LMFDB - Embedded newform 315.2.be.b.236.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.10
Character	$\chi$	$=$	315.236
Dual form			315.2.be.b.311.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.794909 - 0.458941i) q^{2} +(-1.63482 - 0.572153i) q^{3} +(-0.578746 + 1.00242i) q^{4} +1.00000 q^{5} +(-1.56212 + 0.295477i) q^{6} +(-2.55889 + 0.672387i) q^{7} +2.89821i q^{8} +(2.34528 + 1.87074i) q^{9} +O(q^{10})$	\(q+(0.794909 - 0.458941i) q^{2} +(-1.63482 - 0.572153i) q^{3} +(-0.578746 + 1.00242i) q^{4} +1.00000 q^{5} +(-1.56212 + 0.295477i) q^{6} +(-2.55889 + 0.672387i) q^{7} +2.89821i q^{8} +(2.34528 + 1.87074i) q^{9} +(0.794909 - 0.458941i) q^{10} +3.32911i q^{11} +(1.51968 - 1.30764i) q^{12} +(-2.08421 + 1.20332i) q^{13} +(-1.72550 + 1.70886i) q^{14} +(-1.63482 - 0.572153i) q^{15} +(0.172614 + 0.298976i) q^{16} +(-0.514321 - 0.890831i) q^{17} +(2.72284 + 0.410721i) q^{18} +(4.75184 + 2.74348i) q^{19} +(-0.578746 + 1.00242i) q^{20} +(4.56803 + 0.364844i) q^{21} +(1.52787 + 2.64634i) q^{22} +7.46288i q^{23} +(1.65822 - 4.73805i) q^{24} +1.00000 q^{25} +(-1.10450 + 1.91306i) q^{26} +(-2.76377 - 4.40018i) q^{27} +(0.806933 - 2.95421i) q^{28} +(-3.78834 - 2.18720i) q^{29} +(-1.56212 + 0.295477i) q^{30} +(0.455406 + 0.262929i) q^{31} +(-4.74542 - 2.73977i) q^{32} +(1.90476 - 5.44250i) q^{33} +(-0.817678 - 0.472086i) q^{34} +(-2.55889 + 0.672387i) q^{35} +(-3.23258 + 1.26827i) q^{36} +(3.83652 - 6.64504i) q^{37} +5.03638 q^{38} +(4.09579 - 0.774723i) q^{39} +2.89821i q^{40} +(-0.0682512 - 0.118214i) q^{41} +(3.79861 - 1.80644i) q^{42} +(-5.65425 + 9.79344i) q^{43} +(-3.33716 - 1.92671i) q^{44} +(2.34528 + 1.87074i) q^{45} +(3.42502 + 5.93231i) q^{46} +(-4.51482 - 7.81989i) q^{47} +(-0.111132 - 0.587533i) q^{48} +(6.09579 - 3.44112i) q^{49} +(0.794909 - 0.458941i) q^{50} +(0.331132 + 1.75062i) q^{51} -2.78566i q^{52} +(1.24117 - 0.716592i) q^{53} +(-4.21637 - 2.22934i) q^{54} +3.32911i q^{55} +(-1.94871 - 7.41618i) q^{56} +(-6.19872 - 7.20388i) q^{57} -4.01519 q^{58} +(-0.319534 + 0.553449i) q^{59} +(1.51968 - 1.30764i) q^{60} +(8.85068 - 5.10994i) q^{61} +0.482676 q^{62} +(-7.25916 - 3.21007i) q^{63} -5.72002 q^{64} +(-2.08421 + 1.20332i) q^{65} +(-0.983674 - 5.20047i) q^{66} +(2.02545 - 3.50819i) q^{67} +1.19065 q^{68} +(4.26991 - 12.2005i) q^{69} +(-1.72550 + 1.70886i) q^{70} +4.03618i q^{71} +(-5.42178 + 6.79711i) q^{72} +(5.39392 - 3.11418i) q^{73} -7.04294i q^{74} +(-1.63482 - 0.572153i) q^{75} +(-5.50022 + 3.17555i) q^{76} +(-2.23845 - 8.51882i) q^{77} +(2.90023 - 2.49556i) q^{78} +(1.27597 + 2.21005i) q^{79} +(0.172614 + 0.298976i) q^{80} +(2.00068 + 8.77481i) q^{81} +(-0.108507 - 0.0626465i) q^{82} +(-2.30553 + 3.99329i) q^{83} +(-3.00945 + 4.36792i) q^{84} +(-0.514321 - 0.890831i) q^{85} +10.3799i q^{86} +(4.94185 + 5.74320i) q^{87} -9.64845 q^{88} +(-7.33999 + 12.7132i) q^{89} +(2.72284 + 0.410721i) q^{90} +(4.52416 - 4.48055i) q^{91} +(-7.48092 - 4.31911i) q^{92} +(-0.594072 - 0.690404i) q^{93} +(-7.17774 - 4.14407i) q^{94} +(4.75184 + 2.74348i) q^{95} +(6.19034 + 7.19414i) q^{96} +(14.8760 + 8.58869i) q^{97} +(3.26633 - 5.53299i) q^{98} +(-6.22789 + 7.80770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.794909	−	0.458941i	0.562086	−	0.324520i	−0.191896	−	0.981415i	$-0.561464\pi$
$2$	0.794909	−	0.458941i	0.562086	−	0.324520i	0.753982	+	0.656895i	$0.228130\pi$
$3$	−1.63482	−	0.572153i	−0.943864	−	0.330333i
$3$	−1.63482	−	0.572153i	−0.943864	−	0.330333i
$4$	−0.578746	+	1.00242i	−0.289373	+	0.501209i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.56212	+	0.295477i	−0.637733	+	0.120628i
$7$	−2.55889	+	0.672387i	−0.967168	+	0.254138i
$7$	−2.55889	+	0.672387i	−0.967168	+	0.254138i
$8$			2.89821i			1.02467i
$9$	2.34528	+	1.87074i	0.781760	+	0.623579i
$10$	0.794909	−	0.458941i	0.251372	−	0.145130i
$11$			3.32911i			1.00377i	0.864936	+	0.501883i	$0.167359\pi$
$11$			3.32911i			1.00377i	−0.864936	+	0.501883i	$0.832641\pi$
$12$	1.51968	−	1.30764i	0.438695	−	0.377484i
$13$	−2.08421	+	1.20332i	−0.578055	+	0.333740i	−0.760360	−	0.649502i	$-0.774978\pi$
$13$	−2.08421	+	1.20332i	−0.578055	+	0.333740i	0.182305	+	0.983242i	$0.441644\pi$
$14$	−1.72550	+	1.70886i	−0.461158	+	0.456713i
$15$	−1.63482	−	0.572153i	−0.422109	−	0.147729i
$16$	0.172614	+	0.298976i	0.0431534	+	0.0747439i
$17$	−0.514321	−	0.890831i	−0.124741	−	0.216058i	0.796891	−	0.604124i	$-0.206477\pi$
$17$	−0.514321	−	0.890831i	−0.124741	−	0.216058i	−0.921632	+	0.388066i	$0.873143\pi$
$18$	2.72284	+	0.410721i	0.641780	+	0.0968078i
$19$	4.75184	+	2.74348i	1.09015	+	0.629397i	0.933616	−	0.358276i	$-0.116635\pi$
$19$	4.75184	+	2.74348i	1.09015	+	0.629397i	0.156532	+	0.987673i	$0.449969\pi$
$20$	−0.578746	+	1.00242i	−0.129412	+	0.224147i
$21$	4.56803	+	0.364844i	0.996826	+	0.0796154i
$22$	1.52787	+	2.64634i	0.325742	+	0.564202i
$23$			7.46288i			1.55612i	0.628192	+	0.778059i	$0.283795\pi$
$23$			7.46288i			1.55612i	−0.628192	+	0.778059i	$0.716205\pi$
$24$	1.65822	−	4.73805i	0.338482	−	0.967150i
$25$	1.00000			0.200000
$26$	−1.10450	+	1.91306i	−0.216611	+	0.375182i
$27$	−2.76377	−	4.40018i	−0.531887	−	0.846815i
$28$	0.806933	−	2.95421i	0.152496	−	0.558294i
$29$	−3.78834	−	2.18720i	−0.703478	−	0.406153i	0.105164	−	0.994455i	$-0.466463\pi$
$29$	−3.78834	−	2.18720i	−0.703478	−	0.406153i	−0.808641	+	0.588302i	$0.799797\pi$
$30$	−1.56212	+	0.295477i	−0.285203	+	0.0539464i
$31$	0.455406	+	0.262929i	0.0817934	+	0.0472234i	0.540339	−	0.841448i	$-0.318296\pi$
$31$	0.455406	+	0.262929i	0.0817934	+	0.0472234i	−0.458545	+	0.888671i	$0.651629\pi$
$32$	−4.74542	−	2.73977i	−0.838879	−	0.484327i
$33$	1.90476	−	5.44250i	0.331577	−	0.947418i
$34$	−0.817678	−	0.472086i	−0.140231	−	0.0809622i
$35$	−2.55889	+	0.672387i	−0.432531	+	0.113654i
$36$	−3.23258	+	1.26827i	−0.538764	+	0.211378i
$37$	3.83652	−	6.64504i	0.630720	−	1.09244i	−0.356685	−	0.934225i	$-0.616093\pi$
$37$	3.83652	−	6.64504i	0.630720	−	1.09244i	0.987405	−	0.158214i	$-0.0505735\pi$
$38$	5.03638			0.817009
$39$	4.09579	−	0.774723i	0.655851	−	0.124055i
$40$			2.89821i			0.458247i
$41$	−0.0682512	−	0.118214i	−0.0106590	−	0.0184620i	0.860647	−	0.509203i	$-0.170060\pi$
$41$	−0.0682512	−	0.118214i	−0.0106590	−	0.0184620i	−0.871306	+	0.490741i	$0.836726\pi$
$42$	3.79861	−	1.80644i	0.586138	−	0.278740i
$43$	−5.65425	+	9.79344i	−0.862265	+	1.49349i	0.00747323	+	0.999972i	$0.497621\pi$
$43$	−5.65425	+	9.79344i	−0.862265	+	1.49349i	−0.869738	+	0.493514i	$0.835712\pi$
$44$	−3.33716	−	1.92671i	−0.503096	−	0.290463i
$45$	2.34528	+	1.87074i	0.349614	+	0.278873i
$46$	3.42502	+	5.93231i	0.504992	+	0.874671i
$47$	−4.51482	−	7.81989i	−0.658554	−	1.14065i	−0.980990	−	0.194058i	$-0.937835\pi$
$47$	−4.51482	−	7.81989i	−0.658554	−	1.14065i	0.322436	−	0.946591i	$-0.395498\pi$
$48$	−0.111132	−	0.587533i	−0.0160406	−	0.0848031i
$49$	6.09579	−	3.44112i	0.870828	−	0.491589i
$50$	0.794909	−	0.458941i	0.112417	−	0.0649041i
$51$	0.331132	+	1.75062i	0.0463677	+	0.245136i
$52$		−	2.78566i		−	0.386302i
$53$	1.24117	−	0.716592i	0.170488	−	0.0984314i	−0.412328	−	0.911036i	$-0.635284\pi$
$53$	1.24117	−	0.716592i	0.170488	−	0.0984314i	0.582816	+	0.812604i	$0.301951\pi$
$54$	−4.21637	−	2.22934i	−0.573775	−	0.303375i
$55$			3.32911i			0.448897i
$56$	−1.94871	−	7.41618i	−0.260408	−	0.991028i
$57$	−6.19872	−	7.20388i	−0.821041	−	0.954177i
$58$	−4.01519			−0.527220
$59$	−0.319534	+	0.553449i	−0.0415998	+	0.0720529i	−0.886076	−	0.463541i	$-0.846579\pi$
$59$	−0.319534	+	0.553449i	−0.0415998	+	0.0720529i	0.844476	+	0.535594i	$0.179912\pi$
$60$	1.51968	−	1.30764i	0.196190	−	0.168816i
$61$	8.85068	−	5.10994i	1.13321	−	0.654261i	0.188473	−	0.982078i	$-0.439646\pi$
$61$	8.85068	−	5.10994i	1.13321	−	0.654261i	0.944741	+	0.327817i	$0.106313\pi$
$62$	0.482676			0.0612999
$63$	−7.25916	−	3.21007i	−0.914569	−	0.404431i
$64$	−5.72002			−0.715003
$65$	−2.08421	+	1.20332i	−0.258514	+	0.149253i
$66$	−0.983674	−	5.20047i	−0.121082	−	0.640134i
$67$	2.02545	−	3.50819i	0.247448	−	0.428593i	−0.715369	−	0.698747i	$-0.753741\pi$
$67$	2.02545	−	3.50819i	0.247448	−	0.428593i	0.962817	+	0.270154i	$0.0870746\pi$
$68$	1.19065			0.144387
$69$	4.26991	−	12.2005i	0.514037	−	1.46876i
$70$	−1.72550	+	1.70886i	−0.206236	+	0.204248i
$71$			4.03618i			0.479006i	0.970896	+	0.239503i	$0.0769845\pi$
$71$			4.03618i			0.479006i	−0.970896	+	0.239503i	$0.923015\pi$
$72$	−5.42178	+	6.79711i	−0.638963	+	0.801047i
$73$	5.39392	−	3.11418i	0.631311	−	0.364487i	−0.149949	−	0.988694i	$-0.547911\pi$
$73$	5.39392	−	3.11418i	0.631311	−	0.364487i	0.781259	+	0.624206i	$0.214578\pi$
$74$		−	7.04294i		−	0.818725i
$75$	−1.63482	−	0.572153i	−0.188773	−	0.0660666i
$76$	−5.50022	+	3.17555i	−0.630919	+	0.364261i
$77$	−2.23845	−	8.51882i	−0.255095	−	0.970809i
$78$	2.90023	−	2.49556i	0.328386	−	0.282567i
$79$	1.27597	+	2.21005i	0.143558	+	0.248649i	0.928834	−	0.370496i	$-0.120812\pi$
$79$	1.27597	+	2.21005i	0.143558	+	0.248649i	−0.785276	+	0.619146i	$0.787479\pi$
$80$	0.172614	+	0.298976i	0.0192988	+	0.0334265i
$81$	2.00068	+	8.77481i	0.222298	+	0.974979i
$82$	−0.108507	−	0.0626465i	−0.0119826	−	0.00691815i
$83$	−2.30553	+	3.99329i	−0.253065	+	0.438321i	−0.964368	−	0.264564i	$-0.914772\pi$
$83$	−2.30553	+	3.99329i	−0.253065	+	0.438321i	0.711303	+	0.702885i	$0.248105\pi$
$84$	−3.00945	+	4.36792i	−0.328358	+	0.476579i
$85$	−0.514321	−	0.890831i	−0.0557860	−	0.0966242i
$86$			10.3799i			1.11929i
$87$	4.94185	+	5.74320i	0.529822	+	0.615735i
$88$	−9.64845			−1.02853
$89$	−7.33999	+	12.7132i	−0.778037	+	1.34760i	0.155035	+	0.987909i	$0.450451\pi$
$89$	−7.33999	+	12.7132i	−0.778037	+	1.34760i	−0.933072	+	0.359691i	$0.882882\pi$
$90$	2.72284	+	0.410721i	0.287013	+	0.0432938i
$91$	4.52416	−	4.48055i	0.474260	−	0.469689i
$92$	−7.48092	−	4.31911i	−0.779940	−	0.450298i
$93$	−0.594072	−	0.690404i	−0.0616024	−	0.0715916i
$94$	−7.17774	−	4.14407i	−0.740328	−	0.427428i
$95$	4.75184	+	2.74348i	0.487529	+	0.281475i
$96$	6.19034	+	7.19414i	0.631799	+	0.734248i
$97$	14.8760	+	8.58869i	1.51043	+	0.872049i	0.999926	+	0.0121758i	$0.00387577\pi$
$97$	14.8760	+	8.58869i	1.51043	+	0.872049i	0.510507	+	0.859873i	$0.329458\pi$
$98$	3.26633	−	5.53299i	0.329949	−	0.558916i
$99$	−6.22789	+	7.80770i	−0.625927	+	0.784704i
$100$	−0.578746	+	1.00242i	−0.0578746	+	0.100242i
$101$	−0.926445			−0.0921847			−0.0460924	−	0.998937i	$-0.514677\pi$
$101$	−0.926445			−0.0921847			−0.0460924	+	0.998937i	$0.514677\pi$
$102$	1.06665	+	1.23961i	0.105614	+	0.122740i
$103$		−	14.6049i		−	1.43907i	−0.694457	−	0.719534i	$-0.744355\pi$
$103$		−	14.6049i		−	1.43907i	0.694457	−	0.719534i	$-0.255645\pi$
$104$	−3.48746	−	6.04047i	−0.341974	−	0.592316i
$105$	4.56803	+	0.364844i	0.445794	+	0.0356051i
$106$	0.657747	−	1.13925i	0.0638860	−	0.110654i
$107$	15.3708	+	8.87434i	1.48595	+	0.857915i	0.999872	−	0.0159999i	$-0.00509315\pi$
$107$	15.3708	+	8.87434i	1.48595	+	0.857915i	0.486080	+	0.873915i	$0.338426\pi$
$108$	6.01034	−	0.223860i	0.578345	−	0.0215409i
$109$	5.50332	+	9.53203i	0.527122	+	0.913003i	0.999500	+	0.0316067i	$0.0100624\pi$
$109$	5.50332	+	9.53203i	0.527122	+	0.913003i	−0.472378	+	0.881396i	$0.656604\pi$
$110$	1.52787	+	2.64634i	0.145676	+	0.252319i
$111$	−10.0740	+	8.66838i	−0.956182	+	0.822766i
$112$	−0.642726	−	0.648981i	−0.0607319	−	0.0613229i
$113$	7.79331	−	4.49947i	0.733133	−	0.423274i	−0.0864344	−	0.996258i	$-0.527547\pi$
$113$	7.79331	−	4.49947i	0.733133	−	0.423274i	0.819567	+	0.572983i	$0.194214\pi$
$114$	−8.23358	−	2.88158i	−0.771145	−	0.269885i
$115$			7.46288i			0.695917i
$116$	4.38498	−	2.53167i	0.407135	−	0.235059i
$117$	−7.13915	−	1.07689i	−0.660014	−	0.0995583i
$118$			0.586589i			0.0539999i
$119$	1.91507	+	1.93371i	0.175554	+	0.177263i
$120$	1.65822	−	4.73805i	0.151374	−	0.432523i
$121$	−0.0829878			−0.00754435
$122$	4.69033	−	8.12388i	0.424642	−	0.735502i
$123$	0.0439416	+	0.232310i	0.00396208	+	0.0209467i
$124$	−0.527129	+	0.304338i	−0.0473376	+	0.0273304i
$125$	1.00000			0.0894427
$126$	−7.24361	+	0.779816i	−0.645312	+	0.0694715i
$127$	5.07500			0.450334			0.225167	−	0.974320i	$-0.427707\pi$
$127$	5.07500			0.450334			0.225167	+	0.974320i	$0.427707\pi$
$128$	4.94393	−	2.85438i	0.436986	−	0.252294i
$129$	14.8470	−	12.7754i	1.30721	−	1.12481i
$130$	−1.10450	+	1.91306i	−0.0968715	+	0.167786i
$131$	−17.0332			−1.48820			−0.744099	−	0.668070i	$-0.767121\pi$
$131$	−17.0332			−1.48820			−0.744099	+	0.668070i	$0.767121\pi$
$132$	4.35329	+	5.05920i	0.378905	+	0.440346i
$133$	−14.0041	−	3.82517i	−1.21431	−	0.331684i
$134$		−	3.71825i		−	0.321208i
$135$	−2.76377	−	4.40018i	−0.237867	−	0.378707i
$136$	2.58181	−	1.49061i	0.221388	−	0.127819i
$137$			12.4916i			1.06723i	0.845727	+	0.533616i	$0.179167\pi$
$137$			12.4916i			1.06723i	−0.845727	+	0.533616i	$0.820833\pi$
$138$	−2.20510	−	11.6579i	−0.187711	−	0.992387i
$139$	10.7811	−	6.22445i	0.914437	−	0.527951i	0.0325812	−	0.999469i	$-0.489627\pi$
$139$	10.7811	−	6.22445i	0.914437	−	0.527951i	0.881856	+	0.471518i	$0.156294\pi$
$140$	0.806933	−	2.95421i	0.0681983	−	0.249677i
$141$	2.90674	+	15.3673i	0.244792	+	1.29416i
$142$	1.85237	+	3.20840i	0.155447	+	0.269243i
$143$	−4.00598	−	6.93856i	−0.334997	−	0.580232i
$144$	−0.154477	+	1.02410i	−0.0128731	+	0.0853413i
$145$	−3.78834	−	2.18720i	−0.314605	−	0.181637i
$146$	2.85845	−	4.95098i	0.236567	−	0.409746i
$147$	−11.9344	+	2.13789i	−0.984331	+	0.176330i
$148$	4.44074	+	7.69159i	0.365027	+	0.632244i
$149$		−	6.61577i		−	0.541985i	−0.962581	−	0.270993i	$-0.912648\pi$
$149$		−	6.61577i		−	0.541985i	0.962581	−	0.270993i	$-0.0873519\pi$
$150$	−1.56212	+	0.295477i	−0.127547	+	0.0241256i
$151$	10.6503			0.866709			0.433355	−	0.901223i	$-0.357330\pi$
$151$	10.6503			0.866709			0.433355	+	0.901223i	$0.357330\pi$
$152$	−7.95116	+	13.7718i	−0.644925	+	1.11704i
$153$	0.460282	−	3.05141i	0.0372116	−	0.246692i
$154$	−5.68900	−	5.74437i	−0.458433	−	0.462895i
$155$	0.455406	+	0.262929i	0.0365791	+	0.0211190i
$156$	−1.59383	+	4.55406i	−0.127608	+	0.364617i
$157$	−14.6442	−	8.45482i	−1.16873	−	0.674768i	−0.215352	−	0.976537i	$-0.569090\pi$
$157$	−14.6442	−	8.45482i	−1.16873	−	0.674768i	−0.953381	+	0.301768i	$0.902423\pi$
$158$	2.02856	+	1.17119i	0.161384	+	0.0931749i
$159$	−2.43910	+	0.461358i	−0.193433	+	0.0365880i
$160$	−4.74542	−	2.73977i	−0.375158	−	0.216598i
$161$	−5.01794	−	19.0966i	−0.395469	−	1.50503i
$162$	5.61748	+	6.05698i	0.441351	+	0.475881i
$163$	8.04145	−	13.9282i	0.629855	−	1.09094i	−0.357725	−	0.933827i	$-0.616448\pi$
$163$	8.04145	−	13.9282i	0.629855	−	1.09094i	0.987580	−	0.157114i	$-0.0502191\pi$
$164$	0.158000			0.0123378
$165$	1.90476	−	5.44250i	0.148286	−	0.423698i
$166$			4.23241i			0.328498i
$167$	8.02730	+	13.9037i	0.621171	+	1.07590i	0.989268	+	0.146113i	$0.0466762\pi$
$167$	8.02730	+	13.9037i	0.621171	+	1.07590i	−0.368097	+	0.929787i	$0.619990\pi$
$168$	−1.05739	+	13.2391i	−0.0815795	+	1.02142i
$169$	−3.60405	+	6.24240i	−0.277235	+	0.480184i
$170$	−0.817678	−	0.472086i	−0.0627130	−	0.0362074i
$171$	6.01208	+	15.3237i	0.459755	+	1.17183i
$172$	−6.54475	−	11.3358i	−0.499032	−	0.864349i
$173$	11.6602	+	20.1961i	0.886510	+	1.53548i	0.843973	+	0.536386i	$0.180211\pi$
$173$	11.6602	+	20.1961i	0.886510	+	1.53548i	0.0425376	+	0.999095i	$0.486456\pi$
$174$	6.56411	+	2.29730i	0.497624	+	0.174158i
$175$	−2.55889	+	0.672387i	−0.193434	+	0.0508276i
$176$	−0.995323	+	0.574650i	−0.0750253	+	0.0433159i
$177$	0.839038	−	0.721968i	0.0630660	−	0.0542664i
$178$			13.4745i			1.00996i
$179$	−4.26684	+	2.46346i	−0.318919	+	0.184128i	−0.650910	−	0.759154i	$-0.725613\pi$
$179$	−4.26684	+	2.46346i	−0.318919	+	0.184128i	0.331992	+	0.943282i	$0.392279\pi$
$180$	−3.23258	+	1.26827i	−0.240942	+	0.0945312i
$181$			10.3507i			0.769358i	0.923050	+	0.384679i	$0.125688\pi$
$181$			10.3507i			0.769358i	−0.923050	+	0.384679i	$0.874312\pi$
$182$	1.53999	−	5.63795i	0.114151	−	0.417913i
$183$	−17.3930	+	3.28990i	−1.28572	+	0.243196i
$184$	−21.6290			−1.59451
$185$	3.83652	−	6.64504i	0.282066	−	0.488553i
$186$	−0.789088	−	0.276165i	−0.0578588	−	0.0202494i
$187$	2.96568	−	1.71223i	0.216872	−	0.125211i
$188$	10.4517			0.762271
$189$	10.0308	+	9.40124i	0.729632	+	0.683840i
$190$	5.03638			0.365377
$191$	11.2449	−	6.49227i	0.813655	−	0.469764i	−0.0345686	−	0.999402i	$-0.511006\pi$
$191$	11.2449	−	6.49227i	0.813655	−	0.469764i	0.848224	+	0.529638i	$0.177672\pi$
$192$	9.35121	+	3.27273i	0.674866	+	0.236189i
$193$	−7.82634	+	13.5556i	−0.563352	+	0.975755i	0.433849	+	0.900986i	$0.357155\pi$
$193$	−7.82634	+	13.5556i	−0.563352	+	0.975755i	−0.997201	+	0.0747690i	$0.976178\pi$
$194$	15.7668			1.13199
$195$	4.09579	−	0.774723i	0.293306	−	0.0554791i
$196$	−0.0784759	+	8.10207i	−0.00560542	+	0.578719i
$197$		−	20.1861i		−	1.43820i	−0.694908	−	0.719098i	$-0.744555\pi$
$197$		−	20.1861i		−	1.43820i	0.694908	−	0.719098i	$-0.255445\pi$
$198$	−1.36734	+	9.06465i	−0.0971723	+	0.644197i
$199$	1.90446	−	1.09954i	0.135004	−	0.0779443i	−0.430977	−	0.902363i	$-0.641831\pi$
$199$	1.90446	−	1.09954i	0.135004	−	0.0779443i	0.565981	+	0.824419i	$0.308498\pi$
$200$			2.89821i			0.204934i
$201$	−5.31847	+	4.57639i	−0.375136	+	0.322793i
$202$	−0.736440	+	0.425184i	−0.0518157	+	0.0299158i
$203$	11.1646	+	3.04957i	0.783600	+	0.214038i
$204$	−1.94649	−	0.681232i	−0.136282	−	0.0476958i
$205$	−0.0682512	−	0.118214i	−0.00476687	−	0.00825646i
$206$	−6.70281	−	11.6096i	−0.467007	−	0.808880i
$207$	−13.9611	+	17.5025i	−0.970362	+	1.21651i
$208$	−0.719525	−	0.415418i	−0.0498901	−	0.0288041i
$209$	−9.13335	+	15.8194i	−0.631767	+	1.09425i
$210$	3.79861	−	1.80644i	0.262129	−	0.124656i
$211$	−12.5787	−	21.7869i	−0.865952	−	1.49987i	−0.866099	−	0.499873i	$-0.833380\pi$
$211$	−12.5787	−	21.7869i	−0.865952	−	1.49987i	0.000147215	−	1.00000i	$-0.499953\pi$
$212$			1.65890i			0.113934i
$213$	2.30931	−	6.59843i	0.158232	−	0.452117i
$214$	16.2912			1.11364
$215$	−5.65425	+	9.79344i	−0.385616	+	0.667907i
$216$	12.7526	−	8.00996i	0.867707	−	0.545009i
$217$	−1.34212	−	0.366596i	−0.0911092	−	0.0248862i
$218$	8.74928	+	5.05140i	0.592576	+	0.342124i
$219$	−10.5999	+	2.00498i	−0.716274	+	0.135484i
$220$	−3.33716	−	1.92671i	−0.224991	−	0.129899i
$221$	2.14391	+	1.23778i	0.144215	+	0.0832624i
$222$	−4.02964	+	11.5140i	−0.270452	+	0.772766i
$223$	−17.4440	−	10.0713i	−1.16814	−	0.674424i	−0.214897	−	0.976637i	$-0.568942\pi$
$223$	−17.4440	−	10.0713i	−1.16814	−	0.674424i	−0.953241	+	0.302212i	$0.902275\pi$
$224$	13.9852	+	3.82000i	0.934423	+	0.255234i
$225$	2.34528	+	1.87074i	0.156352	+	0.124716i
$226$	4.12998	−	7.15334i	0.274722	−	0.475833i
$227$	−5.05622			−0.335593			−0.167797	−	0.985822i	$-0.553665\pi$
$227$	−5.05622			−0.335593			−0.167797	+	0.985822i	$0.553665\pi$
$228$	10.8088	−	2.04449i	0.715829	−	0.135400i
$229$		−	6.25486i		−	0.413333i	−0.978411	−	0.206666i	$-0.933738\pi$
$229$		−	6.25486i		−	0.413333i	0.978411	−	0.206666i	$-0.0662615\pi$
$230$	3.42502	+	5.93231i	0.225839	+	0.391165i
$231$	−1.21461	+	15.2075i	−0.0799151	+	1.00058i
$232$	6.33896	−	10.9794i	0.416173	−	0.720833i
$233$	−3.18751	−	1.84031i	−0.208821	−	0.120563i	0.391943	−	0.919990i	$-0.371803\pi$
$233$	−3.18751	−	1.84031i	−0.208821	−	0.120563i	−0.600763	+	0.799427i	$0.705137\pi$
$234$	−6.16920	+	2.42042i	−0.403293	+	0.158228i
$235$	−4.51482	−	7.81989i	−0.294514	−	0.510114i
$236$	−0.369858	−	0.640613i	−0.0240757	−	0.0417003i
$237$	−0.821498	−	4.34308i	−0.0533620	−	0.282113i
$238$	2.40977	+	0.658220i	0.156202	+	0.0426661i
$239$	14.3996	−	8.31359i	0.931430	−	0.537761i	0.0441663	−	0.999024i	$-0.485937\pi$
$239$	14.3996	−	8.31359i	0.931430	−	0.537761i	0.887263	+	0.461263i	$0.152604\pi$
$240$	−0.111132	−	0.587533i	−0.00717357	−	0.0379251i
$241$			12.1715i			0.784034i	0.919958	+	0.392017i	$0.128223\pi$
$241$			12.1715i			0.784034i	−0.919958	+	0.392017i	$0.871777\pi$
$242$	−0.0659678	+	0.0380865i	−0.00424057	+	0.00244830i
$243$	1.74978	−	15.4899i	0.112248	−	0.993680i
$244$			11.8294i			0.757302i
$245$	6.09579	−	3.44112i	0.389446	−	0.219845i
$246$	0.141546	+	0.164499i	0.00902465	+	0.0104880i
$247$	−13.2051			−0.840221
$248$	−0.762022	+	1.31986i	−0.0483885	+	0.0838113i
$249$	6.05390	−	5.20920i	0.383650	−	0.330120i
$250$	0.794909	−	0.458941i	0.0502745	−	0.0290260i
$251$	−7.23101			−0.456417			−0.228209	−	0.973612i	$-0.573287\pi$
$251$	−7.23101			−0.456417			−0.228209	+	0.973612i	$0.573287\pi$
$252$	7.41904	−	5.41890i	0.467356	−	0.341359i
$253$	−24.8448			−1.56198
$254$	4.03417	−	2.32913i	0.253126	−	0.146142i
$255$	0.331132	+	1.75062i	0.0207363	+	0.109628i
$256$	8.34001	−	14.4453i	0.521250	−	0.902832i
$257$	−19.3701			−1.20827			−0.604137	−	0.796881i	$-0.706482\pi$
$257$	−19.3701			−1.20827			−0.604137	+	0.796881i	$0.706482\pi$
$258$	5.93888	−	16.9692i	0.369738	−	1.05646i
$259$	−5.34917	+	19.5835i	−0.332381	+	1.21686i
$260$		−	2.78566i		−	0.172760i
$261$	−4.79305	−	12.2166i	−0.296682	−	0.756188i
$262$	−13.5398	+	7.81723i	−0.836495	+	0.482950i
$263$			23.7402i			1.46389i	0.681366	+	0.731943i	$0.261386\pi$
$263$			23.7402i			1.46389i	−0.681366	+	0.731943i	$0.738614\pi$
$264$	15.7735	+	5.52040i	0.970792	+	0.339757i
$265$	1.24117	−	0.716592i	0.0762447	−	0.0440199i
$266$	−12.8875	+	3.38639i	−0.790184	+	0.207633i
$267$	19.2735	−	16.5843i	1.17952	−	1.01494i
$268$	2.34444	+	4.06070i	0.143210	+	0.248047i
$269$	−5.08433	−	8.80631i	−0.309997	−	0.536930i	0.668364	−	0.743834i	$-0.266995\pi$
$269$	−5.08433	−	8.80631i	−0.309997	−	0.536930i	−0.978361	+	0.206904i	$0.933661\pi$
$270$	−4.21637	−	2.22934i	−0.256600	−	0.135673i
$271$	−4.98971	−	2.88081i	−0.303103	−	0.174997i	0.340733	−	0.940160i	$-0.389325\pi$
$271$	−4.98971	−	2.88081i	−0.303103	−	0.174997i	−0.643836	+	0.765163i	$0.722658\pi$
$272$	0.177558	−	0.307539i	0.0107660	−	0.0186473i
$273$	−9.95975	+	4.73638i	−0.602791	+	0.286659i
$274$	5.73292	+	9.92972i	0.346339	+	0.599876i
$275$			3.32911i			0.200753i
$276$	9.75877	+	11.3412i	0.587409	+	0.682660i
$277$	5.79488			0.348180			0.174090	−	0.984730i	$-0.444302\pi$
$277$	5.79488			0.348180			0.174090	+	0.984730i	$0.444302\pi$
$278$	5.71331	−	9.89574i	0.342662	−	0.593507i
$279$	0.576185	+	1.46859i	0.0344953	+	0.0879220i
$280$	−1.94871	−	7.41618i	−0.116458	−	0.443201i
$281$	−2.70317	−	1.56068i	−0.161258	−	0.0931022i	0.417199	−	0.908815i	$-0.363012\pi$
$281$	−2.70317	−	1.56068i	−0.161258	−	0.0931022i	−0.578457	+	0.815713i	$0.696345\pi$
$282$	9.36328	+	10.8816i	0.557575	+	0.647989i
$283$	−0.823546	−	0.475475i	−0.0489548	−	0.0282640i	0.475323	−	0.879811i	$-0.342331\pi$
$283$	−0.823546	−	0.475475i	−0.0489548	−	0.0282640i	−0.524278	+	0.851547i	$0.675665\pi$
$284$	−4.04594	−	2.33592i	−0.240082	−	0.138612i
$285$	−6.19872	−	7.20388i	−0.367181	−	0.426721i
$286$	−6.36878	−	3.67702i	−0.376594	−	0.217427i
$287$	0.254133	+	0.256606i	0.0150010	+	0.0151470i
$288$	−6.00395	−	15.3029i	−0.353786	−	0.901735i
$289$	7.97095	−	13.8061i	0.468879	−	0.812123i
$290$	−4.01519			−0.235780
$291$	−19.4056	−	22.5523i	−1.13758	−	1.32204i
$292$			7.20928i			0.421891i
$293$	−2.53789	−	4.39576i	−0.148265	−	0.256803i	0.782321	−	0.622875i	$-0.214036\pi$
$293$	−2.53789	−	4.39576i	−0.148265	−	0.256803i	−0.930586	+	0.366072i	$0.880702\pi$
$294$	−8.50559	+	7.17661i	−0.496056	+	0.418548i
$295$	−0.319534	+	0.553449i	−0.0186040	+	0.0322230i
$296$	19.2587	+	11.1190i	1.11939	+	0.646280i
$297$	14.6487	−	9.20089i	0.850004	−	0.533890i
$298$	−3.03625	−	5.25894i	−0.175885	−	0.304642i
$299$	−8.98022	−	15.5542i	−0.519339	−	0.899522i
$300$	1.51968	−	1.30764i	0.0877390	−	0.0754968i
$301$	7.88359	−	28.8621i	0.454403	−	1.66359i
$302$	8.46602	−	4.88786i	0.487165	−	0.281265i
$303$	1.51457	+	0.530069i	0.0870099	+	0.0304516i
$304$			1.89425i			0.108642i
$305$	8.85068	−	5.10994i	0.506789	−	0.292595i
$306$	−1.03453	−	2.63684i	−0.0591404	−	0.150738i
$307$			15.3400i			0.875500i	0.899097	+	0.437750i	$0.144224\pi$
$307$			15.3400i			0.875500i	−0.899097	+	0.437750i	$0.855776\pi$
$308$	9.83491	+	2.68637i	0.560396	+	0.153070i
$309$	−8.35627	+	23.8765i	−0.475372	+	1.35829i
$310$	0.482676			0.0274141
$311$	−2.37561	+	4.11468i	−0.134709	+	0.233322i	−0.925486	−	0.378781i	$-0.876343\pi$
$311$	−2.37561	+	4.11468i	−0.134709	+	0.233322i	0.790777	+	0.612104i	$0.209677\pi$
$312$	2.24531	+	11.8704i	0.127116	+	0.672032i
$313$	4.37480	−	2.52579i	0.247278	−	0.142766i	−0.371239	−	0.928537i	$-0.621067\pi$
$313$	4.37480	−	2.52579i	0.247278	−	0.142766i	0.618517	+	0.785771i	$0.287734\pi$
$314$	−15.5211			−0.875904
$315$	−7.25916	−	3.21007i	−0.409008	−	0.180867i
$316$	−2.95385			−0.166167
$317$	5.40787	−	3.12223i	0.303736	−	0.175362i	−0.340384	−	0.940287i	$-0.610557\pi$
$317$	5.40787	−	3.12223i	0.303736	−	0.175362i	0.644120	+	0.764924i	$0.277224\pi$
$318$	−1.72712	+	1.48614i	−0.0968523	+	0.0833385i
$319$	7.28144	−	12.6118i	0.407682	−	0.706126i
$320$	−5.72002			−0.319759
$321$	−20.0510	−	23.3024i	−1.11914	−	1.30061i
$322$	−12.7530	−	12.8772i	−0.710699	−	0.717616i
$323$		−	5.64412i		−	0.314047i
$324$	−9.95391	−	3.07287i	−0.552995	−	0.170715i
$325$	−2.08421	+	1.20332i	−0.115611	+	0.0667481i
$326$		−	14.7622i		−	0.817603i
$327$	−3.54316	−	18.7319i	−0.195937	−	1.03588i
$328$	0.342610	−	0.197806i	0.0189175	−	0.0109220i
$329$	16.8109	+	16.9745i	0.926815	+	0.935835i
$330$	−0.983674	−	5.20047i	−0.0541495	−	0.286276i
$331$	−12.8786	−	22.3064i	−0.707872	−	1.22607i	−0.965645	−	0.259864i	$-0.916322\pi$
$331$	−12.8786	−	22.3064i	−0.707872	−	1.22607i	0.257773	−	0.966205i	$-0.417011\pi$
$332$	−2.66863	−	4.62220i	−0.146460	−	0.253676i
$333$	21.4288	−	8.40738i	1.17429	−	0.460721i
$334$	12.7620	+	7.36812i	0.698303	+	0.403165i
$335$	2.02545	−	3.50819i	0.110662	−	0.191673i
$336$	0.679425	+	1.42871i	0.0370657	+	0.0779423i
$337$	9.57263	+	16.5803i	0.521455	+	0.903186i	0.999689	+	0.0249535i	$0.00794376\pi$
$337$	9.57263	+	16.5803i	0.521455	+	0.903186i	−0.478234	+	0.878232i	$0.658723\pi$
$338$			6.61619i			0.359873i
$339$	−15.3151	+	2.89686i	−0.831799	+	0.157336i
$340$	1.19065			0.0645718
$341$	−0.875320	+	1.51610i	−0.0474012	+	0.0821013i
$342$	11.8117	+	9.42174i	0.638705	+	0.509469i
$343$	−13.2847	+	12.9042i	−0.717305	+	0.696759i
$344$	−28.3834	−	16.3872i	−1.53033	−	0.883537i
$345$	4.26991	−	12.2005i	0.229884	−	0.656851i
$346$	18.5376	+	10.7027i	0.996590	+	0.575381i
$347$	−24.4644	−	14.1245i	−1.31332	−	0.758244i	−0.330673	−	0.943745i	$-0.607276\pi$
$347$	−24.4644	−	14.1245i	−1.31332	−	0.758244i	−0.982644	+	0.185502i	$0.940609\pi$
$348$	−8.61716	+	1.62994i	−0.461928	+	0.0873742i
$349$	−26.7281	−	15.4315i	−1.43072	−	0.826029i	−0.433549	−	0.901130i	$-0.642739\pi$
$349$	−26.7281	−	15.4315i	−1.43072	−	0.826029i	−0.997176	+	0.0751011i	$0.976072\pi$
$350$	−1.72550	+	1.70886i	−0.0922317	+	0.0913426i
$351$	11.0551	+	5.84521i	0.590077	+	0.311994i
$352$	9.12099	−	15.7980i	0.486150	−	0.842037i
$353$	−4.11177			−0.218848			−0.109424	−	0.993995i	$-0.534901\pi$
$353$	−4.11177			−0.218848			−0.109424	+	0.993995i	$0.534901\pi$
$354$	0.335619	−	0.958968i	0.0178379	−	0.0509686i
$355$			4.03618i			0.214218i
$356$	−8.49598	−	14.7155i	−0.450286	−	0.779918i
$357$	−2.02442	−	4.25699i	−0.107144	−	0.225304i
$358$	−2.26117	+	3.91646i	−0.119506	+	0.206991i
$359$	29.5340	+	17.0515i	1.55875	+	0.899943i	0.997377	+	0.0723774i	$0.0230586\pi$
$359$	29.5340	+	17.0515i	1.55875	+	0.899943i	0.561369	+	0.827565i	$0.310275\pi$
$360$	−5.42178	+	6.79711i	−0.285753	+	0.358239i
$361$	5.55334	+	9.61867i	0.292281	+	0.506246i
$362$	4.75034	+	8.22783i	0.249672	+	0.432445i
$363$	0.135670	+	0.0474818i	0.00712084	+	0.00249215i
$364$	1.87304	+	7.12819i	0.0981741	+	0.373619i
$365$	5.39392	−	3.11418i	0.282331	−	0.163004i
$366$	−12.3160	+	10.5975i	−0.643765	+	0.553941i
$367$			4.76142i			0.248544i	0.992248	+	0.124272i	$0.0396595\pi$
$367$			4.76142i			0.248544i	−0.992248	+	0.124272i	$0.960340\pi$
$368$	−2.23122	+	1.28819i	−0.116310	+	0.0671517i
$369$	0.0610801	−	0.404926i	0.00317970	−	0.0210796i
$370$		−	7.04294i		−	0.366145i
$371$	−2.69419	+	2.66822i	−0.139876	+	0.138527i
$372$	1.03589	−	0.195940i	0.0537084	−	0.0101590i
$373$	21.2585			1.10072			0.550362	−	0.834926i	$-0.314490\pi$
$373$	21.2585			1.10072			0.550362	+	0.834926i	$0.314490\pi$
$374$	1.57163	−	2.72214i	0.0812670	−	0.140759i
$375$	−1.63482	−	0.572153i	−0.0844218	−	0.0295459i
$376$	22.6637	−	13.0849i	1.16879	−	0.674801i
$377$	10.5276			0.542199
$378$	12.2882	+	2.86960i	0.632036	+	0.147596i
$379$	13.3283			0.684630			0.342315	−	0.939585i	$-0.388789\pi$
$379$	13.3283			0.684630			0.342315	+	0.939585i	$0.388789\pi$
$380$	−5.50022	+	3.17555i	−0.282155	+	0.162902i
$381$	−8.29672	−	2.90368i	−0.425054	−	0.148760i
$382$	5.95914	−	10.3215i	0.304896	−	0.528095i
$383$	8.06865			0.412289			0.206144	−	0.978522i	$-0.433908\pi$
$383$	8.06865			0.412289			0.206144	+	0.978522i	$0.433908\pi$
$384$	−9.71559	+	1.83771i	−0.495797	+	0.0937805i
$385$	−2.23845	−	8.51882i	−0.114082	−	0.434159i
$386$			14.3673i			0.731277i
$387$	−31.5818	+	12.3908i	−1.60539	+	0.629858i
$388$	−17.2189	+	9.94134i	−0.874157	+	0.504695i
$389$			0.0753201i			0.00381888i	0.999998	+	0.00190944i	$0.000607794\pi$
$389$			0.0753201i			0.00381888i	−0.999998	+	0.00190944i	$0.999392\pi$
$390$	2.90023	−	2.49556i	0.146859	−	0.126368i
$391$	6.64816	−	3.83832i	0.336212	−	0.194112i
$392$	9.97308	+	17.6669i	0.503716	+	0.892311i
$393$	27.8462	+	9.74560i	1.40466	+	0.491601i
$394$	−9.26421	−	16.0461i	−0.466724	−	0.808390i
$395$	1.27597	+	2.21005i	0.0642010	+	0.111199i
$396$	−4.22221	−	10.7616i	−0.212174	−	0.540792i
$397$	19.2310	+	11.1030i	0.965175	+	0.557244i	0.897762	−	0.440481i	$-0.145192\pi$
$397$	19.2310	+	11.1030i	0.965175	+	0.557244i	0.0674134	+	0.997725i	$0.478525\pi$
$398$	1.00925	−	1.74807i	0.0505890	−	0.0876228i
$399$	20.7056	+	14.2660i	1.03658	+	0.714192i
$400$	0.172614	+	0.298976i	0.00863068	+	0.0149488i
$401$		−	30.5299i		−	1.52459i	−0.647228	−	0.762296i	$-0.724072\pi$
$401$		−	30.5299i		−	1.52459i	0.647228	−	0.762296i	$-0.275928\pi$
$402$	−2.12741	+	6.07868i	−0.106106	+	0.303177i
$403$	−1.26555			−0.0630415
$404$	0.536176	−	0.928685i	0.0266758	−	0.0462038i
$405$	2.00068	+	8.77481i	0.0994148	+	0.436024i
$406$	10.2744	−	2.69976i	0.509910	−	0.133987i
$407$	22.1221	+	12.7722i	1.09655	+	0.633094i
$408$	−5.07366	+	0.959688i	−0.251183	+	0.0475116i
$409$	10.2154	+	5.89788i	0.505120	+	0.291631i	0.730826	−	0.682564i	$-0.239135\pi$
$409$	10.2154	+	5.89788i	0.505120	+	0.291631i	−0.225705	+	0.974196i	$0.572469\pi$
$410$	−0.108507	−	0.0626465i	−0.00535878	−	0.00309389i
$411$	7.14713	−	20.4216i	0.352542	−	1.00732i
$412$	14.6403	+	8.45256i	0.721274	+	0.416428i
$413$	0.445519	−	1.63106i	0.0219226	−	0.0802594i
$414$	−3.06516	+	20.3202i	−0.150644	+	0.998686i
$415$	−2.30553	+	3.99329i	−0.113174	+	0.196023i
$416$	13.1872			0.646558
$417$	−21.1864	+	4.00744i	−1.03750	+	0.196245i
$418$			16.7667i			0.820085i
$419$	−10.3221	−	17.8785i	−0.504269	−	0.873419i	−0.999988	−	0.00493642i	$-0.998429\pi$
$419$	−10.3221	−	17.8785i	−0.504269	−	0.873419i	0.495719	−	0.868483i	$-0.334905\pi$
$420$	−3.00945	+	4.36792i	−0.146846	+	0.213133i
$421$	3.04804	−	5.27936i	0.148552	−	0.257300i	−0.782140	−	0.623102i	$-0.785872\pi$
$421$	3.04804	−	5.27936i	0.148552	−	0.257300i	0.930693	+	0.365802i	$0.119205\pi$
$422$	−19.9978	−	11.5457i	−0.973478	−	0.562038i
$423$	4.04045	−	26.7859i	0.196453	−	1.30237i
$424$	2.07683	+	3.59718i	0.100860	+	0.174694i
$425$	−0.514321	−	0.890831i	−0.0249483	−	0.0432116i
$426$	−1.19260	−	6.30499i	−0.0577815	−	0.305478i
$427$	−19.2120	+	19.0268i	−0.929735	+	0.920773i
$428$	−17.7916	+	10.2720i	−0.859989	+	0.496515i
$429$	2.57914	+	13.6353i	0.124522	+	0.658321i
$430$			10.3799i			0.500562i
$431$	6.83329	−	3.94520i	0.329148	−	0.190034i	−0.326315	−	0.945261i	$-0.605807\pi$
$431$	6.83329	−	3.94520i	0.329148	−	0.190034i	0.655463	+	0.755227i	$0.272474\pi$
$432$	0.838483	−	1.58583i	0.0403415	−	0.0762983i
$433$			32.8591i			1.57911i	0.613681	+	0.789554i	$0.289688\pi$
$433$			32.8591i			1.57911i	−0.613681	+	0.789554i	$0.710312\pi$
$434$	−1.23511	+	0.324545i	−0.0592873	+	0.0155786i
$435$	4.94185	+	5.74320i	0.236944	+	0.275365i
$436$	−12.7401			−0.610140
$437$	−20.4742	+	35.4624i	−0.979415	+	1.69640i
$438$	−7.50578	+	6.45850i	−0.358640	+	0.308599i
$439$	24.5966	−	14.2008i	1.17393	−	0.677769i	0.219328	−	0.975651i	$-0.429613\pi$
$439$	24.5966	−	14.2008i	1.17393	−	0.677769i	0.954603	+	0.297882i	$0.0962801\pi$
$440$	−9.64845			−0.459972
$441$	20.7338	+	3.33323i	0.987323	+	0.158725i
$442$	2.27228			0.108081
$443$	−13.1177	+	7.57351i	−0.623241	+	0.359828i	−0.778130	−	0.628104i	$-0.783831\pi$
$443$	−13.1177	+	7.57351i	−0.623241	+	0.359828i	0.154889	+	0.987932i	$0.450498\pi$
$444$	−2.85905	−	15.1152i	−0.135684	−	0.717333i
$445$	−7.33999	+	12.7132i	−0.347949	+	0.602665i
$446$	−18.4885			−0.875458
$447$	−3.78524	+	10.8156i	−0.179036	+	0.511561i
$448$	14.6369	−	3.84607i	0.691528	−	0.181710i
$449$			28.6814i			1.35356i	0.736186	+	0.676779i	$0.236625\pi$
$449$			28.6814i			1.35356i	−0.736186	+	0.676779i	$0.763375\pi$
$450$	2.72284	+	0.410721i	0.128356	+	0.0193616i
$451$	0.393549	−	0.227216i	0.0185315	−	0.0106992i
$452$			10.4162i			0.489937i
$453$	−17.4113	−	6.09361i	−0.818056	−	0.286303i
$454$	−4.01924	+	2.32051i	−0.188632	+	0.108907i
$455$	4.52416	−	4.48055i	0.212096	−	0.210051i
$456$	20.8783	−	17.9652i	0.977717	−	0.841296i
$457$	12.9138	+	22.3674i	0.604084	+	1.04630i	0.992196	+	0.124691i	$0.0397940\pi$
$457$	12.9138	+	22.3674i	0.604084	+	1.04630i	−0.388112	+	0.921612i	$0.626873\pi$
$458$	−2.87061	−	4.97205i	−0.134135	−	0.232329i
$459$	−2.49835	+	4.72516i	−0.116613	+	0.220551i
$460$	−7.48092	−	4.31911i	−0.348800	−	0.201380i
$461$	3.82698	−	6.62853i	0.178240	−	0.308722i	−0.763037	−	0.646354i	$-0.776293\pi$
$461$	3.82698	−	6.62853i	0.178240	−	0.308722i	0.941278	+	0.337633i	$0.109626\pi$
$462$	6.01384	+	12.6460i	0.279789	+	0.588345i
$463$	8.14770	+	14.1122i	0.378656	+	0.655851i	0.990867	−	0.134843i	$-0.0430532\pi$
$463$	8.14770	+	14.1122i	0.378656	+	0.655851i	−0.612211	+	0.790694i	$0.709720\pi$
$464$		−	1.51016i		−	0.0701075i
$465$	−0.594072	−	0.690404i	−0.0275494	−	0.0320167i
$466$	−3.37837			−0.156500
$467$	0.373515	−	0.646947i	0.0172842	−	0.0299371i	−0.857254	−	0.514894i	$-0.827831\pi$
$467$	0.373515	−	0.646947i	0.0172842	−	0.0299371i	0.874538	+	0.484957i	$0.161165\pi$
$468$	5.21124	−	6.53316i	0.240890	−	0.301996i
$469$	−2.82404	+	10.3389i	−0.130402	+	0.477408i
$470$	−7.17774	−	4.14407i	−0.331085	−	0.191152i
$471$	19.1032	+	22.2008i	0.880227	+	1.02296i
$472$	−1.60401	−	0.926075i	−0.0738305	−	0.0426261i
$473$	−32.6035	−	18.8236i	−1.49911	−	0.865511i
$474$	−2.64623	−	3.07533i	−0.121546	−	0.141255i
$475$	4.75184	+	2.74348i	0.218030	+	0.125879i
$476$	−3.04673	+	0.800574i	−0.139647	+	0.0366943i
$477$	4.25145	+	0.641300i	0.194661	+	0.0293631i
$478$	7.63089	−	13.2171i	0.349029	−	0.604536i
$479$	−16.3365			−0.746432			−0.373216	−	0.927745i	$-0.621745\pi$
$479$	−16.3365			−0.746432			−0.373216	+	0.927745i	$0.621745\pi$
$480$	6.19034	+	7.19414i	0.282549	+	0.328366i
$481$			18.4662i			0.841987i
$482$	5.58600	+	9.67523i	0.254435	+	0.440695i
$483$	−2.72278	+	34.0906i	−0.123891	+	1.55118i
$484$	0.0480289	−	0.0831885i	0.00218313	−	0.00378129i
$485$	14.8760	+	8.58869i	0.675486	+	0.389992i
$486$	−5.71806	−	13.1161i	−0.259376	−	0.594960i
$487$	4.37122	+	7.57117i	0.198079	+	0.343083i	0.947905	−	0.318552i	$-0.103196\pi$
$487$	4.37122	+	7.57117i	0.198079	+	0.343083i	−0.749827	+	0.661634i	$0.769863\pi$
$488$	14.8097	+	25.6511i	0.670402	+	1.16117i
$489$	−21.1154	+	18.1692i	−0.954872	+	0.821639i
$490$	3.26633	−	5.53299i	0.147558	−	0.249955i
$491$	−29.3202	+	16.9280i	−1.32320	+	0.763952i	−0.984238	−	0.176847i	$-0.943410\pi$
$491$	−29.3202	+	16.9280i	−1.32320	+	0.763952i	−0.338965	+	0.940799i	$0.610077\pi$
$492$	−0.258302	−	0.0904005i	−0.0116452	−	0.00407557i
$493$			4.49970i			0.202656i
$494$	−10.4969	+	6.06037i	−0.472276	+	0.272669i
$495$	−6.22789	+	7.80770i	−0.279923	+	0.350930i
$496$			0.181540i			0.00815141i
$497$	−2.71387	−	10.3281i	−0.121734	−	0.463280i
$498$	2.42159	−	6.91923i	0.108514	−	0.310058i
$499$	18.9950			0.850331			0.425166	−	0.905116i	$-0.360216\pi$
$499$	18.9950			0.850331			0.425166	+	0.905116i	$0.360216\pi$
$500$	−0.578746	+	1.00242i	−0.0258823	+	0.0448295i
$501$	−5.16816	−	27.3229i	−0.230896	−	1.22070i
$502$	−5.74800	+	3.31861i	−0.256546	+	0.148117i
$503$	−14.6172			−0.651751			−0.325875	−	0.945413i	$-0.605659\pi$
$503$	−14.6172			−0.651751			−0.325875	+	0.945413i	$0.605659\pi$
$504$	9.30344	−	21.0386i	0.414408	−	0.937132i
$505$	−0.926445			−0.0412263
$506$	−19.7493	+	11.4023i	−0.877965	+	0.506893i
$507$	9.46359	−	8.14313i	0.420293	−	0.361649i
$508$	−2.93714	+	5.08727i	−0.130314	+	0.225711i
$509$	3.18456			0.141153			0.0705765	−	0.997506i	$-0.477516\pi$
$509$	3.18456			0.141153			0.0705765	+	0.997506i	$0.477516\pi$
$510$	1.06665	+	1.23961i	0.0472321	+	0.0548910i
$511$	−11.7085	+	11.5956i	−0.517953	+	0.512961i
$512$		−	3.89276i		−	0.172037i
$513$	−1.06118	−	28.4913i	−0.0468523	−	1.25792i
$514$	−15.3975	+	8.88973i	−0.679153	+	0.392109i
$515$		−	14.6049i		−	0.643571i
$516$	4.21365	+	22.2767i	0.185496	+	0.980675i
$517$	26.0333	−	15.0303i	1.14494	−	0.661033i
$518$	4.73558	+	18.0221i	0.208069	+	0.791845i
$519$	−7.50711	−	39.6884i	−0.329526	−	1.74213i
$520$	−3.48746	−	6.04047i	−0.152935	−	0.264892i
$521$	−17.5413	−	30.3824i	−0.768498	−	1.33108i	−0.938377	−	0.345613i	$-0.887671\pi$
$521$	−17.5413	−	30.3824i	−0.768498	−	1.33108i	0.169879	−	0.985465i	$-0.445662\pi$
$522$	−9.41674	−	7.51136i	−0.412159	−	0.328763i
$523$	31.6438	+	18.2695i	1.38369	+	0.798871i	0.992594	−	0.121480i	$-0.0387641\pi$
$523$	31.6438	+	18.2695i	1.38369	+	0.798871i	0.391092	+	0.920352i	$0.372097\pi$
$524$	9.85790	−	17.0744i	0.430644	−	0.745898i
$525$	4.56803	+	0.364844i	0.199365	+	0.0159231i
$526$	10.8954	+	18.8713i	0.475061	+	0.822830i
$527$		−	0.540920i		−	0.0235628i
$528$	1.95596	−	0.369972i	0.0851224	−	0.0161010i
$529$	−32.6945			−1.42150
$530$	0.657747	−	1.13925i	0.0285707	−	0.0494859i
$531$	−1.78475	+	0.700229i	−0.0774517	+	0.0303874i
$532$	11.9392	−	11.8242i	0.517632	−	0.512642i
$533$	0.284499	+	0.164256i	0.0123230	+	0.00711471i
$534$	7.70947	−	22.0284i	0.333622	−	0.953261i
$535$	15.3708	+	8.87434i	0.664538	+	0.383671i
$536$	10.1674	+	5.87018i	0.439167	+	0.253553i
$537$	8.38500	−	1.58603i	0.361839	−	0.0684423i
$538$	−8.08316	−	4.66681i	−0.348490	−	0.201201i
$539$	11.4559	+	20.2936i	0.493440	+	0.874106i
$540$	6.01034	−	0.223860i	0.258644	−	0.00963339i
$541$	4.86502	−	8.42646i	0.209164	−	0.362282i	−0.742288	−	0.670081i	$-0.766259\pi$
$541$	4.86502	−	8.42646i	0.209164	−	0.362282i	0.951451	+	0.307799i	$0.0995926\pi$
$542$	−5.28849			−0.227160
$543$	5.92216	−	16.9215i	0.254144	−	0.726170i
$544$			5.63648i			0.241662i
$545$	5.50332	+	9.53203i	0.235736	+	0.408307i
$546$	−5.74338	+	8.33593i	−0.245794	+	0.356745i
$547$	21.3679	−	37.0103i	0.913626	−	1.58245i	0.104726	−	0.994501i	$-0.466603\pi$
$547$	21.3679	−	37.0103i	0.913626	−	1.58245i	0.808900	−	0.587946i	$-0.200063\pi$
$548$	−12.5218	−	7.22949i	−0.534906	−	0.308828i
$549$	30.3167	+	4.57305i	1.29389	+	0.195173i
$550$	1.52787	+	2.64634i	0.0651484	+	0.112840i
$551$	−12.0011	−	20.7865i	−0.511263	−	0.885533i
$552$	35.3595	+	12.3751i	1.50500	+	0.526718i
$553$	−4.75107	−	4.79731i	−0.202036	−	0.204002i
$554$	4.60640	−	2.65951i	0.195707	−	0.112992i
$555$	−10.0740	+	8.66838i	−0.427618	+	0.367952i
$556$			14.4095i			0.611099i
$557$	−11.3427	+	6.54871i	−0.480606	+	0.277478i	−0.720669	−	0.693280i	$-0.756165\pi$
$557$	−11.3427	+	6.54871i	−0.480606	+	0.277478i	0.240063	+	0.970757i	$0.422832\pi$
$558$	1.13201	+	0.902959i	0.0479218	+	0.0382253i
$559$		−	27.2154i		−	1.15109i
$560$	−0.642726	−	0.648981i	−0.0271601	−	0.0274245i
$561$	−5.82801	+	1.10237i	−0.246059	+	0.0465423i
$562$	−2.86504			−0.120854
$563$	−6.84301	+	11.8524i	−0.288398	+	0.499520i	−0.973428	−	0.228995i	$-0.926456\pi$
$563$	−6.84301	+	11.8524i	−0.288398	+	0.499520i	0.685029	+	0.728516i	$0.259789\pi$
$564$	−17.0867	−	5.98000i	−0.719481	−	0.251803i
$565$	7.79331	−	4.49947i	0.327867	−	0.189294i
$566$	−0.872860			−0.0366890
$567$	−11.0196	−	21.1085i	−0.462779	−	0.886474i
$568$	−11.6977			−0.490824
$569$	3.75268	−	2.16661i	0.157321	−	0.0908291i	−0.419273	−	0.907860i	$-0.637715\pi$
$569$	3.75268	−	2.16661i	0.157321	−	0.0908291i	0.576594	+	0.817031i	$0.304382\pi$
$570$	−8.23358	−	2.88158i	−0.344867	−	0.120696i
$571$	−20.8068	+	36.0384i	−0.870736	+	1.50816i	−0.00949930	+	0.999955i	$0.503024\pi$
$571$	−20.8068	+	36.0384i	−0.870736	+	1.50816i	−0.861237	+	0.508204i	$0.830310\pi$
$572$	9.27379			0.387756
$573$	−22.0980	+	4.17987i	−0.923158	+	0.174616i
$574$	0.319780	+	0.0873467i	0.0133473	+	0.00364578i
$575$			7.46288i			0.311223i
$576$	−13.4151	−	10.7007i	−0.558961	−	0.445861i
$577$	−31.5520	+	18.2166i	−1.31353	+	0.758366i	−0.982679	−	0.185317i	$-0.940669\pi$
$577$	−31.5520	+	18.2166i	−1.31353	+	0.758366i	−0.330850	+	0.943683i	$0.607335\pi$
$578$		−	14.6328i		−	0.608643i
$579$	20.5506	−	17.6831i	0.854052	−	0.734886i
$580$	4.38498	−	2.53167i	0.182076	−	0.105122i
$581$	3.21455	−	11.7686i	0.133362	−	0.488243i
$582$	−25.7759	−	9.02103i	−1.06845	−	0.373934i
$583$	2.38561	+	4.13200i	0.0988020	+	0.171130i
$584$	9.02554	+	15.6327i	0.373479	+	0.646885i
$585$	−7.13915	−	1.07689i	−0.295167	−	0.0445238i
$586$	−4.03479	−	2.32949i	−0.166676	−	0.0962302i
$587$	6.64516	−	11.5097i	0.274275	−	0.475058i	−0.695677	−	0.718355i	$-0.744895\pi$
$587$	6.64516	−	11.5097i	0.274275	−	0.475058i	0.969952	+	0.243297i	$0.0782288\pi$
$588$	4.76392	−	13.2005i	0.196461	−	0.544381i
$589$	1.44268	+	2.49879i	0.0594446	+	0.102961i
$590$			0.586589i			0.0241495i
$591$	−11.5495	+	33.0006i	−0.475084	+	1.35746i
$592$	2.64894			0.108871
$593$	−7.12821	+	12.3464i	−0.292720	+	0.507007i	−0.974452	−	0.224596i	$-0.927894\pi$
$593$	−7.12821	+	12.3464i	−0.292720	+	0.507007i	0.681732	+	0.731602i	$0.261227\pi$
$594$	7.42172	−	14.0368i	0.304517	−	0.575935i
$595$	1.91507	+	1.93371i	0.0785103	+	0.0792744i
$596$	6.63177	+	3.82885i	0.271648	+	0.156836i
$597$	−3.74256	+	0.707908i	−0.153173	+	0.0289728i
$598$	−14.2769	−	8.24278i	−0.583826	−	0.337072i
$599$	9.55886	+	5.51881i	0.390564	+	0.225492i	0.682405	−	0.730975i	$-0.260934\pi$
$599$	9.55886	+	5.51881i	0.390564	+	0.225492i	−0.291840	+	0.956467i	$0.594268\pi$
$600$	1.65822	−	4.73805i	0.0676965	−	0.193430i
$601$	22.2316	+	12.8354i	0.906848	+	0.523569i	0.879416	−	0.476055i	$-0.157934\pi$
$601$	22.2316	+	12.8354i	0.906848	+	0.523569i	0.0274320	+	0.999624i	$0.491267\pi$
$602$	−6.97928	−	26.5609i	−0.284454	−	1.08254i
$603$	11.3131	−	4.43859i	0.460707	−	0.180753i
$604$	−6.16382	+	10.6761i	−0.250802	+	0.434402i
$605$	−0.0829878			−0.00337394
$606$	1.44722	−	0.273743i	0.0587892	−	0.0111200i
$607$			14.6309i			0.593851i	0.954901	+	0.296925i	$0.0959613\pi$
$607$			14.6309i			0.593851i	−0.954901	+	0.296925i	$0.904039\pi$
$608$	−15.0330	−	26.0379i	−0.609668	−	1.05598i
$609$	−16.5073	−	11.3734i	−0.668909	−	0.460871i
$610$	4.69033	−	8.12388i	0.189906	−	0.328926i
$611$	18.8196	+	10.8655i	0.761361	+	0.439572i
$612$	2.79240	+	2.22739i	0.112876	+	0.0900367i
$613$	−14.6538	−	25.3812i	−0.591863	−	1.02514i	−0.993981	−	0.109549i	$-0.965059\pi$
$613$	−14.6538	−	25.3812i	−0.591863	−	1.02514i	0.402119	−	0.915588i	$-0.368274\pi$
$614$	7.04015	+	12.1939i	0.284117	+	0.492106i
$615$	0.0439416	+	0.232310i	0.00177190	+	0.00936763i
$616$	24.6893	−	6.48749i	0.994760	−	0.261388i
$617$	38.5718	−	22.2695i	1.55284	−	0.896535i	0.554935	−	0.831894i	$-0.312743\pi$
$617$	38.5718	−	22.2695i	1.55284	−	0.896535i	0.997909	−	0.0646407i	$-0.0205901\pi$
$618$	4.31542	+	22.8147i	0.173592	+	0.917741i
$619$		−	29.9664i		−	1.20445i	−0.798325	−	0.602226i	$-0.794280\pi$
$619$		−	29.9664i		−	1.20445i	0.798325	−	0.602226i	$-0.205720\pi$
$620$	−0.527129	+	0.304338i	−0.0211700	+	0.0122225i
$621$	32.8380	−	20.6256i	1.31774	−	0.827678i
$622$			4.36107i			0.174863i
$623$	10.2340	−	37.4670i	0.410016	−	1.50108i
$624$	0.938612	+	1.09081i	0.0375746	+	0.0436675i
$625$	1.00000			0.0400000
$626$	2.31838	−	4.01555i	0.0926610	−	0.160494i
$627$	23.9825	−	20.6362i	0.957770	−	0.824132i
$628$	16.9505	−	9.78639i	0.676400	−	0.390520i
$629$	−7.89281			−0.314707
$630$	−7.24361	+	0.779816i	−0.288592	+	0.0310686i
$631$	−37.6515			−1.49888			−0.749441	−	0.662072i	$-0.769677\pi$
$631$	−37.6515			−1.49888			−0.749441	+	0.662072i	$0.769677\pi$
$632$	−6.40517	+	3.69802i	−0.254784	+	0.147099i
$633$	8.09843	+	42.8146i	0.321884	+	1.70173i
$634$	2.86584	−	4.96379i	0.113817	−	0.197137i
$635$	5.07500			0.201395
$636$	0.949145	−	2.71200i	0.0376360	−	0.107538i
$637$	−8.56414	+	14.5072i	−0.339324	+	0.574796i
$638$		−	13.3670i		−	0.529205i
$639$	−7.55063	+	9.46597i	−0.298698	+	0.374468i
$640$	4.94393	−	2.85438i	0.195426	−	0.112829i
$641$			36.2589i			1.43214i	0.698029	+	0.716070i	$0.254061\pi$
$641$			36.2589i			1.43214i	−0.698029	+	0.716070i	$0.745939\pi$
$642$	−26.6332	−	9.32106i	−1.05113	−	0.367873i
$643$	17.1983	−	9.92942i	0.678233	−	0.391578i	−0.120956	−	0.992658i	$-0.538596\pi$
$643$	17.1983	−	9.92942i	0.678233	−	0.391578i	0.799189	+	0.601080i	$0.205263\pi$
$644$	22.0469	+	6.02204i	0.868771	+	0.237302i
$645$	14.8470	−	12.7754i	0.584601	−	0.503032i
$646$	−2.59032	−	4.48656i	−0.101915	−	0.176521i
$647$	19.8660	+	34.4089i	0.781013	+	1.35275i	0.931352	+	0.364120i	$0.118630\pi$
$647$	19.8660	+	34.4089i	0.781013	+	1.35275i	−0.150339	+	0.988635i	$0.548036\pi$
$648$	−25.4312	+	5.79839i	−0.999032	+	0.227782i
$649$	−1.84249	−	1.06376i	−0.0723242	−	0.0417564i
$650$	−1.10450	+	1.91306i	−0.0433222	+	0.0750363i
$651$	1.98438	+	1.36722i	0.0777740	+	0.0535855i
$652$	9.30792	+	16.1218i	0.364526	+	0.631378i
$653$			14.1523i			0.553821i	0.960896	+	0.276911i	$0.0893106\pi$
$653$			14.1523i			0.553821i	−0.960896	+	0.276911i	$0.910689\pi$
$654$	−11.4133	−	13.2641i	−0.446297	−	0.518666i
$655$	−17.0332			−0.665542
$656$	0.0235622	−	0.0408109i	0.000919948	−	0.00159340i
$657$	18.4761	+	2.78698i	0.720820	+	0.108730i
$658$	21.1534	+	5.77799i	0.824647	+	0.225249i
$659$	−0.827193	−	0.477580i	−0.0322229	−	0.0186039i	0.483802	−	0.875177i	$-0.339255\pi$
$659$	−0.827193	−	0.477580i	−0.0322229	−	0.0186039i	−0.516025	+	0.856574i	$0.672589\pi$
$660$	4.35329	+	5.05920i	0.169451	+	0.196929i
$661$	3.56567	+	2.05864i	0.138688	+	0.0800718i	0.567739	−	0.823209i	$-0.307818\pi$
$661$	3.56567	+	2.05864i	0.138688	+	0.0800718i	−0.429050	+	0.903281i	$0.641152\pi$
$662$	−20.4746	−	11.8210i	−0.795769	−	0.459438i
$663$	−2.79670	−	3.25020i	−0.108615	−	0.126227i
$664$	−11.5734	−	6.68189i	−0.449134	−	0.259308i
$665$	−14.0041	−	3.82517i	−0.543056	−	0.148334i
$666$	13.1755	−	16.5177i	0.510540	−	0.640047i
$667$	16.3228	−	28.2719i	0.632022	−	1.09469i
$668$	−18.5831			−0.719001
$669$	22.7555	+	26.4454i	0.879779	+	1.02244i
$670$		−	3.71825i		−	0.143649i
$671$	17.0116	+	29.4649i	0.656725	+	1.13748i
$672$	−20.6776	−	14.2467i	−0.797656	−	0.549577i
$673$	9.85223	−	17.0646i	0.379776	−	0.657791i	−0.611254	−	0.791435i	$-0.709335\pi$
$673$	9.85223	−	17.0646i	0.379776	−	0.657791i	0.991029	+	0.133644i	$0.0426678\pi$
$674$	15.2188	+	8.78655i	0.586204	+	0.338445i
$675$	−2.76377	−	4.40018i	−0.106377	−	0.169363i
$676$	−4.17166	−	7.22553i	−0.160448	−	0.277905i
$677$	−13.0201	−	22.5514i	−0.500402	−	0.866721i	−1.00000		0.000464024i	$-0.999852\pi$
$677$	−13.0201	−	22.5514i	−0.500402	−	0.866721i	0.499598	−	0.866257i	$-0.333481\pi$
$678$	−10.8446	+	9.33145i	−0.416484	+	0.358372i
$679$	−43.8410	−	11.9750i	−1.68246	−	0.459559i
$680$	2.58181	−	1.49061i	0.0990079	−	0.0571623i
$681$	8.26602	+	2.89294i	0.316755	+	0.110858i
$682$			1.60688i			0.0615307i
$683$	24.1050	−	13.9170i	0.922352	−	0.532520i	0.0379673	−	0.999279i	$-0.487912\pi$
$683$	24.1050	−	13.9170i	0.922352	−	0.532520i	0.884385	+	0.466759i	$0.154578\pi$
$684$	−18.8402	−	2.84190i	−0.720373	−	0.108663i
$685$			12.4916i			0.477281i
$686$	−4.63786	+	16.3545i	−0.177074	+	0.624419i
$687$	−3.57874	+	10.2256i	−0.136538	+	0.390130i
$688$	−3.90400			−0.148839
$689$	−1.72458	+	2.98705i	−0.0657011	+	0.113798i
$690$	−2.20510	−	11.6579i	−0.0839469	−	0.443809i
$691$	−30.5959	+	17.6645i	−1.16392	+	0.671990i	−0.952241	−	0.305349i	$-0.901227\pi$
$691$	−30.5959	+	17.6645i	−1.16392	+	0.671990i	−0.211681	+	0.977339i	$0.567894\pi$
$692$	−26.9932			−1.02613
$693$	10.6867	−	24.1666i	0.405953	−	0.918012i
$694$	−25.9293			−0.984262
$695$	10.7811	−	6.22445i	0.408949	−	0.236107i
$696$	−16.6450	+	14.3225i	−0.630926	+	0.542893i
$697$	−0.0702061	+	0.121600i	−0.00265924	+	0.00460595i
$698$	−28.3286			−1.07225
$699$	4.15807	+	4.83232i	0.157273	+	0.182775i
$700$	0.806933	−	2.95421i	0.0304992	−	0.111659i
$701$		−	1.50708i		−	0.0569216i	−0.999595	−	0.0284608i	$-0.990939\pi$
$701$		−	1.50708i		−	0.0569216i	0.999595	−	0.0284608i	$-0.00906057\pi$
$702$	11.4704	−	0.427224i	0.432922	−	0.0161245i
$703$	36.4611	−	21.0508i	1.37515	−	0.793946i
$704$		−	19.0426i		−	0.717695i
$705$	2.90674	+	15.3673i	0.109474	+	0.578766i
$706$	−3.26849	+	1.88706i	−0.123011	+	0.0710205i
$707$	2.37067	−	0.622929i	0.0891581	−	0.0234277i
$708$	0.238123	+	1.25890i	0.00894920	+	0.0473125i
$709$	11.2167	+	19.4279i	0.421252	+	0.729630i	0.996062	−	0.0886568i	$-0.0282574\pi$
$709$	11.2167	+	19.4279i	0.421252	+	0.729630i	−0.574810	+	0.818287i	$0.694924\pi$
$710$	1.85237	+	3.20840i	0.0695181	+	0.120409i
$711$	−1.14191	+	7.57018i	−0.0428248	+	0.283904i
$712$	−36.8456	−	21.2728i	−1.38085	−	0.797232i
$713$	−1.96221	+	3.39864i	−0.0734852	+	0.127280i
$714$	−3.56294	−	2.45483i	−0.133340	−	0.0918697i
$715$	−4.00598	−	6.93856i	−0.149815	−	0.259488i
$716$		−	5.70288i		−	0.213126i
$717$	−28.2973	+	5.35247i	−1.05678	+	0.199892i
$718$	31.3025			1.16820
$719$	8.29632	−	14.3697i	0.309401	−	0.535898i	−0.668831	−	0.743415i	$-0.733205\pi$
$719$	8.29632	−	14.3697i	0.309401	−	0.535898i	0.978231	+	0.207517i	$0.0665383\pi$
$720$	−0.154477	+	1.02410i	−0.00575703	+	0.0381658i
$721$	9.82017	+	37.3724i	0.365722	+	1.39182i
$722$	8.82880	+	5.09731i	0.328574	+	0.189702i
$723$	6.96396	−	19.8982i	0.258992	−	0.740022i
$724$	−10.3757	−	5.99040i	−0.385609	−	0.222632i
$725$	−3.78834	−	2.18720i	−0.140696	−	0.0812306i
$726$	0.129637	−	0.0245210i	0.00481128	−	0.000910058i
$727$	−18.9787	−	10.9574i	−0.703881	−	0.406386i	0.104910	−	0.994482i	$-0.466544\pi$
$727$	−18.9787	−	10.9574i	−0.703881	−	0.406386i	−0.808791	+	0.588096i	$0.799878\pi$
$728$	12.9856	+	13.1119i	0.481277	+	0.485961i
$729$	−11.7232	+	24.3221i	−0.434192	+	0.900820i
$730$	2.85845	−	4.95098i	0.105796	−	0.183244i
$731$	11.6324			0.430240
$732$	6.76826	−	19.3390i	0.250162	−	0.714791i
$733$		−	28.6403i		−	1.05785i	−0.848667	−	0.528927i	$-0.822594\pi$
$733$		−	28.6403i		−	1.05785i	0.848667	−	0.528927i	$-0.177406\pi$
$734$	2.18521	+	3.78489i	0.0806575	+	0.139703i
$735$	−11.9344	+	2.13789i	−0.440206	+	0.0788572i
$736$	20.4465	−	35.4144i	0.753669	−	1.30539i
$737$	11.6791	+	6.74296i	0.430207	+	0.248380i
$738$	−0.137284	−	0.349912i	−0.00505350	−	0.0128804i
$739$	−19.2498	−	33.3415i	−0.708114	−	1.22649i	−0.965556	−	0.260195i	$-0.916213\pi$
$739$	−19.2498	−	33.3415i	−0.708114	−	1.22649i	0.257442	−	0.966294i	$-0.417120\pi$
$740$	4.44074	+	7.69159i	0.163245	+	0.282748i
$741$	21.5880	+	7.55535i	0.793055	+	0.277553i
$742$	−0.917082	+	3.35747i	−0.0336671	+	0.123257i
$743$	−11.8750	+	6.85605i	−0.435653	+	0.251524i	−0.701752	−	0.712421i	$-0.747598\pi$
$743$	−11.8750	+	6.85605i	−0.435653	+	0.251524i	0.266099	+	0.963946i	$0.414265\pi$
$744$	2.00093	−	1.72174i	0.0733578	−	0.0631222i
$745$		−	6.61577i		−	0.242383i
$746$	16.8986	−	9.75641i	0.618702	−	0.357208i
$747$	−12.8775	+	5.05235i	−0.471163	+	0.184856i
$748$			3.96379i			0.144931i
$749$	−45.2991	−	12.3733i	−1.65519	−	0.452110i
$750$	−1.56212	+	0.295477i	−0.0570405	+	0.0107893i
$751$	−47.7091			−1.74093			−0.870464	−	0.492232i	$-0.836181\pi$
$751$	−47.7091			−1.74093			−0.870464	+	0.492232i	$0.836181\pi$
$752$	1.55864	−	2.69964i	0.0568377	−	0.0984457i
$753$	11.8214	+	4.13725i	0.430796	+	0.150770i
$754$	8.36848	−	4.83155i	0.304762	−	0.175955i
$755$	10.6503			0.387604
$756$	−15.2292	+	4.61410i	−0.553882	+	0.167813i
$757$	−25.7065			−0.934318			−0.467159	−	0.884173i	$-0.654722\pi$
$757$	−25.7065			−0.934318			−0.467159	+	0.884173i	$0.654722\pi$
$758$	10.5948	−	6.11692i	0.384821	−	0.222176i
$759$	40.6167	+	14.2150i	1.47429	+	0.515972i
$760$	−7.95116	+	13.7718i	−0.288419	+	0.499556i
$761$	41.0535			1.48819			0.744094	−	0.668075i	$-0.232881\pi$
$761$	41.0535			1.48819			0.744094	+	0.668075i	$0.232881\pi$
$762$	−7.92776	+	1.49954i	−0.287192	+	0.0543227i
$763$	−20.4916	−	20.6910i	−0.741845	−	0.749065i
$764$			15.0295i			0.543748i
$765$	0.460282	−	3.05141i	0.0166415	−	0.110324i
$766$	6.41385	−	3.70304i	0.231742	−	0.133796i
$767$		−	1.53800i		−	0.0555341i
$768$	−21.8994	+	18.8437i	−0.790225	+	0.679965i
$769$	42.5439	−	24.5627i	1.53417	−	0.885755i	0.535009	−	0.844846i	$-0.320308\pi$
$769$	42.5439	−	24.5627i	1.53417	−	0.885755i	0.999163	−	0.0409086i	$-0.0130252\pi$
$770$	−5.68900	−	5.74437i	−0.205017	−	0.207013i
$771$	31.6666	+	11.0827i	1.14045	+	0.399133i
$772$	−9.05893	−	15.6905i	−0.326038	−	0.564714i
$773$	−17.6922	−	30.6437i	−0.636343	−	1.10218i	−0.986229	−	0.165386i	$-0.947113\pi$
$773$	−17.6922	−	30.6437i	−0.636343	−	1.10218i	0.349886	−	0.936792i	$-0.386220\pi$
$774$	−19.4180	+	24.3437i	−0.697966	+	0.875016i
$775$	0.455406	+	0.262929i	0.0163587	+	0.00944469i
$776$	−24.8918	+	43.1138i	−0.893563	+	1.54770i
$777$	19.9497	−	28.9550i	0.715692	−	1.03876i
$778$	0.0345675	+	0.0598727i	0.00123931	+	0.00214654i
$779$		−	0.748982i		−	0.0268351i
$780$	−1.59383	+	4.55406i	−0.0570682	+	0.163062i
$781$	−13.4369			−0.480810
$782$	3.52312	−	6.10223i	0.125987	−	0.218215i
$783$	0.846013	+	22.7143i	0.0302340	+	0.811743i
$784$	2.08103	+	1.22851i	0.0743224	+	0.0438753i
$785$	−14.6442	−	8.45482i	−0.522673	−	0.301766i
$786$	26.6079	−	5.03291i	0.949072	−	0.179518i
$787$	18.4392	+	10.6459i	0.657288	+	0.379486i	0.791243	−	0.611502i	$-0.209434\pi$
$787$	18.4392	+	10.6459i	0.657288	+	0.379486i	−0.133955	+	0.990987i	$0.542768\pi$
$788$	20.2349	+	11.6826i	0.720837	+	0.416175i
$789$	13.5831	−	38.8111i	0.483570	−	1.38171i
$790$	2.02856	+	1.17119i	0.0721730	+	0.0416691i
$791$	−16.9168	+	16.7537i	−0.601492	+	0.595694i
$792$	−22.6283	−	18.0497i	−0.804063	−	0.641369i
$793$	−12.2978	+	21.3004i	−0.436707	+	0.756399i
$794$	20.3825			0.723348
$795$	−2.43910	+	0.461358i	−0.0865058	+	0.0163627i
$796$			2.54542i			0.0902200i
$797$	−10.2546	−	17.7615i	−0.363237	−	0.629145i	0.625255	−	0.780421i	$-0.284995\pi$
$797$	−10.2546	−	17.7615i	−0.363237	−	0.629145i	−0.988492	+	0.151276i	$0.951662\pi$
$798$	23.0063	+	1.83749i	0.814415	+	0.0650465i
$799$	−4.64414	+	8.04388i	−0.164298	+	0.284572i
$800$	−4.74542	−	2.73977i	−0.167776	−	0.0968654i
$801$	−40.9974	+	16.0849i	−1.44857	+	0.568332i
$802$	−14.0114	−	24.2685i	−0.494761	−	0.856952i
$803$	10.3675	+	17.9570i	0.365860	+	0.633688i
$804$	−1.50941	−	7.97990i	−0.0532326	−	0.281429i
$805$	−5.01794	−	19.0966i	−0.176859	−	0.673068i
$806$	−1.00600	+	0.580812i	−0.0354347	+	0.0204582i
$807$	3.27340	+	17.3058i	0.115229	+	0.609192i
$808$		−	2.68503i		−	0.0944590i
$809$	−13.2943	+	7.67546i	−0.467402	+	0.269855i	−0.715152	−	0.698969i	$-0.753642\pi$
$809$	−13.2943	+	7.67546i	−0.467402	+	0.269855i	0.247750	+	0.968824i	$0.420309\pi$
$810$	5.61748	+	6.05698i	0.197378	+	0.212821i
$811$		−	11.9457i		−	0.419470i	−0.977758	−	0.209735i	$-0.932740\pi$
$811$		−	11.9457i		−	0.419470i	0.977758	−	0.209735i	$-0.0672601\pi$
$812$	−9.51840	+	9.42665i	−0.334030	+	0.330811i
$813$	6.50902	+	7.56449i	0.228281	+	0.265298i
$814$	23.4467			0.821808
$815$	8.04145	−	13.9282i	0.281680	−	0.487884i
$816$	−0.466235	+	0.401181i	−0.0163215	+	0.0140441i
$817$	−53.7362	+	31.0246i	−1.87999	+	1.08541i
$818$	10.8271			0.378561
$819$	18.9923	−	2.04464i	0.663646	−	0.0714453i
$820$	0.158000			0.00551761
$821$	3.91641	−	2.26114i	0.136684	−	0.0789143i	−0.430099	−	0.902782i	$-0.641521\pi$
$821$	3.91641	−	2.26114i	0.136684	−	0.0789143i	0.566782	+	0.823867i	$0.308188\pi$
$822$	−3.69098	−	19.5134i	−0.128738	−	0.680609i
$823$	5.33186	−	9.23505i	0.185857	−	0.321914i	−0.758008	−	0.652245i	$-0.773827\pi$
$823$	5.33186	−	9.23505i	0.185857	−	0.321914i	0.943865	+	0.330332i	$0.107161\pi$
$824$	42.3281			1.47457
$825$	1.90476	−	5.44250i	0.0663153	−	0.189484i
$826$	−0.394414	−	1.50101i	−0.0137234	−	0.0522270i
$827$		−	41.3589i		−	1.43819i	−0.694911	−	0.719096i	$-0.744556\pi$
$827$		−	41.3589i		−	1.43819i	0.694911	−	0.719096i	$-0.255444\pi$
$828$	−9.46493	−	24.1244i	−0.328929	−	0.838379i
$829$	−18.1833	+	10.4981i	−0.631531	+	0.364615i	−0.781345	−	0.624100i	$-0.785466\pi$
$829$	−18.1833	+	10.4981i	−0.631531	+	0.364615i	0.149814	+	0.988714i	$0.452133\pi$
$830$			4.23241i			0.146909i
$831$	−9.47359	−	3.31556i	−0.328635	−	0.115015i
$832$	11.9217	−	6.88301i	0.413311	−	0.238625i
$833$	−6.20065	−	3.66048i	−0.214840	−	0.126828i
$834$	−15.0021	+	12.9089i	−0.519481	+	0.446998i
$835$	8.02730	+	13.9037i	0.277796	+	0.481157i
$836$	−10.5718	−	18.3109i	−0.365633	−	0.633294i
$837$	−0.101701	−	2.73054i	−0.00351531	−	0.0943814i
$838$	−16.4103	−	9.47450i	−0.566885	−	0.327291i
$839$	5.38932	−	9.33457i	0.186060	−	0.322265i	−0.757873	−	0.652402i	$-0.773761\pi$
$839$	5.38932	−	9.33457i	0.186060	−	0.322265i	0.943933	+	0.330137i	$0.107095\pi$
$840$	−1.05739	+	13.2391i	−0.0364835	+	0.456792i
$841$	−4.93230	−	8.54300i	−0.170079	−	0.294586i
$842$		−	5.59549i		−	0.192833i
$843$	3.52626	+	4.09806i	0.121451	+	0.141145i
$844$	29.1194			1.00233
$845$	−3.60405	+	6.24240i	−0.123983	+	0.214745i
$846$	−9.08135	−	23.1467i	−0.312223	−	0.795799i
$847$	0.212356	−	0.0557999i	0.00729665	−	0.00191731i
$848$	0.428487	+	0.247387i	0.0147143	+	0.00849530i
$849$	1.07431	+	1.24851i	0.0368701	+	0.0428488i
$850$	−0.817678	−	0.472086i	−0.0280461	−	0.0161924i
$851$	49.5911	+	28.6315i	1.69996	+	0.981474i
$852$	5.27788	+	6.13371i	0.180817	+	0.210138i
$853$	17.6017	+	10.1624i	0.602672	+	0.347953i	0.770092	−	0.637933i	$-0.220210\pi$
$853$	17.6017	+	10.1624i	0.602672	+	0.347953i	−0.167420	+	0.985886i	$0.553544\pi$
$854$	−6.53962	+	23.9418i	−0.223781	+	0.819272i
$855$	6.01208	+	15.3237i	0.205609	+	0.524059i
$856$	−25.7197	+	44.5478i	−0.879080	+	1.52261i
$857$	19.6106			0.669886			0.334943	−	0.942238i	$-0.391283\pi$
$857$	19.6106			0.669886			0.334943	+	0.942238i	$0.391283\pi$
$858$	8.30800	+	9.65519i	0.283631	+	0.329623i
$859$			35.6168i			1.21523i	0.794232	+	0.607614i	$0.207873\pi$
$859$			35.6168i			1.21523i	−0.794232	+	0.607614i	$0.792127\pi$
$860$	−6.54475	−	11.3358i	−0.223174	−	0.386549i
$861$	−0.268643	−	0.564908i	−0.00915535	−	0.0192520i
$862$	3.62123	−	6.27216i	0.123340	−	0.213630i
$863$	−37.2781	−	21.5225i	−1.26896	−	0.732635i	−0.294169	−	0.955753i	$-0.595043\pi$
$863$	−37.2781	−	21.5225i	−1.26896	−	0.732635i	−0.974791	+	0.223119i	$0.928376\pi$
$864$	1.05975	+	28.4528i	0.0360533	+	0.967983i
$865$	11.6602	+	20.1961i	0.396459	+	0.686688i
$866$	15.0804	+	26.1200i	0.512453	+	0.887594i
$867$	−20.9303	+	18.0099i	−0.710829	+	0.611647i
$868$	1.14423	−	1.13320i	0.0388377	−	0.0384634i
$869$	−7.35749	+	4.24785i	−0.249586	+	0.144098i
$870$	6.56411	+	2.29730i	0.222544	+	0.0778858i
$871$			9.74905i			0.330334i
$872$	−27.6258	+	15.9498i	−0.935527	+	0.540127i
$873$	18.8213	+	47.9721i	0.637005	+	1.62361i
$874$			37.5859i			1.27136i
$875$	−2.55889	+	0.672387i	−0.0865061	+	0.0227308i
$876$	4.12482	−	11.7859i	0.139365	−	0.398208i
$877$	−4.99458			−0.168655			−0.0843275	−	0.996438i	$-0.526874\pi$
$877$	−4.99458			−0.168655			−0.0843275	+	0.996438i	$0.526874\pi$
$878$	13.0347	−	22.5768i	0.439900	−	0.761929i
$879$	1.63395	+	8.63834i	0.0551118	+	0.291364i
$880$	−0.995323	+	0.574650i	−0.0335523	+	0.0193714i
$881$	−2.26648			−0.0763596			−0.0381798	−	0.999271i	$-0.512156\pi$
$881$	−2.26648			−0.0763596			−0.0381798	+	0.999271i	$0.512156\pi$
$882$	18.0112	−	6.86597i	0.606470	−	0.231189i
$883$	−0.714022			−0.0240287			−0.0120144	−	0.999928i	$-0.503824\pi$
$883$	−0.714022			−0.0240287			−0.0120144	+	0.999928i	$0.503824\pi$
$884$	−2.48155	+	1.43273i	−0.0834637	+	0.0481878i
$885$	0.839038	−	0.721968i	0.0282040	−	0.0242687i
$886$	−6.95159	+	12.0405i	−0.233543	+	0.404509i
$887$	25.2844			0.848966			0.424483	−	0.905436i	$-0.360456\pi$
$887$	25.2844			0.848966			0.424483	+	0.905436i	$0.360456\pi$
$888$	−25.1228	−	29.1965i	−0.843064	−	0.979772i
$889$	−12.9863	+	3.41236i	−0.435548	+	0.114447i
$890$			13.4745i			0.451666i
$891$	−29.2123	+	6.66050i	−0.978650	+	0.223135i
$892$	20.1913	−	11.6575i	0.676055	−	0.390321i
$893$		−	49.5452i		−	1.65797i
$894$	1.95481	+	10.3346i	0.0653785	+	0.345642i
$895$	−4.26684	+	2.46346i	−0.142625	+	0.0823444i
$896$	−10.7317	+	10.6283i	−0.358521	+	0.355066i
$897$	5.78166	+	30.5664i	0.193044	+	1.02058i
$898$	13.1631	+	22.7991i	0.439257	+	0.760816i
$899$	−1.15016	−	1.99213i	−0.0383599	−	0.0664413i
$900$	−3.23258	+	1.26827i	−0.107753	+	0.0422756i
$901$	−1.27672	−	0.737117i	−0.0425338	−	0.0245569i
$902$	0.208557	−	0.361232i	0.00694420	−	0.0120277i
$903$	−29.4018	+	42.6738i	−0.978432	+	1.42010i
$904$	13.0404	+	22.5866i	0.433717	+	0.751220i
$905$			10.3507i			0.344067i
$906$	−16.6370	+	3.14691i	−0.552729	+	0.104549i
$907$	24.2182			0.804153			0.402077	−	0.915606i	$-0.368289\pi$
$907$	24.2182			0.804153			0.402077	+	0.915606i	$0.368289\pi$
$908$	2.92627	−	5.06845i	0.0971117	−	0.168202i
$909$	−2.17277	−	1.73313i	−0.0720663	−	0.0574845i
$910$	1.53999	−	5.63795i	0.0510501	−	0.186896i
$911$	35.5518	+	20.5259i	1.17788	+	0.680052i	0.955524	−	0.294912i	$-0.0952904\pi$
$911$	35.5518	+	20.5259i	1.17788	+	0.680052i	0.222361	+	0.974964i	$0.428624\pi$
$912$	1.08380	−	3.09675i	0.0358882	−	0.102544i
$913$	−13.2941	−	7.67536i	−0.439971	−	0.254017i
$914$	20.5307	+	11.8534i	0.679094	+	0.392075i
$915$	−17.3930	+	3.28990i	−0.574993	+	0.108761i
$916$	6.26999	+	3.61998i	0.207166	+	0.119607i
$917$	43.5860	−	11.4529i	1.43934	−	0.378208i
$918$	0.182604	+	4.90267i	0.00602682	+	0.161812i
$919$	7.01306	−	12.1470i	0.231340	−	0.400692i	−0.726863	−	0.686782i	$-0.759023\pi$
$919$	7.01306	−	12.1470i	0.231340	−	0.400692i	0.958203	+	0.286091i	$0.0923558\pi$
$920$	−21.6290			−0.713085
$921$	8.77683	−	25.0781i	0.289206	−	0.826353i
$922$		−	7.02544i		−	0.231371i
$923$	−4.85681	−	8.41224i	−0.159864	−	0.276892i
$924$	−14.5413	−	10.0188i	−0.478374	−	0.329595i
$925$	3.83652	−	6.64504i	0.126144	−	0.218488i
$926$	12.9534	+	7.47863i	0.425674	+	0.245763i
$927$	27.3220	−	34.2527i	0.897373	−	1.12501i
$928$	11.9848	+	20.7584i	0.393422	+	0.681426i
$929$	−17.0386	−	29.5118i	−0.559020	−	0.968251i	−0.997579	−	0.0695482i	$-0.977844\pi$
$929$	−17.0386	−	29.5118i	−0.559020	−	0.968251i	0.438559	−	0.898702i	$-0.355489\pi$
$930$	−0.789088	−	0.276165i	−0.0258752	−	0.00905579i
$931$	38.4069	+	0.372006i	1.25873	+	0.0121920i
$932$	3.68952	−	2.13014i	0.120854	−	0.0697752i
$933$	6.23793	−	5.36756i	0.204221	−	0.175726i
$934$		−	0.685686i		−	0.0224363i
$935$	2.96568	−	1.71223i	0.0969880	−	0.0559960i
$936$	3.12104	−	20.6907i	0.102014	−	0.676297i
$937$			26.3889i			0.862087i	0.902331	+	0.431044i	$0.141854\pi$
$937$			26.3889i			0.862087i	−0.902331	+	0.431044i	$0.858146\pi$
$938$	2.50010	+	9.51458i	0.0816313	+	0.310662i
$939$	−8.59715	+	1.62616i	−0.280557	+	0.0530677i
$940$	10.4517			0.340898
$941$	23.9482	−	41.4796i	0.780690	−	1.35219i	−0.150850	−	0.988557i	$-0.548201\pi$
$941$	23.9482	−	41.4796i	0.780690	−	1.35219i	0.931540	−	0.363638i	$-0.118466\pi$
$942$	25.3742	+	8.88043i	0.826735	+	0.289340i
$943$	0.882220	−	0.509350i	0.0287290	−	0.0165867i
$944$	−0.220624			−0.00718068
$945$	10.0308	+	9.40124i	0.326301	+	0.305822i
$946$	−34.5557			−1.12350
$947$	26.5723	−	15.3415i	0.863485	−	0.498533i	−0.00169274	−	0.999999i	$-0.500539\pi$
$947$	26.5723	−	15.3415i	0.863485	−	0.498533i	0.865178	+	0.501465i	$0.167205\pi$
$948$	4.82902	+	1.69006i	0.156839	+	0.0548905i
$949$	−7.49470	+	12.9812i	−0.243288	+	0.421388i
$950$	5.03638			0.163402
$951$	−10.6273	+	2.01016i	−0.344614	+	0.0651840i
$952$	−5.60429	+	5.55027i	−0.181636	+	0.179885i
$953$			9.18788i			0.297625i	0.988865	+	0.148812i	$0.0475450\pi$
$953$			9.18788i			0.297625i	−0.988865	+	0.148812i	$0.952455\pi$
$954$	3.67384	−	1.44139i	0.118945	−	0.0466668i
$955$	11.2449	−	6.49227i	0.363878	−	0.210085i
$956$			19.2458i			0.622455i
$957$	−19.1197	+	16.4520i	−0.618054	+	0.531817i
$958$	−12.9860	+	7.49747i	−0.419559	+	0.242232i
$959$	−8.39921	−	31.9647i	−0.271225	−	1.03219i
$960$	9.35121	+	3.27273i	0.301809	+	0.105627i
$961$	−15.3617	−	26.6073i	−0.495540	−	0.858300i
$962$	8.47490	+	14.6790i	0.273242	+	0.473269i
$963$	19.4473	+	49.5675i	0.626680	+	1.59729i
$964$	−12.2009	−	7.04420i	−0.392965	−	0.226878i
$965$	−7.82634	+	13.5556i	−0.251939	+	0.436371i
$966$	13.4812	+	28.3486i	0.433751	+	0.912100i
$967$	−16.7754	−	29.0558i	−0.539460	−	0.934373i	−0.998933	−	0.0461809i	$-0.985295\pi$
$967$	−16.7754	−	29.0558i	−0.539460	−	0.934373i	0.459473	−	0.888192i	$-0.348038\pi$
$968$		−	0.240516i		−	0.00773047i
$969$	−3.22930	+	9.22712i	−0.103740	+	0.296418i
$970$	15.7668			0.506242
$971$	−8.21003	+	14.2202i	−0.263472	+	0.456348i	−0.967162	−	0.254160i	$-0.918201\pi$
$971$	−8.21003	+	14.2202i	−0.263472	+	0.456348i	0.703690	+	0.710507i	$0.251534\pi$
$972$	14.5147	+	10.7188i	0.465560	+	0.343804i
$973$	−23.4023	+	23.1767i	−0.750242	+	0.743011i
$974$	6.94944	+	4.01226i	0.222675	+	0.128561i
$975$	4.09579	−	0.774723i	0.131170	−	0.0248110i
$976$	3.05550	+	1.76409i	0.0978040	+	0.0564672i
$977$	−10.9846	−	6.34195i	−0.351428	−	0.202897i	0.313886	−	0.949461i	$-0.398369\pi$
$977$	−10.9846	−	6.34195i	−0.351428	−	0.202897i	−0.665314	+	0.746564i	$0.731702\pi$
$978$	−8.44625	+	24.1336i	−0.270081	+	0.771707i
$979$	−42.3238	−	24.4356i	−1.35267	−	0.780966i
$980$	−0.0784759	+	8.10207i	−0.00250682	+	0.258811i
$981$	−4.92509	+	32.6505i	−0.157246	+	1.04245i
$982$	−15.5380	+	26.9125i	−0.495836	+	0.858813i
$983$	43.9531			1.40189			0.700943	−	0.713218i	$-0.252763\pi$
$983$	43.9531			1.40189			0.700943	+	0.713218i	$0.252763\pi$
$984$	−0.673281	+	0.127352i	−0.0214634	+	0.00405983i
$985$		−	20.1861i		−	0.643181i
$986$	2.06510	+	3.57685i	0.0657661	+	0.113910i
$987$	−17.7708	−	37.3687i	−0.565650	−	1.18946i
$988$	7.64241	−	13.2370i	0.243137	−	0.421126i
$989$	−73.0873	−	42.1969i	−2.32404	−	1.34178i
$990$	−1.36734	+	9.06465i	−0.0434568	+	0.288094i
$991$	0.567163	+	0.982355i	0.0180165	+	0.0312055i	0.874893	−	0.484316i	$-0.160932\pi$
$991$	0.567163	+	0.982355i	0.0180165	+	0.0312055i	−0.856877	+	0.515522i	$0.827598\pi$
$992$	−1.44073	−	2.49541i	−0.0457432	−	0.0792295i
$993$	8.29153	+	43.8355i	0.263124	+	1.39108i
$994$	−6.89728	−	6.96441i	−0.218768	−	0.220898i
$995$	1.90446	−	1.09954i	0.0603754	−	0.0348578i
$996$	1.71812	+	9.08334i	0.0544408	+	0.287817i
$997$		−	48.4786i		−	1.53533i	−0.640849	−	0.767667i	$-0.721418\pi$
$997$		−	48.4786i		−	1.53533i	0.640849	−	0.767667i	$-0.278582\pi$
$998$	15.0993	−	8.71757i	0.477959	−	0.275950i
$999$	−39.8426	+	1.48397i	−1.26057	+	0.0469507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.236.10	yes	30
3.2	odd	2		945.2.be.b.656.6		30
7.3	odd	6		315.2.t.b.101.10	✓	30
9.4	even	3		945.2.t.b.341.10		30
9.5	odd	6		315.2.t.b.131.6	yes	30
21.17	even	6		945.2.t.b.521.6		30
63.31	odd	6		945.2.be.b.206.6		30
63.59	even	6	inner	315.2.be.b.311.10	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.10	✓	30	7.3	odd	6
315.2.t.b.131.6	yes	30	9.5	odd	6
315.2.be.b.236.10	yes	30	1.1	even	1	trivial
315.2.be.b.311.10	yes	30	63.59	even	6	inner
945.2.t.b.341.10		30	9.4	even	3
945.2.t.b.521.6		30	21.17	even	6
945.2.be.b.206.6		30	63.31	odd	6
945.2.be.b.656.6		30	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.794909 - 0.458941i) q^{2} +(-1.63482 - 0.572153i) q^{3} +(-0.578746 + 1.00242i) q^{4} +1.00000 q^{5} +(-1.56212 + 0.295477i) q^{6} +(-2.55889 + 0.672387i) q^{7} +2.89821i q^{8} +(2.34528 + 1.87074i) q^{9} +O(q^{10})\)	\(q+(0.794909 - 0.458941i) q^{2} +(-1.63482 - 0.572153i) q^{3} +(-0.578746 + 1.00242i) q^{4} +1.00000 q^{5} +(-1.56212 + 0.295477i) q^{6} +(-2.55889 + 0.672387i) q^{7} +2.89821i q^{8} +(2.34528 + 1.87074i) q^{9} +(0.794909 - 0.458941i) q^{10} +3.32911i q^{11} +(1.51968 - 1.30764i) q^{12} +(-2.08421 + 1.20332i) q^{13} +(-1.72550 + 1.70886i) q^{14} +(-1.63482 - 0.572153i) q^{15} +(0.172614 + 0.298976i) q^{16} +(-0.514321 - 0.890831i) q^{17} +(2.72284 + 0.410721i) q^{18} +(4.75184 + 2.74348i) q^{19} +(-0.578746 + 1.00242i) q^{20} +(4.56803 + 0.364844i) q^{21} +(1.52787 + 2.64634i) q^{22} +7.46288i q^{23} +(1.65822 - 4.73805i) q^{24} +1.00000 q^{25} +(-1.10450 + 1.91306i) q^{26} +(-2.76377 - 4.40018i) q^{27} +(0.806933 - 2.95421i) q^{28} +(-3.78834 - 2.18720i) q^{29} +(-1.56212 + 0.295477i) q^{30} +(0.455406 + 0.262929i) q^{31} +(-4.74542 - 2.73977i) q^{32} +(1.90476 - 5.44250i) q^{33} +(-0.817678 - 0.472086i) q^{34} +(-2.55889 + 0.672387i) q^{35} +(-3.23258 + 1.26827i) q^{36} +(3.83652 - 6.64504i) q^{37} +5.03638 q^{38} +(4.09579 - 0.774723i) q^{39} +2.89821i q^{40} +(-0.0682512 - 0.118214i) q^{41} +(3.79861 - 1.80644i) q^{42} +(-5.65425 + 9.79344i) q^{43} +(-3.33716 - 1.92671i) q^{44} +(2.34528 + 1.87074i) q^{45} +(3.42502 + 5.93231i) q^{46} +(-4.51482 - 7.81989i) q^{47} +(-0.111132 - 0.587533i) q^{48} +(6.09579 - 3.44112i) q^{49} +(0.794909 - 0.458941i) q^{50} +(0.331132 + 1.75062i) q^{51} -2.78566i q^{52} +(1.24117 - 0.716592i) q^{53} +(-4.21637 - 2.22934i) q^{54} +3.32911i q^{55} +(-1.94871 - 7.41618i) q^{56} +(-6.19872 - 7.20388i) q^{57} -4.01519 q^{58} +(-0.319534 + 0.553449i) q^{59} +(1.51968 - 1.30764i) q^{60} +(8.85068 - 5.10994i) q^{61} +0.482676 q^{62} +(-7.25916 - 3.21007i) q^{63} -5.72002 q^{64} +(-2.08421 + 1.20332i) q^{65} +(-0.983674 - 5.20047i) q^{66} +(2.02545 - 3.50819i) q^{67} +1.19065 q^{68} +(4.26991 - 12.2005i) q^{69} +(-1.72550 + 1.70886i) q^{70} +4.03618i q^{71} +(-5.42178 + 6.79711i) q^{72} +(5.39392 - 3.11418i) q^{73} -7.04294i q^{74} +(-1.63482 - 0.572153i) q^{75} +(-5.50022 + 3.17555i) q^{76} +(-2.23845 - 8.51882i) q^{77} +(2.90023 - 2.49556i) q^{78} +(1.27597 + 2.21005i) q^{79} +(0.172614 + 0.298976i) q^{80} +(2.00068 + 8.77481i) q^{81} +(-0.108507 - 0.0626465i) q^{82} +(-2.30553 + 3.99329i) q^{83} +(-3.00945 + 4.36792i) q^{84} +(-0.514321 - 0.890831i) q^{85} +10.3799i q^{86} +(4.94185 + 5.74320i) q^{87} -9.64845 q^{88} +(-7.33999 + 12.7132i) q^{89} +(2.72284 + 0.410721i) q^{90} +(4.52416 - 4.48055i) q^{91} +(-7.48092 - 4.31911i) q^{92} +(-0.594072 - 0.690404i) q^{93} +(-7.17774 - 4.14407i) q^{94} +(4.75184 + 2.74348i) q^{95} +(6.19034 + 7.19414i) q^{96} +(14.8760 + 8.58869i) q^{97} +(3.26633 - 5.53299i) q^{98} +(-6.22789 + 7.80770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

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