LMFDB - Embedded newform 637.2.x.b.80.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.4
Character	$\chi$	$=$	637.80
Dual form			637.2.x.b.215.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0302180 + 0.112775i) q^{2} +2.59871i q^{3} +(1.72025 - 0.993184i) q^{4} +(0.456951 - 1.70537i) q^{5} +(-0.293070 + 0.0785278i) q^{6} +(0.329103 + 0.329103i) q^{8} -3.75328 q^{9} +O(q^{10})$	\(q+(0.0302180 + 0.112775i) q^{2} +2.59871i q^{3} +(1.72025 - 0.993184i) q^{4} +(0.456951 - 1.70537i) q^{5} +(-0.293070 + 0.0785278i) q^{6} +(0.329103 + 0.329103i) q^{8} -3.75328 q^{9} +0.206131 q^{10} +(-1.38433 - 1.38433i) q^{11} +(2.58100 + 4.47042i) q^{12} +(1.85749 + 3.09026i) q^{13} +(4.43175 + 1.18748i) q^{15} +(1.95920 - 3.39343i) q^{16} +(2.13907 + 3.70498i) q^{17} +(-0.113417 - 0.423277i) q^{18} +(3.01787 + 3.01787i) q^{19} +(-0.907674 - 3.38749i) q^{20} +(0.114286 - 0.197949i) q^{22} +(5.53927 + 3.19810i) q^{23} +(-0.855244 + 0.855244i) q^{24} +(1.63066 + 0.941462i) q^{25} +(-0.292376 + 0.302861i) q^{26} -1.95756i q^{27} +(-3.57954 - 6.19995i) q^{29} +0.535675i q^{30} +(-4.13397 + 1.10769i) q^{31} +(1.34103 + 0.359327i) q^{32} +(3.59746 - 3.59746i) q^{33} +(-0.353191 + 0.353191i) q^{34} +(-6.45657 + 3.72770i) q^{36} +(2.73261 - 0.732202i) q^{37} +(-0.249147 + 0.431534i) q^{38} +(-8.03069 + 4.82707i) q^{39} +(0.711626 - 0.410857i) q^{40} +(2.94901 - 11.0059i) q^{41} +(-1.55234 - 0.896243i) q^{43} +(-3.75627 - 1.00649i) q^{44} +(-1.71507 + 6.40072i) q^{45} +(-0.193281 + 0.721333i) q^{46} +(-6.40208 - 1.71543i) q^{47} +(8.81854 + 5.09139i) q^{48} +(-0.0568982 + 0.212347i) q^{50} +(-9.62816 + 5.55882i) q^{51} +(6.26454 + 3.47118i) q^{52} +(-2.13896 + 3.70479i) q^{53} +(0.220765 - 0.0591537i) q^{54} +(-2.99335 + 1.72821i) q^{55} +(-7.84255 + 7.84255i) q^{57} +(0.591034 - 0.591034i) q^{58} +(-1.62980 - 0.436704i) q^{59} +(8.80308 - 2.35878i) q^{60} +3.08259i q^{61} +(-0.249841 - 0.432737i) q^{62} -7.67470i q^{64} +(6.11881 - 1.75560i) q^{65} +(0.514413 + 0.296996i) q^{66} +(0.0139368 - 0.0139368i) q^{67} +(7.35945 + 4.24898i) q^{68} +(-8.31093 + 14.3949i) q^{69} +(1.23109 + 4.59449i) q^{71} +(-1.23522 - 1.23522i) q^{72} +(-0.255666 - 0.954158i) q^{73} +(0.165148 + 0.286046i) q^{74} +(-2.44658 + 4.23761i) q^{75} +(8.18877 + 2.19417i) q^{76} +(-0.787046 - 0.759799i) q^{78} +(2.96860 + 5.14176i) q^{79} +(-4.89178 - 4.89178i) q^{80} -6.17272 q^{81} +1.33030 q^{82} +(-9.87683 - 9.87683i) q^{83} +(7.29580 - 1.95490i) q^{85} +(0.0541654 - 0.202148i) q^{86} +(16.1119 - 9.30218i) q^{87} -0.911173i q^{88} +(-2.07993 - 7.76240i) q^{89} -0.773669 q^{90} +12.7052 q^{92} +(-2.87857 - 10.7430i) q^{93} -0.773833i q^{94} +(6.52558 - 3.76755i) q^{95} +(-0.933785 + 3.48493i) q^{96} +(-14.2676 + 3.82300i) q^{97} +(5.19577 + 5.19577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.0302180	+	0.112775i	0.0213674	+	0.0797441i	0.975786	−	0.218726i	$-0.0701902\pi$
$2$	0.0302180	+	0.112775i	0.0213674	+	0.0797441i	−0.954419	+	0.298471i	$0.903524\pi$
$3$			2.59871i			1.50036i	0.661231	+	0.750182i	$0.270034\pi$
$3$			2.59871i			1.50036i	−0.661231	+	0.750182i	$0.729966\pi$
$4$	1.72025	−	0.993184i	0.860123	−	0.496592i
$5$	0.456951	−	1.70537i	0.204355	−	0.762663i	−0.785290	−	0.619128i	$-0.787486\pi$
$5$	0.456951	−	1.70537i	0.204355	−	0.762663i	0.989645	−	0.143535i	$-0.0458470\pi$
$6$	−0.293070	+	0.0785278i	−0.119645	+	0.0320589i
$7$		0			0
$7$		0			0
$8$	0.329103	+	0.329103i	0.116356	+	0.116356i
$9$	−3.75328			−1.25109
$10$	0.206131			0.0651844
$11$	−1.38433	−	1.38433i	−0.417390	−	0.417390i	0.466913	−	0.884303i	$-0.345366\pi$
$11$	−1.38433	−	1.38433i	−0.417390	−	0.417390i	−0.884303	+	0.466913i	$0.845366\pi$
$12$	2.58100	+	4.47042i	0.745069	+	1.29050i
$13$	1.85749	+	3.09026i	0.515175	+	0.857085i
$13$	1.85749	+	3.09026i	0.515175	+	0.857085i
$14$		0			0
$15$	4.43175	+	1.18748i	1.14427	+	0.306607i
$16$	1.95920	−	3.39343i	0.489800	−	0.848358i
$17$	2.13907	+	3.70498i	0.518801	+	0.898589i	0.999761	+	0.0218471i	$0.00695471\pi$
$17$	2.13907	+	3.70498i	0.518801	+	0.898589i	−0.480960	+	0.876742i	$0.659712\pi$
$18$	−0.113417	−	0.423277i	−0.0267326	−	0.0997674i
$19$	3.01787	+	3.01787i	0.692346	+	0.692346i	0.962748	−	0.270402i	$-0.0871566\pi$
$19$	3.01787	+	3.01787i	0.692346	+	0.692346i	−0.270402	+	0.962748i	$0.587157\pi$
$20$	−0.907674	−	3.38749i	−0.202962	−	0.757465i
$21$		0			0
$22$	0.114286	−	0.197949i	0.0243659	−	0.0422030i
$23$	5.53927	+	3.19810i	1.15502	+	0.666850i	0.950105	−	0.311930i	$-0.100976\pi$
$23$	5.53927	+	3.19810i	1.15502	+	0.666850i	0.204913	+	0.978780i	$0.434309\pi$
$24$	−0.855244	+	0.855244i	−0.174576	+	0.174576i
$25$	1.63066	+	0.941462i	0.326132	+	0.188292i
$26$	−0.292376	+	0.302861i	−0.0573396	+	0.0593959i
$27$		−	1.95756i		−	0.376733i
$28$		0			0
$29$	−3.57954	−	6.19995i	−0.664704	−	1.15130i	−0.979365	−	0.202097i	$-0.935224\pi$
$29$	−3.57954	−	6.19995i	−0.664704	−	1.15130i	0.314661	−	0.949204i	$-0.398109\pi$
$30$			0.535675i			0.0978004i
$31$	−4.13397	+	1.10769i	−0.742483	+	0.198948i	−0.610181	−	0.792262i	$-0.708903\pi$
$31$	−4.13397	+	1.10769i	−0.742483	+	0.198948i	−0.132302	+	0.991210i	$0.542237\pi$
$32$	1.34103	+	0.359327i	0.237062	+	0.0635206i
$33$	3.59746	−	3.59746i	0.626237	−	0.626237i
$34$	−0.353191	+	0.353191i	−0.0605718	+	0.0605718i
$35$		0			0
$36$	−6.45657	+	3.72770i	−1.07609	+	0.621284i
$37$	2.73261	−	0.732202i	0.449239	−	0.120373i	−0.0271042	−	0.999633i	$-0.508629\pi$
$37$	2.73261	−	0.732202i	0.449239	−	0.120373i	0.476343	+	0.879259i	$0.341962\pi$
$38$	−0.249147	+	0.431534i	−0.0404169	+	0.0700041i
$39$	−8.03069	+	4.82707i	−1.28594	+	0.772951i
$40$	0.711626	−	0.410857i	0.112518	−	0.0649623i
$41$	2.94901	−	11.0059i	0.460558	−	1.71883i	−0.210654	−	0.977561i	$-0.567559\pi$
$41$	2.94901	−	11.0059i	0.460558	−	1.71883i	0.671212	−	0.741266i	$-0.265774\pi$
$42$		0			0
$43$	−1.55234	−	0.896243i	−0.236730	−	0.136676i	0.376943	−	0.926236i	$-0.376975\pi$
$43$	−1.55234	−	0.896243i	−0.236730	−	0.136676i	−0.613673	+	0.789561i	$0.710309\pi$
$44$	−3.75627	−	1.00649i	−0.566279	−	0.151734i
$45$	−1.71507	+	6.40072i	−0.255667	+	0.954163i
$46$	−0.193281	+	0.721333i	−0.0284977	+	0.106355i
$47$	−6.40208	−	1.71543i	−0.933839	−	0.250222i	−0.240348	−	0.970687i	$-0.577262\pi$
$47$	−6.40208	−	1.71543i	−0.933839	−	0.250222i	−0.693491	+	0.720465i	$0.743928\pi$
$48$	8.81854	+	5.09139i	1.27285	+	0.734878i
$49$		0			0
$50$	−0.0568982	+	0.212347i	−0.00804663	+	0.0300304i
$51$	−9.62816	+	5.55882i	−1.34821	+	0.778390i
$52$	6.26454	+	3.47118i	0.868736	+	0.481366i
$53$	−2.13896	+	3.70479i	−0.293809	+	0.508893i	−0.974707	−	0.223486i	$-0.928256\pi$
$53$	−2.13896	+	3.70479i	−0.293809	+	0.508893i	0.680898	+	0.732378i	$0.261590\pi$
$54$	0.220765	−	0.0591537i	0.0300423	−	0.00804980i
$55$	−2.99335	+	1.72821i	−0.403624	+	0.233032i
$56$		0			0
$57$	−7.84255	+	7.84255i	−1.03877	+	1.03877i
$58$	0.591034	−	0.591034i	0.0776066	−	0.0776066i
$59$	−1.62980	−	0.436704i	−0.212182	−	0.0568541i	0.151162	−	0.988509i	$-0.451698\pi$
$59$	−1.62980	−	0.436704i	−0.212182	−	0.0568541i	−0.363344	+	0.931655i	$0.618365\pi$
$60$	8.80308	−	2.35878i	1.13647	−	0.304517i
$61$			3.08259i			0.394685i	0.980335	+	0.197342i	$0.0632311\pi$
$61$			3.08259i			0.394685i	−0.980335	+	0.197342i	$0.936769\pi$
$62$	−0.249841	−	0.432737i	−0.0317298	−	0.0549577i
$63$		0			0
$64$		−	7.67470i		−	0.959338i
$65$	6.11881	−	1.75560i	0.758945	−	0.217755i
$66$	0.514413	+	0.296996i	0.0633198	+	0.0365577i
$67$	0.0139368	−	0.0139368i	0.00170265	−	0.00170265i	−0.706255	−	0.707958i	$-0.749617\pi$
$67$	0.0139368	−	0.0139368i	0.00170265	−	0.00170265i	0.707958	+	0.706255i	$0.249617\pi$
$68$	7.35945	+	4.24898i	0.892465	+	0.515265i
$69$	−8.31093	+	14.3949i	−1.00052	+	1.73295i
$70$		0			0
$71$	1.23109	+	4.59449i	0.146104	+	0.545266i	0.999704	+	0.0243373i	$0.00774758\pi$
$71$	1.23109	+	4.59449i	0.146104	+	0.545266i	−0.853600	+	0.520929i	$0.825586\pi$
$72$	−1.23522	−	1.23522i	−0.145572	−	0.145572i
$73$	−0.255666	−	0.954158i	−0.0299234	−	0.111676i	0.949349	−	0.314224i	$-0.101744\pi$
$73$	−0.255666	−	0.954158i	−0.0299234	−	0.111676i	−0.979272	+	0.202548i	$0.935078\pi$
$74$	0.165148	+	0.286046i	0.0191981	+	0.0332521i
$75$	−2.44658	+	4.23761i	−0.282507	+	0.489317i
$76$	8.18877	+	2.19417i	0.939316	+	0.251689i
$77$		0			0
$78$	−0.787046	−	0.759799i	−0.0891154	−	0.0860303i
$79$	2.96860	+	5.14176i	0.333993	+	0.578493i	0.983291	−	0.182041i	$-0.0582704\pi$
$79$	2.96860	+	5.14176i	0.333993	+	0.578493i	−0.649298	+	0.760534i	$0.724937\pi$
$80$	−4.89178	−	4.89178i	−0.546918	−	0.546918i
$81$	−6.17272			−0.685857
$82$	1.33030			0.146907
$83$	−9.87683	−	9.87683i	−1.08412	−	1.08412i	−0.996120	−	0.0880033i	$-0.971951\pi$
$83$	−9.87683	−	9.87683i	−1.08412	−	1.08412i	−0.0880033	−	0.996120i	$-0.528049\pi$
$84$		0			0
$85$	7.29580	−	1.95490i	0.791340	−	0.212039i
$86$	0.0541654	−	0.202148i	0.00584081	−	0.0217982i
$87$	16.1119	−	9.30218i	1.72737	−	0.997299i
$88$		−	0.911173i		−	0.0971314i
$89$	−2.07993	−	7.76240i	−0.220472	−	0.822813i	−0.984168	−	0.177237i	$-0.943284\pi$
$89$	−2.07993	−	7.76240i	−0.220472	−	0.822813i	0.763696	−	0.645576i	$-0.223383\pi$
$90$	−0.773669			−0.0815519
$91$		0			0
$92$	12.7052			1.32461
$93$	−2.87857	−	10.7430i	−0.298494	−	1.11400i
$94$		−	0.773833i		−	0.0798148i
$95$	6.52558	−	3.76755i	0.669511	−	0.386542i
$96$	−0.933785	+	3.48493i	−0.0953041	+	0.355680i
$97$	−14.2676	+	3.82300i	−1.44866	+	0.388167i	−0.895557	−	0.444946i	$-0.853223\pi$
$97$	−14.2676	+	3.82300i	−1.44866	+	0.388167i	−0.553102	+	0.833113i	$0.686556\pi$
$98$		0			0
$99$	5.19577	+	5.19577i	0.522194	+	0.522194i
$100$	3.74018			0.374018
$101$	−16.0096			−1.59301			−0.796506	−	0.604630i	$-0.793321\pi$
$101$	−16.0096			−1.59301			−0.796506	+	0.604630i	$0.793321\pi$
$102$	−0.917841	−	0.917841i	−0.0908798	−	0.0908798i
$103$	−5.90755	−	10.2322i	−0.582088	−	1.00821i	−0.995232	−	0.0975405i	$-0.968902\pi$
$103$	−5.90755	−	10.2322i	−0.582088	−	1.00821i	0.413143	−	0.910666i	$-0.364431\pi$
$104$	−0.405710	+	1.62832i	−0.0397831	+	0.159670i
$105$		0			0
$106$	−0.482444	−	0.129271i	−0.0468591	−	0.0125559i
$107$	−3.99556	+	6.92051i	−0.386265	+	0.669031i	−0.991944	−	0.126678i	$-0.959568\pi$
$107$	−3.99556	+	6.92051i	−0.386265	+	0.669031i	0.605679	+	0.795709i	$0.292902\pi$
$108$	−1.94422	−	3.36749i	−0.187083	−	0.324037i
$109$	−3.20509	−	11.9616i	−0.306992	−	1.14571i	−0.931217	−	0.364465i	$-0.881252\pi$
$109$	−3.20509	−	11.9616i	−0.306992	−	1.14571i	0.624225	−	0.781245i	$-0.285415\pi$
$110$	−0.285353	−	0.285353i	−0.0272073	−	0.0272073i
$111$	1.90278	+	7.10127i	0.180604	+	0.674022i
$112$		0			0
$113$	4.27217	−	7.39961i	0.401892	−	0.696097i	−0.592063	−	0.805892i	$-0.701686\pi$
$113$	4.27217	−	7.39961i	0.401892	−	0.696097i	0.993954	+	0.109795i	$0.0350195\pi$
$114$	−1.12143	−	0.647459i	−0.105032	−	0.0606401i
$115$	7.98511	−	7.98511i	0.744615	−	0.744615i
$116$	−12.3154	−	7.11029i	−1.14345	−	0.660174i
$117$	−6.97169	−	11.5986i	−0.644533	−	1.07229i
$118$		−	0.196998i		−	0.0181351i
$119$		0			0
$120$	1.06770	+	1.84931i	0.0974671	+	0.168818i
$121$		−	7.16728i		−	0.651571i
$122$	−0.347640	+	0.0931497i	−0.0314738	+	0.00843338i
$123$	28.6010	+	7.66362i	2.57887	+	0.691005i
$124$	−6.01130	+	6.01130i	−0.539831	+	0.539831i
$125$	8.59274	−	8.59274i	0.768558	−	0.768558i
$126$		0			0
$127$	−5.29483	+	3.05697i	−0.469840	+	0.271262i	−0.716173	−	0.697923i	$-0.754108\pi$
$127$	−5.29483	+	3.05697i	−0.469840	+	0.271262i	0.246333	+	0.969185i	$0.420774\pi$
$128$	3.54757	−	0.950568i	0.313564	−	0.0840191i
$129$	2.32907	−	4.03408i	0.205064	−	0.355181i
$130$	0.382887	+	0.637000i	0.0335814	+	0.0558686i
$131$	4.99207	−	2.88218i	0.436159	−	0.251817i	−0.265808	−	0.964026i	$-0.585639\pi$
$131$	4.99207	−	2.88218i	0.436159	−	0.251817i	0.701967	+	0.712209i	$0.252305\pi$
$132$	2.61557	−	9.76146i	0.227657	−	0.849626i
$133$		0			0
$134$	0.00199287	+	0.00115058i	0.000172157	+	9.93951e-5i
$135$	−3.33836	−	0.894511i	−0.287320	−	0.0769872i
$136$	−0.515346	+	1.92330i	−0.0441905	+	0.164921i
$137$	1.62427	−	6.06188i	0.138771	−	0.517901i	−0.861183	−	0.508296i	$-0.830276\pi$
$137$	1.62427	−	6.06188i	0.138771	−	0.517901i	0.999954	−	0.00960548i	$-0.00305757\pi$
$138$	−1.87453	−	0.502280i	−0.159571	−	0.0427569i
$139$	18.1314	+	10.4682i	1.53789	+	0.887900i	0.998962	+	0.0455477i	$0.0145033\pi$
$139$	18.1314	+	10.4682i	1.53789	+	0.887900i	0.538927	+	0.842353i	$0.318830\pi$
$140$		0			0
$141$	4.45791	−	16.6371i	0.375424	−	1.40110i
$142$	−0.480944	+	0.277673i	−0.0403599	+	0.0233018i
$143$	1.70656	−	6.84931i	0.142710	−	0.572768i
$144$	−7.35343	+	12.7365i	−0.612786	+	1.06138i
$145$	−12.2089	+	3.27135i	−1.01389	+	0.271671i
$146$	0.0998797	−	0.0576656i	0.00826610	−	0.00477244i
$147$		0			0
$148$	3.97356	−	3.97356i	0.326624	−	0.326624i
$149$	10.9301	−	10.9301i	0.895431	−	0.895431i	−0.0995972	−	0.995028i	$-0.531755\pi$
$149$	10.9301	−	10.9301i	0.895431	−	0.895431i	0.995028	+	0.0995972i	$0.0317554\pi$
$150$	−0.551828	−	0.147862i	−0.0450566	−	0.0120729i
$151$	−4.27019	+	1.14419i	−0.347503	+	0.0931131i	−0.428349	−	0.903614i	$-0.640905\pi$
$151$	−4.27019	+	1.14419i	−0.347503	+	0.0931131i	0.0808459	+	0.996727i	$0.474238\pi$
$152$			1.98638i			0.161117i
$153$	−8.02854	−	13.9058i	−0.649069	−	1.12422i
$154$		0			0
$155$			7.55609i			0.606920i
$156$	−9.02059	+	16.2797i	−0.722225	+	1.30342i
$157$	−6.00211	−	3.46532i	−0.479020	−	0.276563i	0.240988	−	0.970528i	$-0.422529\pi$
$157$	−6.00211	−	3.46532i	−0.479020	−	0.276563i	−0.720008	+	0.693966i	$0.755862\pi$
$158$	−0.490158	+	0.490158i	−0.0389949	+	0.0389949i
$159$	−9.62768	−	5.55854i	−0.763525	−	0.440821i
$160$	1.22557	−	2.12274i	0.0968896	−	0.167818i
$161$		0			0
$162$	−0.186527	−	0.696129i	−0.0146550	−	0.0546931i
$163$	9.14651	+	9.14651i	0.716410	+	0.716410i	0.967868	−	0.251458i	$-0.0809101\pi$
$163$	9.14651	+	9.14651i	0.716410	+	0.716410i	−0.251458	+	0.967868i	$0.580910\pi$
$164$	−5.85782	−	21.8617i	−0.457419	−	1.70711i
$165$	−4.49112	−	7.77885i	−0.349633	−	0.605583i
$166$	0.815404	−	1.41232i	0.0632876	−	0.109617i
$167$	0.900490	+	0.241286i	0.0696820	+	0.0186712i	0.293492	−	0.955962i	$-0.405183\pi$
$167$	0.900490	+	0.241286i	0.0696820	+	0.0186712i	−0.223810	+	0.974633i	$0.571849\pi$
$168$		0			0
$169$	−6.09946	+	11.4803i	−0.469189	+	0.883098i
$170$	0.440929	+	0.763712i	0.0338177	+	0.0585740i
$171$	−11.3269	−	11.3269i	−0.866190	−	0.866190i
$172$	−3.56054			−0.271489
$173$	−0.527560			−0.0401096			−0.0200548	−	0.999799i	$-0.506384\pi$
$173$	−0.527560			−0.0401096			−0.0200548	+	0.999799i	$0.506384\pi$
$174$	1.53592	+	1.53592i	0.116438	+	0.116438i
$175$		0			0
$176$	−7.40979	+	1.98545i	−0.558534	+	0.149659i
$177$	1.13487	−	4.23538i	0.0853018	−	0.318351i
$178$	0.812555	−	0.469129i	0.0609036	−	0.0351627i
$179$			8.27003i			0.618131i	0.951041	+	0.309066i	$0.100016\pi$
$179$			8.27003i			0.618131i	−0.951041	+	0.309066i	$0.899984\pi$
$180$	3.40676	+	12.7142i	0.253925	+	0.947660i
$181$	−14.9785			−1.11334			−0.556672	−	0.830732i	$-0.687922\pi$
$181$	−14.9785			−1.11334			−0.556672	+	0.830732i	$0.687922\pi$
$182$		0			0
$183$	−8.01075			−0.592171
$184$	0.770488	+	2.87550i	0.0568011	+	0.211985i
$185$		−	4.99469i		−	0.367217i
$186$	1.12456	−	0.649263i	0.0824565	−	0.0476063i
$187$	2.16773	−	8.09007i	0.158520	−	0.591605i
$188$	−12.7169	+	3.40748i	−0.927475	+	0.248516i
$189$		0			0
$190$	0.622076	+	0.622076i	0.0451301	+	0.0451301i
$191$	−14.5292			−1.05130			−0.525649	−	0.850702i	$-0.676177\pi$
$191$	−14.5292			−1.05130			−0.525649	+	0.850702i	$0.676177\pi$
$192$	19.9443			1.43936
$193$	13.8436	+	13.8436i	0.996483	+	0.996483i	0.999994	−	0.00351052i	$-0.00111744\pi$
$193$	13.8436	+	13.8436i	0.996483	+	0.996483i	−0.00351052	+	0.999994i	$0.501117\pi$
$194$	−0.862280	−	1.49351i	−0.0619081	−	0.107228i
$195$	4.56229	+	15.9010i	0.326712	+	1.13869i
$196$		0			0
$197$	−21.0175	−	5.63163i	−1.49744	−	0.401237i	−0.585196	−	0.810892i	$-0.698982\pi$
$197$	−21.0175	−	5.63163i	−1.49744	−	0.401237i	−0.912240	+	0.409655i	$0.865649\pi$
$198$	−0.428948	+	0.742960i	−0.0304840	+	0.0527999i
$199$	9.64065	+	16.6981i	0.683408	+	1.18370i	0.973934	+	0.226830i	$0.0728362\pi$
$199$	9.64065	+	16.6981i	0.683408	+	1.18370i	−0.290527	+	0.956867i	$0.593830\pi$
$200$	0.226817	+	0.846494i	0.0160384	+	0.0598562i
$201$	0.0362176	+	0.0362176i	0.00255459	+	0.00255459i
$202$	−0.483778	−	1.80548i	−0.0340385	−	0.127033i
$203$		0			0
$204$	−11.0419	+	19.1251i	−0.773085	+	1.33902i
$205$	−17.4215	−	10.0583i	−1.21677	−	0.702501i
$206$	0.975422	−	0.975422i	0.0679609	−	0.0679609i
$207$	−20.7905	−	12.0034i	−1.44504	−	0.834292i
$208$	14.1258	−	0.248825i	0.979447	−	0.0172529i
$209$		−	8.35542i		−	0.577957i
$210$		0			0
$211$	1.51130	+	2.61764i	0.104042	+	0.180206i	0.913346	−	0.407184i	$-0.133489\pi$
$211$	1.51130	+	2.61764i	0.104042	+	0.180206i	−0.809304	+	0.587389i	$0.800156\pi$
$212$			8.49754i			0.583614i
$213$	−11.9397	+	3.19925i	−0.818098	+	0.219209i
$214$	−0.901200	−	0.241476i	−0.0616048	−	0.0165070i
$215$	−2.23777	+	2.23777i	−0.152614	+	0.152614i
$216$	0.644241	−	0.644241i	0.0438350	−	0.0438350i
$217$		0			0
$218$	1.25212	−	0.722910i	0.0848040	−	0.0489616i
$219$	2.47958	−	0.664401i	0.167554	−	0.0448961i
$220$	−3.43287	+	5.94590i	−0.231444	+	0.400873i
$221$	−7.47606	+	13.4923i	−0.502894	+	0.907587i
$222$	−0.743349	+	0.429173i	−0.0498903	+	0.0288042i
$223$	−1.13865	+	4.24949i	−0.0762495	+	0.284567i	−0.993514	−	0.113712i	$-0.963726\pi$
$223$	−1.13865	+	4.24949i	−0.0762495	+	0.284567i	0.917264	+	0.398279i	$0.130392\pi$
$224$		0			0
$225$	−6.12033	−	3.53357i	−0.408022	−	0.235571i
$226$	0.963589	+	0.258193i	0.0640970	+	0.0171747i
$227$	−1.06086	+	3.95917i	−0.0704116	+	0.262780i	−0.992154	−	0.125024i	$-0.960099\pi$
$227$	−1.06086	+	3.95917i	−0.0704116	+	0.262780i	0.921742	+	0.387803i	$0.126766\pi$
$228$	−5.70202	+	21.2802i	−0.377625	+	1.40932i
$229$	13.1144	+	3.51399i	0.866623	+	0.232211i	0.664627	−	0.747176i	$-0.268591\pi$
$229$	13.1144	+	3.51399i	0.866623	+	0.232211i	0.201996	+	0.979386i	$0.435257\pi$
$230$	1.14182	+	0.659228i	0.0752892	+	0.0434682i
$231$		0			0
$232$	0.862385	−	3.21846i	0.0566183	−	0.211303i
$233$	14.1595	−	8.17501i	0.927622	−	0.535563i	0.0415633	−	0.999136i	$-0.486766\pi$
$233$	14.1595	−	8.17501i	0.927622	−	0.535563i	0.886059	+	0.463573i	$0.153433\pi$
$234$	1.09737	−	1.13672i	0.0717372	−	0.0743098i
$235$	−5.85088	+	10.1340i	−0.381669	+	0.661071i
$236$	−3.23739	+	0.867456i	−0.210736	+	0.0564666i
$237$	−13.3619	+	7.71452i	−0.867951	+	0.501112i
$238$		0			0
$239$	6.11495	−	6.11495i	0.395543	−	0.395543i	−0.481115	−	0.876658i	$-0.659768\pi$
$239$	6.11495	−	6.11495i	0.395543	−	0.395543i	0.876658	+	0.481115i	$0.159768\pi$
$240$	12.7123	−	12.7123i	0.820577	−	0.820577i
$241$	12.9736	+	3.47625i	0.835700	+	0.223925i	0.651199	−	0.758907i	$-0.274266\pi$
$241$	12.9736	+	3.47625i	0.835700	+	0.223925i	0.184501	+	0.982832i	$0.440933\pi$
$242$	0.808292	−	0.216581i	0.0519590	−	0.0139224i
$243$		−	21.9138i		−	1.40577i
$244$	3.06158	+	5.30281i	0.195997	+	0.339478i
$245$		0			0
$246$			3.45707i			0.220414i
$247$	−3.72034	+	14.9317i	−0.236720	+	0.950078i
$248$	−1.72505	−	0.995958i	−0.109541	−	0.0632434i
$249$	25.6670	−	25.6670i	1.62658	−	1.62658i
$250$	1.22870	+	0.709393i	0.0777101	+	0.0448659i
$251$	1.74301	−	3.01899i	0.110018	−	0.190557i	−0.805759	−	0.592243i	$-0.798242\pi$
$251$	1.74301	−	3.01899i	0.110018	−	0.190557i	0.915777	+	0.401686i	$0.131576\pi$
$252$		0			0
$253$	−3.24095	−	12.0954i	−0.203756	−	0.760430i
$254$	−0.504750	−	0.504750i	−0.0316708	−	0.0316708i
$255$	5.08022	+	18.9596i	0.318136	+	1.18730i
$256$	−7.46030	−	12.9216i	−0.466269	−	0.807601i
$257$	−6.72396	+	11.6462i	−0.419429	+	0.726472i	−0.995882	−	0.0906578i	$-0.971103\pi$
$257$	−6.72396	+	11.6462i	−0.419429	+	0.726472i	0.576453	+	0.817130i	$0.304436\pi$
$258$	0.525324	+	0.140760i	0.0327052	+	0.00876334i
$259$		0			0
$260$	8.78223	−	9.09717i	0.544651	−	0.564183i
$261$	13.4350	+	23.2702i	0.831608	+	1.44039i
$262$	0.475889	+	0.475889i	0.0294005	+	0.0294005i
$263$	20.5358			1.26629			0.633147	−	0.774032i	$-0.281763\pi$
$263$	20.5358			1.26629			0.633147	+	0.774032i	$0.281763\pi$
$264$	2.36787			0.145733
$265$	5.34063	+	5.34063i	0.328072	+	0.328072i
$266$		0			0
$267$	20.1722	−	5.40513i	1.23452	−	0.330788i
$268$	0.0101329	−	0.0378165i	0.000618965	−	0.00231001i
$269$	−9.29875	+	5.36864i	−0.566955	+	0.327332i	−0.755932	−	0.654650i	$-0.772816\pi$
$269$	−9.29875	+	5.36864i	−0.566955	+	0.327332i	0.188977	+	0.981981i	$0.439483\pi$
$270$		−	0.403515i		−	0.0245571i
$271$	−0.387901	−	1.44767i	−0.0235633	−	0.0879396i	0.953143	−	0.302521i	$-0.0978281\pi$
$271$	−0.387901	−	1.44767i	−0.0235633	−	0.0879396i	−0.976706	+	0.214581i	$0.931161\pi$
$272$	16.7635			1.01643
$273$		0			0
$274$	0.732712			0.0442647
$275$	−0.954075	−	3.56065i	−0.0575329	−	0.214716i
$276$			33.0171i			1.98740i
$277$	−4.07919	+	2.35512i	−0.245095	+	0.141506i	−0.617516	−	0.786558i	$-0.711861\pi$
$277$	−4.07919	+	2.35512i	−0.245095	+	0.141506i	0.372421	+	0.928064i	$0.378528\pi$
$278$	−0.632656	+	2.36111i	−0.0379442	+	0.141610i
$279$	15.5160	−	4.15749i	0.928916	−	0.248902i
$280$		0			0
$281$	8.01227	+	8.01227i	0.477972	+	0.477972i	0.904483	−	0.426511i	$-0.140257\pi$
$281$	8.01227	+	8.01227i	0.477972	+	0.477972i	−0.426511	+	0.904483i	$0.640257\pi$
$282$	2.01097			0.119751
$283$	−7.87867			−0.468338			−0.234169	−	0.972196i	$-0.575237\pi$
$283$	−7.87867			−0.468338			−0.234169	+	0.972196i	$0.575237\pi$
$284$	6.68096	+	6.68096i	0.396442	+	0.396442i
$285$	9.79075	+	16.9581i	0.579954	+	1.00451i
$286$	0.824001	−	0.0145147i	0.0487242	−	0.000858275i
$287$		0			0
$288$	−5.03325	−	1.34865i	−0.296587	−	0.0794703i
$289$	−0.651246	+	1.12799i	−0.0383086	+	0.0663525i
$290$	−0.737855	−	1.27800i	−0.0433284	−	0.0750469i
$291$	−9.93487	−	37.0774i	−0.582392	−	2.17352i
$292$	−1.38746	−	1.38746i	−0.0811951	−	0.0811951i
$293$	−3.16216	−	11.8013i	−0.184735	−	0.689442i	−0.994687	−	0.102945i	$-0.967173\pi$
$293$	−3.16216	−	11.8013i	−0.184735	−	0.689442i	0.809952	−	0.586497i	$-0.199493\pi$
$294$		0			0
$295$	−1.48948	+	2.57986i	−0.0867210	+	0.150205i
$296$	1.14028	+	0.658343i	0.0662776	+	0.0382654i
$297$	−2.70991	+	2.70991i	−0.157245	+	0.157245i
$298$	1.56293	+	0.902360i	0.0905383	+	0.0522723i
$299$	0.406170	+	23.0582i	0.0234894	+	1.33349i
$300$			9.71963i			0.561163i
$301$		0			0
$302$	−0.258073	−	0.446996i	−0.0148504	−	0.0257217i
$303$		−	41.6042i		−	2.39010i
$304$	16.1535	−	4.32832i	0.926468	−	0.248246i
$305$	5.25694	+	1.40859i	0.301011	+	0.0806558i
$306$	1.32563	−	1.32563i	0.0757811	−	0.0757811i
$307$	7.97207	−	7.97207i	0.454990	−	0.454990i	−0.442017	−	0.897007i	$-0.645737\pi$
$307$	7.97207	−	7.97207i	0.454990	−	0.454990i	0.897007	+	0.442017i	$0.145737\pi$
$308$		0			0
$309$	26.5904	−	15.3520i	1.51268	−	0.873345i
$310$	−0.852140	+	0.228330i	−0.0483983	+	0.0129683i
$311$	−6.52139	+	11.2954i	−0.369794	+	0.640502i	−0.989533	−	0.144306i	$-0.953905\pi$
$311$	−6.52139	+	11.2954i	−0.369794	+	0.640502i	0.619739	+	0.784808i	$0.287238\pi$
$312$	−4.23154	−	1.05432i	−0.239564	−	0.0596892i
$313$	−3.09510	+	1.78696i	−0.174945	+	0.101005i	−0.584916	−	0.811094i	$-0.698872\pi$
$313$	−3.09510	+	1.78696i	−0.174945	+	0.101005i	0.409970	+	0.912099i	$0.365539\pi$
$314$	0.209430	−	0.781604i	0.0118188	−	0.0441085i
$315$		0			0
$316$	10.2134	+	5.89673i	0.574551	+	0.331717i
$317$	−32.0422	−	8.58569i	−1.79967	−	0.482220i	−0.805743	−	0.592265i	$-0.798234\pi$
$317$	−32.0422	−	8.58569i	−1.79967	−	0.482220i	−0.993927	+	0.110045i	$0.964901\pi$
$318$	0.335936	−	1.25373i	0.0188384	−	0.0703058i
$319$	−3.62750	+	13.5380i	−0.203101	+	0.757983i
$320$	−13.0882	−	3.50697i	−0.731651	−	0.196045i
$321$	−17.9844	−	10.3833i	−1.00379	−	0.579539i
$322$		0			0
$323$	−4.72570	+	17.6366i	−0.262945	+	0.981324i
$324$	−10.6186	+	6.13064i	−0.589921	+	0.340591i
$325$	0.119569	+	6.78792i	0.00663249	+	0.376526i
$326$	−0.755110	+	1.30789i	−0.0418217	+	0.0724373i
$327$	31.0846	−	8.32910i	1.71898	−	0.460600i
$328$	4.59260	−	2.65154i	0.253584	−	0.146407i
$329$		0			0
$330$	0.741549	−	0.741549i	0.0408209	−	0.0408209i
$331$	−0.670431	+	0.670431i	−0.0368502	+	0.0368502i	−0.725292	−	0.688442i	$-0.758295\pi$
$331$	−0.670431	+	0.670431i	−0.0368502	+	0.0368502i	0.688442	+	0.725292i	$0.258295\pi$
$332$	−26.8001	−	7.18106i	−1.47085	−	0.394112i
$333$	−10.2563	+	2.74816i	−0.562040	+	0.150598i
$334$			0.108844i			0.00595569i
$335$	−0.0173989	−	0.0301357i	−0.000950602	−	0.00164649i
$336$		0			0
$337$			14.1901i			0.772982i	0.922293	+	0.386491i	$0.126313\pi$
$337$			14.1901i			0.772982i	−0.922293	+	0.386491i	$0.873687\pi$
$338$	−1.47900	−	0.340957i	−0.0804472	−	0.0185456i
$339$	19.2294	+	11.1021i	1.04440	+	0.602984i
$340$	10.6090	−	10.6090i	0.575353	−	0.575353i
$341$	7.25617	+	4.18935i	0.392944	+	0.226866i
$342$	0.935117	−	1.61967i	0.0505654	−	0.0875818i
$343$		0			0
$344$	−0.215923	−	0.805837i	−0.0116418	−	0.0434478i
$345$	20.7510	+	20.7510i	1.11719	+	1.11719i
$346$	−0.0159418	−	0.0594957i	−0.000857038	−	0.00319851i
$347$	−6.92103	−	11.9876i	−0.371540	−	0.643527i	0.618262	−	0.785972i	$-0.287837\pi$
$347$	−6.92103	−	11.9876i	−0.371540	−	0.643527i	−0.989803	+	0.142445i	$0.954504\pi$
$348$	18.4776	−	32.0041i	0.990502	−	1.71560i
$349$	−14.7875	−	3.96231i	−0.791559	−	0.212098i	−0.159684	−	0.987168i	$-0.551048\pi$
$349$	−14.7875	−	3.96231i	−0.791559	−	0.212098i	−0.631875	+	0.775071i	$0.717714\pi$
$350$		0			0
$351$	6.04939	−	3.63615i	0.322892	−	0.194084i
$352$	−1.35899	−	2.35384i	−0.0724345	−	0.125460i
$353$	11.1372	+	11.1372i	0.592773	+	0.592773i	0.938379	−	0.345607i	$-0.112327\pi$
$353$	11.1372	+	11.1372i	0.592773	+	0.592773i	−0.345607	+	0.938379i	$0.612327\pi$
$354$	0.511940			0.0272093
$355$	8.39784			0.445711
$356$	−11.2875	−	11.2875i	−0.598235	−	0.598235i
$357$		0			0
$358$	−0.932655	+	0.249904i	−0.0492924	+	0.0132078i
$359$	−1.71588	+	6.40375i	−0.0905607	+	0.337977i	−0.996309	−	0.0858388i	$-0.972643\pi$
$359$	−1.71588	+	6.40375i	−0.0905607	+	0.337977i	0.905748	+	0.423816i	$0.139310\pi$
$360$	−2.67093	+	1.54206i	−0.140771	+	0.0812739i
$361$		−	0.784981i		−	0.0413148i
$362$	−0.452621	−	1.68920i	−0.0237892	−	0.0887826i
$363$	18.6257			0.977594
$364$		0			0
$365$	−1.74402			−0.0912859
$366$	−0.242069	−	0.903414i	−0.0126531	−	0.0472222i
$367$		−	32.8567i		−	1.71511i	−0.514396	−	0.857553i	$-0.671984\pi$
$367$		−	32.8567i		−	1.71511i	0.514396	−	0.857553i	$-0.328016\pi$
$368$	21.7051	−	12.5314i	1.13145	−	0.653246i
$369$	−11.0685	+	41.3081i	−0.576202	+	2.15041i
$370$	0.563277	−	0.150930i	0.0292834	−	0.00784646i
$371$		0			0
$372$	−15.6216	−	15.6216i	−0.809943	−	0.809943i
$373$	7.87973			0.407997			0.203998	−	0.978971i	$-0.434606\pi$
$373$	7.87973			0.407997			0.203998	+	0.978971i	$0.434606\pi$
$374$	0.977864			0.0505642
$375$	22.3300	+	22.3300i	1.15312	+	1.15312i
$376$	−1.54239	−	2.67150i	−0.0795428	−	0.137772i
$377$	12.5105	−	22.5781i	0.644324	−	1.16283i
$378$		0			0
$379$	10.8095	+	2.89639i	0.555245	+	0.148778i	0.525521	−	0.850781i	$-0.323870\pi$
$379$	10.8095	+	2.89639i	0.555245	+	0.148778i	0.0297243	+	0.999558i	$0.490537\pi$
$380$	7.48374	−	12.9622i	0.383908	−	0.664947i
$381$	−7.94417	−	13.7597i	−0.406992	−	0.704931i
$382$	−0.439044	−	1.63854i	−0.0224635	−	0.0838348i
$383$	1.70452	+	1.70452i	0.0870968	+	0.0870968i	0.749313	−	0.662216i	$-0.230384\pi$
$383$	1.70452	+	1.70452i	0.0870968	+	0.0870968i	−0.662216	+	0.749313i	$0.730384\pi$
$384$	2.47025	+	9.21909i	0.126059	+	0.470460i
$385$		0			0
$386$	−1.14289	+	1.97954i	−0.0581715	+	0.100756i
$387$	5.82637	+	3.36386i	0.296171	+	0.170994i
$388$	−20.7469	+	20.7469i	−1.05326	+	1.05326i
$389$	−14.5674	−	8.41049i	−0.738596	−	0.426429i	0.0829624	−	0.996553i	$-0.473562\pi$
$389$	−14.5674	−	8.41049i	−0.738596	−	0.426429i	−0.821559	+	0.570124i	$0.806895\pi$
$390$	−1.65538	+	0.995011i	−0.0838232	+	0.0503843i
$391$			27.3638i			1.38385i
$392$		0			0
$393$	7.48993	+	12.9729i	0.377817	+	0.654398i
$394$		−	2.54043i		−	0.127985i
$395$	10.1251	−	2.71301i	0.509448	−	0.136506i
$396$	14.0984	+	3.77764i	0.708469	+	0.189834i
$397$	16.6347	−	16.6347i	0.834873	−	0.834873i	−0.153306	−	0.988179i	$-0.548992\pi$
$397$	16.6347	−	16.6347i	0.834873	−	0.834873i	0.988179	+	0.153306i	$0.0489921\pi$
$398$	−1.59181	+	1.59181i	−0.0797903	+	0.0797903i
$399$		0			0
$400$	6.38957	−	3.68902i	0.319479	−	0.184451i
$401$	−8.33434	+	2.23318i	−0.416197	+	0.111520i	−0.460840	−	0.887483i	$-0.652452\pi$
$401$	−8.33434	+	2.23318i	−0.416197	+	0.111520i	0.0446427	+	0.999003i	$0.485785\pi$
$402$	−0.00299003	+	0.00517888i	−0.000149129	+	0.000258299i
$403$	−11.1019	−	10.7175i	−0.553024	−	0.533878i
$404$	−27.5404	+	15.9005i	−1.37019	+	0.791078i
$405$	−2.82063	+	10.5267i	−0.140158	+	0.523078i
$406$		0			0
$407$	−4.79644	−	2.76922i	−0.237751	−	0.137265i
$408$	−4.99809	−	1.33923i	−0.247442	−	0.0663019i
$409$	−3.47744	+	12.9780i	−0.171948	+	0.641720i	0.825103	+	0.564982i	$0.191117\pi$
$409$	−3.47744	+	12.9780i	−0.171948	+	0.641720i	−0.997051	+	0.0767375i	$0.975550\pi$
$410$	0.607883	−	2.26865i	0.0300212	−	0.112041i
$411$	15.7530	+	4.22102i	0.777040	+	0.208207i
$412$	−20.3249	−	11.7346i	−1.00133	−	0.578121i
$413$		0			0
$414$	0.725437	−	2.70737i	0.0356533	−	0.133060i
$415$	−21.3568	+	12.3304i	−1.04837	+	0.605275i
$416$	1.38053	+	4.81157i	0.0676859	+	0.235907i
$417$	−27.2038	+	47.1183i	−1.33217	+	2.30739i
$418$	0.942285	−	0.252484i	0.0460886	−	0.0123494i
$419$	15.0514	−	8.68991i	0.735308	−	0.424530i	−0.0850532	−	0.996376i	$-0.527106\pi$
$419$	15.0514	−	8.68991i	0.735308	−	0.424530i	0.820361	+	0.571846i	$0.193773\pi$
$420$		0			0
$421$	−21.2490	+	21.2490i	−1.03561	+	1.03561i	−0.0362722	+	0.999342i	$0.511548\pi$
$421$	−21.2490	+	21.2490i	−1.03561	+	1.03561i	−0.999342	+	0.0362722i	$0.988452\pi$
$422$	−0.249537	+	0.249537i	−0.0121473	+	0.0121473i
$423$	24.0288	+	6.43850i	1.16832	+	0.313051i
$424$	−1.92320	+	0.515320i	−0.0933989	+	0.0250262i
$425$			8.05541i			0.390745i
$426$	−0.721591	−	1.24983i	−0.0349612	−	0.0605546i
$427$		0			0
$428$			15.8733i			0.767265i
$429$	17.7993	+	4.43485i	0.859361	+	0.214117i
$430$	−0.319986	−	0.184744i	−0.0154311	−	0.00890913i
$431$	−17.0631	+	17.0631i	−0.821902	+	0.821902i	−0.986381	−	0.164479i	$-0.947406\pi$
$431$	−17.0631	+	17.0631i	−0.821902	+	0.821902i	0.164479	+	0.986381i	$0.447406\pi$
$432$	−6.64286	−	3.83525i	−0.319605	−	0.184524i
$433$	2.27124	−	3.93391i	0.109149	−	0.189051i	−0.806277	−	0.591538i	$-0.798521\pi$
$433$	2.27124	−	3.93391i	0.109149	−	0.189051i	0.915426	+	0.402487i	$0.131854\pi$
$434$		0			0
$435$	−8.50129	−	31.7273i	−0.407606	−	1.52121i
$436$	−17.3936	−	17.3936i	−0.833001	−	0.833001i
$437$	7.06534	+	26.3682i	0.337981	+	1.26136i
$438$	0.149856	+	0.259558i	0.00716039	+	0.0124022i
$439$	−8.50036	+	14.7231i	−0.405700	+	0.702693i	−0.994403	−	0.105657i	$-0.966306\pi$
$439$	−8.50036	+	14.7231i	−0.405700	+	0.702693i	0.588703	+	0.808350i	$0.299639\pi$
$440$	−1.55388	−	0.416362i	−0.0740785	−	0.0198493i
$441$		0			0
$442$	−1.74750	−	0.435405i	−0.0831203	−	0.0207101i
$443$	18.3082	+	31.7108i	0.869851	+	1.50663i	0.862149	+	0.506655i	$0.169118\pi$
$443$	18.3082	+	31.7108i	0.869851	+	1.50663i	0.00770183	+	0.999970i	$0.497548\pi$
$444$	10.3261	+	10.3261i	0.490056	+	0.490056i
$445$	−14.1882			−0.672583
$446$	−0.513645			−0.0243218
$447$	28.4042	+	28.4042i	1.34347	+	1.34347i
$448$		0			0
$449$	−32.7480	+	8.77481i	−1.54547	+	0.414109i	−0.928030	−	0.372505i	$-0.878499\pi$
$449$	−32.7480	+	8.77481i	−1.54547	+	0.414109i	−0.617445	+	0.786614i	$0.711832\pi$
$450$	0.213555	−	0.796999i	0.0100671	−	0.0375709i
$451$	−19.3181	+	11.1533i	−0.909654	+	0.525189i
$452$		−	16.9722i		−	0.798305i
$453$	−2.97342	−	11.0970i	−0.139704	−	0.521381i
$454$	−0.478554			−0.0224596
$455$		0			0
$456$	−5.16202			−0.241734
$457$	0.585644	+	2.18565i	0.0273953	+	0.102241i	0.978270	−	0.207336i	$-0.0664793\pi$
$457$	0.585644	+	2.18565i	0.0273953	+	0.102241i	−0.950874	+	0.309577i	$0.899813\pi$
$458$			1.58516i			0.0740698i
$459$	7.25273	−	4.18737i	0.338528	−	0.195449i
$460$	5.80566	−	21.6670i	0.270690	−	1.01023i
$461$	24.5455	−	6.57694i	1.14320	−	0.306319i	0.362961	−	0.931804i	$-0.381766\pi$
$461$	24.5455	−	6.57694i	1.14320	−	0.306319i	0.780235	+	0.625486i	$0.215099\pi$
$462$		0			0
$463$	−22.6265	−	22.6265i	−1.05154	−	1.05154i	−0.998597	−	0.0529442i	$-0.983139\pi$
$463$	−22.6265	−	22.6265i	−1.05154	−	1.05154i	−0.0529442	−	0.998597i	$-0.516861\pi$
$464$	−28.0521			−1.30229
$465$	−19.6361			−0.910601
$466$	1.34981	+	1.34981i	0.0625288	+	0.0625288i
$467$	−5.64704	−	9.78095i	−0.261314	−	0.452609i	0.705278	−	0.708931i	$-0.250822\pi$
$467$	−5.64704	−	9.78095i	−0.261314	−	0.452609i	−0.966591	+	0.256323i	$0.917489\pi$
$468$	−23.5126	−	13.0283i	−1.08687	−	0.602235i
$469$		0			0
$470$	−1.31967	−	0.353604i	−0.0608718	−	0.0163105i
$471$	9.00535	−	15.5977i	0.414945	−	0.718705i
$472$	−0.392653	−	0.680095i	−0.0180733	−	0.0313039i
$473$	0.908251	+	3.38964i	0.0417614	+	0.155856i
$474$	−1.27378	−	1.27378i	−0.0585066	−	0.0585066i
$475$	2.07991	+	7.76231i	0.0954326	+	0.356159i
$476$		0			0
$477$	8.02814	−	13.9051i	0.367583	−	0.636673i
$478$	0.874396	+	0.504833i	0.0399939	+	0.0230905i
$479$	14.1810	−	14.1810i	0.647945	−	0.647945i	−0.304551	−	0.952496i	$-0.598506\pi$
$479$	14.1810	−	14.1810i	0.647945	−	0.647945i	0.952496	+	0.304551i	$0.0985064\pi$
$480$	5.51639	+	3.18489i	0.251788	+	0.145370i
$481$	7.33850	+	7.08444i	0.334607	+	0.323023i
$482$			1.56814i			0.0714269i
$483$		0			0
$484$	−7.11843	−	12.3295i	−0.323565	−	0.560431i
$485$			26.0785i			1.18416i
$486$	2.47133	−	0.662191i	0.112102	−	0.0300376i
$487$	30.3456	+	8.13109i	1.37509	+	0.368455i	0.869336	−	0.494221i	$-0.164547\pi$
$487$	30.3456	+	8.13109i	1.37509	+	0.368455i	0.505756	+	0.862676i	$0.331213\pi$
$488$	−1.01449	+	1.01449i	−0.0459238	+	0.0459238i
$489$	−23.7691	+	23.7691i	−1.07488	+	1.07488i
$490$		0			0
$491$	−16.8341	+	9.71919i	−0.759714	+	0.438621i	−0.829193	−	0.558962i	$-0.811200\pi$
$491$	−16.8341	+	9.71919i	−0.759714	+	0.438621i	0.0694792	+	0.997583i	$0.477866\pi$
$492$	56.8122	−	15.2228i	2.56129	−	0.686296i
$493$	15.3138	−	26.5243i	0.689698	−	1.19459i
$494$	−1.79634	+	0.0316425i	−0.0808213	+	0.00142366i
$495$	11.2349	−	6.48647i	0.504971	−	0.291545i
$496$	−4.34038	+	16.1985i	−0.194889	+	0.727336i
$497$		0			0
$498$	3.67021	+	2.11900i	0.164466	+	0.0949545i
$499$	−16.1261	−	4.32098i	−0.721904	−	0.193434i	−0.120883	−	0.992667i	$-0.538573\pi$
$499$	−16.1261	−	4.32098i	−0.721904	−	0.193434i	−0.601021	+	0.799233i	$0.705239\pi$
$500$	6.24745	−	23.3158i	0.279394	−	1.04271i
$501$	−0.627031	+	2.34011i	−0.0280137	+	0.104548i
$502$	0.393138	+	0.105341i	0.0175466	+	0.00470160i
$503$	−25.9585	−	14.9871i	−1.15743	−	0.668243i	−0.206743	−	0.978395i	$-0.566287\pi$
$503$	−25.9585	−	14.9871i	−1.15743	−	0.668243i	−0.950687	+	0.310153i	$0.899620\pi$
$504$		0			0
$505$	−7.31560	+	27.3022i	−0.325540	+	1.21493i
$506$	1.26612	−	0.730997i	0.0562861	−	0.0324968i
$507$	−29.8339	−	15.8507i	−1.32497	−	0.703955i
$508$	−6.07227	+	10.5175i	−0.269413	+	0.466638i
$509$	−13.5446	+	3.62928i	−0.600356	+	0.160865i	−0.546182	−	0.837667i	$-0.683919\pi$
$509$	−13.5446	+	3.62928i	−0.600356	+	0.160865i	−0.0541739	+	0.998532i	$0.517253\pi$
$510$	−1.98466	+	1.14585i	−0.0878824	+	0.0507389i
$511$		0			0
$512$	6.42580	−	6.42580i	0.283983	−	0.283983i
$513$	5.90766	−	5.90766i	0.260830	−	0.260830i
$514$	−1.51659	−	0.406370i	−0.0668940	−	0.0179242i
$515$	−20.1491	+	5.39893i	−0.887874	+	0.237905i
$516$		−	9.25280i		−	0.407332i
$517$	6.48785	+	11.2373i	0.285335	+	0.494215i
$518$		0			0
$519$		−	1.37097i		−	0.0601791i
$520$	2.59150	+	1.43595i	0.113645	+	0.0629705i
$521$	−0.757986	−	0.437623i	−0.0332080	−	0.0191726i	0.483304	−	0.875453i	$-0.339437\pi$
$521$	−0.757986	−	0.437623i	−0.0332080	−	0.0191726i	−0.516512	+	0.856280i	$0.672770\pi$
$522$	−2.21832	+	2.21832i	−0.0970931	+	0.0970931i
$523$	−11.7198	−	6.76640i	−0.512469	−	0.295874i	0.221379	−	0.975188i	$-0.428944\pi$
$523$	−11.7198	−	6.76640i	−0.512469	−	0.295874i	−0.733848	+	0.679314i	$0.762278\pi$
$524$	5.72506	−	9.91610i	0.250100	−	0.433187i
$525$		0			0
$526$	0.620553	+	2.31593i	0.0270574	+	0.100980i
$527$	−12.9468	−	12.9468i	−0.563973	−	0.563973i
$528$	−5.15960	−	19.2559i	−0.224543	−	0.838004i
$529$	8.95568	+	15.5117i	0.389377	+	0.674421i
$530$	−0.440907	+	0.763674i	−0.0191518	+	0.0331719i
$531$	6.11711	+	1.63908i	0.265460	+	0.0711298i
$532$		0			0
$533$	39.4888	−	11.3301i	1.71045	−	0.490759i
$534$	1.21913	+	2.11159i	0.0527569	+	0.0913776i
$535$	9.97623	+	9.97623i	0.431310	+	0.431310i
$536$	0.00917329			0.000396226
$537$	−21.4914			−0.927423
$538$	−0.886440	−	0.886440i	−0.0382171	−	0.0382171i
$539$		0			0
$540$	−6.63121	+	1.77683i	−0.285362	+	0.0764625i
$541$	3.18000	−	11.8679i	0.136719	−	0.510241i	−0.863266	−	0.504749i	$-0.831585\pi$
$541$	3.18000	−	11.8679i	0.136719	−	0.510241i	0.999985	−	0.00549222i	$-0.00174824\pi$
$542$	0.151539	−	0.0874914i	0.00650918	−	0.00375808i
$543$		−	38.9248i		−	1.67042i
$544$	1.53725	+	5.73710i	0.0659091	+	0.245976i
$545$	−21.8634			−0.936526
$546$		0			0
$547$	16.2786			0.696022			0.348011	−	0.937490i	$-0.386857\pi$
$547$	16.2786			0.696022			0.348011	+	0.937490i	$0.386857\pi$
$548$	−3.22641	−	12.0411i	−0.137825	−	0.514371i
$549$		−	11.5698i		−	0.493788i
$550$	0.372723	−	0.215192i	0.0158930	−	0.00917582i
$551$	7.90803	−	29.5132i	0.336894	−	1.25730i
$552$	−7.47258	+	2.00227i	−0.318054	+	0.0852224i
$553$		0			0
$554$	−0.388865	−	0.388865i	−0.0165213	−	0.0165213i
$555$	12.9797			0.550959
$556$	41.5874			1.76370
$557$	5.84312	+	5.84312i	0.247581	+	0.247581i	0.819977	−	0.572396i	$-0.193986\pi$
$557$	5.84312	+	5.84312i	0.247581	+	0.247581i	−0.572396	+	0.819977i	$0.693986\pi$
$558$	0.937724	+	1.62418i	0.0396970	+	0.0687572i
$559$	−0.113826	−	6.46190i	−0.00481433	−	0.273309i
$560$		0			0
$561$	21.0237	+	5.63329i	0.887623	+	0.237838i
$562$	−0.661470	+	1.14570i	−0.0279024	+	0.0483285i
$563$	−14.0767	−	24.3815i	−0.593261	−	1.02756i	−0.993790	−	0.111274i	$-0.964507\pi$
$563$	−14.0767	−	24.3815i	−0.593261	−	1.02756i	0.400528	−	0.916284i	$-0.368827\pi$
$564$	−8.85505	−	33.0475i	−0.372865	−	1.39155i
$565$	−10.6669	−	10.6669i	−0.448759	−	0.448759i
$566$	−0.238078	−	0.888519i	−0.0100072	−	0.0373472i
$567$		0			0
$568$	−1.10691	+	1.91722i	−0.0464448	+	0.0804447i
$569$	8.62645	+	4.98048i	0.361640	+	0.208793i	0.669800	−	0.742542i	$-0.266380\pi$
$569$	8.62645	+	4.98048i	0.361640	+	0.208793i	−0.308160	+	0.951335i	$0.599713\pi$
$570$	−1.61659	+	1.61659i	−0.0677117	+	0.0677117i
$571$	−4.46188	−	2.57607i	−0.186724	−	0.107805i	0.403724	−	0.914881i	$-0.367716\pi$
$571$	−4.46188	−	2.57607i	−0.186724	−	0.107805i	−0.590448	+	0.807076i	$0.701049\pi$
$572$	−3.86692	−	13.4774i	−0.161684	−	0.563519i
$573$		−	37.7572i		−	1.57733i
$574$		0			0
$575$	6.02177	+	10.4300i	0.251125	+	0.434962i
$576$			28.8053i			1.20022i
$577$	−12.9819	+	3.47849i	−0.540444	+	0.144812i	−0.518707	−	0.854952i	$-0.673586\pi$
$577$	−12.9819	+	3.47849i	−0.540444	+	0.144812i	−0.0217373	+	0.999764i	$0.506920\pi$
$578$	−0.146889	−	0.0393588i	−0.00610978	−	0.00163711i
$579$	−35.9754	+	35.9754i	−1.49509	+	1.49509i
$580$	−17.7532	+	17.7532i	−0.737161	+	0.737161i
$581$		0			0
$582$	3.88120	−	2.24081i	0.160881	−	0.0928847i
$583$	8.08967	−	2.16762i	0.335040	−	0.0897737i
$584$	0.229876	−	0.398157i	0.00951234	−	0.0164759i
$585$	−22.9656	+	6.58926i	−0.949512	+	0.272433i
$586$	1.23535	−	0.713227i	0.0510317	−	0.0294631i
$587$	−9.73498	+	36.3314i	−0.401806	+	1.49956i	0.408066	+	0.912952i	$0.366203\pi$
$587$	−9.73498	+	36.3314i	−0.401806	+	1.49956i	−0.809872	+	0.586607i	$0.800463\pi$
$588$		0			0
$589$	−15.8186	−	9.13289i	−0.651795	−	0.376314i
$590$	−0.335953	−	0.0900184i	−0.0138310	−	0.00370600i
$591$	14.6350	−	54.6184i	0.602001	−	2.24670i
$592$	2.86906	−	10.7075i	0.117918	−	0.440074i
$593$	35.2975	+	9.45795i	1.44950	+	0.388391i	0.895848	−	0.444360i	$-0.146569\pi$
$593$	35.2975	+	9.45795i	1.44950	+	0.388391i	0.553648	+	0.832751i	$0.313235\pi$
$594$	−0.387498	−	0.223722i	−0.0158992	−	0.00917944i
$595$		0			0
$596$	7.94687	−	29.6581i	0.325517	−	1.21484i
$597$	−43.3935	+	25.0532i	−1.77598	+	1.02536i
$598$	−2.58813	+	0.742581i	−0.105836	+	0.0303664i
$599$	−2.66014	+	4.60749i	−0.108690	+	0.188257i	−0.915240	−	0.402909i	$-0.867999\pi$
$599$	−2.66014	+	4.60749i	−0.108690	+	0.188257i	0.806550	+	0.591166i	$0.201332\pi$
$600$	−2.19979	+	0.589432i	−0.0898061	+	0.0240635i
$601$	21.4564	−	12.3879i	0.875225	−	0.505312i	0.00614424	−	0.999981i	$-0.498044\pi$
$601$	21.4564	−	12.3879i	0.875225	−	0.505312i	0.869081	+	0.494669i	$0.164711\pi$
$602$		0			0
$603$	−0.0523087	+	0.0523087i	−0.00213017	+	0.00213017i
$604$	−6.20937	+	6.20937i	−0.252656	+	0.252656i
$605$	−12.2228	−	3.27510i	−0.496929	−	0.133152i
$606$	4.69193	−	1.25720i	0.190596	−	0.0510702i
$607$			22.5591i			0.915644i	0.889044	+	0.457822i	$0.151370\pi$
$607$			22.5591i			0.915644i	−0.889044	+	0.457822i	$0.848630\pi$
$608$	2.96263	+	5.13143i	0.120151	+	0.208107i
$609$		0			0
$610$			0.635418i			0.0257273i
$611$	−6.59066	−	22.9705i	−0.266630	−	0.929288i
$612$	−27.6221	−	15.9476i	−1.11656	−	0.644645i
$613$	16.2662	−	16.2662i	0.656986	−	0.656986i	−0.297680	−	0.954666i	$-0.596213\pi$
$613$	16.2662	−	16.2662i	0.656986	−	0.656986i	0.954666	+	0.297680i	$0.0962128\pi$
$614$	1.13995	+	0.658151i	0.0460047	+	0.0265608i
$615$	26.1385	−	45.2733i	1.05401	−	1.82560i
$616$		0			0
$617$	7.79350	+	29.0858i	0.313755	+	1.17095i	0.925143	+	0.379618i	$0.123945\pi$
$617$	7.79350	+	29.0858i	0.313755	+	1.17095i	−0.611389	+	0.791330i	$0.709389\pi$
$618$	2.53484	+	2.53484i	0.101966	+	0.101966i
$619$	−2.76561	−	10.3214i	−0.111159	−	0.414852i	0.887812	−	0.460207i	$-0.152225\pi$
$619$	−2.76561	−	10.3214i	−0.111159	−	0.414852i	−0.998971	+	0.0453549i	$0.985558\pi$
$620$	7.50459	+	12.9983i	0.301392	+	0.522026i
$621$	6.26048	−	10.8435i	0.251224	−	0.435133i
$622$	−1.47090	−	0.394127i	−0.0589778	−	0.0158031i
$623$		0			0
$624$	0.646624	+	36.7088i	0.0258857	+	1.46953i
$625$	−6.01999	−	10.4269i	−0.240800	−	0.417077i
$626$	−0.295052	−	0.295052i	−0.0117927	−	0.0117927i
$627$	21.7133			0.867146
$628$	−13.7668			−0.549355
$629$	8.55805	+	8.55805i	0.341232	+	0.341232i
$630$		0			0
$631$	13.6759	−	3.66444i	0.544428	−	0.145879i	0.0238855	−	0.999715i	$-0.492396\pi$
$631$	13.6759	−	3.66444i	0.544428	−	0.145879i	0.520543	+	0.853836i	$0.325730\pi$
$632$	−0.715196	+	2.66915i	−0.0284490	+	0.106173i
$633$	−6.80249	+	3.92742i	−0.270375	+	0.156101i
$634$		−	3.87301i		−	0.153817i
$635$	2.79377	+	10.4265i	0.110867	+	0.413763i
$636$	−22.0826			−0.875633
$637$		0			0
$638$	−1.63637			−0.0647844
$639$	−4.62063	−	17.2444i	−0.182789	−	0.682179i
$640$		−	6.48426i		−	0.256313i
$641$	32.0667	−	18.5137i	1.26656	−	0.731248i	0.292224	−	0.956350i	$-0.405605\pi$
$641$	32.0667	−	18.5137i	1.26656	−	0.731248i	0.974335	+	0.225102i	$0.0722714\pi$
$642$	0.627525	−	2.34196i	0.0247664	−	0.0924296i
$643$	33.2886	−	8.91965i	1.31277	−	0.351757i	0.466507	−	0.884517i	$-0.345512\pi$
$643$	33.2886	−	8.91965i	1.31277	−	0.351757i	0.846266	+	0.532761i	$0.178845\pi$
$644$		0			0
$645$	−5.81530	−	5.81530i	−0.228977	−	0.228977i
$646$	−2.13177			−0.0838733
$647$	6.06726			0.238529			0.119264	−	0.992863i	$-0.461946\pi$
$647$	6.06726			0.238529			0.119264	+	0.992863i	$0.461946\pi$
$648$	−2.03146	−	2.03146i	−0.0798034	−	0.0798034i
$649$	1.65164	+	2.86072i	0.0648325	+	0.112293i
$650$	−0.761896	+	0.218602i	−0.0298840	+	0.00857428i
$651$		0			0
$652$	24.8184	+	6.65007i	0.971964	+	0.260437i
$653$	−15.1009	+	26.1555i	−0.590943	+	1.02354i	0.403162	+	0.915129i	$0.367911\pi$
$653$	−15.1009	+	26.1555i	−0.590943	+	1.02354i	−0.994106	+	0.108416i	$0.965422\pi$
$654$	1.87863	+	3.25389i	0.0734603	+	0.127237i
$655$	−2.63403	−	9.83033i	−0.102920	−	0.384103i
$656$	−31.5699	−	31.5699i	−1.23260	−	1.23260i
$657$	0.959586	+	3.58123i	0.0374370	+	0.139717i
$658$		0			0
$659$	4.37179	−	7.57216i	0.170301	−	0.294969i	−0.768224	−	0.640181i	$-0.778859\pi$
$659$	4.37179	−	7.57216i	0.170301	−	0.294969i	0.938525	+	0.345211i	$0.112193\pi$
$660$	−15.4517	−	8.92102i	−0.601455	−	0.347250i
$661$	12.7006	−	12.7006i	0.493996	−	0.493996i	−0.415566	−	0.909563i	$-0.636417\pi$
$661$	12.7006	−	12.7006i	0.493996	−	0.493996i	0.909563	+	0.415566i	$0.136417\pi$
$662$	−0.0958671	−	0.0553489i	−0.00372598	−	0.00215120i
$663$	−35.0624	−	19.4281i	−1.36171	−	0.754525i
$664$		−	6.50100i		−	0.252288i
$665$		0			0
$666$	−0.619849	−	1.07361i	−0.0240187	−	0.0416015i
$667$		−	45.7909i		−	1.77303i
$668$	1.78870	−	0.479282i	0.0692071	−	0.0185440i
$669$	−11.0432	−	2.95901i	−0.426954	−	0.114402i
$670$	0.00287281	−	0.00287281i	0.000110986	−	0.000110986i
$671$	4.26731	−	4.26731i	0.164738	−	0.164738i
$672$		0			0
$673$	22.0524	−	12.7319i	0.850057	−	0.490780i	−0.0106133	−	0.999944i	$-0.503378\pi$
$673$	22.0524	−	12.7319i	0.850057	−	0.490780i	0.860670	+	0.509163i	$0.170045\pi$
$674$	−1.60029	+	0.428796i	−0.0616408	+	0.0165166i
$675$	1.84297	−	3.19212i	0.0709359	−	0.122865i
$676$	0.909453	+	25.8068i	0.0349790	+	0.992568i
$677$	18.9268	−	10.9274i	0.727415	−	0.419973i	−0.0900609	−	0.995936i	$-0.528706\pi$
$677$	18.9268	−	10.9274i	0.727415	−	0.419973i	0.817476	+	0.575963i	$0.195373\pi$
$678$	−0.670968	+	2.50409i	−0.0257684	+	0.0961689i
$679$		0			0
$680$	3.04444	+	1.75771i	0.116749	+	0.0674050i
$681$	−10.2887	−	2.75686i	−0.394265	−	0.105643i
$682$	−0.253188	+	0.944911i	−0.00969507	+	0.0361825i
$683$	−8.29515	+	30.9579i	−0.317405	+	1.18457i	0.604324	+	0.796738i	$0.293443\pi$
$683$	−8.29515	+	30.9579i	−0.317405	+	1.18457i	−0.921729	+	0.387833i	$0.873224\pi$
$684$	−30.7348	−	8.23535i	−1.17517	−	0.314887i
$685$	−9.59550	−	5.53997i	−0.366625	−	0.211671i
$686$		0			0
$687$	−9.13183	+	34.0804i	−0.348401	+	1.30025i
$688$	−6.08268	+	3.51184i	−0.231900	+	0.133888i
$689$	−15.4219	+	0.271656i	−0.587527	+	0.0103493i
$690$	−1.71314	+	2.96725i	−0.0652182	+	0.112961i
$691$	−27.1642	+	7.27863i	−1.03337	+	0.276892i	−0.735365	−	0.677671i	$-0.762989\pi$
$691$	−27.1642	+	7.27863i	−1.03337	+	0.276892i	−0.298010	+	0.954563i	$0.596323\pi$
$692$	−0.907533	+	0.523964i	−0.0344992	+	0.0199181i
$693$		0			0
$694$	1.14276	−	1.14276i	0.0433786	−	0.0433786i
$695$	26.1373	−	26.1373i	0.991444	−	0.991444i
$696$	8.36385	+	2.24109i	0.317031	+	0.0849482i
$697$	47.0846	−	12.6163i	1.78346	−	0.477876i
$698$		−	1.78740i		−	0.0676542i
$699$	21.2445	+	36.7965i	0.803540	+	1.39177i
$700$		0			0
$701$		−	41.8411i		−	1.58032i	−0.612904	−	0.790158i	$-0.709999\pi$
$701$		−	41.8411i		−	1.58032i	0.612904	−	0.790158i	$-0.290001\pi$
$702$	0.592869	+	0.572343i	0.0223764	+	0.0216017i
$703$	10.4563	+	6.03698i	0.394369	+	0.227689i
$704$	−10.6243	+	10.6243i	−0.400418	+	0.400418i
$705$	−26.3354	−	15.2047i	−0.991847	−	0.572643i
$706$	−0.919455	+	1.59254i	−0.0346041	+	0.0599361i
$707$		0			0
$708$	−2.25426	−	8.41303i	−0.0847204	−	0.316181i
$709$	26.4279	+	26.4279i	0.992520	+	0.992520i	0.999972	−	0.00745226i	$-0.00237215\pi$
$709$	26.4279	+	26.4279i	0.992520	+	0.992520i	−0.00745226	+	0.999972i	$0.502372\pi$
$710$	0.253766	+	0.947068i	0.00952368	+	0.0355428i
$711$	−11.1420	−	19.2985i	−0.417857	−	0.723750i
$712$	1.87012	−	3.23914i	0.0700857	−	0.121392i
$713$	−26.4417	−	7.08503i	−0.990249	−	0.265336i
$714$		0			0
$715$	−10.9008	−	6.04011i	−0.407665	−	0.225887i
$716$	8.21367	+	14.2265i	0.306959	+	0.531669i
$717$	15.8910	+	15.8910i	0.593459	+	0.593459i
$718$	−0.774035			−0.0288867
$719$	29.4939			1.09994			0.549968	−	0.835186i	$-0.314640\pi$
$719$	29.4939			1.09994			0.549968	+	0.835186i	$0.314640\pi$
$720$	18.3602	+	18.3602i	0.684246	+	0.684246i
$721$		0			0
$722$	0.0885265	−	0.0237206i	0.00329461	−	0.000882789i
$723$	−9.03377	+	33.7145i	−0.335969	+	1.25386i
$724$	−25.7667	+	14.8764i	−0.957612	+	0.552878i
$725$		−	13.4800i		−	0.500635i
$726$	0.562831	+	2.10051i	0.0208886	+	0.0779574i
$727$	3.04387			0.112891			0.0564455	−	0.998406i	$-0.482023\pi$
$727$	3.04387			0.112891			0.0564455	+	0.998406i	$0.482023\pi$
$728$		0			0
$729$	38.4293			1.42331
$730$	−0.0527007	−	0.196682i	−0.00195054	−	0.00727952i
$731$		−	7.66851i		−	0.283630i
$732$	−13.7805	+	7.95615i	−0.509340	+	0.294068i
$733$	−0.339796	+	1.26813i	−0.0125506	+	0.0468396i	−0.971917	−	0.235323i	$-0.924385\pi$
$733$	−0.339796	+	1.26813i	−0.0125506	+	0.0468396i	0.959367	+	0.282163i	$0.0910518\pi$
$734$	3.70542	−	0.992865i	0.136770	−	0.0366473i
$735$		0			0
$736$	6.27914	+	6.27914i	0.231452	+	0.231452i
$737$	−0.0385861			−0.00142134
$738$	−4.99300			−0.183795
$739$	−21.2184	−	21.2184i	−0.780533	−	0.780533i	0.199388	−	0.979921i	$-0.436105\pi$
$739$	−21.2184	−	21.2184i	−0.780533	−	0.780533i	−0.979921	+	0.199388i	$0.936105\pi$
$740$	−4.96065	−	8.59209i	−0.182357	−	0.315852i
$741$	−38.8030	−	9.66809i	−1.42546	−	0.355166i
$742$		0			0
$743$	−39.4397	−	10.5678i	−1.44690	−	0.387697i	−0.551958	−	0.833872i	$-0.686119\pi$
$743$	−39.4397	−	10.5678i	−1.44690	−	0.387697i	−0.894946	+	0.446175i	$0.852786\pi$
$744$	2.58820	−	4.48290i	0.0948881	−	0.164351i
$745$	−13.6453	−	23.6344i	−0.499926	−	0.865897i
$746$	0.238110	+	0.888638i	0.00871782	+	0.0325354i
$747$	37.0706	+	37.0706i	1.35634	+	1.35634i
$748$	−4.30591	−	16.0699i	−0.157440	−	0.587573i
$749$		0			0
$750$	−1.84350	+	3.19304i	−0.0673153	+	0.116593i
$751$	31.0690	+	17.9377i	1.13372	+	0.654556i	0.944869	−	0.327448i	$-0.106189\pi$
$751$	31.0690	+	17.9377i	1.13372	+	0.654556i	0.188856	+	0.982005i	$0.439522\pi$
$752$	−18.3642	+	18.3642i	−0.669672	+	0.669672i
$753$	7.84547	+	4.52958i	0.285905	+	0.165067i
$754$	2.92429	+	0.728611i	0.106496	+	0.0265345i
$755$			7.80507i			0.284056i
$756$		0			0
$757$	−0.439138	−	0.760610i	−0.0159607	−	0.0276448i	0.857935	−	0.513759i	$-0.171747\pi$
$757$	−0.439138	−	0.760610i	−0.0159607	−	0.0276448i	−0.873895	+	0.486114i	$0.838414\pi$
$758$			1.30656i			0.0474566i
$759$	31.4323	−	8.42227i	1.14092	−	0.305709i
$760$	3.38750	+	0.907679i	0.122878	+	0.0329250i
$761$	25.8663	−	25.8663i	0.937654	−	0.937654i	−0.0605137	−	0.998167i	$-0.519274\pi$
$761$	25.8663	−	25.8663i	0.937654	−	0.937654i	0.998167	+	0.0605137i	$0.0192739\pi$
$762$	1.31170	−	1.31170i	0.0475178	−	0.0475178i
$763$		0			0
$764$	−24.9938	+	14.4302i	−0.904245	+	0.522066i
$765$	−27.3832	+	7.33730i	−0.990041	+	0.265281i
$766$	−0.140720	+	0.243735i	−0.00508443	+	0.00880649i
$767$	−1.67781	−	5.84769i	−0.0605822	−	0.211148i
$768$	33.5795	−	19.3871i	1.21170	−	0.699573i
$769$	−7.85943	+	29.3318i	−0.283418	+	1.05773i	0.666569	+	0.745443i	$0.267762\pi$
$769$	−7.85943	+	29.3318i	−0.283418	+	1.05773i	−0.949987	+	0.312288i	$0.898904\pi$
$770$		0			0
$771$	−30.2652	−	17.4736i	−1.08997	−	0.629297i
$772$	37.5636	+	10.0651i	1.35194	+	0.362252i
$773$	−5.13389	+	19.1599i	−0.184653	+	0.689134i	0.810052	+	0.586359i	$0.199439\pi$
$773$	−5.13389	+	19.1599i	−0.184653	+	0.689134i	−0.994705	+	0.102776i	$0.967228\pi$
$774$	−0.203298	+	0.758719i	−0.00730740	+	0.0272716i
$775$	−7.78395	−	2.08570i	−0.279608	−	0.0749206i
$776$	−5.95369	−	3.43737i	−0.213725	−	0.123394i
$777$		0			0
$778$	0.508297	−	1.89699i	0.0182233	−	0.0680104i
$779$	42.1139	−	24.3145i	1.50889	−	0.871157i
$780$	23.6409	+	22.8224i	0.846480	+	0.817175i
$781$	4.65605	−	8.06451i	0.166606	−	0.288571i
$782$	−3.08596	+	0.826882i	−0.110354	+	0.0295692i
$783$	−12.1368	+	7.00718i	−0.433733	+	0.250416i
$784$		0			0
$785$	−8.65231	+	8.65231i	−0.308814	+	0.308814i
$786$	−1.23670	+	1.23670i	−0.0441115	+	0.0441115i
$787$	8.48989	+	2.27486i	0.302632	+	0.0810900i	0.406940	−	0.913455i	$-0.366596\pi$
$787$	8.48989	+	2.27486i	0.302632	+	0.0810900i	−0.104308	+	0.994545i	$0.533263\pi$
$788$	−41.7485	+	11.1865i	−1.48723	+	0.398502i
$789$			53.3666i			1.89990i
$790$	0.611921	+	1.05988i	0.0217712	+	0.0377087i
$791$		0			0
$792$			3.41989i			0.121521i
$793$	−9.52601	+	5.72588i	−0.338279	+	0.203332i
$794$	2.37865	+	1.37332i	0.0844152	+	0.0487372i
$795$	−13.8787	+	13.8787i	−0.492228	+	0.492228i
$796$	33.1686	+	19.1499i	1.17563	+	0.678750i
$797$	−12.3887	+	21.4579i	−0.438832	+	0.760079i	−0.997600	−	0.0692450i	$-0.977941\pi$
$797$	−12.3887	+	21.4579i	−0.438832	+	0.760079i	0.558768	+	0.829324i	$0.311274\pi$
$798$		0			0
$799$	−7.33886	−	27.3890i	−0.259630	−	0.968953i
$800$	1.84846	+	1.84846i	0.0653531	+	0.0653531i
$801$	7.80656	+	29.1345i	0.275831	+	1.02942i
$802$	−0.503695	−	0.872425i	−0.0177861	−	0.0308064i
$803$	−0.966941	+	1.67479i	−0.0341226	+	0.0591021i
$804$	0.0982740	+	0.0263324i	0.00346586	+	0.000928674i
$805$		0			0
$806$	0.873195	−	1.57588i	0.0307570	−	0.0555080i
$807$	−13.9515	−	24.1647i	−0.491117	−	0.850639i
$808$	−5.26881	−	5.26881i	−0.185356	−	0.185356i
$809$	7.50747			0.263949			0.131974	−	0.991253i	$-0.457868\pi$
$809$	7.50747			0.263949			0.131974	+	0.991253i	$0.457868\pi$
$810$	−1.27239			−0.0447072
$811$	−32.4572	−	32.4572i	−1.13973	−	1.13973i	−0.988499	−	0.151229i	$-0.951677\pi$
$811$	−32.4572	−	32.4572i	−1.13973	−	1.13973i	−0.151229	−	0.988499i	$-0.548323\pi$
$812$		0			0
$813$	3.76207	−	1.00804i	0.131941	−	0.0353536i
$814$	0.167361	−	0.624600i	0.00586600	−	0.0218922i
$815$	19.7777	−	11.4186i	0.692781	−	0.399977i
$816$			43.5633i			1.52502i
$817$	−1.98001	−	7.38949i	−0.0692717	−	0.258526i
$818$	−1.56868			−0.0548475
$819$		0			0
$820$	−39.9589			−1.39543
$821$	−8.15549	−	30.4367i	−0.284629	−	1.06225i	−0.949110	−	0.314944i	$-0.898014\pi$
$821$	−8.15549	−	30.4367i	−0.284629	−	1.06225i	0.664482	−	0.747305i	$-0.268652\pi$
$822$			1.90410i			0.0664133i
$823$	−27.4139	+	15.8274i	−0.955590	+	0.551710i	−0.894813	−	0.446442i	$-0.852691\pi$
$823$	−27.4139	+	15.8274i	−0.955590	+	0.551710i	−0.0607767	+	0.998151i	$0.519358\pi$
$824$	1.42325	−	5.31164i	0.0495813	−	0.185040i
$825$	9.25310	−	2.47936i	0.322152	−	0.0863203i
$826$		0			0
$827$	25.1824	+	25.1824i	0.875678	+	0.875678i	0.993084	−	0.117406i	$-0.0374580\pi$
$827$	25.1824	+	25.1824i	0.875678	+	0.875678i	−0.117406	+	0.993084i	$0.537458\pi$
$828$	−47.6862			−1.65721
$829$	2.10865			0.0732364			0.0366182	−	0.999329i	$-0.488341\pi$
$829$	2.10865			0.0732364			0.0366182	+	0.999329i	$0.488341\pi$
$830$	−2.03592	−	2.03592i	−0.0706679	−	0.0706679i
$831$	−6.12027	−	10.6006i	−0.212310	−	0.367732i
$832$	23.7169	−	14.2557i	0.822234	−	0.494227i
$833$		0			0
$834$	−6.13582	−	1.64409i	−0.212466	−	0.0569302i
$835$	0.822960	−	1.42541i	0.0284797	−	0.0493283i
$836$	−8.29847	−	14.3734i	−0.287009	−	0.497114i
$837$	2.16838	+	8.09251i	0.0749502	+	0.279718i
$838$	1.43483	+	1.43483i	0.0495654	+	0.0495654i
$839$	6.14897	+	22.9483i	0.212286	+	0.792262i	0.987104	+	0.160078i	$0.0511746\pi$
$839$	6.14897	+	22.9483i	0.212286	+	0.792262i	−0.774818	+	0.632184i	$0.782159\pi$
$840$		0			0
$841$	−11.1262	+	19.2712i	−0.383663	+	0.664525i
$842$	−3.03847	−	1.75426i	−0.104713	−	0.0604558i
$843$	−20.8215	+	20.8215i	−0.717132	+	0.717132i
$844$	5.19960	+	3.00199i	0.178978	+	0.103333i
$845$	16.7909	+	15.6477i	0.577625	+	0.538298i
$846$			2.90442i			0.0998559i
$847$		0			0
$848$	8.38131	+	14.5169i	0.287815	+	0.498511i
$849$		−	20.4744i		−	0.702678i
$850$	−0.908451	+	0.243419i	−0.0311596	+	0.00834919i
$851$	17.4783	+	4.68331i	0.599150	+	0.160542i
$852$	−17.3619	+	17.3619i	−0.594807	+	0.594807i
$853$	4.73993	−	4.73993i	0.162292	−	0.162292i	−0.621289	−	0.783581i	$-0.713391\pi$
$853$	4.73993	−	4.73993i	0.162292	−	0.162292i	0.783581	+	0.621289i	$0.213391\pi$
$854$		0			0
$855$	−24.4924	+	14.1407i	−0.837621	+	0.483601i
$856$	−3.59252	+	0.962612i	−0.122790	+	0.0329014i
$857$	−5.66099	+	9.80512i	−0.193376	+	0.334936i	−0.946367	−	0.323094i	$-0.895277\pi$
$857$	−5.66099	+	9.80512i	−0.193376	+	0.334936i	0.752991	+	0.658031i	$0.228610\pi$
$858$	0.0377196	+	2.14134i	0.00128773	+	0.0731041i
$859$	−41.9548	+	24.2226i	−1.43148	+	0.826465i	−0.997234	−	0.0743295i	$-0.976318\pi$
$859$	−41.9548	+	24.2226i	−1.43148	+	0.826465i	−0.434246	+	0.900794i	$0.642985\pi$
$860$	−1.62699	+	6.07202i	−0.0554800	+	0.207054i
$861$		0			0
$862$	−2.43991	−	1.40868i	−0.0831038	−	0.0479800i
$863$	18.1110	+	4.85283i	0.616506	+	0.165192i	0.553539	−	0.832823i	$-0.313277\pi$
$863$	18.1110	+	4.85283i	0.616506	+	0.165192i	0.0629669	+	0.998016i	$0.479944\pi$
$864$	0.703405	−	2.62514i	0.0239303	−	0.0893091i
$865$	−0.241069	+	0.899682i	−0.00819660	+	0.0305901i
$866$	0.512280	+	0.137265i	0.0174080	+	0.00466445i
$867$	−2.93132	−	1.69240i	−0.0995529	−	0.0574769i
$868$		0			0
$869$	3.00837	−	11.2274i	0.102052	−	0.380863i
$870$	3.32116	−	1.91747i	0.112598	−	0.0650083i
$871$	0.0689558	+	0.0171809i	0.00233648	+	0.000582153i
$872$	2.88179	−	4.99140i	0.0975896	−	0.169030i
$873$	53.5505	−	14.3488i	1.81241	−	0.485634i
$874$	−2.76018	+	1.59359i	−0.0933645	+	0.0539040i
$875$		0			0
$876$	3.60561	−	3.60561i	0.121822	−	0.121822i
$877$	5.01143	−	5.01143i	0.169224	−	0.169224i	−0.617414	−	0.786638i	$-0.711820\pi$
$877$	5.01143	−	5.01143i	0.169224	−	0.169224i	0.786638	+	0.617414i	$0.211820\pi$
$878$	−1.91726	−	0.513728i	−0.0647044	−	0.0173375i
$879$	30.6683	−	8.21753i	1.03441	−	0.277171i
$880$			13.5437i			0.456556i
$881$	12.1808	+	21.0977i	0.410380	+	0.710800i	0.994931	−	0.100557i	$-0.0320626\pi$
$881$	12.1808	+	21.0977i	0.410380	+	0.710800i	−0.584551	+	0.811357i	$0.698729\pi$
$882$		0			0
$883$		−	4.51673i		−	0.152000i	−0.997108	−	0.0760000i	$-0.975785\pi$
$883$		−	4.51673i		−	0.152000i	0.997108	−	0.0760000i	$-0.0242149\pi$
$884$	0.539636	+	30.6351i	0.0181499	+	1.03037i
$885$	−6.70430	−	3.87073i	−0.225362	−	0.130113i
$886$	−3.02295	+	3.02295i	−0.101558	+	0.101558i
$887$	38.3035	+	22.1145i	1.28611	+	0.742533i	0.977957	−	0.208805i	$-0.0669575\pi$
$887$	38.3035	+	22.1145i	1.28611	+	0.742533i	0.308148	+	0.951338i	$0.400291\pi$
$888$	−1.71084	+	2.96326i	−0.0574121	+	0.0994406i
$889$		0			0
$890$	−0.428738	−	1.60007i	−0.0143713	−	0.0536346i
$891$	8.54505	+	8.54505i	0.286270	+	0.286270i
$892$	2.26177	+	8.44106i	0.0757298	+	0.282628i
$893$	−14.1437	−	24.4976i	−0.473300	−	0.819780i
$894$	−2.34497	+	4.06161i	−0.0784276	+	0.135841i
$895$	14.1034	+	3.77900i	0.471426	+	0.126318i
$896$		0			0
$897$	−59.9216	+	1.05552i	−2.00073	+	0.0352427i
$898$	−1.97916	−	3.42801i	−0.0660455	−	0.114394i
$899$	21.6654	+	21.6654i	0.722580	+	0.722580i
$900$	−14.0380			−0.467932
$901$	−18.3016			−0.609714
$902$	−1.84157	−	1.84157i	−0.0613176	−	0.0613176i
$903$		0			0
$904$	3.84122	−	1.02925i	0.127757	−	0.0342324i
$905$	−6.84445	+	25.5438i	−0.227517	+	0.849106i
$906$	1.16161	−	0.670657i	0.0385920	−	0.0222811i
$907$			33.8866i			1.12519i	0.826734	+	0.562593i	$0.190196\pi$
$907$			33.8866i			1.12519i	−0.826734	+	0.562593i	$0.809804\pi$
$908$	2.10725	+	7.86438i	0.0699317	+	0.260989i
$909$	60.0885			1.99301
$910$		0			0
$911$	4.66390			0.154522			0.0772610	−	0.997011i	$-0.475383\pi$
$911$	4.66390			0.154522			0.0772610	+	0.997011i	$0.475383\pi$
$912$	11.2480	+	41.9783i	0.372460	+	1.39004i
$913$			27.3455i			0.905005i
$914$	−0.228791	+	0.132092i	−0.00756772	+	0.00436923i
$915$	−3.66052	+	13.6613i	−0.121013	+	0.451627i
$916$	26.0500	−	6.98007i	0.860716	−	0.230628i
$917$		0			0
$918$	0.691394	+	0.691394i	0.0228194	+	0.0228194i
$919$	24.1800			0.797625			0.398812	−	0.917033i	$-0.369422\pi$
$919$	24.1800			0.797625			0.398812	+	0.917033i	$0.369422\pi$
$920$	5.25585			0.173280
$921$	20.7171	+	20.7171i	0.682651	+	0.682651i
$922$	1.48343	+	2.56938i	0.0488542	+	0.0846180i
$923$	−11.9115	+	12.3386i	−0.392070	+	0.406131i
$924$		0			0
$925$	5.14530	+	1.37868i	0.169177	+	0.0453307i
$926$	1.86798	−	3.23543i	0.0613856	−	0.106323i
$927$	22.1727	+	38.4043i	0.728247	+	1.26136i
$928$	−2.57245	−	9.60051i	−0.0844448	−	0.315152i
$929$	−10.9812	−	10.9812i	−0.360282	−	0.360282i	0.503635	−	0.863917i	$-0.331996\pi$
$929$	−10.9812	−	10.9812i	−0.360282	−	0.360282i	−0.863917	+	0.503635i	$0.831996\pi$
$930$	−0.593364	−	2.21446i	−0.0194572	−	0.0726151i
$931$		0			0
$932$	16.2386	−	28.1261i	0.531913	−	0.921300i
$933$	−29.3534	−	16.9472i	−0.960987	−	0.554826i
$934$	0.932407	−	0.932407i	0.0305093	−	0.0305093i
$935$	−12.8060	−	7.39354i	−0.418801	−	0.241795i
$936$	1.52274	−	6.11156i	0.0497725	−	0.199762i
$937$		−	25.4720i		−	0.832134i	−0.909334	−	0.416067i	$-0.863408\pi$
$937$		−	25.4720i		−	0.832134i	0.909334	−	0.416067i	$-0.136592\pi$
$938$		0			0
$939$	−4.64378	−	8.04326i	−0.151544	−	0.262482i
$940$			23.2440i			0.758136i
$941$	−17.3112	+	4.63851i	−0.564328	+	0.151211i	−0.529694	−	0.848189i	$-0.677693\pi$
$941$	−17.3112	+	4.63851i	−0.564328	+	0.151211i	−0.0346338	+	0.999400i	$0.511026\pi$
$942$	2.03116	+	0.544248i	0.0661788	+	0.0177326i
$943$	51.5332	−	51.5332i	1.67815	−	1.67815i
$944$	−4.67503	+	4.67503i	−0.152159	+	0.152159i
$945$		0			0
$946$	−0.354822	+	0.204856i	−0.0115362	+	0.00666046i
$947$	−12.0056	+	3.21690i	−0.390130	+	0.104535i	−0.448552	−	0.893757i	$-0.648060\pi$
$947$	−12.0056	+	3.21690i	−0.390130	+	0.104535i	0.0584214	+	0.998292i	$0.481393\pi$
$948$	−15.3239	+	26.5417i	−0.497696	+	0.862035i
$949$	2.47370	−	2.56241i	0.0802998	−	0.0831795i
$950$	−0.812546	+	0.469124i	−0.0263625	+	0.0152204i
$951$	22.3117	−	83.2684i	0.723506	−	2.70016i
$952$		0			0
$953$	25.0716	+	14.4751i	0.812147	+	0.468893i	0.847701	−	0.530474i	$-0.177986\pi$
$953$	25.0716	+	14.4751i	0.812147	+	0.468893i	−0.0355538	+	0.999368i	$0.511320\pi$
$954$	1.81075	+	0.485189i	0.0586252	+	0.0157086i
$955$	−6.63914	+	24.7776i	−0.214838	+	0.801785i
$956$	4.44594	−	16.5925i	0.143792	−	0.536639i
$957$	−35.1813	−	9.42681i	−1.13725	−	0.304725i
$958$	2.02778	+	1.17074i	0.0655147	+	0.0378249i
$959$		0			0
$960$	9.11358	−	34.0123i	0.294140	−	1.09774i
$961$	−10.9841	+	6.34165i	−0.354325	+	0.204569i
$962$	−0.577195	+	1.04168i	−0.0186095	+	0.0335851i
$963$	14.9965	−	25.9746i	0.483254	−	0.837021i
$964$	25.7703	−	6.90512i	0.830004	−	0.222399i
$965$	29.9342	−	17.2825i	0.963617	−	0.556344i
$966$		0			0
$967$	20.8937	−	20.8937i	0.671895	−	0.671895i	−0.286258	−	0.958153i	$-0.592411\pi$
$967$	20.8937	−	20.8937i	0.671895	−	0.671895i	0.958153	+	0.286258i	$0.0924113\pi$
$968$	2.35878	−	2.35878i	0.0758140	−	0.0758140i
$969$	−45.8323	−	12.2807i	−1.47234	−	0.394513i
$970$	−2.94101	+	0.788040i	−0.0944300	+	0.0253024i
$971$		−	41.0504i		−	1.31737i	−0.752419	−	0.658685i	$-0.771113\pi$
$971$		−	41.0504i		−	1.31737i	0.752419	−	0.658685i	$-0.228887\pi$
$972$	−21.7644	−	37.6971i	−0.698094	−	1.20913i
$973$		0			0
$974$			3.66794i			0.117528i
$975$	−17.6398	+	0.310725i	−0.564927	+	0.00995116i
$976$	10.4606	+	6.03940i	0.334834	+	0.193317i
$977$	16.1451	−	16.1451i	0.516527	−	0.516527i	−0.399992	−	0.916519i	$-0.630987\pi$
$977$	16.1451	−	16.1451i	0.516527	−	0.516527i	0.916519	+	0.399992i	$0.130987\pi$
$978$	−3.39882	−	1.96231i	−0.108682	−	0.0627478i
$979$	−7.86639	+	13.6250i	−0.251411	+	0.435457i
$980$		0			0
$981$	12.0296	+	44.8951i	0.384076	+	1.43339i
$982$	−1.60478	−	1.60478i	−0.0512105	−	0.0512105i
$983$	7.70226	+	28.7452i	0.245664	+	0.916831i	0.973048	+	0.230601i	$0.0740691\pi$
$983$	7.70226	+	28.7452i	0.245664	+	0.916831i	−0.727384	+	0.686230i	$0.759264\pi$
$984$	6.89057	+	11.9348i	0.219663	+	0.380468i
$985$	−19.2080	+	33.2692i	−0.612017	+	1.06004i
$986$	3.45403	+	0.925505i	0.109999	+	0.0294741i
$987$		0			0
$988$	8.42998	+	29.3811i	0.268193	+	0.934737i
$989$	−5.73255	−	9.92907i	−0.182285	−	0.315726i
$990$	1.07101	+	1.07101i	0.0340389	+	0.0340389i
$991$	−2.49766			−0.0793406			−0.0396703	−	0.999213i	$-0.512631\pi$
$991$	−2.49766			−0.0793406			−0.0396703	+	0.999213i	$0.512631\pi$
$992$	−5.94178			−0.188652
$993$	−1.74225	−	1.74225i	−0.0552888	−	0.0552888i
$994$		0			0
$995$	32.8817	−	8.81062i	1.04242	−	0.279315i
$996$	18.6615	−	69.6456i	0.591312	−	2.20681i
$997$	−5.16724	+	2.98331i	−0.163648	+	0.0944823i	−0.579587	−	0.814910i	$-0.696786\pi$
$997$	−5.16724	+	2.98331i	−0.163648	+	0.0944823i	0.415939	+	0.909392i	$0.363453\pi$
$998$		−	1.94920i		−	0.0617008i
$999$	−1.43333	−	5.34926i	−0.0453486	−	0.169243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.80.4		32
7.2	even	3		637.2.bb.b.509.3		32
7.3	odd	6		91.2.bc.a.41.5	yes	32
7.4	even	3		91.2.bc.a.41.6	yes	32
7.5	odd	6		637.2.bb.b.509.4		32
7.6	odd	2	inner	637.2.x.b.80.3		32
13.7	odd	12		637.2.bb.b.423.4		32
21.11	odd	6		819.2.fm.g.496.3		32
21.17	even	6		819.2.fm.g.496.4		32
91.20	even	12		637.2.bb.b.423.3		32
91.33	even	12	inner	637.2.x.b.215.3		32
91.46	odd	12		91.2.bc.a.20.5	✓	32
91.59	even	12		91.2.bc.a.20.6	yes	32
91.72	odd	12	inner	637.2.x.b.215.4		32
273.59	odd	12		819.2.fm.g.748.3		32
273.137	even	12		819.2.fm.g.748.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.5	✓	32	91.46	odd	12
91.2.bc.a.20.6	yes	32	91.59	even	12
91.2.bc.a.41.5	yes	32	7.3	odd	6
91.2.bc.a.41.6	yes	32	7.4	even	3
637.2.x.b.80.3		32	7.6	odd	2	inner
637.2.x.b.80.4		32	1.1	even	1	trivial
637.2.x.b.215.3		32	91.33	even	12	inner
637.2.x.b.215.4		32	91.72	odd	12	inner
637.2.bb.b.423.3		32	91.20	even	12
637.2.bb.b.423.4		32	13.7	odd	12
637.2.bb.b.509.3		32	7.2	even	3
637.2.bb.b.509.4		32	7.5	odd	6
819.2.fm.g.496.3		32	21.11	odd	6
819.2.fm.g.496.4		32	21.17	even	6
819.2.fm.g.748.3		32	273.59	odd	12
819.2.fm.g.748.4		32	273.137	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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0302180 + 0.112775i) q^{2} +2.59871i q^{3} +(1.72025 - 0.993184i) q^{4} +(0.456951 - 1.70537i) q^{5} +(-0.293070 + 0.0785278i) q^{6} +(0.329103 + 0.329103i) q^{8} -3.75328 q^{9} +O(q^{10})\)	\(q+(0.0302180 + 0.112775i) q^{2} +2.59871i q^{3} +(1.72025 - 0.993184i) q^{4} +(0.456951 - 1.70537i) q^{5} +(-0.293070 + 0.0785278i) q^{6} +(0.329103 + 0.329103i) q^{8} -3.75328 q^{9} +0.206131 q^{10} +(-1.38433 - 1.38433i) q^{11} +(2.58100 + 4.47042i) q^{12} +(1.85749 + 3.09026i) q^{13} +(4.43175 + 1.18748i) q^{15} +(1.95920 - 3.39343i) q^{16} +(2.13907 + 3.70498i) q^{17} +(-0.113417 - 0.423277i) q^{18} +(3.01787 + 3.01787i) q^{19} +(-0.907674 - 3.38749i) q^{20} +(0.114286 - 0.197949i) q^{22} +(5.53927 + 3.19810i) q^{23} +(-0.855244 + 0.855244i) q^{24} +(1.63066 + 0.941462i) q^{25} +(-0.292376 + 0.302861i) q^{26} -1.95756i q^{27} +(-3.57954 - 6.19995i) q^{29} +0.535675i q^{30} +(-4.13397 + 1.10769i) q^{31} +(1.34103 + 0.359327i) q^{32} +(3.59746 - 3.59746i) q^{33} +(-0.353191 + 0.353191i) q^{34} +(-6.45657 + 3.72770i) q^{36} +(2.73261 - 0.732202i) q^{37} +(-0.249147 + 0.431534i) q^{38} +(-8.03069 + 4.82707i) q^{39} +(0.711626 - 0.410857i) q^{40} +(2.94901 - 11.0059i) q^{41} +(-1.55234 - 0.896243i) q^{43} +(-3.75627 - 1.00649i) q^{44} +(-1.71507 + 6.40072i) q^{45} +(-0.193281 + 0.721333i) q^{46} +(-6.40208 - 1.71543i) q^{47} +(8.81854 + 5.09139i) q^{48} +(-0.0568982 + 0.212347i) q^{50} +(-9.62816 + 5.55882i) q^{51} +(6.26454 + 3.47118i) q^{52} +(-2.13896 + 3.70479i) q^{53} +(0.220765 - 0.0591537i) q^{54} +(-2.99335 + 1.72821i) q^{55} +(-7.84255 + 7.84255i) q^{57} +(0.591034 - 0.591034i) q^{58} +(-1.62980 - 0.436704i) q^{59} +(8.80308 - 2.35878i) q^{60} +3.08259i q^{61} +(-0.249841 - 0.432737i) q^{62} -7.67470i q^{64} +(6.11881 - 1.75560i) q^{65} +(0.514413 + 0.296996i) q^{66} +(0.0139368 - 0.0139368i) q^{67} +(7.35945 + 4.24898i) q^{68} +(-8.31093 + 14.3949i) q^{69} +(1.23109 + 4.59449i) q^{71} +(-1.23522 - 1.23522i) q^{72} +(-0.255666 - 0.954158i) q^{73} +(0.165148 + 0.286046i) q^{74} +(-2.44658 + 4.23761i) q^{75} +(8.18877 + 2.19417i) q^{76} +(-0.787046 - 0.759799i) q^{78} +(2.96860 + 5.14176i) q^{79} +(-4.89178 - 4.89178i) q^{80} -6.17272 q^{81} +1.33030 q^{82} +(-9.87683 - 9.87683i) q^{83} +(7.29580 - 1.95490i) q^{85} +(0.0541654 - 0.202148i) q^{86} +(16.1119 - 9.30218i) q^{87} -0.911173i q^{88} +(-2.07993 - 7.76240i) q^{89} -0.773669 q^{90} +12.7052 q^{92} +(-2.87857 - 10.7430i) q^{93} -0.773833i q^{94} +(6.52558 - 3.76755i) q^{95} +(-0.933785 + 3.48493i) q^{96} +(-14.2676 + 3.82300i) q^{97} +(5.19577 + 5.19577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more