LMFDB - Embedded newform 315.2.bo.b.4.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(4,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("315.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bo (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.b.79.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40440 - 0.810833i) q^{2} +(-0.306778 + 1.70467i) q^{3} +(0.314901 + 0.545425i) q^{4} +(1.75547 - 1.38504i) q^{5} +(1.81304 - 2.14529i) q^{6} +(-1.09563 - 2.40824i) q^{7} +2.22200i q^{8} +(-2.81177 - 1.04591i) q^{9} +O(q^{10})$	\(q+(-1.40440 - 0.810833i) q^{2} +(-0.306778 + 1.70467i) q^{3} +(0.314901 + 0.545425i) q^{4} +(1.75547 - 1.38504i) q^{5} +(1.81304 - 2.14529i) q^{6} +(-1.09563 - 2.40824i) q^{7} +2.22200i q^{8} +(-2.81177 - 1.04591i) q^{9} +(-3.58842 + 0.521762i) q^{10} +0.738158 q^{11} +(-1.02637 + 0.369477i) q^{12} +(-1.39023 - 0.802650i) q^{13} +(-0.413978 + 4.27051i) q^{14} +(1.82249 + 3.41739i) q^{15} +(2.43148 - 4.21144i) q^{16} +(2.75496 + 1.59058i) q^{17} +(3.10081 + 3.74876i) q^{18} +(-2.94868 - 5.10727i) q^{19} +(1.30823 + 0.521325i) q^{20} +(4.44135 - 1.12888i) q^{21} +(-1.03667 - 0.598523i) q^{22} -7.13616i q^{23} +(-3.78778 - 0.681662i) q^{24} +(1.16334 - 4.86278i) q^{25} +(1.30163 + 2.25449i) q^{26} +(2.64552 - 4.47227i) q^{27} +(0.968498 - 1.35594i) q^{28} +(1.15947 + 2.00826i) q^{29} +(0.211419 - 6.27713i) q^{30} +(-3.47969 - 6.02700i) q^{31} +(-2.98093 + 1.72104i) q^{32} +(-0.226451 + 1.25831i) q^{33} +(-2.57939 - 4.46763i) q^{34} +(-5.25884 - 2.71010i) q^{35} +(-0.314966 - 1.86297i) q^{36} +(0.663945 - 0.383329i) q^{37} +9.56356i q^{38} +(1.79474 - 2.12364i) q^{39} +(3.07756 + 3.90066i) q^{40} +(-1.35331 + 2.34400i) q^{41} +(-7.15279 - 2.01579i) q^{42} +(8.89296 - 5.13435i) q^{43} +(0.232447 + 0.402610i) q^{44} +(-6.38460 + 2.05836i) q^{45} +(-5.78623 + 10.0221i) q^{46} +(3.17928 + 1.83556i) q^{47} +(6.43318 + 5.43683i) q^{48} +(-4.59921 + 5.27705i) q^{49} +(-5.57670 + 5.88604i) q^{50} +(-3.55656 + 4.20833i) q^{51} -1.01102i q^{52} +(-4.84312 - 2.79618i) q^{53} +(-7.34164 + 4.13581i) q^{54} +(1.29581 - 1.02238i) q^{55} +(5.35111 - 2.43448i) q^{56} +(9.61078 - 3.45972i) q^{57} -3.76054i q^{58} +(-1.35066 - 2.33942i) q^{59} +(-1.29002 + 2.07017i) q^{60} +(-2.52264 + 4.36935i) q^{61} +11.2858i q^{62} +(0.561854 + 7.91734i) q^{63} -4.14400 q^{64} +(-3.55221 + 0.516497i) q^{65} +(1.33831 - 1.58357i) q^{66} +(-7.99623 + 4.61662i) q^{67} +2.00350i q^{68} +(12.1648 + 2.18922i) q^{69} +(5.18809 + 8.07012i) q^{70} +3.14092 q^{71} +(2.32401 - 6.24777i) q^{72} +(12.4428 + 7.18386i) q^{73} -1.24326 q^{74} +(7.93253 + 3.47490i) q^{75} +(1.85709 - 3.21657i) q^{76} +(-0.808745 - 1.77766i) q^{77} +(-4.24247 + 1.52722i) q^{78} +(4.88236 - 8.45650i) q^{79} +(-1.56463 - 10.7607i) q^{80} +(6.81215 + 5.88172i) q^{81} +(3.80119 - 2.19462i) q^{82} +(1.49184 - 0.861315i) q^{83} +(2.01431 + 2.06694i) q^{84} +(7.03926 - 1.02352i) q^{85} -16.6524 q^{86} +(-3.77910 + 1.36042i) q^{87} +1.64019i q^{88} +(6.73500 + 11.6654i) q^{89} +(10.6355 + 2.28608i) q^{90} +(-0.409800 + 4.22741i) q^{91} +(3.89224 - 2.24718i) q^{92} +(11.3415 - 4.08276i) q^{93} +(-2.97666 - 5.15573i) q^{94} +(-12.2501 - 4.88161i) q^{95} +(-2.01932 - 5.60947i) q^{96} +(-11.9468 + 6.89747i) q^{97} +(10.7380 - 3.68192i) q^{98} +(-2.07553 - 0.772046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.40440	−	0.810833i	−0.993064	−	0.573346i	−0.0868751	−	0.996219i	$-0.527688\pi$
$2$	−1.40440	−	0.810833i	−0.993064	−	0.573346i	−0.906189	+	0.422874i	$0.861021\pi$
$3$	−0.306778	+	1.70467i	−0.177118	+	0.984190i
$3$	−0.306778	+	1.70467i	−0.177118	+	0.984190i
$4$	0.314901	+	0.545425i	0.157451	+	0.272712i
$5$	1.75547	−	1.38504i	0.785069	−	0.619408i
$5$	1.75547	−	1.38504i	0.785069	−	0.619408i
$6$	1.81304	−	2.14529i	0.740171	−	0.875813i
$7$	−1.09563	−	2.40824i	−0.414107	−	0.910228i
$7$	−1.09563	−	2.40824i	−0.414107	−	0.910228i
$8$			2.22200i			0.785597i
$9$	−2.81177	−	1.04591i	−0.937258	−	0.348636i
$10$	−3.58842	+	0.521762i	−1.13476	+	0.164996i
$11$	0.738158			0.222563			0.111282	−	0.993789i	$-0.464504\pi$
$11$	0.738158			0.222563			0.111282	+	0.993789i	$0.464504\pi$
$12$	−1.02637	+	0.369477i	−0.296288	+	0.106659i
$13$	−1.39023	−	0.802650i	−0.385581	−	0.222615i	0.294663	−	0.955601i	$-0.404793\pi$
$13$	−1.39023	−	0.802650i	−0.385581	−	0.222615i	−0.680243	+	0.732986i	$0.738126\pi$
$14$	−0.413978	+	4.27051i	−0.110640	+	1.14134i
$15$	1.82249	+	3.41739i	0.470565	+	0.882365i
$16$	2.43148	−	4.21144i	0.607869	−	1.05286i
$17$	2.75496	+	1.59058i	0.668176	+	0.385772i	0.795385	−	0.606104i	$-0.207269\pi$
$17$	2.75496	+	1.59058i	0.668176	+	0.385772i	−0.127209	+	0.991876i	$0.540602\pi$
$18$	3.10081	+	3.74876i	0.730868	+	0.883591i
$19$	−2.94868	−	5.10727i	−0.676475	−	1.17169i	−0.976036	−	0.217611i	$-0.930174\pi$
$19$	−2.94868	−	5.10727i	−0.676475	−	1.17169i	0.299561	−	0.954077i	$-0.403160\pi$
$20$	1.30823	+	0.521325i	0.292530	+	0.116572i
$21$	4.44135	−	1.12888i	0.969183	−	0.246342i
$22$	−1.03667	−	0.598523i	−0.221019	−	0.127606i
$23$		−	7.13616i		−	1.48799i	−0.668184	−	0.743996i	$-0.732928\pi$
$23$		−	7.13616i		−	1.48799i	0.668184	−	0.743996i	$-0.267072\pi$
$24$	−3.78778	−	0.681662i	−0.773176	−	0.139144i
$25$	1.16334	−	4.86278i	0.232667	−	0.972556i
$26$	1.30163	+	2.25449i	0.255271	+	0.442142i
$27$	2.64552	−	4.47227i	0.509130	−	0.860690i
$28$	0.968498	−	1.35594i	0.183029	−	0.256248i
$29$	1.15947	+	2.00826i	0.215308	+	0.372924i	0.953368	−	0.301811i	$-0.0975913\pi$
$29$	1.15947	+	2.00826i	0.215308	+	0.372924i	−0.738060	+	0.674735i	$0.764258\pi$
$30$	0.211419	−	6.27713i	0.0385996	−	1.14604i
$31$	−3.47969	−	6.02700i	−0.624970	−	1.08248i	−0.988547	−	0.150916i	$-0.951778\pi$
$31$	−3.47969	−	6.02700i	−0.624970	−	1.08248i	0.363576	−	0.931564i	$-0.381556\pi$
$32$	−2.98093	+	1.72104i	−0.526959	+	0.304240i
$33$	−0.226451	+	1.25831i	−0.0394200	+	0.219044i
$34$	−2.57939	−	4.46763i	−0.442361	−	0.766192i
$35$	−5.25884	−	2.71010i	−0.888906	−	0.458091i
$36$	−0.314966	−	1.86297i	−0.0524944	−	0.310495i
$37$	0.663945	−	0.383329i	0.109152	−	0.0630189i	−0.444430	−	0.895813i	$-0.646594\pi$
$37$	0.663945	−	0.383329i	0.109152	−	0.0630189i	0.553582	+	0.832795i	$0.313260\pi$
$38$			9.56356i			1.55142i
$39$	1.79474	−	2.12364i	0.287389	−	0.340055i
$40$	3.07756	+	3.90066i	0.486605	+	0.616748i
$41$	−1.35331	+	2.34400i	−0.211352	+	0.366072i	−0.952138	−	0.305669i	$-0.901120\pi$
$41$	−1.35331	+	2.34400i	−0.211352	+	0.366072i	0.740786	+	0.671741i	$0.234453\pi$
$42$	−7.15279	−	2.01579i	−1.10370	−	0.311044i
$43$	8.89296	−	5.13435i	1.35616	−	0.782982i	0.367059	−	0.930197i	$-0.380365\pi$
$43$	8.89296	−	5.13435i	1.35616	−	0.782982i	0.989104	+	0.147216i	$0.0470312\pi$
$44$	0.232447	+	0.402610i	0.0350427	+	0.0606957i
$45$	−6.38460	+	2.05836i	−0.951761	+	0.306842i
$46$	−5.78623	+	10.0221i	−0.853134	+	1.47767i
$47$	3.17928	+	1.83556i	0.463746	+	0.267744i	0.713618	−	0.700535i	$-0.247055\pi$
$47$	3.17928	+	1.83556i	0.463746	+	0.267744i	−0.249872	+	0.968279i	$0.580389\pi$
$48$	6.43318	+	5.43683i	0.928549	+	0.784740i
$49$	−4.59921	+	5.27705i	−0.657030	+	0.753864i
$50$	−5.57670	+	5.88604i	−0.788664	+	0.832412i
$51$	−3.55656	+	4.20833i	−0.498019	+	0.589285i
$52$		−	1.01102i		−	0.140203i
$53$	−4.84312	−	2.79618i	−0.665254	−	0.384084i	0.129022	−	0.991642i	$-0.458816\pi$
$53$	−4.84312	−	2.79618i	−0.665254	−	0.384084i	−0.794276	+	0.607557i	$0.792149\pi$
$54$	−7.34164	+	4.13581i	−0.999071	+	0.562812i
$55$	1.29581	−	1.02238i	0.174727	−	0.137857i
$56$	5.35111	−	2.43448i	0.715072	−	0.325322i
$57$	9.61078	−	3.45972i	1.27298	−	0.458252i
$58$		−	3.76054i		−	0.493783i
$59$	−1.35066	−	2.33942i	−0.175841	−	0.304566i	0.764611	−	0.644492i	$-0.222931\pi$
$59$	−1.35066	−	2.33942i	−0.175841	−	0.304566i	−0.940452	+	0.339926i	$0.889598\pi$
$60$	−1.29002	+	2.07017i	−0.166541	+	0.267258i
$61$	−2.52264	+	4.36935i	−0.322991	+	0.559437i	−0.981104	−	0.193482i	$-0.938022\pi$
$61$	−2.52264	+	4.36935i	−0.322991	+	0.559437i	0.658112	+	0.752920i	$0.271355\pi$
$62$			11.2858i			1.43330i
$63$	0.561854	+	7.91734i	0.0707869	+	0.997491i
$64$	−4.14400			−0.518000
$65$	−3.55221	+	0.516497i	−0.440597	+	0.0640635i
$66$	1.33831	−	1.58357i	0.164735	−	0.194924i
$67$	−7.99623	+	4.61662i	−0.976894	+	0.564010i	−0.901331	−	0.433131i	$-0.857409\pi$
$67$	−7.99623	+	4.61662i	−0.976894	+	0.564010i	−0.0755633	+	0.997141i	$0.524076\pi$
$68$			2.00350i			0.242960i
$69$	12.1648	+	2.18922i	1.46447	+	0.263551i
$70$	5.18809	+	8.07012i	0.620096	+	0.964563i
$71$	3.14092			0.372759			0.186379	−	0.982478i	$-0.440325\pi$
$71$	3.14092			0.372759			0.186379	+	0.982478i	$0.440325\pi$
$72$	2.32401	−	6.24777i	0.273888	−	0.736307i
$73$	12.4428	+	7.18386i	1.45632	+	0.840808i	0.998828	−	0.0484049i	$-0.0154138\pi$
$73$	12.4428	+	7.18386i	1.45632	+	0.840808i	0.457494	+	0.889213i	$0.348747\pi$
$74$	−1.24326			−0.144526
$75$	7.93253	+	3.47490i	0.915970	+	0.401246i
$76$	1.85709	−	3.21657i	0.213023	−	0.368966i
$77$	−0.808745	−	1.77766i	−0.0921650	−	0.202583i
$78$	−4.24247	+	1.52722i	−0.480365	+	0.172923i
$79$	4.88236	−	8.45650i	0.549309	−	0.951430i	−0.449014	−	0.893525i	$-0.648225\pi$
$79$	4.88236	−	8.45650i	0.549309	−	0.951430i	0.998322	−	0.0579053i	$-0.0184422\pi$
$80$	−1.56463	−	10.7607i	−0.174931	−	1.20309i
$81$	6.81215	+	5.88172i	0.756905	+	0.653524i
$82$	3.80119	−	2.19462i	0.419772	−	0.242355i
$83$	1.49184	−	0.861315i	0.163751	−	0.0945416i	−0.415885	−	0.909417i	$-0.636528\pi$
$83$	1.49184	−	0.861315i	0.163751	−	0.0945416i	0.579636	+	0.814876i	$0.303195\pi$
$84$	2.01431	+	2.06694i	0.219779	+	0.225521i
$85$	7.03926	−	1.02352i	0.763514	−	0.111016i
$86$	−16.6524			−1.79568
$87$	−3.77910	+	1.36042i	−0.405163	+	0.145852i
$88$			1.64019i			0.174845i
$89$	6.73500	+	11.6654i	0.713908	+	1.23653i	0.963379	+	0.268143i	$0.0864099\pi$
$89$	6.73500	+	11.6654i	0.713908	+	1.23653i	−0.249471	+	0.968382i	$0.580257\pi$
$90$	10.6355	+	2.28608i	1.12109	+	0.240974i
$91$	−0.409800	+	4.22741i	−0.0429587	+	0.443153i
$92$	3.89224	−	2.24718i	0.405794	−	0.234285i
$93$	11.3415	−	4.08276i	1.17606	−	0.423362i
$94$	−2.97666	−	5.15573i	−0.307020	−	0.531773i
$95$	−12.2501	−	4.88161i	−1.25683	−	0.500843i
$96$	−2.01932	−	5.60947i	−0.206096	−	0.572514i
$97$	−11.9468	+	6.89747i	−1.21301	+	0.700332i	−0.963414	−	0.268018i	$-0.913631\pi$
$97$	−11.9468	+	6.89747i	−1.21301	+	0.700332i	−0.249596	+	0.968350i	$0.580298\pi$
$98$	10.7380	−	3.68192i	1.08470	−	0.371930i
$99$	−2.07553	−	0.772046i	−0.208599	−	0.0775936i
$100$	3.01862	−	0.896783i	0.301862	−	0.0896783i
$101$	11.5035			1.14464			0.572321	−	0.820030i	$-0.306043\pi$
$101$	11.5035			1.14464			0.572321	+	0.820030i	$0.306043\pi$
$102$	8.40711	−	3.02642i	0.832428	−	0.299660i
$103$			14.9717i			1.47521i	0.675233	+	0.737604i	$0.264043\pi$
$103$			14.9717i			1.47521i	−0.675233	+	0.737604i	$0.735957\pi$
$104$	1.78349	−	3.08910i	0.174886	−	0.302911i
$105$	6.23311	−	8.13316i	0.608290	−	0.793715i
$106$	4.53447	+	7.85392i	0.440426	+	0.762841i
$107$	−16.9538	+	9.78831i	−1.63899	+	0.946271i	−0.657808	+	0.753186i	$0.728516\pi$
$107$	−16.9538	+	9.78831i	−1.63899	+	0.946271i	−0.981182	+	0.193085i	$0.938151\pi$
$108$	3.27236	+	0.0346059i	0.314883	+	0.00332995i
$109$	−1.08067	+	1.87177i	−0.103509	+	0.179283i	−0.913128	−	0.407673i	$-0.866340\pi$
$109$	−1.08067	+	1.87177i	−0.103509	+	0.179283i	0.809619	+	0.586956i	$0.199674\pi$
$110$	−2.64882	+	0.385143i	−0.252555	+	0.0367220i
$111$	0.449764	+	1.24940i	0.0426897	+	0.118588i
$112$	−12.8061	−	1.24141i	−1.21007	−	0.117302i
$113$	−1.16141	−	0.670538i	−0.109256	−	0.0630789i	0.444376	−	0.895840i	$-0.353425\pi$
$113$	−1.16141	−	0.670538i	−0.109256	−	0.0630789i	−0.553632	+	0.832761i	$0.686759\pi$
$114$	−16.3027	−	2.93389i	−1.52689	−	0.274784i
$115$	−9.88386	−	12.5273i	−0.921674	−	1.16818i
$116$	−0.730235	+	1.26480i	−0.0678006	+	0.117434i
$117$	3.06952	+	3.71092i	0.283777	+	0.343075i
$118$			4.38065i			0.403272i
$119$	0.812083	−	8.37727i	0.0744435	−	0.767943i
$120$	−7.59345	+	4.04958i	−0.693184	+	0.369674i
$121$	−10.4551			−0.950466
$122$	7.08562	−	4.09089i	0.641502	−	0.370371i
$123$	−3.58058	−	3.02603i	−0.322850	−	0.272848i
$124$	2.19151	−	3.79582i	0.196804	−	0.340874i
$125$	−4.69294	−	10.1477i	−0.419749	−	0.907640i
$126$	5.63057	−	11.5747i	0.501611	−	1.03116i
$127$		−	3.17795i		−	0.281997i	−0.990010	−	0.140999i	$-0.954969\pi$
$127$		−	3.17795i		−	0.281997i	0.990010	−	0.140999i	$-0.0450313\pi$
$128$	11.7817	+	6.80217i	1.04137	+	0.601233i
$129$	6.02419	+	16.7346i	0.530401	+	1.47340i
$130$	5.40753	+	2.15488i	0.474271	+	0.188995i
$131$	−3.92153			−0.342626			−0.171313	−	0.985217i	$-0.554801\pi$
$131$	−3.92153			−0.342626			−0.171313	+	0.985217i	$0.554801\pi$
$132$	−0.757625	+	0.272732i	−0.0659428	+	0.0237383i
$133$	−9.06887	+	12.6968i	−0.786370	+	1.10095i
$134$	14.9732			1.29349
$135$	−1.55015	−	11.5151i	−0.133416	−	0.991060i
$136$	−3.53427	+	6.12153i	−0.303061	+	0.524917i
$137$		−	11.8775i		−	1.01476i	−0.861722	−	0.507381i	$-0.830614\pi$
$137$		−	11.8775i		−	1.01476i	0.861722	−	0.507381i	$-0.169386\pi$
$138$	−15.3092	−	12.9381i	−1.30320	−	1.10137i
$139$	3.03996	−	5.26536i	0.257846	−	0.446602i	−0.707819	−	0.706394i	$-0.750321\pi$
$139$	3.03996	−	5.26536i	0.257846	−	0.446602i	0.965665	+	0.259792i	$0.0836540\pi$
$140$	−0.177858	−	3.72171i	−0.0150317	−	0.314542i
$141$	−4.10435	+	4.85650i	−0.345649	+	0.408991i
$142$	−4.41113	−	2.54676i	−0.370173	−	0.213720i
$143$	−1.02621	−	0.592483i	−0.0858160	−	0.0495459i
$144$	−11.2415	+	9.29852i	−0.936796	+	0.774877i
$145$	4.81692	+	1.91952i	0.400023	+	0.159408i
$146$	−11.6498	−	20.1781i	−0.964147	−	1.66995i
$147$	−7.58467	−	9.45900i	−0.625573	−	0.780166i
$148$	0.418154	+	0.241421i	0.0343721	+	0.0198447i
$149$	18.6667			1.52923			0.764617	−	0.644485i	$-0.222928\pi$
$149$	18.6667			1.52923			0.764617	+	0.644485i	$0.222928\pi$
$150$	−8.32293	−	11.3121i	−0.679564	−	0.923631i
$151$	16.5023			1.34294			0.671470	−	0.741032i	$-0.265663\pi$
$151$	16.5023			1.34294			0.671470	+	0.741032i	$0.265663\pi$
$152$	11.3484	−	6.55199i	0.920475	−	0.531436i
$153$	−6.08273	−	7.35378i	−0.491759	−	0.594518i
$154$	−0.305581	+	3.15231i	−0.0246244	+	0.254020i
$155$	−14.4561	−	5.76070i	−1.16114	−	0.462710i
$156$	1.72345	+	0.310159i	0.137987	+	0.0248326i
$157$	6.55466	−	3.78434i	0.523119	−	0.302023i	−0.215091	−	0.976594i	$-0.569005\pi$
$157$	6.55466	−	3.78434i	0.523119	−	0.302023i	0.738210	+	0.674571i	$0.235671\pi$
$158$	−13.7136	+	7.91756i	−1.09100	+	0.629887i
$159$	6.25231	−	7.39810i	0.495841	−	0.586707i
$160$	−2.84922	+	7.14993i	−0.225251	+	0.565252i
$161$	−17.1856	+	7.81855i	−1.35441	+	0.616188i
$162$	−4.79792	−	13.7838i	−0.376960	−	1.08296i
$163$	6.09449	−	3.51865i	0.477357	−	0.275602i	−0.241957	−	0.970287i	$-0.577789\pi$
$163$	6.09449	−	3.51865i	0.477357	−	0.275602i	0.719314	+	0.694685i	$0.244456\pi$
$164$	−1.70464			−0.133110
$165$	1.34529	+	2.52257i	0.104730	+	0.196382i
$166$	−2.79353			−0.216820
$167$	15.8502	+	9.15111i	1.22652	+	0.708134i	0.966301	−	0.257414i	$-0.0828705\pi$
$167$	15.8502	+	9.15111i	1.22652	+	0.708134i	0.260223	+	0.965549i	$0.416204\pi$
$168$	2.50838	+	9.86871i	0.193525	+	0.761387i
$169$	−5.21151	−	9.02659i	−0.400885	−	0.694353i
$170$	−10.7159	−	4.27023i	−0.821869	−	0.327511i
$171$	2.94929	+	17.4445i	0.225538	+	1.33402i
$172$	5.60081	+	3.23363i	0.427057	+	0.246562i
$173$	−15.9562	−	9.21231i	−1.21313	−	0.700399i	−0.249687	−	0.968327i	$-0.580328\pi$
$173$	−15.9562	−	9.21231i	−1.21313	−	0.700399i	−0.963439	+	0.267928i	$0.913661\pi$
$174$	6.41046	+	1.15365i	0.485976	+	0.0874580i
$175$	−12.9853	+	2.52620i	−0.981597	+	0.190963i
$176$	1.79481	−	3.10871i	0.135289	−	0.234328i
$177$	4.40228	−	1.58475i	0.330896	−	0.119117i
$178$		−	21.8438i		−	1.63726i
$179$	−3.01840	+	5.22802i	−0.225606	+	0.390761i	−0.956501	−	0.291729i	$-0.905770\pi$
$179$	−3.01840	+	5.22802i	−0.225606	+	0.390761i	0.730895	+	0.682490i	$0.239103\pi$
$180$	−3.13320	−	2.83414i	−0.233535	−	0.211244i
$181$	5.63935			0.419169			0.209585	−	0.977791i	$-0.432789\pi$
$181$	5.63935			0.419169			0.209585	+	0.977791i	$0.432789\pi$
$182$	4.00325	−	5.60471i	0.296740	−	0.415449i
$183$	−6.67439	−	5.64069i	−0.493385	−	0.416971i
$184$	15.8566			1.16896
$185$	0.634609	−	1.59251i	0.0466574	−	0.117084i
$186$	−19.2385	−	3.46223i	−1.41064	−	0.253863i
$187$	2.03360	+	1.17410i	0.148711	+	0.0858585i
$188$			2.31208i			0.168626i
$189$	−13.6688	−	1.47109i	−0.994258	−	0.107006i
$190$	13.2459	+	16.7885i	0.960959	+	1.21797i
$191$	−12.0790	+	20.9215i	−0.874007	+	1.51383i	−0.0161910	+	0.999869i	$0.505154\pi$
$191$	−12.0790	+	20.9215i	−0.874007	+	1.51383i	−0.857816	+	0.513956i	$0.828179\pi$
$192$	1.27129	−	7.06414i	0.0917474	−	0.509810i
$193$	11.9786	−	6.91583i	0.862236	−	0.497812i	−0.00252430	−	0.999997i	$-0.500804\pi$
$193$	11.9786	−	6.91583i	0.862236	−	0.497812i	0.864760	+	0.502185i	$0.167470\pi$
$194$	22.3708			1.60613
$195$	0.209285	−	6.21378i	0.0149872	−	0.444978i
$196$	−4.32653	−	0.846775i	−0.309038	−	0.0604839i
$197$			7.59901i			0.541407i	0.962663	+	0.270704i	$0.0872563\pi$
$197$			7.59901i			0.541407i	−0.962663	+	0.270704i	$0.912744\pi$
$198$	2.28889	+	2.76718i	0.162664	+	0.196655i
$199$	11.5496	−	20.0045i	0.818729	−	1.41808i	−0.0878897	−	0.996130i	$-0.528012\pi$
$199$	11.5496	−	20.0045i	0.818729	−	1.41808i	0.906619	−	0.421950i	$-0.138654\pi$
$200$	10.8051	+	2.58494i	0.764037	+	0.182783i
$201$	−5.41673	−	15.0472i	−0.382067	−	1.06135i
$202$	−16.1556	−	9.32742i	−1.13670	−	0.656275i
$203$	3.56601	−	4.99257i	0.250285	−	0.350409i
$204$	−3.41529	−	0.614629i	−0.239118	−	0.0430327i
$205$	0.870841	+	5.98921i	0.0608222	+	0.418305i
$206$	12.1396	−	21.0264i	0.845804	−	1.46498i
$207$	−7.46377	+	20.0653i	−0.518768	+	1.39463i
$208$	−6.76063	+	3.90325i	−0.468765	+	0.270642i
$209$	−2.17660	−	3.76997i	−0.150558	−	0.260775i
$210$	−15.3484	+	6.36823i	−1.05914	+	0.439450i
$211$	4.61981	−	8.00175i	0.318041	−	0.550863i	−0.662038	−	0.749470i	$-0.730308\pi$
$211$	4.61981	−	8.00175i	0.318041	−	0.550863i	0.980079	+	0.198607i	$0.0636417\pi$
$212$		−	3.52208i		−	0.241897i
$213$	−0.963567	+	5.35422i	−0.0660225	+	0.366865i
$214$	31.7467			2.17016
$215$	8.50003	−	21.3303i	0.579697	−	1.45471i
$216$	9.93741	+	5.87835i	0.676155	+	0.399971i
$217$	−10.7020	+	14.9832i	−0.726499	+	1.01713i
$218$	3.03538	−	1.75248i	0.205582	−	0.118693i
$219$	−16.0633	+	19.0070i	−1.08546	+	1.28437i
$220$	0.965683	+	0.384821i	0.0651063	+	0.0259446i
$221$	−2.55335	−	4.42254i	−0.171757	−	0.297492i
$222$	0.381406	−	2.11935i	0.0255983	−	0.142241i
$223$	−2.30822	+	1.33265i	−0.154570	+	0.0892411i	−0.575290	−	0.817949i	$-0.695111\pi$
$223$	−2.30822	+	1.33265i	−0.154570	+	0.0892411i	0.420720	+	0.907191i	$0.361777\pi$
$224$	7.41065	+	5.29317i	0.495145	+	0.353665i
$225$	−8.35707	+	12.4563i	−0.557138	+	0.830420i
$226$	1.08739	+	1.88341i	0.0723321	+	0.125283i
$227$			11.9350i			0.792156i	0.918217	+	0.396078i	$0.129629\pi$
$227$			11.9350i			0.792156i	−0.918217	+	0.396078i	$0.870371\pi$
$228$	4.91346	+	4.15249i	0.325402	+	0.275005i
$229$	−1.86489			−0.123236			−0.0616178	−	0.998100i	$-0.519626\pi$
$229$	−1.86489			−0.123236			−0.0616178	+	0.998100i	$0.519626\pi$
$230$	3.72338	+	25.6076i	0.245512	+	1.68851i
$231$	3.27842	−	0.833293i	0.215704	−	0.0548266i
$232$	−4.46235	+	2.57634i	−0.292968	+	0.169145i
$233$	1.76809	−	1.02081i	0.115831	−	0.0668752i	−0.440965	−	0.897524i	$-0.645364\pi$
$233$	1.76809	−	1.02081i	0.115831	−	0.0668752i	0.556796	+	0.830649i	$0.312030\pi$
$234$	−1.30190	−	7.70050i	−0.0851079	−	0.503398i
$235$	8.12345	−	1.18116i	0.529915	−	0.0770505i
$236$	0.850651	−	1.47337i	0.0553727	−	0.0959082i
$237$	12.9177	+	10.9171i	0.839095	+	0.709140i
$238$	−7.93306	+	11.1066i	−0.514224	+	0.719935i
$239$	9.02182	−	15.6262i	0.583573	−	1.01078i	−0.411479	−	0.911419i	$-0.634988\pi$
$239$	9.02182	−	15.6262i	0.583573	−	1.01078i	0.995052	−	0.0993585i	$-0.0316790\pi$
$240$	18.8235	+	0.633990i	1.21505	+	0.0409239i
$241$	26.2550			1.69123			0.845617	−	0.533791i	$-0.179233\pi$
$241$	26.2550			1.69123			0.845617	+	0.533791i	$0.179233\pi$
$242$	14.6832	+	8.47736i	0.943873	+	0.544945i
$243$	−12.1162	+	9.80806i	−0.777254	+	0.629187i
$244$	−3.17753			−0.203421
$245$	−0.764851	+	15.6338i	−0.0488645	+	0.998805i
$246$	2.57497	+	7.15303i	0.164174	+	0.456060i
$247$			9.46704i			0.602374i
$248$	13.3920	−	7.73188i	0.850393	−	0.490975i
$249$	1.01059	+	2.80733i	0.0640436	+	0.177907i
$250$	−1.63732	+	18.0567i	−0.103554	+	1.14201i
$251$	−7.01884			−0.443026			−0.221513	−	0.975157i	$-0.571099\pi$
$251$	−7.01884			−0.443026			−0.221513	+	0.975157i	$0.571099\pi$
$252$	−4.14139	+	2.79963i	−0.260883	+	0.176360i
$253$		−	5.26761i		−	0.331172i
$254$	−2.57678	+	4.46312i	−0.161682	+	0.280041i
$255$	−0.414732	+	12.3136i	−0.0259715	+	0.771106i
$256$	−6.88686	−	11.9284i	−0.430429	−	0.745524i
$257$			0.596367i			0.0372004i	0.999827	+	0.0186002i	$0.00592096\pi$
$257$			0.596367i			0.0372004i	−0.999827	+	0.0186002i	$0.994079\pi$
$258$	5.10860	−	28.3868i	0.318047	−	1.76729i
$259$	−1.65058	−	1.17895i	−0.102562	−	0.0732566i
$260$	−1.40030	−	1.77482i	−0.0868431	−	0.110069i
$261$	−1.15971	−	6.85946i	−0.0717841	−	0.424590i
$262$	5.50741	+	3.17971i	0.340249	+	0.196443i
$263$		−	24.6241i		−	1.51838i	−0.650866	−	0.759192i	$-0.725594\pi$
$263$		−	24.6241i		−	1.51838i	0.650866	−	0.759192i	$-0.274406\pi$
$264$	−2.79598	−	0.503175i	−0.172081	−	0.0309683i
$265$	−12.3748	+	1.79931i	−0.760175	+	0.110531i
$266$	23.0313	−	10.4781i	1.41214	−	0.642452i
$267$	−21.9517	+	7.90224i	−1.34342	+	0.483609i
$268$	−5.03604	−	2.90756i	−0.307625	−	0.177607i
$269$	−7.42285	+	12.8568i	−0.452579	+	0.783890i	−0.998545	−	0.0539172i	$-0.982829\pi$
$269$	−7.42285	+	12.8568i	−0.452579	+	0.783890i	0.545966	+	0.837807i	$0.316163\pi$
$270$	−7.15977	+	17.4287i	−0.435729	+	1.06068i
$271$	11.8666	+	20.5535i	0.720844	+	1.24854i	0.960662	+	0.277721i	$0.0895791\pi$
$271$	11.8666	+	20.5535i	0.720844	+	1.24854i	−0.239817	+	0.970818i	$0.577088\pi$
$272$	13.3972	−	7.73490i	0.812327	−	0.468997i
$273$	−7.08060	−	1.99545i	−0.428538	−	0.120770i
$274$	−9.63067	+	16.6808i	−0.581810	+	1.00772i
$275$	0.858726	−	3.58950i	0.0517831	−	0.216455i
$276$	2.63665	+	7.32435i	0.158707	+	0.440874i
$277$		−	15.8621i		−	0.953060i	−0.879158	−	0.476530i	$-0.841894\pi$
$277$		−	15.8621i		−	0.953060i	0.879158	−	0.476530i	$-0.158106\pi$
$278$	−8.53866	+	4.92980i	−0.512115	+	0.295669i
$279$	3.48041	+	20.5860i	0.208367	+	1.23245i
$280$	6.02185	−	11.6852i	0.359875	−	0.698322i
$281$	0.301741	+	0.522631i	0.0180004	+	0.0311776i	0.874885	−	0.484330i	$-0.160937\pi$
$281$	0.301741	+	0.522631i	0.0180004	+	0.0311776i	−0.856885	+	0.515508i	$0.827603\pi$
$282$	9.70198	−	3.49255i	0.577745	−	0.207978i
$283$	−5.52694	+	3.19098i	−0.328543	+	0.189684i	−0.655194	−	0.755461i	$-0.727413\pi$
$283$	−5.52694	+	3.19098i	−0.328543	+	0.189684i	0.326651	+	0.945145i	$0.394080\pi$
$284$	0.989080	+	1.71314i	0.0586911	+	0.101656i
$285$	12.0796	−	19.3847i	0.715532	−	1.14825i
$286$	0.960809	+	1.66417i	0.0568138	+	0.0984045i
$287$	7.12764	+	0.690945i	0.420731	+	0.0407852i
$288$	10.1818	−	1.72140i	0.599966	−	0.101434i
$289$	−3.44013	−	5.95848i	−0.202361	−	0.350499i
$290$	−5.20849	−	6.60150i	−0.305853	−	0.387654i
$291$	−8.09287	−	22.4812i	−0.474413	−	1.31787i
$292$			9.04883i			0.529543i
$293$	22.1406	+	12.7829i	1.29347	+	0.746784i	0.979267	−	0.202572i	$-0.0649301\pi$
$293$	22.1406	+	12.7829i	1.29347	+	0.746784i	0.314201	+	0.949356i	$0.398263\pi$
$294$	2.98227	+	19.4342i	0.173930	+	1.13342i
$295$	−5.61123	−	2.23605i	−0.326698	−	0.130188i
$296$	0.851759	+	1.47529i	0.0495075	+	0.0857495i
$297$	1.95281	−	3.30125i	0.113314	−	0.191558i
$298$	−26.2156	−	15.1356i	−1.51863	−	0.876780i
$299$	−5.72784	+	9.92091i	−0.331249	+	0.573741i
$300$	0.602670	+	5.42085i	0.0347952	+	0.312973i
$301$	−22.1081	−	15.7910i	−1.27429	−	0.910180i
$302$	−23.1759	−	13.3806i	−1.33362	−	0.769969i
$303$	−3.52902	+	19.6096i	−0.202737	+	1.12654i
$304$	−28.6786			−1.64483
$305$	1.62329	+	11.1642i	0.0929495	+	0.639261i
$306$	2.57992	+	15.2598i	0.147484	+	0.872342i
$307$			2.16590i			0.123614i	0.998088	+	0.0618072i	$0.0196864\pi$
$307$			2.16590i			0.123614i	−0.998088	+	0.0618072i	$0.980314\pi$
$308$	0.714905	−	1.00090i	0.0407355	−	0.0570314i
$309$	−25.5218	−	4.59300i	−1.45188	−	0.261287i
$310$	15.6312	+	19.8118i	0.887795	+	1.12524i
$311$	5.86092	+	10.1514i	0.332342	+	0.575633i	0.982971	−	0.183763i	$-0.0588278\pi$
$311$	5.86092	+	10.1514i	0.332342	+	0.575633i	−0.650629	+	0.759396i	$0.725494\pi$
$312$	4.71874	+	3.98793i	0.267146	+	0.225772i
$313$	−9.87745	−	5.70275i	−0.558306	−	0.322338i	0.194159	−	0.980970i	$-0.437802\pi$
$313$	−9.87745	−	5.70275i	−0.558306	−	0.322338i	−0.752465	+	0.658632i	$0.771136\pi$
$314$	−12.2739			−0.692654
$315$	11.9521	+	13.1205i	0.673427	+	0.739254i
$316$	6.14984			0.345956
$317$	7.54644	+	4.35694i	0.423850	+	0.244710i	0.696723	−	0.717340i	$-0.254641\pi$
$317$	7.54644	+	4.35694i	0.423850	+	0.244710i	−0.272873	+	0.962050i	$0.587974\pi$
$318$	−14.7794	+	5.32034i	−0.828787	+	0.298350i
$319$	0.855870	+	1.48241i	0.0479195	+	0.0829991i
$320$	−7.27466	+	5.73960i	−0.406666	+	0.320853i
$321$	−11.4847	−	31.9035i	−0.641015	−	1.78068i
$322$	30.4750	+	2.95421i	1.69831	+	0.164632i
$323$		−	18.7604i		−	1.04386i
$324$	−1.06288	+	5.56767i	−0.0590490	+	0.309315i
$325$	−5.52042	+	5.82664i	−0.306218	+	0.323204i
$326$	−11.4122			−0.632061
$327$	−2.85922	−	2.41639i	−0.158115	−	0.133627i
$328$	−5.20839	−	3.00706i	−0.287585	−	0.166037i
$329$	0.937161	−	9.66755i	0.0516673	−	0.532989i
$330$	0.156061	−	4.63351i	0.00859086	−	0.255067i
$331$	−2.21516	+	3.83677i	−0.121756	+	0.210888i	−0.920460	−	0.390836i	$-0.872186\pi$
$331$	−2.21516	+	3.83677i	−0.121756	+	0.210888i	0.798704	+	0.601724i	$0.205519\pi$
$332$	0.939565	+	0.542458i	0.0515653	+	0.0297713i
$333$	−2.26779	+	0.383408i	−0.124274	+	0.0210107i
$334$	−14.8400	−	25.7037i	−0.812011	−	1.40644i
$335$	−7.64292	+	19.1794i	−0.417577	+	1.04788i
$336$	6.04484	−	21.4494i	0.329773	−	1.17016i
$337$	13.6016	+	7.85289i	0.740927	+	0.427774i	0.822406	−	0.568901i	$-0.192631\pi$
$337$	13.6016	+	7.85289i	0.740927	+	0.427774i	−0.0814792	+	0.996675i	$0.525964\pi$
$338$			16.9026i			0.919383i
$339$	1.49934	−	1.77410i	0.0814328	−	0.0963561i
$340$	2.77492	+	3.51708i	0.150491	+	0.190740i
$341$	−2.56856	−	4.44888i	−0.139095	−	0.240920i
$342$	10.0026	−	26.8906i	0.540880	−	1.45408i
$343$	17.7474	+	5.29432i	0.958269	+	0.285867i
$344$	11.4086	+	19.7602i	0.615108	+	1.06540i
$345$	24.3870	−	13.0056i	1.31295	−	0.700197i
$346$	14.9393	+	25.8756i	0.803141	+	1.39108i
$347$	−21.5737	+	12.4556i	−1.15814	+	0.668651i	−0.950857	−	0.309630i	$-0.899795\pi$
$347$	−21.5737	+	12.4556i	−1.15814	+	0.668651i	−0.207281	+	0.978281i	$0.566461\pi$
$348$	−1.93205	−	1.63282i	−0.103569	−	0.0875284i
$349$	1.47550	+	2.55565i	0.0789819	+	0.136801i	0.902811	−	0.430038i	$-0.141500\pi$
$349$	1.47550	+	2.55565i	0.0789819	+	0.136801i	−0.823829	+	0.566838i	$0.808166\pi$
$350$	20.2850	+	6.98112i	1.08428	+	0.373157i
$351$	−7.26755	+	4.09407i	−0.387913	+	0.218525i
$352$	−2.20040	+	1.27040i	−0.117282	+	0.0677126i
$353$			15.6839i			0.834767i	0.908730	+	0.417384i	$0.137053\pi$
$353$			15.6839i			0.834767i	−0.908730	+	0.417384i	$0.862947\pi$
$354$	−7.46755	−	1.34389i	−0.396896	−	0.0714269i
$355$	5.51379	−	4.35030i	0.292642	−	0.230890i
$356$	−4.24171	+	7.34687i	−0.224810	+	0.389383i
$357$	14.0313	+	3.95430i	0.742617	+	0.209283i
$358$	8.47811	−	4.89484i	0.448082	−	0.258700i
$359$	−13.7163	−	23.7574i	−0.723919	−	1.25387i	−0.959417	−	0.281990i	$-0.909005\pi$
$359$	−13.7163	−	23.7574i	−0.723919	−	1.25387i	0.235498	−	0.971875i	$-0.424328\pi$
$360$	−4.57368	−	14.1866i	−0.241054	−	0.747700i
$361$	−7.88948	+	13.6650i	−0.415236	+	0.719209i
$362$	−7.91992	−	4.57257i	−0.416262	−	0.240329i
$363$	3.20740	−	17.8225i	0.168345	−	0.935438i
$364$	−2.43478	+	1.10770i	−0.127617	+	0.0580593i
$365$	31.7929	−	4.62274i	1.66412	−	0.241965i
$366$	4.79988	+	13.3336i	0.250894	+	0.696959i
$367$			9.64310i			0.503366i	0.967810	+	0.251683i	$0.0809840\pi$
$367$			9.64310i			0.503366i	−0.967810	+	0.251683i	$0.919016\pi$
$368$	−30.0535	−	17.3514i	−1.56665	−	0.904504i
$369$	6.25682	−	5.17537i	0.325717	−	0.269419i
$370$	−2.18251	+	1.72197i	−0.113463	+	0.0895209i
$371$	−1.42761	+	14.7269i	−0.0741179	+	0.764585i
$372$	5.79829	+	4.90027i	0.300627	+	0.254067i
$373$		−	22.6784i		−	1.17425i	−0.809498	−	0.587123i	$-0.800261\pi$
$373$		−	22.6784i		−	1.17425i	0.809498	−	0.587123i	$-0.199739\pi$
$374$	−1.90399	−	3.29782i	−0.0984532	−	0.170526i
$375$	18.7382	−	4.88680i	0.967635	−	0.252353i
$376$	−4.07862	+	7.06438i	−0.210339	+	0.364317i
$377$		−	3.72258i		−	0.191723i
$378$	18.0037	+	13.1491i	0.926010	+	0.676318i
$379$	−37.4400			−1.92316			−0.961581	−	0.274523i	$-0.911480\pi$
$379$	−37.4400			−1.92316			−0.961581	+	0.274523i	$0.911480\pi$
$380$	−1.19502	−	8.21872i	−0.0613030	−	0.421612i
$381$	5.41734	+	0.974924i	0.277539	+	0.0499469i
$382$	33.9277	−	19.5881i	1.73589	−	1.00222i
$383$		−	5.27232i		−	0.269403i	−0.990886	−	0.134701i	$-0.956992\pi$
$383$		−	5.27232i		−	0.269403i	0.990886	−	0.134701i	$-0.0430075\pi$
$384$	−15.2098	+	17.9971i	−0.776172	+	0.918412i
$385$	−3.88185	−	2.00048i	−0.197838	−	0.101954i
$386$	−22.4303			−1.14167
$387$	−30.3751	+	5.13542i	−1.54405	+	0.261048i
$388$	−7.52410	−	4.34404i	−0.381978	−	0.220535i
$389$	−4.35937			−0.221029			−0.110514	−	0.993875i	$-0.535250\pi$
$389$	−4.35937			−0.221029			−0.110514	+	0.993875i	$0.535250\pi$
$390$	−5.33226	+	8.55696i	−0.270009	+	0.433298i
$391$	11.3506	−	19.6598i	0.574025	−	0.994241i
$392$	−11.7256	−	10.2195i	−0.592234	−	0.516161i
$393$	1.20304	−	6.68490i	0.0606853	−	0.337209i
$394$	6.16153	−	10.6721i	0.310414	−	0.537652i
$395$	−3.14175	−	21.6074i	−0.158078	−	1.08718i
$396$	−0.232495	−	1.37517i	−0.0116833	−	0.0691047i
$397$	28.7294	−	16.5869i	1.44189	−	0.832474i	0.443912	−	0.896070i	$-0.353590\pi$
$397$	28.7294	−	16.5869i	1.44189	−	0.832474i	0.997976	+	0.0635962i	$0.0202570\pi$
$398$	−32.4406	+	18.7296i	−1.62610	+	0.938830i
$399$	−18.8617	−	19.3545i	−0.944264	−	0.968936i
$400$	−17.6507	−	16.7231i	−0.882535	−	0.836153i
$401$	7.97324			0.398164			0.199082	−	0.979983i	$-0.436204\pi$
$401$	7.97324			0.398164			0.199082	+	0.979983i	$0.436204\pi$
$402$	−4.59347	+	25.5244i	−0.229101	+	1.27304i
$403$			11.1719i			0.556511i
$404$	3.62247	+	6.27429i	0.180224	+	0.312158i
$405$	20.1049	+	0.890081i	0.999021	+	0.0442285i
$406$	−9.05626	+	4.12014i	−0.449455	+	0.204479i
$407$	0.490097	−	0.282958i	0.0242932	−	0.0140257i
$408$	−9.35093	−	7.90270i	−0.462940	−	0.391242i
$409$	−4.84444	−	8.39082i	−0.239542	−	0.414900i	0.721041	−	0.692893i	$-0.243664\pi$
$409$	−4.84444	−	8.39082i	−0.239542	−	0.414900i	−0.960583	+	0.277993i	$0.910331\pi$
$410$	3.63324	−	9.11738i	0.179433	−	0.450275i
$411$	20.2472	+	3.64376i	0.998719	+	0.179733i
$412$	−8.16595	+	4.71461i	−0.402308	+	0.232272i
$413$	−4.15405	+	5.81584i	−0.204408	+	0.286179i
$414$	26.7517	−	22.1279i	1.31478	−	1.08753i
$415$	1.42593	−	3.57827i	0.0699959	−	0.175650i
$416$	5.52557			0.270913
$417$	8.04309	+	6.79741i	0.393872	+	0.332871i
$418$			7.05942i			0.345288i
$419$	−17.6524	+	30.5748i	−0.862374	+	1.49368i	0.00725667	+	0.999974i	$0.497690\pi$
$419$	−17.6524	+	30.5748i	−0.862374	+	1.49368i	−0.869631	+	0.493702i	$0.835643\pi$
$420$	6.39884	+	0.838552i	0.312231	+	0.0409172i
$421$	−2.95319	−	5.11507i	−0.143930	−	0.249293i	0.785044	−	0.619441i	$-0.212641\pi$
$421$	−2.95319	−	5.11507i	−0.143930	−	0.249293i	−0.928973	+	0.370147i	$0.879307\pi$
$422$	−12.9762	+	7.49179i	−0.631670	+	0.364695i
$423$	−7.01959	−	8.48642i	−0.341304	−	0.412624i
$424$	6.21312	−	10.7614i	0.301736	−	0.522621i
$425$	10.9396	−	11.5464i	0.530647	−	0.560082i
$426$	5.69462	−	6.73820i	0.275905	−	0.326467i
$427$	13.2863	+	1.28796i	0.642969	+	0.0623286i
$428$	−10.6776	−	6.16470i	−0.516120	−	0.297982i
$429$	1.32480	−	1.56759i	0.0639621	−	0.0756837i
$430$	−29.2328	+	23.0642i	−1.40973	+	1.11226i
$431$	16.5940	−	28.7416i	0.799303	−	1.38443i	−0.120767	−	0.992681i	$-0.538535\pi$
$431$	16.5940	−	28.7416i	0.799303	−	1.38443i	0.920070	−	0.391753i	$-0.128131\pi$
$432$	−12.4022	−	22.0157i	−0.596702	−	1.05923i
$433$		−	16.8698i		−	0.810713i	−0.914159	−	0.405356i	$-0.867147\pi$
$433$		−	16.8698i		−	0.810713i	0.914159	−	0.405356i	$-0.132853\pi$
$434$	27.1788	−	12.3650i	1.30463	−	0.593539i
$435$	−4.74987	+	7.62237i	−0.227739	+	0.365465i
$436$	−1.36121			−0.0651902
$437$	−36.4463	+	21.0423i	−1.74346	+	1.00659i
$438$	37.9708	−	13.6689i	1.81432	−	0.653124i
$439$	−8.68886	+	15.0495i	−0.414697	+	0.718276i	−0.995397	−	0.0958421i	$-0.969446\pi$
$439$	−8.68886	+	15.0495i	−0.414697	+	0.718276i	0.580700	+	0.814118i	$0.302779\pi$
$440$	2.27173	+	2.87930i	0.108300	+	0.137265i
$441$	18.4513	−	10.0275i	0.878631	−	0.477501i
$442$			8.28137i			0.393905i
$443$	3.13752	+	1.81145i	0.149068	+	0.0860645i	0.572679	−	0.819780i	$-0.305904\pi$
$443$	3.13752	+	1.81145i	0.149068	+	0.0860645i	−0.423611	+	0.905844i	$0.639238\pi$
$444$	−0.539824	+	0.638751i	−0.0256189	+	0.0303138i
$445$	27.9800	+	11.1499i	1.32638	+	0.528557i
$446$	4.32224			0.204664
$447$	−5.72653	+	31.8205i	−0.270856	+	1.50506i
$448$	4.54027	+	9.97973i	0.214508	+	0.471498i
$449$	35.7277			1.68609			0.843046	−	0.537841i	$-0.180760\pi$
$449$	35.7277			1.68609			0.843046	+	0.537841i	$0.180760\pi$
$450$	21.8367	−	10.7175i	1.02939	−	0.505228i
$451$	−0.998958	+	1.73025i	−0.0470391	+	0.0814741i
$452$		−	0.844613i		−	0.0397272i
$453$	−5.06255	+	28.1309i	−0.237859	+	1.32171i
$454$	9.67732	−	16.7616i	0.454179	−	0.786661i
$455$	5.13573	+	7.98867i	0.240767	+	0.374515i
$456$	7.68752	+	21.3552i	0.360001	+	1.00005i
$457$	−4.64241	−	2.68029i	−0.217163	−	0.125379i	0.387473	−	0.921881i	$-0.373348\pi$
$457$	−4.64241	−	2.68029i	−0.217163	−	0.125379i	−0.604636	+	0.796502i	$0.706681\pi$
$458$	2.61906	+	1.51212i	0.122381	+	0.0706566i
$459$	14.4018	−	8.11304i	0.672218	−	0.378684i
$460$	3.72026	−	9.33576i	0.173458	−	0.435282i
$461$	7.24565	+	12.5498i	0.337464	+	0.584504i	0.983955	−	0.178417i	$-0.0570977\pi$
$461$	7.24565	+	12.5498i	0.337464	+	0.584504i	−0.646491	+	0.762921i	$0.723764\pi$
$462$	−5.27989	−	1.48797i	−0.245643	−	0.0692268i
$463$	−2.55614	−	1.47579i	−0.118794	−	0.0685856i	0.439426	−	0.898279i	$-0.355182\pi$
$463$	−2.55614	−	1.47579i	−0.118794	−	0.0685856i	−0.558220	+	0.829693i	$0.688515\pi$
$464$	11.2769			0.523515
$465$	14.2549	−	22.8756i	0.661054	−	1.06083i
$466$	−3.31081			−0.153370
$467$	14.3602	−	8.29087i	0.664511	−	0.383656i	−0.129483	−	0.991582i	$-0.541332\pi$
$467$	14.3602	−	8.29087i	0.664511	−	0.383656i	0.793994	+	0.607926i	$0.207998\pi$
$468$	−1.05744	+	2.84276i	−0.0488800	+	0.131407i
$469$	19.8788	+	14.1987i	0.917917	+	0.655636i
$470$	−12.3663	−	4.92793i	−0.570416	−	0.227309i
$471$	4.44020	+	12.3345i	0.204594	+	0.568342i
$472$	5.19820	−	3.00118i	0.239266	−	0.138140i
$473$	6.56441	−	3.78997i	0.301832	−	0.174263i
$474$	−9.28976	−	25.8061i	−0.426693	−	1.18531i
$475$	−28.2659	+	8.39734i	−1.29693	+	0.385296i
$476$	4.82490	−	2.19508i	0.221149	−	0.100611i
$477$	10.6932	+	12.9277i	0.489609	+	0.591918i
$478$	−25.3406	+	14.6304i	−1.15905	+	0.669178i
$479$	−24.3273			−1.11154			−0.555772	−	0.831335i	$-0.687577\pi$
$479$	−24.3273			−1.11154			−0.555772	+	0.831335i	$0.687577\pi$
$480$	−11.3142	−	7.05041i	−0.516419	−	0.321806i
$481$	−1.23072			−0.0561158
$482$	−36.8726	−	21.2884i	−1.67950	−	0.969661i
$483$	−8.05587	−	31.6942i	−0.366555	−	1.44214i
$484$	−3.29233	−	5.70248i	−0.149651	−	0.259204i
$485$	−11.4189	+	28.6550i	−0.518506	+	1.30116i
$486$	24.9687	−	3.95027i	1.13260	−	0.179188i
$487$	−12.4206	−	7.17105i	−0.562832	−	0.324951i	0.191449	−	0.981503i	$-0.438681\pi$
$487$	−12.4206	−	7.17105i	−0.562832	−	0.324951i	−0.754281	+	0.656551i	$0.772015\pi$
$488$	−9.70870	−	5.60532i	−0.439492	−	0.253741i
$489$	4.12847	+	11.4685i	0.186696	+	0.518624i
$490$	13.7505	−	21.3360i	0.621186	−	0.963861i
$491$	−14.5518	+	25.2045i	−0.656714	+	1.13746i	0.324747	+	0.945801i	$0.394721\pi$
$491$	−14.5518	+	25.2045i	−0.656714	+	1.13746i	−0.981461	+	0.191662i	$0.938612\pi$
$492$	0.522945	−	2.90584i	0.0235762	−	0.131005i
$493$			7.37689i			0.332238i
$494$	7.67619	−	13.2956i	0.345368	−	0.598195i
$495$	−4.71285	+	1.51939i	−0.211827	+	0.0682916i
$496$	−33.8431			−1.51960
$497$	−3.44127	−	7.56409i	−0.154362	−	0.339296i
$498$	0.856995	−	4.76204i	0.0384029	−	0.213392i
$499$	33.0622			1.48007			0.740034	−	0.672570i	$-0.234809\pi$
$499$	33.0622			1.48007			0.740034	+	0.672570i	$0.234809\pi$
$500$	4.05701	−	5.75517i	0.181435	−	0.257379i
$501$	−20.4621	+	24.2119i	−0.914178	+	1.08171i
$502$	9.85730	+	5.69111i	0.439953	+	0.254007i
$503$			7.30754i			0.325827i	0.986640	+	0.162914i	$0.0520892\pi$
$503$			7.30754i			0.325827i	−0.986640	+	0.162914i	$0.947911\pi$
$504$	−17.5924	+	1.24844i	−0.783626	+	0.0556100i
$505$	20.1940	−	15.9328i	0.898623	−	0.709000i
$506$	−4.27116	+	7.39786i	−0.189876	+	0.328875i
$507$	16.9861	−	6.11472i	0.754379	−	0.271564i
$508$	1.73333	−	1.00074i	0.0769041	−	0.0444006i
$509$	−23.7290			−1.05177			−0.525885	−	0.850556i	$-0.676266\pi$
$509$	−23.7290			−1.05177			−0.525885	+	0.850556i	$0.676266\pi$
$510$	10.5667	−	16.9570i	0.467902	−	0.750867i
$511$	3.66779	−	37.8361i	0.162253	−	1.67377i
$512$		−	4.87232i		−	0.215328i
$513$	−30.6419	−	0.324044i	−1.35287	−	0.0143069i
$514$	0.483554	−	0.837541i	0.0213287	−	0.0369423i
$515$	20.7364	+	26.2824i	0.913756	+	1.15814i
$516$	−7.23046	+	8.55550i	−0.318303	+	0.376635i
$517$	2.34681	+	1.35493i	0.103213	+	0.0595899i
$518$	1.36215	+	2.99407i	0.0598495	+	0.131552i
$519$	20.5989	−	24.3738i	0.904192	−	1.06989i
$520$	−1.14766	−	7.89302i	−0.0503281	−	0.346132i
$521$	−10.4400	+	18.0825i	−0.457383	+	0.792210i	−0.998822	−	0.0485297i	$-0.984546\pi$
$521$	−10.4400	+	18.0825i	−0.457383	+	0.792210i	0.541439	+	0.840740i	$0.317880\pi$
$522$	−3.93318	+	10.5738i	−0.172151	+	0.462802i
$523$	−1.61770	+	0.933978i	−0.0707370	+	0.0408400i	−0.534951	−	0.844883i	$-0.679670\pi$
$523$	−1.61770	+	0.933978i	−0.0707370	+	0.0408400i	0.464214	+	0.885723i	$0.346337\pi$
$524$	−1.23489	−	2.13890i	−0.0539466	−	0.0934383i
$525$	−0.322712	−	22.9106i	−0.0140843	−	0.999901i
$526$	−19.9660	+	34.5821i	−0.870559	+	1.50785i
$527$		−	22.1388i		−	0.964383i
$528$	4.74870	+	4.01324i	0.206661	+	0.174654i
$529$	−27.9248			−1.21412
$530$	18.8381	+	7.50690i	0.818275	+	0.326079i
$531$	1.35094	+	7.99059i	0.0586259	+	0.346762i
$532$	−9.78094	−	0.948152i	−0.424057	−	0.0411076i
$533$	3.76283	−	2.17247i	0.162986	−	0.0941001i
$534$	37.2364	+	6.70121i	1.61138	+	0.289990i
$535$	−16.2047	+	40.6648i	−0.700592	+	1.75809i
$536$	−10.2582	−	17.7676i	−0.443085	−	0.767445i
$537$	−7.98606	−	6.74921i	−0.344624	−	0.291250i
$538$	20.8494	−	12.0374i	0.898880	−	0.518968i
$539$	−3.39495	+	3.89530i	−0.146231	+	0.167782i
$540$	5.79246	−	4.47160i	0.249268	−	0.192427i
$541$	8.96505	+	15.5279i	0.385438	+	0.667598i	0.991830	−	0.127568i	$-0.0407172\pi$
$541$	8.96505	+	15.5279i	0.385438	+	0.667598i	−0.606392	+	0.795166i	$0.707384\pi$
$542$		−	38.4873i		−	1.65317i
$543$	−1.73003	+	9.61320i	−0.0742426	+	0.412542i
$544$	−10.9498			−0.469468
$545$	0.695397	+	4.78259i	0.0297875	+	0.204864i
$546$	8.32605	+	8.54360i	0.356322	+	0.365633i
$547$	31.5708	−	18.2274i	1.34987	−	0.779347i	0.361638	−	0.932319i	$-0.382218\pi$
$547$	31.5708	−	18.2274i	1.34987	−	0.779347i	0.988231	+	0.152972i	$0.0488844\pi$
$548$	6.47828	−	3.74024i	0.276738	−	0.159775i
$549$	11.6630	−	9.64716i	0.497766	−	0.411731i
$550$	−4.11649	+	4.34483i	−0.175528	+	0.185264i
$551$	6.83780	−	11.8434i	0.291300	−	0.504547i
$552$	−4.86445	+	27.0302i	−0.207045	+	1.15048i
$553$	−25.7145	−	2.49273i	−1.09349	−	0.106002i
$554$	−12.8615	+	22.2768i	−0.546433	+	0.946449i
$555$	2.52002	+	1.57035i	0.106969	+	0.0666574i
$556$	3.82914			0.162392
$557$	−2.74733	−	1.58617i	−0.116408	−	0.0672083i	0.440665	−	0.897671i	$-0.354743\pi$
$557$	−2.74733	−	1.58617i	−0.116408	−	0.0672083i	−0.557074	+	0.830463i	$0.688076\pi$
$558$	11.8039	−	31.7331i	0.499699	−	1.34337i
$559$	−16.4844			−0.697214
$560$	−24.2002	+	15.5577i	−1.02264	+	0.657434i
$561$	−2.62531	+	3.10642i	−0.110841	+	0.131153i
$562$		−	0.978647i		−	0.0412817i
$563$	−8.52906	+	4.92425i	−0.359457	+	0.207533i	−0.668843	−	0.743404i	$-0.733210\pi$
$563$	−8.52906	+	4.92425i	−0.359457	+	0.207533i	0.309386	+	0.950937i	$0.399877\pi$
$564$	−3.94132	−	0.709295i	−0.165960	−	0.0298667i
$565$	−2.96753	+	0.431484i	−0.124845	+	0.0181527i
$566$	10.3494			0.435018
$567$	6.70101	−	22.8494i	0.281416	−	0.959586i
$568$			6.97914i			0.292838i
$569$	11.0251	−	19.0960i	0.462195	−	0.800545i	−0.536875	−	0.843662i	$-0.680395\pi$
$569$	11.0251	−	19.0960i	0.462195	−	0.800545i	0.999070	+	0.0431165i	$0.0137287\pi$
$570$	−32.6824	+	17.4295i	−1.36892	+	0.730041i
$571$	−9.98691	−	17.2978i	−0.417939	−	0.723892i	0.577793	−	0.816183i	$-0.303914\pi$
$571$	−9.98691	−	17.2978i	−0.417939	−	0.723892i	−0.995732	+	0.0922916i	$0.970581\pi$
$572$		−	0.746294i		−	0.0312041i
$573$	−31.9586	−	27.0090i	−1.33509	−	1.12832i
$574$	−9.44985	−	6.74969i	−0.394429	−	0.281727i
$575$	−34.7016	−	8.30175i	−1.44716	−	0.346207i
$576$	11.6520	+	4.33425i	0.485500	+	0.180594i
$577$	−37.2392	−	21.5000i	−1.55029	−	0.895058i	−0.998118	−	0.0613262i	$-0.980467\pi$
$577$	−37.2392	−	21.5000i	−1.55029	−	0.895058i	−0.552169	−	0.833732i	$-0.686200\pi$
$578$			11.1575i			0.464090i
$579$	8.11442	+	22.5411i	0.337224	+	0.936776i
$580$	0.469898	+	3.23173i	0.0195115	+	0.134190i
$581$	−3.70875	−	2.64903i	−0.153865	−	0.109900i
$582$	−6.86287	+	38.1347i	−0.284475	+	1.58074i
$583$	−3.57499	−	2.06402i	−0.148061	−	0.0854830i
$584$	−15.9626	+	27.6480i	−0.660536	+	1.14408i
$585$	10.5282	+	2.26301i	0.435288	+	0.0935641i
$586$	−20.7296	−	35.9047i	−0.856331	−	1.48321i
$587$	7.23754	−	4.17860i	0.298725	−	0.172469i	−0.343145	−	0.939283i	$-0.611492\pi$
$587$	7.23754	−	4.17860i	0.298725	−	0.172469i	0.641870	+	0.766813i	$0.278159\pi$
$588$	2.77075	−	7.11552i	0.114264	−	0.293439i
$589$	−20.5210	+	35.5434i	−0.845553	+	1.46454i
$590$	6.06737	+	7.69009i	0.249790	+	0.316596i
$591$	−12.9538	−	2.33121i	−0.532847	−	0.0958932i
$592$		−	3.72822i		−	0.153229i
$593$	12.3150	−	7.11006i	0.505716	−	0.291975i	−0.225355	−	0.974277i	$-0.572354\pi$
$593$	12.3150	−	7.11006i	0.505716	−	0.291975i	0.731071	+	0.682301i	$0.239021\pi$
$594$	−5.41930	+	3.05288i	−0.222356	+	0.125261i
$595$	−10.1773	−	15.8308i	−0.417227	−	0.649000i
$596$	5.87816	+	10.1813i	0.240779	+	0.417041i
$597$	30.5578	+	25.8251i	1.25065	+	1.05695i
$598$	16.0884	−	9.28864i	0.657904	−	0.379841i
$599$	−7.45561	−	12.9135i	−0.304628	−	0.527631i	0.672551	−	0.740051i	$-0.265199\pi$
$599$	−7.45561	−	12.9135i	−0.304628	−	0.527631i	−0.977178	+	0.212420i	$0.931865\pi$
$600$	−7.72123	+	17.6261i	−0.315218	+	0.719583i
$601$	−15.4440	−	26.7497i	−0.629972	−	1.09114i	−0.987557	−	0.157263i	$-0.949733\pi$
$601$	−15.4440	−	26.7497i	−0.629972	−	1.09114i	0.357584	−	0.933881i	$-0.383600\pi$
$602$	18.2448	+	40.1030i	0.743603	+	1.63447i
$603$	27.3121	−	4.61758i	1.11224	−	0.188042i
$604$	5.19660	+	9.00077i	0.211447	+	0.366236i
$605$	−18.3536	+	14.4807i	−0.746181	+	0.588726i
$606$	20.8563	−	24.6784i	0.847230	−	1.00249i
$607$			16.2436i			0.659309i	0.944102	+	0.329655i	$0.106932\pi$
$607$			16.2436i			0.659309i	−0.944102	+	0.329655i	$0.893068\pi$
$608$	17.5796	+	10.1496i	0.712949	+	0.411621i
$609$	7.41668	+	7.61048i	0.300539	+	0.308392i
$610$	6.77255	−	16.9953i	0.274212	−	0.688119i
$611$	−2.94662	−	5.10370i	−0.119208	−	0.206474i
$612$	2.09548	−	5.63338i	0.0847046	−	0.227716i
$613$	6.77205	+	3.90984i	0.273520	+	0.157917i	0.630486	−	0.776200i	$-0.282855\pi$
$613$	6.77205	+	3.90984i	0.273520	+	0.157917i	−0.356966	+	0.934117i	$0.616189\pi$
$614$	1.75618	−	3.04180i	0.0708737	−	0.122757i
$615$	−10.4768	−	0.352866i	−0.422464	−	0.0142289i
$616$	3.94997	−	1.79703i	0.159149	−	0.0724046i
$617$	−1.96954	−	1.13711i	−0.0792905	−	0.0457784i	0.459831	−	0.888007i	$-0.347910\pi$
$617$	−1.96954	−	1.13711i	−0.0792905	−	0.0457784i	−0.539121	+	0.842228i	$0.681243\pi$
$618$	32.1188	+	27.1444i	1.29201	+	1.09191i
$619$	30.8825			1.24127			0.620637	−	0.784098i	$-0.286874\pi$
$619$	30.8825			1.24127			0.620637	+	0.784098i	$0.286874\pi$
$620$	−1.41022	−	9.69876i	−0.0566356	−	0.389512i
$621$	−31.9149	−	18.8788i	−1.28070	−	0.757581i
$622$		−	19.0089i		−	0.762188i
$623$	20.7139	−	29.0003i	0.829885	−	1.16187i
$624$	−4.57972	−	12.7220i	−0.183336	−	0.509289i
$625$	−22.2933	−	11.3141i	−0.891732	−	0.452564i
$626$	9.24796	+	16.0179i	0.369623	+	0.640205i
$627$	7.09428	−	2.55382i	0.283318	−	0.101990i
$628$	4.12814	+	2.38338i	0.164731	+	0.0951074i
$629$	2.43886			0.0972436
$630$	−6.14714	−	28.1176i	−0.244908	−	1.12023i
$631$	36.2472			1.44298			0.721489	−	0.692425i	$-0.243458\pi$
$631$	36.2472			1.44298			0.721489	+	0.692425i	$0.243458\pi$
$632$	18.7904	+	10.8486i	0.747441	+	0.431535i
$633$	12.2231	+	10.3300i	0.485823	+	0.410581i
$634$	−7.06550	−	12.2378i	−0.280607	−	0.486026i
$635$	−4.40158	−	5.57878i	−0.174671	−	0.221387i
$636$	6.00396	+	1.08050i	0.238073	+	0.0428445i
$637$	10.6296	−	3.64476i	0.421160	−	0.144411i
$638$		−	2.77587i		−	0.109898i
$639$	−8.83157	−	3.28512i	−0.349371	−	0.129957i
$640$	30.1037	−	4.37713i	1.18995	−	0.173021i
$641$	12.4199			0.490555			0.245277	−	0.969453i	$-0.421121\pi$
$641$	12.4199			0.490555			0.245277	+	0.969453i	$0.421121\pi$
$642$	−9.73921	+	54.1176i	−0.384376	+	2.13585i
$643$	22.6778	+	13.0930i	0.894325	+	0.516339i	0.875355	−	0.483481i	$-0.160628\pi$
$643$	22.6778	+	13.0930i	0.894325	+	0.516339i	0.0189702	+	0.999820i	$0.493961\pi$
$644$	−9.67618	−	6.91136i	−0.381295	−	0.272346i
$645$	33.7534	+	21.0334i	1.32904	+	0.828189i
$646$	−15.2116	+	26.3472i	−0.598492	+	1.03662i
$647$	−24.0643	−	13.8935i	−0.946066	−	0.546212i	−0.0542095	−	0.998530i	$-0.517264\pi$
$647$	−24.0643	−	13.8935i	−0.946066	−	0.546212i	−0.891857	+	0.452318i	$0.850597\pi$
$648$	−13.0692	+	15.1366i	−0.513407	+	0.594623i
$649$	−0.997004	−	1.72686i	−0.0391358	−	0.0677852i
$650$	12.4773	−	3.70682i	0.489401	−	0.145393i
$651$	−22.2583	−	22.8399i	−0.872371	−	0.895165i
$652$	3.83832	+	2.21606i	0.150320	+	0.0867874i
$653$		−	9.35849i		−	0.366226i	−0.983092	−	0.183113i	$-0.941383\pi$
$653$		−	9.35849i		−	0.366226i	0.983092	−	0.183113i	$-0.0586174\pi$
$654$	2.05620	+	5.71194i	0.0804039	+	0.223355i
$655$	−6.88412	+	5.43147i	−0.268985	+	0.212225i
$656$	6.58109	+	11.3988i	0.256948	+	0.445048i
$657$	−27.4727	−	33.2135i	−1.07181	−	1.29578i
$658$	−9.15492	+	12.8173i	−0.356896	+	0.499669i
$659$	−5.80798	−	10.0597i	−0.226247	−	0.391871i	0.730446	−	0.682971i	$-0.239312\pi$
$659$	−5.80798	−	10.0597i	−0.226247	−	0.391871i	−0.956693	+	0.291099i	$0.905979\pi$
$660$	−0.952241	+	1.52811i	−0.0370659	+	0.0594817i
$661$	11.2896	+	19.5541i	0.439114	+	0.760567i	0.997621	−	0.0689322i	$-0.0219592\pi$
$661$	11.2896	+	19.5541i	0.439114	+	0.760567i	−0.558508	+	0.829499i	$0.688626\pi$
$662$	6.22196	−	3.59225i	0.241823	−	0.139617i
$663$	8.32226	−	2.99588i	0.323210	−	0.116350i
$664$	1.91385	+	3.31488i	0.0742716	+	0.128642i
$665$	1.66543	+	34.8495i	0.0645827	+	1.35141i
$666$	3.49578	+	1.30034i	0.135459	+	0.0503872i
$667$	14.3312	−	8.27414i	0.554907	−	0.320376i
$668$			11.5268i			0.445984i
$669$	−1.56362	−	4.34358i	−0.0604529	−	0.167932i
$670$	26.2851	−	20.7385i	1.01548	−	0.801199i
$671$	−1.86211	+	3.22527i	−0.0718860	+	0.124510i
$672$	−11.2965	+	11.0089i	−0.435773	+	0.424676i
$673$	−11.0594	+	6.38516i	−0.426309	+	0.246130i	−0.697773	−	0.716319i	$-0.745826\pi$
$673$	−11.0594	+	6.38516i	−0.426309	+	0.246130i	0.271464	+	0.962449i	$0.412492\pi$
$674$	−12.7348	−	22.0573i	−0.490525	−	0.849615i
$675$	−18.6701	−	18.0673i	−0.718611	−	0.695412i
$676$	3.28222	−	5.68497i	0.126239	−	0.218653i
$677$	26.8951	+	15.5279i	1.03366	+	0.596784i	0.918031	−	0.396508i	$-0.129778\pi$
$677$	26.8951	+	15.5279i	1.03366	+	0.596784i	0.115630	+	0.993292i	$0.463111\pi$
$678$	−3.54418	+	1.27585i	−0.136113	+	0.0489986i
$679$	29.6999	+	21.2136i	1.13978	+	0.814103i
$680$	2.27426	+	15.6413i	0.0872140	+	0.599815i
$681$	−20.3452	−	3.66141i	−0.779631	−	0.140305i
$682$			8.33070i			0.318999i
$683$	43.2065	+	24.9453i	1.65325	+	0.954505i	0.975723	+	0.219008i	$0.0702822\pi$
$683$	43.2065	+	24.9453i	1.65325	+	0.954505i	0.677528	+	0.735497i	$0.263051\pi$
$684$	−8.58595	+	7.10192i	−0.328292	+	0.271549i
$685$	−16.4508	−	20.8506i	−0.628552	−	0.796659i
$686$	−20.6317	−	21.8256i	−0.787722	−	0.833303i
$687$	0.572109	−	3.17902i	0.0218273	−	0.121287i
$688$		−	49.9362i		−	1.90380i
$689$	4.48870	+	7.77466i	0.171006	+	0.296191i
$690$	−44.7946	−	1.50872i	−1.70530	−	0.0574360i
$691$	−9.96344	+	17.2572i	−0.379027	+	0.656494i	−0.990921	−	0.134446i	$-0.957075\pi$
$691$	−9.96344	+	17.2572i	−0.379027	+	0.656494i	0.611894	+	0.790940i	$0.290408\pi$
$692$		−	11.6039i		−	0.441113i
$693$	0.414737	+	5.84425i	0.0157546	+	0.222005i
$694$	40.3976			1.53347
$695$	−1.95618	−	13.4536i	−0.0742021	−	0.510325i
$696$	−3.02285	−	8.39719i	−0.114581	−	0.318294i
$697$	−7.45664	+	4.30509i	−0.282440	+	0.163067i
$698$		−	4.78555i		−	0.181136i
$699$	1.19772	+	3.32716i	0.0453020	+	0.125845i
$700$	−5.46694	−	6.28701i	−0.206631	−	0.237627i
$701$	20.3475			0.768513			0.384256	−	0.923226i	$-0.374458\pi$
$701$	20.3475			0.768513			0.384256	+	0.923226i	$0.374458\pi$
$702$	13.5262	+	0.143042i	0.510513	+	0.00539877i
$703$	−3.91553	−	2.26063i	−0.147677	−	0.0852614i
$704$	−3.05893			−0.115288
$705$	−0.478609	+	14.2101i	−0.0180255	+	0.535184i
$706$	12.7170	−	22.0265i	0.478610	−	0.828977i
$707$	−12.6035	−	27.7032i	−0.474004	−	1.04188i
$708$	2.25064	+	1.90207i	0.0845844	+	0.0714843i
$709$	−16.1608	+	27.9914i	−0.606933	+	1.05124i	0.384810	+	0.922996i	$0.374267\pi$
$709$	−16.1608	+	27.9914i	−0.606933	+	1.05124i	−0.991743	+	0.128243i	$0.959066\pi$
$710$	−11.2710	+	1.63882i	−0.422991	+	0.0615036i
$711$	−22.5728	+	18.6713i	−0.846547	+	0.700227i
$712$	−25.9205	+	14.9652i	−0.971411	+	0.560844i
$713$	−43.0096	+	24.8316i	−1.61072	+	0.929951i
$714$	−16.4994	−	16.9305i	−0.617474	−	0.633608i
$715$	−2.62209	+	0.381256i	−0.0980606	+	0.0142582i
$716$	−3.80199			−0.142087
$717$	23.8698	+	20.1730i	0.891435	+	0.753374i
$718$			44.4866i			1.66022i
$719$	16.7323	+	28.9812i	0.624010	+	1.08082i	0.988731	+	0.149701i	$0.0478310\pi$
$719$	16.7323	+	28.9812i	0.624010	+	1.08082i	−0.364721	+	0.931117i	$0.618836\pi$
$720$	−6.85537	+	31.8932i	−0.255485	+	1.18859i
$721$	36.0555	−	16.4034i	1.34278	−	0.610895i
$722$	22.1600	−	12.7941i	0.824711	−	0.476147i
$723$	−8.05446	+	44.7560i	−0.299549	+	1.66449i
$724$	1.77584	+	3.07584i	0.0659984	+	0.114313i
$725$	11.1146	−	3.30196i	0.412784	−	0.122632i
$726$	−18.9556	+	22.4293i	−0.703507	+	0.832430i
$727$	8.93927	−	5.16109i	0.331539	−	0.191414i	−0.324985	−	0.945719i	$-0.605359\pi$
$727$	8.93927	−	5.16109i	0.331539	−	0.191414i	0.656524	+	0.754305i	$0.272026\pi$
$728$	−9.39332	−	0.910577i	−0.348139	−	0.0337482i
$729$	−13.0025	−	23.6630i	−0.481573	−	0.876406i
$730$	−48.3984	−	19.2865i	−1.79130	−	0.713827i
$731$	32.6663			1.20821
$732$	0.974798	−	5.41663i	0.0360296	−	0.200204i
$733$			27.7395i			1.02458i	0.858812	+	0.512290i	$0.171203\pi$
$733$			27.7395i			1.02458i	−0.858812	+	0.512290i	$0.828797\pi$
$734$	7.81894	−	13.5428i	0.288602	−	0.499874i
$735$	−26.4157	−	6.09992i	−0.974359	−	0.224999i
$736$	12.2816	+	21.2724i	0.452706	+	0.784111i
$737$	−5.90248	+	3.40780i	−0.217421	+	0.125528i
$738$	−12.9835	+	2.19507i	−0.477928	+	0.0808018i
$739$	−5.04526	+	8.73865i	−0.185593	+	0.321456i	−0.943776	−	0.330585i	$-0.892754\pi$
$739$	−5.04526	+	8.73865i	−0.185593	+	0.321456i	0.758183	+	0.652042i	$0.226087\pi$
$740$	1.06843	−	0.155352i	0.0392764	−	0.00571086i
$741$	−16.1382	−	2.90428i	−0.592850	−	0.106692i
$742$	13.9460	−	19.5250i	0.511975	−	0.716786i
$743$	21.9920	+	12.6971i	0.806808	+	0.465811i	0.845846	−	0.533427i	$-0.179096\pi$
$743$	21.9920	+	12.6971i	0.806808	+	0.465811i	−0.0390380	+	0.999238i	$0.512429\pi$
$744$	9.07190	+	25.2009i	0.332592	+	0.923909i
$745$	32.7688	−	25.8541i	1.20055	−	0.947220i
$746$	−18.3884	+	31.8497i	−0.673248	+	1.16610i
$747$	−5.09558	+	0.861494i	−0.186438	+	0.0315204i
$748$			1.47890i			0.0540739i
$749$	42.1476	+	30.1046i	1.54004	+	1.10000i
$750$	−30.2784	−	8.33049i	−1.10561	−	0.304187i
$751$	−27.0579			−0.987357			−0.493678	−	0.869645i	$-0.664348\pi$
$751$	−27.0579			−0.987357			−0.493678	+	0.869645i	$0.664348\pi$
$752$	15.4607	−	8.92624i	0.563794	−	0.325506i
$753$	2.15323	−	11.9648i	0.0784680	−	0.436021i
$754$	−3.01839	+	5.22801i	−0.109923	+	0.190393i
$755$	28.9693	−	22.8563i	1.05430	−	0.831828i
$756$	−3.50195	−	7.91855i	−0.127365	−	0.287995i
$757$			3.80197i			0.138185i	0.997610	+	0.0690924i	$0.0220103\pi$
$757$			3.80197i			0.138185i	−0.997610	+	0.0690924i	$0.977990\pi$
$758$	52.5808	+	30.3576i	1.90982	+	1.10264i
$759$	8.97953	+	1.61599i	0.325936	+	0.0586567i
$760$	10.8470	−	27.2197i	0.393460	−	0.987364i
$761$	10.4779			0.379823			0.189912	−	0.981801i	$-0.439180\pi$
$761$	10.4779			0.379823			0.189912	+	0.981801i	$0.439180\pi$
$762$	−6.81763	−	5.76174i	−0.246977	−	0.208726i
$763$	5.69167	+	0.551744i	0.206052	+	0.0199745i
$764$	−15.2148			−0.550452
$765$	−20.8633	−	4.48452i	−0.754314	−	0.162138i
$766$	−4.27497	+	7.40447i	−0.154461	+	0.267534i
$767$			4.33644i			0.156580i
$768$	22.4467	−	8.08042i	0.809974	−	0.291577i
$769$	−1.11645	+	1.93375i	−0.0402603	+	0.0697329i	−0.885453	−	0.464728i	$-0.846152\pi$
$769$	−1.11645	+	1.93375i	−0.0402603	+	0.0697329i	0.845193	+	0.534461i	$0.179485\pi$
$770$	3.82963	+	5.95702i	0.138010	+	0.214676i
$771$	−1.01661	−	0.182952i	−0.0366122	−	0.00658887i
$772$	7.54413	+	4.35560i	0.271519	+	0.156762i
$773$	7.02942	+	4.05844i	0.252831	+	0.145972i	0.621060	−	0.783763i	$-0.286702\pi$
$773$	7.02942	+	4.05844i	0.252831	+	0.145972i	−0.368229	+	0.929735i	$0.620036\pi$
$774$	46.8228	+	17.4169i	1.68301	+	0.626038i
$775$	−33.3560	+	9.90954i	−1.19818	+	0.355961i
$776$	−15.3262	−	26.5458i	−0.550179	−	0.952937i
$777$	2.51608	−	2.45202i	0.0902640	−	0.0879656i
$778$	6.12231	+	3.53472i	0.219496	+	0.126726i
$779$	15.9620			0.571896
$780$	3.45505	−	1.84258i	0.123711	−	0.0659748i
$781$	2.31850			0.0829624
$782$	−31.8817	+	18.4069i	−1.14009	+	0.658230i
$783$	12.0489	+	0.127419i	0.430591	+	0.00455358i
$784$	11.0411	+	32.2003i	0.394325	+	1.15001i
$785$	6.26505	−	15.7217i	0.223609	−	0.561133i
$786$	−7.10989	+	8.41284i	−0.253602	+	0.300076i
$787$	7.78817	−	4.49650i	0.277618	−	0.160283i	−0.354726	−	0.934970i	$-0.615426\pi$
$787$	7.78817	−	4.49650i	0.277618	−	0.160283i	0.632345	+	0.774687i	$0.282093\pi$
$788$	−4.14469	+	2.39294i	−0.147648	+	0.0852449i
$789$	41.9758	+	7.55413i	1.49438	+	0.268934i
$790$	−13.1077	+	32.8929i	−0.466351	+	1.17028i
$791$	−0.342349	+	3.53160i	−0.0121725	+	0.125569i
$792$	1.71549	−	4.61185i	0.0609573	−	0.163875i
$793$	7.01411	−	4.04960i	0.249078	−	0.143805i
$794$	−53.7969			−1.90918
$795$	0.729083	−	21.6468i	0.0258579	−	0.767733i
$796$	14.5479			0.515637
$797$	13.0401	+	7.52872i	0.461905	+	0.266681i	0.712845	−	0.701322i	$-0.247406\pi$
$797$	13.0401	+	7.52872i	0.461905	+	0.266681i	−0.250940	+	0.968003i	$0.580740\pi$
$798$	10.7961	+	42.4752i	0.382179	+	1.50361i
$799$	5.83920	+	10.1138i	0.206576	+	0.357800i
$800$	4.90122	+	16.4978i	0.173284	+	0.583284i
$801$	−6.73639	−	39.8445i	−0.238019	−	1.40784i
$802$	−11.1976	−	6.46497i	−0.395403	−	0.228286i
$803$	9.18477	+	5.30283i	0.324123	+	0.187133i
$804$	6.50137	−	7.69279i	0.229285	−	0.271304i
$805$	−19.3397	+	37.5279i	−0.681635	+	1.32268i
$806$	9.05854	−	15.6898i	0.319073	−	0.552651i
$807$	−19.6393	−	16.5976i	−0.691336	−	0.584265i
$808$			25.5608i			0.899227i
$809$	4.20255	−	7.27903i	0.147754	−	0.255917i	−0.782643	−	0.622471i	$-0.786129\pi$
$809$	4.20255	−	7.27903i	0.147754	−	0.255917i	0.930397	+	0.366554i	$0.119462\pi$
$810$	−27.5137	−	17.5518i	−0.966734	−	0.616706i
$811$	−12.4915			−0.438634			−0.219317	−	0.975654i	$-0.570383\pi$
$811$	−12.4915			−0.438634			−0.219317	+	0.975654i	$0.570383\pi$
$812$	3.84601	+	0.372828i	0.134969	+	0.0130837i
$813$	−38.6774	+	13.9232i	−1.35647	+	0.488308i
$814$	−0.917726			−0.0321663
$815$	5.82520	−	14.6180i	0.204048	−	0.512046i
$816$	9.07544	+	25.2107i	0.317704	+	0.882552i
$817$	−52.4451	−	30.2792i	−1.83482	−	1.05933i
$818$			15.7121i			0.549362i
$819$	5.57375	−	11.4579i	0.194763	−	0.400372i
$820$	−2.99244	+	2.36099i	−0.104500	+	0.0824493i
$821$	2.83369	−	4.90810i	0.0988965	−	0.171294i	−0.812332	−	0.583196i	$-0.801802\pi$
$821$	2.83369	−	4.90810i	0.0988965	−	0.171294i	0.911228	+	0.411902i	$0.135135\pi$
$822$	−25.4807	−	21.5344i	−0.888742	−	0.751098i
$823$	11.3800	−	6.57026i	0.396683	−	0.229025i	−0.288369	−	0.957519i	$-0.593113\pi$
$823$	11.3800	−	6.57026i	0.396683	−	0.229025i	0.685052	+	0.728494i	$0.259780\pi$
$824$	−33.2672			−1.15892
$825$	5.85547	+	2.56502i	0.203861	+	0.0893026i
$826$	10.5496	−	4.79955i	0.367069	−	0.166998i
$827$			16.1033i			0.559968i	0.960005	+	0.279984i	$0.0903292\pi$
$827$			16.1033i			0.559968i	−0.960005	+	0.279984i	$0.909671\pi$
$828$	−13.2944	+	2.24765i	−0.462014	+	0.0781112i
$829$	20.9785	−	36.3358i	0.728612	−	1.26199i	−0.228858	−	0.973460i	$-0.573499\pi$
$829$	20.9785	−	36.3358i	0.728612	−	1.26199i	0.957470	−	0.288533i	$-0.0931676\pi$
$830$	−4.90396	+	3.86915i	−0.170219	+	0.134300i
$831$	27.0396	+	4.86614i	0.937992	+	0.168805i
$832$	5.76111	+	3.32618i	0.199731	+	0.115315i
$833$	−21.0642	+	7.22266i	−0.729831	+	0.250250i
$834$	−5.78418	−	16.0679i	−0.200290	−	0.556386i
$835$	40.4991	−	5.88864i	1.40153	−	0.203785i
$836$	1.37082	−	2.37434i	0.0474110	−	0.0821182i
$837$	−36.1600	−	0.382399i	−1.24987	−	0.0132176i
$838$	49.5821	−	28.6262i	1.71279	−	0.988877i
$839$	−7.00795	−	12.1381i	−0.241941	−	0.419055i	0.719326	−	0.694673i	$-0.244451\pi$
$839$	−7.00795	−	12.1381i	−0.241941	−	0.419055i	−0.961267	+	0.275618i	$0.911117\pi$
$840$	18.0719	+	13.8500i	0.623540	+	0.477870i
$841$	11.8113	−	20.4577i	0.407285	−	0.705439i
$842$			9.57817i			0.330085i
$843$	−0.983479	+	0.354036i	−0.0338728	+	0.0121937i
$844$	5.81913			0.200303
$845$	−21.6508	−	8.62776i	−0.744811	−	0.296804i
$846$	2.97728	+	17.6101i	0.102361	+	0.605447i
$847$	11.4549	+	25.1784i	0.393595	+	0.865141i
$848$	−23.5519	+	13.5977i	−0.808774	+	0.466946i
$849$	−3.74401	−	10.4005i	−0.128494	−	0.356945i
$850$	−24.7258	+	7.34564i	−0.848087	+	0.251953i
$851$	−2.73550	−	4.73802i	−0.0937716	−	0.162417i
$852$	−3.22375	+	1.16050i	−0.110444	+	0.0397580i
$853$	−10.2895	+	5.94065i	−0.352306	+	0.203404i	−0.665700	−	0.746219i	$-0.731867\pi$
$853$	−10.2895	+	5.94065i	−0.352306	+	0.203404i	0.313394	+	0.949623i	$0.398534\pi$
$854$	−17.6150	−	12.5818i	−0.602773	−	0.430540i
$855$	29.3388	+	26.5385i	1.00336	+	0.907596i
$856$	−21.7497	−	37.6715i	−0.743388	−	1.28759i
$857$		−	28.6371i		−	0.978224i	−0.872221	−	0.489112i	$-0.837321\pi$
$857$		−	28.6371i		−	0.978224i	0.872221	−	0.489112i	$-0.162679\pi$
$858$	−3.13161	+	1.12733i	−0.106911	+	0.0384863i
$859$	20.3022			0.692702			0.346351	−	0.938105i	$-0.387421\pi$
$859$	20.3022			0.692702			0.346351	+	0.938105i	$0.387421\pi$
$860$	14.3107	−	2.08080i	0.487992	−	0.0709548i
$861$	−3.36443	+	11.9383i	−0.114660	+	0.406855i
$862$	−46.6093	+	26.9099i	−1.58752	+	0.916554i
$863$	31.2414	−	18.0372i	1.06347	−	0.613994i	0.137079	−	0.990560i	$-0.456229\pi$
$863$	31.2414	−	18.0372i	1.06347	−	0.613994i	0.926390	+	0.376567i	$0.122895\pi$
$864$	−0.189133	+	17.8846i	−0.00643443	+	0.608446i
$865$	−40.7700	+	5.92802i	−1.38622	+	0.201559i
$866$	−13.6786	+	23.6921i	−0.464819	+	0.805090i
$867$	11.2126	−	4.03634i	0.380799	−	0.137081i
$868$	−11.5423	−	1.11890i	−0.391771	−	0.0379778i
$869$	3.60396	−	6.24223i	0.122256	−	0.211753i
$870$	12.8512	−	6.85354i	0.435697	−	0.232357i
$871$	14.8221			0.502229
$872$	−4.15908	−	2.40124i	−0.140844	−	0.0813164i
$873$	40.8057	−	6.89890i	1.38106	−	0.233492i
$874$	68.2471			2.30849
$875$	−19.2964	+	22.4198i	−0.652338	+	0.757928i
$876$	−15.4252	−	2.77598i	−0.521170	−	0.0937918i
$877$			41.3085i			1.39489i	0.716639	+	0.697445i	$0.245680\pi$
$877$			41.3085i			1.39489i	−0.716639	+	0.697445i	$0.754320\pi$
$878$	24.4053	−	14.0904i	0.823640	−	0.475529i
$879$	−28.5828	+	33.8208i	−0.964074	+	1.14075i
$880$	−1.15494	−	7.94313i	−0.0389331	−	0.267763i
$881$	37.7859			1.27304			0.636519	−	0.771261i	$-0.280374\pi$
$881$	37.7859			1.27304			0.636519	+	0.771261i	$0.280374\pi$
$882$	−34.0437	−	0.878204i	−1.14631	−	0.0295707i
$883$		−	2.38661i		−	0.0803159i	−0.999193	−	0.0401580i	$-0.987214\pi$
$883$		−	2.38661i		−	0.0803159i	0.999193	−	0.0401580i	$-0.0127861\pi$
$884$	1.60811	−	2.78532i	0.0540865	−	0.0936806i
$885$	5.53313	−	8.87930i	0.185994	−	0.298475i
$886$	−2.93757	−	5.08801i	−0.0986895	−	0.170935i
$887$		−	40.2504i		−	1.35148i	−0.737141	−	0.675738i	$-0.763825\pi$
$887$		−	40.2504i		−	1.35148i	0.737141	−	0.675738i	$-0.236175\pi$
$888$	−2.77618	+	0.999378i	−0.0931624	+	0.0335369i
$889$	−7.65325	+	3.48184i	−0.256682	+	0.116777i
$890$	−30.2546	−	38.3462i	−1.01413	−	1.28537i
$891$	5.02844	+	4.34164i	0.168459	+	0.145450i
$892$	−1.45372	−	0.839308i	−0.0486743	−	0.0281021i
$893$		−	21.6499i		−	0.724488i
$894$	33.8435	−	40.0455i	1.13189	−	1.33932i
$895$	1.94231	+	13.3582i	0.0649242	+	0.446516i
$896$	3.47291	−	35.8258i	0.116022	−	1.19686i
$897$	−15.1547	−	12.8076i	−0.505999	−	0.427632i
$898$	−50.1761	−	28.9692i	−1.67440	−	0.966714i
$899$	8.06917	−	13.9762i	0.269122	−	0.466133i
$900$	−9.42562	−	0.635647i	−0.314187	−	0.0211882i
$901$	−8.89507	−	15.4067i	−0.296338	−	0.513272i
$902$	2.80588	−	1.61998i	0.0934256	−	0.0539393i
$903$	33.7007	−	32.8426i	1.12149	−	1.09293i
$904$	1.48994	−	2.58065i	0.0495546	−	0.0858311i
$905$	9.89969	−	7.81071i	0.329077	−	0.259637i
$906$	29.9194	−	35.4023i	0.994005	−	1.17616i
$907$			16.4414i			0.545929i	0.962024	+	0.272964i	$0.0880042\pi$
$907$			16.4414i			0.545929i	−0.962024	+	0.272964i	$0.911996\pi$
$908$	−6.50966	+	3.75835i	−0.216031	+	0.124725i
$909$	−32.3453	−	12.0316i	−1.07282	−	0.399063i
$910$	−0.735167	−	15.3835i	−0.0243706	−	0.509959i
$911$	−28.1656	−	48.7843i	−0.933169	−	1.61630i	−0.777866	−	0.628430i	$-0.783698\pi$
$911$	−28.1656	−	48.7843i	−0.933169	−	1.61630i	−0.155303	−	0.987867i	$-0.549635\pi$
$912$	8.79798	−	48.8875i	0.291330	−	1.61883i
$913$	1.10122	−	0.635787i	0.0364449	−	0.0210415i
$914$	4.34654	+	7.52843i	0.143771	+	0.249018i
$915$	−19.5292	−	0.657761i	−0.645617	−	0.0217449i
$916$	−0.587257	−	1.01716i	−0.0194035	−	0.0336079i
$917$	4.29653	+	9.44398i	0.141884	+	0.311868i
$918$	−26.8043	−	0.283460i	−0.884672	−	0.00935558i
$919$	23.7489	+	41.1343i	0.783403	+	1.35689i	0.929948	+	0.367690i	$0.119851\pi$
$919$	23.7489	+	41.1343i	0.783403	+	1.35689i	−0.146545	+	0.989204i	$0.546815\pi$
$920$	27.8357	−	21.9620i	0.917716	−	0.724065i
$921$	−3.69213	−	0.664450i	−0.121660	−	0.0218944i
$922$		−	23.5001i		−	0.773933i
$923$	−4.36661	−	2.52106i	−0.143729	−	0.0829817i
$924$	1.48688	+	1.52573i	0.0489147	+	0.0501928i
$925$	−1.09165	−	3.67456i	−0.0358934	−	0.120819i
$926$	2.39323	+	4.14520i	0.0786465	+	0.136220i
$927$	15.6591	−	42.0971i	0.514311	−	1.38265i
$928$	−6.91258	−	3.99098i	−0.226916	−	0.131010i
$929$	23.7033	−	41.0552i	0.777678	−	1.34698i	−0.155598	−	0.987820i	$-0.549731\pi$
$929$	23.7033	−	41.0552i	0.777678	−	1.34698i	0.933277	−	0.359158i	$-0.116936\pi$
$930$	−38.5679	+	20.5682i	−1.26469	+	0.674459i
$931$	40.5129	+	7.92906i	1.32776	+	0.259865i
$932$	1.11355	+	0.642906i	0.0364754	+	0.0210591i
$933$	−19.1028	+	6.87668i	−0.625396	+	0.225132i
$934$	−26.8900			−0.879869
$935$	5.19608	−	0.755519i	0.169930	−	0.0247081i
$936$	−8.24569	+	6.82048i	−0.269519	+	0.222934i
$937$			23.7269i			0.775123i	0.921844	+	0.387562i	$0.126683\pi$
$937$			23.7269i			0.775123i	−0.921844	+	0.387562i	$0.873317\pi$
$938$	−16.4051	−	36.0591i	−0.535644	−	1.17737i
$939$	12.7515	−	15.0883i	0.416128	−	0.492387i
$940$	3.20232	+	4.05878i	0.104448	+	0.132383i
$941$	−7.13296	−	12.3547i	−0.232528	−	0.402750i	0.726023	−	0.687670i	$-0.241366\pi$
$941$	−7.13296	−	12.3547i	−0.232528	−	0.402750i	−0.958551	+	0.284920i	$0.908033\pi$
$942$	3.76535	−	20.9228i	0.122682	−	0.681703i
$943$	16.7272	+	9.65744i	0.544712	+	0.314490i
$944$	−13.1364			−0.427554
$945$	−26.0327	+	16.3493i	−0.846842	+	0.531844i
$946$	−12.2921			−0.399651
$947$	−3.35383	−	1.93633i	−0.108985	−	0.0629224i	0.444517	−	0.895771i	$-0.353375\pi$
$947$	−3.35383	−	1.93633i	−0.108985	−	0.0629224i	−0.553502	+	0.832848i	$0.686709\pi$
$948$	−1.88664	+	10.4834i	−0.0612751	+	0.340486i
$949$	−11.5323	−	19.9745i	−0.374353	−	0.648398i
$950$	46.5055	+	11.1256i	1.50884	+	0.360963i
$951$	−9.74221	+	11.5276i	−0.315913	+	0.373806i
$952$	18.6143	+	1.80445i	0.603294	+	0.0584826i
$953$			21.5025i			0.696534i	0.937395	+	0.348267i	$0.113230\pi$
$953$			21.5025i			0.696534i	−0.937395	+	0.348267i	$0.886770\pi$
$954$	−4.53540	−	26.8261i	−0.146839	−	0.868527i
$955$	7.77272	+	53.4569i	0.251519	+	1.72982i
$956$	11.3639			0.367535
$957$	−2.78958	+	1.00420i	−0.0901742	+	0.0324612i
$958$	34.1654	+	19.7254i	1.10383	+	0.637299i
$959$	−28.6038	+	13.0133i	−0.923666	+	0.420221i
$960$	−7.55240	−	14.1617i	−0.243753	−	0.457065i
$961$	−8.71645	+	15.0973i	−0.281176	+	0.487011i
$962$	1.72842	+	0.997906i	0.0557266	+	0.0321738i
$963$	57.9081	−	9.79033i	1.86606	−	0.315489i
$964$	8.26773	+	14.3201i	0.266286	+	0.461220i
$965$	11.4493	−	28.7313i	0.368566	−	0.924893i
$966$	−14.3850	+	51.0435i	−0.462830	+	1.64230i
$967$	−39.3820	−	22.7372i	−1.26644	−	0.731180i	−0.292128	−	0.956379i	$-0.594363\pi$
$967$	−39.3820	−	22.7372i	−1.26644	−	0.731180i	−0.974313	+	0.225200i	$0.927697\pi$
$968$		−	23.2313i		−	0.746683i
$969$	31.9803	+	5.75529i	1.02735	+	0.184887i
$970$	39.2712	−	30.9844i	1.26092	−	0.994849i
$971$	−14.4084	−	24.9561i	−0.462389	−	0.800881i	0.536691	−	0.843779i	$-0.319674\pi$
$971$	−14.4084	−	24.9561i	−0.462389	−	0.800881i	−0.999079	+	0.0428984i	$0.986341\pi$
$972$	−9.16496	−	3.51990i	−0.293966	−	0.112901i
$973$	−16.0109	−	1.55208i	−0.513285	−	0.0497573i
$974$	11.6291	+	20.1421i	0.372619	+	0.645395i
$975$	−8.23893	−	11.1980i	−0.263857	−	0.358622i
$976$	12.2675	+	21.2479i	0.392673	+	0.680130i
$977$	−6.24855	+	3.60760i	−0.199909	+	0.115417i	−0.596613	−	0.802529i	$-0.703487\pi$
$977$	−6.24855	+	3.60760i	−0.199909	+	0.115417i	0.396704	+	0.917947i	$0.370154\pi$
$978$	3.50100	−	19.4539i	0.111950	−	0.622068i
$979$	4.97149	+	8.61088i	0.158890	+	0.275205i
$980$	−8.76790	+	4.50592i	−0.280080	+	0.143936i
$981$	4.99629	−	4.13271i	0.159519	−	0.131947i
$982$	40.8733	−	23.5982i	1.30432	−	0.753049i
$983$		−	19.1624i		−	0.611185i	−0.952162	−	0.305592i	$-0.901146\pi$
$983$		−	19.1624i		−	0.611185i	0.952162	−	0.305592i	$-0.0988545\pi$
$984$	6.72386	−	7.95606i	0.214349	−	0.253630i
$985$	10.5249	+	13.3398i	0.335352	+	0.425042i
$986$	5.98142	−	10.3601i	0.190487	−	0.329934i
$987$	16.1924	+	4.56334i	0.515411	+	0.145253i
$988$	−5.16356	+	2.98118i	−0.164275	+	0.0948441i
$989$	−36.6396	−	63.4616i	−1.16507	−	2.01796i
$990$	7.85072	+	1.68749i	0.249512	+	0.0536320i
$991$	−8.28320	+	14.3469i	−0.263125	+	0.455745i	−0.967071	−	0.254508i	$-0.918086\pi$
$991$	−8.28320	+	14.3469i	−0.263125	+	0.455745i	0.703946	+	0.710254i	$0.251420\pi$
$992$	20.7454	+	11.9774i	0.658667	+	0.380282i
$993$	−5.86085	−	4.95315i	−0.185988	−	0.157183i
$994$	−1.30027	+	13.4133i	−0.0412421	+	0.425445i
$995$	−7.43204	−	51.1139i	−0.235612	−	1.62042i
$996$	−1.21295	+	1.43523i	−0.0384337	+	0.0454770i
$997$			45.8282i			1.45139i	0.688015	+	0.725697i	$0.258482\pi$
$997$			45.8282i			1.45139i	−0.688015	+	0.725697i	$0.741518\pi$
$998$	−46.4327	−	26.8079i	−1.46980	−	0.848591i
$999$	0.0421258	−	3.98345i	0.00133280	−	0.126031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bo.b.4.12	yes	84
3.2	odd	2		945.2.bo.b.739.31		84
5.4	even	2	inner	315.2.bo.b.4.31	yes	84
7.2	even	3		315.2.r.b.184.31	yes	84
9.2	odd	6		945.2.r.b.424.12		84
9.7	even	3		315.2.r.b.214.31	yes	84
15.14	odd	2		945.2.bo.b.739.12		84
21.2	odd	6		945.2.r.b.604.12		84
35.9	even	6		315.2.r.b.184.12	✓	84
45.29	odd	6		945.2.r.b.424.31		84
45.34	even	6		315.2.r.b.214.12	yes	84
63.2	odd	6		945.2.bo.b.289.12		84
63.16	even	3	inner	315.2.bo.b.79.31	yes	84
105.44	odd	6		945.2.r.b.604.31		84
315.79	even	6	inner	315.2.bo.b.79.12	yes	84
315.254	odd	6		945.2.bo.b.289.31		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.12	✓	84	35.9	even	6
315.2.r.b.184.31	yes	84	7.2	even	3
315.2.r.b.214.12	yes	84	45.34	even	6
315.2.r.b.214.31	yes	84	9.7	even	3
315.2.bo.b.4.12	yes	84	1.1	even	1	trivial
315.2.bo.b.4.31	yes	84	5.4	even	2	inner
315.2.bo.b.79.12	yes	84	315.79	even	6	inner
315.2.bo.b.79.31	yes	84	63.16	even	3	inner
945.2.r.b.424.12		84	9.2	odd	6
945.2.r.b.424.31		84	45.29	odd	6
945.2.r.b.604.12		84	21.2	odd	6
945.2.r.b.604.31		84	105.44	odd	6
945.2.bo.b.289.12		84	63.2	odd	6
945.2.bo.b.289.31		84	315.254	odd	6
945.2.bo.b.739.12		84	15.14	odd	2
945.2.bo.b.739.31		84	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40440 - 0.810833i) q^{2} +(-0.306778 + 1.70467i) q^{3} +(0.314901 + 0.545425i) q^{4} +(1.75547 - 1.38504i) q^{5} +(1.81304 - 2.14529i) q^{6} +(-1.09563 - 2.40824i) q^{7} +2.22200i q^{8} +(-2.81177 - 1.04591i) q^{9} +O(q^{10})\)	\(q+(-1.40440 - 0.810833i) q^{2} +(-0.306778 + 1.70467i) q^{3} +(0.314901 + 0.545425i) q^{4} +(1.75547 - 1.38504i) q^{5} +(1.81304 - 2.14529i) q^{6} +(-1.09563 - 2.40824i) q^{7} +2.22200i q^{8} +(-2.81177 - 1.04591i) q^{9} +(-3.58842 + 0.521762i) q^{10} +0.738158 q^{11} +(-1.02637 + 0.369477i) q^{12} +(-1.39023 - 0.802650i) q^{13} +(-0.413978 + 4.27051i) q^{14} +(1.82249 + 3.41739i) q^{15} +(2.43148 - 4.21144i) q^{16} +(2.75496 + 1.59058i) q^{17} +(3.10081 + 3.74876i) q^{18} +(-2.94868 - 5.10727i) q^{19} +(1.30823 + 0.521325i) q^{20} +(4.44135 - 1.12888i) q^{21} +(-1.03667 - 0.598523i) q^{22} -7.13616i q^{23} +(-3.78778 - 0.681662i) q^{24} +(1.16334 - 4.86278i) q^{25} +(1.30163 + 2.25449i) q^{26} +(2.64552 - 4.47227i) q^{27} +(0.968498 - 1.35594i) q^{28} +(1.15947 + 2.00826i) q^{29} +(0.211419 - 6.27713i) q^{30} +(-3.47969 - 6.02700i) q^{31} +(-2.98093 + 1.72104i) q^{32} +(-0.226451 + 1.25831i) q^{33} +(-2.57939 - 4.46763i) q^{34} +(-5.25884 - 2.71010i) q^{35} +(-0.314966 - 1.86297i) q^{36} +(0.663945 - 0.383329i) q^{37} +9.56356i q^{38} +(1.79474 - 2.12364i) q^{39} +(3.07756 + 3.90066i) q^{40} +(-1.35331 + 2.34400i) q^{41} +(-7.15279 - 2.01579i) q^{42} +(8.89296 - 5.13435i) q^{43} +(0.232447 + 0.402610i) q^{44} +(-6.38460 + 2.05836i) q^{45} +(-5.78623 + 10.0221i) q^{46} +(3.17928 + 1.83556i) q^{47} +(6.43318 + 5.43683i) q^{48} +(-4.59921 + 5.27705i) q^{49} +(-5.57670 + 5.88604i) q^{50} +(-3.55656 + 4.20833i) q^{51} -1.01102i q^{52} +(-4.84312 - 2.79618i) q^{53} +(-7.34164 + 4.13581i) q^{54} +(1.29581 - 1.02238i) q^{55} +(5.35111 - 2.43448i) q^{56} +(9.61078 - 3.45972i) q^{57} -3.76054i q^{58} +(-1.35066 - 2.33942i) q^{59} +(-1.29002 + 2.07017i) q^{60} +(-2.52264 + 4.36935i) q^{61} +11.2858i q^{62} +(0.561854 + 7.91734i) q^{63} -4.14400 q^{64} +(-3.55221 + 0.516497i) q^{65} +(1.33831 - 1.58357i) q^{66} +(-7.99623 + 4.61662i) q^{67} +2.00350i q^{68} +(12.1648 + 2.18922i) q^{69} +(5.18809 + 8.07012i) q^{70} +3.14092 q^{71} +(2.32401 - 6.24777i) q^{72} +(12.4428 + 7.18386i) q^{73} -1.24326 q^{74} +(7.93253 + 3.47490i) q^{75} +(1.85709 - 3.21657i) q^{76} +(-0.808745 - 1.77766i) q^{77} +(-4.24247 + 1.52722i) q^{78} +(4.88236 - 8.45650i) q^{79} +(-1.56463 - 10.7607i) q^{80} +(6.81215 + 5.88172i) q^{81} +(3.80119 - 2.19462i) q^{82} +(1.49184 - 0.861315i) q^{83} +(2.01431 + 2.06694i) q^{84} +(7.03926 - 1.02352i) q^{85} -16.6524 q^{86} +(-3.77910 + 1.36042i) q^{87} +1.64019i q^{88} +(6.73500 + 11.6654i) q^{89} +(10.6355 + 2.28608i) q^{90} +(-0.409800 + 4.22741i) q^{91} +(3.89224 - 2.24718i) q^{92} +(11.3415 - 4.08276i) q^{93} +(-2.97666 - 5.15573i) q^{94} +(-12.2501 - 4.88161i) q^{95} +(-2.01932 - 5.60947i) q^{96} +(-11.9468 + 6.89747i) q^{97} +(10.7380 - 3.68192i) q^{98} +(-2.07553 - 0.772046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

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