LMFDB - Embedded newform 429.2.bb.a.25.4

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			25.4
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.a.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.897576 - 1.23541i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.102555 + 0.315631i) q^{4} +(0.900087 - 1.23886i) q^{5} +(0.897576 - 1.23541i) q^{6} +(-2.72966 - 0.886920i) q^{7} +(-2.42263 + 0.787161i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.897576 - 1.23541i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.102555 + 0.315631i) q^{4} +(0.900087 - 1.23886i) q^{5} +(0.897576 - 1.23541i) q^{6} +(-2.72966 - 0.886920i) q^{7} +(-2.42263 + 0.787161i) q^{8} +(-0.809017 + 0.587785i) q^{9} -2.33840 q^{10} +(-2.52359 + 2.15209i) q^{11} -0.331874 q^{12} +(-3.21991 - 1.62241i) q^{13} +(1.35437 + 4.16832i) q^{14} +(1.45637 + 0.473204i) q^{15} +(3.68395 + 2.67654i) q^{16} +(-4.09764 - 2.97711i) q^{17} +(1.45231 + 0.471884i) q^{18} +(5.66469 - 1.84057i) q^{19} +(0.298715 + 0.411146i) q^{20} -2.87013i q^{21} +(4.92382 + 1.18599i) q^{22} -7.08980 q^{23} +(-1.49727 - 2.06082i) q^{24} +(0.820459 + 2.52511i) q^{25} +(0.885776 + 5.43413i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.559879 - 0.770607i) q^{28} +(2.11547 - 6.51076i) q^{29} +(-0.722605 - 2.22395i) q^{30} +(0.0788687 + 0.108553i) q^{31} -1.85896i q^{32} +(-2.82659 - 1.73504i) q^{33} +7.73444i q^{34} +(-3.55570 + 2.58337i) q^{35} +(-0.102555 - 0.315631i) q^{36} +(-2.68440 - 0.872214i) q^{37} +(-7.35834 - 5.34615i) q^{38} +(0.547996 - 3.56366i) q^{39} +(-1.20540 + 3.70983i) q^{40} +(-8.76999 + 2.84954i) q^{41} +(-3.54578 + 2.57616i) q^{42} +5.67881 q^{43} +(-0.420462 - 1.01723i) q^{44} +1.53132i q^{45} +(6.36364 + 8.75879i) q^{46} +(-7.76525 + 2.52308i) q^{47} +(-1.40714 + 4.33074i) q^{48} +(1.00129 + 0.727483i) q^{49} +(2.38312 - 3.28008i) q^{50} +(1.56516 - 4.81707i) q^{51} +(0.842298 - 0.849916i) q^{52} +(5.50546 - 3.99995i) q^{53} +1.52705i q^{54} +(0.394704 + 5.06345i) q^{55} +7.31111 q^{56} +(3.50097 + 4.81867i) q^{57} +(-9.94223 + 3.23043i) q^{58} +(12.8943 + 4.18961i) q^{59} +(-0.298715 + 0.411146i) q^{60} +(-8.81938 - 6.40765i) q^{61} +(0.0633171 - 0.194870i) q^{62} +(2.72966 - 0.886920i) q^{63} +(5.07132 - 3.68453i) q^{64} +(-4.90814 + 2.52872i) q^{65} +(0.393603 + 5.04933i) q^{66} -1.96611i q^{67} +(1.35990 - 0.988026i) q^{68} +(-2.19087 - 6.74280i) q^{69} +(6.38303 + 2.07397i) q^{70} +(-1.56752 + 2.15751i) q^{71} +(1.49727 - 2.06082i) q^{72} +(4.32333 + 1.40473i) q^{73} +(1.33191 + 4.09921i) q^{74} +(-2.14799 + 1.56061i) q^{75} +1.97671i q^{76} +(8.79727 - 3.63627i) q^{77} +(-4.89444 + 2.52166i) q^{78} +(1.31096 - 0.952470i) q^{79} +(6.63174 - 2.15478i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.3921 + 8.27683i) q^{82} +(2.15267 - 2.96290i) q^{83} +(0.905903 + 0.294346i) q^{84} +(-7.37647 + 2.39676i) q^{85} +(-5.09717 - 7.01565i) q^{86} +6.84581 q^{87} +(4.41968 - 7.20021i) q^{88} -12.8685i q^{89} +(1.89180 - 1.37448i) q^{90} +(7.35030 + 7.28442i) q^{91} +(0.727092 - 2.23776i) q^{92} +(-0.0788687 + 0.108553i) q^{93} +(10.0869 + 7.32858i) q^{94} +(2.81850 - 8.67445i) q^{95} +(1.76797 - 0.574450i) q^{96} +(2.14642 + 2.95430i) q^{97} -1.88998i q^{98} +(0.776655 - 3.22441i) 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 $

$2$	−0.897576	−	1.23541i	−0.634682	−	0.873565i	0.363636	−	0.931541i	$-0.381535\pi$
$2$	−0.897576	−	1.23541i	−0.634682	−	0.873565i	−0.998318	+	0.0579763i	$0.981535\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.102555	+	0.315631i	−0.0512773	+	0.157815i
$5$	0.900087	−	1.23886i	0.402531	−	0.554037i	−0.558846	−	0.829272i	$-0.688756\pi$
$5$	0.900087	−	1.23886i	0.402531	−	0.554037i	0.961377	+	0.275235i	$0.0887556\pi$
$6$	0.897576	−	1.23541i	0.366434	−	0.504353i
$7$	−2.72966	−	0.886920i	−1.03171	−	0.335224i	−0.256247	−	0.966611i	$-0.582486\pi$
$7$	−2.72966	−	0.886920i	−1.03171	−	0.335224i	−0.775468	+	0.631387i	$0.782486\pi$
$8$	−2.42263	+	0.787161i	−0.856530	+	0.278304i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−2.33840			−0.739466
$11$	−2.52359	+	2.15209i	−0.760890	+	0.648881i
$11$	−2.52359	+	2.15209i	−0.760890	+	0.648881i
$12$	−0.331874			−0.0958037
$13$	−3.21991	−	1.62241i	−0.893041	−	0.449975i
$13$	−3.21991	−	1.62241i	−0.893041	−	0.449975i
$14$	1.35437	+	4.16832i	0.361970	+	1.11403i
$15$	1.45637	+	0.473204i	0.376034	+	0.122181i
$16$	3.68395	+	2.67654i	0.920986	+	0.669136i
$17$	−4.09764	−	2.97711i	−0.993825	−	0.722056i	−0.0330693	−	0.999453i	$-0.510528\pi$
$17$	−4.09764	−	2.97711i	−0.993825	−	0.722056i	−0.960755	+	0.277397i	$0.910528\pi$
$18$	1.45231	+	0.471884i	0.342312	+	0.111224i
$19$	5.66469	−	1.84057i	1.29957	−	0.422255i	0.424137	−	0.905598i	$-0.360577\pi$
$19$	5.66469	−	1.84057i	1.29957	−	0.422255i	0.875431	+	0.483343i	$0.160577\pi$
$20$	0.298715	+	0.411146i	0.0667948	+	0.0919351i
$21$		−	2.87013i		−	0.626315i
$22$	4.92382	+	1.18599i	1.04976	+	0.252854i
$23$	−7.08980			−1.47833			−0.739163	−	0.673527i	$-0.764779\pi$
$23$	−7.08980			−1.47833			−0.739163	+	0.673527i	$0.764779\pi$
$24$	−1.49727	−	2.06082i	−0.305629	−	0.420662i
$25$	0.820459	+	2.52511i	0.164092	+	0.505022i
$26$	0.885776	+	5.43413i	0.173715	+	1.06572i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.559879	−	0.770607i	0.105807	−	0.145631i
$29$	2.11547	−	6.51076i	0.392833	−	1.20902i	−0.537803	−	0.843071i	$-0.680745\pi$
$29$	2.11547	−	6.51076i	0.392833	−	1.20902i	0.930636	−	0.365946i	$-0.119255\pi$
$30$	−0.722605	−	2.22395i	−0.131929	−	0.406036i
$31$	0.0788687	+	0.108553i	0.0141652	+	0.0194968i	0.816041	−	0.577994i	$-0.196164\pi$
$31$	0.0788687	+	0.108553i	0.0141652	+	0.0194968i	−0.801876	+	0.597491i	$0.796164\pi$
$32$		−	1.85896i		−	0.328621i
$33$	−2.82659	−	1.73504i	−0.492047	−	0.302032i
$34$			7.73444i			1.32645i
$35$	−3.55570	+	2.58337i	−0.601024	+	0.436669i
$36$	−0.102555	−	0.315631i	−0.0170924	−	0.0526051i
$37$	−2.68440	−	0.872214i	−0.441313	−	0.143391i	0.0799285	−	0.996801i	$-0.474531\pi$
$37$	−2.68440	−	0.872214i	−0.441313	−	0.143391i	−0.521241	+	0.853409i	$0.674531\pi$
$38$	−7.35834	−	5.34615i	−1.19368	−	0.867260i
$39$	0.547996	−	3.56366i	0.0877495	−	0.570643i
$40$	−1.20540	+	3.70983i	−0.190590	+	0.586575i
$41$	−8.76999	+	2.84954i	−1.36964	+	0.445024i	−0.899250	−	0.437434i	$-0.855887\pi$
$41$	−8.76999	+	2.84954i	−1.36964	+	0.445024i	−0.470392	+	0.882458i	$0.655887\pi$
$42$	−3.54578	+	2.57616i	−0.547126	+	0.397511i
$43$	5.67881			0.866011			0.433005	−	0.901391i	$-0.357453\pi$
$43$	5.67881			0.866011			0.433005	+	0.901391i	$0.357453\pi$
$44$	−0.420462	−	1.01723i	−0.0633870	−	0.153353i
$45$			1.53132i			0.228276i
$46$	6.36364	+	8.75879i	0.938267	+	1.29141i
$47$	−7.76525	+	2.52308i	−1.13268	+	0.368029i	−0.814593	−	0.580033i	$-0.803040\pi$
$47$	−7.76525	+	2.52308i	−1.13268	+	0.368029i	−0.318085	+	0.948062i	$0.603040\pi$
$48$	−1.40714	+	4.33074i	−0.203103	+	0.625088i
$49$	1.00129	+	0.727483i	0.143042	+	0.103926i
$50$	2.38312	−	3.28008i	0.337024	−	0.463873i
$51$	1.56516	−	4.81707i	0.219166	−	0.674525i
$52$	0.842298	−	0.849916i	0.116806	−	0.117862i
$53$	5.50546	−	3.99995i	0.756233	−	0.549435i	−0.141520	−	0.989935i	$-0.545199\pi$
$53$	5.50546	−	3.99995i	0.756233	−	0.549435i	0.897753	+	0.440500i	$0.145199\pi$
$54$			1.52705i			0.207805i
$55$	0.394704	+	5.06345i	0.0532219	+	0.682756i
$56$	7.31111			0.976989
$57$	3.50097	+	4.81867i	0.463715	+	0.638249i
$58$	−9.94223	+	3.23043i	−1.30548	+	0.424176i
$59$	12.8943	+	4.18961i	1.67870	+	0.545441i	0.984658	−	0.174497i	$-0.0558299\pi$
$59$	12.8943	+	4.18961i	1.67870	+	0.545441i	0.694038	+	0.719938i	$0.255830\pi$
$60$	−0.298715	+	0.411146i	−0.0385640	+	0.0530788i
$61$	−8.81938	−	6.40765i	−1.12921	−	0.820416i	−0.143627	−	0.989632i	$-0.545876\pi$
$61$	−8.81938	−	6.40765i	−1.12921	−	0.820416i	−0.985579	+	0.169216i	$0.945876\pi$
$62$	0.0633171	−	0.194870i	0.00804128	−	0.0247485i
$63$	2.72966	−	0.886920i	0.343905	−	0.111741i
$64$	5.07132	−	3.68453i	0.633915	−	0.460566i
$65$	−4.90814	+	2.52872i	−0.608780	+	0.313649i
$66$	0.393603	+	5.04933i	0.0484492	+	0.621529i
$67$		−	1.96611i		−	0.240199i	−0.992762	−	0.120099i	$-0.961679\pi$
$67$		−	1.96611i		−	0.240199i	0.992762	−	0.120099i	$-0.0383213\pi$
$68$	1.35990	−	0.988026i	0.164912	−	0.119816i
$69$	−2.19087	−	6.74280i	−0.263750	−	0.811738i
$70$	6.38303	+	2.07397i	0.762918	+	0.247887i
$71$	−1.56752	+	2.15751i	−0.186031	+	0.256050i	−0.891838	−	0.452354i	$-0.850584\pi$
$71$	−1.56752	+	2.15751i	−0.186031	+	0.256050i	0.705808	+	0.708404i	$0.250584\pi$
$72$	1.49727	−	2.06082i	0.176455	−	0.242869i
$73$	4.32333	+	1.40473i	0.506007	+	0.164412i	0.550886	−	0.834581i	$-0.314290\pi$
$73$	4.32333	+	1.40473i	0.506007	+	0.164412i	−0.0448783	+	0.998992i	$0.514290\pi$
$74$	1.33191	+	4.09921i	0.154832	+	0.476523i
$75$	−2.14799	+	1.56061i	−0.248028	+	0.180203i
$76$			1.97671i			0.226744i
$77$	8.79727	−	3.63627i	1.00254	−	0.414391i
$78$	−4.89444	+	2.52166i	−0.554187	+	0.285522i
$79$	1.31096	−	0.952470i	0.147495	−	0.107161i	−0.511591	−	0.859229i	$-0.670944\pi$
$79$	1.31096	−	0.952470i	0.147495	−	0.107161i	0.659085	+	0.752068i	$0.270944\pi$
$80$	6.63174	−	2.15478i	0.741452	−	0.240912i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	11.3921	+	8.27683i	1.25804	+	0.914023i
$83$	2.15267	−	2.96290i	0.236286	−	0.325220i	−0.674363	−	0.738400i	$-0.735582\pi$
$83$	2.15267	−	2.96290i	0.236286	−	0.325220i	0.910650	+	0.413180i	$0.135582\pi$
$84$	0.905903	+	0.294346i	0.0988421	+	0.0321157i
$85$	−7.37647	+	2.39676i	−0.800091	+	0.259965i
$86$	−5.09717	−	7.01565i	−0.549642	−	0.756517i
$87$	6.84581			0.733948
$88$	4.41968	−	7.20021i	0.471139	−	0.767545i
$89$		−	12.8685i		−	1.36406i	−0.731323	−	0.682031i	$-0.761097\pi$
$89$		−	12.8685i		−	1.36406i	0.731323	−	0.682031i	$-0.238903\pi$
$90$	1.89180	−	1.37448i	0.199414	−	0.144882i
$91$	7.35030	+	7.28442i	0.770521	+	0.763615i
$92$	0.727092	−	2.23776i	0.0758046	−	0.233303i
$93$	−0.0788687	+	0.108553i	−0.00817830	+	0.0112565i
$94$	10.0869	+	7.32858i	1.04039	+	0.755886i
$95$	2.81850	−	8.67445i	0.289172	−	0.889980i
$96$	1.76797	−	0.574450i	0.180443	−	0.0586295i
$97$	2.14642	+	2.95430i	0.217936	+	0.299964i	0.903961	−	0.427614i	$-0.140646\pi$
$97$	2.14642	+	2.95430i	0.217936	+	0.299964i	−0.686025	+	0.727578i	$0.740646\pi$
$98$		−	1.88998i		−	0.190917i
$99$	0.776655	−	3.22441i	0.0780567	−	0.324065i
$100$	−0.881145			−0.0881145
$101$	−16.0155	+	11.6359i	−1.59360	+	1.15782i	−0.695034	+	0.718977i	$0.744611\pi$
$101$	−16.0155	+	11.6359i	−1.59360	+	1.15782i	−0.898565	+	0.438840i	$0.855389\pi$
$102$	−7.35589	+	2.39007i	−0.728342	+	0.236653i
$103$	5.75706	−	17.7184i	0.567260	−	1.74585i	−0.0938797	−	0.995584i	$-0.529927\pi$
$103$	5.75706	−	17.7184i	0.567260	−	1.74585i	0.661140	−	0.750263i	$-0.270073\pi$
$104$	9.07775	+	1.39591i	0.890147	+	0.136881i
$105$	−3.55570	−	2.58337i	−0.347001	−	0.252111i
$106$	−9.88313	−	3.21122i	−0.959935	−	0.311902i
$107$	−3.83803	−	11.8122i	−0.371036	−	1.14193i	−0.946114	−	0.323833i	$-0.895028\pi$
$107$	−3.83803	−	11.8122i	−0.371036	−	1.14193i	0.575078	−	0.818098i	$-0.304972\pi$
$108$	0.268492	−	0.195071i	0.0258356	−	0.0187707i
$109$		−	6.88249i		−	0.659223i	−0.944117	−	0.329611i	$-0.893082\pi$
$109$		−	6.88249i		−	0.659223i	0.944117	−	0.329611i	$-0.106918\pi$
$110$	5.90115	−	5.03245i	0.562652	−	0.479826i
$111$		−	2.82255i		−	0.267904i
$112$	−7.68204	−	10.5734i	−0.725884	−	0.999094i
$113$	−0.676498	−	2.08205i	−0.0636395	−	0.195862i	0.914181	−	0.405306i	$-0.132835\pi$
$113$	−0.676498	−	2.08205i	−0.0636395	−	0.195862i	−0.977821	+	0.209443i	$0.932835\pi$
$114$	2.81064	−	8.65025i	0.263240	−	0.810170i
$115$	−6.38144	+	8.78330i	−0.595072	+	0.819047i
$116$	1.83804	+	1.33542i	0.170658	+	0.123990i
$117$	3.55859	−	0.580058i	0.328991	−	0.0536264i
$118$	−6.39774	−	19.6902i	−0.588960	−	1.81263i
$119$	8.54471	+	11.7608i	0.783292	+	1.07811i
$120$	−3.90074			−0.356087
$121$	1.73698	−	10.8620i	0.157907	−	0.987454i
$122$			16.6469i			1.50714i
$123$	−5.42015	−	7.46020i	−0.488719	−	0.672663i
$124$	−0.0423512	+	0.0137607i	−0.00380325	+	0.00123575i
$125$	11.1486	+	3.62240i	0.997162	+	0.323998i
$126$	−3.54578	−	2.57616i	−0.315884	−	0.229503i
$127$	12.4065	+	9.01387i	1.10090	+	0.799851i	0.981207	−	0.192959i	$-0.0618086\pi$
$127$	12.4065	+	9.01387i	1.10090	+	0.799851i	0.119694	+	0.992811i	$0.461809\pi$
$128$	−12.6397	−	4.10690i	−1.11721	−	0.363002i
$129$	1.75485	+	5.40087i	0.154506	+	0.475520i
$130$	7.52942	+	3.79383i	0.660374	+	0.332741i
$131$	12.4277			1.08581			0.542905	−	0.839794i	$-0.317324\pi$
$131$	12.4277			1.08581			0.542905	+	0.839794i	$0.317324\pi$
$132$	0.837512	−	0.714224i	0.0728961	−	0.0621652i
$133$	−17.0951			−1.48233
$134$	−2.42895	+	1.76474i	−0.209829	+	0.152450i
$135$	−1.45637	+	0.473204i	−0.125345	+	0.0407269i
$136$	12.2706	+	3.98695i	1.05219	+	0.341878i
$137$	2.56231	−	3.52672i	0.218913	−	0.301308i	−0.685409	−	0.728158i	$-0.740377\pi$
$137$	2.56231	−	3.52672i	0.218913	−	0.301308i	0.904323	+	0.426850i	$0.140377\pi$
$138$	−6.36364	+	8.75879i	−0.541709	+	0.745598i
$139$	−3.98164	+	12.2542i	−0.337718	+	1.03939i	0.627650	+	0.778496i	$0.284017\pi$
$139$	−3.98164	+	12.2542i	−0.337718	+	1.03939i	−0.965368	+	0.260893i	$0.915983\pi$
$140$	−0.450737	−	1.38723i	−0.0380942	−	0.117242i
$141$	−4.79919	−	6.60551i	−0.404164	−	0.556285i
$142$	4.07238			0.341746
$143$	11.6173	−	2.83526i	0.971486	−	0.237096i
$144$	−4.55361			−0.379467
$145$	−6.16183	−	8.48103i	−0.511712	−	0.704311i
$146$	−2.14510	−	6.60193i	−0.177529	−	0.546379i
$147$	−0.382461	+	1.17709i	−0.0315448	+	0.0970850i
$148$	0.550595	−	0.757830i	0.0452587	−	0.0622932i
$149$	6.95271	−	9.56958i	0.569588	−	0.783971i	−0.422918	−	0.906168i	$-0.638994\pi$
$149$	6.95271	−	9.56958i	0.569588	−	0.783971i	0.992506	+	0.122197i	$0.0389940\pi$
$150$	3.85597	+	1.25288i	0.314838	+	0.102297i
$151$	−14.3594	+	4.66565i	−1.16855	+	0.379685i	−0.828101	−	0.560578i	$-0.810579\pi$
$151$	−14.3594	+	4.66565i	−1.16855	+	0.379685i	−0.340448	+	0.940263i	$0.610579\pi$
$152$	−12.2746	+	8.91805i	−0.995605	+	0.723349i
$153$	5.06497			0.409478
$154$	−12.3885	−	7.60438i	−0.998293	−	0.612779i
$155$	0.205472			0.0165039
$156$	1.06860	+	0.538435i	0.0855567	+	0.0431093i
$157$	−4.46800	−	13.7511i	−0.356585	−	1.09746i	−0.955085	−	0.296333i	$-0.904236\pi$
$157$	−4.46800	−	13.7511i	−0.356585	−	1.09746i	0.598499	−	0.801123i	$-0.295764\pi$
$158$	−2.35338	−	0.764659i	−0.187225	−	0.0608330i
$159$	5.50546	+	3.99995i	0.436611	+	0.317217i
$160$	−2.30300	−	1.67322i	−0.182068	−	0.132280i
$161$	19.3527	+	6.28809i	1.52521	+	0.495571i
$162$	−1.45231	+	0.471884i	−0.114104	+	0.0370747i
$163$	4.57149	+	6.29211i	0.358067	+	0.492836i	0.949609	−	0.313438i	$-0.101481\pi$
$163$	4.57149	+	6.29211i	0.358067	+	0.492836i	−0.591542	+	0.806274i	$0.701481\pi$
$164$		−	3.06031i		−	0.238970i
$165$	−4.69366	+	1.94008i	−0.365401	+	0.151035i
$166$	−5.59257			−0.434068
$167$	6.28511	+	8.65071i	0.486356	+	0.669412i	0.979711	−	0.200416i	$-0.0642294\pi$
$167$	6.28511	+	8.65071i	0.486356	+	0.669412i	−0.493354	+	0.869828i	$0.664229\pi$
$168$	2.25926	+	6.95328i	0.174306	+	0.536457i
$169$	7.73559	+	10.4480i	0.595045	+	0.803692i
$170$	9.58192	+	6.96167i	0.734900	+	0.533936i
$171$	−3.50097	+	4.81867i	−0.267726	+	0.368493i
$172$	−0.582389	+	1.79241i	−0.0444067	+	0.136670i
$173$	5.08024	+	15.6354i	0.386244	+	1.18874i	0.935574	+	0.353131i	$0.114883\pi$
$173$	5.08024	+	15.6354i	0.386244	+	1.18874i	−0.549330	+	0.835605i	$0.685117\pi$
$174$	−6.14464	−	8.45737i	−0.465824	−	0.641151i
$175$		−	7.62038i		−	0.576046i
$176$	−15.0569	+	1.17371i	−1.13496	+	0.0884719i
$177$			13.5579i			1.01907i
$178$	−15.8979	+	11.5505i	−1.19160	+	0.865746i
$179$	−0.286173	−	0.880749i	−0.0213896	−	0.0658303i	0.939792	−	0.341747i	$-0.111019\pi$
$179$	−0.286173	−	0.880749i	−0.0213896	−	0.0658303i	−0.961182	+	0.275917i	$0.911019\pi$
$180$	−0.483332	−	0.157044i	−0.0360254	−	0.0117054i
$181$	3.71819	+	2.70142i	0.276371	+	0.200795i	0.717333	−	0.696731i	$-0.245363\pi$
$181$	3.71819	+	2.70142i	0.276371	+	0.200795i	−0.440962	+	0.897526i	$0.645363\pi$
$182$	2.40177	−	15.6189i	0.178031	−	1.15775i
$183$	3.36870	−	10.3678i	0.249022	−	0.766410i
$184$	17.1760	−	5.58082i	1.26623	−	0.411423i
$185$	−3.49675	+	2.54054i	−0.257086	+	0.186784i
$186$	0.204898			0.0150239
$187$	16.7478	−	1.30552i	1.22472	−	0.0954689i
$188$		−	2.70970i		−	0.197626i
$189$	1.68702	+	2.32199i	0.122713	+	0.168900i
$190$	−13.2463	+	4.30398i	−0.960987	+	0.312244i
$191$	−1.23007	+	3.78578i	−0.0890050	+	0.273929i	−0.985645	−	0.168831i	$-0.946001\pi$
$191$	−1.23007	+	3.78578i	−0.0890050	+	0.273929i	0.896640	+	0.442760i	$0.146001\pi$
$192$	5.07132	+	3.68453i	0.365991	+	0.265908i
$193$	1.01433	−	1.39611i	0.0730132	−	0.100494i	−0.770948	−	0.636897i	$-0.780217\pi$
$193$	1.01433	−	1.39611i	0.0730132	−	0.100494i	0.843962	+	0.536403i	$0.180217\pi$
$194$	1.72318	−	5.30342i	0.123717	−	0.380763i
$195$	−3.92165	−	3.88650i	−0.280835	−	0.278318i
$196$	−0.332304	+	0.241433i	−0.0237360	+	0.0172452i
$197$		−	6.15199i		−	0.438311i	−0.975690	−	0.219156i	$-0.929670\pi$
$197$		−	6.15199i		−	0.438311i	0.975690	−	0.219156i	$-0.0703302\pi$
$198$	−4.68056	+	1.93467i	−0.332633	+	0.137491i
$199$	−20.1505			−1.42843			−0.714215	−	0.699926i	$-0.753216\pi$
$199$	−20.1505			−1.42843			−0.714215	+	0.699926i	$0.753216\pi$
$200$	−3.97534	−	5.47159i	−0.281099	−	0.386900i
$201$	1.86988	−	0.607562i	0.131891	−	0.0428541i
$202$	28.7502	+	9.34151i	2.02286	+	0.657266i
$203$	−11.5490	+	15.8959i	−0.810584	+	1.11567i
$204$	1.35990	+	0.988026i	0.0952121	+	0.0691756i
$205$	−4.36356	+	13.4297i	−0.304764	+	0.937968i
$206$	−27.0568	+	8.79130i	−1.88514	+	0.612519i
$207$	5.73577	−	4.16728i	0.398664	−	0.289646i
$208$	−7.51951	−	14.5951i	−0.521385	−	1.01199i
$209$	−10.3343	+	16.8358i	−0.714835	+	1.16456i
$210$			6.71151i			0.463139i
$211$	−9.08393	+	6.59986i	−0.625364	+	0.454353i	−0.854791	−	0.518973i	$-0.826315\pi$
$211$	−9.08393	+	6.59986i	−0.625364	+	0.454353i	0.229427	+	0.973326i	$0.426315\pi$
$212$	0.697897	+	2.14791i	0.0479317	+	0.147519i
$213$	−2.53631	−	0.824096i	−0.173785	−	0.0564661i
$214$	−11.1480	+	15.3439i	−0.762061	+	1.04889i
$215$	5.11143	−	7.03528i	0.348596	−	0.479802i
$216$	2.42263	+	0.787161i	0.164839	+	0.0535595i
$217$	−0.119006	−	0.366264i	−0.00807868	−	0.0248636i
$218$	−8.50268	+	6.17756i	−0.575874	+	0.418397i
$219$			4.54582i			0.307178i
$220$	−1.63866	−	0.394700i	−0.110478	−	0.0266107i
$221$	8.36394	+	16.2341i	0.562619	+	1.09202i
$222$	−3.48699	+	2.53345i	−0.234032	+	0.170034i
$223$	−19.7805	+	6.42709i	−1.32460	+	0.430390i	−0.884073	−	0.467348i	$-0.845209\pi$
$223$	−19.7805	+	6.42709i	−1.32460	+	0.430390i	−0.440530	+	0.897738i	$0.645209\pi$
$224$	−1.64875	+	5.07432i	−0.110162	+	0.339043i
$225$	−2.14799	−	1.56061i	−0.143199	−	0.104040i
$226$	−1.96497	+	2.70454i	−0.130708	+	0.179904i
$227$	−18.6188	−	6.04960i	−1.23577	−	0.401526i	−0.382969	−	0.923761i	$-0.625098\pi$
$227$	−18.6188	−	6.04960i	−1.23577	−	0.401526i	−0.852802	+	0.522235i	$0.825098\pi$
$228$	−1.87996	+	0.610837i	−0.124504	+	0.0404536i
$229$	−12.6575	−	17.4215i	−0.836430	−	1.15125i	−0.986692	−	0.162601i	$-0.948012\pi$
$229$	−12.6575	−	17.4215i	−0.836430	−	1.15125i	0.150262	−	0.988646i	$-0.451988\pi$
$230$	16.5788			1.09317
$231$	6.17680	+	7.24303i	0.406404	+	0.476556i
$232$			17.4384i			1.14489i
$233$	−3.00491	+	2.18319i	−0.196858	+	0.143026i	−0.681848	−	0.731494i	$-0.738823\pi$
$233$	−3.00491	+	2.18319i	−0.196858	+	0.143026i	0.484990	+	0.874520i	$0.338823\pi$
$234$	−3.91071	−	3.87566i	−0.255651	−	0.253360i
$235$	−3.86364	+	11.8911i	−0.252036	+	0.775688i
$236$	−2.64474	+	3.64018i	−0.172158	+	0.236955i
$237$	1.31096	+	0.952470i	0.0851562	+	0.0618696i
$238$	6.85983	−	21.1124i	0.444657	−	1.36851i
$239$	9.80947	−	3.18729i	0.634522	−	0.206169i	0.0259446	−	0.999663i	$-0.491741\pi$
$239$	9.80947	−	3.18729i	0.634522	−	0.206169i	0.608577	+	0.793495i	$0.291741\pi$
$240$	4.09864	+	5.64130i	0.264566	+	0.364144i
$241$			2.39783i			0.154458i	0.997013	+	0.0772289i	$0.0246072\pi$
$241$			2.39783i			0.154458i	−0.997013	+	0.0772289i	$0.975393\pi$
$242$	−14.9781	+	7.60359i	−0.962826	+	0.488777i
$243$	1.00000			0.0641500
$244$	2.92692	−	2.12653i	0.187377	−	0.136137i
$245$	1.80251	−	0.585669i	0.115158	−	0.0374171i
$246$	−4.35139	+	13.3922i	−0.277434	+	0.853855i
$247$	−21.2259	−	3.26398i	−1.35057	−	0.207682i
$248$	−0.276519	−	0.200903i	−0.0175590	−	0.0127573i
$249$	3.48309	+	1.13173i	0.220732	+	0.0717202i
$250$	−5.53158	−	17.0245i	−0.349848	−	1.07672i
$251$	7.79775	−	5.66539i	0.492189	−	0.357597i	−0.313836	−	0.949477i	$-0.601614\pi$
$251$	7.79775	−	5.66539i	0.492189	−	0.357597i	0.806026	+	0.591881i	$0.201614\pi$
$252$			0.952522i			0.0600033i
$253$	17.8917	−	15.2579i	1.12484	−	0.959257i
$254$		−	23.4177i		−	1.46936i
$255$	−4.55891	−	6.27480i	−0.285490	−	0.392943i
$256$	2.39729	+	7.37809i	0.149830	+	0.461131i
$257$	−0.856504	+	2.63605i	−0.0534273	+	0.164432i	−0.974210	−	0.225644i	$-0.927551\pi$
$257$	−0.856504	+	2.63605i	−0.0534273	+	0.164432i	0.920783	+	0.390076i	$0.127551\pi$
$258$	5.09717	−	7.01565i	0.317336	−	0.436775i
$259$	6.55391	+	4.76170i	0.407240	+	0.295877i
$260$	−0.294788	−	1.80849i	−0.0182820	−	0.112158i
$261$	2.11547	+	6.51076i	0.130944	+	0.403006i
$262$	−11.1548	−	15.3532i	−0.689144	−	0.948526i
$263$	−23.4694			−1.44719			−0.723593	−	0.690226i	$-0.757511\pi$
$263$	−23.4694			−1.44719			−0.723593	+	0.690226i	$0.757511\pi$
$264$	8.21356	+	1.97838i	0.505510	+	0.121761i
$265$		−	10.4208i		−	0.640145i
$266$	15.3442	+	21.1194i	0.940811	+	1.29491i
$267$	12.2387	−	3.97660i	0.748997	−	0.243364i
$268$	0.620566	+	0.201634i	0.0379071	+	0.0123168i
$269$	−12.3739	−	8.99019i	−0.754452	−	0.548141i	0.142752	−	0.989759i	$-0.454405\pi$
$269$	−12.3739	−	8.99019i	−0.754452	−	0.548141i	−0.897204	+	0.441617i	$0.854405\pi$
$270$	1.89180	+	1.37448i	0.115131	+	0.0836479i
$271$	−9.19919	−	2.98900i	−0.558811	−	0.181569i	0.0159751	−	0.999872i	$-0.494915\pi$
$271$	−9.19919	−	2.98900i	−0.558811	−	0.181569i	−0.574786	+	0.818304i	$0.694915\pi$
$272$	−7.12713	−	21.9350i	−0.432146	−	1.33001i
$273$	−4.65653	+	9.24156i	−0.281826	+	0.559325i
$274$	−6.65681			−0.402153
$275$	−7.50478	−	4.60663i	−0.452555	−	0.277790i
$276$	2.35292			0.141629
$277$	−4.96048	+	3.60400i	−0.298046	+	0.216543i	−0.726750	−	0.686902i	$-0.758970\pi$
$277$	−4.96048	+	3.60400i	−0.298046	+	0.216543i	0.428704	+	0.903445i	$0.358970\pi$
$278$	18.7128	−	6.08015i	1.12232	−	0.364663i
$279$	−0.127612	−	0.0414637i	−0.00763994	−	0.00248237i
$280$	6.58064	−	9.05747i	0.393268	−	0.541288i
$281$	7.18944	−	9.89542i	0.428886	−	0.590311i	−0.538811	−	0.842427i	$-0.681126\pi$
$281$	7.18944	−	9.89542i	0.428886	−	0.590311i	0.967697	+	0.252115i	$0.0811263\pi$
$282$	−3.85287	+	11.8579i	−0.229435	+	0.706128i
$283$	9.57457	+	29.4675i	0.569149	+	1.75166i	0.655289	+	0.755378i	$0.272547\pi$
$283$	9.57457	+	29.4675i	0.569149	+	1.75166i	−0.0861394	+	0.996283i	$0.527453\pi$
$284$	−0.520220	−	0.716022i	−0.0308694	−	0.0424881i
$285$	9.12085			0.540273
$286$	−13.9301	−	11.8072i	−0.823704	−	0.698176i
$287$	26.4664			1.56226
$288$	1.09267	+	1.50393i	0.0643861	+	0.0886199i
$289$	2.67420	+	8.23033i	0.157306	+	0.484137i
$290$	−4.94682	+	15.2247i	−0.290487	+	0.894027i
$291$	−2.14642	+	2.95430i	−0.125826	+	0.173184i
$292$	−0.886755	+	1.22051i	−0.0518934	+	0.0714251i
$293$	−4.94804	−	1.60772i	−0.289068	−	0.0939238i	0.160894	−	0.986972i	$-0.448562\pi$
$293$	−4.94804	−	1.60772i	−0.289068	−	0.0939238i	−0.449962	+	0.893048i	$0.648562\pi$
$294$	1.79748	−	0.584036i	0.104831	−	0.0340616i
$295$	16.7964	−	12.2033i	0.977922	−	0.710502i
$296$	7.18989			0.417904
$297$	3.30659	−	0.257754i	0.191868	−	0.0149564i
$298$	−18.0629			−1.04636
$299$	22.8285	+	11.5025i	1.32021	+	0.665210i
$300$	−0.272289	−	0.838019i	−0.0157206	−	0.0483830i
$301$	−15.5012	−	5.03665i	−0.893476	−	0.290308i
$302$	18.6526	+	13.5519i	1.07334	+	0.779825i
$303$	−16.0155	−	11.6359i	−0.920065	−	0.668466i
$304$	25.7948	+	8.38123i	1.47943	+	0.480696i
$305$	−15.8764	+	5.15856i	−0.909081	+	0.295378i
$306$	−4.54619	−	6.25730i	−0.259888	−	0.357706i
$307$		−	34.4846i		−	1.96814i	−0.177775	−	0.984071i	$-0.556890\pi$
$307$		−	34.4846i		−	1.96814i	0.177775	−	0.984071i	$-0.443110\pi$
$308$	0.245517	+	3.14960i	0.0139896	+	0.179465i
$309$	18.6302			1.05984
$310$	−0.184426	−	0.253841i	−0.0104747	−	0.0144172i
$311$	−3.65021	−	11.2342i	−0.206985	−	0.637033i	−0.999626	−	0.0273449i	$-0.991295\pi$
$311$	−3.65021	−	11.2342i	−0.206985	−	0.637033i	0.792642	−	0.609688i	$-0.208705\pi$
$312$	1.47759	+	9.06481i	0.0836518	+	0.513194i
$313$	−23.2455	−	16.8888i	−1.31391	−	0.954613i	−0.999987	−	0.00516585i	$-0.998356\pi$
$313$	−23.2455	−	16.8888i	−1.31391	−	0.954613i	−0.313926	−	0.949447i	$-0.601644\pi$
$314$	−12.9778	+	17.8624i	−0.732381	+	1.00804i
$315$	1.35816	−	4.17998i	0.0765235	−	0.235515i
$316$	0.166184	+	0.511461i	0.00934856	+	0.0287719i
$317$	−2.17424	−	2.99259i	−0.122118	−	0.168080i	0.743581	−	0.668645i	$-0.233126\pi$
$317$	−2.17424	−	2.99259i	−0.122118	−	0.168080i	−0.865699	+	0.500565i	$0.833126\pi$
$318$		−	10.3917i		−	0.582740i
$319$	8.67319	+	20.9832i	0.485605	+	1.17483i
$320$		−	9.59907i		−	0.536604i
$321$	10.0481	−	7.30036i	0.560829	−	0.407466i
$322$	−9.60221	−	29.5526i	−0.535110	−	1.64690i
$323$	−28.6915	−	9.32242i	−1.59644	−	0.518713i
$324$	0.268492	+	0.195071i	0.0149162	+	0.0108373i
$325$	1.45496	−	9.46174i	0.0807067	−	0.524843i
$326$	3.67006	−	11.2953i	0.203266	−	0.625589i
$327$	6.54564	−	2.12681i	0.361974	−	0.117613i
$328$	19.0034	−	13.8068i	1.04929	−	0.762353i
$329$	23.4343			1.29197
$330$	6.60970	+	4.05721i	0.363852	+	0.223342i
$331$			3.79120i			0.208383i	0.994557	+	0.104192i	$0.0332255\pi$
$331$			3.79120i			0.208383i	−0.994557	+	0.104192i	$0.966774\pi$
$332$	0.714415	+	0.983308i	0.0392086	+	0.0539660i
$333$	2.68440	−	0.872214i	0.147104	−	0.0477971i
$334$	5.04579	−	15.5293i	0.276093	−	0.849728i
$335$	−2.43574	−	1.76967i	−0.133079	−	0.0966875i
$336$	7.68204	−	10.5734i	0.419090	−	0.576827i
$337$	−7.85315	+	24.1695i	−0.427788	+	1.31660i	0.472511	+	0.881325i	$0.343348\pi$
$337$	−7.85315	+	24.1695i	−0.427788	+	1.31660i	−0.900299	+	0.435272i	$0.856652\pi$
$338$	5.96426	−	18.9345i	0.324413	−	1.02990i
$339$	1.77109	−	1.28677i	0.0961926	−	0.0698880i
$340$		−	2.57404i		−	0.139597i
$341$	−0.432649	−	0.104211i	−0.0234293	−	0.00564335i
$342$	9.09541			0.491823
$343$	9.72118	+	13.3801i	0.524894	+	0.722455i
$344$	−13.7577	+	4.47014i	−0.741765	+	0.241014i
$345$	−10.3254	−	3.35492i	−0.555900	−	0.180623i
$346$	14.7562	−	20.3101i	0.793296	−	1.09188i
$347$	18.7051	+	13.5900i	1.00414	+	0.729552i	0.962972	−	0.269601i	$-0.0868917\pi$
$347$	18.7051	+	13.5900i	1.00414	+	0.729552i	0.0411694	+	0.999152i	$0.486892\pi$
$348$	−0.702070	+	2.16075i	−0.0376349	+	0.115828i
$349$	−11.6045	+	3.77054i	−0.621177	+	0.201833i	−0.602663	−	0.797996i	$-0.705894\pi$
$349$	−11.6045	+	3.77054i	−0.621177	+	0.201833i	−0.0185140	+	0.999829i	$0.505894\pi$
$350$	−9.41427	+	6.83987i	−0.503214	+	0.365606i
$351$	1.65133	+	3.20517i	0.0881415	+	0.171079i
$352$	4.00066	+	4.69124i	0.213236	+	0.250044i
$353$			2.01271i			0.107126i	0.998564	+	0.0535629i	$0.0170578\pi$
$353$			2.01271i			0.107126i	−0.998564	+	0.0535629i	$0.982942\pi$
$354$	16.7495	−	12.1692i	0.890226	−	0.646787i
$355$	1.26195	+	3.88390i	0.0669776	+	0.206136i
$356$	4.06171	+	1.31973i	0.215270	+	0.0699455i
$357$	−8.54471	+	11.7608i	−0.452234	+	0.622447i
$358$	−0.831222	+	1.14408i	−0.0439315	+	0.0604665i
$359$	13.4994	+	4.38622i	0.712470	+	0.231496i	0.642756	−	0.766071i	$-0.277791\pi$
$359$	13.4994	+	4.38622i	0.712470	+	0.231496i	0.0697148	+	0.997567i	$0.477791\pi$
$360$	−1.20540	−	3.70983i	−0.0635299	−	0.195525i
$361$	13.3297	−	9.68458i	0.701562	−	0.509714i
$362$		−	7.01821i		−	0.368869i
$363$	10.8671	−	1.70458i	0.570376	−	0.0894671i
$364$	−3.05299	+	1.57293i	−0.160020	+	0.0824439i
$365$	5.63165	−	4.09163i	0.294774	−	0.214166i
$366$	−15.8321	+	5.14417i	−0.827558	+	0.268890i
$367$	1.48685	−	4.57607i	0.0776132	−	0.238869i	−0.904721	−	0.426005i	$-0.859921\pi$
$367$	1.48685	−	4.57607i	0.0776132	−	0.238869i	0.982334	+	0.187136i	$0.0599206\pi$
$368$	−26.1184	−	18.9762i	−1.36152	−	0.989201i
$369$	5.42015	−	7.46020i	0.282162	−	0.388362i
$370$	6.27719	+	2.03958i	0.326336	+	0.106033i
$371$	−18.5757	+	6.03560i	−0.964400	+	0.313353i
$372$	−0.0261745	−	0.0360260i	−0.00135708	−	0.00186786i
$373$	−30.7445			−1.59189			−0.795944	−	0.605370i	$-0.793025\pi$
$373$	−30.7445			−1.59189			−0.795944	+	0.605370i	$0.793025\pi$
$374$	−16.6453	−	19.5185i	−0.860706	−	1.00928i
$375$			11.7223i			0.605339i
$376$	16.8263	−	12.2250i	0.867749	−	0.630456i
$377$	−17.3747	+	17.5319i	−0.894844	+	0.902937i
$378$	1.35437	−	4.16832i	0.0696612	−	0.214395i
$379$	12.4263	−	17.1033i	0.638296	−	0.878539i	−0.360227	−	0.932865i	$-0.617301\pi$
$379$	12.4263	−	17.1033i	0.638296	−	0.878539i	0.998523	+	0.0543255i	$0.0173009\pi$
$380$	2.44887	+	1.77921i	0.125625	+	0.0912715i
$381$	−4.73887	+	14.5847i	−0.242780	+	0.747199i
$382$	5.78106	−	1.87838i	0.295785	−	0.0961063i
$383$	12.6135	+	17.3610i	0.644518	+	0.887104i	0.998846	−	0.0480176i	$-0.0152904\pi$
$383$	12.6135	+	17.3610i	0.644518	+	0.887104i	−0.354328	+	0.935121i	$0.615290\pi$
$384$		−	13.2902i		−	0.678213i
$385$	3.41347	−	14.1716i	0.173967	−	0.722250i
$386$	−2.63520			−0.134128
$387$	−4.59426	+	3.33792i	−0.233539	+	0.169676i
$388$	−1.15259	+	0.374500i	−0.0585141	+	0.0190124i
$389$	−4.38692	+	13.5016i	−0.222426	+	0.684557i	0.776117	+	0.630589i	$0.217187\pi$
$389$	−4.38692	+	13.5016i	−0.222426	+	0.684557i	−0.998543	+	0.0539674i	$0.982813\pi$
$390$	−1.28143	+	8.33326i	−0.0648878	+	0.421971i
$391$	29.0515	+	21.1071i	1.46920	+	1.06743i
$392$	−2.99842	−	0.974245i	−0.151443	−	0.0492068i
$393$	3.84036	+	11.8194i	0.193721	+	0.596211i
$394$	−7.60021	+	5.52188i	−0.382893	+	0.278188i
$395$		−	2.48141i		−	0.124853i
$396$	0.938073	+	0.575814i	0.0471399	+	0.0289358i
$397$			18.6886i			0.937953i	0.883211	+	0.468976i	$0.155377\pi$
$397$			18.6886i			0.937953i	−0.883211	+	0.468976i	$0.844623\pi$
$398$	18.0866	+	24.8941i	0.906599	+	1.24783i
$399$	−5.28268	−	16.2584i	−0.264465	−	0.813939i
$400$	−3.73605	+	11.4984i	−0.186802	+	0.574918i
$401$	−12.0311	+	16.5595i	−0.600807	+	0.826940i	−0.995782	−	0.0917522i	$-0.970753\pi$
$401$	−12.0311	+	16.5595i	−0.600807	+	0.826940i	0.394975	+	0.918692i	$0.370753\pi$
$402$	−2.42895	−	1.76474i	−0.121145	−	0.0880170i
$403$	−0.0778318	−	0.477489i	−0.00387708	−	0.0237854i
$404$	−2.03019	−	6.24829i	−0.101006	−	0.310864i
$405$	−0.900087	−	1.23886i	−0.0447257	−	0.0615596i
$406$	30.0040			1.48908
$407$	8.65140	−	3.57597i	0.428834	−	0.177254i
$408$			12.9020i			0.638746i
$409$	−6.25713	−	8.61220i	−0.309395	−	0.425846i	0.625797	−	0.779986i	$-0.284774\pi$
$409$	−6.25713	−	8.61220i	−0.309395	−	0.425846i	−0.935192	+	0.354140i	$0.884774\pi$
$410$	20.5077	−	6.66336i	1.01280	−	0.329080i
$411$	4.14591	+	1.34709i	0.204503	+	0.0664470i
$412$	5.00206	+	3.63421i	0.246434	+	0.179045i
$413$	−31.4812	−	22.8724i	−1.54909	−	1.12548i
$414$	−10.2966	−	3.34556i	−0.506049	−	0.164425i
$415$	−1.73303	−	5.33373i	−0.0850713	−	0.261822i
$416$	−3.01599	+	5.98567i	−0.147871	+	0.293472i
$417$	−12.8848			−0.630974
$418$	30.0748	−	2.34438i	1.47101	−	0.114667i
$419$	19.3647			0.946026			0.473013	−	0.881055i	$-0.343166\pi$
$419$	19.3647			0.946026			0.473013	+	0.881055i	$0.343166\pi$
$420$	1.18005	−	0.857353i	0.0575803	−	0.0418345i
$421$	7.84714	−	2.54969i	0.382446	−	0.124264i	−0.111483	−	0.993766i	$-0.535560\pi$
$421$	7.84714	−	2.54969i	0.382446	−	0.124264i	0.493929	+	0.869502i	$0.335560\pi$
$422$	16.3070	+	5.29848i	0.793814	+	0.257926i
$423$	4.79919	−	6.60551i	0.233344	−	0.321171i
$424$	−10.1891	+	14.0241i	−0.494826	+	0.681070i
$425$	4.15560	−	12.7896i	0.201576	−	0.620387i
$426$	1.25843	+	3.87306i	0.0609713	+	0.187650i
$427$	18.3908	+	25.3128i	0.889994	+	1.22497i
$428$	4.12191			0.199240
$429$	6.28643	+	10.1726i	0.303512	+	0.491135i
$430$	−13.2793			−0.640386
$431$	−1.71894	−	2.36591i	−0.0827983	−	0.113962i	0.765609	−	0.643307i	$-0.222438\pi$
$431$	−1.71894	−	2.36591i	−0.0827983	−	0.113962i	−0.848407	+	0.529345i	$0.822438\pi$
$432$	−1.40714	−	4.33074i	−0.0677012	−	0.208363i
$433$	2.70440	−	8.32330i	0.129965	−	0.399992i	−0.864808	−	0.502103i	$-0.832560\pi$
$433$	2.70440	−	8.32330i	0.129965	−	0.399992i	0.994773	+	0.102111i	$0.0325597\pi$
$434$	−0.345668	+	0.475771i	−0.0165926	+	0.0228378i
$435$	6.16183	−	8.48103i	0.295437	−	0.406634i
$436$	2.17233	+	0.705831i	0.104036	+	0.0338032i
$437$	−40.1615	+	13.0493i	−1.92119	+	0.624231i
$438$	5.61594	−	4.08022i	0.268340	−	0.194960i
$439$	8.15200			0.389074			0.194537	−	0.980895i	$-0.437680\pi$
$439$	8.15200			0.389074			0.194537	+	0.980895i	$0.437680\pi$
$440$	−4.94198	−	11.9562i	−0.235600	−	0.569989i
$441$	−1.23767			−0.0589366
$442$	12.5484	−	24.9042i	0.596867	−	1.18457i
$443$	1.95236	+	6.00874i	0.0927593	+	0.285484i	0.986663	−	0.162775i	$-0.0520444\pi$
$443$	1.95236	+	6.00874i	0.0927593	+	0.285484i	−0.893904	+	0.448259i	$0.852044\pi$
$444$	0.890882	+	0.289465i	0.0422794	+	0.0137374i
$445$	−15.9424	−	11.5828i	−0.755741	−	0.549078i
$446$	25.6946	+	18.6682i	1.21668	+	0.883966i
$447$	11.2497	+	3.65526i	0.532094	+	0.172888i
$448$	−17.1109	+	5.55966i	−0.808412	+	0.262669i
$449$	6.59978	+	9.08382i	0.311463	+	0.428692i	0.935837	−	0.352434i	$-0.114646\pi$
$449$	6.59978	+	9.08382i	0.311463	+	0.428692i	−0.624374	+	0.781126i	$0.714646\pi$
$450$			4.05440i			0.191126i
$451$	15.9993	−	26.0649i	0.753379	−	1.22735i
$452$	0.726536			0.0341734
$453$	−8.87459	−	12.2148i	−0.416964	−	0.573902i
$454$	9.23803	+	28.4317i	0.433562	+	1.33437i
$455$	15.6403	−	2.54941i	0.733229	−	0.119518i
$456$	−12.2746	−	8.91805i	−0.574813	−	0.417626i
$457$	−14.2172	+	19.5683i	−0.665051	+	0.915364i	−0.999635	−	0.0270016i	$-0.991404\pi$
$457$	−14.2172	+	19.5683i	−0.665051	+	0.915364i	0.334584	+	0.942366i	$0.391404\pi$
$458$	−10.1616	+	31.2743i	−0.474822	+	1.46135i
$459$	1.56516	+	4.81707i	0.0730554	+	0.224842i
$460$	−2.11783	−	2.91495i	−0.0987444	−	0.135910i
$461$		−	21.1788i		−	0.986395i	−0.869917	−	0.493197i	$-0.835828\pi$
$461$		−	21.1788i		−	0.986395i	0.869917	−	0.493197i	$-0.164172\pi$
$462$	3.40395	−	14.1320i	0.158366	−	0.657482i
$463$			1.87180i			0.0869899i	0.999054	+	0.0434949i	$0.0138492\pi$
$463$			1.87180i			0.0869899i	−0.999054	+	0.0434949i	$0.986151\pi$
$464$	25.2196	−	18.3231i	1.17079	−	0.850629i
$465$	0.0634942	+	0.195415i	0.00294447	+	0.00906216i
$466$	5.39427	+	1.75270i	0.249885	+	0.0811925i
$467$	−8.40940	−	6.10979i	−0.389141	−	0.282727i	0.375963	−	0.926635i	$-0.377312\pi$
$467$	−8.40940	−	6.10979i	−0.389141	−	0.282727i	−0.765103	+	0.643908i	$0.777312\pi$
$468$	−0.181865	+	1.18269i	−0.00840673	+	0.0546697i
$469$	−1.74378	+	5.36682i	−0.0805205	+	0.247817i
$470$	18.1582	−	5.89997i	0.837577	−	0.272145i
$471$	11.6974	−	8.49864i	0.538987	−	0.391597i
$472$	−34.5361			−1.58965
$473$	−14.3310	+	12.2213i	−0.658939	+	0.561938i
$474$		−	2.47449i		−	0.113657i
$475$	9.29529	+	12.7939i	0.426497	+	0.587023i
$476$	−4.58837	+	1.49085i	−0.210307	+	0.0683330i
$477$	−2.10290	+	6.47205i	−0.0962851	+	0.296335i
$478$	−12.7423	−	9.25785i	−0.582821	−	0.423444i
$479$	11.1335	−	15.3240i	0.508704	−	0.700171i	−0.474996	−	0.879988i	$-0.657551\pi$
$479$	11.1335	−	15.3240i	0.508704	−	0.700171i	0.983700	+	0.179817i	$0.0575506\pi$
$480$	0.879666	−	2.70733i	0.0401511	−	0.123572i
$481$	7.22843	+	7.16364i	0.329588	+	0.326634i
$482$	2.96230	−	2.15223i	0.134929	−	0.0980316i
$483$			20.3487i			0.925897i
$484$	3.25024	+	1.66219i	0.147738	+	0.0755541i
$485$	5.59194			0.253917
$486$	−0.897576	−	1.23541i	−0.0407149	−	0.0560392i
$487$	−0.793330	+	0.257769i	−0.0359492	+	0.0116806i	−0.326936	−	0.945046i	$-0.606016\pi$
$487$	−0.793330	+	0.257769i	−0.0359492	+	0.0116806i	0.290987	+	0.956727i	$0.406016\pi$
$488$	26.4100	+	8.58112i	1.19552	+	0.388449i
$489$	−4.57149	+	6.29211i	−0.206730	+	0.284539i
$490$	−2.34143	−	1.70115i	−0.105775	−	0.0768499i
$491$	3.47325	−	10.6896i	0.156746	−	0.482414i	−0.841588	−	0.540120i	$-0.818379\pi$
$491$	3.47325	−	10.6896i	0.156746	−	0.482414i	0.998334	+	0.0577065i	$0.0183788\pi$
$492$	2.91053	−	0.945688i	0.131217	−	0.0426349i
$493$	−28.0517	+	20.3808i	−1.26339	+	0.917903i
$494$	15.0195	+	29.1523i	0.675761	+	1.31162i
$495$	−3.29554	−	3.86442i	−0.148124	−	0.173693i
$496$			0.611000i			0.0274347i
$497$	6.19235	−	4.49900i	0.277765	−	0.201808i
$498$	−1.72820	−	5.31885i	−0.0774424	−	0.238343i
$499$	−41.4260	−	13.4601i	−1.85448	−	0.602558i	−0.995961	−	0.0897830i	$-0.971383\pi$
$499$	−41.4260	−	13.4601i	−1.85448	−	0.602558i	−0.858523	−	0.512775i	$-0.828617\pi$
$500$	−2.28668	+	3.14735i	−0.102264	+	0.140754i
$501$	−6.28511	+	8.65071i	−0.280798	+	0.386485i
$502$	−13.9981	−	4.54827i	−0.624767	−	0.202999i
$503$	−7.53416	−	23.1877i	−0.335931	−	1.03389i	−0.966261	−	0.257563i	$-0.917080\pi$
$503$	−7.53416	−	23.1877i	−0.335931	−	1.03389i	0.630330	−	0.776327i	$-0.282920\pi$
$504$	−5.91482	+	4.29737i	−0.263467	+	0.191420i
$505$			30.3143i			1.34897i
$506$	−34.9089	−	8.40842i	−1.55189	−	0.373800i
$507$	−7.54621	+	10.5856i	−0.335139	+	0.470123i
$508$	−4.11740	+	2.99147i	−0.182680	+	0.132725i
$509$	22.3297	−	7.25537i	0.989747	−	0.321588i	0.230986	−	0.972957i	$-0.425805\pi$
$509$	22.3297	−	7.25537i	0.989747	−	0.321588i	0.758761	+	0.651369i	$0.225805\pi$
$510$	−3.65997	+	11.2642i	−0.162066	+	0.498788i
$511$	−10.5553	−	7.66889i	−0.466940	−	0.339252i
$512$	−8.66038	+	11.9200i	−0.382738	+	0.526794i
$513$	−5.66469	−	1.84057i	−0.250102	−	0.0812631i
$514$	4.02537	−	1.30792i	0.177552	−	0.0576900i
$515$	−16.7688	−	23.0803i	−0.738923	−	1.01704i
$516$	−1.88465			−0.0829671
$517$	14.1664	−	23.0788i	0.623036	−	1.01500i
$518$		−	12.3707i		−	0.543539i
$519$	−13.3003	+	9.66320i	−0.583816	+	0.424167i
$520$	9.90011	−	9.98965i	0.434149	−	0.438075i
$521$	−11.0729	+	34.0788i	−0.485111	+	1.49302i	0.346709	+	0.937973i	$0.387299\pi$
$521$	−11.0729	+	34.0788i	−0.485111	+	1.49302i	−0.831820	+	0.555045i	$0.812701\pi$
$522$	6.14464	−	8.45737i	0.268943	−	0.370169i
$523$	12.1935	+	8.85909i	0.533184	+	0.387381i	0.821547	−	0.570140i	$-0.193111\pi$
$523$	12.1935	+	8.85909i	0.533184	+	0.387381i	−0.288363	+	0.957521i	$0.593111\pi$
$524$	−1.27452	+	3.92256i	−0.0556775	+	0.171358i
$525$	7.24741	−	2.35483i	0.316303	−	0.102773i
$526$	21.0656	+	28.9943i	0.918503	+	1.26421i
$527$		−	0.679614i		−	0.0296045i
$528$	−5.76911	−	13.9573i	−0.251068	−	0.607413i
$529$	27.2653			1.18545
$530$	−12.8739	+	9.35347i	−0.559209	+	0.406289i
$531$	−12.8943	+	4.18961i	−0.559565	+	0.181814i
$532$	1.75318	−	5.39574i	0.0760101	−	0.233935i
$533$	32.8617	+	5.05324i	1.42340	+	0.218880i
$534$	−15.8979	−	11.5505i	−0.687969	−	0.499839i
$535$	−18.0883	−	5.87724i	−0.782025	−	0.254095i
$536$	1.54765	+	4.76317i	0.0668482	+	0.205738i
$537$	0.749210	−	0.544333i	0.0323308	−	0.0234897i
$538$			23.3562i			1.00696i
$539$	−4.09247	+	0.319014i	−0.176275	+	0.0137409i
$540$		−	0.508205i		−	0.0218697i
$541$	13.4617	+	18.5285i	0.578765	+	0.796601i	0.993559	−	0.113314i	$-0.0361465\pi$
$541$	13.4617	+	18.5285i	0.578765	+	0.796601i	−0.414794	+	0.909915i	$0.636146\pi$
$542$	4.56434	+	14.0476i	0.196055	+	0.603396i
$543$	−1.42022	+	4.37099i	−0.0609475	+	0.187577i
$544$	−5.53433	+	7.61735i	−0.237282	+	0.326591i
$545$	−8.52646	−	6.19484i	−0.365234	−	0.265358i
$546$	15.5967	−	2.54230i	0.667476	−	0.108800i
$547$	9.71269	+	29.8926i	0.415284	+	1.27811i	0.911996	+	0.410199i	$0.134541\pi$
$547$	9.71269	+	29.8926i	0.415284	+	1.27811i	−0.496712	+	0.867916i	$0.665459\pi$
$548$	0.850365	+	1.17043i	0.0363258	+	0.0499982i
$549$	10.9014			0.465258
$550$	1.04504	+	13.4063i	0.0445607	+	0.571645i
$551$		−	40.7751i		−	1.73708i
$552$	10.6153	+	14.6108i	0.451819	+	0.621876i
$553$	−4.42325	+	1.43720i	−0.188096	+	0.0611160i
$554$	8.90482	+	2.89335i	0.378330	+	0.122927i
$555$	−3.49675	−	2.54054i	−0.148429	−	0.107840i
$556$	−3.45947	−	2.51345i	−0.146714	−	0.106594i
$557$	10.1299	+	3.29141i	0.429219	+	0.139462i	0.515656	−	0.856796i	$-0.327548\pi$
$557$	10.1299	+	3.29141i	0.429219	+	0.139462i	−0.0864372	+	0.996257i	$0.527548\pi$
$558$	0.0633171	+	0.194870i	0.00268043	+	0.00824950i
$559$	−18.2852	−	9.21335i	−0.773383	−	0.389683i
$560$	−20.0135			−0.845726
$561$	6.41697	+	15.5247i	0.270925	+	0.655452i
$562$	−18.6779			−0.787882
$563$	−10.7909	+	7.84006i	−0.454783	+	0.330419i	−0.791481	−	0.611194i	$-0.790690\pi$
$563$	−10.7909	+	7.84006i	−0.454783	+	0.330419i	0.336698	+	0.941613i	$0.390690\pi$
$564$	2.57708	−	0.837345i	0.108515	−	0.0352586i
$565$	−3.18828	−	1.03593i	−0.134132	−	0.0435821i
$566$	27.8105	−	38.2778i	1.16896	−	1.60894i
$567$	−1.68702	+	2.32199i	−0.0708483	+	0.0975143i
$568$	2.09923	−	6.46076i	0.0880816	−	0.271087i
$569$	−5.16220	−	15.8876i	−0.216411	−	0.666043i	−0.999050	−	0.0435685i	$-0.986127\pi$
$569$	−5.16220	−	15.8876i	−0.216411	−	0.666043i	0.782640	−	0.622475i	$-0.213873\pi$
$570$	−8.18666	−	11.2680i	−0.342901	−	0.471963i
$571$	24.4068			1.02139			0.510695	−	0.859762i	$-0.329388\pi$
$571$	24.4068			1.02139			0.510695	+	0.859762i	$0.329388\pi$
$572$	−0.296512	+	3.95754i	−0.0123978	+	0.165473i
$573$	−3.98060			−0.166292
$574$	−23.7556	−	32.6968i	−0.991540	−	1.36474i
$575$	−5.81689	−	17.9025i	−0.242581	−	0.746588i
$576$	−1.93707	+	5.96169i	−0.0807113	+	0.248404i
$577$	9.44955	−	13.0062i	0.393390	−	0.541455i	−0.565680	−	0.824625i	$-0.691386\pi$
$577$	9.44955	−	13.0062i	0.393390	−	0.541455i	0.959070	+	0.283170i	$0.0913861\pi$
$578$	7.76752	−	10.6911i	0.323086	−	0.444690i
$579$	1.64122	+	0.533266i	0.0682069	+	0.0221618i
$580$	3.30880	−	1.07509i	0.137390	−	0.0446408i
$581$	−8.50391	+	6.17845i	−0.352802	+	0.256325i
$582$	5.57634			0.231147
$583$	−5.28523	+	21.9425i	−0.218892	+	0.908765i
$584$	−11.5796			−0.479167
$585$	2.48442	−	4.93071i	0.102718	−	0.203860i
$586$	2.45506	+	7.55590i	0.101418	+	0.312131i
$587$	−7.03344	−	2.28530i	−0.290301	−	0.0943245i	0.160246	−	0.987077i	$-0.448771\pi$
$587$	−7.03344	−	2.28530i	−0.290301	−	0.0943245i	−0.450547	+	0.892753i	$0.648771\pi$
$588$	−0.332304	−	0.241433i	−0.0137040	−	0.00995652i
$589$	0.646567	+	0.469758i	0.0266413	+	0.0193560i
$590$	−30.1520	−	9.79698i	−1.24134	−	0.403335i
$591$	5.85089	−	1.90107i	0.240673	−	0.0781995i
$592$	−7.55466	−	10.3981i	−0.310495	−	0.427359i
$593$		−	40.2226i		−	1.65175i	−0.563856	−	0.825873i	$-0.690683\pi$
$593$		−	40.2226i		−	1.65175i	0.563856	−	0.825873i	$-0.309317\pi$
$594$	−3.28635	−	3.85364i	−0.134841	−	0.158117i
$595$	22.2610			0.912612
$596$	2.30742	+	3.17589i	0.0945157	+	0.130090i
$597$	−6.22685	−	19.1643i	−0.254848	−	0.784341i
$598$	−6.27997	−	38.5269i	−0.256807	−	1.57548i
$599$	−1.65654	−	1.20354i	−0.0676842	−	0.0491754i	0.553429	−	0.832897i	$-0.313319\pi$
$599$	−1.65654	−	1.20354i	−0.0676842	−	0.0491754i	−0.621113	+	0.783721i	$0.713319\pi$
$600$	3.97534	−	5.47159i	0.162293	−	0.223377i
$601$	6.17163	−	18.9943i	0.251746	−	0.774795i	−0.742707	−	0.669616i	$-0.766459\pi$
$601$	6.17163	−	18.9943i	0.251746	−	0.774795i	0.994453	−	0.105178i	$-0.0335414\pi$
$602$	7.69121	+	23.6711i	0.313470	+	0.964762i
$603$	1.15565	+	1.59062i	0.0470618	+	0.0647750i
$604$		−	5.01075i		−	0.203884i
$605$	−11.8931	−	11.9286i	−0.483523	−	0.484967i
$606$			30.2298i			1.22800i
$607$	20.0107	−	14.5386i	0.812209	−	0.590104i	−0.102261	−	0.994758i	$-0.532608\pi$
$607$	20.0107	−	14.5386i	0.812209	−	0.590104i	0.914470	+	0.404653i	$0.132608\pi$
$608$	−3.42154	−	10.5304i	−0.138762	−	0.427065i
$609$	−18.6867	−	6.07169i	−0.757225	−	0.246037i
$610$	20.6232	+	14.9836i	0.835009	+	0.606670i
$611$	29.0968	+	4.47431i	1.17713	+	0.181011i
$612$	−0.519436	+	1.59866i	−0.0209969	+	0.0646220i
$613$	25.2434	−	8.20208i	1.01957	−	0.331279i	0.248912	−	0.968526i	$-0.419927\pi$
$613$	25.2434	−	8.20208i	1.01957	−	0.331279i	0.770660	+	0.637247i	$0.219927\pi$
$614$	−42.6026	+	30.9526i	−1.71930	+	1.24914i
$615$	−14.1208			−0.569405
$616$	−18.4502	+	15.7342i	−0.743381	+	0.633949i
$617$		−	47.5811i		−	1.91554i	−0.287531	−	0.957771i	$-0.592834\pi$
$617$		−	47.5811i		−	1.91554i	0.287531	−	0.957771i	$-0.407166\pi$
$618$	−16.7221	−	23.0159i	−0.672660	−	0.925836i
$619$	−21.5072	+	6.98811i	−0.864447	+	0.280876i	−0.707485	−	0.706729i	$-0.750170\pi$
$619$	−21.5072	+	6.98811i	−0.864447	+	0.280876i	−0.156962	+	0.987605i	$0.550170\pi$
$620$	−0.0210721	+	0.0648532i	−0.000846275	+	0.00260457i
$621$	5.73577	+	4.16728i	0.230169	+	0.167227i
$622$	−10.6025	+	14.5930i	−0.425120	+	0.585128i
$623$	−11.4134	+	35.1267i	−0.457267	+	1.40732i
$624$	11.5571	−	11.6616i	0.462654	−	0.466838i
$625$	3.78244	−	2.74810i	0.151298	−	0.109924i
$626$			43.8767i			1.75366i
$627$	−19.2052	−	4.62592i	−0.766983	−	0.184741i
$628$	4.79848			0.191480
$629$	8.40303	+	11.5658i	0.335051	+	0.461158i
$630$	−6.38303	+	2.07397i	−0.254306	+	0.0826290i
$631$	−9.97216	−	3.24015i	−0.396985	−	0.128988i	0.103719	−	0.994607i	$-0.466926\pi$
$631$	−9.97216	−	3.24015i	−0.396985	−	0.128988i	−0.500705	+	0.865618i	$0.666926\pi$
$632$	−2.42624	+	3.33943i	−0.0965105	+	0.132835i
$633$	−9.08393	−	6.59986i	−0.361054	−	0.262321i
$634$	−1.74552	+	5.37215i	−0.0693233	+	0.213355i
$635$	22.3339	−	7.25673i	0.886294	−	0.287974i
$636$	−1.82712	+	1.32748i	−0.0724499	+	0.0526379i
$637$	−2.04380	−	3.96694i	−0.0809783	−	0.157176i
$638$	18.1379	−	29.5489i	0.718086	−	1.16985i
$639$		−	2.66683i		−	0.105498i
$640$	−16.4648	+	11.9623i	−0.650827	+	0.472853i
$641$	6.78945	+	20.8958i	0.268167	+	0.825334i	0.990947	+	0.134255i	$0.0428643\pi$
$641$	6.78945	+	20.8958i	0.268167	+	0.825334i	−0.722779	+	0.691079i	$0.757136\pi$
$642$	−18.0378	−	5.86085i	−0.711897	−	0.231309i
$643$	−8.23217	+	11.3306i	−0.324645	+	0.446836i	−0.939878	−	0.341510i	$-0.889062\pi$
$643$	−8.23217	+	11.3306i	−0.324645	+	0.446836i	0.615233	+	0.788345i	$0.289062\pi$
$644$	−3.96943	+	5.46345i	−0.156417	+	0.215290i
$645$	8.27046	+	2.68724i	0.325649	+	0.105810i
$646$	14.2358	+	43.8132i	0.560099	+	1.72381i
$647$	29.7896	−	21.6434i	1.17115	−	0.850890i	0.180004	−	0.983666i	$-0.442389\pi$
$647$	29.7896	−	21.6434i	1.17115	−	0.850890i	0.991146	+	0.132776i	$0.0423890\pi$
$648$			2.54731i			0.100068i
$649$	−41.5563	+	17.1769i	−1.63123	+	0.674253i
$650$	−12.9950	+	6.69516i	−0.509708	+	0.262606i
$651$	0.311563	−	0.226364i	0.0122111	−	0.00887189i
$652$	−2.45481	+	0.797617i	−0.0961378	+	0.0312371i
$653$	6.74434	−	20.7569i	0.263926	−	0.812281i	−0.728013	−	0.685564i	$-0.759556\pi$
$653$	6.74434	−	20.7569i	0.263926	−	0.812281i	0.991939	−	0.126718i	$-0.0404442\pi$
$654$	−8.50268	−	6.17756i	−0.332481	−	0.241562i
$655$	11.1860	−	15.3962i	0.437073	−	0.601579i
$656$	−39.9351	−	12.9757i	−1.55920	−	0.506616i
$657$	−4.32333	+	1.40473i	−0.168669	+	0.0548039i
$658$	−21.0340	−	28.9508i	−0.819991	−	1.12862i
$659$	−20.5211			−0.799387			−0.399693	−	0.916649i	$-0.630883\pi$
$659$	−20.5211			−0.799387			−0.399693	+	0.916649i	$0.630883\pi$
$660$	−0.130992	−	1.68043i	−0.00509886	−	0.0654105i
$661$		−	24.6891i		−	0.960294i	−0.877188	−	0.480147i	$-0.840583\pi$
$661$		−	24.6891i		−	0.960294i	0.877188	−	0.480147i	$-0.159417\pi$
$662$	4.68368	−	3.40289i	0.182036	−	0.132257i
$663$	−12.8549	+	12.9712i	−0.499244	+	0.503759i
$664$	−2.88285	+	8.87251i	−0.111876	+	0.344320i
$665$	−15.3871	+	21.1785i	−0.596686	+	0.821267i
$666$	−3.48699	−	2.53345i	−0.135118	−	0.0981691i
$667$	−14.9983	+	46.1600i	−0.580736	+	1.78732i
$668$	−3.37500	+	1.09660i	−0.130583	+	0.0424289i
$669$	−12.2251	−	16.8263i	−0.472648	−	0.650544i
$670$			4.59755i			0.177619i
$671$	36.0463	−	2.80987i	1.39155	−	0.108474i
$672$	−5.33546			−0.205820
$673$	3.32376	−	2.41485i	0.128121	−	0.0930857i	−0.521879	−	0.853020i	$-0.674769\pi$
$673$	3.32376	−	2.41485i	0.128121	−	0.0930857i	0.650000	+	0.759934i	$0.274769\pi$
$674$	36.9080	−	11.9921i	1.42164	−	0.461920i
$675$	0.820459	−	2.52511i	0.0315795	−	0.0971916i
$676$	−4.09103	+	1.37010i	−0.157347	+	0.0526961i
$677$	11.7393	+	8.52913i	0.451180	+	0.327801i	0.790061	−	0.613028i	$-0.210049\pi$
$677$	11.7393	+	8.52913i	0.451180	+	0.327801i	−0.338882	+	0.940829i	$0.610049\pi$
$678$	−3.17938	−	1.03304i	−0.122103	−	0.0396738i
$679$	−3.23878	−	9.96794i	−0.124293	−	0.382534i
$680$	15.9839	−	11.6129i	0.612953	−	0.445336i
$681$		−	19.5769i		−	0.750189i
$682$	0.259592	+	0.628035i	0.00994031	+	0.0240487i
$683$			4.39105i			0.168019i	0.996465	+	0.0840094i	$0.0267726\pi$
$683$			4.39105i			0.168019i	−0.996465	+	0.0840094i	$0.973227\pi$
$684$	−1.16188	−	1.59919i	−0.0444256	−	0.0611466i
$685$	−2.06282	−	6.34871i	−0.0788164	−	0.242572i
$686$	7.80432	−	24.0192i	0.297970	−	0.917059i
$687$	12.6575	−	17.4215i	0.482913	−	0.664673i
$688$	20.9204	+	15.1996i	0.797584	+	0.579479i
$689$	−24.2166	+	3.94736i	−0.922579	+	0.150383i
$690$	5.12312	+	15.7674i	0.195034	+	0.600253i
$691$	−8.29259	−	11.4138i	−0.315465	−	0.434200i	0.621611	−	0.783326i	$-0.286479\pi$
$691$	−8.29259	−	11.4138i	−0.315465	−	0.434200i	−0.937076	+	0.349126i	$0.886479\pi$
$692$	−5.45601			−0.207406
$693$	−4.97980	+	8.11271i	−0.189167	+	0.308176i
$694$		−	35.3065i		−	1.34022i
$695$	11.5975	+	15.9626i	0.439918	+	0.605495i
$696$	−16.5849	+	5.38876i	−0.628649	+	0.204260i
$697$	44.4197	+	14.4328i	1.68252	+	0.546683i
$698$	15.0741	+	10.9520i	0.570564	+	0.414539i
$699$	−3.00491	−	2.18319i	−0.113656	−	0.0825760i
$700$	2.40523	+	0.781505i	0.0909090	+	0.0295381i
$701$	5.62251	+	17.3043i	0.212359	+	0.653574i	0.999331	+	0.0365849i	$0.0116479\pi$
$701$	5.62251	+	17.3043i	0.212359	+	0.653574i	−0.786971	+	0.616990i	$0.788352\pi$
$702$	2.47749	−	4.91695i	0.0935070	−	0.185578i
$703$	−16.8117			−0.634064
$704$	−4.86846	+	20.2122i	−0.183487	+	0.761776i
$705$	−12.5030			−0.470891
$706$	2.48652	−	1.80656i	0.0935814	−	0.0679908i
$707$	54.0369	−	17.5577i	2.03227	−	0.660324i
$708$	−4.27928	−	1.39042i	−0.160825	−	0.0522553i
$709$	−13.0224	+	17.9238i	−0.489066	+	0.673142i	−0.980215	−	0.197934i	$-0.936577\pi$
$709$	−13.0224	+	17.9238i	−0.489066	+	0.673142i	0.491149	+	0.871075i	$0.336577\pi$
$710$	3.66549	−	5.04512i	0.137564	−	0.189340i
$711$	−0.500743	+	1.54113i	−0.0187793	+	0.0577969i
$712$	10.1296	+	31.1758i	0.379623	+	1.16836i
$713$	−0.559163	−	0.769622i	−0.0209408	−	0.0288226i
$714$	22.1989			0.830773
$715$	6.94407	−	16.9442i	0.259694	−	0.633678i
$716$	0.307340			0.0114858
$717$	6.06258	+	8.34443i	0.226411	+	0.311628i
$718$	−6.69796	−	20.6142i	−0.249966	−	0.769315i
$719$	−4.95950	+	15.2638i	−0.184958	+	0.569243i	−0.999948	−	0.0102330i	$-0.996743\pi$
$719$	−4.95950	+	15.2638i	−0.184958	+	0.569243i	0.814989	+	0.579476i	$0.196743\pi$
$720$	−4.09864	+	5.64130i	−0.152747	+	0.210239i
$721$	−31.4296	+	43.2592i	−1.17050	+	1.61106i
$722$	−23.9288	−	7.77494i	−0.890537	−	0.289353i
$723$	−2.28047	+	0.740970i	−0.0848117	+	0.0275570i
$724$	−1.23397	+	0.896531i	−0.0458601	+	0.0333193i
$725$	18.1760			0.675041
$726$	−11.8599	−	11.8953i	−0.440163	−	0.441477i
$727$	5.27678			0.195705			0.0978524	−	0.995201i	$-0.468803\pi$
$727$	5.27678			0.195705			0.0978524	+	0.995201i	$0.468803\pi$
$728$	−23.5411	−	11.8616i	−0.872491	−	0.439620i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−10.1097	−	3.28483i	−0.374175	−	0.121577i
$731$	−23.2698	−	16.9065i	−0.860663	−	0.625308i
$732$	2.92692	+	2.12653i	0.108182	+	0.0785989i
$733$	5.67056	+	1.84248i	0.209447	+	0.0680535i	0.411861	−	0.911247i	$-0.364879\pi$
$733$	5.67056	+	1.84248i	0.209447	+	0.0680535i	−0.202414	+	0.979300i	$0.564879\pi$
$734$	−6.98787	+	2.27050i	−0.257927	+	0.0838056i
$735$	1.11401	+	1.53330i	0.0410909	+	0.0565567i
$736$			13.1796i			0.485808i
$737$	4.23126	+	4.96165i	0.155860	+	0.182765i
$738$	−14.0814			−0.518343
$739$	8.36340	+	11.5112i	0.307653	+	0.423447i	0.934647	−	0.355576i	$-0.115715\pi$
$739$	8.36340	+	11.5112i	0.307653	+	0.423447i	−0.626995	+	0.779023i	$0.715715\pi$
$740$	−0.443264	−	1.36423i	−0.0162947	−	0.0501499i
$741$	−3.45494	−	21.1957i	−0.126921	−	0.778642i
$742$	24.1295	+	17.5311i	0.885821	+	0.643587i
$743$	−14.5578	+	20.0371i	−0.534075	+	0.735091i	−0.987745	−	0.156079i	$-0.950115\pi$
$743$	−14.5578	+	20.0371i	−0.534075	+	0.735091i	0.453670	+	0.891170i	$0.350115\pi$
$744$	0.105621	−	0.325068i	0.00387225	−	0.0119176i
$745$	−5.59737	−	17.2269i	−0.205072	−	0.631145i
$746$	27.5955	+	37.9819i	1.01034	+	1.39062i
$747$			3.66234i			0.133998i
$748$	−1.30550	+	5.42000i	−0.0477339	+	0.198175i
$749$			35.6474i			1.30253i
$750$	14.4819	−	10.5217i	0.528803	−	0.384198i
$751$	−0.350410	−	1.07845i	−0.0127866	−	0.0393532i	0.944460	−	0.328627i	$-0.106586\pi$
$751$	−0.350410	−	1.07845i	−0.0127866	−	0.0393532i	−0.957246	+	0.289274i	$0.906586\pi$
$752$	−35.3599	−	11.4891i	−1.28944	−	0.418965i
$753$	7.79775	+	5.66539i	0.284166	+	0.206458i
$754$	37.2541	+	5.72868i	1.35672	+	0.208626i
$755$	−7.14460	+	21.9888i	−0.260018	+	0.800254i
$756$	−0.905903	+	0.294346i	−0.0329474	+	0.0107052i
$757$	−14.5536	+	10.5738i	−0.528958	+	0.384310i	−0.819968	−	0.572410i	$-0.806009\pi$
$757$	−14.5536	+	10.5738i	−0.528958	+	0.384310i	0.291010	+	0.956720i	$0.406009\pi$
$758$	−32.2831			−1.17258
$759$	20.0400	+	12.3011i	0.727406	+	0.446501i
$760$			23.2336i			0.842772i
$761$	−8.00173	−	11.0134i	−0.290062	−	0.399237i	0.638972	−	0.769230i	$-0.279360\pi$
$761$	−8.00173	−	11.0134i	−0.290062	−	0.399237i	−0.929034	+	0.369993i	$0.879360\pi$
$762$	22.2716	−	7.23648i	0.806815	−	0.262150i
$763$	−6.10422	+	18.7869i	−0.220988	+	0.680130i
$764$	−1.06876	−	0.776498i	−0.0386663	−	0.0280927i
$765$	4.55891	−	6.27480i	0.164828	−	0.226866i
$766$	10.1263	−	31.1656i	0.365878	−	1.12606i
$767$	−34.7212	−	34.4100i	−1.25371	−	1.24247i
$768$	−6.27618	+	4.55991i	−0.226472	+	0.164542i
$769$		−	13.0178i		−	0.469434i	−0.972064	−	0.234717i	$-0.924584\pi$
$769$		−	13.0178i		−	0.469434i	0.972064	−	0.234717i	$-0.0754164\pi$
$770$	−20.5715	+	8.50304i	−0.741346	+	0.306428i
$771$	−2.77171			−0.0998205
$772$	0.336630	+	0.463332i	0.0121156	+	0.0166757i
$773$	18.3992	−	5.97827i	0.661774	−	0.215024i	0.0411757	−	0.999152i	$-0.486890\pi$
$773$	18.3992	−	5.97827i	0.661774	−	0.215024i	0.620599	+	0.784128i	$0.286890\pi$
$774$	8.24739	+	2.67974i	0.296446	+	0.0963212i
$775$	−0.209401	+	0.288216i	−0.00752191	+	0.0103530i
$776$	−7.52551	−	5.46760i	−0.270150	−	0.196275i
$777$	−2.50337	+	7.70459i	−0.0898080	+	0.276401i
$778$	20.6175	−	6.69904i	0.739174	−	0.240172i
$779$	−44.4345	+	32.2835i	−1.59203	+	1.15668i
$780$	1.62888	−	0.839215i	0.0583233	−	0.0300487i
$781$	−0.687387	−	8.81813i	−0.0245967	−	0.315537i
$782$		−	54.8357i		−	1.96092i
$783$	−5.53838	+	4.02387i	−0.197926	+	0.143801i
$784$	1.74158	+	5.36002i	0.0621991	+	0.191429i
$785$	−21.0573	−	6.84194i	−0.751568	−	0.244199i
$786$	11.1548	−	15.3532i	0.397878	−	0.547632i
$787$	−31.9849	+	44.0234i	−1.14014	+	1.56927i	−0.372941	+	0.927855i	$0.621651\pi$
$787$	−31.9849	+	44.0234i	−1.14014	+	1.56927i	−0.767198	+	0.641411i	$0.778349\pi$
$788$	1.94176	+	0.630915i	0.0691722	+	0.0224754i
$789$	−7.25245	−	22.3208i	−0.258194	−	0.794640i
$790$	−3.06555	+	2.22725i	−0.109067	+	0.0792422i
$791$			6.28328i			0.223408i
$792$	0.656580	+	8.42291i	0.0233305	+	0.299295i
$793$	18.0017	+	34.9407i	0.639261	+	1.24078i
$794$	23.0880	−	16.7744i	0.819363	−	0.595302i
$795$	9.91078	−	3.22021i	0.351499	−	0.114209i
$796$	2.06653	−	6.36012i	0.0732461	−	0.225428i
$797$	−18.7720	−	13.6387i	−0.664940	−	0.483107i	0.203388	−	0.979098i	$-0.434805\pi$
$797$	−18.7720	−	13.6387i	−0.664940	−	0.483107i	−0.868327	+	0.495991i	$0.834805\pi$
$798$	−15.3442	+	21.1194i	−0.543177	+	0.747619i
$799$	39.3307	+	12.7793i	1.39142	+	0.452100i
$800$	4.69408	−	1.52520i	0.165961	−	0.0539239i
$801$	7.56394	+	10.4109i	0.267259	+	0.367850i
$802$	31.2565			1.10371
$803$	−13.9334	+	5.75924i	−0.491700	+	0.203239i
$804$			0.652501i			0.0230119i
$805$	25.2092	−	18.3156i	0.888509	−	0.645540i
$806$	−0.520033	+	0.524737i	−0.0183174	+	0.0184831i
$807$	4.72642	−	14.5464i	0.166378	−	0.512059i
$808$	29.6403	−	40.7963i	1.04274	−	1.43521i
$809$	−6.58345	−	4.78316i	−0.231462	−	0.168167i	0.466009	−	0.884780i	$-0.345691\pi$
$809$	−6.58345	−	4.78316i	−0.231462	−	0.168167i	−0.697471	+	0.716613i	$0.745691\pi$
$810$	−0.722605	+	2.22395i	−0.0253897	+	0.0781416i
$811$	−21.4262	+	6.96181i	−0.752377	+	0.244462i	−0.660004	−	0.751262i	$-0.729445\pi$
$811$	−21.4262	+	6.96181i	−0.752377	+	0.244462i	−0.0923732	+	0.995724i	$0.529445\pi$
$812$	−3.83282	−	5.27543i	−0.134506	−	0.185131i
$813$		−	9.67260i		−	0.339233i
$814$	−12.1831	−	7.47830i	−0.427017	−	0.262114i
$815$	11.9098			0.417182
$816$	18.6591	−	13.5566i	0.653198	−	0.474576i
$817$	32.1687	−	10.4522i	1.12544	−	0.365678i
$818$	−5.02332	+	15.4602i	−0.175636	+	0.540553i
$819$	−10.2282	−	1.57282i	−0.357402	−	0.0549588i
$820$	−3.79131	−	2.75455i	−0.132398	−	0.0961930i
$821$	27.3257	+	8.87865i	0.953672	+	0.309867i	0.744207	−	0.667949i	$-0.232828\pi$
$821$	27.3257	+	8.87865i	0.953672	+	0.309867i	0.209465	+	0.977816i	$0.432828\pi$
$822$	−2.05707	−	6.33100i	−0.0717485	−	0.220819i
$823$	40.9503	−	29.7521i	1.42744	−	1.03709i	0.436951	−	0.899485i	$-0.356058\pi$
$823$	40.9503	−	29.7521i	1.42744	−	1.03709i	0.990487	−	0.137608i	$-0.0439416\pi$
$824$			47.4569i			1.65324i
$825$	2.06207	−	8.56100i	0.0717919	−	0.298056i
$826$			59.4219i			2.06755i
$827$	3.23075	+	4.44675i	0.112344	+	0.154629i	0.861486	−	0.507781i	$-0.169534\pi$
$827$	3.23075	+	4.44675i	0.112344	+	0.154629i	−0.749142	+	0.662409i	$0.769534\pi$
$828$	0.727092	+	2.23776i	0.0252682	+	0.0777675i
$829$	−4.46937	+	13.7553i	−0.155228	+	0.477741i	−0.998184	−	0.0602408i	$-0.980813\pi$
$829$	−4.46937	+	13.7553i	−0.155228	+	0.477741i	0.842956	+	0.537982i	$0.180813\pi$
$830$	−5.03380	+	6.92843i	−0.174726	+	0.240489i
$831$	−4.96048	−	3.60400i	−0.172077	−	0.125021i
$832$	−22.3070	+	3.63609i	−0.773355	+	0.126059i
$833$	−1.93715	−	5.96194i	−0.0671183	−	0.206569i
$834$	11.5651	+	15.9180i	0.400468	+	0.551196i
$835$	16.3742			0.566652
$836$	−4.25406	−	4.98840i	−0.147130	−	0.172527i
$837$		−	0.134179i		−	0.00463792i
$838$	−17.3813	−	23.9233i	−0.600426	−	0.826416i
$839$	−4.33203	+	1.40756i	−0.149558	+	0.0485945i	−0.382839	−	0.923815i	$-0.625054\pi$
$839$	−4.33203	+	1.40756i	−0.149558	+	0.0485945i	0.233281	+	0.972409i	$0.425054\pi$
$840$	10.6477	+	3.45965i	0.367381	+	0.119369i
$841$	−14.4532	−	10.5009i	−0.498387	−	0.362099i
$842$	−10.1933	−	7.40587i	−0.351285	−	0.255223i
$843$	11.6328	+	3.77971i	0.400654	+	0.130180i
$844$	−1.15152	−	3.54401i	−0.0396370	−	0.121990i
$845$	19.9063	−	0.179228i	0.684799	−	0.00616562i
$846$	−12.4681			−0.428663
$847$	−14.3751	+	28.1090i	−0.493933	+	0.965836i
$848$	30.9878			1.06413
$849$	−25.0666	+	18.2119i	−0.860282	+	0.625032i
$850$	−19.5303	+	6.34579i	−0.669885	+	0.217659i
$851$	19.0319	+	6.18383i	0.652404	+	0.211979i
$852$	0.520220	−	0.716022i	0.0178225	−	0.0245305i
$853$	29.6938	−	40.8701i	1.01670	−	1.39936i	0.102205	−	0.994763i	$-0.467410\pi$
$853$	29.6938	−	40.8701i	1.01670	−	1.39936i	0.914493	−	0.404601i	$-0.132590\pi$
$854$	14.7645	−	45.4403i	0.505229	−	1.55494i
$855$	2.81850	+	8.67445i	0.0963906	+	0.296660i
$856$	18.5963	+	25.5956i	0.635607	+	0.874838i
$857$	−7.84322			−0.267919			−0.133960	−	0.990987i	$-0.542769\pi$
$857$	−7.84322			−0.267919			−0.133960	+	0.990987i	$0.542769\pi$
$858$	6.92470	−	16.8969i	0.236405	−	0.576852i
$859$	−22.9393			−0.782678			−0.391339	−	0.920247i	$-0.627988\pi$
$859$	−22.9393			−0.782678			−0.391339	+	0.920247i	$0.627988\pi$
$860$	1.69635	+	2.33482i	0.0578450	+	0.0796168i
$861$	8.17857	+	25.1710i	0.278725	+	0.857827i
$862$	−1.37999	+	4.24717i	−0.0470027	+	0.144659i
$863$	6.23551	−	8.58245i	0.212259	−	0.292150i	−0.689591	−	0.724200i	$-0.742209\pi$
$863$	6.23551	−	8.58245i	0.212259	−	0.292150i	0.901850	+	0.432050i	$0.142209\pi$
$864$	−1.09267	+	1.50393i	−0.0371733	+	0.0511647i
$865$	23.9428	+	7.77948i	0.814079	+	0.264510i
$866$	−12.7101	+	4.12975i	−0.431906	+	0.140335i
$867$	−7.00114	+	5.08662i	−0.237771	+	0.172751i
$868$	0.127809			0.00433812
$869$	−1.25852	+	5.22496i	−0.0426924	+	0.177245i
$870$	−16.0082			−0.542730
$871$	−3.18984	+	6.33070i	−0.108083	+	0.214507i
$872$	5.41763	+	16.6737i	0.183464	+	0.564644i
$873$	−3.47299	−	1.12844i	−0.117543	−	0.0381920i
$874$	52.1692	+	37.9031i	1.76465	+	1.28209i
$875$	−27.2191	−	19.7759i	−0.920175	−	0.668546i
$876$	−1.43480	−	0.466195i	−0.0484774	−	0.0157513i
$877$	26.6255	−	8.65115i	0.899080	−	0.292129i	0.177222	−	0.984171i	$-0.443289\pi$
$877$	26.6255	−	8.65115i	0.899080	−	0.292129i	0.721857	+	0.692042i	$0.243289\pi$
$878$	−7.31704	−	10.0710i	−0.246938	−	0.339881i
$879$		−	5.20268i		−	0.175482i
$880$	−12.0985	+	19.7099i	−0.407840	+	0.664421i
$881$	28.7996			0.970285			0.485142	−	0.874435i	$-0.338768\pi$
$881$	28.7996			0.970285			0.485142	+	0.874435i	$0.338768\pi$
$882$	1.11090	+	1.52902i	0.0374060	+	0.0514849i
$883$	−14.6511	−	45.0913i	−0.493048	−	1.51744i	−0.819978	−	0.572396i	$-0.806014\pi$
$883$	−14.6511	−	45.0913i	−0.493048	−	1.51744i	0.326930	−	0.945049i	$-0.393986\pi$
$884$	−5.98173	+	0.975036i	−0.201187	+	0.0327940i
$885$	16.7964	+	12.2033i	0.564603	+	0.410208i
$886$	5.67085	−	7.80525i	0.190516	−	0.262223i
$887$	14.1014	−	43.3996i	0.473479	−	1.45722i	−0.374520	−	0.927219i	$-0.622193\pi$
$887$	14.1014	−	43.3996i	0.473479	−	1.45722i	0.847999	−	0.529998i	$-0.177807\pi$
$888$	2.22180	+	6.83799i	0.0745587	+	0.229468i
$889$	−25.8710	−	35.6084i	−0.867686	−	1.19427i
$890$			30.0918i			1.00868i
$891$	1.26693	+	3.06511i	0.0424438	+	0.102685i
$892$		−	6.90248i		−	0.231112i
$893$	−39.3438	+	28.5849i	−1.31659	+	0.956559i
$894$	−5.58175	−	17.1789i	−0.186682	−	0.574547i
$895$	−1.34871	−	0.438222i	−0.0450824	−	0.0146481i
$896$	30.8597	+	22.4209i	1.03095	+	0.749029i
$897$	−3.88518	+	25.2657i	−0.129722	+	0.843596i
$898$	5.29841	−	16.3068i	0.176810	−	0.544166i
$899$	0.873610	−	0.283853i	0.0291365	−	0.00946703i
$900$	0.712861	−	0.517924i	0.0237620	−	0.0172641i
$901$	−34.4677			−1.14829
$902$	−46.5614	+	3.62954i	−1.55033	+	0.120850i
$903$		−	16.2990i		−	0.542395i
$904$	3.27781	+	4.51152i	0.109018	+	0.150051i
$905$	6.69338	−	2.17481i	0.222496	−	0.0722932i
$906$	−7.12466	+	21.9275i	−0.236701	+	0.728491i
$907$	−15.5894	−	11.3264i	−0.517638	−	0.376086i	0.298076	−	0.954542i	$-0.403655\pi$
$907$	−15.5894	−	11.3264i	−0.517638	−	0.376086i	−0.815713	+	0.578456i	$0.803655\pi$
$908$	3.81888	−	5.25624i	0.126734	−	0.174434i
$909$	6.11737	−	18.8273i	0.202900	−	0.624463i
$910$	−17.1879	−	17.0339i	−0.569774	−	0.564667i
$911$	9.72908	−	7.06859i	0.322339	−	0.234193i	−0.414834	−	0.909897i	$-0.636160\pi$
$911$	9.72908	−	7.06859i	0.322339	−	0.234193i	0.737173	+	0.675704i	$0.236160\pi$
$912$			27.1222i			0.898106i
$913$	0.943984	+	12.1099i	0.0312413	+	0.400778i
$914$	36.9357			1.22173
$915$	−9.81216	−	13.5053i	−0.324380	−	0.446471i
$916$	6.79686	−	2.20843i	0.224574	−	0.0729687i
$917$	−33.9233	−	11.0224i	−1.12025	−	0.363990i
$918$	4.54619	−	6.25730i	0.150047	−	0.206522i
$919$	−21.4070	−	15.5531i	−0.706151	−	0.513049i	0.175779	−	0.984430i	$-0.443756\pi$
$919$	−21.4070	−	15.5531i	−0.706151	−	0.513049i	−0.881930	+	0.471381i	$0.843756\pi$
$920$	8.54602	−	26.3019i	0.281754	−	0.867149i
$921$	32.7968	−	10.6563i	1.08069	−	0.351138i
$922$	−26.1644	+	19.0096i	−0.861680	+	0.626047i
$923$	8.54764	−	4.40382i	0.281349	−	0.144954i
$924$	−2.91958	+	1.20678i	−0.0960472	+	0.0397002i
$925$		−	7.49403i		−	0.246402i
$926$	2.31243	−	1.68008i	0.0759913	−	0.0552109i
$927$	5.75706	+	17.7184i	0.189087	+	0.581949i
$928$	−12.1032	−	3.93258i	−0.397308	−	0.129093i
$929$	4.02982	−	5.54658i	0.132214	−	0.181977i	−0.737777	−	0.675045i	$-0.764124\pi$
$929$	4.02982	−	5.54658i	0.132214	−	0.181977i	0.869991	+	0.493067i	$0.164124\pi$
$930$	0.184426	−	0.253841i	0.00604758	−	0.00832378i
$931$	7.01101	+	2.27801i	0.229776	+	0.0746589i
$932$	−0.380916	−	1.17234i	−0.0124773	−	0.0384012i
$933$	9.55638	−	6.94311i	0.312862	−	0.227307i
$934$			15.8730i			0.519382i
$935$	13.4571	−	21.9233i	0.440095	−	0.716969i
$936$	−8.16455	+	4.20645i	−0.266867	+	0.137492i
$937$	28.8092	−	20.9311i	0.941154	−	0.683789i	−0.00754400	−	0.999972i	$-0.502401\pi$
$937$	28.8092	−	20.9311i	0.941154	−	0.683789i	0.948698	+	0.316183i	$0.102401\pi$
$938$	8.19538	−	2.66284i	0.267589	−	0.0869449i
$939$	8.87899	−	27.3267i	0.289755	−	0.891773i
$940$	−3.35695	−	2.43897i	−0.109492	−	0.0795504i
$941$	−10.3332	+	14.2225i	−0.336854	+	0.463639i	−0.943519	−	0.331318i	$-0.892507\pi$
$941$	−10.3332	+	14.2225i	−0.336854	+	0.463639i	0.606666	+	0.794957i	$0.292507\pi$
$942$	−20.9986	−	6.82285i	−0.684170	−	0.222300i
$943$	62.1775	−	20.2027i	2.02478	−	0.657890i
$944$	36.2882	+	49.9465i	1.18108	+	1.62562i
$945$	4.39509			0.142972
$946$	27.9615	+	6.73501i	0.909106	+	0.218974i
$947$		−	11.4919i		−	0.373438i	−0.982413	−	0.186719i	$-0.940215\pi$
$947$		−	11.4919i		−	0.373438i	0.982413	−	0.186719i	$-0.0597854\pi$
$948$	−0.435074	+	0.316100i	−0.0141306	+	0.0102665i
$949$	−11.6417	−	11.5373i	−0.377904	−	0.374517i
$950$	7.46241	−	22.9669i	0.242112	−	0.745145i
$951$	2.17424	−	2.99259i	0.0705046	−	0.0970413i
$952$	−29.9583	−	21.7660i	−0.970955	−	0.705440i
$953$	17.7499	−	54.6286i	0.574976	−	1.76959i	−0.0612839	−	0.998120i	$-0.519520\pi$
$953$	17.7499	−	54.6286i	0.574976	−	1.76959i	0.636260	−	0.771475i	$-0.280480\pi$
$954$	9.88313	−	3.21122i	0.319978	−	0.103967i
$955$	3.58289	+	4.93142i	0.115940	+	0.159577i
$956$			3.42304i			0.110709i
$957$	−17.2760	+	14.7328i	−0.558454	+	0.476245i
$958$	−28.9246			−0.934510
$959$	−10.1222	+	7.35418i	−0.326862	+	0.237479i
$960$	9.12926	−	2.96628i	0.294646	−	0.0957362i
$961$	9.57396	−	29.4656i	0.308838	−	0.950504i
$962$	2.36195	−	15.3600i	0.0761523	−	0.495225i
$963$	10.0481	+	7.30036i	0.323795	+	0.235251i
$964$	−0.756829	−	0.245909i	−0.0243758	−	0.00792018i
$965$	−0.816600	−	2.51324i	−0.0262873	−	0.0809040i
$966$	25.1389	−	18.2645i	0.808831	−	0.587650i
$967$			43.6144i			1.40254i	0.712894	+	0.701271i	$0.247384\pi$
$967$			43.6144i			1.40254i	−0.712894	+	0.701271i	$0.752616\pi$
$968$	4.34208	+	27.6819i	0.139560	+	0.889730i
$969$		−	30.1680i		−	0.969135i
$970$	−5.01919	−	6.90833i	−0.161157	−	0.221813i
$971$	−1.12494	−	3.46222i	−0.0361011	−	0.111108i	0.931382	−	0.364043i	$-0.118604\pi$
$971$	−1.12494	−	3.46222i	−0.0361011	−	0.111108i	−0.967483	+	0.252935i	$0.918604\pi$
$972$	−0.102555	+	0.315631i	−0.00328944	+	0.0101239i
$973$	21.7370	−	29.9184i	0.696857	−	0.959141i
$974$	1.03052	+	0.748719i	0.0330201	+	0.0239905i
$975$	9.44826	−	1.54009i	0.302586	−	0.0493223i
$976$	−15.3397	−	47.2109i	−0.491013	−	1.51118i
$977$	23.3251	+	32.1043i	0.746236	+	1.02711i	0.998236	+	0.0593788i	$0.0189120\pi$
$977$	23.3251	+	32.1043i	0.746236	+	1.02711i	−0.251999	+	0.967727i	$0.581088\pi$
$978$	11.8766			0.379771
$979$	27.6943	+	32.4749i	0.885114	+	1.03790i
$980$			0.628989i			0.0200923i
$981$	4.04543	+	5.56805i	0.129160	+	0.177774i
$982$	−16.3235	+	5.30382i	−0.520903	+	0.169252i
$983$	−2.95644	−	0.960606i	−0.0942958	−	0.0306386i	0.261489	−	0.965206i	$-0.415786\pi$
$983$	−2.95644	−	0.960606i	−0.0942958	−	0.0306386i	−0.355785	+	0.934568i	$0.615786\pi$
$984$	19.0034	+	13.8068i	0.605807	+	0.440144i
$985$	−7.62148	−	5.53733i	−0.242840	−	0.176434i
$986$	50.3571	+	16.3620i	1.60370	+	0.521072i
$987$	7.24158	+	22.2873i	0.230502	+	0.709412i
$988$	3.20703	−	6.36482i	0.102029	−	0.202492i
$989$	−40.2617			−1.28025
$990$	−1.81613	+	7.53995i	−0.0577203	+	0.239635i
$991$	−1.32044			−0.0419453			−0.0209726	−	0.999780i	$-0.506676\pi$
$991$	−1.32044			−0.0419453			−0.0209726	+	0.999780i	$0.506676\pi$
$992$	0.201796	−	0.146614i	0.00640704	−	0.00465499i
$993$	−3.60565	+	1.17155i	−0.114422	+	0.0371779i
$994$	−11.1162	−	3.61187i	−0.352585	−	0.114562i
$995$	−18.1372	+	24.9637i	−0.574988	+	0.791403i
$996$	−0.714415	+	0.983308i	−0.0226371	+	0.0311573i
$997$	2.23346	−	6.87389i	0.0707345	−	0.217698i	−0.909440	−	0.415836i	$-0.863489\pi$
$997$	2.23346	−	6.87389i	0.0707345	−	0.217698i	0.980174	+	0.198137i	$0.0634892\pi$
$998$	20.5543	+	63.2595i	0.650634	+	2.00245i
$999$	1.65905	+	2.28349i	0.0524900	+	0.0722463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.25.4	✓	56
11.4	even	5	inner	429.2.bb.a.103.11	yes	56
13.12	even	2	inner	429.2.bb.a.25.11	yes	56
143.103	even	10	inner	429.2.bb.a.103.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.25.4	✓	56	1.1	even	1	trivial
429.2.bb.a.25.11	yes	56	13.12	even	2	inner
429.2.bb.a.103.4	yes	56	143.103	even	10	inner
429.2.bb.a.103.11	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)

\(f(q)\)	\(=\)	\(q+(-0.897576 - 1.23541i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.102555 + 0.315631i) q^{4} +(0.900087 - 1.23886i) q^{5} +(0.897576 - 1.23541i) q^{6} +(-2.72966 - 0.886920i) q^{7} +(-2.42263 + 0.787161i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.897576 - 1.23541i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.102555 + 0.315631i) q^{4} +(0.900087 - 1.23886i) q^{5} +(0.897576 - 1.23541i) q^{6} +(-2.72966 - 0.886920i) q^{7} +(-2.42263 + 0.787161i) q^{8} +(-0.809017 + 0.587785i) q^{9} -2.33840 q^{10} +(-2.52359 + 2.15209i) q^{11} -0.331874 q^{12} +(-3.21991 - 1.62241i) q^{13} +(1.35437 + 4.16832i) q^{14} +(1.45637 + 0.473204i) q^{15} +(3.68395 + 2.67654i) q^{16} +(-4.09764 - 2.97711i) q^{17} +(1.45231 + 0.471884i) q^{18} +(5.66469 - 1.84057i) q^{19} +(0.298715 + 0.411146i) q^{20} -2.87013i q^{21} +(4.92382 + 1.18599i) q^{22} -7.08980 q^{23} +(-1.49727 - 2.06082i) q^{24} +(0.820459 + 2.52511i) q^{25} +(0.885776 + 5.43413i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.559879 - 0.770607i) q^{28} +(2.11547 - 6.51076i) q^{29} +(-0.722605 - 2.22395i) q^{30} +(0.0788687 + 0.108553i) q^{31} -1.85896i q^{32} +(-2.82659 - 1.73504i) q^{33} +7.73444i q^{34} +(-3.55570 + 2.58337i) q^{35} +(-0.102555 - 0.315631i) q^{36} +(-2.68440 - 0.872214i) q^{37} +(-7.35834 - 5.34615i) q^{38} +(0.547996 - 3.56366i) q^{39} +(-1.20540 + 3.70983i) q^{40} +(-8.76999 + 2.84954i) q^{41} +(-3.54578 + 2.57616i) q^{42} +5.67881 q^{43} +(-0.420462 - 1.01723i) q^{44} +1.53132i q^{45} +(6.36364 + 8.75879i) q^{46} +(-7.76525 + 2.52308i) q^{47} +(-1.40714 + 4.33074i) q^{48} +(1.00129 + 0.727483i) q^{49} +(2.38312 - 3.28008i) q^{50} +(1.56516 - 4.81707i) q^{51} +(0.842298 - 0.849916i) q^{52} +(5.50546 - 3.99995i) q^{53} +1.52705i q^{54} +(0.394704 + 5.06345i) q^{55} +7.31111 q^{56} +(3.50097 + 4.81867i) q^{57} +(-9.94223 + 3.23043i) q^{58} +(12.8943 + 4.18961i) q^{59} +(-0.298715 + 0.411146i) q^{60} +(-8.81938 - 6.40765i) q^{61} +(0.0633171 - 0.194870i) q^{62} +(2.72966 - 0.886920i) q^{63} +(5.07132 - 3.68453i) q^{64} +(-4.90814 + 2.52872i) q^{65} +(0.393603 + 5.04933i) q^{66} -1.96611i q^{67} +(1.35990 - 0.988026i) q^{68} +(-2.19087 - 6.74280i) q^{69} +(6.38303 + 2.07397i) q^{70} +(-1.56752 + 2.15751i) q^{71} +(1.49727 - 2.06082i) q^{72} +(4.32333 + 1.40473i) q^{73} +(1.33191 + 4.09921i) q^{74} +(-2.14799 + 1.56061i) q^{75} +1.97671i q^{76} +(8.79727 - 3.63627i) q^{77} +(-4.89444 + 2.52166i) q^{78} +(1.31096 - 0.952470i) q^{79} +(6.63174 - 2.15478i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.3921 + 8.27683i) q^{82} +(2.15267 - 2.96290i) q^{83} +(0.905903 + 0.294346i) q^{84} +(-7.37647 + 2.39676i) q^{85} +(-5.09717 - 7.01565i) q^{86} +6.84581 q^{87} +(4.41968 - 7.20021i) q^{88} -12.8685i q^{89} +(1.89180 - 1.37448i) q^{90} +(7.35030 + 7.28442i) q^{91} +(0.727092 - 2.23776i) q^{92} +(-0.0788687 + 0.108553i) q^{93} +(10.0869 + 7.32858i) q^{94} +(2.81850 - 8.67445i) q^{95} +(1.76797 - 0.574450i) q^{96} +(2.14642 + 2.95430i) q^{97} -1.88998i q^{98} +(0.776655 - 3.22441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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