LMFDB - Embedded newform 429.2.bb.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.b.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59022 - 2.18875i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.64379 + 5.05905i) q^{4} +(0.714239 - 0.983066i) q^{5} +(-1.59022 + 2.18875i) q^{6} +(1.83379 + 0.595836i) q^{7} +(8.54091 - 2.77511i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.59022 - 2.18875i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.64379 + 5.05905i) q^{4} +(0.714239 - 0.983066i) q^{5} +(-1.59022 + 2.18875i) q^{6} +(1.83379 + 0.595836i) q^{7} +(8.54091 - 2.77511i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.28748 q^{10} +(0.579858 - 3.26554i) q^{11} +5.31940 q^{12} +(-1.37681 - 3.33232i) q^{13} +(-1.61200 - 4.96122i) q^{14} +(-1.15566 - 0.375498i) q^{15} +(-11.0490 - 8.02753i) q^{16} +(-2.21617 - 1.61014i) q^{17} +(2.57303 + 0.836027i) q^{18} +(-2.24916 + 0.730797i) q^{19} +(3.79933 + 5.22933i) q^{20} -1.92817i q^{21} +(-8.06954 + 3.92376i) q^{22} +0.986462 q^{23} +(-5.27858 - 7.26534i) q^{24} +(1.08880 + 3.35099i) q^{25} +(-5.10419 + 8.31261i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-6.02873 + 8.29784i) q^{28} +(1.88082 - 5.78856i) q^{29} +(1.01589 + 3.12658i) q^{30} +(-6.17431 - 8.49821i) q^{31} +18.9880i q^{32} +(-3.28490 + 0.457630i) q^{33} +7.41111i q^{34} +(1.89551 - 1.37717i) q^{35} +(-1.64379 - 5.05905i) q^{36} +(2.39088 + 0.776844i) q^{37} +(5.17618 + 3.76072i) q^{38} +(-2.74377 + 2.33917i) q^{39} +(3.37214 - 10.3784i) q^{40} +(1.41427 - 0.459524i) q^{41} +(-4.22027 + 3.06620i) q^{42} +9.90380 q^{43} +(15.5674 + 8.30139i) q^{44} +1.21514i q^{45} +(-1.56869 - 2.15911i) q^{46} +(-7.47710 + 2.42946i) q^{47} +(-4.22032 + 12.9888i) q^{48} +(-2.65534 - 1.92922i) q^{49} +(5.60304 - 7.71193i) q^{50} +(-0.846501 + 2.60526i) q^{51} +(19.1216 - 1.48773i) q^{52} +(-7.61762 + 5.53453i) q^{53} -2.70544i q^{54} +(-2.79609 - 2.90242i) q^{55} +17.3158 q^{56} +(1.39006 + 1.91325i) q^{57} +(-15.6606 + 5.08844i) q^{58} +(-3.65969 - 1.18911i) q^{59} +(3.79933 - 5.22933i) q^{60} +(1.34340 + 0.976036i) q^{61} +(-8.78193 + 27.0280i) q^{62} +(-1.83379 + 0.595836i) q^{63} +(19.4620 - 14.1400i) q^{64} +(-4.25927 - 1.02658i) q^{65} +(6.22534 + 6.46208i) q^{66} +15.2525i q^{67} +(11.7887 - 8.56499i) q^{68} +(-0.304833 - 0.938181i) q^{69} +(-6.02856 - 1.95880i) q^{70} +(3.16800 - 4.36038i) q^{71} +(-5.27858 + 7.26534i) q^{72} +(-7.00217 - 2.27514i) q^{73} +(-2.10170 - 6.46838i) q^{74} +(2.85053 - 2.07103i) q^{75} -12.5799i q^{76} +(3.00907 - 5.64283i) q^{77} +(9.48305 + 2.28563i) q^{78} +(2.93694 - 2.13381i) q^{79} +(-15.7832 + 5.12827i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-3.25478 - 2.36474i) q^{82} +(7.83621 - 10.7856i) q^{83} +(9.75469 + 3.16949i) q^{84} +(-3.16575 + 1.02861i) q^{85} +(-15.7492 - 21.6769i) q^{86} -6.08645 q^{87} +(-4.10972 - 29.4999i) q^{88} -7.77969i q^{89} +(2.65963 - 1.93233i) q^{90} +(-0.539270 - 6.93115i) q^{91} +(-1.62153 + 4.99056i) q^{92} +(-6.17431 + 8.49821i) q^{93} +(17.2077 + 12.5021i) q^{94} +(-0.888017 + 2.73304i) q^{95} +(18.0586 - 5.86761i) q^{96} +(0.673437 + 0.926906i) q^{97} +8.87974i q^{98} +(1.45032 + 2.98271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * 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 $

$2$	−1.59022	−	2.18875i	−1.12445	−	1.54768i	−0.798197	−	0.602396i	$-0.794213\pi$
$2$	−1.59022	−	2.18875i	−1.12445	−	1.54768i	−0.326257	−	0.945281i	$-0.605787\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−1.64379	+	5.05905i	−0.821893	+	2.52953i
$5$	0.714239	−	0.983066i	0.319418	−	0.439640i	−0.618872	−	0.785492i	$-0.712410\pi$
$5$	0.714239	−	0.983066i	0.319418	−	0.439640i	0.938289	+	0.345852i	$0.112410\pi$
$6$	−1.59022	+	2.18875i	−0.649204	+	0.893552i
$7$	1.83379	+	0.595836i	0.693109	+	0.225205i	0.634326	−	0.773066i	$-0.281278\pi$
$7$	1.83379	+	0.595836i	0.693109	+	0.225205i	0.0587834	+	0.998271i	$0.481278\pi$
$8$	8.54091	−	2.77511i	3.01967	−	0.981150i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−3.28748			−1.03959
$11$	0.579858	−	3.26554i	0.174834	−	0.984598i
$11$	0.579858	−	3.26554i	0.174834	−	0.984598i
$12$	5.31940			1.53558
$13$	−1.37681	−	3.33232i	−0.381859	−	0.924221i
$13$	−1.37681	−	3.33232i	−0.381859	−	0.924221i
$14$	−1.61200	−	4.96122i	−0.430825	−	1.32594i
$15$	−1.15566	−	0.375498i	−0.298391	−	0.0969531i
$16$	−11.0490	−	8.02753i	−2.76224	−	2.00688i
$17$	−2.21617	−	1.61014i	−0.537500	−	0.390516i	0.285656	−	0.958332i	$-0.407789\pi$
$17$	−2.21617	−	1.61014i	−0.537500	−	0.390516i	−0.823156	+	0.567816i	$0.807789\pi$
$18$	2.57303	+	0.836027i	0.606468	+	0.197053i
$19$	−2.24916	+	0.730797i	−0.515993	+	0.167656i	−0.555426	−	0.831566i	$-0.687445\pi$
$19$	−2.24916	+	0.730797i	−0.515993	+	0.167656i	0.0394332	+	0.999222i	$0.487445\pi$
$20$	3.79933	+	5.22933i	0.849555	+	1.16931i
$21$		−	1.92817i		−	0.420760i
$22$	−8.06954	+	3.92376i	−1.72043	+	0.836548i
$23$	0.986462			0.205691			0.102846	−	0.994697i	$-0.467205\pi$
$23$	0.986462			0.205691			0.102846	+	0.994697i	$0.467205\pi$
$24$	−5.27858	−	7.26534i	−1.07748	−	1.48303i
$25$	1.08880	+	3.35099i	0.217761	+	0.670199i
$26$	−5.10419	+	8.31261i	−1.00101	+	1.63024i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−6.02873	+	8.29784i	−1.13932	+	1.56814i
$29$	1.88082	−	5.78856i	0.349259	−	1.07491i	−0.610005	−	0.792398i	$-0.708833\pi$
$29$	1.88082	−	5.78856i	0.349259	−	1.07491i	0.959264	−	0.282511i	$-0.0911675\pi$
$30$	1.01589	+	3.12658i	0.185475	+	0.570832i
$31$	−6.17431	−	8.49821i	−1.10894	−	1.52632i	−0.822970	−	0.568085i	$-0.807684\pi$
$31$	−6.17431	−	8.49821i	−1.10894	−	1.52632i	−0.285970	−	0.958239i	$-0.592316\pi$
$32$			18.9880i			3.35663i
$33$	−3.28490	+	0.457630i	−0.571828	+	0.0796632i
$34$			7.41111i			1.27099i
$35$	1.89551	−	1.37717i	0.320400	−	0.232784i
$36$	−1.64379	−	5.05905i	−0.273964	−	0.843176i
$37$	2.39088	+	0.776844i	0.393058	+	0.127712i	0.498876	−	0.866673i	$-0.333746\pi$
$37$	2.39088	+	0.776844i	0.393058	+	0.127712i	−0.105818	+	0.994385i	$0.533746\pi$
$38$	5.17618	+	3.76072i	0.839688	+	0.610069i
$39$	−2.74377	+	2.33917i	−0.439355	+	0.374567i
$40$	3.37214	−	10.3784i	0.533182	−	1.64097i
$41$	1.41427	−	0.459524i	0.220872	−	0.0717656i	−0.196491	−	0.980506i	$-0.562955\pi$
$41$	1.41427	−	0.459524i	0.220872	−	0.0717656i	0.417363	+	0.908740i	$0.362955\pi$
$42$	−4.22027	+	3.06620i	−0.651201	+	0.473125i
$43$	9.90380			1.51031			0.755157	−	0.655543i	$-0.227560\pi$
$43$	9.90380			1.51031			0.755157	+	0.655543i	$0.227560\pi$
$44$	15.5674	+	8.30139i	2.34687	+	1.25148i
$45$			1.21514i			0.181142i
$46$	−1.56869	−	2.15911i	−0.231291	−	0.318344i
$47$	−7.47710	+	2.42946i	−1.09065	+	0.354373i	−0.798497	−	0.601999i	$-0.794371\pi$
$47$	−7.47710	+	2.42946i	−1.09065	+	0.354373i	−0.292151	+	0.956372i	$0.594371\pi$
$48$	−4.22032	+	12.9888i	−0.609151	+	1.87477i
$49$	−2.65534	−	1.92922i	−0.379334	−	0.275602i
$50$	5.60304	−	7.71193i	0.792390	−	1.09063i
$51$	−0.846501	+	2.60526i	−0.118534	+	0.364810i
$52$	19.1216	−	1.48773i	2.65169	−	0.206312i
$53$	−7.61762	+	5.53453i	−1.04636	+	0.760226i	−0.971517	−	0.236970i	$-0.923846\pi$
$53$	−7.61762	+	5.53453i	−1.04636	+	0.760226i	−0.0748438	+	0.997195i	$0.523846\pi$
$54$		−	2.70544i		−	0.368164i
$55$	−2.79609	−	2.90242i	−0.377024	−	0.391362i
$56$	17.3158			2.31392
$57$	1.39006	+	1.91325i	0.184118	+	0.253416i
$58$	−15.6606	+	5.08844i	−2.05634	+	0.668145i
$59$	−3.65969	−	1.18911i	−0.476451	−	0.154808i	0.0609402	−	0.998141i	$-0.480590\pi$
$59$	−3.65969	−	1.18911i	−0.476451	−	0.154808i	−0.537391	+	0.843333i	$0.680590\pi$
$60$	3.79933	−	5.22933i	0.490491	−	0.675103i
$61$	1.34340	+	0.976036i	0.172004	+	0.124969i	0.670457	−	0.741949i	$-0.266098\pi$
$61$	1.34340	+	0.976036i	0.172004	+	0.124969i	−0.498452	+	0.866917i	$0.666098\pi$
$62$	−8.78193	+	27.0280i	−1.11531	+	3.43256i
$63$	−1.83379	+	0.595836i	−0.231036	+	0.0750683i
$64$	19.4620	−	14.1400i	2.43275	−	1.76749i
$65$	−4.25927	−	1.02658i	−0.528297	−	0.127332i
$66$	6.22534	+	6.46208i	0.766287	+	0.795428i
$67$			15.2525i			1.86339i	0.363235	+	0.931697i	$0.381672\pi$
$67$			15.2525i			1.86339i	−0.363235	+	0.931697i	$0.618328\pi$
$68$	11.7887	−	8.56499i	1.42959	−	1.03866i
$69$	−0.304833	−	0.938181i	−0.0366976	−	0.112944i
$70$	−6.02856	−	1.95880i	−0.720551	−	0.234121i
$71$	3.16800	−	4.36038i	0.375973	−	0.517482i	−0.578539	−	0.815655i	$-0.696377\pi$
$71$	3.16800	−	4.36038i	0.375973	−	0.517482i	0.954512	+	0.298172i	$0.0963770\pi$
$72$	−5.27858	+	7.26534i	−0.622086	+	0.856228i
$73$	−7.00217	−	2.27514i	−0.819542	−	0.266285i	−0.130908	−	0.991395i	$-0.541789\pi$
$73$	−7.00217	−	2.27514i	−0.819542	−	0.266285i	−0.688634	+	0.725109i	$0.741789\pi$
$74$	−2.10170	−	6.46838i	−0.244318	−	0.751934i
$75$	2.85053	−	2.07103i	0.329150	−	0.239142i
$76$		−	12.5799i		−	1.44301i
$77$	3.00907	−	5.64283i	0.342915	−	0.643060i
$78$	9.48305	+	2.28563i	1.07374	+	0.258797i
$79$	2.93694	−	2.13381i	0.330432	−	0.240073i	−0.410182	−	0.912004i	$-0.634535\pi$
$79$	2.93694	−	2.13381i	0.330432	−	0.240073i	0.740614	+	0.671931i	$0.234535\pi$
$80$	−15.7832	+	5.12827i	−1.76461	+	0.573358i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−3.25478	−	2.36474i	−0.359430	−	0.261141i
$83$	7.83621	−	10.7856i	0.860136	−	1.18388i	−0.121401	−	0.992604i	$-0.538739\pi$
$83$	7.83621	−	10.7856i	0.860136	−	1.18388i	0.981537	−	0.191272i	$-0.0612612\pi$
$84$	9.75469	+	3.16949i	1.06432	+	0.345820i
$85$	−3.16575	+	1.02861i	−0.343374	+	0.111569i
$86$	−15.7492	−	21.6769i	−1.69828	−	2.33748i
$87$	−6.08645			−0.652536
$88$	−4.10972	−	29.4999i	−0.438098	−	3.14470i
$89$		−	7.77969i		−	0.824646i	−0.911038	−	0.412323i	$-0.864718\pi$
$89$		−	7.77969i		−	0.824646i	0.911038	−	0.412323i	$-0.135282\pi$
$90$	2.65963	−	1.93233i	0.280349	−	0.203686i
$91$	−0.539270	−	6.93115i	−0.0565309	−	0.726582i
$92$	−1.62153	+	4.99056i	−0.169056	+	0.520302i
$93$	−6.17431	+	8.49821i	−0.640246	+	0.881224i
$94$	17.2077	+	12.5021i	1.77484	+	1.28950i
$95$	−0.888017	+	2.73304i	−0.0911087	+	0.280404i
$96$	18.0586	−	5.86761i	1.84310	−	0.598860i
$97$	0.673437	+	0.926906i	0.0683772	+	0.0941131i	0.841836	−	0.539734i	$-0.181475\pi$
$97$	0.673437	+	0.926906i	0.0683772	+	0.0941131i	−0.773459	+	0.633847i	$0.781475\pi$
$98$			8.87974i			0.896989i
$99$	1.45032	+	2.98271i	0.145763	+	0.299774i
$100$	−18.7426			−1.87426
$101$	−8.88423	+	6.45477i	−0.884013	+	0.642273i	−0.934310	−	0.356461i	$-0.883983\pi$
$101$	−8.88423	+	6.45477i	−0.884013	+	0.642273i	0.0502968	+	0.998734i	$0.483983\pi$
$102$	7.04838	−	2.29016i	0.697894	−	0.226759i
$103$	4.57973	−	14.0950i	0.451255	−	1.38882i	−0.424222	−	0.905558i	$-0.639452\pi$
$103$	4.57973	−	14.0950i	0.451255	−	1.38882i	0.875477	−	0.483261i	$-0.160548\pi$
$104$	−21.0068	−	24.6403i	−2.05989	−	2.41618i
$105$	−1.89551	−	1.37717i	−0.184983	−	0.134398i
$106$	24.2274	+	7.87194i	2.35317	+	0.764591i
$107$	−0.537531	−	1.65435i	−0.0519650	−	0.159932i	0.921706	−	0.387889i	$-0.126796\pi$
$107$	−0.537531	−	1.65435i	−0.0519650	−	0.159932i	−0.973671	+	0.227957i	$0.926796\pi$
$108$	−4.30349	+	3.12667i	−0.414103	+	0.300864i
$109$			0.825638i			0.0790818i	0.999218	+	0.0395409i	$0.0125895\pi$
$109$			0.825638i			0.0790818i	−0.999218	+	0.0395409i	$0.987410\pi$
$110$	−1.90627	+	10.7354i	−0.181756	+	1.02358i
$111$		−	2.51392i		−	0.238611i
$112$	−15.4784	−	21.3042i	−1.46257	−	2.01306i
$113$	−4.17463	−	12.8482i	−0.392716	−	1.20866i	−0.930726	−	0.365717i	$-0.880824\pi$
$113$	−4.17463	−	12.8482i	−0.392716	−	1.20866i	0.538010	−	0.842939i	$-0.319176\pi$
$114$	1.97713	−	6.08497i	0.185175	−	0.569909i
$115$	0.704570	−	0.969757i	0.0657015	−	0.0904303i
$116$	26.1930	+	19.0303i	2.43196	+	1.76692i
$117$	3.07256	+	1.88664i	0.284058	+	0.174420i
$118$	3.21705	+	9.90107i	0.296154	+	0.911467i
$119$	−3.10462	−	4.27314i	−0.284600	−	0.391718i
$120$	−10.9125			−0.996168
$121$	−10.3275	−	3.78710i	−0.938866	−	0.344282i
$122$		−	4.49247i		−	0.406729i
$123$	−0.874067	−	1.20305i	−0.0788120	−	0.108475i
$124$	53.1422	−	17.2669i	4.77231	−	1.55062i
$125$	9.85023	+	3.20053i	0.881031	+	0.286264i
$126$	4.22027	+	3.06620i	0.375971	+	0.273159i
$127$	18.1094	+	13.1573i	1.60695	+	1.16752i	0.872150	+	0.489238i	$0.162725\pi$
$127$	18.1094	+	13.1573i	1.60695	+	1.16752i	0.734802	+	0.678281i	$0.237275\pi$
$128$	−25.7803	−	8.37652i	−2.27868	−	0.740387i
$129$	−3.06044	−	9.41907i	−0.269457	−	0.829303i
$130$	4.52624	+	10.9549i	0.396977	+	0.960812i
$131$	17.6690			1.54374			0.771872	−	0.635778i	$-0.219321\pi$
$131$	17.6690			1.54374			0.771872	+	0.635778i	$0.219321\pi$
$132$	3.08450	−	17.3707i	0.268471	−	1.51193i
$133$	−4.55993			−0.395396
$134$	33.3840	−	24.2549i	2.88393	−	2.09530i
$135$	1.15566	−	0.375498i	0.0994637	−	0.0323177i
$136$	−23.3964	−	7.60196i	−2.00623	−	0.651863i
$137$	1.74997	−	2.40863i	0.149510	−	0.205783i	−0.727692	−	0.685904i	$-0.759407\pi$
$137$	1.74997	−	2.40863i	0.149510	−	0.205783i	0.877202	+	0.480121i	$0.159407\pi$
$138$	−1.56869	+	2.15911i	−0.133536	+	0.183796i
$139$	0.975748	−	3.00304i	0.0827619	−	0.254715i	−0.901110	−	0.433591i	$-0.857246\pi$
$139$	0.975748	−	3.00304i	0.0827619	−	0.254715i	0.983872	+	0.178876i	$0.0572462\pi$
$140$	3.85136	+	11.8533i	0.325500	+	1.00179i
$141$	4.62110	+	6.36040i	0.389167	+	0.535643i
$142$	−14.5816			−1.22366
$143$	−11.6802	+	2.56376i	−0.976748	+	0.214392i
$144$	13.6573			1.13810
$145$	−4.34718	−	5.98339i	−0.361014	−	0.496893i
$146$	6.15526	+	18.9439i	0.509413	+	1.56781i
$147$	−1.01425	+	3.12154i	−0.0836539	+	0.257460i
$148$	−7.86019	+	10.8186i	−0.646104	+	0.889285i
$149$	−2.59451	+	3.57103i	−0.212550	+	0.292550i	−0.901959	−	0.431823i	$-0.857871\pi$
$149$	−2.59451	+	3.57103i	−0.212550	+	0.292550i	0.689408	+	0.724373i	$0.257871\pi$
$150$	−9.06591	−	2.94569i	−0.740229	−	0.240515i
$151$	11.8185	−	3.84007i	0.961777	−	0.312500i	0.214285	−	0.976771i	$-0.431258\pi$
$151$	11.8185	−	3.84007i	0.961777	−	0.312500i	0.747492	+	0.664271i	$0.231258\pi$
$152$	−17.1818	+	12.4833i	−1.39363	+	1.01253i
$153$	2.73933			0.221462
$154$	−17.1358	+	2.38724i	−1.38084	+	0.192370i
$155$	−12.7642			−1.02525
$156$	−7.32382	−	17.7260i	−0.586375	−	1.41921i
$157$	3.91971	+	12.0636i	0.312827	+	0.962783i	0.976640	+	0.214884i	$0.0689373\pi$
$157$	3.91971	+	12.0636i	0.312827	+	0.962783i	−0.663812	+	0.747899i	$0.731063\pi$
$158$	−9.34075	−	3.03499i	−0.743110	−	0.241451i
$159$	7.61762	+	5.53453i	0.604117	+	0.438917i
$160$	18.6664	+	13.5620i	1.47571	+	1.07217i
$161$	1.80897	+	0.587769i	0.142567	+	0.0463227i
$162$	−2.57303	+	0.836027i	−0.202156	+	0.0656845i
$163$	14.1077	+	19.4176i	1.10500	+	1.52090i	0.828584	+	0.559865i	$0.189147\pi$
$163$	14.1077	+	19.4176i	1.10500	+	1.52090i	0.276417	+	0.961038i	$0.410853\pi$
$164$			7.91023i			0.617685i
$165$	−1.89632	+	3.55613i	−0.147629	+	0.276844i
$166$	−36.0683			−2.79944
$167$	7.60357	+	10.4654i	0.588382	+	0.809838i	0.994583	−	0.103946i	$-0.0331468\pi$
$167$	7.60357	+	10.4654i	0.588382	+	0.809838i	−0.406201	+	0.913784i	$0.633147\pi$
$168$	−5.35087	−	16.4683i	−0.412829	−	1.27056i
$169$	−9.20878	+	9.17597i	−0.708368	+	0.705844i
$170$	7.28561	+	5.29330i	0.558780	+	0.405978i
$171$	1.39006	−	1.91325i	0.106300	−	0.146310i
$172$	−16.2797	+	50.1038i	−1.24132	+	3.82038i
$173$	−4.61494	−	14.2033i	−0.350867	−	1.07986i	−0.958367	−	0.285539i	$-0.907828\pi$
$173$	−4.61494	−	14.2033i	−0.350867	−	1.07986i	0.607500	−	0.794320i	$-0.292172\pi$
$174$	9.67879	+	13.3217i	0.733747	+	1.00992i
$175$			6.79378i			0.513562i
$176$	−32.6211	+	31.4260i	−2.45891	+	2.36882i
$177$			3.84803i			0.289235i
$178$	−17.0278	+	12.3714i	−1.27629	+	0.927276i
$179$	2.02468	+	6.23132i	0.151332	+	0.465751i	0.997771	−	0.0667347i	$-0.0212581\pi$
$179$	2.02468	+	6.23132i	0.151332	+	0.465751i	−0.846439	+	0.532485i	$0.821258\pi$
$180$	−6.14744	−	1.99742i	−0.458203	−	0.148879i
$181$	−1.47906	−	1.07460i	−0.109937	−	0.0798742i	0.531458	−	0.847084i	$-0.321644\pi$
$181$	−1.47906	−	1.07460i	−0.109937	−	0.0798742i	−0.641396	+	0.767210i	$0.721644\pi$
$182$	−14.3130	+	12.2024i	−1.06095	+	0.904499i
$183$	0.513132	−	1.57926i	0.0379318	−	0.116742i
$184$	8.42528	−	2.73754i	0.621120	−	0.201814i
$185$	2.47135	−	1.79554i	0.181697	−	0.132011i
$186$	28.4189			2.08378
$187$	−6.54304	+	6.30334i	−0.478475	+	0.460946i
$188$		−	41.8206i		−	3.05008i
$189$	1.13335	+	1.55992i	0.0824389	+	0.113467i
$190$	7.39407	−	2.40248i	0.536422	−	0.174294i
$191$	6.67318	−	20.5379i	0.482855	−	1.48607i	−0.352209	−	0.935921i	$-0.614570\pi$
$191$	6.67318	−	20.5379i	0.482855	−	1.48607i	0.835064	−	0.550153i	$-0.185430\pi$
$192$	−19.4620	−	14.1400i	−1.40455	−	1.02046i
$193$	5.86319	−	8.06999i	0.422042	−	0.580891i	−0.544062	−	0.839045i	$-0.683114\pi$
$193$	5.86319	−	8.06999i	0.422042	−	0.580891i	0.966104	+	0.258154i	$0.0831143\pi$
$194$	0.957852	−	2.94797i	0.0687698	−	0.211652i
$195$	0.339850	+	4.36804i	0.0243372	+	0.312802i
$196$	14.1248	−	10.2623i	1.00892	−	0.733020i
$197$			1.00508i			0.0716093i	0.999359	+	0.0358047i	$0.0113994\pi$
$197$			1.00508i			0.0716093i	−0.999359	+	0.0358047i	$0.988601\pi$
$198$	4.22207	−	7.91755i	0.300049	−	0.562676i
$199$	12.8185			0.908676			0.454338	−	0.890829i	$-0.349876\pi$
$199$	12.8185			0.908676			0.454338	+	0.890829i	$0.349876\pi$
$200$	18.5988	+	25.5990i	1.31513	+	1.81012i
$201$	14.5060	−	4.71330i	1.02318	−	0.332450i
$202$	28.2557	+	9.18083i	1.98806	+	0.645961i
$203$	6.89806	−	9.49437i	0.484149	−	0.666374i
$204$	−11.7887	−	8.56499i	−0.825374	−	0.599669i
$205$	0.558385	−	1.71853i	0.0389993	−	0.120027i
$206$	−38.1331	+	12.3902i	−2.65686	+	0.863266i
$207$	−0.798064	+	0.579828i	−0.0554693	+	0.0403008i
$208$	−11.5380	+	47.8711i	−0.800018	+	3.31926i
$209$	1.08225	+	7.76849i	0.0748610	+	0.537357i
$210$			6.33880i			0.437419i
$211$	19.0174	−	13.8169i	1.30921	−	0.951197i	0.309210	−	0.950994i	$-0.399935\pi$
$211$	19.0174	−	13.8169i	1.30921	−	0.951197i	1.00000		0.000203014i	$-6.46214e-5\pi$
$212$	−15.4777	−	47.6355i	−1.06301	−	3.27162i
$213$	−5.12594	−	1.66552i	−0.351223	−	0.114119i
$214$	−2.76616	+	3.80729i	−0.189091	+	0.260261i
$215$	7.07368	−	9.73609i	0.482421	−	0.663996i
$216$	8.54091	+	2.77511i	0.581136	+	0.188822i
$217$	−6.25888	−	19.2628i	−0.424880	−	1.30765i
$218$	1.80711	−	1.31294i	0.122393	−	0.0889238i
$219$			7.36252i			0.497513i
$220$	19.2797	−	9.37460i	1.29983	−	0.632035i
$221$	−2.31427	+	9.60185i	−0.155674	+	0.645891i
$222$	−5.50233	+	3.99768i	−0.369292	+	0.268307i
$223$	−5.58334	+	1.81414i	−0.373888	+	0.121484i	−0.489932	−	0.871760i	$-0.662979\pi$
$223$	−5.58334	+	1.81414i	−0.373888	+	0.121484i	0.116044	+	0.993244i	$0.462979\pi$
$224$	−11.3137	+	34.8200i	−0.755930	+	2.32651i
$225$	−2.85053	−	2.07103i	−0.190035	−	0.138069i
$226$	−21.4829	+	29.5686i	−1.42902	+	1.96688i
$227$	8.61807	+	2.80018i	0.572001	+	0.185854i	0.580714	−	0.814108i	$-0.302773\pi$
$227$	8.61807	+	2.80018i	0.572001	+	0.185854i	−0.00871295	+	0.999962i	$0.502773\pi$
$228$	−11.9642	+	3.88740i	−0.792348	+	0.257449i
$229$	12.5498	+	17.2733i	0.829312	+	1.14145i	0.988051	+	0.154130i	$0.0492574\pi$
$229$	12.5498	+	17.2733i	0.829312	+	1.14145i	−0.158738	+	0.987321i	$0.550743\pi$
$230$	−3.24297			−0.213835
$231$	−6.29650	−	1.11806i	−0.414280	−	0.0735631i
$232$		−	54.6591i		−	3.58854i
$233$	0.737126	−	0.535553i	0.0482907	−	0.0350853i	−0.563378	−	0.826199i	$-0.690499\pi$
$233$	0.737126	−	0.535553i	0.0482907	−	0.0350853i	0.611669	+	0.791114i	$0.290499\pi$
$234$	−0.756659	−	9.72521i	−0.0494643	−	0.635757i
$235$	−2.95212	+	9.08570i	−0.192575	+	0.592686i
$236$	12.0315	−	16.5599i	0.783184	−	1.07796i
$237$	−2.93694	−	2.13381i	−0.190775	−	0.138606i
$238$	−4.41580	+	13.5904i	−0.286234	+	0.880937i
$239$	−0.646366	+	0.210017i	−0.0418099	+	0.0135849i	−0.329847	−	0.944034i	$-0.606997\pi$
$239$	−0.646366	+	0.210017i	−0.0418099	+	0.0135849i	0.288037	+	0.957619i	$0.406997\pi$
$240$	9.75455	+	13.4260i	0.629653	+	0.866643i
$241$			9.37549i			0.603928i	0.953319	+	0.301964i	$0.0976423\pi$
$241$			9.37549i			0.603928i	−0.953319	+	0.301964i	$0.902358\pi$
$242$	8.13401	+	28.6267i	0.522874	+	1.84019i
$243$	−1.00000			−0.0641500
$244$	−7.14608	+	5.19193i	−0.457481	+	0.332379i
$245$	−3.79309	+	1.23245i	−0.242332	+	0.0787384i
$246$	−1.24322	+	3.82622i	−0.0792645	+	0.243951i
$247$	5.53192	+	6.48876i	0.351988	+	0.412870i
$248$	−76.3178	−	55.4481i	−4.84618	−	3.52096i
$249$	−12.6793	−	4.11974i	−0.803515	−	0.261078i
$250$	−8.65885	−	26.6492i	−0.547634	−	1.68544i
$251$	−23.9026	+	17.3663i	−1.50872	+	1.09615i	−0.541977	+	0.840393i	$0.682324\pi$
$251$	−23.9026	+	17.3663i	−1.50872	+	1.09615i	−0.966742	+	0.255755i	$0.917676\pi$
$252$		−	10.2567i		−	0.646111i
$253$	0.572008	−	3.22133i	0.0359618	−	0.202523i
$254$		−	60.5599i		−	3.79987i
$255$	1.95654	+	2.69295i	0.122523	+	0.168639i
$256$	7.79454	+	23.9891i	0.487159	+	1.49932i
$257$	−1.24014	+	3.81675i	−0.0773577	+	0.238082i	−0.982256	−	0.187546i	$-0.939947\pi$
$257$	−1.24014	+	3.81675i	−0.0773577	+	0.238082i	0.904898	+	0.425628i	$0.139947\pi$
$258$	−15.7492	+	21.6769i	−0.980502	+	1.34955i
$259$	3.92151	+	2.84914i	0.243671	+	0.177037i
$260$	12.1949	−	19.8604i	0.756293	−	1.23169i
$261$	1.88082	+	5.78856i	0.116420	+	0.358303i
$262$	−28.0975	−	38.6729i	−1.73587	−	2.38922i
$263$	18.7180			1.15420			0.577101	−	0.816673i	$-0.304184\pi$
$263$	18.7180			1.15420			0.577101	+	0.816673i	$0.304184\pi$
$264$	−26.7861	+	13.0245i	−1.64857	+	0.801605i
$265$			11.4416i			0.702852i
$266$	7.25128	+	9.98054i	0.444605	+	0.611946i
$267$	−7.39893	+	2.40406i	−0.452807	+	0.147126i
$268$	−77.1635	−	25.0719i	−4.71351	−	1.53151i
$269$	14.1844	+	10.3056i	0.864839	+	0.628342i	0.929197	−	0.369585i	$-0.120500\pi$
$269$	14.1844	+	10.3056i	0.864839	+	0.628342i	−0.0643584	+	0.997927i	$0.520500\pi$
$270$	−2.65963	−	1.93233i	−0.161860	−	0.117598i
$271$	−16.5748	−	5.38548i	−1.00685	−	0.327145i	−0.241249	−	0.970463i	$-0.577557\pi$
$271$	−16.5748	−	5.38548i	−1.00685	−	0.327145i	−0.765598	+	0.643319i	$0.777557\pi$
$272$	11.5609	+	35.5807i	0.700981	+	2.15740i
$273$	−6.42527	+	2.65472i	−0.388875	+	0.160671i
$274$	−8.05471			−0.486603
$275$	11.5742	−	1.61243i	0.697948	−	0.0972334i
$276$	5.24739			0.315856
$277$	18.2972	−	13.2937i	1.09937	−	0.798742i	0.118416	−	0.992964i	$-0.462218\pi$
$277$	18.2972	−	13.2937i	1.09937	−	0.798742i	0.980958	+	0.194222i	$0.0622182\pi$
$278$	−8.12455	+	2.63983i	−0.487278	+	0.158326i
$279$	9.99025	+	3.24603i	0.598100	+	0.194335i
$280$	12.3676	−	17.0226i	0.739106	−	1.01729i
$281$	−4.36954	+	6.01415i	−0.260665	+	0.358774i	−0.919211	−	0.393766i	$-0.871172\pi$
$281$	−4.36954	+	6.01415i	−0.260665	+	0.358774i	0.658546	+	0.752541i	$0.271172\pi$
$282$	6.57275	−	20.2289i	0.391402	−	1.20461i
$283$	2.73747	+	8.42505i	0.162725	+	0.500817i	0.998861	−	0.0477047i	$-0.0151907\pi$
$283$	2.73747	+	8.42505i	0.162725	+	0.500817i	−0.836136	+	0.548522i	$0.815191\pi$
$284$	16.8519	+	23.1946i	0.999976	+	1.37635i
$285$	2.87368			0.170222
$286$	24.1855	+	21.4881i	1.43012	+	1.27062i
$287$	2.86728			0.169250
$288$	−11.1609	−	15.3616i	−0.657660	−	0.905191i
$289$	−2.93444	−	9.03128i	−0.172614	−	0.531252i
$290$	−6.18315	+	19.0298i	−0.363087	+	1.11747i
$291$	0.673437	−	0.926906i	0.0394776	−	0.0543362i
$292$	23.0201	−	31.6845i	1.34715	−	1.85420i
$293$	−28.9015	−	9.39066i	−1.68844	−	0.548608i	−0.701923	−	0.712253i	$-0.747675\pi$
$293$	−28.9015	−	9.39066i	−1.68844	−	0.548608i	−0.986519	+	0.163645i	$0.947675\pi$
$294$	8.44513	−	2.74399i	0.492530	−	0.160033i
$295$	−3.78286	+	2.74841i	−0.220247	+	0.160019i
$296$	22.5761			1.31221
$297$	2.38855	−	2.30105i	0.138598	−	0.133520i
$298$	11.9419			0.691777
$299$	−1.35817	−	3.28721i	−0.0785451	−	0.190104i
$300$	5.79179	+	17.8253i	0.334389	+	1.02914i
$301$	18.1615	+	5.90104i	1.04681	+	0.340130i
$302$	−27.1989	−	19.7612i	−1.56512	−	1.13713i
$303$	8.88423	+	6.45477i	0.510385	+	0.370817i
$304$	30.7174	+	9.98067i	1.76176	+	0.572431i
$305$	1.91901	−	0.623526i	0.109882	−	0.0357030i
$306$	−4.35614	−	5.99571i	−0.249024	−	0.342752i
$307$		−	15.9993i		−	0.913126i	−0.889691	−	0.456563i	$-0.849080\pi$
$307$		−	15.9993i		−	0.913126i	0.889691	−	0.456563i	$-0.150920\pi$
$308$	23.6011	+	24.4986i	1.34480	+	1.39594i
$309$	−14.8203			−0.843099
$310$	20.2979	+	27.9377i	1.15284	+	1.58675i
$311$	8.68187	+	26.7200i	0.492304	+	1.51515i	0.821117	+	0.570760i	$0.193351\pi$
$311$	8.68187	+	26.7200i	0.492304	+	1.51515i	−0.328813	+	0.944395i	$0.606649\pi$
$312$	−16.9429	+	27.5929i	−0.959200	+	1.56214i
$313$	6.08778	+	4.42303i	0.344102	+	0.250004i	0.746390	−	0.665508i	$-0.231785\pi$
$313$	6.08778	+	4.42303i	0.344102	+	0.250004i	−0.402289	+	0.915513i	$0.631785\pi$
$314$	20.1711	−	27.7631i	1.13832	−	1.56676i
$315$	−0.724022	+	2.22831i	−0.0407940	+	0.125551i
$316$	5.96737	+	18.3657i	0.335691	+	1.03315i
$317$	5.32941	+	7.33530i	0.299329	+	0.411991i	0.932016	−	0.362416i	$-0.118048\pi$
$317$	5.32941	+	7.33530i	0.299329	+	0.411991i	−0.632687	+	0.774408i	$0.718048\pi$
$318$		−	25.4741i		−	1.42852i
$319$	−17.8122	−	9.49843i	−0.997291	−	0.531810i
$320$		−	29.2317i		−	1.63410i
$321$	−1.40727	+	1.02244i	−0.0785463	+	0.0570673i
$322$	−1.59017	−	4.89405i	−0.0886169	−	0.272735i
$323$	6.16120	+	2.00190i	0.342819	+	0.111388i
$324$	4.30349	+	3.12667i	0.239083	+	0.173704i
$325$	9.66752	−	8.24194i	0.536258	−	0.457180i
$326$	20.0659	−	61.7564i	1.11135	−	3.42037i
$327$	0.785228	−	0.255136i	0.0434232	−	0.0141091i
$328$	10.8039	−	7.84952i	0.596547	−	0.433417i
$329$	−15.1590			−0.835744
$330$	10.7990	−	1.50445i	0.594468	−	0.0828172i
$331$		−	26.9610i		−	1.48191i	−0.671554	−	0.740956i	$-0.734373\pi$
$331$		−	26.9610i		−	1.48191i	0.671554	−	0.740956i	$-0.265627\pi$
$332$	41.6840	+	57.3731i	2.28771	+	3.14876i
$333$	−2.39088	+	0.776844i	−0.131019	+	0.0425708i
$334$	10.8148	−	33.2846i	0.591760	−	1.82125i
$335$	14.9943	+	10.8940i	0.819224	+	0.595201i
$336$	−15.4784	+	21.3042i	−0.844416	+	1.16224i
$337$	−4.96834	+	15.2910i	−0.270643	+	0.832953i	0.719696	+	0.694289i	$0.244281\pi$
$337$	−4.96834	+	15.2910i	−0.270643	+	0.832953i	−0.990339	+	0.138664i	$0.955719\pi$
$338$	34.7278	+	5.56390i	1.88895	+	0.302636i
$339$	−10.9293	+	7.94062i	−0.593599	+	0.431275i
$340$		−	17.7065i		−	0.960271i
$341$	−31.3315	+	15.2347i	−1.69670	+	0.825006i
$342$	−6.39811			−0.345970
$343$	−11.6533	−	16.0394i	−0.629218	−	0.866044i
$344$	84.5875	−	27.4841i	4.56065	−	1.48185i
$345$	−1.14002	−	0.370414i	−0.0613765	−	0.0199424i
$346$	−23.7487	+	32.6873i	−1.27674	+	1.75728i
$347$	−1.92069	−	1.39546i	−0.103108	−	0.0749123i	0.535037	−	0.844829i	$-0.320298\pi$
$347$	−1.92069	−	1.39546i	−0.103108	−	0.0749123i	−0.638145	+	0.769917i	$0.720298\pi$
$348$	10.0048	−	30.7917i	0.536315	−	1.65061i
$349$	−10.9577	+	3.56036i	−0.586551	+	0.190582i	−0.587233	−	0.809418i	$-0.699783\pi$
$349$	−10.9577	+	3.56036i	−0.586551	+	0.190582i	0.000682233		1.00000i	$0.499783\pi$
$350$	14.8699	−	10.8036i	0.794828	−	0.577476i
$351$	0.844828	−	3.50518i	0.0450936	−	0.187093i
$352$	62.0060	+	11.0103i	3.30493	+	0.586853i
$353$			20.3791i			1.08467i	0.840162	+	0.542336i	$0.182460\pi$
$353$			20.3791i			1.08467i	−0.840162	+	0.542336i	$0.817540\pi$
$354$	8.42235	−	6.11920i	0.447643	−	0.325232i
$355$	−2.02383	−	6.22871i	−0.107414	−	0.330586i
$356$	39.3579	+	12.7882i	2.08596	+	0.677771i
$357$	−3.10462	+	4.27314i	−0.164314	+	0.226158i
$358$	10.4191	−	14.3407i	0.550667	−	0.757928i
$359$	6.08727	+	1.97787i	0.321274	+	0.104388i	0.465214	−	0.885198i	$-0.345977\pi$
$359$	6.08727	+	1.97787i	0.321274	+	0.104388i	−0.143940	+	0.989586i	$0.545977\pi$
$360$	3.37214	+	10.3784i	0.177727	+	0.546988i
$361$	−10.8467	+	7.88056i	−0.570877	+	0.414766i
$362$			4.94612i			0.259962i
$363$	−0.410365	+	10.9923i	−0.0215386	+	0.576948i
$364$	35.9515	+	8.66513i	1.88437	+	0.454176i
$365$	−7.23784	+	5.25860i	−0.378846	+	0.275248i
$366$	−4.27259	+	1.38825i	−0.223332	+	0.0725649i
$367$	6.88405	−	21.1869i	0.359344	−	1.10595i	−0.594103	−	0.804389i	$-0.702493\pi$
$367$	6.88405	−	21.1869i	0.359344	−	1.10595i	0.953447	−	0.301559i	$-0.0975071\pi$
$368$	−10.8994	−	7.91885i	−0.568169	−	0.412799i
$369$	−0.874067	+	1.20305i	−0.0455021	+	0.0626283i
$370$	−7.85996	−	2.55386i	−0.408620	−	0.132769i
$371$	−17.2668	+	5.61033i	−0.896449	+	0.291274i
$372$	−32.8437	−	45.2054i	−1.70286	−	2.34379i
$373$	17.3557			0.898644			0.449322	−	0.893370i	$-0.351666\pi$
$373$	17.3557			0.898644			0.449322	+	0.893370i	$0.351666\pi$
$374$	24.2013	+	4.29739i	1.25142	+	0.222213i
$375$		−	10.3571i		−	0.534841i
$376$	−57.1193	+	41.4996i	−2.94570	+	2.14018i
$377$	−21.8789	+	1.70226i	−1.12682	+	0.0876710i
$378$	1.61200	−	4.96122i	0.0829122	−	0.255178i
$379$	15.5738	−	21.4355i	0.799973	−	1.10107i	−0.192821	−	0.981234i	$-0.561764\pi$
$379$	15.5738	−	21.4355i	0.799973	−	1.10107i	0.992794	−	0.119835i	$-0.0382365\pi$
$380$	−12.3669	−	8.98506i	−0.634407	−	0.460924i
$381$	6.91719	−	21.2889i	0.354378	−	1.09066i
$382$	−55.5642	+	18.0539i	−2.84291	+	0.923718i
$383$	13.0407	+	17.9490i	0.666350	+	0.917152i	0.999671	−	0.0256618i	$-0.00816929\pi$
$383$	13.0407	+	17.9490i	0.666350	+	0.917152i	−0.333321	+	0.942813i	$0.608169\pi$
$384$			27.1070i			1.38330i
$385$	−3.39808	−	6.98844i	−0.173182	−	0.356164i
$386$	−26.9869			−1.37360
$387$	−8.01234	+	5.82131i	−0.407290	+	0.295914i
$388$	−5.79626	+	1.88332i	−0.294260	+	0.0956110i
$389$	0.854049	−	2.62849i	0.0433020	−	0.133270i	−0.927068	−	0.374893i	$-0.877680\pi$
$389$	0.854049	−	2.62849i	0.0433020	−	0.133270i	0.970370	+	0.241623i	$0.0776796\pi$
$390$	9.02009	−	7.68997i	0.456750	−	0.389397i
$391$	−2.18617	−	1.58834i	−0.110559	−	0.0803259i
$392$	−28.0328	−	9.10841i	−1.41587	−	0.460044i
$393$	−5.46001	−	16.8042i	−0.275421	−	0.847659i
$394$	2.19988	−	1.59830i	0.110828	−	0.0805214i
$395$		−	4.41126i		−	0.221954i
$396$	−17.4737	+	2.43432i	−0.878087	+	0.122329i
$397$		−	11.0032i		−	0.552237i	−0.961124	−	0.276118i	$-0.910952\pi$
$397$		−	11.0032i		−	0.552237i	0.961124	−	0.276118i	$-0.0890482\pi$
$398$	−20.3841	−	28.0563i	−1.02176	−	1.40634i
$399$	1.40910	+	4.33675i	0.0705431	+	0.217109i
$400$	14.8701	−	45.7654i	0.743504	−	2.28827i
$401$	0.00210889	−	0.00290264i	0.000105313	−	0.000144951i	−0.808964	−	0.587858i	$-0.799971\pi$
$401$	0.00210889	−	0.00290264i	0.000105313	−	0.000144951i	0.809070	+	0.587713i	$0.199971\pi$
$402$	−33.3840	−	24.2549i	−1.66504	−	1.20972i
$403$	−19.8179	+	32.2753i	−0.987202	+	1.60774i
$404$	−18.0512	−	55.5560i	−0.898083	−	2.76402i
$405$	−0.714239	−	0.983066i	−0.0354908	−	0.0488489i
$406$	−31.7502			−1.57574
$407$	3.92319	−	7.35706i	0.194465	−	0.364676i
$408$			24.6005i			1.21790i
$409$	6.35460	+	8.74636i	0.314215	+	0.432480i	0.936690	−	0.350160i	$-0.113873\pi$
$409$	6.35460	+	8.74636i	0.314215	+	0.432480i	−0.622475	+	0.782640i	$0.713873\pi$
$410$	−4.64938	+	1.51068i	−0.229617	+	0.0746070i
$411$	−2.83151	−	0.920013i	−0.139668	−	0.0453809i
$412$	63.7791	+	46.3382i	3.14217	+	2.28292i
$413$	−6.00261	−	4.36115i	−0.295369	−	0.214598i
$414$	2.53819	+	0.824708i	0.124745	+	0.0405322i
$415$	−5.00605	−	15.4070i	−0.245737	−	0.756301i
$416$	63.2741	−	26.1429i	3.10227	−	1.28176i
$417$	−3.15759			−0.154628
$418$	15.2822	−	14.7224i	0.747478	−	0.720094i
$419$	−15.4908			−0.756773			−0.378387	−	0.925648i	$-0.623521\pi$
$419$	−15.4908			−0.756773			−0.378387	+	0.925648i	$0.623521\pi$
$420$	10.0830	−	7.32573i	0.492000	−	0.357459i
$421$	27.5394	−	8.94810i	1.34219	−	0.436104i	0.452131	−	0.891951i	$-0.350664\pi$
$421$	27.5394	−	8.94810i	1.34219	−	0.436104i	0.890058	+	0.455848i	$0.150664\pi$
$422$	−60.4835	−	19.6523i	−2.94429	−	0.956658i
$423$	4.62110	−	6.36040i	0.224686	−	0.309253i
$424$	−49.7025	+	68.4097i	−2.41377	+	3.32227i
$425$	2.98260	−	9.17949i	0.144677	−	0.445271i
$426$	4.50596	+	13.8679i	0.218314	+	0.671903i
$427$	1.88196	+	2.59029i	0.0910743	+	0.125353i
$428$	9.25303			0.447262
$429$	6.04766	+	10.3163i	0.291984	+	0.498075i
$430$	−32.5585			−1.57011
$431$	−10.5105	−	14.4665i	−0.506275	−	0.696828i	0.477010	−	0.878898i	$-0.341720\pi$
$431$	−10.5105	−	14.4665i	−0.506275	−	0.696828i	−0.983286	+	0.182070i	$0.941720\pi$
$432$	−4.22032	−	12.9888i	−0.203050	−	0.624925i
$433$	−4.41656	+	13.5928i	−0.212246	+	0.653227i	0.787091	+	0.616837i	$0.211586\pi$
$433$	−4.41656	+	13.5928i	−0.212246	+	0.653227i	−0.999338	+	0.0363908i	$0.988414\pi$
$434$	−32.2085	+	44.3312i	−1.54606	+	2.12797i
$435$	−4.34718	+	5.98339i	−0.208432	+	0.286881i
$436$	−4.17695	−	1.35717i	−0.200039	−	0.0649968i
$437$	−2.21871	+	0.720903i	−0.106135	+	0.0344855i
$438$	16.1147	−	11.7080i	0.769989	−	0.559430i
$439$	−10.3624			−0.494569			−0.247285	−	0.968943i	$-0.579538\pi$
$439$	−10.3624			−0.494569			−0.247285	+	0.968943i	$0.579538\pi$
$440$	−31.9357	−	17.0298i	−1.52247	−	0.811866i
$441$	3.28218			0.156294
$442$	24.6962	−	10.2037i	1.17468	−	0.485340i
$443$	6.34510	+	19.5282i	0.301465	+	0.927814i	0.980973	+	0.194146i	$0.0621934\pi$
$443$	6.34510	+	19.5282i	0.301465	+	0.927814i	−0.679508	+	0.733668i	$0.737807\pi$
$444$	12.7181	+	4.13235i	0.603572	+	0.196112i
$445$	−7.64795	−	5.55656i	−0.362548	−	0.263406i
$446$	12.8494	+	9.33564i	0.608437	+	0.442055i
$447$	4.19800	+	1.36401i	0.198559	+	0.0645156i
$448$	44.1144	−	14.3336i	2.08421	−	0.677200i
$449$	8.80796	+	12.1231i	0.415673	+	0.572125i	0.964591	−	0.263751i	$-0.0849598\pi$
$449$	8.80796	+	12.1231i	0.415673	+	0.572125i	−0.548917	+	0.835877i	$0.684960\pi$
$450$			9.53246i			0.449365i
$451$	−0.680520	−	4.88482i	−0.0320444	−	0.230017i
$452$	71.8619			3.38010
$453$	−7.30424	−	10.0534i	−0.343183	−	0.472351i
$454$	−7.57572	−	23.3157i	−0.355546	−	1.09426i
$455$	−7.19895	−	4.42036i	−0.337492	−	0.207230i
$456$	17.1818	+	12.4833i	0.804614	+	0.584586i
$457$	−8.19652	+	11.2815i	−0.383417	+	0.527728i	−0.956486	−	0.291779i	$-0.905753\pi$
$457$	−8.19652	+	11.2815i	−0.383417	+	0.527728i	0.573069	+	0.819507i	$0.305753\pi$
$458$	17.8500	−	54.9365i	0.834074	−	2.56702i
$459$	−0.846501	−	2.60526i	−0.0395113	−	0.121603i
$460$	3.74789	+	5.15853i	0.174746	+	0.240518i
$461$		−	23.0055i		−	1.07147i	−0.844386	−	0.535736i	$-0.820034\pi$
$461$		−	23.0055i		−	1.07147i	0.844386	−	0.535736i	$-0.179966\pi$
$462$	7.56566	+	15.5594i	0.351986	+	0.723890i
$463$			13.5304i			0.628811i	0.949289	+	0.314405i	$0.101805\pi$
$463$			13.5304i			0.628811i	−0.949289	+	0.314405i	$0.898195\pi$
$464$	−67.2489	+	48.8592i	−3.12195	+	2.26823i
$465$	3.94437	+	12.1395i	0.182916	+	0.562956i
$466$	−2.34438	−	0.761736i	−0.108601	−	0.0352867i
$467$	24.3851	+	17.7168i	1.12841	+	0.819835i	0.985462	−	0.169895i	$-0.0543429\pi$
$467$	24.3851	+	17.7168i	1.12841	+	0.819835i	0.142945	+	0.989731i	$0.454343\pi$
$468$	−14.5952	+	12.4430i	−0.674665	+	0.575178i
$469$	−9.08801	+	27.9700i	−0.419645	+	1.29154i
$470$	24.5808	−	7.98679i	1.13383	−	0.368403i
$471$	10.2619	−	7.45574i	0.472845	−	0.343542i
$472$	−34.5570			−1.59061
$473$	5.74280	−	32.3413i	0.264054	−	1.48705i
$474$			9.82144i			0.451114i
$475$	−4.89779	−	6.74123i	−0.224726	−	0.309309i
$476$	26.7214	−	8.68230i	1.22477	−	0.397952i
$477$	2.90967	−	8.95505i	0.133225	−	0.410024i
$478$	1.48754	+	1.08076i	0.0680383	+	0.0494328i
$479$	−7.77481	+	10.7011i	−0.355240	+	0.488946i	−0.948815	−	0.315833i	$-0.897716\pi$
$479$	−7.77481	+	10.7011i	−0.355240	+	0.488946i	0.593575	+	0.804779i	$0.297716\pi$
$480$	7.12994	−	21.9437i	0.325436	−	1.00159i
$481$	−0.703094	−	9.03675i	−0.0320583	−	0.412041i
$482$	20.5206	−	14.9091i	0.934686	−	0.679089i
$483$		−	1.90206i		−	0.0865468i
$484$	36.1354	−	46.0223i	1.64252	−	2.09192i
$485$	1.39221			0.0632168
$486$	1.59022	+	2.18875i	0.0721337	+	0.0992836i
$487$	−18.3774	+	5.97117i	−0.832759	+	0.270580i	−0.694207	−	0.719775i	$-0.744245\pi$
$487$	−18.3774	+	5.97117i	−0.832759	+	0.270580i	−0.138552	+	0.990355i	$0.544245\pi$
$488$	14.1825	+	4.60816i	0.642009	+	0.208601i
$489$	14.1077	−	19.4176i	0.637972	−	0.878094i
$490$	8.72937	+	6.34226i	0.394353	+	0.286514i
$491$	−7.17345	+	22.0776i	−0.323733	+	0.996348i	0.648276	+	0.761405i	$0.275490\pi$
$491$	−7.17345	+	22.0776i	−0.323733	+	0.996348i	−0.972009	+	0.234943i	$0.924510\pi$
$492$	7.52308	−	2.44440i	0.339166	−	0.110202i
$493$	−13.4886	+	9.80005i	−0.607496	+	0.441372i
$494$	5.40530	−	22.4265i	0.243196	−	1.00902i
$495$	3.96808	+	0.704607i	0.178352	+	0.0316697i
$496$			143.461i			6.44158i
$497$	8.40754	−	6.10844i	0.377130	−	0.274001i
$498$	11.1457	+	34.3030i	0.499451	+	1.53715i
$499$	28.1973	+	9.16187i	1.26229	+	0.410142i	0.862309	−	0.506383i	$-0.169018\pi$
$499$	28.1973	+	9.16187i	1.26229	+	0.410142i	0.399978	+	0.916525i	$0.369018\pi$
$500$	−32.3834	+	44.5719i	−1.44823	+	1.99331i
$501$	7.60357	−	10.4654i	0.339702	−	0.467560i
$502$	76.0207	+	24.7006i	3.39297	+	1.10244i
$503$	−8.98394	−	27.6497i	−0.400574	−	1.23284i	−0.924535	−	0.381098i	$-0.875546\pi$
$503$	−8.98394	−	27.6497i	−0.400574	−	1.23284i	0.523961	−	0.851742i	$-0.324454\pi$
$504$	−14.0088	+	10.1780i	−0.624000	+	0.453363i
$505$			13.3440i			0.593801i
$506$	−7.96030	+	3.87064i	−0.353878	+	0.172071i
$507$	11.5725	+	5.92254i	0.513954	+	0.263029i
$508$	−96.3314	+	69.9889i	−4.27402	+	3.10525i
$509$	−15.1280	+	4.91539i	−0.670537	+	0.217871i	−0.624448	−	0.781067i	$-0.714676\pi$
$509$	−15.1280	+	4.91539i	−0.670537	+	0.217871i	−0.0460894	+	0.998937i	$0.514676\pi$
$510$	2.78285	−	8.56474i	0.123227	−	0.379253i
$511$	−11.4849	−	8.34429i	−0.508063	−	0.369130i
$512$	8.24494	−	11.3482i	0.364378	−	0.501524i
$513$	−2.24916	−	0.730797i	−0.0993029	−	0.0322655i
$514$	10.3260	−	3.35512i	0.455460	−	0.147988i
$515$	−10.5853	−	14.5694i	−0.466442	−	0.642003i
$516$	52.6823			2.31921
$517$	3.59784	+	25.8255i	0.158233	+	1.13581i
$518$		−	13.1139i		−	0.576194i
$519$	−12.0821	+	8.77813i	−0.530344	+	0.385317i
$520$	−39.2269	+	3.05201i	−1.72021	+	0.133839i
$521$	9.01842	−	27.7558i	0.395104	−	1.21601i	−0.533776	−	0.845626i	$-0.679228\pi$
$521$	9.01842	−	27.7558i	0.395104	−	1.21601i	0.928880	−	0.370380i	$-0.120772\pi$
$522$	9.67879	−	13.3217i	0.423629	−	0.583075i
$523$	20.2593	+	14.7193i	0.885879	+	0.643629i	0.934800	−	0.355174i	$-0.115578\pi$
$523$	20.2593	+	14.7193i	0.885879	+	0.643629i	−0.0489215	+	0.998803i	$0.515578\pi$
$524$	−29.0440	+	89.3882i	−1.26879	+	3.90494i
$525$	6.46127	−	2.09939i	0.281993	−	0.0916251i
$526$	−29.7657	−	40.9690i	−1.29785	−	1.78633i
$527$			28.7750i			1.25346i
$528$	39.9683	+	21.3133i	1.73940	+	0.927543i
$529$	−22.0269			−0.957691
$530$	25.0428	−	18.1946i	1.08779	−	0.790324i
$531$	3.65969	−	1.18911i	0.158817	−	0.0516028i
$532$	7.49555	−	23.0689i	0.324973	−	1.00017i
$533$	−3.47847	−	4.08013i	−0.150669	−	0.176730i
$534$	17.0278	+	12.3714i	0.736864	+	0.535363i
$535$	−2.01026	−	0.653173i	−0.0869111	−	0.0282391i
$536$	42.3275	+	130.271i	1.82827	+	5.62684i
$537$	5.30068	−	3.85117i	0.228741	−	0.166190i
$538$		−	47.4342i		−	2.04503i
$539$	−7.83966	+	7.55245i	−0.337678	+	0.325307i
$540$			6.46380i			0.278158i
$541$	−15.2004	−	20.9216i	−0.653516	−	0.899488i	0.345729	−	0.938334i	$-0.387632\pi$
$541$	−15.2004	−	20.9216i	−0.653516	−	0.899488i	−0.999245	+	0.0388464i	$0.987632\pi$
$542$	14.5701	+	44.8421i	0.625839	+	1.92613i
$543$	−0.564949	+	1.73873i	−0.0242443	+	0.0746162i
$544$	30.5733	−	42.0806i	1.31082	−	1.80419i
$545$	0.811657	+	0.589703i	0.0347676	+	0.0252601i
$546$	16.0281	+	9.84171i	0.685939	+	0.421186i
$547$	−7.36010	−	22.6521i	−0.314695	−	0.968532i	−0.975880	−	0.218309i	$-0.929946\pi$
$547$	−7.36010	−	22.6521i	−0.314695	−	0.968532i	0.661185	−	0.750223i	$-0.270054\pi$
$548$	9.30880	+	12.8125i	0.397652	+	0.547321i
$549$	−1.66053			−0.0708697
$550$	−21.9346	−	22.7688i	−0.935297	−	0.970864i
$551$			14.3939i			0.613201i
$552$	−5.20711	−	7.16697i	−0.221629	−	0.305047i
$553$	6.65714	−	2.16304i	0.283091	−	0.0919817i
$554$	−58.1932	−	18.9081i	−2.47239	−	0.803328i
$555$	−2.47135	−	1.79554i	−0.104903	−	0.0762164i
$556$	13.5886	+	9.87272i	0.576287	+	0.418697i
$557$	−20.9212	−	6.79771i	−0.886459	−	0.288028i	−0.169822	−	0.985475i	$-0.554319\pi$
$557$	−20.9212	−	6.79771i	−0.886459	−	0.288028i	−0.716637	+	0.697447i	$0.754319\pi$
$558$	−8.78193	−	27.0280i	−0.371769	−	1.14419i
$559$	−13.6357	−	33.0027i	−0.576727	−	1.39586i
$560$	−31.9987			−1.35219
$561$	8.01674	+	4.27497i	0.338467	+	0.180489i
$562$	20.1120			0.848372
$563$	−18.5761	+	13.4963i	−0.782889	+	0.568802i	−0.905845	−	0.423610i	$-0.860763\pi$
$563$	−18.5761	+	13.4963i	−0.782889	+	0.568802i	0.122956	+	0.992412i	$0.460763\pi$
$564$	−39.7737	+	12.9233i	−1.67478	+	0.544168i
$565$	−15.6123	−	5.07274i	−0.656814	−	0.213412i
$566$	14.0871	−	19.3893i	0.592127	−	0.814992i
$567$	1.13335	−	1.55992i	0.0475961	−	0.0655104i
$568$	14.9571	−	46.0332i	0.627586	−	1.93151i
$569$	0.302125	+	0.929846i	0.0126658	+	0.0389812i	0.957190	−	0.289462i	$-0.0934762\pi$
$569$	0.302125	+	0.929846i	0.0126658	+	0.0389812i	−0.944524	+	0.328443i	$0.893476\pi$
$570$	−4.56978	−	6.28977i	−0.191407	−	0.263449i
$571$	−22.7151			−0.950596			−0.475298	−	0.879825i	$-0.657660\pi$
$571$	−22.7151			−0.950596			−0.475298	+	0.879825i	$0.657660\pi$
$572$	6.22955	−	63.3051i	0.260471	−	2.64692i
$573$	−21.5949			−0.902139
$574$	−4.55960	−	6.27575i	−0.190314	−	0.261945i
$575$	1.07406	+	3.30563i	0.0447915	+	0.137854i
$576$	−7.43381	+	22.8789i	−0.309742	+	0.953289i
$577$	9.68501	−	13.3303i	0.403192	−	0.554946i	−0.558349	−	0.829606i	$-0.688565\pi$
$577$	9.68501	−	13.3303i	0.403192	−	0.554946i	0.961542	+	0.274659i	$0.0885651\pi$
$578$	−15.1008	+	20.7844i	−0.628110	+	0.864519i
$579$	−9.48685	−	3.08246i	−0.394260	−	0.128103i
$580$	37.4161	−	12.1572i	1.55362	−	0.504802i
$581$	20.7965	−	15.1095i	0.862782	−	0.626848i
$582$	−3.09967			−0.128486
$583$	13.6561	+	28.0849i	0.565577	+	1.16316i
$584$	−66.1187			−2.73601
$585$	4.04923	−	1.67301i	0.167415	−	0.0691706i
$586$	25.4059	+	78.1912i	1.04951	+	3.23005i
$587$	13.8937	+	4.51434i	0.573455	+	0.186327i	0.581367	−	0.813642i	$-0.302518\pi$
$587$	13.8937	+	4.51434i	0.573455	+	0.186327i	−0.00791126	+	0.999969i	$0.502518\pi$
$588$	−14.1248	−	10.2623i	−0.582498	−	0.423209i
$589$	20.0975	+	14.6017i	0.828102	+	0.601652i
$590$	12.0311	+	3.90916i	0.495315	+	0.160937i
$591$	0.955893	−	0.310588i	0.0393202	−	0.0127759i
$592$	−20.1806	−	27.7762i	−0.829416	−	1.14159i
$593$			37.8274i			1.55339i	0.629879	+	0.776694i	$0.283105\pi$
$593$			37.8274i			1.55339i	−0.629879	+	0.776694i	$0.716895\pi$
$594$	−8.83473	−	1.56877i	−0.362493	−	0.0643674i
$595$	−6.41822			−0.263121
$596$	−13.8012	−	18.9958i	−0.565321	−	0.778097i
$597$	−3.96112	−	12.1911i	−0.162118	−	0.498947i
$598$	−5.03508	+	8.20007i	−0.205900	+	0.335326i
$599$	21.7624	+	15.8113i	0.889187	+	0.646032i	0.935666	−	0.352887i	$-0.114800\pi$
$599$	21.7624	+	15.8113i	0.889187	+	0.646032i	−0.0464790	+	0.998919i	$0.514800\pi$
$600$	18.5988	−	25.5990i	0.759291	−	1.04507i
$601$	5.84273	−	17.9821i	0.238330	−	0.733505i	−0.758332	−	0.651868i	$-0.773985\pi$
$601$	5.84273	−	17.9821i	0.238330	−	0.733505i	0.996662	−	0.0816361i	$-0.0260145\pi$
$602$	−15.9649	−	49.1349i	−0.650681	−	2.00259i
$603$	−8.96522	−	12.3396i	−0.365092	−	0.502506i
$604$			66.1028i			2.68968i
$605$	−11.0993	+	7.44775i	−0.451251	+	0.302794i
$606$		−	29.7098i		−	1.20688i
$607$	26.5175	−	19.2661i	1.07631	−	0.781986i	0.0992754	−	0.995060i	$-0.468348\pi$
$607$	26.5175	−	19.2661i	1.07631	−	0.781986i	0.977036	+	0.213074i	$0.0683475\pi$
$608$	−13.8763	−	42.7070i	−0.562760	−	1.73200i
$609$	−11.1613	−	3.62653i	−0.452279	−	0.146954i
$610$	−4.41639	−	3.20870i	−0.178814	−	0.129916i
$611$	18.3903	+	21.5712i	0.743992	+	0.872679i
$612$	−4.50288	+	13.8584i	−0.182018	+	0.560194i
$613$	1.93861	−	0.629893i	0.0782998	−	0.0254412i	−0.269605	−	0.962971i	$-0.586893\pi$
$613$	1.93861	−	0.629893i	0.0782998	−	0.0254412i	0.347905	+	0.937530i	$0.386893\pi$
$614$	−35.0183	+	25.4423i	−1.41322	+	1.02677i
$615$	−1.80697			−0.0728641
$616$	10.0407	−	56.5454i	0.404551	−	2.27828i
$617$			23.8751i			0.961176i	0.876947	+	0.480588i	$0.159577\pi$
$617$			23.8751i			0.961176i	−0.876947	+	0.480588i	$0.840423\pi$
$618$	23.5675	+	32.4379i	0.948026	+	1.30485i
$619$	13.6125	−	4.42298i	0.547134	−	0.177775i	−0.0223901	−	0.999749i	$-0.507128\pi$
$619$	13.6125	−	4.42298i	0.547134	−	0.177775i	0.569524	+	0.821975i	$0.307128\pi$
$620$	20.9817	−	64.5750i	0.842645	−	2.59339i
$621$	0.798064	+	0.579828i	0.0320252	+	0.0232677i
$622$	44.6774	−	61.4931i	1.79140	−	2.46565i
$623$	4.63542	−	14.2664i	0.185714	−	0.571569i
$624$	49.0936	−	3.81967i	1.96532	−	0.152909i
$625$	−4.07087	+	2.95766i	−0.162835	+	0.118306i
$626$		−	20.3582i		−	0.813677i
$627$	7.05383	−	3.42988i	0.281703	−	0.136976i
$628$	−67.4738			−2.69250
$629$	−4.04776	−	5.57127i	−0.161395	−	0.222141i
$630$	6.02856	−	1.95880i	0.240184	−	0.0780404i
$631$	−16.7634	−	5.44675i	−0.667339	−	0.216832i	−0.0442953	−	0.999018i	$-0.514104\pi$
$631$	−16.7634	−	5.44675i	−0.667339	−	0.216832i	−0.623044	+	0.782187i	$0.714104\pi$
$632$	19.1626	−	26.3750i	0.762247	−	1.04914i
$633$	−19.0174	−	13.8169i	−0.755873	−	0.549174i
$634$	7.58020	−	23.3294i	0.301048	−	0.926531i
$635$	25.8689	−	8.40533i	1.02658	−	0.333555i
$636$	−40.5212	+	29.4404i	−1.60677	+	1.16739i
$637$	−2.77288	+	11.5046i	−0.109865	+	0.455830i
$638$	7.53558	+	54.0909i	0.298337	+	2.14148i
$639$			5.38973i			0.213214i
$640$	−26.6480	+	19.3609i	−1.05335	+	0.765306i
$641$	−11.8328	−	36.4177i	−0.467369	−	1.43841i	−0.855978	−	0.517012i	$-0.827044\pi$
$641$	−11.8328	−	36.4177i	−0.467369	−	1.43841i	0.388609	−	0.921403i	$-0.372956\pi$
$642$	4.47574	+	1.45426i	0.176643	+	0.0573949i
$643$	−1.78417	+	2.45570i	−0.0703608	+	0.0968433i	−0.842747	−	0.538310i	$-0.819063\pi$
$643$	−1.78417	+	2.45570i	−0.0703608	+	0.0968433i	0.772386	+	0.635153i	$0.219063\pi$
$644$	−5.94711	+	8.18550i	−0.234349	+	0.322554i
$645$	−11.4455	−	3.71885i	−0.450664	−	0.146430i
$646$	−5.41601	−	16.6688i	−0.213090	−	0.655824i
$647$	−16.1606	+	11.7414i	−0.635338	+	0.461600i	−0.858246	−	0.513239i	$-0.828445\pi$
$647$	−16.1606	+	11.7414i	−0.635338	+	0.461600i	0.222907	+	0.974840i	$0.428445\pi$
$648$		−	8.98045i		−	0.352785i
$649$	−6.00517	+	11.2614i	−0.235724	+	0.442047i
$650$	−33.4130	−	8.05329i	−1.31056	−	0.315876i
$651$	−16.3860	+	11.9051i	−0.642216	+	0.466597i
$652$	−121.425	+	39.4533i	−4.75536	+	1.54511i
$653$	−6.53137	+	20.1015i	−0.255592	+	0.786632i	0.738120	+	0.674669i	$0.235714\pi$
$653$	−6.53137	+	20.1015i	−0.255592	+	0.786632i	−0.993712	+	0.111963i	$0.964286\pi$
$654$	−1.80711	−	1.31294i	−0.0706637	−	0.0513402i
$655$	12.6199	−	17.3698i	0.493099	−	0.678692i
$656$	−19.3151	−	6.27584i	−0.754126	−	0.245030i
$657$	7.00217	−	2.27514i	0.273181	−	0.0887618i
$658$	24.1062	+	33.1793i	0.939756	+	1.29346i
$659$	−17.7965			−0.693253			−0.346626	−	0.938003i	$-0.612673\pi$
$659$	−17.7965			−0.693253			−0.346626	+	0.938003i	$0.612673\pi$
$660$	−14.8735	−	15.4391i	−0.578951	−	0.600967i
$661$		−	15.2744i		−	0.594105i	−0.954861	−	0.297052i	$-0.903996\pi$
$661$		−	15.2744i		−	0.594105i	0.954861	−	0.297052i	$-0.0960036\pi$
$662$	−59.0109	+	42.8739i	−2.29352	+	1.66634i
$663$	9.84705	−	0.766139i	0.382428	−	0.0297544i
$664$	36.9971	−	113.865i	1.43577	−	4.41883i
$665$	−3.25688	+	4.48271i	−0.126296	+	0.173832i
$666$	5.50233	+	3.99768i	0.213211	+	0.154907i
$667$	1.85535	−	5.71019i	0.0718396	−	0.221100i
$668$	−65.4437	+	21.2640i	−2.53209	+	0.822727i
$669$	3.45069	+	4.74947i	0.133411	+	0.183625i
$670$		−	50.1424i		−	1.93717i
$671$	3.96626	−	3.82096i	0.153116	−	0.147507i
$672$	36.6120			1.41234
$673$	26.0932	−	18.9578i	1.00582	−	0.730770i	0.0424907	−	0.999097i	$-0.486471\pi$
$673$	26.0932	−	18.9578i	1.00582	−	0.730770i	0.963328	+	0.268327i	$0.0864707\pi$
$674$	41.3689	−	13.4416i	1.59347	−	0.517749i
$675$	−1.08880	+	3.35099i	−0.0419081	+	0.128980i
$676$	−31.2844	−	61.6710i	−1.20325	−	2.37196i
$677$	5.39787	+	3.92178i	0.207457	+	0.150726i	0.686662	−	0.726976i	$-0.259075\pi$
$677$	5.39787	+	3.92178i	0.207457	+	0.150726i	−0.479205	+	0.877703i	$0.659075\pi$
$678$	34.7600	+	11.2942i	1.33495	+	0.433751i
$679$	0.682661	+	2.10101i	0.0261981	+	0.0806295i
$680$	−24.1839	+	17.5706i	−0.927409	+	0.673802i
$681$		−	9.06157i		−	0.347240i
$682$	83.1688	+	44.3502i	3.18470	+	1.69826i
$683$			40.8610i			1.56350i	0.623591	+	0.781751i	$0.285673\pi$
$683$			40.8610i			1.56350i	−0.623591	+	0.781751i	$0.714327\pi$
$684$	7.39428	+	10.1774i	0.282727	+	0.389141i
$685$	−1.11794	−	3.44067i	−0.0427144	−	0.131461i
$686$	−16.5749	+	51.0121i	−0.632831	+	1.94765i
$687$	12.5498	−	17.2733i	0.478804	−	0.659017i
$688$	−109.427	−	79.5031i	−4.17185	−	3.03103i
$689$	28.9309	+	17.7644i	1.10218	+	0.676769i
$690$	1.00213	+	3.08425i	0.0381506	+	0.117415i
$691$	0.617164	+	0.849453i	0.0234780	+	0.0323147i	0.820595	−	0.571511i	$-0.193642\pi$
$691$	0.617164	+	0.849453i	0.0234780	+	0.0323147i	−0.797117	+	0.603825i	$0.793642\pi$
$692$	79.4413			3.01991
$693$	0.882387	+	6.33383i	0.0335191	+	0.240602i
$694$			6.42299i			0.243813i
$695$	−2.25527	−	3.10412i	−0.0855474	−	0.117746i
$696$	−51.9839	+	16.8906i	−1.97044	+	0.640236i
$697$	−3.87416	−	1.25879i	−0.146744	−	0.0476801i
$698$	25.2178	+	18.3218i	0.954509	+	0.693491i
$699$	−0.737126	−	0.535553i	−0.0278807	−	0.0202565i
$700$	−34.3701	−	11.1675i	−1.29907	−	0.422093i
$701$	−10.8894	−	33.5141i	−0.411287	−	1.26581i	−0.915530	−	0.402250i	$-0.868228\pi$
$701$	−10.8894	−	33.5141i	−0.411287	−	1.26581i	0.504243	−	0.863562i	$-0.331772\pi$
$702$	−9.01540	+	3.72488i	−0.340265	+	0.140587i
$703$	−5.94519			−0.224227
$704$	−34.8894	−	71.7531i	−1.31494	−	2.70430i
$705$	9.55327			0.359797
$706$	44.6048	−	32.4073i	1.67872	−	1.21966i
$707$	−20.1378	+	6.54317i	−0.757361	+	0.246081i
$708$	−19.4674	−	6.32533i	−0.731628	−	0.237720i
$709$	−18.8227	+	25.9073i	−0.706903	+	0.972969i	0.292955	+	0.956126i	$0.405361\pi$
$709$	−18.8227	+	25.9073i	−0.706903	+	0.972969i	−0.999858	+	0.0168424i	$0.994639\pi$
$710$	−10.4147	+	14.3347i	−0.390858	+	0.537970i
$711$	−1.12181	+	3.45258i	−0.0420712	+	0.129482i
$712$	−21.5895	−	66.4457i	−0.809101	−	2.49016i
$713$	−6.09072	−	8.38316i	−0.228099	−	0.313952i
$714$	14.2898			0.534784
$715$	−5.82211	+	13.3135i	−0.217735	+	0.497898i
$716$	−34.8527			−1.30251
$717$	0.399476	+	0.549832i	0.0149187	+	0.0205338i
$718$	−5.35102	−	16.4687i	−0.199698	−	0.614608i
$719$	5.25397	−	16.1701i	0.195940	−	0.603042i	−0.804024	−	0.594597i	$-0.797312\pi$
$719$	5.25397	−	16.1701i	0.195940	−	0.603042i	0.999964	−	0.00844517i	$-0.00268821\pi$
$720$	9.75455	−	13.4260i	0.363530	−	0.500357i
$721$	16.7966	−	23.1185i	0.625537	−	0.860978i
$722$	34.4971	+	11.2088i	1.28385	+	0.417148i
$723$	8.91662	−	2.89718i	0.331613	−	0.107747i
$724$	7.86770	−	5.71622i	0.292401	−	0.212441i
$725$	21.4453			0.796458
$726$	24.7120	−	16.5820i	0.917149	−	0.615417i
$727$	36.1247			1.33979			0.669896	−	0.742455i	$-0.266339\pi$
$727$	36.1247			1.33979			0.669896	+	0.742455i	$0.266339\pi$
$728$	−23.8406	−	57.7018i	−0.883591	−	2.13857i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	23.0195	+	7.47948i	0.851989	+	0.276828i
$731$	−21.9485	−	15.9465i	−0.811794	−	0.589803i
$732$	7.14608	+	5.19193i	0.264127	+	0.191899i
$733$	7.13510	+	2.31833i	0.263541	+	0.0856297i	0.437807	−	0.899069i	$-0.355755\pi$
$733$	7.13510	+	2.31833i	0.263541	+	0.0856297i	−0.174266	+	0.984699i	$0.555755\pi$
$734$	−57.3199	+	18.6244i	−2.11572	+	0.687438i
$735$	2.34426	+	3.22660i	0.0864694	+	0.119015i
$736$			18.7309i			0.690431i
$737$	49.8078	+	8.84431i	1.83469	+	0.325784i
$738$	4.02313			0.148093
$739$	11.6254	+	16.0010i	0.427647	+	0.588606i	0.967411	−	0.253211i	$-0.0814866\pi$
$739$	11.6254	+	16.0010i	0.427647	+	0.588606i	−0.539764	+	0.841816i	$0.681487\pi$
$740$	5.02136	+	15.4542i	0.184589	+	0.568107i
$741$	4.46172	−	7.26631i	0.163906	−	0.266935i
$742$	39.7376	+	28.8711i	1.45881	+	1.05989i
$743$	−28.5645	+	39.3157i	−1.04793	+	1.44235i	−0.157341	+	0.987544i	$0.550292\pi$
$743$	−28.5645	+	39.3157i	−1.04793	+	1.44235i	−0.890590	+	0.454808i	$0.849708\pi$
$744$	−29.1508	+	89.7169i	−1.06872	+	3.28918i
$745$	1.65746	+	5.10114i	0.0607247	+	0.186891i
$746$	−27.5993	−	37.9872i	−1.01048	−	1.39081i
$747$			13.3318i			0.487783i
$748$	−21.1336	−	43.4630i	−0.772720	−	1.58916i
$749$		−	3.35402i		−	0.122553i
$750$	−22.6692	+	16.4701i	−0.827761	+	0.601404i
$751$	6.12412	+	18.8481i	0.223472	+	0.687778i	0.998443	+	0.0557802i	$0.0177646\pi$
$751$	6.12412	+	18.8481i	0.223472	+	0.687778i	−0.774971	+	0.631997i	$0.782235\pi$
$752$	102.117	+	33.1797i	3.72381	+	1.20994i
$753$	23.9026	+	17.3663i	0.871059	+	0.632861i
$754$	38.5180	+	45.1804i	1.40274	+	1.64537i
$755$	4.66621	−	14.3611i	0.169821	−	0.522654i
$756$	−9.75469	+	3.16949i	−0.354775	+	0.115273i
$757$	−13.3834	+	9.72364i	−0.486429	+	0.353412i	−0.803809	−	0.594887i	$-0.797197\pi$
$757$	−13.3834	+	9.72364i	−0.486429	+	0.353412i	0.317380	+	0.948298i	$0.397197\pi$
$758$	−71.6827			−2.60363
$759$	−3.24043	+	0.451435i	−0.117620	+	0.0163860i
$760$			25.8070i			0.936117i
$761$	−19.8624	−	27.3383i	−0.720012	−	0.991012i	−0.999523	−	0.0308697i	$-0.990172\pi$
$761$	−19.8624	−	27.3383i	−0.720012	−	0.991012i	0.279511	−	0.960143i	$-0.409828\pi$
$762$	−57.5959	+	18.7140i	−2.08648	+	0.677938i
$763$	−0.491945	+	1.51405i	−0.0178096	+	0.0548123i
$764$	92.9333	+	67.5200i	3.36221	+	2.44279i
$765$	1.95654	−	2.69295i	0.0707389	−	0.0973637i
$766$	18.5483	−	57.0857i	0.670176	−	2.06259i
$767$	1.07622	+	13.8324i	0.0388600	+	0.499461i
$768$	20.4064	−	14.8261i	0.736352	−	0.534991i
$769$			7.92037i			0.285616i	0.989750	+	0.142808i	$0.0456131\pi$
$769$			7.92037i			0.285616i	−0.989750	+	0.142808i	$0.954387\pi$
$770$	−9.89224	+	18.5507i	−0.356492	+	0.668520i
$771$	4.01317			0.144531
$772$	31.1887	+	42.9276i	1.12251	+	1.54500i
$773$	37.2174	−	12.0927i	1.33862	−	0.434944i	0.449770	−	0.893144i	$-0.351506\pi$
$773$	37.2174	−	12.0927i	1.33862	−	0.434944i	0.888849	+	0.458201i	$0.151506\pi$
$774$	25.4827	+	8.27984i	0.915958	+	0.297613i
$775$	21.7548	−	29.9430i	0.781457	−	1.07558i
$776$	8.32404	+	6.04777i	0.298815	+	0.217102i
$777$	1.49788	−	4.61001i	0.0537363	−	0.165383i
$778$	−7.11123	+	2.31058i	−0.254950	+	0.0828383i
$779$	−2.84510	+	2.06709i	−0.101936	+	0.0740611i
$780$	−22.6568	−	5.46080i	−0.811242	−	0.195528i
$781$	−12.4020	−	12.8737i	−0.443779	−	0.460656i
$782$			7.31077i			0.261433i
$783$	4.92404	−	3.57753i	0.175971	−	0.127850i
$784$	13.8519	+	42.6316i	0.494709	+	1.52256i
$785$	14.6590	+	4.76299i	0.523201	+	0.169998i
$786$	−28.0975	+	38.6729i	−1.00220	+	1.37942i
$787$	−26.5689	+	36.5690i	−0.947080	+	1.30354i	0.00573165	+	0.999984i	$0.498176\pi$
$787$	−26.5689	+	36.5690i	−0.947080	+	1.30354i	−0.952812	+	0.303561i	$0.901824\pi$
$788$	−5.08478	−	1.65214i	−0.181138	−	0.0588552i
$789$	−5.78418	−	17.8019i	−0.205922	−	0.633764i
$790$	−9.65513	+	7.01486i	−0.343514	+	0.249577i
$791$		−	26.0483i		−	0.926172i
$792$	20.6644	+	21.4503i	0.734279	+	0.762202i
$793$	1.40286	−	5.82045i	0.0498171	−	0.206690i
$794$	−24.0833	+	17.4975i	−0.854684	+	0.620964i
$795$	10.8816	−	3.53565i	0.385931	−	0.125397i
$796$	−21.0708	+	64.8493i	−0.746835	+	2.29852i
$797$	−14.3464	−	10.4233i	−0.508176	−	0.369212i	0.303955	−	0.952686i	$-0.401693\pi$
$797$	−14.3464	−	10.4233i	−0.508176	−	0.369212i	−0.812131	+	0.583475i	$0.801693\pi$
$798$	7.25128	−	9.98054i	0.256693	−	0.353307i
$799$	20.4823	+	6.65510i	0.724611	+	0.235441i
$800$	−63.6286	+	20.6742i	−2.24961	+	0.730943i
$801$	4.57279	+	6.29390i	0.161572	+	0.222384i
$802$	−0.00970673			−0.000342757
$803$	−11.4898	+	21.5466i	−0.405468	+	0.760364i
$804$			81.1345i			2.86139i
$805$	1.86985	−	1.35853i	0.0659036	−	0.0478818i
$806$	102.157	−	7.94822i	3.59833	−	0.279964i
$807$	5.41796	−	16.6748i	0.190721	−	0.586980i
$808$	−57.9667	+	79.7843i	−2.03926	+	2.80680i
$809$	−24.9891	−	18.1557i	−0.878570	−	0.638319i	0.0543025	−	0.998525i	$-0.482706\pi$
$809$	−24.9891	−	18.1557i	−0.878570	−	0.638319i	−0.932873	+	0.360206i	$0.882706\pi$
$810$	−1.01589	+	3.12658i	−0.0356946	+	0.109857i
$811$	27.4163	−	8.90809i	0.962716	−	0.312806i	0.214844	−	0.976648i	$-0.431076\pi$
$811$	27.4163	−	8.90809i	0.962716	−	0.312806i	0.747872	+	0.663843i	$0.231076\pi$
$812$	36.6936	+	50.5044i	1.28769	+	1.77236i
$813$			17.4278i			0.611219i
$814$	−22.3415	+	3.11246i	−0.783068	+	0.109092i
$815$	29.1650			1.02161
$816$	30.2668	−	21.9901i	1.05955	−	0.769807i
$817$	−22.2752	+	7.23766i	−0.779312	+	0.253214i
$818$	9.03837	−	27.8172i	0.316019	−	0.972607i
$819$	4.51031	+	5.29044i	0.157603	+	0.184863i
$820$	7.77628	+	5.64980i	0.271559	+	0.197299i
$821$	23.8589	+	7.75224i	0.832682	+	0.270555i	0.694175	−	0.719807i	$-0.255769\pi$
$821$	23.8589	+	7.75224i	0.832682	+	0.270555i	0.138508	+	0.990361i	$0.455769\pi$
$822$	2.48904	+	7.66048i	0.0868153	+	0.267190i
$823$	26.1405	−	18.9922i	0.911201	−	0.662027i	−0.0301170	−	0.999546i	$-0.509588\pi$
$823$	26.1405	−	18.9922i	0.911201	−	0.662027i	0.941318	+	0.337520i	$0.109588\pi$
$824$		−	133.093i		−	4.63652i
$825$	−5.11013	−	10.5094i	−0.177912	−	0.365891i
$826$			20.0734i			0.698441i
$827$	2.92957	+	4.03221i	0.101871	+	0.140214i	0.856909	−	0.515467i	$-0.172382\pi$
$827$	2.92957	+	4.03221i	0.101871	+	0.140214i	−0.755038	+	0.655681i	$0.772382\pi$
$828$	−1.62153	−	4.99056i	−0.0563521	−	0.173434i
$829$	−6.03225	+	18.5653i	−0.209509	+	0.644801i	0.789989	+	0.613120i	$0.210086\pi$
$829$	−6.03225	+	18.5653i	−0.209509	+	0.644801i	−0.999498	+	0.0316807i	$0.989914\pi$
$830$	−25.7614	+	35.4575i	−0.894190	+	1.23075i
$831$	−18.2972	−	13.2937i	−0.634724	−	0.461154i
$832$	−73.9144	−	45.3856i	−2.56252	−	1.57346i
$833$	2.77837	+	8.55094i	0.0962647	+	0.296272i
$834$	5.02125	+	6.91116i	0.173872	+	0.239314i
$835$	15.7190			0.543977
$836$	−41.0802	−	7.29455i	−1.42079	−	0.252287i
$837$		−	10.5044i		−	0.363084i
$838$	24.6337	+	33.9053i	0.850956	+	1.17124i
$839$	19.4056	−	6.30525i	0.669955	−	0.217681i	0.0457626	−	0.998952i	$-0.485428\pi$
$839$	19.4056	−	6.30525i	0.669955	−	0.217681i	0.624192	+	0.781271i	$0.285428\pi$
$840$	−20.0112	−	6.50204i	−0.690453	−	0.224342i
$841$	−6.50848	−	4.72868i	−0.224430	−	0.163058i
$842$	−63.3788	−	46.0474i	−2.18418	−	1.58690i
$843$	7.07006	+	2.29720i	0.243506	+	0.0791198i
$844$	38.6401	+	118.922i	1.33005	+	4.09346i
$845$	2.44331	+	15.6067i	0.0840524	+	0.536886i
$846$	−21.2699			−0.731273
$847$	−16.6821	−	13.0983i	−0.573203	−	0.450062i
$848$	128.595			4.41598
$849$	7.16678	−	5.20697i	0.245963	−	0.178703i
$850$	−24.8346	+	8.06924i	−0.851819	+	0.276773i
$851$	2.35851	+	0.766327i	0.0808487	+	0.0262693i
$852$	16.8519	−	23.1946i	0.577336	−	0.794635i
$853$	−11.0558	+	15.2170i	−0.378543	+	0.521019i	−0.955198	−	0.295969i	$-0.904358\pi$
$853$	−11.0558	+	15.2170i	−0.378543	+	0.521019i	0.576655	+	0.816988i	$0.304358\pi$
$854$	2.67677	−	8.23826i	0.0915973	−	0.281907i
$855$	−0.888017	−	2.73304i	−0.0303696	−	0.0934679i
$856$	−9.18200	−	12.6379i	−0.313834	−	0.431956i
$857$	9.11688			0.311427			0.155713	−	0.987802i	$-0.450232\pi$
$857$	9.11688			0.311427			0.155713	+	0.987802i	$0.450232\pi$
$858$	12.9626	−	29.6419i	0.442537	−	1.01196i
$859$	−34.8274			−1.18829			−0.594147	−	0.804356i	$-0.702510\pi$
$859$	−34.8274			−1.18829			−0.594147	+	0.804356i	$0.702510\pi$
$860$	37.6278	+	51.7902i	1.28310	+	1.76603i
$861$	−0.886039	−	2.72695i	−0.0301961	−	0.0929341i
$862$	−14.9495	+	46.0098i	−0.509182	+	1.56710i
$863$	13.7470	−	18.9211i	0.467953	−	0.644082i	−0.508181	−	0.861250i	$-0.669682\pi$
$863$	13.7470	−	18.9211i	0.467953	−	0.644082i	0.976134	+	0.217168i	$0.0696820\pi$
$864$	−11.1609	+	15.3616i	−0.379700	+	0.522612i
$865$	−17.2590	−	5.60778i	−0.586823	−	0.190670i
$866$	36.7745	−	11.9487i	1.24965	−	0.406035i
$867$	−7.68246	+	5.58164i	−0.260910	+	0.189562i
$868$	107.740			3.65694
$869$	−5.26504	−	10.8280i	−0.178604	−	0.367315i
$870$	20.0091			0.678371
$871$	50.8264	−	20.9999i	1.72219	−	0.711554i
$872$	2.29124	+	7.05170i	0.0775911	+	0.238801i
$873$	−1.08964	−	0.354047i	−0.0368789	−	0.0119827i
$874$	5.10611	+	3.70980i	0.172717	+	0.125486i
$875$	16.1563	+	11.7382i	0.546183	+	0.396825i
$876$	−37.2474	−	12.1024i	−1.25847	−	0.408902i
$877$	35.4075	−	11.5046i	1.19563	−	0.388483i	0.357477	−	0.933922i	$-0.383637\pi$
$877$	35.4075	−	11.5046i	1.19563	−	0.388483i	0.838151	+	0.545439i	$0.183637\pi$
$878$	16.4784	+	22.6806i	0.556120	+	0.765434i
$879$			30.3888i			1.02499i
$880$	7.59457	+	54.5143i	0.256013	+	1.83768i
$881$	−12.2069			−0.411259			−0.205630	−	0.978630i	$-0.565924\pi$
$881$	−12.2069			−0.411259			−0.205630	+	0.978630i	$0.565924\pi$
$882$	−5.21938	−	7.18386i	−0.175746	−	0.241893i
$883$	−10.5672	−	32.5225i	−0.355615	−	1.09447i	−0.955652	−	0.294498i	$-0.904848\pi$
$883$	−10.5672	−	32.5225i	−0.355615	−	1.09447i	0.600037	−	0.799972i	$-0.295152\pi$
$884$	−44.7721	−	27.4914i	−1.50585	−	0.924635i
$885$	3.78286	+	2.74841i	0.127160	+	0.0923868i
$886$	32.6522	−	44.9420i	1.09697	−	1.50985i
$887$	10.8775	−	33.4776i	0.365232	−	1.12407i	−0.584604	−	0.811319i	$-0.698750\pi$
$887$	10.8775	−	33.4776i	0.365232	−	1.12407i	0.949836	−	0.312749i	$-0.101250\pi$
$888$	−6.97641	−	21.4712i	−0.234113	−	0.720525i
$889$	25.3694	+	34.9180i	0.850862	+	1.17111i
$890$			25.5756i			0.857295i
$891$	−2.92653	−	1.56059i	−0.0980424	−	0.0522816i
$892$		−	31.2285i		−	1.04561i
$893$	15.0418	−	10.9285i	0.503354	−	0.365708i
$894$	−3.69026	−	11.3574i	−0.123421	−	0.379850i
$895$	7.57190	+	2.46026i	0.253101	+	0.0822375i
$896$	−42.2847	−	30.7216i	−1.41263	−	1.02634i
$897$	−2.70662	+	2.30750i	−0.0903716	+	0.0770453i
$898$	12.5279	−	38.5568i	0.418060	−	1.28666i
$899$	−60.8052	+	19.7568i	−2.02797	+	0.658926i
$900$	15.1631	−	11.0166i	0.505437	−	0.367221i
$901$	25.7933			0.859299
$902$	−9.60946	+	9.25741i	−0.319960	+	0.308238i
$903$		−	19.0962i		−	0.635480i
$904$	−71.3103	−	98.1502i	−2.37175	−	3.26443i
$905$	−2.11280	+	0.686490i	−0.0702318	+	0.0228197i
$906$	−10.3891	+	31.9743i	−0.345154	+	1.06227i
$907$	−42.2606	−	30.7041i	−1.40324	−	1.01951i	−0.994263	−	0.106967i	$-0.965886\pi$
$907$	−42.2606	−	30.7041i	−1.40324	−	1.01951i	−0.408976	−	0.912545i	$-0.634114\pi$
$908$	−28.3325	+	38.9964i	−0.940248	+	1.29414i
$909$	3.39347	−	10.4440i	0.112554	−	0.346407i
$910$	1.77284	+	22.7860i	0.0587691	+	0.755349i
$911$	19.2858	−	14.0119i	0.638966	−	0.464236i	−0.220529	−	0.975380i	$-0.570778\pi$
$911$	19.2858	−	14.0119i	0.638966	−	0.464236i	0.859495	+	0.511145i	$0.170778\pi$
$912$		−	32.2981i		−	1.06950i
$913$	−30.6770	−	31.8436i	−1.01526	−	1.05387i
$914$	37.7267			1.24789
$915$	−1.18602	−	1.63241i	−0.0392085	−	0.0539659i
$916$	−108.016	+	35.0964i	−3.56894	+	1.15962i
$917$	32.4012	+	10.5278i	1.06998	+	0.347659i
$918$	−4.35614	+	5.99571i	−0.143774	+	0.197888i
$919$	−43.4742	−	31.5859i	−1.43408	−	1.04192i	−0.989238	−	0.146314i	$-0.953259\pi$
$919$	−43.4742	−	31.5859i	−1.43408	−	1.04192i	−0.444845	−	0.895608i	$-0.646741\pi$
$920$	3.32649	−	10.2379i	0.109671	−	0.337533i
$921$	−15.2162	+	4.94404i	−0.501391	+	0.162912i
$922$	−50.3531	+	36.5837i	−1.65829	+	1.20482i
$923$	−18.8920	−	4.55339i	−0.621836	−	0.149877i
$924$	16.0064	−	30.0165i	0.526573	−	0.987470i
$925$			8.85765i			0.291238i
$926$	29.6146	−	21.5163i	0.973196	−	0.707069i
$927$	4.57973	+	14.0950i	0.150418	+	0.462940i
$928$	109.913	+	35.7129i	3.60807	+	1.17233i
$929$	−7.71954	+	10.6250i	−0.253270	+	0.348596i	−0.916653	−	0.399684i	$-0.869120\pi$
$929$	−7.71954	+	10.6250i	−0.253270	+	0.348596i	0.663383	+	0.748280i	$0.269120\pi$
$930$	20.2979	−	27.9377i	0.665595	−	0.916113i
$931$	7.38215	+	2.39860i	0.241940	+	0.0786111i
$932$	1.49772	+	4.60949i	0.0490593	+	0.150989i
$933$	22.7294	−	16.5139i	0.744128	−	0.540641i
$934$		−	81.5463i		−	2.66828i
$935$	1.52330	+	10.9343i	0.0498172	+	0.357591i
$936$	31.4781	+	7.58693i	1.02889	+	0.247987i
$937$	−24.2528	+	17.6207i	−0.792305	+	0.575643i	−0.908647	−	0.417566i	$-0.862883\pi$
$937$	−24.2528	+	17.6207i	−0.792305	+	0.575643i	0.116342	+	0.993209i	$0.462883\pi$
$938$	75.6712	−	24.5871i	2.47075	−	0.802796i
$939$	2.32532	−	7.15661i	0.0758841	−	0.233547i
$940$	−41.1124	−	29.8699i	−1.34094	−	0.974249i
$941$	10.3739	−	14.2784i	0.338178	−	0.465462i	−0.605730	−	0.795670i	$-0.707119\pi$
$941$	10.3739	−	14.2784i	0.338178	−	0.465462i	0.943908	+	0.330208i	$0.107119\pi$
$942$	−32.6374	−	10.6045i	−1.06339	−	0.345515i
$943$	1.39512	−	0.453303i	0.0454315	−	0.0147616i
$944$	30.8901	+	42.5166i	1.00539	+	1.38380i
$945$	2.34298			0.0762173
$946$	−79.9191	+	38.8601i	−2.59840	+	1.26345i
$947$			31.6547i			1.02864i	0.857598	+	0.514320i	$0.171956\pi$
$947$			31.6547i			1.02864i	−0.857598	+	0.514320i	$0.828044\pi$
$948$	15.6228	−	11.3506i	0.507404	−	0.368651i
$949$	2.05915	+	26.4660i	0.0668429	+	0.859121i
$950$	−6.96629	+	21.4400i	−0.226016	+	0.695607i
$951$	5.32941	−	7.33530i	0.172818	−	0.237863i
$952$	−38.3747	−	27.8809i	−1.24373	−	0.903624i
$953$	−9.06048	+	27.8853i	−0.293498	+	0.903293i	0.690224	+	0.723596i	$0.257512\pi$
$953$	−9.06048	+	27.8853i	−0.293498	+	0.903293i	−0.983722	+	0.179698i	$0.942488\pi$
$954$	−24.2274	+	7.87194i	−0.784390	+	0.254864i
$955$	−15.4239	−	21.2292i	−0.499106	−	0.686960i
$956$		−	3.61522i		−	0.116925i
$957$	−3.52928	+	19.8756i	−0.114085	+	0.642486i
$958$	35.7857			1.15618
$959$	4.64423	−	3.37423i	0.149970	−	0.108960i
$960$	−27.8010	+	9.03310i	−0.897274	+	0.291542i
$961$	−24.5179	+	75.4585i	−0.790902	+	2.43414i
$962$	−18.6611	+	15.9093i	−0.601658	+	0.512936i
$963$	1.40727	+	1.02244i	0.0453487	+	0.0329478i
$964$	−47.4311	−	15.4113i	−1.52765	−	0.496364i
$965$	−3.74561	−	11.5278i	−0.120576	−	0.371093i
$966$	−4.16313	+	3.02469i	−0.133947	+	0.0973178i
$967$			35.5965i			1.14471i	0.820007	+	0.572353i	$0.193969\pi$
$967$			35.5965i			1.14471i	−0.820007	+	0.572353i	$0.806031\pi$
$968$	−98.7162	−	3.68526i	−3.17286	−	0.118449i
$969$		−	6.47827i		−	0.208112i
$970$	−2.21391	−	3.04718i	−0.0710843	−	0.0978392i
$971$	−4.13149	−	12.7154i	−0.132586	−	0.408057i	0.862621	−	0.505851i	$-0.168821\pi$
$971$	−4.13149	−	12.7154i	−0.132586	−	0.408057i	−0.995207	+	0.0977936i	$0.968821\pi$
$972$	1.64379	−	5.05905i	0.0527245	−	0.162269i
$973$	3.57864	−	4.92558i	0.114726	−	0.157907i
$974$	42.2934	+	30.7280i	1.35517	+	0.984588i
$975$	−10.8260	−	6.64746i	−0.346709	−	0.212889i
$976$	−7.00798	−	21.5683i	−0.224320	−	0.690386i
$977$	−4.57595	−	6.29825i	−0.146398	−	0.201499i	0.729520	−	0.683959i	$-0.239743\pi$
$977$	−4.57595	−	6.29825i	−0.146398	−	0.201499i	−0.875918	+	0.482460i	$0.839743\pi$
$978$	−64.9345			−2.07638
$979$	−25.4049	−	4.51112i	−0.811944	−	0.144176i
$980$		−	21.2154i		−	0.677700i
$981$	−0.485298	−	0.667955i	−0.0154944	−	0.0213262i
$982$	59.7296	−	19.4073i	1.90605	−	0.619313i
$983$	26.3550	+	8.56326i	0.840594	+	0.273126i	0.697501	−	0.716584i	$-0.254295\pi$
$983$	26.3550	+	8.56326i	0.840594	+	0.273126i	0.143093	+	0.989709i	$0.454295\pi$
$984$	−10.8039	−	7.84952i	−0.344417	−	0.250233i
$985$	0.988065	+	0.717871i	0.0314824	+	0.0228733i
$986$	42.8996	+	13.9389i	1.36620	+	0.443906i
$987$	4.68440	+	14.4171i	0.149106	+	0.458901i
$988$	−41.9203	+	17.3201i	−1.33366	+	0.551027i
$989$	9.76972			0.310659
$990$	−4.76790	−	9.80560i	−0.151534	−	0.311642i
$991$	−26.5955			−0.844834			−0.422417	−	0.906402i	$-0.638818\pi$
$991$	−26.5955			−0.844834			−0.422417	+	0.906402i	$0.638818\pi$
$992$	161.364	−	117.238i	5.12331	−	3.72230i
$993$	−25.6415	+	8.33141i	−0.813707	+	0.264389i
$994$	−26.7396	−	8.68823i	−0.848130	−	0.275574i
$995$	9.15544	−	12.6014i	0.290247	−	0.399491i
$996$	41.6840	−	57.3731i	1.32081	−	1.81794i
$997$	−5.63430	+	17.3406i	−0.178440	+	0.549182i	−0.999774	−	0.0212660i	$-0.993230\pi$
$997$	−5.63430	+	17.3406i	−0.178440	+	0.549182i	0.821334	+	0.570448i	$0.193230\pi$
$998$	−24.7869	−	76.2862i	−0.784616	−	2.41480i
$999$	1.47764	+	2.03380i	0.0467506	+	0.0643467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.25.1	✓	56
11.4	even	5	inner	429.2.bb.b.103.14	yes	56
13.12	even	2	inner	429.2.bb.b.25.14	yes	56
143.103	even	10	inner	429.2.bb.b.103.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.25.1	✓	56	1.1	even	1	trivial
429.2.bb.b.25.14	yes	56	13.12	even	2	inner
429.2.bb.b.103.1	yes	56	143.103	even	10	inner
429.2.bb.b.103.14	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)

\(f(q)\)	\(=\)	\(q+(-1.59022 - 2.18875i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.64379 + 5.05905i) q^{4} +(0.714239 - 0.983066i) q^{5} +(-1.59022 + 2.18875i) q^{6} +(1.83379 + 0.595836i) q^{7} +(8.54091 - 2.77511i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.59022 - 2.18875i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.64379 + 5.05905i) q^{4} +(0.714239 - 0.983066i) q^{5} +(-1.59022 + 2.18875i) q^{6} +(1.83379 + 0.595836i) q^{7} +(8.54091 - 2.77511i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.28748 q^{10} +(0.579858 - 3.26554i) q^{11} +5.31940 q^{12} +(-1.37681 - 3.33232i) q^{13} +(-1.61200 - 4.96122i) q^{14} +(-1.15566 - 0.375498i) q^{15} +(-11.0490 - 8.02753i) q^{16} +(-2.21617 - 1.61014i) q^{17} +(2.57303 + 0.836027i) q^{18} +(-2.24916 + 0.730797i) q^{19} +(3.79933 + 5.22933i) q^{20} -1.92817i q^{21} +(-8.06954 + 3.92376i) q^{22} +0.986462 q^{23} +(-5.27858 - 7.26534i) q^{24} +(1.08880 + 3.35099i) q^{25} +(-5.10419 + 8.31261i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-6.02873 + 8.29784i) q^{28} +(1.88082 - 5.78856i) q^{29} +(1.01589 + 3.12658i) q^{30} +(-6.17431 - 8.49821i) q^{31} +18.9880i q^{32} +(-3.28490 + 0.457630i) q^{33} +7.41111i q^{34} +(1.89551 - 1.37717i) q^{35} +(-1.64379 - 5.05905i) q^{36} +(2.39088 + 0.776844i) q^{37} +(5.17618 + 3.76072i) q^{38} +(-2.74377 + 2.33917i) q^{39} +(3.37214 - 10.3784i) q^{40} +(1.41427 - 0.459524i) q^{41} +(-4.22027 + 3.06620i) q^{42} +9.90380 q^{43} +(15.5674 + 8.30139i) q^{44} +1.21514i q^{45} +(-1.56869 - 2.15911i) q^{46} +(-7.47710 + 2.42946i) q^{47} +(-4.22032 + 12.9888i) q^{48} +(-2.65534 - 1.92922i) q^{49} +(5.60304 - 7.71193i) q^{50} +(-0.846501 + 2.60526i) q^{51} +(19.1216 - 1.48773i) q^{52} +(-7.61762 + 5.53453i) q^{53} -2.70544i q^{54} +(-2.79609 - 2.90242i) q^{55} +17.3158 q^{56} +(1.39006 + 1.91325i) q^{57} +(-15.6606 + 5.08844i) q^{58} +(-3.65969 - 1.18911i) q^{59} +(3.79933 - 5.22933i) q^{60} +(1.34340 + 0.976036i) q^{61} +(-8.78193 + 27.0280i) q^{62} +(-1.83379 + 0.595836i) q^{63} +(19.4620 - 14.1400i) q^{64} +(-4.25927 - 1.02658i) q^{65} +(6.22534 + 6.46208i) q^{66} +15.2525i q^{67} +(11.7887 - 8.56499i) q^{68} +(-0.304833 - 0.938181i) q^{69} +(-6.02856 - 1.95880i) q^{70} +(3.16800 - 4.36038i) q^{71} +(-5.27858 + 7.26534i) q^{72} +(-7.00217 - 2.27514i) q^{73} +(-2.10170 - 6.46838i) q^{74} +(2.85053 - 2.07103i) q^{75} -12.5799i q^{76} +(3.00907 - 5.64283i) q^{77} +(9.48305 + 2.28563i) q^{78} +(2.93694 - 2.13381i) q^{79} +(-15.7832 + 5.12827i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-3.25478 - 2.36474i) q^{82} +(7.83621 - 10.7856i) q^{83} +(9.75469 + 3.16949i) q^{84} +(-3.16575 + 1.02861i) q^{85} +(-15.7492 - 21.6769i) q^{86} -6.08645 q^{87} +(-4.10972 - 29.4999i) q^{88} -7.77969i q^{89} +(2.65963 - 1.93233i) q^{90} +(-0.539270 - 6.93115i) q^{91} +(-1.62153 + 4.99056i) q^{92} +(-6.17431 + 8.49821i) q^{93} +(17.2077 + 12.5021i) q^{94} +(-0.888017 + 2.73304i) q^{95} +(18.0586 - 5.86761i) q^{96} +(0.673437 + 0.926906i) q^{97} +8.87974i q^{98} +(1.45032 + 2.98271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

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