LMFDB - Embedded newform 429.2.bb.a.25.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.7
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.a.103.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.150436 - 0.207057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.597792 - 1.83982i) q^{4} +(0.694723 - 0.956204i) q^{5} +(0.150436 - 0.207057i) q^{6} +(-2.82596 - 0.918210i) q^{7} +(-0.957697 + 0.311175i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.150436 - 0.207057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.597792 - 1.83982i) q^{4} +(0.694723 - 0.956204i) q^{5} +(0.150436 - 0.207057i) q^{6} +(-2.82596 - 0.918210i) q^{7} +(-0.957697 + 0.311175i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.302500 q^{10} +(1.49655 - 2.95979i) q^{11} +1.93450 q^{12} +(1.53779 - 3.26117i) q^{13} +(0.235004 + 0.723267i) q^{14} +(1.12409 + 0.365237i) q^{15} +(-2.92158 - 2.12265i) q^{16} +(-1.63053 - 1.18465i) q^{17} +(0.243410 + 0.0790888i) q^{18} +(-3.39640 + 1.10356i) q^{19} +(-1.34394 - 1.84977i) q^{20} -2.97139i q^{21} +(-0.837980 + 0.135386i) q^{22} +6.02963 q^{23} +(-0.591889 - 0.814666i) q^{24} +(1.11340 + 3.42669i) q^{25} +(-0.906586 + 0.172187i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-3.37867 + 4.65034i) q^{28} +(0.590493 - 1.81735i) q^{29} +(-0.0934777 - 0.287695i) q^{30} +(-2.30590 - 3.17381i) q^{31} +2.93822i q^{32} +(3.27738 + 0.508682i) q^{33} +0.515828i q^{34} +(-2.84125 + 2.06429i) q^{35} +(0.597792 + 1.83982i) q^{36} +(2.45374 + 0.797270i) q^{37} +(0.739441 + 0.537235i) q^{38} +(3.57676 + 0.454765i) q^{39} +(-0.367788 + 1.13193i) q^{40} +(6.66338 - 2.16506i) q^{41} +(-0.615247 + 0.447003i) q^{42} -3.94872 q^{43} +(-4.55083 - 4.52272i) q^{44} +1.18193i q^{45} +(-0.907072 - 1.24848i) q^{46} +(7.79196 - 2.53176i) q^{47} +(1.11594 - 3.43452i) q^{48} +(1.47982 + 1.07515i) q^{49} +(0.542026 - 0.746034i) q^{50} +(0.622809 - 1.91681i) q^{51} +(-5.08067 - 4.77874i) q^{52} +(5.23254 - 3.80166i) q^{53} +0.255937i q^{54} +(-1.79047 - 3.48724i) q^{55} +2.99214 q^{56} +(-2.09909 - 2.88915i) q^{57} +(-0.465127 + 0.151129i) q^{58} +(3.67613 + 1.19445i) q^{59} +(1.34394 - 1.84977i) q^{60} +(-1.21460 - 0.882461i) q^{61} +(-0.310268 + 0.954908i) q^{62} +(2.82596 - 0.918210i) q^{63} +(-5.23478 + 3.80329i) q^{64} +(-2.05001 - 3.73604i) q^{65} +(-0.387710 - 0.755130i) q^{66} +13.6191i q^{67} +(-3.15426 + 2.29171i) q^{68} +(1.86326 + 5.73452i) q^{69} +(0.854853 + 0.277758i) q^{70} +(-6.82649 + 9.39585i) q^{71} +(0.591889 - 0.814666i) q^{72} +(9.32054 + 3.02843i) q^{73} +(-0.204051 - 0.628003i) q^{74} +(-2.91492 + 2.11781i) q^{75} +6.90845i q^{76} +(-6.94690 + 6.99008i) q^{77} +(-0.443910 - 0.809006i) q^{78} +(-6.89827 + 5.01189i) q^{79} +(-4.05937 + 1.31897i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.45070 - 1.05400i) q^{82} +(0.175012 - 0.240883i) q^{83} +(-5.46681 - 1.77627i) q^{84} +(-2.26554 + 0.736118i) q^{85} +(0.594029 + 0.817611i) q^{86} +1.91087 q^{87} +(-0.512234 + 3.30027i) q^{88} +3.35850i q^{89} +(0.244728 - 0.177805i) q^{90} +(-7.34015 + 7.80392i) q^{91} +(3.60446 - 11.0934i) q^{92} +(2.30590 - 3.17381i) q^{93} +(-1.69641 - 1.23251i) q^{94} +(-1.30433 + 4.01432i) q^{95} +(-2.79441 + 0.907960i) q^{96} +(7.30845 + 10.0592i) q^{97} -0.468147i q^{98} +(0.528981 + 3.27417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.150436	−	0.207057i	−0.106374	−	0.146412i	0.752511	−	0.658580i	$-0.228842\pi$
$2$	−0.150436	−	0.207057i	−0.106374	−	0.146412i	−0.858885	+	0.512168i	$0.828842\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.597792	−	1.83982i	0.298896	−	0.919908i
$5$	0.694723	−	0.956204i	0.310689	−	0.427627i	−0.624907	−	0.780699i	$-0.714863\pi$
$5$	0.694723	−	0.956204i	0.310689	−	0.427627i	0.935596	+	0.353072i	$0.114863\pi$
$6$	0.150436	−	0.207057i	0.0614152	−	0.0845307i
$7$	−2.82596	−	0.918210i	−1.06811	−	0.347051i	−0.278360	−	0.960477i	$-0.589791\pi$
$7$	−2.82596	−	0.918210i	−1.06811	−	0.347051i	−0.789752	+	0.613426i	$0.789791\pi$
$8$	−0.957697	+	0.311175i	−0.338597	+	0.110017i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.302500			−0.0956589
$11$	1.49655	−	2.95979i	0.451228	−	0.892409i
$11$	1.49655	−	2.95979i	0.451228	−	0.892409i
$12$	1.93450			0.558441
$13$	1.53779	−	3.26117i	0.426505	−	0.904485i
$13$	1.53779	−	3.26117i	0.426505	−	0.904485i
$14$	0.235004	+	0.723267i	0.0628074	+	0.193301i
$15$	1.12409	+	0.365237i	0.290238	+	0.0943039i
$16$	−2.92158	−	2.12265i	−0.730395	−	0.530663i
$17$	−1.63053	−	1.18465i	−0.395463	−	0.287320i	0.372228	−	0.928141i	$-0.378594\pi$
$17$	−1.63053	−	1.18465i	−0.395463	−	0.287320i	−0.767690	+	0.640821i	$0.778594\pi$
$18$	0.243410	+	0.0790888i	0.0573724	+	0.0186414i
$19$	−3.39640	+	1.10356i	−0.779188	+	0.253174i	−0.671494	−	0.741010i	$-0.734347\pi$
$19$	−3.39640	+	1.10356i	−0.779188	+	0.253174i	−0.107695	+	0.994184i	$0.534347\pi$
$20$	−1.34394	−	1.84977i	−0.300514	−	0.413622i
$21$		−	2.97139i		−	0.648410i
$22$	−0.837980	+	0.135386i	−0.178658	+	0.0288643i
$23$	6.02963			1.25726			0.628632	−	0.777703i	$-0.283615\pi$
$23$	6.02963			1.25726			0.628632	+	0.777703i	$0.283615\pi$
$24$	−0.591889	−	0.814666i	−0.120819	−	0.166293i
$25$	1.11340	+	3.42669i	0.222680	+	0.685338i
$26$	−0.906586	+	0.172187i	−0.177796	+	0.0337687i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−3.37867	+	4.65034i	−0.638509	+	0.878832i
$29$	0.590493	−	1.81735i	0.109652	−	0.337473i	−0.881142	−	0.472851i	$-0.843225\pi$
$29$	0.590493	−	1.81735i	0.109652	−	0.337473i	0.990794	+	0.135378i	$0.0432248\pi$
$30$	−0.0934777	−	0.287695i	−0.0170666	−	0.0525256i
$31$	−2.30590	−	3.17381i	−0.414153	−	0.570032i	0.550072	−	0.835117i	$-0.314600\pi$
$31$	−2.30590	−	3.17381i	−0.414153	−	0.570032i	−0.964225	+	0.265085i	$0.914600\pi$
$32$			2.93822i			0.519409i
$33$	3.27738	+	0.508682i	0.570519	+	0.0885502i
$34$			0.515828i			0.0884638i
$35$	−2.84125	+	2.06429i	−0.480260	+	0.348929i
$36$	0.597792	+	1.83982i	0.0996320	+	0.306636i
$37$	2.45374	+	0.797270i	0.403393	+	0.131070i	0.503684	−	0.863888i	$-0.331977\pi$
$37$	2.45374	+	0.797270i	0.403393	+	0.131070i	−0.100291	+	0.994958i	$0.531977\pi$
$38$	0.739441	+	0.537235i	0.119953	+	0.0871510i
$39$	3.57676	+	0.454765i	0.572739	+	0.0728206i
$40$	−0.367788	+	1.13193i	−0.0581523	+	0.178974i
$41$	6.66338	−	2.16506i	1.04064	−	0.338126i	0.261654	−	0.965162i	$-0.415732\pi$
$41$	6.66338	−	2.16506i	1.04064	−	0.338126i	0.778990	+	0.627036i	$0.215732\pi$
$42$	−0.615247	+	0.447003i	−0.0949347	+	0.0689741i
$43$	−3.94872			−0.602175			−0.301087	−	0.953597i	$-0.597350\pi$
$43$	−3.94872			−0.602175			−0.301087	+	0.953597i	$0.597350\pi$
$44$	−4.55083	−	4.52272i	−0.686064	−	0.681825i
$45$			1.18193i			0.176192i
$46$	−0.907072	−	1.24848i	−0.133740	−	0.184078i
$47$	7.79196	−	2.53176i	1.13657	−	0.369295i	0.320503	−	0.947247i	$-0.396148\pi$
$47$	7.79196	−	2.53176i	1.13657	−	0.369295i	0.816071	+	0.577952i	$0.196148\pi$
$48$	1.11594	−	3.43452i	0.161073	−	0.495730i
$49$	1.47982	+	1.07515i	0.211402	+	0.153593i
$50$	0.542026	−	0.746034i	0.0766540	−	0.105505i
$51$	0.622809	−	1.91681i	0.0872107	−	0.268407i
$52$	−5.08067	−	4.77874i	−0.704562	−	0.662692i
$53$	5.23254	−	3.80166i	0.718745	−	0.522199i	−0.167238	−	0.985917i	$-0.553485\pi$
$53$	5.23254	−	3.80166i	0.718745	−	0.522199i	0.885983	+	0.463718i	$0.153485\pi$
$54$			0.255937i			0.0348286i
$55$	−1.79047	−	3.48724i	−0.241427	−	0.470219i
$56$	2.99214			0.399841
$57$	−2.09909	−	2.88915i	−0.278032	−	0.382678i
$58$	−0.465127	+	0.151129i	−0.0610741	+	0.0198442i
$59$	3.67613	+	1.19445i	0.478592	+	0.155504i	0.538371	−	0.842708i	$-0.319040\pi$
$59$	3.67613	+	1.19445i	0.478592	+	0.155504i	−0.0597797	+	0.998212i	$0.519040\pi$
$60$	1.34394	−	1.84977i	0.173502	−	0.238805i
$61$	−1.21460	−	0.882461i	−0.155514	−	0.112988i	0.507307	−	0.861765i	$-0.330641\pi$
$61$	−1.21460	−	0.882461i	−0.155514	−	0.112988i	−0.662821	+	0.748778i	$0.730641\pi$
$62$	−0.310268	+	0.954908i	−0.0394041	+	0.121273i
$63$	2.82596	−	0.918210i	0.356037	−	0.115684i
$64$	−5.23478	+	3.80329i	−0.654347	+	0.475411i
$65$	−2.05001	−	3.73604i	−0.254272	−	0.463399i
$66$	−0.387710	−	0.755130i	−0.0477238	−	0.0929501i
$67$			13.6191i			1.66384i	0.554899	+	0.831918i	$0.312757\pi$
$67$			13.6191i			1.66384i	−0.554899	+	0.831918i	$0.687243\pi$
$68$	−3.15426	+	2.29171i	−0.382511	+	0.277910i
$69$	1.86326	+	5.73452i	0.224310	+	0.690355i
$70$	0.854853	+	0.277758i	0.102174	+	0.0331985i
$71$	−6.82649	+	9.39585i	−0.810155	+	1.11508i	0.181144	+	0.983456i	$0.442020\pi$
$71$	−6.82649	+	9.39585i	−0.810155	+	1.11508i	−0.991299	+	0.131626i	$0.957980\pi$
$72$	0.591889	−	0.814666i	0.0697548	−	0.0960093i
$73$	9.32054	+	3.02843i	1.09089	+	0.354450i	0.798589	−	0.601877i	$-0.205580\pi$
$73$	9.32054	+	3.02843i	1.09089	+	0.354450i	0.292297	+	0.956327i	$0.405580\pi$
$74$	−0.204051	−	0.628003i	−0.0237204	−	0.0730039i
$75$	−2.91492	+	2.11781i	−0.336586	+	0.244544i
$76$			6.90845i			0.792454i
$77$	−6.94690	+	6.99008i	−0.791673	+	0.796594i
$78$	−0.443910	−	0.809006i	−0.0502629	−	0.0916019i
$79$	−6.89827	+	5.01189i	−0.776116	+	0.563881i	−0.903811	−	0.427932i	$-0.859242\pi$
$79$	−6.89827	+	5.01189i	−0.776116	+	0.563881i	0.127695	+	0.991814i	$0.459242\pi$
$80$	−4.05937	+	1.31897i	−0.453852	+	0.147465i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.45070	−	1.05400i	−0.160203	−	0.116394i
$83$	0.175012	−	0.240883i	0.0192101	−	0.0264404i	−0.799304	−	0.600927i	$-0.794798\pi$
$83$	0.175012	−	0.240883i	0.0192101	−	0.0264404i	0.818514	+	0.574487i	$0.194798\pi$
$84$	−5.46681	−	1.77627i	−0.596478	−	0.193807i
$85$	−2.26554	+	0.736118i	−0.245732	+	0.0798432i
$86$	0.594029	+	0.817611i	0.0640558	+	0.0881653i
$87$	1.91087			0.204867
$88$	−0.512234	+	3.30027i	−0.0546043	+	0.351810i
$89$			3.35850i			0.356000i	0.984031	+	0.178000i	$0.0569627\pi$
$89$			3.35850i			0.356000i	−0.984031	+	0.178000i	$0.943037\pi$
$90$	0.244728	−	0.177805i	0.0257966	−	0.0187423i
$91$	−7.34015	+	7.80392i	−0.769457	+	0.818073i
$92$	3.60446	−	11.0934i	0.375791	−	1.15657i
$93$	2.30590	−	3.17381i	0.239111	−	0.329108i
$94$	−1.69641	−	1.23251i	−0.174971	−	0.127124i
$95$	−1.30433	+	4.01432i	−0.133822	+	0.411861i
$96$	−2.79441	+	0.907960i	−0.285204	+	0.0926683i
$97$	7.30845	+	10.0592i	0.742061	+	1.02136i	0.998497	+	0.0547981i	$0.0174515\pi$
$97$	7.30845	+	10.0592i	0.742061	+	1.02136i	−0.256437	+	0.966561i	$0.582548\pi$
$98$		−	0.468147i		−	0.0472900i
$99$	0.528981	+	3.27417i	0.0531646	+	0.329066i
$100$	6.97006			0.697006
$101$	2.49585	−	1.81334i	0.248347	−	0.180435i	−0.456647	−	0.889648i	$-0.650950\pi$
$101$	2.49585	−	1.81334i	0.248347	−	0.180435i	0.704994	+	0.709213i	$0.250950\pi$
$102$	−0.490582	+	0.159400i	−0.0485748	+	0.0157829i
$103$	3.67120	−	11.2988i	0.361734	−	1.11330i	−0.590266	−	0.807208i	$-0.700977\pi$
$103$	3.67120	−	11.2988i	0.361734	−	1.11330i	0.952001	−	0.306095i	$-0.0990227\pi$
$104$	−0.457940	+	3.60173i	−0.0449047	+	0.353179i
$105$	−2.84125	−	2.06429i	−0.277278	−	0.201454i
$106$	−1.57432	−	0.511529i	−0.152912	−	0.0496841i
$107$	5.07114	+	15.6074i	0.490245	+	1.50882i	0.824238	+	0.566244i	$0.191604\pi$
$107$	5.07114	+	15.6074i	0.490245	+	1.50882i	−0.333993	+	0.942576i	$0.608396\pi$
$108$	−1.56504	+	1.13707i	−0.150596	+	0.109414i
$109$		−	6.28756i		−	0.602239i	−0.953586	−	0.301119i	$-0.902640\pi$
$109$		−	6.28756i		−	0.602239i	0.953586	−	0.301119i	$-0.0973603\pi$
$110$	−0.452707	+	0.895335i	−0.0431640	+	0.0853669i
$111$			2.58002i			0.244885i
$112$	6.30722	+	8.68114i	0.595976	+	0.820291i
$113$	−0.452908	−	1.39391i	−0.0426060	−	0.131128i	0.927491	−	0.373846i	$-0.121961\pi$
$113$	−0.452908	−	1.39391i	−0.0426060	−	0.131128i	−0.970097	+	0.242718i	$0.921961\pi$
$114$	−0.282441	+	0.869265i	−0.0264530	+	0.0814141i
$115$	4.18892	−	5.76555i	0.390619	−	0.537641i
$116$	−2.99060	−	2.17280i	−0.277670	−	0.201739i
$117$	0.672772	+	3.54223i	0.0621978	+	0.327479i
$118$	−0.305703	−	0.940857i	−0.0281422	−	0.0866129i
$119$	3.52006	+	4.84495i	0.322684	+	0.444136i
$120$	−1.19019			−0.108649
$121$	−6.52066	−	8.85895i	−0.592787	−	0.805359i
$122$			0.384246i			0.0347880i
$123$	4.11819	+	5.66821i	0.371325	+	0.511085i
$124$	−7.21767	+	2.34516i	−0.648166	+	0.210602i
$125$	9.67054	+	3.14215i	0.864960	+	0.281042i
$126$	−0.615247	−	0.447003i	−0.0548106	−	0.0398222i
$127$	−9.52837	−	6.92277i	−0.845506	−	0.614296i	0.0783971	−	0.996922i	$-0.475020\pi$
$127$	−9.52837	−	6.92277i	−0.845506	−	0.614296i	−0.923903	+	0.382626i	$0.875020\pi$
$128$	7.16382	+	2.32767i	0.633199	+	0.205739i
$129$	−1.22022	−	3.75546i	−0.107435	−	0.330650i
$130$	−0.465180	+	0.986503i	−0.0407990	+	0.0865221i
$131$	−13.3224			−1.16398			−0.581992	−	0.813195i	$-0.697726\pi$
$131$	−13.3224			−1.16398			−0.581992	+	0.813195i	$0.697726\pi$
$132$	2.89508	−	5.72569i	0.251984	−	0.498358i
$133$	10.6114			0.920125
$134$	2.81993	−	2.04880i	0.243605	−	0.176989i
$135$	−1.12409	+	0.365237i	−0.0967458	+	0.0314346i
$136$	1.93019	+	0.627157i	0.165513	+	0.0537783i
$137$	3.74177	−	5.15010i	0.319681	−	0.440003i	−0.618689	−	0.785636i	$-0.712336\pi$
$137$	3.74177	−	5.15010i	0.319681	−	0.440003i	0.938370	+	0.345633i	$0.112336\pi$
$138$	0.907072	−	1.24848i	0.0772151	−	0.106277i
$139$	−1.45954	+	4.49199i	−0.123796	+	0.381006i	−0.993680	−	0.112251i	$-0.964194\pi$
$139$	−1.45954	+	4.49199i	−0.123796	+	0.381006i	0.869884	+	0.493257i	$0.164194\pi$
$140$	2.09944	+	6.46140i	0.177435	+	0.546088i
$141$	4.81569	+	6.62823i	0.405555	+	0.558198i
$142$	2.97243			0.249441
$143$	−7.35098	−	9.43203i	−0.614720	−	0.788746i
$144$	3.61127			0.300939
$145$	−1.32753	−	1.82719i	−0.110245	−	0.151740i
$146$	−0.775085	−	2.38547i	−0.0641465	−	0.197423i
$147$	−0.565239	+	1.73963i	−0.0466202	+	0.143482i
$148$	2.93366	−	4.03783i	0.241145	−	0.331908i
$149$	0.158905	−	0.218714i	0.0130180	−	0.0179177i	−0.802458	−	0.596708i	$-0.796475\pi$
$149$	0.158905	−	0.218714i	0.0130180	−	0.0179177i	0.815476	+	0.578790i	$0.196475\pi$
$150$	0.877016	+	0.284960i	0.0716080	+	0.0232669i
$151$	2.45782	−	0.798595i	0.200015	−	0.0649888i	−0.207296	−	0.978278i	$-0.566466\pi$
$151$	2.45782	−	0.798595i	0.200015	−	0.0649888i	0.407311	+	0.913289i	$0.366466\pi$
$152$	2.90933	−	2.11375i	0.235978	−	0.171448i
$153$	2.01545			0.162940
$154$	2.49241	+	0.386847i	0.200844	+	0.0311730i
$155$	−4.63677			−0.372434
$156$	2.97484	−	6.30872i	0.238178	−	0.505102i
$157$	5.30070	+	16.3139i	0.423042	+	1.30199i	0.904857	+	0.425716i	$0.139978\pi$
$157$	5.30070	+	16.3139i	0.423042	+	1.30199i	−0.481815	+	0.876273i	$0.660022\pi$
$158$	2.07549	+	0.674369i	0.165117	+	0.0536499i
$159$	5.23254	+	3.80166i	0.414967	+	0.301492i
$160$	2.80954	+	2.04125i	0.222113	+	0.161375i
$161$	−17.0395	−	5.53646i	−1.34290	−	0.436334i
$162$	−0.243410	+	0.0790888i	−0.0191241	+	0.00621380i
$163$	−13.2822	−	18.2814i	−1.04034	−	1.43191i	−0.896890	−	0.442254i	$-0.854179\pi$
$163$	−13.2822	−	18.2814i	−1.04034	−	1.43191i	−0.143454	−	0.989657i	$-0.545821\pi$
$164$		−	13.5536i		−	1.05836i
$165$	2.76328	−	2.78045i	0.215121	−	0.216458i
$166$	−0.0762047			−0.00591463
$167$	14.6083	+	20.1066i	1.13043	+	1.55590i	0.787258	+	0.616623i	$0.211500\pi$
$167$	14.6083	+	20.1066i	1.13043	+	1.55590i	0.343168	+	0.939274i	$0.388500\pi$
$168$	0.924621	+	2.84569i	0.0713360	+	0.219550i
$169$	−8.27043	−	10.0300i	−0.636187	−	0.771535i
$170$	0.493237	+	0.358357i	0.0378295	+	0.0274848i
$171$	2.09909	−	2.88915i	0.160522	−	0.220939i
$172$	−2.36052	+	7.26492i	−0.179988	+	0.553945i
$173$	6.32948	+	19.4801i	0.481221	+	1.48105i	0.837380	+	0.546622i	$0.184086\pi$
$173$	6.32948	+	19.4801i	0.481221	+	1.48105i	−0.356158	+	0.934426i	$0.615914\pi$
$174$	−0.287464	−	0.395660i	−0.0217926	−	0.0299949i
$175$		−	10.7060i		−	0.809299i
$176$	−10.6549	+	5.47058i	−0.803142	+	0.412361i
$177$			3.86531i			0.290535i
$178$	0.695401	−	0.505238i	0.0521225	−	0.0378692i
$179$	−4.02167	−	12.3774i	−0.300593	−	0.925131i	−0.981285	−	0.192561i	$-0.938321\pi$
$179$	−4.02167	−	12.3774i	−0.300593	−	0.925131i	0.680692	−	0.732570i	$-0.261679\pi$
$180$	2.17454	+	0.706550i	0.162081	+	0.0526632i
$181$	8.49163	+	6.16953i	0.631178	+	0.458577i	0.856808	−	0.515636i	$-0.172444\pi$
$181$	8.49163	+	6.16953i	0.631178	+	0.458577i	−0.225630	+	0.974213i	$0.572444\pi$
$182$	2.72008	+	0.345843i	0.201626	+	0.0256356i
$183$	0.463937	−	1.42785i	0.0342952	−	0.105550i
$184$	−5.77456	+	1.87627i	−0.425706	+	0.138320i
$185$	2.46702	−	1.79240i	0.181379	−	0.131780i
$186$	−1.00405			−0.0736205
$187$	−5.94650	+	3.05314i	−0.434851	+	0.223267i
$188$		−	15.8492i		−	1.15592i
$189$	1.74654	+	2.40390i	0.127042	+	0.174858i
$190$	1.02741	−	0.333827i	0.0745363	−	0.0242183i
$191$	5.02810	−	15.4749i	0.363821	−	1.11973i	−0.586895	−	0.809663i	$-0.699650\pi$
$191$	5.02810	−	15.4749i	0.363821	−	1.11973i	0.950716	−	0.310062i	$-0.100350\pi$
$192$	−5.23478	−	3.80329i	−0.377787	−	0.274479i
$193$	12.1917	−	16.7805i	0.877580	−	1.20788i	−0.0995058	−	0.995037i	$-0.531726\pi$
$193$	12.1917	−	16.7805i	0.877580	−	1.20788i	0.977085	−	0.212848i	$-0.0682738\pi$
$194$	0.983381	−	3.02653i	0.0706026	−	0.217293i
$195$	2.91970	−	3.10417i	0.209084	−	0.222294i
$196$	2.86270	−	2.07987i	0.204478	−	0.148562i
$197$		−	2.52850i		−	0.180148i	−0.995935	−	0.0900741i	$-0.971290\pi$
$197$		−	2.52850i		−	0.180148i	0.995935	−	0.0900741i	$-0.0287104\pi$
$198$	0.598362	−	0.602082i	0.0425238	−	0.0427881i
$199$	1.72579			0.122338			0.0611692	−	0.998127i	$-0.480517\pi$
$199$	1.72579			0.122338			0.0611692	+	0.998127i	$0.480517\pi$
$200$	−2.13260	−	2.93527i	−0.150797	−	0.207555i
$201$	−12.9525	+	4.20853i	−0.913600	+	0.296847i
$202$	−0.750932	−	0.243993i	−0.0528354	−	0.0171673i
$203$	−3.33742	+	4.59356i	−0.234241	+	0.322405i
$204$	−3.15426	−	2.29171i	−0.220843	−	0.160452i
$205$	2.55896	−	7.87566i	0.178725	−	0.550060i
$206$	−2.89178	+	0.939596i	−0.201480	+	0.0654647i
$207$	−4.87807	+	3.54413i	−0.339049	+	0.246334i
$208$	−11.4151	+	6.26357i	−0.791493	+	0.434301i
$209$	−1.81660	+	11.7042i	−0.125657	+	0.809594i
$210$			0.898845i			0.0620262i
$211$	12.8339	−	9.32437i	0.883522	−	0.641916i	−0.0506588	−	0.998716i	$-0.516132\pi$
$211$	12.8339	−	9.32437i	0.883522	−	0.641916i	0.934181	+	0.356800i	$0.116132\pi$
$212$	−3.86639	−	11.8995i	−0.265545	−	0.817262i
$213$	−11.0455	−	3.58890i	−0.756824	−	0.245907i
$214$	2.46873	−	3.39792i	0.168759	−	0.232277i
$215$	−2.74327	+	3.77578i	−0.187089	+	0.257506i
$216$	0.957697	+	0.311175i	0.0651630	+	0.0211728i
$217$	3.60217	+	11.0863i	0.244531	+	0.752590i
$218$	−1.30188	+	0.945874i	−0.0881747	+	0.0640627i
$219$			9.80019i			0.662236i
$220$	−7.48621	+	1.20949i	−0.504720	+	0.0815436i
$221$	−6.37076	+	3.49570i	−0.428544	+	0.235147i
$222$	0.534211	−	0.388127i	0.0358539	−	0.0260494i
$223$	8.45494	−	2.74718i	0.566185	−	0.183965i	−0.0119174	−	0.999929i	$-0.503794\pi$
$223$	8.45494	−	2.74718i	0.566185	−	0.183965i	0.578102	+	0.815964i	$0.303794\pi$
$224$	2.69790	−	8.30329i	0.180261	−	0.554787i
$225$	−2.91492	−	2.11781i	−0.194328	−	0.141187i
$226$	−0.220485	+	0.303472i	−0.0146665	+	0.0201866i
$227$	−13.0727	−	4.24757i	−0.867664	−	0.281921i	−0.158838	−	0.987305i	$-0.550775\pi$
$227$	−13.0727	−	4.24757i	−0.867664	−	0.281921i	−0.708826	+	0.705384i	$0.750775\pi$
$228$	−6.57033	+	2.13483i	−0.435131	+	0.141383i
$229$	−6.18911	−	8.51857i	−0.408988	−	0.562923i	0.553983	−	0.832528i	$-0.313107\pi$
$229$	−6.18911	−	8.51857i	−0.408988	−	0.562923i	−0.962971	+	0.269604i	$0.913107\pi$
$230$	−1.82396			−0.120269
$231$	−8.79467	−	4.44684i	−0.578647	−	0.292581i
$232$			1.92422i			0.126331i
$233$	9.57648	−	6.95772i	0.627376	−	0.455815i	−0.228114	−	0.973634i	$-0.573256\pi$
$233$	9.57648	−	6.95772i	0.627376	−	0.455815i	0.855490	+	0.517819i	$0.173256\pi$
$234$	0.632235	−	0.672180i	0.0413305	−	0.0439418i
$235$	2.99237	−	9.20957i	0.195201	−	0.600766i
$236$	4.39513	−	6.04937i	0.286098	−	0.393781i
$237$	−6.89827	−	5.01189i	−0.448091	−	0.325557i
$238$	0.473638	−	1.45771i	0.0307014	−	0.0944892i
$239$	−26.6714	+	8.66606i	−1.72523	+	0.560561i	−0.992747	−	0.120226i	$-0.961638\pi$
$239$	−26.6714	+	8.66606i	−1.72523	+	0.560561i	−0.732482	+	0.680787i	$0.761638\pi$
$240$	−2.50883	−	3.45311i	−0.161944	−	0.222897i
$241$		−	25.9815i		−	1.67362i	−0.547495	−	0.836809i	$-0.684419\pi$
$241$		−	25.9815i		−	1.67362i	0.547495	−	0.836809i	$-0.315581\pi$
$242$	−0.853369	+	2.68285i	−0.0548566	+	0.172460i
$243$	1.00000			0.0641500
$244$	−2.34965	+	1.70712i	−0.150421	+	0.109287i
$245$	2.05612	−	0.668075i	0.131361	−	0.0426817i
$246$	0.554119	−	1.70540i	0.0353293	−	0.108733i
$247$	−1.62405	+	12.7733i	−0.103336	+	0.812744i
$248$	3.19597	+	2.32200i	0.202944	+	0.147447i
$249$	0.283175	+	0.0920092i	0.0179455	+	0.00583085i
$250$	−0.804192	−	2.47505i	−0.0508615	−	0.156536i
$251$	15.7869	−	11.4699i	0.996460	−	0.723971i	0.0351338	−	0.999383i	$-0.488814\pi$
$251$	15.7869	−	11.4699i	0.996460	−	0.723971i	0.961326	+	0.275412i	$0.0888143\pi$
$252$		−	5.74814i		−	0.362099i
$253$	9.02366	−	17.8464i	0.567312	−	1.12199i
$254$			3.01435i			0.189137i
$255$	−1.40018	−	1.92718i	−0.0876827	−	0.120685i
$256$	3.40328	+	10.4742i	0.212705	+	0.654638i
$257$	2.64756	−	8.14835i	0.165150	−	0.508280i	−0.833897	−	0.551920i	$-0.813895\pi$
$257$	2.64756	−	8.14835i	0.165150	−	0.508280i	0.999047	+	0.0436399i	$0.0138954\pi$
$258$	−0.594029	+	0.817611i	−0.0369827	+	0.0509023i
$259$	−6.20212	−	4.50610i	−0.385381	−	0.279996i
$260$	−8.09911	+	1.53826i	−0.502285	+	0.0953986i
$261$	0.590493	+	1.81735i	0.0365506	+	0.112491i
$262$	2.00417	+	2.75850i	0.123818	+	0.170421i
$263$	−11.7180			−0.722562			−0.361281	−	0.932457i	$-0.617660\pi$
$263$	−11.7180			−0.722562			−0.361281	+	0.932457i	$0.617660\pi$
$264$	−3.29703	+	0.532675i	−0.202918	+	0.0327839i
$265$		−	7.64448i		−	0.469597i
$266$	−1.59633	−	2.19717i	−0.0978775	−	0.134717i
$267$	−3.19412	+	1.03783i	−0.195477	+	0.0635143i
$268$	25.0566	+	8.14138i	1.53058	+	0.497314i
$269$	18.2871	+	13.2864i	1.11498	+	0.810084i	0.983441	−	0.181227i	$-0.0580068\pi$
$269$	18.2871	+	13.2864i	1.11498	+	0.810084i	0.131543	+	0.991310i	$0.458007\pi$
$270$	0.244728	+	0.177805i	0.0148937	+	0.0108209i
$271$	2.95337	+	0.959607i	0.179404	+	0.0582920i	0.397342	−	0.917671i	$-0.369933\pi$
$271$	2.95337	+	0.959607i	0.179404	+	0.0582920i	−0.217937	+	0.975963i	$0.569933\pi$
$272$	2.24913	+	6.92211i	0.136374	+	0.419715i
$273$	−9.69020	−	4.56936i	−0.586477	−	0.276550i
$274$	−1.62926			−0.0984272
$275$	11.8085	+	1.83280i	0.712081	+	0.110522i
$276$	11.6643			0.702108
$277$	9.50141	−	6.90318i	0.570885	−	0.414772i	−0.264542	−	0.964374i	$-0.585221\pi$
$277$	9.50141	−	6.90318i	0.570885	−	0.414772i	0.835426	+	0.549602i	$0.185221\pi$
$278$	1.14967	−	0.373549i	0.0689523	−	0.0224040i
$279$	3.73103	+	1.21229i	0.223371	+	0.0725777i
$280$	2.07870	−	2.86109i	0.124226	−	0.170983i
$281$	−5.98922	+	8.24346i	−0.357287	+	0.491764i	−0.949390	−	0.314099i	$-0.898298\pi$
$281$	−5.98922	+	8.24346i	−0.357287	+	0.491764i	0.592103	+	0.805862i	$0.298298\pi$
$282$	0.647971	−	1.99425i	0.0385861	−	0.118756i
$283$	3.84091	+	11.8211i	0.228318	+	0.702692i	0.997938	+	0.0641888i	$0.0204460\pi$
$283$	3.84091	+	11.8211i	0.228318	+	0.702692i	−0.769619	+	0.638503i	$0.779554\pi$
$284$	13.2058	+	18.1762i	0.783621	+	1.07856i
$285$	−4.22091			−0.250025
$286$	−0.847118	+	2.94099i	−0.0500911	+	0.173904i
$287$	−20.8184			−1.22887
$288$	−1.72704	−	2.37707i	−0.101767	−	0.140070i
$289$	−3.99805	−	12.3047i	−0.235179	−	0.723808i
$290$	−0.178624	+	0.549748i	−0.0104892	+	0.0322823i
$291$	−7.30845	+	10.0592i	−0.428429	+	0.589682i
$292$	11.1435	−	15.3377i	0.652123	−	0.897571i
$293$	−2.76376	−	0.898001i	−0.161461	−	0.0524618i	0.227171	−	0.973855i	$-0.427052\pi$
$293$	−2.76376	−	0.898001i	−0.161461	−	0.0524618i	−0.388632	+	0.921393i	$0.627052\pi$
$294$	0.445235	−	0.144666i	0.0259666	−	0.00843706i
$295$	3.69603	−	2.68532i	0.215191	−	0.156345i
$296$	−2.59803			−0.151008
$297$	−2.95045	+	1.51486i	−0.171203	+	0.0879014i
$298$	−0.0691912			−0.00400814
$299$	9.27227	−	19.6636i	0.536229	−	1.13718i
$300$	2.15387	+	6.62892i	0.124354	+	0.382721i
$301$	11.1589	+	3.62576i	0.643190	+	0.208985i
$302$	−0.535100	−	0.388773i	−0.0307915	−	0.0223714i
$303$	2.49585	+	1.81334i	0.143383	+	0.104174i
$304$	12.2653	+	3.98525i	0.703465	+	0.228570i
$305$	−1.68763	+	0.548343i	−0.0966331	+	0.0313980i
$306$	−0.303196	−	0.417314i	−0.0173326	−	0.0238562i
$307$			19.7265i			1.12585i	0.826508	+	0.562925i	$0.190324\pi$
$307$			19.7265i			1.12585i	−0.826508	+	0.562925i	$0.809676\pi$
$308$	8.70766	+	16.9596i	0.496165	+	0.966365i
$309$	11.8803			0.675845
$310$	0.697536	+	0.960076i	0.0396174	+	0.0545287i
$311$	−1.54130	−	4.74364i	−0.0873993	−	0.268987i	0.897799	−	0.440405i	$-0.145165\pi$
$311$	−1.54130	−	4.74364i	−0.0873993	−	0.268987i	−0.985198	+	0.171418i	$0.945165\pi$
$312$	−3.56696	+	0.677469i	−0.201939	+	0.0383541i
$313$	11.3359	+	8.23599i	0.640741	+	0.465526i	0.860105	−	0.510117i	$-0.170398\pi$
$313$	11.3359	+	8.23599i	0.640741	+	0.465526i	−0.219363	+	0.975643i	$0.570398\pi$
$314$	2.58049	−	3.55174i	0.145625	−	0.200436i
$315$	1.08526	−	3.34009i	0.0611476	−	0.188193i
$316$	5.09722	+	15.6876i	0.286741	+	0.882497i
$317$	−11.8658	−	16.3319i	−0.666450	−	0.917290i	0.333223	−	0.942848i	$-0.391864\pi$
$317$	−11.8658	−	16.3319i	−0.666450	−	0.917290i	−0.999673	+	0.0255583i	$0.991864\pi$
$318$		−	1.65534i		−	0.0928269i
$319$	−4.49526	−	4.46749i	−0.251686	−	0.250132i
$320$			7.64774i			0.427522i
$321$	−13.2764	+	9.64587i	−0.741017	+	0.538380i
$322$	1.41698	+	4.36103i	0.0789654	+	0.243031i
$323$	6.84529	+	2.22417i	0.380882	+	0.123756i
$324$	−1.56504	−	1.13707i	−0.0869467	−	0.0631705i
$325$	12.8872	+	1.63853i	0.714852	+	0.0908894i
$326$	−1.78718	+	5.50036i	−0.0989825	+	0.304637i
$327$	5.97982	−	1.94296i	0.330685	−	0.107446i
$328$	−5.70778	+	4.14695i	−0.315160	+	0.228977i
$329$	−24.3444			−1.34215
$330$	−0.991409	−	0.153876i	−0.0545753	−	0.00847062i
$331$		−	7.40043i		−	0.406764i	−0.979099	−	0.203382i	$-0.934807\pi$
$331$		−	7.40043i		−	0.406764i	0.979099	−	0.203382i	$-0.0651934\pi$
$332$	−0.338560	−	0.465988i	−0.0185809	−	0.0255744i
$333$	−2.45374	+	0.797270i	−0.134464	+	0.0436901i
$334$	1.96561	−	6.04952i	0.107553	−	0.331015i
$335$	13.0226	+	9.46149i	0.711502	+	0.516936i
$336$	−6.30722	+	8.68114i	−0.344087	+	0.473595i
$337$	0.114298	−	0.351774i	0.00622623	−	0.0191624i	−0.947895	−	0.318582i	$-0.896793\pi$
$337$	0.114298	−	0.351774i	0.00622623	−	0.0191624i	0.954121	+	0.299420i	$0.0967932\pi$
$338$	−0.832604	+	3.22132i	−0.0452877	+	0.175217i
$339$	1.18573	−	0.861483i	0.0644000	−	0.0467893i
$340$			4.60822i			0.249916i
$341$	−12.8447	+	2.07521i	−0.695579	+	0.112379i
$342$	−0.913999			−0.0494234
$343$	9.03108	+	12.4302i	0.487633	+	0.671169i
$344$	3.78168	−	1.22874i	0.203895	−	0.0662493i
$345$	6.77781	+	2.20225i	0.364905	+	0.118565i
$346$	3.08132	−	4.24107i	0.165653	−	0.228002i
$347$	−27.9264	−	20.2897i	−1.49917	−	1.08921i	−0.970712	−	0.240247i	$-0.922772\pi$
$347$	−27.9264	−	20.2897i	−1.49917	−	1.08921i	−0.528455	−	0.848961i	$-0.677228\pi$
$348$	1.14231	−	3.51566i	0.0612340	−	0.188459i
$349$	13.7141	−	4.45597i	0.734097	−	0.238522i	0.0819724	−	0.996635i	$-0.473878\pi$
$349$	13.7141	−	4.45597i	0.734097	−	0.238522i	0.652124	+	0.758112i	$0.273878\pi$
$350$	−2.21676	+	1.61057i	−0.118491	+	0.0860885i
$351$	−3.16096	+	1.73445i	−0.168720	+	0.0925782i
$352$	8.69650	+	4.39720i	0.463525	+	0.234372i
$353$		−	32.9689i		−	1.75476i	−0.479798	−	0.877379i	$-0.659290\pi$
$353$		−	32.9689i		−	1.75476i	0.479798	−	0.877379i	$-0.340710\pi$
$354$	0.800341	−	0.581482i	0.0425376	−	0.0309054i
$355$	4.24184	+	13.0550i	0.225133	+	0.692889i
$356$	6.17901	+	2.00768i	0.327487	+	0.106407i
$357$	−3.52006	+	4.84495i	−0.186302	+	0.256422i
$358$	−1.95783	+	2.69472i	−0.103475	+	0.142420i
$359$	32.7504	+	10.6413i	1.72850	+	0.561624i	0.993232	−	0.116150i	$-0.0370555\pi$
$359$	32.7504	+	10.6413i	1.72850	+	0.561624i	0.735270	+	0.677775i	$0.237055\pi$
$360$	−0.367788	−	1.13193i	−0.0193841	−	0.0596581i
$361$	−5.05361	+	3.67166i	−0.265979	+	0.193245i
$362$		−	2.68637i		−	0.141193i
$363$	6.41037	−	8.93908i	0.336457	−	0.469180i
$364$	9.96988	+	18.1697i	0.522564	+	0.952348i
$365$	9.37098	−	6.80842i	0.490500	−	0.356369i
$366$	−0.365440	+	0.118739i	−0.0191018	+	0.00620656i
$367$	−6.17442	+	19.0029i	−0.322302	+	0.991944i	0.650341	+	0.759642i	$0.274626\pi$
$367$	−6.17442	+	19.0029i	−0.322302	+	0.991944i	−0.972644	+	0.232302i	$0.925374\pi$
$368$	−17.6160	−	12.7988i	−0.918299	−	0.667183i
$369$	−4.11819	+	5.66821i	−0.214385	+	0.295075i
$370$	−0.742258	−	0.241174i	−0.0385881	−	0.0125380i
$371$	−18.2777	+	5.93877i	−0.948929	+	0.308326i
$372$	−4.46076	−	6.13972i	−0.231280	−	0.318329i
$373$	−22.1571			−1.14725			−0.573626	−	0.819117i	$-0.694464\pi$
$373$	−22.1571			−1.14725			−0.573626	+	0.819117i	$0.694464\pi$
$374$	1.52674	+	0.771964i	0.0789459	+	0.0399173i
$375$			10.1682i			0.525084i
$376$	−6.67451	+	4.84932i	−0.344212	+	0.250085i
$377$	−5.01863	−	4.72039i	−0.258473	−	0.243112i
$378$	0.235004	−	0.723267i	0.0120873	−	0.0372008i
$379$	−12.9435	+	17.8152i	−0.664863	+	0.915106i	−0.999630	−	0.0271953i	$-0.991342\pi$
$379$	−12.9435	+	17.8152i	−0.664863	+	0.915106i	0.334767	+	0.942301i	$0.391342\pi$
$380$	6.60589	+	4.79946i	0.338875	+	0.246207i
$381$	3.63951	−	11.2013i	0.186458	−	0.573859i
$382$	−3.96060	+	1.28688i	−0.202642	+	0.0658423i
$383$	14.4553	+	19.8960i	0.738629	+	1.01664i	0.998696	+	0.0510453i	$0.0162553\pi$
$383$	14.4553	+	19.8960i	0.738629	+	1.01664i	−0.260067	+	0.965591i	$0.583745\pi$
$384$			7.53249i			0.384391i
$385$	1.85777	+	11.4988i	0.0946809	+	0.586034i
$386$	−5.30859			−0.270200
$387$	3.19458	−	2.32100i	0.162390	−	0.117983i
$388$	22.8760	−	7.43288i	1.16136	−	0.377347i
$389$	−1.19439	+	3.67595i	−0.0605579	+	0.186378i	−0.976759	−	0.214341i	$-0.931240\pi$
$389$	−1.19439	+	3.67595i	−0.0605579	+	0.186378i	0.916201	+	0.400719i	$0.131240\pi$
$390$	−1.08197	−	0.137566i	−0.0547876	−	0.00696594i
$391$	−9.83152	−	7.14301i	−0.497201	−	0.361238i
$392$	−1.75177	−	0.569186i	−0.0884780	−	0.0287482i
$393$	−4.11685	−	12.6704i	−0.207668	−	0.639135i
$394$	−0.523544	+	0.380377i	−0.0263758	+	0.0191631i
$395$			10.0780i			0.507081i
$396$	6.34009	+	0.984044i	0.318601	+	0.0494501i
$397$		−	19.9974i		−	1.00364i	−0.864971	−	0.501821i	$-0.832664\pi$
$397$		−	19.9974i		−	1.00364i	0.864971	−	0.501821i	$-0.167336\pi$
$398$	−0.259621	−	0.357338i	−0.0130136	−	0.0179117i
$399$	3.27910	+	10.0920i	0.164160	+	0.505234i
$400$	4.02078	−	12.3747i	0.201039	−	0.618735i
$401$	−22.2653	+	30.6456i	−1.11188	+	1.53037i	−0.293253	+	0.956035i	$0.594738\pi$
$401$	−22.2653	+	30.6456i	−1.11188	+	1.53037i	−0.818623	+	0.574332i	$0.805262\pi$
$402$	2.81993	+	2.04880i	0.140645	+	0.102185i
$403$	−13.8963	+	2.63931i	−0.692224	+	0.131473i
$404$	−1.84422	−	5.67592i	−0.0917532	−	0.282387i
$405$	−0.694723	−	0.956204i	−0.0345211	−	0.0475142i
$406$	1.45320			0.0721209
$407$	6.03190	−	6.06940i	0.298990	−	0.300849i
$408$			2.02952i			0.100476i
$409$	−10.0609	−	13.8476i	−0.497479	−	0.684720i	0.484267	−	0.874920i	$-0.339086\pi$
$409$	−10.0609	−	13.8476i	−0.497479	−	0.684720i	−0.981745	+	0.190200i	$0.939086\pi$
$410$	−2.01567	+	0.654931i	−0.0995469	+	0.0323448i
$411$	6.05430	+	1.96716i	0.298637	+	0.0970330i
$412$	−18.5931	−	13.5087i	−0.916016	−	0.665524i
$413$	−9.29184	−	6.75092i	−0.457222	−	0.332191i
$414$	1.46767	+	0.476876i	0.0721322	+	0.0234372i
$415$	−0.108749	−	0.334694i	−0.00533827	−	0.0164295i
$416$	9.58203	+	4.51835i	0.469798	+	0.221531i
$417$	−4.72316			−0.231294
$418$	2.69671	−	1.38458i	0.131901	−	0.0677223i
$419$	−32.2987			−1.57790			−0.788948	−	0.614459i	$-0.789374\pi$
$419$	−32.2987			−1.57790			−0.788948	+	0.614459i	$0.789374\pi$
$420$	−5.49639	+	3.99336i	−0.268197	+	0.194856i
$421$	−13.4491	+	4.36988i	−0.655469	+	0.212975i	−0.617824	−	0.786316i	$-0.711986\pi$
$421$	−13.4491	+	4.36988i	−0.655469	+	0.212975i	−0.0376451	+	0.999291i	$0.511986\pi$
$422$	−3.86136	−	1.25463i	−0.187968	−	0.0610745i
$423$	−4.81569	+	6.62823i	−0.234147	+	0.322276i
$424$	−3.82821	+	5.26908i	−0.185914	+	0.255889i
$425$	2.24400	−	6.90633i	0.108850	−	0.335006i
$426$	0.918530	+	2.82695i	0.0445029	+	0.136966i
$427$	2.62213	+	3.60906i	0.126894	+	0.174655i
$428$	31.7461			1.53451
$429$	6.69881	−	9.90585i	0.323422	−	0.478259i
$430$	1.19449			0.0576034
$431$	6.64913	+	9.15174i	0.320277	+	0.440824i	0.938552	−	0.345138i	$-0.112168\pi$
$431$	6.64913	+	9.15174i	0.320277	+	0.440824i	−0.618274	+	0.785962i	$0.712168\pi$
$432$	1.11594	+	3.43452i	0.0536909	+	0.165243i
$433$	−9.58536	+	29.5007i	−0.460643	+	1.41771i	0.403737	+	0.914875i	$0.367711\pi$
$433$	−9.58536	+	29.5007i	−0.460643	+	1.41771i	−0.864380	+	0.502839i	$0.832289\pi$
$434$	1.75361	−	2.41364i	0.0841761	−	0.115858i
$435$	1.32753	−	1.82719i	0.0636501	−	0.0876068i
$436$	−11.5679	−	3.75865i	−0.554004	−	0.180007i
$437$	−20.4791	+	6.65405i	−0.979646	+	0.318306i
$438$	2.02920	−	1.47430i	0.0969589	−	0.0704448i
$439$	8.50046			0.405705			0.202853	−	0.979209i	$-0.434979\pi$
$439$	8.50046			0.405705			0.202853	+	0.979209i	$0.434979\pi$
$440$	2.79987	+	2.78257i	0.133478	+	0.132654i
$441$	−1.82915			−0.0871025
$442$	1.68220	+	0.793233i	0.0800142	+	0.0377302i
$443$	3.25739	+	10.0252i	0.154763	+	0.476313i	0.998137	−	0.0610150i	$-0.0194338\pi$
$443$	3.25739	+	10.0252i	0.154763	+	0.476313i	−0.843373	+	0.537328i	$0.819434\pi$
$444$	4.74676	+	1.54232i	0.225271	+	0.0731950i
$445$	3.21141	+	2.33322i	0.152235	+	0.110605i
$446$	−1.84075	−	1.33738i	−0.0871620	−	0.0633269i
$447$	0.257113	+	0.0835411i	0.0121610	+	0.00395136i
$448$	18.2855	−	5.94131i	0.863908	−	0.280701i
$449$	11.0494	+	15.2082i	0.521454	+	0.717719i	0.985798	−	0.167935i	$-0.0537100\pi$
$449$	11.0494	+	15.2082i	0.521454	+	0.717719i	−0.464344	+	0.885655i	$0.653710\pi$
$450$			0.922149i			0.0434705i
$451$	3.56398	−	22.9623i	0.167821	−	1.08125i
$452$	−2.83528			−0.133360
$453$	1.51902	+	2.09075i	0.0713697	+	0.0982320i
$454$	1.08711	+	3.34578i	0.0510206	+	0.157025i
$455$	2.36276	+	12.4402i	0.110768	+	0.583208i
$456$	2.90933	+	2.11375i	0.136242	+	0.0989854i
$457$	−15.7526	+	21.6816i	−0.736875	+	1.01422i	0.261918	+	0.965090i	$0.415645\pi$
$457$	−15.7526	+	21.6816i	−0.736875	+	1.01422i	−0.998792	+	0.0491309i	$0.984355\pi$
$458$	−0.832768	+	2.56300i	−0.0389127	+	0.119761i
$459$	0.622809	+	1.91681i	0.0290702	+	0.0894689i
$460$	−8.10345	−	11.1534i	−0.377825	−	0.520032i
$461$			8.61004i			0.401010i	0.979693	+	0.200505i	$0.0642582\pi$
$461$			8.61004i			0.401010i	−0.979693	+	0.200505i	$0.935742\pi$
$462$	0.402284	+	2.48996i	0.0187159	+	0.115844i
$463$			36.9468i			1.71706i	0.512762	+	0.858531i	$0.328622\pi$
$463$			36.9468i			1.71706i	−0.512762	+	0.858531i	$0.671378\pi$
$464$	−5.58277	+	4.05612i	−0.259174	+	0.188301i
$465$	−1.43284	−	4.40983i	−0.0664464	−	0.204501i
$466$	−2.88129	−	0.936189i	−0.133473	−	0.0433681i
$467$	11.4195	+	8.29677i	0.528433	+	0.383929i	0.819771	−	0.572691i	$-0.194101\pi$
$467$	11.4195	+	8.29677i	0.528433	+	0.383929i	−0.291338	+	0.956620i	$0.594101\pi$
$468$	6.91922	+	0.879741i	0.319841	+	0.0406660i
$469$	12.5052	−	38.4870i	0.577435	−	1.77716i
$470$	−2.35707	+	0.765858i	−0.108723	+	0.0353264i
$471$	−13.8774	+	10.0825i	−0.639437	+	0.464578i
$472$	−3.89230			−0.179158
$473$	−5.90947	+	11.6874i	−0.271718	+	0.537386i
$474$			2.18230i			0.100237i
$475$	−7.56310	−	10.4097i	−0.347019	−	0.477631i
$476$	11.0181	−	3.57999i	0.505013	−	0.164089i
$477$	−1.99865	+	6.15122i	−0.0915120	+	0.281645i
$478$	5.80670	+	4.21882i	0.265592	+	0.192964i
$479$	23.3871	−	32.1896i	1.06858	−	1.47078i	0.197084	−	0.980387i	$-0.436853\pi$
$479$	23.3871	−	32.1896i	1.06858	−	1.47078i	0.871501	−	0.490394i	$-0.163147\pi$
$480$	−1.07315	+	3.30281i	−0.0489823	+	0.150752i
$481$	6.37336	−	6.77604i	0.290600	−	0.308961i
$482$	−5.37966	+	3.90855i	−0.245037	+	0.178030i
$483$		−	17.9164i		−	0.815223i
$484$	−20.1968	+	6.70100i	−0.918038	+	0.304591i
$485$	14.6960			0.667312
$486$	−0.150436	−	0.207057i	−0.00682391	−	0.00939230i
$487$	−11.1151	+	3.61152i	−0.503674	+	0.163653i	−0.549823	−	0.835281i	$-0.685305\pi$
$487$	−11.1151	+	3.61152i	−0.503674	+	0.163653i	0.0461496	+	0.998935i	$0.485305\pi$
$488$	1.43782	+	0.467177i	0.0650871	+	0.0211481i
$489$	13.2822	−	18.2814i	0.600643	−	0.826714i
$490$	−0.447644	−	0.325233i	−0.0202225	−	0.0146925i
$491$	−12.3999	+	38.1631i	−0.559601	+	1.72228i	0.123871	+	0.992298i	$0.460469\pi$
$491$	−12.3999	+	38.1631i	−0.559601	+	1.72228i	−0.683472	+	0.729977i	$0.739531\pi$
$492$	12.8903	−	4.18831i	0.581139	−	0.188823i
$493$	−3.11575	+	2.26372i	−0.140326	+	0.101953i
$494$	2.88911	−	1.58529i	0.129987	−	0.0713255i
$495$	3.49827	+	1.76883i	0.157235	+	0.0795028i
$496$			14.1672i			0.636124i
$497$	27.9187	−	20.2841i	1.25233	−	0.909868i
$498$	−0.0235485	−	0.0724750i	−0.00105524	−	0.00324768i
$499$	−37.1451	−	12.0692i	−1.66284	−	0.540290i	−0.681377	−	0.731933i	$-0.738618\pi$
$499$	−37.1451	−	12.0692i	−1.66284	−	0.540290i	−0.981465	+	0.191643i	$0.938618\pi$
$500$	11.5620	−	15.9137i	0.517066	−	0.711681i
$501$	−14.6083	+	20.1066i	−0.652652	+	0.898298i
$502$	−4.74983	−	1.54331i	−0.211995	−	0.0688815i
$503$	3.51313	+	10.8123i	0.156643	+	0.482097i	0.998324	−	0.0578782i	$-0.0184335\pi$
$503$	3.51313	+	10.8123i	0.156643	+	0.482097i	−0.841681	+	0.539975i	$0.818434\pi$
$504$	−2.42069	+	1.75873i	−0.107826	+	0.0783402i
$505$		−	3.64632i		−	0.162259i
$506$	−5.05271	+	0.816326i	−0.224620	+	0.0362901i
$507$	6.98335	−	10.9651i	0.310141	−	0.486976i
$508$	−18.4326	+	13.3921i	−0.817814	+	0.594177i
$509$	4.96183	−	1.61220i	0.219929	−	0.0714593i	−0.196980	−	0.980408i	$-0.563113\pi$
$509$	4.96183	−	1.61220i	0.219929	−	0.0714593i	0.416909	+	0.908948i	$0.363113\pi$
$510$	−0.188400	+	0.579835i	−0.00834248	+	0.0256755i
$511$	−23.5587	−	17.1164i	−1.04218	−	0.757186i
$512$	10.5118	−	14.4682i	0.464559	−	0.639410i
$513$	3.39640	+	1.10356i	0.149955	+	0.0487233i
$514$	−2.08546	+	0.677608i	−0.0919858	+	0.0298880i
$515$	−8.25349	−	11.3600i	−0.363692	−	0.500579i
$516$	−7.63879			−0.336279
$517$	4.16761	−	26.8514i	0.183291	−	1.18092i
$518$			1.96207i			0.0862085i
$519$	−16.5708	+	12.0394i	−0.727377	+	0.528470i
$520$	3.12585	+	2.94009i	0.137077	+	0.128931i
$521$	4.20722	−	12.9485i	0.184322	−	0.567283i	−0.815614	−	0.578596i	$-0.803601\pi$
$521$	4.20722	−	12.9485i	0.184322	−	0.567283i	0.999936	+	0.0113124i	$0.00360091\pi$
$522$	0.287464	−	0.395660i	0.0125820	−	0.0173176i
$523$	27.2466	+	19.7958i	1.19141	+	0.865610i	0.993413	−	0.114592i	$-0.0365562\pi$
$523$	27.2466	+	19.7958i	1.19141	+	0.865610i	0.197998	+	0.980203i	$0.436556\pi$
$524$	−7.96403	+	24.5108i	−0.347910	+	1.07076i
$525$	10.1820	−	3.30834i	0.444380	−	0.144388i
$526$	1.76281	+	2.42629i	0.0768620	+	0.105791i
$527$			7.90669i			0.344421i
$528$	−8.49538	−	8.44290i	−0.369714	−	0.367430i
$529$	13.3564			0.580714
$530$	−1.58284	+	1.15000i	−0.0687543	+	0.0499530i
$531$	−3.67613	+	1.19445i	−0.159531	+	0.0518346i
$532$	6.34341	−	19.5230i	0.275022	−	0.846430i
$533$	3.18621	−	25.0598i	0.138010	−	1.08546i
$534$	0.695401	+	0.505238i	0.0300929	+	0.0218638i
$535$	18.4468	+	5.99374i	0.797527	+	0.259132i
$536$	−4.23791	−	13.0430i	−0.183050	−	0.563370i
$537$	10.5289	−	7.64966i	0.454354	−	0.330107i
$538$		−	5.78522i		−	0.249419i
$539$	5.39683	−	2.77092i	0.232458	−	0.119352i
$540$			2.28645i			0.0983929i
$541$	0.667546	+	0.918798i	0.0287001	+	0.0395022i	0.823126	−	0.567859i	$-0.192228\pi$
$541$	0.667546	+	0.918798i	0.0287001	+	0.0395022i	−0.794426	+	0.607361i	$0.792228\pi$
$542$	−0.245599	−	0.755875i	−0.0105494	−	0.0324676i
$543$	−3.24351	+	9.98251i	−0.139192	+	0.428390i
$544$	3.48077	−	4.79087i	0.149237	−	0.205407i
$545$	−6.01219	−	4.36811i	−0.257534	−	0.187109i
$546$	0.511635	+	2.69382i	0.0218959	+	0.115285i
$547$	−12.8981	−	39.6964i	−0.551484	−	1.69729i	−0.705051	−	0.709156i	$-0.749076\pi$
$547$	−12.8981	−	39.6964i	−0.551484	−	1.69729i	0.153567	−	0.988138i	$-0.450924\pi$
$548$	−7.23843	−	9.96285i	−0.309210	−	0.425592i
$549$	1.50133			0.0640753
$550$	−1.39693	−	2.72076i	−0.0595653	−	0.116014i
$551$			6.82410i			0.290716i
$552$	−3.56887	−	4.91213i	−0.151901	−	0.209074i
$553$	24.0962	−	7.82933i	1.02467	−	0.332937i
$554$	−2.85871	−	0.928850i	−0.121455	−	0.0394631i
$555$	2.46702	+	1.79240i	0.104719	+	0.0760830i
$556$	7.39193	+	5.37055i	0.313488	+	0.227762i
$557$	8.66383	+	2.81505i	0.367098	+	0.119277i	0.486756	−	0.873538i	$-0.338180\pi$
$557$	8.66383	+	2.81505i	0.367098	+	0.119277i	−0.119658	+	0.992815i	$0.538180\pi$
$558$	−0.310268	−	0.954908i	−0.0131347	−	0.0404245i
$559$	−6.07229	+	12.8774i	−0.256830	+	0.544658i
$560$	12.6827			0.535942
$561$	−4.74127	−	4.71198i	−0.200177	−	0.198940i
$562$	2.60786			0.110006
$563$	23.1219	−	16.7990i	0.974471	−	0.707995i	0.0180049	−	0.999838i	$-0.494269\pi$
$563$	23.1219	−	16.7990i	0.974471	−	0.707995i	0.956466	+	0.291843i	$0.0942686\pi$
$564$	15.0735	−	4.89768i	0.634709	−	0.206230i
$565$	−1.64751	−	0.535307i	−0.0693111	−	0.0225206i
$566$	1.86983	−	2.57361i	0.0785950	−	0.108177i
$567$	−1.74654	+	2.40390i	−0.0733477	+	0.100954i
$568$	3.61395	−	11.1226i	0.151638	−	0.466694i
$569$	8.95013	+	27.5457i	0.375209	+	1.15477i	0.943337	+	0.331835i	$0.107668\pi$
$569$	8.95013	+	27.5457i	0.375209	+	1.15477i	−0.568128	+	0.822940i	$0.692332\pi$
$570$	0.634976	+	0.873969i	0.0265962	+	0.0366065i
$571$	−1.73923			−0.0727843			−0.0363922	−	0.999338i	$-0.511587\pi$
$571$	−1.73923			−0.0727843			−0.0363922	+	0.999338i	$0.511587\pi$
$572$	−21.7475	+	7.88605i	−0.909310	+	0.329732i
$573$	16.2713			0.679743
$574$	3.13183	+	4.31060i	0.130720	+	0.179921i
$575$	6.71338	+	20.6617i	0.279967	+	0.861651i
$576$	1.99951	−	6.15385i	0.0833128	−	0.256410i
$577$	−8.13920	+	11.2027i	−0.338840	+	0.466373i	−0.944102	−	0.329653i	$-0.893068\pi$
$577$	−8.13920	+	11.2027i	−0.338840	+	0.466373i	0.605263	+	0.796026i	$0.293068\pi$
$578$	−1.94633	+	2.67890i	−0.0809568	+	0.111427i
$579$	19.7266	+	6.40957i	0.819811	+	0.266373i
$580$	−4.15527	+	1.35013i	−0.172538	+	0.0560611i
$581$	−0.715758	+	0.520029i	−0.0296946	+	0.0215744i
$582$	3.18229			0.131910
$583$	−3.42133	−	21.1766i	−0.141697	−	0.877045i
$584$	−9.86862			−0.408366
$585$	3.85448	+	1.81756i	0.159363	+	0.0751468i
$586$	0.229831	+	0.707348i	0.00949424	+	0.0292203i
$587$	−19.5877	−	6.36443i	−0.808471	−	0.262688i	−0.124521	−	0.992217i	$-0.539739\pi$
$587$	−19.5877	−	6.36443i	−0.808471	−	0.262688i	−0.683950	+	0.729529i	$0.739739\pi$
$588$	2.86270	+	2.07987i	0.118056	+	0.0857725i
$589$	11.3343	+	8.23482i	0.467020	+	0.339310i
$590$	−1.11203	−	0.361321i	−0.0457816	−	0.0148753i
$591$	2.40475	−	0.781349i	0.0989180	−	0.0321404i
$592$	−5.47648	−	7.53773i	−0.225082	−	0.309799i
$593$		−	30.0853i		−	1.23546i	−0.786392	−	0.617728i	$-0.788053\pi$
$593$		−	30.0853i		−	1.23546i	0.786392	−	0.617728i	$-0.211947\pi$
$594$	0.757518	+	0.383023i	0.0310813	+	0.0157156i
$595$	7.07823			0.290179
$596$	−0.307401	−	0.423101i	−0.0125916	−	0.0173309i
$597$	0.533300	+	1.64133i	0.0218265	+	0.0671751i
$598$	−5.46638	+	1.03822i	−0.223537	+	0.0424561i
$599$	20.1877	+	14.6672i	0.824848	+	0.599287i	0.918097	−	0.396356i	$-0.129725\pi$
$599$	20.1877	+	14.6672i	0.824848	+	0.599287i	−0.0932489	+	0.995643i	$0.529725\pi$
$600$	2.13260	−	2.93527i	0.0870629	−	0.119832i
$601$	−2.94022	+	9.04907i	−0.119934	+	0.369119i	−0.992944	−	0.118583i	$-0.962165\pi$
$601$	−2.94022	+	9.04907i	−0.119934	+	0.369119i	0.873010	+	0.487702i	$0.162165\pi$
$602$	−0.927964	−	2.85598i	−0.0378210	−	0.116401i
$603$	−8.00510	−	11.0181i	−0.325993	−	0.448690i
$604$		−	4.99934i		−	0.203420i
$605$	−13.0010	+	0.0805640i	−0.528566	+	0.00327539i
$606$		−	0.789577i		−	0.0320744i
$607$	−14.2678	+	10.3662i	−0.579114	+	0.420751i	−0.838404	−	0.545049i	$-0.816511\pi$
$607$	−14.2678	+	10.3662i	−0.579114	+	0.420751i	0.259291	+	0.965799i	$0.416511\pi$
$608$	−3.24250	−	9.97938i	−0.131501	−	0.404717i
$609$	−5.40005	−	1.75458i	−0.218821	−	0.0710993i
$610$	0.367418	+	0.266945i	0.0148763	+	0.0108083i
$611$	3.72586	−	29.3042i	0.150732	−	1.18552i
$612$	1.20482	−	3.70806i	0.0487020	−	0.149889i
$613$	16.4349	−	5.34002i	0.663798	−	0.215681i	0.0423100	−	0.999105i	$-0.486528\pi$
$613$	16.4349	−	5.34002i	0.663798	−	0.215681i	0.621488	+	0.783423i	$0.286528\pi$
$614$	4.08451	−	2.96757i	0.164837	−	0.119761i
$615$	8.28096			0.333921
$616$	4.47789	−	8.85608i	0.180419	−	0.356822i
$617$			17.5692i			0.707307i	0.935376	+	0.353654i	$0.115061\pi$
$617$			17.5692i			0.707307i	−0.935376	+	0.353654i	$0.884939\pi$
$618$	−1.78722	−	2.45989i	−0.0718924	−	0.0989514i
$619$	−34.1855	+	11.1075i	−1.37403	+	0.446450i	−0.900703	−	0.434436i	$-0.856948\pi$
$619$	−34.1855	+	11.1075i	−1.37403	+	0.446450i	−0.473329	+	0.880886i	$0.656948\pi$
$620$	−2.77182	+	8.53080i	−0.111319	+	0.342605i
$621$	−4.87807	−	3.54413i	−0.195750	−	0.142221i
$622$	−0.750338	+	1.03275i	−0.0300858	+	0.0414096i
$623$	3.08380	−	9.49097i	0.123550	−	0.380248i
$624$	−9.48447	−	8.92084i	−0.379683	−	0.357119i
$625$	−4.85170	+	3.52497i	−0.194068	+	0.140999i
$626$		−	3.58616i		−	0.143332i
$627$	−11.6927	+	1.88909i	−0.466961	+	0.0754431i
$628$	33.1832			1.32416
$629$	−3.05643	−	4.20681i	−0.121868	−	0.167736i
$630$	−0.854853	+	0.277758i	−0.0340581	+	0.0110662i
$631$	5.82733	+	1.89342i	0.231982	+	0.0753757i	0.422701	−	0.906269i	$-0.361082\pi$
$631$	5.82733	+	1.89342i	0.231982	+	0.0753757i	−0.190719	+	0.981645i	$0.561082\pi$
$632$	5.04688	−	6.94644i	0.200754	−	0.276314i
$633$	12.8339	+	9.32437i	0.510102	+	0.370611i
$634$	−1.59659	+	4.91380i	−0.0634087	+	0.195152i
$635$	−13.2392	+	4.30166i	−0.525380	+	0.170706i
$636$	10.1223	−	7.35430i	0.401377	−	0.291617i
$637$	5.78188	−	3.17258i	0.229086	−	0.125702i
$638$	−0.248778	+	1.60285i	−0.00984921	+	0.0634573i
$639$		−	11.6139i		−	0.459439i
$640$	7.20260	−	5.23299i	0.284708	−	0.206852i
$641$	−6.51588	−	20.0538i	−0.257362	−	0.792078i	−0.993355	−	0.115089i	$-0.963285\pi$
$641$	−6.51588	−	20.0538i	−0.257362	−	0.792078i	0.735994	−	0.676989i	$-0.236715\pi$
$642$	3.99449	+	1.29789i	0.157650	+	0.0512236i
$643$	−20.3700	+	28.0369i	−0.803315	+	1.10567i	0.189006	+	0.981976i	$0.439474\pi$
$643$	−20.3700	+	28.0369i	−0.803315	+	1.10567i	−0.992321	+	0.123692i	$0.960526\pi$
$644$	−20.3721	+	28.0398i	−0.802775	+	1.10492i
$645$	−4.43870	−	1.44222i	−0.174774	−	0.0567874i
$646$	−0.569246	−	1.75196i	−0.0223967	−	0.0689300i
$647$	6.42955	−	4.67134i	0.252772	−	0.183649i	−0.454183	−	0.890909i	$-0.650069\pi$
$647$	6.42955	−	4.67134i	0.252772	−	0.183649i	0.706954	+	0.707259i	$0.250069\pi$
$648$			1.00698i			0.0395580i
$649$	9.03683	−	9.09301i	0.354727	−	0.356932i
$650$	−1.59942	−	2.91488i	−0.0627346	−	0.114331i
$651$	−9.43061	+	6.85174i	−0.369615	+	0.268541i
$652$	−41.5744	+	13.5084i	−1.62818	+	0.529028i
$653$	9.09132	−	27.9802i	0.355771	−	1.09495i	−0.599790	−	0.800157i	$-0.704749\pi$
$653$	9.09132	−	27.9802i	0.355771	−	1.09495i	0.955561	−	0.294793i	$-0.0952507\pi$
$654$	−1.30188	−	0.945874i	−0.0509077	−	0.0369866i
$655$	−9.25538	+	12.7389i	−0.361638	+	0.497751i
$656$	−24.0632	−	7.81862i	−0.939512	−	0.305266i
$657$	−9.32054	+	3.02843i	−0.363629	+	0.118150i
$658$	3.66228	+	5.04069i	0.142770	+	0.196507i
$659$	4.13945			0.161250			0.0806251	−	0.996744i	$-0.474308\pi$
$659$	4.13945			0.161250			0.0806251	+	0.996744i	$0.474308\pi$
$660$	−3.46366	−	6.74605i	−0.134823	−	0.262590i
$661$		−	13.8108i		−	0.537178i	−0.963255	−	0.268589i	$-0.913443\pi$
$661$		−	13.8108i		−	0.537178i	0.963255	−	0.268589i	$-0.0865573\pi$
$662$	−1.53231	+	1.11329i	−0.0595550	+	0.0432692i
$663$	−5.29329	−	4.97872i	−0.205574	−	0.193358i
$664$	−0.0926517	+	0.285152i	−0.00359558	+	0.0110661i
$665$	7.37198	−	10.1467i	0.285873	−	0.393470i
$666$	0.534211	+	0.388127i	0.0207003	+	0.0150396i
$667$	3.56045	−	10.9579i	0.137861	−	0.424293i
$668$	45.7252	−	14.8570i	1.76916	−	0.574836i
$669$	5.22544	+	7.19220i	0.202027	+	0.278067i
$670$		−	4.11977i		−	0.159161i
$671$	−4.42961	+	2.27432i	−0.171003	+	0.0877990i
$672$	8.73060			0.336790
$673$	−41.1651	+	29.9082i	−1.58680	+	1.15288i	−0.678461	+	0.734636i	$0.737353\pi$
$673$	−41.1651	+	29.9082i	−1.58680	+	1.15288i	−0.908337	+	0.418240i	$0.862647\pi$
$674$	−0.0900319	+	0.0292531i	−0.00346790	+	0.00112679i
$675$	1.11340	−	3.42669i	0.0428547	−	0.131893i
$676$	−23.3973	+	9.22024i	−0.899895	+	0.354625i
$677$	−2.14128	−	1.55573i	−0.0822961	−	0.0597916i	0.545876	−	0.837866i	$-0.316197\pi$
$677$	−2.14128	−	1.55573i	−0.0822961	−	0.0597916i	−0.628173	+	0.778074i	$0.716197\pi$
$678$	−0.356752	−	0.115916i	−0.0137010	−	0.00445172i
$679$	−11.4169	−	35.1376i	−0.438141	−	1.34846i
$680$	1.94064	−	1.40996i	0.0744201	−	0.0540694i
$681$		−	13.7454i		−	0.526726i
$682$	2.36199	+	2.34740i	0.0904453	+	0.0898865i
$683$		−	11.9875i		−	0.458687i	−0.973346	−	0.229344i	$-0.926342\pi$
$683$		−	11.9875i		−	0.458687i	0.973346	−	0.229344i	$-0.0736580\pi$
$684$	−4.06069	−	5.58906i	−0.155264	−	0.213703i
$685$	−2.32505	−	7.15578i	−0.0888358	−	0.273408i
$686$	1.21517	−	3.73990i	0.0463953	−	0.142790i
$687$	6.18911	−	8.51857i	0.236129	−	0.325004i
$688$	11.5365	+	8.38176i	0.439825	+	0.319552i
$689$	−4.35134	−	22.9103i	−0.165773	−	0.872814i
$690$	−0.563636	−	1.73469i	−0.0214572	−	0.0660386i
$691$	17.3728	+	23.9116i	0.660891	+	0.909639i	0.999511	−	0.0312848i	$-0.00995987\pi$
$691$	17.3728	+	23.9116i	0.660891	+	0.909639i	−0.338619	+	0.940923i	$0.609960\pi$
$692$	39.6236			1.50626
$693$	1.51149	−	9.73838i	0.0574169	−	0.369931i
$694$			8.83466i			0.335359i
$695$	3.28129	+	4.51630i	0.124466	+	0.171313i
$696$	−1.83004	+	0.594616i	−0.0693674	+	0.0225388i
$697$	−13.4297	−	4.36358i	−0.508687	−	0.165282i
$698$	−2.98573	−	2.16926i	−0.113011	−	0.0821076i
$699$	9.57648	+	6.95772i	0.362216	+	0.263165i
$700$	−19.6971	−	6.39997i	−0.744480	−	0.241896i
$701$	4.50313	+	13.8592i	0.170081	+	0.523455i	0.999375	−	0.0353575i	$-0.0112570\pi$
$701$	4.50313	+	13.8592i	0.170081	+	0.523455i	−0.829294	+	0.558813i	$0.811257\pi$
$702$	0.834653	+	0.393576i	0.0315019	+	0.0148546i
$703$	−9.21374			−0.347503
$704$	3.42280	+	21.1856i	0.129001	+	0.798464i
$705$	9.68352			0.364702
$706$	−6.82645	+	4.95971i	−0.256917	+	0.186661i
$707$	−8.71821	+	2.83272i	−0.327882	+	0.106535i
$708$	7.11146	+	2.31065i	0.267265	+	0.0868397i
$709$	18.9591	−	26.0949i	0.712023	−	0.980015i	−0.287729	−	0.957712i	$-0.592900\pi$
$709$	18.9591	−	26.0949i	0.712023	−	0.980015i	0.999751	−	0.0223031i	$-0.00709989\pi$
$710$	2.06501	−	2.84225i	0.0774985	−	0.106668i
$711$	2.63491	−	8.10941i	0.0988167	−	0.304126i
$712$	−1.04508	−	3.21642i	−0.0391660	−	0.120540i
$713$	−13.9037	−	19.1369i	−0.520699	−	0.716681i
$714$	1.53273			0.0573608
$715$	−14.1258	+	0.476392i	−0.528276	+	0.0178161i
$716$	−25.1763			−0.940882
$717$	−16.4838	−	22.6880i	−0.615600	−	0.847300i
$718$	−2.72349	−	8.38204i	−0.101640	−	0.312815i
$719$	−14.5107	+	44.6594i	−0.541158	+	1.66551i	0.188794	+	0.982017i	$0.439542\pi$
$719$	−14.5107	+	44.6594i	−0.541158	+	1.66551i	−0.729953	+	0.683498i	$0.760458\pi$
$720$	2.50883	−	3.45311i	0.0934986	−	0.128690i
$721$	−20.7493	+	28.5590i	−0.772746	+	1.06359i
$722$	1.52049	+	0.494036i	0.0565867	+	0.0183861i
$723$	24.7099	−	8.02873i	0.918971	−	0.298592i
$724$	16.4270	−	11.9349i	0.610505	−	0.443558i
$725$	6.88495			0.255701
$726$	−2.81525	+	0.0174454i	−0.104484	+	0.000647460i
$727$	−9.29786			−0.344839			−0.172419	−	0.985024i	$-0.555158\pi$
$727$	−9.29786			−0.344839			−0.172419	+	0.985024i	$0.555158\pi$
$728$	4.60126	−	9.75786i	0.170534	−	0.361650i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−2.81946	−	0.916099i	−0.104353	−	0.0339063i
$731$	6.43853	+	4.67786i	0.238138	+	0.173017i
$732$	−2.34965	−	1.70712i	−0.0868454	−	0.0630969i
$733$	39.0846	+	12.6994i	1.44362	+	0.469061i	0.923025	−	0.384741i	$-0.125709\pi$
$733$	39.0846	+	12.6994i	1.44362	+	0.469061i	0.520598	+	0.853802i	$0.325709\pi$
$734$	4.86354	−	1.58026i	0.179517	−	0.0583285i
$735$	1.27075	+	1.74904i	0.0468725	+	0.0645144i
$736$			17.7164i			0.653034i
$737$	40.3096	+	20.3817i	1.48482	+	0.750769i
$738$	1.79317			0.0660074
$739$	−24.4483	−	33.6502i	−0.899344	−	1.23784i	−0.970677	−	0.240388i	$-0.922725\pi$
$739$	−24.4483	−	33.6502i	−0.899344	−	1.23784i	0.0713329	−	0.997453i	$-0.477275\pi$
$740$	−1.82291	−	5.61035i	−0.0670116	−	0.206241i
$741$	−12.6500	+	2.40260i	−0.464708	+	0.0882616i
$742$	3.97928	+	2.89112i	0.146084	+	0.106136i
$743$	5.28133	−	7.26912i	0.193753	−	0.266678i	−0.701077	−	0.713086i	$-0.747297\pi$
$743$	5.28133	−	7.26912i	0.193753	−	0.266678i	0.894830	+	0.446408i	$0.147297\pi$
$744$	−1.22075	+	3.75708i	−0.0447549	+	0.137741i
$745$	−0.0987400	−	0.303891i	−0.00361755	−	0.0111337i
$746$	3.33323	+	4.58779i	0.122038	+	0.167971i
$747$			0.297748i			0.0108940i
$748$	2.06244	+	12.7656i	0.0754102	+	0.466757i
$749$		−	48.7621i		−	1.78173i
$750$	2.10540	−	1.52966i	0.0768784	−	0.0558554i
$751$	−7.63213	−	23.4893i	−0.278500	−	0.857136i	−0.988272	−	0.152704i	$-0.951202\pi$
$751$	−7.63213	−	23.4893i	−0.278500	−	0.857136i	0.709772	−	0.704432i	$-0.248798\pi$
$752$	−28.1389	−	9.14287i	−1.02612	−	0.333406i
$753$	15.7869	+	11.4699i	0.575307	+	0.417985i
$754$	−0.222409	+	1.74926i	−0.00809964	+	0.0637043i
$755$	0.943886	−	2.90498i	0.0343515	−	0.105723i
$756$	5.46681	−	1.77627i	0.198826	−	0.0646024i
$757$	−43.5481	+	31.6395i	−1.58278	+	1.14996i	−0.669366	+	0.742933i	$0.733434\pi$
$757$	−43.5481	+	31.6395i	−1.58278	+	1.14996i	−0.913417	+	0.407026i	$0.866566\pi$
$758$	5.63593			0.204706
$759$	19.7614	+	3.06717i	0.717293	+	0.111331i
$760$		−	4.25038i		−	0.154177i
$761$	8.41564	+	11.5831i	0.305067	+	0.419889i	0.933835	−	0.357704i	$-0.116440\pi$
$761$	8.41564	+	11.5831i	0.305067	+	0.419889i	−0.628768	+	0.777593i	$0.716440\pi$
$762$	−2.86682	+	0.931485i	−0.103854	+	0.0337442i
$763$	−5.77330	+	17.7684i	−0.209007	+	0.643259i
$764$	−25.4652	−	18.5016i	−0.921299	−	0.669363i
$765$	1.40018	−	1.92718i	0.0506236	−	0.0696774i
$766$	1.94501	−	5.98613i	0.0702761	−	0.216288i
$767$	9.54840	−	10.1517i	0.344773	−	0.366556i
$768$	−8.90990	+	6.47342i	−0.321508	+	0.233589i
$769$			36.8852i			1.33011i	0.746792	+	0.665057i	$0.231593\pi$
$769$			36.8852i			1.33011i	−0.746792	+	0.665057i	$0.768407\pi$
$770$	2.10144	−	2.11450i	0.0757306	−	0.0762013i
$771$	8.56768			0.308557
$772$	−23.5848	−	32.4618i	−0.848837	−	1.16832i
$773$	7.83740	−	2.54653i	0.281892	−	0.0915922i	−0.164659	−	0.986351i	$-0.552652\pi$
$773$	7.83740	−	2.54653i	0.281892	−	0.0915922i	0.446551	+	0.894758i	$0.352652\pi$
$774$	−0.961160	−	0.312300i	−0.0345482	−	0.0112254i
$775$	8.30825	−	11.4353i	0.298441	−	0.410769i
$776$	−10.1295	−	7.35948i	−0.363626	−	0.264190i
$777$	2.36900	−	7.29103i	0.0849873	−	0.261564i
$778$	0.940810	−	0.305688i	0.0337297	−	0.0109594i
$779$	−20.2422	+	14.7069i	−0.725254	+	0.526928i
$780$	−3.96573	−	7.22736i	−0.141996	−	0.258781i
$781$	17.5935	+	34.2663i	0.629545	+	1.22615i
$782$			3.11025i			0.111222i
$783$	−1.54593	+	1.12318i	−0.0552470	+	0.0401393i
$784$	−2.04123	−	6.28226i	−0.0729011	−	0.224367i
$785$	19.2819	+	6.26507i	0.688201	+	0.223610i
$786$	−2.00417	+	2.75850i	−0.0714863	+	0.0983924i
$787$	27.8176	−	38.2876i	0.991589	−	1.36480i	0.0612424	−	0.998123i	$-0.480494\pi$
$787$	27.8176	−	38.2876i	0.991589	−	1.36480i	0.930346	−	0.366682i	$-0.119506\pi$
$788$	−4.65197	−	1.51152i	−0.165720	−	0.0538456i
$789$	−3.62106	−	11.1445i	−0.128913	−	0.396754i
$790$	2.08673	−	1.51610i	0.0742424	−	0.0539403i
$791$			4.35499i			0.154846i
$792$	−1.52544	−	2.97106i	−0.0542042	−	0.105572i
$793$	−4.74565	+	2.60399i	−0.168523	+	0.0924704i
$794$	−4.14061	+	3.00833i	−0.146945	+	0.106762i
$795$	7.27033	−	2.36227i	0.257852	−	0.0837812i
$796$	1.03167	−	3.17514i	0.0365665	−	0.112540i
$797$	−39.0436	−	28.3668i	−1.38299	−	1.00480i	−0.996593	−	0.0824735i	$-0.973718\pi$
$797$	−39.0436	−	28.3668i	−1.38299	−	1.00480i	−0.386401	−	0.922331i	$-0.626282\pi$
$798$	1.59633	−	2.19717i	0.0565096	−	0.0777788i
$799$	−15.7043	−	5.10264i	−0.555579	−	0.180518i
$800$	−10.0684	+	3.27141i	−0.355971	+	0.115662i
$801$	−1.97407	−	2.71708i	−0.0697505	−	0.0960033i
$802$	9.69488			0.342338
$803$	22.9122	−	23.0546i	0.808553	−	0.813579i
$804$			26.3461i			0.929154i
$805$	−17.1317	+	12.4469i	−0.603813	+	0.438696i
$806$	2.63699	+	2.48028i	0.0928840	+	0.0873642i
$807$	−6.98505	+	21.4978i	−0.245885	+	0.756758i
$808$	−1.82601	+	2.51328i	−0.0642387	+	0.0884169i
$809$	44.5683	+	32.3808i	1.56694	+	1.13845i	0.930015	+	0.367522i	$0.119794\pi$
$809$	44.5683	+	32.3808i	1.56694	+	1.13845i	0.636925	+	0.770926i	$0.280206\pi$
$810$	−0.0934777	+	0.287695i	−0.00328447	+	0.0101086i
$811$	−13.2387	+	4.30153i	−0.464875	+	0.151047i	−0.532083	−	0.846692i	$-0.678591\pi$
$811$	−13.2387	+	4.30153i	−0.464875	+	0.151047i	0.0672084	+	0.997739i	$0.478591\pi$
$812$	6.45622	+	8.88622i	0.226569	+	0.311845i
$813$			3.10535i			0.108909i
$814$	−2.16413	−	0.335894i	−0.0758526	−	0.0117731i
$815$	−26.7082			−0.935548
$816$	−5.88830	+	4.27810i	−0.206132	+	0.149763i
$817$	13.4115	−	4.35765i	0.469208	−	0.152455i
$818$	−1.35373	+	4.16635i	−0.0473321	+	0.145673i
$819$	1.35128	−	10.6279i	0.0472176	−	0.371370i
$820$	−12.9600	−	9.41602i	−0.452584	−	0.328822i
$821$	−12.4870	−	4.05729i	−0.435801	−	0.141600i	0.0828966	−	0.996558i	$-0.473583\pi$
$821$	−12.4870	−	4.05729i	−0.435801	−	0.141600i	−0.518697	+	0.854958i	$0.673583\pi$
$822$	−0.503469	−	1.54952i	−0.0175605	−	0.0540457i
$823$	32.5626	−	23.6581i	1.13506	−	0.824670i	0.148638	−	0.988892i	$-0.452511\pi$
$823$	32.5626	−	23.6581i	1.13506	−	0.824670i	0.986424	+	0.164221i	$0.0525111\pi$
$824$			11.9632i			0.416758i
$825$	1.90594	+	11.7969i	0.0663563	+	0.410717i
$826$			2.93952i			0.102279i
$827$	15.1091	+	20.7959i	0.525396	+	0.723146i	0.986420	−	0.164242i	$-0.0525178\pi$
$827$	15.1091	+	20.7959i	0.525396	+	0.723146i	−0.461024	+	0.887388i	$0.652518\pi$
$828$	3.60446	+	11.0934i	0.125264	+	0.385522i
$829$	−10.3124	+	31.7382i	−0.358164	+	1.10231i	0.595989	+	0.802993i	$0.296760\pi$
$829$	−10.3124	+	31.7382i	−0.358164	+	1.10231i	−0.954152	+	0.299321i	$0.903240\pi$
$830$	−0.0529411	+	0.0728672i	−0.00183761	+	0.00252926i
$831$	9.50141	+	6.90318i	0.329600	+	0.239469i
$832$	4.35320	+	22.9201i	0.150920	+	0.794612i
$833$	−1.13921	−	3.50614i	−0.0394714	−	0.121480i
$834$	0.710532	+	0.977964i	0.0246037	+	0.0338641i
$835$	29.3748			1.01656
$836$	20.4475	+	10.3389i	0.707193	+	0.357577i
$837$			3.92304i			0.135600i
$838$	4.85889	+	6.68769i	0.167848	+	0.231022i
$839$	22.0263	−	7.15677i	0.760432	−	0.247079i	0.0969678	−	0.995288i	$-0.469086\pi$
$839$	22.0263	−	7.15677i	0.760432	−	0.247079i	0.663464	+	0.748208i	$0.269086\pi$
$840$	3.36342	+	1.09284i	0.116049	+	0.0377066i
$841$	20.5074	+	14.8995i	0.707152	+	0.513776i
$842$	2.92804	+	2.12735i	0.100907	+	0.0733132i
$843$	−9.69077	−	3.14872i	−0.333768	−	0.108448i
$844$	−9.48312	−	29.1860i	−0.326422	−	1.00463i
$845$	−15.3363	+	0.940182i	−0.527586	+	0.0323432i
$846$	2.09688			0.0720921
$847$	10.2927	+	31.0224i	0.353663	+	1.06594i
$848$	−23.3569			−0.802079
$849$	−10.0556	+	7.30584i	−0.345108	+	0.250736i
$850$	−1.76758	+	0.574322i	−0.0606276	+	0.0196991i
$851$	14.7952	+	4.80724i	0.507172	+	0.164790i
$852$	−13.2058	+	18.1762i	−0.452424	+	0.622708i
$853$	−8.02164	+	11.0408i	−0.274656	+	0.378031i	−0.923955	−	0.382502i	$-0.875062\pi$
$853$	−8.02164	+	11.0408i	−0.274656	+	0.378031i	0.649299	+	0.760533i	$0.275062\pi$
$854$	0.352819	−	1.08586i	0.0120732	−	0.0371575i
$855$	−1.30433	−	4.01432i	−0.0446072	−	0.137287i
$856$	−9.71322	−	13.3691i	−0.331991	−	0.456947i
$857$	21.5848			0.737323			0.368661	−	0.929564i	$-0.379816\pi$
$857$	21.5848			0.737323			0.368661	+	0.929564i	$0.379816\pi$
$858$	−3.05882	+	0.103158i	−0.104426	+	0.00352177i
$859$	−8.60414			−0.293570			−0.146785	−	0.989168i	$-0.546892\pi$
$859$	−8.60414			−0.293570			−0.146785	+	0.989168i	$0.546892\pi$
$860$	5.30684	+	7.30424i	0.180962	+	0.249073i
$861$	−6.43324	−	19.7995i	−0.219244	−	0.674765i
$862$	0.894667	−	2.75350i	0.0304725	−	0.0937846i
$863$	26.5321	−	36.5183i	0.903162	−	1.24310i	−0.0662863	−	0.997801i	$-0.521115\pi$
$863$	26.5321	−	36.5183i	0.903162	−	1.24310i	0.969448	−	0.245295i	$-0.0788849\pi$
$864$	1.72704	−	2.37707i	0.0587552	−	0.0808696i
$865$	23.0242	+	7.48102i	0.782847	+	0.254362i
$866$	7.55031	−	2.45325i	0.256570	−	0.0833647i
$867$	10.4670	−	7.60474i	0.355479	−	0.258271i
$868$	22.5502			0.765403
$869$	4.51048	+	27.9180i	0.153008	+	0.947052i
$870$	−0.578040			−0.0195974
$871$	44.4141	+	20.9432i	1.50491	+	0.709634i
$872$	1.95653	+	6.02158i	0.0662564	+	0.203916i
$873$	−11.8253	−	3.84228i	−0.400227	−	0.130041i
$874$	4.45855	+	3.23933i	0.150813	+	0.109572i
$875$	−24.4434	−	17.7592i	−0.826338	−	0.600370i
$876$	18.0305	+	5.85848i	0.609196	+	0.197940i
$877$	−2.13092	+	0.692378i	−0.0719560	+	0.0233799i	−0.344774	−	0.938686i	$-0.612044\pi$
$877$	−2.13092	+	0.692378i	−0.0719560	+	0.0233799i	0.272818	+	0.962066i	$0.412044\pi$
$878$	−1.27877	−	1.76008i	−0.0431565	−	0.0593999i
$879$		−	2.90599i		−	0.0980166i
$880$	−2.17120	+	13.9888i	−0.0731911	+	0.471562i
$881$	−35.4761			−1.19522			−0.597610	−	0.801787i	$-0.703883\pi$
$881$	−35.4761			−1.19522			−0.597610	+	0.801787i	$0.703883\pi$
$882$	0.275170	+	0.378739i	0.00926546	+	0.0127528i
$883$	1.35473	+	4.16944i	0.0455904	+	0.140313i	0.971261	−	0.238019i	$-0.0764979\pi$
$883$	1.35473	+	4.16944i	0.0455904	+	0.140313i	−0.925670	+	0.378332i	$0.876498\pi$
$884$	2.62306	+	13.8107i	0.0882230	+	0.464505i
$885$	3.69603	+	2.68532i	0.124241	+	0.0902661i
$886$	1.58577	−	2.18262i	0.0532749	−	0.0733266i
$887$	−10.2985	+	31.6956i	−0.345791	+	1.06423i	0.615369	+	0.788239i	$0.289007\pi$
$887$	−10.2985	+	31.6956i	−0.345791	+	1.06423i	−0.961159	+	0.275994i	$0.910993\pi$
$888$	−0.802836	−	2.47088i	−0.0269414	−	0.0829172i
$889$	20.5702	+	28.3125i	0.689903	+	0.949571i
$890$		−	1.01595i		−	0.0340546i
$891$	−2.35246	−	2.33793i	−0.0788105	−	0.0783236i
$892$		−	17.1978i		−	0.575824i
$893$	−23.6707	+	17.1978i	−0.792109	+	0.575501i
$894$	−0.0213812	−	0.0658047i	−0.000715096	−	0.00220084i
$895$	−14.6293	−	4.75334i	−0.489003	−	0.158887i
$896$	−18.1074	−	13.1558i	−0.604925	−	0.439504i
$897$	21.5665	+	2.74206i	0.720085	+	0.0915548i
$898$	1.48674	−	4.57572i	0.0496132	−	0.152694i
$899$	−7.12953	+	2.31653i	−0.237783	+	0.0772605i
$900$	−5.63889	+	4.09690i	−0.187963	+	0.136563i
$901$	−13.0355			−0.434275
$902$	−5.29066	+	2.71641i	−0.176160	+	0.0904464i
$903$			11.7332i			0.390456i
$904$	0.867498	+	1.19401i	0.0288526	+	0.0397121i
$905$	11.7987	−	3.83361i	0.392201	−	0.127434i
$906$	0.204390	−	0.629047i	0.00679040	−	0.0208987i
$907$	−35.0026	−	25.4309i	−1.16224	−	0.844420i	−0.172184	−	0.985065i	$-0.555082\pi$
$907$	−35.0026	−	25.4309i	−1.16224	−	0.844420i	−0.990060	+	0.140645i	$0.955082\pi$
$908$	−15.6295	+	21.5121i	−0.518683	+	0.713906i
$909$	−0.953332	+	2.93405i	−0.0316200	+	0.0973164i
$910$	2.22040	−	2.36069i	0.0736055	−	0.0782560i
$911$	35.2826	−	25.6343i	1.16896	−	0.849303i	0.178080	−	0.984016i	$-0.443011\pi$
$911$	35.2826	−	25.6343i	1.16896	−	0.849303i	0.990885	+	0.134713i	$0.0430113\pi$
$912$			12.8965i			0.427047i
$913$	−0.451048	−	0.878492i	−0.0149275	−	0.0290739i
$914$	6.85908			0.226878
$915$	−1.04301	−	1.43558i	−0.0344808	−	0.0474588i
$916$	−19.3724	+	6.29448i	−0.640082	+	0.207975i
$917$	37.6486	+	12.2328i	1.24327	+	0.403961i
$918$	0.303196	−	0.417314i	0.0100070	−	0.0137734i
$919$	6.66098	+	4.83949i	0.219726	+	0.159640i	0.692203	−	0.721703i	$-0.256640\pi$
$919$	6.66098	+	4.83949i	0.219726	+	0.159640i	−0.472478	+	0.881343i	$0.656640\pi$
$920$	−2.21762	+	6.82514i	−0.0731128	+	0.225018i
$921$	−18.7610	+	6.09582i	−0.618196	+	0.200864i
$922$	1.78277	−	1.29526i	0.0587124	−	0.0426571i
$923$	20.1438	+	36.7111i	0.663041	+	1.20836i
$924$	−13.4388	+	13.5223i	−0.442103	+	0.444851i
$925$			9.29590i			0.305647i
$926$	7.65009	−	5.55812i	0.251398	−	0.182651i
$927$	3.67120	+	11.2988i	0.120578	+	0.371101i
$928$	5.33977	+	1.73500i	0.175287	+	0.0569541i
$929$	−17.8204	+	24.5276i	−0.584668	+	0.804726i	−0.994197	−	0.107571i	$-0.965693\pi$
$929$	−17.8204	+	24.5276i	−0.584668	+	0.804726i	0.409530	+	0.912297i	$0.365693\pi$
$930$	−0.697536	+	0.960076i	−0.0228731	+	0.0314821i
$931$	−6.21254	−	2.01858i	−0.203608	−	0.0661562i
$932$	−7.07618	−	21.7782i	−0.231788	−	0.713370i
$933$	4.03518	−	2.93173i	0.132106	−	0.0959806i
$934$		−	3.61263i		−	0.118209i
$935$	−1.21175	+	7.80715i	−0.0396284	+	0.255321i
$936$	−1.74656	−	3.18303i	−0.0570882	−	0.104041i
$937$	4.54409	−	3.30148i	0.148449	−	0.107855i	−0.511082	−	0.859532i	$-0.670755\pi$
$937$	4.54409	−	3.30148i	0.148449	−	0.107855i	0.659531	+	0.751678i	$0.270755\pi$
$938$	−9.85023	+	3.20053i	−0.321621	+	0.104501i
$939$	−4.32992	+	13.3261i	−0.141302	+	0.434881i
$940$	−15.1551	−	11.0108i	−0.494305	−	0.359133i
$941$	−5.84392	+	8.04346i	−0.190506	+	0.262209i	−0.893576	−	0.448911i	$-0.851812\pi$
$941$	−5.84392	+	8.04346i	−0.190506	+	0.262209i	0.703070	+	0.711121i	$0.251812\pi$
$942$	4.17532	+	1.35664i	0.136039	+	0.0442018i
$943$	40.1777	−	13.0545i	1.30837	−	0.425114i
$944$	−8.20471	−	11.2928i	−0.267041	−	0.367550i
$945$	3.51198			0.114245
$946$	3.30895	−	0.534601i	0.107583	−	0.0173814i
$947$		−	41.7341i		−	1.35618i	−0.734980	−	0.678088i	$-0.762809\pi$
$947$		−	41.7341i		−	1.35618i	0.734980	−	0.678088i	$-0.237191\pi$
$948$	−13.3447	+	9.69548i	−0.433415	+	0.314895i
$949$	24.2092	−	25.7388i	0.785864	−	0.835516i
$950$	−1.01765	+	3.13199i	−0.0330168	+	0.101615i
$951$	11.8658	−	16.3319i	0.384775	−	0.529597i
$952$	−4.87878	−	3.54464i	−0.158122	−	0.114882i
$953$	−5.17392	+	15.9237i	−0.167600	+	0.515818i	−0.999218	−	0.0395283i	$-0.987414\pi$
$953$	−5.17392	+	15.9237i	−0.167600	+	0.515818i	0.831619	+	0.555347i	$0.187414\pi$
$954$	1.57432	−	0.511529i	0.0509706	−	0.0165614i
$955$	−11.3040	−	15.5587i	−0.365790	−	0.503466i
$956$			54.2509i			1.75460i
$957$	2.85972	−	5.65578i	0.0924418	−	0.182825i
$958$	−10.1833			−0.329009
$959$	−15.3029	+	11.1182i	−0.494158	+	0.359027i
$960$	−7.27344	+	2.36328i	−0.234749	+	0.0762746i
$961$	4.82368	−	14.8458i	0.155603	−	0.478896i
$962$	−2.36181	−	0.300291i	−0.0761478	−	0.00968177i
$963$	−13.2764	−	9.64587i	−0.427826	−	0.310834i
$964$	−47.8012	−	15.5316i	−1.53957	−	0.500238i
$965$	−7.57568	−	23.3155i	−0.243870	−	0.750554i
$966$	−3.70971	+	2.69526i	−0.119358	+	0.0867187i
$967$			48.1352i			1.54793i	0.633231	+	0.773963i	$0.281728\pi$
$967$			48.1352i			1.54793i	−0.633231	+	0.773963i	$0.718272\pi$
$968$	9.00150	+	6.45513i	0.289319	+	0.207476i
$969$			7.19756i			0.231219i
$970$	−2.21081	−	3.04292i	−0.0709847	−	0.0977021i
$971$	−0.0646764	−	0.199053i	−0.00207556	−	0.00638793i	0.950013	−	0.312209i	$-0.101069\pi$
$971$	−0.0646764	−	0.199053i	−0.00207556	−	0.00638793i	−0.952089	+	0.305821i	$0.901069\pi$
$972$	0.597792	−	1.83982i	0.0191742	−	0.0590121i
$973$	8.24918	−	11.3540i	0.264456	−	0.363993i
$974$	2.41990	+	1.75816i	0.0775386	+	0.0563351i
$975$	2.42402	+	12.7628i	0.0776308	+	0.408736i
$976$	1.67540	+	5.15636i	0.0536283	+	0.165051i
$977$	−5.92397	−	8.15364i	−0.189525	−	0.260858i	0.703672	−	0.710525i	$-0.251543\pi$
$977$	−5.92397	−	8.15364i	−0.189525	−	0.260858i	−0.893196	+	0.449667i	$0.851543\pi$
$978$	−5.78342			−0.184933
$979$	9.94043	+	5.02617i	0.317697	+	0.160637i
$980$		−	4.18226i		−	0.133597i
$981$	3.69573	+	5.08674i	0.117996	+	0.162407i
$982$	9.76733	−	3.17360i	0.311688	−	0.101274i
$983$	−21.0237	−	6.83100i	−0.670550	−	0.217875i	−0.0460968	−	0.998937i	$-0.514678\pi$
$983$	−21.0237	−	6.83100i	−0.670550	−	0.217875i	−0.624454	+	0.781062i	$0.714678\pi$
$984$	−5.70778	−	4.14695i	−0.181957	−	0.132200i
$985$	−2.41776	−	1.75661i	−0.0770363	−	0.0559701i
$986$	0.937440	+	0.304593i	0.0298542	+	0.00970021i
$987$	−7.52285	−	23.1529i	−0.239455	−	0.736966i
$988$	22.5296	+	10.6237i	0.716763	+	0.337986i
$989$	−23.8093			−0.757093
$990$	−0.160017	−	0.990436i	−0.00508567	−	0.0314781i
$991$	−23.1859			−0.736524			−0.368262	−	0.929722i	$-0.620047\pi$
$991$	−23.1859			−0.736524			−0.368262	+	0.929722i	$0.620047\pi$
$992$	9.32534	−	6.77526i	0.296080	−	0.215115i
$993$	7.03823	−	2.28686i	0.223351	−	0.0725713i
$994$	−8.39996	−	2.72931i	−0.266430	−	0.0865685i
$995$	1.19895	−	1.65021i	0.0380092	−	0.0523152i
$996$	0.338560	−	0.465988i	0.0107277	−	0.0147654i
$997$	1.45520	−	4.47863i	0.0460865	−	0.141840i	−0.925365	−	0.379076i	$-0.876242\pi$
$997$	1.45520	−	4.47863i	0.0460865	−	0.141840i	0.971452	+	0.237237i	$0.0762417\pi$
$998$	3.08894	+	9.50679i	0.0977787	+	0.300932i
$999$	−1.51650	−	2.08728i	−0.0479798	−	0.0660386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.25.7	✓	56
11.4	even	5	inner	429.2.bb.a.103.8	yes	56
13.12	even	2	inner	429.2.bb.a.25.8	yes	56
143.103	even	10	inner	429.2.bb.a.103.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.25.7	✓	56	1.1	even	1	trivial
429.2.bb.a.25.8	yes	56	13.12	even	2	inner
429.2.bb.a.103.7	yes	56	143.103	even	10	inner
429.2.bb.a.103.8	yes	56	11.4	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.150436 - 0.207057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.597792 - 1.83982i) q^{4} +(0.694723 - 0.956204i) q^{5} +(0.150436 - 0.207057i) q^{6} +(-2.82596 - 0.918210i) q^{7} +(-0.957697 + 0.311175i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.150436 - 0.207057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.597792 - 1.83982i) q^{4} +(0.694723 - 0.956204i) q^{5} +(0.150436 - 0.207057i) q^{6} +(-2.82596 - 0.918210i) q^{7} +(-0.957697 + 0.311175i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.302500 q^{10} +(1.49655 - 2.95979i) q^{11} +1.93450 q^{12} +(1.53779 - 3.26117i) q^{13} +(0.235004 + 0.723267i) q^{14} +(1.12409 + 0.365237i) q^{15} +(-2.92158 - 2.12265i) q^{16} +(-1.63053 - 1.18465i) q^{17} +(0.243410 + 0.0790888i) q^{18} +(-3.39640 + 1.10356i) q^{19} +(-1.34394 - 1.84977i) q^{20} -2.97139i q^{21} +(-0.837980 + 0.135386i) q^{22} +6.02963 q^{23} +(-0.591889 - 0.814666i) q^{24} +(1.11340 + 3.42669i) q^{25} +(-0.906586 + 0.172187i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-3.37867 + 4.65034i) q^{28} +(0.590493 - 1.81735i) q^{29} +(-0.0934777 - 0.287695i) q^{30} +(-2.30590 - 3.17381i) q^{31} +2.93822i q^{32} +(3.27738 + 0.508682i) q^{33} +0.515828i q^{34} +(-2.84125 + 2.06429i) q^{35} +(0.597792 + 1.83982i) q^{36} +(2.45374 + 0.797270i) q^{37} +(0.739441 + 0.537235i) q^{38} +(3.57676 + 0.454765i) q^{39} +(-0.367788 + 1.13193i) q^{40} +(6.66338 - 2.16506i) q^{41} +(-0.615247 + 0.447003i) q^{42} -3.94872 q^{43} +(-4.55083 - 4.52272i) q^{44} +1.18193i q^{45} +(-0.907072 - 1.24848i) q^{46} +(7.79196 - 2.53176i) q^{47} +(1.11594 - 3.43452i) q^{48} +(1.47982 + 1.07515i) q^{49} +(0.542026 - 0.746034i) q^{50} +(0.622809 - 1.91681i) q^{51} +(-5.08067 - 4.77874i) q^{52} +(5.23254 - 3.80166i) q^{53} +0.255937i q^{54} +(-1.79047 - 3.48724i) q^{55} +2.99214 q^{56} +(-2.09909 - 2.88915i) q^{57} +(-0.465127 + 0.151129i) q^{58} +(3.67613 + 1.19445i) q^{59} +(1.34394 - 1.84977i) q^{60} +(-1.21460 - 0.882461i) q^{61} +(-0.310268 + 0.954908i) q^{62} +(2.82596 - 0.918210i) q^{63} +(-5.23478 + 3.80329i) q^{64} +(-2.05001 - 3.73604i) q^{65} +(-0.387710 - 0.755130i) q^{66} +13.6191i q^{67} +(-3.15426 + 2.29171i) q^{68} +(1.86326 + 5.73452i) q^{69} +(0.854853 + 0.277758i) q^{70} +(-6.82649 + 9.39585i) q^{71} +(0.591889 - 0.814666i) q^{72} +(9.32054 + 3.02843i) q^{73} +(-0.204051 - 0.628003i) q^{74} +(-2.91492 + 2.11781i) q^{75} +6.90845i q^{76} +(-6.94690 + 6.99008i) q^{77} +(-0.443910 - 0.809006i) q^{78} +(-6.89827 + 5.01189i) q^{79} +(-4.05937 + 1.31897i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.45070 - 1.05400i) q^{82} +(0.175012 - 0.240883i) q^{83} +(-5.46681 - 1.77627i) q^{84} +(-2.26554 + 0.736118i) q^{85} +(0.594029 + 0.817611i) q^{86} +1.91087 q^{87} +(-0.512234 + 3.30027i) q^{88} +3.35850i q^{89} +(0.244728 - 0.177805i) q^{90} +(-7.34015 + 7.80392i) q^{91} +(3.60446 - 11.0934i) q^{92} +(2.30590 - 3.17381i) q^{93} +(-1.69641 - 1.23251i) q^{94} +(-1.30433 + 4.01432i) q^{95} +(-2.79441 + 0.907960i) q^{96} +(7.30845 + 10.0592i) q^{97} -0.468147i q^{98} +(0.528981 + 3.27417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Introduction

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