LMFDB - Embedded newform 637.2.q.i.589.5

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			589.5
Root			$-1.38488 + 0.286553i$ of defining polynomial
Character	$\chi$	$=$	637.589
Dual form			637.2.q.i.491.5

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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	0.858790	−	0.512328i	$-0.171217\pi$
$2$	1.19430	+	0.689527i	0.844495	+	0.487570i	−0.0142944	+	0.999898i	$0.504550\pi$
$3$	1.44060	−	2.49520i	0.831732	−	1.44060i	−0.0649323	−	0.997890i	$-0.520683\pi$
$3$	1.44060	−	2.49520i	0.831732	−	1.44060i	0.896664	−	0.442712i	$-0.145984\pi$
$4$	−0.0491037	−	0.0850501i	−0.0245518	−	0.0425250i
$5$			0.805948i			0.360431i	0.983627	+	0.180216i	$0.0576795\pi$
$5$			0.805948i			0.360431i	−0.983627	+	0.180216i	$0.942320\pi$
$6$	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	−0.384760	−	0.923017i	$-0.625716\pi$
$11$	−4.56532	−	2.63579i	−1.37650	−	0.794720i	−0.991736	+	0.128296i	$0.959049\pi$
$12$	−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	0.897987	−	0.440023i	$-0.145030\pi$
$17$	0.280051	+	0.485062i	0.0679223	+	0.117645i	−0.830064	+	0.557668i	$0.811696\pi$
$18$		−	7.31083i		−	1.72318i
$19$	5.06165	−	2.92234i	1.16122	−	0.670431i	0.209625	−	0.977782i	$-0.432776\pi$
$19$	5.06165	−	2.92234i	1.16122	−	0.670431i	0.951596	+	0.307351i	$0.0994424\pi$
$20$	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	$0.220178\pi$
$24$	−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	−0.952249	−	0.305323i	$-0.901236\pi$
$29$	−1.14008	+	1.97467i	−0.211707	+	0.366687i	0.740542	+	0.672010i	$0.234569\pi$
$30$	1.60115	+	2.77328i	0.292329	+	0.506329i
$31$			3.47590i			0.624290i	0.950034	+	0.312145i	$0.101048\pi$
$31$			3.47590i			0.624290i	−0.950034	+	0.312145i	$0.898952\pi$
$32$	−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	0.408977	−	0.912545i	$-0.365886\pi$
$37$	−1.07557	−	0.620979i	−0.176822	−	0.102088i	−0.585799	+	0.810457i	$0.699219\pi$
$38$	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	0.435950	−	0.899971i	$-0.356412\pi$
$41$	−0.803413	−	0.463851i	−0.125472	−	0.0724413i	−0.561422	+	0.827529i	$0.689746\pi$
$42$		0			0
$43$	2.22356	+	3.85131i	0.339089	+	0.587320i	0.984262	−	0.176717i	$-0.0565478\pi$
$43$	2.22356	+	3.85131i	0.339089	+	0.587320i	−0.645172	+	0.764037i	$0.723214\pi$
$44$			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	$0.0904556\pi$
$47$			3.84418i			0.560731i	−0.959893	+	0.280365i	$0.909544\pi$
$48$	−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	0.270537	−	0.962710i	$-0.412799\pi$
$59$	9.52106	−	5.49698i	1.23954	−	0.715646i	0.968999	+	0.247063i	$0.0794655\pi$
$60$		−	0.228047i		−	0.0294408i
$61$	3.65107	+	6.32385i	0.467472	+	0.809686i	0.999309	−	0.0371610i	$-0.0118314\pi$
$61$	3.65107	+	6.32385i	0.467472	+	0.809686i	−0.531837	+	0.846847i	$0.678498\pi$
$62$	−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	0.0582541	−	0.998302i	$-0.481447\pi$
$67$	−6.36144	−	3.67278i	−0.777174	−	0.448701i	−0.835428	+	0.549600i	$0.814780\pi$
$68$	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	−0.895353	−	0.445357i	$-0.853077\pi$
$71$	−8.06668	+	4.65730i	−0.957339	+	0.552720i	−0.0619857	+	0.998077i	$0.519743\pi$
$72$	−13.2845	+	7.66982i	−1.56559	+	0.903896i
$73$			5.00146i			0.585376i	0.956208	+	0.292688i	$0.0945498\pi$
$73$			5.00146i			0.585376i	−0.956208	+	0.292688i	$0.905450\pi$
$74$	−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	$-0.896521\pi$
$83$		−	5.81962i		−	0.638786i	0.947622	−	0.319393i	$-0.103479\pi$
$84$		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	0.711986	−	0.702194i	$-0.247796\pi$
$89$	4.33832	+	2.50473i	0.459861	+	0.265501i	−0.252125	+	0.967695i	$0.581129\pi$
$90$	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	−0.888806	−	0.458284i	$-0.848464\pi$
$97$	−9.22171	+	5.32416i	−0.936323	+	0.540586i	−0.0475172	+	0.998870i	$0.515131\pi$
$98$		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	−0.946837	−	0.321715i	$-0.895741\pi$
$101$	−1.95777	+	3.39096i	−0.194805	+	0.337413i	0.752031	+	0.659127i	$0.229074\pi$
$102$	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	−0.531648	−	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
$109$			14.5638i			1.39496i	0.716606	+	0.697478i	$0.245695\pi$
$109$			14.5638i			1.39496i	−0.716606	+	0.697478i	$0.754305\pi$
$110$	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	−0.802838	−	0.596197i	$-0.796678\pi$
$113$	−9.75572	−	16.8974i	−0.917741	−	1.58957i	−0.114903	−	0.993377i	$-0.536656\pi$
$114$	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	−0.905420	−	0.424517i	$-0.860444\pi$
$127$	−0.958656	+	1.66044i	−0.0850670	+	0.147340i	0.820353	+	0.571858i	$0.193777\pi$
$128$	−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	−0.761489	−	0.648178i	$-0.775531\pi$
$137$	−6.79921	+	3.92553i	−0.580896	+	0.335380i	0.180594	+	0.983558i	$0.442198\pi$
$138$			6.37671i			0.542822i
$139$	4.96241	+	8.59514i	0.420906	+	0.729030i	0.996028	−	0.0890370i	$-0.0283789\pi$
$139$	4.96241	+	8.59514i	0.420906	+	0.729030i	−0.575122	+	0.818067i	$0.695046\pi$
$140$		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	−0.753888	−	0.657003i	$-0.771824\pi$
$149$	−6.85827	+	3.95962i	−0.561851	+	0.324385i	0.192037	+	0.981388i	$0.438491\pi$
$150$	14.9699	−	8.64290i	1.22229	−	0.705690i
$151$		−	1.50116i		−	0.122163i	−0.998133	−	0.0610815i	$-0.980545\pi$
$151$		−	1.50116i		−	0.122163i	0.998133	−	0.0610815i	$-0.0194550\pi$
$152$	−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	−0.900493	−	0.434871i	$-0.856794\pi$
$163$	−12.4369	+	7.18042i	−0.974130	+	0.562414i	−0.0736372	+	0.997285i	$0.523461\pi$
$164$			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	0.643790	−	0.765202i	$-0.277361\pi$
$167$	3.91563	+	2.26069i	0.303000	+	0.174937i	−0.340790	+	0.940140i	$0.610694\pi$
$168$		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	0.951602	+	0.307334i	$0.0994369\pi$
$173$	9.75896	+	16.9030i	0.741960	+	1.28511i	−0.209642	+	0.977778i	$0.567230\pi$
$174$			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	−0.154990	−	0.987916i	$-0.549535\pi$
$179$	10.4098	−	18.0303i	0.778065	−	1.34765i	0.933055	−	0.359733i	$-0.117132\pi$
$180$	−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	0.932608	−	0.360892i	$-0.117528\pi$
$191$	2.12504	+	3.68068i	0.153762	+	0.266324i	−0.778845	+	0.627216i	$0.784194\pi$
$192$	−12.0338	+	20.8431i	−0.868463	+	1.50422i
$193$	10.0435	+	5.79861i	0.722946	+	0.417393i	0.815836	−	0.578283i	$-0.196277\pi$
$193$	10.0435	+	5.79861i	0.722946	+	0.417393i	−0.0928898	+	0.995676i	$0.529610\pi$
$194$	−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	−0.0159371	−	0.999873i	$-0.505073\pi$
$197$	−12.4892	−	7.21066i	−0.889821	−	0.513738i	−0.873884	+	0.486135i	$0.838406\pi$
$198$	−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	$0.913832\pi$
$200$		−	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	0.0947513	−	0.995501i	$-0.469794\pi$
$211$	13.2113	−	22.8827i	0.909505	−	1.57531i	0.814754	−	0.579807i	$-0.196872\pi$
$212$	−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	−0.347987	−	0.937499i	$-0.613135\pi$
$223$	−19.9191	−	11.5003i	−1.33388	−	0.770115i	−0.985892	+	0.167384i	$0.946468\pi$
$224$		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	−0.512973	−	0.858405i	$-0.671456\pi$
$227$	−0.392628	+	0.226684i	−0.0260596	+	0.0150455i	0.486914	+	0.873450i	$0.338123\pi$
$228$	−1.43222	+	0.826893i	−0.0948511	+	0.0547623i
$229$		−	17.3335i		−	1.14543i	−0.819755	−	0.572714i	$-0.805890\pi$
$229$		−	17.3335i		−	1.14543i	0.819755	−	0.572714i	$-0.194110\pi$
$230$	−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	$0.144185\pi$
$239$			13.5314i			0.875276i	−0.899151	+	0.437638i	$0.855815\pi$
$240$	7.62961	−	4.40496i	0.492489	−	0.284339i
$241$	−19.5369	+	11.2796i	−1.25848	+	0.726583i	−0.972779	−	0.231736i	$-0.925560\pi$
$241$	−19.5369	+	11.2796i	−1.25848	+	0.726583i	−0.285701	+	0.958319i	$0.592226\pi$
$242$			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	0.952487	−	0.304578i	$-0.0985154\pi$
$251$	3.36618	+	5.83039i	0.212471	+	0.368011i	−0.740016	+	0.672589i	$0.765182\pi$
$252$		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	0.484021	+	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
$261$	12.0878			0.748219
$262$	−18.6090	−	10.7439i	−1.14967	−	0.663761i
$263$	5.01137	−	8.67994i	0.309014	−	0.535228i	−0.669133	−	0.743143i	$-0.733334\pi$
$263$	5.01137	−	8.67994i	0.309014	−	0.535228i	0.978147	+	0.207915i	$0.0666676\pi$
$264$	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	0.520395	−	0.853925i	$-0.325785\pi$
$269$	−7.86149	−	13.6165i	−0.479323	−	0.830212i	−0.999719	+	0.0237130i	$0.992451\pi$
$270$	3.68478	−	6.38223i	0.224249	−	0.388410i
$271$	−4.51734	−	2.60809i	−0.274409	−	0.158430i	0.356481	−	0.934303i	$-0.383977\pi$
$271$	−4.51734	−	2.60809i	−0.274409	−	0.158430i	−0.630890	+	0.775873i	$0.717310\pi$
$272$	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	−0.995596	−	0.0937439i	$-0.970117\pi$
$277$	−9.63619	−	16.6904i	−0.578983	−	1.00283i	0.416614	−	0.909084i	$-0.363217\pi$
$278$			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	$0.0203588\pi$
$281$			2.14283i			0.127831i	−0.997955	+	0.0639153i	$0.979641\pi$
$282$	7.63711	+	13.2279i	0.454783	+	0.787707i
$283$	7.87512	−	13.6401i	0.468127	−	0.810820i	−0.531209	−	0.847241i	$-0.678262\pi$
$283$	7.87512	−	13.6401i	0.468127	−	0.810820i	0.999337	+	0.0364203i	$0.0115955\pi$
$284$	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	0.217223	−	0.976122i	$-0.430300\pi$
$293$	20.0474	−	11.5744i	1.17118	−	0.676182i	0.953958	+	0.299940i	$0.0969668\pi$
$294$		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	$0.0385709\pi$
$307$			4.23590i			0.241756i	−0.992667	+	0.120878i	$0.961429\pi$
$308$		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	$0.236273\pi$
$317$			24.0705i			1.35193i	−0.736933	+	0.675966i	$0.763727\pi$
$318$	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	−0.514677	−	0.857384i	$-0.672088\pi$
$331$	−0.536696	+	0.309862i	−0.0294995	+	0.0170315i	0.485178	+	0.874416i	$0.338755\pi$
$332$	−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	0.889968	−	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	0.918290	−	0.395909i	$-0.129571\pi$
$349$	19.3273	+	11.1586i	1.03457	+	0.597307i	0.116277	+	0.993217i	$0.462904\pi$
$350$		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	0.552781	−	0.833326i	$-0.313566\pi$
$353$	2.01956	+	1.16600i	0.107491	+	0.0620597i	−0.445291	+	0.895386i	$0.646900\pi$
$354$	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	$-0.972489\pi$
$359$		−	3.27105i		−	0.172639i	0.996267	−	0.0863197i	$-0.0275107\pi$
$360$	−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	−0.806728	−	0.590923i	$-0.798764\pi$
$367$	2.07645	−	3.59652i	0.108390	−	0.187737i	0.915118	+	0.403186i	$0.132097\pi$
$368$	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	0.973236	−	0.229807i	$-0.0738096\pi$
$373$	5.55446	+	9.62061i	0.287599	+	0.498136i	−0.685637	+	0.727944i	$0.740476\pi$
$374$	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	0.393225	−	0.919442i	$-0.371359\pi$
$379$	−4.01862	−	2.32015i	−0.206422	−	0.119178i	−0.599648	+	0.800264i	$0.704693\pi$
$380$	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	−0.578985	−	0.815338i	$-0.696551\pi$
$383$	−3.17773	+	1.83466i	−0.162374	+	0.0937469i	0.416611	+	0.909085i	$0.363218\pi$
$384$	−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	−0.817041	−	0.576579i	$-0.804387\pi$
$397$	−14.4700	+	8.35428i	−0.726230	+	0.419289i	0.0908114	+	0.995868i	$0.471054\pi$
$398$		−	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	−0.159902	−	0.987133i	$-0.551118\pi$
$401$	−21.9221	−	12.6567i	−1.09474	−	0.632046i	−0.934833	+	0.355087i	$0.884451\pi$
$402$	−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	−0.372192	−	0.928156i	$-0.621394\pi$
$409$	4.96529	−	2.86671i	0.245518	−	0.141750i	0.617710	+	0.786406i	$0.288060\pi$
$410$	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	0.0518229	+	0.998656i	$0.483497\pi$
$419$	−17.1729	+	29.7443i	−0.838950	+	1.45310i	−0.890773	+	0.454448i	$0.849836\pi$
$420$		0			0
$421$			2.94167i			0.143368i	0.997427	+	0.0716842i	$0.0228374\pi$
$421$			2.94167i			0.143368i	−0.997427	+	0.0716842i	$0.977163\pi$
$422$	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	−0.974578	−	0.224048i	$-0.928073\pi$
$431$	−34.3773	−	19.8478i	−1.65590	−	0.956033i	−0.681321	−	0.731985i	$-0.738594\pi$
$432$	−12.5781	+	21.7858i	−0.605162	+	1.04817i
$433$	4.91827	+	8.51869i	0.236357	+	0.409382i	0.959666	−	0.281142i	$-0.0907133\pi$
$433$	4.91827	+	8.51869i	0.236357	+	0.409382i	−0.723309	+	0.690524i	$0.757380\pi$
$434$		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	0.293381	+	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
$443$	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	−0.0800136	−	0.996794i	$-0.525496\pi$
$449$	15.7487	−	9.09253i	0.743228	−	0.429103i	0.823242	+	0.567691i	$0.192163\pi$
$450$		−	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	0.312651	−	0.949868i	$-0.398783\pi$
$457$	−7.55982	−	4.36466i	−0.353633	−	0.204170i	−0.666284	+	0.745698i	$0.732116\pi$
$458$	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	−0.453495	−	0.891259i	$-0.649823\pi$
$461$	1.96695	−	1.13562i	0.0916099	−	0.0528910i	0.545105	+	0.838368i	$0.316490\pi$
$462$		0			0
$463$			5.48326i			0.254829i	0.991850	+	0.127414i	$0.0406678\pi$
$463$			5.48326i			0.254829i	−0.991850	+	0.127414i	$0.959332\pi$
$464$	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	−0.328869	−	0.944375i	$-0.606668\pi$
$479$	−28.6961	−	16.5677i	−1.31116	−	0.756997i	−0.982288	+	0.187378i	$0.940001\pi$
$480$	−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	−0.153093	−	0.988212i	$-0.548923\pi$
$487$	13.8185	−	7.97814i	0.626178	−	0.361524i	0.779270	+	0.626688i	$0.215590\pi$
$488$	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	0.247769	+	0.968819i	$0.420303\pi$
$491$	−15.8464	+	27.4468i	−0.715138	+	1.23866i	−0.962906	+	0.269836i	$0.913031\pi$
$492$	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	$0.182364\pi$
$499$			24.2184i			1.08417i	−0.840325	+	0.542083i	$0.817636\pi$
$500$	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	0.875393	−	0.483411i	$-0.160602\pi$
$503$	0.427249	+	0.740017i	0.0190501	+	0.0329957i	−0.856343	+	0.516407i	$0.827269\pi$
$504$		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	0.474842	−	0.880071i	$-0.342505\pi$
$509$	−1.12583	−	0.650000i	−0.0499017	−	0.0288108i	−0.524743	+	0.851261i	$0.675839\pi$
$510$	−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	−0.691101	−	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
$527$	−1.68603	+	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	$-0.787975\pi$
$541$		−	28.7449i		−	1.23584i	0.786241	−	0.617920i	$-0.212025\pi$
$542$	−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	−0.424695	−	0.905336i	$-0.639619\pi$
$557$	−33.5389	−	19.3637i	−1.42109	−	0.820465i	−0.996392	+	0.0848711i	$0.972952\pi$
$558$	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	0.784005	−	0.620754i	$-0.213173\pi$
$563$	−3.45441	−	5.98321i	−0.145586	−	0.252162i	−0.929591	+	0.368592i	$0.879840\pi$
$564$		−	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	−0.894230	−	0.447607i	$-0.852276\pi$
$569$	−1.41872	+	2.45730i	−0.0594759	+	0.103015i	0.834754	+	0.550623i	$0.185610\pi$
$570$	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	$-0.923679\pi$
$577$		−	11.4088i		−	0.474955i	0.971393	−	0.237478i	$-0.0763207\pi$
$578$	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	0.972702	+	0.232057i	$0.0745456\pi$
$587$	40.2191	+	23.2205i	1.66002	+	0.958413i	0.687318	+	0.726356i	$0.258788\pi$
$588$		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	$-0.863431\pi$
$593$		−	20.2606i		−	0.832002i	0.909364	−	0.416001i	$-0.136569\pi$
$594$	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	−0.602147	−	0.798385i	$-0.705688\pi$
$601$	9.56951	−	16.5749i	0.390348	−	0.676103i	0.992495	+	0.122282i	$0.0390212\pi$
$602$		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	0.851970	+	0.523590i	$0.175408\pi$
$607$	21.6668	+	37.5280i	0.879428	+	1.52321i	0.0274572	+	0.999623i	$0.491259\pi$
$608$	−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	0.308737	−	0.951147i	$-0.400094\pi$
$613$	−8.92834	−	5.15478i	−0.360612	−	0.208200i	−0.669349	+	0.742948i	$0.733427\pi$
$614$	−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	−0.680405	−	0.732837i	$-0.738196\pi$
$617$	−9.58684	+	5.53497i	−0.385952	+	0.222829i	0.294453	+	0.955666i	$0.404863\pi$
$618$	29.0896	−	16.7949i	1.17015	−	0.675589i
$619$			33.7616i			1.35700i	0.734603	+	0.678498i	$0.237369\pi$
$619$			33.7616i			1.35700i	−0.734603	+	0.678498i	$0.762631\pi$
$620$	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	0.345280	−	0.938500i	$-0.387784\pi$
$631$	33.4264	−	19.2987i	1.33068	−	0.768271i	0.985405	+	0.170229i	$0.0544507\pi$
$632$		−	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	0.991846	−	0.127445i	$-0.0406775\pi$
$641$	9.76141	+	16.9073i	0.385553	+	0.667797i	−0.606293	+	0.795241i	$0.707344\pi$
$642$		−	38.4429i		−	1.51722i
$643$	−10.8009	+	6.23589i	−0.425945	+	0.245920i	−0.697618	−	0.716470i	$-0.745757\pi$
$643$	−10.8009	+	6.23589i	−0.425945	+	0.245920i	0.271673	+	0.962390i	$0.412423\pi$
$644$		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	0.259709	+	0.965687i	$0.416373\pi$
$647$	−17.9695	+	31.1241i	−0.706455	+	1.22362i	−0.966164	+	0.257929i	$0.916960\pi$
$648$	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	−0.909638	−	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
$655$		−	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	0.998964	−	0.0455166i	$-0.0144934\pi$
$659$	11.8103	+	20.4560i	0.460063	+	0.796853i	−0.538900	+	0.842370i	$0.681160\pi$
$660$	−0.601085	+	1.04111i	−0.0233972	+	0.0405251i
$661$	14.1970	+	8.19662i	0.552198	+	0.318812i	0.750008	−	0.661429i	$-0.230050\pi$
$661$	14.1970	+	8.19662i	0.552198	+	0.318812i	−0.197810	+	0.980240i	$0.563383\pi$
$662$	−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	−0.970064	−	0.242851i	$-0.921918\pi$
$673$	−7.12678	+	12.3439i	−0.274717	+	0.475824i	0.695347	+	0.718675i	$0.255251\pi$
$674$	−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	−0.536364	−	0.843987i	$-0.680203\pi$
$683$	−1.92432	+	1.11101i	−0.0736321	+	0.0425115i	0.462732	+	0.886498i	$0.346869\pi$
$684$			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	0.542859	−	0.839824i	$-0.317342\pi$
$691$	2.28643	+	1.32007i	0.0869800	+	0.0502179i	−0.455879	+	0.890042i	$0.650675\pi$
$692$	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	0.336527	−	0.941674i	$-0.390748\pi$
$709$	35.1558	−	20.2972i	1.32030	−	0.762278i	0.983777	+	0.179396i	$0.0574143\pi$
$710$		−	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	0.698393	−	0.715715i	$-0.253899\pi$
$719$	−7.25674	−	12.5690i	−0.270631	−	0.468746i	−0.969024	+	0.246968i	$0.920566\pi$
$720$		−	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	$0.0787765\pi$
$733$			13.2644i			0.489930i	−0.969532	+	0.244965i	$0.921223\pi$
$734$	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	0.611087	−	0.791564i	$-0.290733\pi$
$739$	6.28279	+	3.62737i	0.231116	+	0.133435i	−0.379971	+	0.924999i	$0.624066\pi$
$740$	−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	−0.470608	−	0.882342i	$-0.655965\pi$
$743$	−40.0705	−	23.1347i	−1.47004	−	0.848730i	−0.999435	+	0.0336128i	$0.989299\pi$
$744$	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	0.324006	+	0.946055i	$0.394970\pi$
$751$	−18.0130	+	31.1995i	−0.657305	+	1.13848i	−0.981311	+	0.192430i	$0.938363\pi$
$752$	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	−0.753945	−	0.656938i	$-0.771851\pi$
$757$	5.28132	−	9.14751i	0.191953	−	0.332472i	0.945897	+	0.324466i	$0.105185\pi$
$758$	−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	−0.372340	−	0.928097i	$-0.621444\pi$
$761$	6.76541	−	3.90601i	0.245246	−	0.141593i	0.617585	+	0.786504i	$0.288111\pi$
$762$			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	0.0500637	−	0.998746i	$-0.484058\pi$
$769$	−21.9030	−	12.6457i	−0.789844	−	0.456017i	−0.839908	+	0.542729i	$0.817391\pi$
$770$		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	−0.998569	−	0.0534716i	$-0.982971\pi$
$773$	−40.3572	+	23.3002i	−1.45155	+	0.838051i	−0.452977	+	0.891522i	$0.649638\pi$
$774$	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	0.260268	−	0.965536i	$-0.416189\pi$
$787$	34.4099	−	19.8666i	1.22658	−	0.708167i	0.966313	+	0.257369i	$0.0828556\pi$
$788$			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	0.889642	−	0.456659i	$-0.150954\pi$
$797$	1.39299	+	2.41273i	0.0493422	+	0.0854632i	−0.840299	+	0.542123i	$0.817621\pi$
$798$		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	−0.228586	−	0.973524i	$-0.573410\pi$
$809$	20.7293	−	35.9042i	0.728803	−	1.26232i	0.957389	−	0.288801i	$-0.0932565\pi$
$810$	−1.77838	−	3.08024i	−0.0624859	−	0.108229i
$811$			27.8622i			0.978375i	0.872179	+	0.489188i	$0.162707\pi$
$811$			27.8622i			0.978375i	−0.872179	+	0.489188i	$0.837293\pi$
$812$		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	0.798965	−	0.601378i	$-0.205381\pi$
$821$	19.4164	+	11.2101i	0.677638	+	0.391235i	−0.121326	+	0.992613i	$0.538715\pi$
$822$	−15.5974	+	27.0156i	−0.544023	+	0.942276i
$823$	−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	$0.846439\pi$
$824$		−	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	$-0.728557\pi$
$827$		−	43.3148i		−	1.50620i	0.657904	−	0.753102i	$-0.271443\pi$
$828$	−0.417773	−	0.723604i	−0.0145186	−	0.0251470i
$829$	27.4640	−	47.5690i	0.953864	−	1.65214i	0.216917	−	0.976190i	$-0.430400\pi$
$829$	27.4640	−	47.5690i	0.953864	−	1.65214i	0.736947	−	0.675951i	$-0.236267\pi$
$830$	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	−0.263174	−	0.964748i	$-0.584769\pi$
$839$	12.7661	−	7.37052i	0.440735	−	0.254459i	0.703910	+	0.710290i	$0.251436\pi$
$840$		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	$0.135396\pi$
$853$			24.1038i			0.825297i	−0.910890	+	0.412649i	$0.864604\pi$
$854$		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	$-0.897219\pi$
$863$		−	18.6435i		−	0.634631i	0.948320	−	0.317315i	$-0.102781\pi$
$864$	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	0.166731	−	0.986002i	$-0.446679\pi$
$877$	32.6941	−	18.8759i	1.10400	−	0.637395i	0.937269	+	0.348608i	$0.113345\pi$
$878$	−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	0.497499	+	0.867464i	$0.334252\pi$
$881$	−14.9149	+	25.8334i	−0.502497	+	0.870350i	−0.999996	+	0.00288515i	$0.999082\pi$
$882$		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	−0.997308	−	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
$891$	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	−0.707680	−	0.706533i	$-0.750258\pi$
$907$	7.77113	−	13.4600i	0.258036	−	0.446931i	0.965716	+	0.259602i	$0.0835914\pi$
$908$	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	−0.955309	−	0.295608i	$-0.904478\pi$
$919$	−22.2409	−	38.5223i	−0.733659	−	1.27073i	0.221651	−	0.975126i	$-0.428856\pi$
$920$	−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	−0.541223	−	0.840879i	$-0.682039\pi$
$929$	−2.54846	+	1.47135i	−0.0836121	+	0.0482735i	0.457611	+	0.889152i	$0.348705\pi$
$930$	−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	$-0.882873\pi$
$941$		−	22.0692i		−	0.719436i	0.933061	−	0.359718i	$-0.117127\pi$
$942$	−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	0.997854	−	0.0654762i	$-0.0208567\pi$
$947$	44.3160	+	25.5859i	1.44008	+	0.831429i	0.442223	+	0.896905i	$0.354190\pi$
$948$	−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	0.951324	+	0.308194i	$0.0997245\pi$
$953$	22.9235	+	39.7047i	0.742565	+	1.28616i	−0.208758	+	0.977967i	$0.566942\pi$
$954$		−	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	$-0.899773\pi$
$967$		−	19.2609i		−	0.619387i	0.950836	−	0.309694i	$-0.100227\pi$
$968$	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	0.943112	+	0.332474i	$0.107883\pi$
$971$	23.6663	+	40.9912i	0.759487	+	1.31547i	−0.183625	+	0.982996i	$0.558783\pi$
$972$	−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	−0.341285	−	0.939960i	$-0.610862\pi$
$977$	−41.4454	−	23.9285i	−1.32596	−	0.765541i	−0.984672	+	0.174418i	$0.944195\pi$
$978$	−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	$0.0809142\pi$
$983$			15.7686i			0.502941i	−0.967865	+	0.251471i	$0.919086\pi$
$984$	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	−0.753387	−	0.657578i	$-0.771581\pi$
$991$	6.06892	−	10.5117i	0.192786	−	0.333914i	0.946172	+	0.323663i	$0.104914\pi$
$992$	−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	0.999162	+	0.0409358i	$0.0130339\pi$
$997$	16.8938	+	29.2609i	0.535032	+	0.926703i	−0.464129	+	0.885767i	$0.653633\pi$
$998$	−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.589.5		12
7.2	even	3		637.2.k.i.459.2		12
7.3	odd	6		91.2.u.b.30.2	yes	12
7.4	even	3		637.2.u.g.30.2		12
7.5	odd	6		91.2.k.b.4.2	✓	12
7.6	odd	2		637.2.q.g.589.5		12
13.6	odd	12		8281.2.a.co.1.3		12
13.7	odd	12		8281.2.a.co.1.10		12
13.10	even	6	inner	637.2.q.i.491.5		12
21.5	even	6		819.2.bm.f.550.5		12
21.17	even	6		819.2.do.e.667.5		12
91.6	even	12		8281.2.a.cp.1.3		12
91.10	odd	6		91.2.k.b.23.5	yes	12
91.19	even	12		1183.2.e.j.508.10		24
91.20	even	12		8281.2.a.cp.1.10		12
91.23	even	6		637.2.u.g.361.2		12
91.33	even	12		1183.2.e.j.508.3		24
91.45	even	12		1183.2.e.j.170.10		24
91.59	even	12		1183.2.e.j.170.3		24
91.62	odd	6		637.2.q.g.491.5		12
91.75	odd	6		91.2.u.b.88.2	yes	12
91.88	even	6		637.2.k.i.569.5		12
273.101	even	6		819.2.bm.f.478.2		12
273.257	even	6		819.2.do.e.361.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.2	✓	12	7.5	odd	6
91.2.k.b.23.5	yes	12	91.10	odd	6
91.2.u.b.30.2	yes	12	7.3	odd	6
91.2.u.b.88.2	yes	12	91.75	odd	6
637.2.k.i.459.2		12	7.2	even	3
637.2.k.i.569.5		12	91.88	even	6
637.2.q.g.491.5		12	91.62	odd	6
637.2.q.g.589.5		12	7.6	odd	2
637.2.q.i.491.5		12	13.10	even	6	inner
637.2.q.i.589.5		12	1.1	even	1	trivial
637.2.u.g.30.2		12	7.4	even	3
637.2.u.g.361.2		12	91.23	even	6
819.2.bm.f.478.2		12	273.101	even	6
819.2.bm.f.550.5		12	21.5	even	6
819.2.do.e.361.5		12	273.257	even	6
819.2.do.e.667.5		12	21.17	even	6
1183.2.e.j.170.3		24	91.59	even	12
1183.2.e.j.170.10		24	91.45	even	12
1183.2.e.j.508.3		24	91.33	even	12
1183.2.e.j.508.10		24	91.19	even	12
8281.2.a.co.1.3		12	13.6	odd	12
8281.2.a.co.1.10		12	13.7	odd	12
8281.2.a.cp.1.3		12	91.6	even	12
8281.2.a.cp.1.10		12	91.20	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

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Groups

Database

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