LMFDB - Embedded newform 429.2.n.c.157.5

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			157.5
Character	$\chi$	$=$	429.157
Dual form			429.2.n.c.235.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.788916 - 0.573181i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.324182 + 0.997729i) q^{4} +(-2.91208 - 2.11575i) q^{5} +(-0.788916 - 0.573181i) q^{6} +(-1.06635 + 3.28188i) q^{7} +(0.918806 + 2.82779i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.788916 - 0.573181i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.324182 + 0.997729i) q^{4} +(-2.91208 - 2.11575i) q^{5} +(-0.788916 - 0.573181i) q^{6} +(-1.06635 + 3.28188i) q^{7} +(0.918806 + 2.82779i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.51009 q^{10} +(0.466640 + 3.28363i) q^{11} +1.04907 q^{12} +(-0.809017 + 0.587785i) q^{13} +(1.03985 + 3.20034i) q^{14} +(-1.11231 + 3.42335i) q^{15} +(0.648261 + 0.470989i) q^{16} +(-6.51477 - 4.73326i) q^{17} +(-0.301339 + 0.927427i) q^{18} +(1.40012 + 4.30911i) q^{19} +(3.05498 - 2.21958i) q^{20} +3.45077 q^{21} +(2.25026 + 2.32304i) q^{22} +5.38284 q^{23} +(2.40546 - 1.74767i) q^{24} +(2.45872 + 7.56715i) q^{25} +(-0.301339 + 0.927427i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.92873 - 2.12785i) q^{28} +(-0.565134 + 1.73930i) q^{29} +(1.08468 + 3.33829i) q^{30} +(-6.04966 + 4.39534i) q^{31} -5.16525 q^{32} +(2.97872 - 1.45850i) q^{33} -7.85262 q^{34} +(10.0489 - 7.30095i) q^{35} +(-0.324182 - 0.997729i) q^{36} +(0.848128 - 2.61027i) q^{37} +(3.57448 + 2.59701i) q^{38} +(0.809017 + 0.587785i) q^{39} +(3.30726 - 10.1787i) q^{40} +(-2.68180 - 8.25373i) q^{41} +(2.72237 - 1.97792i) q^{42} -6.68750 q^{43} +(-3.42745 - 0.598914i) q^{44} +3.59952 q^{45} +(4.24661 - 3.08534i) q^{46} +(0.462046 + 1.42203i) q^{47} +(0.247614 - 0.762077i) q^{48} +(-3.97050 - 2.88474i) q^{49} +(6.27707 + 4.56056i) q^{50} +(-2.48842 + 7.65857i) q^{51} +(-0.324182 - 0.997729i) q^{52} +(-6.30053 + 4.57760i) q^{53} +0.975154 q^{54} +(5.58845 - 10.5495i) q^{55} -10.2602 q^{56} +(3.66555 - 2.66318i) q^{57} +(0.551093 + 1.69609i) q^{58} +(-1.57629 + 4.85133i) q^{59} +(-3.05498 - 2.21958i) q^{60} +(-1.09627 - 0.796490i) q^{61} +(-2.25335 + 6.93511i) q^{62} +(-1.06635 - 3.28188i) q^{63} +(-5.37147 + 3.90260i) q^{64} +3.59952 q^{65} +(1.51398 - 2.85798i) q^{66} +4.00675 q^{67} +(6.83448 - 4.96554i) q^{68} +(-1.66339 - 5.11939i) q^{69} +(3.74297 - 11.5197i) q^{70} +(7.39649 + 5.37386i) q^{71} +(-2.40546 - 1.74767i) q^{72} +(2.38841 - 7.35076i) q^{73} +(-0.827056 - 2.54542i) q^{74} +(6.43700 - 4.67675i) q^{75} -4.75322 q^{76} +(-11.2741 - 1.97004i) q^{77} +0.975154 q^{78} +(2.72499 - 1.97982i) q^{79} +(-0.891291 - 2.74311i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-6.84660 - 4.97435i) q^{82} +(4.69889 + 3.41395i) q^{83} +(-1.11868 + 3.44293i) q^{84} +(8.95713 + 27.5672i) q^{85} +(-5.27588 + 3.83315i) q^{86} +1.82881 q^{87} +(-8.85668 + 4.33658i) q^{88} +16.5060 q^{89} +(2.83972 - 2.06318i) q^{90} +(-1.06635 - 3.28188i) q^{91} +(-1.74502 + 5.37062i) q^{92} +(6.04966 + 4.39534i) q^{93} +(1.17960 + 0.857027i) q^{94} +(5.03975 - 15.5108i) q^{95} +(1.59615 + 4.91244i) q^{96} +(-0.0735643 + 0.0534476i) q^{97} -4.78587 q^{98} +(-2.30759 - 2.38223i) 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 $

$2$	0.788916	−	0.573181i	0.557848	−	0.405300i	−0.272823	−	0.962064i	$-0.587957\pi$
$2$	0.788916	−	0.573181i	0.557848	−	0.405300i	0.830671	+	0.556764i	$0.187957\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.324182	+	0.997729i	−0.162091	+	0.498864i
$5$	−2.91208	−	2.11575i	−1.30232	−	0.946191i	−0.302344	−	0.953199i	$-0.597769\pi$
$5$	−2.91208	−	2.11575i	−1.30232	−	0.946191i	−0.999975	+	0.00700796i	$0.997769\pi$
$6$	−0.788916	−	0.573181i	−0.322074	−	0.234000i
$7$	−1.06635	+	3.28188i	−0.403041	+	1.24043i	0.519479	+	0.854483i	$0.326126\pi$
$7$	−1.06635	+	3.28188i	−0.403041	+	1.24043i	−0.922520	+	0.385949i	$0.873874\pi$
$8$	0.918806	+	2.82779i	0.324847	+	0.999776i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−3.51009			−1.10999
$11$	0.466640	+	3.28363i	0.140697	+	0.990053i
$11$	0.466640	+	3.28363i	0.140697	+	0.990053i
$12$	1.04907			0.302842
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	1.03985	+	3.20034i	0.277912	+	0.855326i
$15$	−1.11231	+	3.42335i	−0.287198	+	0.883905i
$16$	0.648261	+	0.470989i	0.162065	+	0.117747i
$17$	−6.51477	−	4.73326i	−1.58006	−	1.14798i	−0.916621	−	0.399756i	$-0.869095\pi$
$17$	−6.51477	−	4.73326i	−1.58006	−	1.14798i	−0.663443	−	0.748227i	$-0.730905\pi$
$18$	−0.301339	+	0.927427i	−0.0710263	+	0.218597i
$19$	1.40012	+	4.30911i	0.321209	+	0.988579i	0.973123	+	0.230286i	$0.0739662\pi$
$19$	1.40012	+	4.30911i	0.321209	+	0.988579i	−0.651914	+	0.758293i	$0.726034\pi$
$20$	3.05498	−	2.21958i	0.683115	−	0.496312i
$21$	3.45077			0.753020
$22$	2.25026	+	2.32304i	0.479756	+	0.495274i
$23$	5.38284			1.12240			0.561200	−	0.827680i	$-0.310340\pi$
$23$	5.38284			1.12240			0.561200	+	0.827680i	$0.310340\pi$
$24$	2.40546	−	1.74767i	0.491013	−	0.356742i
$25$	2.45872	+	7.56715i	0.491743	+	1.51343i
$26$	−0.301339	+	0.927427i	−0.0590975	+	0.181883i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−2.92873	−	2.12785i	−0.553478	−	0.402126i
$29$	−0.565134	+	1.73930i	−0.104943	+	0.322981i	−0.989717	−	0.143039i	$-0.954313\pi$
$29$	−0.565134	+	1.73930i	−0.104943	+	0.322981i	0.884774	+	0.466020i	$0.154313\pi$
$30$	1.08468	+	3.33829i	0.198034	+	0.609486i
$31$	−6.04966	+	4.39534i	−1.08655	+	0.789426i	−0.978814	−	0.204753i	$-0.934361\pi$
$31$	−6.04966	+	4.39534i	−1.08655	+	0.789426i	−0.107738	+	0.994179i	$0.534361\pi$
$32$	−5.16525			−0.913096
$33$	2.97872	−	1.45850i	0.518529	−	0.253892i
$34$	−7.85262			−1.34671
$35$	10.0489	−	7.30095i	1.69857	−	1.23409i
$36$	−0.324182	−	0.997729i	−0.0540303	−	0.166288i
$37$	0.848128	−	2.61027i	0.139431	−	0.429126i	−0.856822	−	0.515613i	$-0.827564\pi$
$37$	0.848128	−	2.61027i	0.139431	−	0.429126i	0.996253	+	0.0864874i	$0.0275642\pi$
$38$	3.57448	+	2.59701i	0.579857	+	0.421291i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	3.30726	−	10.1787i	0.522924	−	1.60940i
$41$	−2.68180	−	8.25373i	−0.418827	−	1.28902i	−0.908783	−	0.417269i	$-0.862987\pi$
$41$	−2.68180	−	8.25373i	−0.418827	−	1.28902i	0.489956	−	0.871747i	$-0.337013\pi$
$42$	2.72237	−	1.97792i	0.420071	−	0.305199i
$43$	−6.68750			−1.01983			−0.509917	−	0.860224i	$-0.670324\pi$
$43$	−6.68750			−1.01983			−0.509917	+	0.860224i	$0.670324\pi$
$44$	−3.42745	−	0.598914i	−0.516708	−	0.0902897i
$45$	3.59952			0.536585
$46$	4.24661	−	3.08534i	0.626129	−	0.454909i
$47$	0.462046	+	1.42203i	0.0673963	+	0.207425i	0.979083	−	0.203462i	$-0.0652193\pi$
$47$	0.462046	+	1.42203i	0.0673963	+	0.207425i	−0.911687	+	0.410886i	$0.865219\pi$
$48$	0.247614	−	0.762077i	0.0357400	−	0.109996i
$49$	−3.97050	−	2.88474i	−0.567214	−	0.412105i
$50$	6.27707	+	4.56056i	0.887712	+	0.644960i
$51$	−2.48842	+	7.65857i	−0.348449	+	1.07241i
$52$	−0.324182	−	0.997729i	−0.0449559	−	0.138360i
$53$	−6.30053	+	4.57760i	−0.865444	+	0.628782i	−0.929361	−	0.369173i	$-0.879641\pi$
$53$	−6.30053	+	4.57760i	−0.865444	+	0.628782i	0.0639162	+	0.997955i	$0.479641\pi$
$54$	0.975154			0.132702
$55$	5.58845	−	10.5495i	0.753546	−	1.42249i
$56$	−10.2602			−1.37108
$57$	3.66555	−	2.66318i	0.485514	−	0.352747i
$58$	0.551093	+	1.69609i	0.0723621	+	0.222708i
$59$	−1.57629	+	4.85133i	−0.205216	+	0.631589i	0.794489	+	0.607279i	$0.207739\pi$
$59$	−1.57629	+	4.85133i	−0.205216	+	0.631589i	−0.999704	+	0.0243100i	$0.992261\pi$
$60$	−3.05498	−	2.21958i	−0.394397	−	0.286546i
$61$	−1.09627	−	0.796490i	−0.140363	−	0.101980i	0.515388	−	0.856957i	$-0.327648\pi$
$61$	−1.09627	−	0.796490i	−0.140363	−	0.101980i	−0.655751	+	0.754977i	$0.727648\pi$
$62$	−2.25335	+	6.93511i	−0.286176	+	0.880760i
$63$	−1.06635	−	3.28188i	−0.134347	−	0.413478i
$64$	−5.37147	+	3.90260i	−0.671434	+	0.487825i
$65$	3.59952			0.446466
$66$	1.51398	−	2.85798i	0.186358	−	0.351793i
$67$	4.00675			0.489502			0.244751	−	0.969586i	$-0.421294\pi$
$67$	4.00675			0.489502			0.244751	+	0.969586i	$0.421294\pi$
$68$	6.83448	−	4.96554i	0.828802	−	0.602160i
$69$	−1.66339	−	5.11939i	−0.200249	−	0.616302i
$70$	3.74297	−	11.5197i	0.447371	−	1.37687i
$71$	7.39649	+	5.37386i	0.877802	+	0.637760i	0.932669	−	0.360733i	$-0.117474\pi$
$71$	7.39649	+	5.37386i	0.877802	+	0.637760i	−0.0548672	+	0.998494i	$0.517474\pi$
$72$	−2.40546	−	1.74767i	−0.283487	−	0.205965i
$73$	2.38841	−	7.35076i	0.279542	−	0.860342i	−0.708440	−	0.705771i	$-0.750601\pi$
$73$	2.38841	−	7.35076i	0.279542	−	0.860342i	0.987982	−	0.154571i	$-0.0493994\pi$
$74$	−0.827056	−	2.54542i	−0.0961433	−	0.295899i
$75$	6.43700	−	4.67675i	0.743281	−	0.540025i
$76$	−4.75322			−0.545232
$77$	−11.2741	−	1.97004i	−1.28480	−	0.224506i
$78$	0.975154			0.110414
$79$	2.72499	−	1.97982i	0.306585	−	0.222747i	−0.423845	−	0.905735i	$-0.639320\pi$
$79$	2.72499	−	1.97982i	0.306585	−	0.222747i	0.730430	+	0.682988i	$0.239320\pi$
$80$	−0.891291	−	2.74311i	−0.0996494	−	0.306689i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−6.84660	−	4.97435i	−0.756081	−	0.549325i
$83$	4.69889	+	3.41395i	0.515771	+	0.374729i	0.815008	−	0.579449i	$-0.196732\pi$
$83$	4.69889	+	3.41395i	0.515771	+	0.374729i	−0.299238	+	0.954179i	$0.596732\pi$
$84$	−1.11868	+	3.44293i	−0.122058	+	0.375655i
$85$	8.95713	+	27.5672i	0.971537	+	2.99008i
$86$	−5.27588	+	3.83315i	−0.568912	+	0.413339i
$87$	1.82881			0.196069
$88$	−8.85668	+	4.33658i	−0.944126	+	0.462281i
$89$	16.5060			1.74963			0.874817	−	0.484454i	$-0.160982\pi$
$89$	16.5060			1.74963			0.874817	+	0.484454i	$0.160982\pi$
$90$	2.83972	−	2.06318i	0.299333	−	0.217478i
$91$	−1.06635	−	3.28188i	−0.111783	−	0.344034i
$92$	−1.74502	+	5.37062i	−0.181931	+	0.559926i
$93$	6.04966	+	4.39534i	0.627321	+	0.455775i
$94$	1.17960	+	0.857027i	0.121666	+	0.0883956i
$95$	5.03975	−	15.5108i	0.517068	−	1.59137i
$96$	1.59615	+	4.91244i	0.162906	+	0.501374i
$97$	−0.0735643	+	0.0534476i	−0.00746932	+	0.00542678i	−0.591514	−	0.806295i	$-0.701469\pi$
$97$	−0.0735643	+	0.0534476i	−0.00746932	+	0.00542678i	0.584044	+	0.811722i	$0.301469\pi$
$98$	−4.78587			−0.483446
$99$	−2.30759	−	2.38223i	−0.231922	−	0.239423i
$100$	−8.34703			−0.834703
$101$	0.434294	−	0.315533i	0.0432139	−	0.0313967i	−0.565969	−	0.824427i	$-0.691498\pi$
$101$	0.434294	−	0.315533i	0.0432139	−	0.0313967i	0.609183	+	0.793030i	$0.291498\pi$
$102$	2.42659	+	7.46829i	0.240269	+	0.739471i
$103$	−0.742505	+	2.28520i	−0.0731612	+	0.225167i	−0.980950	−	0.194261i	$-0.937769\pi$
$103$	−0.742505	+	2.28520i	−0.0731612	+	0.225167i	0.907789	+	0.419428i	$0.137769\pi$
$104$	−2.40546	−	1.74767i	−0.235875	−	0.171373i
$105$	−10.0489	−	7.30095i	−0.980672	−	0.712500i
$106$	−2.34680	+	7.22269i	−0.227941	+	0.701530i
$107$	−5.04349	−	15.5223i	−0.487573	−	1.50059i	−0.828220	−	0.560403i	$-0.810646\pi$
$107$	−5.04349	−	15.5223i	−0.487573	−	1.50059i	0.340647	−	0.940191i	$-0.389354\pi$
$108$	−0.848719	+	0.616630i	−0.0816680	+	0.0593353i
$109$	5.50310			0.527101			0.263551	−	0.964646i	$-0.415106\pi$
$109$	5.50310			0.527101			0.263551	+	0.964646i	$0.415106\pi$
$110$	−1.63795	−	11.5259i	−0.156172	−	1.09895i
$111$	−2.74460			−0.260506
$112$	−2.23700	+	1.62528i	−0.211377	+	0.153574i
$113$	4.50820	+	13.8748i	0.424096	+	1.30523i	0.903858	+	0.427833i	$0.140723\pi$
$113$	4.50820	+	13.8748i	0.424096	+	1.30523i	−0.479762	+	0.877399i	$0.659277\pi$
$114$	1.36533	−	4.20205i	0.127875	−	0.393558i
$115$	−15.6752	−	11.3887i	−1.46172	−	1.06200i
$116$	−1.55215	−	1.12770i	−0.144113	−	0.104704i
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$	1.53713	+	4.73079i	0.141504	+	0.435505i
$119$	22.4810	−	16.3334i	2.06083	−	1.49728i
$120$	−10.7025			−0.977003
$121$	−10.5645	+	3.06455i	−0.960409	+	0.278595i
$122$	−1.32140			−0.119634
$123$	−7.02104	+	5.10109i	−0.633066	+	0.459949i
$124$	−2.42416	−	7.46081i	−0.217696	−	0.670001i
$125$	3.28863	−	10.1214i	0.294144	−	0.905283i
$126$	−2.72237	−	1.97792i	−0.242528	−	0.176207i
$127$	−1.54386	−	1.12168i	−0.136996	−	0.0995331i	0.517177	−	0.855879i	$-0.326983\pi$
$127$	−1.54386	−	1.12168i	−0.136996	−	0.0995331i	−0.654172	+	0.756345i	$0.726983\pi$
$128$	1.19156	−	3.66723i	0.105320	−	0.324141i
$129$	2.06655	+	6.36019i	0.181950	+	0.559983i
$130$	2.83972	−	2.06318i	0.249060	−	0.180953i
$131$	−9.46219			−0.826716			−0.413358	−	0.910569i	$-0.635644\pi$
$131$	−9.46219			−0.826716			−0.413358	+	0.910569i	$0.635644\pi$
$132$	0.489540	+	3.44478i	0.0426090	+	0.299829i
$133$	−15.6350			−1.35573
$134$	3.16099	−	2.29659i	0.273068	−	0.198396i
$135$	−1.11231	−	3.42335i	−0.0957327	−	0.294635i
$136$	7.39887	−	22.7714i	0.634448	−	1.95263i
$137$	9.21812	+	6.69736i	0.787557	+	0.572194i	0.907238	−	0.420619i	$-0.138187\pi$
$137$	9.21812	+	6.69736i	0.787557	+	0.572194i	−0.119680	+	0.992812i	$0.538187\pi$
$138$	−4.24661	−	3.08534i	−0.361496	−	0.262642i
$139$	−3.91169	+	12.0390i	−0.331786	+	1.02113i	0.636498	+	0.771278i	$0.280382\pi$
$139$	−3.91169	+	12.0390i	−0.331786	+	1.02113i	−0.968284	+	0.249853i	$0.919618\pi$
$140$	4.02670	+	12.3929i	0.340318	+	1.04739i
$141$	1.20965	−	0.878864i	0.101871	−	0.0740137i
$142$	8.91541			0.748165
$143$	−2.30759	−	2.38223i	−0.192970	−	0.199212i
$144$	−0.801295			−0.0667746
$145$	5.32564	−	3.86931i	0.442271	−	0.321328i
$146$	−2.32907	−	7.16813i	−0.192755	−	0.593239i
$147$	−1.51660	+	4.66760i	−0.125087	+	0.384977i
$148$	2.32939	+	1.69240i	0.191475	+	0.139115i
$149$	1.05367	+	0.765538i	0.0863202	+	0.0627153i	0.630108	−	0.776507i	$-0.283010\pi$
$149$	1.05367	+	0.765538i	0.0863202	+	0.0627153i	−0.543788	+	0.839223i	$0.683010\pi$
$150$	2.39763	−	7.37914i	0.195765	−	0.602504i
$151$	4.72220	+	14.5334i	0.384288	+	1.18272i	0.936996	+	0.349341i	$0.113594\pi$
$151$	4.72220	+	14.5334i	0.384288	+	1.18272i	−0.552708	+	0.833375i	$0.686406\pi$
$152$	−10.8988	+	7.91848i	−0.884013	+	0.642273i
$153$	8.05270			0.651022
$154$	−10.0235	+	4.90790i	−0.807716	+	0.395490i
$155$	26.9165			2.16199
$156$	−0.848719	+	0.616630i	−0.0679519	+	0.0493699i
$157$	1.07631	+	3.31255i	0.0858991	+	0.264370i	0.984775	−	0.173833i	$-0.0556152\pi$
$157$	1.07631	+	3.31255i	0.0858991	+	0.264370i	−0.898876	+	0.438203i	$0.855615\pi$
$158$	1.01499	−	3.12382i	0.0807483	−	0.248518i
$159$	6.30053	+	4.57760i	0.499665	+	0.363028i
$160$	15.0416	+	10.9284i	1.18914	+	0.863963i
$161$	−5.73997	+	17.6658i	−0.452373	+	1.39226i
$162$	−0.301339	−	0.927427i	−0.0236754	−	0.0728655i
$163$	4.08300	−	2.96647i	0.319805	−	0.232352i	−0.416287	−	0.909233i	$-0.636669\pi$
$163$	4.08300	−	2.96647i	0.319805	−	0.232352i	0.736092	+	0.676881i	$0.236669\pi$
$164$	9.10438			0.710932
$165$	−11.7601	−	2.05496i	−0.915521	−	0.159978i
$166$	5.66384			0.439600
$167$	−16.3880	+	11.9066i	−1.26814	+	0.921360i	−0.999127	−	0.0417761i	$-0.986698\pi$
$167$	−16.3880	+	11.9066i	−1.26814	+	0.921360i	−0.269016	+	0.963136i	$0.586698\pi$
$168$	3.17059	+	9.75806i	0.244616	+	0.752851i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	22.8674	+	16.6142i	1.75385	+	1.27425i
$171$	−3.66555	−	2.66318i	−0.280312	−	0.203658i
$172$	2.16796	−	6.67231i	0.165306	−	0.508759i
$173$	−1.22295	−	3.76386i	−0.0929793	−	0.286161i	0.893743	−	0.448580i	$-0.148070\pi$
$173$	−1.22295	−	3.76386i	−0.0929793	−	0.286161i	−0.986722	+	0.162420i	$0.948070\pi$
$174$	1.44278	−	1.04824i	0.109377	−	0.0794670i
$175$	−27.4563			−2.07550
$176$	−1.24405	+	2.34843i	−0.0937739	+	0.177020i
$177$	5.10099			0.383414
$178$	13.0219	−	9.46094i	0.976030	−	0.709127i
$179$	−5.55628	−	17.1005i	−0.415296	−	1.27815i	−0.911986	−	0.410222i	$-0.865451\pi$
$179$	−5.55628	−	17.1005i	−0.415296	−	1.27815i	0.496690	−	0.867928i	$-0.334549\pi$
$180$	−1.16690	+	3.59135i	−0.0869756	+	0.267683i
$181$	10.8595	+	7.88988i	0.807180	+	0.586450i	0.913012	−	0.407934i	$-0.133751\pi$
$181$	10.8595	+	7.88988i	0.807180	+	0.586450i	−0.105832	+	0.994384i	$0.533751\pi$
$182$	−2.72237	−	1.97792i	−0.201795	−	0.146613i
$183$	−0.418739	+	1.28875i	−0.0309541	+	0.0952669i
$184$	4.94579	+	15.2216i	0.364608	+	1.12215i
$185$	−7.99248	+	5.80688i	−0.587619	+	0.426930i
$186$	7.29200			0.534676
$187$	12.5022	−	23.6008i	0.914254	−	1.72586i
$188$	−1.56859			−0.114401
$189$	−2.79173	+	2.02831i	−0.203069	+	0.147538i
$190$	−4.91453	−	15.1254i	−0.356538	−	1.09731i
$191$	−0.868334	+	2.67246i	−0.0628304	+	0.193372i	−0.977544	−	0.210730i	$-0.932416\pi$
$191$	−0.868334	+	2.67246i	−0.0628304	+	0.193372i	0.914714	+	0.404102i	$0.132416\pi$
$192$	5.37147	+	3.90260i	0.387653	+	0.281646i
$193$	17.0374	+	12.3784i	1.22638	+	0.891017i	0.996613	−	0.0822291i	$-0.0262039\pi$
$193$	17.0374	+	12.3784i	1.22638	+	0.891017i	0.229766	+	0.973246i	$0.426204\pi$
$194$	−0.0274009	+	0.0843313i	−0.00196727	+	0.00605464i
$195$	−1.11231	−	3.42335i	−0.0796545	−	0.245151i
$196$	4.16535	−	3.02630i	0.297525	−	0.216164i
$197$	−5.16249			−0.367812			−0.183906	−	0.982944i	$-0.558874\pi$
$197$	−5.16249			−0.367812			−0.183906	+	0.982944i	$0.558874\pi$
$198$	−3.18595	−	0.556713i	−0.226415	−	0.0395639i
$199$	26.3950			1.87109			0.935547	−	0.353202i	$-0.114907\pi$
$199$	26.3950			1.87109			0.935547	+	0.353202i	$0.114907\pi$
$200$	−19.1392	+	13.9055i	−1.35335	+	0.983266i
$201$	−1.23815	−	3.81065i	−0.0873326	−	0.268782i
$202$	0.161764	−	0.497858i	0.0113817	−	0.0350292i
$203$	−5.10555	−	3.70940i	−0.358340	−	0.260349i
$204$	−6.83448	−	4.96554i	−0.478509	−	0.347657i
$205$	−9.65320	+	29.7095i	−0.674209	+	2.07500i
$206$	0.724057	+	2.22842i	0.0504475	+	0.155261i
$207$	−4.35481	+	3.16396i	−0.302680	+	0.219910i
$208$	−0.801295			−0.0555598
$209$	−13.4962	+	6.60827i	−0.933552	+	0.457104i
$210$	−12.1125			−0.835843
$211$	−6.15420	+	4.47129i	−0.423673	+	0.307816i	−0.779114	−	0.626882i	$-0.784331\pi$
$211$	−6.15420	+	4.47129i	−0.423673	+	0.307816i	0.355441	+	0.934699i	$0.384331\pi$
$212$	−2.52469	−	7.77020i	−0.173396	−	0.533659i
$213$	2.82521	−	8.69509i	0.193580	−	0.595778i
$214$	−12.8760	−	9.35494i	−0.880183	−	0.639490i
$215$	19.4745	+	14.1491i	1.32815	+	0.964957i
$216$	−0.918806	+	2.82779i	−0.0625168	+	0.192407i
$217$	−7.97392	−	24.5412i	−0.541305	−	1.66597i
$218$	4.34149	−	3.15427i	0.294042	−	0.213634i
$219$	−7.72905			−0.522281
$220$	8.71385	+	8.99570i	0.587488	+	0.606490i
$221$	8.05270			0.541683
$222$	−2.16526	+	1.57315i	−0.145323	+	0.105583i
$223$	1.33792	+	4.11769i	0.0895936	+	0.275741i	0.985807	−	0.167882i	$-0.0536929\pi$
$223$	1.33792	+	4.11769i	0.0895936	+	0.275741i	−0.896213	+	0.443623i	$0.853693\pi$
$224$	5.50794	−	16.9517i	0.368015	−	1.13263i
$225$	−6.43700	−	4.67675i	−0.429133	−	0.311784i
$226$	11.5094	+	8.36205i	0.765592	+	0.556235i
$227$	3.11528	−	9.58785i	0.206768	−	0.636368i	−0.792868	−	0.609394i	$-0.791413\pi$
$227$	3.11528	−	9.58785i	0.206768	−	0.636368i	0.999636	−	0.0269740i	$-0.00858714\pi$
$228$	1.46883	+	4.52058i	0.0972754	+	0.299383i
$229$	−9.91078	+	7.20061i	−0.654923	+	0.475829i	−0.864945	−	0.501867i	$-0.832647\pi$
$229$	−9.91078	+	7.20061i	−0.654923	+	0.475829i	0.210022	+	0.977697i	$0.432647\pi$
$230$	−18.8943			−1.24585
$231$	1.61027	+	11.3311i	0.105948	+	0.745529i
$232$	−5.43764			−0.356999
$233$	3.67299	−	2.66859i	0.240626	−	0.174825i	−0.460936	−	0.887433i	$-0.652486\pi$
$233$	3.67299	−	2.66859i	0.240626	−	0.174825i	0.701562	+	0.712608i	$0.252486\pi$
$234$	−0.301339	−	0.927427i	−0.0196992	−	0.0606278i
$235$	1.66315	−	5.11863i	0.108492	−	0.333903i
$236$	−4.32930	−	3.14542i	−0.281814	−	0.204750i
$237$	−2.72499	−	1.97982i	−0.177007	−	0.128603i
$238$	8.37362	−	25.7713i	0.542781	−	1.67051i
$239$	5.99242	+	18.4428i	0.387618	+	1.19296i	0.934563	+	0.355796i	$0.115790\pi$
$239$	5.99242	+	18.4428i	0.387618	+	1.19296i	−0.546946	+	0.837168i	$0.684210\pi$
$240$	−2.33343	+	1.69534i	−0.150622	+	0.109434i
$241$	−20.0668			−1.29261			−0.646307	−	0.763078i	$-0.723687\pi$
$241$	−20.0668			−1.29261			−0.646307	+	0.763078i	$0.723687\pi$
$242$	−6.57796	+	8.47304i	−0.422847	+	0.544668i
$243$	−1.00000			−0.0641500
$244$	1.15007	−	0.835577i	0.0736259	−	0.0534923i
$245$	5.45902	+	16.8011i	0.348764	+	1.07339i
$246$	−2.61517	+	8.04866i	−0.166737	+	0.513164i
$247$	−3.66555	−	2.66318i	−0.233233	−	0.169454i
$248$	−17.9876	−	13.0687i	−1.14221	−	0.829866i
$249$	1.79482	−	5.52388i	0.113742	−	0.350062i
$250$	−3.20693	−	9.86990i	−0.202824	−	0.624227i
$251$	−19.0356	+	13.8301i	−1.20151	+	0.872951i	−0.994433	−	0.105373i	$-0.966396\pi$
$251$	−19.0356	+	13.8301i	−1.20151	+	0.872951i	−0.207081	+	0.978324i	$0.566396\pi$
$252$	3.62011			0.228046
$253$	2.51185	+	17.6753i	0.157919	+	1.11124i
$254$	−1.86090			−0.116764
$255$	23.4501	−	17.0375i	1.46850	−	1.06693i
$256$	−5.26539	−	16.2052i	−0.329087	−	1.01283i
$257$	−3.08890	+	9.50666i	−0.192680	+	0.593009i	0.807315	+	0.590120i	$0.200920\pi$
$257$	−3.08890	+	9.50666i	−0.192680	+	0.593009i	−0.999996	+	0.00288904i	$0.999080\pi$
$258$	5.27588	+	3.83315i	0.328462	+	0.238641i
$259$	7.66218	+	5.56690i	0.476105	+	0.345910i
$260$	−1.16690	+	3.59135i	−0.0723681	+	0.222726i
$261$	−0.565134	−	1.73930i	−0.0349809	−	0.107660i
$262$	−7.46488	+	5.42355i	−0.461182	+	0.335068i
$263$	−4.34580			−0.267973			−0.133987	−	0.990983i	$-0.542778\pi$
$263$	−4.34580			−0.267973			−0.133987	+	0.990983i	$0.542778\pi$
$264$	6.86120	+	7.08313i	0.422278	+	0.435937i
$265$	28.0327			1.72203
$266$	−12.3347	+	8.96168i	−0.756289	+	0.549476i
$267$	−5.10064	−	15.6981i	−0.312154	−	0.960711i
$268$	−1.29892	+	3.99765i	−0.0793439	+	0.244195i
$269$	−13.8368	−	10.0530i	−0.843645	−	0.612944i	0.0797415	−	0.996816i	$-0.474591\pi$
$269$	−13.8368	−	10.0530i	−0.843645	−	0.612944i	−0.923386	+	0.383872i	$0.874591\pi$
$270$	−2.83972	−	2.06318i	−0.172820	−	0.125561i
$271$	−3.11505	+	9.58714i	−0.189226	+	0.582377i	−0.999996	−	0.00298814i	$-0.999049\pi$
$271$	−3.11505	+	9.58714i	−0.189226	+	0.582377i	0.810770	+	0.585365i	$0.199049\pi$
$272$	−1.99396	−	6.13677i	−0.120902	−	0.372097i
$273$	−2.79173	+	2.02831i	−0.168963	+	0.122759i
$274$	11.1111			0.671248
$275$	−23.7004	+	11.6047i	−1.42919	+	0.699787i
$276$	5.64700			0.339909
$277$	−2.30454	+	1.67435i	−0.138467	+	0.100602i	−0.654862	−	0.755748i	$-0.727273\pi$
$277$	−2.30454	+	1.67435i	−0.138467	+	0.100602i	0.516396	+	0.856350i	$0.327273\pi$
$278$	3.81451	+	11.7398i	0.228779	+	0.704109i
$279$	2.31077	−	7.11181i	0.138342	−	0.425773i
$280$	29.8786	+	21.7081i	1.78559	+	1.29730i
$281$	−26.8784	−	19.5283i	−1.60343	−	1.16496i	−0.880502	−	0.474042i	$-0.842794\pi$
$281$	−26.8784	−	19.5283i	−1.60343	−	1.16496i	−0.722931	−	0.690920i	$-0.757206\pi$
$282$	0.450566	−	1.38670i	0.0268308	−	0.0825768i
$283$	−7.41358	−	22.8166i	−0.440691	−	1.35631i	−0.887141	−	0.461499i	$-0.847312\pi$
$283$	−7.41358	−	22.8166i	−0.440691	−	1.35631i	0.446449	−	0.894809i	$-0.352688\pi$
$284$	−7.75947	+	5.63758i	−0.460440	+	0.334529i
$285$	−16.3090			−0.966060
$286$	−3.18595	−	0.556713i	−0.188389	−	0.0329191i
$287$	29.9475			1.76774
$288$	4.17877	−	3.03606i	0.246237	−	0.178901i
$289$	14.7852	+	45.5042i	0.869719	+	2.67672i
$290$	1.98367	−	6.10512i	0.116485	−	0.358505i
$291$	0.0735643	+	0.0534476i	0.00431241	+	0.00313315i
$292$	6.55979	+	4.76597i	0.383883	+	0.278907i
$293$	−1.27879	+	3.93570i	−0.0747076	+	0.229926i	−0.981436	−	0.191788i	$-0.938571\pi$
$293$	−1.27879	+	3.93570i	−0.0747076	+	0.229926i	0.906729	+	0.421714i	$0.138571\pi$
$294$	1.47891	+	4.55163i	0.0862521	+	0.265457i
$295$	14.8545	−	10.7924i	0.864860	−	0.628357i
$296$	8.16057			0.474323
$297$	−1.55255	+	2.93080i	−0.0900882	+	0.170062i
$298$	1.27005			0.0735721
$299$	−4.35481	+	3.16396i	−0.251845	+	0.182976i
$300$	2.57938	+	7.93850i	0.148920	+	0.458330i
$301$	7.13119	−	21.9475i	0.411035	−	1.26504i
$302$	12.0557	+	8.75900i	0.693729	+	0.504024i
$303$	−0.434294	−	0.315533i	−0.0249495	−	0.0181269i
$304$	−1.12191	+	3.45287i	−0.0643457	+	0.198036i
$305$	1.50726	+	4.63888i	0.0863056	+	0.265621i
$306$	6.35291	−	4.61566i	0.363171	−	0.263860i
$307$	7.71681			0.440422			0.220211	−	0.975452i	$-0.429325\pi$
$307$	7.71681			0.440422			0.220211	+	0.975452i	$0.429325\pi$
$308$	5.62041	−	10.6098i	0.320253	−	0.604551i
$309$	2.40280			0.136690
$310$	21.2349	−	15.4280i	1.20606	−	0.876254i
$311$	9.69726	+	29.8451i	0.549881	+	1.69236i	0.709093	+	0.705115i	$0.249105\pi$
$311$	9.69726	+	29.8451i	0.549881	+	1.69236i	−0.159211	+	0.987245i	$0.550895\pi$
$312$	−0.918806	+	2.82779i	−0.0520171	+	0.160092i
$313$	4.12939	+	3.00017i	0.233407	+	0.169580i	0.698341	−	0.715765i	$-0.253922\pi$
$313$	4.12939	+	3.00017i	0.233407	+	0.169580i	−0.464934	+	0.885345i	$0.653922\pi$
$314$	2.74781	+	1.99640i	0.155068	+	0.112663i
$315$	−3.83834	+	11.8132i	−0.216266	+	0.665598i
$316$	1.09193	+	3.36062i	0.0614259	+	0.189049i
$317$	5.06307	−	3.67854i	0.284370	−	0.206607i	−0.436451	−	0.899728i	$-0.643765\pi$
$317$	5.06307	−	3.67854i	0.284370	−	0.206607i	0.720821	+	0.693121i	$0.243765\pi$
$318$	7.59439			0.425872
$319$	−5.97495	−	1.04407i	−0.334533	−	0.0584564i
$320$	23.8991			1.33600
$321$	−13.2040	+	9.59329i	−0.736977	+	0.535445i
$322$	5.59736	+	17.2269i	0.311929	+	0.960018i
$323$	11.2747	−	34.7000i	0.627342	−	1.93076i
$324$	0.848719	+	0.616630i	0.0471510	+	0.0342572i
$325$	−6.43700	−	4.67675i	−0.357061	−	0.259420i
$326$	1.52082	−	4.68060i	0.0842303	−	0.259234i
$327$	−1.70055	−	5.23376i	−0.0940407	−	0.289428i
$328$	20.8758	−	15.1672i	1.15267	−	0.837466i
$329$	−5.15963			−0.284460
$330$	−10.4556	+	5.11946i	−0.575561	+	0.281817i
$331$	−24.1969			−1.32998			−0.664991	−	0.746851i	$-0.731565\pi$
$331$	−24.1969			−1.32998			−0.664991	+	0.746851i	$0.731565\pi$
$332$	−4.92949	+	3.58148i	−0.270541	+	0.196559i
$333$	0.848128	+	2.61027i	0.0464771	+	0.143042i
$334$	−6.10414	+	18.7866i	−0.334004	+	1.02796i
$335$	−11.6680	−	8.47727i	−0.637489	−	0.463163i
$336$	2.23700	+	1.62528i	0.122038	+	0.0886660i
$337$	5.22924	−	16.0939i	0.284855	−	0.876693i	−0.701587	−	0.712584i	$-0.747525\pi$
$337$	5.22924	−	16.0939i	0.284855	−	0.876693i	0.986442	−	0.164110i	$-0.0524751\pi$
$338$	−0.301339	−	0.927427i	−0.0163907	−	0.0504454i
$339$	11.8026	−	8.57510i	0.641030	−	0.465736i
$340$	−30.4083			−1.64912
$341$	−17.2557	−	17.8138i	−0.934448	−	0.964673i
$342$	−4.41830			−0.238914
$343$	−5.84084	+	4.24362i	−0.315376	+	0.229134i
$344$	−6.14451	−	18.9109i	−0.331290	−	1.01961i
$345$	−5.98741	+	18.4274i	−0.322351	+	0.992095i
$346$	−3.12218	−	2.26840i	−0.167849	−	0.121950i
$347$	−7.33189	−	5.32693i	−0.393596	−	0.285964i	0.373331	−	0.927698i	$-0.378215\pi$
$347$	−7.33189	−	5.32693i	−0.393596	−	0.285964i	−0.766928	+	0.641734i	$0.778215\pi$
$348$	−0.592868	+	1.82466i	−0.0317811	+	0.0978120i
$349$	9.12335	+	28.0788i	0.488362	+	1.50302i	0.827052	+	0.562125i	$0.190016\pi$
$349$	9.12335	+	28.0788i	0.488362	+	1.50302i	−0.338690	+	0.940898i	$0.609984\pi$
$350$	−21.6607	+	15.7374i	−1.15781	+	0.841201i
$351$	−1.00000			−0.0533761
$352$	−2.41031	−	16.9608i	−0.128470	−	0.904013i
$353$	9.51258			0.506304			0.253152	−	0.967427i	$-0.418533\pi$
$353$	9.51258			0.506304			0.253152	+	0.967427i	$0.418533\pi$
$354$	4.02425	−	2.92379i	0.213887	−	0.155398i
$355$	−10.1694	−	31.2982i	−0.539736	−	1.66114i
$356$	−5.35095	+	16.4685i	−0.283600	+	0.872830i
$357$	−22.4810	−	16.3334i	−1.18982	−	0.864454i
$358$	−14.1851	−	10.3061i	−0.749707	−	0.544694i
$359$	6.36899	−	19.6017i	0.336143	−	1.03454i	−0.630014	−	0.776584i	$-0.716951\pi$
$359$	6.36899	−	19.6017i	0.336143	−	1.03454i	0.966156	−	0.257957i	$-0.0830492\pi$
$360$	3.30726	+	10.1787i	0.174308	+	0.536465i
$361$	−1.23682	+	0.898599i	−0.0650956	+	0.0472947i
$362$	13.0896			0.687972
$363$	6.17917	+	9.10043i	0.324322	+	0.477649i
$364$	3.62011			0.189745
$365$	−22.5076	+	16.3527i	−1.17810	+	0.855940i
$366$	0.408335	+	1.25673i	0.0213440	+	0.0656902i
$367$	4.84907	−	14.9239i	0.253120	−	0.779022i	−0.741075	−	0.671422i	$-0.765684\pi$
$367$	4.84907	−	14.9239i	0.253120	−	0.779022i	0.994194	−	0.107599i	$-0.0343164\pi$
$368$	3.48949	+	2.53526i	0.181902	+	0.132160i
$369$	7.02104	+	5.10109i	0.365501	+	0.265552i
$370$	−2.97701	+	9.16228i	−0.154767	+	0.476324i
$371$	−8.30458	−	25.5589i	−0.431152	−	1.32695i
$372$	−6.34655	+	4.61104i	−0.329053	+	0.239071i
$373$	16.4971			0.854188			0.427094	−	0.904207i	$-0.359537\pi$
$373$	16.4971			0.854188			0.427094	+	0.904207i	$0.359537\pi$
$374$	−3.66435	−	25.7851i	−0.189479	−	1.33332i
$375$	−10.6422			−0.549563
$376$	−3.59668	+	2.61314i	−0.185485	+	0.134762i
$377$	−0.565134	−	1.73930i	−0.0291059	−	0.0895787i
$378$	−1.03985	+	3.20034i	−0.0534842	+	0.164608i
$379$	25.0141	+	18.1738i	1.28489	+	0.933527i	0.999689	−	0.0249403i	$-0.00793956\pi$
$379$	25.0141	+	18.1738i	1.28489	+	0.933527i	0.285201	+	0.958468i	$0.407940\pi$
$380$	13.8417	+	10.0566i	0.710066	+	0.515893i
$381$	−0.589703	+	1.81492i	−0.0302114	+	0.0929811i
$382$	0.846759	+	2.60606i	0.0433240	+	0.133338i
$383$	28.9288	−	21.0180i	1.47819	−	1.07397i	0.500057	−	0.865992i	$-0.333312\pi$
$383$	28.9288	−	21.0180i	1.47819	−	1.07397i	0.978134	−	0.207976i	$-0.0666877\pi$
$384$	−3.85596			−0.196774
$385$	28.6629	+	29.5900i	1.46080	+	1.50805i
$386$	20.5362			1.04526
$387$	5.41030	−	3.93081i	0.275021	−	0.199814i
$388$	−0.0294780	−	0.0907239i	−0.00149652	−	0.00460581i
$389$	−8.84943	+	27.2358i	−0.448684	+	1.38091i	0.429708	+	0.902968i	$0.358616\pi$
$389$	−8.84943	+	27.2358i	−0.448684	+	1.38091i	−0.878393	+	0.477940i	$0.841384\pi$
$390$	−2.83972	−	2.06318i	−0.143795	−	0.104473i
$391$	−35.0680	−	25.4784i	−1.77346	−	1.28850i
$392$	4.50932	−	13.8783i	0.227755	−	0.700958i
$393$	2.92398	+	8.99908i	0.147495	+	0.453944i
$394$	−4.07277	+	2.95904i	−0.205183	+	0.149074i
$395$	−12.1242			−0.610033
$396$	3.12490	−	1.53007i	0.157032	−	0.0768891i
$397$	−16.7426			−0.840286			−0.420143	−	0.907458i	$-0.638020\pi$
$397$	−16.7426			−0.840286			−0.420143	+	0.907458i	$0.638020\pi$
$398$	20.8235	−	15.1291i	1.04379	−	0.758355i
$399$	4.83148	+	14.8698i	0.241876	+	0.744419i
$400$	−1.97016	+	6.06352i	−0.0985078	+	0.303176i
$401$	−28.9160	−	21.0087i	−1.44400	−	1.04913i	−0.987188	−	0.159561i	$-0.948992\pi$
$401$	−28.9160	−	21.0087i	−1.44400	−	1.04913i	−0.456809	−	0.889565i	$-0.651008\pi$
$402$	−3.16099	−	2.29659i	−0.157656	−	0.114544i
$403$	2.31077	−	7.11181i	0.115107	−	0.354264i
$404$	0.174026	+	0.535598i	0.00865813	+	0.0266470i
$405$	−2.91208	+	2.11575i	−0.144702	+	0.105132i
$406$	−6.15401			−0.305419
$407$	8.96694	+	1.56689i	0.444475	+	0.0776676i
$408$	−23.9432			−1.18537
$409$	12.4228	−	9.02568i	0.614267	−	0.446291i	−0.236647	−	0.971596i	$-0.576049\pi$
$409$	12.4228	−	9.02568i	0.614267	−	0.446291i	0.850914	+	0.525304i	$0.176049\pi$
$410$	9.41336	+	28.9713i	0.464893	+	1.43079i
$411$	3.52101	−	10.8366i	0.173679	−	0.534528i
$412$	−2.03930	−	1.48164i	−0.100469	−	0.0729951i
$413$	−14.2406	−	10.3464i	−0.700733	−	0.509112i
$414$	−1.62206	+	4.99219i	−0.0797200	+	0.245353i
$415$	−6.46049	−	19.8833i	−0.317133	−	0.976035i
$416$	4.17877	−	3.03606i	0.204881	−	0.148855i
$417$	12.6585			0.619890
$418$	−6.85964	+	12.9491i	−0.335516	+	0.633363i
$419$	−25.7895			−1.25990			−0.629949	−	0.776636i	$-0.716924\pi$
$419$	−25.7895			−1.25990			−0.629949	+	0.776636i	$0.716924\pi$
$420$	10.5420	−	7.65924i	0.514399	−	0.373733i
$421$	2.84403	+	8.75302i	0.138609	+	0.426596i	0.996134	−	0.0878470i	$-0.0279987\pi$
$421$	2.84403	+	8.75302i	0.138609	+	0.426596i	−0.857524	+	0.514443i	$0.827999\pi$
$422$	−2.29229	+	7.05495i	−0.111587	+	0.343429i
$423$	−1.20965	−	0.878864i	−0.0588153	−	0.0427318i
$424$	−18.7335	−	13.6107i	−0.909778	−	0.660993i
$425$	19.7993	−	60.9360i	0.960407	−	2.95583i
$426$	−2.75501	−	8.47906i	−0.133481	−	0.410812i
$427$	3.78299	−	2.74850i	0.183072	−	0.133009i
$428$	17.1220			0.827624
$429$	−1.55255	+	2.93080i	−0.0749579	+	0.141500i
$430$	23.4737			1.13200
$431$	2.23576	−	1.62438i	0.107693	−	0.0782435i	−0.532635	−	0.846345i	$-0.678798\pi$
$431$	2.23576	−	1.62438i	0.107693	−	0.0782435i	0.640328	+	0.768101i	$0.278798\pi$
$432$	0.247614	+	0.762077i	0.0119133	+	0.0366654i
$433$	9.44391	−	29.0654i	0.453846	−	1.39679i	−0.418640	−	0.908152i	$-0.637493\pi$
$433$	9.44391	−	29.0654i	0.453846	−	1.39679i	0.872485	−	0.488641i	$-0.162507\pi$
$434$	−20.3573	−	14.7905i	−0.977182	−	0.709964i
$435$	−5.32564	−	3.86931i	−0.255345	−	0.185519i
$436$	−1.78400	+	5.49060i	−0.0854383	+	0.262952i
$437$	7.53660	+	23.1953i	0.360525	+	1.10958i
$438$	−6.09758	+	4.43015i	−0.291353	+	0.211681i
$439$	32.6429			1.55796			0.778980	−	0.627049i	$-0.215738\pi$
$439$	32.6429			1.55796			0.778980	+	0.627049i	$0.215738\pi$
$440$	34.9664	+	6.11005i	1.66696	+	0.291285i
$441$	4.90781			0.233705
$442$	6.35291	−	4.61566i	0.302177	−	0.219544i
$443$	−8.08711	−	24.8896i	−0.384230	−	1.18254i	−0.937037	−	0.349230i	$-0.886443\pi$
$443$	−8.08711	−	24.8896i	−0.384230	−	1.18254i	0.552807	−	0.833309i	$-0.313557\pi$
$444$	0.889749	−	2.73837i	0.0422256	−	0.129957i
$445$	−48.0668	−	34.9225i	−2.27858	−	1.65549i
$446$	3.41569	+	2.48164i	0.161738	+	0.117509i
$447$	0.402467	−	1.23867i	0.0190360	−	0.0585869i
$448$	−7.08001	−	21.7900i	−0.334499	−	1.02948i
$449$	6.76729	−	4.91672i	0.319368	−	0.232034i	−0.416538	−	0.909118i	$-0.636757\pi$
$449$	6.76729	−	4.91672i	0.319368	−	0.232034i	0.735906	+	0.677084i	$0.236757\pi$
$450$	−7.75888			−0.365757
$451$	25.8508	−	12.6576i	1.21727	−	0.596022i
$452$	−15.3048			−0.719876
$453$	12.3629	−	8.98217i	0.580859	−	0.422019i
$454$	−3.03788	−	9.34963i	−0.142575	−	0.438800i
$455$	−3.83834	+	11.8132i	−0.179944	+	0.553811i
$456$	10.8988	+	7.91848i	0.510385	+	0.370817i
$457$	−19.2928	−	14.0170i	−0.902478	−	0.655689i	0.0366232	−	0.999329i	$-0.488340\pi$
$457$	−19.2928	−	14.0170i	−0.902478	−	0.655689i	−0.939101	+	0.343640i	$0.888340\pi$
$458$	−3.69153	+	11.3614i	−0.172494	+	0.530881i
$459$	−2.48842	−	7.65857i	−0.116150	−	0.357472i
$460$	16.4445	−	11.9476i	0.766728	−	0.557061i
$461$	−23.8611			−1.11132			−0.555662	−	0.831408i	$-0.687535\pi$
$461$	−23.8611			−1.11132			−0.555662	+	0.831408i	$0.687535\pi$
$462$	7.76512	+	8.01628i	0.361266	+	0.372951i
$463$	−15.1085			−0.702152			−0.351076	−	0.936347i	$-0.614184\pi$
$463$	−15.1085			−0.702152			−0.351076	+	0.936347i	$0.614184\pi$
$464$	−1.18555	+	0.861351i	−0.0550377	+	0.0399872i
$465$	−8.31766	−	25.5991i	−0.385722	−	1.18713i
$466$	1.36810	−	4.21058i	0.0633761	−	0.195051i
$467$	−15.5595	−	11.3046i	−0.720007	−	0.523116i	0.166380	−	0.986062i	$-0.446792\pi$
$467$	−15.5595	−	11.3046i	−0.720007	−	0.523116i	−0.886386	+	0.462946i	$0.846792\pi$
$468$	0.848719	+	0.616630i	0.0392320	+	0.0285037i
$469$	−4.27258	+	13.1497i	−0.197290	+	0.607195i
$470$	−1.62182	−	4.99146i	−0.0748091	−	0.230239i
$471$	2.81782	−	2.04727i	0.129838	−	0.0943331i
$472$	−15.1668			−0.698111
$473$	−3.12065	−	21.9593i	−0.143488	−	1.00969i
$474$	−3.28458			−0.150866
$475$	−29.1652	+	21.1898i	−1.33819	+	0.972253i
$476$	9.00836	+	27.7249i	0.412898	+	1.27077i
$477$	2.40659	−	7.40672i	0.110190	−	0.339130i
$478$	15.2986	+	11.1151i	0.699741	+	0.508391i
$479$	17.3873	+	12.6326i	0.794447	+	0.577200i	0.909280	−	0.416185i	$-0.136633\pi$
$479$	17.3873	+	12.6326i	0.794447	+	0.577200i	−0.114833	+	0.993385i	$0.536633\pi$
$480$	5.74538	−	17.6825i	0.262239	−	0.807090i
$481$	0.848128	+	2.61027i	0.0386713	+	0.119018i
$482$	−15.8310	+	11.5019i	−0.721082	+	0.523897i
$483$	18.5749			0.845189
$484$	0.367229	−	11.5340i	0.0166922	−	0.524271i
$485$	0.327306			0.0148622
$486$	−0.788916	+	0.573181i	−0.0357860	+	0.0260000i
$487$	9.68532	+	29.8084i	0.438884	+	1.35075i	0.889054	+	0.457803i	$0.151363\pi$
$487$	9.68532	+	29.8084i	0.438884	+	1.35075i	−0.450170	+	0.892943i	$0.648637\pi$
$488$	1.24505	−	3.83185i	0.0563605	−	0.173460i
$489$	−4.08300	−	2.96647i	−0.184640	−	0.134149i
$490$	13.9368	+	10.1257i	0.629601	+	0.457432i
$491$	−5.01272	+	15.4276i	−0.226221	+	0.696236i	0.771945	+	0.635690i	$0.219284\pi$
$491$	−5.01272	+	15.4276i	−0.226221	+	0.696236i	−0.998165	+	0.0605463i	$0.980716\pi$
$492$	−2.81341	−	8.65878i	−0.126838	−	0.390368i
$493$	11.9143	−	8.65624i	0.536593	−	0.389858i
$494$	−4.41830			−0.198789
$495$	1.67968	+	11.8195i	0.0754960	+	0.531248i
$496$	−5.99192			−0.269045
$497$	−25.5236	+	18.5440i	−1.14489	+	0.831810i
$498$	−1.75022	−	5.38664i	−0.0784294	−	0.241381i
$499$	5.00853	−	15.4147i	0.224212	−	0.690055i	−0.774158	−	0.632992i	$-0.781826\pi$
$499$	5.00853	−	15.4147i	0.224212	−	0.690055i	0.998371	−	0.0570628i	$-0.0181735\pi$
$500$	9.03227	+	6.56233i	0.403936	+	0.293476i
$501$	16.3880	+	11.9066i	0.732163	+	0.531947i
$502$	−7.09029	+	21.8217i	−0.316455	+	0.973948i
$503$	3.01691	+	9.28510i	0.134517	+	0.414002i	0.995515	−	0.0946076i	$-0.0301596\pi$
$503$	3.01691	+	9.28510i	0.134517	+	0.414002i	−0.860997	+	0.508610i	$0.830160\pi$
$504$	8.30070	−	6.03081i	0.369743	−	0.268634i
$505$	−1.93228			−0.0859855
$506$	12.1128	+	12.5046i	0.538479	+	0.555896i
$507$	−1.00000			−0.0444116
$508$	1.61963	−	1.17673i	0.0718593	−	0.0522088i
$509$	6.85866	+	21.1088i	0.304005	+	0.935631i	0.980047	+	0.198768i	$0.0636939\pi$
$509$	6.85866	+	21.1088i	0.304005	+	0.935631i	−0.676042	+	0.736863i	$0.736306\pi$
$510$	8.73458	−	26.8823i	0.386774	−	1.19037i
$511$	21.5774	+	15.6769i	0.954529	+	0.693506i
$512$	−7.20340	−	5.23358i	−0.318348	−	0.231294i
$513$	−1.40012	+	4.30911i	−0.0618166	+	0.190252i
$514$	3.01215	+	9.27046i	0.132860	+	0.408902i
$515$	6.99713	−	5.08371i	0.308330	−	0.224015i
$516$	−7.01568			−0.308848
$517$	−4.45382	+	2.18077i	−0.195879	+	0.0959100i
$518$	9.23567			0.405792
$519$	−3.20173	+	2.32619i	−0.140540	+	0.102109i
$520$	3.30726	+	10.1787i	0.145033	+	0.446366i
$521$	8.20347	−	25.2477i	0.359400	−	1.10612i	−0.594013	−	0.804455i	$-0.702457\pi$
$521$	8.20347	−	25.2477i	0.359400	−	1.10612i	0.953414	−	0.301666i	$-0.0975426\pi$
$522$	−1.44278	−	1.04824i	−0.0631488	−	0.0458803i
$523$	0.214500	+	0.155843i	0.00937943	+	0.00681456i	0.592465	−	0.805596i	$-0.298155\pi$
$523$	0.214500	+	0.155843i	0.00937943	+	0.00681456i	−0.583086	+	0.812411i	$0.698155\pi$
$524$	3.06747	−	9.44070i	0.134003	−	0.412419i
$525$	8.48446	+	26.1125i	0.370292	+	1.13964i
$526$	−3.42847	+	2.49093i	−0.149488	+	0.108610i
$527$	60.2164			2.62307
$528$	2.61793	+	0.457457i	0.113931	+	0.0199083i
$529$	5.97499			0.259782
$530$	22.1154	−	16.0678i	0.960633	−	0.697941i
$531$	−1.57629	−	4.85133i	−0.0684052	−	0.210530i
$532$	5.06858	−	15.5995i	0.219751	−	0.676323i
$533$	7.02104	+	5.10109i	0.304115	+	0.220953i
$534$	−13.0219	−	9.46094i	−0.563511	−	0.409415i
$535$	−18.1542	+	55.8728i	−0.784873	+	2.41559i
$536$	3.68143	+	11.3303i	0.159013	+	0.489393i
$537$	−14.5465	+	10.5687i	−0.627730	+	0.456072i
$538$	−16.6783			−0.719052
$539$	7.61962	−	14.3838i	0.328200	−	0.619554i
$540$	3.77617			0.162500
$541$	−19.0666	+	13.8527i	−0.819739	+	0.595575i	−0.916638	−	0.399719i	$-0.869108\pi$
$541$	−19.0666	+	13.8527i	−0.819739	+	0.595575i	0.0968986	+	0.995294i	$0.469108\pi$
$542$	3.03765	+	9.34894i	0.130478	+	0.401571i
$543$	4.14796	−	12.7661i	0.178006	−	0.547846i
$544$	33.6504	+	24.4485i	1.44275	+	1.04822i
$545$	−16.0254	−	11.6432i	−0.686455	−	0.498738i
$546$	−1.03985	+	3.20034i	−0.0445016	+	0.136962i
$547$	6.26515	+	19.2821i	0.267878	+	0.824445i	0.991016	+	0.133741i	$0.0426990\pi$
$547$	6.26515	+	19.2821i	0.267878	+	0.824445i	−0.723138	+	0.690704i	$0.757301\pi$
$548$	−9.67049	+	7.02602i	−0.413103	+	0.300137i
$549$	1.35507			0.0578329
$550$	−12.0461	+	22.7397i	−0.513646	+	0.969625i
$551$	−8.28612			−0.353000
$552$	12.9482	−	9.40744i	0.551113	−	0.400407i
$553$	3.59174	+	11.0542i	0.152736	+	0.470074i
$554$	−0.858387	+	2.64184i	−0.0364694	+	0.112241i
$555$	7.99248	+	5.80688i	0.339262	+	0.246488i
$556$	−10.7435	−	7.80562i	−0.455627	−	0.331032i
$557$	−3.39898	+	10.4610i	−0.144019	+	0.443246i	−0.996884	−	0.0788868i	$-0.974863\pi$
$557$	−3.39898	+	10.4610i	−0.144019	+	0.443246i	0.852864	+	0.522133i	$0.174863\pi$
$558$	−2.25335	−	6.93511i	−0.0953920	−	0.293587i
$559$	5.41030	−	3.93081i	0.228831	−	0.166256i
$560$	9.95298			0.420590
$561$	−26.3091	−	4.59727i	−1.11077	−	0.194097i
$562$	−32.3981			−1.36663
$563$	−22.0934	+	16.0518i	−0.931126	+	0.676502i	−0.946268	−	0.323383i	$-0.895180\pi$
$563$	−22.0934	+	16.0518i	−0.931126	+	0.676502i	0.0151425	+	0.999885i	$0.495180\pi$
$564$	0.484720	+	1.49182i	0.0204104	+	0.0628168i
$565$	16.2274	−	49.9427i	0.682690	−	2.10110i
$566$	−18.9268	−	13.7511i	−0.795551	−	0.578002i
$567$	2.79173	+	2.02831i	0.117242	+	0.0851811i
$568$	−8.40024	+	25.8533i	−0.352466	+	1.08478i
$569$	0.414645	+	1.27615i	0.0173828	+	0.0534988i	0.959372	−	0.282145i	$-0.0910460\pi$
$569$	0.414645	+	1.27615i	0.0173828	+	0.0534988i	−0.941989	+	0.335644i	$0.891046\pi$
$570$	−12.8664	+	9.34800i	−0.538915	+	0.391545i
$571$	35.9461			1.50430			0.752150	−	0.658992i	$-0.229017\pi$
$571$	35.9461			1.50430			0.752150	+	0.658992i	$0.229017\pi$
$572$	3.12490	−	1.53007i	0.130659	−	0.0639756i
$573$	2.80999			0.117389
$574$	23.6260	−	17.1653i	0.986132	−	0.716467i
$575$	13.2349	+	40.7328i	0.551933	+	1.69867i
$576$	2.05172	−	6.31454i	0.0854883	−	0.263106i
$577$	19.3160	+	14.0339i	0.804135	+	0.584239i	0.912124	−	0.409914i	$-0.134441\pi$
$577$	19.3160	+	14.0339i	0.804135	+	0.584239i	−0.107989	+	0.994152i	$0.534441\pi$
$578$	37.7465	+	27.4244i	1.57005	+	1.14071i
$579$	6.50771	−	20.0287i	0.270451	−	0.832363i
$580$	2.13404	+	6.56791i	0.0886113	+	0.272717i
$581$	−16.2148	+	11.7807i	−0.672703	+	0.488747i
$582$	0.0886712			0.00367554
$583$	−17.9712	−	18.5525i	−0.744293	−	0.768368i
$584$	22.9809			0.950957
$585$	−2.91208	+	2.11575i	−0.120400	+	0.0874754i
$586$	1.24702	+	3.83792i	0.0515137	+	0.158543i
$587$	−7.98885	+	24.5871i	−0.329735	+	1.01482i	0.639523	+	0.768772i	$0.279132\pi$
$587$	−7.98885	+	24.5871i	−0.329735	+	1.01482i	−0.969258	+	0.246048i	$0.920868\pi$
$588$	−4.16535	−	3.02630i	−0.171776	−	0.124803i
$589$	−27.4102	−	19.9147i	−1.12942	−	0.820571i
$590$	5.53292	−	17.0286i	0.227787	−	0.701056i
$591$	1.59530	+	4.90982i	0.0656218	+	0.201963i
$592$	1.77922	−	1.29268i	0.0731254	−	0.0531287i
$593$	−15.3155			−0.628934			−0.314467	−	0.949268i	$-0.601826\pi$
$593$	−15.3155			−0.628934			−0.314467	+	0.949268i	$0.601826\pi$
$594$	0.455046	+	3.20205i	0.0186708	+	0.131382i
$595$	−100.024			−4.10057
$596$	−1.10538	+	0.803106i	−0.0452782	+	0.0328965i
$597$	−8.15651	−	25.1032i	−0.333824	−	1.02740i
$598$	−1.62206	+	4.99219i	−0.0663310	+	0.204146i
$599$	−33.6533	−	24.4505i	−1.37504	−	0.999022i	−0.997325	−	0.0730989i	$-0.976711\pi$
$599$	−33.6533	−	24.4505i	−1.37504	−	0.999022i	−0.377711	−	0.925923i	$-0.623289\pi$
$600$	19.1392	+	13.9055i	0.781357	+	0.567689i
$601$	−8.19403	+	25.2186i	−0.334242	+	1.02869i	0.632853	+	0.774272i	$0.281884\pi$
$601$	−8.19403	+	25.2186i	−0.334242	+	1.02869i	−0.967094	+	0.254418i	$0.918116\pi$
$602$	−6.95401	−	21.4022i	−0.283424	−	0.872290i
$603$	−3.24153	+	2.35511i	−0.132005	+	0.0959074i
$604$	−16.0313			−0.652304
$605$	37.2484	+	13.4276i	1.51436	+	0.545910i
$606$	−0.523479			−0.0212649
$607$	−4.75411	+	3.45407i	−0.192964	+	0.140196i	−0.680072	−	0.733145i	$-0.738052\pi$
$607$	−4.75411	+	3.45407i	−0.192964	+	0.140196i	0.487109	+	0.873341i	$0.338052\pi$
$608$	−7.23195	−	22.2576i	−0.293294	−	0.902667i
$609$	−1.95015	+	6.00194i	−0.0790240	+	0.243211i
$610$	3.84802	+	2.79575i	0.155802	+	0.113197i
$611$	−1.20965	−	0.878864i	−0.0489373	−	0.0355550i
$612$	−2.61054	+	8.03441i	−0.105525	+	0.324772i
$613$	−8.48776	−	26.1227i	−0.342818	−	1.05508i	−0.962742	−	0.270422i	$-0.912837\pi$
$613$	−8.48776	−	26.1227i	−0.342818	−	1.05508i	0.619924	−	0.784662i	$-0.287163\pi$
$614$	6.08792	−	4.42313i	0.245688	−	0.178503i
$615$	31.2384			1.25965
$616$	−4.78783	−	33.6908i	−0.192907	−	1.35744i
$617$	17.2096			0.692832			0.346416	−	0.938081i	$-0.387399\pi$
$617$	17.2096			0.692832			0.346416	+	0.938081i	$0.387399\pi$
$618$	1.89561	−	1.37724i	0.0762525	−	0.0554007i
$619$	−2.36986	−	7.29368i	−0.0952528	−	0.293158i	0.892067	−	0.451904i	$-0.149255\pi$
$619$	−2.36986	−	7.29368i	−0.0952528	−	0.293158i	−0.987319	+	0.158746i	$0.949255\pi$
$620$	−8.72584	+	26.8554i	−0.350438	+	1.07854i
$621$	4.35481	+	3.16396i	0.174753	+	0.126965i
$622$	24.7570	+	17.9870i	0.992664	+	0.721213i
$623$	−17.6011	+	54.1707i	−0.705174	+	2.17030i
$624$	0.247614	+	0.762077i	0.00991248	+	0.0305075i
$625$	1.19398	−	0.867476i	0.0477592	−	0.0346991i
$626$	4.97738			0.198936
$627$	10.4554	+	10.7936i	0.417548	+	0.431054i
$628$	−3.65395			−0.145808
$629$	−17.8804	+	12.9909i	−0.712940	+	0.517981i
$630$	3.74297	+	11.5197i	0.149124	+	0.458955i
$631$	−0.975564	+	3.00248i	−0.0388366	+	0.119527i	−0.968595	−	0.248643i	$-0.920015\pi$
$631$	−0.975564	+	3.00248i	−0.0388366	+	0.119527i	0.929759	+	0.368170i	$0.120015\pi$
$632$	8.10225	+	5.88663i	0.322290	+	0.234157i
$633$	6.15420	+	4.47129i	0.244608	+	0.177718i
$634$	1.88587	−	5.80411i	0.0748975	−	0.230511i
$635$	2.12265	+	6.53284i	0.0842348	+	0.259248i
$636$	−6.60972	+	4.80225i	−0.262093	+	0.190421i
$637$	4.90781			0.194454
$638$	−5.31218	+	2.60105i	−0.210311	+	0.102977i
$639$	−9.14256			−0.361674
$640$	−11.2288	+	8.15823i	−0.443859	+	0.322482i
$641$	−2.74336	−	8.44319i	−0.108356	−	0.333486i	0.882147	−	0.470973i	$-0.156097\pi$
$641$	−2.74336	−	8.44319i	−0.108356	−	0.333486i	−0.990503	+	0.137488i	$0.956097\pi$
$642$	−4.91818	+	15.1366i	−0.194105	+	0.597394i
$643$	20.0644	+	14.5776i	0.791262	+	0.574885i	0.908338	−	0.418238i	$-0.137352\pi$
$643$	20.0644	+	14.5776i	0.791262	+	0.574885i	−0.117076	+	0.993123i	$0.537352\pi$
$644$	−15.7649	−	11.4539i	−0.621224	−	0.451346i
$645$	7.43860	−	22.8936i	0.292894	−	0.901437i
$646$	−10.9946	−	33.8379i	−0.432576	−	1.33133i
$647$	2.66450	−	1.93587i	0.104752	−	0.0761071i	−0.534176	−	0.845373i	$-0.679378\pi$
$647$	2.66450	−	1.93587i	0.104752	−	0.0761071i	0.638928	+	0.769266i	$0.279378\pi$
$648$	2.97332			0.116803
$649$	−16.6655	−	2.91214i	−0.654179	−	0.114312i
$650$	−7.75888			−0.304328
$651$	−20.8760	+	15.1673i	−0.818195	+	0.594453i
$652$	1.63610	+	5.03540i	0.0640747	+	0.197202i
$653$	8.29862	−	25.5405i	0.324750	−	0.999478i	−0.646803	−	0.762657i	$-0.723894\pi$
$653$	8.29862	−	25.5405i	0.324750	−	0.999478i	0.971553	−	0.236821i	$-0.0761056\pi$
$654$	−4.34149	−	3.15427i	−0.169766	−	0.123342i
$655$	27.5546	+	20.0196i	1.07665	+	0.782231i
$656$	2.14891	−	6.61367i	0.0839009	−	0.258221i
$657$	2.38841	+	7.35076i	0.0931807	+	0.286781i
$658$	−4.07052	+	2.95740i	−0.158685	+	0.115292i
$659$	13.0411			0.508011			0.254005	−	0.967203i	$-0.418252\pi$
$659$	13.0411			0.508011			0.254005	+	0.967203i	$0.418252\pi$
$660$	5.86270	−	11.0672i	0.228205	−	0.430790i
$661$	−8.88151			−0.345451			−0.172725	−	0.984970i	$-0.555257\pi$
$661$	−8.88151			−0.345451			−0.172725	+	0.984970i	$0.555257\pi$
$662$	−19.0893	+	13.8692i	−0.741928	+	0.539042i
$663$	−2.48842	−	7.65857i	−0.0966423	−	0.297434i
$664$	−5.33656	+	16.4243i	−0.207099	+	0.637385i
$665$	45.5303	+	33.0797i	1.76559	+	1.28277i
$666$	2.16526	+	1.57315i	0.0839021	+	0.0609584i
$667$	−3.04203	+	9.36240i	−0.117788	+	0.362514i
$668$	−6.56685	−	20.2107i	−0.254079	−	0.781975i
$669$	3.50272	−	2.54487i	0.135423	−	0.0983904i
$670$	−14.0641			−0.543342
$671$	2.10381	−	3.97143i	0.0812169	−	0.153316i
$672$	−17.8241			−0.687579
$673$	4.43775	−	3.22422i	0.171063	−	0.124284i	−0.498960	−	0.866625i	$-0.666284\pi$
$673$	4.43775	−	3.22422i	0.171063	−	0.124284i	0.670023	+	0.742341i	$0.266284\pi$
$674$	−5.09932	−	15.6941i	−0.196418	−	0.604513i
$675$	−2.45872	+	7.56715i	−0.0946360	+	0.291260i
$676$	0.848719	+	0.616630i	0.0326430	+	0.0237166i
$677$	8.79714	+	6.39149i	0.338101	+	0.245645i	0.743860	−	0.668335i	$-0.232993\pi$
$677$	8.79714	+	6.39149i	0.338101	+	0.245645i	−0.405759	+	0.913980i	$0.632993\pi$
$678$	4.39619	−	13.5301i	0.168835	−	0.519619i
$679$	−0.0969633	−	0.298422i	−0.00372111	−	0.0114524i
$680$	−69.7245	+	50.6578i	−2.67381	+	1.94264i
$681$	−10.0813			−0.386315
$682$	−23.8239	−	4.16299i	−0.912263	−	0.159409i
$683$	14.6191			0.559386			0.279693	−	0.960090i	$-0.409767\pi$
$683$	14.6191			0.559386			0.279693	+	0.960090i	$0.409767\pi$
$684$	3.84544	−	2.79387i	0.147034	−	0.106826i
$685$	−12.6740	−	39.0064i	−0.484247	−	1.49036i
$686$	−2.17557	+	6.69572i	−0.0830637	+	0.255644i
$687$	9.91078	+	7.20061i	0.378120	+	0.274720i
$688$	−4.33524	−	3.14974i	−0.165280	−	0.120083i
$689$	2.40659	−	7.40672i	0.0916837	−	0.282173i
$690$	5.83865	+	17.9695i	0.222274	+	0.684088i
$691$	−7.07864	+	5.14293i	−0.269284	+	0.195646i	−0.714230	−	0.699911i	$-0.753223\pi$
$691$	−7.07864	+	5.14293i	−0.269284	+	0.195646i	0.444946	+	0.895557i	$0.353223\pi$
$692$	4.15177			0.157827
$693$	10.2789	−	5.03294i	0.390462	−	0.191186i
$694$	−8.83754			−0.335468
$695$	36.8625	−	26.7822i	1.39828	−	1.01591i
$696$	1.68032	+	5.17151i	0.0636925	+	0.196025i
$697$	−21.5957	+	66.4648i	−0.817997	+	2.51753i
$698$	23.2918	+	16.9225i	0.881608	+	0.640525i
$699$	−3.67299	−	2.66859i	−0.138925	−	0.100935i
$700$	8.90083	−	27.3939i	0.336420	−	1.03539i
$701$	−11.3874	−	35.0469i	−0.430097	−	1.32370i	−0.898028	−	0.439938i	$-0.855000\pi$
$701$	−11.3874	−	35.0469i	−0.430097	−	1.32370i	0.467931	−	0.883765i	$-0.345000\pi$
$702$	−0.788916	+	0.573181i	−0.0297757	+	0.0216333i
$703$	12.4354			0.469011
$704$	−15.3213	−	15.8168i	−0.577442	−	0.596119i
$705$	−5.38205			−0.202700
$706$	7.50463	−	5.45243i	0.282441	−	0.205205i
$707$	0.572432	+	1.76177i	0.0215285	+	0.0662580i
$708$	−1.65365	+	5.08940i	−0.0621478	+	0.191271i
$709$	−30.2905	−	22.0073i	−1.13758	−	0.826502i	−0.150802	−	0.988564i	$-0.548186\pi$
$709$	−30.2905	−	22.0073i	−1.13758	−	0.826502i	−0.986781	+	0.162062i	$0.948186\pi$
$710$	−25.9623	−	18.8628i	−0.974350	−	0.707906i
$711$	−1.04085	+	3.20341i	−0.0390350	+	0.120137i
$712$	15.1658	+	46.6756i	0.568363	+	1.74924i
$713$	−32.5644	+	23.6594i	−1.21955	+	0.886052i
$714$	−27.0976			−1.01410
$715$	1.67968	+	11.8195i	0.0628165	+	0.442025i
$716$	18.8629			0.704939
$717$	15.6884	−	11.3983i	0.585893	−	0.425676i
$718$	−6.21075	−	19.1147i	−0.231783	−	0.713355i
$719$	−7.35174	+	22.6263i	−0.274174	+	0.843820i	0.715263	+	0.698855i	$0.246307\pi$
$719$	−7.35174	+	22.6263i	−0.274174	+	0.843820i	−0.989437	+	0.144965i	$0.953693\pi$
$720$	2.33343	+	1.69534i	0.0869618	+	0.0631815i
$721$	−6.70796	−	4.87362i	−0.249818	−	0.181503i
$722$	−0.460684	+	1.41784i	−0.0171449	+	0.0527665i
$723$	6.20097	+	19.0846i	0.230616	+	0.709764i
$724$	−11.3924	+	8.27707i	−0.423396	+	0.307615i
$725$	−14.5511			−0.540414
$726$	10.0910	+	3.63770i	0.374514	+	0.135008i
$727$	−38.9674			−1.44522			−0.722611	−	0.691255i	$-0.757058\pi$
$727$	−38.9674			−1.44522			−0.722611	+	0.691255i	$0.757058\pi$
$728$	8.30070	−	6.03081i	0.307645	−	0.223517i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−8.38353	+	25.8019i	−0.310288	+	0.954969i
$731$	43.5675	+	31.6537i	1.61140	+	1.17075i
$732$	−1.15007	−	0.835577i	−0.0425079	−	0.0308838i
$733$	0.553803	−	1.70443i	0.0204552	−	0.0629545i	−0.940308	−	0.340325i	$-0.889463\pi$
$733$	0.553803	−	1.70443i	0.0204552	−	0.0629545i	0.960763	+	0.277370i	$0.0894629\pi$
$734$	−4.72859	−	14.5531i	−0.174536	−	0.537165i
$735$	14.2919	−	10.3837i	0.527165	−	0.383008i
$736$	−27.8037			−1.02486
$737$	1.86971	+	13.1567i	0.0688716	+	0.484633i
$738$	8.46286			0.311522
$739$	−30.5011	+	22.1603i	−1.12200	+	0.815181i	−0.984511	−	0.175322i	$-0.943903\pi$
$739$	−30.5011	+	22.1603i	−1.12200	+	0.815181i	−0.137489	+	0.990503i	$0.543903\pi$
$740$	−3.20267	−	9.85681i	−0.117733	−	0.362344i
$741$	−1.40012	+	4.30911i	−0.0514345	+	0.158299i
$742$	−21.2015	−	15.4038i	−0.778331	−	0.565491i
$743$	36.7180	+	26.6772i	1.34705	+	0.978691i	0.999153	+	0.0411601i	$0.0131054\pi$
$743$	36.7180	+	26.6772i	1.34705	+	0.978691i	0.347901	+	0.937531i	$0.386895\pi$
$744$	−6.87064	+	21.1457i	−0.251890	+	0.775237i
$745$	−1.44869	−	4.45861i	−0.0530759	−	0.163351i
$746$	13.0148	−	9.45584i	0.476507	−	0.346203i
$747$	−5.80815			−0.212509
$748$	19.4942	+	20.1248i	0.712780	+	0.735836i
$749$	56.3203			2.05790
$750$	−8.39584	+	6.09994i	−0.306573	+	0.222738i
$751$	−1.84965	−	5.69264i	−0.0674947	−	0.207727i	0.911621	−	0.411032i	$-0.134832\pi$
$751$	−1.84965	−	5.69264i	−0.0674947	−	0.207727i	−0.979115	+	0.203305i	$0.934832\pi$
$752$	−0.370235	+	1.13947i	−0.0135011	+	0.0415521i
$753$	19.0356	+	13.8301i	0.693694	+	0.503998i
$754$	−1.44278	−	1.04824i	−0.0525430	−	0.0381747i
$755$	16.9977	−	52.3135i	0.618609	−	1.90388i
$756$	−1.11868	−	3.44293i	−0.0406859	−	0.125218i
$757$	33.5229	−	24.3558i	1.21841	−	0.885228i	0.222445	−	0.974945i	$-0.428596\pi$
$757$	33.5229	−	24.3558i	1.21841	−	0.885228i	0.995967	+	0.0897169i	$0.0285962\pi$
$758$	30.1510			1.09513
$759$	16.0340	−	7.85087i	0.581997	−	0.284969i
$760$	48.4918			1.75898
$761$	12.3817	−	8.99582i	0.448836	−	0.326098i	−0.340300	−	0.940317i	$-0.610529\pi$
$761$	12.3817	−	8.99582i	0.448836	−	0.326098i	0.789136	+	0.614219i	$0.210529\pi$
$762$	0.575051	+	1.76983i	0.0208319	+	0.0641140i
$763$	−5.86821	+	18.0605i	−0.212443	+	0.653834i
$764$	−2.38489	−	1.73272i	−0.0862823	−	0.0626877i
$765$	−23.4501	−	17.0375i	−0.847839	−	0.615991i
$766$	10.7753	−	33.1629i	0.389326	−	1.19822i
$767$	−1.57629	−	4.85133i	−0.0569166	−	0.175171i
$768$	−13.7850	+	10.0154i	−0.497422	+	0.361398i
$769$	24.0709			0.868018			0.434009	−	0.900909i	$-0.357099\pi$
$769$	24.0709			0.868018			0.434009	+	0.900909i	$0.357099\pi$
$770$	39.5730	+	6.91501i	1.42611	+	0.249200i
$771$	9.99589			0.359993
$772$	−17.8735	+	12.9859i	−0.643282	+	0.467371i
$773$	10.5409	+	32.4415i	0.379129	+	1.16684i	0.940650	+	0.339378i	$0.110216\pi$
$773$	10.5409	+	32.4415i	0.379129	+	1.16684i	−0.561521	+	0.827463i	$0.689784\pi$
$774$	2.01521	−	6.20216i	0.0724351	−	0.222932i
$775$	−48.1346	−	34.9718i	−1.72904	−	1.25622i
$776$	−0.218730	−	0.158917i	−0.00785195	−	0.00570477i
$777$	2.92669	−	9.00744i	0.104995	−	0.323140i
$778$	8.62956	+	26.5591i	0.309385	+	0.952188i
$779$	31.8114	−	23.1124i	1.13976	−	0.828086i
$780$	3.77617			0.135208
$781$	−14.1943	+	26.7950i	−0.507912	+	0.958801i
$782$	−42.2694			−1.51155
$783$	−1.47954	+	1.07495i	−0.0528745	+	0.0384156i
$784$	−1.21524	−	3.74013i	−0.0434014	−	0.133576i
$785$	3.87421	−	11.9236i	0.138277	−	0.425571i
$786$	7.46488	+	5.42355i	0.266263	+	0.193452i
$787$	−7.14984	−	5.19466i	−0.254864	−	0.185170i	0.453016	−	0.891503i	$-0.350348\pi$
$787$	−7.14984	−	5.19466i	−0.254864	−	0.185170i	−0.707880	+	0.706333i	$0.750348\pi$
$788$	1.67359	−	5.15077i	0.0596190	−	0.183488i
$789$	1.34293	+	4.13310i	0.0478094	+	0.147142i
$790$	−9.56495	+	6.94934i	−0.340305	+	0.247246i
$791$	−50.3427			−1.78998
$792$	4.61623	−	8.71420i	0.164031	−	0.309645i
$793$	1.35507			0.0481199
$794$	−13.2085	+	9.59653i	−0.468752	+	0.340568i
$795$	−8.66257	−	26.6607i	−0.307230	−	0.945556i
$796$	−8.55679	+	26.3351i	−0.303287	+	0.933422i
$797$	25.1042	+	18.2393i	0.889236	+	0.646068i	0.935679	−	0.352853i	$-0.114788\pi$
$797$	25.1042	+	18.2393i	0.889236	+	0.646068i	−0.0464424	+	0.998921i	$0.514788\pi$
$798$	12.3347	+	8.96168i	0.436644	+	0.317240i
$799$	3.72072	−	11.4512i	0.131629	−	0.405114i
$800$	−12.6999	−	39.0862i	−0.449009	−	1.38191i
$801$	−13.3536	+	9.70199i	−0.471828	+	0.342803i
$802$	−34.8541			−1.23074
$803$	25.2517	+	4.41250i	0.891115	+	0.155714i
$804$	4.20338			0.148242
$805$	54.0916	−	39.2999i	1.90648	−	1.38514i
$806$	−2.25335	−	6.93511i	−0.0793710	−	0.244279i
$807$	−5.28519	+	16.2661i	−0.186047	+	0.572595i
$808$	1.29129	+	0.938180i	0.0454275	+	0.0330050i
$809$	−9.39939	−	6.82906i	−0.330465	−	0.240097i	0.410163	−	0.912012i	$-0.365472\pi$
$809$	−9.39939	−	6.82906i	−0.330465	−	0.240097i	−0.740628	+	0.671915i	$0.765472\pi$
$810$	−1.08468	+	3.33829i	−0.0381117	+	0.117296i
$811$	−4.45764	−	13.7192i	−0.156529	−	0.481746i	0.841784	−	0.539815i	$-0.181506\pi$
$811$	−4.45764	−	13.7192i	−0.156529	−	0.481746i	−0.998313	+	0.0580686i	$0.981506\pi$
$812$	5.35611	−	3.89144i	0.187962	−	0.136563i
$813$	10.0805			0.353539
$814$	7.97227	−	3.90354i	0.279428	−	0.136819i
$815$	−18.1663			−0.636338
$816$	−5.22025	+	3.79273i	−0.182745	+	0.132772i
$817$	−9.36327	−	28.8172i	−0.327579	−	1.00819i
$818$	4.62719	−	14.2410i	0.161786	−	0.497925i
$819$	2.79173	+	2.02831i	0.0975510	+	0.0708749i
$820$	−26.5126	−	19.2626i	−0.925861	−	0.672678i
$821$	8.15624	−	25.1023i	0.284655	−	0.876077i	−0.701847	−	0.712327i	$-0.747641\pi$
$821$	8.15624	−	25.1023i	0.284655	−	0.876077i	0.986502	−	0.163750i	$-0.0523589\pi$
$822$	−3.43353	−	10.5673i	−0.119758	−	0.368577i
$823$	10.9551	−	7.95936i	0.381871	−	0.277446i	−0.380245	−	0.924886i	$-0.624160\pi$
$823$	10.9551	−	7.95936i	0.381871	−	0.277446i	0.762116	+	0.647440i	$0.224160\pi$
$824$	−7.14428			−0.248883
$825$	18.3605	+	18.9544i	0.639231	+	0.659907i
$826$	−17.1650			−0.597246
$827$	−5.81710	+	4.22637i	−0.202280	+	0.146965i	−0.684314	−	0.729187i	$-0.739898\pi$
$827$	−5.81710	+	4.22637i	−0.202280	+	0.146965i	0.482034	+	0.876153i	$0.339898\pi$
$828$	−1.74502	−	5.37062i	−0.0606436	−	0.186642i
$829$	−15.0065	+	46.1853i	−0.521198	+	1.60408i	0.250516	+	0.968112i	$0.419400\pi$
$829$	−15.0065	+	46.1853i	−0.521198	+	1.60408i	−0.771714	+	0.635970i	$0.780600\pi$
$830$	−16.4935	−	11.9833i	−0.572499	−	0.415945i
$831$	2.30454	+	1.67435i	0.0799437	+	0.0580825i
$832$	2.05172	−	6.31454i	0.0711306	−	0.218917i
$833$	12.2127	+	37.5868i	0.423145	+	1.30231i
$834$	9.98651	−	7.25562i	0.345804	−	0.251242i
$835$	72.9145			2.52331
$836$	−2.21804	−	15.6078i	−0.0767126	−	0.539808i
$837$	−7.47780			−0.258470
$838$	−20.3457	+	14.7820i	−0.702832	+	0.510637i
$839$	−9.93676	−	30.5822i	−0.343055	−	1.05582i	−0.962617	−	0.270867i	$-0.912690\pi$
$839$	−9.93676	−	30.5822i	−0.343055	−	1.05582i	0.619562	−	0.784948i	$-0.287310\pi$
$840$	11.4126	−	35.1244i	0.393772	−	1.21191i
$841$	20.7557	+	15.0799i	0.715713	+	0.519996i
$842$	7.26077	+	5.27526i	0.250223	+	0.181797i
$843$	−10.2666	+	31.5975i	−0.353602	+	1.08828i
$844$	−2.46605	−	7.58974i	−0.0848851	−	0.261249i
$845$	−2.91208	+	2.11575i	−0.100178	+	0.0727839i
$846$	−1.45806			−0.0501292
$847$	1.20794	−	37.9392i	0.0415054	−	1.30361i
$848$	−6.24039			−0.214296
$849$	−19.4090	+	14.1015i	−0.666115	+	0.483961i
$850$	−19.3074	−	59.4220i	−0.662237	−	2.03816i
$851$	4.56534	−	14.0507i	0.156498	−	0.481651i
$852$	7.75947	+	5.63758i	0.265835	+	0.193140i
$853$	39.3020	+	28.5546i	1.34568	+	0.977691i	0.999215	+	0.0396267i	$0.0126169\pi$
$853$	39.3020	+	28.5546i	1.34568	+	0.977691i	0.346461	+	0.938064i	$0.387383\pi$
$854$	1.40907	−	4.33668i	0.0482174	−	0.148398i
$855$	5.03975	+	15.5108i	0.172356	+	0.530457i
$856$	39.2598	−	28.5239i	1.34187	−	0.974927i
$857$	8.19897			0.280071			0.140036	−	0.990146i	$-0.455278\pi$
$857$	8.19897			0.280071			0.140036	+	0.990146i	$0.455278\pi$
$858$	0.455046	+	3.20205i	0.0155350	+	0.109316i
$859$	19.8006			0.675589			0.337795	−	0.941220i	$-0.390319\pi$
$859$	19.8006			0.675589			0.337795	+	0.941220i	$0.390319\pi$
$860$	−20.4302	+	14.8434i	−0.696664	+	0.506156i
$861$	−9.25427	−	28.4817i	−0.315385	−	0.970654i
$862$	0.832767	−	2.56299i	0.0283642	−	0.0872959i
$863$	−12.9159	−	9.38392i	−0.439661	−	0.319432i	0.345839	−	0.938294i	$-0.387594\pi$
$863$	−12.9159	−	9.38392i	−0.439661	−	0.319432i	−0.785500	+	0.618861i	$0.787594\pi$
$864$	−4.17877	−	3.03606i	−0.142165	−	0.103289i
$865$	−4.40204	+	13.5481i	−0.149674	+	0.460649i
$866$	−9.20927	−	28.3432i	−0.312944	−	0.963142i
$867$	38.7082	−	28.1232i	1.31460	−	0.955112i
$868$	27.0705			0.918831
$869$	7.77258	+	8.02399i	0.263667	+	0.272195i
$870$	−6.41930			−0.217635
$871$	−3.24153	+	2.35511i	−0.109835	+	0.0797998i
$872$	5.05628	+	15.5616i	0.171227	+	0.526983i
$873$	0.0280991	−	0.0864800i	0.000951009	−	0.00292690i
$874$	19.2408	+	13.9793i	0.650831	+	0.472857i
$875$	29.7103	+	21.5858i	1.00439	+	0.729733i
$876$	2.50562	−	7.71150i	0.0846570	−	0.260547i
$877$	7.64594	+	23.5318i	0.258185	+	0.794612i	0.993185	+	0.116545i	$0.0371820\pi$
$877$	7.64594	+	23.5318i	0.258185	+	0.794612i	−0.735000	+	0.678067i	$0.762818\pi$
$878$	25.7525	−	18.7103i	0.869104	−	0.631441i
$879$	4.13824			0.139580
$880$	8.59146	−	4.20672i	0.289618	−	0.141808i
$881$	56.9520			1.91876			0.959381	−	0.282113i	$-0.0910354\pi$
$881$	56.9520			1.91876			0.959381	+	0.282113i	$0.0910354\pi$
$882$	3.87185	−	2.81306i	0.130372	−	0.0947208i
$883$	−8.59376	−	26.4489i	−0.289203	−	0.890076i	−0.985107	−	0.171941i	$-0.944996\pi$
$883$	−8.59376	−	26.4489i	−0.289203	−	0.890076i	0.695904	−	0.718135i	$-0.255004\pi$
$884$	−2.61054	+	8.03441i	−0.0878019	+	0.270226i
$885$	−14.8545	−	10.7924i	−0.499327	−	0.362782i
$886$	−20.6463	−	15.0004i	−0.693626	−	0.503949i
$887$	−4.57256	+	14.0729i	−0.153532	+	0.472522i	−0.998009	−	0.0630693i	$-0.979911\pi$
$887$	−4.57256	+	14.0729i	−0.153532	+	0.472522i	0.844478	+	0.535591i	$0.179911\pi$
$888$	−2.52175	−	7.76116i	−0.0846245	−	0.260447i
$889$	5.32751	−	3.87066i	0.178679	−	0.129818i
$890$	−57.9376			−1.94207
$891$	3.26712	+	0.570898i	0.109453	+	0.0191258i
$892$	−4.54207			−0.152080
$893$	−5.48078	+	3.98202i	−0.183407	+	0.133253i
$894$	−0.392468	−	1.20789i	−0.0131261	−	0.0403979i
$895$	−20.0000	+	61.5536i	−0.668525	+	2.05751i
$896$	10.7648	+	7.82108i	0.359627	+	0.261284i
$897$	4.35481	+	3.16396i	0.145403	+	0.105641i
$898$	2.52065	−	7.75776i	0.0841152	−	0.258880i
$899$	−4.22596	−	13.0062i	−0.140944	−	0.433780i
$900$	6.75289	−	4.90626i	0.225096	−	0.163542i
$901$	62.7135			2.08929
$902$	13.1390	−	24.8030i	0.437482	−	0.825848i
$903$	−23.0770			−0.767955
$904$	−35.0929	+	25.4965i	−1.16717	+	0.848001i
$905$	−14.9307	−	45.9519i	−0.496312	−	1.52749i
$906$	4.60488	−	14.1724i	0.152987	−	0.470845i
$907$	−7.48813	−	5.44045i	−0.248639	−	0.180647i	0.456484	−	0.889732i	$-0.349108\pi$
$907$	−7.48813	−	5.44045i	−0.248639	−	0.180647i	−0.705124	+	0.709084i	$0.749108\pi$
$908$	8.55616	+	6.21641i	0.283946	+	0.206299i
$909$	−0.165885	+	0.510543i	−0.00550207	+	0.0169336i
$910$	3.74297	+	11.5197i	0.124078	+	0.381874i
$911$	4.14946	−	3.01476i	0.137478	−	0.0998834i	−0.516921	−	0.856033i	$-0.672922\pi$
$911$	4.14946	−	3.01476i	0.137478	−	0.0998834i	0.654399	+	0.756150i	$0.272922\pi$
$912$	3.63056			0.120220
$913$	−9.01746	+	17.0225i	−0.298434	+	0.563363i
$914$	−23.2547			−0.769197
$915$	3.94606	−	2.86698i	0.130453	−	0.0947795i
$916$	−3.97136	−	12.2226i	−0.131217	−	0.403845i
$917$	10.0900	−	31.0538i	0.333200	−	1.02549i
$918$	−6.35291	−	4.61566i	−0.209677	−	0.152339i
$919$	−17.6132	−	12.7968i	−0.581007	−	0.422126i	0.258080	−	0.966124i	$-0.416910\pi$
$919$	−17.6132	−	12.7968i	−0.581007	−	0.422126i	−0.839087	+	0.543997i	$0.816910\pi$
$920$	17.8025	−	54.7904i	0.586930	−	1.80639i
$921$	−2.38463	−	7.33913i	−0.0785761	−	0.241832i
$922$	−18.8244	+	13.6768i	−0.619950	+	0.450420i
$923$	−9.14256			−0.300931
$924$	−11.8273	−	2.06671i	−0.389091	−	0.0679899i
$925$	21.8376			0.718016
$926$	−11.9193	+	8.65991i	−0.391694	+	0.284582i
$927$	−0.742505	−	2.28520i	−0.0243871	−	0.0750557i
$928$	2.91906	−	8.98394i	0.0958228	−	0.294912i
$929$	−33.3216	−	24.2096i	−1.09325	−	0.794291i	−0.113303	−	0.993561i	$-0.536143\pi$
$929$	−33.3216	−	24.2096i	−1.09325	−	0.794291i	−0.979945	+	0.199270i	$0.936143\pi$
$930$	−21.2349	−	15.4280i	−0.696319	−	0.505905i
$931$	6.87150	−	21.1483i	0.225204	−	0.693108i
$932$	1.47181	+	4.52976i	0.0482107	+	0.148377i
$933$	25.3878	−	18.4453i	0.831158	−	0.603871i
$934$	−18.7547			−0.613673
$935$	−86.3409	+	42.2759i	−2.82365	+	1.38257i
$936$	2.97332			0.0971859
$937$	47.6127	−	34.5927i	1.55544	−	1.13009i	0.615813	−	0.787892i	$-0.288828\pi$
$937$	47.6127	−	34.5927i	1.55544	−	1.13009i	0.939627	−	0.342201i	$-0.111172\pi$
$938$	4.16643	+	12.8229i	0.136039	+	0.418684i
$939$	1.57728	−	4.85438i	0.0514727	−	0.158417i
$940$	4.56785	+	3.31874i	0.148987	+	0.108245i
$941$	29.5661	+	21.4810i	0.963827	+	0.700261i	0.954036	−	0.299691i	$-0.0968835\pi$
$941$	29.5661	+	21.4810i	0.963827	+	0.700261i	0.00979074	+	0.999952i	$0.496883\pi$
$942$	1.04957	−	3.23025i	0.0341969	−	0.105247i
$943$	−14.4357	−	44.4285i	−0.470091	−	1.44679i
$944$	−3.30677	+	2.40251i	−0.107626	+	0.0781950i
$945$	12.4211			0.404059
$946$	−15.0486	−	15.5353i	−0.489272	−	0.505098i
$947$	−24.8578			−0.807770			−0.403885	−	0.914810i	$-0.632340\pi$
$947$	−24.8578			−0.807770			−0.403885	+	0.914810i	$0.632340\pi$
$948$	2.85871	−	2.07698i	0.0928466	−	0.0674570i
$949$	2.38841	+	7.35076i	0.0775310	+	0.238616i
$950$	−10.8633	+	33.4339i	−0.352453	+	1.08474i
$951$	−5.06307	−	3.67854i	−0.164181	−	0.119285i
$952$	66.8431	+	48.5643i	2.16640	+	1.57398i
$953$	−0.884064	+	2.72087i	−0.0286376	+	0.0881376i	−0.964354	−	0.264616i	$-0.914755\pi$
$953$	−0.884064	+	2.72087i	−0.0286376	+	0.0881376i	0.935716	+	0.352754i	$0.114755\pi$
$954$	−2.34680	−	7.22269i	−0.0759803	−	0.233843i
$955$	8.18290	−	5.94522i	0.264792	−	0.192383i
$956$	−20.3435			−0.657957
$957$	0.853397	+	6.00515i	0.0275864	+	0.194119i
$958$	20.9579			0.677120
$959$	−31.8096	+	23.1110i	−1.02719	+	0.746294i
$960$	−7.38521	−	22.7293i	−0.238357	−	0.733587i
$961$	7.69991	−	23.6979i	0.248384	−	0.764448i
$962$	2.16526	+	1.57315i	0.0698108	+	0.0507205i
$963$	13.2040	+	9.59329i	0.425494	+	0.309139i
$964$	6.50527	−	20.0212i	0.209521	−	0.644839i
$965$	−23.4247	−	72.0937i	−0.754066	−	2.32078i
$966$	14.6541	−	10.6468i	0.471487	−	0.342556i
$967$	−21.8776			−0.703536			−0.351768	−	0.936087i	$-0.614419\pi$
$967$	−21.8776			−0.703536			−0.351768	+	0.936087i	$0.614419\pi$
$968$	−18.3726	−	27.0585i	−0.590519	−	0.869693i
$969$	−36.4857			−1.17209
$970$	0.258217	−	0.187606i	0.00829086	−	0.00602366i
$971$	13.5570	+	41.7240i	0.435063	+	1.33899i	0.893022	+	0.450014i	$0.148581\pi$
$971$	13.5570	+	41.7240i	0.435063	+	1.33899i	−0.457958	+	0.888974i	$0.651419\pi$
$972$	0.324182	−	0.997729i	0.0103981	−	0.0320022i
$973$	−35.3392	−	25.6754i	−1.13292	−	0.823115i
$974$	24.7265	+	17.9649i	0.792288	+	0.575631i
$975$	−2.45872	+	7.56715i	−0.0787419	+	0.242343i
$976$	−0.335534	−	1.03267i	−0.0107402	−	0.0330548i
$977$	−46.7323	+	33.9530i	−1.49510	+	1.08625i	−0.522815	+	0.852446i	$0.675118\pi$
$977$	−46.7323	+	33.9530i	−1.49510	+	1.08625i	−0.972283	+	0.233807i	$0.924882\pi$
$978$	−4.92147			−0.157371
$979$	7.70236	+	54.1997i	0.246168	+	1.73223i
$980$	−18.5327			−0.592005
$981$	−4.45210	+	3.23464i	−0.142145	+	0.103274i
$982$	4.88817	+	15.0443i	0.155988	+	0.480081i
$983$	−14.8878	+	45.8201i	−0.474849	+	1.46143i	0.371313	+	0.928508i	$0.378908\pi$
$983$	−14.8878	+	45.8201i	−0.474849	+	1.46143i	−0.846162	+	0.532926i	$0.821092\pi$
$984$	−20.8758	−	15.1672i	−0.665496	−	0.483511i
$985$	15.0336	+	10.9225i	0.479009	+	0.348020i
$986$	4.43779	−	13.6581i	0.141328	−	0.434963i
$987$	1.59441	+	4.90710i	0.0507507	+	0.156195i
$988$	3.84544	−	2.79387i	0.122340	−	0.0888849i
$989$	−35.9977			−1.14466
$990$	8.09985	+	8.36185i	0.257430	+	0.265757i
$991$	−4.09824			−0.130185			−0.0650925	−	0.997879i	$-0.520734\pi$
$991$	−4.09824			−0.130185			−0.0650925	+	0.997879i	$0.520734\pi$
$992$	31.2480	−	22.7030i	0.992126	−	0.720821i
$993$	7.47726	+	23.0126i	0.237284	+	0.730284i
$994$	−9.50691	+	29.2593i	−0.301541	+	0.928048i
$995$	−76.8643	−	55.8452i	−2.43676	−	1.77041i
$996$	4.92949	+	3.58148i	0.156197	+	0.113484i
$997$	8.55282	−	26.3229i	0.270871	−	0.833654i	−0.719412	−	0.694584i	$-0.755589\pi$
$997$	8.55282	−	26.3229i	0.270871	−	0.833654i	0.990283	−	0.139070i	$-0.0444114\pi$
$998$	−4.88409	−	15.0317i	−0.154603	−	0.475819i
$999$	2.22043	−	1.61324i	0.0702512	−	0.0510405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.157.5	✓	28
11.2	odd	10		4719.2.a.bo.1.10		14
11.4	even	5	inner	429.2.n.c.235.5	yes	28
11.9	even	5		4719.2.a.bp.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.157.5	✓	28	1.1	even	1	trivial
429.2.n.c.235.5	yes	28	11.4	even	5	inner
4719.2.a.bo.1.10		14	11.2	odd	10
4719.2.a.bp.1.5		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)

\(f(q)\)	\(=\)	\(q+(0.788916 - 0.573181i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.324182 + 0.997729i) q^{4} +(-2.91208 - 2.11575i) q^{5} +(-0.788916 - 0.573181i) q^{6} +(-1.06635 + 3.28188i) q^{7} +(0.918806 + 2.82779i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.788916 - 0.573181i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.324182 + 0.997729i) q^{4} +(-2.91208 - 2.11575i) q^{5} +(-0.788916 - 0.573181i) q^{6} +(-1.06635 + 3.28188i) q^{7} +(0.918806 + 2.82779i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.51009 q^{10} +(0.466640 + 3.28363i) q^{11} +1.04907 q^{12} +(-0.809017 + 0.587785i) q^{13} +(1.03985 + 3.20034i) q^{14} +(-1.11231 + 3.42335i) q^{15} +(0.648261 + 0.470989i) q^{16} +(-6.51477 - 4.73326i) q^{17} +(-0.301339 + 0.927427i) q^{18} +(1.40012 + 4.30911i) q^{19} +(3.05498 - 2.21958i) q^{20} +3.45077 q^{21} +(2.25026 + 2.32304i) q^{22} +5.38284 q^{23} +(2.40546 - 1.74767i) q^{24} +(2.45872 + 7.56715i) q^{25} +(-0.301339 + 0.927427i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.92873 - 2.12785i) q^{28} +(-0.565134 + 1.73930i) q^{29} +(1.08468 + 3.33829i) q^{30} +(-6.04966 + 4.39534i) q^{31} -5.16525 q^{32} +(2.97872 - 1.45850i) q^{33} -7.85262 q^{34} +(10.0489 - 7.30095i) q^{35} +(-0.324182 - 0.997729i) q^{36} +(0.848128 - 2.61027i) q^{37} +(3.57448 + 2.59701i) q^{38} +(0.809017 + 0.587785i) q^{39} +(3.30726 - 10.1787i) q^{40} +(-2.68180 - 8.25373i) q^{41} +(2.72237 - 1.97792i) q^{42} -6.68750 q^{43} +(-3.42745 - 0.598914i) q^{44} +3.59952 q^{45} +(4.24661 - 3.08534i) q^{46} +(0.462046 + 1.42203i) q^{47} +(0.247614 - 0.762077i) q^{48} +(-3.97050 - 2.88474i) q^{49} +(6.27707 + 4.56056i) q^{50} +(-2.48842 + 7.65857i) q^{51} +(-0.324182 - 0.997729i) q^{52} +(-6.30053 + 4.57760i) q^{53} +0.975154 q^{54} +(5.58845 - 10.5495i) q^{55} -10.2602 q^{56} +(3.66555 - 2.66318i) q^{57} +(0.551093 + 1.69609i) q^{58} +(-1.57629 + 4.85133i) q^{59} +(-3.05498 - 2.21958i) q^{60} +(-1.09627 - 0.796490i) q^{61} +(-2.25335 + 6.93511i) q^{62} +(-1.06635 - 3.28188i) q^{63} +(-5.37147 + 3.90260i) q^{64} +3.59952 q^{65} +(1.51398 - 2.85798i) q^{66} +4.00675 q^{67} +(6.83448 - 4.96554i) q^{68} +(-1.66339 - 5.11939i) q^{69} +(3.74297 - 11.5197i) q^{70} +(7.39649 + 5.37386i) q^{71} +(-2.40546 - 1.74767i) q^{72} +(2.38841 - 7.35076i) q^{73} +(-0.827056 - 2.54542i) q^{74} +(6.43700 - 4.67675i) q^{75} -4.75322 q^{76} +(-11.2741 - 1.97004i) q^{77} +0.975154 q^{78} +(2.72499 - 1.97982i) q^{79} +(-0.891291 - 2.74311i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-6.84660 - 4.97435i) q^{82} +(4.69889 + 3.41395i) q^{83} +(-1.11868 + 3.44293i) q^{84} +(8.95713 + 27.5672i) q^{85} +(-5.27588 + 3.83315i) q^{86} +1.82881 q^{87} +(-8.85668 + 4.33658i) q^{88} +16.5060 q^{89} +(2.83972 - 2.06318i) q^{90} +(-1.06635 - 3.28188i) q^{91} +(-1.74502 + 5.37062i) q^{92} +(6.04966 + 4.39534i) q^{93} +(1.17960 + 0.857027i) q^{94} +(5.03975 - 15.5108i) q^{95} +(1.59615 + 4.91244i) q^{96} +(-0.0735643 + 0.0534476i) q^{97} -4.78587 q^{98} +(-2.30759 - 2.38223i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more