LMFDB - Embedded newform 429.2.n.c.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	429.157
Dual form			429.2.n.c.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44143 + 1.04726i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.362933 - 1.11699i) q^{4} +(2.24980 + 1.63458i) q^{5} +(1.44143 + 1.04726i) q^{6} +(-0.0806900 + 0.248338i) q^{7} +(-0.454515 - 1.39885i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.44143 + 1.04726i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.362933 - 1.11699i) q^{4} +(2.24980 + 1.63458i) q^{5} +(1.44143 + 1.04726i) q^{6} +(-0.0806900 + 0.248338i) q^{7} +(-0.454515 - 1.39885i) q^{8} +(-0.809017 + 0.587785i) q^{9} -4.95476 q^{10} +(0.650478 + 3.25221i) q^{11} -1.17448 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.143766 - 0.442466i) q^{14} +(0.859348 - 2.64480i) q^{15} +(4.02046 + 2.92103i) q^{16} +(3.03587 + 2.20569i) q^{17} +(0.550577 - 1.69450i) q^{18} +(-1.80841 - 5.56572i) q^{19} +(2.64234 - 1.91977i) q^{20} +0.261118 q^{21} +(-4.34353 - 4.00662i) q^{22} +7.50231 q^{23} +(-1.18994 + 0.864539i) q^{24} +(0.844682 + 2.59966i) q^{25} +(0.550577 - 1.69450i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.248107 + 0.180260i) q^{28} +(-2.17401 + 6.69093i) q^{29} +(1.53110 + 4.71226i) q^{30} +(-7.33192 + 5.32695i) q^{31} -5.91261 q^{32} +(2.89203 - 1.62363i) q^{33} -6.68592 q^{34} +(-0.587464 + 0.426818i) q^{35} +(0.362933 + 1.11699i) q^{36} +(-2.58363 + 7.95161i) q^{37} +(8.43545 + 6.12871i) q^{38} +(0.809017 + 0.587785i) q^{39} +(1.26396 - 3.89008i) q^{40} +(1.24079 + 3.81875i) q^{41} +(-0.376384 + 0.273459i) q^{42} +1.53022 q^{43} +(3.86878 + 0.453756i) q^{44} -2.78091 q^{45} +(-10.8141 + 7.85688i) q^{46} +(2.73242 + 8.40951i) q^{47} +(1.53568 - 4.72633i) q^{48} +(5.60796 + 4.07442i) q^{49} +(-3.94007 - 2.86263i) q^{50} +(1.15960 - 3.56888i) q^{51} +(0.362933 + 1.11699i) q^{52} +(1.20436 - 0.875022i) q^{53} -1.78171 q^{54} +(-3.85254 + 8.38009i) q^{55} +0.384064 q^{56} +(-4.73448 + 3.43980i) q^{57} +(-3.87345 - 11.9213i) q^{58} +(2.10986 - 6.49350i) q^{59} +(-2.64234 - 1.91977i) q^{60} +(-8.26202 - 6.00271i) q^{61} +(4.98975 - 15.3569i) q^{62} +(-0.0806900 - 0.248338i) q^{63} +(0.481696 - 0.349972i) q^{64} -2.78091 q^{65} +(-2.46829 + 5.36906i) q^{66} +8.40802 q^{67} +(3.56555 - 2.59053i) q^{68} +(-2.31834 - 7.13513i) q^{69} +(0.399800 - 1.23046i) q^{70} +(-5.01275 - 3.64197i) q^{71} +(1.18994 + 0.864539i) q^{72} +(0.191681 - 0.589933i) q^{73} +(-4.60328 - 14.1674i) q^{74} +(2.21141 - 1.60668i) q^{75} -6.87319 q^{76} +(-0.860136 - 0.100882i) q^{77} -1.78171 q^{78} +(6.87105 - 4.99211i) q^{79} +(4.27058 + 13.1435i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.78773 - 4.20503i) q^{82} +(-1.59707 - 1.16034i) q^{83} +(0.0947684 - 0.291667i) q^{84} +(3.22474 + 9.92472i) q^{85} +(-2.20570 + 1.60253i) q^{86} +7.03526 q^{87} +(4.25372 - 2.38810i) q^{88} -10.2488 q^{89} +(4.00848 - 2.91233i) q^{90} +(-0.0806900 - 0.248338i) q^{91} +(2.72284 - 8.38003i) q^{92} +(7.33192 + 5.32695i) q^{93} +(-12.7455 - 9.26017i) q^{94} +(5.02902 - 15.4777i) q^{95} +(1.82710 + 5.62322i) q^{96} +(9.86280 - 7.16574i) q^{97} -12.3505 q^{98} +(-2.43785 - 2.24875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) $ 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.44143	+	1.04726i	−1.01925	+	0.740525i	−0.966128	−	0.258063i	$-0.916916\pi$
$2$	−1.44143	+	1.04726i	−1.01925	+	0.740525i	−0.0531171	+	0.998588i	$0.516916\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.362933	−	1.11699i	0.181466	−	0.558496i
$5$	2.24980	+	1.63458i	1.00614	+	0.731005i	0.963396	−	0.268081i	$-0.0863895\pi$
$5$	2.24980	+	1.63458i	1.00614	+	0.731005i	0.0427455	+	0.999086i	$0.486390\pi$
$6$	1.44143	+	1.04726i	0.588461	+	0.427542i
$7$	−0.0806900	+	0.248338i	−0.0304980	+	0.0938630i	−0.965147	−	0.261709i	$-0.915714\pi$
$7$	−0.0806900	+	0.248338i	−0.0304980	+	0.0938630i	0.934649	+	0.355572i	$0.115714\pi$
$8$	−0.454515	−	1.39885i	−0.160695	−	0.494570i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−4.95476			−1.56683
$11$	0.650478	+	3.25221i	0.196126	+	0.980579i
$11$	0.650478	+	3.25221i	0.196126	+	0.980579i
$12$	−1.17448			−0.339042
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−0.143766	−	0.442466i	−0.0384230	−	0.118254i
$15$	0.859348	−	2.64480i	0.221883	−	0.682885i
$16$	4.02046	+	2.92103i	1.00511	+	0.730258i
$17$	3.03587	+	2.20569i	0.736307	+	0.534958i	0.891552	−	0.452918i	$-0.149617\pi$
$17$	3.03587	+	2.20569i	0.736307	+	0.534958i	−0.155246	+	0.987876i	$0.549617\pi$
$18$	0.550577	−	1.69450i	0.129772	−	0.399398i
$19$	−1.80841	−	5.56572i	−0.414878	−	1.27686i	−0.912360	−	0.409389i	$-0.865742\pi$
$19$	−1.80841	−	5.56572i	−0.414878	−	1.27686i	0.497482	−	0.867474i	$-0.334258\pi$
$20$	2.64234	−	1.91977i	0.590844	−	0.429274i
$21$	0.261118			0.0569807
$22$	−4.34353	−	4.00662i	−0.926044	−	0.854213i
$23$	7.50231			1.56434			0.782170	−	0.623065i	$-0.214113\pi$
$23$	7.50231			1.56434			0.782170	+	0.623065i	$0.214113\pi$
$24$	−1.18994	+	0.864539i	−0.242895	+	0.176473i
$25$	0.844682	+	2.59966i	0.168936	+	0.519933i
$26$	0.550577	−	1.69450i	0.107977	−	0.332319i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.248107	+	0.180260i	0.0468878	+	0.0340660i
$29$	−2.17401	+	6.69093i	−0.403704	+	1.24247i	0.518268	+	0.855218i	$0.326577\pi$
$29$	−2.17401	+	6.69093i	−0.403704	+	1.24247i	−0.921972	+	0.387256i	$0.873423\pi$
$30$	1.53110	+	4.71226i	0.279540	+	0.860336i
$31$	−7.33192	+	5.32695i	−1.31685	+	0.956749i	−0.316886	+	0.948464i	$0.602637\pi$
$31$	−7.33192	+	5.32695i	−1.31685	+	0.956749i	−0.999966	+	0.00828546i	$0.997363\pi$
$32$	−5.91261			−1.04521
$33$	2.89203	−	1.62363i	0.503437	−	0.282638i
$34$	−6.68592			−1.14663
$35$	−0.587464	+	0.426818i	−0.0992996	+	0.0721454i
$36$	0.362933	+	1.11699i	0.0604888	+	0.186165i
$37$	−2.58363	+	7.95161i	−0.424747	+	1.30724i	0.478489	+	0.878093i	$0.341185\pi$
$37$	−2.58363	+	7.95161i	−0.424747	+	1.30724i	−0.903236	+	0.429143i	$0.858815\pi$
$38$	8.43545	+	6.12871i	1.36841	+	0.994209i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	1.26396	−	3.89008i	0.199850	−	0.615076i
$41$	1.24079	+	3.81875i	0.193778	+	0.596388i	0.999989	+	0.00475910i	$0.00151488\pi$
$41$	1.24079	+	3.81875i	0.193778	+	0.596388i	−0.806211	+	0.591629i	$0.798485\pi$
$42$	−0.376384	+	0.273459i	−0.0580773	+	0.0421956i
$43$	1.53022			0.233356			0.116678	−	0.993170i	$-0.462775\pi$
$43$	1.53022			0.233356			0.116678	+	0.993170i	$0.462775\pi$
$44$	3.86878	+	0.453756i	0.583240	+	0.0684062i
$45$	−2.78091			−0.414553
$46$	−10.8141	+	7.85688i	−1.59445	+	1.15843i
$47$	2.73242	+	8.40951i	0.398564	+	1.22665i	0.926151	+	0.377153i	$0.123097\pi$
$47$	2.73242	+	8.40951i	0.398564	+	1.22665i	−0.527587	+	0.849501i	$0.676903\pi$
$48$	1.53568	−	4.72633i	0.221656	−	0.682187i
$49$	5.60796	+	4.07442i	0.801137	+	0.582060i
$50$	−3.94007	−	2.86263i	−0.557211	−	0.404837i
$51$	1.15960	−	3.56888i	0.162376	−	0.499743i
$52$	0.362933	+	1.11699i	0.0503297	+	0.154899i
$53$	1.20436	−	0.875022i	0.165432	−	0.120194i	−0.501989	−	0.864874i	$-0.667398\pi$
$53$	1.20436	−	0.875022i	0.165432	−	0.120194i	0.667421	+	0.744681i	$0.267398\pi$
$54$	−1.78171			−0.242459
$55$	−3.85254	+	8.38009i	−0.519477	+	1.12997i
$56$	0.384064			0.0513227
$57$	−4.73448	+	3.43980i	−0.627097	+	0.455613i
$58$	−3.87345	−	11.9213i	−0.508609	−	1.56534i
$59$	2.10986	−	6.49350i	0.274681	−	0.845381i	−0.714623	−	0.699510i	$-0.753402\pi$
$59$	2.10986	−	6.49350i	0.274681	−	0.845381i	0.989304	−	0.145871i	$-0.0465985\pi$
$60$	−2.64234	−	1.91977i	−0.341124	−	0.247841i
$61$	−8.26202	−	6.00271i	−1.05784	−	0.768568i	−0.0841550	−	0.996453i	$-0.526819\pi$
$61$	−8.26202	−	6.00271i	−1.05784	−	0.768568i	−0.973688	+	0.227885i	$0.926819\pi$
$62$	4.98975	−	15.3569i	0.633698	−	1.95032i
$63$	−0.0806900	−	0.248338i	−0.0101660	−	0.0312877i
$64$	0.481696	−	0.349972i	0.0602120	−	0.0437466i
$65$	−2.78091			−0.344929
$66$	−2.46829	+	5.36906i	−0.303826	+	0.660885i
$67$	8.40802			1.02720			0.513601	−	0.858029i	$-0.328311\pi$
$67$	8.40802			1.02720			0.513601	+	0.858029i	$0.328311\pi$
$68$	3.56555	−	2.59053i	0.432387	−	0.314148i
$69$	−2.31834	−	7.13513i	−0.279096	−	0.858968i
$70$	0.399800	−	1.23046i	0.0477852	−	0.147068i
$71$	−5.01275	−	3.64197i	−0.594904	−	0.432223i	0.249163	−	0.968462i	$-0.419845\pi$
$71$	−5.01275	−	3.64197i	−0.594904	−	0.432223i	−0.844066	+	0.536239i	$0.819845\pi$
$72$	1.18994	+	0.864539i	0.140235	+	0.101887i
$73$	0.191681	−	0.589933i	0.0224345	−	0.0690464i	−0.939212	−	0.343337i	$-0.888443\pi$
$73$	0.191681	−	0.589933i	0.0224345	−	0.0690464i	0.961647	+	0.274290i	$0.0884429\pi$
$74$	−4.60328	−	14.1674i	−0.535120	−	1.64693i
$75$	2.21141	−	1.60668i	0.255351	−	0.185523i
$76$	−6.87319			−0.788409
$77$	−0.860136	−	0.100882i	−0.0980216	−	0.0114966i
$78$	−1.78171			−0.201738
$79$	6.87105	−	4.99211i	0.773054	−	0.561656i	−0.129832	−	0.991536i	$-0.541444\pi$
$79$	6.87105	−	4.99211i	0.773054	−	0.561656i	0.902886	+	0.429879i	$0.141444\pi$
$80$	4.27058	+	13.1435i	0.477465	+	1.46949i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.78773	−	4.20503i	−0.639148	−	0.464368i
$83$	−1.59707	−	1.16034i	−0.175301	−	0.127363i	0.496675	−	0.867937i	$-0.334554\pi$
$83$	−1.59707	−	1.16034i	−0.175301	−	0.127363i	−0.671976	+	0.740573i	$0.734554\pi$
$84$	0.0947684	−	0.291667i	0.0103401	−	0.0318235i
$85$	3.22474	+	9.92472i	0.349772	+	1.07649i
$86$	−2.20570	+	1.60253i	−0.237847	+	0.172806i
$87$	7.03526			0.754259
$88$	4.25372	−	2.38810i	0.453448	−	0.254573i
$89$	−10.2488			−1.08637			−0.543184	−	0.839613i	$-0.682782\pi$
$89$	−10.2488			−1.08637			−0.543184	+	0.839613i	$0.682782\pi$
$90$	4.00848	−	2.91233i	0.422531	−	0.306987i
$91$	−0.0806900	−	0.248338i	−0.00845861	−	0.0260329i
$92$	2.72284	−	8.38003i	0.283875	−	0.873678i
$93$	7.33192	+	5.32695i	0.760285	+	0.552379i
$94$	−12.7455	−	9.26017i	−1.31460	−	0.955114i
$95$	5.02902	−	15.4777i	0.515967	−	1.58798i
$96$	1.82710	+	5.62322i	0.186477	+	0.573918i
$97$	9.86280	−	7.16574i	1.00142	−	0.727571i	0.0390242	−	0.999238i	$-0.487575\pi$
$97$	9.86280	−	7.16574i	1.00142	−	0.727571i	0.962391	+	0.271667i	$0.0875751\pi$
$98$	−12.3505			−1.24758
$99$	−2.43785	−	2.24875i	−0.245013	−	0.226008i
$100$	3.21037			0.321037
$101$	5.19745	−	3.77617i	0.517165	−	0.375743i	−0.298370	−	0.954450i	$-0.596443\pi$
$101$	5.19745	−	3.77617i	0.517165	−	0.375743i	0.815535	+	0.578708i	$0.196443\pi$
$102$	2.06606	+	6.35869i	0.204571	+	0.629604i
$103$	5.71361	−	17.5847i	0.562979	−	1.73267i	−0.110904	−	0.993831i	$-0.535374\pi$
$103$	5.71361	−	17.5847i	0.562979	−	1.73267i	0.673882	−	0.738839i	$-0.264626\pi$
$104$	1.18994	+	0.864539i	0.116683	+	0.0847750i
$105$	0.587464	+	0.426818i	0.0573307	+	0.0416532i
$106$	−0.819632	+	2.52257i	−0.0796097	+	0.245013i
$107$	−0.489502	−	1.50653i	−0.0473220	−	0.145642i	0.924604	−	0.380931i	$-0.124396\pi$
$107$	−0.489502	−	1.50653i	−0.0473220	−	0.145642i	−0.971925	+	0.235289i	$0.924396\pi$
$108$	0.950171	−	0.690339i	0.0914302	−	0.0664279i
$109$	6.75764			0.647265			0.323632	−	0.946183i	$-0.395096\pi$
$109$	6.75764			0.647265			0.323632	+	0.946183i	$0.395096\pi$
$110$	−3.22296	−	16.1139i	−0.307297	−	1.53640i
$111$	8.36082			0.793574
$112$	−1.04982	+	0.762735i	−0.0991982	+	0.0720717i
$113$	6.44675	+	19.8410i	0.606459	+	1.86649i	0.486433	+	0.873718i	$0.338298\pi$
$113$	6.44675	+	19.8410i	0.606459	+	1.86649i	0.120025	+	0.992771i	$0.461702\pi$
$114$	3.22206	−	9.91647i	0.301773	−	0.928762i
$115$	16.8787	+	12.2631i	1.57395	+	1.14354i
$116$	6.68469	+	4.85671i	0.620658	+	0.450935i
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$	3.75916	+	11.5695i	0.346059	+	1.06506i
$119$	−0.792721	+	0.575946i	−0.0726686	+	0.0527969i
$120$	−4.09028			−0.373389
$121$	−10.1538	+	4.23098i	−0.923069	+	0.384635i
$122$	18.1955			1.64735
$123$	3.24842	−	2.36011i	0.292900	−	0.212804i
$124$	3.28917	+	10.1230i	0.295376	+	0.909075i
$125$	1.94776	−	5.99458i	0.174213	−	0.536171i
$126$	0.376384	+	0.273459i	0.0335309	+	0.0243617i
$127$	−17.1833	−	12.4844i	−1.52477	−	1.10781i	−0.959059	−	0.283206i	$-0.908602\pi$
$127$	−17.1833	−	12.4844i	−1.52477	−	1.10781i	−0.565710	−	0.824604i	$-0.691398\pi$
$128$	3.32637	−	10.2375i	0.294013	−	0.904878i
$129$	−0.472863	−	1.45532i	−0.0416332	−	0.128134i
$130$	4.00848	−	2.91233i	0.351567	−	0.255429i
$131$	2.93483			0.256418			0.128209	−	0.991747i	$-0.459077\pi$
$131$	2.93483			0.256418			0.128209	+	0.991747i	$0.459077\pi$
$132$	−0.763970	−	3.81964i	−0.0664951	−	0.332457i
$133$	1.52810			0.132503
$134$	−12.1196	+	8.80538i	−1.04697	+	0.760669i
$135$	0.859348	+	2.64480i	0.0739609	+	0.227628i
$136$	1.70559	−	5.24926i	0.146253	−	0.450120i
$137$	4.11520	+	2.98987i	0.351585	+	0.255442i	0.749534	−	0.661966i	$-0.230278\pi$
$137$	4.11520	+	2.98987i	0.351585	+	0.255442i	−0.397948	+	0.917408i	$0.630278\pi$
$138$	10.8141	+	7.85688i	0.920554	+	0.668822i
$139$	0.656649	−	2.02096i	0.0556963	−	0.171415i	−0.919339	−	0.393467i	$-0.871275\pi$
$139$	0.656649	−	2.02096i	0.0556963	−	0.171415i	0.975035	+	0.222052i	$0.0712754\pi$
$140$	0.263542	+	0.811100i	0.0222734	+	0.0685504i
$141$	7.15356	−	5.19736i	0.602438	−	0.437697i
$142$	11.0396			0.926424
$143$	−2.43785	−	2.24875i	−0.203863	−	0.188050i
$144$	−4.96956			−0.414130
$145$	−15.8279	+	11.4997i	−1.31444	+	0.954995i
$146$	0.341519	+	1.05109i	0.0282643	+	0.0869886i
$147$	2.14205	−	6.59255i	0.176673	−	0.543744i
$148$	7.94420	+	5.77180i	0.653009	+	0.474439i
$149$	−13.0256	−	9.46365i	−1.06710	−	0.775292i	−0.0917097	−	0.995786i	$-0.529233\pi$
$149$	−13.0256	−	9.46365i	−1.06710	−	0.775292i	−0.975388	+	0.220494i	$0.929233\pi$
$150$	−1.50497	+	4.63184i	−0.122881	+	0.378188i
$151$	0.171834	+	0.528852i	0.0139837	+	0.0430374i	0.957805	−	0.287419i	$-0.0927973\pi$
$151$	0.171834	+	0.528852i	0.0139837	+	0.0430374i	−0.943821	+	0.330457i	$0.892797\pi$
$152$	−6.96367	+	5.05940i	−0.564828	+	0.410372i
$153$	−3.75254			−0.303375
$154$	1.34548	−	0.755371i	0.108422	−	0.0608695i
$155$	−25.2027			−2.02433
$156$	0.950171	−	0.690339i	0.0760745	−	0.0552714i
$157$	−2.90065	−	8.92728i	−0.231497	−	0.712474i	−0.997567	−	0.0697169i	$-0.977790\pi$
$157$	−2.90065	−	8.92728i	−0.231497	−	0.712474i	0.766070	−	0.642757i	$-0.222210\pi$
$158$	−4.67610	+	14.3916i	−0.372011	+	1.14493i
$159$	−1.20436	−	0.875022i	−0.0955123	−	0.0693938i
$160$	−13.3022	−	9.66461i	−1.05163	−	0.764054i
$161$	−0.605362	+	1.86311i	−0.0477092	+	0.146834i
$162$	0.550577	+	1.69450i	0.0432574	+	0.133133i
$163$	11.5949	−	8.42420i	0.908184	−	0.659834i	−0.0323711	−	0.999476i	$-0.510306\pi$
$163$	11.5949	−	8.42420i	0.908184	−	0.659834i	0.940555	+	0.339642i	$0.110306\pi$
$164$	4.71583			0.368245
$165$	9.16044	+	1.07440i	0.713139	+	0.0836417i
$166$	3.51723			0.272990
$167$	−16.1627	+	11.7429i	−1.25070	+	0.908690i	−0.998263	−	0.0589217i	$-0.981234\pi$
$167$	−16.1627	+	11.7429i	−1.25070	+	0.908690i	−0.252442	+	0.967612i	$0.581234\pi$
$168$	−0.118682	−	0.365266i	−0.00915653	−	0.0281809i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−15.0420	−	10.9287i	−1.15367	−	0.838190i
$171$	4.73448	+	3.43980i	0.362055	+	0.263048i
$172$	0.555366	−	1.70924i	0.0423462	−	0.130328i
$173$	1.60549	+	4.94120i	0.122063	+	0.375672i	0.993355	−	0.115094i	$-0.0367169\pi$
$173$	1.60549	+	4.94120i	0.122063	+	0.375672i	−0.871291	+	0.490766i	$0.836717\pi$
$174$	−10.1408	+	7.36775i	−0.768774	+	0.558547i
$175$	−0.713753			−0.0539547
$176$	−6.88460	+	14.9754i	−0.518946	+	1.12882i
$177$	−6.82767			−0.513199
$178$	14.7729	−	10.7331i	1.10728	−	0.804483i
$179$	−2.94786	−	9.07259i	−0.220334	−	0.678117i	−0.998732	−	0.0503463i	$-0.983967\pi$
$179$	−2.94786	−	9.07259i	−0.220334	−	0.678117i	0.778398	−	0.627771i	$-0.216033\pi$
$180$	−1.00928	+	3.10625i	−0.0752275	+	0.231526i
$181$	6.21104	+	4.51259i	0.461663	+	0.335418i	0.794183	−	0.607678i	$-0.207899\pi$
$181$	6.21104	+	4.51259i	0.461663	+	0.335418i	−0.332520	+	0.943096i	$0.607899\pi$
$182$	0.376384	+	0.273459i	0.0278994	+	0.0202701i
$183$	−3.15581	+	9.71259i	−0.233284	+	0.717975i
$184$	−3.40992	−	10.4946i	−0.251382	−	0.773675i
$185$	−18.8102	+	13.6664i	−1.38295	+	1.00477i
$186$	−16.1472			−1.18397
$187$	−5.19860	+	11.3080i	−0.380159	+	0.826926i
$188$	10.3850			0.757407
$189$	−0.211249	+	0.153481i	−0.0153661	+	0.0111641i
$190$	8.96024	+	27.5768i	0.650044	+	2.00063i
$191$	8.01159	−	24.6571i	0.579698	−	1.78413i	−0.0398935	−	0.999204i	$-0.512702\pi$
$191$	8.01159	−	24.6571i	0.579698	−	1.78413i	0.619592	−	0.784924i	$-0.287298\pi$
$192$	−0.481696	−	0.349972i	−0.0347634	−	0.0252571i
$193$	4.78611	+	3.47731i	0.344512	+	0.250302i	0.746563	−	0.665315i	$-0.231703\pi$
$193$	4.78611	+	3.47731i	0.344512	+	0.250302i	−0.402051	+	0.915617i	$0.631703\pi$
$194$	−6.71214	+	20.6578i	−0.481903	+	1.48315i
$195$	0.859348	+	2.64480i	0.0615392	+	0.189398i
$196$	6.58641	−	4.78531i	0.470458	−	0.341808i
$197$	−0.605953			−0.0431724			−0.0215862	−	0.999767i	$-0.506872\pi$
$197$	−0.605953			−0.0431724			−0.0215862	+	0.999767i	$0.506872\pi$
$198$	5.86902	+	0.688358i	0.417093	+	0.0489194i
$199$	−0.794098			−0.0562921			−0.0281461	−	0.999604i	$-0.508960\pi$
$199$	−0.794098			−0.0562921			−0.0281461	+	0.999604i	$0.508960\pi$
$200$	3.25263	−	2.36317i	0.229996	−	0.167102i
$201$	−2.59822	−	7.99650i	−0.183264	−	0.564030i
$202$	−3.53713	+	10.8862i	−0.248871	+	0.765948i
$203$	−1.48619	−	1.07978i	−0.104310	−	0.0757858i
$204$	−3.56555	−	2.59053i	−0.249639	−	0.181373i
$205$	−3.45051	+	10.6196i	−0.240994	+	0.741704i
$206$	10.1800	+	31.3307i	0.709272	+	2.18291i
$207$	−6.06950	+	4.40975i	−0.421859	+	0.306499i
$208$	−4.96956			−0.344577
$209$	16.9246	−	9.50171i	1.17070	−	0.657247i
$210$	−1.29378			−0.0892792
$211$	19.4008	−	14.0955i	1.33561	−	0.970375i	0.336013	−	0.941857i	$-0.390921\pi$
$211$	19.4008	−	14.0955i	1.33561	−	0.970375i	0.999593	−	0.0285172i	$-0.00907854\pi$
$212$	−0.540290	−	1.66284i	−0.0371072	−	0.114204i
$213$	−1.91470	+	5.89284i	−0.131193	+	0.403771i
$214$	2.28332	+	1.65893i	0.156084	+	0.113402i
$215$	3.44268	+	2.50125i	0.234789	+	0.170584i
$216$	0.454515	−	1.39885i	0.0309258	−	0.0951799i
$217$	−0.731274	−	2.25063i	−0.0496421	−	0.152783i
$218$	−9.74067	+	7.07701i	−0.659721	+	0.479316i
$219$	−0.620292			−0.0419155
$220$	7.96228	+	7.34467i	0.536817	+	0.495178i
$221$	−3.75254			−0.252423
$222$	−12.0515	+	8.75595i	−0.808846	+	0.587661i
$223$	−4.77098	−	14.6836i	−0.319488	−	0.983284i	−0.973867	−	0.227117i	$-0.927070\pi$
$223$	−4.77098	−	14.6836i	−0.319488	−	0.983284i	0.654379	−	0.756167i	$-0.272930\pi$
$224$	0.477088	−	1.46833i	0.0318768	−	0.0981067i
$225$	−2.21141	−	1.60668i	−0.147427	−	0.107112i
$226$	−30.0713	−	21.8481i	−2.00031	−	1.45331i
$227$	0.673593	−	2.07311i	0.0447080	−	0.137597i	−0.926211	−	0.377006i	$-0.876954\pi$
$227$	0.673593	−	2.07311i	0.0447080	−	0.137597i	0.970919	+	0.239409i	$0.0769536\pi$
$228$	2.12393	+	6.53680i	0.140661	+	0.432910i
$229$	−24.0086	+	17.4433i	−1.58653	+	1.15268i	−0.677846	+	0.735204i	$0.737087\pi$
$229$	−24.0086	+	17.4433i	−1.58653	+	1.15268i	−0.908686	+	0.417480i	$0.862913\pi$
$230$	−37.1722			−2.45106
$231$	0.169852	+	0.849212i	0.0111754	+	0.0558740i
$232$	10.3478			0.679363
$233$	10.1013	−	7.33900i	0.661756	−	0.480794i	−0.205499	−	0.978657i	$-0.565882\pi$
$233$	10.1013	−	7.33900i	0.661756	−	0.480794i	0.867256	+	0.497863i	$0.165882\pi$
$234$	0.550577	+	1.69450i	0.0359924	+	0.110773i
$235$	−7.59860	+	23.3861i	−0.495678	+	1.52554i
$236$	−6.48745	−	4.71341i	−0.422297	−	0.306817i
$237$	−6.87105	−	4.99211i	−0.446323	−	0.324273i
$238$	0.539487	−	1.66037i	0.0349698	−	0.107626i
$239$	−1.74658	−	5.37541i	−0.112977	−	0.347706i	0.878543	−	0.477663i	$-0.158516\pi$
$239$	−1.74658	−	5.37541i	−0.112977	−	0.347706i	−0.991520	+	0.129957i	$0.958516\pi$
$240$	11.1805	−	8.12312i	0.721700	−	0.524345i
$241$	12.4206			0.800082			0.400041	−	0.916497i	$-0.368996\pi$
$241$	12.4206			0.800082			0.400041	+	0.916497i	$0.368996\pi$
$242$	10.2050	−	16.7323i	0.656002	−	1.07559i
$243$	−1.00000			−0.0641500
$244$	−9.70354	+	7.05003i	−0.621205	+	0.451332i
$245$	5.95684	+	18.3333i	0.380569	+	1.17127i
$246$	−2.21072	+	6.80388i	−0.140950	+	0.433800i
$247$	4.73448	+	3.43980i	0.301248	+	0.218869i
$248$	10.7841	+	7.83511i	0.684791	+	0.497530i
$249$	−0.610025	+	1.87746i	−0.0386588	+	0.118979i
$250$	3.47033	+	10.6806i	0.219483	+	0.675499i
$251$	0.631953	−	0.459141i	0.0398885	−	0.0289807i	−0.567662	−	0.823261i	$-0.692152\pi$
$251$	0.631953	−	0.459141i	0.0398885	−	0.0289807i	0.607551	+	0.794281i	$0.292152\pi$
$252$	−0.306677			−0.0193188
$253$	4.88009	+	24.3991i	0.306809	+	1.53396i
$254$	37.8429			2.37447
$255$	8.44247	−	6.13382i	0.528688	−	0.384114i
$256$	6.29460	+	19.3728i	0.393413	+	1.21080i
$257$	5.27155	−	16.2242i	0.328830	−	1.01204i	−0.640852	−	0.767665i	$-0.721419\pi$
$257$	5.27155	−	16.2242i	0.328830	−	1.01204i	0.969682	−	0.244371i	$-0.0785814\pi$
$258$	2.20570	+	1.60253i	0.137321	+	0.0997694i
$259$	−1.76622	−	1.28323i	−0.109747	−	0.0797361i
$260$	−1.00928	+	3.10625i	−0.0625931	+	0.192642i
$261$	−2.17401	−	6.69093i	−0.134568	−	0.414158i
$262$	−4.23036	+	3.07354i	−0.261352	+	0.189884i
$263$	19.3208			1.19137			0.595686	−	0.803217i	$-0.296880\pi$
$263$	19.3208			1.19137			0.595686	+	0.803217i	$0.296880\pi$
$264$	−3.58569	−	3.30756i	−0.220684	−	0.203566i
$265$	4.13987			0.254310
$266$	−2.20265	+	1.60032i	−0.135053	+	0.0981219i
$267$	3.16705	+	9.74717i	0.193820	+	0.596517i
$268$	3.05155	−	9.39169i	0.186403	−	0.573689i
$269$	−17.2954	−	12.5658i	−1.05452	−	0.766152i	−0.0814509	−	0.996677i	$-0.525955\pi$
$269$	−17.2954	−	12.5658i	−1.05452	−	0.766152i	−0.973066	+	0.230526i	$0.925955\pi$
$270$	−4.00848	−	2.91233i	−0.243949	−	0.177239i
$271$	−5.61986	+	17.2962i	−0.341382	+	1.05067i	0.622110	+	0.782930i	$0.286276\pi$
$271$	−5.61986	+	17.2962i	−0.341382	+	1.05067i	−0.963492	+	0.267737i	$0.913724\pi$
$272$	5.76269	+	17.7358i	0.349415	+	1.07539i
$273$	−0.211249	+	0.153481i	−0.0127854	+	0.00928912i
$274$	−9.06295			−0.547513
$275$	−7.90521	+	4.43811i	−0.476702	+	0.267628i
$276$	−8.81128			−0.530377
$277$	9.40760	−	6.83502i	0.565248	−	0.410677i	−0.268128	−	0.963383i	$-0.586405\pi$
$277$	9.40760	−	6.83502i	0.565248	−	0.410677i	0.833376	+	0.552707i	$0.186405\pi$
$278$	1.16996	+	3.60075i	0.0701693	+	0.215959i
$279$	2.80054	−	8.61919i	0.167664	−	0.516017i
$280$	0.864067	+	0.627782i	0.0516379	+	0.0375171i
$281$	−9.49657	−	6.89966i	−0.566518	−	0.411599i	0.267321	−	0.963608i	$-0.413862\pi$
$281$	−9.49657	−	6.89966i	−0.566518	−	0.411599i	−0.833839	+	0.552008i	$0.813862\pi$
$282$	−4.86836	+	14.9833i	−0.289907	+	0.892241i
$283$	1.11866	+	3.44289i	0.0664976	+	0.204659i	0.978784	−	0.204894i	$-0.0656849\pi$
$283$	1.11866	+	3.44289i	0.0664976	+	0.204659i	−0.912287	+	0.409552i	$0.865685\pi$
$284$	−5.88735	+	4.27741i	−0.349350	+	0.253817i
$285$	−16.2743			−0.964004
$286$	5.86902	+	0.688358i	0.347042	+	0.0407034i
$287$	−1.04846			−0.0618886
$288$	4.78340	−	3.47534i	0.281865	−	0.204787i
$289$	−0.901846	−	2.77560i	−0.0530498	−	0.163270i
$290$	10.7717	−	33.1519i	0.632537	−	1.94675i
$291$	−9.86280	−	7.16574i	−0.578167	−	0.420063i
$292$	−0.589383	−	0.428212i	−0.0344911	−	0.0250592i
$293$	−5.37569	+	16.5447i	−0.314051	+	0.966550i	0.662092	+	0.749423i	$0.269669\pi$
$293$	−5.37569	+	16.5447i	−0.314051	+	0.966550i	−0.976143	+	0.217128i	$0.930331\pi$
$294$	3.81650	+	11.7460i	0.222583	+	0.685040i
$295$	15.3609	−	11.1603i	0.894346	−	0.649780i
$296$	12.2974			0.714774
$297$	−1.38535	+	3.01344i	−0.0803864	+	0.174857i
$298$	28.6864			1.66176
$299$	−6.06950	+	4.40975i	−0.351008	+	0.255022i
$300$	−0.992058	−	3.05324i	−0.0572765	−	0.176279i
$301$	−0.123473	+	0.380011i	−0.00711687	+	0.0219035i
$302$	−0.801533	−	0.582348i	−0.0461230	−	0.0335104i
$303$	−5.19745	−	3.77617i	−0.298586	−	0.216935i
$304$	8.98700	−	27.6591i	0.515440	−	1.58636i
$305$	−8.77602	−	27.0098i	−0.502513	−	1.54658i
$306$	5.40903	−	3.92989i	0.309213	−	0.224657i
$307$	−4.40067			−0.251160			−0.125580	−	0.992084i	$-0.540079\pi$
$307$	−4.40067			−0.251160			−0.125580	+	0.992084i	$0.540079\pi$
$308$	−0.424856	+	0.924151i	−0.0242084	+	0.0526584i
$309$	−18.4896			−1.05184
$310$	36.3279	−	26.3938i	2.06329	−	1.49907i
$311$	6.65953	+	20.4959i	0.377627	+	1.16222i	0.941689	+	0.336485i	$0.109238\pi$
$311$	6.65953	+	20.4959i	0.377627	+	1.16222i	−0.564062	+	0.825733i	$0.690762\pi$
$312$	0.454515	−	1.39885i	0.0257319	−	0.0791945i
$313$	−12.9497	−	9.40849i	−0.731959	−	0.531799i	0.158224	−	0.987403i	$-0.449423\pi$
$313$	−12.9497	−	9.40849i	−0.731959	−	0.531799i	−0.890183	+	0.455604i	$0.849423\pi$
$314$	13.5303	+	9.83031i	0.763557	+	0.554757i
$315$	0.224391	−	0.690606i	0.0126430	−	0.0389112i
$316$	−3.08242	−	9.48672i	−0.173400	−	0.533669i
$317$	17.8777	−	12.9889i	1.00411	−	0.729530i	0.0411464	−	0.999153i	$-0.486899\pi$
$317$	17.8777	−	12.9889i	1.00411	−	0.729530i	0.962966	+	0.269623i	$0.0868990\pi$
$318$	2.65238			0.148738
$319$	−23.1745	−	2.71805i	−1.29752	−	0.152182i
$320$	1.65578			0.0925607
$321$	−1.28153	+	0.931088i	−0.0715282	+	0.0519683i
$322$	−1.07858	−	3.31952i	−0.0601067	−	0.184989i
$323$	6.78614	−	20.8856i	0.377591	−	1.16210i
$324$	−0.950171	−	0.690339i	−0.0527873	−	0.0383522i
$325$	−2.21141	−	1.60668i	−0.122667	−	0.0891226i
$326$	−7.89093	+	24.2858i	−0.437038	+	1.34507i
$327$	−2.08823	−	6.42690i	−0.115479	−	0.355408i
$328$	4.77791	−	3.47136i	0.263816	−	0.191674i
$329$	−2.30888			−0.127293
$330$	−14.3293	+	8.04469i	−0.788802	+	0.442846i
$331$	−3.01935			−0.165959			−0.0829793	−	0.996551i	$-0.526444\pi$
$331$	−3.01935			−0.165959			−0.0829793	+	0.996551i	$0.526444\pi$
$332$	−1.87572	+	1.36279i	−0.102943	+	0.0747926i
$333$	−2.58363	−	7.95161i	−0.141582	−	0.435746i
$334$	10.9995	−	33.8530i	0.601867	−	1.85236i
$335$	18.9164	+	13.7435i	1.03351	+	0.750890i
$336$	1.04982	+	0.762735i	0.0572721	+	0.0416106i
$337$	−3.39794	+	10.4578i	−0.185098	+	0.569673i	−0.999950	−	0.00999621i	$-0.996818\pi$
$337$	−3.39794	+	10.4578i	−0.185098	+	0.569673i	0.814852	+	0.579669i	$0.196818\pi$
$338$	0.550577	+	1.69450i	0.0299475	+	0.0921688i
$339$	16.8778	−	12.2624i	0.916676	−	0.666004i
$340$	12.2562			0.664686
$341$	−22.0936	−	20.3799i	−1.19644	−	1.10363i
$342$	−10.4268			−0.563816
$343$	−2.94308	+	2.13828i	−0.158912	+	0.115456i
$344$	−0.695506	−	2.14055i	−0.0374992	−	0.115411i
$345$	6.44710	−	19.8421i	0.347100	−	1.06826i
$346$	−7.48893	−	5.44103i	−0.402607	−	0.292511i
$347$	15.1912	+	11.0370i	0.815506	+	0.592499i	0.915422	−	0.402496i	$-0.131857\pi$
$347$	15.1912	+	11.0370i	0.815506	+	0.592499i	−0.0999160	+	0.994996i	$0.531857\pi$
$348$	2.55333	−	7.85833i	0.136873	−	0.421251i
$349$	2.84663	+	8.76102i	0.152376	+	0.468967i	0.997886	−	0.0649943i	$-0.0207029\pi$
$349$	2.84663	+	8.76102i	0.152376	+	0.468967i	−0.845509	+	0.533961i	$0.820703\pi$
$350$	1.02883	−	0.747486i	0.0549930	−	0.0399548i
$351$	−1.00000			−0.0533761
$352$	−3.84602	−	19.2290i	−0.204994	−	1.02491i
$353$	4.11864			0.219213			0.109607	−	0.993975i	$-0.465041\pi$
$353$	4.11864			0.219213			0.109607	+	0.993975i	$0.465041\pi$
$354$	9.84160	−	7.15034i	0.523075	−	0.380037i
$355$	−5.32460	−	16.3874i	−0.282600	−	0.869755i
$356$	−3.71962	+	11.4478i	−0.197139	+	0.606733i
$357$	0.792721	+	0.575946i	0.0419553	+	0.0304823i
$358$	13.7505	+	9.99032i	0.726737	+	0.528005i
$359$	−8.50887	+	26.1876i	−0.449081	+	1.38213i	0.428865	+	0.903369i	$0.358914\pi$
$359$	−8.50887	+	26.1876i	−0.449081	+	1.38213i	−0.877946	+	0.478760i	$0.841086\pi$
$360$	1.26396	+	3.89008i	0.0666168	+	0.205025i
$361$	−12.3355	+	8.96228i	−0.649238	+	0.471699i
$362$	−13.6786			−0.718933
$363$	7.16159	+	8.34935i	0.375886	+	0.438227i
$364$	−0.306677			−0.0160742
$365$	1.39553	−	1.01392i	0.0730456	−	0.0530707i
$366$	−5.62273	−	17.3050i	−0.293905	−	0.904545i
$367$	−3.33320	+	10.2585i	−0.173992	+	0.535491i	−0.999586	−	0.0287729i	$-0.990840\pi$
$367$	−3.33320	+	10.2585i	−0.173992	+	0.535491i	0.825594	+	0.564264i	$0.190840\pi$
$368$	30.1627	+	21.9145i	1.57234	+	1.14237i
$369$	−3.24842	−	2.36011i	−0.169106	−	0.122863i
$370$	12.8013	−	39.3983i	0.665507	−	2.04822i
$371$	0.120121	+	0.369695i	0.00623639	+	0.0191936i
$372$	8.61116	−	6.25637i	0.446468	−	0.324378i
$373$	15.7686			0.816467			0.408234	−	0.912878i	$-0.366145\pi$
$373$	15.7686			0.816467			0.408234	+	0.912878i	$0.366145\pi$
$374$	−4.34904	−	21.7440i	−0.224884	−	1.12436i
$375$	−6.30307			−0.325489
$376$	10.5218	−	7.64450i	0.542618	−	0.394235i
$377$	−2.17401	−	6.69093i	−0.111967	−	0.344600i
$378$	0.143766	−	0.442466i	0.00739452	−	0.0227580i
$379$	−3.26751	−	2.37399i	−0.167841	−	0.121944i	0.500694	−	0.865624i	$-0.333078\pi$
$379$	−3.26751	−	2.37399i	−0.167841	−	0.121944i	−0.668535	+	0.743681i	$0.733078\pi$
$380$	−15.4633	−	11.2348i	−0.793252	−	0.576331i
$381$	−6.56343	+	20.2002i	−0.336255	+	1.03489i
$382$	14.2743	+	43.9318i	0.730337	+	2.24774i
$383$	−10.2113	+	7.41896i	−0.521774	+	0.379091i	−0.817272	−	0.576252i	$-0.804515\pi$
$383$	−10.2113	+	7.41896i	−0.521774	+	0.379091i	0.295497	+	0.955344i	$0.404515\pi$
$384$	−10.7644			−0.549317
$385$	−1.77023	−	1.63292i	−0.0902195	−	0.0832215i
$386$	−10.5405			−0.536497
$387$	−1.23797	+	0.899438i	−0.0629296	+	0.0457210i
$388$	−4.42455	−	13.6174i	−0.224622	−	0.691316i
$389$	−4.95653	+	15.2546i	−0.251306	+	0.773440i	0.743229	+	0.669037i	$0.233293\pi$
$389$	−4.95653	+	15.2546i	−0.251306	+	0.773440i	−0.994535	+	0.104403i	$0.966707\pi$
$390$	−4.00848	−	2.91233i	−0.202978	−	0.147472i
$391$	22.7760	+	16.5478i	1.15183	+	0.836857i
$392$	3.15062	−	9.69660i	0.159130	−	0.489752i
$393$	−0.906914	−	2.79119i	−0.0457477	−	0.140797i
$394$	0.873439	−	0.634591i	0.0440032	−	0.0319702i
$395$	23.6185			1.18838
$396$	−3.39662	+	1.90691i	−0.170686	+	0.0958260i
$397$	0.563043			0.0282583			0.0141292	−	0.999900i	$-0.495502\pi$
$397$	0.563043			0.0282583			0.0141292	+	0.999900i	$0.495502\pi$
$398$	1.14464	−	0.831627i	0.0573755	−	0.0416857i
$399$	−0.472209	−	1.45331i	−0.0236400	−	0.0727565i
$400$	−4.19770	+	12.9192i	−0.209885	+	0.645959i
$401$	−4.29687	−	3.12186i	−0.214576	−	0.155898i	0.475306	−	0.879821i	$-0.342337\pi$
$401$	−4.29687	−	3.12186i	−0.214576	−	0.155898i	−0.689882	+	0.723922i	$0.742337\pi$
$402$	12.1196	+	8.80538i	0.604469	+	0.439173i
$403$	2.80054	−	8.61919i	0.139505	−	0.429352i
$404$	−2.33163	−	7.17600i	−0.116003	−	0.357020i
$405$	2.24980	−	1.63458i	0.111794	−	0.0812228i
$406$	3.27305			0.162439
$407$	−27.5409	−	3.23018i	−1.36515	−	0.160114i
$408$	−5.51940			−0.273251
$409$	2.73520	−	1.98724i	0.135247	−	0.0982627i	−0.518105	−	0.855317i	$-0.673362\pi$
$409$	2.73520	−	1.98724i	0.135247	−	0.0982627i	0.653352	+	0.757054i	$0.273362\pi$
$410$	−6.14779	−	18.9210i	−0.303618	−	0.934440i
$411$	1.57187	−	4.83771i	0.0775345	−	0.238627i
$412$	−17.5683	−	12.7641i	−0.865528	−	0.628843i
$413$	1.44234	+	1.04792i	0.0709729	+	0.0515648i
$414$	4.13060	−	12.7127i	0.203008	−	0.624795i
$415$	−1.69642	−	5.22105i	−0.0832742	−	0.256291i
$416$	4.78340	−	3.47534i	0.234525	−	0.170393i
$417$	−2.12496			−0.104060
$418$	−14.4448	+	31.4205i	−0.706518	+	1.53682i
$419$	6.81167			0.332772			0.166386	−	0.986061i	$-0.446790\pi$
$419$	6.81167			0.332772			0.166386	+	0.986061i	$0.446790\pi$
$420$	0.689963	−	0.501287i	0.0336667	−	0.0244603i
$421$	−8.68556	−	26.7314i	−0.423308	−	1.30281i	−0.904605	−	0.426251i	$-0.859834\pi$
$421$	−8.68556	−	26.7314i	−0.423308	−	1.30281i	0.481297	−	0.876558i	$-0.340166\pi$
$422$	−13.2032	+	40.6354i	−0.642723	+	1.97810i
$423$	−7.15356	−	5.19736i	−0.347818	−	0.252705i
$424$	−1.77143	−	1.28702i	−0.0860283	−	0.0625032i
$425$	−3.16970	+	9.75534i	−0.153753	+	0.473204i
$426$	−3.41143	−	10.4993i	−0.165284	−	0.508693i
$427$	2.15736	−	1.56742i	0.104402	−	0.0758526i
$428$	−1.86044			−0.0899279
$429$	−1.38535	+	3.01344i	−0.0668855	+	0.145490i
$430$	−7.58185			−0.365629
$431$	4.58021	−	3.32771i	0.220621	−	0.160290i	−0.471985	−	0.881606i	$-0.656462\pi$
$431$	4.58021	−	3.32771i	0.220621	−	0.160290i	0.692606	+	0.721316i	$0.256462\pi$
$432$	1.53568	+	4.72633i	0.0738853	+	0.227396i
$433$	5.31116	−	16.3461i	0.255238	−	0.785542i	−0.738545	−	0.674205i	$-0.764487\pi$
$433$	5.31116	−	16.3461i	0.255238	−	0.785542i	0.993783	−	0.111338i	$-0.0355135\pi$
$434$	3.41107	+	2.47829i	0.163737	+	0.118962i
$435$	15.8279	+	11.4997i	0.758891	+	0.551367i
$436$	2.45257	−	7.54824i	0.117457	−	0.361495i
$437$	−13.5673	−	41.7557i	−0.649010	−	1.99745i
$438$	0.894108	−	0.649608i	0.0427221	−	0.0310394i
$439$	−32.2484			−1.53913			−0.769567	−	0.638567i	$-0.779528\pi$
$439$	−32.2484			−1.53913			−0.769567	+	0.638567i	$0.779528\pi$
$440$	13.4736	+	1.58027i	0.642327	+	0.0753363i
$441$	−6.93182			−0.330087
$442$	5.40903	−	3.92989i	0.257281	−	0.186926i
$443$	−0.166327	−	0.511902i	−0.00790244	−	0.0243212i	0.947028	−	0.321152i	$-0.104070\pi$
$443$	−0.166327	−	0.511902i	−0.00790244	−	0.0243212i	−0.954930	+	0.296831i	$0.904070\pi$
$444$	3.03442	−	9.33897i	0.144007	−	0.443208i
$445$	−23.0577	−	16.7524i	−1.09304	−	0.794141i
$446$	22.2545	+	16.1689i	1.05378	+	0.765618i
$447$	−4.97533	+	15.3125i	−0.235325	+	0.724257i
$448$	0.0480435	+	0.147863i	0.00226984	+	0.00698586i
$449$	−10.7441	+	7.80608i	−0.507047	+	0.368392i	−0.811702	−	0.584071i	$-0.801459\pi$
$449$	−10.7441	+	7.80608i	−0.507047	+	0.368392i	0.304655	+	0.952463i	$0.401459\pi$
$450$	4.87020			0.229583
$451$	−11.6123	+	6.51931i	−0.546800	+	0.306982i
$452$	24.5020			1.15248
$453$	0.449868	−	0.326848i	0.0211367	−	0.0153567i
$454$	1.20015	+	3.69367i	0.0563256	+	0.173352i
$455$	0.224391	−	0.690606i	0.0105196	−	0.0323761i
$456$	6.96367	+	5.05940i	0.326104	+	0.236928i
$457$	32.9032	+	23.9056i	1.53915	+	1.11826i	0.950866	+	0.309601i	$0.100196\pi$
$457$	32.9032	+	23.9056i	1.53915	+	1.11826i	0.588282	+	0.808656i	$0.299804\pi$
$458$	16.3391	−	50.2865i	0.763475	−	2.34973i
$459$	1.15960	+	3.56888i	0.0541254	+	0.166581i
$460$	19.8236	−	14.4027i	0.924282	−	0.671530i
$461$	0.816957			0.0380495			0.0190247	−	0.999819i	$-0.493944\pi$
$461$	0.816957			0.0380495			0.0190247	+	0.999819i	$0.493944\pi$
$462$	−1.13418	−	1.04620i	−0.0527666	−	0.0486737i
$463$	3.97474			0.184722			0.0923610	−	0.995726i	$-0.470559\pi$
$463$	3.97474			0.184722			0.0923610	+	0.995726i	$0.470559\pi$
$464$	−28.2849	+	20.5502i	−1.31310	+	0.954020i
$465$	7.78806	+	23.9692i	0.361162	+	1.11154i
$466$	−6.87443	+	21.1573i	−0.318452	+	0.980094i
$467$	−8.44629	−	6.13659i	−0.390848	−	0.283967i	0.374955	−	0.927043i	$-0.377658\pi$
$467$	−8.44629	−	6.13659i	−0.390848	−	0.283967i	−0.765803	+	0.643076i	$0.777658\pi$
$468$	−0.950171	−	0.690339i	−0.0439216	−	0.0319109i
$469$	−0.678443	+	2.08803i	−0.0313276	+	0.0964164i
$470$	−13.5385	−	41.6671i	−0.624483	−	1.92196i
$471$	−7.59399	+	5.51736i	−0.349913	+	0.254227i
$472$	−10.0424			−0.462240
$473$	0.995371	+	4.97658i	0.0457672	+	0.228824i
$474$	15.1322			0.695044
$475$	12.9415	−	9.40252i	0.593795	−	0.431417i
$476$	0.355622	+	1.09449i	0.0162999	+	0.0501660i
$477$	−0.460026	+	1.41582i	−0.0210632	+	0.0648257i
$478$	8.14702	+	5.91916i	0.372636	+	0.270736i
$479$	13.8637	+	10.0726i	0.633448	+	0.460227i	0.857593	−	0.514329i	$-0.171959\pi$
$479$	13.8637	+	10.0726i	0.633448	+	0.460227i	−0.224145	+	0.974556i	$0.571959\pi$
$480$	−5.08099	+	15.6377i	−0.231914	+	0.713758i
$481$	−2.58363	−	7.95161i	−0.117804	−	0.362562i
$482$	−17.9034	+	13.0076i	−0.815479	+	0.592480i
$483$	1.95899			0.0891372
$484$	1.04084	+	12.8772i	0.0473111	+	0.585329i
$485$	33.9023			1.53942
$486$	1.44143	−	1.04726i	0.0653846	−	0.0475047i
$487$	−4.75274	−	14.6274i	−0.215367	−	0.662832i	−0.999127	−	0.0417681i	$-0.986701\pi$
$487$	−4.75274	−	14.6274i	−0.215367	−	0.662832i	0.783760	−	0.621063i	$-0.213299\pi$
$488$	−4.64170	+	14.2857i	−0.210120	+	0.646682i
$489$	−11.5949	−	8.42420i	−0.524340	−	0.380955i
$490$	−27.7861	−	20.1878i	−1.25525	−	0.911991i
$491$	−0.784290	+	2.41380i	−0.0353945	+	0.108933i	−0.967193	−	0.254043i	$-0.918239\pi$
$491$	−0.784290	+	2.41380i	−0.0353945	+	0.108933i	0.931798	+	0.362976i	$0.118239\pi$
$492$	−1.45727	−	4.48502i	−0.0656989	−	0.202200i
$493$	−21.3581	+	15.5176i	−0.961921	+	0.698877i
$494$	−10.4268			−0.469123
$495$	−1.80892	−	9.04410i	−0.0813048	−	0.406502i
$496$	−45.0379			−2.02226
$497$	1.30892	−	0.950986i	0.0587131	−	0.0426576i
$498$	−1.08689	−	3.34509i	−0.0487045	−	0.149897i
$499$	−0.169619	+	0.522032i	−0.00759317	+	0.0233694i	−0.954781	−	0.297309i	$-0.903911\pi$
$499$	−0.169619	+	0.522032i	−0.00759317	+	0.0233694i	0.947188	+	0.320678i	$0.103911\pi$
$500$	−5.98899	−	4.35126i	−0.267836	−	0.194594i
$501$	16.1627	+	11.7429i	0.722095	+	0.524633i
$502$	−0.430076	+	1.32364i	−0.0191952	+	0.0590769i
$503$	10.8915	+	33.5207i	0.485630	+	1.49462i	0.831066	+	0.556173i	$0.187731\pi$
$503$	10.8915	+	33.5207i	0.485630	+	1.49462i	−0.345436	+	0.938442i	$0.612269\pi$
$504$	−0.310714	+	0.225747i	−0.0138403	+	0.0100556i
$505$	17.8657			0.795011
$506$	−32.5865	−	30.0589i	−1.44865	−	1.33628i
$507$	−1.00000			−0.0444116
$508$	−20.1813	+	14.6626i	−0.895402	+	0.650548i
$509$	3.04605	+	9.37477i	0.135014	+	0.415529i	0.995592	−	0.0937885i	$-0.0298977\pi$
$509$	3.04605	+	9.37477i	0.135014	+	0.415529i	−0.860578	+	0.509318i	$0.829898\pi$
$510$	−5.74553	+	17.6829i	−0.254417	+	0.783014i
$511$	0.131036	+	0.0952034i	0.00579670	+	0.00421155i
$512$	−11.9445	−	8.67816i	−0.527876	−	0.383524i
$513$	1.80841	−	5.56572i	0.0798433	−	0.245732i
$514$	9.39235	+	28.9067i	0.414279	+	1.27502i
$515$	41.5980	−	30.2227i	1.83303	−	1.33177i
$516$	−1.79720			−0.0791173
$517$	−25.5721	+	14.3566i	−1.12466	+	0.631402i
$518$	3.88975			0.170906
$519$	4.20324	−	3.05383i	0.184502	−	0.134048i
$520$	1.26396	+	3.89008i	0.0554285	+	0.170591i
$521$	−6.04754	+	18.6124i	−0.264948	+	0.815425i	0.726758	+	0.686894i	$0.241026\pi$
$521$	−6.04754	+	18.6124i	−0.264948	+	0.815425i	−0.991705	+	0.128531i	$0.958974\pi$
$522$	10.1408	+	7.36775i	0.443852	+	0.322477i
$523$	−23.8691	−	17.3419i	−1.04372	−	0.758310i	−0.0727154	−	0.997353i	$-0.523166\pi$
$523$	−23.8691	−	17.3419i	−1.04372	−	0.758310i	−0.971009	+	0.239042i	$0.923166\pi$
$524$	1.06515	−	3.27819i	0.0465312	−	0.143208i
$525$	0.220562	+	0.678820i	0.00962611	+	0.0296261i
$526$	−27.8496	+	20.2339i	−1.21430	+	0.882241i
$527$	−34.0084			−1.48143
$528$	16.3700	+	1.91998i	0.712411	+	0.0835562i
$529$	33.2847			1.44716
$530$	−5.96734	+	4.33552i	−0.259205	+	0.188323i
$531$	2.10986	+	6.49350i	0.0915603	+	0.281794i
$532$	0.554598	−	1.70688i	0.0240449	−	0.0740025i
$533$	−3.24842	−	2.36011i	−0.140705	−	0.102228i
$534$	−14.7729	−	10.7331i	−0.639286	−	0.464469i
$535$	1.36126	−	4.18953i	0.0588524	−	0.181129i
$536$	−3.82157	−	11.7616i	−0.165067	−	0.508023i
$537$	−7.71761	+	5.60717i	−0.333039	+	0.241967i
$538$	38.0897			1.64217
$539$	−9.60302	+	20.8886i	−0.413631	+	0.899735i
$540$	3.26611			0.140551
$541$	−9.90730	+	7.19807i	−0.425948	+	0.309469i	−0.780027	−	0.625746i	$-0.784795\pi$
$541$	−9.90730	+	7.19807i	−0.425948	+	0.309469i	0.354079	+	0.935216i	$0.384795\pi$
$542$	−10.0129	−	30.8167i	−0.430093	−	1.32369i
$543$	2.37241	−	7.30152i	0.101810	−	0.313338i
$544$	−17.9499	−	13.0414i	−0.769596	−	0.559144i
$545$	15.2034	+	11.0459i	0.651240	+	0.473154i
$546$	0.143766	−	0.442466i	0.00615261	−	0.0189358i
$547$	−4.74263	−	14.5963i	−0.202780	−	0.624093i	−0.999797	−	0.0201364i	$-0.993590\pi$
$547$	−4.74263	−	14.5963i	−0.202780	−	0.624093i	0.797017	−	0.603957i	$-0.206410\pi$
$548$	4.83320	−	3.51153i	0.206464	−	0.150005i
$549$	10.2124			0.435855
$550$	6.74695	−	14.6760i	0.287691	−	0.625788i
$551$	41.1713			1.75396
$552$	−8.92728	+	6.48605i	−0.379970	+	0.276064i
$553$	0.685307	+	2.10916i	0.0291422	+	0.0896906i
$554$	−6.40235	+	19.7044i	−0.272010	+	0.837160i
$555$	18.8102	+	13.6664i	0.798448	+	0.580106i
$556$	−2.01908	−	1.46694i	−0.0856279	−	0.0622123i
$557$	13.9991	−	43.0849i	0.593162	−	1.82556i	0.0294909	−	0.999565i	$-0.490611\pi$
$557$	13.9991	−	43.0849i	0.593162	−	1.82556i	0.563671	−	0.825999i	$-0.309389\pi$
$558$	4.98975	+	15.3569i	0.211233	+	0.650108i
$559$	−1.23797	+	0.899438i	−0.0523606	+	0.0380422i
$560$	−3.60862			−0.152492
$561$	12.3610	+	1.44978i	0.521884	+	0.0612100i
$562$	20.9144			0.882220
$563$	16.8740	−	12.2597i	0.711153	−	0.516683i	−0.172392	−	0.985028i	$-0.555150\pi$
$563$	16.8740	−	12.2597i	0.711153	−	0.516683i	0.883546	+	0.468345i	$0.155150\pi$
$564$	−3.20916	−	9.87677i	−0.135130	−	0.415887i
$565$	−17.9278	+	55.1761i	−0.754228	+	2.32128i
$566$	−5.21808	−	3.79116i	−0.219332	−	0.159354i
$567$	0.211249	+	0.153481i	0.00887163	+	0.00644562i
$568$	−2.81622	+	8.66743i	−0.118166	+	0.363677i
$569$	9.28516	+	28.5768i	0.389254	+	1.19800i	0.933347	+	0.358976i	$0.116874\pi$
$569$	9.28516	+	28.5768i	0.389254	+	1.19800i	−0.544093	+	0.839025i	$0.683126\pi$
$570$	23.4582	−	17.0434i	0.982556	−	0.713869i
$571$	−16.4888			−0.690034			−0.345017	−	0.938596i	$-0.612127\pi$
$571$	−16.4888			−0.690034			−0.345017	+	0.938596i	$0.612127\pi$
$572$	−3.39662	+	1.90691i	−0.142020	+	0.0797320i
$573$	−25.9261			−1.08308
$574$	1.51128	−	1.09801i	0.0630797	−	0.0458301i
$575$	6.33707	+	19.5035i	0.264274	+	0.813352i
$576$	−0.183991	+	0.566267i	−0.00766631	+	0.0235945i
$577$	−10.1029	−	7.34021i	−0.420591	−	0.305577i	0.357285	−	0.933996i	$-0.383703\pi$
$577$	−10.1029	−	7.34021i	−0.420591	−	0.305577i	−0.777876	+	0.628418i	$0.783703\pi$
$578$	4.20672	+	3.05636i	0.174976	+	0.127128i
$579$	1.82813	−	5.62641i	0.0759745	−	0.233825i
$580$	7.10056	+	21.8533i	0.294835	+	0.907408i
$581$	0.417023	−	0.302985i	0.0173010	−	0.0125699i
$582$	21.7209			0.900362
$583$	3.62917	+	3.34767i	0.150305	+	0.138646i
$584$	−0.912352			−0.0377534
$585$	2.24980	−	1.63458i	0.0930179	−	0.0675814i
$586$	−9.57790	−	29.4777i	−0.395659	−	1.21771i
$587$	12.1640	−	37.4370i	0.502063	−	1.54519i	−0.303590	−	0.952803i	$-0.598185\pi$
$587$	12.1640	−	37.4370i	0.502063	−	1.54519i	0.805653	−	0.592388i	$-0.201815\pi$
$588$	−6.58641	−	4.78531i	−0.271619	−	0.197343i
$589$	42.9074	+	31.1741i	1.76797	+	1.28451i
$590$	−10.4539	+	32.1737i	−0.430379	+	1.32457i
$591$	0.187250	+	0.576296i	0.00770243	+	0.0237056i
$592$	−33.6143	+	24.4222i	−1.38154	+	1.00375i
$593$	6.14138			0.252196			0.126098	−	0.992018i	$-0.459755\pi$
$593$	6.14138			0.252196			0.126098	+	0.992018i	$0.459755\pi$
$594$	−1.15896	−	5.79448i	−0.0475527	−	0.237751i
$595$	−2.72489			−0.111710
$596$	−15.2982	+	11.1148i	−0.626640	+	0.455281i
$597$	0.245390	+	0.755232i	0.0100431	+	0.0309096i
$598$	4.13060	−	12.7127i	0.168913	−	0.519861i
$599$	0.323531	+	0.235059i	0.0132191	+	0.00960425i	0.594375	−	0.804188i	$-0.297399\pi$
$599$	0.323531	+	0.235059i	0.0132191	+	0.00960425i	−0.581156	+	0.813792i	$0.697399\pi$
$600$	−3.25263	−	2.36317i	−0.132788	−	0.0964761i
$601$	3.99729	−	12.3024i	0.163053	−	0.501825i	−0.835835	−	0.548981i	$-0.815016\pi$
$601$	3.99729	−	12.3024i	0.163053	−	0.501825i	0.998888	+	0.0471561i	$0.0150158\pi$
$602$	−0.219993	−	0.677068i	−0.00896623	−	0.0275952i
$603$	−6.80223	+	4.94211i	−0.277008	+	0.201258i
$604$	0.653088			0.0265738
$605$	−29.7598	−	7.07822i	−1.20991	−	0.287771i
$606$	11.4464			0.464978
$607$	32.7475	−	23.7924i	1.32918	−	0.965705i	0.329411	−	0.944187i	$-0.393150\pi$
$607$	32.7475	−	23.7924i	1.32918	−	0.965705i	0.999768	−	0.0215185i	$-0.00685008\pi$
$608$	10.6924	+	32.9079i	0.433635	+	1.33459i
$609$	−0.567675	+	1.74712i	−0.0230033	+	0.0707970i
$610$	40.9363	+	29.7420i	1.65746	+	1.20422i
$611$	−7.15356	−	5.19736i	−0.289402	−	0.210263i
$612$	−1.36192	+	4.19156i	−0.0550524	+	0.169434i
$613$	−3.40767	−	10.4877i	−0.137634	−	0.423595i	0.858356	−	0.513054i	$-0.171486\pi$
$613$	−3.40767	−	10.4877i	−0.137634	−	0.423595i	−0.995990	+	0.0894593i	$0.971486\pi$
$614$	6.34326	−	4.60865i	0.255993	−	0.185990i
$615$	11.1661			0.450260
$616$	0.249825	+	1.24906i	0.0100657	+	0.0503259i
$617$	−28.3608			−1.14176			−0.570882	−	0.821032i	$-0.693399\pi$
$617$	−28.3608			−1.14176			−0.570882	+	0.821032i	$0.693399\pi$
$618$	26.6515	−	19.3635i	1.07208	−	0.778912i
$619$	−0.930970	−	2.86523i	−0.0374188	−	0.115163i	0.930602	−	0.366032i	$-0.119284\pi$
$619$	−0.930970	−	2.86523i	−0.0374188	−	0.115163i	−0.968021	+	0.250868i	$0.919284\pi$
$620$	−9.14688	+	28.1512i	−0.367348	+	1.13058i
$621$	6.06950	+	4.40975i	0.243561	+	0.176957i
$622$	−31.0638	−	22.5692i	−1.24555	−	0.904942i
$623$	0.826974	−	2.54516i	0.0331320	−	0.101970i
$624$	1.53568	+	4.72633i	0.0614763	+	0.189205i
$625$	25.2377	−	18.3363i	1.00951	−	0.733450i
$626$	28.5192			1.13986
$627$	−14.2666	−	13.1600i	−0.569755	−	0.525560i
$628$	−11.0244			−0.439923
$629$	−25.3824	+	18.4414i	−1.01206	+	0.735305i
$630$	0.399800	+	1.23046i	0.0159284	+	0.0490226i
$631$	−1.00130	+	3.08170i	−0.0398613	+	0.122680i	−0.969007	−	0.247033i	$-0.920544\pi$
$631$	−1.00130	+	3.08170i	−0.0398613	+	0.122680i	0.929146	+	0.369714i	$0.120544\pi$
$632$	−10.1062	−	7.34261i	−0.402004	−	0.292073i
$633$	−19.4008	−	14.0955i	−0.771113	−	0.560246i
$634$	−12.1667	+	37.4452i	−0.483201	+	1.48714i
$635$	−18.2523	−	56.1748i	−0.724320	−	2.22923i
$636$	−1.41450	+	1.02769i	−0.0560884	+	0.0407506i
$637$	−6.93182			−0.274649
$638$	36.2509	−	20.3518i	1.43519	−	0.805736i
$639$	6.19610			0.245114
$640$	24.2177	−	17.5952i	0.957289	−	0.695511i
$641$	−5.15915	−	15.8782i	−0.203774	−	0.627153i	−0.999761	−	0.0218393i	$-0.993048\pi$
$641$	−5.15915	−	15.8782i	−0.203774	−	0.627153i	0.795987	−	0.605313i	$-0.206952\pi$
$642$	0.872149	−	2.68420i	0.0344210	−	0.105937i
$643$	−21.1581	−	15.3722i	−0.834393	−	0.606222i	0.0864058	−	0.996260i	$-0.472462\pi$
$643$	−21.1581	−	15.3722i	−0.834393	−	0.606222i	−0.920799	+	0.390038i	$0.872462\pi$
$644$	1.86138	+	1.35237i	0.0733485	+	0.0532908i
$645$	1.31499	−	4.04711i	0.0517776	−	0.159355i
$646$	12.0909	+	37.2120i	0.475710	+	1.46408i
$647$	25.7933	−	18.7400i	1.01404	−	0.736744i	0.0489879	−	0.998799i	$-0.484400\pi$
$647$	25.7933	−	18.7400i	1.01404	−	0.736744i	0.965053	+	0.262056i	$0.0844004\pi$
$648$	−1.47084			−0.0577801
$649$	22.4906	+	2.63785i	0.882835	+	0.103545i
$650$	4.87020			0.191025
$651$	−1.91450	+	1.39096i	−0.0750351	+	0.0545162i
$652$	−5.20159	−	16.0089i	−0.203710	−	0.626955i
$653$	−10.3282	+	31.7868i	−0.404172	+	1.24391i	0.517413	+	0.855736i	$0.326895\pi$
$653$	−10.3282	+	31.7868i	−0.404172	+	1.24391i	−0.921585	+	0.388177i	$0.873105\pi$
$654$	9.74067	+	7.07701i	0.380890	+	0.276733i
$655$	6.60280	+	4.79721i	0.257993	+	0.187443i
$656$	−6.16616	+	18.9775i	−0.240748	+	0.740946i
$657$	0.191681	+	0.589933i	0.00747818	+	0.0230155i
$658$	3.32809	−	2.41800i	0.129743	−	0.0942635i
$659$	−27.8630			−1.08539			−0.542694	−	0.839930i	$-0.682596\pi$
$659$	−27.8630			−1.08539			−0.542694	+	0.839930i	$0.682596\pi$
$660$	4.52472	−	9.84220i	0.176124	−	0.383107i
$661$	13.4100			0.521589			0.260795	−	0.965394i	$-0.416015\pi$
$661$	13.4100			0.521589			0.260795	+	0.965394i	$0.416015\pi$
$662$	4.35219	−	3.16205i	0.169153	−	0.122897i
$663$	1.15960	+	3.56888i	0.0450351	+	0.138604i
$664$	−0.897250	+	2.76145i	−0.0348201	+	0.107165i
$665$	3.43792	+	2.49780i	0.133317	+	0.0968604i
$666$	12.0515	+	8.75595i	0.466988	+	0.339286i
$667$	−16.3101	+	50.1974i	−0.631531	+	1.94365i
$668$	7.25073	+	22.3155i	0.280539	+	0.863411i
$669$	−12.4906	+	9.07494i	−0.482914	+	0.350857i
$670$	−41.6597			−1.60945
$671$	14.1478	−	30.7745i	0.546170	−	1.18803i
$672$	−1.54389			−0.0595568
$673$	−12.3679	+	8.98578i	−0.476746	+	0.346376i	−0.800065	−	0.599914i	$-0.795202\pi$
$673$	−12.3679	+	8.98578i	−0.476746	+	0.346376i	0.323318	+	0.946290i	$0.395202\pi$
$674$	−6.05414	−	18.6327i	−0.233197	−	0.717706i
$675$	−0.844682	+	2.59966i	−0.0325118	+	0.100061i
$676$	−0.950171	−	0.690339i	−0.0365450	−	0.0265515i
$677$	28.9412	+	21.0270i	1.11230	+	0.808133i	0.983024	−	0.183476i	$-0.0587349\pi$
$677$	28.9412	+	21.0270i	1.11230	+	0.808133i	0.129275	+	0.991609i	$0.458735\pi$
$678$	−11.4862	+	35.3509i	−0.441125	+	1.35764i
$679$	0.983699	+	3.02751i	0.0377509	+	0.116185i
$680$	12.4175	−	9.02187i	0.476191	−	0.345973i
$681$	−2.17979			−0.0835299
$682$	53.1895	+	6.23841i	2.03673	+	0.238881i
$683$	35.0550			1.34134			0.670671	−	0.741755i	$-0.266006\pi$
$683$	35.0550			1.34134			0.670671	+	0.741755i	$0.266006\pi$
$684$	5.56053	−	4.03996i	0.212612	−	0.154472i
$685$	4.37122	+	13.4532i	0.167016	+	0.514021i
$686$	2.00292	−	6.16435i	0.0764718	−	0.235356i
$687$	24.0086	+	17.4433i	0.915985	+	0.665502i
$688$	6.15217	+	4.46981i	0.234549	+	0.170410i
$689$	−0.460026	+	1.41582i	−0.0175256	+	0.0539383i
$690$	11.4868	+	35.3528i	0.437296	+	1.34586i
$691$	4.01224	−	2.91506i	0.152633	−	0.110894i	−0.508848	−	0.860856i	$-0.669928\pi$
$691$	4.01224	−	2.91506i	0.152633	−	0.110894i	0.661481	+	0.749962i	$0.269928\pi$
$692$	6.10197			0.231962
$693$	0.755162	−	0.423959i	0.0286862	−	0.0161049i
$694$	−33.4557			−1.26996
$695$	4.78074	−	3.47341i	0.181344	−	0.131754i
$696$	−3.19763	−	9.84130i	−0.121206	−	0.373033i
$697$	−4.65610	+	14.3300i	−0.176362	+	0.542787i
$698$	−13.2783	−	9.64724i	−0.502590	−	0.365153i
$699$	−10.1013	−	7.33900i	−0.382065	−	0.277587i
$700$	−0.259045	+	0.797257i	−0.00979096	+	0.0301335i
$701$	−11.2706	−	34.6873i	−0.425684	−	1.31012i	−0.902338	−	0.431030i	$-0.858150\pi$
$701$	−11.2706	−	34.6873i	−0.425684	−	1.31012i	0.476654	−	0.879091i	$-0.341850\pi$
$702$	1.44143	−	1.04726i	0.0544033	−	0.0395263i
$703$	48.9287			1.84538
$704$	1.45152	+	1.33893i	0.0547061	+	0.0504627i
$705$	24.5896			0.926097
$706$	−5.93673	+	4.31329i	−0.223432	+	0.162333i
$707$	0.518385	+	1.59542i	0.0194959	+	0.0600021i
$708$	−2.47798	+	7.62645i	−0.0931284	+	0.286620i
$709$	−10.2052	−	7.41448i	−0.383263	−	0.278457i	0.379426	−	0.925222i	$-0.376121\pi$
$709$	−10.2052	−	7.41448i	−0.383263	−	0.278457i	−0.762689	+	0.646765i	$0.776121\pi$
$710$	24.8370	+	18.0451i	0.932114	+	0.677221i
$711$	−2.62451	+	8.07741i	−0.0984268	+	0.302926i
$712$	4.65823	+	14.3365i	0.174574	+	0.537285i
$713$	−55.0064	+	39.9645i	−2.06001	+	1.49668i
$714$	−1.74582			−0.0653356
$715$	−1.80892	−	9.04410i	−0.0676497	−	0.338230i
$716$	−11.2039			−0.418709
$717$	−4.57259	+	3.32218i	−0.170767	+	0.124069i
$718$	−15.1603	−	46.6586i	−0.565777	−	1.74128i
$719$	0.568102	−	1.74844i	0.0211866	−	0.0652058i	−0.939904	−	0.341438i	$-0.889086\pi$
$719$	0.568102	−	1.74844i	0.0211866	−	0.0652058i	0.961091	+	0.276232i	$0.0890860\pi$
$720$	−11.1805	−	8.12312i	−0.416673	−	0.302731i
$721$	3.90592	+	2.83782i	0.145464	+	0.105686i
$722$	8.39495	−	25.8370i	0.312428	−	0.961553i
$723$	−3.83818	−	11.8127i	−0.142743	−	0.439319i
$724$	7.29472	−	5.29992i	0.271106	−	0.196970i
$725$	−19.2305			−0.714203
$726$	−19.0669	−	4.53496i	−0.707638	−	0.168308i
$727$	−28.5435			−1.05862			−0.529309	−	0.848429i	$-0.677549\pi$
$727$	−28.5435			−1.05862			−0.529309	+	0.848429i	$0.677549\pi$
$728$	−0.310714	+	0.225747i	−0.0115158	+	0.00836674i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−0.949733	+	2.92298i	−0.0351512	+	0.108184i
$731$	4.64553	+	3.37518i	0.171821	+	0.124835i
$732$	9.70354	+	7.05003i	0.358653	+	0.260577i
$733$	6.10695	−	18.7952i	0.225565	−	0.694218i	−0.772669	−	0.634810i	$-0.781079\pi$
$733$	6.10695	−	18.7952i	0.225565	−	0.694218i	0.998234	−	0.0594086i	$-0.0189215\pi$
$734$	−5.93878	−	18.2777i	−0.219204	−	0.674642i
$735$	15.5952	−	11.3306i	0.575238	−	0.417935i
$736$	−44.3582			−1.63507
$737$	5.46923	+	27.3446i	0.201462	+	1.00725i
$738$	7.15402			0.263343
$739$	−25.0077	+	18.1691i	−0.919922	+	0.668362i	−0.943505	−	0.331359i	$-0.892493\pi$
$739$	−25.0077	+	18.1691i	−0.919922	+	0.668362i	0.0235827	+	0.999722i	$0.492493\pi$
$740$	8.43843	+	25.9708i	0.310203	+	0.954706i
$741$	1.80841	−	5.56572i	0.0664336	−	0.204462i
$742$	−0.560314	−	0.407092i	−0.0205698	−	0.0149448i
$743$	−29.7872	−	21.6417i	−1.09279	−	0.793957i	−0.112920	−	0.993604i	$-0.536020\pi$
$743$	−29.7872	−	21.6417i	−1.09279	−	0.793957i	−0.979868	+	0.199647i	$0.936020\pi$
$744$	4.11916	−	12.6775i	0.151016	−	0.464779i
$745$	−13.8359	−	42.5827i	−0.506910	−	1.56011i
$746$	−22.7293	+	16.5138i	−0.832180	+	0.604614i
$747$	1.97408			0.0722279
$748$	10.7443	+	9.91086i	0.392849	+	0.362377i
$749$	0.413628			0.0151136
$750$	9.08544	−	6.60096i	0.331753	−	0.241033i
$751$	9.61814	+	29.6016i	0.350971	+	1.08018i	0.958309	+	0.285734i	$0.0922373\pi$
$751$	9.61814	+	29.6016i	0.350971	+	1.08018i	−0.607338	+	0.794443i	$0.707763\pi$
$752$	−13.5789	+	41.7916i	−0.495172	+	1.52398i
$753$	−0.631953	−	0.459141i	−0.0230296	−	0.0167320i
$754$	10.1408	+	7.36775i	0.369307	+	0.268317i
$755$	−0.477856	+	1.47069i	−0.0173909	+	0.0535238i
$756$	0.0947684	+	0.291667i	0.00344669	+	0.0106078i
$757$	−37.0926	+	26.9494i	−1.34815	+	0.979492i	−0.349054	+	0.937103i	$0.613497\pi$
$757$	−37.0926	+	26.9494i	−1.34815	+	0.979492i	−0.999101	+	0.0423892i	$0.986503\pi$
$758$	7.19607			0.261373
$759$	21.6969	−	12.1810i	0.787548	−	0.442142i
$760$	−23.9369			−0.868281
$761$	5.29497	−	3.84702i	0.191942	−	0.139454i	−0.487664	−	0.873032i	$-0.662151\pi$
$761$	5.29497	−	3.84702i	0.191942	−	0.139454i	0.679606	+	0.733577i	$0.262151\pi$
$762$	−11.6941	−	35.9907i	−0.423632	−	1.30381i
$763$	−0.545274	+	1.67818i	−0.0197402	+	0.0607542i
$764$	−24.6342	−	17.8978i	−0.891233	−	0.647519i
$765$	−8.44247	−	6.13382i	−0.305238	−	0.221769i
$766$	6.94933	−	21.3878i	0.251089	−	0.772774i
$767$	2.10986	+	6.49350i	0.0761828	+	0.234467i
$768$	16.4795	−	11.9730i	0.594652	−	0.432040i
$769$	47.3207			1.70643			0.853214	−	0.521560i	$-0.174650\pi$
$769$	47.3207			1.70643			0.853214	+	0.521560i	$0.174650\pi$
$770$	4.26177	+	0.499848i	0.153583	+	0.0180133i
$771$	−17.0591			−0.614368
$772$	5.62116	−	4.08402i	0.202310	−	0.146987i
$773$	−4.19890	−	12.9229i	−0.151024	−	0.464804i	0.846712	−	0.532051i	$-0.178579\pi$
$773$	−4.19890	−	12.9229i	−0.151024	−	0.464804i	−0.997736	+	0.0672468i	$0.978579\pi$
$774$	0.842502	−	2.59295i	0.0302831	−	0.0932018i
$775$	−20.0414	−	14.5609i	−0.719909	−	0.523045i
$776$	−14.5066	−	10.5397i	−0.520757	−	0.378352i
$777$	−0.674634	+	2.07631i	−0.0242024	+	0.0744873i
$778$	−8.83107	−	27.1792i	−0.316609	−	0.974423i
$779$	19.0102	−	13.8117i	0.681111	−	0.494856i
$780$	3.26611			0.116945
$781$	8.58379	−	18.6715i	0.307152	−	0.668120i
$782$	−50.1599			−1.79371
$783$	−5.69164	+	4.13522i	−0.203403	+	0.147781i
$784$	10.6450	+	32.7621i	0.380180	+	1.17007i
$785$	8.06643	−	24.8259i	0.287903	−	0.886075i
$786$	4.23036	+	3.07354i	0.150892	+	0.109629i
$787$	−40.0542	−	29.1011i	−1.42778	−	1.03734i	−0.990425	−	0.138053i	$-0.955915\pi$
$787$	−40.0542	−	29.1011i	−1.42778	−	1.03734i	−0.437355	−	0.899289i	$-0.644085\pi$
$788$	−0.219920	+	0.676845i	−0.00783434	+	0.0241116i
$789$	−5.97046	−	18.3752i	−0.212554	−	0.654174i
$790$	−34.0444	+	24.7347i	−1.21125	+	0.880022i
$791$	−5.44748			−0.193690
$792$	−2.03764	+	4.43229i	−0.0724043	+	0.157494i
$793$	10.2124			0.362654
$794$	−0.811588	+	0.589653i	−0.0288022	+	0.0209260i
$795$	−1.27929	−	3.93725i	−0.0453718	−	0.139640i
$796$	−0.288204	+	0.887002i	−0.0102151	+	0.0314389i
$797$	−16.3965	−	11.9128i	−0.580795	−	0.421973i	0.258215	−	0.966087i	$-0.416866\pi$
$797$	−16.3965	−	11.9128i	−0.580795	−	0.421973i	−0.839011	+	0.544115i	$0.816866\pi$
$798$	2.20265	+	1.60032i	0.0779730	+	0.0566507i
$799$	−10.2535	+	31.5570i	−0.362743	+	1.11641i
$800$	−4.99427	−	15.3708i	−0.176574	−	0.543439i
$801$	8.29144	−	6.02408i	0.292964	−	0.212850i
$802$	9.46305			0.334152
$803$	2.04327	+	0.239648i	0.0721055	+	0.00845701i
$804$	−9.87501			−0.348265
$805$	−4.40734	+	3.20212i	−0.155338	+	0.112860i
$806$	4.98975	+	15.3569i	0.175756	+	0.540922i
$807$	−6.60624	+	20.3319i	−0.232551	+	0.715718i
$808$	−7.64462	−	5.55414i	−0.268937	−	0.195394i
$809$	33.3414	+	24.2240i	1.17222	+	0.851669i	0.991273	−	0.131823i	$-0.0420831\pi$
$809$	33.3414	+	24.2240i	1.17222	+	0.851669i	0.180949	+	0.983492i	$0.442083\pi$
$810$	−1.53110	+	4.71226i	−0.0537975	+	0.165572i
$811$	2.56544	+	7.89561i	0.0900847	+	0.277252i	0.985942	−	0.167091i	$-0.0534372\pi$
$811$	2.56544	+	7.89561i	0.0900847	+	0.277252i	−0.895857	+	0.444343i	$0.853437\pi$
$812$	−1.74550	+	1.26818i	−0.0612549	+	0.0445043i
$813$	18.1863			0.637820
$814$	43.0811	−	24.1864i	1.50999	−	0.847734i
$815$	39.8563			1.39610
$816$	15.0869	−	10.9613i	0.528148	−	0.383722i
$817$	−2.76726	−	8.51674i	−0.0968141	−	0.297963i
$818$	−1.86144	+	5.72894i	−0.0650839	+	0.200308i
$819$	0.211249	+	0.153481i	0.00738164	+	0.00536308i
$820$	10.6097	+	7.70839i	0.370506	+	0.269189i
$821$	12.1834	−	37.4967i	0.425204	−	1.30864i	−0.477595	−	0.878580i	$-0.658491\pi$
$821$	12.1834	−	37.4967i	0.425204	−	1.30864i	0.902799	−	0.430063i	$-0.141509\pi$
$822$	2.80060	+	8.61937i	0.0976823	+	0.300635i
$823$	−38.3188	+	27.8403i	−1.33571	+	0.970450i	−0.336120	+	0.941819i	$0.609115\pi$
$823$	−38.3188	+	27.8403i	−1.33571	+	0.970450i	−0.999590	+	0.0286310i	$0.990885\pi$
$824$	−27.1953			−0.947394
$825$	6.66373	+	6.14685i	0.232001	+	0.214006i
$826$	−3.17648			−0.110524
$827$	−33.9908	+	24.6958i	−1.18198	+	0.858756i	−0.992393	−	0.123108i	$-0.960714\pi$
$827$	−33.9908	+	24.6958i	−1.18198	+	0.858756i	−0.189583	+	0.981865i	$0.560714\pi$
$828$	2.72284	+	8.38003i	0.0946251	+	0.291226i
$829$	3.26522	−	10.0493i	0.113406	−	0.349028i	−0.878205	−	0.478284i	$-0.841259\pi$
$829$	3.26522	−	10.0493i	0.113406	−	0.349028i	0.991611	+	0.129256i	$0.0412590\pi$
$830$	7.91308	+	5.74919i	0.274667	+	0.199557i
$831$	−9.40760	−	6.83502i	−0.326346	−	0.237104i
$832$	−0.183991	+	0.566267i	−0.00637875	+	0.0196318i
$833$	8.03813	+	24.7388i	0.278505	+	0.857149i
$834$	3.06298	−	2.22539i	0.106062	−	0.0770589i
$835$	−55.5574			−1.92264
$836$	−4.47086	−	22.3531i	−0.154628	−	0.773097i
$837$	−9.06275			−0.313255
$838$	−9.81854	+	7.13359i	−0.339176	+	0.246426i
$839$	13.2785	+	40.8669i	0.458423	+	1.41088i	0.867069	+	0.498188i	$0.166001\pi$
$839$	13.2785	+	40.8669i	0.458423	+	1.41088i	−0.408646	+	0.912693i	$0.633999\pi$
$840$	0.330044	−	1.01577i	0.0113876	−	0.0350475i
$841$	−16.5807	−	12.0466i	−0.571747	−	0.415399i
$842$	40.5144	+	29.4354i	1.39622	+	1.01441i
$843$	−3.62737	+	11.1639i	−0.124933	+	0.384505i
$844$	−8.70339	−	26.7863i	−0.299583	−	0.922021i
$845$	2.24980	−	1.63458i	0.0773955	−	0.0562311i
$846$	15.7544			0.541646
$847$	−0.231408	−	2.86296i	−0.00795128	−	0.0983726i
$848$	7.39807			0.254051
$849$	2.92870	−	2.12782i	0.100513	−	0.0730267i
$850$	−5.64748	−	17.3812i	−0.193707	−	0.596169i
$851$	−19.3832	+	59.6555i	−0.664449	+	2.04496i
$852$	5.88735	+	4.27741i	0.201697	+	0.146542i
$853$	−4.74673	−	3.44870i	−0.162525	−	0.118081i	0.503550	−	0.863966i	$-0.332027\pi$
$853$	−4.74673	−	3.44870i	−0.162525	−	0.118081i	−0.666075	+	0.745885i	$0.732027\pi$
$854$	−1.46820	+	4.51864i	−0.0502407	+	0.154625i
$855$	5.02902	+	15.4777i	0.171989	+	0.529328i
$856$	−1.88493	+	1.36948i	−0.0644257	+	0.0468080i
$857$	5.70581			0.194907			0.0974533	−	0.995240i	$-0.468930\pi$
$857$	5.70581			0.194907			0.0974533	+	0.995240i	$0.468930\pi$
$858$	−1.15896	−	5.79448i	−0.0395662	−	0.197820i
$859$	8.02997			0.273979			0.136990	−	0.990572i	$-0.456257\pi$
$859$	8.02997			0.273979			0.136990	+	0.990572i	$0.456257\pi$
$860$	4.04334	−	2.93766i	0.137877	−	0.100173i
$861$	0.323992	+	0.997144i	0.0110416	+	0.0339826i
$862$	−3.11706	+	9.59333i	−0.106168	+	0.326750i
$863$	20.5017	+	14.8953i	0.697885	+	0.507043i	0.879243	−	0.476374i	$-0.158049\pi$
$863$	20.5017	+	14.8953i	0.697885	+	0.507043i	−0.181358	+	0.983417i	$0.558049\pi$
$864$	−4.78340	−	3.47534i	−0.162735	−	0.118234i
$865$	−4.46473	+	13.7410i	−0.151805	+	0.467209i
$866$	9.46293	+	29.1239i	0.321563	+	0.989670i
$867$	−2.36106	+	1.71541i	−0.0801859	+	0.0582585i
$868$	−2.77934			−0.0943369
$869$	20.7049	+	19.0989i	0.702365	+	0.647884i
$870$	−34.8580			−1.18180
$871$	−6.80223	+	4.94211i	−0.230485	+	0.167457i
$872$	−3.07145	−	9.45295i	−0.104012	−	0.320117i
$873$	−3.76725	+	11.5944i	−0.127502	+	0.392411i
$874$	63.2854	+	45.9795i	2.14066	+	1.55528i
$875$	1.33152	+	0.967405i	0.0450135	+	0.0327043i
$876$	−0.225124	+	0.692862i	−0.00760625	+	0.0234096i
$877$	4.41097	+	13.5756i	0.148948	+	0.458414i	0.997498	−	0.0707015i	$-0.0225238\pi$
$877$	4.41097	+	13.5756i	0.148948	+	0.458414i	−0.848550	+	0.529116i	$0.822524\pi$
$878$	46.4838	−	33.7725i	1.56875	−	1.13977i
$879$	17.3961			0.586756
$880$	−39.9675	+	22.4384i	−1.34730	+	0.756397i
$881$	21.1535			0.712681			0.356340	−	0.934356i	$-0.384024\pi$
$881$	21.1535			0.712681			0.356340	+	0.934356i	$0.384024\pi$
$882$	9.99173	−	7.25942i	0.336439	−	0.244437i
$883$	−15.6058	−	48.0297i	−0.525177	−	1.61633i	−0.763966	−	0.645256i	$-0.776751\pi$
$883$	−15.6058	−	48.0297i	−0.525177	−	1.61633i	0.238789	−	0.971071i	$-0.423249\pi$
$884$	−1.36192	+	4.19156i	−0.0458063	+	0.140977i
$885$	−15.3609	−	11.1603i	−0.516351	−	0.375151i
$886$	0.775844	+	0.563683i	0.0260650	+	0.0189373i
$887$	5.67780	−	17.4745i	0.190642	−	0.586735i	−0.809358	−	0.587315i	$-0.800185\pi$
$887$	5.67780	−	17.4745i	0.190642	−	0.586735i	1.00000		0.000580564i	$0.000184799\pi$
$888$	−3.80012	−	11.6956i	−0.127524	−	0.392477i
$889$	4.48687	−	3.25990i	0.150485	−	0.109334i
$890$	50.7802			1.70216
$891$	3.29405	+	0.386347i	0.110355	+	0.0129431i
$892$	−18.1330			−0.607137
$893$	41.8636	−	30.4157i	1.40091	−	1.01782i
$894$	−8.86458	−	27.2824i	−0.296476	−	0.912459i
$895$	8.19774	−	25.2300i	0.274020	−	0.843347i
$896$	2.27396	+	1.65213i	0.0759678	+	0.0551938i
$897$	6.06950	+	4.40975i	0.202655	+	0.147237i
$898$	7.31194	−	22.5038i	0.244003	−	0.750963i
$899$	−19.7026	−	60.6382i	−0.657117	−	2.02240i
$900$	−2.59724	+	1.88701i	−0.0865747	+	0.0629002i
$901$	5.58632			0.186107
$902$	9.91086	−	21.5582i	0.329995	−	0.717809i
$903$	0.399567			0.0132968
$904$	24.8246	−	18.0361i	0.825653	−	0.599872i
$905$	6.59745	+	20.3048i	0.219306	+	0.674956i
$906$	−0.306158	+	0.942259i	−0.0101714	+	0.0313044i
$907$	7.32638	+	5.32292i	0.243268	+	0.176745i	0.702738	−	0.711449i	$-0.251961\pi$
$907$	7.32638	+	5.32292i	0.243268	+	0.176745i	−0.459470	+	0.888193i	$0.651961\pi$
$908$	−2.07118	−	1.50480i	−0.0687344	−	0.0499385i
$909$	−1.98525	+	6.10997i	−0.0658465	+	0.202655i
$910$	0.399800	+	1.23046i	0.0132532	+	0.0407892i
$911$	−28.8084	+	20.9305i	−0.954465	+	0.693460i	−0.951859	−	0.306537i	$-0.900830\pi$
$911$	−28.8084	+	20.9305i	−0.954465	+	0.693460i	−0.00260665	+	0.999997i	$0.500830\pi$
$912$	−29.0825			−0.963019
$913$	2.73480	−	5.94877i	0.0905088	−	0.196876i
$914$	−72.4631			−2.39687
$915$	−22.9759	+	16.6930i	−0.759560	+	0.551853i
$916$	10.7705	+	33.1482i	0.355867	+	1.09525i
$917$	−0.236812	+	0.728832i	−0.00782021	+	0.0240681i
$918$	−5.40903	−	3.92989i	−0.178524	−	0.129706i
$919$	40.2574	+	29.2487i	1.32797	+	0.964826i	0.999796	+	0.0202090i	$0.00643316\pi$
$919$	40.2574	+	29.2487i	1.32797	+	0.964826i	0.328174	+	0.944617i	$0.393567\pi$
$920$	9.48266	−	29.1846i	0.312634	−	0.962189i
$921$	1.35988	+	4.18529i	0.0448096	+	0.137910i
$922$	−1.17759	+	0.855567i	−0.0387818	+	0.0281766i
$923$	6.19610			0.203947
$924$	1.01021	+	0.118484i	0.0332334	+	0.00389783i
$925$	−22.8539			−0.751430
$926$	−5.72931	+	4.16259i	−0.188277	+	0.136791i
$927$	5.71361	+	17.5847i	0.187660	+	0.577557i
$928$	12.8541	−	39.5608i	0.421956	−	1.29865i
$929$	−3.29776	−	2.39596i	−0.108196	−	0.0786089i	0.532372	−	0.846511i	$-0.321301\pi$
$929$	−3.29776	−	2.39596i	−0.108196	−	0.0786089i	−0.640568	+	0.767902i	$0.721301\pi$
$930$	−36.3279	−	26.3938i	−1.19124	−	0.865486i
$931$	12.5356	−	38.5805i	0.410837	−	1.26443i
$932$	−4.53153	−	13.9466i	−0.148435	−	0.456836i
$933$	17.4349	−	12.6672i	0.570792	−	0.414705i
$934$	18.6013			0.608654
$935$	−30.1797	+	16.9433i	−0.986981	+	0.554106i
$936$	−1.47084			−0.0480760
$937$	−13.7703	+	10.0047i	−0.449858	+	0.326841i	−0.789540	−	0.613700i	$-0.789681\pi$
$937$	−13.7703	+	10.0047i	−0.449858	+	0.326841i	0.339682	+	0.940540i	$0.389681\pi$
$938$	−1.20879	−	3.72026i	−0.0394682	−	0.121471i
$939$	−4.94634	+	15.2233i	−0.161418	+	0.496792i
$940$	23.3643	+	16.9752i	0.762059	+	0.553668i
$941$	−36.3001	−	26.3736i	−1.18335	−	0.859755i	−0.190805	−	0.981628i	$-0.561110\pi$
$941$	−36.3001	−	26.3736i	−1.18335	−	0.859755i	−0.992546	+	0.121873i	$0.961110\pi$
$942$	5.16810	−	15.9058i	0.168386	−	0.518238i
$943$	9.30877	+	28.6494i	0.303135	+	0.932954i
$944$	27.4503	−	19.9438i	0.893432	−	0.649117i
$945$	−0.726146			−0.0236215
$946$	−6.64654	−	6.13099i	−0.216098	−	0.199336i
$947$	47.4472			1.54183			0.770914	−	0.636940i	$-0.219800\pi$
$947$	47.4472			1.54183			0.770914	+	0.636940i	$0.219800\pi$
$948$	−8.06988	+	5.86311i	−0.262098	+	0.190425i
$949$	0.191681	+	0.589933i	0.00622222	+	0.0191500i
$950$	−8.80732	+	27.1061i	−0.285747	+	0.879440i
$951$	−17.8777	−	12.9889i	−0.579725	−	0.421195i
$952$	1.16597	+	0.847125i	0.0377892	+	0.0274555i
$953$	−5.35317	+	16.4754i	−0.173406	+	0.533689i	−0.999557	−	0.0297595i	$-0.990526\pi$
$953$	−5.35317	+	16.4754i	−0.173406	+	0.533689i	0.826151	+	0.563449i	$0.190526\pi$
$954$	−0.819632	−	2.52257i	−0.0265366	−	0.0816711i
$955$	58.3285	−	42.3781i	1.88747	−	1.37132i
$956$	−6.63818			−0.214694
$957$	4.57628	+	22.8801i	0.147930	+	0.739610i
$958$	−30.5321			−0.986448
$959$	−1.07455	+	0.780709i	−0.0346992	+	0.0252104i
$960$	−0.511663	−	1.57474i	−0.0165139	−	0.0508244i
$961$	15.8011	−	48.6309i	0.509714	−	1.56874i
$962$	12.0515	+	8.75595i	0.388557	+	0.282303i
$963$	1.28153	+	0.931088i	0.0412968	+	0.0300039i
$964$	4.50785	−	13.8737i	0.145188	−	0.446843i
$965$	5.08386	+	15.6465i	0.163655	+	0.503679i
$966$	−2.82375	+	2.05157i	−0.0908527	+	0.0660083i
$967$	28.8159			0.926658			0.463329	−	0.886186i	$-0.346655\pi$
$967$	28.8159			0.926658			0.463329	+	0.886186i	$0.346655\pi$
$968$	10.5336	+	12.2806i	0.338562	+	0.394713i
$969$	−21.9604			−0.705470
$970$	−48.8678	+	35.5045i	−1.56905	+	1.13998i
$971$	−0.225123	−	0.692859i	−0.00722456	−	0.0222349i	0.947379	−	0.320113i	$-0.103721\pi$
$971$	−0.225123	−	0.692859i	−0.00722456	−	0.0222349i	−0.954604	+	0.297878i	$0.903721\pi$
$972$	−0.362933	+	1.11699i	−0.0116411	+	0.0358275i
$973$	0.448896	+	0.326142i	0.0143910	+	0.0104556i
$974$	22.1695	+	16.1071i	0.710355	+	0.516103i
$975$	−0.844682	+	2.59966i	−0.0270515	+	0.0832559i
$976$	−15.6830	−	48.2673i	−0.502000	−	1.54500i
$977$	−16.2530	+	11.8085i	−0.519978	+	0.377786i	−0.816596	−	0.577210i	$-0.804141\pi$
$977$	−16.2530	+	11.8085i	−0.519978	+	0.377786i	0.296617	+	0.954996i	$0.404141\pi$
$978$	25.5356			0.816538
$979$	−6.66660	−	33.3312i	−0.213066	−	1.06527i
$980$	22.6401			0.723210
$981$	−5.46705	+	3.97204i	−0.174549	+	0.126818i
$982$	−1.39737	−	4.30067i	−0.0445920	−	0.137240i
$983$	6.55980	−	20.1890i	0.209225	−	0.643929i	−0.790288	−	0.612735i	$-0.790069\pi$
$983$	6.55980	−	20.1890i	0.209225	−	0.643929i	0.999513	−	0.0311933i	$-0.00993076\pi$
$984$	−4.77791	−	3.47136i	−0.152314	−	0.110663i
$985$	−1.36327	−	0.990477i	−0.0434375	−	0.0315592i
$986$	14.5353	−	44.7350i	0.462898	−	1.42465i
$987$	0.713484	+	2.19588i	0.0227104	+	0.0698956i
$988$	5.56053	−	4.03996i	0.176904	−	0.128528i
$989$	11.4802			0.365048
$990$	12.0790	+	11.1420i	0.383894	+	0.354117i
$991$	1.09694			0.0348454			0.0174227	−	0.999848i	$-0.494454\pi$
$991$	1.09694			0.0348454			0.0174227	+	0.999848i	$0.494454\pi$
$992$	43.3508	−	31.4962i	1.37639	−	1.00000i
$993$	0.933032	+	2.87158i	0.0296089	+	0.0911267i
$994$	−0.890787	+	2.74156i	−0.0282540	+	0.0869570i
$995$	−1.78656	−	1.29801i	−0.0566379	−	0.0411498i
$996$	1.87572	+	1.36279i	0.0594343	+	0.0431816i
$997$	12.0672	−	37.1390i	0.382172	−	1.17621i	−0.556339	−	0.830956i	$-0.687794\pi$
$997$	12.0672	−	37.1390i	0.382172	−	1.17621i	0.938511	−	0.345249i	$-0.112206\pi$
$998$	−0.302210	−	0.930108i	−0.00956631	−	0.0294421i
$999$	−6.76404	+	4.91437i	−0.214005	+	0.155484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.157.2	✓	28
11.2	odd	10		4719.2.a.bo.1.4		14
11.4	even	5	inner	429.2.n.c.235.2	yes	28
11.9	even	5		4719.2.a.bp.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.157.2	✓	28	1.1	even	1	trivial
429.2.n.c.235.2	yes	28	11.4	even	5	inner
4719.2.a.bo.1.4		14	11.2	odd	10
4719.2.a.bp.1.11		14	11.9	even	5

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44143 + 1.04726i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.362933 - 1.11699i) q^{4} +(2.24980 + 1.63458i) q^{5} +(1.44143 + 1.04726i) q^{6} +(-0.0806900 + 0.248338i) q^{7} +(-0.454515 - 1.39885i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.44143 + 1.04726i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.362933 - 1.11699i) q^{4} +(2.24980 + 1.63458i) q^{5} +(1.44143 + 1.04726i) q^{6} +(-0.0806900 + 0.248338i) q^{7} +(-0.454515 - 1.39885i) q^{8} +(-0.809017 + 0.587785i) q^{9} -4.95476 q^{10} +(0.650478 + 3.25221i) q^{11} -1.17448 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.143766 - 0.442466i) q^{14} +(0.859348 - 2.64480i) q^{15} +(4.02046 + 2.92103i) q^{16} +(3.03587 + 2.20569i) q^{17} +(0.550577 - 1.69450i) q^{18} +(-1.80841 - 5.56572i) q^{19} +(2.64234 - 1.91977i) q^{20} +0.261118 q^{21} +(-4.34353 - 4.00662i) q^{22} +7.50231 q^{23} +(-1.18994 + 0.864539i) q^{24} +(0.844682 + 2.59966i) q^{25} +(0.550577 - 1.69450i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.248107 + 0.180260i) q^{28} +(-2.17401 + 6.69093i) q^{29} +(1.53110 + 4.71226i) q^{30} +(-7.33192 + 5.32695i) q^{31} -5.91261 q^{32} +(2.89203 - 1.62363i) q^{33} -6.68592 q^{34} +(-0.587464 + 0.426818i) q^{35} +(0.362933 + 1.11699i) q^{36} +(-2.58363 + 7.95161i) q^{37} +(8.43545 + 6.12871i) q^{38} +(0.809017 + 0.587785i) q^{39} +(1.26396 - 3.89008i) q^{40} +(1.24079 + 3.81875i) q^{41} +(-0.376384 + 0.273459i) q^{42} +1.53022 q^{43} +(3.86878 + 0.453756i) q^{44} -2.78091 q^{45} +(-10.8141 + 7.85688i) q^{46} +(2.73242 + 8.40951i) q^{47} +(1.53568 - 4.72633i) q^{48} +(5.60796 + 4.07442i) q^{49} +(-3.94007 - 2.86263i) q^{50} +(1.15960 - 3.56888i) q^{51} +(0.362933 + 1.11699i) q^{52} +(1.20436 - 0.875022i) q^{53} -1.78171 q^{54} +(-3.85254 + 8.38009i) q^{55} +0.384064 q^{56} +(-4.73448 + 3.43980i) q^{57} +(-3.87345 - 11.9213i) q^{58} +(2.10986 - 6.49350i) q^{59} +(-2.64234 - 1.91977i) q^{60} +(-8.26202 - 6.00271i) q^{61} +(4.98975 - 15.3569i) q^{62} +(-0.0806900 - 0.248338i) q^{63} +(0.481696 - 0.349972i) q^{64} -2.78091 q^{65} +(-2.46829 + 5.36906i) q^{66} +8.40802 q^{67} +(3.56555 - 2.59053i) q^{68} +(-2.31834 - 7.13513i) q^{69} +(0.399800 - 1.23046i) q^{70} +(-5.01275 - 3.64197i) q^{71} +(1.18994 + 0.864539i) q^{72} +(0.191681 - 0.589933i) q^{73} +(-4.60328 - 14.1674i) q^{74} +(2.21141 - 1.60668i) q^{75} -6.87319 q^{76} +(-0.860136 - 0.100882i) q^{77} -1.78171 q^{78} +(6.87105 - 4.99211i) q^{79} +(4.27058 + 13.1435i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.78773 - 4.20503i) q^{82} +(-1.59707 - 1.16034i) q^{83} +(0.0947684 - 0.291667i) q^{84} +(3.22474 + 9.92472i) q^{85} +(-2.20570 + 1.60253i) q^{86} +7.03526 q^{87} +(4.25372 - 2.38810i) q^{88} -10.2488 q^{89} +(4.00848 - 2.91233i) q^{90} +(-0.0806900 - 0.248338i) q^{91} +(2.72284 - 8.38003i) q^{92} +(7.33192 + 5.32695i) q^{93} +(-12.7455 - 9.26017i) q^{94} +(5.02902 - 15.4777i) q^{95} +(1.82710 + 5.62322i) q^{96} +(9.86280 - 7.16574i) q^{97} -12.3505 q^{98} +(-2.43785 - 2.24875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

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