LMFDB - Embedded newform 429.2.bb.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	429.64
Dual form			429.2.bb.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.53943 - 0.825112i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(4.14988 + 3.01506i) q^{4} +(-1.45528 + 0.472849i) q^{5} +(2.53943 - 0.825112i) q^{6} +(-0.367708 + 0.506107i) q^{7} +(-4.91166 - 6.76032i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-2.53943 - 0.825112i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(4.14988 + 3.01506i) q^{4} +(-1.45528 + 0.472849i) q^{5} +(2.53943 - 0.825112i) q^{6} +(-0.367708 + 0.506107i) q^{7} +(-4.91166 - 6.76032i) q^{8} +(0.309017 - 0.951057i) q^{9} +4.08574 q^{10} +(2.83831 + 1.71581i) q^{11} -5.12953 q^{12} +(3.60482 + 0.0724610i) q^{13} +(1.35137 - 0.981824i) q^{14} +(0.899413 - 1.23794i) q^{15} +(3.72458 + 11.4631i) q^{16} +(-0.515319 - 1.58599i) q^{17} +(-1.56946 + 2.16017i) q^{18} +(-1.49052 - 2.05152i) q^{19} +(-7.46490 - 2.42549i) q^{20} -0.625583i q^{21} +(-5.79197 - 6.69910i) q^{22} -6.23335 q^{23} +(7.94723 + 2.58221i) q^{24} +(-2.15083 + 1.56267i) q^{25} +(-9.09442 - 3.15839i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-3.05189 + 0.991618i) q^{28} +(5.91852 + 4.30005i) q^{29} +(-3.30543 + 2.40154i) q^{30} +(0.716521 + 0.232812i) q^{31} -15.4705i q^{32} +(-3.30477 + 0.280202i) q^{33} +4.45270i q^{34} +(0.295806 - 0.910398i) q^{35} +(4.14988 - 3.01506i) q^{36} +(-5.91282 + 8.13830i) q^{37} +(2.09234 + 6.43955i) q^{38} +(-2.95895 + 2.06024i) q^{39} +(10.3444 + 7.51568i) q^{40} +(0.806337 + 1.10983i) q^{41} +(-0.516176 + 1.58863i) q^{42} -2.56053 q^{43} +(6.60538 + 15.6781i) q^{44} +1.53017i q^{45} +(15.8292 + 5.14321i) q^{46} +(4.34991 + 5.98714i) q^{47} +(-9.75109 - 7.08458i) q^{48} +(2.04218 + 6.28520i) q^{49} +(6.75127 - 2.19362i) q^{50} +(1.34912 + 0.980194i) q^{51} +(14.7411 + 11.1695i) q^{52} +(-1.76580 + 5.43457i) q^{53} -2.67012i q^{54} +(-4.94186 - 1.15489i) q^{55} +5.22750 q^{56} +(2.41171 + 0.783613i) q^{57} +(-11.4816 - 15.8031i) q^{58} +(-5.99019 + 8.24479i) q^{59} +(7.46490 - 2.42549i) q^{60} +(-2.23034 - 6.86429i) q^{61} +(-1.62746 - 1.18242i) q^{62} +(0.367708 + 0.506107i) q^{63} +(-5.31575 + 16.3602i) q^{64} +(-5.28029 + 1.59909i) q^{65} +(8.62343 + 2.01525i) q^{66} -11.9234i q^{67} +(2.64334 - 8.13537i) q^{68} +(5.04288 - 3.66387i) q^{69} +(-1.50236 + 2.06782i) q^{70} +(-7.15157 + 2.32369i) q^{71} +(-7.94723 + 2.58221i) q^{72} +(-4.84058 + 6.66248i) q^{73} +(21.7302 - 15.7879i) q^{74} +(0.821544 - 2.52845i) q^{75} -13.0076i q^{76} +(-1.91205 + 0.805573i) q^{77} +(9.21399 - 2.79037i) q^{78} +(-4.58787 + 14.1200i) q^{79} +(-10.8406 - 14.9208i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.13191 - 3.48365i) q^{82} +(4.50551 - 1.46393i) q^{83} +(1.88617 - 2.59609i) q^{84} +(1.49987 + 2.06439i) q^{85} +(6.50228 + 2.11272i) q^{86} -7.31569 q^{87} +(-2.34142 - 27.6153i) q^{88} +7.30731i q^{89} +(1.26256 - 3.88577i) q^{90} +(-1.36220 + 1.79778i) q^{91} +(-25.8676 - 18.7939i) q^{92} +(-0.716521 + 0.232812i) q^{93} +(-6.10625 - 18.7931i) q^{94} +(3.13919 + 2.28075i) q^{95} +(9.09335 + 12.5159i) q^{96} +(-10.8203 - 3.51573i) q^{97} -17.6459i q^{98} +(2.50891 - 2.16918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−2.53943	−	0.825112i	−1.79565	−	0.583442i	−0.795892	−	0.605438i	$-0.792998\pi$
$2$	−2.53943	−	0.825112i	−1.79565	−	0.583442i	−0.999758	+	0.0219963i	$0.992998\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	4.14988	+	3.01506i	2.07494	+	1.50753i
$5$	−1.45528	+	0.472849i	−0.650821	+	0.211465i	−0.615776	−	0.787921i	$-0.711157\pi$
$5$	−1.45528	+	0.472849i	−0.650821	+	0.211465i	−0.0350450	+	0.999386i	$0.511157\pi$
$6$	2.53943	−	0.825112i	1.03672	−	0.336850i
$7$	−0.367708	+	0.506107i	−0.138981	+	0.191290i	−0.872834	−	0.488018i	$-0.837720\pi$
$7$	−0.367708	+	0.506107i	−0.138981	+	0.191290i	0.733853	+	0.679308i	$0.237720\pi$
$8$	−4.91166	−	6.76032i	−1.73653	−	2.39013i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	4.08574			1.29202
$11$	2.83831	+	1.71581i	0.855783	+	0.517335i
$11$	2.83831	+	1.71581i	0.855783	+	0.517335i
$12$	−5.12953			−1.48077
$13$	3.60482	+	0.0724610i	0.999798	+	0.0200971i
$13$	3.60482	+	0.0724610i	0.999798	+	0.0200971i
$14$	1.35137	−	0.981824i	0.361168	−	0.262404i
$15$	0.899413	−	1.23794i	0.232227	−	0.319634i
$16$	3.72458	+	11.4631i	0.931146	+	2.86577i
$17$	−0.515319	−	1.58599i	−0.124983	−	0.384658i	0.868915	−	0.494962i	$-0.164818\pi$
$17$	−0.515319	−	1.58599i	−0.124983	−	0.384658i	−0.993898	+	0.110303i	$0.964818\pi$
$18$	−1.56946	+	2.16017i	−0.369924	+	0.509157i
$19$	−1.49052	−	2.05152i	−0.341949	−	0.470652i	0.603061	−	0.797695i	$-0.293948\pi$
$19$	−1.49052	−	2.05152i	−0.341949	−	0.470652i	−0.945009	+	0.327043i	$0.893948\pi$
$20$	−7.46490	−	2.42549i	−1.66920	−	0.542357i
$21$		−	0.625583i		−	0.136513i
$22$	−5.79197	−	6.69910i	−1.23485	−	1.42825i
$23$	−6.23335			−1.29974			−0.649871	−	0.760044i	$-0.725177\pi$
$23$	−6.23335			−1.29974			−0.649871	+	0.760044i	$0.725177\pi$
$24$	7.94723	+	2.58221i	1.62222	+	0.527092i
$25$	−2.15083	+	1.56267i	−0.430166	+	0.312534i
$26$	−9.09442	−	3.15839i	−1.78356	−	0.619412i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−3.05189	+	0.991618i	−0.576752	+	0.187398i
$29$	5.91852	+	4.30005i	1.09904	+	0.798500i	0.980903	−	0.194497i	$-0.0623075\pi$
$29$	5.91852	+	4.30005i	1.09904	+	0.798500i	0.118138	+	0.992997i	$0.462308\pi$
$30$	−3.30543	+	2.40154i	−0.603487	+	0.438459i
$31$	0.716521	+	0.232812i	0.128691	+	0.0418142i	0.372654	−	0.927970i	$-0.378448\pi$
$31$	0.716521	+	0.232812i	0.128691	+	0.0418142i	−0.243963	+	0.969784i	$0.578448\pi$
$32$		−	15.4705i		−	2.73483i
$33$	−3.30477	+	0.280202i	−0.575286	+	0.0487768i
$34$			4.45270i			0.763632i
$35$	0.295806	−	0.910398i	0.0500004	−	0.153885i
$36$	4.14988	−	3.01506i	0.691646	−	0.502510i
$37$	−5.91282	+	8.13830i	−0.972062	+	1.33793i	−0.0310634	+	0.999517i	$0.509889\pi$
$37$	−5.91282	+	8.13830i	−0.972062	+	1.33793i	−0.940998	+	0.338411i	$0.890111\pi$
$38$	2.09234	+	6.43955i	0.339422	+	1.04463i
$39$	−2.95895	+	2.06024i	−0.473812	+	0.329902i
$40$	10.3444	+	7.51568i	1.63560	+	1.18833i
$41$	0.806337	+	1.10983i	0.125929	+	0.173326i	0.867326	−	0.497740i	$-0.165837\pi$
$41$	0.806337	+	1.10983i	0.125929	+	0.173326i	−0.741398	+	0.671066i	$0.765837\pi$
$42$	−0.516176	+	1.58863i	−0.0796476	+	0.245130i
$43$	−2.56053			−0.390476			−0.195238	−	0.980756i	$-0.562548\pi$
$43$	−2.56053			−0.390476			−0.195238	+	0.980756i	$0.562548\pi$
$44$	6.60538	+	15.6781i	0.995798	+	2.36356i
$45$			1.53017i			0.228105i
$46$	15.8292	+	5.14321i	2.33388	+	0.758325i
$47$	4.34991	+	5.98714i	0.634499	+	0.873314i	0.998307	−	0.0581604i	$-0.0185235\pi$
$47$	4.34991	+	5.98714i	0.634499	+	0.873314i	−0.363808	+	0.931474i	$0.618523\pi$
$48$	−9.75109	−	7.08458i	−1.40745	−	1.02257i
$49$	2.04218	+	6.28520i	0.291741	+	0.897885i
$50$	6.75127	−	2.19362i	0.954773	−	0.310225i
$51$	1.34912	+	0.980194i	0.188915	+	0.137255i
$52$	14.7411	+	11.1695i	2.04422	+	1.54893i
$53$	−1.76580	+	5.43457i	−0.242551	+	0.746495i	0.753479	+	0.657473i	$0.228374\pi$
$53$	−1.76580	+	5.43457i	−0.242551	+	0.746495i	−0.996030	+	0.0890229i	$0.971626\pi$
$54$		−	2.67012i		−	0.363357i
$55$	−4.94186	−	1.15489i	−0.666360	−	0.155725i
$56$	5.22750			0.698554
$57$	2.41171	+	0.783613i	0.319439	+	0.103792i
$58$	−11.4816	−	15.8031i	−1.50761	−	2.07505i
$59$	−5.99019	+	8.24479i	−0.779857	+	1.07338i	0.215441	+	0.976517i	$0.430881\pi$
$59$	−5.99019	+	8.24479i	−0.779857	+	1.07338i	−0.995298	+	0.0968640i	$0.969119\pi$
$60$	7.46490	−	2.42549i	0.963715	−	0.313130i
$61$	−2.23034	−	6.86429i	−0.285566	−	0.878882i	−0.986228	−	0.165389i	$-0.947112\pi$
$61$	−2.23034	−	6.86429i	−0.285566	−	0.878882i	0.700662	−	0.713493i	$-0.252888\pi$
$62$	−1.62746	−	1.18242i	−0.206688	−	0.150167i
$63$	0.367708	+	0.506107i	0.0463269	+	0.0637635i
$64$	−5.31575	+	16.3602i	−0.664468	+	2.04502i
$65$	−5.28029	+	1.59909i	−0.654940	+	0.198342i
$66$	8.62343	+	2.01525i	1.06147	+	0.248060i
$67$		−	11.9234i		−	1.45668i	−0.685218	−	0.728338i	$-0.740293\pi$
$67$		−	11.9234i		−	1.45668i	0.685218	−	0.728338i	$-0.259707\pi$
$68$	2.64334	−	8.13537i	0.320552	−	0.986558i
$69$	5.04288	−	3.66387i	0.607092	−	0.441078i
$70$	−1.50236	+	2.06782i	−0.179566	+	0.247152i
$71$	−7.15157	+	2.32369i	−0.848736	+	0.275771i	−0.700916	−	0.713243i	$-0.747225\pi$
$71$	−7.15157	+	2.32369i	−0.848736	+	0.275771i	−0.147819	+	0.989014i	$0.547225\pi$
$72$	−7.94723	+	2.58221i	−0.936590	+	0.304316i
$73$	−4.84058	+	6.66248i	−0.566547	+	0.779785i	−0.992140	−	0.125130i	$-0.960065\pi$
$73$	−4.84058	+	6.66248i	−0.566547	+	0.779785i	0.425594	+	0.904914i	$0.360065\pi$
$74$	21.7302	−	15.7879i	2.52609	−	1.83531i
$75$	0.821544	−	2.52845i	0.0948637	−	0.291961i
$76$		−	13.0076i		−	1.49207i
$77$	−1.91205	+	0.805573i	−0.217899	+	0.0918036i
$78$	9.21399	−	2.79037i	1.04328	−	0.315947i
$79$	−4.58787	+	14.1200i	−0.516176	+	1.58863i	0.264956	+	0.964261i	$0.414643\pi$
$79$	−4.58787	+	14.1200i	−0.516176	+	1.58863i	−0.781132	+	0.624366i	$0.785357\pi$
$80$	−10.8406	−	14.9208i	−1.21202	−	1.66820i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.13191	−	3.48365i	−0.124998	−	0.384705i
$83$	4.50551	−	1.46393i	0.494544	−	0.160687i	−0.0511175	−	0.998693i	$-0.516278\pi$
$83$	4.50551	−	1.46393i	0.494544	−	0.160687i	0.545662	+	0.838005i	$0.316278\pi$
$84$	1.88617	−	2.59609i	0.205798	−	0.283257i
$85$	1.49987	+	2.06439i	0.162683	+	0.223914i
$86$	6.50228	+	2.11272i	0.701159	+	0.227820i
$87$	−7.31569			−0.784324
$88$	−2.34142	−	27.6153i	−0.249596	−	2.94380i
$89$			7.30731i			0.774573i	0.921959	+	0.387286i	$0.126588\pi$
$89$			7.30731i			0.774573i	−0.921959	+	0.387286i	$0.873412\pi$
$90$	1.26256	−	3.88577i	0.133086	−	0.409596i
$91$	−1.36220	+	1.79778i	−0.142797	+	0.188459i
$92$	−25.8676	−	18.7939i	−2.69689	−	1.95940i
$93$	−0.716521	+	0.232812i	−0.0742998	+	0.0241415i
$94$	−6.10625	−	18.7931i	−0.629811	−	1.93836i
$95$	3.13919	+	2.28075i	0.322074	+	0.234000i
$96$	9.09335	+	12.5159i	0.928086	+	1.27740i
$97$	−10.8203	−	3.51573i	−1.09864	−	0.356969i	−0.297059	−	0.954859i	$-0.596006\pi$
$97$	−10.8203	−	3.51573i	−1.09864	−	0.356969i	−0.801578	+	0.597891i	$0.796006\pi$
$98$		−	17.6459i		−	1.78250i
$99$	2.50891	−	2.16918i	0.252155	−	0.218011i
$100$	−13.6372			−1.36372
$101$	0.764165	−	2.35186i	0.0760372	−	0.234019i	−0.905813	−	0.423679i	$-0.860739\pi$
$101$	0.764165	−	2.35186i	0.0760372	−	0.234019i	0.981850	+	0.189660i	$0.0607386\pi$
$102$	−2.61723	−	3.60231i	−0.259145	−	0.356682i
$103$	4.21730	+	3.06405i	0.415543	+	0.301910i	0.775842	−	0.630927i	$-0.217325\pi$
$103$	4.21730	+	3.06405i	0.415543	+	0.301910i	−0.360299	+	0.932837i	$0.617325\pi$
$104$	−17.2158	−	24.7256i	−1.68815	−	2.42455i
$105$	0.295806	+	0.910398i	0.0288677	+	0.0888458i
$106$	8.96825	−	12.3437i	0.871074	−	1.19893i
$107$	−10.2035	+	7.41328i	−0.986410	+	0.716669i	−0.959132	−	0.282959i	$-0.908684\pi$
$107$	−10.2035	+	7.41328i	−0.986410	+	0.716669i	−0.0272779	+	0.999628i	$0.508684\pi$
$108$	−1.58511	+	4.87847i	−0.152527	+	0.469431i
$109$		−	7.31737i		−	0.700877i	−0.936586	−	0.350438i	$-0.886033\pi$
$109$		−	7.31737i		−	0.700877i	0.936586	−	0.350438i	$-0.113967\pi$
$110$	11.5966	+	7.01034i	1.10569	+	0.668409i
$111$		−	10.0595i		−	0.954805i
$112$	−7.17111	−	2.33003i	−0.677606	−	0.220168i
$113$	13.8904	−	10.0919i	1.30670	−	0.949370i	0.306698	−	0.951807i	$-0.400776\pi$
$113$	13.8904	−	10.0919i	1.30670	−	0.949370i	0.999997	+	0.00243685i	$0.000775676\pi$
$114$	−5.47781	−	3.97986i	−0.513044	−	0.372748i
$115$	9.07127	−	2.94743i	0.845900	−	0.274850i
$116$	11.5962	+	35.6894i	1.07668	+	3.31368i
$117$	1.18287	−	3.40600i	0.109356	−	0.314885i
$118$	22.0146	−	15.9945i	2.02661	−	1.47242i
$119$	0.992166	+	0.322374i	0.0909517	+	0.0295520i
$120$	−12.7864			−1.16724
$121$	5.11202	+	9.73998i	0.464729	+	0.885453i
$122$			19.2717i			1.74478i
$123$	−1.30468	−	0.423916i	−0.117639	−	0.0382232i
$124$	2.27153	+	3.12649i	0.203990	+	0.280768i
$125$	6.88822	−	9.48082i	0.616101	−	0.847990i
$126$	−0.516176	−	1.58863i	−0.0459846	−	0.141526i
$127$	−0.843759	−	2.59682i	−0.0748715	−	0.230431i	0.906616	−	0.421956i	$-0.138656\pi$
$127$	−0.843759	−	2.59682i	−0.0748715	−	0.230431i	−0.981488	+	0.191526i	$0.938656\pi$
$128$	8.81126	−	12.1277i	0.778813	−	1.07194i
$129$	2.07151	−	1.50504i	0.182386	−	0.132511i
$130$	14.7284	+	0.296057i	1.29176	+	0.0259659i
$131$	−21.0346			−1.83780			−0.918901	−	0.394488i	$-0.870922\pi$
$131$	−21.0346			−1.83780			−0.918901	+	0.394488i	$0.870922\pi$
$132$	−14.5592	−	8.80127i	−1.26722	−	0.766053i
$133$	1.58637			0.137555
$134$	−9.83815	+	30.2787i	−0.849887	+	2.61568i
$135$	−0.899413	−	1.23794i	−0.0774091	−	0.106545i
$136$	−8.19071	+	11.2735i	−0.702347	+	0.966698i
$137$	4.29194	−	1.39454i	0.366685	−	0.119143i	−0.119878	−	0.992789i	$-0.538250\pi$
$137$	4.29194	−	1.39454i	0.366685	−	0.119143i	0.486563	+	0.873645i	$0.338250\pi$
$138$	−15.8292	+	5.14321i	−1.34747	+	0.437819i
$139$	11.3442	+	8.24201i	0.962198	+	0.699078i	0.953660	−	0.300886i	$-0.0972822\pi$
$139$	11.3442	+	8.24201i	0.962198	+	0.699078i	0.00853810	+	0.999964i	$0.497282\pi$
$140$	3.97247	−	2.88617i	0.335735	−	0.243925i
$141$	−7.03830	−	2.28688i	−0.592732	−	0.192590i
$142$	20.0782			1.68493
$143$	10.1073	+	6.39084i	0.845213	+	0.534429i
$144$	12.0530			1.00442
$145$	−10.6464	−	3.45922i	−0.884134	−	0.287272i
$146$	17.7896	−	12.9249i	1.47228	−	1.06967i
$147$	−5.34651	−	3.88446i	−0.440972	−	0.320385i
$148$	−49.0749	+	15.9454i	−4.03394	+	1.31071i
$149$	19.0516	−	6.19025i	1.56077	−	0.507125i	0.603757	−	0.797168i	$-0.293670\pi$
$149$	19.0516	−	6.19025i	1.56077	−	0.507125i	0.957014	+	0.290043i	$0.0936696\pi$
$150$	−4.17251	+	5.74297i	−0.340684	+	0.468912i
$151$	−9.38564	−	12.9182i	−0.763793	−	1.05127i	−0.996889	−	0.0788171i	$-0.974886\pi$
$151$	−9.38564	−	12.9182i	−0.763793	−	1.05127i	0.233096	−	0.972454i	$-0.425114\pi$
$152$	−6.54803	+	20.1528i	−0.531115	+	1.63461i
$153$	−1.66761			−0.134818
$154$	5.52021	−	0.468043i	0.444832	−	0.0377160i
$155$	−1.15282			−0.0925970
$156$	−18.4910	−	0.371691i	−1.48047	−	0.0297591i
$157$	−1.93015	+	1.40234i	−0.154043	+	0.111919i	−0.662137	−	0.749383i	$-0.730350\pi$
$157$	−1.93015	+	1.40234i	−0.154043	+	0.111919i	0.508094	+	0.861302i	$0.330350\pi$
$158$	23.3012	−	32.0713i	1.85374	−	2.55146i
$159$	−1.76580	−	5.43457i	−0.140037	−	0.430989i
$160$	7.31523	+	22.5140i	0.578319	+	1.77988i
$161$	2.29205	−	3.15474i	0.180639	−	0.248628i
$162$	1.56946	+	2.16017i	0.123308	+	0.169719i
$163$	−9.38305	−	3.04874i	−0.734937	−	0.238796i	−0.0824500	−	0.996595i	$-0.526274\pi$
$163$	−9.38305	−	3.04874i	−0.734937	−	0.238796i	−0.652487	+	0.757800i	$0.726274\pi$
$164$			7.03680i			0.549482i
$165$	4.67687	−	1.97043i	0.364094	−	0.153398i
$166$	−12.6494			−0.981780
$167$	1.18220	+	0.384120i	0.0914812	+	0.0297241i	0.354400	−	0.935094i	$-0.384685\pi$
$167$	1.18220	+	0.384120i	0.0914812	+	0.0297241i	−0.262919	+	0.964818i	$0.584685\pi$
$168$	−4.22914	+	3.07265i	−0.326285	+	0.237060i
$169$	12.9895	+	0.522418i	0.999192	+	0.0401860i
$170$	−2.10546	−	6.47993i	−0.161481	−	0.496988i
$171$	−2.41171	+	0.783613i	−0.184428	+	0.0599244i
$172$	−10.6259	−	7.72014i	−0.810214	−	0.588655i
$173$	7.72514	−	5.61264i	0.587331	−	0.426721i	−0.254028	−	0.967197i	$-0.581756\pi$
$173$	7.72514	−	5.61264i	0.587331	−	0.426721i	0.841360	+	0.540476i	$0.181756\pi$
$174$	18.5777	+	6.03626i	1.40837	+	0.457608i
$175$		−	1.66316i		−	0.125723i
$176$	−9.09691	+	38.9265i	−0.685705	+	2.93419i
$177$		−	10.1911i		−	0.766012i
$178$	6.02934	−	18.5564i	0.451918	−	1.39086i
$179$	−18.5206	+	13.4560i	−1.38429	+	1.00575i	−0.387827	+	0.921732i	$0.626774\pi$
$179$	−18.5206	+	13.4560i	−1.38429	+	1.00575i	−0.996464	+	0.0840150i	$0.973226\pi$
$180$	−4.61356	+	6.35003i	−0.343875	+	0.473303i
$181$	5.63333	+	17.3376i	0.418722	+	1.28869i	0.908879	+	0.417060i	$0.136939\pi$
$181$	5.63333	+	17.3376i	0.418722	+	1.28869i	−0.490157	+	0.871634i	$0.663061\pi$
$182$	4.94258	−	3.44138i	0.366368	−	0.255092i
$183$	5.83912	+	4.24237i	0.431640	+	0.313605i
$184$	30.6161	+	42.1394i	2.25705	+	3.10656i
$185$	4.75662	−	14.6394i	0.349714	−	1.07631i
$186$	2.01165			0.147502
$187$	1.25861	−	5.38571i	0.0920388	−	0.393842i
$188$			37.9611i			2.76860i
$189$	−0.594964	−	0.193316i	−0.0432773	−	0.0140616i
$190$	−6.08988	−	8.38200i	−0.441806	−	0.608094i
$191$	−5.09105	−	3.69886i	−0.368375	−	0.267640i	0.388162	−	0.921591i	$-0.373110\pi$
$191$	−5.09105	−	3.69886i	−0.368375	−	0.267640i	−0.756537	+	0.653951i	$0.773110\pi$
$192$	−5.31575	−	16.3602i	−0.383631	−	1.18069i
$193$	7.17601	−	2.33163i	0.516541	−	0.167834i	−0.0391342	−	0.999234i	$-0.512460\pi$
$193$	7.17601	−	2.33163i	0.516541	−	0.167834i	0.555675	+	0.831400i	$0.312460\pi$
$194$	24.5766	+	17.8559i	1.76450	+	1.28198i
$195$	3.33193	−	4.39737i	0.238604	−	0.314902i
$196$	−10.4754	+	32.2401i	−0.748246	+	2.30286i
$197$			21.9700i			1.56530i	0.622463	+	0.782649i	$0.286132\pi$
$197$			21.9700i			1.56530i	−0.622463	+	0.782649i	$0.713868\pi$
$198$	−8.16104	+	3.43836i	−0.579980	+	0.244353i
$199$	3.53941			0.250902			0.125451	−	0.992100i	$-0.459962\pi$
$199$	3.53941			0.250902			0.125451	+	0.992100i	$0.459962\pi$
$200$	21.1283	+	6.86499i	1.49399	+	0.485428i
$201$	7.00841	+	9.64624i	0.494335	+	0.680394i
$202$	−3.88109	+	5.34186i	−0.273073	+	0.375852i
$203$	−4.35257	+	1.41424i	−0.305491	+	0.0992600i
$204$	2.64334	+	8.13537i	0.185071	+	0.569590i
$205$	−1.69823	−	1.23383i	−0.118609	−	0.0861747i
$206$	−8.18138	−	11.2607i	−0.570024	−	0.784570i
$207$	−1.92621	+	5.92827i	−0.133881	+	0.412043i
$208$	12.5958	+	41.5923i	0.873364	+	2.88391i
$209$	−0.710542	−	8.38031i	−0.0491492	−	0.579678i
$210$		−	2.55597i		−	0.176379i
$211$	3.17525	−	9.77242i	0.218593	−	0.672761i	−0.780286	−	0.625423i	$-0.784926\pi$
$211$	3.17525	−	9.77242i	0.218593	−	0.672761i	0.998879	−	0.0473378i	$-0.0150737\pi$
$212$	−23.7134	+	17.2288i	−1.62864	+	1.18328i
$213$	4.41992	−	6.08349i	0.302848	−	0.416834i
$214$	32.0279	−	10.4065i	2.18938	−	0.711373i
$215$	3.72628	−	1.21074i	0.254130	−	0.0825720i
$216$	4.91166	−	6.76032i	0.334196	−	0.459981i
$217$	−0.381298	+	0.277029i	−0.0258842	+	0.0188060i
$218$	−6.03765	+	18.5820i	−0.408921	+	1.25853i
$219$		−	8.23528i		−	0.556489i
$220$	−17.0260	−	19.6926i	−1.14790	−	1.32768i
$221$	−1.74271	−	5.75454i	−0.117227	−	0.387093i
$222$	−8.30021	+	25.5454i	−0.557073	+	1.71450i
$223$	13.3848	+	18.4226i	0.896312	+	1.23367i	0.971630	+	0.236508i	$0.0760028\pi$
$223$	13.3848	+	18.4226i	0.896312	+	1.23367i	−0.0753179	+	0.997160i	$0.523997\pi$
$224$	7.82974	+	5.68864i	0.523147	+	0.380088i
$225$	0.821544	+	2.52845i	0.0547696	+	0.168564i
$226$	−43.6006	+	14.1667i	−2.90027	+	0.942355i
$227$	0.0871870	−	0.120003i	0.00578680	−	0.00796485i	−0.806114	−	0.591761i	$-0.798433\pi$
$227$	0.0871870	−	0.120003i	0.00578680	−	0.00796485i	0.811901	+	0.583796i	$0.198433\pi$
$228$	7.64566	+	10.5234i	0.506346	+	0.696926i
$229$	14.8757	+	4.83340i	0.983012	+	0.319400i	0.756058	−	0.654505i	$-0.227123\pi$
$229$	14.8757	+	4.83340i	0.983012	+	0.319400i	0.226955	+	0.973905i	$0.427123\pi$
$230$	−25.4678			−1.67930
$231$	1.07338	−	1.77560i	0.0706231	−	0.116826i
$232$		−	61.1314i		−	4.01347i
$233$	1.80127	−	5.54373i	0.118005	−	0.363182i	−0.874557	−	0.484923i	$-0.838848\pi$
$233$	1.80127	−	5.54373i	0.118005	−	0.363182i	0.992562	+	0.121741i	$0.0388477\pi$
$234$	−5.81414	+	7.67331i	−0.380082	+	0.501620i
$235$	−9.16135	−	6.65611i	−0.597621	−	0.434197i
$236$	−49.7171	+	16.1541i	−3.23631	+	1.05154i
$237$	−4.58787	−	14.1200i	−0.298014	−	0.917194i
$238$	−2.25354	−	1.63730i	−0.146076	−	0.106130i
$239$	3.90165	+	5.37016i	0.252377	+	0.347367i	0.916342	−	0.400397i	$-0.131128\pi$
$239$	3.90165	+	5.37016i	0.252377	+	0.347367i	−0.663965	+	0.747764i	$0.731128\pi$
$240$	17.5405	+	5.69926i	1.13223	+	0.367885i
$241$			1.29184i			0.0832146i	0.999134	+	0.0416073i	$0.0132478\pi$
$241$			1.29184i			0.0832146i	−0.999134	+	0.0416073i	$0.986752\pi$
$242$	−4.94506	−	28.9520i	−0.317881	−	1.86111i
$243$	1.00000			0.0641500
$244$	11.4406	−	35.2106i	0.732410	−	2.25413i
$245$	−5.94390	−	8.18108i	−0.379742	−	0.522670i
$246$	2.96337	+	2.15301i	0.188938	+	0.137271i
$247$	−5.22440	−	7.50339i	−0.332421	−	0.477429i
$248$	−1.94542	−	5.98740i	−0.123535	−	0.380200i
$249$	−2.78456	+	3.83262i	−0.176464	+	0.242882i
$250$	−25.3149	+	18.3924i	−1.60105	+	1.16323i
$251$	4.98840	−	15.3527i	0.314865	−	0.969055i	−0.660945	−	0.750435i	$-0.729844\pi$
$251$	4.98840	−	15.3527i	0.314865	−	0.969055i	0.975810	−	0.218621i	$-0.0701558\pi$
$252$			3.20894i			0.202144i
$253$	−17.6922	−	10.6952i	−1.11230	−	0.672402i
$254$			7.29065i			0.457456i
$255$	−2.42683	−	0.788526i	−0.151974	−	0.0493794i
$256$	−4.54868	+	3.30481i	−0.284293	+	0.206551i
$257$	23.7283	+	17.2396i	1.48013	+	1.07538i	0.977515	+	0.210864i	$0.0676278\pi$
$257$	23.7283	+	17.2396i	1.48013	+	1.07538i	0.502613	+	0.864512i	$0.332372\pi$
$258$	−6.50228	+	2.11272i	−0.404814	+	0.131532i
$259$	−1.94466	−	5.98504i	−0.120835	−	0.371892i
$260$	−26.7339	−	9.28439i	−1.65797	−	0.575793i
$261$	5.91852	−	4.30005i	0.366347	−	0.266167i
$262$	53.4160	+	17.3559i	3.30005	+	1.07225i
$263$	2.45902			0.151630			0.0758149	−	0.997122i	$-0.475844\pi$
$263$	2.45902			0.151630			0.0758149	+	0.997122i	$0.475844\pi$
$264$	18.1261	+	20.9650i	1.11559	+	1.29031i
$265$		−	8.74378i		−	0.537126i
$266$	−4.02847	−	1.30893i	−0.247002	−	0.0802557i
$267$	−4.29513	−	5.91173i	−0.262857	−	0.361792i
$268$	35.9498	−	49.4807i	2.19598	−	3.02251i
$269$	−3.54876	−	10.9219i	−0.216371	−	0.665923i	−0.999053	−	0.0435009i	$-0.986149\pi$
$269$	−3.54876	−	10.9219i	−0.216371	−	0.665923i	0.782682	−	0.622422i	$-0.213851\pi$
$270$	1.26256	+	3.88577i	0.0768372	+	0.236480i
$271$	2.46622	−	3.39446i	0.149812	−	0.206199i	−0.727515	−	0.686092i	$-0.759325\pi$
$271$	2.46622	−	3.39446i	0.149812	−	0.206199i	0.877327	+	0.479893i	$0.159325\pi$
$272$	16.2610	−	11.8143i	0.985966	−	0.716346i
$273$	0.0453303	−	2.25511i	0.00274352	−	0.136486i
$274$	−12.0497			−0.727951
$275$	−8.78596	+	0.744936i	−0.529814	+	0.0449213i
$276$	31.9741			1.92462
$277$	5.57657	−	17.1629i	0.335064	−	1.03122i	−0.631627	−	0.775272i	$-0.717613\pi$
$277$	5.57657	−	17.1629i	0.335064	−	1.03122i	0.966691	−	0.255948i	$-0.0823874\pi$
$278$	−22.0071	−	30.2902i	−1.31990	−	1.81669i
$279$	0.442834	−	0.609509i	0.0265118	−	0.0364904i
$280$	−7.60748	+	2.47182i	−0.454634	+	0.147719i
$281$	−12.7930	+	4.15669i	−0.763166	+	0.247968i	−0.664637	−	0.747167i	$-0.731414\pi$
$281$	−12.7930	+	4.15669i	−0.763166	+	0.247968i	−0.0985288	+	0.995134i	$0.531414\pi$
$282$	15.9864	+	11.6148i	0.951974	+	0.691649i
$283$	−26.3941	+	19.1765i	−1.56897	+	1.13992i	−0.640833	+	0.767681i	$0.721411\pi$
$283$	−26.3941	+	19.1765i	−1.56897	+	1.13992i	−0.928136	+	0.372242i	$0.878589\pi$
$284$	−36.6842	−	11.9194i	−2.17681	−	0.707287i
$285$	−3.88025			−0.229846
$286$	−20.3936	−	24.5688i	−1.20590	−	1.45278i
$287$	−0.858188			−0.0506572
$288$	−14.7133	−	4.78066i	−0.866992	−	0.281703i
$289$	11.5035	−	8.35777i	0.676676	−	0.491634i
$290$	24.1815	+	17.5689i	1.41999	+	1.03168i
$291$	10.8203	−	3.51573i	0.634298	−	0.206096i
$292$	−40.1756	+	13.0538i	−2.35110	+	0.763918i
$293$	−0.719500	+	0.990307i	−0.0420336	+	0.0578543i	−0.829516	−	0.558482i	$-0.811384\pi$
$293$	−0.719500	+	0.990307i	−0.0420336	+	0.0578543i	0.787483	+	0.616337i	$0.211384\pi$
$294$	10.3720	+	14.2758i	0.604906	+	0.832582i
$295$	4.81887	−	14.8309i	0.280565	−	0.863491i
$296$	84.0592			4.88584
$297$	−0.754742	+	3.22961i	−0.0437946	+	0.187401i
$298$	−53.4880			−3.09848
$299$	−22.4701	−	0.451675i	−1.29948	−	0.0261210i
$300$	11.0327	−	8.01576i	0.636976	−	0.462790i
$301$	0.941526	−	1.29590i	0.0542687	−	0.0746944i
$302$	13.1752	+	40.5492i	0.758149	+	2.33334i
$303$	0.764165	+	2.35186i	0.0439001	+	0.135111i
$304$	17.9652	−	24.7270i	1.03038	−	1.41819i
$305$	6.49155	+	8.93485i	0.371705	+	0.511608i
$306$	4.23477	+	1.37596i	0.242086	+	0.0786585i
$307$			14.2676i			0.814298i	0.913362	+	0.407149i	$0.133477\pi$
$307$			14.2676i			0.814298i	−0.913362	+	0.407149i	$0.866523\pi$
$308$	−10.3636	−	2.42192i	−0.590523	−	0.138002i
$309$	−5.21288			−0.296550
$310$	2.92752	+	0.951209i	0.166272	+	0.0540250i
$311$	19.0425	−	13.8352i	1.07980	−	0.784523i	0.102154	−	0.994769i	$-0.467426\pi$
$311$	19.0425	−	13.8352i	1.07980	−	0.784523i	0.977649	+	0.210246i	$0.0674264\pi$
$312$	28.4612	+	9.88428i	1.61130	+	0.559587i
$313$	9.10672	+	28.0276i	0.514742	+	1.58421i	0.783751	+	0.621076i	$0.213304\pi$
$313$	9.10672	+	28.0276i	0.514742	+	1.58421i	−0.269008	+	0.963138i	$0.586696\pi$
$314$	6.05857	−	1.96855i	0.341905	−	0.111092i
$315$	−0.774431	−	0.562657i	−0.0436342	−	0.0317021i
$316$	−61.6118	+	44.7636i	−3.46594	+	2.51815i
$317$	20.5020	+	6.66151i	1.15151	+	0.374148i	0.821711	−	0.569904i	$-0.193020\pi$
$317$	20.5020	+	6.66151i	1.15151	+	0.374148i	0.329797	+	0.944052i	$0.393020\pi$
$318$			15.2577i			0.855610i
$319$	9.42053	+	22.3599i	0.527449	+	1.25191i
$320$		−	26.3222i		−	1.47146i
$321$	3.89739	−	11.9949i	0.217531	−	0.669492i
$322$	−8.42353	+	6.12005i	−0.469425	+	0.341057i
$323$	−2.48560	+	3.42113i	−0.138302	+	0.190357i
$324$	−1.58511	−	4.87847i	−0.0880617	−	0.271026i
$325$	−7.86660	+	5.47730i	−0.436360	+	0.303826i
$326$	21.3121	+	15.4841i	1.18037	+	0.857587i
$327$	4.30104	+	5.91988i	0.237848	+	0.327370i
$328$	3.54233	−	10.9022i	0.195593	−	0.601972i
$329$	−4.62963			−0.255240
$330$	−13.5024	+	1.14483i	−0.743284	+	0.0630209i
$331$		−	19.7925i		−	1.08789i	−0.839120	−	0.543946i	$-0.816930\pi$
$331$		−	19.7925i		−	1.08789i	0.839120	−	0.543946i	$-0.183070\pi$
$332$	23.1112	+	7.50927i	1.26839	+	0.412125i
$333$	5.91282	+	8.13830i	0.324021	+	0.445976i
$334$	−2.68517	−	1.95089i	−0.146926	−	0.106748i
$335$	5.63798	+	17.3519i	0.308036	+	0.948036i
$336$	7.17111	−	2.33003i	0.391216	−	0.127114i
$337$	−1.63615	−	1.18873i	−0.0891269	−	0.0647545i	0.542329	−	0.840166i	$-0.317542\pi$
$337$	−1.63615	−	1.18873i	−0.0891269	−	0.0647545i	−0.631456	+	0.775411i	$0.717542\pi$
$338$	−32.5549	−	12.0444i	−1.77075	−	0.655131i
$339$	−5.30565	+	16.3291i	−0.288163	+	0.886875i
$340$			13.0891i			0.709859i
$341$	1.63425	+	1.89020i	0.0884996	+	0.102360i
$342$	6.77095			0.366131
$343$	−8.09666	−	2.63076i	−0.437179	−	0.142048i
$344$	12.5764	+	17.3100i	0.678075	+	0.933290i
$345$	−5.60635	+	7.71648i	−0.301836	+	0.415441i
$346$	−24.2485	+	7.87882i	−1.30361	+	0.423568i
$347$	−9.78768	−	30.1234i	−0.525430	−	1.61711i	−0.763464	−	0.645851i	$-0.776503\pi$
$347$	−9.78768	−	30.1234i	−0.525430	−	1.61711i	0.238033	−	0.971257i	$-0.423497\pi$
$348$	−30.3592	−	22.0572i	−1.62742	−	1.18239i
$349$	−2.90028	−	3.99189i	−0.155248	−	0.213681i	0.724307	−	0.689478i	$-0.242160\pi$
$349$	−2.90028	−	3.99189i	−0.155248	−	0.213681i	−0.879555	+	0.475797i	$0.842160\pi$
$350$	−1.37229	+	4.22347i	−0.0733520	+	0.225754i
$351$	1.04504	+	3.45078i	0.0557800	+	0.184189i
$352$	26.5444	−	43.9102i	1.41482	−	2.34042i
$353$		−	1.75396i		−	0.0933540i	−0.998910	−	0.0466770i	$-0.985137\pi$
$353$		−	1.75396i		−	0.0933540i	0.998910	−	0.0466770i	$-0.0148631\pi$
$354$	−8.40882	+	25.8797i	−0.446924	+	1.37549i
$355$	9.30879	−	6.76323i	0.494059	−	0.358955i
$356$	−22.0320	+	30.3244i	−1.16769	+	1.60719i
$357$	−0.992166	+	0.322374i	−0.0525110	+	0.0170619i
$358$	58.1344	−	18.8890i	3.07250	−	0.998316i
$359$	12.2101	−	16.8057i	0.644422	−	0.886971i	−0.354420	−	0.935086i	$-0.615322\pi$
$359$	12.2101	−	16.8057i	0.644422	−	0.886971i	0.998842	+	0.0481155i	$0.0153216\pi$
$360$	10.3444	−	7.51568i	0.545200	−	0.396111i
$361$	3.88422	−	11.9544i	0.204433	−	0.629179i
$362$		−	48.6758i		−	2.55834i
$363$	−9.86073	−	4.87504i	−0.517554	−	0.255873i
$364$	−11.0734	+	3.35347i	−0.580402	+	0.175769i
$365$	3.89405	−	11.9846i	0.203824	−	0.627305i
$366$	−11.3276	−	15.5911i	−0.592104	−	0.814961i
$367$	27.5503	+	20.0165i	1.43811	+	1.04485i	0.988432	+	0.151663i	$0.0484628\pi$
$367$	27.5503	+	20.0165i	1.43811	+	1.04485i	0.449682	+	0.893189i	$0.351537\pi$
$368$	−23.2166	−	71.4534i	−1.21025	−	3.72477i
$369$	1.30468	−	0.423916i	0.0679189	−	0.0220682i
$370$	−24.1583	+	33.2510i	−1.25593	+	1.72864i
$371$	−2.10117	−	2.89202i	−0.109088	−	0.150146i
$372$	−3.67541	−	1.19421i	−0.190561	−	0.0619171i
$373$	−8.22630			−0.425942			−0.212971	−	0.977059i	$-0.568314\pi$
$373$	−8.22630			−0.425942			−0.212971	+	0.977059i	$0.568314\pi$
$374$	−7.63998	+	12.6382i	−0.395054	+	0.653504i
$375$			11.7189i			0.605163i
$376$	19.1097	−	58.8135i	0.985506	−	3.03308i
$377$	21.0236	+	15.9298i	1.08277	+	0.820426i
$378$	1.35137	+	0.981824i	0.0695067	+	0.0504996i
$379$	−27.3222	+	8.87751i	−1.40344	+	0.456007i	−0.910303	−	0.413942i	$-0.864152\pi$
$379$	−27.3222	+	8.87751i	−1.40344	+	0.456007i	−0.493142	+	0.869949i	$0.664152\pi$
$380$	6.15062	+	18.9297i	0.315520	+	0.971072i
$381$	2.20899	+	1.60492i	0.113170	+	0.0822228i
$382$	9.87640	+	13.5937i	0.505321	+	0.695514i
$383$	−4.89922	−	1.59185i	−0.250339	−	0.0813399i	0.181160	−	0.983454i	$-0.442015\pi$
$383$	−4.89922	−	1.59185i	−0.250339	−	0.0813399i	−0.431498	+	0.902114i	$0.642015\pi$
$384$			14.9906i			0.764987i
$385$	2.40166	−	2.07645i	0.122400	−	0.105826i
$386$	−20.1469			−1.02545
$387$	−0.791246	+	2.43520i	−0.0402213	+	0.123788i
$388$	−34.3028	−	47.2138i	−1.74146	−	2.39692i
$389$	−13.2786	−	9.64749i	−0.673253	−	0.489147i	0.197860	−	0.980230i	$-0.436601\pi$
$389$	−13.2786	−	9.64749i	−0.673253	−	0.489147i	−0.871113	+	0.491083i	$0.836601\pi$
$390$	−12.0895	+	8.41760i	−0.612177	+	0.426242i
$391$	3.21216	+	9.88601i	0.162446	+	0.499957i
$392$	32.4594	−	44.6765i	1.63945	−	2.25651i
$393$	17.0174	−	12.3638i	0.858412	−	0.623673i
$394$	18.1277	−	55.7914i	0.913261	−	2.81073i
$395$		−	22.7180i		−	1.14306i
$396$	16.9519	−	1.43730i	0.851865	−	0.0722271i
$397$			30.0730i			1.50932i	0.656116	+	0.754660i	$0.272198\pi$
$397$			30.0730i			1.50932i	−0.656116	+	0.754660i	$0.727802\pi$
$398$	−8.98809	−	2.92041i	−0.450532	−	0.146387i
$399$	−1.28340	+	0.932443i	−0.0642503	+	0.0466806i
$400$	−25.9240	−	18.8349i	−1.29620	−	0.941743i
$401$	−10.3364	+	3.35849i	−0.516174	+	0.167715i	−0.555508	−	0.831511i	$-0.687476\pi$
$401$	−10.3364	+	3.35849i	−0.516174	+	0.167715i	0.0393341	+	0.999226i	$0.487476\pi$
$402$	−9.83815	−	30.2787i	−0.490682	−	1.51016i
$403$	2.56606	+	0.891165i	0.127825	+	0.0443921i
$404$	10.2622	−	7.45591i	0.510563	−	0.370945i
$405$	1.45528	+	0.472849i	0.0723135	+	0.0234961i
$406$	12.2200			0.606467
$407$	−30.7462	+	12.9538i	−1.52403	+	0.642095i
$408$		−	13.9349i		−	0.689879i
$409$	34.0247	+	11.0553i	1.68241	+	0.546650i	0.985377	−	0.170386i	$-0.0545013\pi$
$409$	34.0247	+	11.0553i	1.68241	+	0.546650i	0.697037	+	0.717035i	$0.254501\pi$
$410$	3.29448	+	4.53447i	0.162703	+	0.223941i
$411$	−2.65256	+	3.65094i	−0.130841	+	0.180088i
$412$	8.26299	+	25.4309i	0.407088	+	1.25289i
$413$	−1.97010	−	6.06336i	−0.0969425	−	0.298358i
$414$	9.78296	−	13.4651i	0.480806	−	0.661773i
$415$	−5.86457	+	4.26086i	−0.287880	+	0.209157i
$416$	1.12101	−	55.7685i	0.0549620	−	2.73428i
$417$	−14.0221			−0.686667
$418$	−5.11032	+	21.8675i	−0.249954	+	1.06957i
$419$	−5.90468			−0.288463			−0.144231	−	0.989544i	$-0.546071\pi$
$419$	−5.90468			−0.288463			−0.144231	+	0.989544i	$0.546071\pi$
$420$	−1.51735	+	4.66991i	−0.0740389	+	0.227868i
$421$	0.920266	+	1.26664i	0.0448510	+	0.0617322i	0.830853	−	0.556491i	$-0.187853\pi$
$421$	0.920266	+	1.26664i	0.0448510	+	0.0617322i	−0.786002	+	0.618223i	$0.787853\pi$
$422$	−16.1267	+	22.1965i	−0.785034	+	1.08051i
$423$	7.03830	−	2.28688i	0.342214	−	0.111192i
$424$	45.4124	−	14.7554i	2.20542	−	0.716585i
$425$	3.58674	+	2.60592i	0.173982	+	0.126406i
$426$	−16.2436	+	11.8017i	−0.787007	+	0.571794i
$427$	4.29418	+	1.39526i	0.207810	+	0.0675216i
$428$	−64.6948			−3.12714
$429$	−11.9334	+	0.770610i	−0.576150	+	0.0372054i
$430$	−10.4616			−0.504505
$431$	−19.9890	−	6.49481i	−0.962835	−	0.312844i	−0.214915	−	0.976633i	$-0.568947\pi$
$431$	−19.9890	−	6.49481i	−0.962835	−	0.312844i	−0.747920	+	0.663789i	$0.768947\pi$
$432$	−9.75109	+	7.08458i	−0.469149	+	0.340857i
$433$	7.28570	+	5.29337i	0.350129	+	0.254383i	0.748923	−	0.662657i	$-0.230571\pi$
$433$	7.28570	+	5.29337i	0.350129	+	0.254383i	−0.398794	+	0.917040i	$0.630571\pi$
$434$	1.19686	−	0.388884i	0.0574512	−	0.0186670i
$435$	10.6464	−	3.45922i	0.510455	−	0.165857i
$436$	22.0623	−	30.3662i	1.05659	−	1.45428i
$437$	9.29093	+	12.7879i	0.444445	+	0.611727i
$438$	−6.79503	+	20.9129i	−0.324679	+	0.999259i
$439$	−15.2673			−0.728669			−0.364334	−	0.931268i	$-0.618704\pi$
$439$	−15.2673			−0.728669			−0.364334	+	0.931268i	$0.618704\pi$
$440$	16.4653	+	39.0809i	0.784953	+	1.86311i
$441$	6.60865			0.314697
$442$	−0.322647	+	16.0512i	−0.0153468	+	0.763478i
$443$	−1.17945	+	0.856923i	−0.0560375	+	0.0407137i	−0.615451	−	0.788175i	$-0.711026\pi$
$443$	−1.17945	+	0.856923i	−0.0560375	+	0.0407137i	0.559414	+	0.828888i	$0.311026\pi$
$444$	30.3300	−	41.7456i	1.43940	−	1.98116i
$445$	−3.45525	−	10.6342i	−0.163795	−	0.504108i
$446$	−18.7891	−	57.8269i	−0.889689	−	2.73818i
$447$	−11.7746	+	16.2063i	−0.556918	+	0.766531i
$448$	−6.32536	−	8.70611i	−0.298845	−	0.411325i
$449$	−34.6712	−	11.2654i	−1.63624	−	0.531646i	−0.660544	−	0.750788i	$-0.729674\pi$
$449$	−34.6712	−	11.2654i	−1.63624	−	0.531646i	−0.975693	+	0.219142i	$0.929674\pi$
$450$		−	7.09870i		−	0.334636i
$451$	0.384387	+	4.53355i	0.0181001	+	0.213477i
$452$	88.0711			4.14252
$453$	15.1863	+	4.93433i	0.713514	+	0.231835i
$454$	−0.320421	+	0.232799i	−0.0150381	+	0.0109258i
$455$	1.13230	−	3.26039i	0.0530829	−	0.152849i
$456$	−6.54803	−	20.1528i	−0.306640	−	0.943740i
$457$	7.97709	−	2.59191i	0.373152	−	0.121245i	−0.116436	−	0.993198i	$-0.537147\pi$
$457$	7.97709	−	2.59191i	0.373152	−	0.121245i	0.489588	+	0.871954i	$0.337147\pi$
$458$	−33.7877	−	24.5482i	−1.57879	−	1.14706i
$459$	1.34912	−	0.980194i	0.0629716	−	0.0457515i
$460$	46.5313	+	15.1189i	2.16953	+	0.704925i
$461$		−	5.12918i		−	0.238890i	−0.992841	−	0.119445i	$-0.961889\pi$
$461$		−	5.12918i		−	0.238890i	0.992841	−	0.119445i	$-0.0381114\pi$
$462$	−4.19084	+	3.62336i	−0.194975	+	0.168574i
$463$			32.8222i			1.52538i	0.646766	+	0.762689i	$0.276121\pi$
$463$			32.8222i			1.52538i	−0.646766	+	0.762689i	$0.723879\pi$
$464$	−27.2479	+	83.8604i	−1.26495	+	3.89312i
$465$	0.932654	−	0.677613i	0.0432508	−	0.0314235i
$466$	−9.14839	+	12.5917i	−0.423791	+	0.583298i
$467$	−3.95160	−	12.1618i	−0.182858	−	0.562780i	0.817047	−	0.576571i	$-0.195610\pi$
$467$	−3.95160	−	12.1618i	−0.182858	−	0.562780i	−0.999905	+	0.0137919i	$0.995610\pi$
$468$	15.1780	−	10.5681i	0.701605	−	0.488509i
$469$	6.03452	+	4.38434i	0.278648	+	0.202450i
$470$	17.7726	+	24.4619i	0.819789	+	1.12834i
$471$	0.737252	−	2.26903i	0.0339708	−	0.104551i
$472$	85.1592			3.91977
$473$	−7.26757	−	4.39336i	−0.334163	−	0.202007i
$474$			39.6424i			1.82083i
$475$	6.41171	+	2.08329i	0.294189	+	0.0955879i
$476$	3.14539	+	4.32926i	0.144169	+	0.198431i
$477$	4.62292	+	3.35875i	0.211669	+	0.153787i
$478$	−5.47700	−	16.8565i	−0.250512	−	0.770997i
$479$	26.0277	−	8.45691i	1.18924	−	0.386406i	0.353446	−	0.935455i	$-0.385010\pi$
$479$	26.0277	−	8.45691i	1.18924	−	0.386406i	0.835790	+	0.549049i	$0.185010\pi$
$480$	−19.1515	−	13.9144i	−0.874143	−	0.635102i
$481$	−21.9044	+	28.9087i	−0.998754	+	1.31812i
$482$	1.06591	−	3.28054i	0.0485509	−	0.149424i
$483$			3.89947i			0.177432i
$484$	−8.15239	+	55.8328i	−0.370563	+	2.53785i
$485$	17.4090			0.790502
$486$	−2.53943	−	0.825112i	−0.115191	−	0.0374278i
$487$	11.8249	+	16.2755i	0.535835	+	0.737514i	0.988006	−	0.154418i	$-0.0493501\pi$
$487$	11.8249	+	16.2755i	0.535835	+	0.737514i	−0.452170	+	0.891932i	$0.649350\pi$
$488$	−35.4501	+	48.7929i	−1.60475	+	2.20875i
$489$	9.38305	−	3.04874i	0.424316	−	0.137869i
$490$	8.34383	+	25.6797i	0.376936	+	1.16009i
$491$	21.6814	+	15.7524i	0.978466	+	0.710897i	0.957365	−	0.288880i	$-0.0932830\pi$
$491$	21.6814	+	15.7524i	0.978466	+	0.710897i	0.0211006	+	0.999777i	$0.493283\pi$
$492$	−4.13613	−	5.69289i	−0.186471	−	0.256655i
$493$	3.76991	−	11.6026i	0.169788	−	0.522554i
$494$	7.07589	+	23.3651i	0.318359	+	1.05124i
$495$	−2.62548	+	4.34311i	−0.118006	+	0.195208i
$496$			9.08067i			0.407734i
$497$	1.45366	−	4.47390i	0.0652055	−	0.200682i
$498$	10.2335	−	7.43510i	0.458576	−	0.333175i
$499$	2.22118	−	3.05720i	0.0994338	−	0.136859i	−0.756401	−	0.654108i	$-0.773044\pi$
$499$	2.22118	−	3.05720i	0.0994338	−	0.136859i	0.855835	+	0.517249i	$0.173044\pi$
$500$	57.1705	−	18.5758i	2.55674	−	0.830736i
$501$	−1.18220	+	0.384120i	−0.0528167	+	0.0171612i
$502$	−25.3354	+	34.8712i	−1.13078	+	1.55638i
$503$	28.1747	−	20.4701i	1.25625	−	0.912719i	0.257682	−	0.966230i	$-0.417041\pi$
$503$	28.1747	−	20.4701i	1.25625	−	0.912719i	0.998567	+	0.0535110i	$0.0170412\pi$
$504$	1.61539	−	4.97165i	0.0719550	−	0.221455i
$505$			3.78395i			0.168383i
$506$	36.1034	+	41.7578i	1.60499	+	1.85636i
$507$	−10.8158	+	7.21239i	−0.480346	+	0.320314i
$508$	4.32809	−	13.3205i	0.192028	−	0.591001i
$509$	−3.97194	−	5.46691i	−0.176053	−	0.242316i	0.711867	−	0.702315i	$-0.247850\pi$
$509$	−3.97194	−	5.46691i	−0.176053	−	0.242316i	−0.887920	+	0.459998i	$0.847850\pi$
$510$	5.51216	+	4.00482i	0.244083	+	0.177336i
$511$	−1.59201	−	4.89970i	−0.0704263	−	0.216750i
$512$	−14.2359	+	4.62554i	−0.629145	+	0.204422i
$513$	1.49052	−	2.05152i	0.0658081	−	0.0905770i
$514$	−46.0317	−	63.3572i	−2.03037	−	2.79457i
$515$	−7.58620	−	2.46490i	−0.334288	−	0.108617i
$516$	13.1343			0.578205
$517$	2.07363	+	24.4570i	0.0911983	+	1.07562i
$518$			16.8032i			0.738289i
$519$	−2.95074	+	9.08144i	−0.129523	+	0.398631i
$520$	36.7453	+	27.8423i	1.61139	+	1.22096i
$521$	−21.6745	−	15.7474i	−0.949575	−	0.689907i	0.00113133	−	0.999999i	$-0.499640\pi$
$521$	−21.6745	−	15.7474i	−0.949575	−	0.689907i	−0.950706	+	0.310093i	$0.899640\pi$
$522$	−18.5777	+	6.03626i	−0.813124	+	0.264200i
$523$	−12.9262	−	39.7829i	−0.565225	−	1.73958i	−0.667282	−	0.744805i	$-0.732542\pi$
$523$	−12.9262	−	39.7829i	−0.565225	−	1.73958i	0.102057	−	0.994779i	$-0.467458\pi$
$524$	−87.2910	−	63.4206i	−3.81333	−	2.77054i
$525$	0.977579	+	1.34552i	0.0426650	+	0.0587234i
$526$	−6.24452	−	2.02897i	−0.272274	−	0.0884672i
$527$		−	1.25637i		−	0.0547281i
$528$	−15.5209	−	36.8392i	−0.675459	−	1.60322i
$529$	15.8546			0.689331
$530$	−7.21459	+	22.2042i	−0.313382	+	0.964490i
$531$	5.99019	+	8.24479i	0.259952	+	0.357794i
$532$	6.58323	+	4.78299i	0.285419	+	0.207369i
$533$	2.82628	+	4.05916i	0.122420	+	0.175822i
$534$	6.02934	+	18.5564i	0.260915	+	0.803015i
$535$	11.3436	−	15.6131i	0.490426	−	0.675014i
$536$	−80.6060	+	58.5637i	−3.48165	+	2.52957i
$537$	7.07423	−	21.7722i	0.305275	−	0.939541i
$538$			30.6637i			1.32200i
$539$	−4.98782	+	21.3433i	−0.214841	+	0.919322i
$540$		−	7.84906i		−	0.337770i
$541$	−32.4530	−	10.5446i	−1.39526	−	0.453349i	−0.487608	−	0.873063i	$-0.662130\pi$
$541$	−32.4530	−	10.5446i	−1.39526	−	0.453349i	−0.907656	+	0.419714i	$0.862130\pi$
$542$	−9.06360	+	6.58509i	−0.389315	+	0.282854i
$543$	−14.7482	−	10.7152i	−0.632908	−	0.459835i
$544$	−24.5361	+	7.97225i	−1.05197	+	0.341807i
$545$	3.46001	+	10.6488i	0.148211	+	0.456146i
$546$	−1.97584	+	5.68931i	−0.0845579	+	0.243480i
$547$	−1.98490	+	1.44212i	−0.0848682	+	0.0616604i	−0.629410	−	0.777073i	$-0.716703\pi$
$547$	−1.98490	+	1.44212i	−0.0848682	+	0.0616604i	0.544542	+	0.838734i	$0.316703\pi$
$548$	22.0156	+	7.15331i	0.940461	+	0.305574i
$549$	−7.21754			−0.308037
$550$	22.9260	+	5.35769i	0.977569	+	0.228453i
$551$		−	18.5513i		−	0.790312i
$552$	−49.5378	−	16.0958i	−2.10847	−	0.685083i
$553$	−5.45924	−	7.51400i	−0.232151	−	0.319528i
$554$	−28.3227	+	38.9828i	−1.20331	+	1.65622i
$555$	4.75662	+	14.6394i	0.201907	+	0.621407i
$556$	22.2267	+	68.4066i	0.942620	+	2.90109i
$557$	4.77923	−	6.57804i	0.202502	−	0.278721i	−0.695672	−	0.718359i	$-0.744893\pi$
$557$	4.77923	−	6.57804i	0.202502	−	0.278721i	0.898175	+	0.439639i	$0.144893\pi$
$558$	−1.62746	+	1.18242i	−0.0688959	+	0.0500558i
$559$	−9.23024	−	0.185538i	−0.390398	−	0.00784743i
$560$	11.5377			0.487558
$561$	2.14740	+	5.09693i	0.0906635	+	0.215192i
$562$	35.9167			1.51505
$563$	−3.08233	+	9.48642i	−0.129905	+	0.399805i	−0.994763	−	0.102211i	$-0.967408\pi$
$563$	−3.08233	+	9.48642i	−0.129905	+	0.399805i	0.864858	+	0.502016i	$0.167408\pi$
$564$	−22.3130	−	30.7112i	−0.939546	−	1.29317i
$565$	−15.4424	+	21.2547i	−0.649667	+	0.894190i
$566$	82.8489	−	26.9192i	3.48240	−	1.13150i
$567$	0.594964	−	0.193316i	0.0249862	−	0.00811849i
$568$	50.8349	+	36.9337i	2.13299	+	1.54971i
$569$	6.15231	−	4.46992i	0.257918	−	0.187389i	−0.451311	−	0.892367i	$-0.649043\pi$
$569$	6.15231	−	4.46992i	0.257918	−	0.187389i	0.709229	+	0.704978i	$0.249043\pi$
$570$	9.85363	+	3.20164i	0.412723	+	0.134102i
$571$	3.60928			0.151044			0.0755218	−	0.997144i	$-0.475938\pi$
$571$	3.60928			0.151044			0.0755218	+	0.997144i	$0.475938\pi$
$572$	22.6752	+	56.9953i	0.948097	+	2.38309i
$573$	6.29288			0.262889
$574$	2.17931	+	0.708101i	0.0909627	+	0.0295556i
$575$	13.4069	−	9.74066i	0.559105	−	0.406214i
$576$	13.9168	+	10.1111i	0.579867	+	0.421298i
$577$	11.9096	−	3.86966i	0.495802	−	0.161096i	−0.0504334	−	0.998727i	$-0.516060\pi$
$577$	11.9096	−	3.86966i	0.495802	−	0.161096i	0.546236	+	0.837631i	$0.316060\pi$
$578$	−36.1084	+	11.7323i	−1.50191	+	0.488001i
$579$	−4.43502	+	6.10428i	−0.184313	+	0.253685i
$580$	−33.7514	−	46.4548i	−1.40145	−	1.92893i
$581$	−0.915809	+	2.81857i	−0.0379942	+	0.116934i
$582$	−30.3783			−1.25922
$583$	−14.3365	+	12.3952i	−0.593759	+	0.513358i
$584$	68.8157			2.84762
$585$	−0.110878	+	5.51600i	−0.00458423	+	0.228059i
$586$	2.64424	−	1.92115i	0.109232	−	0.0793620i
$587$	−10.5714	+	14.5503i	−0.436328	+	0.600555i	−0.969391	−	0.245521i	$-0.921041\pi$
$587$	−10.5714	+	14.5503i	−0.436328	+	0.600555i	0.533063	+	0.846076i	$0.321041\pi$
$588$	−10.4754	−	32.2401i	−0.432000	−	1.32956i
$589$	−0.590370	−	1.81697i	−0.0243258	−	0.0748670i
$590$	−24.4744	+	33.6861i	−1.00759	+	1.38683i
$591$	−12.9136	−	17.7741i	−0.531196	−	0.731129i
$592$	−115.313	−	37.4674i	−4.73933	−	1.53990i
$593$		−	13.9728i		−	0.573793i	−0.957962	−	0.286897i	$-0.907376\pi$
$593$		−	13.9728i		−	0.573793i	0.957962	−	0.286897i	$-0.0926237\pi$
$594$	4.58140	−	7.57863i	0.187977	−	0.310955i
$595$	−1.59631			−0.0654425
$596$	97.7259	+	31.7531i	4.00301	+	1.30066i
$597$	−2.86344	+	2.08041i	−0.117193	+	0.0851456i
$598$	56.6887	+	19.6874i	2.31817	+	0.805076i
$599$	6.38432	+	19.6489i	0.260856	+	0.802833i	0.992619	+	0.121274i	$0.0386978\pi$
$599$	6.38432	+	19.6489i	0.260856	+	0.802833i	−0.731763	+	0.681559i	$0.761302\pi$
$600$	−21.1283	+	6.86499i	−0.862558	+	0.280262i
$601$	−25.6589	−	18.6423i	−1.04665	−	0.760434i	−0.0750760	−	0.997178i	$-0.523920\pi$
$601$	−25.6589	−	18.6423i	−1.04665	−	0.760434i	−0.971572	+	0.236743i	$0.923920\pi$
$602$	−3.46021	+	2.51399i	−0.141027	+	0.102462i
$603$	−11.3398	−	3.68454i	−0.461794	−	0.150046i
$604$		−	81.9073i		−	3.33276i
$605$	−12.0450	−	11.7572i	−0.489698	−	0.477998i
$606$		−	6.60290i		−	0.268225i
$607$	5.98929	−	18.4331i	0.243098	−	0.748178i	−0.752846	−	0.658197i	$-0.771319\pi$
$607$	5.98929	−	18.4331i	0.243098	−	0.748178i	0.995943	−	0.0899810i	$-0.0286806\pi$
$608$	−31.7382	+	23.0591i	−1.28715	+	0.935171i
$609$	2.69004	−	3.70252i	0.109006	−	0.150034i
$610$	−9.11260	−	28.0457i	−0.368959	−	1.13554i
$611$	15.2468	+	21.8978i	0.616820	+	0.885889i
$612$	−6.92036	−	5.02793i	−0.279739	−	0.203242i
$613$	0.269133	+	0.370430i	0.0108702	+	0.0149615i	0.814417	−	0.580279i	$-0.197057\pi$
$613$	0.269133	+	0.370430i	0.0108702	+	0.0149615i	−0.803547	+	0.595241i	$0.797057\pi$
$614$	11.7724	−	36.2317i	0.475096	−	1.46219i
$615$	2.09912			0.0846448
$616$	14.8373	+	8.96937i	0.597811	+	0.361386i
$617$		−	33.9249i		−	1.36577i	−0.730528	−	0.682883i	$-0.760726\pi$
$617$		−	33.9249i		−	1.36577i	0.730528	−	0.682883i	$-0.239274\pi$
$618$	13.2377	+	4.30120i	0.532500	+	0.173020i
$619$	13.1013	+	18.0324i	0.526586	+	0.724784i	0.986605	−	0.163125i	$-0.0521574\pi$
$619$	13.1013	+	18.0324i	0.526586	+	0.724784i	−0.460019	+	0.887909i	$0.652157\pi$
$620$	−4.78408	−	3.47583i	−0.192133	−	0.139593i
$621$	−1.92621	−	5.92827i	−0.0772962	−	0.237893i
$622$	−59.7728	+	19.4214i	−2.39667	+	0.778726i
$623$	−3.69828	−	2.68696i	−0.148168	−	0.107651i
$624$	−34.6376	−	26.2452i	−1.38661	−	1.05065i
$625$	−1.43357	+	4.41208i	−0.0573428	+	0.176483i
$626$		−	78.6883i		−	3.14502i
$627$	5.50066	+	6.36217i	0.219675	+	0.254080i
$628$	−12.2380			−0.488350
$629$	15.9542	+	5.18384i	0.636137	+	0.206693i
$630$	1.50236	+	2.06782i	0.0598555	+	0.0823840i
$631$	−1.68268	+	2.31601i	−0.0669864	+	0.0921988i	−0.841196	−	0.540731i	$-0.818148\pi$
$631$	−1.68268	+	2.31601i	−0.0669864	+	0.0921988i	0.774209	+	0.632930i	$0.218148\pi$
$632$	117.990	−	38.3372i	4.69339	−	1.52497i
$633$	3.17525	+	9.77242i	0.126205	+	0.388419i
$634$	−46.5670	−	33.8329i	−1.84941	−	1.34368i
$635$	2.45581	+	3.38013i	0.0974559	+	0.134137i
$636$	9.05771	−	27.8768i	0.359162	−	1.10539i
$637$	6.90628	+	22.8050i	0.273637	+	0.903567i
$638$	−5.47339	−	64.5545i	−0.216693	−	2.55574i
$639$			7.51961i			0.297471i
$640$	−7.08830	+	21.8155i	−0.280190	+	0.862335i
$641$	4.60289	−	3.34419i	0.181803	−	0.132088i	−0.493162	−	0.869938i	$-0.664159\pi$
$641$	4.60289	−	3.34419i	0.181803	−	0.132088i	0.674965	+	0.737850i	$0.264159\pi$
$642$	−19.7943	+	27.2446i	−0.781220	+	1.07526i
$643$	36.0106	−	11.7006i	1.42012	−	0.461425i	0.504480	−	0.863423i	$-0.331684\pi$
$643$	36.0106	−	11.7006i	1.42012	−	0.461425i	0.915641	+	0.401998i	$0.131684\pi$
$644$	19.0235	−	6.18110i	0.749630	−	0.243570i
$645$	−2.30297	+	3.16977i	−0.0906793	+	0.124809i
$646$	9.13483	−	6.63684i	0.359405	−	0.261123i
$647$	−7.72805	+	23.7845i	−0.303821	+	0.935065i	0.676294	+	0.736632i	$0.263585\pi$
$647$	−7.72805	+	23.7845i	−0.303821	+	0.935065i	−0.980115	+	0.198432i	$0.936415\pi$
$648$			8.35621i			0.328263i
$649$	−31.1485	+	13.1233i	−1.22269	+	0.515134i
$650$	24.4961	−	7.41841i	0.960815	−	0.290974i
$651$	0.145643	−	0.448243i	0.00570820	−	0.0175680i
$652$	−29.7464	−	40.9424i	−1.16496	−	1.60343i
$653$	−1.56011	−	1.13349i	−0.0610520	−	0.0443569i	0.556841	−	0.830619i	$-0.312013\pi$
$653$	−1.56011	−	1.13349i	−0.0610520	−	0.0443569i	−0.617893	+	0.786262i	$0.712013\pi$
$654$	−6.03765	−	18.5820i	−0.236091	−	0.726612i
$655$	30.6113	−	9.94620i	1.19608	−	0.388630i
$656$	−9.71878	+	13.3768i	−0.379455	+	0.522274i
$657$	4.84058	+	6.66248i	0.188849	+	0.259928i
$658$	11.7566	+	3.81996i	0.458321	+	0.148918i
$659$	−35.8703			−1.39731			−0.698654	−	0.715459i	$-0.746218\pi$
$659$	−35.8703			−1.39731			−0.698654	+	0.715459i	$0.746218\pi$
$660$	25.3494	+	5.92402i	0.986724	+	0.230592i
$661$		−	23.1888i		−	0.901940i	−0.892539	−	0.450970i	$-0.851078\pi$
$661$		−	23.1888i		−	0.901940i	0.892539	−	0.450970i	$-0.148922\pi$
$662$	−16.3310	+	50.2616i	−0.634722	+	1.95347i
$663$	4.79232	+	3.63119i	0.186118	+	0.141024i
$664$	−32.0262	−	23.2684i	−1.24286	−	0.902988i
$665$	−2.30861	+	0.750113i	−0.0895240	+	0.0290881i
$666$	−8.30021	−	25.5454i	−0.321626	−	0.989864i
$667$	−36.8922	−	26.8037i	−1.42847	−	1.03784i
$668$	3.74783	+	5.15845i	0.145008	+	0.199586i
$669$	−21.6570	−	7.03680i	−0.837310	−	0.272058i
$670$		−	48.7160i		−	1.88206i
$671$	5.44738	−	23.3098i	0.210294	−	0.899866i
$672$	−9.67809			−0.373341
$673$	−12.0913	+	37.2131i	−0.466084	+	1.43446i	0.391530	+	0.920165i	$0.371946\pi$
$673$	−12.0913	+	37.2131i	−0.466084	+	1.43446i	−0.857614	+	0.514293i	$0.828054\pi$
$674$	3.17406	+	4.36872i	0.122260	+	0.168277i
$675$	−2.15083	−	1.56267i	−0.0827855	−	0.0601472i
$676$	52.3297	+	41.3321i	2.01268	+	1.58970i
$677$	−13.2713	−	40.8447i	−0.510056	−	1.56979i	−0.792101	−	0.610390i	$-0.791013\pi$
$677$	−13.2713	−	40.8447i	−0.510056	−	1.56979i	0.282045	−	0.959401i	$-0.408987\pi$
$678$	26.9467	−	37.0889i	1.03488	−	1.42439i
$679$	5.75806	−	4.18347i	0.220974	−	0.160547i
$680$	6.58909	−	20.2791i	0.252680	−	0.777669i
$681$			0.148331i			0.00568407i
$682$	−2.59044	−	6.14848i	−0.0991930	−	0.235438i
$683$		−	15.5957i		−	0.596752i	−0.954448	−	0.298376i	$-0.903555\pi$
$683$		−	15.5957i		−	0.596752i	0.954448	−	0.298376i	$-0.0964449\pi$
$684$	−12.3709	−	4.01956i	−0.473015	−	0.153692i
$685$	−5.58657	+	4.05888i	−0.213452	+	0.155082i
$686$	18.3903	+	13.3613i	0.702143	+	0.510137i
$687$	−14.8757	+	4.83340i	−0.567542	+	0.184406i
$688$	−9.53689	−	29.3515i	−0.363591	−	1.11902i
$689$	−6.75919	+	19.4627i	−0.257504	+	0.741470i
$690$	20.6039	−	14.9696i	0.784378	−	0.569884i
$691$	−32.1257	−	10.4383i	−1.22212	−	0.397091i	−0.374266	−	0.927321i	$-0.622105\pi$
$691$	−32.1257	−	10.4383i	−1.22212	−	0.397091i	−0.847853	+	0.530231i	$0.822105\pi$
$692$	48.9808			1.86197
$693$	0.175289	+	2.06741i	0.00665869	+	0.0785342i
$694$			84.5722i			3.21032i
$695$	−20.4061	−	6.63036i	−0.774049	−	0.251504i
$696$	35.9322	+	49.4564i	1.36200	+	1.87464i
$697$	1.34465	−	1.85075i	0.0509323	−	0.0701023i
$698$	4.07131	+	12.5302i	0.154101	+	0.474275i
$699$	1.80127	+	5.54373i	0.0681302	+	0.209683i
$700$	5.01452	−	6.90189i	0.189531	−	0.260867i
$701$	17.9163	−	13.0170i	0.676690	−	0.491644i	−0.195568	−	0.980690i	$-0.562655\pi$
$701$	17.9163	−	13.0170i	0.676690	−	0.491644i	0.872258	+	0.489046i	$0.162655\pi$
$702$	0.193479	−	9.62530i	0.00730241	−	0.363284i
$703$	25.5091			0.962094
$704$	−43.1586	+	37.3145i	−1.62660	+	1.40634i
$705$	11.3241			0.426488
$706$	−1.44721	+	4.45407i	−0.0544666	+	0.167631i
$707$	0.909302	+	1.25155i	0.0341978	+	0.0470692i
$708$	30.7269	−	42.2919i	1.15479	−	1.58943i
$709$	−26.5490	+	8.62630i	−0.997070	+	0.323968i	−0.761694	−	0.647937i	$-0.775632\pi$
$709$	−26.5490	+	8.62630i	−0.997070	+	0.323968i	−0.235376	+	0.971904i	$0.575632\pi$
$710$	−29.2195	+	9.49398i	−1.09659	+	0.356303i
$711$	12.0112	+	8.72665i	0.450456	+	0.327275i
$712$	49.3997	−	35.8910i	1.85133	−	1.34507i
$713$	−4.46632	−	1.45120i	−0.167265	−	0.0543477i
$714$	2.78553			0.104246
$715$	−17.7308	−	4.52125i	−0.663096	−	0.169085i
$716$	−117.429			−4.38851
$717$	−6.31301	−	2.05122i	−0.235764	−	0.0766042i
$718$	−44.8732	+	32.6023i	−1.67465	+	1.21671i
$719$	18.4225	+	13.3847i	0.687043	+	0.499166i	0.875687	−	0.482879i	$-0.160409\pi$
$719$	18.4225	+	13.3847i	0.687043	+	0.499166i	−0.188643	+	0.982046i	$0.560409\pi$
$720$	−17.5405	+	5.69926i	−0.653696	+	0.212399i
$721$	−3.10148	+	1.00773i	−0.115505	+	0.0375298i
$722$	−19.7274	+	27.1525i	−0.734179	+	1.01051i
$723$	−0.759324	−	1.04512i	−0.0282395	−	0.0388684i
$724$	−28.8963	+	88.9337i	−1.07392	+	3.30520i
$725$	−19.4493			−0.722328
$726$	21.0182	+	20.5160i	0.780059	+	0.761422i
$727$	26.3797			0.978368			0.489184	−	0.872181i	$-0.337295\pi$
$727$	26.3797			0.978368			0.489184	+	0.872181i	$0.337295\pi$
$728$	18.8442	+	0.378790i	0.698413	+	0.0140389i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−19.7773	+	27.2212i	−0.731992	+	1.00750i
$731$	1.31949	+	4.06096i	0.0488030	+	0.150200i
$732$	11.4406	+	35.2106i	0.422857	+	1.30142i
$733$	16.9336	−	23.3070i	0.625455	−	0.860865i	−0.372281	−	0.928120i	$-0.621424\pi$
$733$	16.9336	−	23.3070i	0.625455	−	0.860865i	0.997736	+	0.0672552i	$0.0214242\pi$
$734$	−53.4463	−	73.5626i	−1.97274	−	2.71524i
$735$	9.61743	+	3.12489i	0.354744	+	0.115263i
$736$			96.4332i			3.55457i
$737$	20.4583	−	33.8424i	0.753590	−	1.24660i
$738$	−3.66293			−0.134834
$739$	4.15409	+	1.34974i	0.152811	+	0.0496512i	0.384423	−	0.923157i	$-0.374400\pi$
$739$	4.15409	+	1.34974i	0.152811	+	0.0496512i	−0.231613	+	0.972808i	$0.574400\pi$
$740$	63.8780	−	46.4101i	2.34820	−	1.70607i
$741$	8.63701	+	2.99954i	0.317289	+	0.110191i
$742$	2.94955	+	9.07779i	0.108282	+	0.333256i
$743$	−12.4039	+	4.03028i	−0.455056	+	0.147857i	−0.527571	−	0.849511i	$-0.676897\pi$
$743$	−12.4039	+	4.03028i	−0.455056	+	0.147857i	0.0725156	+	0.997367i	$0.476897\pi$
$744$	5.09319	+	3.70042i	0.186725	+	0.135664i
$745$	−24.7984	+	18.0171i	−0.908544	+	0.660096i
$746$	20.8901	+	6.78762i	0.764843	+	0.248512i
$747$		−	4.73738i		−	0.173332i
$748$	21.4613	−	18.5552i	0.784704	−	0.678447i
$749$		−	7.88999i		−	0.288294i
$750$	9.66943	−	29.7595i	0.353078	−	1.08666i
$751$	17.8949	−	13.0014i	0.652996	−	0.474429i	−0.211294	−	0.977422i	$-0.567768\pi$
$751$	17.8949	−	13.0014i	0.652996	−	0.474429i	0.864290	+	0.502993i	$0.167768\pi$
$752$	−52.4295	+	72.1630i	−1.91191	+	2.63151i
$753$	4.98840	+	15.3527i	0.181788	+	0.559484i
$754$	−40.2442	−	57.7995i	−1.46561	−	2.10493i
$755$	19.7671	+	14.3617i	0.719399	+	0.522674i
$756$	−1.88617	−	2.59609i	−0.0685993	−	0.0944189i
$757$	13.9210	−	42.8446i	0.505969	−	1.55721i	−0.293167	−	0.956061i	$-0.594709\pi$
$757$	13.9210	−	42.8446i	0.505969	−	1.55721i	0.799136	−	0.601151i	$-0.205291\pi$
$758$	76.7077			2.78615
$759$	20.5998	−	1.74659i	0.747724	−	0.0633973i
$760$		−	32.4242i		−	1.17615i
$761$	32.5173	+	10.5655i	1.17875	+	0.383000i	0.831903	−	0.554921i	$-0.187252\pi$
$761$	32.5173	+	10.5655i	1.17875	+	0.383000i	0.346849	+	0.937921i	$0.387252\pi$
$762$	−4.28534	−	5.89826i	−0.155241	−	0.213671i
$763$	3.70337	+	2.69066i	0.134071	+	0.0974083i
$764$	−9.97492	−	30.6996i	−0.360880	−	1.11067i
$765$	2.42683	−	0.788526i	0.0877424	−	0.0285092i
$766$	11.1278	+	8.08481i	0.402063	+	0.292116i
$767$	−22.1910	+	29.2870i	−0.801271	+	1.05749i
$768$	1.73744	−	5.34729i	0.0626945	−	0.192954i
$769$			1.77172i			0.0638898i	0.999490	+	0.0319449i	$0.0101701\pi$
$769$			1.77172i			0.0638898i	−0.999490	+	0.0319449i	$0.989830\pi$
$770$	−7.81215	+	3.29136i	−0.281530	+	0.118612i
$771$	−29.3297			−1.05628
$772$	36.8096	+	11.9601i	1.32480	+	0.430455i
$773$	−15.1375	−	20.8350i	−0.544457	−	0.749381i	0.444790	−	0.895635i	$-0.353278\pi$
$773$	−15.1375	−	20.8350i	−0.544457	−	0.749381i	−0.989247	+	0.146254i	$0.953278\pi$
$774$	4.01863	−	5.53117i	0.144447	−	0.198814i
$775$	−1.90492	+	0.618947i	−0.0684269	+	0.0222332i
$776$	29.3782	+	90.4168i	1.05462	+	3.24577i
$777$	5.09118	+	3.69896i	0.182645	+	0.132699i
$778$	25.7599	+	35.4555i	0.923538	+	1.27114i
$779$	1.07498	−	3.30844i	0.0385150	−	0.118537i
$780$	27.0854	−	8.20256i	0.969813	−	0.293699i
$781$	−24.2854	−	5.67536i	−0.868999	−	0.203080i
$782$		−	27.7553i		−	0.992526i
$783$	−2.26067	+	6.95763i	−0.0807898	+	0.248646i
$784$	−64.4415	+	46.8195i	−2.30148	+	1.67212i
$785$	2.14582	−	2.95346i	0.0765875	−	0.105414i
$786$	−53.4160	+	17.3559i	−1.90528	+	0.619064i
$787$	−1.31080	+	0.425906i	−0.0467251	+	0.0151819i	−0.332286	−	0.943179i	$-0.607820\pi$
$787$	−1.31080	+	0.425906i	−0.0467251	+	0.0151819i	0.285561	+	0.958360i	$0.407820\pi$
$788$	−66.2409	+	91.1728i	−2.35973	+	3.24790i
$789$	−1.98939	+	1.44538i	−0.0708242	+	0.0514568i
$790$	−18.7449	+	57.6908i	−0.666912	+	2.05254i
$791$			10.7409i			0.381902i
$792$	−26.9873	−	6.30678i	−0.958951	−	0.224102i
$793$	−7.54260	−	24.9062i	−0.267846	−	0.884444i
$794$	24.8136	−	76.3683i	0.880601	−	2.71021i
$795$	5.13946	+	7.07387i	0.182278	+	0.250884i
$796$	14.6881	+	10.6715i	0.520606	+	0.378242i
$797$	11.0742	+	34.0829i	0.392269	+	1.20728i	0.931068	+	0.364845i	$0.118878\pi$
$797$	11.0742	+	34.0829i	0.392269	+	1.20728i	−0.538800	+	0.842434i	$0.681122\pi$
$798$	4.02847	−	1.30893i	0.142606	−	0.0463356i
$799$	7.25393	−	9.98418i	0.256626	−	0.353215i
$800$	24.1753	+	33.2745i	0.854727	+	1.17643i
$801$	6.94966	+	2.25808i	0.245554	+	0.0797854i
$802$	29.0197			1.02472
$803$	−25.1706	+	10.6047i	−0.888251	+	0.374232i
$804$			61.1615i			2.15700i
$805$	−1.84386	+	5.67483i	−0.0649876	+	0.200011i
$806$	−5.78103	−	4.38034i	−0.203628	−	0.154291i
$807$	9.29076	+	6.75013i	0.327050	+	0.237616i
$808$	−19.6526	+	6.38552i	−0.691376	+	0.224642i
$809$	15.9768	+	49.1717i	0.561716	+	1.72878i	0.677513	+	0.735511i	$0.263058\pi$
$809$	15.9768	+	49.1717i	0.561716	+	1.72878i	−0.115797	+	0.993273i	$0.536942\pi$
$810$	−3.30543	−	2.40154i	−0.116141	−	0.0843814i
$811$	−4.99948	−	6.88119i	−0.175555	−	0.241631i	0.712167	−	0.702010i	$-0.247714\pi$
$811$	−4.99948	−	6.88119i	−0.175555	−	0.241631i	−0.887723	+	0.460378i	$0.847714\pi$
$812$	−22.3267	−	7.25437i	−0.783512	−	0.254578i
$813$			4.19578i			0.147152i
$814$	88.7661	−	7.52622i	3.11125	−	0.263794i
$815$	15.0966			0.528810
$816$	−6.21114	+	19.1159i	−0.217433	+	0.669191i
$817$	3.81651	+	5.25298i	0.133523	+	0.183779i
$818$	−77.2816	−	56.1484i	−2.70209	−	1.96318i
$819$	1.28885	+	1.85107i	0.0450361	+	0.0646816i
$820$	−3.32735	−	10.2405i	−0.116196	−	0.357614i
$821$	7.10633	−	9.78102i	0.248013	−	0.341360i	−0.666801	−	0.745235i	$-0.732337\pi$
$821$	7.10633	−	9.78102i	0.248013	−	0.341360i	0.914814	+	0.403875i	$0.132337\pi$
$822$	9.74844	−	7.08266i	0.340016	−	0.247036i
$823$	14.4039	−	44.3306i	0.502088	−	1.54527i	−0.303523	−	0.952824i	$-0.598163\pi$
$823$	14.4039	−	44.3306i	0.502088	−	1.54527i	0.805611	−	0.592444i	$-0.201837\pi$
$824$		−	43.5599i		−	1.51748i
$825$	6.67013	−	5.76693i	0.232224	−	0.200779i
$826$			17.0230i			0.592308i
$827$	26.3203	+	8.55198i	0.915247	+	0.297382i	0.728515	−	0.685029i	$-0.240211\pi$
$827$	26.3203	+	8.55198i	0.915247	+	0.297382i	0.186731	+	0.982411i	$0.440211\pi$
$828$	−25.8676	+	18.7939i	−0.898962	+	0.653134i
$829$	26.9714	+	19.5959i	0.936756	+	0.680593i	0.947638	−	0.319348i	$-0.103464\pi$
$829$	26.9714	+	19.5959i	0.936756	+	0.680593i	−0.0108818	+	0.999941i	$0.503464\pi$
$830$	18.4084	−	5.98124i	0.638964	−	0.207612i
$831$	5.57657	+	17.1629i	0.193449	+	0.595375i
$832$	−20.3478	+	58.5904i	−0.705433	+	2.03126i
$833$	8.91587	−	6.47776i	0.308916	−	0.224441i
$834$	35.6083	+	11.5698i	1.23301	+	0.400631i
$835$	−1.90206			−0.0658235
$836$	22.3185	−	36.9196i	0.771901	−	1.27689i
$837$			0.753395i			0.0260411i
$838$	14.9945	+	4.87202i	0.517978	+	0.168301i
$839$	2.17582	+	2.99476i	0.0751176	+	0.103390i	0.844922	−	0.534889i	$-0.179647\pi$
$839$	2.17582	+	2.99476i	0.0751176	+	0.103390i	−0.769805	+	0.638279i	$0.779647\pi$
$840$	4.70168	−	6.47131i	0.162223	−	0.223281i
$841$	7.57688	+	23.3192i	0.261272	+	0.804112i
$842$	−1.29184	−	3.97587i	−0.0445196	−	0.137017i
$843$	7.90650	−	10.8824i	0.272314	−	0.374809i
$844$	42.6413	−	30.9807i	1.46778	−	1.06640i
$845$	−19.1504	+	5.38181i	−0.658793	+	0.185140i
$846$	−19.7602			−0.679371
$847$	−6.80921	−	0.994242i	−0.233967	−	0.0341625i
$848$	−68.8738			−2.36514
$849$	10.0817	−	31.0282i	0.346002	−	1.06488i
$850$	−6.95811	−	9.57701i	−0.238661	−	0.328489i
$851$	36.8567	−	50.7289i	1.26343	−	1.73896i
$852$	36.6842	−	11.9194i	1.25678	−	0.408353i
$853$	45.0130	−	14.6256i	1.54122	−	0.500772i	0.589505	−	0.807765i	$-0.299323\pi$
$853$	45.0130	−	14.6256i	1.54122	−	0.500772i	0.951712	+	0.306993i	$0.0993229\pi$
$854$	−9.75354	−	7.08636i	−0.333759	−	0.242490i
$855$	3.13919	−	2.28075i	0.107358	−	0.0780001i
$856$	100.232	+	32.5674i	3.42587	+	1.11313i
$857$	−20.1676			−0.688914			−0.344457	−	0.938802i	$-0.611937\pi$
$857$	−20.1676			−0.688914			−0.344457	+	0.938802i	$0.611937\pi$
$858$	30.9399	+	7.88948i	1.05627	+	0.269342i
$859$	−4.70408			−0.160501			−0.0802505	−	0.996775i	$-0.525572\pi$
$859$	−4.70408			−0.160501			−0.0802505	+	0.996775i	$0.525572\pi$
$860$	19.1141	+	6.21054i	0.651784	+	0.211778i
$861$	0.694289	−	0.504430i	0.0236613	−	0.0171909i
$862$	45.4017	+	32.9863i	1.54639	+	1.12352i
$863$	−40.0682	+	13.0190i	−1.36394	+	0.443171i	−0.897356	−	0.441307i	$-0.854515\pi$
$863$	−40.0682	+	13.0190i	−1.36394	+	0.443171i	−0.466583	+	0.884478i	$0.654515\pi$
$864$	14.7133	−	4.78066i	0.500558	−	0.162641i
$865$	−8.58831	+	11.8208i	−0.292011	+	0.401919i
$866$	−14.1339	−	19.4537i	−0.480291	−	0.661063i
$867$	−4.39394	+	13.5232i	−0.149226	+	0.459271i
$868$	−2.41760			−0.0820587
$869$	−37.2490	+	32.2051i	−1.26359	+	1.09248i
$870$	−29.8900			−1.01337
$871$	0.863982	−	42.9818i	0.0292749	−	1.45638i
$872$	−49.4677	+	35.9404i	−1.67519	+	1.21710i
$873$	−6.68732	+	9.20431i	−0.226332	+	0.311519i
$874$	−13.0423	−	40.1400i	−0.441161	−	1.35776i
$875$	2.26545	+	6.97235i	0.0765863	+	0.235708i
$876$	24.8299	−	34.1754i	0.838924	−	1.15468i
$877$	2.80949	+	3.86694i	0.0948698	+	0.130577i	0.853813	−	0.520580i	$-0.174284\pi$
$877$	2.80949	+	3.86694i	0.0948698	+	0.130577i	−0.758943	+	0.651157i	$0.774284\pi$
$878$	38.7703	+	12.5972i	1.30843	+	0.425136i
$879$		−	1.22409i		−	0.0412874i
$880$	−5.16781	−	60.9504i	−0.174207	−	2.05464i
$881$	5.57645			0.187875			0.0939377	−	0.995578i	$-0.470055\pi$
$881$	5.57645			0.187875			0.0939377	+	0.995578i	$0.470055\pi$
$882$	−16.7822	−	5.45287i	−0.565087	−	0.183608i
$883$	−4.98472	+	3.62161i	−0.167749	+	0.121877i	−0.668492	−	0.743719i	$-0.733060\pi$
$883$	−4.98472	+	3.62161i	−0.167749	+	0.121877i	0.500743	+	0.865596i	$0.333060\pi$
$884$	10.1183	−	29.1350i	0.340314	−	0.979917i
$885$	4.81887	+	14.8309i	0.161984	+	0.498537i
$886$	3.70220	−	1.20292i	0.124378	−	0.0404128i
$887$	29.1450	+	21.1751i	0.978593	+	0.710989i	0.957394	−	0.288786i	$-0.0932516\pi$
$887$	29.1450	+	21.1751i	0.978593	+	0.710989i	0.0211993	+	0.999775i	$0.493252\pi$
$888$	−68.0053	+	49.4088i	−2.28211	+	1.65805i
$889$	1.62453	+	0.527841i	0.0544849	+	0.0177032i
$890$			29.8558i			1.00077i
$891$	−1.28772	−	3.05643i	−0.0431401	−	0.102394i
$892$			116.807i			3.91100i
$893$	5.79913	−	17.8479i	0.194061	−	0.597257i
$894$	43.2727	−	31.4395i	1.44726	−	1.05149i
$895$	20.5900	−	28.3397i	0.688247	−	0.947290i
$896$	2.89792	+	8.91888i	0.0968127	+	0.297959i
$897$	18.4442	−	12.8422i	0.615834	−	0.428788i
$898$	78.7501	+	57.2153i	2.62792	+	1.90930i
$899$	3.23964	+	4.45898i	0.108048	+	0.148715i
$900$	−4.21413	+	12.9698i	−0.140471	+	0.432326i
$901$	9.52911			0.317461
$902$	2.76456	−	11.8298i	0.0920499	−	0.393890i
$903$			1.60182i			0.0533052i
$904$	−136.449	−	44.3351i	−4.53824	−	1.47456i
$905$	−16.3961	−	22.5674i	−0.545026	−	0.750165i
$906$	−34.4932	−	25.0608i	−1.14596	−	0.832589i
$907$	−5.19064	−	15.9751i	−0.172352	−	0.530446i	0.827150	−	0.561981i	$-0.189960\pi$
$907$	−5.19064	−	15.9751i	−0.172352	−	0.530446i	−0.999503	+	0.0315349i	$0.989960\pi$
$908$	0.723630	−	0.235122i	0.0240145	−	0.00780279i
$909$	−2.00061	−	1.45353i	−0.0663560	−	0.0482105i
$910$	−5.56558	+	7.34527i	−0.184497	+	0.243493i
$911$	−1.87423	+	5.76827i	−0.0620959	+	0.191111i	−0.977292	−	0.211898i	$-0.932036\pi$
$911$	−1.87423	+	5.76827i	−0.0620959	+	0.191111i	0.915196	+	0.403009i	$0.132036\pi$
$912$			30.5643i			1.01209i
$913$	15.2999	+	3.57550i	0.506352	+	0.118332i
$914$	−22.3959			−0.740790
$915$	−10.5035	−	3.41281i	−0.347237	−	0.112824i
$916$	47.1592	+	64.9091i	1.55818	+	2.14466i
$917$	7.73460	−	10.6458i	0.255419	−	0.351554i
$918$	−4.23477	+	1.37596i	−0.139768	+	0.0454135i
$919$	−0.539142	−	1.65931i	−0.0177847	−	0.0547356i	0.941770	−	0.336257i	$-0.109161\pi$
$919$	−0.539142	−	1.65931i	−0.0177847	−	0.0547356i	−0.959555	+	0.281521i	$0.909161\pi$
$920$	−64.4805	−	46.8479i	−2.12586	−	1.54453i
$921$	−8.38631	−	11.5428i	−0.276338	−	0.380347i
$922$	−4.23214	+	13.0252i	−0.139378	+	0.428962i
$923$	−25.9485	+	7.85827i	−0.854106	+	0.258658i
$924$	9.80792	−	4.13221i	0.322657	−	0.135940i
$925$		−	26.7439i		−	0.879334i
$926$	27.0820	−	83.3498i	0.889970	−	2.73904i
$927$	4.21730	−	3.06405i	0.138514	−	0.100637i
$928$	66.5241	−	91.5626i	2.18376	−	3.00569i
$929$	−26.7538	+	8.69285i	−0.877765	+	0.285203i	−0.713029	−	0.701134i	$-0.752677\pi$
$929$	−26.7538	+	8.69285i	−0.877765	+	0.285203i	−0.164736	+	0.986338i	$0.552677\pi$
$930$	−2.92752	+	0.951209i	−0.0959971	+	0.0311914i
$931$	9.85032	−	13.5578i	0.322831	−	0.444339i
$932$	24.1897	−	17.5749i	0.792360	−	0.575684i
$933$	−7.27360	+	22.3858i	−0.238127	+	0.732879i
$934$			34.1445i			1.11724i
$935$	0.714997	+	8.43286i	0.0233829	+	0.275784i
$936$	−28.8355	+	8.73255i	−0.942516	+	0.285432i
$937$	−7.18308	+	22.1072i	−0.234661	+	0.722212i	0.762505	+	0.646982i	$0.223969\pi$
$937$	−7.18308	+	22.1072i	−0.234661	+	0.722212i	−0.997166	+	0.0752302i	$0.976031\pi$
$938$	−11.7067	−	16.1129i	−0.382237	−	0.526104i
$939$	−23.8417	−	17.3220i	−0.778044	−	0.565282i
$940$	−17.9499	−	55.2441i	−0.585461	−	1.80186i
$941$	−8.72636	+	2.83537i	−0.284471	+	0.0924303i	−0.447777	−	0.894145i	$-0.647784\pi$
$941$	−8.72636	+	2.83537i	−0.284471	+	0.0924303i	0.163306	+	0.986575i	$0.447784\pi$
$942$	−3.74440	+	5.15373i	−0.121999	+	0.167918i
$943$	−5.02618	−	6.91794i	−0.163675	−	0.225279i
$944$	−116.822	−	37.9577i	−3.80223	−	1.23542i
$945$	0.957249			0.0311393
$946$	14.8305	+	17.1532i	0.482181	+	0.557699i
$947$		−	21.2836i		−	0.691624i	−0.938304	−	0.345812i	$-0.887603\pi$
$947$		−	21.2836i		−	0.691624i	0.938304	−	0.345812i	$-0.112397\pi$
$948$	23.5336	−	72.4291i	0.764337	−	2.35239i
$949$	−17.9322	+	23.6663i	−0.582104	+	0.768241i
$950$	−14.5632	−	10.5808i	−0.472491	−	0.343285i
$951$	−20.5020	+	6.66151i	−0.664823	+	0.216014i
$952$	−2.69383	−	8.29075i	−0.0873075	−	0.268705i
$953$	−4.28942	−	3.11645i	−0.138948	−	0.100952i	0.516140	−	0.856504i	$-0.327368\pi$
$953$	−4.28942	−	3.11645i	−0.138948	−	0.100952i	−0.655088	+	0.755553i	$0.727368\pi$
$954$	−8.96825	−	12.3437i	−0.290358	−	0.399643i
$955$	9.15791	+	2.97558i	0.296343	+	0.0962877i
$956$			34.0492i			1.10123i
$957$	−20.7642	−	12.5523i	−0.671211	−	0.405758i
$958$	−73.0735			−2.36090
$959$	−0.872397	+	2.68496i	−0.0281712	+	0.0867020i
$960$	15.4718	+	21.2951i	0.499350	+	0.687297i
$961$	−24.6203	−	17.8877i	−0.794204	−	0.577023i
$962$	79.4776	−	55.3381i	2.56246	−	1.78417i
$963$	3.89739	+	11.9949i	0.125592	+	0.386531i
$964$	−3.89497	+	5.36097i	−0.125449	+	0.172665i
$965$	−9.34060	+	6.78634i	−0.300685	+	0.218460i
$966$	3.21750	−	9.90245i	0.103521	−	0.318606i
$967$			5.98311i			0.192404i	0.995362	+	0.0962019i	$0.0306695\pi$
$967$			5.98311i			0.192404i	−0.995362	+	0.0962019i	$0.969331\pi$
$968$	40.7369	−	82.3983i	1.30933	−	2.64838i
$969$		−	4.22875i		−	0.135847i
$970$	−44.2090	−	14.3644i	−1.41947	−	0.461212i
$971$	12.7917	−	9.29372i	0.410505	−	0.298250i	−0.363301	−	0.931672i	$-0.618350\pi$
$971$	12.7917	−	9.29372i	0.410505	−	0.298250i	0.773806	+	0.633422i	$0.218350\pi$
$972$	4.14988	+	3.01506i	0.133107	+	0.0967081i
$973$	−8.34268	+	2.71070i	−0.267454	+	0.0869010i
$974$	−16.5993	−	51.0874i	−0.531876	−	1.63695i
$975$	3.14474	−	9.05509i	0.100712	−	0.289995i
$976$	70.3789	−	51.1333i	2.25277	−	1.63674i
$977$	40.6894	+	13.2208i	1.30177	+	0.422971i	0.876197	−	0.481954i	$-0.160073\pi$
$977$	40.6894	+	13.2208i	1.30177	+	0.422971i	0.425573	+	0.904924i	$0.360073\pi$
$978$	−26.3432			−0.842362
$979$	−12.5379	+	20.7404i	−0.400714	+	0.662866i
$980$		−	51.8717i		−	1.65698i
$981$	−6.95923	−	2.26119i	−0.222191	−	0.0721943i
$982$	−42.0608	−	57.8918i	−1.34221	−	1.84740i
$983$	−14.3965	+	19.8151i	−0.459178	+	0.632004i	−0.974338	−	0.225090i	$-0.927733\pi$
$983$	−14.3965	+	19.8151i	−0.459178	+	0.632004i	0.515160	+	0.857094i	$0.327733\pi$
$984$	3.54233	+	10.9022i	0.112925	+	0.347549i
$985$	−10.3885	−	31.9725i	−0.331005	−	1.01873i
$986$	−19.1469	+	26.3534i	−0.609760	+	0.839263i
$987$	3.74545	−	2.72123i	0.119219	−	0.0866176i
$988$	0.942542	−	46.8900i	0.0299863	−	1.49177i
$989$	15.9606			0.507519
$990$	10.2508	−	8.86271i	0.325791	−	0.281675i
$991$	31.1305			0.988893			0.494447	−	0.869208i	$-0.335371\pi$
$991$	31.1305			0.988893			0.494447	+	0.869208i	$0.335371\pi$
$992$	3.60172	−	11.0850i	0.114355	−	0.351948i
$993$	11.6337	+	16.0124i	0.369185	+	0.508139i
$994$	−7.38293	+	10.1617i	−0.234172	+	0.322311i
$995$	−5.15083	+	1.67361i	−0.163292	+	0.0530569i
$996$	−23.1112	+	7.50927i	−0.732305	+	0.237940i
$997$	−24.2734	−	17.6357i	−0.768747	−	0.558528i	0.132833	−	0.991138i	$-0.457592\pi$
$997$	−24.2734	−	17.6357i	−0.768747	−	0.558528i	−0.901581	+	0.432611i	$0.857592\pi$
$998$	−8.16307	+	5.93082i	−0.258398	+	0.187737i
$999$	−9.56715	−	3.10855i	−0.302691	−	0.0983503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.64.1	✓	56
11.5	even	5	inner	429.2.bb.a.181.14	yes	56
13.12	even	2	inner	429.2.bb.a.64.14	yes	56
143.38	even	10	inner	429.2.bb.a.181.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.64.1	✓	56	1.1	even	1	trivial
429.2.bb.a.64.14	yes	56	13.12	even	2	inner
429.2.bb.a.181.1	yes	56	143.38	even	10	inner
429.2.bb.a.181.14	yes	56	11.5	even	5	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.53943 - 0.825112i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(4.14988 + 3.01506i) q^{4} +(-1.45528 + 0.472849i) q^{5} +(2.53943 - 0.825112i) q^{6} +(-0.367708 + 0.506107i) q^{7} +(-4.91166 - 6.76032i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-2.53943 - 0.825112i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(4.14988 + 3.01506i) q^{4} +(-1.45528 + 0.472849i) q^{5} +(2.53943 - 0.825112i) q^{6} +(-0.367708 + 0.506107i) q^{7} +(-4.91166 - 6.76032i) q^{8} +(0.309017 - 0.951057i) q^{9} +4.08574 q^{10} +(2.83831 + 1.71581i) q^{11} -5.12953 q^{12} +(3.60482 + 0.0724610i) q^{13} +(1.35137 - 0.981824i) q^{14} +(0.899413 - 1.23794i) q^{15} +(3.72458 + 11.4631i) q^{16} +(-0.515319 - 1.58599i) q^{17} +(-1.56946 + 2.16017i) q^{18} +(-1.49052 - 2.05152i) q^{19} +(-7.46490 - 2.42549i) q^{20} -0.625583i q^{21} +(-5.79197 - 6.69910i) q^{22} -6.23335 q^{23} +(7.94723 + 2.58221i) q^{24} +(-2.15083 + 1.56267i) q^{25} +(-9.09442 - 3.15839i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-3.05189 + 0.991618i) q^{28} +(5.91852 + 4.30005i) q^{29} +(-3.30543 + 2.40154i) q^{30} +(0.716521 + 0.232812i) q^{31} -15.4705i q^{32} +(-3.30477 + 0.280202i) q^{33} +4.45270i q^{34} +(0.295806 - 0.910398i) q^{35} +(4.14988 - 3.01506i) q^{36} +(-5.91282 + 8.13830i) q^{37} +(2.09234 + 6.43955i) q^{38} +(-2.95895 + 2.06024i) q^{39} +(10.3444 + 7.51568i) q^{40} +(0.806337 + 1.10983i) q^{41} +(-0.516176 + 1.58863i) q^{42} -2.56053 q^{43} +(6.60538 + 15.6781i) q^{44} +1.53017i q^{45} +(15.8292 + 5.14321i) q^{46} +(4.34991 + 5.98714i) q^{47} +(-9.75109 - 7.08458i) q^{48} +(2.04218 + 6.28520i) q^{49} +(6.75127 - 2.19362i) q^{50} +(1.34912 + 0.980194i) q^{51} +(14.7411 + 11.1695i) q^{52} +(-1.76580 + 5.43457i) q^{53} -2.67012i q^{54} +(-4.94186 - 1.15489i) q^{55} +5.22750 q^{56} +(2.41171 + 0.783613i) q^{57} +(-11.4816 - 15.8031i) q^{58} +(-5.99019 + 8.24479i) q^{59} +(7.46490 - 2.42549i) q^{60} +(-2.23034 - 6.86429i) q^{61} +(-1.62746 - 1.18242i) q^{62} +(0.367708 + 0.506107i) q^{63} +(-5.31575 + 16.3602i) q^{64} +(-5.28029 + 1.59909i) q^{65} +(8.62343 + 2.01525i) q^{66} -11.9234i q^{67} +(2.64334 - 8.13537i) q^{68} +(5.04288 - 3.66387i) q^{69} +(-1.50236 + 2.06782i) q^{70} +(-7.15157 + 2.32369i) q^{71} +(-7.94723 + 2.58221i) q^{72} +(-4.84058 + 6.66248i) q^{73} +(21.7302 - 15.7879i) q^{74} +(0.821544 - 2.52845i) q^{75} -13.0076i q^{76} +(-1.91205 + 0.805573i) q^{77} +(9.21399 - 2.79037i) q^{78} +(-4.58787 + 14.1200i) q^{79} +(-10.8406 - 14.9208i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.13191 - 3.48365i) q^{82} +(4.50551 - 1.46393i) q^{83} +(1.88617 - 2.59609i) q^{84} +(1.49987 + 2.06439i) q^{85} +(6.50228 + 2.11272i) q^{86} -7.31569 q^{87} +(-2.34142 - 27.6153i) q^{88} +7.30731i q^{89} +(1.26256 - 3.88577i) q^{90} +(-1.36220 + 1.79778i) q^{91} +(-25.8676 - 18.7939i) q^{92} +(-0.716521 + 0.232812i) q^{93} +(-6.10625 - 18.7931i) q^{94} +(3.13919 + 2.28075i) q^{95} +(9.09335 + 12.5159i) q^{96} +(-10.8203 - 3.51573i) q^{97} -17.6459i q^{98} +(2.50891 - 2.16918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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