LMFDB - Embedded newform 637.2.q.i.491.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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([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("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (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:	$5.08647060876$
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			491.5
Root			$-1.38488 - 0.286553i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.i.589.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19430 - 0.689527i) q^{2} +(1.44060 + 2.49520i) q^{3} +(-0.0491037 + 0.0850501i) q^{4} -0.805948i q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +O(q^{10})$	\(q+(1.19430 - 0.689527i) q^{2} +(1.44060 + 2.49520i) q^{3} +(-0.0491037 + 0.0850501i) q^{4} -0.805948i q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +(-0.555723 - 0.962541i) q^{10} +(-4.56532 + 2.63579i) q^{11} -0.282955 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} +7.31083i q^{18} +(5.06165 + 2.92234i) q^{19} +(0.0685460 + 0.0395750i) q^{20} +(-3.63490 + 6.29583i) q^{22} +(-0.802438 - 1.38986i) q^{23} +(-7.21995 + 4.16844i) q^{24} +4.35045 q^{25} +(0.949380 - 4.88078i) q^{26} -6.63060 q^{27} +(-1.14008 - 1.97467i) q^{29} +(1.60115 - 2.77328i) q^{30} -3.47590i q^{31} +(-0.480674 - 0.277517i) q^{32} +(-13.1536 - 7.59424i) q^{33} -0.772411i q^{34} +(-0.260315 - 0.450879i) q^{36} +(-1.07557 + 0.620979i) q^{37} +8.06014 q^{38} +(10.1972 + 1.98350i) q^{39} +2.33205 q^{40} +(-0.803413 + 0.463851i) q^{41} +(2.22356 - 3.85131i) q^{43} -0.517708i q^{44} +(3.70018 + 2.13630i) q^{45} +(-1.91670 - 1.10661i) q^{46} -3.84418i q^{47} +(-5.46556 + 9.46662i) q^{48} +(5.19572 - 2.99975i) q^{50} +1.61377 q^{51} +(0.115238 + 0.334815i) q^{52} +5.45454 q^{53} +(-7.91890 + 4.57198i) q^{54} +(2.12431 + 3.67941i) q^{55} +16.8397i q^{57} +(-2.72318 - 1.57223i) q^{58} +(9.52106 + 5.49698i) q^{59} +0.228047i q^{60} +(3.65107 - 6.32385i) q^{61} +(-2.39673 - 4.15126i) q^{62} -8.35330 q^{64} +(-2.19286 - 1.90672i) q^{65} -20.9458 q^{66} +(-6.36144 + 3.67278i) q^{67} +(0.0275031 + 0.0476367i) q^{68} +(2.31199 - 4.00448i) q^{69} +(-8.06668 - 4.65730i) q^{71} +(-13.2845 - 7.66982i) q^{72} -5.00146i 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} +11.3687 q^{79} +(2.64806 - 1.52886i) q^{80} +(-1.60006 - 2.77138i) q^{81} +(-0.639676 + 1.10795i) q^{82} +5.81962i q^{83} +(-0.390935 - 0.225707i) q^{85} -6.13281i q^{86} +(3.28479 - 5.68943i) q^{87} +(-7.62677 - 13.2100i) q^{88} +(4.33832 - 2.50473i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(8.67305 - 5.00739i) q^{93} +(-2.65067 - 4.59109i) q^{94} +(2.35526 - 4.07942i) q^{95} -1.59917i q^{96} +(-9.22171 - 5.32416i) q^{97} -27.9464i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9	$ 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9} - 12 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 3 q^{23} + 15 q^{24} + 10 q^{25} - 15 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} - 6 q^{33} - 13 q^{36} - 15 q^{37} + 38 q^{38} + 5 q^{39} - 2 q^{40} + 6 q^{41} + 11 q^{43} - 9 q^{45} + 30 q^{46} - 19 q^{48} + 18 q^{50} - 8 q^{51} + 40 q^{52} + 16 q^{53} + 6 q^{54} + 15 q^{55} + 24 q^{58} + 27 q^{59} - 5 q^{61} - 41 q^{62} + 2 q^{64} - 18 q^{65} - 68 q^{66} - 15 q^{67} + 11 q^{68} - 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} + 70 q^{79} - 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 10 q^{87} - 14 q^{88} + 48 q^{89} - 66 q^{92} + 81 q^{93} - q^{94} + 2 q^{95} + 3 q^{97}+O(q^{100}) $ 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9 - 12 * q^10 - 12 * q^11 - 2 * q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 3 * q^23 + 15 * q^24 + 10 * q^25 - 15 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 - 6 * q^33 - 13 * q^36 - 15 * q^37 + 38 * q^38 + 5 * q^39 - 2 * q^40 + 6 * q^41 + 11 * q^43 - 9 * q^45 + 30 * q^46 - 19 * q^48 + 18 * q^50 - 8 * q^51 + 40 * q^52 + 16 * q^53 + 6 * q^54 + 15 * q^55 + 24 * q^58 + 27 * q^59 - 5 * q^61 - 41 * q^62 + 2 * q^64 - 18 * q^65 - 68 * q^66 - 15 * q^67 + 11 * q^68 - 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 + 70 * q^79 - 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 10 * q^87 - 14 * q^88 + 48 * q^89 - 66 * q^92 + 81 * q^93 - q^94 + 2 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.19430	−	0.689527i	0.844495	−	0.487570i	−0.0142944	−	0.999898i	$-0.504550\pi$
$2$	1.19430	−	0.689527i	0.844495	−	0.487570i	0.858790	+	0.512328i	$0.171217\pi$
$3$	1.44060	+	2.49520i	0.831732	+	1.44060i	0.896664	+	0.442712i	$0.145984\pi$
$3$	1.44060	+	2.49520i	0.831732	+	1.44060i	−0.0649323	+	0.997890i	$0.520683\pi$
$4$	−0.0491037	+	0.0850501i	−0.0245518	+	0.0425250i
$5$		−	0.805948i		−	0.360431i	−0.983627	−	0.180216i	$-0.942320\pi$
$5$		−	0.805948i		−	0.360431i	0.983627	−	0.180216i	$-0.0576795\pi$
$6$	3.44101	+	1.98667i	1.40479	+	0.811054i
$7$		0			0
$7$		0			0
$8$			2.89354i			1.02302i
$9$	−2.65067	+	4.59109i	−0.883555	+	1.53036i
$10$	−0.555723	−	0.962541i	−0.175735	−	0.304382i
$11$	−4.56532	+	2.63579i	−1.37650	+	0.794720i	−0.991736	−	0.128296i	$-0.959049\pi$
$11$	−4.56532	+	2.63579i	−1.37650	+	0.794720i	−0.384760	+	0.923017i	$0.625716\pi$
$12$	−0.282955			−0.0816822
$13$	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	−0.830064	−	0.557668i	$-0.811696\pi$
$17$	0.280051	−	0.485062i	0.0679223	−	0.117645i	0.897987	+	0.440023i	$0.145030\pi$
$18$			7.31083i			1.72318i
$19$	5.06165	+	2.92234i	1.16122	+	0.670431i	0.951596	−	0.307351i	$-0.0994424\pi$
$19$	5.06165	+	2.92234i	1.16122	+	0.670431i	0.209625	+	0.977782i	$0.432776\pi$
$20$	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	0.770157	−	0.637855i	$-0.220178\pi$
$23$	−0.802438	−	1.38986i	−0.167320	−	0.289807i	−0.937477	+	0.348048i	$0.886845\pi$
$24$	−7.21995	+	4.16844i	−1.47377	+	0.850880i
$25$	4.35045			0.870089
$26$	0.949380	−	4.88078i	0.186189	−	0.957199i
$27$	−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	$0.901236\pi$
$30$	1.60115	−	2.77328i	0.292329	−	0.506329i
$31$		−	3.47590i		−	0.624290i	−0.950034	−	0.312145i	$-0.898952\pi$
$31$		−	3.47590i		−	0.624290i	0.950034	−	0.312145i	$-0.101048\pi$
$32$	−0.480674	−	0.277517i	−0.0849719	−	0.0490585i
$33$	−13.1536	−	7.59424i	−2.28975	−	1.32199i
$34$		−	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	$-0.699219\pi$
$37$	−1.07557	+	0.620979i	−0.176822	+	0.102088i	0.408977	+	0.912545i	$0.365886\pi$
$38$	8.06014			1.30753
$39$	10.1972	+	1.98350i	1.63286	+	0.317614i
$40$	2.33205			0.368729
$41$	−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	$0.0565478\pi$
$44$		−	0.517708i		−	0.0780474i
$45$	3.70018	+	2.13630i	0.551590	+	0.318461i
$46$	−1.91670	−	1.10661i	−0.282602	−	0.163160i
$47$		−	3.84418i		−	0.560731i	−0.959893	−	0.280365i	$-0.909544\pi$
$47$		−	3.84418i		−	0.560731i	0.959893	−	0.280365i	$-0.0904556\pi$
$48$	−5.46556	+	9.46662i	−0.788885	+	1.36639i
$49$		0			0
$50$	5.19572	−	2.99975i	0.734786	−	0.424229i
$51$	1.61377			0.225973
$52$	0.115238	+	0.334815i	0.0159806	+	0.0464305i
$53$	5.45454			0.749239			0.374620	−	0.927179i	$-0.377773\pi$
$53$	5.45454			0.749239			0.374620	+	0.927179i	$0.377773\pi$
$54$	−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
$58$	−2.72318	−	1.57223i	−0.357571	−	0.206444i
$59$	9.52106	+	5.49698i	1.23954	+	0.715646i	0.968999	−	0.247063i	$-0.0794655\pi$
$59$	9.52106	+	5.49698i	1.23954	+	0.715646i	0.270537	+	0.962710i	$0.412799\pi$
$60$			0.228047i			0.0294408i
$61$	3.65107	−	6.32385i	0.467472	−	0.809686i	−0.531837	−	0.846847i	$-0.678498\pi$
$61$	3.65107	−	6.32385i	0.467472	−	0.809686i	0.999309	+	0.0371610i	$0.0118314\pi$
$62$	−2.39673	−	4.15126i	−0.304385	−	0.527210i
$63$		0			0
$64$	−8.35330			−1.04416
$65$	−2.19286	−	1.90672i	−0.271990	−	0.236499i
$66$	−20.9458			−2.57824
$67$	−6.36144	+	3.67278i	−0.777174	+	0.448701i	−0.835428	−	0.549600i	$-0.814780\pi$
$67$	−6.36144	+	3.67278i	−0.777174	+	0.448701i	0.0582541	+	0.998302i	$0.481447\pi$
$68$	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	$0.853077\pi$
$72$	−13.2845	−	7.66982i	−1.56559	−	0.903896i
$73$		−	5.00146i		−	0.585376i	−0.956208	−	0.292688i	$-0.905450\pi$
$73$		−	5.00146i		−	0.585376i	0.956208	−	0.292688i	$-0.0945498\pi$
$74$	−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
$79$	11.3687			1.27908			0.639542	−	0.768756i	$-0.279124\pi$
$79$	11.3687			1.27908			0.639542	+	0.768756i	$0.279124\pi$
$80$	2.64806	−	1.52886i	0.296062	−	0.170932i
$81$	−1.60006	−	2.77138i	−0.177784	−	0.307931i
$82$	−0.639676	+	1.10795i	−0.0706404	+	0.122353i
$83$			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
$86$		−	6.13281i		−	0.661318i
$87$	3.28479	−	5.68943i	0.352167	−	0.609971i
$88$	−7.62677	−	13.2100i	−0.813016	−	1.40819i
$89$	4.33832	−	2.50473i	0.459861	−	0.265501i	−0.252125	−	0.967695i	$-0.581129\pi$
$89$	4.33832	−	2.50473i	0.459861	−	0.265501i	0.711986	+	0.702194i	$0.247796\pi$
$90$	5.89215			0.621087
$91$		0			0
$92$	0.157611			0.0164320
$93$	8.67305	−	5.00739i	0.899354	−	0.519242i
$94$	−2.65067	−	4.59109i	−0.273395	−	0.473534i
$95$	2.35526	−	4.07942i	0.241644	−	0.418540i
$96$		−	1.59917i		−	0.163214i
$97$	−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
$100$	−0.213623	+	0.370006i	−0.0213623	+	0.0370006i
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	0.752031	−	0.659127i	$-0.229074\pi$
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	−0.946837	+	0.321715i	$0.895741\pi$
$102$	1.92732	−	1.11274i	0.190833	−	0.110177i
$103$	8.45379			0.832977			0.416488	−	0.909141i	$-0.363261\pi$
$103$	8.45379			0.832977			0.416488	+	0.909141i	$0.363261\pi$
$104$	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	0.999318	−	0.0369379i	$-0.0117604\pi$
$107$	4.83761	+	8.37899i	0.467670	+	0.810028i	−0.531648	+	0.846965i	$0.678427\pi$
$108$	0.325587	−	0.563933i	0.0313296	−	0.0542645i
$109$		−	14.5638i		−	1.39496i	−0.716606	−	0.697478i	$-0.754305\pi$
$109$		−	14.5638i		−	1.39496i	0.716606	−	0.697478i	$-0.245695\pi$
$110$	5.07411	+	2.92954i	0.483798	+	0.279321i
$111$	−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
$115$	−1.12016	+	0.646723i	−0.104455	+	0.0603073i
$116$	0.223928			0.0207912
$117$	6.22065	+	18.0737i	0.575100	+	1.67091i
$118$	15.1613			1.39571
$119$		0			0
$120$	3.35955	+	5.81891i	0.306683	+	0.531191i
$121$	8.39477	−	14.5402i	0.763161	−	1.32183i
$122$		−	10.0701i		−	0.911701i
$123$	−2.31480	−	1.33645i	−0.208718	−	0.120503i
$124$	0.295626	+	0.170680i	0.0265480	+	0.0153275i
$125$		−	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
$129$	12.8130			1.12813
$130$	−3.93365	−	0.765151i	−0.345004	−	0.0671082i
$131$	−15.5816			−1.36137			−0.680684	−	0.732577i	$-0.738317\pi$
$131$	−15.5816			−1.36137			−0.680684	+	0.732577i	$0.738317\pi$
$132$	1.29178	−	0.745811i	0.112435	−	0.0649145i
$133$		0			0
$134$	−5.06496	+	8.77278i	−0.437546	+	0.757852i
$135$			5.34392i			0.459932i
$136$	1.40355	+	0.810339i	0.120353	+	0.0694860i
$137$	−6.79921	−	3.92553i	−0.580896	−	0.335380i	0.180594	−	0.983558i	$-0.442198\pi$
$137$	−6.79921	−	3.92553i	−0.580896	−	0.335380i	−0.761489	+	0.648178i	$0.775531\pi$
$138$		−	6.37671i		−	0.542822i
$139$	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
$142$	−12.8453			−1.07796
$143$	−3.62910	+	18.6573i	−0.303481	+	1.56020i
$144$	−20.1129			−1.67608
$145$	−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
$149$	−6.85827	−	3.95962i	−0.561851	−	0.324385i	0.192037	−	0.981388i	$-0.438491\pi$
$149$	−6.85827	−	3.95962i	−0.561851	−	0.324385i	−0.753888	+	0.657003i	$0.771824\pi$
$150$	14.9699	+	8.64290i	1.22229	+	0.705690i
$151$			1.50116i			0.122163i	0.998133	+	0.0610815i	$0.0194550\pi$
$151$			1.50116i			0.122163i	−0.998133	+	0.0610815i	$0.980545\pi$
$152$	−8.45592	+	14.6461i	−0.685866	+	1.18795i
$153$	1.48464	+	2.57148i	0.120026	+	0.207892i
$154$		0			0
$155$	−2.80140			−0.225014
$156$	−0.669417	+	0.769876i	−0.0535963	+	0.0616394i
$157$	−3.85692			−0.307816			−0.153908	−	0.988085i	$-0.549186\pi$
$157$	−3.85692			−0.307816			−0.153908	+	0.988085i	$0.549186\pi$
$158$	13.5777	−	7.83906i	1.08018	−	0.623642i
$159$	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
$163$	−12.4369	−	7.18042i	−0.974130	−	0.562414i	−0.0736372	−	0.997285i	$-0.523461\pi$
$163$	−12.4369	−	7.18042i	−0.974130	−	0.562414i	−0.900493	+	0.434871i	$0.856794\pi$
$164$		−	0.0911072i		−	0.00711427i
$165$	−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
$170$	−0.622523			−0.0477454
$171$	−26.8335	+	15.4923i	−2.05201	+	1.18473i
$172$	0.218370	+	0.378227i	0.0166505	+	0.0288396i
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	−0.209642	−	0.977778i	$-0.567230\pi$
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	0.951602	−	0.307334i	$-0.0994369\pi$
$174$		−	9.05982i		−	0.686823i
$175$		0			0
$176$	−17.3206	−	10.0000i	−1.30559	−	0.753780i
$177$			31.6759i			2.38090i
$178$	3.45416	−	5.98278i	0.258900	−	0.448428i
$179$	10.4098	+	18.0303i	0.778065	+	1.34765i	0.933055	+	0.359733i	$0.117132\pi$
$179$	10.4098	+	18.0303i	0.778065	+	1.34765i	−0.154990	+	0.987916i	$0.549535\pi$
$180$	−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
$185$	0.500477	+	0.866851i	0.0367958	+	0.0637322i
$186$	6.90546	−	11.9606i	0.506333	−	0.876995i
$187$			2.95262i			0.215917i
$188$	0.326948	+	0.188763i	0.0238451	+	0.0137670i
$189$		0			0
$190$		−	6.49606i		−	0.471274i
$191$	2.12504	−	3.68068i	0.153762	−	0.266324i	−0.778845	−	0.627216i	$-0.784194\pi$
$191$	2.12504	−	3.68068i	0.153762	−	0.266324i	0.932608	+	0.360892i	$0.117528\pi$
$192$	−12.0338	−	20.8431i	−0.868463	−	1.50422i
$193$	10.0435	−	5.79861i	0.722946	−	0.417393i	−0.0928898	−	0.995676i	$-0.529610\pi$
$193$	10.0435	−	5.79861i	0.722946	−	0.417393i	0.815836	+	0.578283i	$0.196277\pi$
$194$	−14.6846			−1.05429
$195$	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	−0.963583	−	0.267409i	$-0.913832\pi$
$199$	−3.52962	+	6.11348i	−0.250208	+	0.433373i	0.713375	+	0.700783i	$0.247166\pi$
$200$			12.5882i			0.890121i
$201$	−18.3286	−	10.5820i	−1.29280	−	0.746398i
$202$	−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
$206$	10.0963	−	5.82912i	0.703445	−	0.406134i
$207$	8.50798			0.591345
$208$	13.4276	+	2.61185i	0.931035	+	0.181099i
$209$	−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	$0.469794\pi$
$212$	−0.267838	+	0.463909i	−0.0183952	+	0.0318614i
$213$		−	26.8372i		−	1.83886i
$214$	11.5551	+	6.67133i	0.789890	+	0.456043i
$215$	−3.10396	−	1.79207i	−0.211688	−	0.122218i
$216$		−	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
$220$	−0.417246			−0.0281307
$221$	−0.657231	−	1.90954i	−0.0442101	−	0.128449i
$222$	−4.93472			−0.331197
$223$	−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
$226$			26.9073i			1.78985i
$227$	−0.392628	−	0.226684i	−0.0260596	−	0.0150455i	0.486914	−	0.873450i	$-0.338123\pi$
$227$	−0.392628	−	0.226684i	−0.0260596	−	0.0150455i	−0.512973	+	0.858405i	$0.671456\pi$
$228$	−1.43222	−	0.826893i	−0.0948511	−	0.0547623i
$229$			17.3335i			1.14543i	0.819755	+	0.572714i	$0.194110\pi$
$229$			17.3335i			1.14543i	−0.819755	+	0.572714i	$0.805890\pi$
$230$	−0.891867	+	1.54476i	−0.0588080	+	0.101858i
$231$		0			0
$232$	5.71380	−	3.29886i	0.375129	−	0.216581i
$233$	−7.81511			−0.511985			−0.255992	−	0.966679i	$-0.582402\pi$
$233$	−7.81511			−0.511985			−0.255992	+	0.966679i	$0.582402\pi$
$234$	19.8916	+	17.2960i	1.30035	+	1.13067i
$235$	−3.09821			−0.202105
$236$	−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	$-0.144185\pi$
$240$	7.62961	+	4.40496i	0.492489	+	0.284339i
$241$	−19.5369	−	11.2796i	−1.25848	−	0.726583i	−0.285701	−	0.958319i	$-0.592226\pi$
$241$	−19.5369	−	11.2796i	−1.25848	−	0.726583i	−0.972779	+	0.231736i	$0.925560\pi$
$242$		−	23.1537i		−	1.48838i
$243$	−5.33581	+	9.24189i	−0.342292	+	0.592868i
$244$	0.358563	+	0.621049i	0.0229546	+	0.0397586i
$245$		0			0
$246$	−3.68607			−0.235015
$247$	19.9261	−	6.85823i	1.26787	−	0.436379i
$248$	10.0577			0.638663
$249$	−14.5211	+	8.38375i	−0.920236	+	0.531299i
$250$	−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
$254$	−2.28984	−	1.32204i	−0.143677	−	0.0829521i
$255$		−	1.30061i		−	0.0814475i
$256$	1.17560	−	2.03620i	0.0734750	−	0.127262i
$257$	−8.26907	−	14.3225i	−0.515811	−	0.893410i	−0.999832	−	0.0183536i	$-0.994158\pi$
$257$	−8.26907	−	14.3225i	−0.515811	−	0.893410i	0.484021	−	0.875056i	$-0.339176\pi$
$258$	15.3026	−	8.83494i	0.952696	−	0.550039i
$259$		0			0
$260$	0.269844	−	0.0928757i	0.0167350	−	0.00575991i
$261$	12.0878			0.748219
$262$	−18.6090	+	10.7439i	−1.14967	+	0.663761i
$263$	5.01137	+	8.67994i	0.309014	+	0.535228i	0.978147	−	0.207915i	$-0.0666676\pi$
$263$	5.01137	+	8.67994i	0.309014	+	0.535228i	−0.669133	+	0.743143i	$0.733334\pi$
$264$	21.9743	−	38.0606i	1.35242	−	2.34247i
$265$		−	4.39608i		−	0.270049i
$266$		0			0
$267$	12.4996	+	7.21663i	0.764962	+	0.441651i
$268$		−	0.721388i		−	0.0440658i
$269$	−7.86149	+	13.6165i	−0.479323	+	0.830212i	−0.999719	−	0.0237130i	$-0.992451\pi$
$269$	−7.86149	+	13.6165i	−0.479323	+	0.830212i	0.520395	+	0.853925i	$0.325785\pi$
$270$	3.68478	+	6.38223i	0.224249	+	0.388410i
$271$	−4.51734	+	2.60809i	−0.274409	+	0.158430i	−0.630890	−	0.775873i	$-0.717310\pi$
$271$	−4.51734	+	2.60809i	−0.274409	+	0.158430i	0.356481	+	0.934303i	$0.383977\pi$
$272$	2.12499			0.128847
$273$		0			0
$274$	−10.8270			−0.654085
$275$	−19.8612	+	11.4669i	−1.19767	+	0.691478i
$276$	0.227054	+	0.393269i	0.0136671	+	0.0236720i
$277$	−9.63619	+	16.6904i	−0.578983	+	1.00283i	0.416614	+	0.909084i	$0.363217\pi$
$277$	−9.63619	+	16.6904i	−0.578983	+	1.00283i	−0.995596	+	0.0937439i	$0.970117\pi$
$278$		−	13.6869i		−	0.820884i
$279$	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	$-0.0203588\pi$
$282$	7.63711	−	13.2279i	0.454783	−	0.787707i
$283$	7.87512	+	13.6401i	0.468127	+	0.810820i	0.999337	−	0.0364203i	$-0.0115955\pi$
$283$	7.87512	+	13.6401i	0.468127	+	0.810820i	−0.531209	+	0.847241i	$0.678262\pi$
$284$	0.792207	−	0.457381i	0.0470089	−	0.0271406i
$285$	13.5719			0.803933
$286$	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
$291$		−	30.6800i		−	1.79849i
$292$	0.425374	+	0.245590i	0.0248932	+	0.0143721i
$293$	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
$297$	30.2708	−	17.4769i	1.75649	−	1.01411i
$298$	−10.9211			−0.632641
$299$	−5.68001	−	1.10484i	−0.328483	−	0.0638946i
$300$	−1.23098			−0.0710708
$301$		0			0
$302$	1.03509	+	1.79283i	0.0595629	+	0.103166i
$303$	5.64073	−	9.77003i	0.324052	−	0.561274i
$304$			22.1744i			1.27179i
$305$	−5.09669	−	2.94258i	−0.291836	−	0.168491i
$306$	3.54621	+	2.04740i	0.202723	+	0.117042i
$307$		−	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
$311$	27.2501			1.54521			0.772606	−	0.634885i	$-0.218953\pi$
$311$	27.2501			1.54521			0.772606	+	0.634885i	$0.218953\pi$
$312$	−5.73934	+	29.5061i	−0.324926	+	1.67045i
$313$	−2.69697			−0.152442			−0.0762209	−	0.997091i	$-0.524285\pi$
$313$	−2.69697			−0.152442			−0.0762209	+	0.997091i	$0.524285\pi$
$314$	−4.60631	+	2.65945i	−0.259949	+	0.150082i
$315$		0			0
$316$	−0.558247	+	0.966913i	−0.0314039	+	0.0543931i
$317$		−	24.0705i		−	1.35193i	−0.736933	−	0.675966i	$-0.763727\pi$
$317$		−	24.0705i		−	1.35193i	0.736933	−	0.675966i	$-0.236273\pi$
$318$	18.7691	+	10.8364i	1.05252	+	0.607674i
$319$	10.4096	+	6.01000i	0.582828	+	0.336496i
$320$			6.73233i			0.376349i
$321$	−13.9381	+	24.1416i	−0.777951	+	1.34745i
$322$		0			0
$323$	2.83504	−	1.63681i	0.157746	−	0.0910745i
$324$	0.314275			0.0174597
$325$	10.2923	−	11.8369i	0.570915	−	0.656591i
$326$	−19.8044			−1.09686
$327$	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
$331$	−0.536696	−	0.309862i	−0.0294995	−	0.0170315i	0.485178	−	0.874416i	$-0.338755\pi$
$331$	−0.536696	−	0.309862i	−0.0294995	−	0.0170315i	−0.514677	+	0.857384i	$0.672088\pi$
$332$	−0.494959	−	0.285765i	−0.0271644	−	0.0156834i
$333$		−	6.58403i		−	0.360803i
$334$	3.11762	−	5.39987i	0.170588	−	0.295468i
$335$	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	$0.549804\pi$
$338$	−11.0338	−	14.1301i	−0.600158	−	0.768575i
$339$	−56.2164			−3.05326
$340$	0.0383927	−	0.0221660i	0.00208214	−	0.00120212i
$341$	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
$345$	−3.22740	−	1.86334i	−0.173757	−	0.100319i
$346$		−	26.9163i		−	1.44703i
$347$	0.932429	−	1.61501i	0.0500554	−	0.0866985i	−0.839912	−	0.542722i	$-0.817394\pi$
$347$	0.932429	−	1.61501i	0.0500554	−	0.0866985i	0.889968	+	0.456024i	$0.150727\pi$
$348$	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
$352$	2.92591			0.155951
$353$	2.01956	−	1.16600i	0.107491	−	0.0620597i	−0.445291	−	0.895386i	$-0.646900\pi$
$353$	2.01956	−	1.16600i	0.107491	−	0.0620597i	0.552781	+	0.833326i	$0.313566\pi$
$354$	21.8414	+	37.8304i	1.16086	+	2.01066i
$355$	−3.75354	+	6.50133i	−0.199217	+	0.345055i
$356$			0.491966i			0.0260741i
$357$		0			0
$358$	24.8648	+	14.3557i	1.31415	+	0.758722i
$359$			3.27105i			0.172639i	0.996267	+	0.0863197i	$0.0275107\pi$
$359$			3.27105i			0.172639i	−0.996267	+	0.0863197i	$0.972489\pi$
$360$	−6.18147	+	10.7066i	−0.325792	+	0.564289i
$361$	7.58017	+	13.1292i	0.398956	+	0.691013i
$362$	−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
$367$	2.07645	+	3.59652i	0.108390	+	0.187737i	0.915118	−	0.403186i	$-0.132097\pi$
$367$	2.07645	+	3.59652i	0.108390	+	0.187737i	−0.806728	+	0.590923i	$0.798764\pi$
$368$	3.04440	−	5.27306i	0.158700	−	0.274877i
$369$		−	4.91805i		−	0.256024i
$370$	1.19544	+	0.690185i	0.0621477	+	0.0358810i
$371$		0			0
$372$			0.983525i			0.0509934i
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	−0.685637	−	0.727944i	$-0.740476\pi$
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	0.973236	+	0.229807i	$0.0738096\pi$
$374$	2.03591	+	3.52630i	0.105275	+	0.182341i
$375$	18.8037	−	10.8563i	0.971021	−	0.560619i
$376$	11.1233			0.573640
$377$	−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
$382$		−	5.86109i		−	0.299880i
$383$	−3.17773	−	1.83466i	−0.162374	−	0.0937469i	0.416611	−	0.909085i	$-0.363218\pi$
$383$	−3.17773	−	1.83466i	−0.162374	−	0.0937469i	−0.578985	+	0.815338i	$0.696551\pi$
$384$	−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
$388$	0.905640	−	0.522872i	0.0459769	−	0.0265448i
$389$	−16.8831			−0.856008			−0.428004	−	0.903777i	$-0.640783\pi$
$389$	−16.8831			−0.856008			−0.428004	+	0.903777i	$0.640783\pi$
$390$	−3.75763	−	10.9175i	−0.190275	−	0.552830i
$391$	−0.898894			−0.0454590
$392$		0			0
$393$	−22.4468	−	38.8790i	−1.13229	−	1.96119i
$394$	−9.94390	+	17.2233i	−0.500966	+	0.867699i
$395$		−	9.16262i		−	0.461021i
$396$	2.37684	+	1.37227i	0.119441	+	0.0689592i
$397$	−14.4700	−	8.35428i	−0.726230	−	0.419289i	0.0908114	−	0.995868i	$-0.471054\pi$
$397$	−14.4700	−	8.35428i	−0.726230	−	0.419289i	−0.817041	+	0.576579i	$0.804387\pi$
$398$			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	$-0.884451\pi$
$401$	−21.9221	+	12.6567i	−1.09474	+	0.632046i	−0.159902	+	0.987133i	$0.551118\pi$
$402$	−29.1864			−1.45568
$403$	−9.45737	−	8.22331i	−0.471105	−	0.409632i
$404$	0.384535			0.0191313
$405$	−2.23359	+	1.28956i	−0.110988	+	0.0640789i
$406$		0			0
$407$	3.27354	−	5.66994i	0.162263	−	0.281048i
$408$			4.66950i			0.231175i
$409$	4.96529	+	2.86671i	0.245518	+	0.141750i	0.617710	−	0.786406i	$-0.288060\pi$
$409$	4.96529	+	2.86671i	0.245518	+	0.141750i	−0.372192	+	0.928156i	$0.621394\pi$
$410$	0.892951	+	0.515546i	0.0440997	+	0.0254610i
$411$		−	22.6205i		−	1.11579i
$412$	−0.415112	+	0.718996i	−0.0204511	+	0.0354224i
$413$		0			0
$414$	10.1610	−	5.86648i	0.499388	−	0.288322i
$415$	4.69031			0.230238
$416$	−1.89226	+	0.651284i	−0.0927756	+	0.0319318i
$417$	28.5954			1.40032
$418$	−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	$-0.0228374\pi$
$422$	31.5565	+	18.2191i	1.53614	+	0.886894i
$423$	17.6489	+	10.1896i	0.858121	+	0.495437i
$424$			15.7830i			0.766488i
$425$	1.21835	−	2.11024i	0.0590985	−	0.102362i
$426$	−18.5050	−	32.0516i	−0.896571	−	1.55291i
$427$		0			0
$428$	−0.950178			−0.0459286
$429$	−51.7816	+	17.8224i	−2.50004	+	0.860472i
$430$	−4.94273			−0.238360
$431$	−34.3773	+	19.8478i	−1.65590	+	0.956033i	−0.681321	+	0.731985i	$0.738594\pi$
$431$	−34.3773	+	19.8478i	−1.65590	+	0.956033i	−0.974578	+	0.224048i	$0.928073\pi$
$432$	−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
$436$	1.23865	+	0.715135i	0.0593206	+	0.0342488i
$437$		−	9.37999i		−	0.448706i
$438$	9.93624	−	17.2101i	0.474772	−	0.822329i
$439$	−14.2733	−	24.7220i	−0.681226	−	1.17992i	−0.974607	−	0.223922i	$-0.928114\pi$
$439$	−14.2733	−	24.7220i	−0.681226	−	1.17992i	0.293381	−	0.955996i	$-0.405220\pi$
$440$	−10.6465	+	6.14678i	−0.507554	+	0.293036i
$441$		0			0
$442$	−2.10161	−	1.82737i	−0.0999632	−	0.0869193i
$443$	3.33901			0.158641			0.0793207	−	0.996849i	$-0.474725\pi$
$443$	3.33901			0.158641			0.0793207	+	0.996849i	$0.474725\pi$
$444$	0.304337	−	0.175709i	0.0144432	−	0.00833880i
$445$	−2.01868	−	3.49646i	−0.0956947	−	0.165748i
$446$	−15.8595	+	27.4695i	−0.750969	+	1.30072i
$447$		−	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	$0.525496\pi$
$450$			31.8054i			1.49932i
$451$	2.44523	−	4.23526i	0.115141	−	0.199430i
$452$	−0.958084	−	1.65945i	−0.0450645	−	0.0780539i
$453$	−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	$-0.732116\pi$
$457$	−7.55982	+	4.36466i	−0.353633	+	0.204170i	0.312651	+	0.949868i	$0.398783\pi$
$458$	11.9519	+	20.7013i	0.558476	+	0.967309i
$459$	−1.85691	+	3.21625i	−0.0866729	+	0.150122i
$460$		−	0.127026i		−	0.00592262i
$461$	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	$-0.0406678\pi$
$464$	4.32538	−	7.49178i	0.200801	−	0.347797i
$465$	−4.03570	−	6.99003i	−0.187151	−	0.324155i
$466$	−9.33356	+	5.38873i	−0.432369	+	0.249628i
$467$	18.8819			0.873750			0.436875	−	0.899522i	$-0.356085\pi$
$467$	18.8819			0.873750			0.436875	+	0.899522i	$0.356085\pi$
$468$	−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
$473$			23.4433i			1.07792i
$474$	39.1200	+	22.5859i	1.79684	+	1.03741i
$475$	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
$479$	−28.6961	+	16.5677i	−1.31116	+	0.756997i	−0.982288	−	0.187378i	$-0.940001\pi$
$479$	−28.6961	+	16.5677i	−1.31116	+	0.756997i	−0.328869	+	0.944375i	$0.606668\pi$
$480$	−1.28884			−0.0588275
$481$	−0.854998	+	4.39556i	−0.0389846	+	0.200420i
$482$	−31.1104			−1.41704
$483$		0			0
$484$	0.824428	+	1.42795i	0.0374740	+	0.0649069i
$485$	−4.29100	+	7.43222i	−0.194844	+	0.337480i
$486$			14.7168i			0.667565i
$487$	13.8185	+	7.97814i	0.626178	+	0.361524i	0.779270	−	0.626688i	$-0.215590\pi$
$487$	13.8185	+	7.97814i	0.626178	+	0.361524i	−0.153093	+	0.988212i	$0.548923\pi$
$488$	18.2983	+	10.5645i	0.828326	+	0.478234i
$489$		−	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
$493$	−1.27712			−0.0575185
$494$	19.0687	−	21.9304i	0.857942	−	0.986693i
$495$	−22.5233			−1.01235
$496$	11.4206	−	6.59368i	0.512800	−	0.296065i
$497$		0			0
$498$	−11.5617	+	20.0254i	−0.518090	+	0.897358i
$499$		−	24.2184i		−	1.08417i	−0.840325	−	0.542083i	$-0.817636\pi$
$499$		−	24.2184i		−	1.08417i	0.840325	−	0.542083i	$-0.182364\pi$
$500$	0.640935	+	0.370044i	0.0286635	+	0.0165489i
$501$	11.2817	+	6.51351i	0.504030	+	0.291002i
$502$		−	9.28429i		−	0.414378i
$503$	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
$506$	11.6671			0.518667
$507$	29.5214	−	23.0524i	1.31109	−	1.02379i
$508$	0.188294			0.00835420
$509$	−1.12583	+	0.650000i	−0.0499017	+	0.0288108i	−0.524743	−	0.851261i	$-0.675839\pi$
$509$	−1.12583	+	0.650000i	−0.0499017	+	0.0288108i	0.474842	+	0.880071i	$0.342505\pi$
$510$	−0.896808	−	1.55332i	−0.0397113	−	0.0687820i
$511$		0			0
$512$		−	24.0616i		−	1.06338i
$513$	−33.5618	−	19.3769i	−1.48179	−	0.855511i
$514$	−19.7514	−	11.4035i	−0.871199	−	0.502987i
$515$		−	6.81332i		−	0.300231i
$516$	−0.629167	+	1.08975i	−0.0276976	+	0.0479736i
$517$	10.1324	+	17.5499i	0.445624	+	0.771844i
$518$		0			0
$519$	56.2351			2.46845
$520$	5.51717	−	6.34512i	0.241944	−	0.278252i
$521$	25.0455			1.09726			0.548632	−	0.836064i	$-0.315149\pi$
$521$	25.0455			1.09726			0.548632	+	0.836064i	$0.315149\pi$
$522$	14.4365	−	8.33490i	0.631867	−	0.364809i
$523$	6.41197	+	11.1059i	0.280376	+	0.485625i	0.971477	−	0.237133i	$-0.0762076\pi$
$523$	6.41197	+	11.1059i	0.280376	+	0.485625i	−0.691101	+	0.722758i	$0.742874\pi$
$524$	0.765112	−	1.32521i	0.0334241	−	0.0578922i
$525$		0			0
$526$	11.9701	+	6.91095i	0.521922	+	0.301332i
$527$	−1.68603	−	0.973429i	−0.0734446	−	0.0424032i
$528$		−	57.6242i		−	2.50777i
$529$	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
$534$	19.9043			0.861342
$535$	6.75303	−	3.89886i	0.291959	−	0.168563i
$536$	−10.6273	−	18.4071i	−0.459031	−	0.795066i
$537$	−29.9928	+	51.9490i	−1.29428	+	2.24176i
$538$			21.6828i			0.934814i
$539$		0			0
$540$	−0.454501	−	0.262406i	−0.0195586	−	0.0112922i
$541$			28.7449i			1.23584i	0.786241	+	0.617920i	$0.212025\pi$
$541$			28.7449i			1.23584i	−0.786241	+	0.617920i	$0.787975\pi$
$542$	−3.59670	+	6.22966i	−0.154491	+	0.267587i
$543$	−23.8451	−	41.3009i	−1.02329	−	1.77239i
$544$	−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
$549$	19.3556	+	33.5248i	0.826075	+	1.43080i
$550$	−15.8134	+	27.3897i	−0.674287	+	1.16790i
$551$		−	13.3268i		−	0.567740i
$552$	11.5871	+	6.68983i	0.493181	+	0.284738i
$553$		0			0
$554$			26.5777i			1.12918i
$555$	−1.44198	+	2.49757i	−0.0612084	+	0.106016i
$556$	0.487345	+	0.844106i	0.0206680	+	0.0357981i
$557$	−33.5389	+	19.3637i	−1.42109	+	0.820465i	−0.996392	−	0.0848711i	$-0.972952\pi$
$557$	−33.5389	+	19.3637i	−1.42109	+	0.820465i	−0.424695	+	0.905336i	$0.639619\pi$
$558$	25.4117			1.07576
$559$	−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	−0.929591	−	0.368592i	$-0.879840\pi$
$563$	−3.45441	+	5.98321i	−0.145586	+	0.252162i	0.784005	+	0.620754i	$0.213173\pi$
$564$			1.08773i			0.0458017i
$565$	13.6184	+	7.86260i	0.572932	+	0.330782i
$566$	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	0.834754	−	0.550623i	$-0.185610\pi$
$569$	−1.41872	−	2.45730i	−0.0594759	−	0.103015i	−0.894230	+	0.447607i	$0.852276\pi$
$570$	16.2089	−	9.35823i	0.678917	−	0.391973i
$571$	46.6724			1.95318			0.976589	−	0.215113i	$-0.0690119\pi$
$571$	46.6724			1.95318			0.976589	+	0.215113i	$0.0690119\pi$
$572$	−1.40860	−	1.22480i	−0.0588965	−	0.0512113i
$573$	12.2453			0.511557
$574$		0			0
$575$	−3.49096	−	6.04653i	−0.145583	−	0.252158i
$576$	22.1418	−	38.3507i	0.922576	−	1.59795i
$577$			11.4088i			0.474955i	0.971393	+	0.237478i	$0.0763207\pi$
$577$			11.4088i			0.474955i	−0.971393	+	0.237478i	$0.923679\pi$
$578$	19.9284	+	11.5057i	0.828911	+	0.478572i
$579$	28.9373	+	16.7070i	1.20259	+	0.694318i
$580$		−	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
$584$	14.4719			0.598853
$585$	14.5664	−	5.01352i	0.602248	−	0.207284i
$586$	31.9234			1.31874
$587$	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
$590$		−	12.2192i		−	0.503057i
$591$	−35.9840	−	20.7754i	−1.48018	−	0.854585i
$592$	−4.08064	−	2.35596i	−0.167713	−	0.0968292i
$593$			20.2606i			0.832002i	0.909364	+	0.416001i	$0.136569\pi$
$593$			20.2606i			0.832002i	−0.909364	+	0.416001i	$0.863431\pi$
$594$	24.1016	−	41.7451i	0.988899	−	1.71282i
$595$		0			0
$596$	0.673533	−	0.388864i	0.0275890	−	0.0159285i
$597$	−20.3391			−0.832424
$598$	−7.54543	+	2.59701i	−0.308556	+	0.106200i
$599$	−38.9876			−1.59299			−0.796494	−	0.604646i	$-0.793315\pi$
$599$	−38.9876			−1.59299			−0.796494	+	0.604646i	$0.793315\pi$
$600$	−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
$604$	−0.127674	−	0.0737127i	−0.00519499	−	0.00299933i
$605$	−11.7186	−	6.76575i	−0.476430	−	0.275067i
$606$		−	15.5578i		−	0.631991i
$607$	21.6668	−	37.5280i	0.879428	−	1.52321i	0.0274572	−	0.999623i	$-0.491259\pi$
$607$	21.6668	−	37.5280i	0.879428	−	1.52321i	0.851970	−	0.523590i	$-0.175408\pi$
$608$	−1.62200	−	2.80939i	−0.0657808	−	0.113936i
$609$		0			0
$610$	−8.11595			−0.328605
$611$	−10.4594	−	9.09457i	−0.423141	−	0.367927i
$612$	−0.291606			−0.0117875
$613$	−8.92834	+	5.15478i	−0.360612	+	0.208200i	−0.669349	−	0.742948i	$-0.733427\pi$
$613$	−8.92834	+	5.15478i	−0.360612	+	0.208200i	0.308737	+	0.951147i	$0.400094\pi$
$614$	−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	$0.738196\pi$
$618$	29.0896	+	16.7949i	1.17015	+	0.675589i
$619$		−	33.7616i		−	1.35700i	−0.734603	−	0.678498i	$-0.762631\pi$
$619$		−	33.7616i		−	1.35700i	0.734603	−	0.678498i	$-0.237369\pi$
$620$	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
$625$	15.6786			0.627145
$626$	−3.22098	+	1.85964i	−0.128736	+	0.0743260i
$627$	−44.3860	−	76.8787i	−1.77260	−	3.07024i
$628$	0.189389	−	0.328031i	0.00755745	−	0.0130899i
$629$			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	$0.387784\pi$
$632$			32.8959i			1.30853i
$633$	−38.0645	+	65.9296i	−1.51293	+	2.62047i
$634$	−16.5972	−	28.7473i	−0.659161	−	1.14170i
$635$	−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
$640$	4.19480	+	7.26560i	0.165814	+	0.287198i
$641$	9.76141	−	16.9073i	0.385553	−	0.667797i	−0.606293	−	0.795241i	$-0.707344\pi$
$641$	9.76141	−	16.9073i	0.385553	−	0.667797i	0.991846	+	0.127445i	$0.0406775\pi$
$642$			38.4429i			1.51722i
$643$	−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
$646$	2.25725	−	3.90967i	0.0888103	−	0.153824i
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	−0.966164	−	0.257929i	$-0.916960\pi$
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	0.259709	−	0.965687i	$-0.416373\pi$
$648$	8.01911	−	4.62984i	0.315021	−	0.181877i
$649$	−57.9556			−2.27496
$650$	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	0.814567	−	0.580069i	$-0.196975\pi$
$653$	−2.42944	−	4.20791i	−0.0950713	−	0.164668i	−0.909638	+	0.415401i	$0.863641\pi$
$654$	28.9334	−	50.1141i	1.13138	−	1.95962i
$655$			12.5579i			0.490679i
$656$	−3.04810	−	1.75982i	−0.119008	−	0.0687095i
$657$	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
$661$	14.1970	−	8.19662i	0.552198	−	0.318812i	−0.197810	−	0.980240i	$-0.563383\pi$
$661$	14.1970	−	8.19662i	0.552198	−	0.318812i	0.750008	+	0.661429i	$0.230050\pi$
$662$	−0.854633			−0.0332162
$663$	3.81786	−	4.39080i	0.148273	−	0.170525i
$664$	−16.8393			−0.653492
$665$		0			0
$666$	−4.53987	−	7.86328i	−0.175916	−	0.304696i
$667$	−1.82968	+	3.16910i	−0.0708456	+	0.122708i
$668$			0.444033i			0.0171801i
$669$	−57.3908	−	33.1346i	−2.21886	−	1.28106i
$670$	7.07040	+	4.08210i	0.273154	+	0.157705i
$671$			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
$675$	−28.8461			−1.11029
$676$	1.18361	+	0.478564i	0.0455234	+	0.0184063i
$677$	10.2715			0.394765			0.197383	−	0.980327i	$-0.436756\pi$
$677$	10.2715			0.394765			0.197383	+	0.980327i	$0.436756\pi$
$678$	−67.1391	+	38.7628i	−2.57846	+	1.48867i
$679$		0			0
$680$	0.653092	−	1.13119i	0.0250449	−	0.0433791i
$681$		−	1.30624i		−	0.0500554i
$682$	21.8837	+	12.6345i	0.837969	+	0.483802i
$683$	−1.92432	−	1.11101i	−0.0736321	−	0.0425115i	0.462732	−	0.886498i	$-0.346869\pi$
$683$	−1.92432	−	1.11101i	−0.0736321	−	0.0425115i	−0.536364	+	0.843987i	$0.680203\pi$
$684$		−	3.04292i		−	0.116349i
$685$	−3.16377	+	5.47981i	−0.120881	+	0.209373i
$686$		0			0
$687$	−43.2504	+	24.9706i	−1.65011	+	0.952689i
$688$	16.8721			0.643242
$689$	12.9044	−	14.8409i	0.491618	−	0.565395i
$690$	−5.13930			−0.195650
$691$	2.28643	−	1.32007i	0.0869800	−	0.0502179i	−0.455879	−	0.890042i	$-0.650675\pi$
$691$	2.28643	−	1.32007i	0.0869800	−	0.0502179i	0.542859	+	0.839824i	$0.317342\pi$
$692$	0.958402	+	1.66000i	0.0364330	+	0.0631038i
$693$		0			0
$694$		−	2.57174i		−	0.0976220i
$695$	−6.92724	−	3.99944i	−0.262765	−	0.151708i
$696$	16.4626	+	9.50469i	0.624014	+	0.360274i
$697$			0.519607i			0.0196815i
$698$	15.3884	−	26.6534i	0.582458	−	1.00885i
$699$	−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	$0.553754\pi$
$702$	−6.29496	+	32.3625i	−0.237588	+	1.22144i
$703$	−7.25885			−0.273773
$704$	38.1355	−	22.0175i	1.43729	−	0.829818i
$705$	−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
$709$	35.1558	+	20.2972i	1.32030	+	0.762278i	0.983777	−	0.179396i	$-0.0574143\pi$
$709$	35.1558	+	20.2972i	1.32030	+	0.762278i	0.336527	+	0.941674i	$0.390748\pi$
$710$			10.3527i			0.388529i
$711$	−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
$716$	−2.04464			−0.0764118
$717$	33.7636	−	19.4934i	1.26092	−	0.727995i
$718$	2.25548	+	3.90661i	0.0841738	+	0.145793i
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	−0.969024	−	0.246968i	$-0.920566\pi$
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	0.698393	+	0.715715i	$0.253899\pi$
$720$			16.2100i			0.604110i
$721$		0			0
$722$	18.1059	+	10.4535i	0.673834	+	0.389038i
$723$		−	64.9977i		−	2.41729i
$724$	0.812773	−	1.40776i	0.0302065	−	0.0523191i
$725$	−4.95984	−	8.59070i	−0.184204	−	0.319051i
$726$	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
$731$	−1.24542	−	2.15713i	−0.0460635	−	0.0797842i
$732$	−1.03309	+	1.78937i	−0.0381842	+	0.0661369i
$733$		−	13.2644i		−	0.489930i	−0.969532	−	0.244965i	$-0.921223\pi$
$733$		−	13.2644i		−	0.489930i	0.969532	−	0.244965i	$-0.0787765\pi$
$734$	4.95980	+	2.86354i	0.183069	+	0.105695i
$735$		0			0
$736$			0.890761i			0.0328339i
$737$	19.3613	−	33.5348i	0.713184	−	1.23527i
$738$	−3.39113	−	5.87361i	−0.124829	−	0.216211i
$739$	6.28279	−	3.62737i	0.231116	−	0.133435i	−0.379971	−	0.924999i	$-0.624066\pi$
$739$	6.28279	−	3.62737i	0.231116	−	0.133435i	0.611087	+	0.791564i	$0.290733\pi$
$740$	−0.0983010			−0.00361362
$741$	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
$746$		−	15.3198i		−	0.560898i
$747$	−26.7184	−	15.4259i	−0.977574	−	0.564403i
$748$	−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	−0.981311	−	0.192430i	$-0.938363\pi$
$751$	−18.0130	−	31.1995i	−0.657305	−	1.13848i	0.324006	−	0.946055i	$-0.394970\pi$
$752$	12.6306	−	7.29229i	0.460591	−	0.265922i
$753$	19.3973			0.706877
$754$	−10.7203	+	3.68975i	−0.390410	+	0.134373i
$755$	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	$0.771851\pi$
$758$	−3.19961	+	5.54189i	−0.116215	+	0.201291i
$759$			24.3756i			0.884780i
$760$	11.8040	+	6.81504i	0.428176	+	0.247207i
$761$	6.76541	+	3.90601i	0.245246	+	0.141593i	0.617585	−	0.786504i	$-0.288111\pi$
$761$	6.76541	+	3.90601i	0.245246	+	0.141593i	−0.372340	+	0.928097i	$0.621444\pi$
$762$		−	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
$766$	−5.06020			−0.182833
$767$	37.4814	−	12.9005i	1.35337	−	0.465809i
$768$	6.77429			0.244446
$769$	−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
$772$			1.13893i			0.0409911i
$773$	−40.3572	−	23.3002i	−1.45155	−	0.838051i	−0.452977	−	0.891522i	$-0.649638\pi$
$773$	−40.3572	−	23.3002i	−1.45155	−	0.838051i	−0.998569	+	0.0534716i	$0.982971\pi$
$774$	28.1563	+	16.2560i	1.01206	+	0.584311i
$775$		−	15.1217i		−	0.543188i
$776$	15.4057	−	26.6834i	0.553032	−	0.957879i
$777$		0			0
$778$	−20.1634	+	11.6414i	−0.722895	+	0.417363i
$779$	−5.42212			−0.194268
$780$	0.620480	+	0.539516i	0.0222168	+	0.0193178i
$781$	49.1026			1.75703
$782$	−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
$786$	−53.6163	−	30.9554i	−1.91243	−	1.10414i
$787$	34.4099	+	19.8666i	1.22658	+	0.708167i	0.966313	−	0.257369i	$-0.0828556\pi$
$787$	34.4099	+	19.8666i	1.22658	+	0.708167i	0.260268	+	0.965536i	$0.416189\pi$
$788$		−	1.41628i		−	0.0504529i
$789$	−14.4388	+	25.0087i	−0.514034	+	0.890333i
$790$	−6.31788	−	10.9429i	−0.224780	−	0.389330i
$791$		0			0
$792$	80.8641			2.87338
$793$	−8.56844	−	24.8950i	−0.304274	−	0.884047i
$794$	−23.0420			−0.817730
$795$	10.9691	−	6.33300i	0.389033	−	0.224608i
$796$	−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
$800$	−2.09115	−	1.20732i	−0.0739332	−	0.0426853i
$801$			26.5568i			0.938338i
$802$	−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
$807$	−45.3011			−1.59467
$808$	9.81188	−	5.66489i	0.345181	−	0.199290i
$809$	20.7293	+	35.9042i	0.728803	+	1.26232i	0.957389	+	0.288801i	$0.0932565\pi$
$809$	20.7293	+	35.9042i	0.728803	+	1.26232i	−0.228586	+	0.973524i	$0.573410\pi$
$810$	−1.77838	+	3.08024i	−0.0624859	+	0.108229i
$811$		−	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
$814$		−	9.02878i		−	0.316459i
$815$	−5.78705	+	10.0235i	−0.202712	+	0.351107i
$816$	3.06127	+	5.30227i	0.107166	+	0.185617i
$817$	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	$-0.538715\pi$
$821$	19.4164	−	11.2101i	0.677638	−	0.391235i	0.798965	+	0.601378i	$0.205381\pi$
$822$	−15.5974	−	27.0156i	−0.544023	−	0.942276i
$823$	−1.18083	+	2.04525i	−0.0411611	+	0.0712931i	−0.885872	−	0.463930i	$-0.846439\pi$
$823$	−1.18083	+	2.04525i	−0.0411611	+	0.0712931i	0.844711	+	0.535223i	$0.179772\pi$
$824$			24.4614i			0.852154i
$825$	−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	$0.728557\pi$
$828$	−0.417773	+	0.723604i	−0.0145186	+	0.0251470i
$829$	27.4640	+	47.5690i	0.953864	+	1.65214i	0.736947	+	0.675951i	$0.236267\pi$
$829$	27.4640	+	47.5690i	0.953864	+	1.65214i	0.216917	+	0.976190i	$0.430400\pi$
$830$	5.60162	−	3.23410i	0.194435	−	0.112257i
$831$	−55.5277			−1.92623
$832$	−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
$837$			23.0473i			0.796632i
$838$	−41.0190	−	23.6824i	−1.41698	−	0.818093i
$839$	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
$843$	5.34678	−	3.08697i	0.184153	−	0.106321i
$844$	−2.59490			−0.0893201
$845$	−10.3757	+	1.45549i	−0.356936	+	0.0500703i
$846$	28.1041			0.966239
$847$		0			0
$848$	10.3471	+	17.9217i	0.355321	+	0.615434i
$849$	−22.6898	+	39.2999i	−0.778713	+	1.34877i
$850$		−	3.36033i		−	0.115258i
$851$	1.72615	+	0.996594i	0.0591717	+	0.0341628i
$852$	2.28251	+	1.31781i	0.0781975	+	0.0451474i
$853$		−	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
$857$	−18.5850			−0.634851			−0.317425	−	0.948283i	$-0.602818\pi$
$857$	−18.5850			−0.634851			−0.317425	+	0.948283i	$0.602818\pi$
$858$	−49.5536	+	56.9900i	−1.69173	+	1.94561i
$859$	−29.4975			−1.00644			−0.503221	−	0.864158i	$-0.667852\pi$
$859$	−29.4975			−1.00644			−0.503221	+	0.864158i	$0.667852\pi$
$860$	0.304832	−	0.175995i	0.0103947	−	0.00600137i
$861$		0			0
$862$	−27.3712	+	47.4083i	−0.932266	+	1.61473i
$863$			18.6435i			0.634631i	0.948320	+	0.317315i	$0.102781\pi$
$863$			18.6435i			0.634631i	−0.948320	+	0.317315i	$0.897219\pi$
$864$	3.18716	+	1.84010i	0.108429	+	0.0626016i
$865$	−13.6230	−	7.86522i	−0.463194	−	0.267425i
$866$		−	13.5651i		−	0.460961i
$867$	−24.0383	+	41.6355i	−0.816383	+	1.41402i
$868$		0			0
$869$	−51.9020	+	29.9656i	−1.76065	+	1.01651i
$870$	−7.30175			−0.247552
$871$	−5.05689	+	25.9975i	−0.171346	+	0.880893i
$872$	42.1409			1.42707
$873$	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
$877$	32.6941	+	18.8759i	1.10400	+	0.637395i	0.937269	−	0.348608i	$-0.113345\pi$
$877$	32.6941	+	18.8759i	1.10400	+	0.637395i	0.166731	+	0.986002i	$0.446679\pi$
$878$	−34.0930	−	19.6836i	−1.15058	−	0.664290i
$879$			66.6962i			2.24961i
$880$	−8.05950	+	13.9595i	−0.271686	+	0.470574i
$881$	−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	$0.683523\pi$
$884$	0.194679	+	0.0378677i	0.00654775	+	0.00127363i
$885$	25.5291			0.858151
$886$	3.98777	−	2.30234i	0.133972	−	0.0773487i
$887$	−12.9599	−	22.4472i	−0.435151	−	0.753703i	0.562157	−	0.827030i	$-0.309972\pi$
$887$	−12.9599	−	22.4472i	−0.435151	−	0.753703i	−0.997308	+	0.0733272i	$0.976638\pi$
$888$	5.17703	−	8.96688i	0.173730	−	0.300909i
$889$		0			0
$890$	−4.82181	−	2.78387i	−0.161627	−	0.0933156i
$891$	14.6096	+	8.43483i	0.489439	+	0.282577i
$892$		−	2.25882i		−	0.0756310i
$893$	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
$898$	25.0782			0.836870
$899$	−6.86376	+	3.96280i	−0.228919	+	0.132167i
$900$	−1.13249	−	1.96152i	−0.0377495	−	0.0653841i
$901$	1.52755	−	2.64579i	0.0508901	−	0.0881442i
$902$		−	6.74420i		−	0.224557i
$903$		0			0
$904$	−48.8934	−	28.2286i	−1.62617	−	0.938869i
$905$			13.3402i			0.443443i
$906$	−2.98231	+	5.16552i	−0.0990808	+	0.171613i
$907$	7.77113	+	13.4600i	0.258036	+	0.446931i	0.965716	−	0.259602i	$-0.0835914\pi$
$907$	7.77113	+	13.4600i	0.258036	+	0.446931i	−0.707680	+	0.706533i	$0.750258\pi$
$908$	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
$913$	−15.3393	−	26.5684i	−0.507656	−	0.879287i
$914$	−6.01911	+	10.4254i	−0.199094	+	0.344842i
$915$		−	16.9563i		−	0.560559i
$916$	−1.47421	−	0.851138i	−0.0487094	−	0.0281224i
$917$		0			0
$918$			5.12155i			0.169036i
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	0.221651	+	0.975126i	$0.428856\pi$
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	−0.955309	+	0.295608i	$0.904478\pi$
$920$	−1.87132	−	3.24123i	−0.0616957	−	0.106860i
$921$	10.5694	−	6.10224i	0.348273	−	0.201076i
$922$	3.13216			0.103152
$923$	−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
$928$			1.26556i			0.0415441i
$929$	−2.54846	−	1.47135i	−0.0836121	−	0.0482735i	0.457611	−	0.889152i	$-0.348705\pi$
$929$	−2.54846	−	1.47135i	−0.0836121	−	0.0482735i	−0.541223	+	0.840879i	$0.682039\pi$
$930$	−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
$934$	22.5506	−	13.0196i	0.737878	−	0.426014i
$935$	2.37966			0.0778232
$936$	−52.2969	+	17.9997i	−1.70938	+	0.588339i
$937$	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
$940$	0.152133	−	0.263503i	0.00496205	−	0.00859451i
$941$			22.0692i			0.719436i	0.933061	+	0.359718i	$0.117127\pi$
$941$			22.0692i			0.719436i	−0.933061	+	0.359718i	$0.882873\pi$
$942$	−13.2717	−	7.66242i	−0.432416	−	0.249655i
$943$	1.28938	+	0.744423i	0.0419879	+	0.0242417i
$944$			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	$-0.354190\pi$
$947$	44.3160	−	25.5859i	1.44008	−	0.831429i	0.997854	+	0.0654762i	$0.0208567\pi$
$948$	−3.21685			−0.104478
$949$	−13.6082	−	11.8325i	−0.441740	−	0.384098i
$950$	35.0652			1.13767
$951$	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	$-0.0997245\pi$
$954$			39.8772i			1.29107i
$955$	−2.96644	−	1.71267i	−0.0959916	−	0.0554208i
$956$	1.15085	+	0.664444i	0.0372212	+	0.0214896i
$957$			34.6321i			1.11950i
$958$	−22.8478	+	39.5735i	−0.738177	+	1.27856i
$959$		0			0
$960$	−16.7985	+	9.69861i	−0.542169	+	0.313021i
$961$	18.9181			0.610262
$962$	2.00974	+	5.83915i	0.0647965	+	0.188262i
$963$	−51.2916			−1.65285
$964$	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	$0.899773\pi$
$968$	42.0726	+	24.2906i	1.35226	+	0.780730i
$969$	8.16832	+	4.71598i	0.262404	+	0.151499i
$970$			11.8350i			0.380000i
$971$	23.6663	−	40.9912i	0.759487	−	1.31547i	−0.183625	−	0.982996i	$-0.558783\pi$
$971$	23.6663	−	40.9912i	0.759487	−	1.31547i	0.943112	−	0.332474i	$-0.107883\pi$
$972$	−0.524016	−	0.907622i	−0.0168078	−	0.0291120i
$973$		0			0
$974$	22.0046			0.705072
$975$	44.3624	+	8.62911i	1.42073	+	0.276353i
$976$	27.7039			0.886781
$977$	−41.4454	+	23.9285i	−1.32596	+	0.765541i	−0.984672	−	0.174418i	$-0.944195\pi$
$977$	−41.4454	+	23.9285i	−1.32596	+	0.765541i	−0.341285	+	0.939960i	$0.610862\pi$
$978$	−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
$982$	−37.8506	−	21.8531i	−1.20786	−	0.697359i
$983$		−	15.7686i		−	0.502941i	−0.967865	−	0.251471i	$-0.919086\pi$
$983$		−	15.7686i		−	0.502941i	0.967865	−	0.251471i	$-0.0809142\pi$
$984$	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
$989$	−7.13707			−0.226945
$990$	−26.8995	+	15.5305i	−0.854924	+	0.493590i
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	0.946172	−	0.323663i	$-0.104914\pi$
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	−0.753387	+	0.657578i	$0.771581\pi$
$992$	−0.964622	+	1.67077i	−0.0306268	+	0.0530471i
$993$		−	1.78555i		−	0.0566627i
$994$		0			0
$995$	4.92715	+	2.84469i	0.156201	+	0.0901828i
$996$		−	1.64669i		−	0.0521775i
$997$	16.8938	−	29.2609i	0.535032	−	0.926703i	−0.464129	−	0.885767i	$-0.653633\pi$
$997$	16.8938	−	29.2609i	0.535032	−	0.926703i	0.999162	−	0.0409358i	$-0.0130339\pi$
$998$	−16.6993	−	28.9240i	−0.528607	−	0.915574i
$999$	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.q.i.491.5		12
7.2	even	3		637.2.u.g.361.2		12
7.3	odd	6		91.2.k.b.23.5	yes	12
7.4	even	3		637.2.k.i.569.5		12
7.5	odd	6		91.2.u.b.88.2	yes	12
7.6	odd	2		637.2.q.g.491.5		12
13.2	odd	12		8281.2.a.co.1.10		12
13.4	even	6	inner	637.2.q.i.589.5		12
13.11	odd	12		8281.2.a.co.1.3		12
21.5	even	6		819.2.do.e.361.5		12
21.17	even	6		819.2.bm.f.478.2		12
91.4	even	6		637.2.u.g.30.2		12
91.17	odd	6		91.2.u.b.30.2	yes	12
91.24	even	12		1183.2.e.j.170.10		24
91.30	even	6		637.2.k.i.459.2		12
91.41	even	12		8281.2.a.cp.1.10		12
91.54	even	12		1183.2.e.j.508.3		24
91.69	odd	6		637.2.q.g.589.5		12
91.76	even	12		8281.2.a.cp.1.3		12
91.80	even	12		1183.2.e.j.170.3		24
91.82	odd	6		91.2.k.b.4.2	✓	12
91.89	even	12		1183.2.e.j.508.10		24
273.17	even	6		819.2.do.e.667.5		12
273.173	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	91.82	odd	6
91.2.k.b.23.5	yes	12	7.3	odd	6
91.2.u.b.30.2	yes	12	91.17	odd	6
91.2.u.b.88.2	yes	12	7.5	odd	6
637.2.k.i.459.2		12	91.30	even	6
637.2.k.i.569.5		12	7.4	even	3
637.2.q.g.491.5		12	7.6	odd	2
637.2.q.g.589.5		12	91.69	odd	6
637.2.q.i.491.5		12	1.1	even	1	trivial
637.2.q.i.589.5		12	13.4	even	6	inner
637.2.u.g.30.2		12	91.4	even	6
637.2.u.g.361.2		12	7.2	even	3
819.2.bm.f.478.2		12	21.17	even	6
819.2.bm.f.550.5		12	273.173	even	6
819.2.do.e.361.5		12	21.5	even	6
819.2.do.e.667.5		12	273.17	even	6
1183.2.e.j.170.3		24	91.80	even	12
1183.2.e.j.170.10		24	91.24	even	12
1183.2.e.j.508.3		24	91.54	even	12
1183.2.e.j.508.10		24	91.89	even	12
8281.2.a.co.1.3		12	13.11	odd	12
8281.2.a.co.1.10		12	13.2	odd	12
8281.2.a.cp.1.3		12	91.76	even	12
8281.2.a.cp.1.10		12	91.41	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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19430 - 0.689527i) q^{2} +(1.44060 + 2.49520i) q^{3} +(-0.0491037 + 0.0850501i) q^{4} -0.805948i q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +O(q^{10})\)	\(q+(1.19430 - 0.689527i) q^{2} +(1.44060 + 2.49520i) q^{3} +(-0.0491037 + 0.0850501i) q^{4} -0.805948i q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +(-2.65067 + 4.59109i) q^{9} +(-0.555723 - 0.962541i) q^{10} +(-4.56532 + 2.63579i) q^{11} -0.282955 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} +7.31083i q^{18} +(5.06165 + 2.92234i) q^{19} +(0.0685460 + 0.0395750i) q^{20} +(-3.63490 + 6.29583i) q^{22} +(-0.802438 - 1.38986i) q^{23} +(-7.21995 + 4.16844i) q^{24} +4.35045 q^{25} +(0.949380 - 4.88078i) q^{26} -6.63060 q^{27} +(-1.14008 - 1.97467i) q^{29} +(1.60115 - 2.77328i) q^{30} -3.47590i q^{31} +(-0.480674 - 0.277517i) q^{32} +(-13.1536 - 7.59424i) q^{33} -0.772411i q^{34} +(-0.260315 - 0.450879i) q^{36} +(-1.07557 + 0.620979i) q^{37} +8.06014 q^{38} +(10.1972 + 1.98350i) q^{39} +2.33205 q^{40} +(-0.803413 + 0.463851i) q^{41} +(2.22356 - 3.85131i) q^{43} -0.517708i q^{44} +(3.70018 + 2.13630i) q^{45} +(-1.91670 - 1.10661i) q^{46} -3.84418i q^{47} +(-5.46556 + 9.46662i) q^{48} +(5.19572 - 2.99975i) q^{50} +1.61377 q^{51} +(0.115238 + 0.334815i) q^{52} +5.45454 q^{53} +(-7.91890 + 4.57198i) q^{54} +(2.12431 + 3.67941i) q^{55} +16.8397i q^{57} +(-2.72318 - 1.57223i) q^{58} +(9.52106 + 5.49698i) q^{59} +0.228047i q^{60} +(3.65107 - 6.32385i) q^{61} +(-2.39673 - 4.15126i) q^{62} -8.35330 q^{64} +(-2.19286 - 1.90672i) q^{65} -20.9458 q^{66} +(-6.36144 + 3.67278i) q^{67} +(0.0275031 + 0.0476367i) q^{68} +(2.31199 - 4.00448i) q^{69} +(-8.06668 - 4.65730i) q^{71} +(-13.2845 - 7.66982i) q^{72} -5.00146i 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} +11.3687 q^{79} +(2.64806 - 1.52886i) q^{80} +(-1.60006 - 2.77138i) q^{81} +(-0.639676 + 1.10795i) q^{82} +5.81962i q^{83} +(-0.390935 - 0.225707i) q^{85} -6.13281i q^{86} +(3.28479 - 5.68943i) q^{87} +(-7.62677 - 13.2100i) q^{88} +(4.33832 - 2.50473i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(8.67305 - 5.00739i) q^{93} +(-2.65067 - 4.59109i) q^{94} +(2.35526 - 4.07942i) q^{95} -1.59917i q^{96} +(-9.22171 - 5.32416i) q^{97} -27.9464i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9	\( 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9} - 12 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 3 q^{23} + 15 q^{24} + 10 q^{25} - 15 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} - 6 q^{33} - 13 q^{36} - 15 q^{37} + 38 q^{38} + 5 q^{39} - 2 q^{40} + 6 q^{41} + 11 q^{43} - 9 q^{45} + 30 q^{46} - 19 q^{48} + 18 q^{50} - 8 q^{51} + 40 q^{52} + 16 q^{53} + 6 q^{54} + 15 q^{55} + 24 q^{58} + 27 q^{59} - 5 q^{61} - 41 q^{62} + 2 q^{64} - 18 q^{65} - 68 q^{66} - 15 q^{67} + 11 q^{68} - 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} + 70 q^{79} - 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 10 q^{87} - 14 q^{88} + 48 q^{89} - 66 q^{92} + 81 q^{93} - q^{94} + 2 q^{95} + 3 q^{97}+O(q^{100}) \) 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9 - 12 * q^10 - 12 * q^11 - 2 * q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 3 * q^23 + 15 * q^24 + 10 * q^25 - 15 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 - 6 * q^33 - 13 * q^36 - 15 * q^37 + 38 * q^38 + 5 * q^39 - 2 * q^40 + 6 * q^41 + 11 * q^43 - 9 * q^45 + 30 * q^46 - 19 * q^48 + 18 * q^50 - 8 * q^51 + 40 * q^52 + 16 * q^53 + 6 * q^54 + 15 * q^55 + 24 * q^58 + 27 * q^59 - 5 * q^61 - 41 * q^62 + 2 * q^64 - 18 * q^65 - 68 * q^66 - 15 * q^67 + 11 * q^68 - 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 + 70 * q^79 - 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 10 * q^87 - 14 * q^88 + 48 * q^89 - 66 * q^92 + 81 * q^93 - q^94 + 2 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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