$119$	−0.681644	−	3.92390i	−0.0624862	−	0.359703i
$120$	−2.35824	−	3.13579i	−0.215277	−	0.286257i
$121$	−6.30039			−0.572763
$122$	−3.92163	+	6.79246i	−0.355047	+	0.614960i
$123$	4.66993	−	10.9722i	0.421073	−	0.989329i
$124$	2.89367	+	5.01199i	0.259859	+	0.450090i
$125$	−1.00000			−0.0894427
$126$	−12.7059	−	1.39283i	−1.13193	−	0.124083i
$127$	−17.6396			−1.56526			−0.782630	−	0.622488i	$-0.786122\pi$
$127$	−17.6396			−1.56526			−0.782630	+	0.622488i	$0.786122\pi$
$128$	6.81993	+	11.8125i	0.602802	+	1.04408i
$129$	21.1963	−	2.58179i	1.86623	−	0.227314i
$130$	−3.56393	+	6.17291i	−0.312577	+	0.541400i
$131$	−21.5579			−1.88352			−0.941760	−	0.336286i	$-0.890829\pi$
$131$	−21.5579			−1.88352			−0.941760	+	0.336286i	$0.890829\pi$
$132$	2.21150	−	0.269371i	0.192487	−	0.0234457i
$133$	0.673042	−	0.561850i	0.0583601	−	0.0487185i
$134$	−21.2945			−1.83957
$135$	4.85640	−	1.84807i	0.417973	−	0.159056i
$136$	−1.70497	−	2.95309i	−0.146200	−	0.253226i
$137$	−1.79472			−0.153333			−0.0766666	−	0.997057i	$-0.524428\pi$
$137$	−1.79472			−0.153333			−0.0766666	+	0.997057i	$0.524428\pi$
$138$	2.07482	−	4.87486i	0.176620	−	0.414976i
$139$	3.05809	+	5.29676i	0.259383	+	0.449265i	0.966077	−	0.258255i	$-0.0831473\pi$
$139$	3.05809	+	5.29676i	0.259383	+	0.449265i	−0.706693	+	0.707520i	$0.749814\pi$
$140$	1.20509	−	1.00600i	0.101848	−	0.0850222i
$141$	−1.23244	+	2.89566i	−0.103790	+	0.243858i
$142$	12.0240	+	20.8261i	1.00903	+	1.74769i
$143$	4.79768	+	8.30983i	0.401202	+	0.694903i
$144$	−14.0798	+	3.48161i	−1.17331	+	0.290134i
$145$	1.99635	−	3.45777i	0.165787	−	0.287152i
$146$	8.56145	−	14.8289i	0.708550	−	1.22725i
$147$	−0.707572	+	12.1037i	−0.0583595	+	0.998296i
$148$	−0.652051	−	1.12939i	−0.0535983	−	0.0928349i
$149$	14.2934			1.17096			0.585480	−	0.810687i	$-0.300906\pi$
$149$	14.2934			1.17096			0.585480	+	0.810687i	$0.300906\pi$
$150$	−1.09233	+	2.56648i	−0.0891885	+	0.209552i
$151$	−0.413699			−0.0336664			−0.0168332	−	0.999858i	$-0.505358\pi$
$151$	−0.413699			−0.0336664			−0.0168332	+	0.999858i	$0.505358\pi$
$152$	0.375327	−	0.650086i	0.0304431	−	0.0527289i
$153$	4.38388	−	1.08403i	0.354416	−	0.0876388i
$154$	−1.58086	−	9.10023i	−0.127389	−	0.733318i
$155$	−4.87703	+	8.44726i	−0.391732	+	0.678500i
$156$	2.73396	+	3.63538i	0.218892	+	0.291063i
$157$	−1.97318	+	3.41764i	−0.157477	+	0.272757i	−0.933958	−	0.357383i	$-0.883669\pi$
$157$	−1.97318	+	3.41764i	−0.157477	+	0.272757i	0.776481	+	0.630140i	$0.217003\pi$
$158$	4.11553	−	7.12831i	0.327414	−	0.567098i
$159$	−1.79938	+	4.22771i	−0.142700	+	0.335279i
$160$	1.62751	−	2.81893i	0.128666	−	0.222856i
$161$	−4.71800	−	1.73076i	−0.371830	−	0.136403i
$162$	0.561774	−	14.4825i	0.0441372	−	1.13786i
$163$	−7.52899	+	13.0406i	−0.589716	+	1.02142i	0.404553	+	0.914514i	$0.367427\pi$
$163$	−7.52899	+	13.0406i	−0.589716	+	1.02142i	−0.994269	+	0.106904i	$0.965906\pi$
$164$	4.08488			0.318975
$165$	2.25682	+	3.00093i	0.175693	+	0.233622i
$166$	9.65390			0.749288
$167$	−4.78399	−	8.28611i	−0.370196	−	0.641199i	0.619399	−	0.785076i	$-0.287376\pi$
$167$	−4.78399	−	8.28611i	−0.370196	−	0.641199i	−0.989596	+	0.143877i	$0.954043\pi$
$168$	3.00030	+	9.93778i	0.231478	+	0.766716i
$169$	−3.29561	+	5.70816i	−0.253508	+	0.439089i
$170$	−1.21206	+	2.09935i	−0.0929606	+	0.161012i
$171$	0.689192	+	0.716444i	0.0527038	+	0.0547878i
$172$	3.65731	+	6.33464i	0.278867	+	0.483012i
$173$	8.57844	+	14.8583i	0.652207	+	1.12966i	0.982586	+	0.185807i	$0.0594901\pi$
$173$	8.57844	+	14.8583i	0.652207	+	1.12966i	−0.330379	+	0.943848i	$0.607177\pi$
$174$	−6.69361	−	8.90060i	−0.507442	−	0.674753i
$175$	2.48389	+	0.911196i	0.187765	+	0.0688799i
$176$	−5.24038	−	9.07661i	−0.395009	−	0.684175i
$177$	−13.0275	+	1.58680i	−0.979203	+	0.119271i
$178$	−9.63718			−0.722337
$179$	−12.1937	−	21.1200i	−0.911397	−	1.57859i	−0.812092	−	0.583529i	$-0.801671\pi$
$179$	−12.1937	−	21.1200i	−0.911397	−	1.57859i	−0.0993046	−	0.995057i	$-0.531662\pi$
$180$	1.23400	+	1.28280i	0.0919772	+	0.0956141i
$181$	2.08440			0.154932			0.0774660	−	0.996995i	$-0.475317\pi$
$181$	2.08440			0.154932			0.0774660	+	0.996995i	$0.475317\pi$
$182$	14.4772	−	12.0854i	1.07312	−	0.895830i
$183$	−3.30364	+	7.76204i	−0.244212	+	0.573787i
$184$	−4.30276			−0.317203
$185$	1.09897	−	1.90348i	0.0807982	−	0.139947i
$186$	16.3523	+	21.7440i	1.19901	+	1.59435i
$187$	1.63164	+	2.82609i	0.119318	+	0.206664i
$188$	−1.07804			−0.0786239
$189$	−13.7467	+	0.165272i	−0.999928	+	0.0120217i
$190$	−0.533638			−0.0387142
$191$	−6.04829	−	10.4759i	−0.437639	−	0.758013i	0.559868	−	0.828582i	$-0.310852\pi$
$191$	−6.04829	−	10.4759i	−0.437639	−	0.758013i	−0.997507	+	0.0705689i	$0.977519\pi$
$192$	4.60911	+	6.12880i	0.332634	+	0.442308i
$193$	1.68614	−	2.92048i	0.121371	−	0.210220i	−0.798938	−	0.601414i	$-0.794604\pi$
$193$	1.68614	−	2.92048i	0.121371	−	0.210220i	0.920309	+	0.391193i	$0.127938\pi$
$194$	10.0242			0.719696
$195$	−3.00231	+	7.05406i	−0.215000	+	0.505152i
$196$	−3.90996	+	1.40072i	−0.279283	+	0.100051i
$197$	−13.8266			−0.985107			−0.492554	−	0.870282i	$-0.663936\pi$
$197$	−13.8266			−0.985107			−0.492554	+	0.870282i	$0.663936\pi$
$198$	10.1670	−	2.51407i	0.722538	−	0.178667i
$199$	9.36690	+	16.2240i	0.664002	+	1.15009i	0.979555	+	0.201177i	$0.0644768\pi$
$199$	9.36690	+	16.2240i	0.664002	+	1.15009i	−0.315553	+	0.948908i	$0.602190\pi$
$200$	2.26528			0.160179
$201$	−22.7354	+	2.76926i	−1.60363	+	0.195329i
$202$	−6.24603	−	10.8184i	−0.439469	−	0.761183i
$203$	−8.10941	+	6.76967i	−0.569169	+	0.475138i
$204$	0.929791	+	1.23636i	0.0650984	+	0.0865623i
$205$	3.44235	+	5.96232i	0.240424	+	0.416427i
$206$	−10.1194	−	17.5272i	−0.705049	−	1.22118i
$207$	1.58125	−	5.47453i	0.109904	−	0.380506i
$208$	10.6995	−	18.5320i	0.741876	−	1.28497i
$209$	−0.359186	+	0.622128i	−0.0248454	+	0.0430335i
$210$	5.05179	−	5.37952i	0.348607	−	0.371222i
$211$	12.8766	+	22.3029i	0.886459	+	1.53539i	0.844032	+	0.536292i	$0.180176\pi$
$211$	12.8766	+	22.3029i	0.886459	+	1.53539i	0.0424267	+	0.999100i	$0.486491\pi$
$212$	−1.57395			−0.108099
$213$	15.5459	+	20.6716i	1.06519	+	1.41640i
$214$	−2.44299			−0.166999
$215$	−6.16406	+	10.6765i	−0.420385	+	0.728129i
$216$	−11.0011	+	4.18639i	−0.748530	+	0.284848i
$217$	19.8111	−	16.5382i	1.34487	−	1.12268i
$218$	−12.8251	+	22.2138i	−0.868628	+	1.50451i
$219$	7.21230	−	16.9456i	0.487362	−	1.14508i
$220$	−0.643125	+	1.11392i	−0.0433595	+	0.0751008i
$221$	−3.33139	+	5.77014i	−0.224093	+	0.388141i
$222$	−3.68479	−	4.89972i	−0.247307	−	0.328848i
$223$	−1.86363	+	3.22790i	−0.124798	+	0.216156i	−0.921654	−	0.388013i	$-0.873162\pi$
$223$	−1.86363	+	3.22790i	−0.124798	+	0.216156i	0.796856	+	0.604169i	$0.206495\pi$
$224$	−6.61115	+	5.51894i	−0.441726	+	0.368749i
$225$	−0.832482	+	2.88218i	−0.0554988	+	0.192145i
$226$	−0.918150	+	1.59028i	−0.0610745	+	0.105784i
$227$	−28.0027			−1.85860			−0.929301	−	0.369322i	$-0.879590\pi$
$227$	−28.0027			−1.85860			−0.929301	+	0.369322i	$0.879590\pi$
$228$	−0.133364	+	0.313344i	−0.00883224	+	0.0207517i
$229$	8.32459			0.550104			0.275052	−	0.961429i	$-0.411305\pi$
$229$	8.32459			0.550104			0.275052	+	0.961429i	$0.411305\pi$
$230$	1.52941	+	2.64901i	0.100846	+	0.174671i
$231$	−2.87127	−	9.51040i	−0.188916	−	0.625738i
$232$	−4.52228	+	7.83282i	−0.296902	+	0.514250i
$233$	1.58936	−	2.75285i	0.104122	−	0.180345i	−0.809257	−	0.587455i	$-0.800130\pi$
$233$	1.58936	−	2.75285i	0.104122	−	0.180345i	0.913379	+	0.407110i	$0.133463\pi$
$234$	14.8245	+	15.4107i	0.969111	+	1.00743i
$235$	−0.908467	−	1.57351i	−0.0592618	−	0.102644i
$236$	−2.24782	−	3.89334i	−0.146321	−	0.253435i
$237$	3.46699	−	8.14583i	0.225205	−	0.529129i
$238$	4.92354	−	4.11013i	0.319146	−	0.266420i
$239$	4.20403	+	7.28160i	0.271936	+	0.471008i	0.969358	−	0.245654i	$-0.0790026\pi$
$239$	4.20403	+	7.28160i	0.271936	+	0.471008i	−0.697421	+	0.716661i	$0.745669\pi$
$240$	3.27935	−	7.70496i	0.211681	−	0.497353i
$241$	22.4484			1.44603			0.723014	−	0.690834i	$-0.242756\pi$
$241$	22.4484			1.44603			0.723014	+	0.690834i	$0.242756\pi$
$242$	−5.07301	−	8.78672i	−0.326106	−	0.564832i
$243$	−1.28361	−	15.5355i	−0.0823434	−	0.996604i
$244$	−2.88976			−0.184998
$245$	−5.33944	−	4.52663i	−0.341125	−	0.289196i
$246$	19.0623	−	2.32187i	1.21537	−	0.148037i
$247$	−1.46673			−0.0933255
$248$	11.0478	−	19.1354i	0.701538	−	1.21510i
$249$	10.3071	−	1.25545i	0.653186	−	0.0795608i
$250$	−0.805191	−	1.39463i	−0.0509247	−	0.0882042i
$251$	30.1109			1.90058			0.950292	−	0.311359i	$-0.100784\pi$
$251$	30.1109			1.90058			0.950292	+	0.311359i	$0.100784\pi$
$252$	−1.89625	−	4.31075i	−0.119453	−	0.271552i
$253$	4.11771			0.258878
$254$	−14.2032	−	24.6007i	−0.891189	−	1.54359i
$255$	−1.02106	+	2.39902i	−0.0639411	+	0.150232i
$256$	−6.55527	+	11.3541i	−0.409705	+	0.709629i
$257$	20.1420			1.25642			0.628211	−	0.778043i	$-0.283788\pi$
$257$	20.1420			1.25642			0.628211	+	0.778043i	$0.283788\pi$
$258$	20.6677	+	27.4821i	1.28671	+	1.71096i
$259$	−4.46417	+	3.72666i	−0.277390	+	0.231563i
$260$	−2.62618			−0.162869
$261$	−8.30401	−	8.63236i	−0.514005	−	0.534330i
$262$	−17.3582	−	30.0653i	−1.07239	−	1.85744i
$263$	−5.91285			−0.364602			−0.182301	−	0.983243i	$-0.558355\pi$
$263$	−5.91285			−0.364602			−0.182301	+	0.983243i	$0.558355\pi$
$264$	−5.11233	−	6.79795i	−0.314642	−	0.418385i
$265$	−1.32638	−	2.29735i	−0.0814787	−	0.141125i
$266$	1.32550	+	0.486249i	0.0812716	+	0.0298138i
$267$	−10.2893	+	1.25327i	−0.629692	+	0.0766991i
$268$	−3.92287	−	6.79461i	−0.239627	−	0.415047i
$269$	10.3002	+	17.8405i	0.628017	+	1.08776i	0.987949	+	0.154779i	$0.0494665\pi$
$269$	10.3002	+	17.8405i	0.628017	+	1.08776i	−0.359932	+	0.932979i	$0.617200\pi$
$270$	6.48770	+	5.28484i	0.394829	+	0.321625i
$271$	−12.8109	+	22.1892i	−0.778208	+	1.34790i	0.154765	+	0.987951i	$0.450538\pi$
$271$	−12.8109	+	22.1892i	−0.778208	+	1.34790i	−0.932973	+	0.359945i	$0.882795\pi$
$272$	3.63879	−	6.30257i	0.220634	−	0.382149i
$273$	13.8851	−	14.7858i	0.840362	−	0.894879i
$274$	−1.44509	−	2.50297i	−0.0873011	−	0.151210i
$275$	−2.16786			−0.130727
$276$	1.93768	−	0.236018i	0.116635	−	0.0142066i
$277$	12.1705			0.731256			0.365628	−	0.930761i	$-0.380854\pi$
$277$	12.1705			0.731256			0.365628	+	0.930761i	$0.380854\pi$
$278$	−4.92468	+	8.52980i	−0.295363	+	0.511583i
$279$	20.2865	+	21.0887i	1.21452	+	1.26255i
$280$	−5.62671	−	2.06411i	−0.336260	−	0.123354i
$281$	2.00102	−	3.46586i	0.119371	−	0.206756i	−0.800148	−	0.599803i	$-0.795246\pi$
$281$	2.00102	−	3.46586i	0.119371	−	0.206756i	0.919518	+	0.393047i	$0.128579\pi$
$282$	−5.03072	+	0.612763i	−0.299575	+	0.0364895i
$283$	−2.36998	+	4.10492i	−0.140880	+	0.244012i	−0.927828	−	0.373007i	$-0.878327\pi$
$283$	−2.36998	+	4.10492i	−0.140880	+	0.244012i	0.786948	+	0.617019i	$0.211660\pi$
$284$	−4.43010	+	7.67316i	−0.262878	+	0.455318i
$285$	−0.569745	+	0.0693974i	−0.0337488	+	0.00411075i
$286$	−7.72610	+	13.3820i	−0.456854	+	0.791294i
$287$	−3.11758	−	17.9464i	−0.184025	−	1.05934i
$288$	−6.76979	−	7.03748i	−0.398914	−	0.414688i
$289$	7.36703	−	12.7601i	0.433355	−	0.750592i
$290$	6.42975			0.377568
$291$	10.7025	−	1.30361i	0.627390	−	0.0764187i
$292$	6.30874			0.369191
$293$	−12.1285	−	21.0071i	−0.708553	−	1.22725i	−0.965394	−	0.260795i	$-0.916015\pi$
$293$	−12.1285	−	21.0071i	−0.708553	−	1.22725i	0.256842	−	0.966454i	$-0.417318\pi$
$294$	−17.4499	+	8.75898i	−1.01770	+	0.510834i
$295$	3.78850	−	6.56187i	0.220575	−	0.382047i
$296$	−2.48948	+	4.31191i	−0.144698	+	0.250625i
$297$	10.5280	−	4.00635i	0.610896	−	0.232472i
$298$	11.5089	+	19.9340i	0.666693	+	1.15475i
$299$	4.20364	+	7.28092i	0.243103	+	0.421067i
$300$	−1.02013	+	0.124257i	−0.0588974	+	0.00717395i
$301$	25.0392	−	20.9025i	1.44324	−	1.20480i
$302$	−0.333107	−	0.576958i	−0.0191681	−	0.0332002i
$303$	−8.07554	−	10.7382i	−0.463928	−	0.616892i
$304$	1.60207			0.0918848
$305$	−2.43522	−	4.21792i	−0.139440	−	0.241517i
$306$	5.04168	+	5.24104i	0.288214	+	0.299610i
$307$	−9.11593			−0.520273			−0.260137	−	0.965572i	$-0.583768\pi$
$307$	−9.11593			−0.520273			−0.260137	+	0.965572i	$0.583768\pi$
$308$	2.61246	−	2.18086i	0.148859	−	0.124266i
$309$	−13.0834	−	17.3972i	−0.744289	−	0.989692i
$310$	−15.7077			−0.892140
$311$	−6.90047	+	11.9520i	−0.391290	+	0.677734i	−0.992620	−	0.121267i	$-0.961304\pi$
$311$	−6.90047	+	11.9520i	−0.391290	+	0.677734i	0.601330	+	0.799001i	$0.294638\pi$
$312$	6.80108	−	15.9794i	0.385035	−	0.904656i
$313$	−3.94106	−	6.82611i	−0.222762	−	0.385835i	0.732884	−	0.680354i	$-0.238174\pi$
$313$	−3.94106	−	6.82611i	−0.222762	−	0.385835i	−0.955646	+	0.294519i	$0.904841\pi$
$314$	−6.35513			−0.358641
$315$	4.69403	−	6.40048i	0.264478	−	0.360626i
$316$	3.03264			0.170600
$317$	−6.35262	−	11.0031i	−0.356798	−	0.617993i	0.630626	−	0.776087i	$-0.282798\pi$
$317$	−6.35262	−	11.0031i	−0.356798	−	0.617993i	−0.987424	+	0.158094i	$0.949465\pi$
$318$	−7.34494	+	0.894645i	−0.411884	+	0.0501692i
$319$	4.32779	−	7.49596i	0.242310	−	0.419693i
$320$	−4.42741			−0.247500
$321$	−2.60829	+	0.317701i	−0.145581	+	0.0177323i
$322$	−1.38512	−	7.97346i	−0.0771896	−	0.444344i
$323$	−0.498819			−0.0277550
$324$	4.72454	−	2.48872i	0.262475	−	0.138262i
$325$	−2.21310	−	3.83320i	−0.122761	−	0.212628i
$326$	−24.2491			−1.34303
$327$	−10.8041	+	25.3847i	−0.597468	+	1.40378i
$328$	−7.79788	−	13.5063i	−0.430566	−	0.745762i
$329$	0.822757	+	4.73622i	0.0453601	+	0.261116i
$330$	−2.36802	+	5.56375i	−0.130355	+	0.306275i
$331$	−2.62749	−	4.55095i	−0.144420	−	0.250143i	0.784736	−	0.619830i	$-0.212798\pi$
$331$	−2.62749	−	4.55095i	−0.144420	−	0.250143i	−0.929156	+	0.369687i	$0.879465\pi$
$332$	1.77844	+	3.08034i	0.0976044	+	0.169056i
$333$	−4.57130	−	4.75205i	−0.250505	−	0.260411i
$334$	7.70405	−	13.3438i	0.421547	−	0.730140i
$335$	6.61165	−	11.4517i	0.361233	−	0.625674i
$336$	−15.1663	+	16.1502i	−0.827389	+	0.881064i
$337$	7.33922	+	12.7119i	0.399793	+	0.692461i	0.993700	−	0.112072i	$-0.0357488\pi$
$337$	7.33922	+	12.7119i	0.399793	+	0.692461i	−0.593907	+	0.804533i	$0.702415\pi$
$338$	−10.6144			−0.577345
$339$	−0.773465	+	1.81729i	−0.0420089	+	0.0987015i
$340$	−0.893139			−0.0484373
$341$	−10.5727	+	18.3125i	−0.572544	+	0.991675i
$342$	−0.444244	+	1.53804i	−0.0240220	+	0.0831678i
$343$	9.13796	+	16.1089i	0.493404	+	0.869801i
$344$	13.9633	−	24.1852i	0.752852	−	1.30398i
$345$	1.97739	+	2.62936i	0.106459	+	0.141560i
$346$	−13.8146	+	23.9275i	−0.742676	+	1.28635i
$347$	15.2925	−	26.4875i	0.820947	−	1.42192i	−0.0840317	−	0.996463i	$-0.526780\pi$
$347$	15.2925	−	26.4875i	0.820947	−	1.42192i	0.904978	−	0.425458i	$-0.139887\pi$
$348$	1.60689	−	3.77545i	0.0861382	−	0.202385i
$349$	−10.5415	+	18.2585i	−0.564275	+	0.977353i	0.432842	+	0.901470i	$0.357511\pi$
$349$	−10.5415	+	18.2585i	−0.564275	+	0.977353i	−0.997117	+	0.0758828i	$0.975823\pi$
$350$	0.729225	+	4.19780i	0.0389787	+	0.224382i
$351$	17.8317	+	14.5256i	0.951786	+	0.775319i
$352$	3.52821	−	6.11104i	0.188054	−	0.325719i
$353$	−7.78719			−0.414470			−0.207235	−	0.978291i	$-0.566447\pi$
$353$	−7.78719			−0.414470			−0.207235	+	0.978291i	$0.566447\pi$
$354$	−12.7026	−	16.8908i	−0.675135	−	0.897737i
$355$	−14.9331			−0.792565
$356$	−1.77536	−	3.07501i	−0.0940937	−	0.162975i
$357$	4.72217	−	5.02851i	0.249924	−	0.266137i
$358$	19.6364	−	34.0113i	1.03782	−	1.79755i
$359$	8.52548	−	14.7666i	0.449958	−	0.779349i	−0.548425	−	0.836200i	$-0.684772\pi$
$359$	8.52548	−	14.7666i	0.449958	−	0.779349i	0.998383	+	0.0568504i	$0.0181058\pi$
$360$	1.88580	−	6.52895i	0.0993906	−	0.344106i
$361$	9.44510	+	16.3594i	0.497110	+	0.861020i
$362$	1.67834	+	2.90697i	0.0882115	+	0.152787i
$363$	−6.55894	−	8.72153i	−0.344255	−	0.457761i
$364$	6.52316	+	2.39297i	0.341906	+	0.125426i
$365$	5.31641	+	9.20829i	0.278274	+	0.481984i
$366$	−13.4852	+	1.64256i	−0.704885	+	0.0858579i
$367$	16.0561			0.838122			0.419061	−	0.907958i	$-0.362359\pi$
$367$	16.0561			0.838122			0.419061	+	0.907958i	$0.362359\pi$
$368$	−4.59153	−	7.95276i	−0.239350	−	0.414566i
$369$	20.0502	−	4.95795i	1.04377	−	0.258101i
$370$	3.53953			0.184012
$371$	1.20124	+	6.91497i	0.0623653	+	0.359007i
$372$	−3.92559	+	9.22333i	−0.203532	+	0.478207i
$373$	−11.7970			−0.610827			−0.305413	−	0.952220i	$-0.598795\pi$
$373$	−11.7970			−0.610827			−0.305413	+	0.952220i	$0.598795\pi$
$374$	−2.62757	+	4.55108i	−0.135868	+	0.235331i
$375$	−1.04104	−	1.38428i	−0.0537589	−	0.0714841i
$376$	2.05793	+	3.56444i	0.106130	+	0.183822i
$377$	17.6724			0.910176
$378$	−11.2992	−	19.0385i	−0.581170	−	0.979237i
$379$	−29.0464			−1.49202			−0.746008	−	0.665937i	$-0.768032\pi$
$379$	−29.0464			−1.49202			−0.746008	+	0.665937i	$0.768032\pi$
$380$	−0.0983066	−	0.170272i	−0.00504302	−	0.00873477i
$381$	−18.3635	−	24.4182i	−0.940789	−	1.25098i
$382$	9.74005	−	16.8703i	0.498345	−	0.863158i
$383$	24.6357			1.25882			0.629412	−	0.777072i	$-0.283296\pi$
$383$	24.6357			1.25882			0.629412	+	0.777072i	$0.283296\pi$
$384$	−9.25200	+	21.7379i	−0.472139	+	1.10931i
$385$	5.38473	+	1.97534i	0.274431	+	0.100673i
$386$	5.43065			0.276413
$387$	25.6401	+	26.6539i	1.30336	+	1.35489i
$388$	1.84666	+	3.19850i	0.0937497	+	0.162379i
$389$	25.4164			1.28866			0.644331	−	0.764747i	$-0.277136\pi$
$389$	25.4164			1.28866			0.644331	+	0.764747i	$0.277136\pi$
$390$	−12.2552	+	1.49274i	−0.620568	+	0.0755878i
$391$	1.42962	+	2.47617i	0.0722989	+	0.125225i
$392$	12.0953	+	10.2541i	0.610906	+	0.517909i
$393$	−22.4426	−	29.8422i	−1.13208	−	1.50534i
$394$	−11.1331	−	19.2831i	−0.560876	−	0.971467i
$395$	2.55562	+	4.42647i	0.128587	+	0.222720i
$396$	2.67514	+	2.78092i	0.134431	+	0.139747i
$397$	1.83289	−	3.17467i	0.0919904	−	0.159332i	−0.816358	−	0.577546i	$-0.804010\pi$
$397$	1.83289	−	3.17467i	0.0919904	−	0.159332i	0.908349	+	0.418214i	$0.137344\pi$
$398$	−15.0843	+	26.1267i	−0.756107	+	1.30962i
$399$	1.47842	+	0.346774i	0.0740136	+	0.0173604i
$400$	2.41731	+	4.18690i	0.120865	+	0.209345i
$401$	32.7873			1.63732			0.818659	−	0.574280i	$-0.194718\pi$
$401$	32.7873			1.63732			0.818659	+	0.574280i	$0.194718\pi$
$402$	−22.1684	−	29.4777i	−1.10566	−	1.47021i
$403$	−43.1733			−2.15062
$404$	2.30128	−	3.98594i	0.114493	−	0.198308i
$405$	7.61395	+	4.79873i	0.378340	+	0.238451i
$406$	−15.9708	−	5.85876i	−0.792618	−	0.290766i
$407$	2.38242	−	4.12647i	0.118092	−	0.204542i
$408$	2.31298	−	5.43444i	0.114510	−	0.269045i
$409$	17.0763	−	29.5769i	0.844367	−	1.46249i	−0.0418034	−	0.999126i	$-0.513310\pi$
$409$	17.0763	−	29.5769i	0.844367	−	1.46249i	0.886170	−	0.463360i	$-0.153356\pi$
$410$	−5.54349	+	9.60161i	−0.273774	+	0.474190i
$411$	−1.86837	−	2.48440i	−0.0921599	−	0.122546i
$412$	3.72837	−	6.45772i	0.183683	−	0.318149i
$413$	−15.3894	+	12.8469i	−0.757261	+	0.632155i
$414$	8.90815	−	2.20278i	0.437812	−	0.108261i
$415$	−2.99740	+	5.19164i	−0.147136	+	0.254848i
$416$	14.4073			0.706378
$417$	−4.14863	+	9.74738i	−0.203159	+	0.477331i
$418$	−1.15685			−0.0565835
$419$	11.9929	+	20.7724i	0.585894	+	1.01480i	0.994763	+	0.102205i	$0.0325897\pi$
$419$	11.9929	+	20.7724i	0.585894	+	1.01480i	−0.408870	+	0.912593i	$0.634077\pi$
$420$	2.64712	+	0.620902i	0.129166	+	0.0302969i
$421$	−6.78545	+	11.7527i	−0.330703	+	0.572794i	−0.982650	−	0.185471i	$-0.940619\pi$
$421$	−6.78545	+	11.7527i	−0.330703	+	0.572794i	0.651947	+	0.758264i	$0.273952\pi$
$422$	−20.7362	+	35.9161i	−1.00942	+	1.74837i
$423$	−5.29143	+	1.30845i	−0.257278	+	0.0636189i
$424$	3.00462	+	5.20415i	0.145917	+	0.252736i
$425$	−0.752653	−	1.30363i	−0.0365090	−	0.0632355i
$426$	−16.3119	+	38.3254i	−0.790312	+	1.85687i
$427$	2.20547	+	12.6958i	0.106730	+	0.614393i
$428$	−0.450047	−	0.779504i	−0.0217538	−	0.0376787i
$429$	−6.50859	+	15.2922i	−0.314238	+	0.738314i
$430$	−19.8530			−0.957395
$431$	4.73995	+	8.20983i	0.228315	+	0.395454i	0.957309	−	0.289067i	$-0.0933450\pi$
$431$	4.73995	+	8.20983i	0.228315	+	0.395454i	−0.728994	+	0.684520i	$0.760012\pi$
$432$	−19.4771	−	15.8659i	−0.937093	−	0.763350i
$433$	4.53611			0.217991			0.108996	−	0.994042i	$-0.465237\pi$
$433$	4.53611			0.217991			0.108996	+	0.994042i	$0.465237\pi$
$434$	39.0163	+	14.3128i	1.87284	+	0.687038i
$435$	6.86481	−	0.836162i	0.329142	−	0.0400909i
$436$	−9.45056			−0.452600
$437$	−0.314712	+	0.545097i	−0.0150547	+	0.0260755i
$438$	29.4401	−	3.58593i	1.40670	−	0.171342i
$439$	−8.81764	−	15.2726i	−0.420843	−	0.728921i	0.575179	−	0.818027i	$-0.304932\pi$
$439$	−8.81764	−	15.2726i	−0.420843	−	0.728921i	−0.996022	+	0.0891062i	$0.971599\pi$
$440$	4.91080			0.234113
$441$	−17.4915	+	11.6209i	−0.832931	+	0.553377i
$442$	−10.7296			−0.510356
$443$	−18.7328	−	32.4461i	−0.890020	−	1.54156i	−0.839850	−	0.542819i	$-0.817357\pi$
$443$	−18.7328	−	32.4461i	−0.890020	−	1.54156i	−0.0501704	−	0.998741i	$-0.515976\pi$
$444$	0.884580	−	2.07836i	0.0419803	−	0.0986344i
$445$	2.99220	−	5.18265i	0.141844	−	0.245681i
$446$	−6.00230			−0.284217
$447$	14.8799	+	19.7861i	0.703797	+	0.935850i
$448$	10.9972	+	4.03424i	0.519570	+	0.190600i
$449$	20.2196			0.954224			0.477112	−	0.878842i	$-0.341684\pi$
$449$	20.2196			0.954224			0.477112	+	0.878842i	$0.341684\pi$
$450$	−4.68989	+	1.15970i	−0.221083	+	0.0546688i
$451$	7.46252	+	12.9255i	0.351396	+	0.608636i
$452$	−0.676565			−0.0318229
$453$	−0.430676	−	0.572677i	−0.0202349	−	0.0269067i
$454$	−22.5475	−	39.0534i	−1.05821	−	1.83287i
$455$	2.00430	+	11.5378i	0.0939632	+	0.540901i
$456$	1.29063	−	0.157204i	0.0604394	−	0.00736177i
$457$	−11.7130	−	20.2876i	−0.547912	−	0.949012i	−0.998417	−	0.0562378i	$-0.982089\pi$
$457$	−11.7130	−	20.2876i	−0.547912	−	0.949012i	0.450505	−	0.892774i	$-0.351244\pi$
$458$	6.70288	+	11.6097i	0.313205	+	0.542487i
$459$	6.06439	+	4.94001i	0.283061	+	0.230580i
$460$	−0.563494	+	0.976001i	−0.0262731	+	0.0455063i
$461$	−11.7643	+	20.3763i	−0.547916	+	0.949019i	0.450501	+	0.892776i	$0.351245\pi$
$461$	−11.7643	+	20.3763i	−0.547916	+	0.949019i	−0.998417	+	0.0562429i	$0.982088\pi$
$462$	10.9516	−	11.6620i	0.509513	−	0.542567i
$463$	7.26578	+	12.5847i	0.337669	+	0.584861i	0.983994	−	0.178202i	$-0.0570281\pi$
$463$	7.26578	+	12.5847i	0.337669	+	0.584861i	−0.646325	+	0.763063i	$0.723695\pi$
$464$	−19.3031			−0.896125
$465$	−16.7706	+	2.04272i	−0.777716	+	0.0947291i
$466$	5.11895			0.237131
$467$	1.15245	−	1.99611i	0.0533292	−	0.0923689i	−0.838128	−	0.545473i	$-0.816350\pi$
$467$	1.15245	−	1.99611i	0.0533292	−	0.0923689i	0.891458	+	0.453104i	$0.149683\pi$
$468$	−2.18625	+	7.56914i	−0.101059	+	0.349884i
$469$	−26.8574	+	22.4203i	−1.24016	+	1.03527i
$470$	1.46298	−	2.53395i	0.0674821	−	0.116882i
$471$	−6.78513	+	0.826458i	−0.312643	+	0.0380812i
$472$	−8.58200	+	14.8645i	−0.395019	+	0.684192i
$473$	−13.3628	+	23.1451i	−0.614423	+	1.06421i
$474$	14.1520	−	1.72377i	0.650024	−	0.0791756i
$475$	0.165687	−	0.286978i	0.00760224	−	0.0131675i
$476$	2.21846	+	0.813825i	0.101683	+	0.0373016i
$477$	−7.72557	+	1.91036i	−0.353730	+	0.0874692i
$478$	−6.77010	+	11.7262i	−0.309657	+	0.536342i
$479$	7.65132			0.349598			0.174799	−	0.984604i	$-0.444073\pi$
$479$	7.65132			0.349598			0.174799	+	0.984604i	$0.444073\pi$
$480$	5.59649	−	0.681676i	0.255444	−	0.0311141i
$481$	9.72855			0.443584
$482$	18.0752	+	31.3072i	0.823304	+	1.42600i
$483$	−2.51575	−	8.33284i	−0.114471	−	0.379157i
$484$	1.86910	−	3.23737i	0.0849589	−	0.147153i
$485$	−3.11237	+	5.39079i	−0.141326	+	0.244783i
$486$	20.6328	−	14.2992i	0.935921	−	0.648625i
$487$	9.17052	+	15.8838i	0.415556	+	0.719764i	0.995487	−	0.0949017i	$-0.0302537\pi$
$487$	9.17052	+	15.8838i	0.415556	+	0.719764i	−0.579931	+	0.814666i	$0.696920\pi$
$488$	5.51644	+	9.55476i	0.249718	+	0.432524i
$489$	−25.8898	+	3.15349i	−1.17078	+	0.142606i
$490$	2.01370	−	11.0913i	0.0909698	−	0.501056i
$491$	−9.66801	−	16.7455i	−0.436311	−	0.755713i	0.561091	−	0.827754i	$-0.310382\pi$
$491$	−9.66801	−	16.7455i	−0.436311	−	0.755713i	−0.997402	+	0.0720414i	$0.977049\pi$
$492$	4.25251	+	5.65463i	0.191718	+	0.254930i
$493$	6.01022			0.270687
$494$	−1.18099	−	2.04554i	−0.0531354	−	0.0920332i
$495$	−1.80470	+	6.24816i	−0.0811153	+	0.280834i
$496$	47.1571			2.11742
$497$	37.0922	+	13.6070i	1.66381	+	0.610355i
$498$	10.0501	+	13.3637i	0.450354	+	0.598843i
$499$	3.88879			0.174086			0.0870430	−	0.996205i	$-0.472258\pi$
$499$	3.88879			0.174086			0.0870430	+	0.996205i	$0.472258\pi$
$500$	0.296664	−	0.513837i	0.0132672	−	0.0229795i
$501$	6.49002	−	15.2486i	0.289953	−	0.681255i
$502$	24.2450	+	41.9936i	1.08211	+	1.87427i
$503$	22.2956			0.994111			0.497055	−	0.867719i	$-0.334415\pi$
$503$	22.2956			0.994111			0.497055	+	0.867719i	$0.334415\pi$
$504$	−10.6333	+	14.4989i	−0.473644	+	0.645831i
$505$	7.75721			0.345191
$506$	3.31554	+	5.74269i	0.147394	+	0.255294i
$507$	−11.3326	+	1.38035i	−0.503297	+	0.0613036i
$508$	5.23302	−	9.06386i	0.232178	−	0.402144i
$509$	−10.1696			−0.450758			−0.225379	−	0.974271i	$-0.572362\pi$
$509$	−10.1696			−0.450758			−0.225379	+	0.974271i	$0.572362\pi$
$510$	−4.16789	+	0.507666i	−0.184557	+	0.0224798i
$511$	−4.81483	−	27.7167i	−0.212996	−	1.22611i
$512$	6.16675			0.272534
$513$	−0.274287	+	1.69988i	−0.0121101	+	0.0750516i
$514$	16.2181	+	28.0906i	0.715351	+	1.23902i
$515$	12.5677			0.553797
$516$	−4.96154	+	11.6573i	−0.218420	+	0.513186i
$517$	−1.96943	−	3.41115i	−0.0866153	−	0.150022i
$518$	−8.79182	−	3.22521i	−0.386290	−	0.141708i
$519$	−11.6376	+	27.3430i	−0.510835	+	1.20023i
$520$	5.01328	+	8.68326i	0.219847	+	0.380786i
$521$	11.5067	+	19.9301i	0.504117	+	0.873156i	0.999989	+	0.00475997i	$0.00151515\pi$
$521$	11.5067	+	19.9301i	0.504117	+	0.873156i	−0.495872	+	0.868396i	$0.665152\pi$
$522$	5.35265	−	18.5317i	0.234279	−	0.811111i
$523$	7.30479	−	12.6523i	0.319416	−	0.553245i	−0.660950	−	0.750430i	$-0.729847\pi$
$523$	7.30479	−	12.6523i	0.319416	−	0.553245i	0.980366	+	0.197185i	$0.0631799\pi$
$524$	6.39544	−	11.0772i	0.279386	−	0.483911i
$525$	1.32447	+	4.38700i	0.0578047	+	0.191464i
$526$	−4.76097	−	8.24625i	−0.207588	−	0.359554i
$527$	−14.6828			−0.639594
$528$	7.10916	−	16.7033i	0.309387	−	0.726916i
$529$	−19.3921			−0.843136
$530$	2.13597	−	3.69961i	0.0927807	−	0.160701i
$531$	−15.7586	−	16.3818i	−0.683867	−	0.710908i
$532$	0.0890318	+	0.512514i	0.00386002	+	0.0222203i
$533$	−15.2365	+	26.3904i	−0.659966	+	1.14310i
$534$	−10.0327	−	13.3406i	−0.434156	−	0.577303i
$535$	0.758514	−	1.31378i	0.0327934	−	0.0567998i
$536$	−14.9772	+	25.9413i	−0.646918	+	1.12049i
$537$	16.5421	−	38.8662i	0.713843	−	1.67720i
$538$	−16.5873	+	28.7301i	−0.715130	+	1.23864i
$539$	−11.5752	−	9.81308i	−0.498577	−	0.422679i
$540$	−0.491112	+	3.04365i	−0.0211341	+	0.130978i
$541$	−2.67729	+	4.63720i	−0.115106	+	0.199369i	−0.917822	−	0.396992i	$-0.870054\pi$
$541$	−2.67729	+	4.63720i	−0.115106	+	0.199369i	0.802716	+	0.596361i	$0.203387\pi$
$542$	−41.2610			−1.77231
$543$	2.16994	+	2.88540i	0.0931209	+	0.123824i
$544$	4.89980			0.210077
$545$	−7.96403	−	13.7941i	−0.341142	−	0.590875i
$546$	31.8009	+	7.45912i	1.36095	+	0.319221i
$547$	1.00726	−	1.74463i	0.0430675	−	0.0745951i	−0.843688	−	0.536834i	$-0.819620\pi$
$547$	1.00726	−	1.74463i	0.0430675	−	0.0745951i	0.886756	+	0.462239i	$0.152954\pi$
$548$	0.532428	−	0.922192i	0.0227442	−	0.0393941i
$549$	−14.1841	+	3.50740i	−0.605362	+	0.149692i
$550$	−1.74554	−	3.02336i	−0.0744300	−	0.128917i
$551$	0.661537	+	1.14581i	0.0281824	+	0.0488134i
$552$	−4.47933	−	5.95624i	−0.190653	−	0.253514i
$553$	−2.31451	−	13.3236i	−0.0984231	−	0.566575i
$554$	9.79960	+	16.9734i	0.416345	+	0.721131i
$555$	3.77903	−	0.460301i	0.160411	−	0.0195387i
$556$	−3.62889			−0.153899
$557$	1.51801	+	2.62927i	0.0643201	+	0.111406i	0.896392	−	0.443262i	$-0.146179\pi$
$557$	1.51801	+	2.62927i	0.0643201	+	0.111406i	−0.832072	+	0.554668i	$0.812845\pi$
$558$	−13.0764	+	45.2726i	−0.553568	+	1.91654i
$559$	−54.5667			−2.30792
$560$	−2.18925	−	12.6025i	−0.0925126	−	0.532551i
$561$	−2.21351	+	5.20073i	−0.0934544	+	0.219575i
$562$	6.44480			0.271858
$563$	15.3868	−	26.6507i	0.648475	−	1.12319i	−0.335012	−	0.942214i	$-0.608740\pi$
$563$	15.3868	−	26.6507i	0.648475	−	1.12319i	0.983487	−	0.180978i	$-0.0579263\pi$
$564$	−1.12228	−	1.49231i	−0.0472563	−	0.0628375i
$565$	−0.570145	−	0.987520i	−0.0239862	−	0.0415453i
$566$	−7.63313			−0.320844
$567$	−14.5396	−	18.8573i	−0.610608	−	0.791933i
$568$	33.8276			1.41937
$569$	−6.93719	−	12.0156i	−0.290822	−	0.503719i	0.683182	−	0.730248i	$-0.260595\pi$
$569$	−6.93719	−	12.0156i	−0.290822	−	0.503719i	−0.974004	+	0.226529i	$0.927262\pi$
$570$	−0.555537	−	0.738707i	−0.0232689	−	0.0309410i
$571$	20.1657	−	34.9280i	0.843908	−	1.46169i	−0.0426576	−	0.999090i	$-0.513582\pi$
$571$	20.1657	−	34.9280i	0.843908	−	1.46169i	0.886566	−	0.462602i	$-0.153084\pi$
$572$	−5.69319			−0.238044
$573$	8.20518	−	19.2784i	0.342776	−	0.805367i
$574$	22.5184	−	18.7982i	0.939899	−	0.784620i
$575$	−1.89944			−0.0792120
$576$	−3.68574	+	12.7606i	−0.153573	+	0.531692i
$577$	6.11697	+	10.5949i	0.254653	+	0.441072i	0.964801	−	0.262980i	$-0.0847054\pi$
$577$	6.11697	+	10.5949i	0.254653	+	0.441072i	−0.710148	+	0.704052i	$0.751372\pi$
$578$	23.7274			0.986932
$579$	5.79810	−	0.706233i	0.240961	−	0.0293500i
$580$	1.18449	+	2.05159i	0.0491831	+	0.0851876i
$581$	12.1758	−	10.1643i	0.505138	−	0.421685i
$582$	10.4356	+	13.8764i	0.432569	+	0.575193i
$583$	−2.87540	−	4.98034i	−0.119087	−	0.206264i
$584$	−12.0432	−	20.8594i	−0.498349	−	0.863166i
$585$	−12.8903	+	3.18748i	−0.532950	+	0.131786i
$586$	19.5315	−	33.8295i	0.806837	−	1.39748i
$587$	−10.1698	+	17.6146i	−0.419753	+	0.727034i	−0.995914	−	0.0903021i	$-0.971217\pi$
$587$	−10.1698	+	17.6146i	−0.419753	+	0.727034i	0.576161	+	0.817336i	$0.304550\pi$
$588$	−6.00941	−	3.95430i	−0.247824	−	0.163073i
$589$	−1.61612	−	2.79920i	−0.0665910	−	0.115339i
$590$	12.2018			0.502342
$591$	−14.3941	−	19.1400i	−0.592092	−	0.787314i
$592$	−10.6262			−0.436736
$593$	6.17555	−	10.6964i	0.253599	−	0.439247i	−0.710915	−	0.703278i	$-0.751719\pi$
$593$	6.17555	−	10.6964i	0.253599	−	0.439247i	0.964514	+	0.264031i	$0.0850522\pi$
$594$	14.0644	+	11.4568i	0.577070	+	0.470078i
$595$	0.681644	+	3.92390i	0.0279447	+	0.160864i
$596$	−4.24033	+	7.34446i	−0.173691	+	0.300841i
$597$	−12.7073	+	29.8562i	−0.520073	+	1.22193i
$598$	−6.76947	+	11.7251i	−0.276824	+	0.479473i
$599$	−6.27154	+	10.8626i	−0.256248	+	0.443835i	−0.965234	−	0.261388i	$-0.915820\pi$
$599$	−6.27154	+	10.8626i	−0.256248	+	0.443835i	0.708986	+	0.705223i	$0.249153\pi$
$600$	2.35824	+	3.13579i	0.0962748	+	0.128018i
$601$	−3.00706	+	5.20838i	−0.122661	+	0.212454i	−0.920816	−	0.389997i	$-0.872476\pi$
$601$	−3.00706	+	5.20838i	−0.122661	+	0.212454i	0.798155	+	0.602452i	$0.205809\pi$
$602$	49.3127	+	18.0900i	2.00983	+	0.737291i
$603$	−27.5018	−	28.5893i	−1.11996	−	1.16425i
$604$	0.122730	−	0.212574i	0.00499379	−	0.00864950i
$605$	6.30039			0.256147
$606$	8.47344	−	19.9087i	0.344210	−	0.808735i
$607$	−22.0220			−0.893846			−0.446923	−	0.894573i	$-0.647480\pi$
$607$	−22.0220			−0.893846			−0.446923	+	0.894573i	$0.647480\pi$
$608$	0.539314	+	0.934119i	0.0218721	+	0.0378835i
$609$	−17.8133	−	4.17825i	−0.721833	−	0.169311i
$610$	3.92163	−	6.79246i	0.158782	−	0.275018i
$611$	4.02105	−	6.96467i	0.162674	−	0.281760i
$612$	−0.743522	+	2.57419i	−0.0300551	+	0.104055i
$613$	−1.51893	−	2.63087i	−0.0613491	−	0.106260i	0.833720	−	0.552188i	$-0.186207\pi$
$613$	−1.51893	−	2.63087i	−0.0613491	−	0.106260i	−0.895069	+	0.445928i	$0.852874\pi$
$614$	−7.34006	−	12.7134i	−0.296221	−	0.513069i
$615$	−4.66993	+	10.9722i	−0.188310	+	0.442441i
$616$	−12.1979	−	4.47470i	−0.491468	−	0.180291i
$617$	−17.4520	−	30.2277i	−0.702590	−	1.21692i	−0.967554	−	0.252664i	$-0.918693\pi$
$617$	−17.4520	−	30.2277i	−0.702590	−	1.21692i	0.264964	−	0.964258i	$-0.414640\pi$
$618$	13.7280	−	32.2546i	0.552223	−	1.29747i
$619$	−16.6709			−0.670060			−0.335030	−	0.942207i	$-0.608746\pi$
$619$	−16.6709			−0.670060			−0.335030	+	0.942207i	$0.608746\pi$
$620$	−2.89367	−	5.01199i	−0.116213	−	0.201286i
$621$	9.22443	−	3.51029i	0.370164	−	0.140863i
$622$	−22.2248			−0.891133
$623$	−12.1547	+	10.1467i	−0.486969	+	0.406517i
$624$	36.7922	−	4.48144i	1.47287	−	0.179401i
$625$	1.00000			0.0400000
$626$	6.34660	−	10.9926i	0.253661	−	0.439354i
$627$	−1.23513	+	0.150444i	−0.0493262	+	0.00600814i
$628$	−1.17074	−	2.02778i	−0.0467176	−	0.0809172i
$629$	3.30858			0.131922
$630$	12.7059	+	1.39283i	0.506215	+	0.0554918i
$631$	−24.1920			−0.963068			−0.481534	−	0.876427i	$-0.659920\pi$
$631$	−24.1920			−0.963068			−0.481534	+	0.876427i	$0.659920\pi$
$632$	−5.78920	−	10.0272i	−0.230282	−	0.398860i
$633$	−17.4685	+	41.0429i	−0.694310	+	1.63131i
$634$	10.2301	−	17.7191i	0.406290	−	0.703716i
$635$	17.6396			0.700005
$636$	−1.63854	−	2.17880i	−0.0649725	−	0.0863949i
$637$	5.53474	−	30.4850i	0.219294	−	1.20786i
$638$	13.9388			0.551842
$639$	−12.4315	+	43.0398i	−0.491783	+	1.70263i
$640$	−6.81993	−	11.8125i	−0.269581	−	0.466929i
$641$	−12.8188			−0.506314			−0.253157	−	0.967425i	$-0.581469\pi$
$641$	−12.8188			−0.506314			−0.253157	+	0.967425i	$0.581469\pi$
$642$	−2.54325	−	3.38179i	−0.100374	−	0.133469i
$643$	−6.83164	−	11.8327i	−0.269414	−	0.466638i	0.699297	−	0.714831i	$-0.253497\pi$
$643$	−6.83164	−	11.8327i	−0.269414	−	0.466638i	−0.968711	+	0.248193i	$0.920163\pi$
$644$	2.28899	−	1.91083i	0.0901987	−	0.0752971i
$645$	−21.1963	+	2.58179i	−0.834603	+	0.101658i
$646$	−0.401644	−	0.695668i	−0.0158025	−	0.0273707i
$647$	−14.3903	−	24.9247i	−0.565740	−	0.979890i	−0.996980	−	0.0776530i	$-0.975257\pi$
$647$	−14.3903	−	24.9247i	−0.565740	−	0.979890i	0.431241	−	0.902237i	$-0.358076\pi$
$648$	−17.2477	−	10.8705i	−0.677554	−	0.427032i
$649$	8.21292	−	14.2252i	0.322385	−	0.558388i
$650$	3.56393	−	6.17291i	0.139789	−	0.242121i
$651$	43.5176	+	10.2074i	1.70559	+	0.400058i
$652$	−4.46716	−	7.73734i	−0.174947	−	0.303018i
$653$	−22.9272			−0.897212			−0.448606	−	0.893730i	$-0.648079\pi$
$653$	−22.9272			−0.897212			−0.448606	+	0.893730i	$0.648079\pi$
$654$	−44.1016	+	5.37176i	−1.72451	+	0.210052i
$655$	21.5579			0.842336
$656$	16.6424	−	28.8255i	0.649778	−	1.12545i
$657$	30.9658	−	7.65713i	1.20809	−	0.298733i
$658$	−5.94280	+	4.96100i	−0.231675	+	0.193400i
$659$	18.0569	−	31.2755i	0.703399	−	1.21832i	−0.263868	−	0.964559i	$-0.584998\pi$
$659$	18.0569	−	31.2755i	0.703399	−	1.21832i	0.967266	−	0.253763i	$-0.0816684\pi$
$660$	−2.21150	+	0.269371i	−0.0860827	+	0.0104852i
$661$	−8.55839	+	14.8236i	−0.332883	+	0.576570i	−0.983076	−	0.183199i	$-0.941355\pi$
$661$	−8.55839	+	14.8236i	−0.332883	+	0.576570i	0.650193	+	0.759769i	$0.274688\pi$
$662$	4.23127	−	7.32877i	0.164453	−	0.284841i
$663$	−11.4556	+	1.39534i	−0.444899	+	0.0541905i
$664$	6.78994	−	11.7605i	0.263501	−	0.456396i
$665$	−0.673042	+	0.561850i	−0.0260994	+	0.0217876i
$666$	2.94660	−	10.2016i	0.114178	−	0.395303i
$667$	3.79193	−	6.56782i	0.146824	−	0.254307i
$668$	5.67694			0.219648
$669$	−6.40843	+	0.780573i	−0.247764	+	0.0301787i
$670$	21.2945			0.822680
$671$	−5.27920	−	9.14385i	−0.203801	−	0.352994i
$672$	−14.5222	−	3.40629i	−0.560207	−	0.131401i
$673$	3.85331	−	6.67413i	0.148534	−	0.257269i	−0.782152	−	0.623088i	$-0.785878\pi$
$673$	3.85331	−	6.67413i	0.148534	−	0.257269i	0.930686	+	0.365819i	$0.119211\pi$
$674$	−11.8189	+	20.4710i	−0.455248	+	0.788513i
$675$	−4.85640	+	1.84807i	−0.186923	+	0.0711322i
$676$	−1.95537	−	3.38681i	−0.0752067	−	0.130262i
$677$	−2.37556	−	4.11459i	−0.0913001	−	0.158136i	0.816758	−	0.576980i	$-0.195769\pi$
$677$	−2.37556	−	4.11459i	−0.0913001	−	0.158136i	−0.908058	+	0.418843i	$0.862436\pi$
$678$	−3.15723	+	0.384564i	−0.121253	+	0.0147691i
$679$	12.6429	−	10.5542i	0.485189	−	0.405031i
$680$	1.70497	+	2.95309i	0.0653826	+	0.113246i
$681$	−29.1518	−	38.7636i	−1.11710	−	1.48543i
$682$	−34.0522			−1.30392
$683$	−14.9574	−	25.9070i	−0.572329	−	0.991302i	−0.996326	−	0.0856390i	$-0.972707\pi$
$683$	−14.9574	−	25.9070i	−0.572329	−	0.991302i	0.423998	−	0.905663i	$-0.360626\pi$
$684$	−0.572593	+	0.141589i	−0.0218937	+	0.00541380i
$685$	1.79472			0.0685727
$686$	−15.1082	+	25.7148i	−0.576834	+	0.981797i
$687$	8.66621	+	11.5236i	0.330636	+	0.439652i
$688$	59.6018			2.27230
$689$	5.87081	−	10.1685i	0.223660	−	0.387390i
$690$	−2.07482	+	4.87486i	−0.0789869	+	0.185583i
$691$	−10.5506	−	18.2741i	−0.401362	−	0.695179i	0.592529	−	0.805549i	$-0.298130\pi$
$691$	−10.5506	−	18.2741i	−0.401362	−	0.695179i	−0.993891	+	0.110370i	$0.964796\pi$
$692$	−10.1797			−0.386972
$693$	10.1760	−	13.8753i	0.386554	−	0.527080i
$694$	49.2536			1.86964
$695$	−3.05809	−	5.29676i	−0.116000	−	0.200918i
$696$	−15.5507	+	1.89414i	−0.589448	+	0.0717972i
$697$	−5.18179	+	8.97512i	−0.196274	+	0.339957i
$698$	−33.9517			−1.28509
$699$	5.46531	−	0.665698i	0.206717	−	0.0251790i
$700$	−1.20509	+	1.00600i	−0.0455480	+	0.0380231i
$701$	−2.33628			−0.0882402			−0.0441201	−	0.999026i	$-0.514048\pi$
$701$	−2.33628			−0.0882402			−0.0441201	+	0.999026i	$0.514048\pi$
$702$	−5.89992	+	36.5645i	−0.222678	+	1.38004i
$703$	0.364171	+	0.630763i	0.0137350	+	0.0237897i
$704$	−9.59801			−0.361739
$705$	1.23244	−	2.89566i	0.0464162	−	0.109057i
$706$	−6.27017	−	10.8603i	−0.235981	−	0.408731i
$707$	−19.2681	−	7.06834i	−0.724650	−	0.265832i
$708$	3.04942	−	7.16473i	0.114604	−	0.269267i
$709$	11.3318	+	19.6272i	0.425574	+	0.737116i	0.996474	−	0.0839035i	$-0.0267388\pi$
$709$	11.3318	+	19.6272i	0.425574	+	0.737116i	−0.570900	+	0.821020i	$0.693405\pi$
$710$	−12.0240	−	20.8261i	−0.451252	−	0.781591i
$711$	14.8854	−	3.68082i	0.558246	−	0.138042i
$712$	−6.77818	+	11.7401i	−0.254023	+	0.439981i
$713$	−9.26361	+	16.0450i	−0.346925	+	0.600891i
$714$	10.8152	+	2.53677i	0.404748	+	0.0949364i
$715$	−4.79768	−	8.30983i	−0.179423	−	0.310770i
$716$	14.4697			0.540757
$717$	−5.70324	+	13.4000i	−0.212991	+	0.500432i
$718$	27.4585			1.02474
$719$	0.849707	−	1.47173i	0.0316887	−	0.0548865i	−0.849746	−	0.527192i	$-0.823245\pi$
$719$	0.849707	−	1.47173i	0.0316887	−	0.0548865i	0.881435	+	0.472306i	$0.156578\pi$
$720$	14.0798	−	3.48161i	0.524722	−	0.129752i
$721$	−31.2167	−	11.4516i	−1.16257	−	0.426480i
$722$	−15.2102	+	26.3448i	−0.566065	+	0.980454i
$723$	23.3696	+	31.0749i	0.869125	+	1.15569i
$724$	−0.618365	+	1.07104i	−0.0229814	+	0.0398049i
$725$	−1.99635	+	3.45777i	−0.0741424	+	0.128418i
$726$	6.88211	−	16.1698i	0.255419	−	0.600117i
$727$	10.4857	−	18.1617i	0.388891	−	0.673580i	−0.603409	−	0.797432i	$-0.706191\pi$
$727$	10.4857	−	18.1617i	0.388891	−	0.673580i	0.992301	+	0.123852i	$0.0395248\pi$
$728$	−4.54031	−	26.1364i	−0.168275	−	0.968679i
$729$	20.1693	−	17.9499i	0.747010	−	0.664812i
$730$	−8.56145	+	14.8289i	−0.316873	+	0.548841i
$731$	−18.5576			−0.686377
$732$	−3.00835	−	4.00025i	−0.111192	−	0.147853i
$733$	44.5545			1.64566			0.822828	−	0.568290i	$-0.192395\pi$
$733$	44.5545			1.64566			0.822828	+	0.568290i	$0.192395\pi$
$734$	12.9282	+	22.3923i	0.477190	+	0.826517i
$735$	0.707572	−	12.1037i	0.0260992	−	0.446451i
$736$	3.09135	−	5.35438i	0.113949	−	0.197365i
$737$	14.3331	−	24.8257i	0.527967	−	0.914466i
$738$	23.0587	+	23.9705i	0.848804	+	0.882367i
$739$	3.97950	+	6.89270i	0.146388	+	0.253552i	0.929890	−	0.367838i	$-0.119902\pi$
$739$	3.97950	+	6.89270i	0.146388	+	0.253552i	−0.783502	+	0.621390i	$0.786568\pi$
$740$	0.652051	+	1.12939i	0.0239699	+	0.0415170i
$741$	−1.52692	−	2.03036i	−0.0560927	−	0.0745873i
$742$	−8.67660	+	7.24315i	−0.318528	+	0.265905i
$743$	23.7220	+	41.0877i	0.870275	+	1.50736i	0.861713	+	0.507396i	$0.169392\pi$
$743$	23.7220	+	41.0877i	0.870275	+	1.50736i	0.00856172	+	0.999963i	$0.497275\pi$
$744$	37.9900	−	4.62734i	1.39278	−	0.169647i
$745$	−14.2934			−0.523669
$746$	−9.49885	−	16.4525i	−0.347778	−	0.602368i
$747$	12.4680	+	12.9610i	0.456179	+	0.474218i
$748$	−1.93620			−0.0707944
$749$	−3.08118	+	2.57214i	−0.112584	+	0.0939841i
$750$	1.09233	−	2.56648i	0.0398863	−	0.0937144i
$751$	−14.4200			−0.526194			−0.263097	−	0.964769i	$-0.584744\pi$
$751$	−14.4200			−0.526194			−0.263097	+	0.964769i	$0.584744\pi$
$752$	−4.39209	+	7.60732i	−0.160163	+	0.277410i
$753$	31.3466	+	41.6821i	1.14233	+	1.51898i
$754$	14.2297	+	24.6465i	0.518214	+	0.897573i
$755$	0.413699			0.0150561
$756$	3.99323	−	7.11260i	0.145233	−	0.258683i
$757$	24.9373			0.906361			0.453181	−	0.891419i	$-0.350289\pi$
$757$	24.9373			0.906361			0.453181	+	0.891419i	$0.350289\pi$
$758$	−23.3879	−	40.5091i	−0.849488	−	1.47136i
$759$	4.28669	+	5.70008i	0.155597	+	0.206900i
$760$	−0.375327	+	0.650086i	−0.0136145	+	0.0235811i
$761$	−17.4750			−0.633468			−0.316734	−	0.948514i	$-0.602586\pi$
$761$	−17.4750			−0.633468			−0.316734	+	0.948514i	$0.602586\pi$
$762$	19.2683	−	45.2715i	0.698015	−	1.64001i
$763$	7.21267	+	41.5199i	0.261116	+	1.50312i
$764$	7.17723			0.259663
$765$	−4.38388	+	1.08403i	−0.158499	+	0.0391933i
$766$	19.8364	+	34.3576i	0.716718	+	1.24139i
$767$	33.5373			1.21096
$768$	−22.5415	+	2.74565i	−0.813397	+	0.0990752i
$769$	17.7197	+	30.6913i	0.638987	+	1.10676i	0.985655	+	0.168770i	$0.0539795\pi$
$769$	17.7197	+	30.6913i	0.638987	+	1.10676i	−0.346669	+	0.937988i	$0.612687\pi$
$770$	1.58086	+	9.10023i	0.0569701	+	0.327950i
$771$	20.9685	+	27.8822i	0.755164	+	1.00415i
$772$	1.00043	+	1.73280i	0.0360063	+	0.0623648i
$773$	8.12332	+	14.0700i	0.292176	+	0.506063i	0.974324	−	0.225151i	$-0.0722875\pi$
$773$	8.12332	+	14.0700i	0.292176	+	0.506063i	−0.682148	+	0.731214i	$0.738954\pi$
$774$	−16.5272	+	57.2199i	−0.594059	+	2.05673i
$775$	4.87703	−	8.44726i	0.175188	−	0.303434i
$776$	7.05039	−	12.2116i	0.253094	−	0.438372i
$777$	−9.80612	−	2.30010i	−0.351793	−	0.0825155i
$778$	20.4650	+	35.4465i	0.733707	+	1.27082i
$779$	−2.28141			−0.0817399
$780$	−2.73396	−	3.63538i	−0.0978913	−	0.130168i
$781$	−32.3728			−1.15839
$782$	−2.30223	+	3.98758i	−0.0823275	+	0.142595i
$783$	3.30485	−	20.4817i	0.118106	−	0.731957i
$784$	−6.04545	+	33.2980i	−0.215909	+	1.18921i
$785$	1.97318	−	3.41764i	0.0704257	−	0.121981i
$786$	23.5483	−	55.3277i	0.839941	−	1.97347i
$787$	9.51672	−	16.4834i	0.339234	−	0.587571i	−0.645055	−	0.764136i	$-0.723165\pi$
$787$	9.51672	−	16.4834i	0.339234	−	0.587571i	0.984289	+	0.176565i	$0.0564987\pi$
$788$	4.10186	−	7.10463i	0.146123	−	0.253092i
$789$	−6.15550	−	8.18507i	−0.219142	−	0.291396i
$790$	−4.11553	+	7.12831i	−0.146424	+	0.253614i
$791$	0.516354	+	2.97241i	0.0183594	+	0.105687i
$792$	4.08815	−	14.1538i	0.145266	−	0.502935i
$793$	10.7787	−	18.6693i	0.382764	−	0.662967i
$794$	5.90332			0.209501
$795$	1.79938	−	4.22771i	0.0638174	−	0.149942i
$796$	−11.1153			−0.393971
$797$	−1.57566	−	2.72912i	−0.0558126	−	0.0966703i	0.836769	−	0.547556i	$-0.184442\pi$
$797$	−1.57566	−	2.72912i	−0.0558126	−	0.0966703i	−0.892582	+	0.450885i	$0.851108\pi$
$798$	0.706789	+	2.34107i	0.0250201	+	0.0828730i
$799$	1.36752	−	2.36861i	0.0483794	−	0.0837955i
$800$	−1.62751	+	2.81893i	−0.0575411	+	0.0996642i
$801$	−12.4464	−	12.9385i	−0.439771	−	0.457161i
$802$	26.4000	+	45.7262i	0.932217	+	1.61465i
$803$	11.5252	+	19.9623i	0.406716	+	0.704453i
$804$	5.32181	−	12.5038i	0.187686	−	0.440975i
$805$	4.71800	+	1.73076i	0.166288	+	0.0610013i
$806$	−34.7628	−	60.2109i	−1.22447	−	2.12084i
$807$	−13.9734	+	32.8311i	−0.491888	+	1.15571i
$808$	−17.5722			−0.618189
$809$	−10.6077	−	18.3730i	−0.372946	−	0.645961i	0.617071	−	0.786907i	$-0.288319\pi$
$809$	−10.6077	−	18.3730i	−0.372946	−	0.645961i	−0.990017	+	0.140946i	$0.954986\pi$
$810$	−0.561774	+	14.4825i	−0.0197387	+	0.508865i
$811$	11.4309			0.401393			0.200696	−	0.979654i	$-0.435680\pi$
$811$	11.4309			0.401393			0.200696	+	0.979654i	$0.435680\pi$
$812$	−1.07274	−	6.17523i	−0.0376456	−	0.216708i
$813$	−44.0528	+	5.36581i	−1.54500	+	0.188187i
$814$	7.67321			0.268946
$815$	7.52899	−	13.0406i	0.263729	−	0.456792i
$816$	12.5127	−	1.52409i	0.438031	−	0.0533539i
$817$	−2.04261	−	3.53790i	−0.0714618	−	0.123776i
$818$	54.9986			1.92298
$819$	34.9226	+	3.82826i	1.22030	+	0.133770i
$820$	−4.08488			−0.142650
$821$	22.3319	+	38.6800i	0.779388	+	1.34994i	0.932295	+	0.361699i	$0.117803\pi$
$821$	22.3319	+	38.6800i	0.779388	+	1.34994i	−0.152907	+	0.988241i	$0.548863\pi$
$822$	1.96043	−	4.60610i	0.0683778	−	0.160656i
$823$	−4.00611	+	6.93879i	−0.139644	+	0.241871i	−0.927362	−	0.374165i	$-0.877929\pi$
$823$	−4.00611	+	6.93879i	−0.139644	+	0.241871i	0.787718	+	0.616036i	$0.211263\pi$
$824$	−28.4692			−0.991773
$825$	−2.25682	−	3.00093i	−0.0785725	−	0.104479i
$826$	−30.3081	−	11.1183i	−1.05455	−	0.386854i
$827$	−31.4963			−1.09523			−0.547617	−	0.836729i	$-0.684465\pi$
$827$	−31.4963			−1.09523			−0.547617	+	0.836729i	$0.684465\pi$
$828$	2.34391	+	2.43660i	0.0814566	+	0.0846775i
$829$	−7.67081	−	13.2862i	−0.266418	−	0.461450i	0.701516	−	0.712654i	$-0.252507\pi$
$829$	−7.67081	−	13.2862i	−0.266418	−	0.461450i	−0.967934	+	0.251204i	$0.919174\pi$
$830$	−9.65390			−0.335092
$831$	12.6700	+	16.8475i	0.439517	+	0.584432i
$832$	−9.79830	−	16.9712i	−0.339695	−	0.588369i
$833$	1.88231	−	10.3677i	0.0652182	−	0.359218i
$834$	−16.9344	+	2.06269i	−0.586392	+	0.0714250i
$835$	4.78399	+	8.28611i	0.165557	+	0.286753i
$836$	−0.213115	−	0.369126i	−0.00737073	−	0.0127665i
$837$	−8.07368	+	50.0364i	−0.279067	+	1.72951i
$838$	−19.3132	+	33.4515i	−0.667164	+	1.15556i
$839$	−9.33924	+	16.1760i	−0.322426	+	0.558459i	−0.980988	−	0.194068i	$-0.937832\pi$
$839$	−9.33924	+	16.1760i	−0.322426	+	0.558459i	0.658562	+	0.752527i	$0.271165\pi$
$840$	−3.00030	−	9.93778i	−0.103520	−	0.342886i
$841$	6.52921	+	11.3089i	0.225145	+	0.389963i
$842$	−21.8543			−0.753150
$843$	6.88087	−	0.838119i	0.236990	−	0.0288664i
$844$	−15.2800			−0.525960
$845$	3.29561	−	5.70816i	0.113372	−	0.196367i
$846$	−6.08541	−	6.32604i	−0.209221	−	0.217494i
$847$	−15.6495	−	5.74089i	−0.537723	−	0.197259i
$848$	−6.41253	+	11.1068i	−0.220207	+	0.381410i
$849$	−8.14960	+	0.992656i	−0.279694	+	0.0340679i
$850$	1.21206	−	2.09935i	0.0415732	−	0.0720070i
$851$	2.08743	−	3.61554i	0.0715563	−	0.123939i
$852$	−15.2337	+	1.85553i	−0.521899	+	0.0635695i
$853$	−16.9041	+	29.2787i	−0.578784	+	1.00248i	0.416835	+	0.908982i	$0.363139\pi$
$853$	−16.9041	+	29.2787i	−0.578784	+	1.00248i	−0.995619	+	0.0935009i	$0.970194\pi$
$854$	−15.9302	+	13.2984i	−0.545119	+	0.455060i
$855$	−0.689192	−	0.716444i	−0.0235699	−	0.0245019i
$856$	−1.71825	+	2.97609i	−0.0587284	+	0.101721i
$857$	31.8946			1.08950			0.544749	−	0.838599i	$-0.316625\pi$
$857$	31.8946			1.08950			0.544749	+	0.838599i	$0.316625\pi$
$858$	−26.5676	+	3.23605i	−0.907004	+	0.110477i
$859$	−54.8464			−1.87133			−0.935667	−	0.352883i	$-0.885201\pi$
$859$	−54.8464			−1.87133			−0.935667	+	0.352883i	$0.885201\pi$
$860$	−3.65731	−	6.33464i	−0.124713	−	0.216009i
$861$	21.5974	−	22.9985i	0.736038	−	0.783787i
$862$	−7.63312	+	13.2210i	−0.259985	+	0.450308i
$863$	7.40110	−	12.8191i	0.251936	−	0.436367i	−0.712122	−	0.702055i	$-0.752266\pi$
$863$	7.40110	−	12.8191i	0.251936	−	0.436367i	0.964059	+	0.265689i	$0.0855993\pi$
$864$	2.69426	−	16.6976i	0.0916607	−	0.568064i
$865$	−8.57844	−	14.8583i	−0.291676	−	0.505197i
$866$	3.65243	+	6.32619i	0.124115	+	0.214973i
$867$	25.3329	−	3.08565i	0.860350	−	0.104794i
$868$	2.62067	+	15.0859i	0.0889513	+	0.512050i
$869$	5.54023	+	9.59596i	0.187940	+	0.325521i
$870$	6.69361	+	8.90060i	0.226935	+	0.301759i
$871$	58.5289			1.98318
$872$	18.0408	+	31.2475i	0.610937	+	1.05817i
$873$	12.9462	+	13.4582i	0.438164	+	0.455490i
$874$	−1.01361			−0.0342860
$875$	−2.48389	−	0.911196i	−0.0839709	−	0.0308040i
$876$	6.56764	+	8.73309i	0.221900	+	0.295064i
$877$	30.7272			1.03759			0.518793	−	0.854900i	$-0.326382\pi$
$877$	30.7272			1.03759			0.518793	+	0.854900i	$0.326382\pi$
$878$	14.1998	−	24.5947i	0.479219	−	0.830031i
$879$	16.4536	−	38.6584i	0.554967	−	1.30392i
$880$	5.24038	+	9.07661i	0.176653	+	0.305972i
$881$	−56.6033			−1.90701			−0.953507	−	0.301371i	$-0.902556\pi$
$881$	−56.6033			−1.90701			−0.953507	+	0.301371i	$0.902556\pi$
$882$	−30.2909	−	15.0372i	−1.01995	−	0.506329i
$883$	−17.4137			−0.586018			−0.293009	−	0.956110i	$-0.594657\pi$
$883$	−17.4137			−0.586018			−0.293009	+	0.956110i	$0.594657\pi$
$884$	−1.97660	−	3.42358i	−0.0664804	−	0.115147i
$885$	13.0275	−	1.58680i	0.437913	−	0.0533396i
$886$	30.1669	−	52.2506i	1.01348	−	1.75539i
$887$	−31.0546			−1.04271			−0.521356	−	0.853339i	$-0.674574\pi$
$887$	−31.0546			−1.04271			−0.521356	+	0.853339i	$0.674574\pi$
$888$	−8.56055	+	1.04271i	−0.287273	+	0.0349911i
$889$	−43.8148	−	16.0731i	−1.46950	−	0.539075i
$890$	9.63718			0.323039
$891$	16.5060	+	10.4030i	0.552971	+	0.348512i
$892$	−1.10574	−	1.91520i	−0.0370229	−	0.0641256i
$893$	0.602084			0.0201480
$894$	−15.6131	+	36.6836i	−0.522180	+	1.22688i
$895$	12.1937	+	21.1200i	0.407589	+	0.705965i
$896$	6.17650	+	35.5552i	0.206342	+	1.18782i
$897$	−5.70271	+	13.3987i	−0.190408	+	0.447371i
$898$	16.2807	+	28.1989i	0.543293	+	0.941011i
$899$	19.4725	+	33.7273i	0.649443	+	1.12487i
$900$	−1.23400	−	1.28280i	−0.0411334	−	0.0427599i
$901$	1.99660	−	3.45822i	0.0665165	−	0.115210i
$902$	−12.0175	+	20.8149i	−0.400139	+	0.693061i
$903$	55.0018	+	12.9011i	1.83035	+	0.429320i
$904$	1.29154	+	2.23701i	0.0429559	+	0.0744018i
$905$	−2.08440			−0.0692877
$906$	0.451897	−	1.06175i	0.0150133	−	0.0352742i
$907$	−45.1972			−1.50075			−0.750375	−	0.661013i	$-0.770127\pi$
$907$	−45.1972			−1.50075			−0.750375	+	0.661013i	$0.770127\pi$
$908$	8.30737	−	14.3888i	0.275690	−	0.477509i
$909$	6.45773	−	22.3577i	0.214189	−	0.741558i
$910$	−14.4772	+	12.0854i	−0.479913	+	0.400627i
$911$	19.1706	−	33.2044i	0.635149	−	1.10011i	−0.351335	−	0.936250i	$-0.614272\pi$
$911$	19.1706	−	33.2044i	0.635149	−	1.10011i	0.986484	−	0.163860i	$-0.0523946\pi$
$912$	1.66781	+	2.21771i	0.0552267	+	0.0734358i
$913$	−6.49793	+	11.2547i	−0.215050	+	0.372478i
$914$	18.8624	−	32.6707i	0.623914	−	1.08065i
$915$	3.30364	−	7.76204i	0.109215	−	0.256605i
$916$	−2.46960	+	4.27748i	−0.0815980	+	0.141332i
$917$	−53.5474	−	19.6434i	−1.76829	−	0.648684i
$918$	−2.00650	+	12.4352i	−0.0662245	+	0.410424i
$919$	25.3037	−	43.8273i	0.834693	−	1.44573i	−0.0595876	−	0.998223i	$-0.518979\pi$
$919$	25.3037	−	43.8273i	0.834693	−	1.44573i	0.894280	−	0.447507i	$-0.147688\pi$
$920$	4.30276			0.141858
$921$	−9.49002	−	12.6190i	−0.312707	−	0.415811i
$922$	−37.8899			−1.24784
$923$	−33.0484	−	57.2414i	−1.08780	−	1.88412i
$924$	5.73859	+	1.34603i	0.188786	+	0.0442810i
$925$	−1.09897	+	1.90348i	−0.0361340	+	0.0625860i
$926$	−11.7007	+	20.2662i	−0.384508	+	0.665987i
$927$	10.4623	−	36.2223i	0.343628	−	1.18970i
$928$	−6.49814	−	11.2551i	−0.213312	−	0.369467i
$929$	7.83701	+	13.5741i	0.257124	+	0.445352i	0.965470	−	0.260513i	$-0.0838918\pi$
$929$	7.83701	+	13.5741i	0.257124	+	0.445352i	−0.708346	+	0.705865i	$0.750559\pi$
$930$	−16.3523	−	21.7440i	−0.536215	−	0.713013i
$931$	2.18372	−	0.782301i	0.0715685	−	0.0256389i
$932$	0.943010	+	1.63334i	0.0308893	+	0.0535019i
$933$	−23.7286	+	2.89024i	−0.776839	+	0.0946222i
$934$	3.71178			0.121453
$935$	−1.63164	−	2.82609i	−0.0533605	−	0.0924231i
$936$	29.2002	−	7.22054i	0.954439	−	0.236011i
$937$	28.8469			0.942387			0.471193	−	0.882030i	$-0.343823\pi$
$937$	28.8469			0.942387			0.471193	+	0.882030i	$0.343823\pi$
$938$	−52.8934	−	19.4035i	−1.72703	−	0.633547i
$939$	5.34648	−	12.5618i	0.174476	−	0.409938i
$940$	1.07804			0.0351617
$941$	16.6635	−	28.8620i	0.543215	−	0.940876i	−0.455502	−	0.890235i	$-0.650540\pi$
$941$	16.6635	−	28.8620i	0.543215	−	0.940876i	0.998717	−	0.0506410i	$-0.0161264\pi$
$942$	−6.61593	−	8.79730i	−0.215559	−	0.286632i
$943$	6.53853	+	11.3251i	0.212924	+	0.368795i
$944$	−36.6319			−1.19227
$945$	13.7467	−	0.165272i	0.447181	−	0.00537629i
$946$	−43.0384			−1.39930
$947$	14.1195	+	24.4556i	0.458821	+	0.794701i	0.998899	−	0.0469138i	$-0.0149386\pi$
$947$	14.1195	+	24.4556i	0.458821	+	0.794701i	−0.540078	+	0.841615i	$0.681605\pi$
$948$	3.15710	+	4.19804i	0.102538	+	0.136346i
$949$	−23.5315	+	40.7577i	−0.763864	+	1.32305i
$950$	0.533638			0.0173135
$951$	8.61803	−	20.2484i	0.279459	−	0.656600i
$952$	−1.54411	−	8.88873i	−0.0500450	−	0.288085i
$953$	−3.08541			−0.0999463			−0.0499732	−	0.998751i	$-0.515914\pi$
$953$	−3.08541			−0.0999463			−0.0499732	+	0.998751i	$0.515914\pi$
$954$	−8.88480	−	9.23612i	−0.287656	−	0.299031i
$955$	6.04829	+	10.4759i	0.195718	+	0.338994i
$956$	−4.98874			−0.161347
$957$	14.8819	−	1.81268i	0.481064	−	0.0585956i
$958$	6.16077	+	10.6708i	0.199045	+	0.344757i
$959$	−4.45789	−	1.63534i	−0.143953	−	0.0528079i
$960$	−4.60911	−	6.12880i	−0.148758	−	0.197806i
$961$	−32.0708	−	55.5482i	−1.03454	−	1.79188i
$962$	7.83333	+	13.5677i	0.252557	+	0.437441i
$963$	−3.15512	−	3.27988i	−0.101672	−	0.105693i
$964$	−6.65962	+	11.5348i	−0.214492	+	0.371511i
$965$	−1.68614	+	2.92048i	−0.0542787	+	0.0940135i
$966$	9.59557	−	10.2181i	0.308732	−	0.328761i
$967$	0.585963	+	1.01492i	0.0188433	+	0.0326375i	0.875293	−	0.483592i	$-0.160668\pi$
$967$	0.585963	+	1.01492i	0.0188433	+	0.0326375i	−0.856450	+	0.516230i	$0.827335\pi$
$968$	−14.2721			−0.458724
$969$	−0.519289	−	0.690507i	−0.0166820	−	0.0221823i
$970$	−10.0242			−0.321858
$971$	−4.62475	+	8.01029i	−0.148415	+	0.257063i	−0.930642	−	0.365931i	$-0.880751\pi$
$971$	−4.62475	+	8.01029i	−0.148415	+	0.257063i	0.782227	+	0.622994i	$0.214084\pi$
$972$	8.36352	+	3.94926i	0.268260	+	0.126673i
$973$	2.76957	+	15.9431i	0.0887883	+	0.511112i
$974$	−14.7680	+	25.5790i	−0.473198	+	0.819604i
$975$	3.00231	−	7.05406i	0.0961510	−	0.225911i
$976$	−11.7733	+	20.3920i	−0.376855	+	0.652733i
$977$	−22.5289	+	39.0212i	−0.720763	+	1.24840i	0.239931	+	0.970790i	$0.422875\pi$
$977$	−22.5289	+	39.0212i	−0.720763	+	1.24840i	−0.960694	+	0.277609i	$0.910458\pi$
$978$	−25.2442	−	33.5676i	−0.807221	−	1.07337i
$979$	6.48667	−	11.2352i	0.207315	−	0.359080i
$980$	3.90996	−	1.40072i	0.124899	−	0.0447442i
$981$	−46.3871	+	11.4705i	−1.48102	+	0.366223i
$982$	15.5692	−	26.9666i	0.496832	−	0.860539i
$983$	57.2057			1.82458			0.912289	−	0.409547i	$-0.134313\pi$
$983$	57.2057			1.82458			0.912289	+	0.409547i	$0.134313\pi$
$984$	10.5787	−	24.8551i	0.337236	−	0.792350i
$985$	13.8266			0.440553
$986$	4.83937	+	8.38204i	0.154117	+	0.266938i
$987$	−5.69975	+	6.06951i	−0.181425	+	0.193195i
$988$	0.435124	−	0.753657i	0.0138431	−	0.0239770i
$989$	−11.7083	+	20.2793i	−0.372301	+	0.644844i
$990$	−10.1670	+	2.51407i	−0.323129	+	0.0799023i
$991$	−10.0718	−	17.4449i	−0.319943	−	0.554157i	0.660533	−	0.750797i	$-0.270330\pi$
$991$	−10.0718	−	17.4449i	−0.319943	−	0.554157i	−0.980476	+	0.196640i	$0.936997\pi$
$992$	15.8748	+	27.4960i	0.504026	+	0.872998i
$993$	3.56449	−	8.37491i	0.113116	−	0.265770i
$994$	10.8896	+	62.6861i	0.345396	+	1.98828i
$995$	−9.36690	−	16.2240i	−0.296951	−	0.514334i
$996$	−2.41265	+	5.66861i	−0.0764477	+	0.179617i
$997$	0.614633			0.0194656			0.00973281	−	0.999953i	$-0.496902\pi$
$997$	0.614633			0.0194656			0.00973281	+	0.999953i	$0.496902\pi$
$998$	3.13121	+	5.42342i	0.0991168	+	0.171675i
$999$	1.81930	−	11.2750i	0.0575601	−	0.356726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.16.10	✓	24
3.2	odd	2		945.2.k.b.856.3		24
7.4	even	3		315.2.l.b.151.3	yes	24
9.4	even	3		315.2.l.b.121.3	yes	24
9.5	odd	6		945.2.l.b.226.10		24
21.11	odd	6		945.2.l.b.46.10		24
63.4	even	3	inner	315.2.k.b.256.10	yes	24
63.32	odd	6		945.2.k.b.361.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.10	✓	24	1.1	even	1	trivial
315.2.k.b.256.10	yes	24	63.4	even	3	inner
315.2.l.b.121.3	yes	24	9.4	even	3
315.2.l.b.151.3	yes	24	7.4	even	3
945.2.k.b.361.3		24	63.32	odd	6
945.2.k.b.856.3		24	3.2	odd	2
945.2.l.b.46.10		24	21.11	odd	6
945.2.l.b.226.10		24	9.5	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.805191 + 1.39463i) q^{2} +(1.04104 + 1.38428i) q^{3} +(-0.296664 + 0.513837i) q^{4} -1.00000 q^{5} +(-1.09233 + 2.56648i) q^{6} +(2.48389 + 0.911196i) q^{7} +2.26528 q^{8} +(-0.832482 + 2.88218i) q^{9} +O(q^{10})\)	\(q+(0.805191 + 1.39463i) q^{2} +(1.04104 + 1.38428i) q^{3} +(-0.296664 + 0.513837i) q^{4} -1.00000 q^{5} +(-1.09233 + 2.56648i) q^{6} +(2.48389 + 0.911196i) q^{7} +2.26528 q^{8} +(-0.832482 + 2.88218i) q^{9} +(-0.805191 - 1.39463i) q^{10} -2.16786 q^{11} +(-1.02013 + 0.124257i) q^{12} +(-2.21310 - 3.83320i) q^{13} +(0.729225 + 4.19780i) q^{14} +(-1.04104 - 1.38428i) q^{15} +(2.41731 + 4.18690i) q^{16} +(-0.752653 - 1.30363i) q^{17} +(-4.68989 + 1.15970i) q^{18} +(0.165687 - 0.286978i) q^{19} +(0.296664 - 0.513837i) q^{20} +(1.32447 + 4.38700i) q^{21} +(-1.74554 - 3.02336i) q^{22} -1.89944 q^{23} +(2.35824 + 3.13579i) q^{24} +1.00000 q^{25} +(3.56393 - 6.17291i) q^{26} +(-4.85640 + 1.84807i) q^{27} +(-1.20509 + 1.00600i) q^{28} +(-1.99635 + 3.45777i) q^{29} +(1.09233 - 2.56648i) q^{30} +(4.87703 - 8.44726i) q^{31} +(-1.62751 + 2.81893i) q^{32} +(-2.25682 - 3.00093i) q^{33} +(1.21206 - 2.09935i) q^{34} +(-2.48389 - 0.911196i) q^{35} +(-1.23400 - 1.28280i) q^{36} +(-1.09897 + 1.90348i) q^{37} +0.533638 q^{38} +(3.00231 - 7.05406i) q^{39} -2.26528 q^{40} +(-3.44235 - 5.96232i) q^{41} +(-5.05179 + 5.37952i) q^{42} +(6.16406 - 10.6765i) q^{43} +(0.643125 - 1.11392i) q^{44} +(0.832482 - 2.88218i) q^{45} +(-1.52941 - 2.64901i) q^{46} +(0.908467 + 1.57351i) q^{47} +(-3.27935 + 7.70496i) q^{48} +(5.33944 + 4.52663i) q^{49} +(0.805191 + 1.39463i) q^{50} +(1.02106 - 2.39902i) q^{51} +2.62618 q^{52} +(1.32638 + 2.29735i) q^{53} +(-6.48770 - 5.28484i) q^{54} +2.16786 q^{55} +(5.62671 + 2.06411i) q^{56} +(0.569745 - 0.0693974i) q^{57} -6.42975 q^{58} +(-3.78850 + 6.56187i) q^{59} +(1.02013 - 0.124257i) q^{60} +(2.43522 + 4.21792i) q^{61} +15.7077 q^{62} +(-4.69403 + 6.40048i) q^{63} +4.42741 q^{64} +(2.21310 + 3.83320i) q^{65} +(2.36802 - 5.56375i) q^{66} +(-6.61165 + 11.4517i) q^{67} +0.893139 q^{68} +(-1.97739 - 2.62936i) q^{69} +(-0.729225 - 4.19780i) q^{70} +14.9331 q^{71} +(-1.88580 + 6.52895i) q^{72} +(-5.31641 - 9.20829i) q^{73} -3.53953 q^{74} +(1.04104 + 1.38428i) q^{75} +(0.0983066 + 0.170272i) q^{76} +(-5.38473 - 1.97534i) q^{77} +(12.2552 - 1.49274i) q^{78} +(-2.55562 - 4.42647i) q^{79} +(-2.41731 - 4.18690i) q^{80} +(-7.61395 - 4.79873i) q^{81} +(5.54349 - 9.60161i) q^{82} +(2.99740 - 5.19164i) q^{83} +(-2.64712 - 0.620902i) q^{84} +(0.752653 + 1.30363i) q^{85} +19.8530 q^{86} +(-6.86481 + 0.836162i) q^{87} -4.91080 q^{88} +(-2.99220 + 5.18265i) q^{89} +(4.68989 - 1.15970i) q^{90} +(-2.00430 - 11.5378i) q^{91} +(0.563494 - 0.976001i) q^{92} +(16.7706 - 2.04272i) q^{93} +(-1.46298 + 2.53395i) q^{94} +(-0.165687 + 0.286978i) q^{95} +(-5.59649 + 0.681676i) q^{96} +(3.11237 - 5.39079i) q^{97} +(-2.01370 + 11.0913i) q^{98} +(1.80470 - 6.24816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more