LMFDB - Embedded newform 637.2.u.g.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-1.38488 + 0.286553i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.g.30.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19430 - 0.689527i) q^{2} -2.88120 q^{3} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +5.30133 q^{9} +O(q^{10})$	\(q+(-1.19430 - 0.689527i) q^{2} -2.88120 q^{3} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +5.30133 q^{9} +1.11145 q^{10} -5.27158i q^{11} +(0.141478 + 0.245047i) q^{12} +(2.36581 - 2.72084i) q^{13} +(2.01100 - 1.16105i) q^{15} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +(-6.33136 - 3.65541i) q^{18} -5.84469i q^{19} +(0.0685460 + 0.0395750i) q^{20} +(-3.63490 + 6.29583i) q^{22} +(-0.802438 + 1.38986i) q^{23} -8.33689i q^{24} +(-2.17522 + 3.76760i) q^{25} +(-4.70157 + 1.61820i) q^{26} -6.63060 q^{27} +(-1.14008 - 1.97467i) q^{29} -3.20230 q^{30} +(3.01022 + 1.73795i) q^{31} +(0.480674 - 0.277517i) q^{32} +15.1885i q^{33} -0.772411i q^{34} +(-0.260315 - 0.450879i) q^{36} +(1.07557 + 0.620979i) q^{37} +(-4.03007 + 6.98029i) q^{38} +(-6.81636 + 7.83929i) q^{39} +(-1.16602 - 2.01961i) q^{40} +(-0.803413 + 0.463851i) q^{41} +(2.22356 - 3.85131i) q^{43} +(-0.448348 + 0.258854i) q^{44} +(-3.70018 + 2.13630i) q^{45} +(1.91670 - 1.10661i) q^{46} +(-3.32915 + 1.92209i) q^{47} +(-5.46556 + 9.46662i) q^{48} +(5.19572 - 2.99975i) q^{50} +(-0.806883 - 1.39756i) q^{51} +(-0.347577 - 0.0676087i) q^{52} +(-2.72727 + 4.72377i) q^{53} +(7.91890 + 4.57198i) q^{54} +(2.12431 + 3.67941i) q^{55} +16.8397i q^{57} +3.14446i q^{58} +(-9.52106 + 5.49698i) q^{59} +(-0.197495 - 0.114024i) q^{60} -7.30215 q^{61} +(-2.39673 - 4.15126i) q^{62} -8.35330 q^{64} +(-0.554837 + 2.85243i) q^{65} +(10.4729 - 18.1396i) q^{66} -7.34556i q^{67} +(0.0275031 - 0.0476367i) q^{68} +(2.31199 - 4.00448i) q^{69} +(-8.06668 - 4.65730i) q^{71} +15.3396i q^{72} +(4.33139 + 2.50073i) q^{73} +(-0.856364 - 1.48327i) q^{74} +(6.26726 - 10.8552i) q^{75} +(-0.497091 + 0.286996i) q^{76} +(13.5462 - 4.66237i) q^{78} +(-5.68437 - 9.84562i) q^{79} +3.05772i q^{80} +3.20012 q^{81} +1.27935 q^{82} +5.81962i q^{83} +(-0.390935 - 0.225707i) q^{85} +(-5.31117 + 3.06641i) q^{86} +(3.28479 + 5.68943i) q^{87} +15.2535 q^{88} +(-4.33832 - 2.50473i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(-8.67305 - 5.00739i) q^{93} +5.30133 q^{94} +(2.35526 + 4.07942i) q^{95} +(-1.38492 + 0.799583i) q^{96} +(-9.22171 - 5.32416i) q^{97} -27.9464i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.19430	−	0.689527i	−0.844495	−	0.487570i	0.0142944	−	0.999898i	$-0.495450\pi$
$2$	−1.19430	−	0.689527i	−0.844495	−	0.487570i	−0.858790	+	0.512328i	$0.828783\pi$
$3$	−2.88120			−1.66346			−0.831732	−	0.555178i	$-0.812650\pi$
$3$	−2.88120			−1.66346			−0.831732	+	0.555178i	$0.812650\pi$
$4$	−0.0491037	−	0.0850501i	−0.0245518	−	0.0425250i
$5$	−0.697972	+	0.402974i	−0.312142	+	0.180216i	−0.647885	−	0.761738i	$-0.724346\pi$
$5$	−0.697972	+	0.402974i	−0.312142	+	0.180216i	0.335742	+	0.941954i	$0.391013\pi$
$6$	3.44101	+	1.98667i	1.40479	+	0.811054i
$7$		0			0
$7$		0			0
$8$			2.89354i			1.02302i
$9$	5.30133			1.76711
$10$	1.11145			0.351470
$11$		−	5.27158i		−	1.58944i	−0.606976	−	0.794720i	$-0.707618\pi$
$11$		−	5.27158i		−	1.58944i	0.606976	−	0.794720i	$-0.292382\pi$
$12$	0.141478	+	0.245047i	0.0408411	+	0.0707389i
$13$	2.36581	−	2.72084i	0.656156	−	0.754625i
$13$	2.36581	−	2.72084i	0.656156	−	0.754625i
$14$		0			0
$15$	2.01100	−	1.16105i	0.519237	−	0.299782i
$16$	1.89697	−	3.28565i	0.474243	−	0.821412i
$17$	0.280051	+	0.485062i	0.0679223	+	0.117645i	0.897987	−	0.440023i	$-0.145030\pi$
$17$	0.280051	+	0.485062i	0.0679223	+	0.117645i	−0.830064	+	0.557668i	$0.811696\pi$
$18$	−6.33136	−	3.65541i	−1.49232	−	0.861589i
$19$		−	5.84469i		−	1.34086i	−0.741972	−	0.670431i	$-0.766109\pi$
$19$		−	5.84469i		−	1.34086i	0.741972	−	0.670431i	$-0.233891\pi$
$20$	0.0685460	+	0.0395750i	0.0153273	+	0.00884925i
$21$		0			0
$22$	−3.63490	+	6.29583i	−0.774963	+	1.34228i
$23$	−0.802438	+	1.38986i	−0.167320	+	0.289807i	−0.937477	−	0.348048i	$-0.886845\pi$
$23$	−0.802438	+	1.38986i	−0.167320	+	0.289807i	0.770157	+	0.637855i	$0.220178\pi$
$24$		−	8.33689i		−	1.70176i
$25$	−2.17522	+	3.76760i	−0.435045	+	0.753520i
$26$	−4.70157	+	1.61820i	−0.922053	+	0.317355i
$27$	−6.63060			−1.27606
$28$		0			0
$29$	−1.14008	−	1.97467i	−0.211707	−	0.366687i	0.740542	−	0.672010i	$-0.234569\pi$
$29$	−1.14008	−	1.97467i	−0.211707	−	0.366687i	−0.952249	+	0.305323i	$0.901236\pi$
$30$	−3.20230			−0.584658
$31$	3.01022	+	1.73795i	0.540651	+	0.312145i	0.745343	−	0.666681i	$-0.232286\pi$
$31$	3.01022	+	1.73795i	0.540651	+	0.312145i	−0.204692	+	0.978827i	$0.565619\pi$
$32$	0.480674	−	0.277517i	0.0849719	−	0.0490585i
$33$			15.1885i			2.64398i
$34$		−	0.772411i		−	0.132467i
$35$		0			0
$36$	−0.260315	−	0.450879i	−0.0433858	−	0.0751464i
$37$	1.07557	+	0.620979i	0.176822	+	0.102088i	0.585799	−	0.810457i	$-0.300781\pi$
$37$	1.07557	+	0.620979i	0.176822	+	0.102088i	−0.408977	+	0.912545i	$0.634114\pi$
$38$	−4.03007	+	6.98029i	−0.653764	+	1.13235i
$39$	−6.81636	+	7.83929i	−1.09149	+	1.25529i
$40$	−1.16602	−	2.01961i	−0.184364	−	0.319329i
$41$	−0.803413	+	0.463851i	−0.125472	+	0.0724413i	−0.561422	−	0.827529i	$-0.689746\pi$
$41$	−0.803413	+	0.463851i	−0.125472	+	0.0724413i	0.435950	+	0.899971i	$0.356412\pi$
$42$		0			0
$43$	2.22356	−	3.85131i	0.339089	−	0.587320i	−0.645172	−	0.764037i	$-0.723214\pi$
$43$	2.22356	−	3.85131i	0.339089	−	0.587320i	0.984262	+	0.176717i	$0.0565478\pi$
$44$	−0.448348	+	0.258854i	−0.0675910	+	0.0390237i
$45$	−3.70018	+	2.13630i	−0.551590	+	0.318461i
$46$	1.91670	−	1.10661i	0.282602	−	0.163160i
$47$	−3.32915	+	1.92209i	−0.485607	+	0.280365i	−0.722750	−	0.691109i	$-0.757122\pi$
$47$	−3.32915	+	1.92209i	−0.485607	+	0.280365i	0.237143	+	0.971475i	$0.423789\pi$
$48$	−5.46556	+	9.46662i	−0.788885	+	1.36639i
$49$		0			0
$50$	5.19572	−	2.99975i	0.734786	−	0.424229i
$51$	−0.806883	−	1.39756i	−0.112986	−	0.195698i
$52$	−0.347577	−	0.0676087i	−0.0482003	−	0.00937564i
$53$	−2.72727	+	4.72377i	−0.374620	+	0.648860i	−0.990270	−	0.139159i	$-0.955560\pi$
$53$	−2.72727	+	4.72377i	−0.374620	+	0.648860i	0.615650	+	0.788019i	$0.288893\pi$
$54$	7.91890	+	4.57198i	1.07763	+	0.622168i
$55$	2.12431	+	3.67941i	0.286442	+	0.496132i
$56$		0			0
$57$			16.8397i			2.23048i
$58$			3.14446i			0.412887i
$59$	−9.52106	+	5.49698i	−1.23954	+	0.715646i	−0.968999	−	0.247063i	$-0.920534\pi$
$59$	−9.52106	+	5.49698i	−1.23954	+	0.715646i	−0.270537	+	0.962710i	$0.587201\pi$
$60$	−0.197495	−	0.114024i	−0.0254965	−	0.0147204i
$61$	−7.30215			−0.934944			−0.467472	−	0.884008i	$-0.654835\pi$
$61$	−7.30215			−0.934944			−0.467472	+	0.884008i	$0.654835\pi$
$62$	−2.39673	−	4.15126i	−0.304385	−	0.527210i
$63$		0			0
$64$	−8.35330			−1.04416
$65$	−0.554837	+	2.85243i	−0.0688191	+	0.353800i
$66$	10.4729	−	18.1396i	1.28912	−	2.23283i
$67$		−	7.34556i		−	0.897403i	−0.893682	−	0.448701i	$-0.851887\pi$
$67$		−	7.34556i		−	0.897403i	0.893682	−	0.448701i	$-0.148113\pi$
$68$	0.0275031	−	0.0476367i	0.00333524	−	0.00577680i
$69$	2.31199	−	4.00448i	0.278330	−	0.482083i
$70$		0			0
$71$	−8.06668	−	4.65730i	−0.957339	−	0.552720i	−0.0619857	−	0.998077i	$-0.519743\pi$
$71$	−8.06668	−	4.65730i	−0.957339	−	0.552720i	−0.895353	+	0.445357i	$0.853077\pi$
$72$			15.3396i			1.80779i
$73$	4.33139	+	2.50073i	0.506951	+	0.292688i	0.731579	−	0.681756i	$-0.238784\pi$
$73$	4.33139	+	2.50073i	0.506951	+	0.292688i	−0.224629	+	0.974444i	$0.572117\pi$
$74$	−0.856364	−	1.48327i	−0.0995503	−	0.172426i
$75$	6.26726	−	10.8552i	0.723681	−	1.25345i
$76$	−0.497091	+	0.286996i	−0.0570202	+	0.0329207i
$77$		0			0
$78$	13.5462	−	4.66237i	1.53380	−	0.527909i
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	−0.985533	−	0.169481i	$-0.945791\pi$
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	0.345992	−	0.938238i	$-0.387543\pi$
$80$			3.05772i			0.341863i
$81$	3.20012			0.355568
$82$	1.27935			0.141281
$83$			5.81962i			0.638786i	0.947622	+	0.319393i	$0.103479\pi$
$83$			5.81962i			0.638786i	−0.947622	+	0.319393i	$0.896521\pi$
$84$		0			0
$85$	−0.390935	−	0.225707i	−0.0424029	−	0.0244813i
$86$	−5.31117	+	3.06641i	−0.572719	+	0.330659i
$87$	3.28479	+	5.68943i	0.352167	+	0.609971i
$88$	15.2535			1.62603
$89$	−4.33832	−	2.50473i	−0.459861	−	0.265501i	0.252125	−	0.967695i	$-0.418871\pi$
$89$	−4.33832	−	2.50473i	−0.459861	−	0.265501i	−0.711986	+	0.702194i	$0.752204\pi$
$90$	5.89215			0.621087
$91$		0			0
$92$	0.157611			0.0164320
$93$	−8.67305	−	5.00739i	−0.899354	−	0.519242i
$94$	5.30133			0.546791
$95$	2.35526	+	4.07942i	0.241644	+	0.418540i
$96$	−1.38492	+	0.799583i	−0.141348	+	0.0816071i
$97$	−9.22171	−	5.32416i	−0.936323	−	0.540586i	−0.0475172	−	0.998870i	$-0.515131\pi$
$97$	−9.22171	−	5.32416i	−0.936323	−	0.540586i	−0.888806	+	0.458284i	$0.848464\pi$
$98$		0			0
$99$		−	27.9464i		−	2.80872i
$100$	0.427246			0.0427246
$101$	3.91554			0.389611			0.194805	−	0.980842i	$-0.437592\pi$
$101$	3.91554			0.389611			0.194805	+	0.980842i	$0.437592\pi$
$102$			2.22547i			0.220355i
$103$	−4.22690	−	7.32120i	−0.416488	−	0.721379i	0.579095	−	0.815260i	$-0.303406\pi$
$103$	−4.22690	−	7.32120i	−0.416488	−	0.721379i	−0.995583	+	0.0938810i	$0.970073\pi$
$104$	7.87287	+	6.84556i	0.771998	+	0.671262i
$105$		0			0
$106$	6.51434	−	3.76106i	0.632729	−	0.365306i
$107$	4.83761	−	8.37899i	0.467670	−	0.810028i	−0.531648	−	0.846965i	$-0.678427\pi$
$107$	4.83761	−	8.37899i	0.467670	−	0.810028i	0.999318	+	0.0369379i	$0.0117604\pi$
$108$	0.325587	+	0.563933i	0.0313296	+	0.0542645i
$109$	12.6126	+	7.28189i	1.20807	+	0.697478i	0.962337	−	0.271860i	$-0.0876388\pi$
$109$	12.6126	+	7.28189i	1.20807	+	0.697478i	0.245731	+	0.969338i	$0.420972\pi$
$110$		−	5.85908i		−	0.558641i
$111$	−3.09893	−	1.78917i	−0.294137	−	0.169820i
$112$		0			0
$113$	−9.75572	+	16.8974i	−0.917741	+	1.58957i	−0.114903	+	0.993377i	$0.536656\pi$
$113$	−9.75572	+	16.8974i	−0.917741	+	1.58957i	−0.802838	+	0.596197i	$0.796678\pi$
$114$	11.6115	−	20.1116i	1.08751	−	1.88363i
$115$		−	1.29345i		−	0.120615i
$116$	−0.111964	+	0.193927i	−0.0103956	+	0.0180057i
$117$	12.5419	−	14.4241i	1.15950	−	1.33351i
$118$	15.1613			1.39571
$119$		0			0
$120$	3.35955	+	5.81891i	0.306683	+	0.531191i
$121$	−16.7895			−1.52632
$122$	8.72093	+	5.03503i	0.789556	+	0.455850i
$123$	2.31480	−	1.33645i	0.208718	−	0.120503i
$124$		−	0.341359i		−	0.0306550i
$125$		−	7.53598i		−	0.674038i
$126$		0			0
$127$	−0.958656	−	1.66044i	−0.0850670	−	0.147340i	0.820353	−	0.571858i	$-0.193777\pi$
$127$	−0.958656	−	1.66044i	−0.0850670	−	0.147340i	−0.905420	+	0.424517i	$0.860444\pi$
$128$	9.01498	+	5.20480i	0.796819	+	0.460044i
$129$	−6.40652	+	11.0964i	−0.564063	+	0.976985i
$130$	2.62947	−	3.02407i	0.230619	−	0.265228i
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	0.974772	+	0.223201i	$0.0716506\pi$
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	−0.294089	+	0.955778i	$0.595016\pi$
$132$	1.29178	−	0.745811i	0.112435	−	0.0649145i
$133$		0			0
$134$	−5.06496	+	8.77278i	−0.437546	+	0.757852i
$135$	4.62797	−	2.67196i	0.398312	−	0.229966i
$136$	−1.40355	+	0.810339i	−0.120353	+	0.0694860i
$137$	6.79921	−	3.92553i	0.580896	−	0.335380i	−0.180594	−	0.983558i	$-0.557802\pi$
$137$	6.79921	−	3.92553i	0.580896	−	0.335380i	0.761489	+	0.648178i	$0.224469\pi$
$138$	−5.52240	+	3.18836i	−0.470098	+	0.271411i
$139$	4.96241	−	8.59514i	0.420906	−	0.729030i	−0.575122	−	0.818067i	$-0.695046\pi$
$139$	4.96241	−	8.59514i	0.420906	−	0.729030i	0.996028	+	0.0890370i	$0.0283789\pi$
$140$		0			0
$141$	9.59197	−	5.53793i	0.807790	−	0.466378i
$142$	6.42267	+	11.1244i	0.538979	+	0.933538i
$143$	−14.3431	−	12.4715i	−1.19943	−	1.04292i
$144$	10.0565	−	17.4183i	0.838039	−	1.45153i
$145$	1.59148	+	0.918843i	0.132165	+	0.0763058i
$146$	−3.44864	−	5.97322i	−0.285412	−	0.494347i
$147$		0			0
$148$		−	0.121969i		−	0.0100258i
$149$			7.91925i			0.648770i	0.945925	+	0.324385i	$0.105157\pi$
$149$			7.91925i			0.648770i	−0.945925	+	0.324385i	$0.894843\pi$
$150$	−14.9699	+	8.64290i	−1.22229	+	0.705690i
$151$	−1.30005	−	0.750582i	−0.105796	−	0.0610815i	0.446168	−	0.894949i	$-0.352788\pi$
$151$	−1.30005	−	0.750582i	−0.105796	−	0.0610815i	−0.551965	+	0.833868i	$0.686122\pi$
$152$	16.9118			1.37173
$153$	1.48464	+	2.57148i	0.120026	+	0.207892i
$154$		0			0
$155$	−2.80140			−0.225014
$156$	1.00144	+	0.194794i	0.0801794	+	0.0155960i
$157$	1.92846	−	3.34019i	0.153908	−	0.266576i	−0.778753	−	0.627331i	$-0.784147\pi$
$157$	1.92846	−	3.34019i	0.153908	−	0.266576i	0.932661	+	0.360754i	$0.117481\pi$
$158$			15.6781i			1.24728i
$159$	7.85782	−	13.6102i	0.623166	−	1.07936i
$160$	−0.223664	+	0.387398i	−0.0176822	+	0.0306265i
$161$		0			0
$162$	−3.82189	−	2.20657i	−0.300276	−	0.173364i
$163$			14.3608i			1.12483i	0.826856	+	0.562414i	$0.190127\pi$
$163$			14.3608i			1.12483i	−0.826856	+	0.562414i	$0.809873\pi$
$164$	0.0789011	+	0.0455536i	0.00616114	+	0.00355714i
$165$	−6.12057	−	10.6011i	−0.476486	−	0.825297i
$166$	4.01279	−	6.95035i	0.311453	−	0.539452i
$167$	3.91563	−	2.26069i	0.303000	−	0.174937i	−0.340790	−	0.940140i	$-0.610694\pi$
$167$	3.91563	−	2.26069i	0.303000	−	0.174937i	0.643790	+	0.765202i	$0.277361\pi$
$168$		0			0
$169$	−1.80593	−	12.8740i	−0.138918	−	0.990304i
$170$	0.311262	+	0.539121i	0.0238727	+	0.0413487i
$171$		−	30.9846i		−	2.36945i
$172$	−0.436739			−0.0333011
$173$	−19.5179			−1.48392			−0.741960	−	0.670444i	$-0.766104\pi$
$173$	−19.5179			−1.48392			−0.741960	+	0.670444i	$0.766104\pi$
$174$		−	9.05982i		−	0.686823i
$175$		0			0
$176$	−17.3206	−	10.0000i	−1.30559	−	0.753780i
$177$	27.4321	−	15.8379i	2.06192	−	1.19045i
$178$	3.45416	+	5.98278i	0.258900	+	0.448428i
$179$	−20.8196			−1.55613			−0.778065	−	0.628183i	$-0.783799\pi$
$179$	−20.8196			−1.55613			−0.778065	+	0.628183i	$0.783799\pi$
$180$	0.363385	+	0.209800i	0.0270851	+	0.0156376i
$181$	−16.5522			−1.23031			−0.615157	−	0.788405i	$-0.710907\pi$
$181$	−16.5522			−1.23031			−0.615157	+	0.788405i	$0.710907\pi$
$182$		0			0
$183$	21.0390			1.55525
$184$	−4.02163	−	2.32189i	−0.296478	−	0.171172i
$185$	−1.00095			−0.0735916
$186$	6.90546	+	11.9606i	0.506333	+	0.876995i
$187$	2.55704	−	1.47631i	0.186990	−	0.107958i
$188$	0.326948	+	0.188763i	0.0238451	+	0.0137670i
$189$		0			0
$190$		−	6.49606i		−	0.471274i
$191$	−4.25008			−0.307525			−0.153762	−	0.988108i	$-0.549139\pi$
$191$	−4.25008			−0.307525			−0.153762	+	0.988108i	$0.549139\pi$
$192$	24.0676			1.73693
$193$			11.5972i			0.834787i	0.908726	+	0.417393i	$0.137056\pi$
$193$			11.5972i			0.834787i	−0.908726	+	0.417393i	$0.862944\pi$
$194$	7.34231	+	12.7172i	0.527147	+	0.913045i
$195$	1.59860	−	8.21842i	0.114478	−	0.588533i
$196$		0			0
$197$	−12.4892	+	7.21066i	−0.889821	+	0.513738i	−0.873884	−	0.486135i	$-0.838406\pi$
$197$	−12.4892	+	7.21066i	−0.889821	+	0.513738i	−0.0159371	+	0.999873i	$0.505073\pi$
$198$	−19.2698	+	33.3763i	−1.36944	+	2.37195i
$199$	−3.52962	−	6.11348i	−0.250208	−	0.433373i	0.713375	−	0.700783i	$-0.247166\pi$
$199$	−3.52962	−	6.11348i	−0.250208	−	0.433373i	−0.963583	+	0.267409i	$0.913832\pi$
$200$	−10.9017	−	6.29410i	−0.770867	−	0.445060i
$201$			21.1640i			1.49280i
$202$	−4.67632	−	2.69987i	−0.329024	−	0.189962i
$203$		0			0
$204$	−0.0792419	+	0.137251i	−0.00554804	+	0.00960949i
$205$	0.373840	−	0.647509i	0.0261101	−	0.0452240i
$206$			11.6582i			0.812268i
$207$	−4.25399	+	7.36812i	−0.295673	+	0.512120i
$208$	−4.45186	−	12.9346i	−0.308681	−	0.896850i
$209$	−30.8107			−2.13122
$210$		0			0
$211$	13.2113	+	22.8827i	0.909505	+	1.57531i	0.814754	+	0.579807i	$0.196872\pi$
$211$	13.2113	+	22.8827i	0.909505	+	1.57531i	0.0947513	+	0.995501i	$0.469794\pi$
$212$	0.535677			0.0367904
$213$	23.2417	+	13.4186i	1.59250	+	0.919429i
$214$	−11.5551	+	6.67133i	−0.789890	+	0.456043i
$215$			3.58414i			0.244437i
$216$		−	19.1859i		−	1.30544i
$217$		0			0
$218$	−10.0421	−	17.3935i	−0.680138	−	1.17803i
$219$	−12.4796	−	7.20511i	−0.843294	−	0.486876i
$220$	0.208623	−	0.361345i	0.0140654	−	0.0243619i
$221$	1.98232	+	0.385590i	0.133345	+	0.0259376i
$222$	2.46736	+	4.27359i	0.165598	+	0.286825i
$223$	−19.9191	+	11.5003i	−1.33388	+	0.770115i	−0.985892	−	0.167384i	$-0.946468\pi$
$223$	−19.9191	+	11.5003i	−1.33388	+	0.770115i	−0.347987	+	0.937499i	$0.613135\pi$
$224$		0			0
$225$	−11.5316	+	19.9733i	−0.768772	+	1.33155i
$226$	23.3024	−	13.4537i	1.55006	−	0.894925i
$227$	0.392628	−	0.226684i	0.0260596	−	0.0150455i	−0.486914	−	0.873450i	$-0.661877\pi$
$227$	0.392628	−	0.226684i	0.0260596	−	0.0150455i	0.512973	+	0.858405i	$0.328544\pi$
$228$	1.43222	−	0.826893i	0.0948511	−	0.0547623i
$229$	15.0112	−	8.66674i	0.991970	−	0.572714i	0.0861077	−	0.996286i	$-0.472557\pi$
$229$	15.0112	−	8.66674i	0.991970	−	0.572714i	0.905863	+	0.423571i	$0.139224\pi$
$230$	−0.891867	+	1.54476i	−0.0588080	+	0.101858i
$231$		0			0
$232$	5.71380	−	3.29886i	0.375129	−	0.216581i
$233$	3.90756	+	6.76809i	0.255992	+	0.443392i	0.965165	−	0.261643i	$-0.0842644\pi$
$233$	3.90756	+	6.76809i	0.255992	+	0.443392i	−0.709172	+	0.705035i	$0.750931\pi$
$234$	−24.9246	+	8.57862i	−1.62937	+	0.560802i
$235$	1.54910	−	2.68313i	0.101052	−	0.175028i
$236$	0.935038	+	0.539844i	0.0608658	+	0.0351409i
$237$	16.3778	+	28.3672i	1.06385	+	1.84265i
$238$		0			0
$239$		−	13.5314i		−	0.875276i	−0.899151	−	0.437638i	$-0.855815\pi$
$239$		−	13.5314i		−	0.875276i	0.899151	−	0.437638i	$-0.144185\pi$
$240$		−	8.80991i		−	0.568677i
$241$	19.5369	−	11.2796i	1.25848	−	0.726583i	0.285701	−	0.958319i	$-0.407774\pi$
$241$	19.5369	−	11.2796i	1.25848	−	0.726583i	0.972779	+	0.231736i	$0.0744404\pi$
$242$	20.0517	+	11.5768i	1.28897	+	0.744188i
$243$	10.6716			0.684585
$244$	0.358563	+	0.621049i	0.0229546	+	0.0397586i
$245$		0			0
$246$	−3.68607			−0.235015
$247$	−15.9024	−	13.8274i	−1.01185	−	0.879815i
$248$	−5.02884	+	8.71020i	−0.319331	+	0.553098i
$249$		−	16.7675i		−	1.06260i
$250$	−5.19626	+	9.00019i	−0.328641	+	0.569222i
$251$	3.36618	−	5.83039i	0.212471	−	0.368011i	−0.740016	−	0.672589i	$-0.765182\pi$
$251$	3.36618	−	5.83039i	0.212471	−	0.368011i	0.952487	+	0.304578i	$0.0985154\pi$
$252$		0			0
$253$	7.32677	+	4.23011i	0.460630	+	0.265945i
$254$			2.64408i			0.165904i
$255$	1.12636	+	0.650306i	0.0705356	+	0.0407238i
$256$	1.17560	+	2.03620i	0.0734750	+	0.127262i
$257$	−8.26907	+	14.3225i	−0.515811	+	0.893410i	0.484021	+	0.875056i	$0.339176\pi$
$257$	−8.26907	+	14.3225i	−0.515811	+	0.893410i	−0.999832	+	0.0183536i	$0.994158\pi$
$258$	15.3026	−	8.83494i	0.952696	−	0.550039i
$259$		0			0
$260$	0.269844	−	0.0928757i	0.0167350	−	0.00575991i
$261$	−6.04392	−	10.4684i	−0.374110	−	0.647977i
$262$		−	21.4878i		−	1.32752i
$263$	−10.0227			−0.618028			−0.309014	−	0.951057i	$-0.599999\pi$
$263$	−10.0227			−0.618028			−0.309014	+	0.951057i	$0.599999\pi$
$264$	−43.9485			−2.70485
$265$		−	4.39608i		−	0.270049i
$266$		0			0
$267$	12.4996	+	7.21663i	0.764962	+	0.441651i
$268$	−0.624740	+	0.360694i	−0.0381621	+	0.0220329i
$269$	−7.86149	−	13.6165i	−0.479323	−	0.830212i	0.520395	−	0.853925i	$-0.325785\pi$
$269$	−7.86149	−	13.6165i	−0.479323	−	0.830212i	−0.999719	+	0.0237130i	$0.992451\pi$
$270$	−7.36956			−0.448497
$271$	4.51734	+	2.60809i	0.274409	+	0.158430i	0.630890	−	0.775873i	$-0.282690\pi$
$271$	4.51734	+	2.60809i	0.274409	+	0.158430i	−0.356481	+	0.934303i	$0.616023\pi$
$272$	2.12499			0.128847
$273$		0			0
$274$	−10.8270			−0.654085
$275$	19.8612	+	11.4669i	1.19767	+	0.691478i
$276$	−0.454108			−0.0273341
$277$	−9.63619	−	16.6904i	−0.578983	−	1.00283i	−0.995596	−	0.0937439i	$-0.970117\pi$
$277$	−9.63619	−	16.6904i	−0.578983	−	1.00283i	0.416614	−	0.909084i	$-0.363217\pi$
$278$	−11.8532	+	6.84343i	−0.710906	+	0.410442i
$279$	15.9582	+	9.21345i	0.955390	+	0.551595i
$280$		0			0
$281$		−	2.14283i		−	0.127831i	−0.997955	−	0.0639153i	$-0.979641\pi$
$281$		−	2.14283i		−	0.127831i	0.997955	−	0.0639153i	$-0.0203588\pi$
$282$	−15.2742			−0.909566
$283$	−15.7502			−0.936255			−0.468127	−	0.883661i	$-0.655071\pi$
$283$	−15.7502			−0.936255			−0.468127	+	0.883661i	$0.655071\pi$
$284$			0.914762i			0.0542812i
$285$	−6.78597	−	11.7537i	−0.401966	−	0.696226i
$286$	8.53048	+	24.7847i	0.504418	+	1.46555i
$287$		0			0
$288$	2.54821	−	1.47121i	0.150155	−	0.0866919i
$289$	8.34314	−	14.4507i	0.490773	−	0.850044i
$290$	−1.26714	−	2.19474i	−0.0744087	−	0.128880i
$291$	26.5696	+	15.3400i	1.55754	+	0.899246i
$292$		−	0.491180i		−	0.0287441i
$293$	20.0474	+	11.5744i	1.17118	+	0.676182i	0.953958	−	0.299940i	$-0.0969668\pi$
$293$	20.0474	+	11.5744i	1.17118	+	0.676182i	0.217223	+	0.976122i	$0.430300\pi$
$294$		0			0
$295$	4.43029	−	7.67348i	0.257941	−	0.446767i
$296$	−1.79683	+	3.11220i	−0.104439	+	0.180893i
$297$			34.9537i			2.02822i
$298$	5.46054	−	9.45793i	0.316320	−	0.547883i
$299$	1.88318	+	5.47145i	0.108907	+	0.316422i
$300$	−1.23098			−0.0710708
$301$		0			0
$302$	1.03509	+	1.79283i	0.0595629	+	0.103166i
$303$	−11.2815			−0.648103
$304$	−19.2036	−	11.0872i	−1.10140	−	0.635894i
$305$	5.09669	−	2.94258i	0.291836	−	0.168491i
$306$		−	4.09481i		−	0.234085i
$307$		−	4.23590i		−	0.241756i	−0.992667	−	0.120878i	$-0.961429\pi$
$307$		−	4.23590i		−	0.241756i	0.992667	−	0.120878i	$-0.0385709\pi$
$308$		0			0
$309$	12.1785	+	21.0939i	0.692813	+	1.19999i
$310$	3.34570	+	1.93164i	0.190023	+	0.109710i
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	0.163524	+	0.986539i	$0.447714\pi$
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	−0.936130	+	0.351654i	$0.885619\pi$
$312$	−22.6833	−	19.7234i	−1.28419	−	1.11662i
$313$	1.34849	+	2.33565i	0.0762209	+	0.132018i	0.901617	−	0.432536i	$-0.142381\pi$
$313$	1.34849	+	2.33565i	0.0762209	+	0.132018i	−0.825396	+	0.564555i	$0.809048\pi$
$314$	−4.60631	+	2.65945i	−0.259949	+	0.150082i
$315$		0			0
$316$	−0.558247	+	0.966913i	−0.0314039	+	0.0543931i
$317$	−20.8456	+	12.0352i	−1.17081	+	0.675966i	−0.953870	−	0.300220i	$-0.902940\pi$
$317$	−20.8456	+	12.0352i	−1.17081	+	0.675966i	−0.216937	+	0.976186i	$0.569607\pi$
$318$	−18.7691	+	10.8364i	−1.05252	+	0.607674i
$319$	−10.4096	+	6.01000i	−0.582828	+	0.336496i
$320$	5.83037	−	3.36617i	0.325928	−	0.188174i
$321$	−13.9381	+	24.1416i	−0.777951	+	1.34745i
$322$		0			0
$323$	2.83504	−	1.63681i	0.157746	−	0.0910745i
$324$	−0.157138	−	0.272170i	−0.00872986	−	0.0151206i
$325$	5.10487	+	14.8318i	0.283167	+	0.822722i
$326$	9.90220	−	17.1511i	0.548432	−	0.949912i
$327$	−36.3394	−	20.9806i	−2.00958	−	1.16023i
$328$	−1.34217	−	2.32471i	−0.0741091	−	0.128361i
$329$		0			0
$330$			16.8812i			0.929279i
$331$			0.619723i			0.0340631i	0.999855	+	0.0170315i	$0.00542157\pi$
$331$			0.619723i			0.0340631i	−0.999855	+	0.0170315i	$0.994578\pi$
$332$	0.494959	−	0.285765i	0.0271644	−	0.0156834i
$333$	5.70194	+	3.29201i	0.312464	+	0.180401i
$334$	−6.23523			−0.341177
$335$	2.96007	+	5.12699i	0.161726	+	0.280117i
$336$		0			0
$337$	−5.72118			−0.311652			−0.155826	−	0.987784i	$-0.549804\pi$
$337$	−5.72118			−0.311652			−0.155826	+	0.987784i	$0.549804\pi$
$338$	−6.72012	+	16.6206i	−0.365527	+	0.904039i
$339$	28.1082	−	48.6848i	1.52663	−	2.64420i
$340$			0.0443321i			0.00240425i
$341$	9.16174	−	15.8686i	0.496136	−	0.859333i
$342$	−21.3647	+	37.0048i	−1.15527	+	2.00099i
$343$		0			0
$344$	11.1439	+	6.43396i	0.600841	+	0.346896i
$345$			3.72668i			0.200638i
$346$	23.3102	+	13.4581i	1.25316	+	0.723514i
$347$	0.932429	+	1.61501i	0.0500554	+	0.0866985i	0.889968	−	0.456024i	$-0.150727\pi$
$347$	0.932429	+	1.61501i	0.0500554	+	0.0866985i	−0.839912	+	0.542722i	$0.817394\pi$
$348$	0.322591	−	0.558744i	0.0172927	−	0.0299518i
$349$	19.3273	−	11.1586i	1.03457	−	0.597307i	0.116277	−	0.993217i	$-0.462904\pi$
$349$	19.3273	−	11.1586i	1.03457	−	0.597307i	0.918290	+	0.395909i	$0.129571\pi$
$350$		0			0
$351$	−15.6867	+	18.0408i	−0.837295	+	0.962947i
$352$	−1.46295	−	2.53391i	−0.0779756	−	0.135058i
$353$			2.33199i			0.124119i	0.998072	+	0.0620597i	$0.0197669\pi$
$353$			2.33199i			0.124119i	−0.998072	+	0.0620597i	$0.980233\pi$
$354$	−43.6827			−2.32171
$355$	7.50708			0.398435
$356$			0.491966i			0.0260741i
$357$		0			0
$358$	24.8648	+	14.3557i	1.31415	+	0.758722i
$359$	2.83281	−	1.63553i	0.149510	−	0.0863197i	−0.423379	−	0.905953i	$-0.639156\pi$
$359$	2.83281	−	1.63553i	0.149510	−	0.0863197i	0.572889	+	0.819633i	$0.305823\pi$
$360$	−6.18147	−	10.7066i	−0.325792	−	0.564289i
$361$	−15.1603			−0.797913
$362$	19.7682	+	11.4132i	1.03899	+	0.599863i
$363$	48.3741			2.53898
$364$		0			0
$365$	−4.03092			−0.210988
$366$	−25.1268	−	14.5070i	−1.31340	−	0.758291i
$367$	−4.15290			−0.216780			−0.108390	−	0.994108i	$-0.534569\pi$
$367$	−4.15290			−0.216780			−0.108390	+	0.994108i	$0.534569\pi$
$368$	3.04440	+	5.27306i	0.158700	+	0.274877i
$369$	−4.25916	+	2.45903i	−0.221723	+	0.128012i
$370$	1.19544	+	0.690185i	0.0621477	+	0.0358810i
$371$		0			0
$372$			0.983525i			0.0509934i
$373$	−11.1089			−0.575198			−0.287599	−	0.957751i	$-0.592857\pi$
$373$	−11.1089			−0.575198			−0.287599	+	0.957751i	$0.592857\pi$
$374$	−4.07183			−0.210549
$375$			21.7127i			1.12124i
$376$	−5.56165	−	9.63305i	−0.286820	−	0.496787i
$377$	−8.06996	−	1.56972i	−0.415624	−	0.0808447i
$378$		0			0
$379$	−4.01862	+	2.32015i	−0.206422	+	0.119178i	−0.599648	−	0.800264i	$-0.704693\pi$
$379$	−4.01862	+	2.32015i	−0.206422	+	0.119178i	0.393225	+	0.919442i	$0.371359\pi$
$380$	0.231304	−	0.400630i	0.0118656	−	0.0205519i
$381$	2.76208	+	4.78407i	0.141506	+	0.245095i
$382$	5.07586	+	2.93055i	0.259703	+	0.149940i
$383$			3.66933i			0.187494i	0.995596	+	0.0937469i	$0.0298845\pi$
$383$			3.66933i			0.187494i	−0.995596	+	0.0937469i	$0.970116\pi$
$384$	−25.9740	−	14.9961i	−1.32548	−	0.765266i
$385$		0			0
$386$	7.99661	−	13.8505i	0.407017	−	0.704973i
$387$	11.7878	−	20.4171i	0.599208	−	1.03786i
$388$			1.04574i			0.0530896i
$389$	8.44156	−	14.6212i	0.428004	−	0.741324i	−0.568692	−	0.822551i	$-0.692550\pi$
$389$	8.44156	−	14.6212i	0.428004	−	0.741324i	0.996696	+	0.0812262i	$0.0258836\pi$
$390$	−7.57603	+	8.71296i	−0.383627	+	0.441198i
$391$	−0.898894			−0.0454590
$392$		0			0
$393$	−22.4468	−	38.8790i	−1.13229	−	1.96119i
$394$	19.8878			1.00193
$395$	7.93506	+	4.58131i	0.399256	+	0.230511i
$396$	−2.37684	+	1.37227i	−0.119441	+	0.0689592i
$397$			16.7086i			0.838578i	0.907853	+	0.419289i	$0.137721\pi$
$397$			16.7086i			0.838578i	−0.907853	+	0.419289i	$0.862279\pi$
$398$			9.73508i			0.487976i
$399$		0			0
$400$	8.25267	+	14.2940i	0.412633	+	0.714702i
$401$	21.9221	+	12.6567i	1.09474	+	0.632046i	0.934833	−	0.355087i	$-0.115549\pi$
$401$	21.9221	+	12.6567i	1.09474	+	0.632046i	0.159902	+	0.987133i	$0.448882\pi$
$402$	14.5932	−	25.2761i	0.727842	−	1.26066i
$403$	11.8503	−	4.07867i	0.590304	−	0.203173i
$404$	−0.192267	−	0.333017i	−0.00956566	−	0.0165682i
$405$	−2.23359	+	1.28956i	−0.110988	+	0.0640789i
$406$		0			0
$407$	3.27354	−	5.66994i	0.162263	−	0.281048i
$408$	4.04391	−	2.33475i	0.200203	−	0.115587i
$409$	−4.96529	+	2.86671i	−0.245518	+	0.141750i	−0.617710	−	0.786406i	$-0.711940\pi$
$409$	−4.96529	+	2.86671i	−0.245518	+	0.141750i	0.372192	+	0.928156i	$0.378606\pi$
$410$	−0.892951	+	0.515546i	−0.0440997	+	0.0254610i
$411$	−19.5899	+	11.3102i	−0.966299	+	0.557893i
$412$	−0.415112	+	0.718996i	−0.0204511	+	0.0354224i
$413$		0			0
$414$	10.1610	−	5.86648i	0.499388	−	0.288322i
$415$	−2.34516	−	4.06193i	−0.115119	−	0.199392i
$416$	0.382101	−	1.96439i	0.0187340	−	0.0963120i
$417$	−14.2977	+	24.7643i	−0.700161	+	1.21272i
$418$	36.7971	+	21.2448i	1.79981	+	1.03912i
$419$	−17.1729	−	29.7443i	−0.838950	−	1.45310i	−0.890773	−	0.454448i	$-0.849836\pi$
$419$	−17.1729	−	29.7443i	−0.838950	−	1.45310i	0.0518229	−	0.998656i	$-0.483497\pi$
$420$		0			0
$421$		−	2.94167i		−	0.143368i	−0.997427	−	0.0716842i	$-0.977163\pi$
$421$		−	2.94167i		−	0.143368i	0.997427	−	0.0716842i	$-0.0228374\pi$
$422$		−	36.4383i		−	1.77379i
$423$	−17.6489	+	10.1896i	−0.858121	+	0.495437i
$424$	−13.6684	−	7.89148i	−0.663798	−	0.383244i
$425$	−2.43669			−0.118197
$426$	−18.5050	−	32.0516i	−0.896571	−	1.55291i
$427$		0			0
$428$	−0.950178			−0.0459286
$429$	41.3254	+	35.9330i	1.99521	+	1.73486i
$430$	2.47137	−	4.28053i	0.119180	−	0.206426i
$431$		−	39.6955i		−	1.91207i	−0.293258	−	0.956033i	$-0.594739\pi$
$431$		−	39.6955i		−	1.91207i	0.293258	−	0.956033i	$-0.405261\pi$
$432$	−12.5781	+	21.7858i	−0.605162	+	1.04817i
$433$	4.91827	−	8.51869i	0.236357	−	0.409382i	−0.723309	−	0.690524i	$-0.757380\pi$
$433$	4.91827	−	8.51869i	0.236357	−	0.409382i	0.959666	+	0.281142i	$0.0907133\pi$
$434$		0			0
$435$	−4.58538	−	2.64737i	−0.219852	−	0.126932i
$436$		−	1.43027i		−	0.0684975i
$437$	8.12331	+	4.69000i	0.388591	+	0.224353i
$438$	9.93624	+	17.2101i	0.474772	+	0.822329i
$439$	−14.2733	+	24.7220i	−0.681226	+	1.17992i	0.293381	+	0.955996i	$0.405220\pi$
$439$	−14.2733	+	24.7220i	−0.681226	+	1.17992i	−0.974607	+	0.223922i	$0.928114\pi$
$440$	−10.6465	+	6.14678i	−0.507554	+	0.293036i
$441$		0			0
$442$	−2.10161	−	1.82737i	−0.0999632	−	0.0869193i
$443$	−1.66951	−	2.89167i	−0.0793207	−	0.137387i	0.823636	−	0.567118i	$-0.191942\pi$
$443$	−1.66951	−	2.89167i	−0.0793207	−	0.137387i	−0.902957	+	0.429731i	$0.858608\pi$
$444$			0.351419i			0.0166776i
$445$	4.03736			0.191389
$446$	31.7190			1.50194
$447$		−	22.8170i		−	1.07921i
$448$		0			0
$449$	15.7487	+	9.09253i	0.743228	+	0.429103i	0.823242	−	0.567691i	$-0.192163\pi$
$449$	15.7487	+	9.09253i	0.743228	+	0.429103i	−0.0800136	+	0.996794i	$0.525496\pi$
$450$	27.5443	−	15.9027i	1.29845	−	0.749660i
$451$	2.44523	+	4.23526i	0.115141	+	0.199430i
$452$	1.91617			0.0901289
$453$	3.74570	+	2.16258i	0.175988	+	0.101607i
$454$	−0.625219			−0.0293430
$455$		0			0
$456$	−48.7265			−2.28183
$457$	7.55982	+	4.36466i	0.353633	+	0.204170i	0.666284	−	0.745698i	$-0.267884\pi$
$457$	7.55982	+	4.36466i	0.353633	+	0.204170i	−0.312651	+	0.949868i	$0.601217\pi$
$458$	−23.9038			−1.11695
$459$	−1.85691	−	3.21625i	−0.0866729	−	0.150122i
$460$	−0.110008	+	0.0635130i	−0.00512914	+	0.00296131i
$461$	1.96695	+	1.13562i	0.0916099	+	0.0528910i	0.545105	−	0.838368i	$-0.316490\pi$
$461$	1.96695	+	1.13562i	0.0916099	+	0.0528910i	−0.453495	+	0.891259i	$0.649823\pi$
$462$		0			0
$463$		−	5.48326i		−	0.254829i	−0.991850	−	0.127414i	$-0.959332\pi$
$463$		−	5.48326i		−	0.254829i	0.991850	−	0.127414i	$-0.0406678\pi$
$464$	−8.65077			−0.401602
$465$	8.07139			0.374302
$466$		−	10.7775i		−	0.499257i
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	0.560572	−	0.828106i	$-0.310581\pi$
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	−0.997447	+	0.0714164i	$0.977248\pi$
$468$	−1.84262	−	0.358416i	−0.0851753	−	0.0165678i
$469$		0			0
$470$	−3.70018	+	2.13630i	−0.170677	+	0.0985401i
$471$	−5.55629	+	9.62377i	−0.256020	+	0.443440i
$472$	−15.9058	−	27.5496i	−0.732122	−	1.26807i
$473$	−20.3025	−	11.7217i	−0.933510	−	0.538962i
$474$		−	45.1718i		−	2.07481i
$475$	22.0204	+	12.7135i	1.01037	+	0.583335i
$476$		0			0
$477$	−14.4582	+	25.0423i	−0.661994	+	1.14661i
$478$	−9.33030	+	16.1606i	−0.426758	+	0.739166i
$479$		−	33.1354i		−	1.51399i	−0.653418	−	0.756997i	$-0.726666\pi$
$479$		−	33.1354i		−	1.51399i	0.653418	−	0.756997i	$-0.273334\pi$
$480$	0.644422	−	1.11617i	0.0294137	−	0.0509461i
$481$	4.23417	−	1.45733i	0.193061	−	0.0664485i
$482$	−31.1104			−1.41704
$483$		0			0
$484$	0.824428	+	1.42795i	0.0374740	+	0.0649069i
$485$	8.58199			0.389688
$486$	−12.7451	−	7.35838i	−0.578129	−	0.333783i
$487$	−13.8185	+	7.97814i	−0.626178	+	0.361524i	−0.779270	−	0.626688i	$-0.784410\pi$
$487$	−13.8185	+	7.97814i	−0.626178	+	0.361524i	0.153093	+	0.988212i	$0.451077\pi$
$488$		−	21.1291i		−	0.956469i
$489$		−	41.3765i		−	1.87111i
$490$		0			0
$491$	−15.8464	−	27.4468i	−0.715138	−	1.23866i	−0.962906	−	0.269836i	$-0.913031\pi$
$491$	−15.8464	−	27.4468i	−0.715138	−	1.23866i	0.247769	−	0.968819i	$-0.420303\pi$
$492$	−0.227330	−	0.131249i	−0.0102488	−	0.00591717i
$493$	0.638559	−	1.10602i	0.0287593	−	0.0498125i
$494$	9.45788	+	27.4792i	0.425530	+	1.23635i
$495$	11.2617	+	19.5058i	0.506174	+	0.876720i
$496$	11.4206	−	6.59368i	0.512800	−	0.296065i
$497$		0			0
$498$	−11.5617	+	20.0254i	−0.518090	+	0.897358i
$499$	−20.9738	+	12.1092i	−0.938916	+	0.542083i	−0.889620	−	0.456701i	$-0.849031\pi$
$499$	−20.9738	+	12.1092i	−0.938916	+	0.542083i	−0.0492955	+	0.998784i	$0.515698\pi$
$500$	−0.640935	+	0.370044i	−0.0286635	+	0.0165489i
$501$	−11.2817	+	6.51351i	−0.504030	+	0.291002i
$502$	−8.04043	+	4.64215i	−0.358862	+	0.207189i
$503$	0.427249	−	0.740017i	0.0190501	−	0.0329957i	−0.856343	−	0.516407i	$-0.827269\pi$
$503$	0.427249	−	0.740017i	0.0190501	−	0.0329957i	0.875393	+	0.483411i	$0.160602\pi$
$504$		0			0
$505$	−2.73294	+	1.57786i	−0.121614	+	0.0702139i
$506$	−5.83356	−	10.1040i	−0.259333	−	0.449179i
$507$	5.20326	+	37.0925i	0.231085	+	1.64733i
$508$	−0.0941471	+	0.163068i	−0.00417710	+	0.00723495i
$509$	1.12583	+	0.650000i	0.0499017	+	0.0288108i	0.524743	−	0.851261i	$-0.324161\pi$
$509$	1.12583	+	0.650000i	0.0499017	+	0.0288108i	−0.474842	+	0.880071i	$0.657495\pi$
$510$	−0.896808	−	1.55332i	−0.0397113	−	0.0687820i
$511$		0			0
$512$		−	24.0616i		−	1.06338i
$513$			38.7538i			1.71102i
$514$	19.7514	−	11.4035i	0.871199	−	0.502987i
$515$	5.90051	+	3.40666i	0.260007	+	0.150115i
$516$	1.25833			0.0553951
$517$	10.1324	+	17.5499i	0.445624	+	0.771844i
$518$		0			0
$519$	56.2351			2.46845
$520$	−8.25362	−	1.60545i	−0.361945	−	0.0704034i
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	0.449736	+	0.893161i	$0.351518\pi$
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	−0.998369	+	0.0570974i	$0.981815\pi$
$522$			16.6698i			0.729618i
$523$	6.41197	−	11.1059i	0.280376	−	0.485625i	−0.691101	−	0.722758i	$-0.742874\pi$
$523$	6.41197	−	11.1059i	0.280376	−	0.485625i	0.971477	+	0.237133i	$0.0762076\pi$
$524$	0.765112	−	1.32521i	0.0334241	−	0.0578922i
$525$		0			0
$526$	11.9701	+	6.91095i	0.521922	+	0.301332i
$527$			1.94686i			0.0848065i
$528$	49.9040	+	28.8121i	2.17179	+	1.25389i
$529$	10.2122	+	17.6880i	0.444008	+	0.769045i
$530$	−3.03122	+	5.25022i	−0.131668	+	0.228055i
$531$	−50.4743	+	29.1413i	−2.19040	+	1.26463i
$532$		0			0
$533$	−0.638656	+	3.28334i	−0.0276632	+	0.142217i
$534$	−9.95213	−	17.2376i	−0.430671	−	0.745944i
$535$			7.79773i			0.337125i
$536$	21.2547			0.918063
$537$	59.9855			2.58857
$538$			21.6828i			0.934814i
$539$		0			0
$540$	−0.454501	−	0.262406i	−0.0195586	−	0.0112922i
$541$	24.8938	−	14.3725i	1.07027	−	0.617920i	0.142014	−	0.989865i	$-0.454642\pi$
$541$	24.8938	−	14.3725i	1.07027	−	0.617920i	0.928255	+	0.371944i	$0.121309\pi$
$542$	−3.59670	−	6.22966i	−0.154491	−	0.267587i
$543$	47.6902			2.04658
$544$	0.269226	+	0.155438i	0.0115430	+	0.00666434i
$545$	−11.7376			−0.502785
$546$		0			0
$547$	−8.88085			−0.379718			−0.189859	−	0.981811i	$-0.560803\pi$
$547$	−8.88085			−0.379718			−0.189859	+	0.981811i	$0.560803\pi$
$548$	−0.667733	−	0.385516i	−0.0285241	−	0.0164684i
$549$	−38.7111			−1.65215
$550$	−15.8134	−	27.3897i	−0.674287	−	1.16790i
$551$	−11.5413	+	6.66339i	−0.491677	+	0.283870i
$552$	11.5871	+	6.68983i	0.493181	+	0.284738i
$553$		0			0
$554$			26.5777i			1.12918i
$555$	2.88395			0.122417
$556$	−0.974690			−0.0413361
$557$		−	38.7273i		−	1.64093i	−0.571696	−	0.820465i	$-0.693714\pi$
$557$		−	38.7273i		−	1.64093i	0.571696	−	0.820465i	$-0.306286\pi$
$558$	−12.7059	−	22.0072i	−0.537882	−	0.931639i
$559$	−5.21830	−	15.1614i	−0.220711	−	0.641259i
$560$		0			0
$561$	−7.36736	+	4.25355i	−0.311050	+	0.179585i
$562$	−1.47754	+	2.55918i	−0.0623263	+	0.107952i
$563$	−3.45441	−	5.98321i	−0.145586	−	0.252162i	0.784005	−	0.620754i	$-0.213173\pi$
$563$	−3.45441	−	5.98321i	−0.145586	−	0.252162i	−0.929591	+	0.368592i	$0.879840\pi$
$564$	−0.942002	−	0.543865i	−0.0396655	−	0.0229009i
$565$		−	15.7252i		−	0.661565i
$566$	18.8105	+	10.8602i	0.790663	+	0.456489i
$567$		0			0
$568$	13.4761	−	23.3413i	0.565444	−	0.979379i
$569$	−1.41872	+	2.45730i	−0.0594759	+	0.103015i	−0.894230	−	0.447607i	$-0.852276\pi$
$569$	−1.41872	+	2.45730i	−0.0594759	+	0.103015i	0.834754	+	0.550623i	$0.185610\pi$
$570$			18.7165i			0.783946i
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.302001	+	0.953307i	$0.597655\pi$
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.674588	+	0.738195i	$0.735679\pi$
$572$	−0.356404	+	1.83228i	−0.0149020	+	0.0766115i
$573$	12.2453			0.511557
$574$		0			0
$575$	−3.49096	−	6.04653i	−0.145583	−	0.252158i
$576$	−44.2836			−1.84515
$577$	−9.88033	−	5.70441i	−0.411323	−	0.237478i	0.280035	−	0.959990i	$-0.409654\pi$
$577$	−9.88033	−	5.70441i	−0.411323	−	0.237478i	−0.691358	+	0.722512i	$0.742987\pi$
$578$	−19.9284	+	11.5057i	−0.828911	+	0.478572i
$579$		−	33.4140i		−	1.38864i
$580$		−	0.180474i		−	0.00749379i
$581$		0			0
$582$	−21.1547	−	36.6410i	−0.876890	−	1.51882i
$583$	24.9017	+	14.3770i	1.03132	+	0.595436i
$584$	−7.23597	+	12.5331i	−0.299426	+	0.518622i
$585$	−2.94138	+	15.1217i	−0.121611	+	0.625204i
$586$	−15.9617	−	27.6465i	−0.659371	−	1.14206i
$587$	40.2191	−	23.2205i	1.66002	−	0.958413i	0.687318	−	0.726356i	$-0.258788\pi$
$587$	40.2191	−	23.2205i	1.66002	−	0.958413i	0.972702	−	0.232057i	$-0.0745456\pi$
$588$		0			0
$589$	10.1578	−	17.5938i	0.418544	−	0.724939i
$590$	−10.5821	+	6.10961i	−0.435660	+	0.251529i
$591$	35.9840	−	20.7754i	1.48018	−	0.854585i
$592$	4.08064	−	2.35596i	0.167713	−	0.0968292i
$593$	17.5462	−	10.1303i	0.720535	−	0.416001i	−0.0944146	−	0.995533i	$-0.530098\pi$
$593$	17.5462	−	10.1303i	0.720535	−	0.416001i	0.814950	+	0.579532i	$0.196765\pi$
$594$	24.1016	−	41.7451i	0.988899	−	1.71282i
$595$		0			0
$596$	0.673533	−	0.388864i	0.0275890	−	0.0159285i
$597$	10.1696	+	17.6142i	0.416212	+	0.720901i
$598$	1.52364	−	7.83304i	0.0623061	−	0.320317i
$599$	19.4938	−	33.7642i	0.796494	−	1.37957i	−0.125391	−	0.992107i	$-0.540019\pi$
$599$	19.4938	−	33.7642i	0.796494	−	1.37957i	0.921886	−	0.387462i	$-0.126648\pi$
$600$	31.4100	+	18.1346i	1.28231	+	0.740342i
$601$	9.56951	+	16.5749i	0.390348	+	0.676103i	0.992495	−	0.122282i	$-0.0390212\pi$
$601$	9.56951	+	16.5749i	0.390348	+	0.676103i	−0.602147	+	0.798385i	$0.705688\pi$
$602$		0			0
$603$		−	38.9412i		−	1.58581i
$604$			0.147425i			0.00599865i
$605$	11.7186	−	6.76575i	0.476430	−	0.275067i
$606$	13.4734	+	7.77888i	0.547320	+	0.315995i
$607$	−43.3336			−1.75886			−0.879428	−	0.476033i	$-0.842074\pi$
$607$	−43.3336			−1.75886			−0.879428	+	0.476033i	$0.842074\pi$
$608$	−1.62200	−	2.80939i	−0.0657808	−	0.113936i
$609$		0			0
$610$	−8.11595			−0.328605
$611$	−2.64644	+	13.6054i	−0.107063	+	0.550415i
$612$	0.145803	−	0.252538i	0.00589373	−	0.0102082i
$613$		−	10.3096i		−	0.416399i	−0.978086	−	0.208200i	$-0.933240\pi$
$613$		−	10.3096i		−	0.416399i	0.978086	−	0.208200i	$-0.0667604\pi$
$614$	−2.92077	+	5.05892i	−0.117873	+	0.204161i
$615$	−1.07711	+	1.86561i	−0.0434332	+	0.0752285i
$616$		0			0
$617$	−9.58684	−	5.53497i	−0.385952	−	0.222829i	0.294453	−	0.955666i	$-0.404863\pi$
$617$	−9.58684	−	5.53497i	−0.385952	−	0.222829i	−0.680405	+	0.732837i	$0.738196\pi$
$618$		−	33.5898i		−	1.35118i
$619$	29.2384	+	16.8808i	1.17519	+	0.678498i	0.954897	−	0.296936i	$-0.0959647\pi$
$619$	29.2384	+	16.8808i	1.17519	+	0.678498i	0.220295	+	0.975433i	$0.429298\pi$
$620$	0.137559	+	0.238259i	0.00552450	+	0.00956871i
$621$	5.32065	−	9.21563i	0.213510	−	0.369810i
$622$	32.5447	−	18.7897i	1.30492	−	0.753399i
$623$		0			0
$624$	12.8267	+	37.2671i	0.513480	+	1.49188i
$625$	−7.83931	−	13.5781i	−0.313573	−	0.543124i
$626$		−	3.71927i		−	0.148652i
$627$	88.7719			3.54521
$628$	−0.378778			−0.0151149
$629$			0.695623i			0.0277363i
$630$		0			0
$631$	33.4264	+	19.2987i	1.33068	+	0.768271i	0.985405	−	0.170229i	$-0.0544507\pi$
$631$	33.4264	+	19.2987i	1.33068	+	0.768271i	0.345280	+	0.938500i	$0.387784\pi$
$632$	28.4887	−	16.4480i	1.13322	−	0.654265i
$633$	−38.0645	−	65.9296i	−1.51293	−	2.62047i
$634$	33.1945			1.31832
$635$	1.33823	+	0.772627i	0.0531060	+	0.0306608i
$636$	−1.54339			−0.0611995
$637$		0			0
$638$	16.5763			0.656260
$639$	−42.7641	−	24.6899i	−1.69172	−	0.976717i
$640$	−8.38960			−0.331628
$641$	9.76141	+	16.9073i	0.385553	+	0.667797i	0.991846	−	0.127445i	$-0.0406775\pi$
$641$	9.76141	+	16.9073i	0.385553	+	0.667797i	−0.606293	+	0.795241i	$0.707344\pi$
$642$	33.2926	−	19.2215i	1.31395	−	0.758611i
$643$	−10.8009	−	6.23589i	−0.425945	−	0.245920i	0.271673	−	0.962390i	$-0.412423\pi$
$643$	−10.8009	−	6.23589i	−0.425945	−	0.245920i	−0.697618	+	0.716470i	$0.745757\pi$
$644$		0			0
$645$		−	10.3266i		−	0.406611i
$646$	−4.51450			−0.177621
$647$	35.9391			1.41291			0.706455	−	0.707758i	$-0.250293\pi$
$647$	35.9391			1.41291			0.706455	+	0.707758i	$0.250293\pi$
$648$			9.25967i			0.363754i
$649$	28.9778	+	50.1910i	1.13748	+	1.97017i
$650$	4.13023	−	21.2336i	0.162001	−	0.832849i
$651$		0			0
$652$	1.22139	−	0.705171i	0.0478334	−	0.0276166i
$653$	−2.42944	+	4.20791i	−0.0950713	+	0.164668i	−0.909638	−	0.415401i	$-0.863641\pi$
$653$	−2.42944	+	4.20791i	−0.0950713	+	0.164668i	0.814567	+	0.580069i	$0.196975\pi$
$654$	28.9334	+	50.1141i	1.13138	+	1.95962i
$655$	−10.8755	−	6.27897i	−0.424941	−	0.245340i
$656$			3.51964i			0.137419i
$657$	22.9621	+	13.2572i	0.895838	+	0.517212i
$658$		0			0
$659$	11.8103	−	20.4560i	0.460063	−	0.796853i	−0.538900	−	0.842370i	$-0.681160\pi$
$659$	11.8103	−	20.4560i	0.460063	−	0.796853i	0.998964	+	0.0455166i	$0.0144934\pi$
$660$	−0.601085	+	1.04111i	−0.0233972	+	0.0405251i
$661$			16.3932i			0.637623i	0.947818	+	0.318812i	$0.103284\pi$
$661$			16.3932i			0.637623i	−0.947818	+	0.318812i	$0.896716\pi$
$662$	0.427316	−	0.740134i	0.0166081	−	0.0287661i
$663$	−5.71147	−	1.11096i	−0.221815	−	0.0431462i
$664$	−16.8393			−0.653492
$665$		0			0
$666$	−4.53987	−	7.86328i	−0.175916	−	0.304696i
$667$	3.65936			0.141691
$668$	−0.384544	−	0.222016i	−0.0148784	−	0.00859007i
$669$	57.3908	−	33.1346i	2.21886	−	1.28106i
$670$		−	8.16420i		−	0.315410i
$671$			38.4939i			1.48604i
$672$		0			0
$673$	−7.12678	−	12.3439i	−0.274717	−	0.475824i	0.695347	−	0.718675i	$-0.255251\pi$
$673$	−7.12678	−	12.3439i	−0.274717	−	0.475824i	−0.970064	+	0.242851i	$0.921918\pi$
$674$	6.83278	+	3.94491i	0.263189	+	0.151952i
$675$	14.4230	−	24.9814i	0.555143	−	0.961536i
$676$	−1.00625	+	0.785753i	−0.0387020	+	0.0302213i
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	0.750296	−	0.661102i	$-0.229911\pi$
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	−0.947679	+	0.319225i	$0.896577\pi$
$678$	−67.1391	+	38.7628i	−2.57846	+	1.48867i
$679$		0			0
$680$	0.653092	−	1.13119i	0.0250449	−	0.0433791i
$681$	−1.13124	+	0.653122i	−0.0433492	+	0.0250277i
$682$	−21.8837	+	12.6345i	−0.837969	+	0.483802i
$683$	1.92432	−	1.11101i	0.0736321	−	0.0425115i	−0.462732	−	0.886498i	$-0.653131\pi$
$683$	1.92432	−	1.11101i	0.0736321	−	0.0425115i	0.536364	+	0.843987i	$0.319797\pi$
$684$	−2.63524	+	1.52146i	−0.100761	+	0.0581744i
$685$	−3.16377	+	5.47981i	−0.120881	+	0.209373i
$686$		0			0
$687$	−43.2504	+	24.9706i	−1.65011	+	0.952689i
$688$	−8.43604	−	14.6117i	−0.321621	−	0.557064i
$689$	6.40044	+	18.5960i	0.243837	+	0.708451i
$690$	2.56965	−	4.45076i	0.0978249	−	0.169438i
$691$	−2.28643	−	1.32007i	−0.0869800	−	0.0502179i	0.455879	−	0.890042i	$-0.349325\pi$
$691$	−2.28643	−	1.32007i	−0.0869800	−	0.0502179i	−0.542859	+	0.839824i	$0.682658\pi$
$692$	0.958402	+	1.66000i	0.0364330	+	0.0631038i
$693$		0			0
$694$		−	2.57174i		−	0.0976220i
$695$			7.99889i			0.303415i
$696$	−16.4626	+	9.50469i	−0.624014	+	0.360274i
$697$	−0.449993	−	0.259804i	−0.0170447	−	0.00984077i
$698$	−30.7767			−1.16492
$699$	−11.2585	−	19.5002i	−0.425834	−	0.737566i
$700$		0			0
$701$	−8.89991			−0.336145			−0.168072	−	0.985775i	$-0.553754\pi$
$701$	−8.89991			−0.336145			−0.168072	+	0.985775i	$0.553754\pi$
$702$	31.1742	−	10.7296i	1.17659	−	0.404965i
$703$	3.62943	−	6.28635i	0.136886	−	0.237094i
$704$			44.0351i			1.65964i
$705$	−4.46328	+	7.73063i	−0.168097	+	0.291152i
$706$	1.60797	−	2.78509i	0.0605168	−	0.104818i
$707$		0			0
$708$	−2.69403	−	1.55540i	−0.101248	−	0.0584556i
$709$		−	40.5944i		−	1.52456i	−0.647250	−	0.762278i	$-0.724081\pi$
$709$		−	40.5944i		−	1.52456i	0.647250	−	0.762278i	$-0.275919\pi$
$710$	−8.96569	−	5.17634i	−0.336476	−	0.194265i
$711$	−30.1347	−	52.1949i	−1.13014	−	1.95746i
$712$	7.24754	−	12.5531i	0.271613	−	0.470448i
$713$	−4.83103	+	2.78920i	−0.180923	+	0.104456i
$714$		0			0
$715$	15.0368	+	2.92487i	0.562344	+	0.109384i
$716$	1.02232	+	1.77071i	0.0382059	+	0.0661745i
$717$			38.9868i			1.45599i
$718$	−4.51096			−0.168348
$719$	14.5135			0.541262			0.270631	−	0.962683i	$-0.412768\pi$
$719$	14.5135			0.541262			0.270631	+	0.962683i	$0.412768\pi$
$720$			16.2100i			0.604110i
$721$		0			0
$722$	18.1059	+	10.4535i	0.673834	+	0.389038i
$723$	−56.2896	+	32.4988i	−2.09343	+	1.20864i
$724$	0.812773	+	1.40776i	0.0302065	+	0.0523191i
$725$	9.91969			0.368408
$726$	−57.7730	−	33.3552i	−2.14416	−	1.23793i
$727$	−30.6942			−1.13839			−0.569193	−	0.822204i	$-0.692744\pi$
$727$	−30.6942			−1.13839			−0.569193	+	0.822204i	$0.692744\pi$
$728$		0			0
$729$	−40.3475			−1.49435
$730$	4.81411	+	2.77943i	0.178178	+	0.102871i
$731$	2.49084			0.0921269
$732$	−1.03309	−	1.78937i	−0.0381842	−	0.0661369i
$733$	−11.4873	+	6.63218i	−0.424292	+	0.244965i	−0.696912	−	0.717157i	$-0.745443\pi$
$733$	−11.4873	+	6.63218i	−0.424292	+	0.244965i	0.272620	+	0.962122i	$0.412110\pi$
$734$	4.95980	+	2.86354i	0.183069	+	0.105695i
$735$		0			0
$736$			0.890761i			0.0328339i
$737$	−38.7227			−1.42637
$738$	6.78227			0.249659
$739$			7.25474i			0.266870i	0.991058	+	0.133435i	$0.0426008\pi$
$739$			7.25474i			0.266870i	−0.991058	+	0.133435i	$0.957399\pi$
$740$	0.0491505	+	0.0851312i	0.00180681	+	0.00312948i
$741$	45.8182	+	39.8395i	1.68317	+	1.46354i
$742$		0			0
$743$	−40.0705	+	23.1347i	−1.47004	+	0.848730i	−0.999435	−	0.0336128i	$-0.989299\pi$
$743$	−40.0705	+	23.1347i	−1.47004	+	0.848730i	−0.470608	+	0.882342i	$0.655965\pi$
$744$	14.4891	−	25.0959i	0.531196	−	0.920059i
$745$	−3.19125	−	5.52741i	−0.116918	−	0.202509i
$746$	13.2673	+	7.65991i	0.485752	+	0.280449i
$747$			30.8517i			1.12881i
$748$	−0.251121	−	0.144985i	−0.00918188	−	0.00530116i
$749$		0			0
$750$	14.9715	−	25.9314i	0.546681	−	0.946880i
$751$	−18.0130	+	31.1995i	−0.657305	+	1.13848i	0.324006	+	0.946055i	$0.394970\pi$
$751$	−18.0130	+	31.1995i	−0.657305	+	1.13848i	−0.981311	+	0.192430i	$0.938363\pi$
$752$			14.5846i			0.531845i
$753$	−9.69865	+	16.7985i	−0.353438	+	0.612173i
$754$	8.55556	+	7.43917i	0.311575	+	0.270919i
$755$	1.20986			0.0440313
$756$		0			0
$757$	5.28132	+	9.14751i	0.191953	+	0.332472i	0.945897	−	0.324466i	$-0.105185\pi$
$757$	5.28132	+	9.14751i	0.191953	+	0.332472i	−0.753945	+	0.656938i	$0.771851\pi$
$758$	6.39923			0.232430
$759$	−21.1099	−	12.1878i	−0.766242	−	0.442390i
$760$	−11.8040	+	6.81504i	−0.428176	+	0.247207i
$761$		−	7.81202i		−	0.283185i	−0.989925	−	0.141593i	$-0.954778\pi$
$761$		−	7.81202i		−	0.283185i	0.989925	−	0.141593i	$-0.0452223\pi$
$762$		−	7.61813i		−	0.275976i
$763$		0			0
$764$	0.208695	+	0.361470i	0.00755031	+	0.0130775i
$765$	−2.07248	−	1.19654i	−0.0749305	−	0.0432612i
$766$	2.53010	−	4.38226i	0.0914163	−	0.158338i
$767$	−7.56855	+	38.9101i	−0.273285	+	1.40496i
$768$	−3.38714	−	5.86671i	−0.122223	−	0.211696i
$769$	−21.9030	+	12.6457i	−0.789844	+	0.456017i	−0.839908	−	0.542729i	$-0.817391\pi$
$769$	−21.9030	+	12.6457i	−0.789844	+	0.456017i	0.0500637	+	0.998746i	$0.484058\pi$
$770$		0			0
$771$	23.8249	−	41.2659i	0.858032	−	1.48615i
$772$	0.986345	−	0.569467i	0.0354993	−	0.0204956i
$773$	40.3572	−	23.3002i	1.45155	−	0.838051i	0.452977	−	0.891522i	$-0.350362\pi$
$773$	40.3572	−	23.3002i	1.45155	−	0.838051i	0.998569	+	0.0534716i	$0.0170287\pi$
$774$	−28.1563	+	16.2560i	−1.01206	+	0.584311i
$775$	−13.0958	+	7.56086i	−0.470415	+	0.271594i
$776$	15.4057	−	26.6834i	0.553032	−	0.957879i
$777$		0			0
$778$	−20.1634	+	11.6414i	−0.722895	+	0.417363i
$779$	2.71106	+	4.69570i	0.0971339	+	0.168241i
$780$	−0.777475	+	0.267594i	−0.0278381	+	0.00958140i
$781$	−24.5513	+	42.5241i	−0.878515	+	1.52163i
$782$	1.07355	+	0.619812i	0.0383899	+	0.0221644i
$783$	7.55940	+	13.0933i	0.270151	+	0.467915i
$784$		0			0
$785$			3.10848i			0.110946i
$786$			61.9108i			2.20829i
$787$	−34.4099	+	19.8666i	−1.22658	+	0.708167i	−0.966313	−	0.257369i	$-0.917144\pi$
$787$	−34.4099	+	19.8666i	−1.22658	+	0.708167i	−0.260268	+	0.965536i	$0.583811\pi$
$788$	1.22653	+	0.708140i	0.0436935	+	0.0252265i
$789$	28.8775			1.02807
$790$	−6.31788	−	10.9429i	−0.224780	−	0.389330i
$791$		0			0
$792$	80.8641			2.87338
$793$	−17.2755	+	19.8680i	−0.613470	+	0.705533i
$794$	11.5210	−	19.9550i	0.408865	−	0.708175i
$795$			12.6660i			0.449217i
$796$	−0.346635	+	0.600389i	−0.0122861	+	0.0212802i
$797$	1.39299	−	2.41273i	0.0493422	−	0.0854632i	−0.840299	−	0.542123i	$-0.817621\pi$
$797$	1.39299	−	2.41273i	0.0493422	−	0.0854632i	0.889642	+	0.456659i	$0.150954\pi$
$798$		0			0
$799$	−1.86467	−	1.07656i	−0.0659671	−	0.0380861i
$800$			2.41465i			0.0853706i
$801$	−22.9989	−	13.2784i	−0.812625	−	0.469169i
$802$	−17.4543	−	30.2317i	−0.616333	−	1.06752i
$803$	13.1828	−	22.8333i	0.465210	−	0.805768i
$804$	1.80000	−	1.03923i	0.0634812	−	0.0366509i
$805$		0			0
$806$	−16.9651	−	3.29995i	−0.597570	−	0.116236i
$807$	22.6505	+	39.2319i	0.797337	+	1.38103i
$808$			11.3298i			0.398580i
$809$	−41.4586			−1.45761			−0.728803	−	0.684723i	$-0.759923\pi$
$809$	−41.4586			−1.45761			−0.728803	+	0.684723i	$0.759923\pi$
$810$	3.55676			0.124972
$811$		−	27.8622i		−	0.978375i	−0.872179	−	0.489188i	$-0.837293\pi$
$811$		−	27.8622i		−	0.978375i	0.872179	−	0.489188i	$-0.162707\pi$
$812$		0			0
$813$	−13.0154	−	7.51443i	−0.456469	−	0.263543i
$814$	−7.81915	+	4.51439i	−0.274061	+	0.158229i
$815$	−5.78705	−	10.0235i	−0.202712	−	0.351107i
$816$	−6.12254			−0.214332
$817$	−22.5097	−	12.9960i	−0.787515	−	0.454672i
$818$	7.90671			0.276452
$819$		0			0
$820$	−0.0734276			−0.00256420
$821$	−19.4164	−	11.2101i	−0.677638	−	0.391235i	0.121326	−	0.992613i	$-0.461285\pi$
$821$	−19.4164	−	11.2101i	−0.677638	−	0.391235i	−0.798965	+	0.601378i	$0.794619\pi$
$822$	31.1949			1.08805
$823$	−1.18083	−	2.04525i	−0.0411611	−	0.0712931i	0.844711	−	0.535223i	$-0.179772\pi$
$823$	−1.18083	−	2.04525i	−0.0411611	−	0.0712931i	−0.885872	+	0.463930i	$0.846439\pi$
$824$	21.1842	−	12.2307i	0.737987	−	0.426077i
$825$	−57.2241	−	33.0384i	−1.99229	−	1.15025i
$826$		0			0
$827$			43.3148i			1.50620i	0.657904	+	0.753102i	$0.271443\pi$
$827$			43.3148i			1.50620i	−0.657904	+	0.753102i	$0.728557\pi$
$828$	0.835546			0.0290372
$829$	−54.9280			−1.90773			−0.953864	−	0.300239i	$-0.902933\pi$
$829$	−54.9280			−1.90773			−0.953864	+	0.300239i	$0.902933\pi$
$830$			6.46820i			0.224514i
$831$	27.7638	+	48.0884i	0.963117	+	1.66817i
$832$	−19.7623	+	22.7280i	−0.685134	+	0.787951i
$833$		0			0
$834$	34.1514	−	19.7173i	1.18257	−	0.682755i
$835$	−1.82200	+	3.15579i	−0.0630529	+	0.109211i
$836$	1.51292	+	2.62045i	0.0523254	+	0.0906303i
$837$	−19.9596	−	11.5237i	−0.689903	−	0.398316i
$838$			47.3647i			1.63619i
$839$	12.7661	+	7.37052i	0.440735	+	0.254459i	0.703910	−	0.710290i	$-0.251436\pi$
$839$	12.7661	+	7.37052i	0.440735	+	0.254459i	−0.263174	+	0.964748i	$0.584769\pi$
$840$		0			0
$841$	11.9004	−	20.6122i	0.410360	−	0.710765i
$842$	−2.02837	+	3.51323i	−0.0699021	+	0.121074i
$843$			6.17393i			0.212642i
$844$	1.29745	−	2.24725i	0.0446600	−	0.0773535i
$845$	6.44836	+	8.25791i	0.221830	+	0.284081i
$846$	28.1041			0.966239
$847$		0			0
$848$	10.3471	+	17.9217i	0.355321	+	0.615434i
$849$	45.3796			1.55743
$850$	2.91013	+	1.68017i	0.0998168	+	0.0576292i
$851$	−1.72615	+	0.996594i	−0.0591717	+	0.0341628i
$852$		−	2.63562i		−	0.0902947i
$853$		−	24.1038i		−	0.825297i	−0.910890	−	0.412649i	$-0.864604\pi$
$853$		−	24.1038i		−	0.825297i	0.910890	−	0.412649i	$-0.135396\pi$
$854$		0			0
$855$	12.4860	+	21.6264i	0.427012	+	0.739607i
$856$	24.2450	+	13.9978i	0.828676	+	0.478436i
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	−0.662525	−	0.749040i	$-0.730515\pi$
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	0.979950	+	0.199243i	$0.0638483\pi$
$858$	−24.5780	−	71.4097i	−0.839080	−	2.43789i
$859$	14.7487	+	25.5456i	0.503221	+	0.871604i	0.999993	+	0.00372294i	$0.00118505\pi$
$859$	14.7487	+	25.5456i	0.503221	+	0.871604i	−0.496772	+	0.867881i	$0.665482\pi$
$860$	0.304832	−	0.175995i	0.0103947	−	0.00600137i
$861$		0			0
$862$	−27.3712	+	47.4083i	−0.932266	+	1.61473i
$863$	16.1457	−	9.32173i	0.549606	−	0.317315i	−0.199357	−	0.979927i	$-0.563885\pi$
$863$	16.1457	−	9.32173i	0.549606	−	0.317315i	0.748963	+	0.662612i	$0.230552\pi$
$864$	−3.18716	+	1.84010i	−0.108429	+	0.0626016i
$865$	13.6230	−	7.86522i	0.463194	−	0.267425i
$866$	−11.7477	+	6.78256i	−0.399204	+	0.230481i
$867$	−24.0383	+	41.6355i	−0.816383	+	1.41402i
$868$		0			0
$869$	−51.9020	+	29.9656i	−1.76065	+	1.01651i
$870$	3.65087	+	6.32350i	0.123776	+	0.214387i
$871$	−19.9861	−	17.3782i	−0.677203	−	0.588836i
$872$	−21.0705	+	36.4951i	−0.713536	+	1.23588i
$873$	−48.8873	−	28.2251i	−1.65459	−	0.955276i
$874$	−6.46776	−	11.2025i	−0.218775	−	0.378930i
$875$		0			0
$876$			1.41519i			0.0478148i
$877$		−	37.7518i		−	1.27479i	−0.770538	−	0.637395i	$-0.780012\pi$
$877$		−	37.7518i		−	1.27479i	0.770538	−	0.637395i	$-0.219988\pi$
$878$	34.0930	−	19.6836i	1.15058	−	0.664290i
$879$	−57.7606	−	33.3481i	−1.94822	−	1.12480i
$880$	16.1190			0.543372
$881$	−14.9149	−	25.8334i	−0.502497	−	0.870350i	−0.999996	−	0.00288515i	$-0.999082\pi$
$881$	−14.9149	−	25.8334i	−0.502497	−	0.870350i	0.497499	−	0.867464i	$-0.334252\pi$
$882$		0			0
$883$	−32.3979			−1.09028			−0.545138	−	0.838346i	$-0.683523\pi$
$883$	−32.3979			−1.09028			−0.545138	+	0.838346i	$0.683523\pi$
$884$	−0.0645449	−	0.187531i	−0.00217088	−	0.00630734i
$885$	−12.7646	+	22.1089i	−0.429076	+	0.743181i
$886$			4.60468i			0.154697i
$887$	−12.9599	+	22.4472i	−0.435151	+	0.753703i	−0.997308	−	0.0733272i	$-0.976638\pi$
$887$	−12.9599	+	22.4472i	−0.435151	+	0.753703i	0.562157	+	0.827030i	$0.309972\pi$
$888$	5.17703	−	8.96688i	0.173730	−	0.300909i
$889$		0			0
$890$	−4.82181	−	2.78387i	−0.161627	−	0.0933156i
$891$		−	16.8697i		−	0.565155i
$892$	1.95620	+	1.12941i	0.0654984	+	0.0378155i
$893$	11.2340	+	19.4579i	0.375931	+	0.651132i
$894$	−15.7329	+	27.2502i	−0.526188	+	0.911384i
$895$	14.5315	−	8.38976i	0.485734	−	0.280439i
$896$		0			0
$897$	−5.42583	−	15.7644i	−0.181163	−	0.526357i
$898$	−12.5391	−	21.7184i	−0.418435	−	0.724751i
$899$		−	7.92559i		−	0.264333i
$900$	2.26497			0.0754991
$901$	−3.05510			−0.101780
$902$		−	6.74420i		−	0.224557i
$903$		0			0
$904$	−48.8934	−	28.2286i	−1.62617	−	0.938869i
$905$	11.5529	−	6.67010i	0.384033	−	0.221722i
$906$	−2.98231	−	5.16552i	−0.0990808	−	0.171613i
$907$	−15.5423			−0.516072			−0.258036	−	0.966135i	$-0.583075\pi$
$907$	−15.5423			−0.516072			−0.258036	+	0.966135i	$0.583075\pi$
$908$	−0.0385589	−	0.0222620i	−0.00127962	−	0.000738791i
$909$	20.7576			0.688485
$910$		0			0
$911$	23.6358			0.783090			0.391545	−	0.920159i	$-0.371941\pi$
$911$	23.6358			0.783090			0.391545	+	0.920159i	$0.371941\pi$
$912$	55.3294	+	31.9445i	1.83214	+	1.05779i
$913$	30.6786			1.01531
$914$	−6.01911	−	10.4254i	−0.199094	−	0.344842i
$915$	−14.6846	+	8.47816i	−0.485458	+	0.280279i
$916$	−1.47421	−	0.851138i	−0.0487094	−	0.0281224i
$917$		0			0
$918$			5.12155i			0.169036i
$919$	44.4817			1.46732			0.733659	−	0.679518i	$-0.237811\pi$
$919$	44.4817			1.46732			0.733659	+	0.679518i	$0.237811\pi$
$920$	3.74264			0.123391
$921$			12.2045i			0.402151i
$922$	−1.56608	−	2.71253i	−0.0515761	−	0.0893324i
$923$	−31.7560	+	10.9299i	−1.04526	+	0.359761i
$924$		0			0
$925$	−4.67920	+	2.70154i	−0.153851	+	0.0888259i
$926$	−3.78086	+	6.54864i	−0.124247	+	0.215202i
$927$	−22.4082	−	38.8121i	−0.735981	−	1.27476i
$928$	−1.09601	−	0.632782i	−0.0359783	−	0.0207721i
$929$			2.94270i			0.0965470i	0.998834	+	0.0482735i	$0.0153719\pi$
$929$			2.94270i			0.0965470i	−0.998834	+	0.0482735i	$0.984628\pi$
$930$	−9.63964	−	5.56545i	−0.316096	−	0.182498i
$931$		0			0
$932$	0.383751	−	0.664676i	0.0125702	−	0.0217722i
$933$	39.2566	−	67.9944i	1.28520	−	2.22604i
$934$			26.0392i			0.852028i
$935$	−1.18983	+	2.06085i	−0.0389116	+	0.0673968i
$936$	41.7367	+	36.2906i	1.36421	+	1.18619i
$937$	0.951020			0.0310685			0.0155342	−	0.999879i	$-0.495055\pi$
$937$	0.951020			0.0310685			0.0155342	+	0.999879i	$0.495055\pi$
$938$		0			0
$939$	−3.88526	−	6.72947i	−0.126791	−	0.219608i
$940$	−0.304267			−0.00992409
$941$	−19.1125	−	11.0346i	−0.623050	−	0.359718i	0.155006	−	0.987914i	$-0.450460\pi$
$941$	−19.1125	−	11.0346i	−0.623050	−	0.359718i	−0.778056	+	0.628196i	$0.783794\pi$
$942$	13.2717	−	7.66242i	0.432416	−	0.249655i
$943$		−	1.48885i		−	0.0484835i
$944$			41.7105i			1.35756i
$945$		0			0
$946$	16.1648	+	27.9983i	0.525563	+	0.910302i
$947$	−44.3160	−	25.5859i	−1.44008	−	0.831429i	−0.442223	−	0.896905i	$-0.645810\pi$
$947$	−44.3160	−	25.5859i	−1.44008	−	0.831429i	−0.997854	+	0.0654762i	$0.979143\pi$
$948$	1.60842	−	2.78587i	0.0522392	−	0.0904809i
$949$	17.0513	−	5.86878i	0.553509	−	0.190509i
$950$	−17.5326	−	30.3674i	−0.568833	−	0.985248i
$951$	60.0605	−	34.6759i	1.94759	−	1.12444i
$952$		0			0
$953$	22.9235	−	39.7047i	0.742565	−	1.28616i	−0.208758	−	0.977967i	$-0.566942\pi$
$953$	22.9235	−	39.7047i	0.742565	−	1.28616i	0.951324	−	0.308194i	$-0.0997245\pi$
$954$	34.5347	−	19.9386i	1.11810	−	0.645536i
$955$	2.96644	−	1.71267i	0.0959916	−	0.0554208i
$956$	−1.15085	+	0.664444i	−0.0372212	+	0.0214896i
$957$	29.9923	−	17.3160i	0.969512	−	0.559748i
$958$	−22.8478	+	39.5735i	−0.738177	+	1.27856i
$959$		0			0
$960$	−16.7985	+	9.69861i	−0.542169	+	0.313021i
$961$	−9.45905	−	16.3836i	−0.305131	−	0.528502i
$962$	−6.06172	−	1.17909i	−0.195438	−	0.0380154i
$963$	25.6458	−	44.4198i	0.826424	−	1.43141i
$964$	−1.91866	−	1.10774i	−0.0617960	−	0.0356779i
$965$	−4.67338	−	8.09453i	−0.150441	−	0.260572i
$966$		0			0
$967$			19.2609i			0.619387i	0.950836	+	0.309694i	$0.100227\pi$
$967$			19.2609i			0.619387i	−0.950836	+	0.309694i	$0.899773\pi$
$968$		−	48.5813i		−	1.56146i
$969$	−8.16832	+	4.71598i	−0.262404	+	0.151499i
$970$	−10.2494	−	5.91752i	−0.329090	−	0.190000i
$971$	−47.3326			−1.51897			−0.759487	−	0.650522i	$-0.774550\pi$
$971$	−47.3326			−1.51897			−0.759487	+	0.650522i	$0.774550\pi$
$972$	−0.524016	−	0.907622i	−0.0168078	−	0.0291120i
$973$		0			0
$974$	22.0046			0.705072
$975$	−14.7082	−	42.7335i	−0.471039	−	1.36857i
$976$	−13.8520	+	23.9923i	−0.443390	+	0.767975i
$977$		−	47.8571i		−	1.53108i	−0.643387	−	0.765541i	$-0.722471\pi$
$977$		−	47.8571i		−	1.53108i	0.643387	−	0.765541i	$-0.277529\pi$
$978$	−28.5302	+	49.4158i	−0.912297	+	1.58014i
$979$	−13.2039	+	22.8698i	−0.421998	+	0.730921i
$980$		0			0
$981$	66.8635	+	38.6037i	2.13479	+	1.23252i
$982$			43.7061i			1.39472i
$983$	13.6560	+	7.88432i	0.435560	+	0.251471i	0.701712	−	0.712460i	$-0.252419\pi$
$983$	13.6560	+	7.88432i	0.435560	+	0.251471i	−0.266152	+	0.963931i	$0.585752\pi$
$984$	3.86707	+	6.69796i	0.123278	+	0.213523i
$985$	5.81142	−	10.0657i	0.185167	−	0.320719i
$986$	−1.52526	+	0.880608i	−0.0485741	+	0.0280443i
$987$		0			0
$988$	−0.395151	+	2.03148i	−0.0125714	+	0.0646300i
$989$	3.56853	+	6.18088i	0.113473	+	0.196541i
$990$		−	31.0609i		−	0.987181i
$991$	−12.1378			−0.385571			−0.192786	−	0.981241i	$-0.561752\pi$
$991$	−12.1378			−0.385571			−0.192786	+	0.981241i	$0.561752\pi$
$992$	1.92924			0.0612536
$993$		−	1.78555i		−	0.0566627i
$994$		0			0
$995$	4.92715	+	2.84469i	0.156201	+	0.0901828i
$996$	−1.42608	+	0.823346i	−0.0451870	+	0.0260887i
$997$	16.8938	+	29.2609i	0.535032	+	0.926703i	0.999162	+	0.0409358i	$0.0130339\pi$
$997$	16.8938	+	29.2609i	0.535032	+	0.926703i	−0.464129	+	0.885767i	$0.653633\pi$
$998$	33.3986			1.05721
$999$	−7.13166	−	4.11746i	−0.225636	−	0.130271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.g.361.2		12
7.2	even	3		637.2.k.i.569.5		12
7.3	odd	6		637.2.q.g.491.5		12
7.4	even	3		637.2.q.i.491.5		12
7.5	odd	6		91.2.k.b.23.5	yes	12
7.6	odd	2		91.2.u.b.88.2	yes	12
13.4	even	6		637.2.k.i.459.2		12
21.5	even	6		819.2.bm.f.478.2		12
21.20	even	2		819.2.do.e.361.5		12
91.4	even	6		637.2.q.i.589.5		12
91.11	odd	12		8281.2.a.co.1.3		12
91.17	odd	6		637.2.q.g.589.5		12
91.24	even	12		8281.2.a.cp.1.3		12
91.30	even	6	inner	637.2.u.g.30.2		12
91.41	even	12		1183.2.e.j.508.3		24
91.54	even	12		1183.2.e.j.170.3		24
91.67	odd	12		8281.2.a.co.1.10		12
91.69	odd	6		91.2.k.b.4.2	✓	12
91.76	even	12		1183.2.e.j.508.10		24
91.80	even	12		8281.2.a.cp.1.10		12
91.82	odd	6		91.2.u.b.30.2	yes	12
91.89	even	12		1183.2.e.j.170.10		24
273.173	even	6		819.2.do.e.667.5		12
273.251	even	6		819.2.bm.f.550.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.2	✓	12	91.69	odd	6
91.2.k.b.23.5	yes	12	7.5	odd	6
91.2.u.b.30.2	yes	12	91.82	odd	6
91.2.u.b.88.2	yes	12	7.6	odd	2
637.2.k.i.459.2		12	13.4	even	6
637.2.k.i.569.5		12	7.2	even	3
637.2.q.g.491.5		12	7.3	odd	6
637.2.q.g.589.5		12	91.17	odd	6
637.2.q.i.491.5		12	7.4	even	3
637.2.q.i.589.5		12	91.4	even	6
637.2.u.g.30.2		12	91.30	even	6	inner
637.2.u.g.361.2		12	1.1	even	1	trivial
819.2.bm.f.478.2		12	21.5	even	6
819.2.bm.f.550.5		12	273.251	even	6
819.2.do.e.361.5		12	21.20	even	2
819.2.do.e.667.5		12	273.173	even	6
1183.2.e.j.170.3		24	91.54	even	12
1183.2.e.j.170.10		24	91.89	even	12
1183.2.e.j.508.3		24	91.41	even	12
1183.2.e.j.508.10		24	91.76	even	12
8281.2.a.co.1.3		12	91.11	odd	12
8281.2.a.co.1.10		12	91.67	odd	12
8281.2.a.cp.1.3		12	91.24	even	12
8281.2.a.cp.1.10		12	91.80	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.19430 - 0.689527i) q^{2} -2.88120 q^{3} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +5.30133 q^{9} +O(q^{10})\)	\(q+(-1.19430 - 0.689527i) q^{2} -2.88120 q^{3} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +5.30133 q^{9} +1.11145 q^{10} -5.27158i q^{11} +(0.141478 + 0.245047i) q^{12} +(2.36581 - 2.72084i) q^{13} +(2.01100 - 1.16105i) q^{15} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +(-6.33136 - 3.65541i) q^{18} -5.84469i q^{19} +(0.0685460 + 0.0395750i) q^{20} +(-3.63490 + 6.29583i) q^{22} +(-0.802438 + 1.38986i) q^{23} -8.33689i q^{24} +(-2.17522 + 3.76760i) q^{25} +(-4.70157 + 1.61820i) q^{26} -6.63060 q^{27} +(-1.14008 - 1.97467i) q^{29} -3.20230 q^{30} +(3.01022 + 1.73795i) q^{31} +(0.480674 - 0.277517i) q^{32} +15.1885i q^{33} -0.772411i q^{34} +(-0.260315 - 0.450879i) q^{36} +(1.07557 + 0.620979i) q^{37} +(-4.03007 + 6.98029i) q^{38} +(-6.81636 + 7.83929i) q^{39} +(-1.16602 - 2.01961i) q^{40} +(-0.803413 + 0.463851i) q^{41} +(2.22356 - 3.85131i) q^{43} +(-0.448348 + 0.258854i) q^{44} +(-3.70018 + 2.13630i) q^{45} +(1.91670 - 1.10661i) q^{46} +(-3.32915 + 1.92209i) q^{47} +(-5.46556 + 9.46662i) q^{48} +(5.19572 - 2.99975i) q^{50} +(-0.806883 - 1.39756i) q^{51} +(-0.347577 - 0.0676087i) q^{52} +(-2.72727 + 4.72377i) q^{53} +(7.91890 + 4.57198i) q^{54} +(2.12431 + 3.67941i) q^{55} +16.8397i q^{57} +3.14446i q^{58} +(-9.52106 + 5.49698i) q^{59} +(-0.197495 - 0.114024i) q^{60} -7.30215 q^{61} +(-2.39673 - 4.15126i) q^{62} -8.35330 q^{64} +(-0.554837 + 2.85243i) q^{65} +(10.4729 - 18.1396i) q^{66} -7.34556i q^{67} +(0.0275031 - 0.0476367i) q^{68} +(2.31199 - 4.00448i) q^{69} +(-8.06668 - 4.65730i) q^{71} +15.3396i q^{72} +(4.33139 + 2.50073i) q^{73} +(-0.856364 - 1.48327i) q^{74} +(6.26726 - 10.8552i) q^{75} +(-0.497091 + 0.286996i) q^{76} +(13.5462 - 4.66237i) q^{78} +(-5.68437 - 9.84562i) q^{79} +3.05772i q^{80} +3.20012 q^{81} +1.27935 q^{82} +5.81962i q^{83} +(-0.390935 - 0.225707i) q^{85} +(-5.31117 + 3.06641i) q^{86} +(3.28479 + 5.68943i) q^{87} +15.2535 q^{88} +(-4.33832 - 2.50473i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(-8.67305 - 5.00739i) q^{93} +5.30133 q^{94} +(2.35526 + 4.07942i) q^{95} +(-1.38492 + 0.799583i) q^{96} +(-9.22171 - 5.32416i) q^{97} -27.9464i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more