LMFDB - Embedded newform 637.2.q.g.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.g.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	$0.479317\pi$
$3$	−1.44060	+	2.49520i	−0.831732	+	1.44060i	−0.896664	+	0.442712i	$0.854016\pi$
$4$	−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	−0.384760	−	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	0.830064	−	0.557668i	$-0.188304\pi$
$17$	−0.280051	−	0.485062i	−0.0679223	−	0.117645i	−0.897987	+	0.440023i	$0.854970\pi$
$18$		−	7.31083i		−	1.72318i
$19$	−5.06165	+	2.92234i	−1.16122	+	0.670431i	−0.951596	−	0.307351i	$-0.900558\pi$
$19$	−5.06165	+	2.92234i	−1.16122	+	0.670431i	−0.209625	+	0.977782i	$0.567224\pi$
$20$	−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	$-0.898952\pi$
$31$		−	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	0.408977	−	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	0.561422	−	0.827529i	$-0.310254\pi$
$41$	0.803413	+	0.463851i	0.125472	+	0.0724413i	−0.435950	+	0.899971i	$0.643588\pi$
$42$		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	$-0.909544\pi$
$47$		−	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	$-0.920534\pi$
$59$	−9.52106	+	5.49698i	−1.23954	+	0.715646i	−0.270537	+	0.962710i	$0.587201\pi$
$60$		−	0.228047i		−	0.0294408i
$61$	−3.65107	−	6.32385i	−0.467472	−	0.809686i	0.531837	−	0.846847i	$-0.321502\pi$
$61$	−3.65107	−	6.32385i	−0.467472	−	0.809686i	−0.999309	+	0.0371610i	$0.988169\pi$
$62$	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	$-0.905450\pi$
$73$		−	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	$-0.418871\pi$
$89$	−4.33832	−	2.50473i	−0.459861	−	0.265501i	−0.711986	+	0.702194i	$0.752204\pi$
$90$	−5.89215			−0.621087
$91$		0			0
$92$	0.157611			0.0164320
$93$	8.67305	+	5.00739i	0.899354	+	0.519242i
$94$	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	$-0.484869\pi$
$97$	9.22171	−	5.32416i	0.936323	−	0.540586i	0.888806	+	0.458284i	$0.151536\pi$
$98$		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	$-0.770926\pi$
$101$	1.95777	−	3.39096i	0.194805	−	0.337413i	0.946837	+	0.321715i	$0.104259\pi$
$102$	1.92732	+	1.11274i	0.190833	+	0.110177i
$103$	−8.45379			−0.832977			−0.416488	−	0.909141i	$-0.636739\pi$
$103$	−8.45379			−0.832977			−0.416488	+	0.909141i	$0.636739\pi$
$104$	−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	$-0.261683\pi$
$131$	15.5816			1.36137			0.680684	+	0.732577i	$0.261683\pi$
$132$	−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	0.575122	−	0.818067i	$-0.304954\pi$
$139$	−4.96241	−	8.59514i	−0.420906	−	0.729030i	−0.996028	+	0.0890370i	$0.971621\pi$
$140$		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	$-0.450814\pi$
$157$	3.85692			0.307816			0.153908	+	0.988085i	$0.450814\pi$
$158$	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	0.340790	−	0.940140i	$-0.389306\pi$
$167$	−3.91563	−	2.26069i	−0.303000	−	0.174937i	−0.643790	+	0.765202i	$0.722639\pi$
$168$		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	$-0.900563\pi$
$173$	−9.75896	−	16.9030i	−0.741960	−	1.28511i	0.209642	−	0.977778i	$-0.432770\pi$
$174$		−	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	$-0.289093\pi$
$181$	16.5522			1.23031			0.615157	+	0.788405i	$0.289093\pi$
$182$		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	0.963583	−	0.267409i	$-0.0861676\pi$
$199$	3.52962	+	6.11348i	0.250208	+	0.433373i	−0.713375	+	0.700783i	$0.752834\pi$
$200$		−	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	0.985892	−	0.167384i	$-0.0535321\pi$
$223$	19.9191	+	11.5003i	1.33388	+	0.770115i	0.347987	+	0.937499i	$0.386865\pi$
$224$		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	$-0.661877\pi$
$227$	0.392628	−	0.226684i	0.0260596	−	0.0150455i	0.512973	+	0.858405i	$0.328544\pi$
$228$	−1.43222	+	0.826893i	−0.0948511	+	0.0547623i
$229$			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	$0.144185\pi$
$239$			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	0.285701	−	0.958319i	$-0.407774\pi$
$241$	19.5369	−	11.2796i	1.25848	−	0.726583i	0.972779	+	0.231736i	$0.0744404\pi$
$242$			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	$-0.234818\pi$
$251$	−3.36618	−	5.83039i	−0.212471	−	0.368011i	−0.952487	+	0.304578i	$0.901485\pi$
$252$		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	$-0.660824\pi$
$257$	8.26907	−	14.3225i	0.515811	−	0.893410i	0.999832	−	0.0183536i	$-0.00584248\pi$
$258$	−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	0.999719	−	0.0237130i	$-0.00754880\pi$
$269$	7.86149	+	13.6165i	0.479323	+	0.830212i	−0.520395	+	0.853925i	$0.674215\pi$
$270$	3.68478	−	6.38223i	0.224249	−	0.388410i
$271$	4.51734	+	2.60809i	0.274409	+	0.158430i	0.630890	−	0.775873i	$-0.282690\pi$
$271$	4.51734	+	2.60809i	0.274409	+	0.158430i	−0.356481	+	0.934303i	$0.616023\pi$
$272$	−2.12499			−0.128847
$273$		0			0
$274$	−10.8270			−0.654085
$275$	−19.8612	−	11.4669i	−1.19767	−	0.691478i
$276$	−0.227054	+	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	−0.999337	−	0.0364203i	$-0.988405\pi$
$283$	−7.87512	+	13.6401i	−0.468127	+	0.810820i	0.531209	+	0.847241i	$0.321738\pi$
$284$	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	$-0.903033\pi$
$293$	−20.0474	+	11.5744i	−1.17118	+	0.676182i	−0.217223	+	0.976122i	$0.569700\pi$
$294$		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	$-0.781047\pi$
$311$	−27.2501			−1.54521			−0.772606	+	0.634885i	$0.781047\pi$
$312$	−5.73934	−	29.5061i	−0.324926	−	1.67045i
$313$	2.69697			0.152442			0.0762209	−	0.997091i	$-0.475715\pi$
$313$	2.69697			0.152442			0.0762209	+	0.997091i	$0.475715\pi$
$314$	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	−0.116277	−	0.993217i	$-0.537096\pi$
$349$	−19.3273	−	11.1586i	−1.03457	−	0.597307i	−0.918290	+	0.395909i	$0.870429\pi$
$350$		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	$-0.353100\pi$
$353$	−2.01956	−	1.16600i	−0.107491	−	0.0620597i	−0.552781	+	0.833326i	$0.686434\pi$
$354$	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	−0.915118	−	0.403186i	$-0.867903\pi$
$367$	−2.07645	+	3.59652i	−0.108390	+	0.187737i	0.806728	+	0.590923i	$0.201236\pi$
$368$	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	−0.416611	−	0.909085i	$-0.636782\pi$
$383$	3.17773	−	1.83466i	0.162374	−	0.0937469i	0.578985	+	0.815338i	$0.303449\pi$
$384$	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	$-0.528946\pi$
$397$	14.4700	−	8.35428i	0.726230	−	0.419289i	0.817041	+	0.576579i	$0.195613\pi$
$398$			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	−0.617710	−	0.786406i	$-0.711940\pi$
$409$	−4.96529	+	2.86671i	−0.245518	+	0.141750i	0.372192	+	0.928156i	$0.378606\pi$
$410$	0.892951	−	0.515546i	0.0440997	−	0.0254610i
$411$		−	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	$-0.516503\pi$
$419$	17.1729	−	29.7443i	0.838950	−	1.45310i	0.890773	−	0.454448i	$-0.150164\pi$
$420$		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	0.723309	−	0.690524i	$-0.242620\pi$
$433$	−4.91827	−	8.51869i	−0.236357	−	0.409382i	−0.959666	+	0.281142i	$0.909287\pi$
$434$		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	$-0.594780\pi$
$439$	14.2733	−	24.7220i	0.681226	−	1.17992i	0.974607	−	0.223922i	$-0.0718863\pi$
$440$	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	−0.545105	−	0.838368i	$-0.683510\pi$
$461$	−1.96695	+	1.13562i	−0.0916099	+	0.0528910i	0.453495	+	0.891259i	$0.350177\pi$
$462$		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	$-0.643915\pi$
$467$	−18.8819			−0.873750			−0.436875	+	0.899522i	$0.643915\pi$
$468$	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	$-0.0599991\pi$
$479$	28.6961	+	16.5677i	1.31116	+	0.756997i	0.328869	+	0.944375i	$0.393332\pi$
$480$	−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	0.856343	−	0.516407i	$-0.172731\pi$
$503$	−0.427249	−	0.740017i	−0.0190501	−	0.0329957i	−0.875393	+	0.483411i	$0.839398\pi$
$504$		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	$-0.324161\pi$
$509$	1.12583	+	0.650000i	0.0499017	+	0.0288108i	−0.474842	+	0.880071i	$0.657495\pi$
$510$	0.896808	−	1.55332i	0.0397113	−	0.0687820i
$511$		0			0
$512$			24.0616i			1.06338i
$513$	−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	$-0.684851\pi$
$521$	−25.0455			−1.09726			−0.548632	+	0.836064i	$0.684851\pi$
$522$	14.4365	+	8.33490i	0.631867	+	0.364809i
$523$	−6.41197	+	11.1059i	−0.280376	+	0.485625i	−0.971477	−	0.237133i	$-0.923792\pi$
$523$	−6.41197	+	11.1059i	−0.280376	+	0.485625i	0.691101	+	0.722758i	$0.257126\pi$
$524$	−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	0.929591	−	0.368592i	$-0.120160\pi$
$563$	3.45441	+	5.98321i	0.145586	+	0.252162i	−0.784005	+	0.620754i	$0.786827\pi$
$564$		−	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	$0.0763207\pi$
$577$			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	−0.972702	−	0.232057i	$-0.925454\pi$
$587$	−40.2191	−	23.2205i	−1.66002	−	0.958413i	−0.687318	−	0.726356i	$-0.741212\pi$
$588$		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	$-0.960979\pi$
$601$	−9.56951	+	16.5749i	−0.390348	+	0.676103i	0.602147	+	0.798385i	$0.294312\pi$
$602$		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	$-0.824592\pi$
$607$	−21.6668	−	37.5280i	−0.879428	−	1.52321i	−0.0274572	−	0.999623i	$-0.508741\pi$
$608$	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	$-0.762631\pi$
$619$		−	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	0.345280	−	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	−0.271673	−	0.962390i	$-0.587577\pi$
$643$	10.8009	−	6.23589i	0.425945	−	0.245920i	0.697618	+	0.716470i	$0.254243\pi$
$644$		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	$-0.583627\pi$
$647$	17.9695	−	31.1241i	0.706455	−	1.22362i	0.966164	−	0.257929i	$-0.0830401\pi$
$648$	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	0.197810	−	0.980240i	$-0.436617\pi$
$661$	−14.1970	−	8.19662i	−0.552198	−	0.318812i	−0.750008	+	0.661429i	$0.769950\pi$
$662$	−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	$-0.563244\pi$
$677$	−10.2715			−0.394765			−0.197383	+	0.980327i	$0.563244\pi$
$678$	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	0.455879	−	0.890042i	$-0.349325\pi$
$691$	−2.28643	−	1.32007i	−0.0869800	−	0.0502179i	−0.542859	+	0.839824i	$0.682658\pi$
$692$	−0.958402	+	1.66000i	−0.0364330	+	0.0631038i
$693$		0			0
$694$			2.57174i			0.0976220i
$695$	−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	0.969024	−	0.246968i	$-0.0794344\pi$
$719$	7.25674	+	12.5690i	0.270631	+	0.468746i	−0.698393	+	0.715715i	$0.746101\pi$
$720$			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	$-0.307256\pi$
$727$	30.6942			1.13839			0.569193	+	0.822204i	$0.307256\pi$
$728$		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	0.611087	−	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	−0.617585	−	0.786504i	$-0.711889\pi$
$761$	−6.76541	+	3.90601i	−0.245246	+	0.141593i	0.372340	+	0.928097i	$0.378556\pi$
$762$		−	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	$-0.182609\pi$
$769$	21.9030	+	12.6457i	0.789844	+	0.456017i	−0.0500637	+	0.998746i	$0.515942\pi$
$770$		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	$-0.350362\pi$
$773$	40.3572	−	23.3002i	1.45155	−	0.838051i	0.998569	+	0.0534716i	$0.0170287\pi$
$774$	28.1563	−	16.2560i	1.01206	−	0.584311i
$775$		−	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	$-0.917144\pi$
$787$	−34.4099	+	19.8666i	−1.22658	+	0.708167i	−0.260268	+	0.965536i	$0.583811\pi$
$788$			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	$-0.182379\pi$
$797$	−1.39299	−	2.41273i	−0.0493422	−	0.0854632i	−0.889642	+	0.456659i	$0.849046\pi$
$798$		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	$-0.837293\pi$
$811$		−	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	0.798965	−	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	$0.569600\pi$
$829$	−27.4640	+	47.5690i	−0.953864	+	1.65214i	−0.736947	+	0.675951i	$0.763733\pi$
$830$	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	$-0.748564\pi$
$839$	−12.7661	+	7.37052i	−0.440735	+	0.254459i	0.263174	+	0.964748i	$0.415231\pi$
$840$		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	$-0.397182\pi$
$857$	18.5850			0.634851			0.317425	+	0.948283i	$0.397182\pi$
$858$	−49.5536	−	56.9900i	−1.69173	−	1.94561i
$859$	29.4975			1.00644			0.503221	−	0.864158i	$-0.332148\pi$
$859$	29.4975			1.00644			0.503221	+	0.864158i	$0.332148\pi$
$860$	−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	$-0.665748\pi$
$881$	14.9149	−	25.8334i	0.502497	−	0.870350i	0.999996	−	0.00288515i	$-0.000918372\pi$
$882$		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	$-0.690028\pi$
$887$	12.9599	−	22.4472i	0.435151	−	0.753703i	0.997308	+	0.0733272i	$0.0233617\pi$
$888$	−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	−0.457611	−	0.889152i	$-0.651295\pi$
$929$	2.54846	−	1.47135i	0.0836121	−	0.0482735i	0.541223	+	0.840879i	$0.317961\pi$
$930$	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	$-0.504945\pi$
$937$	−0.951020			−0.0310685			−0.0155342	+	0.999879i	$0.504945\pi$
$938$		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	0.997854	−	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	$-0.892117\pi$
$971$	−23.6663	−	40.9912i	−0.759487	−	1.31547i	0.183625	−	0.982996i	$-0.441217\pi$
$972$	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	$-0.919086\pi$
$983$		−	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	−0.753387	−	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	$-0.986966\pi$
$997$	−16.8938	−	29.2609i	−0.535032	−	0.926703i	0.464129	−	0.885767i	$-0.346367\pi$
$998$	−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.g.589.5		12
7.2	even	3		91.2.k.b.4.2	✓	12
7.3	odd	6		637.2.u.g.30.2		12
7.4	even	3		91.2.u.b.30.2	yes	12
7.5	odd	6		637.2.k.i.459.2		12
7.6	odd	2		637.2.q.i.589.5		12
13.6	odd	12		8281.2.a.cp.1.3		12
13.7	odd	12		8281.2.a.cp.1.10		12
13.10	even	6	inner	637.2.q.g.491.5		12
21.2	odd	6		819.2.bm.f.550.5		12
21.11	odd	6		819.2.do.e.667.5		12
91.6	even	12		8281.2.a.co.1.3		12
91.10	odd	6		637.2.k.i.569.5		12
91.20	even	12		8281.2.a.co.1.10		12
91.23	even	6		91.2.u.b.88.2	yes	12
91.32	odd	12		1183.2.e.j.170.10		24
91.46	odd	12		1183.2.e.j.170.3		24
91.58	odd	12		1183.2.e.j.508.10		24
91.62	odd	6		637.2.q.i.491.5		12
91.72	odd	12		1183.2.e.j.508.3		24
91.75	odd	6		637.2.u.g.361.2		12
91.88	even	6		91.2.k.b.23.5	yes	12
273.23	odd	6		819.2.do.e.361.5		12
273.179	odd	6		819.2.bm.f.478.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.2	✓	12	7.2	even	3
91.2.k.b.23.5	yes	12	91.88	even	6
91.2.u.b.30.2	yes	12	7.4	even	3
91.2.u.b.88.2	yes	12	91.23	even	6
637.2.k.i.459.2		12	7.5	odd	6
637.2.k.i.569.5		12	91.10	odd	6
637.2.q.g.491.5		12	13.10	even	6	inner
637.2.q.g.589.5		12	1.1	even	1	trivial
637.2.q.i.491.5		12	91.62	odd	6
637.2.q.i.589.5		12	7.6	odd	2
637.2.u.g.30.2		12	7.3	odd	6
637.2.u.g.361.2		12	91.75	odd	6
819.2.bm.f.478.2		12	273.179	odd	6
819.2.bm.f.550.5		12	21.2	odd	6
819.2.do.e.361.5		12	273.23	odd	6
819.2.do.e.667.5		12	21.11	odd	6
1183.2.e.j.170.3		24	91.46	odd	12
1183.2.e.j.170.10		24	91.32	odd	12
1183.2.e.j.508.3		24	91.72	odd	12
1183.2.e.j.508.10		24	91.58	odd	12
8281.2.a.co.1.3		12	91.6	even	12
8281.2.a.co.1.10		12	91.20	even	12
8281.2.a.cp.1.3		12	13.6	odd	12
8281.2.a.cp.1.10		12	13.7	odd	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

Related objects

Downloads

Learn more