LMFDB - Embedded newform 950.2.h.e.381.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.6
Character	$\chi$	$=$	950.381
Dual form			950.2.h.e.571.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.417797 + 0.303547i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.20950 - 1.88072i) q^{5} +(0.417797 + 0.303547i) q^{6} +0.938984 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.844638 + 2.59953i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.417797 + 0.303547i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.20950 - 1.88072i) q^{5} +(0.417797 + 0.303547i) q^{6} +0.938984 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.844638 + 2.59953i) q^{9} +(-1.41492 + 1.73148i) q^{10} +(0.530443 + 1.63253i) q^{11} +(0.159584 - 0.491150i) q^{12} +(1.63887 - 5.04394i) q^{13} +(-0.290162 - 0.893027i) q^{14} +(1.07621 + 0.418619i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.14206 - 2.28284i) q^{17} +2.73330 q^{18} +(-0.809017 - 0.587785i) q^{19} +(2.08397 + 0.810609i) q^{20} +(-0.392305 + 0.285026i) q^{21} +(1.38872 - 1.00896i) q^{22} +(-1.52440 - 4.69161i) q^{23} -0.516426 q^{24} +(-2.07422 + 4.54946i) q^{25} -5.30351 q^{26} +(-0.914945 - 2.81591i) q^{27} +(-0.759654 + 0.551921i) q^{28} +(-3.43793 + 2.49780i) q^{29} +(0.0655622 - 1.15290i) q^{30} +(-6.13673 - 4.45859i) q^{31} -1.00000 q^{32} +(-0.717169 - 0.521054i) q^{33} +(-1.20016 + 3.69371i) q^{34} +(-1.13570 - 1.76597i) q^{35} +(-0.844638 - 2.59953i) q^{36} +(-2.97867 + 9.16739i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(0.846357 + 2.60482i) q^{39} +(0.126954 - 2.23246i) q^{40} +(0.997480 - 3.06993i) q^{41} +(0.392305 + 0.285026i) q^{42} +6.94457 q^{43} +(-1.38872 - 1.00896i) q^{44} +(5.91057 - 1.55560i) q^{45} +(-3.99092 + 2.89957i) q^{46} +(-6.53866 + 4.75062i) q^{47} +(0.159584 + 0.491150i) q^{48} -6.11831 q^{49} +(4.96777 + 0.566839i) q^{50} +2.00569 q^{51} +(1.63887 + 5.04394i) q^{52} +(-4.78183 + 3.47420i) q^{53} +(-2.39536 + 1.74033i) q^{54} +(2.42877 - 2.97217i) q^{55} +(0.759654 + 0.551921i) q^{56} +0.516426 q^{57} +(3.43793 + 2.49780i) q^{58} +(0.990585 - 3.04871i) q^{59} +(-1.11673 + 0.293912i) q^{60} +(1.48098 + 4.55799i) q^{61} +(-2.34402 + 7.21415i) q^{62} +(-0.793101 + 2.44091i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-11.4685 + 3.01838i) q^{65} +(-0.273934 + 0.843083i) q^{66} +(-13.0397 - 9.47390i) q^{67} +3.88380 q^{68} +(2.06101 + 1.49741i) q^{69} +(-1.32858 + 1.62583i) q^{70} +(-3.47362 + 2.52373i) q^{71} +(-2.21129 + 1.60660i) q^{72} +(0.389377 + 1.19838i) q^{73} +9.63916 q^{74} +(-0.514374 - 2.53038i) q^{75} +1.00000 q^{76} +(0.498077 + 1.53292i) q^{77} +(2.21579 - 1.60987i) q^{78} +(-5.75286 + 4.17970i) q^{79} +(-2.16243 + 0.569128i) q^{80} +(-5.39685 - 3.92104i) q^{81} -3.22791 q^{82} +(0.751363 + 0.545897i) q^{83} +(0.149847 - 0.461182i) q^{84} +(-0.493063 + 8.67042i) q^{85} +(-2.14599 - 6.60468i) q^{86} +(0.678156 - 2.08715i) q^{87} +(-0.530443 + 1.63253i) q^{88} +(-4.22840 - 13.0137i) q^{89} +(-3.30593 - 5.14058i) q^{90} +(1.53888 - 4.73617i) q^{91} +(3.99092 + 2.89957i) q^{92} +3.91730 q^{93} +(6.53866 + 4.75062i) q^{94} +(-0.126954 + 2.23246i) q^{95} +(0.417797 - 0.303547i) q^{96} +(14.5434 - 10.5664i) q^{97} +(1.89066 + 5.81886i) q^{98} -4.69185 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.417797	+	0.303547i	−0.241215	+	0.175253i	−0.701825	−	0.712350i	$-0.747631\pi$
$3$	−0.417797	+	0.303547i	−0.241215	+	0.175253i	0.460609	+	0.887603i	$0.347631\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.20950	−	1.88072i	−0.540905	−	0.841084i
$5$	−1.20950	−	1.88072i	−0.540905	−	0.841084i
$6$	0.417797	+	0.303547i	0.170565	+	0.123923i
$7$	0.938984			0.354902			0.177451	−	0.984130i	$-0.443215\pi$
$7$	0.938984			0.354902			0.177451	+	0.984130i	$0.443215\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.844638	+	2.59953i	−0.281546	+	0.866509i
$10$	−1.41492	+	1.73148i	−0.447436	+	0.547541i
$11$	0.530443	+	1.63253i	0.159934	+	0.492228i	0.998627	−	0.0523769i	$-0.0166797\pi$
$11$	0.530443	+	1.63253i	0.159934	+	0.492228i	−0.838693	+	0.544605i	$0.816680\pi$
$12$	0.159584	−	0.491150i	0.0460680	−	0.141783i
$13$	1.63887	−	5.04394i	0.454542	−	1.39894i	−0.417130	−	0.908847i	$-0.636964\pi$
$13$	1.63887	−	5.04394i	0.454542	−	1.39894i	0.871672	−	0.490090i	$-0.163036\pi$
$14$	−0.290162	−	0.893027i	−0.0775490	−	0.238671i
$15$	1.07621	+	0.418619i	0.277877	+	0.108087i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.14206	−	2.28284i	−0.762061	−	0.553670i	0.137481	−	0.990504i	$-0.456099\pi$
$17$	−3.14206	−	2.28284i	−0.762061	−	0.553670i	−0.899542	+	0.436835i	$0.856099\pi$
$18$	2.73330			0.644246
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$20$	2.08397	+	0.810609i	0.465989	+	0.181258i
$21$	−0.392305	+	0.285026i	−0.0856079	+	0.0621978i
$22$	1.38872	−	1.00896i	0.296075	−	0.215111i
$23$	−1.52440	−	4.69161i	−0.317858	−	0.978268i	−0.974562	−	0.224119i	$-0.928050\pi$
$23$	−1.52440	−	4.69161i	−0.317858	−	0.978268i	0.656703	−	0.754149i	$-0.271950\pi$
$24$	−0.516426			−0.105415
$25$	−2.07422	+	4.54946i	−0.414844	+	0.909893i
$26$	−5.30351			−1.04010
$27$	−0.914945	−	2.81591i	−0.176081	−	0.541922i
$28$	−0.759654	+	0.551921i	−0.143561	+	0.104303i
$29$	−3.43793	+	2.49780i	−0.638408	+	0.463830i	−0.859303	−	0.511467i	$-0.829102\pi$
$29$	−3.43793	+	2.49780i	−0.638408	+	0.463830i	0.220895	+	0.975298i	$0.429102\pi$
$30$	0.0655622	−	1.15290i	0.0119700	−	0.210490i
$31$	−6.13673	−	4.45859i	−1.10219	−	0.800787i	−0.120773	−	0.992680i	$-0.538537\pi$
$31$	−6.13673	−	4.45859i	−1.10219	−	0.800787i	−0.981416	+	0.191893i	$0.938537\pi$
$32$	−1.00000			−0.176777
$33$	−0.717169	−	0.521054i	−0.124843	−	0.0907038i
$34$	−1.20016	+	3.69371i	−0.205826	+	0.633466i
$35$	−1.13570	−	1.76597i	−0.191968	−	0.298503i
$36$	−0.844638	−	2.59953i	−0.140773	−	0.433255i
$37$	−2.97867	+	9.16739i	−0.489690	+	1.50711i	0.335382	+	0.942082i	$0.391134\pi$
$37$	−2.97867	+	9.16739i	−0.489690	+	1.50711i	−0.825072	+	0.565028i	$0.808866\pi$
$38$	−0.309017	+	0.951057i	−0.0501292	+	0.154282i
$39$	0.846357	+	2.60482i	0.135526	+	0.417105i
$40$	0.126954	−	2.23246i	0.0200732	−	0.352983i
$41$	0.997480	−	3.06993i	0.155780	−	0.479442i	−0.842459	−	0.538761i	$-0.818893\pi$
$41$	0.997480	−	3.06993i	0.155780	−	0.479442i	0.998239	+	0.0593183i	$0.0188927\pi$
$42$	0.392305	+	0.285026i	0.0605339	+	0.0439805i
$43$	6.94457			1.05904			0.529518	−	0.848298i	$-0.322373\pi$
$43$	6.94457			1.05904			0.529518	+	0.848298i	$0.322373\pi$
$44$	−1.38872	−	1.00896i	−0.209357	−	0.152107i
$45$	5.91057	−	1.55560i	0.881096	−	0.231895i
$46$	−3.99092	+	2.89957i	−0.588429	+	0.427519i
$47$	−6.53866	+	4.75062i	−0.953762	+	0.692949i	−0.951694	−	0.307049i	$-0.900658\pi$
$47$	−6.53866	+	4.75062i	−0.953762	+	0.692949i	−0.00206843	+	0.999998i	$0.500658\pi$
$48$	0.159584	+	0.491150i	0.0230340	+	0.0708914i
$49$	−6.11831			−0.874044
$50$	4.96777	+	0.566839i	0.702548	+	0.0801632i
$51$	2.00569			0.280853
$52$	1.63887	+	5.04394i	0.227271	+	0.699468i
$53$	−4.78183	+	3.47420i	−0.656835	+	0.477219i	−0.865593	−	0.500749i	$-0.833058\pi$
$53$	−4.78183	+	3.47420i	−0.656835	+	0.477219i	0.208758	+	0.977967i	$0.433058\pi$
$54$	−2.39536	+	1.74033i	−0.325967	+	0.236829i
$55$	2.42877	−	2.97217i	0.327495	−	0.400767i
$56$	0.759654	+	0.551921i	0.101513	+	0.0737535i
$57$	0.516426			0.0684022
$58$	3.43793	+	2.49780i	0.451422	+	0.327978i
$59$	0.990585	−	3.04871i	0.128963	−	0.396908i	−0.865639	−	0.500668i	$-0.833088\pi$
$59$	0.990585	−	3.04871i	0.128963	−	0.396908i	0.994602	+	0.103761i	$0.0330876\pi$
$60$	−1.11673	+	0.293912i	−0.144170	+	0.0379439i
$61$	1.48098	+	4.55799i	0.189620	+	0.583591i	0.999997	−	0.00231789i	$-0.000737806\pi$
$61$	1.48098	+	4.55799i	0.189620	+	0.583591i	−0.810377	+	0.585908i	$0.800738\pi$
$62$	−2.34402	+	7.21415i	−0.297691	+	0.916199i
$63$	−0.793101	+	2.44091i	−0.0999213	+	0.307526i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−11.4685	+	3.01838i	−1.42249	+	0.374384i
$66$	−0.273934	+	0.843083i	−0.0337190	+	0.103776i
$67$	−13.0397	−	9.47390i	−1.59305	−	1.15742i	−0.899413	−	0.437099i	$-0.856006\pi$
$67$	−13.0397	−	9.47390i	−1.59305	−	1.15742i	−0.693640	−	0.720322i	$-0.743994\pi$
$68$	3.88380			0.470979
$69$	2.06101	+	1.49741i	0.248117	+	0.180267i
$70$	−1.32858	+	1.62583i	−0.158796	+	0.194324i
$71$	−3.47362	+	2.52373i	−0.412242	+	0.299512i	−0.774509	−	0.632563i	$-0.782003\pi$
$71$	−3.47362	+	2.52373i	−0.412242	+	0.299512i	0.362267	+	0.932075i	$0.382003\pi$
$72$	−2.21129	+	1.60660i	−0.260603	+	0.189339i
$73$	0.389377	+	1.19838i	0.0455732	+	0.140260i	0.971254	−	0.238046i	$-0.0765068\pi$
$73$	0.389377	+	1.19838i	0.0455732	+	0.140260i	−0.925681	+	0.378306i	$0.876507\pi$
$74$	9.63916			1.12053
$75$	−0.514374	−	2.53038i	−0.0593948	−	0.292183i
$76$	1.00000			0.114708
$77$	0.498077	+	1.53292i	0.0567611	+	0.174693i
$78$	2.21579	−	1.60987i	0.250889	−	0.182281i
$79$	−5.75286	+	4.17970i	−0.647247	+	0.470253i	−0.862332	−	0.506343i	$-0.830997\pi$
$79$	−5.75286	+	4.17970i	−0.647247	+	0.470253i	0.215085	+	0.976595i	$0.430997\pi$
$80$	−2.16243	+	0.569128i	−0.241767	+	0.0636305i
$81$	−5.39685	−	3.92104i	−0.599650	−	0.435671i
$82$	−3.22791			−0.356463
$83$	0.751363	+	0.545897i	0.0824728	+	0.0599200i	0.628258	−	0.778005i	$-0.283768\pi$
$83$	0.751363	+	0.545897i	0.0824728	+	0.0599200i	−0.545785	+	0.837925i	$0.683768\pi$
$84$	0.149847	−	0.461182i	0.0163497	−	0.0503190i
$85$	−0.493063	+	8.67042i	−0.0534802	+	0.940440i
$86$	−2.14599	−	6.60468i	−0.231408	−	0.712201i
$87$	0.678156	−	2.08715i	0.0727059	−	0.223766i
$88$	−0.530443	+	1.63253i	−0.0565454	+	0.174029i
$89$	−4.22840	−	13.0137i	−0.448209	−	1.37945i	−0.878926	−	0.476959i	$-0.841739\pi$
$89$	−4.22840	−	13.0137i	−0.448209	−	1.37945i	0.430716	−	0.902487i	$-0.358261\pi$
$90$	−3.30593	−	5.14058i	−0.348476	−	0.541865i
$91$	1.53888	−	4.73617i	0.161318	−	0.496486i
$92$	3.99092	+	2.89957i	0.416082	+	0.302301i
$93$	3.91730			0.406205
$94$	6.53866	+	4.75062i	0.674412	+	0.489989i
$95$	−0.126954	+	2.23246i	−0.0130252	+	0.229046i
$96$	0.417797	−	0.303547i	0.0426412	−	0.0309807i
$97$	14.5434	−	10.5664i	1.47666	−	1.07286i	0.498044	−	0.867152i	$-0.334052\pi$
$97$	14.5434	−	10.5664i	1.47666	−	1.07286i	0.978614	−	0.205704i	$-0.0659483\pi$
$98$	1.89066	+	5.81886i	0.190986	+	0.587793i
$99$	−4.69185			−0.471549
$100$	−0.996028	−	4.89979i	−0.0996028	−	0.489979i
$101$	−16.7883			−1.67050			−0.835251	−	0.549869i	$-0.814678\pi$
$101$	−16.7883			−1.67050			−0.835251	+	0.549869i	$0.814678\pi$
$102$	−0.619793	−	1.90753i	−0.0613686	−	0.188873i
$103$	12.4801	−	9.06733i	1.22970	−	0.893431i	0.232834	−	0.972516i	$-0.425200\pi$
$103$	12.4801	−	9.06733i	1.22970	−	0.893431i	0.996868	+	0.0790858i	$0.0252001\pi$
$104$	4.29063	−	3.11732i	0.420731	−	0.305679i
$105$	1.01055	+	0.393076i	0.0986192	+	0.0383603i
$106$	4.78183	+	3.47420i	0.464452	+	0.337444i
$107$	−12.8856			−1.24570			−0.622849	−	0.782342i	$-0.714025\pi$
$107$	−12.8856			−1.24570			−0.622849	+	0.782342i	$0.714025\pi$
$108$	2.39536	+	1.74033i	0.230493	+	0.167463i
$109$	−1.68034	+	5.17156i	−0.160948	+	0.495346i	−0.998715	−	0.0506817i	$-0.983861\pi$
$109$	−1.68034	+	5.17156i	−0.160948	+	0.495346i	0.837767	+	0.546027i	$0.183861\pi$
$110$	−3.57723	−	1.39145i	−0.341075	−	0.132669i
$111$	−1.53826	−	4.73427i	−0.146005	−	0.449357i
$112$	0.290162	−	0.893027i	0.0274177	−	0.0843831i
$113$	2.84453	−	8.75458i	0.267591	−	0.823561i	−0.723494	−	0.690331i	$-0.757465\pi$
$113$	2.84453	−	8.75458i	0.267591	−	0.823561i	0.991085	−	0.133230i	$-0.0425350\pi$
$114$	−0.159584	−	0.491150i	−0.0149464	−	0.0460004i
$115$	−6.97985	+	8.54146i	−0.650874	+	0.796495i
$116$	1.31317	−	4.04153i	0.121925	−	0.375247i
$117$	11.7276	+	8.52060i	1.08422	+	0.787730i
$118$	−3.20560			−0.295099
$119$	−2.95034	−	2.14355i	−0.270457	−	0.196499i
$120$	0.624617	+	0.971252i	0.0570194	+	0.0886628i
$121$	6.51539	−	4.73371i	0.592308	−	0.430337i
$122$	3.87726	−	2.81699i	0.351030	−	0.255038i
$123$	0.515124	+	1.58539i	0.0464472	+	0.142950i
$124$	7.58541			0.681190
$125$	11.0650	−	1.60155i	0.989687	−	0.143247i
$126$	2.56653			0.228645
$127$	5.45930	+	16.8020i	0.484434	+	1.49094i	0.832798	+	0.553577i	$0.186737\pi$
$127$	5.45930	+	16.8020i	0.484434	+	1.49094i	−0.348364	+	0.937359i	$0.613263\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−2.90142	+	2.10801i	−0.255456	+	0.185599i
$130$	6.41459	+	9.97442i	0.562597	+	0.874814i
$131$	−14.3197	−	10.4039i	−1.25112	−	0.908990i	−0.252832	−	0.967510i	$-0.581362\pi$
$131$	−14.3197	−	10.4039i	−1.25112	−	0.908990i	−0.998286	+	0.0585198i	$0.981362\pi$
$132$	0.886469			0.0771573
$133$	−0.759654	−	0.551921i	−0.0658703	−	0.0478576i
$134$	−4.98072	+	15.3291i	−0.430269	+	1.32423i
$135$	−4.18932	+	5.12660i	−0.360559	+	0.441228i
$136$	−1.20016	−	3.69371i	−0.102913	−	0.316733i
$137$	−1.12459	+	3.46112i	−0.0960799	+	0.295703i	−0.987534	−	0.157408i	$-0.949686\pi$
$137$	−1.12459	+	3.46112i	−0.0960799	+	0.295703i	0.891454	+	0.453112i	$0.149686\pi$
$138$	0.787237	−	2.42287i	0.0670140	−	0.206248i
$139$	0.855580	+	2.63321i	0.0725694	+	0.223346i	0.980762	−	0.195207i	$-0.0625377\pi$
$139$	0.855580	+	2.63321i	0.0725694	+	0.223346i	−0.908193	+	0.418552i	$0.862538\pi$
$140$	1.95681	+	0.761148i	0.165381	+	0.0643288i
$141$	1.28980	−	3.96959i	0.108621	−	0.334300i
$142$	3.47362	+	2.52373i	0.291499	+	0.211787i
$143$	9.10373			0.761292
$144$	2.21129	+	1.60660i	0.184274	+	0.133883i
$145$	8.85584	+	3.44469i	0.735438	+	0.286066i
$146$	1.01940	−	0.740640i	0.0843664	−	0.0612958i
$147$	2.55621	−	1.85720i	0.210833	−	0.153179i
$148$	−2.97867	−	9.16739i	−0.244845	−	0.753555i
$149$	4.72198			0.386840			0.193420	−	0.981116i	$-0.438042\pi$
$149$	4.72198			0.386840			0.193420	+	0.981116i	$0.438042\pi$
$150$	−2.24758	+	1.27113i	−0.183514	+	0.103787i
$151$	20.0275			1.62982			0.814909	−	0.579589i	$-0.196787\pi$
$151$	20.0275			1.62982			0.814909	+	0.579589i	$0.196787\pi$
$152$	−0.309017	−	0.951057i	−0.0250646	−	0.0771409i
$153$	8.58820	−	6.23969i	0.694315	−	0.504449i
$154$	1.30398	−	0.947399i	0.105078	−	0.0763436i
$155$	−0.962997	+	16.9341i	−0.0773498	+	1.36018i
$156$	−2.21579	−	1.60987i	−0.177405	−	0.128892i
$157$	17.7232			1.41446			0.707232	−	0.706982i	$-0.249944\pi$
$157$	17.7232			1.41446			0.707232	+	0.706982i	$0.249944\pi$
$158$	5.75286	+	4.17970i	0.457673	+	0.332519i
$159$	0.943250	−	2.90302i	0.0748046	−	0.230225i
$160$	1.20950	+	1.88072i	0.0956194	+	0.148684i
$161$	−1.43138	−	4.40534i	−0.112809	−	0.347190i
$162$	−2.06141	+	6.34437i	−0.161960	+	0.498461i
$163$	−1.28598	+	3.95785i	−0.100726	+	0.310003i	−0.988704	−	0.149884i	$-0.952110\pi$
$163$	−1.28598	+	3.95785i	−0.100726	+	0.310003i	0.887978	+	0.459887i	$0.152110\pi$
$164$	0.997480	+	3.06993i	0.0778901	+	0.239721i
$165$	−0.112541	+	1.97901i	−0.00876128	+	0.154066i
$166$	0.286995	−	0.883280i	0.0222751	−	0.0685558i
$167$	−5.84482	−	4.24651i	−0.452286	−	0.328605i	0.338212	−	0.941070i	$-0.390178\pi$
$167$	−5.84482	−	4.24651i	−0.452286	−	0.328605i	−0.790498	+	0.612465i	$0.790178\pi$
$168$	−0.484915			−0.0374120
$169$	−12.2382	−	8.89155i	−0.941398	−	0.683966i
$170$	8.39843	−	2.21038i	0.644130	−	0.169528i
$171$	2.21129	−	1.60660i	0.169102	−	0.122859i
$172$	−5.61827	+	4.08191i	−0.428389	+	0.311243i
$173$	1.08251	+	3.33161i	0.0823014	+	0.253298i	0.983737	−	0.179616i	$-0.0574855\pi$
$173$	1.08251	+	3.33161i	0.0823014	+	0.253298i	−0.901435	+	0.432914i	$0.857485\pi$
$174$	−2.19456			−0.166369
$175$	−1.94766	+	4.27187i	−0.147229	+	0.322923i
$176$	1.71655			0.129390
$177$	0.511563	+	1.57443i	0.0384514	+	0.118341i
$178$	−11.0701	+	8.04289i	−0.829738	+	0.602840i
$179$	−10.2341	+	7.43548i	−0.764930	+	0.555754i	−0.900419	−	0.435025i	$-0.856740\pi$
$179$	−10.2341	+	7.43548i	−0.764930	+	0.555754i	0.135488	+	0.990779i	$0.456740\pi$
$180$	−3.86740	+	4.73266i	−0.288259	+	0.352751i
$181$	7.52402	+	5.46652i	0.559256	+	0.406323i	0.831186	−	0.555994i	$-0.187662\pi$
$181$	7.52402	+	5.46652i	0.559256	+	0.406323i	−0.271931	+	0.962317i	$0.587662\pi$
$182$	−4.97991			−0.369135
$183$	−2.00231	−	1.45477i	−0.148015	−	0.107539i
$184$	1.52440	−	4.69161i	0.112380	−	0.345870i
$185$	20.8440	−	5.48592i	1.53248	−	0.403333i
$186$	−1.21051	−	3.72557i	−0.0887591	−	0.273172i
$187$	2.06013	−	6.34043i	0.150652	−	0.463658i
$188$	2.49755	−	7.68666i	0.182152	−	0.560607i
$189$	−0.859119	−	2.64410i	−0.0624917	−	0.192330i
$190$	2.16243	−	0.569128i	0.156879	−	0.0412889i
$191$	1.04588	−	3.21888i	0.0756770	−	0.232910i	−0.906061	−	0.423147i	$-0.860926\pi$
$191$	1.04588	−	3.21888i	0.0756770	−	0.232910i	0.981738	+	0.190237i	$0.0609256\pi$
$192$	−0.417797	−	0.303547i	−0.0301519	−	0.0219066i
$193$	25.0518			1.80327			0.901635	−	0.432498i	$-0.142368\pi$
$193$	25.0518			1.80327			0.901635	+	0.432498i	$0.142368\pi$
$194$	−14.5434	−	10.5664i	−1.04416	−	0.758623i
$195$	3.87527	−	4.74229i	0.277514	−	0.339602i
$196$	4.94982	−	3.59625i	0.353558	−	0.256875i
$197$	9.81800	−	7.13320i	0.699504	−	0.508219i	−0.180267	−	0.983618i	$-0.557696\pi$
$197$	9.81800	−	7.13320i	0.699504	−	0.508219i	0.879771	+	0.475399i	$0.157696\pi$
$198$	1.44986	+	4.46221i	0.103037	+	0.317116i
$199$	−8.98861			−0.637185			−0.318593	−	0.947892i	$-0.603210\pi$
$199$	−8.98861			−0.637185			−0.318593	+	0.947892i	$0.603210\pi$
$200$	−4.35219	+	2.46140i	−0.307746	+	0.174047i
$201$	8.32373			0.587110
$202$	5.18788	+	15.9667i	0.365018	+	1.12341i
$203$	−3.22816	+	2.34540i	−0.226572	+	0.164615i
$204$	−1.62264	+	1.17892i	−0.113607	+	0.0825406i
$205$	−6.98013	+	1.83710i	−0.487513	+	0.128308i
$206$	−12.4801	−	9.06733i	−0.869530	−	0.631751i
$207$	13.4835			0.937170
$208$	−4.29063	−	3.11732i	−0.297502	−	0.216148i
$209$	0.530443	−	1.63253i	0.0366915	−	0.112925i
$210$	0.0615618	−	1.08255i	0.00424817	−	0.0747033i
$211$	−6.03797	−	18.5830i	−0.415671	−	1.27930i	−0.911649	−	0.410969i	$-0.865191\pi$
$211$	−6.03797	−	18.5830i	−0.415671	−	1.27930i	0.495978	−	0.868335i	$-0.334809\pi$
$212$	1.82650	−	5.62138i	0.125444	−	0.386078i
$213$	0.685195	−	2.10881i	0.0469488	−	0.144494i
$214$	3.98187	+	12.2549i	0.272195	+	0.837730i
$215$	−8.39945	−	13.0608i	−0.572838	−	0.890739i
$216$	0.914945	−	2.81591i	0.0622541	−	0.191599i
$217$	−5.76229	−	4.18655i	−0.391169	−	0.284201i
$218$	5.43770			0.368288
$219$	−0.526446	−	0.382485i	−0.0355739	−	0.0258460i
$220$	−0.217922	+	3.83213i	−0.0146923	+	0.258362i
$221$	−16.6639	+	12.1071i	−1.12094	+	0.814409i
$222$	−4.02721	+	2.92594i	−0.270289	+	0.196376i
$223$	−4.61267	−	14.1963i	−0.308887	−	0.950658i	−0.978198	−	0.207675i	$-0.933410\pi$
$223$	−4.61267	−	14.1963i	−0.308887	−	0.950658i	0.669310	−	0.742983i	$-0.266590\pi$
$224$	−0.938984			−0.0627385
$225$	−10.0745	−	9.23464i	−0.671633	−	0.615643i
$226$	−9.20511			−0.612315
$227$	−7.55328	−	23.2466i	−0.501329	−	1.54293i	−0.806856	−	0.590748i	$-0.798833\pi$
$227$	−7.55328	−	23.2466i	−0.501329	−	1.54293i	0.305528	−	0.952183i	$-0.401167\pi$
$228$	−0.417797	+	0.303547i	−0.0276693	+	0.0201029i
$229$	−11.8264	+	8.59241i	−0.781513	+	0.567802i	−0.905433	−	0.424490i	$-0.860453\pi$
$229$	−11.8264	+	8.59241i	−0.781513	+	0.567802i	0.123920	+	0.992292i	$0.460453\pi$
$230$	10.2803	+	3.99877i	0.677863	+	0.263671i
$231$	−0.673410	−	0.489261i	−0.0443071	−	0.0321910i
$232$	−4.24952			−0.278994
$233$	−13.2655	−	9.63792i	−0.869049	−	0.631401i	0.0612823	−	0.998120i	$-0.480481\pi$
$233$	−13.2655	−	9.63792i	−0.869049	−	0.631401i	−0.930332	+	0.366719i	$0.880481\pi$
$234$	4.47954	−	13.7866i	0.292837	−	0.901259i
$235$	16.8431	+	6.55153i	1.09872	+	0.427375i
$236$	0.990585	+	3.04871i	0.0644816	+	0.198454i
$237$	1.13479	−	3.49253i	0.0737127	−	0.226864i
$238$	−1.12693	+	3.46833i	−0.0730480	+	0.224819i
$239$	−4.55487	−	14.0185i	−0.294630	−	0.906778i	−0.983345	−	0.181746i	$-0.941825\pi$
$239$	−4.55487	−	14.0185i	−0.294630	−	0.906778i	0.688715	−	0.725032i	$-0.258175\pi$
$240$	0.730698	−	0.894179i	0.0471664	−	0.0577190i
$241$	−3.86290	+	11.8888i	−0.248831	+	0.765824i	0.746151	+	0.665776i	$0.231899\pi$
$241$	−3.86290	+	11.8888i	−0.248831	+	0.765824i	−0.994983	+	0.100047i	$0.968101\pi$
$242$	−6.51539	−	4.73371i	−0.418825	−	0.304294i
$243$	12.3275			0.790808
$244$	−3.87726	−	2.81699i	−0.248216	−	0.180339i
$245$	7.40009	+	11.5068i	0.472775	+	0.735144i
$246$	1.34861	−	0.979825i	0.0859844	−	0.0624713i
$247$	−4.29063	+	3.11732i	−0.273006	+	0.198351i
$248$	−2.34402	−	7.21415i	−0.148845	−	0.458099i
$249$	−0.479623			−0.0303949
$250$	−4.94245	−	10.0286i	−0.312588	−	0.634262i
$251$	20.6736			1.30491			0.652453	−	0.757829i	$-0.273740\pi$
$251$	20.6736			1.30491			0.652453	+	0.757829i	$0.273740\pi$
$252$	−0.793101	−	2.44091i	−0.0499607	−	0.153763i
$253$	6.85061	−	4.97726i	0.430694	−	0.312917i
$254$	14.2926	−	10.3842i	0.896799	−	0.651563i
$255$	−2.42588	−	3.77215i	−0.151915	−	0.236221i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−0.946492			−0.0590406			−0.0295203	−	0.999564i	$-0.509398\pi$
$257$	−0.946492			−0.0590406			−0.0295203	+	0.999564i	$0.509398\pi$
$258$	2.90142	+	2.10801i	0.180635	+	0.131239i
$259$	−2.79692	+	8.60803i	−0.173792	+	0.534877i
$260$	7.50402	−	9.18291i	0.465379	−	0.569500i
$261$	−3.58930	−	11.0467i	−0.222172	−	0.683775i
$262$	−5.46964	+	16.8338i	−0.337915	+	1.04000i
$263$	3.24925	−	10.0002i	0.200357	−	0.616637i	−0.799515	−	0.600646i	$-0.794910\pi$
$263$	3.24925	−	10.0002i	0.200357	−	0.616637i	0.999872	−	0.0159901i	$-0.00509003\pi$
$264$	−0.273934	−	0.843083i	−0.0168595	−	0.0518881i
$265$	12.3176	+	4.79124i	0.756666	+	0.294323i
$266$	−0.290162	+	0.893027i	−0.0177910	+	0.0547550i
$267$	5.71688	+	4.15355i	0.349867	+	0.254193i
$268$	16.1180			0.984561
$269$	24.0485	+	17.4722i	1.46626	+	1.06530i	0.981676	+	0.190556i	$0.0610292\pi$
$269$	24.0485	+	17.4722i	1.46626	+	1.06530i	0.484585	+	0.874744i	$0.338971\pi$
$270$	6.17026	+	2.40007i	0.375510	+	0.146064i
$271$	−0.729469	+	0.529990i	−0.0443121	+	0.0321946i	−0.609721	−	0.792616i	$-0.708718\pi$
$271$	−0.729469	+	0.529990i	−0.0443121	+	0.0321946i	0.565409	+	0.824811i	$0.308718\pi$
$272$	−3.14206	+	2.28284i	−0.190515	+	0.138417i
$273$	0.794715	+	2.44588i	0.0480983	+	0.148031i
$274$	3.63924			0.219854
$275$	−8.52741	−	0.973007i	−0.514222	−	0.0586745i
$276$	−2.54755			−0.153345
$277$	7.73399	+	23.8028i	0.464691	+	1.43017i	0.859371	+	0.511352i	$0.170855\pi$
$277$	7.73399	+	23.8028i	0.464691	+	1.43017i	−0.394681	+	0.918818i	$0.629145\pi$
$278$	2.23994	−	1.62741i	0.134343	−	0.0976056i
$279$	16.7735	−	12.1867i	1.00421	−	0.729598i
$280$	0.119208	−	2.09624i	0.00712402	−	0.125275i
$281$	17.9770	+	13.0611i	1.07242	+	0.779158i	0.976345	−	0.216216i	$-0.0693717\pi$
$281$	17.9770	+	13.0611i	1.07242	+	0.779158i	0.0960734	+	0.995374i	$0.469372\pi$
$282$	−4.17387			−0.248550
$283$	−10.3037	−	7.48607i	−0.612491	−	0.445001i	0.237800	−	0.971314i	$-0.423574\pi$
$283$	−10.3037	−	7.48607i	−0.612491	−	0.445001i	−0.850291	+	0.526313i	$0.823574\pi$
$284$	1.32680	−	4.08348i	0.0787313	−	0.242310i
$285$	−0.624617	−	0.971252i	−0.0369991	−	0.0575320i
$286$	−2.81321	−	8.65816i	−0.166348	−	0.511968i
$287$	0.936618	−	2.88261i	0.0552868	−	0.170155i
$288$	0.844638	−	2.59953i	0.0497707	−	0.153179i
$289$	−0.592116	−	1.82235i	−0.0348303	−	0.107197i
$290$	0.539492	−	9.48688i	0.0316801	−	0.557089i
$291$	−2.86879	+	8.82922i	−0.168171	+	0.517578i
$292$	−1.01940	−	0.740640i	−0.0596560	−	0.0433426i
$293$	5.49339			0.320927			0.160464	−	0.987042i	$-0.448701\pi$
$293$	5.49339			0.320927			0.160464	+	0.987042i	$0.448701\pi$
$294$	−2.55621	−	1.85720i	−0.149081	−	0.108314i
$295$	−6.93188	+	1.82440i	−0.403590	+	0.106220i
$296$	−7.79825	+	5.66576i	−0.453264	+	0.329316i
$297$	4.11175	−	2.98736i	0.238588	−	0.173344i
$298$	−1.45917	−	4.49087i	−0.0845276	−	0.260149i
$299$	−26.1625			−1.51301
$300$	1.90346	+	1.74478i	0.109896	+	0.100735i
$301$	6.52084			0.375855
$302$	−6.18885	−	19.0473i	−0.356128	−	1.09605i
$303$	7.01412	−	5.09605i	0.402950	−	0.292761i
$304$	−0.809017	+	0.587785i	−0.0464003	+	0.0337118i
$305$	6.78106	−	8.29820i	0.388282	−	0.475153i
$306$	−8.58820	−	6.23969i	−0.490955	−	0.356699i
$307$	−0.527239			−0.0300911			−0.0150456	−	0.999887i	$-0.504789\pi$
$307$	−0.527239			−0.0300911			−0.0150456	+	0.999887i	$0.504789\pi$
$308$	−1.30398	−	0.947399i	−0.0743013	−	0.0539831i
$309$	−2.46179	+	7.57661i	−0.140046	+	0.431018i
$310$	16.4029	−	4.31707i	0.931622	−	0.245193i
$311$	−0.714354	−	2.19856i	−0.0405073	−	0.124669i	0.928758	−	0.370687i	$-0.120878\pi$
$311$	−0.714354	−	2.19856i	−0.0405073	−	0.124669i	−0.969265	+	0.246018i	$0.920878\pi$
$312$	−0.846357	+	2.60482i	−0.0479155	+	0.147469i
$313$	−2.88893	+	8.89121i	−0.163292	+	0.502561i	−0.998906	−	0.0467554i	$-0.985112\pi$
$313$	−2.88893	+	8.89121i	−0.163292	+	0.502561i	0.835614	+	0.549317i	$0.185112\pi$
$314$	−5.47676	−	16.8557i	−0.309072	−	0.951224i
$315$	5.54993	−	1.46068i	0.312703	−	0.0823002i
$316$	2.19740	−	6.76289i	0.123613	−	0.380443i
$317$	13.9904	+	10.1646i	0.785780	+	0.570902i	0.906708	−	0.421759i	$-0.138587\pi$
$317$	13.9904	+	10.1646i	0.785780	+	0.570902i	−0.120928	+	0.992661i	$0.538587\pi$
$318$	−3.05242			−0.171171
$319$	−5.90137	−	4.28760i	−0.330413	−	0.240059i
$320$	1.41492	−	1.73148i	0.0790962	−	0.0967925i
$321$	5.38356	−	3.91139i	0.300481	−	0.218312i
$322$	−3.74741	+	2.72265i	−0.208835	+	0.151727i
$323$	1.20016	+	3.69371i	0.0667786	+	0.205524i
$324$	6.67087			0.370604
$325$	19.5478	+	17.9182i	1.08432	+	0.993925i
$326$	4.16153			0.230486
$327$	−0.867772	−	2.67073i	−0.0479879	−	0.147692i
$328$	2.61144	−	1.89732i	0.144193	−	0.104762i
$329$	−6.13970	+	4.46075i	−0.338493	+	0.245929i
$330$	1.91693	−	0.504515i	0.105523	−	0.0277726i
$331$	−14.9782	−	10.8823i	−0.823274	−	0.598144i	0.0943743	−	0.995537i	$-0.469915\pi$
$331$	−14.9782	−	10.8823i	−0.823274	−	0.598144i	−0.917648	+	0.397393i	$0.869915\pi$
$332$	−0.928736			−0.0509710
$333$	−21.3150	−	15.4862i	−1.16805	−	0.848641i
$334$	−2.23252	+	6.87100i	−0.122158	+	0.375964i
$335$	−2.04624	+	35.9827i	−0.111798	+	1.96595i
$336$	0.149847	+	0.461182i	0.00817483	+	0.0251595i
$337$	3.50252	−	10.7797i	0.190795	−	0.587205i	−0.809205	−	0.587526i	$-0.800102\pi$
$337$	3.50252	−	10.7797i	0.190795	−	0.587205i	1.00000		0.000320483i	$0.000102013\pi$
$338$	−4.67457	+	14.3868i	−0.254263	+	0.782541i
$339$	1.46899	+	4.52109i	0.0797846	+	0.245552i
$340$	−4.69745	−	7.30434i	−0.254755	−	0.396133i
$341$	4.02363	−	12.3834i	0.217892	−	0.670601i
$342$	−2.21129	−	1.60660i	−0.119573	−	0.0868748i
$343$	−12.3179			−0.665103
$344$	5.61827	+	4.08191i	0.302917	+	0.220082i
$345$	0.323422	−	5.68731i	0.0174124	−	0.306194i
$346$	2.83404	−	2.05905i	0.152359	−	0.110695i
$347$	−12.9291	+	9.39355i	−0.694071	+	0.504272i	−0.877996	−	0.478668i	$-0.841120\pi$
$347$	−12.9291	+	9.39355i	−0.694071	+	0.504272i	0.183925	+	0.982940i	$0.441120\pi$
$348$	0.678156	+	2.08715i	0.0363530	+	0.111883i
$349$	−29.8307			−1.59680			−0.798401	−	0.602126i	$-0.794320\pi$
$349$	−29.8307			−1.59680			−0.798401	+	0.602126i	$0.794320\pi$
$350$	4.66465	+	0.532253i	0.249336	+	0.0284501i
$351$	−15.7028			−0.838151
$352$	−0.530443	−	1.63253i	−0.0282727	−	0.0870144i
$353$	5.50114	−	3.99681i	0.292796	−	0.212729i	−0.431683	−	0.902025i	$-0.642080\pi$
$353$	5.50114	−	3.99681i	0.292796	−	0.212729i	0.724480	+	0.689296i	$0.242080\pi$
$354$	1.33929	−	0.973051i	0.0711825	−	0.0517171i
$355$	8.94777	+	3.48045i	0.474898	+	0.184723i
$356$	11.0701	+	8.04289i	0.586713	+	0.426272i
$357$	1.88331			0.0996754
$358$	10.2341	+	7.43548i	0.540887	+	0.392978i
$359$	−9.37605	+	28.8565i	−0.494849	+	1.52299i	0.322343	+	0.946623i	$0.395530\pi$
$359$	−9.37605	+	28.8565i	−0.494849	+	1.52299i	−0.817192	+	0.576366i	$0.804470\pi$
$360$	5.69611	+	2.21564i	0.300212	+	0.116775i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	2.87392	−	8.84501i	0.151050	−	0.464883i
$363$	−1.28521	+	3.95546i	−0.0674558	+	0.207608i
$364$	1.53888	+	4.73617i	0.0806590	+	0.248243i
$365$	1.78287	−	2.18175i	0.0933195	−	0.114198i
$366$	−0.764816	+	2.35386i	−0.0399776	+	0.123038i
$367$	1.17137	+	0.851049i	0.0611450	+	0.0444244i	0.617938	−	0.786227i	$-0.287968\pi$
$367$	1.17137	+	0.851049i	0.0611450	+	0.0444244i	−0.556793	+	0.830651i	$0.687968\pi$
$368$	−4.93305			−0.257153
$369$	7.13785	+	5.18595i	0.371582	+	0.269970i
$370$	−11.6586	−	18.1286i	−0.606100	−	0.942460i
$371$	−4.49006	+	3.26222i	−0.233112	+	0.169366i
$372$	−3.16916	+	2.30253i	−0.164313	+	0.119381i
$373$	0.129543	+	0.398694i	0.00670751	+	0.0206436i	0.954354	−	0.298677i	$-0.0965453\pi$
$373$	0.129543	+	0.398694i	0.00670751	+	0.0206436i	−0.947647	+	0.319321i	$0.896545\pi$
$374$	−6.66672			−0.344728
$375$	−4.13679	+	4.02788i	−0.213623	+	0.207999i
$376$	−8.08223			−0.416809
$377$	6.96442	+	21.4343i	0.358686	+	1.10392i
$378$	−2.24920	+	1.63414i	−0.115686	+	0.0840511i
$379$	20.7169	−	15.0517i	1.06416	−	0.773155i	0.0893039	−	0.996004i	$-0.471536\pi$
$379$	20.7169	−	15.0517i	1.06416	−	0.773155i	0.974853	+	0.222849i	$0.0715358\pi$
$380$	−1.20950	−	1.88072i	−0.0620460	−	0.0964789i
$381$	−7.38108	−	5.36267i	−0.378144	−	0.274738i
$382$	−3.38453			−0.173167
$383$	0.969536	+	0.704409i	0.0495410	+	0.0359936i	0.612280	−	0.790641i	$-0.290252\pi$
$383$	0.969536	+	0.704409i	0.0495410	+	0.0359936i	−0.562739	+	0.826635i	$0.690252\pi$
$384$	−0.159584	+	0.491150i	−0.00814375	+	0.0250639i
$385$	2.28058	−	2.79081i	0.116229	−	0.142233i
$386$	−7.74144	−	23.8257i	−0.394029	−	1.21270i
$387$	−5.86564	+	18.0526i	−0.298167	+	0.917665i
$388$	−5.55508	+	17.0968i	−0.282017	+	0.867958i
$389$	−11.7695	−	36.2229i	−0.596739	−	1.83657i	−0.545873	−	0.837868i	$-0.683802\pi$
$389$	−11.7695	−	36.2229i	−0.596739	−	1.83657i	−0.0508659	−	0.998705i	$-0.516198\pi$
$390$	−5.70771	−	2.22015i	−0.289021	−	0.112422i
$391$	−5.92044	+	18.2212i	−0.299410	+	0.921488i
$392$	−4.94982	−	3.59625i	−0.250003	−	0.181638i
$393$	9.14079			0.461092
$394$	−9.81800	−	7.13320i	−0.494624	−	0.359365i
$395$	14.8189	+	5.76418i	0.745621	+	0.290027i
$396$	3.79579	−	2.75780i	0.190745	−	0.138585i
$397$	−29.8084	+	21.6571i	−1.49604	+	1.08694i	−0.524115	+	0.851648i	$0.675604\pi$
$397$	−29.8084	+	21.6571i	−1.49604	+	1.08694i	−0.971925	+	0.235289i	$0.924396\pi$
$398$	2.77763	+	8.54867i	0.139230	+	0.428506i
$399$	0.484915			0.0242761
$400$	3.68583	+	3.37856i	0.184291	+	0.168928i
$401$	32.3975			1.61785			0.808927	−	0.587909i	$-0.200049\pi$
$401$	32.3975			1.61785			0.808927	+	0.587909i	$0.200049\pi$
$402$	−2.57217	−	7.91633i	−0.128288	−	0.394831i
$403$	−32.5462	+	23.6462i	−1.62124	+	1.17790i
$404$	13.5820	−	9.86793i	0.675732	−	0.490948i
$405$	−0.846893	+	14.8925i	−0.0420824	+	0.740012i
$406$	3.22816	+	2.34540i	0.160211	+	0.116400i
$407$	−16.5461			−0.820159
$408$	1.62264	+	1.17892i	0.0803326	+	0.0583650i
$409$	−1.81702	+	5.59223i	−0.0898461	+	0.276518i	−0.985876	−	0.167475i	$-0.946439\pi$
$409$	−1.81702	+	5.59223i	−0.0898461	+	0.276518i	0.896030	+	0.443993i	$0.146439\pi$
$410$	3.90416	+	6.07080i	0.192813	+	0.299816i
$411$	−0.580765	−	1.78741i	−0.0286470	−	0.0881665i
$412$	−4.76698	+	14.6712i	−0.234852	+	0.722801i
$413$	0.930143	−	2.86269i	0.0457693	−	0.140864i
$414$	−4.16664	−	12.8236i	−0.204779	−	0.630245i
$415$	0.117907	−	2.07337i	0.00578781	−	0.101778i
$416$	−1.63887	+	5.04394i	−0.0803524	+	0.247299i
$417$	−1.15676	−	0.840436i	−0.0566468	−	0.0411563i
$418$	−1.71655			−0.0839591
$419$	−7.01243	−	5.09483i	−0.342580	−	0.248899i	0.403170	−	0.915125i	$-0.367908\pi$
$419$	−7.01243	−	5.09483i	−0.342580	−	0.248899i	−0.745749	+	0.666227i	$0.767908\pi$
$420$	−1.04859	+	0.275979i	−0.0511661	+	0.0134664i
$421$	1.84407	−	1.33980i	0.0898747	−	0.0652978i	−0.541940	−	0.840417i	$-0.682310\pi$
$421$	1.84407	−	1.33980i	0.0898747	−	0.0652978i	0.631815	+	0.775119i	$0.282310\pi$
$422$	−15.8076	+	11.4849i	−0.769502	+	0.559076i
$423$	−6.82656	−	21.0100i	−0.331919	−	1.02154i
$424$	−5.91067			−0.287047
$425$	16.9030	−	9.55956i	0.819916	−	0.463707i
$426$	−2.21734			−0.107430
$427$	1.39062	+	4.27988i	0.0672966	+	0.207118i
$428$	10.4247	−	7.57396i	0.503895	−	0.366101i
$429$	−3.80351	+	2.76341i	−0.183635	+	0.133419i
$430$	−9.82598	+	12.0244i	−0.473851	+	0.579866i
$431$	15.2329	+	11.0673i	0.733743	+	0.533095i	0.890745	−	0.454503i	$-0.150183\pi$
$431$	15.2329	+	11.0673i	0.733743	+	0.533095i	−0.157002	+	0.987598i	$0.550183\pi$
$432$	−2.96082			−0.142453
$433$	−10.5560	−	7.66938i	−0.507289	−	0.368567i	0.304505	−	0.952511i	$-0.401509\pi$
$433$	−10.5560	−	7.66938i	−0.507289	−	0.368567i	−0.811794	+	0.583944i	$0.801509\pi$
$434$	−2.20100	+	6.77397i	−0.105651	+	0.325161i
$435$	−4.74557	+	1.24898i	−0.227533	+	0.0598842i
$436$	−1.68034	−	5.17156i	−0.0804738	−	0.247673i
$437$	−1.52440	+	4.69161i	−0.0729217	+	0.224430i
$438$	−0.201084	+	0.618874i	−0.00960818	+	0.0295709i
$439$	6.90753	+	21.2592i	0.329678	+	1.01465i	0.969284	+	0.245943i	$0.0790974\pi$
$439$	6.90753	+	21.2592i	0.329678	+	1.01465i	−0.639606	+	0.768703i	$0.720903\pi$
$440$	3.71191	−	0.976936i	0.176958	−	0.0465736i
$441$	5.16775	−	15.9047i	0.246084	−	0.757367i
$442$	16.6639	+	12.1071i	0.792622	+	0.575874i
$443$	20.4392			0.971096			0.485548	−	0.874210i	$-0.338620\pi$
$443$	20.4392			0.971096			0.485548	+	0.874210i	$0.338620\pi$
$444$	4.02721	+	2.92594i	0.191123	+	0.138859i
$445$	−19.3608	+	23.6925i	−0.917791	+	1.12313i
$446$	−12.0761	+	8.77383i	−0.571822	+	0.415453i
$447$	−1.97283	+	1.43335i	−0.0933117	+	0.0677949i
$448$	0.290162	+	0.893027i	0.0137089	+	0.0421915i
$449$	13.8638			0.654273			0.327137	−	0.944977i	$-0.393916\pi$
$449$	13.8638			0.654273			0.327137	+	0.944977i	$0.393916\pi$
$450$	−5.66948	+	12.4351i	−0.267262	+	0.586195i
$451$	5.54087			0.260909
$452$	2.84453	+	8.75458i	0.133796	+	0.411781i
$453$	−8.36745	+	6.07931i	−0.393137	+	0.285631i
$454$	−19.7747	+	14.3672i	−0.928074	+	0.674286i
$455$	−10.7687	+	2.83421i	−0.504844	+	0.132870i
$456$	0.417797	+	0.303547i	0.0195651	+	0.0142149i
$457$	31.8806			1.49131			0.745656	−	0.666331i	$-0.232136\pi$
$457$	31.8806			1.49131			0.745656	+	0.666331i	$0.232136\pi$
$458$	11.8264	+	8.59241i	0.552613	+	0.401497i
$459$	−3.55346	+	10.9364i	−0.165861	+	0.510469i
$460$	0.626269	−	11.0128i	0.0292000	−	0.513476i
$461$	−2.93523	−	9.03370i	−0.136707	−	0.420741i	0.859145	−	0.511733i	$-0.170996\pi$
$461$	−2.93523	−	9.03370i	−0.136707	−	0.420741i	−0.995852	+	0.0909918i	$0.970996\pi$
$462$	−0.257220	+	0.791641i	−0.0119669	+	0.0368305i
$463$	−1.59251	+	4.90124i	−0.0740101	+	0.227780i	−0.981218	−	0.192903i	$-0.938210\pi$
$463$	−1.59251	+	4.90124i	−0.0740101	+	0.227780i	0.907208	+	0.420683i	$0.138210\pi$
$464$	1.31317	+	4.04153i	0.0609625	+	0.187623i
$465$	−4.73797	−	7.36735i	−0.219718	−	0.341652i
$466$	−5.06696	+	15.5945i	−0.234722	+	0.722401i
$467$	−9.07793	−	6.59550i	−0.420077	−	0.305203i	0.357592	−	0.933878i	$-0.383598\pi$
$467$	−9.07793	−	6.59550i	−0.420077	−	0.305203i	−0.777669	+	0.628674i	$0.783598\pi$
$468$	−14.4961			−0.670083
$469$	−12.2441	−	8.89584i	−0.565379	−	0.410772i
$470$	1.02607	−	18.0433i	0.0473291	−	0.832274i
$471$	−7.40469	+	5.37982i	−0.341190	+	0.247889i
$472$	2.59338	−	1.88420i	0.119370	−	0.0867275i
$473$	3.68370	+	11.3372i	0.169376	+	0.521287i
$474$	−3.67226			−0.168673
$475$	4.35219	−	2.46140i	0.199692	−	0.112937i
$476$	3.64682			0.167152
$477$	−4.99237	−	15.3649i	−0.228585	−	0.703512i
$478$	−11.9248	+	8.66388i	−0.545428	+	0.396277i
$479$	10.0358	−	7.29143i	0.458547	−	0.333154i	−0.334414	−	0.942426i	$-0.608538\pi$
$479$	10.0358	−	7.29143i	0.458547	−	0.333154i	0.792961	+	0.609272i	$0.208538\pi$
$480$	−1.07621	−	0.418619i	−0.0491222	−	0.0191073i
$481$	41.3581	+	30.0484i	1.88577	+	1.37009i
$482$	12.5006			0.569387
$483$	1.93526	+	1.40605i	0.0880573	+	0.0639773i
$484$	−2.48866	+	7.65930i	−0.113121	+	0.348150i
$485$	−37.4627	−	14.5720i	−1.70109	−	0.661681i
$486$	−3.80940	−	11.7241i	−0.172798	−	0.531817i
$487$	2.56723	−	7.90113i	0.116332	−	0.358034i	−0.875890	−	0.482510i	$-0.839725\pi$
$487$	2.56723	−	7.90113i	0.116332	−	0.358034i	0.992223	+	0.124476i	$0.0397250\pi$
$488$	−1.48098	+	4.55799i	−0.0670408	+	0.206330i
$489$	−0.664115	−	2.04394i	−0.0300323	−	0.0924300i
$490$	8.65689	−	10.5937i	0.391078	−	0.478575i
$491$	−10.4571	+	32.1838i	−0.471924	+	1.45243i	0.378136	+	0.925750i	$0.376565\pi$
$491$	−10.4571	+	32.1838i	−0.471924	+	1.45243i	−0.850061	+	0.526684i	$0.823435\pi$
$492$	−1.34861	−	0.979825i	−0.0608002	−	0.0441739i
$493$	16.5043			0.743314
$494$	4.29063	+	3.11732i	0.193045	+	0.140255i
$495$	5.67479	+	8.82406i	0.255063	+	0.396612i
$496$	−6.13673	+	4.45859i	−0.275547	+	0.200197i
$497$	−3.26167	+	2.36974i	−0.146306	+	0.106297i
$498$	0.148212	+	0.456148i	0.00664152	+	0.0204405i
$499$	7.60947			0.340647			0.170323	−	0.985388i	$-0.445519\pi$
$499$	7.60947			0.340647			0.170323	+	0.985388i	$0.445519\pi$
$500$	−8.01044	+	7.79954i	−0.358238	+	0.348806i
$501$	3.73096			0.166687
$502$	−6.38850	−	19.6618i	−0.285133	−	0.877548i
$503$	−29.7540	+	21.6175i	−1.32666	+	0.963878i	−0.326840	+	0.945080i	$0.605984\pi$
$503$	−29.7540	+	21.6175i	−1.32666	+	0.963878i	−0.999823	+	0.0187981i	$0.994016\pi$
$504$	−2.07637	+	1.50857i	−0.0924887	+	0.0671969i
$505$	20.3055	+	31.5742i	0.903582	+	1.40503i
$506$	−6.85061	−	4.97726i	−0.304547	−	0.221266i
$507$	7.81208			0.346947
$508$	−14.2926	−	10.3842i	−0.634133	−	0.460725i
$509$	−6.43559	+	19.8067i	−0.285252	+	0.877916i	0.701071	+	0.713092i	$0.252706\pi$
$509$	−6.43559	+	19.8067i	−0.285252	+	0.877916i	−0.986323	+	0.164825i	$0.947294\pi$
$510$	−2.83788	+	3.47281i	−0.125664	+	0.153779i
$511$	0.365619	+	1.12526i	0.0161740	+	0.0497785i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−0.914945	+	2.81591i	−0.0403958	+	0.124326i
$514$	0.292482	+	0.900168i	0.0129008	+	0.0397047i
$515$	−32.1478	−	12.5047i	−1.41660	−	0.551021i
$516$	1.10824	−	3.41082i	0.0487877	−	0.150153i
$517$	−11.2239	−	8.15466i	−0.493628	−	0.358642i
$518$	9.05102			0.397679
$519$	−1.46357	−	1.06335i	−0.0642436	−	0.0466757i
$520$	−11.0523	−	4.29907i	−0.484677	−	0.188527i
$521$	−2.18228	+	1.58552i	−0.0956075	+	0.0694629i	−0.634562	−	0.772872i	$-0.718819\pi$
$521$	−2.18228	+	1.58552i	−0.0956075	+	0.0694629i	0.538954	+	0.842335i	$0.318819\pi$
$522$	−9.39691	+	6.82725i	−0.411292	+	0.298821i
$523$	−8.87749	−	27.3221i	−0.388186	−	1.19471i	−0.934143	−	0.356899i	$-0.883834\pi$
$523$	−8.87749	−	27.3221i	−0.388186	−	1.19471i	0.545957	−	0.837813i	$-0.316166\pi$
$524$	17.7001			0.773233
$525$	−0.482989	−	2.37598i	−0.0210794	−	0.103696i
$526$	−10.5148			−0.458467
$527$	9.10370	+	28.0183i	0.396563	+	1.22050i
$528$	−0.717169	+	0.521054i	−0.0312108	+	0.0226760i
$529$	−1.08000	+	0.784669i	−0.0469567	+	0.0341160i
$530$	0.750382	−	13.1953i	0.0325945	−	0.573169i
$531$	7.08851	+	5.15010i	0.307615	+	0.223495i
$532$	0.938984			0.0407101
$533$	−13.8498	−	10.0625i	−0.599901	−	0.435853i
$534$	2.18365	−	6.72059i	0.0944959	−	0.290828i
$535$	15.5851	+	24.2342i	0.673804	+	1.04774i
$536$	−4.98072	−	15.3291i	−0.215134	−	0.662116i
$537$	2.01874	−	6.21305i	0.0871151	−	0.268113i
$538$	9.18570	−	28.2707i	0.396024	−	1.21884i
$539$	−3.24541	−	9.98835i	−0.139790	−	0.430229i
$540$	0.375888	−	6.60993i	0.0161756	−	0.284446i
$541$	9.07337	−	27.9250i	0.390095	−	1.20059i	−0.542622	−	0.839977i	$-0.682568\pi$
$541$	9.07337	−	27.9250i	0.390095	−	1.20059i	0.932716	−	0.360611i	$-0.117432\pi$
$542$	0.729469	+	0.529990i	0.0313334	+	0.0227650i
$543$	−4.80286			−0.206110
$544$	3.14206	+	2.28284i	0.134715	+	0.0978759i
$545$	11.7586	−	3.09475i	0.503685	−	0.132564i
$546$	2.08059	−	1.51164i	0.0890411	−	0.0646921i
$547$	−3.56161	+	2.58766i	−0.152283	+	0.110640i	−0.661318	−	0.750106i	$-0.730003\pi$
$547$	−3.56161	+	2.58766i	−0.152283	+	0.110640i	0.509034	+	0.860746i	$0.330003\pi$
$548$	−1.12459	−	3.46112i	−0.0480399	−	0.147852i
$549$	−13.0995			−0.559073
$550$	1.70973	+	8.41073i	0.0729031	+	0.358635i
$551$	4.24952			0.181035
$552$	0.787237	+	2.42287i	0.0335070	+	0.103124i
$553$	−5.40184	+	3.92467i	−0.229710	+	0.166894i
$554$	20.2479	−	14.7109i	0.860249	−	0.625007i
$555$	−7.04332	+	8.61914i	−0.298972	+	0.365862i
$556$	−2.23994	−	1.62741i	−0.0949945	−	0.0690176i
$557$	29.2847			1.24083			0.620417	−	0.784273i	$-0.286964\pi$
$557$	29.2847			1.24083			0.620417	+	0.784273i	$0.286964\pi$
$558$	−16.7735	−	12.1867i	−0.710081	−	0.515904i
$559$	11.3813	−	35.0280i	0.481377	−	1.48153i
$560$	−2.03048	+	0.534402i	−0.0858036	+	0.0225826i
$561$	1.06390	+	3.27436i	0.0449181	+	0.138244i
$562$	6.86661	−	21.1332i	0.289650	−	0.891452i
$563$	8.19986	−	25.2366i	0.345583	−	1.06359i	−0.615688	−	0.787990i	$-0.711122\pi$
$563$	8.19986	−	25.2366i	0.345583	−	1.06359i	0.961271	−	0.275604i	$-0.0888780\pi$
$564$	1.28980	+	3.96959i	0.0543103	+	0.167150i
$565$	−19.9054	+	5.23889i	−0.837426	+	0.220402i
$566$	−3.93566	+	12.1127i	−0.165428	+	0.509136i
$567$	−5.06755	−	3.68179i	−0.212817	−	0.154621i
$568$	−4.29363			−0.180157
$569$	−28.0809	−	20.4020i	−1.17721	−	0.855296i	−0.185359	−	0.982671i	$-0.559345\pi$
$569$	−28.0809	−	20.4020i	−1.17721	−	0.855296i	−0.991855	+	0.127375i	$0.959345\pi$
$570$	−0.730698	+	0.894179i	−0.0306056	+	0.0374530i
$571$	−12.6393	+	9.18297i	−0.528937	+	0.384295i	−0.819960	−	0.572421i	$-0.806004\pi$
$571$	−12.6393	+	9.18297i	−0.528937	+	0.384295i	0.291023	+	0.956716i	$0.406004\pi$
$572$	−7.36507	+	5.35104i	−0.307949	+	0.223738i
$573$	0.540117	+	1.66231i	0.0225637	+	0.0694440i
$574$	−3.03096			−0.126510
$575$	24.5062	+	2.79624i	1.02198	+	0.116611i
$576$	−2.73330			−0.113888
$577$	3.20445	+	9.86228i	0.133403	+	0.410572i	0.995338	−	0.0964464i	$-0.0307476\pi$
$577$	3.20445	+	9.86228i	0.133403	+	0.410572i	−0.861935	+	0.507018i	$0.830748\pi$
$578$	−1.55018	+	1.12627i	−0.0644790	+	0.0468467i
$579$	−10.4666	+	7.60441i	−0.434976	+	0.316029i
$580$	−9.18927	+	2.41852i	−0.381564	+	0.100424i
$581$	0.705518	+	0.512589i	0.0292698	+	0.0212658i
$582$	9.28359			0.384817
$583$	−8.20824	−	5.96364i	−0.339951	−	0.246989i
$584$	−0.389377	+	1.19838i	−0.0161125	+	0.0495893i
$585$	1.84034	−	32.3620i	0.0760886	−	1.33800i
$586$	−1.69755	−	5.22452i	−0.0701252	−	0.215823i
$587$	−1.73013	+	5.32480i	−0.0714102	+	0.219778i	−0.980392	−	0.197058i	$-0.936861\pi$
$587$	−1.73013	+	5.32480i	−0.0714102	+	0.219778i	0.908982	+	0.416836i	$0.136861\pi$
$588$	−0.976386	+	3.00501i	−0.0402655	+	0.123924i
$589$	2.34402	+	7.21415i	0.0965837	+	0.297254i
$590$	3.87717	+	6.02884i	0.159621	+	0.248203i
$591$	−1.93667	+	5.96046i	−0.0796639	+	0.245180i
$592$	7.79825	+	5.66576i	0.320506	+	0.232861i
$593$	−33.1692			−1.36210			−0.681048	−	0.732239i	$-0.738475\pi$
$593$	−33.1692			−1.36210			−0.681048	+	0.732239i	$0.738475\pi$
$594$	−4.11175	−	2.98736i	−0.168707	−	0.122573i
$595$	−0.462978	+	8.14139i	−0.0189802	+	0.333764i
$596$	−3.82016	+	2.77551i	−0.156480	+	0.113689i
$597$	3.75541	−	2.72847i	0.153699	−	0.111669i
$598$	8.08465	+	24.8820i	0.330606	+	1.01750i
$599$	−43.3225			−1.77011			−0.885055	−	0.465487i	$-0.845879\pi$
$599$	−43.3225			−1.77011			−0.885055	+	0.465487i	$0.845879\pi$
$600$	1.07118	−	2.34946i	0.0437307	−	0.0959162i
$601$	32.6800			1.33305			0.666523	−	0.745484i	$-0.267782\pi$
$601$	32.6800			1.33305			0.666523	+	0.745484i	$0.267782\pi$
$602$	−2.01505	−	6.20168i	−0.0821273	−	0.252762i
$603$	35.6415	−	25.8951i	1.45143	−	1.05453i
$604$	−16.2026	+	11.7719i	−0.659275	+	0.478992i
$605$	−16.7831	−	6.52821i	−0.682332	−	0.265409i
$606$	−7.01412	−	5.09605i	−0.284929	−	0.207013i
$607$	−5.62425			−0.228281			−0.114141	−	0.993465i	$-0.536411\pi$
$607$	−5.62425			−0.228281			−0.114141	+	0.993465i	$0.536411\pi$
$608$	0.809017	+	0.587785i	0.0328100	+	0.0238378i
$609$	0.636777	−	1.95980i	0.0258035	−	0.0794151i
$610$	−9.98752	−	3.88488i	−0.404383	−	0.157294i
$611$	13.2458	+	40.7663i	0.535866	+	1.64923i
$612$	−3.28040	+	10.0960i	−0.132602	+	0.408108i
$613$	−0.856463	+	2.63592i	−0.0345922	+	0.106464i	−0.966862	−	0.255301i	$-0.917826\pi$
$613$	−0.856463	+	2.63592i	−0.0345922	+	0.106464i	0.932270	+	0.361765i	$0.117826\pi$
$614$	0.162926	+	0.501434i	0.00657516	+	0.0202362i
$615$	2.35863	−	2.88633i	0.0951092	−	0.116388i
$616$	−0.498077	+	1.53292i	−0.0200681	+	0.0617632i
$617$	−22.0613	−	16.0285i	−0.888154	−	0.645282i	0.0472418	−	0.998883i	$-0.484957\pi$
$617$	−22.0613	−	16.0285i	−0.888154	−	0.645282i	−0.935396	+	0.353602i	$0.884957\pi$
$618$	7.96652			0.320460
$619$	1.35779	+	0.986493i	0.0545742	+	0.0396505i	0.614738	−	0.788731i	$-0.289262\pi$
$619$	1.35779	+	0.986493i	0.0545742	+	0.0396505i	−0.560164	+	0.828382i	$0.689262\pi$
$620$	−9.17455	−	14.2660i	−0.368459	−	0.572938i
$621$	−11.8164	+	8.58513i	−0.474176	+	0.344509i
$622$	−1.87020	+	1.35878i	−0.0749883	+	0.0544822i
$623$	−3.97040	−	12.2196i	−0.159071	−	0.489569i
$624$	2.73887			0.109642
$625$	−16.3952	−	18.8732i	−0.655809	−	0.754927i
$626$	9.34878			0.373652
$627$	0.273934	+	0.843083i	0.0109399	+	0.0336695i
$628$	−14.3383	+	10.4174i	−0.572162	+	0.415700i
$629$	30.2868	−	22.0047i	1.20761	−	0.877383i
$630$	−3.10422	−	4.82692i	−0.123675	−	0.192309i
$631$	−4.50831	−	3.27548i	−0.179473	−	0.130395i	0.494422	−	0.869222i	$-0.335380\pi$
$631$	−4.50831	−	3.27548i	−0.179473	−	0.130395i	−0.673895	+	0.738827i	$0.735380\pi$
$632$	−7.11093			−0.282858
$633$	8.16345	+	5.93110i	0.324468	+	0.235740i
$634$	5.34386	−	16.4467i	0.212232	−	0.653182i
$635$	24.9968	−	30.5894i	0.991969	−	1.21390i
$636$	0.943250	+	2.90302i	0.0374023	+	0.115112i
$637$	−10.0271	+	30.8604i	−0.397290	+	1.22273i
$638$	−2.25412	+	6.93748i	−0.0892416	+	0.274658i
$639$	−3.62656	−	11.1614i	−0.143464	−	0.441538i
$640$	−2.08397	−	0.810609i	−0.0823760	−	0.0320421i
$641$	−2.02982	+	6.24714i	−0.0801730	+	0.246747i	−0.983107	−	0.183032i	$-0.941409\pi$
$641$	−2.02982	+	6.24714i	−0.0801730	+	0.246747i	0.902934	+	0.429779i	$0.141409\pi$
$642$	−5.38356	−	3.91139i	−0.212472	−	0.154370i
$643$	−31.2499			−1.23237			−0.616187	−	0.787600i	$-0.711323\pi$
$643$	−31.2499			−1.23237			−0.616187	+	0.787600i	$0.711323\pi$
$644$	3.74741	+	2.72265i	0.147669	+	0.107287i
$645$	7.47384	+	2.90713i	0.294282	+	0.114468i
$646$	3.14206	−	2.28284i	0.123623	−	0.0898171i
$647$	33.7124	−	24.4935i	1.32537	−	0.962940i	0.325524	−	0.945534i	$-0.394459\pi$
$647$	33.7124	−	24.4935i	1.32537	−	0.962940i	0.999849	−	0.0174062i	$-0.00554086\pi$
$648$	−2.06141	−	6.34437i	−0.0809799	−	0.249231i
$649$	5.50257			0.215995
$650$	11.0006	−	24.1281i	0.431481	−	0.946383i
$651$	3.67828			0.144163
$652$	−1.28598	−	3.95785i	−0.0503630	−	0.155001i
$653$	−7.92465	+	5.75759i	−0.310115	+	0.225312i	−0.731946	−	0.681363i	$-0.761388\pi$
$653$	−7.92465	+	5.75759i	−0.310115	+	0.225312i	0.421831	+	0.906675i	$0.361388\pi$
$654$	−2.27186	+	1.65060i	−0.0888366	+	0.0645436i
$655$	−2.24710	+	39.5148i	−0.0878014	+	1.54397i
$656$	−2.61144	−	1.89732i	−0.101960	−	0.0740779i
$657$	−3.44410			−0.134367
$658$	6.13970	+	4.46075i	0.239350	+	0.173898i
$659$	2.25936	−	6.95360i	0.0880122	−	0.270874i	−0.897357	−	0.441304i	$-0.854516\pi$
$659$	2.25936	−	6.95360i	0.0880122	−	0.270874i	0.985370	+	0.170431i	$0.0545159\pi$
$660$	−1.07218	−	1.66720i	−0.0417347	−	0.0648957i
$661$	5.11308	+	15.7364i	0.198876	+	0.612077i	0.999909	+	0.0134574i	$0.00428374\pi$
$661$	5.11308	+	15.7364i	0.198876	+	0.612077i	−0.801034	+	0.598619i	$0.795716\pi$
$662$	−5.72115	+	17.6079i	−0.222359	+	0.684350i
$663$	3.28708	−	10.1166i	0.127659	−	0.392895i
$664$	0.286995	+	0.883280i	0.0111376	+	0.0342779i
$665$	−0.119208	+	2.09624i	−0.00462267	+	0.0812889i
$666$	−8.14160	+	25.0573i	−0.315481	+	0.970949i
$667$	16.9595	+	12.3218i	0.656673	+	0.477101i
$668$	7.22459			0.279528
$669$	6.23642	+	4.53103i	0.241114	+	0.175180i
$670$	34.8539	−	9.17318i	1.34652	−	0.354391i
$671$	−6.65550	+	4.83550i	−0.256933	+	0.186673i
$672$	0.392305	−	0.285026i	0.0151335	−	0.0109951i
$673$	−2.87969	−	8.86277i	−0.111004	−	0.341635i	0.880089	−	0.474809i	$-0.157483\pi$
$673$	−2.87969	−	8.86277i	−0.111004	−	0.341635i	−0.991093	+	0.133174i	$0.957483\pi$
$674$	−11.3344			−0.436585
$675$	14.7087	+	1.67831i	0.566137	+	0.0645982i
$676$	15.1272			0.581816
$677$	−1.80345	−	5.55044i	−0.0693121	−	0.213321i	0.910401	−	0.413728i	$-0.135773\pi$
$677$	−1.80345	−	5.55044i	−0.0693121	−	0.213321i	−0.979713	+	0.200407i	$0.935773\pi$
$678$	3.84587	−	2.79419i	0.147700	−	0.107310i
$679$	13.6560	−	9.92168i	0.524070	−	0.380759i
$680$	−5.49524	+	6.72471i	−0.210733	+	0.257881i
$681$	10.2122	+	7.41958i	0.391332	+	0.284319i
$682$	−13.0207			−0.498589
$683$	12.0290	+	8.73957i	0.460276	+	0.334410i	0.793640	−	0.608388i	$-0.208184\pi$
$683$	12.0290	+	8.73957i	0.460276	+	0.334410i	−0.333363	+	0.942798i	$0.608184\pi$
$684$	−0.844638	+	2.59953i	−0.0322955	+	0.0993954i
$685$	7.86959	−	2.07119i	0.300682	−	0.0791362i
$686$	3.80643	+	11.7150i	0.145330	+	0.447281i
$687$	2.33285	−	7.17976i	0.0890037	−	0.273925i
$688$	2.14599	−	6.60468i	0.0818151	−	0.251801i
$689$	9.68684	+	29.8130i	0.369039	+	1.13579i
$690$	−5.50890	+	1.44988i	−0.209720	+	0.0551961i
$691$	−8.89948	+	27.3898i	−0.338552	+	1.04196i	0.626394	+	0.779507i	$0.284530\pi$
$691$	−8.89948	+	27.3898i	−0.338552	+	1.04196i	−0.964946	+	0.262449i	$0.915470\pi$
$692$	−2.83404	−	2.05905i	−0.107734	−	0.0782733i
$693$	−4.40557			−0.167354
$694$	12.9291	+	9.39355i	0.490782	+	0.356574i
$695$	3.91750	−	4.79397i	0.148599	−	0.181846i
$696$	1.77543	−	1.28993i	0.0672977	−	0.0488946i
$697$	−10.1423	+	7.36881i	−0.384167	+	0.279113i
$698$	9.21820	+	28.3707i	0.348914	+	1.07385i
$699$	8.46784			0.320283
$700$	−0.935254	−	4.60082i	−0.0353493	−	0.173895i
$701$	−17.9356			−0.677417			−0.338708	−	0.940891i	$-0.609990\pi$
$701$	−17.9356			−0.677417			−0.338708	+	0.940891i	$0.609990\pi$
$702$	4.85242	+	14.9342i	0.183143	+	0.563656i
$703$	7.79825	−	5.66576i	0.294116	−	0.213688i
$704$	−1.38872	+	1.00896i	−0.0523392	+	0.0380267i
$705$	−9.02569	+	2.37547i	−0.339927	+	0.0894653i
$706$	−5.50114	−	3.99681i	−0.207038	−	0.150422i
$707$	−15.7640			−0.592865
$708$	−1.33929	−	0.973051i	−0.0503336	−	0.0365695i
$709$	1.58151	−	4.86740i	0.0593950	−	0.182799i	−0.916957	−	0.398986i	$-0.869362\pi$
$709$	1.58151	−	4.86740i	0.0593950	−	0.182799i	0.976352	+	0.216187i	$0.0693622\pi$
$710$	0.545092	−	9.58535i	0.0204570	−	0.359732i
$711$	−6.00616	−	18.4851i	−0.225248	−	0.693244i
$712$	4.22840	−	13.0137i	0.158466	−	0.487708i
$713$	−11.5632	+	35.5878i	−0.433044	+	1.33277i
$714$	−0.581975	−	1.79114i	−0.0217799	−	0.0670316i
$715$	−11.0110	−	17.1216i	−0.411787	−	0.640311i
$716$	3.90907	−	12.0309i	0.146089	−	0.449615i
$717$	6.15828	+	4.47425i	0.229985	+	0.167094i
$718$	30.3415			1.13234
$719$	−16.9031	−	12.2808i	−0.630380	−	0.457998i	0.226152	−	0.974092i	$-0.427385\pi$
$719$	−16.9031	−	12.2808i	−0.630380	−	0.457998i	−0.856532	+	0.516094i	$0.827385\pi$
$720$	0.347004	−	6.10200i	0.0129321	−	0.227408i
$721$	11.7186	−	8.51408i	0.436424	−	0.317081i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	−1.99490	−	6.13967i	−0.0741911	−	0.228337i
$724$	−9.30019			−0.345639
$725$	−4.23264	−	20.8217i	−0.157196	−	0.773299i
$726$	4.15901			0.154355
$727$	−8.47901	−	26.0957i	−0.314469	−	0.967836i	−0.975972	−	0.217894i	$-0.930081\pi$
$727$	−8.47901	−	26.0957i	−0.314469	−	0.967836i	0.661503	−	0.749942i	$-0.269919\pi$
$728$	4.02883	−	2.92712i	0.149318	−	0.108486i
$729$	11.0402	−	8.02114i	0.408895	−	0.297079i
$730$	−2.62590	−	1.02141i	−0.0971891	−	0.0378040i
$731$	−21.8202	−	15.8533i	−0.807050	−	0.586356i
$732$	2.47500			0.0914785
$733$	−20.6639	−	15.0132i	−0.763238	−	0.554525i	0.136664	−	0.990617i	$-0.456362\pi$
$733$	−20.6639	−	15.0132i	−0.763238	−	0.554525i	−0.899902	+	0.436093i	$0.856362\pi$
$734$	0.447423	−	1.37703i	0.0165147	−	0.0508270i
$735$	−6.58460	−	2.56124i	−0.242877	−	0.0944728i
$736$	1.52440	+	4.69161i	0.0561900	+	0.172935i
$737$	8.54965	−	26.3131i	0.314931	−	0.969257i
$738$	2.72642	−	8.39105i	0.100361	−	0.308879i
$739$	7.56063	+	23.2692i	0.278122	+	0.855972i	0.988376	+	0.152027i	$0.0485800\pi$
$739$	7.56063	+	23.2692i	0.278122	+	0.855972i	−0.710254	+	0.703945i	$0.751420\pi$
$740$	−13.6386	+	16.6900i	−0.501365	+	0.613536i
$741$	0.846357	−	2.60482i	0.0310917	−	0.0956904i
$742$	4.49006	+	3.26222i	0.164835	+	0.119760i
$743$	42.7860			1.56967			0.784833	−	0.619707i	$-0.212748\pi$
$743$	42.7860			1.56967			0.784833	+	0.619707i	$0.212748\pi$
$744$	3.16916	+	2.30253i	0.116187	+	0.0844149i
$745$	−5.71124	−	8.88073i	−0.209244	−	0.325365i
$746$	0.339149	−	0.246406i	0.0124171	−	0.00902158i
$747$	−2.05370	+	1.49210i	−0.0751411	+	0.0545932i
$748$	2.06013	+	6.34043i	0.0753259	+	0.231829i
$749$	−12.0994			−0.442101
$750$	5.10908	+	2.68964i	0.186557	+	0.0982118i
$751$	33.1270			1.20882			0.604412	−	0.796672i	$-0.293408\pi$
$751$	33.1270			1.20882			0.604412	+	0.796672i	$0.293408\pi$
$752$	2.49755	+	7.68666i	0.0910762	+	0.280304i
$753$	−8.63737	+	6.27542i	−0.314763	+	0.228689i
$754$	18.2331	−	13.2471i	0.664010	−	0.482432i
$755$	−24.2233	−	37.6662i	−0.881577	−	1.37081i
$756$	2.24920	+	1.63414i	0.0818027	+	0.0594331i
$757$	−5.85860			−0.212934			−0.106467	−	0.994316i	$-0.533954\pi$
$757$	−5.85860			−0.212934			−0.106467	+	0.994316i	$0.533954\pi$
$758$	−20.7169	−	15.0517i	−0.752473	−	0.546703i
$759$	−1.35133	+	4.15897i	−0.0490502	+	0.150961i
$760$	−1.41492	+	1.73148i	−0.0513244	+	0.0628073i
$761$	−7.30690	−	22.4883i	−0.264875	−	0.815201i	−0.991722	−	0.128402i	$-0.959015\pi$
$761$	−7.30690	−	22.4883i	−0.264875	−	0.815201i	0.726847	−	0.686799i	$-0.240985\pi$
$762$	−2.81932	+	8.67698i	−0.102133	+	0.314334i
$763$	−1.57781	+	4.85601i	−0.0571207	+	0.175799i
$764$	1.04588	+	3.21888i	0.0378385	+	0.116455i
$765$	−22.1225	−	8.60510i	−0.799842	−	0.311118i
$766$	0.370330	−	1.13976i	0.0133806	−	0.0411811i
$767$	−13.7540	−	9.99290i	−0.496630	−	0.360823i
$768$	0.516426			0.0186349
$769$	10.5596	+	7.67203i	0.380790	+	0.276660i	0.761671	−	0.647964i	$-0.224379\pi$
$769$	10.5596	+	7.67203i	0.380790	+	0.276660i	−0.380881	+	0.924624i	$0.624379\pi$
$770$	−3.35896	−	1.30655i	−0.121048	−	0.0470847i
$771$	0.395442	−	0.287305i	0.0142415	−	0.0103470i
$772$	−20.2674	+	14.7251i	−0.729438	+	0.529968i
$773$	14.5294	+	44.7168i	0.522585	+	1.60835i	0.769043	+	0.639197i	$0.220733\pi$
$773$	14.5294	+	44.7168i	0.522585	+	1.60835i	−0.246458	+	0.969154i	$0.579267\pi$
$774$	18.9816			0.682280
$775$	33.0131	−	18.6707i	1.18587	−	0.670672i
$776$	17.9766			0.645323
$777$	−1.44440	−	4.44541i	−0.0518176	−	0.159478i
$778$	−30.8130	+	22.3870i	−1.10470	+	0.802612i
$779$	−2.61144	+	1.89732i	−0.0935645	+	0.0679786i
$780$	−0.347710	+	6.11442i	−0.0124500	+	0.218931i
$781$	−5.96263	−	4.33211i	−0.213360	−	0.155015i
$782$	19.1590			0.685123
$783$	10.1791	+	7.39556i	0.363772	+	0.264296i
$784$	−1.89066	+	5.81886i	−0.0675236	+	0.207816i
$785$	−21.4362	−	33.3323i	−0.765090	−	1.18968i
$786$	−2.82466	−	8.69341i	−0.100752	−	0.310084i
$787$	6.99053	−	21.5146i	0.249185	−	0.766914i	−0.745735	−	0.666243i	$-0.767901\pi$
$787$	6.99053	−	21.5146i	0.249185	−	0.766914i	0.994920	−	0.100670i	$-0.0320987\pi$
$788$	−3.75014	+	11.5418i	−0.133593	+	0.411158i
$789$	1.67800	+	5.16434i	0.0597382	+	0.183855i
$790$	0.902760	−	15.8749i	0.0321188	−	0.564803i
$791$	2.67097	−	8.22041i	0.0949688	−	0.292284i
$792$	−3.79579	−	2.75780i	−0.134877	−	0.0979942i
$793$	25.4173			0.902596
$794$	29.8084	+	21.6571i	1.05786	+	0.768580i
$795$	−6.60064	+	1.73722i	−0.234100	+	0.0616128i
$796$	7.27194	−	5.28337i	0.257747	−	0.187264i
$797$	44.4525	−	32.2967i	1.57459	−	1.14401i	0.652002	−	0.758217i	$-0.273929\pi$
$797$	44.4525	−	32.2967i	1.57459	−	1.14401i	0.922587	−	0.385789i	$-0.126071\pi$
$798$	−0.149847	−	0.461182i	−0.00530453	−	0.0163257i
$799$	31.3897			1.11049
$800$	2.07422	−	4.54946i	0.0733348	−	0.160848i
$801$	37.4008			1.32149
$802$	−10.0114	−	30.8119i	−0.353514	−	1.08800i
$803$	−1.74985	+	1.27134i	−0.0617510	+	0.0448647i
$804$	−6.73404	+	4.89256i	−0.237491	+	0.172547i
$805$	−6.55396	+	8.02029i	−0.230997	+	0.282678i
$806$	32.5462	+	23.6462i	1.14639	+	0.832901i
$807$	−15.3510			−0.540382
$808$	−13.5820	−	9.86793i	−0.477815	−	0.347153i
$809$	−12.5878	+	38.7411i	−0.442562	+	1.36206i	0.442574	+	0.896732i	$0.354065\pi$
$809$	−12.5878	+	38.7411i	−0.442562	+	1.36206i	−0.885136	+	0.465333i	$0.845935\pi$
$810$	14.4253	−	3.79658i	0.506852	−	0.133398i
$811$	−3.59117	−	11.0525i	−0.126103	−	0.388105i	0.867998	−	0.496569i	$-0.165407\pi$
$811$	−3.59117	−	11.0525i	−0.126103	−	0.388105i	−0.994100	+	0.108464i	$0.965407\pi$
$812$	1.23305	−	3.79493i	0.0432715	−	0.133176i
$813$	0.143893	−	0.442856i	0.00504654	−	0.0155317i
$814$	5.11302	+	15.7363i	0.179211	+	0.551556i
$815$	8.99901	−	2.36844i	0.315222	−	0.0829630i
$816$	0.619793	−	1.90753i	0.0216971	−	0.0667768i
$817$	−5.61827	−	4.08191i	−0.196559	−	0.142808i
$818$	5.88001			0.205590
$819$	11.0120	+	8.00070i	0.384791	+	0.279567i
$820$	4.56723	−	5.58906i	0.159494	−	0.195178i
$821$	−14.4635	+	10.5084i	−0.504781	+	0.366745i	−0.810840	−	0.585268i	$-0.800989\pi$
$821$	−14.4635	+	10.5084i	−0.504781	+	0.366745i	0.306059	+	0.952012i	$0.400989\pi$
$822$	−1.52046	+	1.10468i	−0.0530322	+	0.0385302i
$823$	2.13415	+	6.56823i	0.0743917	+	0.228954i	0.981338	−	0.192293i	$-0.0615925\pi$
$823$	2.13415	+	6.56823i	0.0743917	+	0.228954i	−0.906946	+	0.421247i	$0.861592\pi$
$824$	15.4263			0.537399
$825$	3.85808	−	2.18195i	0.134321	−	0.0759659i
$826$	−3.01001			−0.104732
$827$	−16.9249	−	52.0896i	−0.588538	−	1.81133i	−0.584573	−	0.811341i	$-0.698738\pi$
$827$	−16.9249	−	52.0896i	−0.588538	−	1.81133i	−0.00396504	−	0.999992i	$-0.501262\pi$
$828$	−10.9084	+	7.92542i	−0.379093	+	0.275427i
$829$	3.52332	−	2.55984i	0.122370	−	0.0889069i	−0.524917	−	0.851153i	$-0.675904\pi$
$829$	3.52332	−	2.55984i	0.122370	−	0.0889069i	0.647287	+	0.762247i	$0.275904\pi$
$830$	−2.00832	+	0.528570i	−0.0697099	+	0.0183469i
$831$	−10.4565	−	7.59710i	−0.362732	−	0.263540i
$832$	5.30351			0.183866
$833$	19.2241	+	13.9671i	0.666075	+	0.483932i
$834$	−0.441843	+	1.35985i	−0.0152998	+	0.0470879i
$835$	−0.917190	+	16.1286i	−0.0317407	+	0.558154i
$836$	0.530443	+	1.63253i	0.0183457	+	0.0564624i
$837$	−6.94023	+	21.3598i	−0.239890	+	0.738304i
$838$	−2.67851	+	8.24360i	−0.0925276	+	0.284771i
$839$	−4.51349	−	13.8911i	−0.155823	−	0.479574i	0.842420	−	0.538821i	$-0.181130\pi$
$839$	−4.51349	−	13.8911i	−0.155823	−	0.479574i	−0.998243	+	0.0592469i	$0.981130\pi$
$840$	0.586505	+	0.911990i	0.0202363	+	0.0314666i
$841$	−3.38115	+	10.4061i	−0.116591	+	0.358831i
$842$	−1.84407	−	1.33980i	−0.0635510	−	0.0461725i
$843$	−11.4754			−0.395234
$844$	15.8076	+	11.4849i	0.544120	+	0.395327i
$845$	−1.92046	+	33.7709i	−0.0660658	+	1.16175i
$846$	−17.8722	+	12.9849i	−0.614458	+	0.446430i
$847$	6.11784	−	4.44487i	0.210212	−	0.152728i
$848$	1.82650	+	5.62138i	0.0627222	+	0.193039i
$849$	6.57723			0.225730
$850$	−14.3150	−	13.1216i	−0.491000	−	0.450069i
$851$	47.5505			1.63001
$852$	0.685195	+	2.10881i	0.0234744	+	0.0722468i
$853$	−32.4628	+	23.5856i	−1.11151	+	0.807556i	−0.982900	−	0.184139i	$-0.941050\pi$
$853$	−32.4628	+	23.5856i	−1.11151	+	0.807556i	−0.128606	+	0.991696i	$0.541050\pi$
$854$	3.64068	−	2.64511i	0.124582	−	0.0905138i
$855$	−5.69611	−	2.21564i	−0.194803	−	0.0757733i
$856$	−10.4247	−	7.57396i	−0.356308	−	0.258873i
$857$	1.98031			0.0676463			0.0338231	−	0.999428i	$-0.489232\pi$
$857$	1.98031			0.0676463			0.0338231	+	0.999428i	$0.489232\pi$
$858$	3.80351	+	2.76341i	0.129850	+	0.0943414i
$859$	11.6673	−	35.9081i	0.398082	−	1.22517i	−0.528454	−	0.848962i	$-0.677228\pi$
$859$	11.6673	−	35.9081i	0.398082	−	1.22517i	0.926535	−	0.376207i	$-0.122772\pi$
$860$	14.4722	+	5.62933i	0.493499	+	0.191958i
$861$	0.483693	+	1.48866i	0.0164842	+	0.0507332i
$862$	5.81845	−	17.9073i	0.198177	−	0.609927i
$863$	11.1890	−	34.4363i	0.380879	−	1.17223i	−0.558546	−	0.829473i	$-0.688641\pi$
$863$	11.1890	−	34.4363i	0.380879	−	1.17223i	0.939426	−	0.342753i	$-0.111359\pi$
$864$	0.914945	+	2.81591i	0.0311271	+	0.0957993i
$865$	4.95654	−	6.06548i	0.168527	−	0.206232i
$866$	−4.03203	+	12.4093i	−0.137014	+	0.421686i
$867$	0.800552	+	0.581635i	0.0271882	+	0.0197534i
$868$	7.12258			0.241756
$869$	−9.87507	−	7.17466i	−0.334989	−	0.243384i
$870$	2.65432	+	4.12735i	0.0899898	+	0.139930i
$871$	−69.1562	+	50.2449i	−2.34327	+	1.70248i
$872$	−4.39919	+	3.19620i	−0.148975	+	0.108237i
$873$	15.1837	+	46.7307i	0.513892	+	1.58160i
$874$	4.93305			0.166863
$875$	10.3899	−	1.50383i	0.351242	−	0.0508386i
$876$	0.650723			0.0219859
$877$	5.92174	+	18.2253i	0.199963	+	0.615423i	0.999883	+	0.0153159i	$0.00487538\pi$
$877$	5.92174	+	18.2253i	0.199963	+	0.615423i	−0.799920	+	0.600107i	$0.795125\pi$
$878$	18.0841	−	13.1389i	0.610310	−	0.443416i
$879$	−2.29512	+	1.66750i	−0.0774125	+	0.0562435i
$880$	−2.07617	−	3.22835i	−0.0699875	−	0.108828i
$881$	−21.0865	−	15.3202i	−0.710423	−	0.516152i	0.172887	−	0.984942i	$-0.444690\pi$
$881$	−21.0865	−	15.3202i	−0.710423	−	0.516152i	−0.883310	+	0.468789i	$0.844690\pi$
$882$	−16.7232			−0.563100
$883$	−32.9188	−	23.9169i	−1.10781	−	0.804868i	−0.125490	−	0.992095i	$-0.540050\pi$
$883$	−32.9188	−	23.9169i	−1.10781	−	0.804868i	−0.982317	+	0.187226i	$0.940050\pi$
$884$	6.36505	−	19.5896i	0.214080	−	0.658870i
$885$	2.34233	−	2.86638i	0.0787365	−	0.0963523i
$886$	−6.31606	−	19.4388i	−0.212192	−	0.653060i
$887$	0.783642	−	2.41180i	0.0263121	−	0.0809804i	−0.937038	−	0.349227i	$-0.886444\pi$
$887$	0.783642	−	2.41180i	0.0263121	−	0.0809804i	0.963350	+	0.268247i	$0.0864442\pi$
$888$	1.53826	−	4.73427i	0.0516206	−	0.158872i
$889$	5.12619	+	15.7768i	0.171927	+	0.529137i
$890$	28.5157	+	11.0919i	0.955848	+	0.371800i
$891$	3.53851	−	10.8904i	0.118545	−	0.364843i
$892$	12.0761	+	8.77383i	0.404339	+	0.293769i
$893$	8.08223			0.270462
$894$	1.97283	+	1.43335i	0.0659813	+	0.0479382i
$895$	26.3622	+	10.2542i	0.881190	+	0.342760i
$896$	0.759654	−	0.551921i	0.0253783	−	0.0184384i
$897$	10.9306	−	7.94155i	0.364962	−	0.265160i
$898$	−4.28415	−	13.1853i	−0.142964	−	0.439998i
$899$	32.2343			1.07507
$900$	13.5784	+	1.54934i	0.452614	+	0.0516448i
$901$	22.9558			0.764770
$902$	−1.71222	−	5.26968i	−0.0570108	−	0.175461i
$903$	−2.72439	+	1.97938i	−0.0906619	+	0.0658697i
$904$	7.44709	−	5.41063i	0.247686	−	0.179955i
$905$	1.18070	−	20.7623i	0.0392476	−	0.690163i
$906$	8.36745	+	6.07931i	0.277990	+	0.201971i
$907$	−42.2612			−1.40326			−0.701630	−	0.712542i	$-0.747544\pi$
$907$	−42.2612			−1.40326			−0.701630	+	0.712542i	$0.747544\pi$
$908$	19.7747	+	14.3672i	0.656248	+	0.476792i
$909$	14.1801	−	43.6417i	0.470323	−	1.44750i
$910$	6.02320	+	9.36582i	0.199667	+	0.310474i
$911$	−1.97839	−	6.08885i	−0.0655469	−	0.201733i	0.912919	−	0.408140i	$-0.133823\pi$
$911$	−1.97839	−	6.08885i	−0.0655469	−	0.201733i	−0.978466	+	0.206408i	$0.933823\pi$
$912$	0.159584	−	0.491150i	0.00528436	−	0.0162636i
$913$	−0.492641	+	1.51619i	−0.0163040	+	0.0501787i
$914$	−9.85165	−	30.3203i	−0.325864	−	1.00291i
$915$	−0.314210	+	5.52533i	−0.0103875	+	0.182662i
$916$	4.51730	−	13.9028i	0.149256	−	0.459362i
$917$	−13.4460	−	9.76907i	−0.444025	−	0.322603i
$918$	11.4992			0.379531
$919$	24.1056	+	17.5138i	0.795172	+	0.577726i	0.909494	−	0.415718i	$-0.136470\pi$
$919$	24.1056	+	17.5138i	0.795172	+	0.577726i	−0.114322	+	0.993444i	$0.536470\pi$
$920$	−10.6674	+	2.80754i	−0.351692	+	0.0925617i
$921$	0.220279	−	0.160042i	0.00725844	−	0.00527357i
$922$	−7.68452	+	5.58313i	−0.253076	+	0.183871i
$923$	7.03672	+	21.6568i	0.231616	+	0.712842i
$924$	0.832380			0.0273833
$925$	−35.5283	−	32.5665i	−1.16816	−	1.07078i
$926$	5.15347			0.169353
$927$	13.0296	+	40.1010i	0.427948	+	1.31709i
$928$	3.43793	−	2.49780i	0.112856	−	0.0819944i
$929$	−9.86777	+	7.16936i	−0.323751	+	0.235219i	−0.737774	−	0.675047i	$-0.764123\pi$
$929$	−9.86777	+	7.16936i	−0.323751	+	0.235219i	0.414023	+	0.910266i	$0.364123\pi$
$930$	−5.54265	+	6.78272i	−0.181751	+	0.222414i
$931$	4.94982	+	3.59625i	0.162224	+	0.117862i
$932$	16.3970			0.537102
$933$	0.965821	+	0.701710i	0.0316195	+	0.0229729i
$934$	−3.46746	+	10.6717i	−0.113459	+	0.349190i
$935$	−14.4163	+	3.79422i	−0.471464	+	0.124084i
$936$	4.47954	+	13.7866i	0.146418	+	0.450630i
$937$	3.18036	−	9.78815i	0.103898	−	0.319765i	−0.885572	−	0.464502i	$-0.846233\pi$
$937$	3.18036	−	9.78815i	0.103898	−	0.319765i	0.989470	+	0.144737i	$0.0462335\pi$
$938$	−4.67682	+	14.3938i	−0.152704	+	0.469973i
$939$	−1.49192	−	4.59165i	−0.0486869	−	0.149843i
$940$	−17.4772	+	4.59983i	−0.570045	+	0.150030i
$941$	−2.33083	+	7.17355i	−0.0759828	+	0.233851i	−0.981833	−	0.189747i	$-0.939233\pi$
$941$	−2.33083	+	7.17355i	−0.0759828	+	0.233851i	0.905850	+	0.423598i	$0.139233\pi$
$942$	7.40469	+	5.37982i	0.241258	+	0.175284i
$943$	−15.9235			−0.518539
$944$	−2.59338	−	1.88420i	−0.0844075	−	0.0613256i
$945$	−3.93370	+	4.81380i	−0.127963	+	0.156593i
$946$	9.64404	−	7.00681i	0.313555	−	0.227811i
$947$	36.6065	−	26.5962i	1.18955	−	0.864260i	0.196335	−	0.980537i	$-0.437096\pi$
$947$	36.6065	−	26.5962i	1.18955	−	0.864260i	0.993217	+	0.116276i	$0.0370959\pi$
$948$	1.13479	+	3.49253i	0.0368563	+	0.113432i
$949$	6.68269			0.216929
$950$	−3.68583	−	3.37856i	−0.119584	−	0.109615i
$951$	−8.93059			−0.289594
$952$	−1.12693	−	3.46833i	−0.0365240	−	0.112409i
$953$	−15.1600	+	11.0144i	−0.491080	+	0.356791i	−0.805600	−	0.592460i	$-0.798157\pi$
$953$	−15.1600	+	11.0144i	−0.491080	+	0.356791i	0.314519	+	0.949251i	$0.398157\pi$
$954$	−13.0702	+	9.49606i	−0.423163	+	0.307446i
$955$	−7.31880	+	1.92623i	−0.236831	+	0.0623313i
$956$	11.9248	+	8.66388i	0.385676	+	0.280210i
$957$	3.76707			0.121772
$958$	−10.0358	−	7.29143i	−0.324242	−	0.235575i
$959$	−1.05597	+	3.24994i	−0.0340990	+	0.104946i
$960$	−0.0655622	+	1.15290i	−0.00211601	+	0.0372097i
$961$	8.20083	+	25.2396i	0.264543	+	0.814180i
$962$	15.7974	−	48.6193i	0.509328	−	1.56755i
$963$	10.8837	−	33.4965i	0.350721	−	1.07941i
$964$	−3.86290	−	11.8888i	−0.124416	−	0.382912i
$965$	−30.3002	−	47.1155i	−0.975397	−	1.51670i
$966$	0.739202	−	2.27503i	0.0237834	−	0.0731979i
$967$	−21.9346	−	15.9364i	−0.705369	−	0.512481i	0.176307	−	0.984335i	$-0.443585\pi$
$967$	−21.9346	−	15.9364i	−0.705369	−	0.512481i	−0.881676	+	0.471854i	$0.843585\pi$
$968$	8.05346			0.258848
$969$	−1.62264	−	1.17892i	−0.0521267	−	0.0378722i
$970$	−2.28220	+	40.1321i	−0.0732771	+	1.28857i
$971$	−10.5603	+	7.67251i	−0.338896	+	0.246222i	−0.744196	−	0.667961i	$-0.767167\pi$
$971$	−10.5603	+	7.67251i	−0.338896	+	0.246222i	0.405300	+	0.914184i	$0.367167\pi$
$972$	−9.97314	+	7.24591i	−0.319889	+	0.232413i
$973$	0.803376	+	2.47254i	0.0257551	+	0.0792659i
$974$	−8.30774			−0.266197
$975$	−13.6061	−	1.55250i	−0.435742	−	0.0497197i
$976$	4.79255			0.153406
$977$	1.89418	+	5.82969i	0.0606003	+	0.186508i	0.976774	−	0.214274i	$-0.0687384\pi$
$977$	1.89418	+	5.82969i	0.0606003	+	0.186508i	−0.916173	+	0.400782i	$0.868738\pi$
$978$	−1.73868	+	1.26322i	−0.0555967	+	0.0403934i
$979$	19.0023	−	13.8060i	0.607318	−	0.441242i
$980$	−12.7503	−	4.95956i	−0.407295	−	0.158427i
$981$	−12.0243	−	8.73619i	−0.383907	−	0.278925i
$982$	33.8400			1.07988
$983$	2.91989	+	2.12142i	0.0931300	+	0.0676629i	0.633376	−	0.773844i	$-0.281669\pi$
$983$	2.91989	+	2.12142i	0.0931300	+	0.0676629i	−0.540246	+	0.841507i	$0.681669\pi$
$984$	−0.515124	+	1.58539i	−0.0164216	+	0.0505404i
$985$	−25.2904	−	9.83732i	−0.805820	−	0.313443i
$986$	−5.10009	−	15.6965i	−0.162420	−	0.499878i
$987$	1.21110	−	3.72738i	0.0385497	−	0.118644i
$988$	1.63887	−	5.04394i	0.0521395	−	0.160469i
$989$	−10.5863	−	32.5812i	−0.336624	−	1.03602i
$990$	6.63857	−	8.12383i	0.210988	−	0.258192i
$991$	14.1298	−	43.4869i	0.448846	−	1.38141i	−0.429364	−	0.903132i	$-0.641262\pi$
$991$	14.1298	−	43.4869i	0.448846	−	1.38141i	0.878210	−	0.478275i	$-0.158738\pi$
$992$	6.13673	+	4.45859i	0.194841	+	0.141560i
$993$	9.56111			0.303413
$994$	3.26167	+	2.36974i	0.103454	+	0.0751636i
$995$	10.8717	+	16.9051i	0.344657	+	0.535926i
$996$	0.388023	−	0.281915i	0.0122950	−	0.00893283i
$997$	41.4261	−	30.0978i	1.31198	−	0.953207i	0.311982	−	0.950088i	$-0.399007\pi$
$997$	41.4261	−	30.0978i	1.31198	−	0.953207i	0.999995	−	0.00311929i	$-0.000992902\pi$
$998$	−2.35145	−	7.23703i	−0.0744340	−	0.229084i
$999$	28.5399			0.902962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.e.381.6	✓	44
25.21	even	5	inner	950.2.h.e.571.6	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.e.381.6	✓	44	1.1	even	1	trivial
950.2.h.e.571.6	yes	44	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.417797 + 0.303547i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.20950 - 1.88072i) q^{5} +(0.417797 + 0.303547i) q^{6} +0.938984 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.844638 + 2.59953i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.417797 + 0.303547i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.20950 - 1.88072i) q^{5} +(0.417797 + 0.303547i) q^{6} +0.938984 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.844638 + 2.59953i) q^{9} +(-1.41492 + 1.73148i) q^{10} +(0.530443 + 1.63253i) q^{11} +(0.159584 - 0.491150i) q^{12} +(1.63887 - 5.04394i) q^{13} +(-0.290162 - 0.893027i) q^{14} +(1.07621 + 0.418619i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.14206 - 2.28284i) q^{17} +2.73330 q^{18} +(-0.809017 - 0.587785i) q^{19} +(2.08397 + 0.810609i) q^{20} +(-0.392305 + 0.285026i) q^{21} +(1.38872 - 1.00896i) q^{22} +(-1.52440 - 4.69161i) q^{23} -0.516426 q^{24} +(-2.07422 + 4.54946i) q^{25} -5.30351 q^{26} +(-0.914945 - 2.81591i) q^{27} +(-0.759654 + 0.551921i) q^{28} +(-3.43793 + 2.49780i) q^{29} +(0.0655622 - 1.15290i) q^{30} +(-6.13673 - 4.45859i) q^{31} -1.00000 q^{32} +(-0.717169 - 0.521054i) q^{33} +(-1.20016 + 3.69371i) q^{34} +(-1.13570 - 1.76597i) q^{35} +(-0.844638 - 2.59953i) q^{36} +(-2.97867 + 9.16739i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(0.846357 + 2.60482i) q^{39} +(0.126954 - 2.23246i) q^{40} +(0.997480 - 3.06993i) q^{41} +(0.392305 + 0.285026i) q^{42} +6.94457 q^{43} +(-1.38872 - 1.00896i) q^{44} +(5.91057 - 1.55560i) q^{45} +(-3.99092 + 2.89957i) q^{46} +(-6.53866 + 4.75062i) q^{47} +(0.159584 + 0.491150i) q^{48} -6.11831 q^{49} +(4.96777 + 0.566839i) q^{50} +2.00569 q^{51} +(1.63887 + 5.04394i) q^{52} +(-4.78183 + 3.47420i) q^{53} +(-2.39536 + 1.74033i) q^{54} +(2.42877 - 2.97217i) q^{55} +(0.759654 + 0.551921i) q^{56} +0.516426 q^{57} +(3.43793 + 2.49780i) q^{58} +(0.990585 - 3.04871i) q^{59} +(-1.11673 + 0.293912i) q^{60} +(1.48098 + 4.55799i) q^{61} +(-2.34402 + 7.21415i) q^{62} +(-0.793101 + 2.44091i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-11.4685 + 3.01838i) q^{65} +(-0.273934 + 0.843083i) q^{66} +(-13.0397 - 9.47390i) q^{67} +3.88380 q^{68} +(2.06101 + 1.49741i) q^{69} +(-1.32858 + 1.62583i) q^{70} +(-3.47362 + 2.52373i) q^{71} +(-2.21129 + 1.60660i) q^{72} +(0.389377 + 1.19838i) q^{73} +9.63916 q^{74} +(-0.514374 - 2.53038i) q^{75} +1.00000 q^{76} +(0.498077 + 1.53292i) q^{77} +(2.21579 - 1.60987i) q^{78} +(-5.75286 + 4.17970i) q^{79} +(-2.16243 + 0.569128i) q^{80} +(-5.39685 - 3.92104i) q^{81} -3.22791 q^{82} +(0.751363 + 0.545897i) q^{83} +(0.149847 - 0.461182i) q^{84} +(-0.493063 + 8.67042i) q^{85} +(-2.14599 - 6.60468i) q^{86} +(0.678156 - 2.08715i) q^{87} +(-0.530443 + 1.63253i) q^{88} +(-4.22840 - 13.0137i) q^{89} +(-3.30593 - 5.14058i) q^{90} +(1.53888 - 4.73617i) q^{91} +(3.99092 + 2.89957i) q^{92} +3.91730 q^{93} +(6.53866 + 4.75062i) q^{94} +(-0.126954 + 2.23246i) q^{95} +(0.417797 - 0.303547i) q^{96} +(14.5434 - 10.5664i) q^{97} +(1.89066 + 5.81886i) q^{98} -4.69185 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Introduction

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