LMFDB - Embedded newform 315.2.be.c.236.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.7
Character	$\chi$	$=$	315.236
Dual form			315.2.be.c.311.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.454062 + 0.262153i) q^{2} +(0.322156 - 1.70183i) q^{3} +(-0.862552 + 1.49398i) q^{4} -1.00000 q^{5} +(0.299860 + 0.857190i) q^{6} +(-1.09499 + 2.40853i) q^{7} -1.95309i q^{8} +(-2.79243 - 1.09651i) q^{9} +O(q^{10})$	\(q+(-0.454062 + 0.262153i) q^{2} +(0.322156 - 1.70183i) q^{3} +(-0.862552 + 1.49398i) q^{4} -1.00000 q^{5} +(0.299860 + 0.857190i) q^{6} +(-1.09499 + 2.40853i) q^{7} -1.95309i q^{8} +(-2.79243 - 1.09651i) q^{9} +(0.454062 - 0.262153i) q^{10} -0.685395i q^{11} +(2.26463 + 1.94921i) q^{12} +(-5.48168 + 3.16485i) q^{13} +(-0.134208 - 1.38068i) q^{14} +(-0.322156 + 1.70183i) q^{15} +(-1.21309 - 2.10114i) q^{16} +(1.00830 + 1.74642i) q^{17} +(1.55539 - 0.234162i) q^{18} +(-5.11150 - 2.95112i) q^{19} +(0.862552 - 1.49398i) q^{20} +(3.74614 + 2.63940i) q^{21} +(0.179678 + 0.311212i) q^{22} +8.06526i q^{23} +(-3.32383 - 0.629200i) q^{24} +1.00000 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} +(-0.299860 - 0.857190i) q^{30} +(3.98213 + 2.29908i) q^{31} +(4.48450 + 2.58913i) q^{32} +(-1.16642 - 0.220804i) 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} +3.09458 q^{38} +(3.62007 + 10.3484i) q^{39} +1.95309i q^{40} +(-3.16732 - 5.48596i) q^{41} +(-2.39291 - 0.216393i) q^{42} +(-1.53520 + 2.65905i) q^{43} +(1.02397 + 0.591189i) q^{44} +(2.79243 + 1.09651i) q^{45} +(-2.11433 - 3.66213i) q^{46} +(-5.57784 - 9.66111i) q^{47} +(-3.96658 + 1.38758i) q^{48} +(-4.60199 - 5.27462i) q^{49} +(-0.454062 + 0.262153i) q^{50} +(3.29694 - 1.15333i) q^{51} -10.9194i q^{52} +(8.01159 - 4.62549i) q^{53} +(0.102574 - 2.72244i) q^{54} +0.685395i q^{55} +(4.70408 + 2.13862i) q^{56} +(-6.66900 + 7.74816i) q^{57} -0.149392 q^{58} +(3.63772 - 6.30071i) q^{59} +(-2.26463 - 1.94921i) q^{60} +(-1.70164 + 0.982445i) q^{61} -2.41085 q^{62} +(5.69865 - 5.52498i) q^{63} +2.13738 q^{64} +(5.48168 - 3.16485i) q^{65} +(0.587514 - 0.205523i) q^{66} +(-2.06833 + 3.58246i) q^{67} -3.47883 q^{68} +(13.7257 + 2.59827i) q^{69} +(0.134208 + 1.38068i) q^{70} +3.56258i q^{71} +(-2.14158 + 5.45388i) q^{72} +(-3.24977 + 1.87626i) q^{73} -0.622440i q^{74} +(0.322156 - 1.70183i) q^{75} +(8.81786 - 5.09099i) q^{76} +(1.65079 + 0.750501i) q^{77} +(-4.35662 - 3.74983i) q^{78} +(2.42665 + 4.20308i) q^{79} +(1.21309 + 2.10114i) q^{80} +(6.59535 + 6.12384i) q^{81} +(2.87632 + 1.66065i) q^{82} +(2.12987 - 3.68905i) q^{83} +(-7.17446 + 3.32004i) q^{84} +(-1.00830 - 1.74642i) q^{85} -1.60983i q^{86} +(0.321949 - 0.374046i) q^{87} -1.33864 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} +(5.19551 - 6.03624i) q^{93} +(5.06538 + 2.92450i) q^{94} +(5.11150 + 2.95112i) q^{95} +(5.85095 - 6.79774i) 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} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.454062	+	0.262153i	−0.321071	+	0.185370i	−0.651870	−	0.758331i	$-0.726015\pi$
$2$	−0.454062	+	0.262153i	−0.321071	+	0.185370i	0.330799	+	0.943701i	$0.392682\pi$
$3$	0.322156	−	1.70183i	0.185997	−	0.982550i
$3$	0.322156	−	1.70183i	0.185997	−	0.982550i
$4$	−0.862552	+	1.49398i	−0.431276	+	0.746992i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.299860	+	0.857190i	0.122418	+	0.349946i
$7$	−1.09499	+	2.40853i	−0.413867	+	0.910337i
$7$	−1.09499	+	2.40853i	−0.413867	+	0.910337i
$8$		−	1.95309i		−	0.690523i
$9$	−2.79243	−	1.09651i	−0.930811	−	0.365502i
$10$	0.454062	−	0.262153i	0.143587	−	0.0829001i
$11$		−	0.685395i		−	0.206654i	−0.994647	−	0.103327i	$-0.967051\pi$
$11$		−	0.685395i		−	0.206654i	0.994647	−	0.103327i	$-0.0329489\pi$
$12$	2.26463	+	1.94921i	0.653741	+	0.562688i
$13$	−5.48168	+	3.16485i	−1.52034	+	0.877772i	−0.520633	+	0.853781i	$0.674304\pi$
$13$	−5.48168	+	3.16485i	−1.52034	+	0.877772i	−0.999712	+	0.0239908i	$0.992363\pi$
$14$	−0.134208	−	1.38068i	−0.0358687	−	0.369001i
$15$	−0.322156	+	1.70183i	−0.0831802	+	0.439410i
$16$	−1.21309	−	2.10114i	−0.303273	−	0.525285i
$17$	1.00830	+	1.74642i	0.244548	+	0.423569i	0.962004	−	0.273034i	$-0.0880271\pi$
$17$	1.00830	+	1.74642i	0.244548	+	0.423569i	−0.717457	+	0.696603i	$0.754694\pi$
$18$	1.55539	−	0.234162i	0.366609	−	0.0551926i
$19$	−5.11150	−	2.95112i	−1.17266	−	0.677034i	−0.218353	−	0.975870i	$-0.570068\pi$
$19$	−5.11150	−	2.95112i	−1.17266	−	0.677034i	−0.954305	+	0.298836i	$0.903402\pi$
$20$	0.862552	−	1.49398i	0.192872	−	0.334065i
$21$	3.74614	+	2.63940i	0.817474	+	0.575965i
$22$	0.179678	+	0.311212i	0.0383076	+	0.0663507i
$23$			8.06526i			1.68172i	0.541250	+	0.840862i	$0.317951\pi$
$23$			8.06526i			1.68172i	−0.541250	+	0.840862i	$0.682049\pi$
$24$	−3.32383	−	0.629200i	−0.678474	−	0.128435i
$25$	1.00000			0.200000
$26$	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	$0.658245\pi$
$30$	−0.299860	−	0.857190i	−0.0547468	−	0.156501i
$31$	3.98213	+	2.29908i	0.715212	+	0.412928i	0.812988	−	0.582281i	$-0.197839\pi$
$31$	3.98213	+	2.29908i	0.715212	+	0.412928i	−0.0977759	+	0.995208i	$0.531173\pi$
$32$	4.48450	+	2.58913i	0.792755	+	0.457697i
$33$	−1.16642	−	0.220804i	−0.203048	−	0.0384370i
$34$	−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	−0.910684	−	0.413103i	$-0.864445\pi$
$37$	−0.593585	+	1.02812i	−0.0975847	+	0.169022i	0.813100	+	0.582124i	$0.197778\pi$
$38$	3.09458			0.502008
$39$	3.62007	+	10.3484i	0.579676	+	1.65708i
$40$			1.95309i			0.308811i
$41$	−3.16732	−	5.48596i	−0.494653	−	0.856763i	0.505328	−	0.862927i	$-0.331371\pi$
$41$	−3.16732	−	5.48596i	−0.494653	−	0.856763i	−0.999981	+	0.00616369i	$0.998038\pi$
$42$	−2.39291	−	0.216393i	−0.369234	−	0.0333902i
$43$	−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
$45$	2.79243	+	1.09651i	0.416271	+	0.163457i
$46$	−2.11433	−	3.66213i	−0.311742	−	0.539952i
$47$	−5.57784	−	9.66111i	−0.813612	−	1.40922i	−0.910320	−	0.413905i	$-0.864165\pi$
$47$	−5.57784	−	9.66111i	−0.813612	−	1.40922i	0.0967082	−	0.995313i	$-0.469169\pi$
$48$	−3.96658	+	1.38758i	−0.572527	+	0.200280i
$49$	−4.60199	−	5.27462i	−0.657427	−	0.753518i
$50$	−0.454062	+	0.262153i	−0.0642141	+	0.0370740i
$51$	3.29694	−	1.15333i	0.461663	−	0.161498i
$52$		−	10.9194i		−	1.51425i
$53$	8.01159	−	4.62549i	1.10048	−	0.635360i	0.164130	−	0.986439i	$-0.447518\pi$
$53$	8.01159	−	4.62549i	1.10048	−	0.635360i	0.936346	+	0.351079i	$0.114185\pi$
$54$	0.102574	−	2.72244i	0.0139586	−	0.370478i
$55$			0.685395i			0.0924187i
$56$	4.70408	+	2.13862i	0.628609	+	0.285785i
$57$	−6.66900	+	7.74816i	−0.883331	+	1.02627i
$58$	−0.149392			−0.0196162
$59$	3.63772	−	6.30071i	0.473590	−	0.820283i	−0.525952	−	0.850514i	$-0.676291\pi$
$59$	3.63772	−	6.30071i	0.473590	−	0.820283i	0.999543	+	0.0302312i	$0.00962436\pi$
$60$	−2.26463	−	1.94921i	−0.292362	−	0.251642i
$61$	−1.70164	+	0.982445i	−0.217873	+	0.125789i	−0.604965	−	0.796252i	$-0.706813\pi$
$61$	−1.70164	+	0.982445i	−0.217873	+	0.125789i	0.387092	+	0.922041i	$0.373480\pi$
$62$	−2.41085			−0.306178
$63$	5.69865	−	5.52498i	0.717962	−	0.696082i
$64$	2.13738			0.267173
$65$	5.48168	−	3.16485i	0.679919	−	0.392551i
$66$	0.587514	−	0.205523i	0.0723180	−	0.0252981i
$67$	−2.06833	+	3.58246i	−0.252687	+	0.437667i	−0.964265	−	0.264940i	$-0.914648\pi$
$67$	−2.06833	+	3.58246i	−0.252687	+	0.437667i	0.711578	+	0.702608i	$0.247981\pi$
$68$	−3.47883			−0.421870
$69$	13.7257	+	2.59827i	1.65238	+	0.312795i
$70$	0.134208	+	1.38068i	0.0160410	+	0.165022i
$71$			3.56258i			0.422801i	0.977400	+	0.211400i	$0.0678024\pi$
$71$			3.56258i			0.422801i	−0.977400	+	0.211400i	$0.932198\pi$
$72$	−2.14158	+	5.45388i	−0.252388	+	0.642746i
$73$	−3.24977	+	1.87626i	−0.380357	+	0.219599i	−0.677974	−	0.735086i	$-0.737142\pi$
$73$	−3.24977	+	1.87626i	−0.380357	+	0.219599i	0.297617	+	0.954685i	$0.403808\pi$
$74$		−	0.622440i		−	0.0723572i
$75$	0.322156	−	1.70183i	0.0371993	−	0.196510i
$76$	8.81786	−	5.09099i	1.01148	−	0.583977i
$77$	1.65079	+	0.750501i	0.188125	+	0.0855275i
$78$	−4.35662	−	3.74983i	−0.493290	−	0.424584i
$79$	2.42665	+	4.20308i	0.273019	+	0.472883i	0.969633	−	0.244563i	$-0.0786444\pi$
$79$	2.42665	+	4.20308i	0.273019	+	0.472883i	−0.696614	+	0.717446i	$0.745311\pi$
$80$	1.21309	+	2.10114i	0.135628	+	0.234915i
$81$	6.59535	+	6.12384i	0.732816	+	0.680426i
$82$	2.87632	+	1.66065i	0.317637	+	0.183388i
$83$	2.12987	−	3.68905i	0.233784	−	0.404925i	−0.725135	−	0.688607i	$-0.758223\pi$
$83$	2.12987	−	3.68905i	0.233784	−	0.404925i	0.958919	+	0.283682i	$0.0915559\pi$
$84$	−7.17446	+	3.32004i	−0.782798	+	0.362246i
$85$	−1.00830	−	1.74642i	−0.109365	−	0.189426i
$86$		−	1.60983i		−	0.173593i
$87$	0.321949	−	0.374046i	0.0345165	−	0.0401019i
$88$	−1.33864			−0.142700
$89$	−2.97729	+	5.15681i	−0.315592	+	0.546621i	−0.979563	−	0.201137i	$-0.935536\pi$
$89$	−2.97729	+	5.15681i	−0.315592	+	0.546621i	0.663971	+	0.747758i	$0.268870\pi$
$90$	−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
$93$	5.19551	−	6.03624i	0.538749	−	0.625929i
$94$	5.06538	+	2.92450i	0.522454	+	0.301639i
$95$	5.11150	+	2.95112i	0.524428	+	0.302779i
$96$	5.85095	−	6.79774i	0.597160	−	0.693792i
$97$	8.55461	+	4.93901i	0.868589	+	0.501480i	0.866879	−	0.498518i	$-0.166122\pi$
$97$	8.55461	+	4.93901i	0.868589	+	0.501480i	0.00170992	+	0.999999i	$0.499456\pi$
$98$	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
$101$	6.76222			0.672866			0.336433	−	0.941707i	$-0.390779\pi$
$101$	6.76222			0.672866			0.336433	+	0.941707i	$0.390779\pi$
$102$	−1.19467	+	1.38798i	−0.118290	+	0.137431i
$103$			17.3681i			1.71133i	0.517529	+	0.855666i	$0.326852\pi$
$103$			17.3681i			1.71133i	−0.517529	+	0.855666i	$0.673148\pi$
$104$	6.18125	+	10.7062i	0.606122	+	1.04983i
$105$	−3.74614	−	2.63940i	−0.365586	−	0.257579i
$106$	−2.42517	+	4.20052i	−0.235554	+	0.407991i
$107$	−12.6434	−	7.29966i	−1.22228	−	0.705685i	−0.256878	−	0.966444i	$-0.582694\pi$
$107$	−12.6434	−	7.29966i	−1.22228	−	0.705685i	−0.965404	+	0.260759i	$0.916027\pi$
$108$	−4.18649	−	7.92621i	−0.402845	−	0.762700i
$109$	−0.585706	−	1.01447i	−0.0561005	−	0.0971688i	0.836611	−	0.547797i	$-0.184533\pi$
$109$	−0.585706	−	1.01447i	−0.0561005	−	0.0971688i	−0.892712	+	0.450628i	$0.851200\pi$
$110$	−0.179678	−	0.311212i	−0.0171317	−	0.0296729i
$111$	1.55845	+	1.34139i	0.147922	+	0.127319i
$112$	6.38897	−	0.621039i	0.603701	−	0.0586827i
$113$	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	$0.274870\pi$
$114$	0.996938	−	5.26645i	0.0933718	−	0.493248i
$115$		−	8.06526i		−	0.752090i
$116$	−0.425686	+	0.245770i	−0.0395239	+	0.0228191i
$117$	18.7775	−	2.82693i	1.73598	−	0.261350i
$118$			3.81456i			0.351158i
$119$	−5.31038	+	0.516194i	−0.486801	+	0.0473194i
$120$	3.32383	+	0.629200i	0.303423	+	0.0574379i
$121$	10.5302			0.957294
$122$	0.515102	−	0.892183i	0.0466351	−	0.0807744i
$123$	−10.3565	+	3.62290i	−0.933817	+	0.326666i
$124$	−6.86959	+	3.96616i	−0.616907	+	0.356172i
$125$	−1.00000			−0.0894427
$126$	−1.13915	+	4.00260i	−0.101484	+	0.356580i
$127$	−10.6893			−0.948522			−0.474261	−	0.880384i	$-0.657285\pi$
$127$	−10.6893			−0.948522			−0.474261	+	0.880384i	$0.657285\pi$
$128$	−9.93950	+	5.73858i	−0.878536	+	0.507223i
$129$	4.03067	+	3.46927i	0.354880	+	0.305453i
$130$	−1.65935	+	2.87408i	−0.145535	+	0.252073i
$131$	−9.99010			−0.872839			−0.436420	−	0.899743i	$-0.643754\pi$
$131$	−9.99010			−0.872839			−0.436420	+	0.899743i	$0.643754\pi$
$132$	1.33598	−	1.55216i	0.116282	−	0.135098i
$133$	12.7049	−	9.07972i	1.10165	−	0.787311i
$134$		−	2.16888i		−	0.187363i
$135$	2.76566	−	4.39899i	0.238030	−	0.378605i
$136$	3.41093	−	1.96930i	0.292484	−	0.168866i
$137$			19.2422i			1.64397i	0.569509	+	0.821985i	$0.307133\pi$
$137$			19.2422i			1.64397i	−0.569509	+	0.821985i	$0.692867\pi$
$138$	−6.91346	+	2.41845i	−0.588513	+	0.205872i
$139$	−17.6387	+	10.1837i	−1.49609	+	0.863769i	−0.999990	−	0.00449501i	$-0.998569\pi$
$139$	−17.6387	+	10.1837i	−1.49609	+	0.863769i	−0.496102	+	0.868264i	$0.665236\pi$
$140$	2.65381	+	3.71337i	0.224288	+	0.313837i
$141$	−18.2385	+	6.38015i	−1.53596	+	0.537305i
$142$	−0.933942	−	1.61764i	−0.0783747	−	0.135749i
$143$	2.16917	+	3.75712i	0.181395	+	0.314186i
$144$	1.08357	+	7.19745i	0.0902973	+	0.599788i
$145$	−0.246759	−	0.142467i	−0.0204923	−	0.0118312i
$146$	0.983733	−	1.70388i	0.0814143	−	0.141014i
$147$	−10.4591	+	6.13255i	−0.862649	+	0.505804i
$148$	−1.02399	−	1.77361i	−0.0841718	−	0.145790i
$149$		−	0.531041i		−	0.0435045i	−0.999763	−	0.0217523i	$-0.993075\pi$
$149$		−	0.531041i		−	0.0435045i	0.999763	−	0.0217523i	$-0.00692451\pi$
$150$	0.299860	+	0.857190i	0.0244835	+	0.0699893i
$151$	15.1591			1.23363			0.616814	−	0.787109i	$-0.288423\pi$
$151$	15.1591			1.23363			0.616814	+	0.787109i	$0.288423\pi$
$152$	−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
$156$	−18.5829	−	3.51774i	−1.48782	−	0.281645i
$157$	−5.42288	−	3.13090i	−0.432793	−	0.249873i	0.267743	−	0.963490i	$-0.413722\pi$
$157$	−5.42288	−	3.13090i	−0.432793	−	0.249873i	−0.700536	+	0.713617i	$0.747056\pi$
$158$	−2.20370	−	1.27231i	−0.175317	−	0.101219i
$159$	−5.29081	−	15.1245i	−0.419589	−	1.19945i
$160$	−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	0.264368	+	0.964422i	$0.414837\pi$
$163$	−8.97569	+	15.5463i	−0.703030	+	1.21768i	−0.967398	+	0.253262i	$0.918497\pi$
$164$	10.9279			0.853327
$165$	1.16642	+	0.220804i	0.0908060	+	0.0171896i
$166$			2.23341i			0.173346i
$167$	−12.5882	−	21.8033i	−0.974101	−	1.68719i	−0.682872	−	0.730538i	$-0.739269\pi$
$167$	−12.5882	−	21.8033i	−0.974101	−	1.68719i	−0.291229	−	0.956653i	$-0.594064\pi$
$168$	5.15501	−	7.31656i	0.397717	−	0.564485i
$169$	13.5326	−	23.4391i	1.04097	−	1.80301i
$170$	0.915659	+	0.528656i	0.0702279	+	0.0405461i
$171$	11.0376	+	13.8456i	0.844065	+	1.05880i
$172$	−2.64838	−	4.58713i	−0.201937	−	0.349765i
$173$	2.67485	+	4.63298i	0.203365	+	0.352239i	0.949611	−	0.313432i	$-0.101479\pi$
$173$	2.67485	+	4.63298i	0.203365	+	0.352239i	−0.746245	+	0.665671i	$0.768145\pi$
$174$	−0.0481276	+	0.254240i	−0.00364854	+	0.0192739i
$175$	−1.09499	+	2.40853i	−0.0827735	+	0.182067i
$176$	−1.44011	+	0.831448i	−0.108552	+	0.0626728i
$177$	−9.55081	−	8.22058i	−0.717883	−	0.617896i
$178$		−	3.12202i		−	0.234005i
$179$	−7.73789	+	4.46747i	−0.578357	+	0.333915i	−0.760480	−	0.649361i	$-0.775036\pi$
$179$	−7.73789	+	4.46747i	−0.578357	+	0.333915i	0.182123	+	0.983276i	$0.441703\pi$
$180$	−4.04678	+	3.22605i	−0.301629	+	0.240456i
$181$			3.02129i			0.224571i	0.993676	+	0.112286i	$0.0358171\pi$
$181$			3.02129i			0.224571i	−0.993676	+	0.112286i	$0.964183\pi$
$182$	5.10532	+	7.14368i	0.378432	+	0.529525i
$183$	1.12376	+	3.21241i	0.0830705	+	0.237468i
$184$	15.7522			1.16127
$185$	0.593585	−	1.02812i	0.0436412	−	0.0755888i
$186$	−0.776668	+	4.10285i	−0.0569481	+	0.300835i
$187$	1.19699	−	0.691082i	0.0875325	−	0.0505369i
$188$	19.2447			1.40356
$189$	−7.56671	−	11.4780i	−0.550397	−	0.834903i
$190$	−3.09458			−0.224505
$191$	−22.8315	+	13.1818i	−1.65203	+	0.953800i	−0.675794	+	0.737091i	$0.736199\pi$
$191$	−22.8315	+	13.1818i	−1.65203	+	0.953800i	−0.976236	+	0.216709i	$0.930468\pi$
$192$	0.688570	−	3.63746i	0.0496932	−	0.262511i
$193$	−6.49750	+	11.2540i	−0.467701	+	0.810081i	−0.999319	−	0.0369029i	$-0.988251\pi$
$193$	−6.49750	+	11.2540i	−0.467701	+	0.810081i	0.531618	+	0.846984i	$0.321584\pi$
$194$	−5.17910			−0.371838
$195$	−3.62007	−	10.3484i	−0.259239	−	0.741068i
$196$	11.8497	−	2.32566i	0.846404	−	0.166119i
$197$			8.97314i			0.639310i	0.947534	+	0.319655i	$0.103567\pi$
$197$			8.97314i			0.639310i	−0.947534	+	0.319655i	$0.896433\pi$
$198$	−0.160494	−	1.06606i	−0.0114058	−	0.0757614i
$199$	−9.18073	+	5.30050i	−0.650805	+	0.375742i	−0.788764	−	0.614696i	$-0.789279\pi$
$199$	−9.18073	+	5.30050i	−0.650805	+	0.375742i	0.137960	+	0.990438i	$0.455946\pi$
$200$		−	1.95309i		−	0.138105i
$201$	5.43040	+	4.67406i	0.383031	+	0.329683i
$202$	−3.07047	+	1.77274i	−0.216037	+	0.124729i
$203$	−0.613334	+	0.438327i	−0.0430476	+	0.0307645i
$204$	−1.12072	+	5.92037i	−0.0784664	+	0.414509i
$205$	3.16732	+	5.48596i	0.221215	+	0.383156i
$206$	−4.55311	−	7.88621i	−0.317230	−	0.549458i
$207$	8.84361	−	22.5217i	0.614674	−	1.56537i
$208$	13.2996	+	7.67852i	0.922160	+	0.532409i
$209$	−2.02269	+	3.50340i	−0.139912	+	0.242335i
$210$	2.39291	+	0.216393i	0.165126	+	0.0149325i
$211$	−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	$0.884828\pi$
$212$			15.9589i			1.09606i
$213$	6.06290	+	1.14771i	0.415423	+	0.0786395i
$214$	7.65452			0.523252
$215$	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
$219$	2.14613	+	6.13500i	0.145022	+	0.414565i
$220$	−1.02397	−	0.591189i	−0.0690360	−	0.0398579i
$221$	−11.0543	−	6.38222i	−0.743594	−	0.429314i
$222$	−1.05929	−	0.200523i	−0.0710946	−	0.0134582i
$223$	14.6072	+	8.43348i	0.978171	+	0.564748i	0.901718	−	0.432326i	$-0.142307\pi$
$223$	14.6072	+	8.43348i	0.978171	+	0.564748i	0.0764539	+	0.997073i	$0.475640\pi$
$224$	−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
$227$	20.4852			1.35965			0.679827	−	0.733373i	$-0.262055\pi$
$227$	20.4852			1.35965			0.679827	+	0.733373i	$0.262055\pi$
$228$	−5.82327	−	16.6466i	−0.385655	−	1.10245i
$229$		−	4.40000i		−	0.290760i	−0.989376	−	0.145380i	$-0.953560\pi$
$229$		−	4.40000i		−	0.290760i	0.989376	−	0.145380i	$-0.0464405\pi$
$230$	2.11433	+	3.66213i	0.139415	+	0.241474i
$231$	1.80904	−	2.56758i	0.119026	−	0.168935i
$232$	0.278251	−	0.481945i	0.0182681	−	0.0316412i
$233$	16.1414	+	9.31924i	1.05746	+	0.610524i	0.924728	−	0.380628i	$-0.124292\pi$
$233$	16.1414	+	9.31924i	1.05746	+	0.610524i	0.132730	+	0.991152i	$0.457626\pi$
$234$	−7.78507	+	6.20618i	−0.508926	+	0.405711i
$235$	5.57784	+	9.66111i	0.363858	+	0.630221i
$236$	6.27544	+	10.8694i	0.408496	+	0.707536i
$237$	7.93467	−	2.77569i	0.515412	−	0.180300i
$238$	2.27592	−	1.62652i	0.147526	−	0.105431i
$239$	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	$0.292868\pi$
$240$	3.96658	−	1.38758i	0.256042	−	0.0895680i
$241$		−	8.98836i		−	0.578991i	−0.957179	−	0.289495i	$-0.906512\pi$
$241$		−	8.98836i		−	0.578991i	0.957179	−	0.289495i	$-0.0934875\pi$
$242$	−4.78138	+	2.76053i	−0.307359	+	0.177454i
$243$	12.5464	−	9.25132i	0.804855	−	0.593472i
$244$		−	3.38964i		−	0.216999i
$245$	4.60199	+	5.27462i	0.294010	+	0.336983i
$246$	3.75276	−	4.36002i	0.239267	−	0.277985i
$247$	37.3595			2.37713
$248$	4.49033	−	7.77748i	0.285136	−	0.493870i
$249$	−5.59197	−	4.81312i	−0.354377	−	0.305019i
$250$	0.454062	−	0.262153i	0.0287174	−	0.0165800i
$251$	−11.8323			−0.746846			−0.373423	−	0.927661i	$-0.621816\pi$
$251$	−11.8323			−0.746846			−0.373423	+	0.927661i	$0.621816\pi$
$252$	3.33885	+	13.2793i	0.210328	+	0.836515i
$253$	5.52789			0.347536
$254$	4.85361	−	2.80223i	0.304543	−	0.175828i
$255$	−3.29694	+	1.15333i	−0.206462	+	0.0722242i
$256$	0.871387	−	1.50929i	0.0544617	−	0.0943304i
$257$	29.2599			1.82518			0.912592	−	0.408872i	$-0.134078\pi$
$257$	29.2599			1.82518			0.912592	+	0.408872i	$0.134078\pi$
$258$	−2.73965	−	0.518616i	−0.170563	−	0.0322876i
$259$	−1.82628	−	2.55544i	−0.113480	−	0.158788i
$260$			10.9194i			0.677192i
$261$	−0.532843	−	0.668402i	−0.0329822	−	0.0413730i
$262$	4.53613	−	2.61894i	0.280243	−	0.161798i
$263$			5.14677i			0.317363i	0.987330	+	0.158682i	$0.0507244\pi$
$263$			5.14677i			0.317363i	−0.987330	+	0.158682i	$0.949276\pi$
$264$	−0.431251	+	2.27814i	−0.0265417	+	0.140210i
$265$	−8.01159	+	4.62549i	−0.492148	+	0.284142i
$266$	−3.38854	+	7.45339i	−0.207765	+	0.456996i
$267$	7.81685	+	6.72812i	0.478384	+	0.411754i
$268$	−3.56809	−	6.18011i	−0.217956	−	0.377510i
$269$	−3.25506	−	5.63794i	−0.198465	−	0.343751i	0.749566	−	0.661930i	$-0.230262\pi$
$269$	−3.25506	−	5.63794i	−0.198465	−	0.343751i	−0.948031	+	0.318178i	$0.896929\pi$
$270$	−0.102574	+	2.72244i	−0.00624246	+	0.165683i
$271$	−7.92293	−	4.57431i	−0.481284	−	0.277869i	0.239668	−	0.970855i	$-0.422962\pi$
$271$	−7.92293	−	4.57431i	−0.481284	−	0.277869i	−0.720951	+	0.692986i	$0.756295\pi$
$272$	2.44632	−	4.23714i	0.148330	−	0.256915i
$273$	−28.8885	−	2.61241i	−1.74841	−	0.158110i
$274$	−5.04440	−	8.73715i	−0.304743	−	0.527831i
$275$		−	0.685395i		−	0.0413309i
$276$	−15.7209	+	18.2648i	−0.946286	+	1.09941i
$277$	−8.06846			−0.484787			−0.242393	−	0.970178i	$-0.577932\pi$
$277$	−8.06846			−0.484787			−0.242393	+	0.970178i	$0.577932\pi$
$278$	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	$0.461642\pi$
$282$	6.60883	−	7.67826i	0.393550	−	0.457233i
$283$	−22.3829	−	12.9228i	−1.33052	−	0.768178i	−0.345144	−	0.938550i	$-0.612170\pi$
$283$	−22.3829	−	12.9228i	−1.33052	−	0.768178i	−0.985380	+	0.170372i	$0.945503\pi$
$284$	−5.32244	−	3.07291i	−0.315829	−	0.182344i
$285$	6.66900	−	7.74816i	0.395037	−	0.458962i
$286$	−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
$290$	0.149392			0.00877262
$291$	11.1613	−	12.9673i	0.654284	−	0.760159i
$292$		−	6.47347i		−	0.378831i
$293$	0.740371	+	1.28236i	0.0432529	+	0.0749162i	0.886841	−	0.462074i	$-0.152895\pi$
$293$	0.740371	+	1.28236i	0.0432529	+	0.0749162i	−0.843588	+	0.536990i	$0.819561\pi$
$294$	3.14140	−	5.52643i	0.183210	−	0.322308i
$295$	−3.63772	+	6.30071i	−0.211796	+	0.366842i
$296$	2.00801	+	1.15933i	0.116713	+	0.0673845i
$297$	3.01505	+	1.89557i	0.174951	+	0.109992i
$298$	0.139214	+	0.241126i	0.00806445	+	0.0139680i
$299$	−25.5254	−	44.2112i	−1.47617	−	2.55680i
$300$	2.26463	+	1.94921i	0.130748	+	0.112538i
$301$	−4.72335	−	6.60920i	−0.272250	−	0.380948i
$302$	−6.88317	+	3.97400i	−0.396082	+	0.228678i
$303$	2.17849	−	11.5081i	0.125151	−	0.661125i
$304$			14.3200i			0.821306i
$305$	1.70164	−	0.982445i	0.0974359	−	0.0562546i
$306$	1.97724	+	2.48026i	0.113031	+	0.141787i
$307$		−	31.9466i		−	1.82329i	−0.410977	−	0.911646i	$-0.634812\pi$
$307$		−	31.9466i		−	1.82329i	0.410977	−	0.911646i	$-0.365188\pi$
$308$	−2.54513	+	1.81891i	−0.145022	+	0.103642i
$309$	29.5575	+	5.59524i	1.68147	+	0.318302i
$310$	2.41085			0.136927
$311$	−5.80572	+	10.0558i	−0.329212	+	0.570212i	−0.982356	−	0.187022i	$-0.940117\pi$
$311$	−5.80572	+	10.0558i	−0.329212	+	0.570212i	0.653143	+	0.757234i	$0.273450\pi$
$312$	20.2115	−	7.07035i	1.14425	−	0.400280i
$313$	−18.8101	+	10.8600i	−1.06321	+	0.613846i	−0.926319	−	0.376740i	$-0.877045\pi$
$313$	−18.8101	+	10.8600i	−1.06321	+	0.613846i	−0.136893	+	0.990586i	$0.543712\pi$
$314$	3.28310			0.185276
$315$	−5.69865	+	5.52498i	−0.321082	+	0.311297i
$316$	−8.37243			−0.470986
$317$	−7.14807	+	4.12694i	−0.401475	+	0.231792i	−0.687120	−	0.726544i	$-0.741126\pi$
$317$	−7.14807	+	4.12694i	−0.401475	+	0.231792i	0.285645	+	0.958336i	$0.407792\pi$
$318$	6.36728	+	5.48045i	0.357059	+	0.307328i
$319$	0.0976460	−	0.169128i	0.00546712	−	0.00946934i
$320$	−2.13738			−0.119483
$321$	−16.4959	+	19.1652i	−0.920711	+	1.06970i
$322$	11.1355	−	1.08243i	0.620558	−	0.0603213i
$323$		−	11.9024i		−	0.662269i
$324$	−14.8377	+	4.57121i	−0.824319	+	0.253956i
$325$	−5.48168	+	3.16485i	−0.304069	+	0.175554i
$326$		−	9.41202i		−	0.521283i
$327$	−1.91515	+	0.669952i	−0.105908	+	0.0370484i
$328$	−10.7146	+	6.18608i	−0.591615	+	0.341569i
$329$	29.3767	−	2.85556i	1.61959	−	0.157432i
$330$	−0.587514	+	0.205523i	−0.0323416	+	0.0113137i
$331$	5.05808	+	8.76086i	0.278017	+	0.481540i	0.970892	−	0.239518i	$-0.0769893\pi$
$331$	5.05808	+	8.76086i	0.278017	+	0.481540i	−0.692874	+	0.721058i	$0.743656\pi$
$332$	3.67425	+	6.36399i	0.201651	+	0.349269i
$333$	2.78488	−	2.22008i	0.152611	−	0.121660i
$334$	11.4316	+	6.60005i	0.625510	+	0.361138i
$335$	2.06833	−	3.58246i	0.113005	−	0.195731i
$336$	1.00134	−	11.0730i	0.0546277	−	0.604082i
$337$	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	$0.736856\pi$
$338$			14.1904i			0.771856i
$339$	−2.22072	−	6.34821i	−0.120613	−	0.344788i
$340$	3.47883			0.188666
$341$	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
$345$	−13.7257	−	2.59827i	−0.738966	−	0.139886i
$346$	−2.42910	−	1.40244i	−0.130589	−	0.0753958i
$347$	−31.7697	−	18.3423i	−1.70549	−	0.984664i	−0.939975	−	0.341242i	$-0.889152\pi$
$347$	−31.7697	−	18.3423i	−1.70549	−	0.984664i	−0.765512	−	0.643422i	$-0.777514\pi$
$348$	0.281121	+	0.803619i	0.0150696	+	0.0430785i
$349$	24.4021	+	14.0886i	1.30622	+	0.754144i	0.981462	−	0.191655i	$-0.0613854\pi$
$349$	24.4021	+	14.0886i	1.30622	+	0.754144i	0.324753	+	0.945799i	$0.394719\pi$
$350$	−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
$353$	−9.59560			−0.510723			−0.255361	−	0.966846i	$-0.582194\pi$
$353$	−9.59560			−0.510723			−0.255361	+	0.966846i	$0.582194\pi$
$354$	6.49171	+	1.22888i	0.345031	+	0.0653142i
$355$		−	3.56258i		−	0.189082i
$356$	−5.13613	−	8.89603i	−0.272214	−	0.471489i
$357$	−0.832294	+	9.20364i	−0.0440496	+	0.487108i
$358$	2.34232	−	4.05702i	0.123796	−	0.214420i
$359$	−8.31863	−	4.80277i	−0.439041	−	0.253480i	0.264150	−	0.964482i	$-0.414909\pi$
$359$	−8.31863	−	4.80277i	−0.439041	−	0.253480i	−0.703191	+	0.711001i	$0.748242\pi$
$360$	2.14158	−	5.45388i	0.112871	−	0.287445i
$361$	7.91826	+	13.7148i	0.416751	+	0.721834i
$362$	−0.792042	−	1.37186i	−0.0416288	−	0.0721032i
$363$	3.39237	−	17.9206i	0.178053	−	0.940590i
$364$	26.2996	+	11.9566i	1.37847	+	0.626697i
$365$	3.24977	−	1.87626i	0.170101	−	0.0982078i
$366$	−1.35240	−	1.16404i	−0.0706910	−	0.0608451i
$367$			16.3695i			0.854481i	0.904138	+	0.427241i	$0.140514\pi$
$367$			16.3695i			0.854481i	−0.904138	+	0.427241i	$0.859486\pi$
$368$	16.9462	−	9.78392i	0.883384	−	0.510022i
$369$	2.82914	+	18.7922i	0.147279	+	0.978281i
$370$			0.622440i			0.0323591i
$371$	2.36801	+	24.3610i	0.122941	+	1.26476i
$372$	4.53664	+	12.9686i	0.235214	+	0.672389i
$373$	−3.61850			−0.187359			−0.0936794	−	0.995602i	$-0.529863\pi$
$373$	−3.61850			−0.187359			−0.0936794	+	0.995602i	$0.529863\pi$
$374$	−0.362338	+	0.627589i	−0.0187361	+	0.0324518i
$375$	−0.322156	+	1.70183i	−0.0166360	+	0.0878820i
$376$	−18.8691	+	10.8941i	−0.973097	+	0.561818i
$377$	−1.80354			−0.0928872
$378$	6.44476	+	3.22810i	0.331482	+	0.166036i
$379$	31.9510			1.64121			0.820607	−	0.571493i	$-0.193636\pi$
$379$	31.9510			1.64121			0.820607	+	0.571493i	$0.193636\pi$
$380$	−8.81786	+	5.09099i	−0.452347	+	0.261162i
$381$	−3.44362	+	18.1913i	−0.176422	+	0.931970i
$382$	6.91129	−	11.9707i	0.353612	−	0.612474i
$383$	−31.7797			−1.62387			−0.811934	−	0.583750i	$-0.801585\pi$
$383$	−31.7797			−1.62387			−0.811934	+	0.583750i	$0.801585\pi$
$384$	6.56400	+	18.7640i	0.334968	+	0.957548i
$385$	−1.65079	−	0.750501i	−0.0841322	−	0.0382491i
$386$		−	6.81336i		−	0.346791i
$387$	7.20261	−	5.74185i	0.366129	−	0.291875i
$388$	−14.7576	+	8.52029i	−0.749203	+	0.432552i
$389$		−	17.4446i		−	0.884477i	−0.896897	−	0.442239i	$-0.854184\pi$
$389$		−	17.4446i		−	0.884477i	0.896897	−	0.442239i	$-0.145816\pi$
$390$	4.35662	+	3.74983i	0.220606	+	0.189880i
$391$	−14.0853	+	8.13218i	−0.712327	+	0.411262i
$392$	−10.3018	+	8.98813i	−0.520322	+	0.453969i
$393$	−3.21837	+	17.0014i	−0.162345	+	0.857609i
$394$	−2.35234	−	4.07436i	−0.118509	−	0.205264i
$395$	−2.42665	−	4.20308i	−0.122098	−	0.211480i
$396$	−2.21112	−	2.77364i	−0.111113	−	0.139381i
$397$	14.9631	+	8.63892i	0.750974	+	0.433575i	0.826046	−	0.563603i	$-0.190585\pi$
$397$	14.9631	+	8.63892i	0.750974	+	0.433575i	−0.0750716	+	0.997178i	$0.523919\pi$
$398$	2.77908	−	4.81351i	0.139303	−	0.241280i
$399$	−11.3592	−	24.5466i	−0.568669	−	1.22887i
$400$	−1.21309	−	2.10114i	−0.0606547	−	0.105057i
$401$		−	12.2208i		−	0.610280i	−0.952307	−	0.305140i	$-0.901297\pi$
$401$		−	12.2208i		−	0.610280i	0.952307	−	0.305140i	$-0.0987033\pi$
$402$	−3.69106	−	0.698717i	−0.184093	−	0.0348488i
$403$	−29.1050			−1.44983
$404$	−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
$408$	−2.25256	−	6.43923i	−0.111518	−	0.318789i
$409$	−19.1440	−	11.0528i	−0.946610	−	0.546525i	−0.0545835	−	0.998509i	$-0.517383\pi$
$409$	−19.1440	−	11.0528i	−0.946610	−	0.546525i	−0.892026	+	0.451984i	$0.850716\pi$
$410$	−2.87632	−	1.66065i	−0.142052	−	0.0820135i
$411$	32.7469	+	6.19897i	1.61528	+	0.305773i
$412$	−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
$416$	−32.7768			−1.60701
$417$	11.6485	+	33.2987i	0.570429	+	1.63064i
$418$		−	2.12101i		−	0.103742i
$419$	16.4445	+	28.4827i	0.803365	+	1.39147i	0.917389	+	0.397992i	$0.130293\pi$
$419$	16.4445	+	28.4827i	0.803365	+	1.39147i	−0.114024	+	0.993478i	$0.536374\pi$
$420$	7.17446	−	3.32004i	0.350078	−	0.162002i
$421$	−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
$423$	4.98228	+	33.0941i	0.242247	+	1.60909i
$424$	−9.03402	−	15.6474i	−0.438731	−	0.759904i
$425$	1.00830	+	1.74642i	0.0489096	+	0.0847139i
$426$	−3.05381	+	1.06828i	−0.147958	+	0.0517582i
$427$	−0.502960	−	5.17422i	−0.0243399	−	0.250398i
$428$	21.8111	−	12.5927i	1.05428	−	0.608690i
$429$	7.09278	−	2.48118i	0.342443	−	0.119793i
$430$			1.60983i			0.0776330i
$431$	2.47525	−	1.42909i	0.119229	−	0.0688368i	−0.439200	−	0.898390i	$-0.644738\pi$
$431$	2.47525	−	1.42909i	0.119229	−	0.0688368i	0.558428	+	0.829553i	$0.311405\pi$
$432$	12.5979	+	0.474654i	0.606117	+	0.0228368i
$433$		−	2.73608i		−	0.131488i	−0.997837	−	0.0657438i	$-0.979058\pi$
$433$		−	2.73608i		−	0.131488i	0.997837	−	0.0657438i	$-0.0209420\pi$
$434$	2.63986	−	5.80659i	0.126717	−	0.278725i
$435$	−0.321949	+	0.374046i	−0.0154363	+	0.0179341i
$436$	2.02081			0.0967791
$437$	23.8016	−	41.2256i	1.13858	−	1.97209i
$438$	−2.58279	−	2.22306i	−0.123410	−	0.106222i
$439$	−10.9015	+	6.29398i	−0.520300	+	0.300395i	−0.737057	−	0.675830i	$-0.763785\pi$
$439$	−10.9015	+	6.29398i	−0.520300	+	0.300395i	0.216757	+	0.976225i	$0.430452\pi$
$440$	1.33864			0.0638172
$441$	7.06709	+	19.7751i	0.336528	+	0.941673i
$442$	6.69247			0.318328
$443$	9.13673	−	5.27509i	0.434099	−	0.250627i	−0.266992	−	0.963699i	$-0.586030\pi$
$443$	9.13673	−	5.27509i	0.434099	−	0.250627i	0.701091	+	0.713072i	$0.252697\pi$
$444$	−3.34826	+	1.17128i	−0.158902	+	0.0555866i
$445$	2.97729	−	5.15681i	0.141137	−	0.244456i
$446$	−8.84345			−0.418750
$447$	−0.903739	−	0.171078i	−0.0427454	−	0.00809170i
$448$	−2.34041	+	5.14794i	−0.110574	+	0.243217i
$449$			14.4733i			0.683039i	0.939875	+	0.341520i	$0.110942\pi$
$449$			14.4733i			0.683039i	−0.939875	+	0.341520i	$0.889058\pi$
$450$	1.55539	−	0.234162i	0.0733218	−	0.0110385i
$451$	−3.76005	+	2.17087i	−0.177054	+	0.102222i
$452$			6.69845i			0.315069i
$453$	4.88358	−	25.7981i	0.229451	−	1.21210i
$454$	−9.30158	+	5.37027i	−0.436545	+	0.252039i
$455$	1.62023	+	16.6683i	0.0759578	+	0.781420i
$456$	15.1329	+	13.0252i	0.708663	+	0.609960i
$457$	−12.2771	−	21.2646i	−0.574300	−	0.994717i	−0.996117	−	0.0880360i	$-0.971941\pi$
$457$	−12.2771	−	21.2646i	−0.574300	−	0.994717i	0.421817	−	0.906681i	$-0.361392\pi$
$458$	1.15347	+	1.99787i	0.0538982	+	0.0933545i
$459$	−10.4711	−	0.394522i	−0.488749	−	0.0184147i
$460$	12.0494	+	6.95671i	0.561805	+	0.324358i
$461$	2.17057	−	3.75954i	0.101094	−	0.175099i	−0.811042	−	0.584988i	$-0.801099\pi$
$461$	2.17057	−	3.75954i	0.101094	−	0.175099i	0.912136	+	0.409889i	$0.134432\pi$
$462$	−0.148315	+	1.64009i	−0.00690022	+	0.0763038i
$463$	−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	$0.893307\pi$
$464$		−	0.691301i		−	0.0320929i
$465$	−5.19551	+	6.03624i	−0.240936	+	0.279924i
$466$	−9.77227			−0.452692
$467$	9.85389	−	17.0674i	0.455984	−	0.789787i	−0.542760	−	0.839888i	$-0.682621\pi$
$467$	9.85389	−	17.0674i	0.455984	−	0.789787i	0.998744	+	0.0501005i	$0.0159542\pi$
$468$	−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
$471$	−7.07526	+	8.22016i	−0.326011	+	0.378765i
$472$	−12.3059	−	7.10481i	−0.566424	−	0.327025i
$473$	1.82250	+	1.05222i	0.0837986	+	0.0483811i
$474$	−2.87518	+	3.34043i	−0.132061	+	0.153431i
$475$	−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
$479$	14.9645			0.683745			0.341873	−	0.939746i	$-0.388939\pi$
$479$	14.9645			0.683745			0.341873	+	0.939746i	$0.388939\pi$
$480$	−5.85095	+	6.79774i	−0.267058	+	0.310273i
$481$		−	7.51443i		−	0.342628i
$482$	2.35633	+	4.08128i	0.107328	+	0.185897i
$483$	−21.2875	+	30.2136i	−0.968614	+	1.37477i
$484$	−9.08287	+	15.7320i	−0.412858	+	0.715090i
$485$	−8.55461	−	4.93901i	−0.388445	−	0.224269i
$486$	−3.27161	+	7.48976i	−0.148403	+	0.339743i
$487$	−0.207370	−	0.359175i	−0.00939682	−	0.0162758i	0.861289	−	0.508116i	$-0.169658\pi$
$487$	−0.207370	−	0.359175i	−0.00939682	−	0.0162758i	−0.870686	+	0.491840i	$0.836324\pi$
$488$	1.91881	+	3.32347i	0.0868604	+	0.150447i
$489$	23.5656	+	20.2834i	1.06567	+	0.917248i
$490$	−3.47235	−	1.18858i	−0.156865	−	0.0536947i
$491$	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	$0.172709\pi$
$492$	3.52049	−	18.5974i	0.158716	−	0.838436i
$493$			0.574595i			0.0258784i
$494$	−16.9635	+	9.79390i	−0.763225	+	0.440648i
$495$	0.751540	−	1.91392i	0.0337792	−	0.0860243i
$496$		−	11.1560i		−	0.500920i
$497$	−8.58057	−	3.90099i	−0.384891	−	0.174984i
$498$	3.80088	+	0.719505i	0.170321	+	0.0322418i
$499$	25.3449			1.13460			0.567298	−	0.823513i	$-0.307989\pi$
$499$	25.3449			1.13460			0.567298	+	0.823513i	$0.307989\pi$
$500$	0.862552	−	1.49398i	0.0385745	−	0.0668130i
$501$	−41.1608	+	14.3988i	−1.83893	+	0.643291i
$502$	5.37258	−	3.10186i	0.239790	−	0.138443i
$503$	−2.51829			−0.112285			−0.0561424	−	0.998423i	$-0.517880\pi$
$503$	−2.51829			−0.112285			−0.0561424	+	0.998423i	$0.517880\pi$
$504$	−10.7908	−	11.1300i	−0.480661	−	0.495770i
$505$	−6.76222			−0.300915
$506$	−2.51001	+	1.44915i	−0.111584	+	0.0644228i
$507$	−35.5297	−	30.5811i	−1.57793	−	1.35815i
$508$	9.22007	−	15.9696i	0.409074	−	0.708538i
$509$	−9.63202			−0.426932			−0.213466	−	0.976951i	$-0.568475\pi$
$509$	−9.63202			−0.426932			−0.213466	+	0.976951i	$0.568475\pi$
$510$	1.19467	−	1.38798i	0.0529007	−	0.0614610i
$511$	−0.960544	−	9.88164i	−0.0424919	−	0.437138i
$512$		−	22.0406i		−	0.974064i
$513$	27.1186	−	14.3236i	1.19732	−	0.632403i
$514$	−13.2858	+	7.67058i	−0.586013	+	0.338335i
$515$		−	17.3681i		−	0.765331i
$516$	−8.65969	+	3.02932i	−0.381222	+	0.133358i
$517$	−6.62168	+	3.82303i	−0.291221	+	0.168137i
$518$	1.49916	+	0.681566i	0.0658694	+	0.0299463i
$519$	8.74626	−	3.05960i	0.383918	−	0.134301i
$520$	−6.18125	−	10.7062i	−0.271066	−	0.469500i
$521$	−4.60032	−	7.96798i	−0.201544	−	0.349084i	0.747482	−	0.664282i	$-0.231262\pi$
$521$	−4.60032	−	7.96798i	−0.201544	−	0.349084i	−0.949026	+	0.315198i	$0.897929\pi$
$522$	0.417168	+	0.163810i	0.0182589	+	0.00716975i
$523$	−3.19809	−	1.84642i	−0.139843	−	0.0807382i	0.428446	−	0.903567i	$-0.359061\pi$
$523$	−3.19809	−	1.84642i	−0.139843	−	0.0807382i	−0.568289	+	0.822829i	$0.692394\pi$
$524$	8.61698	−	14.9250i	0.376434	−	0.652004i
$525$	3.74614	+	2.63940i	0.163495	+	0.115193i
$526$	−1.34924	−	2.33695i	−0.0588297	−	0.101896i
$527$			9.27264i			0.403923i
$528$	0.951042	+	2.71868i	0.0413888	+	0.118315i
$529$	−42.0485			−1.82820
$530$	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
$534$	−5.31314	−	1.00578i	−0.229922	−	0.0435242i
$535$	12.6434	+	7.29966i	0.546621	+	0.315592i
$536$	6.99688	+	4.03965i	0.302219	+	0.174486i
$537$	5.11006	+	14.6078i	0.220516	+	0.630372i
$538$	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	−0.479074	−	0.877775i	$-0.659027\pi$
$541$	12.1097	−	20.9747i	0.520638	−	0.901772i	0.999712	−	0.0239973i	$-0.00763931\pi$
$542$	4.79667			0.206035
$543$	5.14172	+	0.973327i	0.220652	+	0.0417694i
$544$			10.4424i			0.447716i
$545$	0.585706	+	1.01447i	0.0250889	+	0.0434552i
$546$	13.8020	−	6.38700i	0.590672	−	0.273338i
$547$	−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
$549$	5.82898	−	0.877547i	0.248775	−	0.0374528i
$550$	0.179678	+	0.311212i	0.00766152	+	0.0132701i
$551$	−0.840873	−	1.45644i	−0.0358224	−	0.0620462i
$552$	5.07467	−	26.8076i	0.215992	−	1.14101i
$553$	−12.7804	+	1.24231i	−0.543477	+	0.0528286i
$554$	3.66358	−	2.11517i	0.155651	−	0.0898650i
$555$	−1.55845	−	1.34139i	−0.0661527	−	0.0569389i
$556$		−	35.1358i		−	1.49009i
$557$	17.3868	−	10.0383i	0.736703	−	0.425336i	−0.0841662	−	0.996452i	$-0.526823\pi$
$557$	17.3868	−	10.0383i	0.736703	−	0.425336i	0.820869	+	0.571116i	$0.193489\pi$
$558$	6.73213	+	2.64351i	0.284994	+	0.111909i
$559$		−	19.4347i		−	0.822002i
$560$	−6.38897	+	0.621039i	−0.269983	+	0.0262437i
$561$	−0.790485	−	2.25970i	−0.0333743	−	0.0954048i
$562$	−10.5552			−0.445245
$563$	−16.0759	+	27.8443i	−0.677518	+	1.17350i	0.298208	+	0.954501i	$0.403611\pi$
$563$	−16.0759	+	27.8443i	−0.677518	+	1.17350i	−0.975726	+	0.218995i	$0.929722\pi$
$564$	6.19979	−	32.7512i	0.261058	−	1.37907i
$565$	−3.36272	+	1.94146i	−0.141470	+	0.0816780i
$566$	13.5510			0.569589
$567$	−21.9713	+	9.17952i	−0.922706	+	0.385504i
$568$	6.95806			0.291954
$569$	−20.5812	+	11.8826i	−0.862808	+	0.498143i	−0.864952	−	0.501855i	$-0.832651\pi$
$569$	−20.5812	+	11.8826i	−0.862808	+	0.498143i	0.00214339	+	0.999998i	$0.499318\pi$
$570$	−0.996938	+	5.26645i	−0.0417571	+	0.220587i
$571$	−3.79027	+	6.56494i	−0.158618	+	0.274734i	−0.934371	−	0.356303i	$-0.884037\pi$
$571$	−3.79027	+	6.56494i	−0.158618	+	0.274734i	0.775753	+	0.631037i	$0.217370\pi$
$572$	−7.48409			−0.312926
$573$	15.0778	+	43.1019i	0.629885	+	1.80061i
$574$	−7.14926	+	5.10931i	−0.298404	+	0.213258i
$575$			8.06526i			0.336345i
$576$	−5.96850	−	2.34365i	−0.248687	−	0.0976522i
$577$	−20.4203	+	11.7897i	−0.850108	+	0.490810i	−0.860687	−	0.509134i	$-0.829966\pi$
$577$	−20.4203	+	11.7897i	−0.850108	+	0.490810i	0.0105795	+	0.999944i	$0.496632\pi$
$578$			6.78104i			0.282054i
$579$	17.0592	+	14.6832i	0.708955	+	0.610212i
$580$	0.425686	−	0.245770i	0.0176756	−	0.0102050i
$581$	6.55297	+	9.16932i	0.271863	+	0.380408i
$582$	−1.66848	+	8.81394i	−0.0691606	+	0.365349i
$583$	−3.17029	−	5.49110i	−0.131300	−	0.227418i
$584$	3.66451	+	6.34711i	0.151638	+	0.262645i
$585$	−18.7775	+	2.82693i	−0.776354	+	0.116879i
$586$	−0.672349	−	0.388181i	−0.0277745	−	0.0160356i
$587$	1.23062	−	2.13150i	0.0507932	−	0.0879765i	−0.839511	−	0.543343i	$-0.817158\pi$
$587$	1.23062	−	2.13150i	0.0507932	−	0.0879765i	0.890304	+	0.455366i	$0.150492\pi$
$588$	−0.140444	−	20.9153i	−0.00579180	−	0.862532i
$589$	−13.5698	−	23.5035i	−0.559133	−	0.968446i
$590$		−	3.81456i		−	0.157043i
$591$	15.2707	+	2.89075i	0.628154	+	0.118909i
$592$	2.88029			0.118379
$593$	15.5216	−	26.8842i	0.637397	−	1.10400i	−0.348605	−	0.937270i	$-0.613345\pi$
$593$	15.5216	−	26.8842i	0.637397	−	1.10400i	0.986002	−	0.166734i	$-0.0533221\pi$
$594$	−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
$597$	6.06291	+	17.3316i	0.248138	+	0.709335i
$598$	23.1802	+	13.3831i	0.947909	+	0.547276i
$599$	22.0823	+	12.7492i	0.902257	+	0.520919i	0.877932	−	0.478786i	$-0.158923\pi$
$599$	22.0823	+	12.7492i	0.902257	+	0.520919i	0.0243255	+	0.999704i	$0.492256\pi$
$600$	−3.32383	−	0.629200i	−0.135695	−	0.0256870i
$601$	19.3792	+	11.1886i	0.790493	+	0.456391i	0.840136	−	0.542376i	$-0.182475\pi$
$601$	19.3792	+	11.1886i	0.790493	+	0.456391i	−0.0496432	+	0.998767i	$0.515808\pi$
$602$	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
$605$	−10.5302			−0.428115
$606$	2.02772	+	5.79651i	0.0823706	+	0.235467i
$607$			35.7447i			1.45083i	0.688310	+	0.725416i	$0.258353\pi$
$607$			35.7447i			1.45083i	−0.688310	+	0.725416i	$0.741647\pi$
$608$	−15.2817	−	26.4686i	−0.619753	−	1.07344i
$609$	0.548368	+	1.18500i	0.0222210	+	0.0480185i
$610$	−0.515102	+	0.892183i	−0.0208559	+	0.0361234i
$611$	61.1519	+	35.3061i	2.47394	+	1.42833i
$612$	9.71440	+	3.81456i	0.392681	+	0.154194i
$613$	−5.29560	−	9.17224i	−0.213887	−	0.370463i	0.739041	−	0.673661i	$-0.235279\pi$
$613$	−5.29560	−	9.17224i	−0.213887	−	0.370463i	−0.952928	+	0.303198i	$0.901946\pi$
$614$	8.37491	+	14.5058i	0.337984	+	0.585405i
$615$	10.3565	−	3.62290i	0.417616	−	0.146089i
$616$	1.46580	−	3.22415i	0.0590588	−	0.129905i
$617$	−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	$0.481931\pi$
$618$	−14.8878	+	5.20801i	−0.598874	+	0.209497i
$619$		−	1.53400i		−	0.0616568i	−0.999525	−	0.0308284i	$-0.990185\pi$
$619$		−	1.53400i		−	0.0616568i	0.999525	−	0.0308284i	$-0.00981454\pi$
$620$	6.86959	−	3.96616i	0.275889	−	0.159285i
$621$	−35.4790	−	22.3058i	−1.42372	−	0.895101i
$622$		−	6.08795i		−	0.244105i
$623$	−9.16021	−	12.8175i	−0.366996	−	0.513523i
$624$	17.3520	−	20.1599i	0.694638	−	0.807042i
$625$	1.00000			0.0400000
$626$	5.69399	−	9.86228i	0.227578	−	0.394176i
$627$	5.31055	+	4.57090i	0.212083	+	0.182544i
$628$	9.35502	−	5.40112i	0.373306	−	0.215528i
$629$	−2.39404			−0.0954565
$630$	1.13915	−	4.00260i	0.0453849	−	0.159468i
$631$	11.0346			0.439281			0.219641	−	0.975581i	$-0.429512\pi$
$631$	11.0346			0.439281			0.219641	+	0.975581i	$0.429512\pi$
$632$	8.20901	−	4.73947i	0.326537	−	0.188526i
$633$	−7.65033	+	2.67622i	−0.304073	+	0.106370i
$634$	2.16378	−	3.74777i	0.0859346	−	0.148843i
$635$	10.6893			0.424192
$636$	27.1593	+	5.14125i	1.07694	+	0.203864i
$637$	41.9201	+	14.3492i	1.66093	+	0.568536i
$638$			0.102393i			0.00405377i
$639$	3.90639	−	9.94827i	0.154535	−	0.393547i
$640$	9.93950	−	5.73858i	0.392893	−	0.226837i
$641$		−	46.3489i		−	1.83067i	−0.402691	−	0.915336i	$-0.631925\pi$
$641$		−	46.3489i		−	1.83067i	0.402691	−	0.915336i	$-0.368075\pi$
$642$	2.46594	−	13.0267i	0.0973231	−	0.514121i
$643$	27.1868	−	15.6963i	1.07214	−	0.619001i	0.143376	−	0.989668i	$-0.454204\pi$
$643$	27.1868	−	15.6963i	1.07214	−	0.619001i	0.928766	+	0.370667i	$0.120871\pi$
$644$	29.9493	−	21.4037i	1.18017	−	0.843423i
$645$	−4.03067	−	3.46927i	−0.158707	−	0.136603i
$646$	3.12026	+	5.40445i	0.122765	+	0.212635i
$647$	−1.50230	−	2.60206i	−0.0590616	−	0.102298i	0.834983	−	0.550276i	$-0.185478\pi$
$647$	−1.50230	−	2.60206i	−0.0590616	−	0.102298i	−0.894044	+	0.447978i	$0.852144\pi$
$648$	11.9604	−	12.8813i	0.469850	−	0.506027i
$649$	−4.31848	−	2.49327i	−0.169515	−	0.0978696i
$650$	1.65935	−	2.87408i	0.0650851	−	0.112731i
$651$	8.84940	+	19.1231i	0.346835	+	0.749495i
$652$	−15.4840	−	26.8190i	−0.606400	−	1.05032i
$653$		−	26.0804i		−	1.02060i	−0.859996	−	0.510302i	$-0.829534\pi$
$653$		−	26.0804i		−	1.02060i	0.859996	−	0.510302i	$-0.170466\pi$
$654$	0.693965	−	0.806261i	0.0271362	−	0.0315273i
$655$	9.99010			0.390346
$656$	−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	$0.911116\pi$
$660$	−1.33598	+	1.55216i	−0.0520029	+	0.0604179i
$661$	4.58323	+	2.64613i	0.178267	+	0.102922i	0.586478	−	0.809965i	$-0.300514\pi$
$661$	4.58323	+	2.64613i	0.178267	+	0.102922i	−0.408211	+	0.912888i	$0.633847\pi$
$662$	−4.59337	−	2.65199i	−0.178527	−	0.103072i
$663$	−14.4226	+	16.7565i	−0.560129	+	0.650768i
$664$	−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
$668$	43.4317			1.68042
$669$	19.0581	−	22.1421i	0.736830	−	0.856062i
$670$			2.16888i			0.0837912i
$671$	0.673363	+	1.16630i	0.0259949	+	0.0450245i
$672$	9.96580	+	21.5356i	0.384439	+	0.830755i
$673$	−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
$675$	−2.76566	+	4.39899i	−0.106450	+	0.169317i
$676$	23.3451	+	40.4348i	0.897887	+	1.55519i
$677$	−12.0277	−	20.8327i	−0.462264	−	0.800664i	0.536810	−	0.843703i	$-0.319629\pi$
$677$	−12.0277	−	20.8327i	−0.462264	−	0.800664i	−0.999073	+	0.0430392i	$0.986296\pi$
$678$	2.67255	+	2.30032i	0.102639	+	0.0883431i
$679$	−21.2629	+	15.1958i	−0.815997	+	0.583163i
$680$	−3.41093	+	1.96930i	−0.130803	+	0.0755192i
$681$	6.59943	−	34.8623i	0.252891	−	1.33593i
$682$			1.65238i			0.0632731i
$683$	2.83022	−	1.63403i	0.108295	−	0.0625243i	−0.444874	−	0.895593i	$-0.646752\pi$
$683$	2.83022	−	1.63403i	0.108295	−	0.0625243i	0.553169	+	0.833069i	$0.313418\pi$
$684$	−30.2056	+	4.54741i	−1.15494	+	0.173875i
$685$		−	19.2422i		−	0.735206i
$686$	−6.66492	+	7.06176i	−0.254468	+	0.269619i
$687$	−7.48803	−	1.41748i	−0.285686	−	0.0540803i
$688$	7.44937			0.284005
$689$	−29.2780	+	50.7109i	−1.11540	+	1.93193i
$690$	6.91346	−	2.41845i	0.263191	−	0.0920690i
$691$	−14.6708	+	8.47018i	−0.558103	+	0.322221i	−0.752384	−	0.658725i	$-0.771096\pi$
$691$	−14.6708	+	8.47018i	−0.558103	+	0.322221i	0.194281	+	0.980946i	$0.437763\pi$
$692$	−9.22880			−0.350826
$693$	−3.78679	−	3.90583i	−0.143848	−	0.148370i
$694$	19.2339			0.730109
$695$	17.6387	−	10.1837i	0.669073	−	0.386289i
$696$	−0.730546	−	0.628796i	−0.0276913	−	0.0238344i
$697$	6.38720	−	11.0630i	0.241932	−	0.419039i
$698$	−14.7734			−0.559183
$699$	21.0598	−	24.4676i	0.796554	−	0.925451i
$700$	−2.65381	−	3.71337i	−0.100305	−	0.140352i
$701$			25.9872i			0.981524i	0.871294	+	0.490762i	$0.163282\pi$
$701$			25.9872i			0.981524i	−0.871294	+	0.490762i	$0.836718\pi$
$702$	8.05385	+	15.2482i	0.303973	+	0.575506i
$703$	6.06821	−	3.50348i	0.228867	−	0.132136i
$704$		−	1.46495i		−	0.0552125i
$705$	18.2385	−	6.38015i	0.686900	−	0.240290i
$706$	4.35700	−	2.51552i	0.163978	−	0.0946727i
$707$	−7.40456	+	16.2870i	−0.278477	+	0.612535i
$708$	20.5195	−	7.17808i	0.771169	−	0.269769i
$709$	5.90396	+	10.2260i	0.221728	+	0.384044i	0.955333	−	0.295532i	$-0.0954971\pi$
$709$	5.90396	+	10.2260i	0.221728	+	0.384044i	−0.733605	+	0.679576i	$0.762164\pi$
$710$	0.933942	+	1.61764i	0.0350502	+	0.0607088i
$711$	−2.16755	−	14.3976i	−0.0812894	−	0.539954i
$712$	10.0717	+	5.81492i	0.377454	+	0.217923i
$713$	−18.5427	+	32.1169i	−0.694431	+	1.20279i
$714$	−2.03485	−	4.39721i	−0.0761523	−	0.164562i
$715$	−2.16917	−	3.75712i	−0.0811225	−	0.140508i
$716$		−	15.4137i		−	0.576037i
$717$	−2.24195	−	6.40890i	−0.0837271	−	0.239345i
$718$	5.03624			0.187951
$719$	−10.0996	+	17.4931i	−0.376653	+	0.652383i	−0.990573	−	0.136986i	$-0.956259\pi$
$719$	−10.0996	+	17.4931i	−0.376653	+	0.652383i	0.613920	+	0.789369i	$0.289592\pi$
$720$	−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
$723$	−15.2966	−	2.89565i	−0.568888	−	0.107690i
$724$	−4.51376	−	2.60602i	−0.167753	−	0.0968520i
$725$	0.246759	+	0.142467i	0.00916442	+	0.00529108i
$726$	3.15760	+	9.02641i	0.117190	+	0.335001i
$727$	−9.44302	−	5.45193i	−0.350222	−	0.202201i	0.314561	−	0.949237i	$-0.398143\pi$
$727$	−9.44302	−	5.45193i	−0.350222	−	0.202201i	−0.664783	+	0.747036i	$0.731476\pi$
$728$	−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
$731$	−6.19175			−0.229010
$732$	−5.76858	−	1.09199i	−0.213213	−	0.0403611i
$733$		−	18.8843i		−	0.697509i	−0.937214	−	0.348754i	$-0.886605\pi$
$733$		−	18.8843i		−	0.697509i	0.937214	−	0.348754i	$-0.113395\pi$
$734$	−4.29132	−	7.43278i	−0.158395	−	0.274349i
$735$	10.4591	−	6.13255i	0.385788	−	0.226202i
$736$	−20.8820	+	36.1687i	−0.769720	+	1.33319i
$737$	2.45540	+	1.41763i	0.0904459	+	0.0522189i
$738$	−6.21103	−	7.79115i	−0.228631	−	0.286796i
$739$	3.98391	+	6.90033i	0.146550	+	0.253833i	0.929950	−	0.367685i	$-0.119850\pi$
$739$	3.98391	+	6.90033i	0.146550	+	0.253833i	−0.783400	+	0.621518i	$0.786516\pi$
$740$	1.02399	+	1.77361i	0.0376428	+	0.0651992i
$741$	12.0356	−	63.5793i	0.442137	−	2.33565i
$742$	−7.46153	−	10.4406i	−0.273921	−	0.383287i
$743$	−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	$0.392778\pi$
$744$	−11.7893	−	10.1473i	−0.432218	−	0.372019i
$745$			0.531041i			0.0194558i
$746$	1.64302	−	0.948601i	0.0601554	−	0.0347307i
$747$	−9.99258	+	7.96599i	−0.365610	+	0.291460i
$748$			2.38437i			0.0871814i
$749$	31.4258	−	22.4589i	1.14827	−	0.820629i
$750$	−0.299860	−	0.857190i	−0.0109494	−	0.0313001i
$751$	11.2999			0.412339			0.206169	−	0.978516i	$-0.433900\pi$
$751$	11.2999			0.412339			0.206169	+	0.978516i	$0.433900\pi$
$752$	−13.5329	+	23.4397i	−0.493494	+	0.854756i
$753$	−3.81183	+	20.1365i	−0.138911	+	0.733813i
$754$	0.818921	−	0.472804i	0.0298233	−	0.0172185i
$755$	−15.1591			−0.551695
$756$	23.6746	−	1.40415i	0.861038	−	0.0510685i
$757$	52.7826			1.91842			0.959208	−	0.282701i	$-0.0912305\pi$
$757$	52.7826			1.91842			0.959208	+	0.282701i	$0.0912305\pi$
$758$	−14.5078	+	8.37606i	−0.526946	+	0.304232i
$759$	1.78084	−	9.40752i	0.0646405	−	0.341471i
$760$	5.76382	−	9.98324i	0.209076	−	0.362130i
$761$	25.3090			0.917452			0.458726	−	0.888578i	$-0.348306\pi$
$761$	25.3090			0.917452			0.458726	+	0.888578i	$0.348306\pi$
$762$	−3.20530	−	9.16276i	−0.116116	−	0.331932i
$763$	3.08473	−	0.299850i	0.111675	−	0.0108553i
$764$		−	45.4799i		−	1.64540i
$765$	0.900638	+	5.98237i	0.0325626	+	0.216293i
$766$	14.4300	−	8.33115i	0.521376	−	0.301017i
$767$			46.0513i			1.66282i
$768$	−2.28782	−	1.96918i	−0.0825547	−	0.0710565i
$769$	3.30938	−	1.91067i	0.119339	−	0.0689007i	−0.439142	−	0.898418i	$-0.644718\pi$
$769$	3.30938	−	1.91067i	0.119339	−	0.0689007i	0.558481	+	0.829517i	$0.311384\pi$
$770$	0.946309	−	0.0919858i	0.0341026	−	0.00331494i
$771$	9.42625	−	49.7953i	0.339478	−	1.79334i
$772$	−11.2089	−	19.4143i	−0.403416	−	0.698737i
$773$	−1.34544	−	2.33038i	−0.0483922	−	0.0838178i	0.840815	−	0.541323i	$-0.182076\pi$
$773$	−1.34544	−	2.33038i	−0.0483922	−	0.0838178i	−0.889207	+	0.457505i	$0.848743\pi$
$774$	−1.76519	+	4.49534i	−0.0634484	+	0.161582i
$775$	3.98213	+	2.29908i	0.143042	+	0.0825856i
$776$	9.64635	−	16.7080i	0.346284	−	0.599781i
$777$	−4.93727	+	2.28476i	−0.177124	+	0.0819655i
$778$	4.57316	+	7.92095i	0.163956	+	0.283980i
$779$			37.3886i			1.33959i
$780$	18.5829	+	3.51774i	0.665375	+	0.125955i
$781$	2.44178			0.0873737
$782$	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
$786$	−2.99564	−	8.56342i	−0.106851	−	0.305447i
$787$	19.9334	+	11.5086i	0.710549	+	0.410236i	0.811264	−	0.584680i	$-0.198780\pi$
$787$	19.9334	+	11.5086i	0.710549	+	0.410236i	−0.100715	+	0.994915i	$0.532113\pi$
$788$	−13.4057	−	7.73979i	−0.477559	−	0.275719i
$789$	8.75891	+	1.65806i	0.311825	+	0.0590285i
$790$	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
$794$	−9.05888			−0.321488
$795$	5.29081	+	15.1245i	0.187646	+	0.536409i
$796$		−	18.2878i		−	0.648194i
$797$	3.95223	+	6.84546i	0.139995	+	0.242479i	0.927495	−	0.373837i	$-0.121958\pi$
$797$	3.95223	+	6.84546i	0.139995	+	0.242479i	−0.787499	+	0.616315i	$0.788625\pi$
$798$	11.5927	+	8.16786i	0.410379	+	0.289139i
$799$	11.2482	−	19.4825i	0.397934	−	0.689242i
$800$	4.48450	+	2.58913i	0.158551	+	0.0915395i
$801$	13.9683	−	11.1354i	0.493547	−	0.393451i
$802$	3.20373	+	5.54903i	0.113128	+	0.195943i
$803$	1.28598	+	2.22738i	0.0453812	+	0.0786025i
$804$	−11.6670	+	4.08131i	−0.411462	+	0.143937i
$805$	19.4254	+	8.83139i	0.684655	+	0.311265i
$806$	13.2155	−	7.62998i	0.465496	−	0.268754i
$807$	−10.6434	+	3.72326i	−0.374667	+	0.131065i
$808$		−	13.2073i		−	0.464629i
$809$	−20.3186	+	11.7309i	−0.714363	+	0.412438i	−0.812675	−	0.582718i	$-0.801989\pi$
$809$	−20.3186	+	11.7309i	−0.714363	+	0.412438i	0.0983112	+	0.995156i	$0.468656\pi$
$810$	4.60008	+	1.05161i	0.161630	+	0.0369499i
$811$			31.6614i			1.11178i	0.831255	+	0.555891i	$0.187623\pi$
$811$			31.6614i			1.11178i	−0.831255	+	0.555891i	$0.812377\pi$
$812$	−0.125821	−	1.29439i	−0.00441545	−	0.0454242i
$813$	−10.3371	+	12.0098i	−0.362538	+	0.421203i
$814$	−0.426617			−0.0149529
$815$	8.97569	−	15.5463i	0.314405	−	0.544565i
$816$	−6.42279	−	5.52823i	−0.224843	−	0.193527i
$817$	15.6944	−	9.06114i	0.549076	−	0.317009i
$818$	11.5901			0.405238
$819$	−13.7524	+	48.3215i	−0.480549	+	1.68849i
$820$	−10.9279			−0.381619
$821$	15.0132	−	8.66787i	0.523964	−	0.302511i	−0.214591	−	0.976704i	$-0.568842\pi$
$821$	15.0132	−	8.66787i	0.523964	−	0.302511i	0.738555	+	0.674193i	$0.235508\pi$
$822$	−16.4942	+	5.76997i	−0.575301	+	0.201251i
$823$	5.60580	−	9.70952i	0.195406	−	0.338453i	−0.751628	−	0.659588i	$-0.770731\pi$
$823$	5.60580	−	9.70952i	0.195406	−	0.338453i	0.947033	+	0.321135i	$0.104064\pi$
$824$	33.9216			1.18171
$825$	−1.16642	−	0.220804i	−0.0406097	−	0.00768740i
$826$	−9.18745	−	4.17690i	−0.319672	−	0.145333i
$827$			17.4250i			0.605927i	0.953002	+	0.302963i	$0.0979760\pi$
$827$			17.4250i			0.605927i	−0.953002	+	0.302963i	$0.902024\pi$
$828$	26.0190	+	32.6383i	0.904222	+	1.13426i
$829$	18.4407	−	10.6467i	0.640472	−	0.369777i	−0.144324	−	0.989530i	$-0.546101\pi$
$829$	18.4407	−	10.6467i	0.640472	−	0.369777i	0.784796	+	0.619754i	$0.212767\pi$
$830$		−	2.23341i		−	0.0775228i
$831$	−2.59930	+	13.7311i	−0.0901687	+	0.476327i
$832$	−11.7165	+	6.76450i	−0.406195	+	0.234517i
$833$	4.57154	−	13.3554i	0.158395	−	0.462737i
$834$	−14.0185	−	12.0660i	−0.485421	−	0.417811i
$835$	12.5882	+	21.8033i	0.435631	+	0.754535i
$836$	−3.48934	−	6.04372i	−0.120681	−	0.209026i
$837$	−21.1269	+	11.1589i	−0.730252	+	0.385707i
$838$	−14.9336	−	8.62194i	−0.515874	−	0.297840i
$839$	−21.5972	+	37.4075i	−0.745619	+	1.29145i	0.204286	+	0.978911i	$0.434513\pi$
$839$	−21.5972	+	37.4075i	−0.745619	+	1.29145i	−0.949905	+	0.312539i	$0.898821\pi$
$840$	−5.15501	+	7.31656i	−0.177865	+	0.252445i
$841$	−14.4594	−	25.0444i	−0.498600	−	0.863601i
$842$		−	4.95858i		−	0.170884i
$843$	22.7471	−	26.4280i	0.783451	−	0.910228i
$844$	8.07241			0.277864
$845$	−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
$849$	−29.2031	+	33.9286i	−1.00225	+	1.16443i
$850$	−0.915659	−	0.528656i	−0.0314069	−	0.0181328i
$851$	−8.29205	−	4.78742i	−0.284248	−	0.164111i
$852$	−6.94422	+	8.06792i	−0.237905	+	0.276402i
$853$	12.0459	+	6.95468i	0.412442	+	0.238124i	0.691839	−	0.722052i	$-0.256801\pi$
$853$	12.0459	+	6.95468i	0.412442	+	0.238124i	−0.279396	+	0.960176i	$0.590134\pi$
$854$	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
$857$	19.1284			0.653414			0.326707	−	0.945126i	$-0.394061\pi$
$857$	19.1284			0.653414			0.326707	+	0.945126i	$0.394061\pi$
$858$	−2.57011	+	2.98600i	−0.0877423	+	0.101941i
$859$		−	9.68336i		−	0.330392i	−0.986261	−	0.165196i	$-0.947174\pi$
$859$		−	9.68336i		−	0.330392i	0.986261	−	0.165196i	$-0.0528257\pi$
$860$	2.64838	+	4.58713i	0.0903090	+	0.156420i
$861$	2.61445	−	28.9110i	0.0891002	−	0.985285i
$862$	−0.749280	+	1.29779i	−0.0255206	+	0.0442029i
$863$	−22.1631	−	12.7959i	−0.754440	−	0.435576i	0.0728560	−	0.997342i	$-0.476789\pi$
$863$	−22.1631	−	12.7959i	−0.754440	−	0.435576i	−0.827296	+	0.561766i	$0.810122\pi$
$864$	−23.7921	+	12.5666i	−0.809425	+	0.427525i
$865$	−2.67485	−	4.63298i	−0.0909478	−	0.157526i
$866$	0.717272	+	1.24235i	0.0243739	+	0.0422168i
$867$	−16.9782	−	14.6135i	−0.576611	−	0.496301i
$868$	−2.03046	−	20.8885i	−0.0689184	−	0.709001i
$869$	2.88077	−	1.66321i	0.0977234	−	0.0564206i
$870$	0.0481276	−	0.254240i	0.00163168	−	0.00861954i
$871$		−	26.1839i		−	0.887207i
$872$	−1.98136	+	1.14394i	−0.0670973	+	0.0387387i
$873$	−18.4725	−	23.1720i	−0.625200	−	0.784254i
$874$			24.9586i			0.844239i
$875$	1.09499	−	2.40853i	0.0370174	−	0.0814230i
$876$	−11.0167	−	2.08547i	−0.372221	−	0.0704613i
$877$	−6.97429			−0.235505			−0.117753	−	0.993043i	$-0.537569\pi$
$877$	−6.97429			−0.235505			−0.117753	+	0.993043i	$0.537569\pi$
$878$	3.29997	−	5.71572i	0.111369	−	0.192896i
$879$	2.42087	−	0.846864i	0.0816539	−	0.0285640i
$880$	1.44011	−	0.831448i	0.0485461	−	0.0280281i
$881$	−14.9270			−0.502904			−0.251452	−	0.967870i	$-0.580908\pi$
$881$	−14.9270			−0.502904			−0.251452	+	0.967870i	$0.580908\pi$
$882$	−8.39301	−	7.12649i	−0.282607	−	0.239961i
$883$	38.7784			1.30500			0.652499	−	0.757790i	$-0.273721\pi$
$883$	38.7784			1.30500			0.652499	+	0.757790i	$0.273721\pi$
$884$	19.0698	−	11.0100i	0.641388	−	0.370306i
$885$	9.55081	+	8.22058i	0.321047	+	0.276332i
$886$	−2.76576	+	4.79044i	−0.0929176	+	0.160938i
$887$	21.4992			0.721871			0.360936	−	0.932591i	$-0.382457\pi$
$887$	21.4992			0.721871			0.360936	+	0.932591i	$0.382457\pi$
$888$	2.61987	−	3.04381i	0.0879170	−	0.102143i
$889$	11.7047	−	25.7454i	0.392562	−	0.863475i
$890$			3.12202i			0.104650i
$891$	4.19725	−	4.52042i	0.140613	−	0.151440i
$892$	−25.1990	+	14.5486i	−0.843723	+	0.487124i
$893$			65.8436i			2.20337i
$894$	0.455203	−	0.159238i	0.0152243	−	0.00532572i
$895$	7.73789	−	4.46747i	0.258649	−	0.149331i
$896$	−2.93785	−	30.2232i	−0.0981465	−	1.00969i
$897$	−83.4630	+	29.1969i	−2.78675	+	0.974855i
$898$	−3.79423	−	6.57180i	−0.126615	−	0.219304i
$899$	0.655086	+	1.13464i	0.0218483	+	0.0378424i
$900$	4.04678	−	3.22605i	0.134893	−	0.107535i
$901$	16.1561	+	9.32774i	0.538238	+	0.310752i
$902$	1.13820	−	1.97142i	0.0378979	−	0.0656411i
$903$	−12.7694	+	5.90914i	−0.424938	+	0.196644i
$904$	−3.79186	−	6.56770i	−0.126116	−	0.218438i
$905$		−	3.02129i		−	0.100431i
$906$	4.54561	+	12.9942i	0.151018	+	0.431704i
$907$	−33.5611			−1.11438			−0.557189	−	0.830386i	$-0.688120\pi$
$907$	−33.5611			−1.11438			−0.557189	+	0.830386i	$0.688120\pi$
$908$	−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	$0.357437\pi$
$912$	24.3701	+	4.61325i	0.806974	+	0.152760i
$913$	−2.52845	−	1.45980i	−0.0836796	−	0.0483125i
$914$	11.1492	+	6.43698i	0.368782	+	0.212916i
$915$	−1.12376	−	3.21241i	−0.0371503	−	0.106199i
$916$	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	0.491735	+	0.870745i	$0.336363\pi$
$919$	−15.4067	+	26.6852i	−0.508220	+	0.880263i	−0.999955	+	0.00951786i	$0.996970\pi$
$920$	−15.7522			−0.519335
$921$	−54.3677	−	10.2918i	−1.79148	−	0.339126i
$922$			2.27609i			0.0749590i
$923$	−11.2750	−	19.5289i	−0.371123	−	0.642803i
$924$	2.27554	+	4.91734i	0.0748598	+	0.161769i
$925$	−0.593585	+	1.02812i	−0.0195169	+	0.0338043i
$926$	3.65997	+	2.11308i	0.120274	+	0.0694402i
$927$	19.0443	−	48.4993i	0.625495	−	1.59293i
$928$	0.737728	+	1.27778i	0.0242171	+	0.0419453i
$929$	10.7316	+	18.5876i	0.352091	+	0.609840i	0.986616	−	0.163063i	$-0.0521373\pi$
$929$	10.7316	+	18.5876i	0.352091	+	0.609840i	−0.634524	+	0.772903i	$0.718804\pi$
$930$	0.776668	−	4.10285i	0.0254680	−	0.134538i
$931$	7.95700	+	40.5423i	0.260780	+	1.32872i
$932$	−27.8456	+	16.0767i	−0.912112	+	0.526608i
$933$	15.2429	+	13.1199i	0.499030	+	0.429525i
$934$			10.3329i			0.338103i
$935$	−1.19699	+	0.691082i	−0.0391457	+	0.0226008i
$936$	−5.52126	−	36.6742i	−0.180468	−	1.19873i
$937$			20.2097i			0.660223i	0.943942	+	0.330111i	$0.107086\pi$
$937$			20.2097i			0.660223i	−0.943942	+	0.330111i	$0.892914\pi$
$938$	5.22381	+	2.37490i	0.170563	+	0.0775434i
$939$	12.4221	+	35.5102i	0.405381	+	1.15883i
$940$	−19.2447			−0.627693
$941$	−28.1404	+	48.7405i	−0.917349	+	1.58890i	−0.113925	+	0.993489i	$0.536342\pi$
$941$	−28.1404	+	48.7405i	−0.917349	+	1.58890i	−0.803425	+	0.595406i	$0.796991\pi$
$942$	1.05767	−	5.58727i	0.0344607	−	0.182043i
$943$	44.2457	−	25.5453i	1.44084	−	0.831869i
$944$	−17.6516			−0.574509
$945$	7.56671	+	11.4780i	0.246145	+	0.373380i
$946$	−1.10337			−0.0358737
$947$	−18.0367	+	10.4135i	−0.586114	+	0.338393i	−0.763559	−	0.645738i	$-0.776550\pi$
$947$	−18.0367	+	10.4135i	−0.586114	+	0.338393i	0.177445	+	0.984131i	$0.443217\pi$
$948$	−2.69723	+	14.2484i	−0.0876018	+	0.462768i
$949$	11.8761	−	20.5701i	0.385516	−	0.667733i
$950$	3.09458			0.100402
$951$	4.72055	+	13.4943i	0.153074	+	0.437582i
$952$	1.00818	+	10.3717i	0.0326752	+	0.336148i
$953$			3.82448i			0.123887i	0.998080	+	0.0619435i	$0.0197298\pi$
$953$			3.82448i			0.123887i	−0.998080	+	0.0619435i	$0.980270\pi$
$954$	11.3780	−	9.07046i	0.368377	−	0.293667i
$955$	22.8315	−	13.1818i	0.738810	−	0.426552i
$956$			6.76248i			0.218714i
$957$	−0.256369	−	0.220662i	−0.00828723	−	0.00713299i
$958$	−6.79481	+	3.92299i	−0.219530	+	0.126746i
$959$	−46.3453	−	21.0700i	−1.49657	−	0.680386i
$960$	−0.688570	+	3.63746i	−0.0222235	+	0.117398i
$961$	−4.92842	−	8.53627i	−0.158981	−	0.275363i
$962$	1.96993	+	3.41202i	0.0635131	+	0.110008i
$963$	27.3017	+	34.2474i	0.879784	+	1.10361i
$964$	13.4285	+	7.75292i	0.432501	+	0.249705i
$965$	6.49750	−	11.2540i	0.209162	−	0.362279i
$966$	1.74527	−	19.2994i	0.0561530	−	0.620949i
$967$	−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	$-0.371308\pi$
$968$		−	20.5665i		−	0.661034i
$969$	−20.2559	−	3.83444i	−0.650713	−	0.123180i
$970$	5.17910			0.166291
$971$	15.7637	−	27.3034i	0.505880	−	0.876209i	−0.494097	−	0.869407i	$-0.664501\pi$
$971$	15.7637	−	27.3034i	0.505880	−	0.876209i	0.999977	−	0.00680264i	$-0.00216537\pi$
$972$	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
$975$	3.62007	+	10.3484i	0.115935	+	0.331416i
$976$	4.12851	+	2.38360i	0.132150	+	0.0762970i
$977$	47.7466	+	27.5665i	1.52755	+	0.881930i	0.999464	+	0.0327380i	$0.0104227\pi$
$977$	47.7466	+	27.5665i	1.52755	+	0.881930i	0.528084	+	0.849192i	$0.322911\pi$
$978$	−16.0176	−	3.03213i	−0.512187	−	0.0969569i
$979$	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
$983$	−42.7506			−1.36353			−0.681766	−	0.731571i	$-0.738788\pi$
$983$	−42.7506			−1.36353			−0.681766	+	0.731571i	$0.738788\pi$
$984$	7.07587	+	20.2273i	0.225570	+	0.644822i
$985$		−	8.97314i		−	0.285908i
$986$	−0.150632	−	0.260902i	−0.00479709	−	0.00830881i
$987$	4.60420	−	50.9140i	0.146553	−	1.62061i
$988$	−32.2245	+	55.8144i	−1.02520	+	1.77569i
$989$	−21.4459	−	12.3818i	−0.681941	−	0.393719i
$990$	0.160494	+	1.06606i	0.00510082	+	0.0338815i
$991$	19.6274	+	33.9957i	0.623485	+	1.07991i	0.988832	+	0.149036i	$0.0476172\pi$
$991$	19.6274	+	33.9957i	0.623485	+	1.07991i	−0.365347	+	0.930872i	$0.619050\pi$
$992$	11.9052	+	20.6205i	0.377992	+	0.654701i
$993$	16.5390	−	5.78563i	0.524848	−	0.183601i
$994$	4.91877	−	0.478129i	0.156014	−	0.0151653i
$995$	9.18073	−	5.30050i	0.291049	−	0.168037i
$996$	12.0141	−	4.20274i	0.380681	−	0.133169i
$997$			43.4034i			1.37460i	0.726374	+	0.687300i	$0.241204\pi$
$997$			43.4034i			1.37460i	−0.726374	+	0.687300i	$0.758796\pi$
$998$	−11.5082	+	6.64425i	−0.364285	+	0.210320i
$999$	−2.88103	−	5.45460i	−0.0911518	−	0.172576i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.7	✓	32	7.3	odd	6
315.2.t.c.131.10	yes	32	9.5	odd	6
315.2.be.c.236.7	yes	32	1.1	even	1	trivial
315.2.be.c.311.7	yes	32	63.59	even	6	inner
945.2.t.c.341.7		32	9.4	even	3
945.2.t.c.521.10		32	21.17	even	6
945.2.be.c.206.10		32	63.31	odd	6
945.2.be.c.656.10		32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.454062 + 0.262153i) q^{2} +(0.322156 - 1.70183i) q^{3} +(-0.862552 + 1.49398i) q^{4} -1.00000 q^{5} +(0.299860 + 0.857190i) q^{6} +(-1.09499 + 2.40853i) q^{7} -1.95309i q^{8} +(-2.79243 - 1.09651i) q^{9} +O(q^{10})\)	\(q+(-0.454062 + 0.262153i) q^{2} +(0.322156 - 1.70183i) q^{3} +(-0.862552 + 1.49398i) q^{4} -1.00000 q^{5} +(0.299860 + 0.857190i) q^{6} +(-1.09499 + 2.40853i) q^{7} -1.95309i q^{8} +(-2.79243 - 1.09651i) q^{9} +(0.454062 - 0.262153i) q^{10} -0.685395i q^{11} +(2.26463 + 1.94921i) q^{12} +(-5.48168 + 3.16485i) q^{13} +(-0.134208 - 1.38068i) q^{14} +(-0.322156 + 1.70183i) q^{15} +(-1.21309 - 2.10114i) q^{16} +(1.00830 + 1.74642i) q^{17} +(1.55539 - 0.234162i) q^{18} +(-5.11150 - 2.95112i) q^{19} +(0.862552 - 1.49398i) q^{20} +(3.74614 + 2.63940i) q^{21} +(0.179678 + 0.311212i) q^{22} +8.06526i q^{23} +(-3.32383 - 0.629200i) q^{24} +1.00000 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} +(-0.299860 - 0.857190i) q^{30} +(3.98213 + 2.29908i) q^{31} +(4.48450 + 2.58913i) q^{32} +(-1.16642 - 0.220804i) 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} +3.09458 q^{38} +(3.62007 + 10.3484i) q^{39} +1.95309i q^{40} +(-3.16732 - 5.48596i) q^{41} +(-2.39291 - 0.216393i) q^{42} +(-1.53520 + 2.65905i) q^{43} +(1.02397 + 0.591189i) q^{44} +(2.79243 + 1.09651i) q^{45} +(-2.11433 - 3.66213i) q^{46} +(-5.57784 - 9.66111i) q^{47} +(-3.96658 + 1.38758i) q^{48} +(-4.60199 - 5.27462i) q^{49} +(-0.454062 + 0.262153i) q^{50} +(3.29694 - 1.15333i) q^{51} -10.9194i q^{52} +(8.01159 - 4.62549i) q^{53} +(0.102574 - 2.72244i) q^{54} +0.685395i q^{55} +(4.70408 + 2.13862i) q^{56} +(-6.66900 + 7.74816i) q^{57} -0.149392 q^{58} +(3.63772 - 6.30071i) q^{59} +(-2.26463 - 1.94921i) q^{60} +(-1.70164 + 0.982445i) q^{61} -2.41085 q^{62} +(5.69865 - 5.52498i) q^{63} +2.13738 q^{64} +(5.48168 - 3.16485i) q^{65} +(0.587514 - 0.205523i) q^{66} +(-2.06833 + 3.58246i) q^{67} -3.47883 q^{68} +(13.7257 + 2.59827i) q^{69} +(0.134208 + 1.38068i) q^{70} +3.56258i q^{71} +(-2.14158 + 5.45388i) q^{72} +(-3.24977 + 1.87626i) q^{73} -0.622440i q^{74} +(0.322156 - 1.70183i) q^{75} +(8.81786 - 5.09099i) q^{76} +(1.65079 + 0.750501i) q^{77} +(-4.35662 - 3.74983i) q^{78} +(2.42665 + 4.20308i) q^{79} +(1.21309 + 2.10114i) q^{80} +(6.59535 + 6.12384i) q^{81} +(2.87632 + 1.66065i) q^{82} +(2.12987 - 3.68905i) q^{83} +(-7.17446 + 3.32004i) q^{84} +(-1.00830 - 1.74642i) q^{85} -1.60983i q^{86} +(0.321949 - 0.374046i) q^{87} -1.33864 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} +(5.19551 - 6.03624i) q^{93} +(5.06538 + 2.92450i) q^{94} +(5.11150 + 2.95112i) q^{95} +(5.85095 - 6.79774i) q^{96} +(8.55461 + 4.93901i) q^{97} +(3.47235 + 1.18858i) q^{98} +(-0.751540 + 1.91392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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