LMFDB - Embedded newform 315.2.t.c.101.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.7
Character	$\chi$	$=$	315.101
Dual form			315.2.t.c.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.524306i q^{2} +(1.63490 - 0.571919i) q^{3} +1.72510 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.299860 - 0.857190i) q^{6} +(-1.53835 + 2.15255i) q^{7} -1.95309i q^{8} +(2.34582 - 1.87006i) q^{9} +O(q^{10})$	\(q-0.524306i q^{2} +(1.63490 - 0.571919i) q^{3} +1.72510 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.299860 - 0.857190i) q^{6} +(-1.53835 + 2.15255i) q^{7} -1.95309i q^{8} +(2.34582 - 1.87006i) q^{9} +(0.454062 + 0.262153i) q^{10} +(-0.593570 + 0.342698i) q^{11} +(2.82038 - 0.986619i) q^{12} +(5.48168 - 3.16485i) q^{13} +(1.12860 + 0.806566i) q^{14} +(-0.322156 + 1.70183i) q^{15} +2.42619 q^{16} +(-1.00830 + 1.74642i) q^{17} +(-0.980486 - 1.22993i) q^{18} +(-5.11150 + 2.95112i) q^{19} +(-0.862552 + 1.49398i) q^{20} +(-1.28397 + 4.39903i) q^{21} +(0.179678 + 0.311212i) q^{22} +(-6.98472 - 4.03263i) q^{23} +(-1.11701 - 3.19312i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.65935 - 2.87408i) q^{26} +(2.76566 - 4.39899i) q^{27} +(-2.65381 + 3.71337i) q^{28} +(0.246759 + 0.142467i) q^{29} +(0.892278 + 0.168908i) q^{30} +4.59817i q^{31} -5.17825i q^{32} +(-0.774434 + 0.899751i) q^{33} +(0.915659 + 0.528656i) q^{34} +(-1.09499 - 2.40853i) q^{35} +(4.04678 - 3.22605i) q^{36} +(-0.593585 - 1.02812i) q^{37} +(1.54729 + 2.67999i) q^{38} +(7.15198 - 8.30930i) q^{39} +(1.69143 + 0.976547i) q^{40} +(3.16732 + 5.48596i) q^{41} +(2.30644 + 0.673192i) q^{42} +(-1.53520 + 2.65905i) q^{43} +(-1.02397 + 0.591189i) q^{44} +(0.446614 + 2.96657i) q^{45} +(-2.11433 + 3.66213i) q^{46} -11.1557 q^{47} +(3.96658 - 1.38758i) q^{48} +(-2.26696 - 6.62275i) q^{49} +(-0.454062 + 0.262153i) q^{50} +(-0.649657 + 3.43189i) q^{51} +(9.45647 - 5.45969i) q^{52} +(-8.01159 - 4.62549i) q^{53} +(-2.30642 - 1.45005i) q^{54} -0.685395i q^{55} +(4.20414 + 3.00454i) q^{56} +(-6.66900 + 7.74816i) q^{57} +(0.0746961 - 0.129378i) q^{58} +7.27543 q^{59} +(-0.555752 + 2.93583i) q^{60} +1.96489i q^{61} +2.41085 q^{62} +(0.416722 + 7.92631i) q^{63} +2.13738 q^{64} +6.32970i q^{65} +(0.471745 + 0.406040i) q^{66} +4.13667 q^{67} +(-1.73942 + 3.01276i) q^{68} +(-13.7257 - 2.59827i) q^{69} +(-1.26280 + 0.574110i) q^{70} +3.56258i q^{71} +(-3.65241 - 4.58160i) q^{72} +(-3.24977 - 1.87626i) q^{73} +(-0.539049 + 0.311220i) q^{74} +(-1.31275 - 1.12991i) q^{75} +(-8.81786 + 5.09099i) q^{76} +(0.175443 - 1.80488i) q^{77} +(-4.35662 - 3.74983i) q^{78} -4.85329 q^{79} +(-1.21309 + 2.10114i) q^{80} +(2.00572 - 8.77366i) q^{81} +(2.87632 - 1.66065i) q^{82} +(-2.12987 + 3.68905i) q^{83} +(-2.21498 + 7.58877i) q^{84} +(-1.00830 - 1.74642i) q^{85} +(1.39415 + 0.804916i) q^{86} +(0.484907 + 0.0917928i) q^{87} +(0.669321 + 1.15930i) q^{88} +(2.97729 + 5.15681i) q^{89} +(1.55539 - 0.234162i) q^{90} +(-1.62023 + 16.6683i) q^{91} +(-12.0494 - 6.95671i) q^{92} +(2.62978 + 7.51756i) q^{93} +5.84899i q^{94} -5.90225i q^{95} +(-2.96154 - 8.46594i) q^{96} +(-8.55461 - 4.93901i) q^{97} +(-3.47235 + 1.18858i) q^{98} +(-0.751540 + 1.91392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	0.524306i		−	0.370740i	−0.982669	−	0.185370i	$-0.940652\pi$
$2$		−	0.524306i		−	0.370740i	0.982669	−	0.185370i	$-0.0593484\pi$
$3$	1.63490	−	0.571919i	0.943912	−	0.330197i
$3$	1.63490	−	0.571919i	0.943912	−	0.330197i
$4$	1.72510			0.862552
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.299860	−	0.857190i	−0.122418	−	0.349946i
$7$	−1.53835	+	2.15255i	−0.581441	+	0.813588i
$7$	−1.53835	+	2.15255i	−0.581441	+	0.813588i
$8$		−	1.95309i		−	0.690523i
$9$	2.34582	−	1.87006i	0.781939	−	0.623355i
$10$	0.454062	+	0.262153i	0.143587	+	0.0829001i
$11$	−0.593570	+	0.342698i	−0.178968	+	0.103327i	−0.586808	−	0.809726i	$-0.699616\pi$
$11$	−0.593570	+	0.342698i	−0.178968	+	0.103327i	0.407840	+	0.913054i	$0.366282\pi$
$12$	2.82038	−	0.986619i	0.814173	−	0.284812i
$13$	5.48168	−	3.16485i	1.52034	−	0.877772i	0.520633	−	0.853781i	$-0.325696\pi$
$13$	5.48168	−	3.16485i	1.52034	−	0.877772i	0.999712	−	0.0239908i	$-0.00763723\pi$
$14$	1.12860	+	0.806566i	0.301630	+	0.215564i
$15$	−0.322156	+	1.70183i	−0.0831802	+	0.439410i
$16$	2.42619			0.606547
$17$	−1.00830	+	1.74642i	−0.244548	+	0.423569i	−0.962004	−	0.273034i	$-0.911973\pi$
$17$	−1.00830	+	1.74642i	−0.244548	+	0.423569i	0.717457	+	0.696603i	$0.245306\pi$
$18$	−0.980486	−	1.22993i	−0.231103	−	0.289897i
$19$	−5.11150	+	2.95112i	−1.17266	+	0.677034i	−0.954305	−	0.298836i	$-0.903402\pi$
$19$	−5.11150	+	2.95112i	−1.17266	+	0.677034i	−0.218353	+	0.975870i	$0.570068\pi$
$20$	−0.862552	+	1.49398i	−0.192872	+	0.334065i
$21$	−1.28397	+	4.39903i	−0.280185	+	0.959946i
$22$	0.179678	+	0.311212i	0.0383076	+	0.0663507i
$23$	−6.98472	−	4.03263i	−1.45642	−	0.840862i	−0.457583	−	0.889167i	$-0.651285\pi$
$23$	−6.98472	−	4.03263i	−1.45642	−	0.840862i	−0.998833	+	0.0483050i	$0.984618\pi$
$24$	−1.11701	−	3.19312i	−0.228009	−	0.651793i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.65935	−	2.87408i	−0.325425	−	0.563653i
$27$	2.76566	−	4.39899i	0.532252	−	0.846586i
$28$	−2.65381	+	3.71337i	−0.501523	+	0.701762i
$29$	0.246759	+	0.142467i	0.0458221	+	0.0264554i	0.522736	−	0.852495i	$-0.324911\pi$
$29$	0.246759	+	0.142467i	0.0458221	+	0.0264554i	−0.476914	+	0.878950i	$0.658245\pi$
$30$	0.892278	+	0.168908i	0.162907	+	0.0308383i
$31$			4.59817i			0.825856i	0.910764	+	0.412928i	$0.135494\pi$
$31$			4.59817i			0.825856i	−0.910764	+	0.412928i	$0.864506\pi$
$32$		−	5.17825i		−	0.915395i
$33$	−0.774434	+	0.899751i	−0.134812	+	0.156627i
$34$	0.915659	+	0.528656i	0.157034	+	0.0906638i
$35$	−1.09499	−	2.40853i	−0.185087	−	0.407115i
$36$	4.04678	−	3.22605i	0.674463	−	0.537675i
$37$	−0.593585	−	1.02812i	−0.0975847	−	0.169022i	0.813100	−	0.582124i	$-0.197778\pi$
$37$	−0.593585	−	1.02812i	−0.0975847	−	0.169022i	−0.910684	+	0.413103i	$0.864445\pi$
$38$	1.54729	+	2.67999i	0.251004	+	0.434752i
$39$	7.15198	−	8.30930i	1.14523	−	1.33055i
$40$	1.69143	+	0.976547i	0.267438	+	0.154406i
$41$	3.16732	+	5.48596i	0.494653	+	0.856763i	0.999981	−	0.00616369i	$-0.00196198\pi$
$41$	3.16732	+	5.48596i	0.494653	+	0.856763i	−0.505328	+	0.862927i	$0.668629\pi$
$42$	2.30644	+	0.673192i	0.355891	+	0.103876i
$43$	−1.53520	+	2.65905i	−0.234116	+	0.405501i	−0.959015	−	0.283354i	$-0.908553\pi$
$43$	−1.53520	+	2.65905i	−0.234116	+	0.405501i	0.724899	+	0.688855i	$0.241886\pi$
$44$	−1.02397	+	0.591189i	−0.154369	+	0.0891250i
$45$	0.446614	+	2.96657i	0.0665772	+	0.442230i
$46$	−2.11433	+	3.66213i	−0.311742	+	0.539952i
$47$	−11.1557			−1.62722			−0.813612	−	0.581408i	$-0.802502\pi$
$47$	−11.1557			−1.62722			−0.813612	+	0.581408i	$0.802502\pi$
$48$	3.96658	−	1.38758i	0.572527	−	0.200280i
$49$	−2.26696	−	6.62275i	−0.323852	−	0.946108i
$50$	−0.454062	+	0.262153i	−0.0642141	+	0.0370740i
$51$	−0.649657	+	3.43189i	−0.0909701	+	0.480561i
$52$	9.45647	−	5.45969i	1.31138	−	0.757123i
$53$	−8.01159	−	4.62549i	−1.10048	−	0.635360i	−0.164130	−	0.986439i	$-0.552482\pi$
$53$	−8.01159	−	4.62549i	−1.10048	−	0.635360i	−0.936346	+	0.351079i	$0.885815\pi$
$54$	−2.30642	−	1.45005i	−0.313864	−	0.197327i
$55$		−	0.685395i		−	0.0924187i
$56$	4.20414	+	3.00454i	0.561802	+	0.401499i
$57$	−6.66900	+	7.74816i	−0.883331	+	1.02627i
$58$	0.0746961	−	0.129378i	0.00980808	−	0.0169881i
$59$	7.27543			0.947181			0.473590	−	0.880745i	$-0.342958\pi$
$59$	7.27543			0.947181			0.473590	+	0.880745i	$0.342958\pi$
$60$	−0.555752	+	2.93583i	−0.0717472	+	0.379014i
$61$			1.96489i			0.251578i	0.992057	+	0.125789i	$0.0401463\pi$
$61$			1.96489i			0.251578i	−0.992057	+	0.125789i	$0.959854\pi$
$62$	2.41085			0.306178
$63$	0.416722	+	7.92631i	0.0525021	+	0.998621i
$64$	2.13738			0.267173
$65$			6.32970i			0.785103i
$66$	0.471745	+	0.406040i	0.0580678	+	0.0499801i
$67$	4.13667			0.505375			0.252687	−	0.967548i	$-0.418686\pi$
$67$	4.13667			0.505375			0.252687	+	0.967548i	$0.418686\pi$
$68$	−1.73942	+	3.01276i	−0.210935	+	0.365350i
$69$	−13.7257	−	2.59827i	−1.65238	−	0.312795i
$70$	−1.26280	+	0.574110i	−0.150934	+	0.0686193i
$71$			3.56258i			0.422801i	0.977400	+	0.211400i	$0.0678024\pi$
$71$			3.56258i			0.422801i	−0.977400	+	0.211400i	$0.932198\pi$
$72$	−3.65241	−	4.58160i	−0.430441	−	0.539947i
$73$	−3.24977	−	1.87626i	−0.380357	−	0.219599i	0.297617	−	0.954685i	$-0.403808\pi$
$73$	−3.24977	−	1.87626i	−0.380357	−	0.219599i	−0.677974	+	0.735086i	$0.737142\pi$
$74$	−0.539049	+	0.311220i	−0.0626632	+	0.0361786i
$75$	−1.31275	−	1.12991i	−0.151583	−	0.130471i
$76$	−8.81786	+	5.09099i	−1.01148	+	0.583977i
$77$	0.175443	−	1.80488i	0.0199936	−	0.205685i
$78$	−4.35662	−	3.74983i	−0.493290	−	0.424584i
$79$	−4.85329			−0.546038			−0.273019	−	0.962009i	$-0.588022\pi$
$79$	−4.85329			−0.546038			−0.273019	+	0.962009i	$0.588022\pi$
$80$	−1.21309	+	2.10114i	−0.135628	+	0.234915i
$81$	2.00572	−	8.77366i	0.222858	−	0.974851i
$82$	2.87632	−	1.66065i	0.317637	−	0.183388i
$83$	−2.12987	+	3.68905i	−0.233784	+	0.404925i	−0.958919	−	0.283682i	$-0.908444\pi$
$83$	−2.12987	+	3.68905i	−0.233784	+	0.404925i	0.725135	+	0.688607i	$0.241777\pi$
$84$	−2.21498	+	7.58877i	−0.241674	+	0.828003i
$85$	−1.00830	−	1.74642i	−0.109365	−	0.189426i
$86$	1.39415	+	0.804916i	0.150336	+	0.0867963i
$87$	0.484907	+	0.0917928i	0.0519875	+	0.00984123i
$88$	0.669321	+	1.15930i	0.0713498	+	0.123582i
$89$	2.97729	+	5.15681i	0.315592	+	0.546621i	0.979563	−	0.201137i	$-0.0644637\pi$
$89$	2.97729	+	5.15681i	0.315592	+	0.546621i	−0.663971	+	0.747758i	$0.731130\pi$
$90$	1.55539	−	0.234162i	0.163953	−	0.0246829i
$91$	−1.62023	+	16.6683i	−0.169847	+	1.74731i
$92$	−12.0494	−	6.95671i	−1.25623	−	0.725287i
$93$	2.62978	+	7.51756i	0.272695	+	0.779535i
$94$			5.84899i			0.603278i
$95$		−	5.90225i		−	0.605558i
$96$	−2.96154	−	8.46594i	−0.302261	−	0.864052i
$97$	−8.55461	−	4.93901i	−0.868589	−	0.501480i	−0.00170992	−	0.999999i	$-0.500544\pi$
$97$	−8.55461	−	4.93901i	−0.868589	−	0.501480i	−0.866879	+	0.498518i	$0.833878\pi$
$98$	−3.47235	+	1.18858i	−0.350760	+	0.120065i
$99$	−0.751540	+	1.91392i	−0.0755326	+	0.192356i
$100$	−0.862552	−	1.49398i	−0.0862552	−	0.149398i
$101$	3.38111	+	5.85625i	0.336433	+	0.582719i	0.983759	−	0.179494i	$-0.0574461\pi$
$101$	3.38111	+	5.85625i	0.336433	+	0.582719i	−0.647326	+	0.762213i	$0.724113\pi$
$102$	1.79936	+	0.340619i	0.178163	+	0.0337263i
$103$	15.0412	+	8.68406i	1.48206	+	0.855666i	0.999793	−	0.0203601i	$-0.00648125\pi$
$103$	15.0412	+	8.68406i	1.48206	+	0.855666i	0.482264	+	0.876026i	$0.339815\pi$
$104$	−6.18125	−	10.7062i	−0.606122	−	1.04983i
$105$	−3.16768	−	3.31146i	−0.309134	−	0.323166i
$106$	−2.42517	+	4.20052i	−0.235554	+	0.407991i
$107$	12.6434	−	7.29966i	1.22228	−	0.705685i	0.256878	−	0.966444i	$-0.417306\pi$
$107$	12.6434	−	7.29966i	1.22228	−	0.705685i	0.965404	+	0.260759i	$0.0839727\pi$
$108$	4.77105	−	7.58871i	0.459095	−	0.730224i
$109$	−0.585706	+	1.01447i	−0.0561005	+	0.0971688i	−0.892712	−	0.450628i	$-0.851200\pi$
$109$	−0.585706	+	1.01447i	−0.0561005	+	0.0971688i	0.836611	+	0.547797i	$0.184533\pi$
$110$	−0.359357			−0.0342633
$111$	−1.55845	−	1.34139i	−0.147922	−	0.127319i
$112$	−3.73232	+	5.22249i	−0.352671	+	0.493479i
$113$	3.36272	−	1.94146i	0.316338	−	0.182638i	−0.333421	−	0.942778i	$-0.608203\pi$
$113$	3.36272	−	1.94146i	0.316338	−	0.182638i	0.649759	+	0.760140i	$0.274870\pi$
$114$	4.06241	+	3.49660i	0.380480	+	0.327486i
$115$	6.98472	−	4.03263i	0.651329	−	0.376045i
$116$	0.425686	+	0.245770i	0.0395239	+	0.0228191i
$117$	6.94056	−	17.6753i	0.641655	−	1.63408i
$118$		−	3.81456i		−	0.351158i
$119$	−2.20815	−	4.85702i	−0.202421	−	0.445242i
$120$	3.32383	+	0.629200i	0.303423	+	0.0574379i
$121$	−5.26512	+	9.11945i	−0.478647	+	0.829041i
$122$	1.03020			0.0932703
$123$	8.31579	+	7.15757i	0.749810	+	0.645376i
$124$			7.93232i			0.712343i
$125$	1.00000			0.0894427
$126$	4.15581	−	0.218490i	0.370229	−	0.0194646i
$127$	−10.6893			−0.948522			−0.474261	−	0.880384i	$-0.657285\pi$
$127$	−10.6893			−0.948522			−0.474261	+	0.880384i	$0.657285\pi$
$128$		−	11.4772i		−	1.01445i
$129$	−0.989147	+	5.22530i	−0.0870896	+	0.460062i
$130$	3.31870			0.291069
$131$	−4.99505	+	8.65168i	−0.436420	+	0.755901i	−0.997410	−	0.0719211i	$-0.977087\pi$
$131$	−4.99505	+	8.65168i	−0.436420	+	0.755901i	0.560991	+	0.827822i	$0.310420\pi$
$132$	−1.33598	+	1.55216i	−0.116282	+	0.135098i
$133$	1.51082	−	15.5426i	0.131005	−	1.34772i
$134$		−	2.16888i		−	0.187363i
$135$	2.42681	+	4.59463i	0.208866	+	0.395443i
$136$	3.41093	+	1.96930i	0.292484	+	0.168866i
$137$	16.6642	−	9.62109i	1.42372	−	0.821985i	0.427105	−	0.904202i	$-0.359533\pi$
$137$	16.6642	−	9.62109i	1.42372	−	0.821985i	0.996614	+	0.0822169i	$0.0262000\pi$
$138$	−1.36229	+	7.19646i	−0.115966	+	0.612603i
$139$	17.6387	−	10.1837i	1.49609	−	0.863769i	0.496102	−	0.868264i	$-0.334764\pi$
$139$	17.6387	−	10.1837i	1.49609	−	0.863769i	0.999990	+	0.00449501i	$0.00143081\pi$
$140$	−1.88897	−	4.15496i	−0.159647	−	0.351158i
$141$	−18.2385	+	6.38015i	−1.53596	+	0.537305i
$142$	1.86788			0.156749
$143$	−2.16917	+	3.75712i	−0.181395	+	0.314186i
$144$	5.69139	−	4.53712i	0.474283	−	0.378094i
$145$	−0.246759	+	0.142467i	−0.0204923	+	0.0118312i
$146$	−0.983733	+	1.70388i	−0.0814143	+	0.141014i
$147$	−7.49394	−	9.53105i	−0.618090	−	0.786107i
$148$	−1.02399	−	1.77361i	−0.0841718	−	0.145790i
$149$	0.459895	+	0.265520i	0.0376760	+	0.0217523i	0.518720	−	0.854944i	$-0.326409\pi$
$149$	0.459895	+	0.265520i	0.0376760	+	0.0217523i	−0.481044	+	0.876697i	$0.659742\pi$
$150$	−0.592418	+	0.688282i	−0.0483707	+	0.0561980i
$151$	−7.57954	−	13.1281i	−0.616814	−	1.06835i	−0.990063	−	0.140622i	$-0.955090\pi$
$151$	−7.57954	−	13.1281i	−0.616814	−	1.06835i	0.373249	−	0.927731i	$-0.378244\pi$
$152$	5.76382	+	9.98324i	0.467508	+	0.809747i
$153$	0.900638	+	5.98237i	0.0728123	+	0.483646i
$154$	−0.946309	−	0.0919858i	−0.0762557	−	0.00741243i
$155$	−3.98213	−	2.29908i	−0.319853	−	0.184667i
$156$	12.3379	−	14.3344i	0.987823	−	1.14767i
$157$		−	6.26180i		−	0.499746i	−0.968279	−	0.249873i	$-0.919611\pi$
$157$		−	6.26180i		−	0.499746i	0.968279	−	0.249873i	$-0.0803889\pi$
$158$			2.54461i			0.202438i
$159$	−15.7436	−	2.98026i	−1.24855	−	0.236350i
$160$	4.48450	+	2.58913i	0.354531	+	0.204688i
$161$	19.4254	−	8.83139i	1.53094	−	0.696011i
$162$	−4.60008	−	1.05161i	−0.361417	−	0.0826226i
$163$	−8.97569	−	15.5463i	−0.703030	−	1.21768i	−0.967398	−	0.253262i	$-0.918497\pi$
$163$	−8.97569	−	15.5463i	−0.703030	−	1.21768i	0.264368	−	0.964422i	$-0.414837\pi$
$164$	5.46396	+	9.46385i	0.426663	+	0.739003i
$165$	−0.391990	−	1.12055i	−0.0305164	−	0.0872351i
$166$	1.93419	+	1.11671i	0.150122	+	0.0866731i
$167$	12.5882	+	21.8033i	0.974101	+	1.68719i	0.682872	+	0.730538i	$0.260731\pi$
$167$	12.5882	+	21.8033i	0.974101	+	1.68719i	0.291229	+	0.956653i	$0.405936\pi$
$168$	8.59171	+	2.50771i	0.662865	+	0.193474i
$169$	13.5326	−	23.4391i	1.04097	−	1.80301i
$170$	−0.915659	+	0.528656i	−0.0702279	+	0.0405461i
$171$	−6.47185	+	16.4816i	−0.494915	+	1.26038i
$172$	−2.64838	+	4.58713i	−0.201937	+	0.349765i
$173$	5.34971			0.406731			0.203365	−	0.979103i	$-0.434812\pi$
$173$	5.34971			0.406731			0.203365	+	0.979103i	$0.434812\pi$
$174$	0.0481276	−	0.254240i	0.00364854	−	0.0192739i
$175$	2.63334	+	0.255973i	0.199062	+	0.0193498i
$176$	−1.44011	+	0.831448i	−0.108552	+	0.0626728i
$177$	11.8946	−	4.16096i	0.894055	−	0.312757i
$178$	2.70375	−	1.56101i	0.202654	−	0.117003i
$179$	7.73789	+	4.46747i	0.578357	+	0.333915i	0.760480	−	0.649361i	$-0.224964\pi$
$179$	7.73789	+	4.46747i	0.578357	+	0.333915i	−0.182123	+	0.983276i	$0.558297\pi$
$180$	0.770454	+	5.11764i	0.0574263	+	0.381446i
$181$		−	3.02129i		−	0.224571i	−0.993676	−	0.112286i	$-0.964183\pi$
$181$		−	3.02129i		−	0.224571i	0.993676	−	0.112286i	$-0.0358171\pi$
$182$	8.73927	+	0.849499i	0.647798	+	0.0629691i
$183$	1.12376	+	3.21241i	0.0830705	+	0.237468i
$184$	−7.87611	+	13.6418i	−0.580635	+	1.00569i
$185$	1.18717			0.0872824
$186$	3.94150	−	1.37881i	0.289005	−	0.101099i
$187$		−	1.38216i		−	0.101074i
$188$	−19.2447			−1.40356
$189$	5.21450	+	12.7204i	0.379299	+	0.925274i
$190$	−3.09458			−0.224505
$191$		−	26.3636i		−	1.90760i	−0.300442	−	0.953800i	$-0.597134\pi$
$191$		−	26.3636i		−	1.90760i	0.300442	−	0.953800i	$-0.402866\pi$
$192$	3.49441	−	1.22241i	0.252188	−	0.0882198i
$193$	12.9950			0.935401			0.467701	−	0.883887i	$-0.345083\pi$
$193$	12.9950			0.935401			0.467701	+	0.883887i	$0.345083\pi$
$194$	−2.58955	+	4.48523i	−0.185919	+	0.322021i
$195$	3.62007	+	10.3484i	0.259239	+	0.741068i
$196$	−3.91074	−	11.4249i	−0.279339	−	0.816067i
$197$			8.97314i			0.639310i	0.947534	+	0.319655i	$0.103567\pi$
$197$			8.97314i			0.639310i	−0.947534	+	0.319655i	$0.896433\pi$
$198$	1.00348	+	0.394037i	0.0713142	+	0.0280030i
$199$	−9.18073	−	5.30050i	−0.650805	−	0.375742i	0.137960	−	0.990438i	$-0.455946\pi$
$199$	−9.18073	−	5.30050i	−0.650805	−	0.375742i	−0.788764	+	0.614696i	$0.789279\pi$
$200$	−1.69143	+	0.976547i	−0.119602	+	0.0690523i
$201$	6.76305	−	2.36584i	0.477029	−	0.166873i
$202$	3.07047	−	1.77274i	0.216037	−	0.124729i
$203$	−0.686269	+	0.311999i	−0.0481667	+	0.0218981i
$204$	−1.12072	+	5.92037i	−0.0784664	+	0.414509i
$205$	−6.33464			−0.442431
$206$	4.55311	−	7.88621i	0.317230	−	0.549458i
$207$	−23.9262	+	3.60206i	−1.66298	+	0.250360i
$208$	13.2996	−	7.67852i	0.922160	−	0.532409i
$209$	2.02269	−	3.50340i	0.139912	−	0.242335i
$210$	−1.73622	+	1.66084i	−0.119811	+	0.114609i
$211$	−2.33969	−	4.05246i	−0.161071	−	0.278983i	0.774182	−	0.632963i	$-0.218161\pi$
$211$	−2.33969	−	4.05246i	−0.161071	−	0.278983i	−0.935253	+	0.353980i	$0.884828\pi$
$212$	−13.8208	−	7.97945i	−0.949217	−	0.548031i
$213$	2.03751	+	5.82448i	0.139608	+	0.399087i
$214$	−3.82726	−	6.62900i	−0.261626	−	0.453149i
$215$	−1.53520	−	2.65905i	−0.104700	−	0.181346i
$216$	−8.59164	−	5.40160i	−0.584587	−	0.367532i
$217$	−9.89780	−	7.07359i	−0.671907	−	0.480187i
$218$	0.531894	+	0.307089i	0.0360244	+	0.0207987i
$219$	−6.38613	−	1.20889i	−0.431535	−	0.0816894i
$220$		−	1.18238i		−	0.0797159i
$221$			12.7644i			0.858629i
$222$	−0.703300	+	0.817107i	−0.0472024	+	0.0548406i
$223$	−14.6072	−	8.43348i	−0.978171	−	0.564748i	−0.0764539	−	0.997073i	$-0.524360\pi$
$223$	−14.6072	−	8.43348i	−0.978171	−	0.564748i	−0.901718	+	0.432326i	$0.857693\pi$
$224$	11.1465	+	7.96596i	0.744754	+	0.532248i
$225$	−2.79243	−	1.09651i	−0.186162	−	0.0731004i
$226$	−1.01792	−	1.76309i	−0.0677112	−	0.117279i
$227$	10.2426	+	17.7407i	0.679827	+	1.17749i	0.975033	+	0.222061i	$0.0712783\pi$
$227$	10.2426	+	17.7407i	0.679827	+	1.17749i	−0.295206	+	0.955434i	$0.595388\pi$
$228$	−11.5047	+	13.3664i	−0.761918	+	0.885210i
$229$	−3.81051	−	2.20000i	−0.251805	−	0.145380i	0.368785	−	0.929515i	$-0.379774\pi$
$229$	−3.81051	−	2.20000i	−0.251805	−	0.145380i	−0.620591	+	0.784135i	$0.713107\pi$
$230$	−2.11433	−	3.66213i	−0.139415	−	0.241474i
$231$	−0.745411	−	3.05114i	−0.0490445	−	0.200750i
$232$	0.278251	−	0.481945i	0.0182681	−	0.0316412i
$233$	−16.1414	+	9.31924i	−1.05746	+	0.610524i	−0.924728	−	0.380628i	$-0.875708\pi$
$233$	−16.1414	+	9.31924i	−1.05746	+	0.610524i	−0.132730	+	0.991152i	$0.542374\pi$
$234$	−9.26725	−	3.63898i	−0.605819	−	0.237887i
$235$	5.57784	−	9.66111i	0.363858	−	0.630221i
$236$	12.5509			0.816992
$237$	−7.93467	+	2.77569i	−0.515412	+	0.180300i
$238$	−2.54656	+	1.15775i	−0.165069	+	0.0750456i
$239$	3.39486	−	1.96002i	0.219595	−	0.126783i	−0.386168	−	0.922429i	$-0.626201\pi$
$239$	3.39486	−	1.96002i	0.219595	−	0.126783i	0.605763	+	0.795645i	$0.292868\pi$
$240$	−0.781610	+	4.12895i	−0.0504527	+	0.266523i
$241$	7.78415	−	4.49418i	0.501421	−	0.289495i	−0.227879	−	0.973689i	$-0.573179\pi$
$241$	7.78415	−	4.49418i	0.501421	−	0.289495i	0.729300	+	0.684194i	$0.239846\pi$
$242$	4.78138	+	2.76053i	0.307359	+	0.177454i
$243$	−1.73865	−	15.4912i	−0.111535	−	0.993761i
$244$			3.38964i			0.216999i
$245$	6.86896	+	1.34813i	0.438841	+	0.0861288i
$246$	3.75276	−	4.36002i	0.239267	−	0.277985i
$247$	−18.6797	+	32.3542i	−1.18856	+	2.05865i
$248$	8.98066			0.570272
$249$	−1.37230	+	7.24935i	−0.0869660	+	0.459409i
$250$		−	0.524306i		−	0.0331600i
$251$	11.8323			0.746846			0.373423	−	0.927661i	$-0.378184\pi$
$251$	11.8323			0.746846			0.373423	+	0.927661i	$0.378184\pi$
$252$	0.718889	+	13.6737i	0.0452858	+	0.861362i
$253$	5.52789			0.347536
$254$			5.60446i			0.351655i
$255$	−2.64728	−	2.27857i	−0.165779	−	0.142689i
$256$	−1.74277			−0.108923
$257$	14.6300	−	25.3398i	0.912592	−	1.58066i	0.102203	−	0.994764i	$-0.467411\pi$
$257$	14.6300	−	25.3398i	0.912592	−	1.58066i	0.810389	−	0.585892i	$-0.199256\pi$
$258$	2.73965	+	0.518616i	0.170563	+	0.0322876i
$259$	3.12622	+	0.303884i	0.194254	+	0.0188824i
$260$			10.9194i			0.677192i
$261$	0.845275	−	0.127255i	0.0523212	−	0.00787689i
$262$	4.53613	+	2.61894i	0.280243	+	0.161798i
$263$	4.45723	−	2.57338i	0.274845	−	0.158682i	−0.356243	−	0.934394i	$-0.615942\pi$
$263$	4.45723	−	2.57338i	0.274845	−	0.158682i	0.631087	+	0.775712i	$0.282609\pi$
$264$	1.75730	+	1.51254i	0.108154	+	0.0930906i
$265$	8.01159	−	4.62549i	0.492148	−	0.284142i
$266$	−8.14909	−	0.792131i	−0.499653	−	0.0485687i
$267$	7.81685	+	6.72812i	0.478384	+	0.411754i
$268$	7.13618			0.435912
$269$	3.25506	−	5.63794i	0.198465	−	0.343751i	−0.749566	−	0.661930i	$-0.769738\pi$
$269$	3.25506	−	5.63794i	0.198465	−	0.343751i	0.948031	+	0.318178i	$0.103071\pi$
$270$	2.40899	−	1.27239i	0.146607	−	0.0774352i
$271$	−7.92293	+	4.57431i	−0.481284	+	0.277869i	−0.720951	−	0.692986i	$-0.756295\pi$
$271$	−7.92293	+	4.57431i	−0.481284	+	0.277869i	0.239668	+	0.970855i	$0.422962\pi$
$272$	−2.44632	+	4.23714i	−0.148330	+	0.256915i
$273$	6.88396	+	28.1776i	0.416636	+	1.70539i
$274$	−5.04440	−	8.73715i	−0.304743	−	0.527831i
$275$	0.593570	+	0.342698i	0.0357936	+	0.0206654i
$276$	−23.6782	−	4.48228i	−1.42526	−	0.269802i
$277$	4.03423	+	6.98749i	0.242393	+	0.419837i	0.961396	−	0.275170i	$-0.0887342\pi$
$277$	4.03423	+	6.98749i	0.242393	+	0.419837i	−0.719002	+	0.695008i	$0.755401\pi$
$278$	−5.33937	−	9.24806i	−0.320234	−	0.554662i
$279$	8.59887	+	10.7865i	0.514801	+	0.645769i
$280$	−4.70408	+	2.13862i	−0.281122	+	0.127807i
$281$	17.4346	+	10.0659i	1.04006	+	0.600481i	0.919851	−	0.392267i	$-0.128309\pi$
$281$	17.4346	+	10.0659i	1.04006	+	0.600481i	0.120213	+	0.992748i	$0.461642\pi$
$282$	3.34515	+	9.56254i	0.199201	+	0.569441i
$283$		−	25.8455i		−	1.53636i	−0.640236	−	0.768178i	$-0.721164\pi$
$283$		−	25.8455i		−	1.53636i	0.640236	−	0.768178i	$-0.278836\pi$
$284$			6.14582i			0.364688i
$285$	−3.37561	−	9.64960i	−0.199954	−	0.571593i
$286$	1.96988	+	1.13731i	0.116481	+	0.0672506i
$287$	−16.6813	−	1.62150i	−0.984664	−	0.0957141i
$288$	−9.68366	−	12.1472i	−0.570615	−	0.715783i
$289$	6.46668	+	11.2006i	0.380393	+	0.658859i
$290$	0.0746961	+	0.129378i	0.00438631	+	0.00759731i
$291$	−16.8107	−	3.18226i	−0.985459	−	0.186547i
$292$	−5.60619	−	3.23674i	−0.328078	−	0.189416i
$293$	−0.740371	−	1.28236i	−0.0432529	−	0.0749162i	0.843588	−	0.536990i	$-0.180439\pi$
$293$	−0.740371	−	1.28236i	−0.0432529	−	0.0749162i	−0.886841	+	0.462074i	$0.847105\pi$
$294$	−4.99719	+	3.92912i	−0.291442	+	0.229151i
$295$	−3.63772	+	6.30071i	−0.211796	+	0.366842i
$296$	−2.00801	+	1.15933i	−0.116713	+	0.0673845i
$297$	−0.134089	+	3.55889i	−0.00778064	+	0.206508i
$298$	0.139214	−	0.241126i	0.00806445	−	0.0139680i
$299$	−51.0507			−2.95234
$300$	−2.26463	−	1.94921i	−0.130748	−	0.112538i
$301$	−3.36206	−	7.39515i	−0.193786	−	0.426249i
$302$	−6.88317	+	3.97400i	−0.396082	+	0.228678i
$303$	8.87709	+	7.64069i	0.509975	+	0.438946i
$304$	−12.4014	+	7.15998i	−0.711272	+	0.410653i
$305$	−1.70164	−	0.982445i	−0.0974359	−	0.0562546i
$306$	3.13659	−	0.472210i	0.179307	−	0.0269945i
$307$			31.9466i			1.82329i	0.410977	+	0.911646i	$0.365188\pi$
$307$			31.9466i			1.82329i	−0.410977	+	0.911646i	$0.634812\pi$
$308$	0.302657	−	3.11360i	0.0172455	−	0.177414i
$309$	29.5575	+	5.59524i	1.68147	+	0.318302i
$310$	−1.20542	+	2.08786i	−0.0684635	+	0.118582i
$311$	−11.6114			−0.658425			−0.329212	−	0.944256i	$-0.606783\pi$
$311$	−11.6114			−0.658425			−0.329212	+	0.944256i	$0.606783\pi$
$312$	−16.2288	−	13.9685i	−0.918778	−	0.790810i
$313$			21.7201i			1.22769i	0.789426	+	0.613846i	$0.210378\pi$
$313$			21.7201i			1.22769i	−0.789426	+	0.613846i	$0.789622\pi$
$314$	−3.28310			−0.185276
$315$	−7.07274	−	3.60226i	−0.398504	−	0.202964i
$316$	−8.37243			−0.470986
$317$		−	8.25388i		−	0.463584i	−0.972765	−	0.231792i	$-0.925541\pi$
$317$		−	8.25388i		−	0.463584i	0.972765	−	0.231792i	$-0.0744588\pi$
$318$	−1.56257	+	8.25445i	−0.0876244	+	0.462887i
$319$	−0.195292			−0.0109342
$320$	−1.06869	+	1.85103i	−0.0597417	+	0.103476i
$321$	16.4959	−	19.1652i	0.920711	−	1.06970i
$322$	−4.63035	−	10.1849i	−0.258039	−	0.567580i
$323$		−	11.9024i		−	0.662269i
$324$	3.46008	−	15.1355i	0.192227	−	0.840859i
$325$	−5.48168	−	3.16485i	−0.304069	−	0.175554i
$326$	−8.15104	+	4.70601i	−0.451445	+	0.260642i
$327$	−0.377377	+	1.99354i	−0.0208690	+	0.110243i
$328$	10.7146	−	6.18608i	0.591615	−	0.341569i
$329$	17.1613	−	24.0132i	0.946135	−	1.32389i
$330$	−0.587514	+	0.205523i	−0.0323416	+	0.0113137i
$331$	−10.1162			−0.556035			−0.278017	−	0.960576i	$-0.589677\pi$
$331$	−10.1162			−0.556035			−0.278017	+	0.960576i	$0.589677\pi$
$332$	−3.67425	+	6.36399i	−0.201651	+	0.349269i
$333$	−3.31509	−	1.30174i	−0.181666	−	0.0713348i
$334$	11.4316	−	6.60005i	0.625510	−	0.361138i
$335$	−2.06833	+	3.58246i	−0.113005	+	0.195731i
$336$	−3.11514	+	10.6729i	−0.169945	+	0.582252i
$337$	5.47922	+	9.49029i	0.298472	+	0.516969i	0.975787	−	0.218725i	$-0.0701897\pi$
$337$	5.47922	+	9.49029i	0.298472	+	0.516969i	−0.677315	+	0.735694i	$0.736856\pi$
$338$	−12.2892	−	7.09520i	−0.668447	−	0.385928i
$339$	4.38735	−	5.09731i	0.238288	−	0.276848i
$340$	−1.73942	−	3.01276i	−0.0943331	−	0.163390i
$341$	−1.57578	−	2.72933i	−0.0853334	−	0.147802i
$342$	8.64142	+	3.39323i	0.467274	+	0.183485i
$343$	17.7432	+	5.30835i	0.958043	+	0.286624i
$344$	5.19337	+	2.99839i	0.280008	+	0.161663i
$345$	9.11301	−	10.5877i	0.490628	−	0.570020i
$346$		−	2.80488i		−	0.150792i
$347$			36.6845i			1.96933i	0.174464	+	0.984664i	$0.444181\pi$
$347$			36.6845i			1.96933i	−0.174464	+	0.984664i	$0.555819\pi$
$348$	0.836515	+	0.158352i	0.0448419	+	0.00848856i
$349$	−24.4021	−	14.0886i	−1.30622	−	0.754144i	−0.324753	−	0.945799i	$-0.605281\pi$
$349$	−24.4021	−	14.0886i	−1.30622	−	0.754144i	−0.981462	+	0.191655i	$0.938615\pi$
$350$	0.134208	−	1.38068i	0.00717374	−	0.0738002i
$351$	1.23833	−	32.8668i	0.0660971	−	1.75430i
$352$	1.77458	+	3.07365i	0.0945852	+	0.163826i
$353$	−4.79780	−	8.31004i	−0.255361	−	0.442299i	0.709632	−	0.704572i	$-0.248861\pi$
$353$	−4.79780	−	8.31004i	−0.255361	−	0.442299i	−0.964994	+	0.262274i	$0.915528\pi$
$354$	−2.18162	−	6.23643i	−0.115952	−	0.331462i
$355$	−3.08529	−	1.78129i	−0.163750	−	0.0945411i
$356$	5.13613	+	8.89603i	0.272214	+	0.471489i
$357$	−6.38793	−	6.67787i	−0.338085	−	0.353430i
$358$	2.34232	−	4.05702i	0.123796	−	0.214420i
$359$	8.31863	−	4.80277i	0.439041	−	0.253480i	−0.264150	−	0.964482i	$-0.585091\pi$
$359$	8.31863	−	4.80277i	0.439041	−	0.253480i	0.703191	+	0.711001i	$0.251758\pi$
$360$	5.79399	−	0.872279i	0.305370	−	0.0459731i
$361$	7.91826	−	13.7148i	0.416751	−	0.721834i
$362$	−1.58408			−0.0832576
$363$	−3.39237	+	17.9206i	−0.178053	+	0.940590i
$364$	−2.79507	+	28.7545i	−0.146502	+	1.50714i
$365$	3.24977	−	1.87626i	0.170101	−	0.0982078i
$366$	1.68428	−	0.589193i	0.0880389	−	0.0307976i
$367$	−14.1764	+	8.18475i	−0.740003	+	0.427241i	−0.822070	−	0.569386i	$-0.807181\pi$
$367$	−14.1764	+	8.18475i	−0.740003	+	0.427241i	0.0820677	+	0.996627i	$0.473848\pi$
$368$	−16.9462	−	9.78392i	−0.883384	−	0.510022i
$369$	17.6891	+	6.94598i	0.920856	+	0.361593i
$370$		−	0.622440i		−	0.0323591i
$371$	22.2812	−	10.1297i	1.15678	−	0.525910i
$372$	4.53664	+	12.9686i	0.235214	+	0.672389i
$373$	1.80925	−	3.13371i	0.0936794	−	0.162257i	−0.815377	−	0.578930i	$-0.803470\pi$
$373$	1.80925	−	3.13371i	0.0936794	−	0.162257i	0.909057	+	0.416672i	$0.136804\pi$
$374$	−0.724677			−0.0374721
$375$	1.63490	−	0.571919i	0.0844260	−	0.0295338i
$376$			21.7881i			1.12364i
$377$	1.80354			0.0928872
$378$	6.66939	−	2.73400i	0.343036	−	0.140622i
$379$	31.9510			1.64121			0.820607	−	0.571493i	$-0.193636\pi$
$379$	31.9510			1.64121			0.820607	+	0.571493i	$0.193636\pi$
$380$		−	10.1820i		−	0.522325i
$381$	−17.4760	+	6.11341i	−0.895321	+	0.313199i
$382$	−13.8226			−0.707224
$383$	−15.8899	+	27.5220i	−0.811934	+	1.40631i	0.0995751	+	0.995030i	$0.468252\pi$
$383$	−15.8899	+	27.5220i	−0.811934	+	1.40631i	−0.911509	+	0.411280i	$0.865082\pi$
$384$	−6.56400	−	18.7640i	−0.334968	−	0.957548i
$385$	1.47535	+	1.05438i	0.0751908	+	0.0537360i
$386$		−	6.81336i		−	0.346791i
$387$	1.37128	+	9.10857i	0.0697063	+	0.463014i
$388$	−14.7576	−	8.52029i	−0.749203	−	0.432552i
$389$	−15.1075	+	8.72231i	−0.765980	+	0.442239i	−0.831439	−	0.555617i	$-0.812482\pi$
$389$	−15.1075	+	8.72231i	−0.765980	+	0.442239i	0.0654589	+	0.997855i	$0.479149\pi$
$390$	5.42576	−	1.89803i	0.274744	−	0.0961103i
$391$	14.0853	−	8.13218i	0.712327	−	0.411262i
$392$	−12.9349	+	4.42759i	−0.653309	+	0.223627i
$393$	−3.21837	+	17.0014i	−0.162345	+	0.857609i
$394$	4.70467			0.237018
$395$	2.42665	−	4.20308i	0.122098	−	0.211480i
$396$	−1.29648	+	3.30171i	−0.0651508	+	0.165917i
$397$	14.9631	−	8.63892i	0.750974	−	0.433575i	−0.0750716	−	0.997178i	$-0.523919\pi$
$397$	14.9631	−	8.63892i	0.750974	−	0.433575i	0.826046	+	0.563603i	$0.190585\pi$
$398$	−2.77908	+	4.81351i	−0.139303	+	0.241280i
$399$	−6.41907	−	26.2748i	−0.321356	−	1.31538i
$400$	−1.21309	−	2.10114i	−0.0606547	−	0.105057i
$401$	10.5836	+	6.11042i	0.528518	+	0.305140i	0.740413	−	0.672152i	$-0.234630\pi$
$401$	10.5836	+	6.11042i	0.528518	+	0.305140i	−0.211895	+	0.977292i	$0.567963\pi$
$402$	−1.24042	−	3.54591i	−0.0618667	−	0.176854i
$403$	14.5525	+	25.2057i	0.724913	+	1.25559i
$404$	5.83276	+	10.1026i	0.290191	+	0.502625i
$405$	6.59535	+	6.12384i	0.327725	+	0.304296i
$406$	0.163583	+	0.359815i	0.00811849	+	0.0178573i
$407$	0.704668	+	0.406840i	0.0349291	+	0.0201663i
$408$	6.70281	+	1.26884i	0.331839	+	0.0628170i
$409$		−	22.1056i		−	1.09305i	−0.837443	−	0.546525i	$-0.815950\pi$
$409$		−	22.1056i		−	1.09305i	0.837443	−	0.546525i	$-0.184050\pi$
$410$			3.32129i			0.164027i
$411$	21.7419	−	25.2601i	1.07245	−	1.24599i
$412$	25.9477	+	14.9809i	1.27835	+	0.738056i
$413$	−11.1922	+	15.6608i	−0.550730	+	0.770615i
$414$	1.88858	+	12.5446i	0.0928187	+	0.616535i
$415$	−2.12987	−	3.68905i	−0.104551	−	0.181088i
$416$	−16.3884	−	28.3855i	−0.803507	−	1.39172i
$417$	23.0133	−	26.7372i	1.12696	−	1.30933i
$418$	−1.83685	−	1.06051i	−0.0898434	−	0.0518711i
$419$	−16.4445	−	28.4827i	−0.803365	−	1.39147i	−0.917389	−	0.397992i	$-0.869707\pi$
$419$	−16.4445	−	28.4827i	−0.803365	−	1.39147i	0.114024	−	0.993478i	$-0.463626\pi$
$420$	−5.46458	−	5.71261i	−0.266644	−	0.278747i
$421$	−4.72871	+	8.19036i	−0.230463	+	0.399174i	−0.957944	−	0.286954i	$-0.907357\pi$
$421$	−4.72871	+	8.19036i	−0.230463	+	0.399174i	0.727481	+	0.686127i	$0.240691\pi$
$422$	−2.12473	+	1.22671i	−0.103430	+	0.0597155i
$423$	−26.1692	+	20.8618i	−1.27239	+	1.01434i
$424$	−9.03402	+	15.6474i	−0.438731	+	0.759904i
$425$	2.01659			0.0978191
$426$	3.05381	−	1.06828i	0.147958	−	0.0517582i
$427$	−4.22953	−	3.02269i	−0.204681	−	0.146278i
$428$	21.8111	−	12.5927i	1.05428	−	0.608690i
$429$	−1.39762	+	7.38312i	−0.0674778	+	0.356460i
$430$	−1.39415	+	0.804916i	−0.0672321	+	0.0388165i
$431$	−2.47525	−	1.42909i	−0.119229	−	0.0688368i	0.439200	−	0.898390i	$-0.355262\pi$
$431$	−2.47525	−	1.42909i	−0.119229	−	0.0688368i	−0.558428	+	0.829553i	$0.688595\pi$
$432$	6.71001	−	10.6728i	0.322836	−	0.513494i
$433$			2.73608i			0.131488i	0.997837	+	0.0657438i	$0.0209420\pi$
$433$			2.73608i			0.131488i	−0.997837	+	0.0657438i	$0.979058\pi$
$434$	−3.70873	+	5.18948i	−0.178025	+	0.249103i
$435$	−0.321949	+	0.374046i	−0.0154363	+	0.0179341i
$436$	−1.01040	+	1.75007i	−0.0483895	+	0.0838131i
$437$	47.6032			2.27717
$438$	−0.633830	+	3.34829i	−0.0302856	+	0.159987i
$439$			12.5880i			0.600791i	0.953815	+	0.300395i	$0.0971186\pi$
$439$			12.5880i			0.600791i	−0.953815	+	0.300395i	$0.902881\pi$
$440$	−1.33864			−0.0638172
$441$	−17.7029	−	11.2964i	−0.842993	−	0.537924i
$442$	6.69247			0.318328
$443$			10.5502i			0.501254i	0.968084	+	0.250627i	$0.0806368\pi$
$443$			10.5502i			0.501254i	−0.968084	+	0.250627i	$0.919363\pi$
$444$	−2.68849	−	2.31404i	−0.127590	−	0.109819i
$445$	−5.95457			−0.282274
$446$	−4.42173	+	7.65865i	−0.209375	+	0.362648i
$447$	0.903739	+	0.171078i	0.0427454	+	0.00809170i
$448$	−3.28804	+	4.60083i	−0.155345	+	0.217369i
$449$			14.4733i			0.683039i	0.939875	+	0.341520i	$0.110942\pi$
$449$			14.4733i			0.683039i	−0.939875	+	0.341520i	$0.889058\pi$
$450$	−0.574905	+	1.46409i	−0.0271013	+	0.0690178i
$451$	−3.76005	−	2.17087i	−0.177054	−	0.102222i
$452$	5.80103	−	3.34923i	0.272858	−	0.157534i
$453$	−19.9001	−	17.1284i	−0.934986	−	0.804761i
$454$	9.30158	−	5.37027i	0.436545	−	0.252039i
$455$	−13.6250	−	9.73729i	−0.638750	−	0.456491i
$456$	15.1329	+	13.0252i	0.708663	+	0.609960i
$457$	24.5543			1.14860			0.574300	−	0.818645i	$-0.305274\pi$
$457$	24.5543			1.14860			0.574300	+	0.818645i	$0.305274\pi$
$458$	−1.15347	+	1.99787i	−0.0538982	+	0.0933545i
$459$	4.89388	+	9.26550i	0.228427	+	0.432476i
$460$	12.0494	−	6.95671i	0.561805	−	0.324358i
$461$	−2.17057	+	3.75954i	−0.101094	+	0.175099i	−0.912136	−	0.409889i	$-0.865568\pi$
$461$	−2.17057	+	3.75954i	−0.101094	+	0.175099i	0.811042	+	0.584988i	$0.198901\pi$
$462$	−1.59973	+	0.390824i	−0.0744263	+	0.0181828i
$463$	−4.03025	−	6.98059i	−0.187301	−	0.324416i	0.757048	−	0.653359i	$-0.226641\pi$
$463$	−4.03025	−	6.98059i	−0.187301	−	0.324416i	−0.944350	+	0.328943i	$0.893307\pi$
$464$	0.598685	+	0.345651i	0.0277932	+	0.0160464i
$465$	−7.82529	−	1.48133i	−0.362889	−	0.0686948i
$466$	4.88614	+	8.46304i	0.226346	+	0.392043i
$467$	−9.85389	−	17.0674i	−0.455984	−	0.789787i	0.542760	−	0.839888i	$-0.317379\pi$
$467$	−9.85389	−	17.0674i	−0.455984	−	0.789787i	−0.998744	+	0.0501005i	$0.984046\pi$
$468$	11.9732	−	30.4916i	0.553460	−	1.40948i
$469$	−6.36364	+	8.90440i	−0.293846	+	0.411167i
$470$	−5.06538	−	2.92450i	−0.233648	−	0.134897i
$471$	−3.58124	−	10.2374i	−0.165015	−	0.471716i
$472$		−	14.2096i		−	0.654050i
$473$		−	2.10444i		−	0.0967622i
$474$	1.45531	+	4.16020i	0.0668447	+	0.191084i
$475$	5.11150	+	2.95112i	0.234532	+	0.135407i
$476$	−3.80929	−	8.37886i	−0.174598	−	0.384044i
$477$	−27.4437	+	4.13161i	−1.25656	+	0.189174i
$478$	−1.02765	−	1.77995i	−0.0470037	−	0.0814128i
$479$	7.48225	+	12.9596i	0.341873	+	0.592141i	0.984780	−	0.173803i	$-0.0556056\pi$
$479$	7.48225	+	12.9596i	0.341873	+	0.592141i	−0.642908	+	0.765943i	$0.722272\pi$
$480$	8.81249	+	1.66820i	0.402233	+	0.0761427i
$481$	−6.50768	−	3.75721i	−0.296725	−	0.171314i
$482$	−2.35633	−	4.08128i	−0.107328	−	0.185897i
$483$	26.7078	−	25.5482i	1.21525	−	1.16248i
$484$	−9.08287	+	15.7320i	−0.412858	+	0.715090i
$485$	8.55461	−	4.93901i	0.388445	−	0.224269i
$486$	−8.12213	+	0.911587i	−0.368427	+	0.0413504i
$487$	−0.207370	+	0.359175i	−0.00939682	+	0.0162758i	−0.870686	−	0.491840i	$-0.836324\pi$
$487$	−0.207370	+	0.359175i	−0.00939682	+	0.0162758i	0.861289	+	0.508116i	$0.169658\pi$
$488$	3.83762			0.173721
$489$	−23.5656	−	20.2834i	−1.06567	−	0.917248i
$490$	0.706833	−	3.60144i	0.0319314	−	0.162696i
$491$	18.5555	−	10.7130i	0.837396	−	0.483471i	−0.0189822	−	0.999820i	$-0.506043\pi$
$491$	18.5555	−	10.7130i	0.837396	−	0.483471i	0.856378	+	0.516349i	$0.172709\pi$
$492$	14.3456	+	12.3475i	0.646749	+	0.556670i
$493$	−0.497614	+	0.287297i	−0.0224114	+	0.0129392i
$494$	16.9635	+	9.79390i	0.763225	+	0.440648i
$495$	−1.28173	−	1.60781i	−0.0576096	−	0.0722658i
$496$			11.1560i			0.500920i
$497$	−7.66865	−	5.48050i	−0.343986	−	0.245834i
$498$	3.80088	+	0.719505i	0.170321	+	0.0322418i
$499$	−12.6725	+	21.9494i	−0.567298	+	0.982588i	0.429534	+	0.903051i	$0.358678\pi$
$499$	−12.6725	+	21.9494i	−0.567298	+	0.982588i	−0.996832	+	0.0795378i	$0.974656\pi$
$500$	1.72510			0.0771490
$501$	33.0501	+	28.4469i	1.47657	+	1.27091i
$502$		−	6.20373i		−	0.276886i
$503$	2.51829			0.112285			0.0561424	−	0.998423i	$-0.482120\pi$
$503$	2.51829			0.112285			0.0561424	+	0.998423i	$0.482120\pi$
$504$	15.4808	−	0.813898i	0.689571	−	0.0362539i
$505$	−6.76222			−0.300915
$506$		−	2.89831i		−	0.128846i
$507$	8.71917	−	46.0601i	0.387232	−	2.04560i
$508$	−18.4401			−0.818149
$509$	−4.81601	+	8.34158i	−0.213466	+	0.369734i	−0.952797	−	0.303608i	$-0.901809\pi$
$509$	−4.81601	+	8.34158i	−0.213466	+	0.369734i	0.739331	+	0.673342i	$0.235142\pi$
$510$	−1.19467	+	1.38798i	−0.0529007	+	0.0614610i
$511$	9.03802	−	4.10897i	0.399819	−	0.181770i
$512$		−	22.0406i		−	0.974064i
$513$	−1.15470	+	30.6472i	−0.0509814	+	1.35311i
$514$	−13.2858	−	7.67058i	−0.586013	−	0.338335i
$515$	−15.0412	+	8.68406i	−0.662796	+	0.382665i
$516$	−1.70638	+	9.01417i	−0.0751192	+	0.396827i
$517$	6.62168	−	3.82303i	0.291221	−	0.168137i
$518$	0.159328	−	1.63910i	0.00700047	−	0.0720178i
$519$	8.74626	−	3.05960i	0.383918	−	0.134301i
$520$	12.3625			0.542132
$521$	4.60032	−	7.96798i	0.201544	−	0.349084i	−0.747482	−	0.664282i	$-0.768738\pi$
$521$	4.60032	−	7.96798i	0.201544	−	0.349084i	0.949026	+	0.315198i	$0.102071\pi$
$522$	−0.0667206	−	0.443183i	−0.00292028	−	0.0193976i
$523$	−3.19809	+	1.84642i	−0.139843	+	0.0807382i	−0.568289	−	0.822829i	$-0.692394\pi$
$523$	−3.19809	+	1.84642i	−0.139843	+	0.0807382i	0.428446	+	0.903567i	$0.359061\pi$
$524$	−8.61698	+	14.9250i	−0.376434	+	0.652004i
$525$	4.45165	−	1.08756i	0.194286	−	0.0474652i
$526$	−1.34924	−	2.33695i	−0.0588297	−	0.101896i
$527$	−8.03034	−	4.63632i	−0.349807	−	0.201961i
$528$	−1.87892	+	2.18296i	−0.0817695	+	0.0950013i
$529$	21.0242	+	36.4151i	0.914098	+	1.58326i
$530$	−2.42517	−	4.20052i	−0.105343	−	0.182459i
$531$	17.0668	−	13.6055i	0.740638	−	0.590430i
$532$	2.60632	−	26.8126i	0.112998	−	1.16247i
$533$	34.7245	+	20.0482i	1.50409	+	0.868384i
$534$	3.52760	−	4.09842i	0.152654	−	0.177356i
$535$			14.5993i			0.631184i
$536$		−	8.07930i		−	0.348973i
$537$	15.2057	+	2.87844i	0.656176	+	0.124214i
$538$	−2.95601	−	1.70665i	−0.127442	−	0.0735789i
$539$	3.61520	+	3.15418i	0.155718	+	0.135860i
$540$	4.18649	+	7.92621i	0.180158	+	0.341090i
$541$	12.1097	+	20.9747i	0.520638	+	0.901772i	0.999712	+	0.0239973i	$0.00763931\pi$
$541$	12.1097	+	20.9747i	0.520638	+	0.901772i	−0.479074	+	0.877775i	$0.659027\pi$
$542$	2.39834	+	4.15404i	0.103017	+	0.178431i
$543$	−1.72793	−	4.93952i	−0.0741528	−	0.211975i
$544$	9.04341	+	5.22122i	0.387733	+	0.223858i
$545$	−0.585706	−	1.01447i	−0.0250889	−	0.0434552i
$546$	14.7737	−	3.60930i	0.632256	−	0.154464i
$547$	−13.4234	+	23.2500i	−0.573943	+	0.994098i	0.422213	+	0.906497i	$0.361254\pi$
$547$	−13.4234	+	23.2500i	−0.573943	+	0.994098i	−0.996156	+	0.0876016i	$0.972080\pi$
$548$	28.7475	−	16.5974i	1.22803	−	0.709004i
$549$	3.67447	+	4.60927i	0.156823	+	0.196719i
$550$	0.179678	−	0.311212i	0.00766152	−	0.0132701i
$551$	−1.68175			−0.0716448
$552$	−5.07467	+	26.8076i	−0.215992	+	1.14101i
$553$	7.46606	−	10.4470i	0.317489	−	0.444250i
$554$	3.66358	−	2.11517i	0.155651	−	0.0898650i
$555$	1.94091	−	0.678964i	0.0823869	−	0.0288204i
$556$	30.4285	−	17.5679i	1.29046	−	0.745045i
$557$	−17.3868	−	10.0383i	−0.736703	−	0.425336i	0.0841662	−	0.996452i	$-0.473177\pi$
$557$	−17.3868	−	10.0383i	−0.736703	−	0.425336i	−0.820869	+	0.571116i	$0.806511\pi$
$558$	5.65541	−	4.50844i	0.239413	−	0.190858i
$559$			19.4347i			0.822002i
$560$	−2.65665	−	5.84353i	−0.112264	−	0.246934i
$561$	−0.790485	−	2.25970i	−0.0333743	−	0.0954048i
$562$	5.27761	−	9.14109i	0.222623	−	0.385594i
$563$	−32.1518			−1.35504			−0.677518	−	0.735506i	$-0.736945\pi$
$563$	−32.1518			−1.35504			−0.677518	+	0.735506i	$0.736945\pi$
$564$	−31.4632	+	11.0064i	−1.32484	+	0.463453i
$565$			3.88293i			0.163356i
$566$	−13.5510			−0.569589
$567$	15.8003	+	17.8144i	0.663548	+	0.748133i
$568$	6.95806			0.291954
$569$		−	23.7651i		−	0.996285i	−0.867095	−	0.498143i	$-0.834016\pi$
$569$		−	23.7651i		−	0.996285i	0.867095	−	0.498143i	$-0.165984\pi$
$570$	−5.05935	+	1.76985i	−0.211913	+	0.0741309i
$571$	7.58054			0.317236			0.158618	−	0.987340i	$-0.449296\pi$
$571$	7.58054			0.317236			0.158618	+	0.987340i	$0.449296\pi$
$572$	−3.74205	+	6.48142i	−0.156463	+	0.271002i
$573$	−15.0778	−	43.1019i	−0.629885	−	1.80061i
$574$	−0.850163	+	8.74609i	−0.0354851	+	0.365055i
$575$			8.06526i			0.336345i
$576$	5.01391	−	3.99704i	0.208913	−	0.166543i
$577$	−20.4203	−	11.7897i	−0.850108	−	0.490810i	0.0105795	−	0.999944i	$-0.496632\pi$
$577$	−20.4203	−	11.7897i	−0.850108	−	0.490810i	−0.860687	+	0.509134i	$0.829966\pi$
$578$	5.87255	−	3.39052i	0.244266	−	0.141027i
$579$	21.2456	−	7.43209i	0.882936	−	0.308867i
$580$	−0.425686	+	0.245770i	−0.0176756	+	0.0102050i
$581$	−4.66438	−	10.2597i	−0.193511	−	0.425644i
$582$	−1.66848	+	8.81394i	−0.0691606	+	0.365349i
$583$	6.34058			0.262600
$584$	−3.66451	+	6.34711i	−0.151638	+	0.262645i
$585$	11.8369	+	14.8483i	0.489397	+	0.613903i
$586$	−0.672349	+	0.388181i	−0.0277745	+	0.0160356i
$587$	−1.23062	+	2.13150i	−0.0507932	+	0.0879765i	−0.890304	−	0.455366i	$-0.849508\pi$
$587$	−1.23062	+	2.13150i	−0.0507932	+	0.0879765i	0.839511	+	0.543343i	$0.182842\pi$
$588$	−12.9278	−	16.4420i	−0.533134	−	0.678058i
$589$	−13.5698	−	23.5035i	−0.559133	−	0.968446i
$590$	3.30350	+	1.90728i	0.136003	+	0.0785214i
$591$	5.13191	+	14.6702i	0.211098	+	0.603452i
$592$	−1.44015	−	2.49441i	−0.0591897	−	0.102520i
$593$	−15.5216	−	26.8842i	−0.637397	−	1.10400i	−0.986002	−	0.166734i	$-0.946678\pi$
$593$	−15.5216	−	26.8842i	−0.637397	−	1.10400i	0.348605	−	0.937270i	$-0.386655\pi$
$594$	1.86595	+	0.0703038i	0.0765608	+	0.00288460i
$595$	5.31038	+	0.516194i	0.217704	+	0.0211619i
$596$	0.793366	+	0.458050i	0.0324975	+	0.0187625i
$597$	−18.0411	−	3.41517i	−0.738371	−	0.139774i
$598$			26.7662i			1.09455i
$599$		−	25.4984i		−	1.04184i	−0.853606	−	0.520919i	$-0.825590\pi$
$599$		−	25.4984i		−	1.04184i	0.853606	−	0.520919i	$-0.174410\pi$
$600$	−2.20682	+	2.56392i	−0.0900930	+	0.104672i
$601$	−19.3792	−	11.1886i	−0.790493	−	0.456391i	0.0496432	−	0.998767i	$-0.484192\pi$
$601$	−19.3792	−	11.1886i	−0.790493	−	0.456391i	−0.840136	+	0.542376i	$0.817525\pi$
$602$	−3.87732	+	1.76275i	−0.158028	+	0.0718443i
$603$	9.70387	−	7.73583i	0.395172	−	0.315027i
$604$	−13.0755	−	22.6474i	−0.532034	−	0.921510i
$605$	−5.26512	−	9.11945i	−0.214057	−	0.370758i
$606$	4.00606	−	4.65431i	0.162735	−	0.189068i
$607$	30.9558	+	17.8724i	1.25646	+	0.725416i	0.972384	−	0.233386i	$-0.0749806\pi$
$607$	30.9558	+	17.8724i	1.25646	+	0.725416i	0.284074	+	0.958802i	$0.408314\pi$
$608$	15.2817	+	26.4686i	0.619753	+	1.07344i
$609$	−0.943546	+	0.902579i	−0.0382344	+	0.0365743i
$610$	−0.515102	+	0.892183i	−0.0208559	+	0.0361234i
$611$	−61.1519	+	35.3061i	−2.47394	+	1.42833i
$612$	1.55369	+	10.3202i	0.0628043	+	0.417169i
$613$	−5.29560	+	9.17224i	−0.213887	+	0.370463i	−0.952928	−	0.303198i	$-0.901946\pi$
$613$	−5.29560	+	9.17224i	−0.213887	+	0.370463i	0.739041	+	0.673661i	$0.235279\pi$
$614$	16.7498			0.675968
$615$	−10.3565	+	3.62290i	−0.417616	+	0.146089i
$616$	−3.52510	−	0.342657i	−0.142030	−	0.0138060i
$617$	−19.3631	+	11.1793i	−0.779527	+	0.450060i	−0.836263	−	0.548329i	$-0.815264\pi$
$617$	−19.3631	+	11.1793i	−0.779527	+	0.450060i	0.0567356	+	0.998389i	$0.481931\pi$
$618$	2.93362	−	15.4972i	0.118007	−	0.623389i
$619$	1.32849	−	0.767002i	0.0533964	−	0.0308284i	−0.473064	−	0.881028i	$-0.656852\pi$
$619$	1.32849	−	0.767002i	0.0533964	−	0.0308284i	0.526461	+	0.850200i	$0.323519\pi$
$620$	−6.86959	−	3.96616i	−0.275889	−	0.159285i
$621$	−37.0569	+	19.5728i	−1.48704	+	0.785431i
$622$			6.08795i			0.244105i
$623$	−15.6804	−	1.52421i	−0.628222	−	0.0610663i
$624$	17.3520	−	20.1599i	0.694638	−	0.807042i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.3880			0.455155
$627$	1.30324	−	6.88452i	0.0520464	−	0.274941i
$628$		−	10.8022i		−	0.431057i
$629$	2.39404			0.0954565
$630$	−1.88869	+	3.70828i	−0.0752471	+	0.147742i
$631$	11.0346			0.439281			0.219641	−	0.975581i	$-0.429512\pi$
$631$	11.0346			0.439281			0.219641	+	0.975581i	$0.429512\pi$
$632$			9.47894i			0.377052i
$633$	−6.14284	−	5.28727i	−0.244156	−	0.210150i
$634$	−4.32756			−0.171869
$635$	5.34465	−	9.25720i	0.212096	−	0.367361i
$636$	−27.1593	−	5.14125i	−1.07694	−	0.203864i
$637$	−33.3868	−	29.1292i	−1.32283	−	1.15414i
$638$			0.102393i			0.00405377i
$639$	6.66226	+	8.35717i	0.263555	+	0.330605i
$640$	9.93950	+	5.73858i	0.392893	+	0.226837i
$641$	−40.1393	+	23.1745i	−1.58541	+	0.915336i	−0.591359	+	0.806408i	$0.701408\pi$
$641$	−40.1393	+	23.1745i	−1.58541	+	0.915336i	−0.994050	+	0.108928i	$0.965258\pi$
$642$	−10.0484	−	8.64890i	−0.396581	−	0.341345i
$643$	−27.1868	+	15.6963i	−1.07214	+	0.619001i	−0.928766	−	0.370667i	$-0.879129\pi$
$643$	−27.1868	+	15.6963i	−1.07214	+	0.619001i	−0.143376	+	0.989668i	$0.545796\pi$
$644$	33.5108	−	15.2351i	1.32051	−	0.600345i
$645$	−4.03067	−	3.46927i	−0.158707	−	0.136603i
$646$	−6.24052			−0.245530
$647$	1.50230	−	2.60206i	0.0590616	−	0.102298i	−0.834983	−	0.550276i	$-0.814522\pi$
$647$	1.50230	−	2.60206i	0.0590616	−	0.102298i	0.894044	+	0.447978i	$0.147856\pi$
$648$	−17.1358	−	3.91737i	−0.673157	−	0.153889i
$649$	−4.31848	+	2.49327i	−0.169515	+	0.0978696i
$650$	−1.65935	+	2.87408i	−0.0650851	+	0.112731i
$651$	−20.2275	−	5.90390i	−0.792777	−	0.231392i
$652$	−15.4840	−	26.8190i	−0.606400	−	1.05032i
$653$	22.5863	+	13.0402i	0.883868	+	0.510302i	0.871932	−	0.489627i	$-0.162867\pi$
$653$	22.5863	+	13.0402i	0.883868	+	0.510302i	0.0119364	+	0.999929i	$0.496200\pi$
$654$	1.04523	+	0.197861i	0.0408716	+	0.00773698i
$655$	−4.99505	−	8.65168i	−0.195173	−	0.338049i
$656$	7.68451	+	13.3100i	0.300030	+	0.519667i
$657$	−11.1321	+	1.67592i	−0.434304	+	0.0653840i
$658$	−12.5903	−	8.99780i	−0.490820	−	0.350771i
$659$	−30.8874	−	17.8329i	−1.20320	−	0.694669i	−0.241937	−	0.970292i	$-0.577783\pi$
$659$	−30.8874	−	17.8329i	−1.20320	−	0.694669i	−0.961266	+	0.275623i	$0.911116\pi$
$660$	−0.676224	−	1.93307i	−0.0263220	−	0.0752448i
$661$			5.29226i			0.205845i	0.994689	+	0.102922i	$0.0328194\pi$
$661$			5.29226i			0.205845i	−0.994689	+	0.102922i	$0.967181\pi$
$662$			5.30397i			0.206145i
$663$	7.30022	+	20.8686i	0.283517	+	0.810470i
$664$	7.20506	+	4.15984i	0.279610	+	0.161433i
$665$	12.7049	+	9.07972i	0.492675	+	0.352096i
$666$	−0.682509	+	1.73812i	−0.0264467	+	0.0673508i
$667$	−1.14903	−	1.99018i	−0.0444907	−	0.0770601i
$668$	21.7159	+	37.6130i	0.840212	+	1.45529i
$669$	−28.7046	−	5.43378i	−1.10979	−	0.210082i
$670$	1.87831	+	1.08444i	0.0725653	+	0.0418956i
$671$	−0.673363	−	1.16630i	−0.0259949	−	0.0450245i
$672$	22.7793	+	6.64871i	0.878729	+	0.256480i
$673$	−7.09437	+	12.2878i	−0.273468	+	0.473661i	−0.969747	−	0.244110i	$-0.921504\pi$
$673$	−7.09437	+	12.2878i	−0.273468	+	0.473661i	0.696279	+	0.717771i	$0.254837\pi$
$674$	4.97581	−	2.87279i	0.191661	−	0.110656i
$675$	−5.19247	−	0.195638i	−0.199858	−	0.00753010i
$676$	23.3451	−	40.4348i	0.897887	−	1.55519i
$677$	−24.0555			−0.924527			−0.462264	−	0.886743i	$-0.652963\pi$
$677$	−24.0555			−0.924527			−0.462264	+	0.886743i	$0.652963\pi$
$678$	−2.67255	−	2.30032i	−0.102639	−	0.0883431i
$679$	23.7914	−	10.8163i	0.913032	−	0.415093i
$680$	−3.41093	+	1.96930i	−0.130803	+	0.0755192i
$681$	26.8920	+	23.1464i	1.03050	+	0.886974i
$682$	−1.43101	+	0.826192i	−0.0547961	+	0.0316365i
$683$	−2.83022	−	1.63403i	−0.108295	−	0.0625243i	0.444874	−	0.895593i	$-0.353248\pi$
$683$	−2.83022	−	1.63403i	−0.108295	−	0.0625243i	−0.553169	+	0.833069i	$0.686582\pi$
$684$	−11.1646	+	28.4325i	−0.426890	+	1.08714i
$685$			19.2422i			0.735206i
$686$	2.78320	−	9.30287i	0.106263	−	0.355185i
$687$	−7.48803	−	1.41748i	−0.285686	−	0.0540803i
$688$	−3.72469	+	6.45134i	−0.142002	+	0.245955i
$689$	−58.5559			−2.23080
$690$	−5.55117	−	4.77801i	−0.211330	−	0.181896i
$691$			16.9404i			0.644442i	0.946664	+	0.322221i	$0.104429\pi$
$691$			16.9404i			0.644442i	−0.946664	+	0.322221i	$0.895571\pi$
$692$	9.22880			0.350826
$693$	−2.96368	−	4.56201i	−0.112581	−	0.173296i
$694$	19.2339			0.730109
$695$			20.3674i			0.772579i
$696$	0.179280	−	0.947070i	0.00679559	−	0.0358986i
$697$	−12.7744			−0.483865
$698$	−7.38672	+	12.7942i	−0.279592	+	0.484267i
$699$	−21.0598	+	24.4676i	−0.796554	+	0.925451i
$700$	4.54278	+	0.441580i	0.171701	+	0.0166902i
$701$			25.9872i			0.981524i	0.871294	+	0.490762i	$0.163282\pi$
$701$			25.9872i			0.981524i	−0.871294	+	0.490762i	$0.836718\pi$
$702$	−17.2322	−	0.649263i	−0.650389	−	0.0245049i
$703$	6.06821	+	3.50348i	0.228867	+	0.132136i
$704$	−1.26869	+	0.732476i	−0.0478154	+	0.0276062i
$705$	3.59387	−	18.9851i	0.135353	−	0.715018i
$706$	−4.35700	+	2.51552i	−0.163978	+	0.0946727i
$707$	−17.8072	−	1.73095i	−0.669709	−	0.0650990i
$708$	20.5195	−	7.17808i	0.771169	−	0.269769i
$709$	−11.8079			−0.443455			−0.221728	−	0.975109i	$-0.571170\pi$
$709$	−11.8079			−0.443455			−0.221728	+	0.975109i	$0.571170\pi$
$710$	−0.933942	+	1.61764i	−0.0350502	+	0.0607088i
$711$	−11.3849	+	9.07597i	−0.426969	+	0.340375i
$712$	10.0717	−	5.81492i	0.377454	−	0.217923i
$713$	18.5427	−	32.1169i	0.694431	−	1.20279i
$714$	−3.50125	+	3.34923i	−0.131031	+	0.125342i
$715$	−2.16917	−	3.75712i	−0.0811225	−	0.140508i
$716$	13.3487	+	7.70685i	0.498863	+	0.288019i
$717$	4.42929	−	5.14603i	0.165415	−	0.192182i
$718$	−2.51812	−	4.36151i	−0.0939754	−	0.162770i
$719$	10.0996	+	17.4931i	0.376653	+	0.652383i	0.990573	−	0.136986i	$-0.0437415\pi$
$719$	10.0996	+	17.4931i	0.376653	+	0.652383i	−0.613920	+	0.789369i	$0.710408\pi$
$720$	1.08357	+	7.19745i	0.0403822	+	0.268233i
$721$	−41.8316	+	19.0179i	−1.55789	+	0.708265i
$722$	−7.19077	−	4.15159i	−0.267613	−	0.154506i
$723$	10.1560	−	11.7994i	0.377706	−	0.438826i
$724$		−	5.21204i		−	0.193704i
$725$		−	0.284933i		−	0.0105822i
$726$	9.39590	+	1.77864i	0.348715	+	0.0660116i
$727$	9.44302	+	5.45193i	0.350222	+	0.202201i	0.664783	−	0.747036i	$-0.268524\pi$
$727$	9.44302	+	5.45193i	0.350222	+	0.202201i	−0.314561	+	0.949237i	$0.601857\pi$
$728$	32.5547	+	3.16447i	1.20656	+	0.117283i
$729$	−11.7022	−	24.3322i	−0.433416	−	0.901194i
$730$	−0.983733	−	1.70388i	−0.0364096	−	0.0630633i
$731$	−3.09588	−	5.36222i	−0.114505	−	0.198329i
$732$	1.93860	+	5.54173i	0.0716526	+	0.204828i
$733$	−16.3543	−	9.44217i	−0.604060	−	0.348754i	0.166577	−	0.986028i	$-0.446729\pi$
$733$	−16.3543	−	9.44217i	−0.604060	−	0.348754i	−0.770637	+	0.637274i	$0.780062\pi$
$734$	4.29132	+	7.43278i	0.158395	+	0.274349i
$735$	12.0011	−	1.72442i	0.442667	−	0.0636063i
$736$	−20.8820	+	36.1687i	−0.769720	+	1.33319i
$737$	−2.45540	+	1.41763i	−0.0904459	+	0.0522189i
$738$	3.64182	−	9.27448i	0.134057	−	0.341398i
$739$	3.98391	−	6.90033i	0.146550	−	0.253833i	−0.783400	−	0.621518i	$-0.786516\pi$
$739$	3.98391	−	6.90033i	0.146550	−	0.253833i	0.929950	+	0.367685i	$0.119850\pi$
$740$	2.04799			0.0752856
$741$	−12.0356	+	63.5793i	−0.442137	+	2.33565i
$742$	−5.31108	−	11.6822i	−0.194976	−	0.428867i
$743$	−8.76571	+	5.06089i	−0.321583	+	0.185666i	−0.652098	−	0.758135i	$-0.726111\pi$
$743$	−8.76571	+	5.06089i	−0.321583	+	0.185666i	0.330515	+	0.943801i	$0.392778\pi$
$744$	14.6825	−	5.13621i	0.538287	−	0.188303i
$745$	−0.459895	+	0.265520i	−0.0168492	+	0.00972791i
$746$	−1.64302	−	0.948601i	−0.0601554	−	0.0347307i
$747$	1.90246	+	12.6368i	0.0696074	+	0.462357i
$748$		−	2.38437i		−	0.0871814i
$749$	−3.73704	+	38.4450i	−0.136548	+	1.40475i
$750$	−0.299860	−	0.857190i	−0.0109494	−	0.0313001i
$751$	−5.64994	+	9.78599i	−0.206169	+	0.357096i	−0.950505	−	0.310710i	$-0.899433\pi$
$751$	−5.64994	+	9.78599i	−0.206169	+	0.357096i	0.744335	+	0.667806i	$0.232766\pi$
$752$	−27.0658			−0.986987
$753$	19.3446	−	6.76709i	0.704956	−	0.246606i
$754$		−	0.945608i		−	0.0344370i
$755$	15.1591			0.551695
$756$	8.99556	+	21.9440i	0.327165	+	0.798097i
$757$	52.7826			1.91842			0.959208	−	0.282701i	$-0.0912305\pi$
$757$	52.7826			1.91842			0.959208	+	0.282701i	$0.0912305\pi$
$758$		−	16.7521i		−	0.608464i
$759$	9.03757	−	3.16151i	0.328043	−	0.114755i
$760$	−11.5276			−0.418152
$761$	12.6545	−	21.9183i	0.458726	−	0.794536i	−0.540168	−	0.841557i	$-0.681639\pi$
$761$	12.6545	−	21.9183i	0.458726	−	0.794536i	0.998894	+	0.0470208i	$0.0149727\pi$
$762$	3.20530	+	9.16276i	0.116116	+	0.331932i
$763$	−1.28268	−	2.82138i	−0.0464363	−	0.102141i
$764$		−	45.4799i		−	1.64540i
$765$	−5.63120	−	2.21121i	−0.203596	−	0.0799464i
$766$	14.4300	+	8.33115i	0.521376	+	0.301017i
$767$	39.8816	−	23.0257i	1.44004	−	0.831408i
$768$	−2.84927	+	0.996725i	−0.102814	+	0.0359662i
$769$	−3.30938	+	1.91067i	−0.119339	+	0.0689007i	−0.558481	−	0.829517i	$-0.688616\pi$
$769$	−3.30938	+	1.91067i	−0.119339	+	0.0689007i	0.439142	+	0.898418i	$0.355282\pi$
$770$	0.552816	−	0.773535i	0.0199221	−	0.0278763i
$771$	9.42625	−	49.7953i	0.339478	−	1.79334i
$772$	22.4177			0.806832
$773$	1.34544	−	2.33038i	0.0483922	−	0.0838178i	−0.840815	−	0.541323i	$-0.817924\pi$
$773$	1.34544	−	2.33038i	0.0483922	−	0.0838178i	0.889207	+	0.457505i	$0.151257\pi$
$774$	4.77568	−	0.718973i	0.171658	−	0.0258429i
$775$	3.98213	−	2.29908i	0.143042	−	0.0825856i
$776$	−9.64635	+	16.7080i	−0.346284	+	0.599781i
$777$	5.28486	−	1.29112i	0.189593	−	0.0463188i
$778$	4.57316	+	7.92095i	0.163956	+	0.283980i
$779$	−32.3795	−	18.6943i	−1.16012	−	0.669793i
$780$	6.24500	+	17.8521i	0.223607	+	0.639209i
$781$	−1.22089	−	2.11464i	−0.0436868	−	0.0756678i
$782$	−4.26375	−	7.38503i	−0.152471	−	0.264088i
$783$	1.30916	−	0.691478i	0.0467857	−	0.0247114i
$784$	−5.50008	−	16.0680i	−0.196431	−	0.573859i
$785$	5.42288	+	3.13090i	0.193551	+	0.111747i
$786$	8.91395	+	1.68741i	0.317950	+	0.0601879i
$787$			23.0171i			0.820471i	0.911980	+	0.410236i	$0.134554\pi$
$787$			23.0171i			0.820471i	−0.911980	+	0.410236i	$0.865446\pi$
$788$			15.4796i			0.551437i
$789$	5.81538	−	6.75641i	0.207033	−	0.240535i
$790$	−2.20370	−	1.27231i	−0.0784041	−	0.0452666i
$791$	−0.993927	+	10.2251i	−0.0353400	+	0.363562i
$792$	3.73807	+	1.46783i	0.132826	+	0.0521570i
$793$	6.21858	+	10.7709i	0.220828	+	0.382486i
$794$	−4.52944	−	7.84522i	−0.160744	−	0.278417i
$795$	10.4528	−	12.1442i	0.370721	−	0.430711i
$796$	−15.8377	−	9.14390i	−0.561352	−	0.324097i
$797$	−3.95223	−	6.84546i	−0.139995	−	0.242479i	0.787499	−	0.616315i	$-0.211375\pi$
$797$	−3.95223	−	6.84546i	−0.139995	−	0.242479i	−0.927495	+	0.373837i	$0.878042\pi$
$798$	−13.7760	+	3.36556i	−0.487666	+	0.119140i
$799$	11.2482	−	19.4825i	0.397934	−	0.689242i
$800$	−4.48450	+	2.58913i	−0.158551	+	0.0915395i
$801$	16.6277	+	6.52923i	0.587512	+	0.230699i
$802$	3.20373	−	5.54903i	0.113128	−	0.195943i
$803$	2.57195			0.0907623
$804$	11.6670	−	4.08131i	0.411462	−	0.143937i
$805$	−2.06449	+	21.2386i	−0.0727638	+	0.748562i
$806$	13.2155	−	7.62998i	0.465496	−	0.268754i
$807$	2.09727	−	11.0791i	0.0738276	−	0.390003i
$808$	11.4378	−	6.60363i	0.402381	−	0.232315i
$809$	20.3186	+	11.7309i	0.714363	+	0.412438i	0.812675	−	0.582718i	$-0.198011\pi$
$809$	20.3186	+	11.7309i	0.714363	+	0.412438i	−0.0983112	+	0.995156i	$0.531344\pi$
$810$	3.21077	−	3.45798i	0.112815	−	0.121501i
$811$		−	31.6614i		−	1.11178i	−0.831255	−	0.555891i	$-0.812377\pi$
$811$		−	31.6614i		−	1.11178i	0.831255	−	0.555891i	$-0.187623\pi$
$812$	−1.18389	+	0.538231i	−0.0415462	+	0.0188882i
$813$	−10.3371	+	12.0098i	−0.362538	+	0.421203i
$814$	0.213309	−	0.369462i	0.00747647	−	0.0129496i
$815$	17.9514			0.628809
$816$	−1.57619	+	8.32641i	−0.0551776	+	0.291483i
$817$		−	18.1223i		−	0.634018i
$818$	−11.5901			−0.405238
$819$	27.3699	+	42.1306i	0.956382	+	1.47216i
$820$	−10.9279			−0.381619
$821$			17.3357i			0.605022i	0.953146	+	0.302511i	$0.0978249\pi$
$821$			17.3357i			0.605022i	−0.953146	+	0.302511i	$0.902175\pi$
$822$	−13.2440	−	11.3994i	−0.461939	−	0.397600i
$823$	−11.2116			−0.390812			−0.195406	−	0.980722i	$-0.562602\pi$
$823$	−11.2116			−0.390812			−0.195406	+	0.980722i	$0.562602\pi$
$824$	16.9608	−	29.3769i	0.590857	−	1.02339i
$825$	1.16642	+	0.220804i	0.0406097	+	0.00768740i
$826$	8.21103	+	5.86812i	0.285698	+	0.204178i
$827$			17.4250i			0.605927i	0.953002	+	0.302963i	$0.0979760\pi$
$827$			17.4250i			0.605927i	−0.953002	+	0.302963i	$0.902024\pi$
$828$	−41.2751	+	6.21392i	−1.43441	+	0.215949i
$829$	18.4407	+	10.6467i	0.640472	+	0.369777i	0.784796	−	0.619754i	$-0.212767\pi$
$829$	18.4407	+	10.6467i	0.640472	+	0.369777i	−0.144324	+	0.989530i	$0.546101\pi$
$830$	−1.93419	+	1.11671i	−0.0671367	+	0.0387614i
$831$	10.5918	+	9.11662i	0.367427	+	0.316252i
$832$	11.7165	−	6.76450i	0.406195	−	0.234517i
$833$	13.8519	+	2.71863i	0.479940	+	0.0941949i
$834$	−14.0185	−	12.0660i	−0.485421	−	0.417811i
$835$	−25.1763			−0.871262
$836$	3.48934	−	6.04372i	0.120681	−	0.209026i
$837$	20.2273	+	12.7170i	0.699158	+	0.439563i
$838$	−14.9336	+	8.62194i	−0.515874	+	0.297840i
$839$	21.5972	−	37.4075i	0.745619	−	1.29145i	−0.204286	−	0.978911i	$-0.565487\pi$
$839$	21.5972	−	37.4075i	0.745619	−	1.29145i	0.949905	−	0.312539i	$-0.101179\pi$
$840$	−6.46760	+	6.18679i	−0.223153	+	0.213464i
$841$	−14.4594	−	25.0444i	−0.498600	−	0.863601i
$842$	4.29426	+	2.47929i	0.147990	+	0.0854420i
$843$	34.2608	+	6.48557i	1.18001	+	0.223375i
$844$	−4.03620	−	6.99091i	−0.138932	−	0.240637i
$845$	13.5326	+	23.4391i	0.465534	+	0.806329i
$846$	10.9380	+	13.7207i	0.376056	+	0.471727i
$847$	−11.5305	−	25.3623i	−0.396193	−	0.871460i
$848$	−19.4376	−	11.2223i	−0.667490	−	0.385376i
$849$	−14.7815	−	42.2549i	−0.507301	−	1.45018i
$850$		−	1.05731i		−	0.0362655i
$851$			9.57483i			0.328221i
$852$	3.51491	+	10.0478i	0.120419	+	0.344233i
$853$	−12.0459	−	6.95468i	−0.412442	−	0.238124i	0.279396	−	0.960176i	$-0.409866\pi$
$853$	−12.0459	−	6.95468i	−0.412442	−	0.238124i	−0.691839	+	0.722052i	$0.743199\pi$
$854$	−1.58481	+	2.21757i	−0.0542312	+	0.0758836i
$855$	−11.0376	−	13.8456i	−0.377477	−	0.473510i
$856$	−14.2569	−	24.6937i	−0.487292	−	0.844014i
$857$	9.56421	+	16.5657i	0.326707	+	0.565873i	0.981856	−	0.189626i	$-0.0607276\pi$
$857$	9.56421	+	16.5657i	0.326707	+	0.565873i	−0.655149	+	0.755499i	$0.727394\pi$
$858$	3.87101	+	0.732782i	0.132154	+	0.0250168i
$859$	−8.38604	−	4.84168i	−0.286128	−	0.165196i	0.350066	−	0.936725i	$-0.386159\pi$
$859$	−8.38604	−	4.84168i	−0.286128	−	0.165196i	−0.636194	+	0.771529i	$0.719492\pi$
$860$	−2.64838	−	4.58713i	−0.0903090	−	0.156420i
$861$	−28.1996	+	6.88933i	−0.961041	+	0.234788i
$862$	−0.749280	+	1.29779i	−0.0255206	+	0.0442029i
$863$	22.1631	−	12.7959i	0.754440	−	0.435576i	−0.0728560	−	0.997342i	$-0.523211\pi$
$863$	22.1631	−	12.7959i	0.754440	−	0.435576i	0.827296	+	0.561766i	$0.189878\pi$
$864$	−22.7791	−	14.3213i	−0.774960	−	0.487220i
$865$	−2.67485	+	4.63298i	−0.0909478	+	0.157526i
$866$	1.43454			0.0487478
$867$	16.9782	+	14.6135i	0.576611	+	0.496301i
$868$	−17.0747	−	12.2027i	−0.579554	−	0.414186i
$869$	2.88077	−	1.66321i	0.0977234	−	0.0564206i
$870$	0.196114	+	0.168800i	0.00664890	+	0.00572284i
$871$	22.6759	−	13.0919i	0.768344	−	0.443603i
$872$	1.98136	+	1.14394i	0.0670973	+	0.0387387i
$873$	−29.3038	+	4.41165i	−0.991784	+	0.149312i
$874$		−	24.9586i		−	0.844239i
$875$	−1.53835	+	2.15255i	−0.0520057	+	0.0727696i
$876$	−11.0167	−	2.08547i	−0.372221	−	0.0704613i
$877$	3.48715	−	6.03991i	0.117753	−	0.203953i	−0.801124	−	0.598498i	$-0.795764\pi$
$877$	3.48715	−	6.03991i	0.117753	−	0.203953i	0.918877	+	0.394545i	$0.129098\pi$
$878$	6.59994			0.222737
$879$	−1.94384	−	1.67310i	−0.0655641	−	0.0564323i
$880$		−	1.66290i		−	0.0560562i
$881$	14.9270			0.502904			0.251452	−	0.967870i	$-0.419092\pi$
$881$	14.9270			0.502904			0.251452	+	0.967870i	$0.419092\pi$
$882$	−5.92278	+	9.28172i	−0.199430	+	0.312532i
$883$	38.7784			1.30500			0.652499	−	0.757790i	$-0.273721\pi$
$883$	38.7784			1.30500			0.652499	+	0.757790i	$0.273721\pi$
$884$			22.0200i			0.740611i
$885$	−2.34382	+	12.3815i	−0.0787867	+	0.416201i
$886$	5.53153			0.185835
$887$	10.7496	−	18.6188i	0.360936	−	0.625159i	−0.627180	−	0.778875i	$-0.715791\pi$
$887$	10.7496	−	18.6188i	0.360936	−	0.625159i	0.988115	+	0.153716i	$0.0491241\pi$
$888$	−2.61987	+	3.04381i	−0.0879170	+	0.102143i
$889$	16.4439	−	23.0093i	0.551510	−	0.771706i
$890$			3.12202i			0.104650i
$891$	1.81617	+	5.89513i	0.0608441	+	0.197494i
$892$	−25.1990	−	14.5486i	−0.843723	−	0.487124i
$893$	57.0223	−	32.9218i	1.90818	−	1.10169i
$894$	0.0896971	−	0.473836i	0.00299992	−	0.0158475i
$895$	−7.73789	+	4.46747i	−0.258649	+	0.149331i
$896$	24.7052	+	17.6559i	0.825342	+	0.589841i
$897$	−83.4630	+	29.1969i	−2.78675	+	0.974855i
$898$	7.58846			0.253230
$899$	−0.655086	+	1.13464i	−0.0218483	+	0.0378424i
$900$	−4.81723	−	1.89159i	−0.160574	−	0.0630529i
$901$	16.1561	−	9.32774i	0.538238	−	0.310752i
$902$	−1.13820	+	1.97142i	−0.0378979	+	0.0656411i
$903$	−9.72607	−	10.1675i	−0.323663	−	0.338354i
$904$	−3.79186	−	6.56770i	−0.126116	−	0.218438i
$905$	2.61652	+	1.51065i	0.0869760	+	0.0502156i
$906$	−8.98051	+	10.4337i	−0.298358	+	0.346637i
$907$	16.7806	+	29.0648i	0.557189	+	0.965080i	0.997730	+	0.0673471i	$0.0214535\pi$
$907$	16.7806	+	29.0648i	0.557189	+	0.965080i	−0.440540	+	0.897733i	$0.645213\pi$
$908$	17.6696	+	30.6046i	0.586385	+	1.01565i
$909$	18.8830	+	7.41481i	0.626311	+	0.245934i
$910$	−5.10532	+	7.14368i	−0.169240	+	0.236811i
$911$	43.1670	+	24.9225i	1.43019	+	0.825719i	0.997134	−	0.0756501i	$-0.0241032\pi$
$911$	43.1670	+	24.9225i	1.43019	+	0.825719i	0.433052	+	0.901369i	$0.357437\pi$
$912$	−16.1802	+	18.7985i	−0.535781	+	0.622480i
$913$		−	2.91961i		−	0.0966249i
$914$		−	12.8740i		−	0.425833i
$915$	−3.34390	−	0.633000i	−0.110546	−	0.0209263i
$916$	−6.57352	−	3.79522i	−0.217195	−	0.125398i
$917$	−10.9391	−	24.0614i	−0.361240	−	0.794578i
$918$	4.85796	−	2.56589i	0.160336	−	0.0846871i
$919$	−15.4067	−	26.6852i	−0.508220	−	0.880263i	−0.999955	−	0.00951786i	$-0.996970\pi$
$919$	−15.4067	−	26.6852i	−0.508220	−	0.880263i	0.491735	−	0.870745i	$-0.336363\pi$
$920$	−7.87611	−	13.6418i	−0.259668	−	0.449758i
$921$	18.2709	+	52.2297i	0.602046	+	1.72103i
$922$	1.97115	+	1.13804i	0.0649164	+	0.0374795i
$923$	11.2750	+	19.5289i	0.371123	+	0.642803i
$924$	−1.28591	−	5.26353i	−0.0423034	−	0.173158i
$925$	−0.593585	+	1.02812i	−0.0195169	+	0.0338043i
$926$	−3.65997	+	2.11308i	−0.120274	+	0.0694402i
$927$	51.5237	−	7.75684i	1.69226	−	0.254768i
$928$	0.737728	−	1.27778i	0.0242171	−	0.0419453i
$929$	21.4631			0.704183			0.352091	−	0.935966i	$-0.385471\pi$
$929$	21.4631			0.704183			0.352091	+	0.935966i	$0.385471\pi$
$930$	−0.776668	+	4.10285i	−0.0254680	+	0.134538i
$931$	31.1321	+	27.1621i	1.02031	+	0.890202i
$932$	−27.8456	+	16.0767i	−0.912112	+	0.526608i
$933$	−18.9836	+	6.64080i	−0.621495	+	0.217410i
$934$	−8.94857	+	5.16646i	−0.292806	+	0.169052i
$935$	1.19699	+	0.691082i	0.0391457	+	0.0226008i
$936$	−34.5214	−	13.5556i	−1.12837	−	0.443077i
$937$		−	20.2097i		−	0.660223i	−0.943942	−	0.330111i	$-0.892914\pi$
$937$		−	20.2097i		−	0.660223i	0.943942	−	0.330111i	$-0.107086\pi$
$938$	4.66863	+	3.33650i	0.152436	+	0.108940i
$939$	12.4221	+	35.5102i	0.405381	+	1.15883i
$940$	9.62235	−	16.6664i	0.313847	−	0.543598i
$941$	−56.2807			−1.83470			−0.917349	−	0.398083i	$-0.869676\pi$
$941$	−56.2807			−1.83470			−0.917349	+	0.398083i	$0.869676\pi$
$942$	−5.36755	+	1.87767i	−0.174884	+	0.0611777i
$943$		−	51.0906i		−	1.66374i
$944$	17.6516			0.574509
$945$	−13.6235	−	1.84431i	−0.443171	−	0.0599956i
$946$	−1.10337			−0.0358737
$947$		−	20.8270i		−	0.676786i	−0.941005	−	0.338393i	$-0.890117\pi$
$947$		−	20.8270i		−	0.676786i	0.941005	−	0.338393i	$-0.109883\pi$
$948$	−13.6881	+	4.78835i	−0.444569	+	0.155518i
$949$	−23.7523			−0.771032
$950$	1.54729	−	2.67999i	0.0502008	−	0.0869503i
$951$	−4.72055	−	13.4943i	−0.153074	−	0.437582i
$952$	−9.48621	+	4.31273i	−0.307450	+	0.139776i
$953$			3.82448i			0.123887i	0.998080	+	0.0619435i	$0.0197298\pi$
$953$			3.82448i			0.123887i	−0.998080	+	0.0619435i	$0.980270\pi$
$954$	2.16623	+	14.3889i	0.0701343	+	0.465858i
$955$	22.8315	+	13.1818i	0.738810	+	0.426552i
$956$	5.85648	−	3.38124i	0.189412	−	0.109357i
$957$	−0.319283	+	0.111691i	−0.0103210	+	0.00361046i
$958$	6.79481	−	3.92299i	0.219530	−	0.126746i
$959$	−4.92548	+	50.6712i	−0.159052	+	1.63626i
$960$	−0.688570	+	3.63746i	−0.0222235	+	0.117398i
$961$	9.85683			0.317962
$962$	−1.96993	+	3.41202i	−0.0635131	+	0.110008i
$963$	16.0082	−	40.7676i	0.515859	−	1.31372i
$964$	13.4285	−	7.75292i	0.432501	−	0.249705i
$965$	−6.49750	+	11.2540i	−0.209162	+	0.362279i
$966$	−13.3951	−	14.0031i	−0.430980	−	0.450541i
$967$	−18.6430	−	32.2907i	−0.599520	−	1.03840i	−0.992892	−	0.119019i	$-0.962025\pi$
$967$	−18.6430	−	32.2907i	−0.599520	−	1.03840i	0.393372	−	0.919379i	$-0.371308\pi$
$968$	17.8111	+	10.2833i	0.572472	+	0.330517i
$969$	−6.80722	−	19.4593i	−0.218680	−	0.625124i
$970$	−2.58955	−	4.48523i	−0.0831455	−	0.144012i
$971$	−15.7637	−	27.3034i	−0.505880	−	0.876209i	−0.999977	−	0.00680264i	$-0.997835\pi$
$971$	−15.7637	−	27.3034i	−0.505880	−	0.876209i	0.494097	−	0.869407i	$-0.335499\pi$
$972$	−2.99936	−	26.7239i	−0.0962044	−	0.857170i
$973$	−5.21351	+	53.6342i	−0.167137	+	1.71943i
$974$	0.188318	+	0.108725i	0.00603409	+	0.00348378i
$975$	−10.7721	−	2.03915i	−0.344982	−	0.0653050i
$976$			4.76719i			0.152594i
$977$		−	55.1330i		−	1.76386i	−0.471380	−	0.881930i	$-0.656244\pi$
$977$		−	55.1330i		−	1.76386i	0.471380	−	0.881930i	$-0.343756\pi$
$978$	−10.6347	+	12.3556i	−0.340061	+	0.395089i
$979$	−3.53445	−	2.04062i	−0.112962	−	0.0652184i
$980$	11.8497	+	2.32566i	0.378523	+	0.0742906i
$981$	0.523168	+	3.47508i	0.0167035	+	0.110951i
$982$	−5.61689	−	9.72874i	−0.179242	−	0.310457i
$983$	−21.3753	−	37.0231i	−0.681766	−	1.18085i	−0.974442	−	0.224641i	$-0.927879\pi$
$983$	−21.3753	−	37.0231i	−0.681766	−	1.18085i	0.292676	−	0.956212i	$-0.405454\pi$
$984$	13.9794	−	16.2415i	0.445647	−	0.517761i
$985$	−7.77096	−	4.48657i	−0.247604	−	0.142954i
$986$	0.150632	+	0.260902i	0.00479709	+	0.00830881i
$987$	14.3235	−	49.0742i	0.455923	−	1.56205i
$988$	−32.2245	+	55.8144i	−1.02520	+	1.77569i
$989$	21.4459	−	12.3818i	0.681941	−	0.393719i
$990$	−0.842986	+	0.672020i	−0.0267919	+	0.0213582i
$991$	19.6274	−	33.9957i	0.623485	−	1.07991i	−0.365347	−	0.930872i	$-0.619050\pi$
$991$	19.6274	−	33.9957i	0.623485	−	1.07991i	0.988832	−	0.149036i	$-0.0476172\pi$
$992$	23.8105			0.755984
$993$	−16.5390	+	5.78563i	−0.524848	+	0.183601i
$994$	−2.87346	+	4.02072i	−0.0911406	+	0.127529i
$995$	9.18073	−	5.30050i	0.291049	−	0.168037i
$996$	−2.36736	+	12.5059i	−0.0750127	+	0.396264i
$997$	−37.5885	+	21.7017i	−1.19044	+	0.687300i	−0.958406	−	0.285408i	$-0.907871\pi$
$997$	−37.5885	+	21.7017i	−1.19044	+	0.687300i	−0.232033	+	0.972708i	$0.574538\pi$
$998$	11.5082	+	6.64425i	0.364285	+	0.210320i
$999$	−6.16434	−	0.232255i	−0.195031	−	0.00734823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.c.101.7	✓	32
3.2	odd	2		945.2.t.c.521.10		32
7.5	odd	6		315.2.be.c.236.7	yes	32
9.4	even	3		945.2.be.c.206.10		32
9.5	odd	6		315.2.be.c.311.7	yes	32
21.5	even	6		945.2.be.c.656.10		32
63.5	even	6	inner	315.2.t.c.131.10	yes	32
63.40	odd	6		945.2.t.c.341.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.7	✓	32	1.1	even	1	trivial
315.2.t.c.131.10	yes	32	63.5	even	6	inner
315.2.be.c.236.7	yes	32	7.5	odd	6
315.2.be.c.311.7	yes	32	9.5	odd	6
945.2.t.c.341.7		32	63.40	odd	6
945.2.t.c.521.10		32	3.2	odd	2
945.2.be.c.206.10		32	9.4	even	3
945.2.be.c.656.10		32	21.5	even	6

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.524306i q^{2} +(1.63490 - 0.571919i) q^{3} +1.72510 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.299860 - 0.857190i) q^{6} +(-1.53835 + 2.15255i) q^{7} -1.95309i q^{8} +(2.34582 - 1.87006i) q^{9} +O(q^{10})\)	\(q-0.524306i q^{2} +(1.63490 - 0.571919i) q^{3} +1.72510 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.299860 - 0.857190i) q^{6} +(-1.53835 + 2.15255i) q^{7} -1.95309i q^{8} +(2.34582 - 1.87006i) q^{9} +(0.454062 + 0.262153i) q^{10} +(-0.593570 + 0.342698i) q^{11} +(2.82038 - 0.986619i) q^{12} +(5.48168 - 3.16485i) q^{13} +(1.12860 + 0.806566i) q^{14} +(-0.322156 + 1.70183i) q^{15} +2.42619 q^{16} +(-1.00830 + 1.74642i) q^{17} +(-0.980486 - 1.22993i) q^{18} +(-5.11150 + 2.95112i) q^{19} +(-0.862552 + 1.49398i) q^{20} +(-1.28397 + 4.39903i) q^{21} +(0.179678 + 0.311212i) q^{22} +(-6.98472 - 4.03263i) q^{23} +(-1.11701 - 3.19312i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.65935 - 2.87408i) q^{26} +(2.76566 - 4.39899i) q^{27} +(-2.65381 + 3.71337i) q^{28} +(0.246759 + 0.142467i) q^{29} +(0.892278 + 0.168908i) q^{30} +4.59817i q^{31} -5.17825i q^{32} +(-0.774434 + 0.899751i) q^{33} +(0.915659 + 0.528656i) q^{34} +(-1.09499 - 2.40853i) q^{35} +(4.04678 - 3.22605i) q^{36} +(-0.593585 - 1.02812i) q^{37} +(1.54729 + 2.67999i) q^{38} +(7.15198 - 8.30930i) q^{39} +(1.69143 + 0.976547i) q^{40} +(3.16732 + 5.48596i) q^{41} +(2.30644 + 0.673192i) q^{42} +(-1.53520 + 2.65905i) q^{43} +(-1.02397 + 0.591189i) q^{44} +(0.446614 + 2.96657i) q^{45} +(-2.11433 + 3.66213i) q^{46} -11.1557 q^{47} +(3.96658 - 1.38758i) q^{48} +(-2.26696 - 6.62275i) q^{49} +(-0.454062 + 0.262153i) q^{50} +(-0.649657 + 3.43189i) q^{51} +(9.45647 - 5.45969i) q^{52} +(-8.01159 - 4.62549i) q^{53} +(-2.30642 - 1.45005i) q^{54} -0.685395i q^{55} +(4.20414 + 3.00454i) q^{56} +(-6.66900 + 7.74816i) q^{57} +(0.0746961 - 0.129378i) q^{58} +7.27543 q^{59} +(-0.555752 + 2.93583i) q^{60} +1.96489i q^{61} +2.41085 q^{62} +(0.416722 + 7.92631i) q^{63} +2.13738 q^{64} +6.32970i q^{65} +(0.471745 + 0.406040i) q^{66} +4.13667 q^{67} +(-1.73942 + 3.01276i) q^{68} +(-13.7257 - 2.59827i) q^{69} +(-1.26280 + 0.574110i) q^{70} +3.56258i q^{71} +(-3.65241 - 4.58160i) q^{72} +(-3.24977 - 1.87626i) q^{73} +(-0.539049 + 0.311220i) q^{74} +(-1.31275 - 1.12991i) q^{75} +(-8.81786 + 5.09099i) q^{76} +(0.175443 - 1.80488i) q^{77} +(-4.35662 - 3.74983i) q^{78} -4.85329 q^{79} +(-1.21309 + 2.10114i) q^{80} +(2.00572 - 8.77366i) q^{81} +(2.87632 - 1.66065i) q^{82} +(-2.12987 + 3.68905i) q^{83} +(-2.21498 + 7.58877i) q^{84} +(-1.00830 - 1.74642i) q^{85} +(1.39415 + 0.804916i) q^{86} +(0.484907 + 0.0917928i) q^{87} +(0.669321 + 1.15930i) q^{88} +(2.97729 + 5.15681i) q^{89} +(1.55539 - 0.234162i) q^{90} +(-1.62023 + 16.6683i) q^{91} +(-12.0494 - 6.95671i) q^{92} +(2.62978 + 7.51756i) q^{93} +5.84899i q^{94} -5.90225i q^{95} +(-2.96154 - 8.46594i) q^{96} +(-8.55461 - 4.93901i) q^{97} +(-3.47235 + 1.18858i) q^{98} +(-0.751540 + 1.91392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

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