LMFDB - Embedded newform 637.2.bb.a.227.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.2
Character	$\chi$	$=$	637.227
Dual form			637.2.bb.a.362.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984398 + 0.984398i) q^{2} +(1.25446 - 0.724265i) q^{3} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-0.521927 + 1.94786i) q^{6} +(-2.02975 - 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +O(q^{10})$	\(q+(-0.984398 + 0.984398i) q^{2} +(1.25446 - 0.724265i) q^{3} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-0.521927 + 1.94786i) q^{6} +(-2.02975 - 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +(0.463421 + 0.802669i) q^{10} +(-1.24780 + 4.65687i) q^{11} +(0.0448464 + 0.0776763i) q^{12} +(-3.60544 + 0.0282257i) q^{13} +(-0.249600 - 0.931519i) q^{15} +3.87233 q^{16} -0.467904 q^{17} +(-0.324918 - 1.21261i) q^{18} +(-3.26172 + 0.873976i) q^{19} +(0.0398194 + 0.0106696i) q^{20} +(-3.35587 - 5.81255i) q^{22} +6.95512i q^{23} +(-4.01633 - 1.07617i) q^{24} +(3.94627 + 2.27838i) q^{25} +(3.52140 - 3.57698i) q^{26} +5.65182i q^{27} +(-2.01911 + 3.49720i) q^{29} +(1.16269 + 0.671280i) q^{30} +(4.10087 - 1.09883i) q^{31} +(0.247590 - 0.247590i) q^{32} +(1.80748 + 6.74561i) q^{33} +(0.460604 - 0.460604i) q^{34} +(-0.0483562 - 0.0279185i) q^{36} +(-2.38729 - 2.38729i) q^{37} +(2.35049 - 4.07117i) q^{38} +(-4.50245 + 2.64670i) q^{39} +(-1.65504 + 0.955538i) q^{40} +(-3.68025 + 0.986119i) q^{41} +(3.42191 - 1.97564i) q^{43} +(-0.288353 - 0.0772639i) q^{44} +(0.424518 + 0.424518i) q^{45} +(-6.84661 - 6.84661i) q^{46} +(9.64648 + 2.58477i) q^{47} +(4.85769 - 2.80459i) q^{48} +(-6.12753 + 1.64187i) q^{50} +(-0.586968 + 0.338886i) q^{51} +(-0.00174773 - 0.223249i) q^{52} +(2.20051 - 3.81140i) q^{53} +(-5.56364 - 5.56364i) q^{54} +(2.77972 + 1.60487i) q^{55} +(-3.45872 + 3.45872i) q^{57} +(-1.45503 - 5.43025i) q^{58} +(-4.33306 + 4.33306i) q^{59} +(0.0576796 - 0.0154552i) q^{60} +(-4.21802 - 2.43528i) q^{61} +(-2.95521 + 5.11858i) q^{62} +8.23211i q^{64} +(-0.603111 + 2.32344i) q^{65} +(-8.41965 - 4.86109i) q^{66} +(-9.03697 - 2.42145i) q^{67} -0.0289726i q^{68} +(5.03735 + 8.72495i) q^{69} +(3.19935 + 0.857263i) q^{71} +(2.50030 - 0.669954i) q^{72} +(0.0301918 + 0.112678i) q^{73} +4.70008 q^{74} +6.60060 q^{75} +(-0.0541165 - 0.201966i) q^{76} +(1.82680 - 7.03762i) q^{78} +(0.194920 + 0.337611i) q^{79} +(0.667250 - 2.49021i) q^{80} +(2.74077 + 4.74716i) q^{81} +(2.65209 - 4.59356i) q^{82} +(-11.5572 - 11.5572i) q^{83} +(-0.0806256 + 0.300899i) q^{85} +(-1.42371 + 5.31334i) q^{86} +5.84949i q^{87} +(11.9850 - 6.91955i) q^{88} +(-6.83819 + 6.83819i) q^{89} -0.835790 q^{90} -0.430661 q^{92} +(4.34856 - 4.34856i) q^{93} +(-12.0404 + 6.95154i) q^{94} +2.24814i q^{95} +(0.131272 - 0.489913i) q^{96} +(4.61378 - 17.2188i) q^{97} +(-3.07416 - 3.07416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.984398	+	0.984398i	−0.696075	+	0.696075i	−0.963562	−	0.267487i	$-0.913807\pi$
$2$	−0.984398	+	0.984398i	−0.696075	+	0.696075i	0.267487	+	0.963562i	$0.413807\pi$
$3$	1.25446	−	0.724265i	0.724265	−	0.418155i	−0.0920554	−	0.995754i	$-0.529344\pi$
$3$	1.25446	−	0.724265i	0.724265	−	0.418155i	0.816320	+	0.577599i	$0.196010\pi$
$4$			0.0619199i			0.0309600i
$5$	0.172312	−	0.643078i	0.0770604	−	0.287593i	−0.916632	−	0.399732i	$-0.869103\pi$
$5$	0.172312	−	0.643078i	0.0770604	−	0.287593i	0.993693	+	0.112138i	$0.0357700\pi$
$6$	−0.521927	+	1.94786i	−0.213076	+	0.795210i
$7$		0			0
$7$		0			0
$8$	−2.02975	−	2.02975i	−0.717625	−	0.717625i
$9$	−0.450880	+	0.780947i	−0.150293	+	0.260316i
$10$	0.463421	+	0.802669i	0.146547	+	0.253826i
$11$	−1.24780	+	4.65687i	−0.376227	+	1.40410i	0.475317	+	0.879815i	$0.342333\pi$
$11$	−1.24780	+	4.65687i	−0.376227	+	1.40410i	−0.851544	+	0.524283i	$0.824333\pi$
$12$	0.0448464	+	0.0776763i	0.0129461	+	0.0224232i
$13$	−3.60544	+	0.0282257i	−0.999969	+	0.00782840i
$13$	−3.60544	+	0.0282257i	−0.999969	+	0.00782840i
$14$		0			0
$15$	−0.249600	−	0.931519i	−0.0644463	−	0.240517i
$16$	3.87233			0.968082
$17$	−0.467904			−0.113483			−0.0567417	−	0.998389i	$-0.518071\pi$
$17$	−0.467904			−0.113483			−0.0567417	+	0.998389i	$0.518071\pi$
$18$	−0.324918	−	1.21261i	−0.0765838	−	0.285815i
$19$	−3.26172	+	0.873976i	−0.748290	+	0.200504i	−0.612760	−	0.790269i	$-0.709941\pi$
$19$	−3.26172	+	0.873976i	−0.748290	+	0.200504i	−0.135531	+	0.990773i	$0.543274\pi$
$20$	0.0398194	+	0.0106696i	0.00890388	+	0.00238579i
$21$		0			0
$22$	−3.35587	−	5.81255i	−0.715475	−	1.23924i
$23$			6.95512i			1.45024i	0.688621	+	0.725122i	$0.258217\pi$
$23$			6.95512i			1.45024i	−0.688621	+	0.725122i	$0.741783\pi$
$24$	−4.01633	−	1.07617i	−0.819829	−	0.219673i
$25$	3.94627	+	2.27838i	0.789254	+	0.455676i
$26$	3.52140	−	3.57698i	0.690604	−	0.701503i
$27$			5.65182i			1.08769i
$28$		0			0
$29$	−2.01911	+	3.49720i	−0.374940	+	0.649414i	−0.990318	−	0.138817i	$-0.955670\pi$
$29$	−2.01911	+	3.49720i	−0.374940	+	0.649414i	0.615378	+	0.788232i	$0.289003\pi$
$30$	1.16269	+	0.671280i	0.212277	+	0.122558i
$31$	4.10087	−	1.09883i	0.736539	−	0.197355i	0.129000	−	0.991645i	$-0.458823\pi$
$31$	4.10087	−	1.09883i	0.736539	−	0.197355i	0.607539	+	0.794290i	$0.292157\pi$
$32$	0.247590	−	0.247590i	0.0437681	−	0.0437681i
$33$	1.80748	+	6.74561i	0.314642	+	1.17426i
$34$	0.460604	−	0.460604i	0.0789929	−	0.0789929i
$35$		0			0
$36$	−0.0483562	−	0.0279185i	−0.00805937	−	0.00465308i
$37$	−2.38729	−	2.38729i	−0.392467	−	0.392467i	0.483099	−	0.875566i	$-0.339511\pi$
$37$	−2.38729	−	2.38729i	−0.392467	−	0.392467i	−0.875566	+	0.483099i	$0.839511\pi$
$38$	2.35049	−	4.07117i	0.381300	−	0.660432i
$39$	−4.50245	+	2.64670i	−0.720969	+	0.423812i
$40$	−1.65504	+	0.955538i	−0.261685	+	0.151084i
$41$	−3.68025	+	0.986119i	−0.574758	+	0.154006i	−0.534478	−	0.845182i	$-0.679492\pi$
$41$	−3.68025	+	0.986119i	−0.574758	+	0.154006i	−0.0402801	+	0.999188i	$0.512825\pi$
$42$		0			0
$43$	3.42191	−	1.97564i	0.521836	−	0.301282i	−0.215849	−	0.976427i	$-0.569252\pi$
$43$	3.42191	−	1.97564i	0.521836	−	0.301282i	0.737686	+	0.675144i	$0.235919\pi$
$44$	−0.288353	−	0.0772639i	−0.0434708	−	0.0116480i
$45$	0.424518	+	0.424518i	0.0632834	+	0.0632834i
$46$	−6.84661	−	6.84661i	−1.00948	−	1.00948i
$47$	9.64648	+	2.58477i	1.40708	+	0.377027i	0.880883	−	0.473333i	$-0.156949\pi$
$47$	9.64648	+	2.58477i	1.40708	+	0.377027i	0.526201	+	0.850360i	$0.323616\pi$
$48$	4.85769	−	2.80459i	0.701148	−	0.404808i
$49$		0			0
$50$	−6.12753	+	1.64187i	−0.866564	+	0.232195i
$51$	−0.586968	+	0.338886i	−0.0821920	+	0.0474536i
$52$	−0.00174773	−	0.223249i	−0.000242367	−	0.0309590i
$53$	2.20051	−	3.81140i	0.302264	−	0.523537i	−0.674384	−	0.738380i	$-0.735591\pi$
$53$	2.20051	−	3.81140i	0.302264	−	0.523537i	0.976648	+	0.214844i	$0.0689243\pi$
$54$	−5.56364	−	5.56364i	−0.757115	−	0.757115i
$55$	2.77972	+	1.60487i	0.374817	+	0.216401i
$56$		0			0
$57$	−3.45872	+	3.45872i	−0.458119	+	0.458119i
$58$	−1.45503	−	5.43025i	−0.191055	−	0.713027i
$59$	−4.33306	+	4.33306i	−0.564117	+	0.564117i	−0.930474	−	0.366358i	$-0.880605\pi$
$59$	−4.33306	+	4.33306i	−0.564117	+	0.564117i	0.366358	+	0.930474i	$0.380605\pi$
$60$	0.0576796	−	0.0154552i	0.00744640	−	0.00199526i
$61$	−4.21802	−	2.43528i	−0.540062	−	0.311805i	0.205042	−	0.978753i	$-0.434267\pi$
$61$	−4.21802	−	2.43528i	−0.540062	−	0.311805i	−0.745104	+	0.666948i	$0.767600\pi$
$62$	−2.95521	+	5.11858i	−0.375312	+	0.650060i
$63$		0			0
$64$			8.23211i			1.02901i
$65$	−0.603111	+	2.32344i	−0.0748067	+	0.288188i
$66$	−8.41965	−	4.86109i	−1.03639	−	0.598358i
$67$	−9.03697	−	2.42145i	−1.10404	−	0.295827i	−0.339633	−	0.940558i	$-0.610303\pi$
$67$	−9.03697	−	2.42145i	−1.10404	−	0.295827i	−0.764409	+	0.644731i	$0.776969\pi$
$68$		−	0.0289726i		−	0.00351344i
$69$	5.03735	+	8.72495i	0.606426	+	1.05036i
$70$		0			0
$71$	3.19935	+	0.857263i	0.379693	+	0.101738i	0.443617	−	0.896216i	$-0.353695\pi$
$71$	3.19935	+	0.857263i	0.379693	+	0.101738i	−0.0639244	+	0.997955i	$0.520362\pi$
$72$	2.50030	−	0.669954i	0.294663	−	0.0789548i
$73$	0.0301918	+	0.112678i	0.00353369	+	0.0131879i	0.967670	−	0.252219i	$-0.0811604\pi$
$73$	0.0301918	+	0.112678i	0.00353369	+	0.0131879i	−0.964136	+	0.265407i	$0.914494\pi$
$74$	4.70008			0.546373
$75$	6.60060			0.762172
$76$	−0.0541165	−	0.201966i	−0.00620759	−	0.0231670i
$77$		0			0
$78$	1.82680	−	7.03762i	0.206844	−	0.796853i
$79$	0.194920	+	0.337611i	0.0219302	+	0.0379842i	0.876782	−	0.480888i	$-0.159686\pi$
$79$	0.194920	+	0.337611i	0.0219302	+	0.0379842i	−0.854852	+	0.518872i	$0.826352\pi$
$80$	0.667250	−	2.49021i	0.0746008	−	0.278414i
$81$	2.74077	+	4.74716i	0.304530	+	0.527462i
$82$	2.65209	−	4.59356i	0.292875	−	0.507274i
$83$	−11.5572	−	11.5572i	−1.26857	−	1.26857i	−0.946828	−	0.321741i	$-0.895732\pi$
$83$	−11.5572	−	11.5572i	−1.26857	−	1.26857i	−0.321741	−	0.946828i	$-0.604268\pi$
$84$		0			0
$85$	−0.0806256	+	0.300899i	−0.00874507	+	0.0326371i
$86$	−1.42371	+	5.31334i	−0.153522	+	0.572952i
$87$			5.84949i			0.627131i
$88$	11.9850	−	6.91955i	1.27761	−	0.737626i
$89$	−6.83819	+	6.83819i	−0.724847	+	0.724847i	−0.969588	−	0.244742i	$-0.921297\pi$
$89$	−6.83819	+	6.83819i	−0.724847	+	0.724847i	0.244742	+	0.969588i	$0.421297\pi$
$90$	−0.835790			−0.0881000
$91$		0			0
$92$	−0.430661			−0.0448995
$93$	4.34856	−	4.34856i	0.450924	−	0.450924i
$94$	−12.0404	+	6.95154i	−1.24187	+	0.716997i
$95$			2.24814i			0.230654i
$96$	0.131272	−	0.489913i	0.0133979	−	0.0500015i
$97$	4.61378	−	17.2188i	0.468458	−	1.74831i	−0.176705	−	0.984264i	$-0.556544\pi$
$97$	4.61378	−	17.2188i	0.468458	−	1.74831i	0.645163	−	0.764045i	$-0.276790\pi$
$98$		0			0
$99$	−3.07416	−	3.07416i	−0.308964	−	0.308964i
$100$	−0.141077	+	0.244353i	−0.0141077	+	0.0244353i
$101$	5.57293	+	9.65259i	0.554527	+	0.960469i	0.997940	+	0.0641517i	$0.0204342\pi$
$101$	5.57293	+	9.65259i	0.554527	+	0.960469i	−0.443413	+	0.896317i	$0.646233\pi$
$102$	0.244212	−	0.911410i	0.0241805	−	0.0902430i
$103$	−3.73616	−	6.47122i	−0.368135	−	0.637628i	0.621139	−	0.783700i	$-0.286670\pi$
$103$	−3.73616	−	6.47122i	−0.368135	−	0.637628i	−0.989274	+	0.146072i	$0.953337\pi$
$104$	7.37544	+	7.26085i	0.723221	+	0.711985i
$105$		0			0
$106$	1.58576	+	5.91812i	0.154022	+	0.574819i
$107$	−4.15105			−0.401297			−0.200649	−	0.979663i	$-0.564305\pi$
$107$	−4.15105			−0.401297			−0.200649	+	0.979663i	$0.564305\pi$
$108$	−0.349960			−0.0336749
$109$	−1.59208	−	5.94172i	−0.152493	−	0.569113i	−0.999307	−	0.0372233i	$-0.988149\pi$
$109$	−1.59208	−	5.94172i	−0.152493	−	0.569113i	0.846814	−	0.531890i	$-0.178518\pi$
$110$	−4.31618	+	1.15652i	−0.411532	+	0.110270i
$111$	−4.72379	−	1.26574i	−0.448363	−	0.120138i
$112$		0			0
$113$	−0.554932	−	0.961171i	−0.0522036	−	0.0904194i	0.838743	−	0.544528i	$-0.183291\pi$
$113$	−0.554932	−	0.961171i	−0.0522036	−	0.0904194i	−0.890946	+	0.454109i	$0.849958\pi$
$114$		−	6.80952i		−	0.637770i
$115$	4.47269	+	1.19845i	0.417080	+	0.111756i
$116$	−0.216547	−	0.125023i	−0.0201058	−	0.0116081i
$117$	1.60358	−	2.82839i	0.148251	−	0.261484i
$118$		−	8.53092i		−	0.785335i
$119$		0			0
$120$	−1.38413	+	2.39738i	−0.126353	+	0.218849i
$121$	−10.6031	−	6.12170i	−0.963918	−	0.556519i
$122$	6.54950	−	1.75493i	0.592963	−	0.158884i
$123$	−3.90253	+	3.90253i	−0.351879	+	0.351879i
$124$	0.0680392	+	0.253926i	0.00611010	+	0.0228032i
$125$	4.49900	−	4.49900i	0.402403	−	0.402403i
$126$		0			0
$127$	17.2552	+	9.96228i	1.53115	+	0.884009i	0.999309	+	0.0371647i	$0.0118326\pi$
$127$	17.2552	+	9.96228i	1.53115	+	0.884009i	0.531840	+	0.846845i	$0.321501\pi$
$128$	−7.60849	−	7.60849i	−0.672502	−	0.672502i
$129$	2.86178	−	4.95674i	0.251965	−	0.436417i
$130$	−1.69349	−	2.88090i	−0.148529	−	0.252671i
$131$	−6.61385	+	3.81851i	−0.577855	+	0.333625i	−0.760280	−	0.649595i	$-0.774938\pi$
$131$	−6.61385	+	3.81851i	−0.577855	+	0.333625i	0.182426	+	0.983220i	$0.441605\pi$
$132$	−0.417688	+	0.111919i	−0.0363550	+	0.00974131i
$133$		0			0
$134$	11.2797	−	6.51231i	0.974414	−	0.562578i
$135$	3.63456	+	0.973878i	0.312813	+	0.0838181i
$136$	0.949728	+	0.949728i	0.0814385	+	0.0814385i
$137$	9.31142	+	9.31142i	0.795528	+	0.795528i	0.982387	−	0.186859i	$-0.0598306\pi$
$137$	9.31142	+	9.31142i	0.795528	+	0.795528i	−0.186859	+	0.982387i	$0.559831\pi$
$138$	−13.5476	−	3.63007i	−1.15325	−	0.309012i
$139$	14.9082	−	8.60724i	1.26449	−	0.730056i	0.290554	−	0.956859i	$-0.406161\pi$
$139$	14.9082	−	8.60724i	1.26449	−	0.730056i	0.973941	+	0.226802i	$0.0728272\pi$
$140$		0			0
$141$	13.9732	−	3.74411i	1.17676	−	0.315311i
$142$	−3.99332	+	2.30555i	−0.335112	+	0.193477i
$143$	4.36744	−	16.8253i	0.365223	−	1.40700i
$144$	−1.74595	+	3.02408i	−0.145496	+	0.252007i
$145$	1.90106	+	1.90106i	0.157874	+	0.157874i
$146$	−0.140640	−	0.0811987i	−0.0116395	−	0.00672006i
$147$		0			0
$148$	0.147821	−	0.147821i	0.0121508	−	0.0121508i
$149$	0.973843	+	3.63443i	0.0797804	+	0.297744i	0.994275	−	0.106854i	$-0.0340779\pi$
$149$	0.973843	+	3.63443i	0.0797804	+	0.297744i	−0.914494	+	0.404599i	$0.867411\pi$
$150$	−6.49762	+	6.49762i	−0.530529	+	0.530529i
$151$	7.30304	−	1.95684i	0.594313	−	0.159246i	0.0508895	−	0.998704i	$-0.483794\pi$
$151$	7.30304	−	1.95684i	0.594313	−	0.159246i	0.543424	+	0.839459i	$0.317128\pi$
$152$	8.39443	+	4.84653i	0.680879	+	0.393105i
$153$	0.210968	−	0.365408i	0.0170558	−	0.0295415i
$154$		0			0
$155$		−	2.82653i		−	0.227032i
$156$	−0.163884	−	0.278792i	−0.0131212	−	0.0223212i
$157$	21.3379	+	12.3194i	1.70295	+	0.983199i	0.942744	+	0.333518i	$0.108236\pi$
$157$	21.3379	+	12.3194i	1.70295	+	0.983199i	0.760207	+	0.649681i	$0.225097\pi$
$158$	−0.524222	−	0.140465i	−0.0417049	−	0.0111748i
$159$		−	6.37502i		−	0.505572i
$160$	−0.116557	−	0.201882i	−0.00921463	−	0.0159602i
$161$		0			0
$162$	−7.37111	−	1.97508i	−0.579129	−	0.155177i
$163$	20.0547	−	5.37364i	1.57081	−	0.420896i	0.634742	−	0.772724i	$-0.281107\pi$
$163$	20.0547	−	5.37364i	1.57081	−	0.420896i	0.936065	+	0.351828i	$0.114440\pi$
$164$	−0.0610604	−	0.227881i	−0.00476802	−	0.0177945i
$165$	4.64941			0.361956
$166$	22.7538			1.76604
$167$	4.53457	+	16.9233i	0.350896	+	1.30956i	0.885571	+	0.464503i	$0.153767\pi$
$167$	4.53457	+	16.9233i	0.350896	+	1.30956i	−0.534676	+	0.845057i	$0.679566\pi$
$168$		0			0
$169$	12.9984	−	0.203532i	0.999877	−	0.0156563i
$170$	−0.216837	−	0.375572i	−0.0166306	−	0.0288051i
$171$	0.788117	−	2.94129i	0.0602688	−	0.224926i
$172$	0.122332	+	0.211884i	0.00932769	+	0.0161560i
$173$	−2.96030	+	5.12740i	−0.225068	+	0.389829i	−0.956340	−	0.292257i	$-0.905594\pi$
$173$	−2.96030	+	5.12740i	−0.225068	+	0.389829i	0.731272	+	0.682086i	$0.238927\pi$
$174$	−5.75823	−	5.75823i	−0.436530	−	0.436530i
$175$		0			0
$176$	−4.83190	+	18.0329i	−0.364218	+	1.35928i
$177$	−2.29738	+	8.57396i	−0.172682	+	0.644458i
$178$		−	13.4630i		−	1.00910i
$179$	3.26505	−	1.88508i	0.244041	−	0.140897i	−0.372992	−	0.927835i	$-0.621668\pi$
$179$	3.26505	−	1.88508i	0.244041	−	0.140897i	0.617033	+	0.786938i	$0.288335\pi$
$180$	−0.0262861	+	0.0262861i	−0.00195925	+	0.00195925i
$181$	−5.68899			−0.422859			−0.211430	−	0.977393i	$-0.567812\pi$
$181$	−5.68899			−0.422859			−0.211430	+	0.977393i	$0.567812\pi$
$182$		0			0
$183$	−7.05514			−0.521531
$184$	14.1172	−	14.1172i	1.04073	−	1.04073i
$185$	−1.94657	+	1.12385i	−0.143115	+	0.0826273i
$186$			8.56143i			0.627754i
$187$	0.583852	−	2.17896i	0.0426955	−	0.159342i
$188$	−0.160049	+	0.597309i	−0.0116727	+	0.0435633i
$189$		0			0
$190$	−2.21307	−	2.21307i	−0.160553	−	0.160553i
$191$	4.58382	−	7.93941i	0.331674	−	0.574476i	−0.651167	−	0.758935i	$-0.725720\pi$
$191$	4.58382	−	7.93941i	0.331674	−	0.574476i	0.982840	+	0.184459i	$0.0590534\pi$
$192$	5.96223	+	10.3269i	0.430287	+	0.745278i
$193$	−6.57695	+	24.5455i	−0.473419	+	1.76682i	0.153926	+	0.988082i	$0.450808\pi$
$193$	−6.57695	+	24.5455i	−0.473419	+	1.76682i	−0.627345	+	0.778742i	$0.715858\pi$
$194$	12.4084	+	21.4920i	0.890872	+	1.54304i
$195$	0.926209	+	3.35149i	0.0663272	+	0.240005i
$196$		0			0
$197$	−0.371638	−	1.38697i	−0.0264781	−	0.0988175i	0.951422	−	0.307889i	$-0.0996225\pi$
$197$	−0.371638	−	1.38697i	−0.0264781	−	0.0988175i	−0.977900	+	0.209071i	$0.932956\pi$
$198$	6.05239			0.430125
$199$	−11.0158			−0.780892			−0.390446	−	0.920626i	$-0.627679\pi$
$199$	−11.0158			−0.780892			−0.390446	+	0.920626i	$0.627679\pi$
$200$	−3.38540	−	12.6345i	−0.239384	−	0.893393i
$201$	−13.0903	+	3.50754i	−0.923321	+	0.247403i
$202$	−14.9880	−	4.01602i	−1.05455	−	0.282566i
$203$		0			0
$204$	−0.0209838	−	0.0363450i	−0.00146916	−	0.00254466i
$205$			2.53661i			0.177164i
$206$	10.0481	+	2.69239i	0.700086	+	0.187588i
$207$	−5.43158	−	3.13593i	−0.377521	−	0.217962i
$208$	−13.9614	+	0.109299i	−0.968052	+	0.00757853i
$209$		−	16.2800i		−	1.12611i
$210$		0			0
$211$	11.5485	−	20.0025i	0.795029	−	1.37703i	−0.127792	−	0.991801i	$-0.540789\pi$
$211$	11.5485	−	20.0025i	0.795029	−	1.37703i	0.922821	−	0.385229i	$-0.125878\pi$
$212$	0.236002	+	0.136256i	0.0162087	+	0.00935808i
$213$	4.63435	−	1.24177i	0.317541	−	0.0850848i
$214$	4.08629	−	4.08629i	0.279333	−	0.279333i
$215$	−0.680855	−	2.54098i	−0.0464339	−	0.173294i
$216$	11.4718	−	11.4718i	0.780556	−	0.780556i
$217$		0			0
$218$	7.41625	+	4.28178i	0.502292	+	0.289998i
$219$	0.119483	+	0.119483i	0.00807391	+	0.00807391i
$220$	−0.0993735	+	0.172120i	−0.00669976	+	0.0116043i
$221$	1.68700	−	0.0132069i	0.113480	−	0.000888393i
$222$	5.89608	−	3.40410i	0.395719	−	0.228469i
$223$	3.57776	−	0.958657i	0.239584	−	0.0641964i	−0.137029	−	0.990567i	$-0.543755\pi$
$223$	3.57776	−	0.958657i	0.239584	−	0.0641964i	0.376613	+	0.926371i	$0.377089\pi$
$224$		0			0
$225$	−3.55859	+	2.05455i	−0.237239	+	0.136970i
$226$	1.49245	+	0.399901i	0.0992763	+	0.0266010i
$227$	−17.0467	−	17.0467i	−1.13143	−	1.13143i	−0.989939	−	0.141493i	$-0.954810\pi$
$227$	−17.0467	−	17.0467i	−1.13143	−	1.13143i	−0.141493	−	0.989939i	$-0.545190\pi$
$228$	−0.214164	−	0.214164i	−0.0141833	−	0.0141833i
$229$	−18.0095	−	4.82564i	−1.19010	−	0.318887i	−0.391176	−	0.920316i	$-0.627932\pi$
$229$	−18.0095	−	4.82564i	−1.19010	−	0.318887i	−0.798926	+	0.601429i	$0.794598\pi$
$230$	−5.58266	+	3.22315i	−0.368110	+	0.212528i
$231$		0			0
$232$	11.1967	−	3.00016i	0.735102	−	0.196970i
$233$	−3.91672	+	2.26132i	−0.256593	+	0.148144i	−0.622779	−	0.782398i	$-0.713997\pi$
$233$	−3.91672	+	2.26132i	−0.256593	+	0.148144i	0.366187	+	0.930541i	$0.380663\pi$
$234$	1.20570	+	4.36282i	0.0788189	+	0.285206i
$235$	3.32442	−	5.75806i	0.216861	−	0.375614i
$236$	−0.268303	−	0.268303i	−0.0174650	−	0.0174650i
$237$	0.489040	+	0.282347i	0.0317665	+	0.0183404i
$238$		0			0
$239$	−11.1608	+	11.1608i	−0.721931	+	0.721931i	−0.968998	−	0.247067i	$-0.920533\pi$
$239$	−11.1608	+	11.1608i	−0.721931	+	0.721931i	0.247067	+	0.968998i	$0.420533\pi$
$240$	−0.966531	−	3.60714i	−0.0623893	−	0.232840i
$241$	5.35165	−	5.35165i	0.344730	−	0.344730i	−0.513412	−	0.858142i	$-0.671619\pi$
$241$	5.35165	−	5.35165i	0.344730	−	0.344730i	0.858142	+	0.513412i	$0.171619\pi$
$242$	16.4639	−	4.41148i	1.05834	−	0.283581i
$243$	−7.80745	−	4.50763i	−0.500848	−	0.289165i
$244$	0.150792	−	0.261180i	0.00965348	−	0.0167203i
$245$		0			0
$246$		−	7.68328i		−	0.489868i
$247$	11.7353	−	3.24313i	0.746698	−	0.206356i
$248$	−10.5541	−	6.09341i	−0.670186	−	0.386932i
$249$	−22.8686	−	6.12762i	−1.44924	−	0.388322i
$250$			8.85761i			0.560205i
$251$	10.6165	+	18.3883i	0.670106	+	1.16066i	0.977874	+	0.209197i	$0.0670849\pi$
$251$	10.6165	+	18.3883i	0.670106	+	1.16066i	−0.307767	+	0.951462i	$0.599582\pi$
$252$		0			0
$253$	−32.3891	−	8.67863i	−2.03628	−	0.545621i
$254$	−26.7928	+	7.17911i	−1.68113	+	0.450458i
$255$	0.116789	+	0.435861i	0.00731359	+	0.0272947i
$256$	−1.48464			−0.0927899
$257$	25.2410			1.57449			0.787245	−	0.616640i	$-0.211506\pi$
$257$	25.2410			1.57449			0.787245	+	0.616640i	$0.211506\pi$
$258$	2.06228	+	7.69653i	0.128392	+	0.479165i
$259$		0			0
$260$	−0.143868	−	0.0373446i	−0.00892229	−	0.00231601i
$261$	−1.82075	−	3.15364i	−0.112702	−	0.195205i
$262$	2.75173	−	10.2696i	0.170002	−	0.634458i
$263$	−0.152018	−	0.263302i	−0.00937381	−	0.0162359i	0.861300	−	0.508096i	$-0.169650\pi$
$263$	−0.152018	−	0.263302i	−0.00937381	−	0.0162359i	−0.870674	+	0.491860i	$0.836317\pi$
$264$	10.0232	−	17.3606i	0.616884	−	1.06847i
$265$	−2.07186	−	2.07186i	−0.127273	−	0.127273i
$266$		0			0
$267$	−3.62560	+	13.5309i	−0.221883	+	0.828079i
$268$	0.149936	−	0.559569i	0.00915880	−	0.0341811i
$269$			17.9385i			1.09373i	0.837221	+	0.546865i	$0.184179\pi$
$269$			17.9385i			1.09373i	−0.837221	+	0.546865i	$0.815821\pi$
$270$	−4.53654	+	2.61917i	−0.276085	+	0.159398i
$271$	9.18147	−	9.18147i	0.557734	−	0.557734i	−0.370927	−	0.928662i	$-0.620960\pi$
$271$	9.18147	−	9.18147i	0.557734	−	0.557734i	0.928662	+	0.370927i	$0.120960\pi$
$272$	−1.81188			−0.109861
$273$		0			0
$274$	−18.3323			−1.10749
$275$	−15.5343	+	15.5343i	−0.936752	+	0.936752i
$276$	−0.540248	+	0.311913i	−0.0325191	+	0.0187749i
$277$			6.21287i			0.373295i	0.982427	+	0.186648i	$0.0597623\pi$
$277$			6.21287i			0.373295i	−0.982427	+	0.186648i	$0.940238\pi$
$278$	−6.20263	+	23.1485i	−0.372009	+	1.38836i
$279$	−0.990877	+	3.69801i	−0.0593223	+	0.221394i
$280$		0			0
$281$	1.72841	+	1.72841i	0.103108	+	0.103108i	0.756779	−	0.653671i	$-0.226772\pi$
$281$	1.72841	+	1.72841i	0.103108	+	0.103108i	−0.653671	+	0.756779i	$0.726772\pi$
$282$	−10.0695	+	17.4409i	−0.599631	+	1.03859i
$283$	9.00809	+	15.6025i	0.535475	+	0.927471i	0.999140	+	0.0414599i	$0.0132009\pi$
$283$	9.00809	+	15.6025i	0.535475	+	0.927471i	−0.463665	+	0.886011i	$0.653466\pi$
$284$	−0.0530817	+	0.198103i	−0.00314982	+	0.0117553i
$285$	1.62825	+	2.82021i	0.0964492	+	0.167055i
$286$	12.2635	+	20.8621i	0.725154	+	1.23360i
$287$		0			0
$288$	0.0817212	+	0.304988i	0.00481547	+	0.0179716i
$289$	−16.7811			−0.987122
$290$	−3.74280			−0.219785
$291$	−6.68319	−	24.9420i	−0.391776	−	1.46213i
$292$	−0.00697698	+	0.00186948i	−0.000408297	+	0.000109403i
$293$	−4.38187	−	1.17412i	−0.255992	−	0.0685927i	0.128541	−	0.991704i	$-0.458971\pi$
$293$	−4.38187	−	1.17412i	−0.255992	−	0.0685927i	−0.384532	+	0.923111i	$0.625637\pi$
$294$		0			0
$295$	2.03986	+	3.53314i	0.118765	+	0.205707i
$296$			9.69119i			0.563289i
$297$	−26.3198	−	7.05236i	−1.52723	−	0.409219i
$298$	−4.53638	−	2.61908i	−0.262785	−	0.151719i
$299$	−0.196313	−	25.0763i	−0.0113531	−	1.45020i
$300$			0.408709i			0.0235968i
$301$		0			0
$302$	−5.26279	+	9.11542i	−0.302839	+	0.524533i
$303$	13.9821	+	8.07256i	0.803249	+	0.463756i
$304$	−12.6305	+	3.38432i	−0.724406	+	0.194104i
$305$	−2.29289	+	2.29289i	−0.131291	+	0.131291i
$306$	0.152030	+	0.567384i	0.00869098	+	0.0324352i
$307$	−11.5340	+	11.5340i	−0.658282	+	0.658282i	−0.954973	−	0.296691i	$-0.904117\pi$
$307$	−11.5340	+	11.5340i	−0.658282	+	0.658282i	0.296691	+	0.954973i	$0.404117\pi$
$308$		0			0
$309$	−9.37376	−	5.41194i	−0.533254	−	0.307875i
$310$	2.78243	+	2.78243i	0.158031	+	0.158031i
$311$	−5.42435	+	9.39525i	−0.307587	+	0.532756i	−0.977834	−	0.209382i	$-0.932855\pi$
$311$	−5.42435	+	9.39525i	−0.307587	+	0.532756i	0.670247	+	0.742138i	$0.266188\pi$
$312$	14.5110	+	3.76671i	0.821524	+	0.213248i
$313$	6.22407	−	3.59347i	0.351805	−	0.203115i	−0.313675	−	0.949530i	$-0.601560\pi$
$313$	6.22407	−	3.59347i	0.351805	−	0.203115i	0.665480	+	0.746416i	$0.268227\pi$
$314$	−33.1322	+	8.87776i	−1.86976	+	0.501001i
$315$		0			0
$316$	−0.0209048	+	0.0120694i	−0.00117599	+	0.000678958i
$317$	9.14677	+	2.45087i	0.513734	+	0.137655i	0.506367	−	0.862318i	$-0.330988\pi$
$317$	9.14677	+	2.45087i	0.513734	+	0.137655i	0.00736711	+	0.999973i	$0.497655\pi$
$318$	6.27556	+	6.27556i	0.351916	+	0.351916i
$319$	−13.7666	−	13.7666i	−0.770779	−	0.770779i
$320$	5.29389	+	1.41849i	0.295937	+	0.0792962i
$321$	−5.20734	+	3.00646i	−0.290646	+	0.167804i
$322$		0			0
$323$	1.52617	−	0.408937i	0.0849185	−	0.0227538i
$324$	−0.293944	+	0.169709i	−0.0163302	+	0.00942825i
$325$	−14.2923	−	8.10318i	−0.792797	−	0.449483i
$326$	−14.4520	+	25.0316i	−0.800423	+	1.38637i
$327$	−6.30058	−	6.30058i	−0.348423	−	0.348423i
$328$	9.47156	+	5.46841i	0.522979	+	0.301942i
$329$		0			0
$330$	−4.57687	+	4.57687i	−0.251948	+	0.251948i
$331$	1.53579	+	5.73166i	0.0844148	+	0.315040i	0.995203	−	0.0978341i	$-0.0311915\pi$
$331$	1.53579	+	5.73166i	0.0844148	+	0.315040i	−0.910788	+	0.412875i	$0.864525\pi$
$332$	0.715621	−	0.715621i	0.0392748	−	0.0392748i
$333$	2.94072	−	0.787965i	0.161151	−	0.0431802i
$334$	−21.1230	−	12.1954i	−1.15580	−	0.667302i
$335$	−3.11436	+	5.39424i	−0.170156	+	0.294719i
$336$		0			0
$337$		−	16.0448i		−	0.874014i	−0.899458	−	0.437007i	$-0.856039\pi$
$337$		−	16.0448i		−	0.874014i	0.899458	−	0.437007i	$-0.143961\pi$
$338$	−12.5953	+	12.9960i	−0.685091	+	0.706887i
$339$	−1.39229	−	0.803836i	−0.0756185	−	0.0436584i
$340$	−0.0186316	−	0.00499233i	−0.00101044	−	0.000270747i
$341$			20.4683i			1.10842i
$342$	2.11958	+	3.67122i	0.114614	+	0.198517i
$343$		0			0
$344$	−10.9557	−	2.93557i	−0.590691	−	0.158275i
$345$	6.47883	−	1.73600i	0.348808	−	0.0934629i
$346$	−2.13328	−	7.96152i	−0.114686	−	0.428014i
$347$	22.9374			1.23135			0.615673	−	0.788002i	$-0.288884\pi$
$347$	22.9374			1.23135			0.615673	+	0.788002i	$0.288884\pi$
$348$	−0.362200			−0.0194160
$349$	3.69715	+	13.7979i	0.197904	+	0.738587i	0.991496	+	0.130137i	$0.0415417\pi$
$349$	3.69715	+	13.7979i	0.197904	+	0.738587i	−0.793592	+	0.608450i	$0.791792\pi$
$350$		0			0
$351$	−0.159526	−	20.3773i	−0.00851489	−	1.08766i
$352$	0.844049	+	1.46194i	0.0449880	+	0.0779214i
$353$	−1.20372	+	4.49235i	−0.0640677	+	0.239104i	−0.990533	−	0.137277i	$-0.956165\pi$
$353$	−1.20372	+	4.49235i	−0.0640677	+	0.239104i	0.926465	+	0.376381i	$0.122832\pi$
$354$	−6.17865	−	10.7017i	−0.328391	−	0.568790i
$355$	1.10257	−	1.90972i	0.0585186	−	0.101357i
$356$	−0.423420	−	0.423420i	−0.0224412	−	0.0224412i
$357$		0			0
$358$	−1.35844	+	5.06977i	−0.0717959	+	0.267946i
$359$	4.70405	−	17.5557i	0.248270	−	0.926557i	−0.723441	−	0.690386i	$-0.757441\pi$
$359$	4.70405	−	17.5557i	0.248270	−	0.926557i	0.971711	−	0.236171i	$-0.0758926\pi$
$360$		−	1.72333i		−	0.0908275i
$361$	−6.57949	+	3.79867i	−0.346289	+	0.199930i
$362$	5.60023	−	5.60023i	0.294342	−	0.294342i
$363$	−17.7349			−0.930843
$364$		0			0
$365$	0.0776629			0.00406506
$366$	6.94507	−	6.94507i	0.363025	−	0.363025i
$367$	−12.6911	+	7.32723i	−0.662472	+	0.382478i	−0.793218	−	0.608937i	$-0.791596\pi$
$367$	−12.6911	+	7.32723i	−0.662472	+	0.382478i	0.130746	+	0.991416i	$0.458263\pi$
$368$			26.9325i			1.40395i
$369$	0.889243	−	3.31870i	0.0462921	−	0.172765i
$370$	0.809882	−	3.02252i	0.0421038	−	0.157133i
$371$		0			0
$372$	0.269262	+	0.269262i	0.0139606	+	0.0139606i
$373$	2.86259	−	4.95816i	0.148220	−	0.256724i	−0.782350	−	0.622839i	$-0.785979\pi$
$373$	2.86259	−	4.95816i	0.148220	−	0.256724i	0.930569	+	0.366115i	$0.119312\pi$
$374$	1.57023	+	2.71971i	0.0811945	+	0.140633i
$375$	2.38536	−	8.90230i	0.123180	−	0.459713i
$376$	−14.3335	−	24.8264i	−0.739195	−	1.28032i
$377$	7.18108	−	12.6660i	0.369844	−	0.652330i
$378$		0			0
$379$	−0.283332	−	1.05741i	−0.0145538	−	0.0543156i	0.958267	−	0.285875i	$-0.0922840\pi$
$379$	−0.283332	−	1.05741i	−0.0145538	−	0.0543156i	−0.972821	+	0.231559i	$0.925617\pi$
$380$	−0.139205			−0.00714105
$381$	28.8613			1.47861
$382$	3.30324	+	12.3278i	0.169008	+	0.630747i
$383$	0.492561	−	0.131981i	0.0251687	−	0.00674393i	−0.246213	−	0.969216i	$-0.579186\pi$
$383$	0.492561	−	0.131981i	0.0251687	−	0.00674393i	0.271381	+	0.962472i	$0.412520\pi$
$384$	−15.0551	−	4.03401i	−0.768280	−	0.205860i
$385$		0			0
$386$	−17.6882	−	30.6369i	−0.900306	−	1.55938i
$387$			3.56311i			0.181123i
$388$	1.06619	+	0.285685i	0.0541276	+	0.0145034i
$389$	−17.8137	−	10.2847i	−0.903191	−	0.521457i	−0.0249566	−	0.999689i	$-0.507945\pi$
$389$	−17.8137	−	10.2847i	−0.903191	−	0.521457i	−0.878234	+	0.478231i	$0.841278\pi$
$390$	−4.21096	−	2.38744i	−0.213230	−	0.120893i
$391$		−	3.25433i		−	0.164578i
$392$		0			0
$393$	−5.53122	+	9.58036i	−0.279013	+	0.483265i
$394$	1.73117	+	0.999492i	0.0872151	+	0.0503537i
$395$	0.250697	−	0.0671742i	0.0126140	−	0.00337990i
$396$	0.190352	−	0.190352i	0.00956552	−	0.00956552i
$397$	7.65009	+	28.5505i	0.383947	+	1.43291i	0.839820	+	0.542864i	$0.182660\pi$
$397$	7.65009	+	28.5505i	0.383947	+	1.43291i	−0.455874	+	0.890045i	$0.650673\pi$
$398$	10.8440	−	10.8440i	0.543559	−	0.543559i
$399$		0			0
$400$	15.2812	+	8.82263i	0.764062	+	0.441131i
$401$	−4.67580	−	4.67580i	−0.233499	−	0.233499i	0.580653	−	0.814151i	$-0.302797\pi$
$401$	−4.67580	−	4.67580i	−0.233499	−	0.233499i	−0.814151	+	0.580653i	$0.802797\pi$
$402$	9.43328	−	16.3389i	0.470489	−	0.814911i
$403$	−14.7544	+	4.07750i	−0.734971	+	0.203115i
$404$	−0.597688	+	0.345075i	−0.0297361	+	0.0171681i
$405$	3.52507	−	0.944538i	0.175162	−	0.0469345i
$406$		0			0
$407$	14.0961	−	8.13841i	0.698719	−	0.403406i
$408$	1.87925	+	0.503545i	0.0930369	+	0.0249292i
$409$	−1.68995	−	1.68995i	−0.0835625	−	0.0835625i	0.664090	−	0.747653i	$-0.268819\pi$
$409$	−1.68995	−	1.68995i	−0.0835625	−	0.0835625i	−0.747653	+	0.664090i	$0.768819\pi$
$410$	−2.49703	−	2.49703i	−0.123320	−	0.123320i
$411$	18.4248	+	4.93690i	0.908827	+	0.243520i
$412$	0.400697	−	0.231343i	0.0197409	−	0.0113974i
$413$		0			0
$414$	8.43384	−	2.25984i	0.414501	−	0.111065i
$415$	−9.42364	+	5.44074i	−0.462588	+	0.267076i
$416$	−0.885682	+	0.899659i	−0.0434241	+	0.0441094i
$417$	12.4678	−	21.5949i	0.610553	−	1.05751i
$418$	16.0260	+	16.0260i	0.783855	+	0.783855i
$419$	−13.1791	−	7.60897i	−0.643842	−	0.371722i	0.142251	−	0.989831i	$-0.454566\pi$
$419$	−13.1791	−	7.60897i	−0.643842	−	0.371722i	−0.786093	+	0.618108i	$0.787899\pi$
$420$		0			0
$421$	−15.0076	+	15.0076i	−0.731425	+	0.731425i	−0.970902	−	0.239477i	$-0.923024\pi$
$421$	−15.0076	+	15.0076i	−0.731425	+	0.731425i	0.239477	+	0.970902i	$0.423024\pi$
$422$	8.32216	+	31.0587i	0.405116	+	1.51192i
$423$	−6.36797	+	6.36797i	−0.309621	+	0.309621i
$424$	−12.2027	+	3.26970i	−0.592615	+	0.158791i
$425$	−1.84647	−	1.06606i	−0.0895671	−	0.0517116i
$426$	−3.33965	+	5.78445i	−0.161807	+	0.280257i
$427$		0			0
$428$		−	0.257033i		−	0.0124241i
$429$	−6.70716	−	24.2699i	−0.323825	−	1.17176i
$430$	3.17157	+	1.83111i	0.152947	+	0.0883039i
$431$	29.0180	+	7.77536i	1.39775	+	0.374526i	0.877536	−	0.479511i	$-0.159186\pi$
$431$	29.0180	+	7.77536i	1.39775	+	0.374526i	0.520213	+	0.854037i	$0.325853\pi$
$432$			21.8857i			1.05298i
$433$	7.75396	+	13.4302i	0.372631	+	0.645417i	0.989969	−	0.141281i	$-0.0451222\pi$
$433$	7.75396	+	13.4302i	0.372631	+	0.645417i	−0.617338	+	0.786698i	$0.711789\pi$
$434$		0			0
$435$	3.76168	+	1.00794i	0.180359	+	0.0483270i
$436$	0.367911	−	0.0985813i	0.0176197	−	0.00472119i
$437$	−6.07861	−	22.6857i	−0.290779	−	1.08520i
$438$	−0.235238			−0.0112401
$439$	−14.4339			−0.688894			−0.344447	−	0.938806i	$-0.611933\pi$
$439$	−14.4339			−0.688894			−0.344447	+	0.938806i	$0.611933\pi$
$440$	−2.38465	−	8.89962i	−0.113684	−	0.424273i
$441$		0			0
$442$	−1.64768	+	1.67368i	−0.0783721	+	0.0796088i
$443$	6.23855	+	10.8055i	0.296403	+	0.513384i	0.975310	−	0.220839i	$-0.0708797\pi$
$443$	6.23855	+	10.8055i	0.296403	+	0.513384i	−0.678908	+	0.734224i	$0.737546\pi$
$444$	0.0783743	−	0.292497i	0.00371948	−	0.0138813i
$445$	3.21919	+	5.57580i	0.152604	+	0.264318i
$446$	−2.57824	+	4.46564i	−0.122083	+	0.211454i
$447$	3.85394	+	3.85394i	0.182285	+	0.182285i
$448$		0			0
$449$	−7.24956	+	27.0557i	−0.342128	+	1.27684i	0.553804	+	0.832647i	$0.313176\pi$
$449$	−7.24956	+	27.0557i	−0.342128	+	1.27684i	−0.895932	+	0.444191i	$0.853491\pi$
$450$	1.48057	−	5.52556i	0.0697948	−	0.260478i
$451$		−	18.3689i		−	0.864958i
$452$	0.0595156	−	0.0343614i	0.00279938	−	0.00161622i
$453$	7.74413	−	7.74413i	0.363851	−	0.363851i
$454$	33.5616			1.57512
$455$		0			0
$456$	14.0407			0.657515
$457$	−12.4557	+	12.4557i	−0.582653	+	0.582653i	−0.935631	−	0.352978i	$-0.885169\pi$
$457$	−12.4557	+	12.4557i	−0.582653	+	0.582653i	0.352978	+	0.935631i	$0.385169\pi$
$458$	22.4789	−	12.9782i	1.05037	−	0.606431i
$459$		−	2.64451i		−	0.123435i
$460$	−0.0742082	+	0.276949i	−0.00345997	+	0.0129128i
$461$	−1.39627	+	5.21097i	−0.0650310	+	0.242699i	−0.990788	−	0.135419i	$-0.956762\pi$
$461$	−1.39627	+	5.21097i	−0.0650310	+	0.242699i	0.925757	+	0.378118i	$0.123429\pi$
$462$		0			0
$463$	−19.4789	−	19.4789i	−0.905259	−	0.905259i	0.0906259	−	0.995885i	$-0.471113\pi$
$463$	−19.4789	−	19.4789i	−0.905259	−	0.905259i	−0.995885	+	0.0906259i	$0.971113\pi$
$464$	−7.81866	+	13.5423i	−0.362972	+	0.628686i
$465$	−2.04715	−	3.54577i	−0.0949345	−	0.164431i
$466$	1.62957	−	6.08165i	0.0754885	−	0.281727i
$467$	−4.79805	−	8.31047i	−0.222027	−	0.384563i	0.733396	−	0.679802i	$-0.237934\pi$
$467$	−4.79805	−	8.31047i	−0.222027	−	0.384563i	−0.955423	+	0.295239i	$0.904601\pi$
$468$	0.175133	+	0.0992935i	0.00809554	+	0.00458984i
$469$		0			0
$470$	2.39567	+	8.94077i	0.110504	+	0.412407i
$471$	35.6902			1.64452
$472$	17.5901			0.809649
$473$	4.93042	+	18.4006i	0.226701	+	0.846060i
$474$	−0.759352	+	0.203468i	−0.0348782	+	0.00934558i
$475$	−14.8629	−	3.98250i	−0.681956	−	0.182729i
$476$		0			0
$477$	1.98434	+	3.43697i	0.0908565	+	0.157368i
$478$		−	21.9733i		−	1.00504i
$479$	29.8944	+	8.01018i	1.36591	+	0.365994i	0.865983	−	0.500073i	$-0.166694\pi$
$479$	29.8944	+	8.01018i	1.36591	+	0.365994i	0.499927	+	0.866068i	$0.333360\pi$
$480$	−0.292433	−	0.168836i	−0.0133477	−	0.00770628i
$481$	8.67460	+	8.53984i	0.395528	+	0.389383i
$482$			10.5363i			0.479916i
$483$		0			0
$484$	0.379055	−	0.656543i	0.0172298	−	0.0298429i
$485$	−10.2781	−	5.93404i	−0.466703	−	0.269451i
$486$	12.1229	−	3.24833i	0.549908	−	0.147347i
$487$	3.95701	−	3.95701i	0.179309	−	0.179309i	−0.611745	−	0.791055i	$-0.709532\pi$
$487$	3.95701	−	3.95701i	0.179309	−	0.179309i	0.791055	+	0.611745i	$0.209532\pi$
$488$	3.61853	+	13.5045i	0.163803	+	0.611322i
$489$	21.2660	−	21.2660i	0.961680	−	0.961680i
$490$		0			0
$491$	12.0113	+	6.93474i	0.542063	+	0.312960i	0.745915	−	0.666041i	$-0.232013\pi$
$491$	12.0113	+	6.93474i	0.542063	+	0.312960i	−0.203851	+	0.979002i	$0.565346\pi$
$492$	−0.241644	−	0.241644i	−0.0108942	−	0.0108942i
$493$	0.944750	−	1.63635i	0.0425494	−	0.0736977i
$494$	−8.35965	+	14.7447i	−0.376119	+	0.663396i
$495$	−2.50664	+	1.44721i	−0.112665	+	0.0650472i
$496$	15.8799	−	4.25501i	0.713030	−	0.191056i
$497$		0			0
$498$	28.5438	−	16.4798i	1.27908	−	0.738477i
$499$	8.83159	+	2.36642i	0.395356	+	0.105935i	0.451019	−	0.892514i	$-0.351061\pi$
$499$	8.83159	+	2.36642i	0.395356	+	0.105935i	−0.0556630	+	0.998450i	$0.517727\pi$
$500$	0.278578	+	0.278578i	0.0124584	+	0.0124584i
$501$	17.9454	+	17.9454i	0.801740	+	0.801740i
$502$	−28.5522	−	7.65055i	−1.27435	−	0.341461i
$503$	27.9587	−	16.1420i	1.24662	−	0.719736i	0.276185	−	0.961104i	$-0.410930\pi$
$503$	27.9587	−	16.1420i	1.24662	−	0.719736i	0.970434	+	0.241369i	$0.0775963\pi$
$504$		0			0
$505$	7.16766	−	1.92057i	0.318957	−	0.0854642i
$506$	40.4270	−	23.3405i	1.79720	−	1.03761i
$507$	16.1586	−	9.66962i	0.717630	−	0.429443i
$508$	−0.616864	+	1.06844i	−0.0273689	+	0.0474043i
$509$	8.53926	+	8.53926i	0.378496	+	0.378496i	0.870559	−	0.492063i	$-0.163757\pi$
$509$	8.53926	+	8.53926i	0.378496	+	0.378496i	−0.492063	+	0.870559i	$0.663757\pi$
$510$	−0.544027	−	0.314094i	−0.0240899	−	0.0139083i
$511$		0			0
$512$	16.6785	−	16.6785i	0.737091	−	0.737091i
$513$	−4.93955	−	18.4347i	−0.218087	−	0.813910i
$514$	−24.8472	+	24.8472i	−1.09596	+	1.09596i
$515$	−4.80529	+	1.28757i	−0.211746	+	0.0567372i
$516$	0.306921	+	0.177201i	0.0135114	+	0.00780084i
$517$	−24.0738	+	41.6971i	−1.05877	+	1.83384i
$518$		0			0
$519$			8.57618i			0.376452i
$520$	5.94018	−	3.49185i	0.260494	−	0.153128i
$521$	−10.1929	−	5.88486i	−0.446558	−	0.257821i	0.259817	−	0.965658i	$-0.416338\pi$
$521$	−10.1929	−	5.88486i	−0.446558	−	0.257821i	−0.706376	+	0.707837i	$0.749671\pi$
$522$	4.89678	+	1.31209i	0.214326	+	0.0574286i
$523$		−	15.3301i		−	0.670337i	−0.942158	−	0.335168i	$-0.891207\pi$
$523$		−	15.3301i		−	0.670337i	0.942158	−	0.335168i	$-0.108793\pi$
$524$	−0.236442	−	0.409529i	−0.0103290	−	0.0178904i
$525$		0			0
$526$	0.408840	+	0.109548i	0.0178263	+	0.00477654i
$527$	−1.91881	+	0.514145i	−0.0835849	+	0.0223965i
$528$	6.99916	+	26.1212i	0.304599	+	1.13678i
$529$	−25.3737			−1.10321
$530$	4.07906			0.177183
$531$	−1.43020	−	5.33758i	−0.0620654	−	0.231631i
$532$		0			0
$533$	13.2411	−	3.65927i	0.573535	−	0.158501i
$534$	−9.75079	−	16.8889i	−0.421958	−	0.730852i
$535$	−0.715277	+	2.66945i	−0.0309241	+	0.115410i
$536$	13.4279	+	23.2577i	0.579995	+	1.00458i
$537$	2.73059	−	4.72952i	0.117834	−	0.204094i
$538$	−17.6586	−	17.6586i	−0.761318	−	0.761318i
$539$		0			0
$540$	−0.0603024	+	0.225052i	−0.00259500	+	0.00968469i
$541$	−3.88929	+	14.5150i	−0.167214	+	0.624050i	0.830534	+	0.556968i	$0.188036\pi$
$541$	−3.88929	+	14.5150i	−0.167214	+	0.624050i	−0.997747	+	0.0670818i	$0.978631\pi$
$542$			18.0764i			0.776450i
$543$	−7.13663	+	4.12034i	−0.306262	+	0.176821i
$544$	−0.115848	+	0.115848i	−0.00496695	+	0.00496695i
$545$	−4.09532			−0.175424
$546$		0			0
$547$	20.0277			0.856322			0.428161	−	0.903702i	$-0.359162\pi$
$547$	20.0277			0.856322			0.428161	+	0.903702i	$0.359162\pi$
$548$	−0.576562	+	0.576562i	−0.0246295	+	0.0246295i
$549$	3.80364	−	2.19603i	0.162336	−	0.0937245i
$550$		−	30.5838i		−	1.30410i
$551$	3.52931	−	13.1716i	0.150354	−	0.561127i
$552$	7.48490	−	27.9340i	0.318579	−	1.18895i
$553$		0			0
$554$	−6.11594	−	6.11594i	−0.259841	−	0.259841i
$555$	−1.62794	+	2.81967i	−0.0691020	+	0.119688i
$556$	0.532959	+	0.923113i	0.0226025	+	0.0391487i
$557$	0.644961	−	2.40703i	0.0273279	−	0.101989i	−0.950915	−	0.309453i	$-0.899854\pi$
$557$	0.644961	−	2.40703i	0.0273279	−	0.101989i	0.978243	+	0.207464i	$0.0665209\pi$
$558$	−2.66489	−	4.61573i	−0.112814	−	0.195399i
$559$	−12.2817	+	7.21964i	−0.519462	+	0.305358i
$560$		0			0
$561$	−0.845727	−	3.15630i	−0.0357066	−	0.133259i
$562$	−3.40288			−0.143542
$563$	−19.7161			−0.830933			−0.415467	−	0.909608i	$-0.636382\pi$
$563$	−19.7161			−0.830933			−0.415467	+	0.909608i	$0.636382\pi$
$564$	0.231835	+	0.865221i	0.00976202	+	0.0364324i
$565$	−0.713730	+	0.191243i	−0.0300268	+	0.00804567i
$566$	−24.2266	−	6.49150i	−1.01832	−	0.272858i
$567$		0			0
$568$	−4.75385	−	8.23391i	−0.199467	−	0.345487i
$569$		−	44.6858i		−	1.87333i	−0.350230	−	0.936664i	$-0.613897\pi$
$569$		−	44.6858i		−	1.87333i	0.350230	−	0.936664i	$-0.386103\pi$
$570$	−4.37906	−	1.17336i	−0.183418	−	0.0491468i
$571$	23.8503	+	13.7700i	0.998103	+	0.576255i	0.907686	−	0.419649i	$-0.137847\pi$
$571$	23.8503	+	13.7700i	0.998103	+	0.576255i	0.0904162	+	0.995904i	$0.471180\pi$
$572$	1.04182	+	0.270431i	0.0435607	+	0.0113073i
$573$		−	13.2796i		−	0.554763i
$574$		0			0
$575$	−15.8464	+	27.4468i	−0.660841	+	1.14461i
$576$	−6.42884	−	3.71169i	−0.267868	−	0.154654i
$577$	−17.7698	+	4.76139i	−0.739765	+	0.198219i	−0.608974	−	0.793190i	$-0.708418\pi$
$577$	−17.7698	+	4.76139i	−0.739765	+	0.198219i	−0.130791	+	0.991410i	$0.541752\pi$
$578$	16.5193	−	16.5193i	0.687110	−	0.687110i
$579$	9.52691	+	35.5549i	0.395925	+	1.47761i
$580$	−0.117713	+	0.117713i	−0.00488778	+	0.00488778i
$581$		0			0
$582$	31.1318	+	17.9740i	1.29046	+	0.745045i
$583$	15.0034	+	15.0034i	0.621377	+	0.621377i
$584$	0.167425	−	0.289989i	0.00692811	−	0.0119998i
$585$	−1.54256	−	1.51859i	−0.0637769	−	0.0627861i
$586$	5.46930	−	3.15770i	0.225935	−	0.130444i
$587$	20.1767	−	5.40633i	0.832781	−	0.223143i	0.182855	−	0.983140i	$-0.441466\pi$
$587$	20.1767	−	5.40633i	0.832781	−	0.223143i	0.649927	+	0.759997i	$0.274800\pi$
$588$		0			0
$589$	−12.4156	+	7.16813i	−0.511574	+	0.295358i
$590$	−5.48605	−	1.46998i	−0.225857	−	0.0605182i
$591$	−1.47074	−	1.47074i	−0.0604982	−	0.0604982i
$592$	−9.24435	−	9.24435i	−0.379940	−	0.379940i
$593$	−8.55614	−	2.29261i	−0.351358	−	0.0941462i	0.0788231	−	0.996889i	$-0.474884\pi$
$593$	−8.55614	−	2.29261i	−0.351358	−	0.0941462i	−0.430182	+	0.902742i	$0.641550\pi$
$594$	32.8514	−	18.9668i	1.34791	−	0.778217i
$595$		0			0
$596$	−0.225044	+	0.0603003i	−0.00921815	+	0.00247000i
$597$	−13.8190	+	7.97838i	−0.565573	+	0.326534i
$598$	24.8783	+	24.4918i	1.01735	+	1.00154i
$599$	18.1377	−	31.4154i	0.741087	−	1.28360i	−0.210914	−	0.977505i	$-0.567644\pi$
$599$	18.1377	−	31.4154i	0.741087	−	1.28360i	0.952001	−	0.306096i	$-0.0990227\pi$
$600$	−13.3976	−	13.3976i	−0.546954	−	0.546954i
$601$	−30.7163	−	17.7340i	−1.25294	−	0.723387i	−0.281250	−	0.959635i	$-0.590749\pi$
$601$	−30.7163	−	17.7340i	−1.25294	−	0.723387i	−0.971693	+	0.236248i	$0.924082\pi$
$602$		0			0
$603$	5.96562	−	5.96562i	0.242939	−	0.242939i
$604$	0.121168	+	0.452204i	0.00493024	+	0.0183999i
$605$	−5.76378	+	5.76378i	−0.234331	+	0.234331i
$606$	−21.7105	+	5.81732i	−0.881930	+	0.236313i
$607$	22.2647	+	12.8545i	0.903697	+	0.521749i	0.878398	−	0.477930i	$-0.158613\pi$
$607$	22.2647	+	12.8545i	0.903697	+	0.521749i	0.0252989	+	0.999680i	$0.491946\pi$
$608$	−0.591182	+	1.02396i	−0.0239756	+	0.0415269i
$609$		0			0
$610$		−	4.51424i		−	0.182776i
$611$	−34.8528	−	9.04695i	−1.40999	−	0.366000i
$612$	0.0226260	+	0.0130632i	0.000914604	+	0.000528047i
$613$	44.0688	+	11.8082i	1.77992	+	0.476928i	0.990569	−	0.137013i	$-0.0437501\pi$
$613$	44.0688	+	11.8082i	1.77992	+	0.476928i	0.789352	+	0.613941i	$0.210417\pi$
$614$		−	22.7082i		−	0.916427i
$615$	1.83718	+	3.18208i	0.0740821	+	0.128314i
$616$		0			0
$617$	35.5733	+	9.53183i	1.43213	+	0.383737i	0.889769	−	0.456411i	$-0.150865\pi$
$617$	35.5733	+	9.53183i	1.43213	+	0.383737i	0.542357	+	0.840148i	$0.317532\pi$
$618$	14.5550	−	3.90000i	0.585489	−	0.156881i
$619$	1.37524	+	5.13248i	0.0552757	+	0.206292i	0.988041	−	0.154193i	$-0.0492778\pi$
$619$	1.37524	+	5.13248i	0.0552757	+	0.206292i	−0.932765	+	0.360485i	$0.882611\pi$
$620$	0.175018			0.00702890
$621$	−39.3091			−1.57742
$622$	−3.90895	−	14.5884i	−0.156734	−	0.584941i
$623$		0			0
$624$	−17.4350	+	10.2489i	−0.697957	+	0.410284i
$625$	9.27392	+	16.0629i	0.370957	+	0.642516i
$626$	−2.58956	+	9.66437i	−0.103500	+	0.386266i
$627$	−11.7910	−	20.4226i	−0.470887	−	0.815601i
$628$	−0.762819	+	1.32124i	−0.0304398	+	0.0527233i
$629$	1.11702	+	1.11702i	0.0445385	+	0.0445385i
$630$		0			0
$631$	−3.50380	+	13.0763i	−0.139484	+	0.520561i	0.860455	+	0.509526i	$0.170179\pi$
$631$	−3.50380	+	13.0763i	−0.139484	+	0.520561i	−0.999939	+	0.0110350i	$0.996487\pi$
$632$	0.289627	−	1.08090i	0.0115208	−	0.0429961i
$633$		−	33.4566i		−	1.32978i
$634$	−11.4167	+	6.59143i	−0.453415	+	0.261779i
$635$	9.37981	−	9.37981i	0.372226	−	0.372226i
$636$	0.394741			0.0156525
$637$		0			0
$638$	27.1035			1.07304
$639$	−2.11200	+	2.11200i	−0.0835494	+	0.0835494i
$640$	−6.20389	+	3.58182i	−0.245230	+	0.141584i
$641$		−	21.4184i		−	0.845978i	−0.906135	−	0.422989i	$-0.860981\pi$
$641$		−	21.4184i		−	0.845978i	0.906135	−	0.422989i	$-0.139019\pi$
$642$	2.16654	−	8.08566i	0.0855067	−	0.319115i
$643$	3.68080	−	13.7369i	0.145157	−	0.541732i	−0.854592	−	0.519300i	$-0.826193\pi$
$643$	3.68080	−	13.7369i	0.145157	−	0.541732i	0.999748	−	0.0224315i	$-0.00714075\pi$
$644$		0			0
$645$	−2.69445	−	2.69445i	−0.106094	−	0.106094i
$646$	−1.09980	+	1.90492i	−0.0432712	+	0.0749480i
$647$	−10.2738	−	17.7948i	−0.403906	−	0.699585i	0.590288	−	0.807193i	$-0.299014\pi$
$647$	−10.2738	−	17.7948i	−0.403906	−	0.699585i	−0.994193	+	0.107608i	$0.965681\pi$
$648$	4.07246	−	15.1986i	0.159981	−	0.597059i
$649$	−14.7717	−	25.5853i	−0.579839	−	1.00431i
$650$	22.0461	−	6.09261i	0.864720	−	0.238972i
$651$		0			0
$652$	0.332736	+	1.24179i	0.0130309	+	0.0486321i
$653$	−43.6957			−1.70994			−0.854972	−	0.518675i	$-0.826426\pi$
$653$	−43.6957			−1.70994			−0.854972	+	0.518675i	$0.826426\pi$
$654$	12.4046			0.485057
$655$	1.31595	+	4.91120i	0.0514185	+	0.191896i
$656$	−14.2511	+	3.81857i	−0.556413	+	0.149090i
$657$	−0.101608	−	0.0272258i	−0.00396411	−	0.00106218i
$658$		0			0
$659$	−6.26381	−	10.8492i	−0.244003	−	0.422626i	0.717848	−	0.696200i	$-0.245127\pi$
$659$	−6.26381	−	10.8492i	−0.244003	−	0.422626i	−0.961851	+	0.273574i	$0.911794\pi$
$660$			0.287891i			0.0112061i
$661$	−22.2227	−	5.95454i	−0.864361	−	0.231605i	−0.200713	−	0.979650i	$-0.564326\pi$
$661$	−22.2227	−	5.95454i	−0.864361	−	0.231605i	−0.663648	+	0.748045i	$0.730993\pi$
$662$	−7.15407	−	4.13040i	−0.278051	−	0.160533i
$663$	2.10671	−	1.23840i	0.0818180	−	0.0480956i
$664$			46.9165i			1.82071i
$665$		0			0
$666$	−2.11917	+	3.67051i	−0.0821163	+	0.142230i
$667$	−24.3235	−	14.0432i	−0.941809	−	0.543754i
$668$	−1.04789	+	0.280780i	−0.0405439	+	0.0108637i
$669$	3.79385	−	3.79385i	0.146679	−	0.146679i
$670$	−2.24430	−	8.37585i	−0.0867050	−	0.323587i
$671$	16.6040	−	16.6040i	0.640991	−	0.640991i
$672$		0			0
$673$	−12.0684	−	6.96769i	−0.465202	−	0.268585i	0.249027	−	0.968497i	$-0.419889\pi$
$673$	−12.0684	−	6.96769i	−0.465202	−	0.268585i	−0.714229	+	0.699912i	$0.753223\pi$
$674$	15.7944	+	15.7944i	0.608379	+	0.608379i
$675$	−12.8770	+	22.3036i	−0.495635	+	0.858466i
$676$	0.0126027	+	0.804860i	0.000484719	+	0.0309562i
$677$	−44.8299	+	25.8826i	−1.72295	+	0.994747i	−0.810296	+	0.586020i	$0.800694\pi$
$677$	−44.8299	+	25.8826i	−1.72295	+	0.994747i	−0.912657	+	0.408727i	$0.865973\pi$
$678$	2.16186	−	0.579268i	0.0830257	−	0.0222467i
$679$		0			0
$680$	0.774399	−	0.447100i	0.0296969	−	0.0171455i
$681$	−33.7309	−	9.03816i	−1.29257	−	0.346343i
$682$	−20.1490	−	20.1490i	−0.771545	−	0.771545i
$683$	−20.1791	−	20.1791i	−0.772131	−	0.772131i	0.206348	−	0.978479i	$-0.433842\pi$
$683$	−20.1791	−	20.1791i	−0.772131	−	0.772131i	−0.978479	+	0.206348i	$0.933842\pi$
$684$	0.182125	+	0.0488001i	0.00696371	+	0.00186592i
$685$	7.59245	−	4.38350i	0.290092	−	0.167485i
$686$		0			0
$687$	−26.0873	+	6.99008i	−0.995294	+	0.266688i
$688$	13.2508	−	7.65033i	0.505180	−	0.291666i
$689$	−7.82625	+	13.8039i	−0.298156	+	0.525887i
$690$	−4.66883	+	8.08666i	−0.177739	+	0.307854i
$691$	13.2476	+	13.2476i	0.503963	+	0.503963i	0.912667	−	0.408704i	$-0.134019\pi$
$691$	13.2476	+	13.2476i	0.503963	+	0.503963i	−0.408704	+	0.912667i	$0.634019\pi$
$692$	−0.317488	−	0.183302i	−0.0120691	−	0.00696809i
$693$		0			0
$694$	−22.5796	+	22.5796i	−0.857108	+	0.857108i
$695$	−2.96627	−	11.0703i	−0.112517	−	0.419919i
$696$	11.8730	−	11.8730i	0.450045	−	0.450045i
$697$	1.72200	−	0.461409i	0.0652254	−	0.0174771i
$698$	−17.2221	−	9.94320i	−0.651867	−	0.376356i
$699$	−3.27559	+	5.67348i	−0.123894	+	0.214591i
$700$		0			0
$701$			20.1282i			0.760231i	0.924939	+	0.380115i	$0.124116\pi$
$701$			20.1282i			0.760231i	−0.924939	+	0.380115i	$0.875884\pi$
$702$	20.2164	+	19.9023i	0.763019	+	0.751165i
$703$	9.87309	+	5.70023i	0.372371	+	0.214988i
$704$	−38.3358	−	10.2720i	−1.44484	−	0.387142i
$705$		−	9.63103i		−	0.362726i
$706$	−3.23732	−	5.60721i	−0.121838	−	0.211030i
$707$		0			0
$708$	−0.530899	−	0.142254i	−0.0199524	−	0.00534623i
$709$	4.16243	−	1.11532i	0.156323	−	0.0418867i	−0.179809	−	0.983702i	$-0.557548\pi$
$709$	4.16243	−	1.11532i	0.156323	−	0.0418867i	0.336132	+	0.941815i	$0.390881\pi$
$710$	0.794548	+	2.96529i	0.0298189	+	0.111285i
$711$	−0.351542			−0.0131838
$712$	27.7596			1.04034
$713$	7.64247	+	28.5221i	0.286213	+	1.06816i
$714$		0			0
$715$	−10.0674	−	5.70781i	−0.376500	−	0.213460i
$716$	0.116724	+	0.202172i	0.00436217	+	0.00755550i
$717$	−5.91744	+	22.0842i	−0.220991	+	0.824749i
$718$	12.6512	+	21.9125i	0.472138	+	0.817767i
$719$	15.9230	−	27.5794i	0.593827	−	1.02854i	−0.399884	−	0.916566i	$-0.630950\pi$
$719$	15.9230	−	27.5794i	0.593827	−	1.02854i	0.993711	−	0.111973i	$-0.0357171\pi$
$720$	1.64387	+	1.64387i	0.0612635	+	0.0612635i
$721$		0			0
$722$	2.73743	−	10.2162i	0.101877	−	0.380209i
$723$	2.83744	−	10.5895i	0.105525	−	0.393826i
$724$		−	0.352262i		−	0.0130917i
$725$	−15.9359	+	9.20060i	−0.591845	+	0.341702i
$726$	17.4583	−	17.4583i	0.647936	−	0.647936i
$727$	49.3169			1.82906			0.914531	−	0.404516i	$-0.132560\pi$
$727$	49.3169			1.82906			0.914531	+	0.404516i	$0.132560\pi$
$728$		0			0
$729$	−29.5035			−1.09272
$730$	−0.0764512	+	0.0764512i	−0.00282959	+	0.00282959i
$731$	−1.60112	+	0.924410i	−0.0592197	+	0.0341905i
$732$		−	0.436854i		−	0.0161466i
$733$	−4.21647	+	15.7361i	−0.155739	+	0.581226i	0.843302	+	0.537440i	$0.180609\pi$
$733$	−4.21647	+	15.7361i	−0.155739	+	0.581226i	−0.999041	+	0.0437858i	$0.986058\pi$
$734$	5.28022	−	19.7061i	0.194896	−	0.727364i
$735$		0			0
$736$	1.72202	+	1.72202i	0.0634744	+	0.0634744i
$737$	22.5527	−	39.0625i	0.830741	−	1.43888i
$738$	2.39155	+	4.14229i	0.0880343	+	0.152480i
$739$	6.53382	−	24.3845i	0.240350	−	0.897000i	−0.735313	−	0.677727i	$-0.762965\pi$
$739$	6.53382	−	24.3845i	0.240350	−	0.897000i	0.975664	−	0.219273i	$-0.0703684\pi$
$740$	−0.0695889	−	0.120532i	−0.00255814	−	0.00443083i
$741$	12.3726	−	12.5678i	0.454519	−	0.461691i
$742$		0			0
$743$	2.17652	+	8.12290i	0.0798489	+	0.298000i	0.994289	−	0.106721i	$-0.0340352\pi$
$743$	2.17652	+	8.12290i	0.0798489	+	0.298000i	−0.914440	+	0.404721i	$0.867369\pi$
$744$	−17.6530			−0.647189
$745$	2.50503			0.0917772
$746$	2.06287	+	7.69874i	0.0755270	+	0.281871i
$747$	14.2365	−	3.81465i	0.520886	−	0.139571i
$748$	0.134921	+	0.0361521i	0.00493321	+	0.00132185i
$749$		0			0
$750$	6.41526	+	11.1116i	0.234252	+	0.405737i
$751$			34.1800i			1.24725i	0.781725	+	0.623623i	$0.214340\pi$
$751$			34.1800i			1.24725i	−0.781725	+	0.623623i	$0.785660\pi$
$752$	37.3543	+	10.0091i	1.36217	+	0.364993i
$753$	26.6360	+	15.3783i	0.970669	+	0.560416i
$754$	5.39930	+	19.5374i	0.196631	+	0.711509i
$755$		−	5.03362i		−	0.183192i
$756$		0			0
$757$	−6.77459	+	11.7339i	−0.246227	+	0.426477i	−0.962476	−	0.271368i	$-0.912524\pi$
$757$	−6.77459	+	11.7339i	−0.246227	+	0.426477i	0.716249	+	0.697845i	$0.245857\pi$
$758$	1.31983	+	0.762002i	0.0479382	+	0.0276771i
$759$	−46.9166	+	12.5713i	−1.70296	+	0.456308i
$760$	4.56316	−	4.56316i	0.165523	−	0.165523i
$761$	5.17326	+	19.3069i	0.187531	+	0.699873i	0.994075	+	0.108700i	$0.0346686\pi$
$761$	5.17326	+	19.3069i	0.187531	+	0.699873i	−0.806544	+	0.591174i	$0.798665\pi$
$762$	−28.4110	+	28.4110i	−1.02922	+	1.02922i
$763$		0			0
$764$	0.491608	+	0.283830i	0.0177857	+	0.0102686i
$765$	−0.198634	−	0.198634i	−0.00718161	−	0.00718161i
$766$	−0.354954	+	0.614799i	−0.0128250	+	0.0222136i
$767$	15.5003	−	15.7449i	0.559683	−	0.568515i
$768$	−1.86243	+	1.07527i	−0.0672045	+	0.0388005i
$769$	−30.3963	+	8.14467i	−1.09612	+	0.293704i	−0.761184	−	0.648536i	$-0.775381\pi$
$769$	−30.3963	+	8.14467i	−1.09612	+	0.293704i	−0.334936	+	0.942241i	$0.608715\pi$
$770$		0			0
$771$	31.6639	−	18.2812i	1.14035	−	0.658381i
$772$	−1.51986	−	0.407244i	−0.0547008	−	0.0146570i
$773$	27.0775	+	27.0775i	0.973910	+	0.973910i	0.999668	−	0.0257585i	$-0.00820008\pi$
$773$	27.0775	+	27.0775i	0.973910	+	0.973910i	−0.0257585	+	0.999668i	$0.508200\pi$
$774$	−3.50752	−	3.50752i	−0.126075	−	0.126075i
$775$	18.6867	+	5.00708i	0.671246	+	0.179860i
$776$	−44.3148	+	25.5852i	−1.59081	+	0.918453i
$777$		0			0
$778$	27.6601	−	7.41149i	0.991661	−	0.265715i
$779$	11.1421	−	6.43289i	0.399207	−	0.230482i
$780$	−0.207524	+	0.0573508i	−0.00743055	+	0.00205349i
$781$	−7.98432	+	13.8292i	−0.285701	+	0.494849i
$782$	3.20356	+	3.20356i	0.114559	+	0.114559i
$783$	−19.7656	−	11.4116i	−0.706363	−	0.407819i
$784$		0			0
$785$	11.5992	−	11.5992i	0.413992	−	0.413992i
$786$	−3.98596	−	14.8758i	−0.142175	−	0.530603i
$787$	15.6978	−	15.6978i	0.559566	−	0.559566i	−0.369618	−	0.929184i	$-0.620511\pi$
$787$	15.6978	−	15.6978i	0.559566	−	0.559566i	0.929184	+	0.369618i	$0.120511\pi$
$788$	0.0858811	−	0.0230118i	0.00305939	−	0.000819760i
$789$	−0.381401	−	0.220202i	−0.0135782	−	0.00783940i
$790$	−0.180660	+	0.312912i	−0.00642759	+	0.0111329i
$791$		0			0
$792$			12.4795i			0.443441i
$793$	15.2766	+	8.66119i	0.542487	+	0.307568i
$794$	−35.6358	−	20.5743i	−1.26467	−	0.730156i
$795$	−4.09964	−	1.09850i	−0.145399	−	0.0389596i
$796$		−	0.682100i		−	0.0241764i
$797$	−15.2784	−	26.4630i	−0.541189	−	0.937367i	−0.998836	−	0.0482334i	$-0.984641\pi$
$797$	−15.2784	−	26.4630i	−0.541189	−	0.937367i	0.457647	−	0.889134i	$-0.348692\pi$
$798$		0			0
$799$	−4.51362	−	1.20942i	−0.159681	−	0.0427863i
$800$	1.54116	−	0.412952i	0.0544882	−	0.0146001i
$801$	−2.25706	−	8.42347i	−0.0797494	−	0.297629i
$802$	9.20571			0.325065
$803$	−0.562397			−0.0198466
$804$	−0.217187	−	0.810552i	−0.00765959	−	0.0285860i
$805$		0			0
$806$	10.5104	−	18.5381i	0.370212	−	0.652978i
$807$	12.9922	+	22.5032i	0.457349	+	0.792151i
$808$	8.28071	−	30.9040i	0.291314	−	1.08720i
$809$	−13.3877	−	23.1882i	−0.470688	−	0.815255i	0.528750	−	0.848778i	$-0.322661\pi$
$809$	−13.3877	−	23.1882i	−0.470688	−	0.815255i	−0.999438	+	0.0335223i	$0.989328\pi$
$810$	−2.54027	+	4.39987i	−0.0892559	+	0.154596i
$811$	7.94016	+	7.94016i	0.278817	+	0.278817i	0.832637	−	0.553820i	$-0.186830\pi$
$811$	7.94016	+	7.94016i	0.278817	+	0.278817i	−0.553820	+	0.832637i	$0.686830\pi$
$812$		0			0
$813$	4.86800	−	18.1676i	0.170728	−	0.637167i
$814$	−5.86478	+	21.8876i	−0.205560	+	0.767161i
$815$		−	13.8227i		−	0.484188i
$816$	−2.27293	+	1.31228i	−0.0795686	+	0.0459389i
$817$	−9.43466	+	9.43466i	−0.330077	+	0.330077i
$818$	3.32716			0.116331
$819$		0			0
$820$	−0.157067			−0.00548500
$821$	6.49943	−	6.49943i	0.226832	−	0.226832i	−0.584536	−	0.811368i	$-0.698723\pi$
$821$	6.49943	−	6.49943i	0.226832	−	0.226832i	0.811368	+	0.584536i	$0.198723\pi$
$822$	−22.9972	+	13.2774i	−0.802119	+	0.463104i
$823$			34.6382i			1.20741i	0.797208	+	0.603705i	$0.206310\pi$
$823$			34.6382i			1.20741i	−0.797208	+	0.603705i	$0.793690\pi$
$824$	−5.55149	+	20.7184i	−0.193395	+	0.721761i
$825$	−8.23625	+	30.7381i	−0.286750	+	1.07016i
$826$		0			0
$827$	−18.6739	−	18.6739i	−0.649355	−	0.649355i	0.303482	−	0.952837i	$-0.401851\pi$
$827$	−18.6739	−	18.6739i	−0.649355	−	0.649355i	−0.952837	+	0.303482i	$0.901851\pi$
$828$	0.194176	−	0.336323i	0.00674809	−	0.0116880i
$829$	−16.3278	−	28.2806i	−0.567089	−	0.982228i	−0.996852	−	0.0792856i	$-0.974736\pi$
$829$	−16.3278	−	28.2806i	−0.567089	−	0.982228i	0.429763	−	0.902942i	$-0.358597\pi$
$830$	3.92076	−	14.6325i	0.136092	−	0.507901i
$831$	4.49977	+	7.79382i	0.156095	+	0.270365i
$832$	−0.232357	−	29.6804i	−0.00805552	−	1.02898i
$833$		0			0
$834$	8.98470	+	33.5313i	0.311115	+	1.16110i
$835$	11.6643			0.403661
$836$	1.00805			0.0348643
$837$	6.21036	+	23.1774i	0.214662	+	0.801128i
$838$	20.4638	−	5.48325i	0.706909	−	0.189416i
$839$	38.6060	+	10.3444i	1.33283	+	0.357130i	0.853768	−	0.520654i	$-0.174312\pi$
$839$	38.6060	+	10.3444i	1.33283	+	0.357130i	0.479058	+	0.877783i	$0.340978\pi$
$840$		0			0
$841$	6.34638	+	10.9922i	0.218841	+	0.379043i
$842$		−	29.5469i		−	1.01825i
$843$	3.42005	+	0.916400i	0.117793	+	0.0315625i
$844$	1.23855	+	0.715080i	0.0426328	+	0.0246141i
$845$	2.10890	−	8.39407i	0.0725483	−	0.288765i
$846$		−	12.5372i		−	0.431039i
$847$		0			0
$848$	8.52111	−	14.7590i	0.292616	−	0.506826i
$849$	22.6007	+	13.0485i	0.775652	+	0.447823i
$850$	2.86710	−	0.768236i	0.0983406	−	0.0263503i
$851$	16.6039	−	16.6039i	0.569173	−	0.569173i
$852$	0.0768904	+	0.286959i	0.00263422	+	0.00983105i
$853$	−20.1071	+	20.1071i	−0.688454	+	0.688454i	−0.961890	−	0.273436i	$-0.911840\pi$
$853$	−20.1071	+	20.1071i	−0.688454	+	0.688454i	0.273436	+	0.961890i	$0.411840\pi$
$854$		0			0
$855$	−1.75568	−	1.01364i	−0.0600429	−	0.0346658i
$856$	8.42560	+	8.42560i	0.287981	+	0.287981i
$857$	−6.66400	+	11.5424i	−0.227638	+	0.394280i	−0.957108	−	0.289733i	$-0.906434\pi$
$857$	−6.66400	+	11.5424i	−0.227638	+	0.394280i	0.729470	+	0.684013i	$0.239767\pi$
$858$	30.4938	+	17.2887i	1.04104	+	0.590227i
$859$	11.1463	−	6.43532i	0.380307	−	0.219570i	−0.297645	−	0.954677i	$-0.596201\pi$
$859$	11.1463	−	6.43532i	0.380307	−	0.219570i	0.677952	+	0.735106i	$0.262868\pi$
$860$	0.157338	−	0.0421585i	0.00536517	−	0.00143759i
$861$		0			0
$862$	−36.2193	+	20.9112i	−1.23364	+	0.712240i
$863$	14.4716	+	3.87766i	0.492620	+	0.131997i	0.496573	−	0.867995i	$-0.334592\pi$
$863$	14.4716	+	3.87766i	0.492620	+	0.131997i	−0.00395268	+	0.999992i	$0.501258\pi$
$864$	1.39933	+	1.39933i	0.0476062	+	0.0476062i
$865$	2.78722	+	2.78722i	0.0947683	+	0.0947683i
$866$	−20.8537	−	5.58773i	−0.708638	−	0.189879i
$867$	−21.0512	+	12.1539i	−0.714938	+	0.412769i
$868$		0			0
$869$	−1.81543	+	0.486443i	−0.0615842	+	0.0165014i
$870$	−4.69520	+	2.71078i	−0.159182	+	0.0919040i
$871$	32.6506	+	8.47532i	1.10632	+	0.287175i
$872$	−8.82868	+	15.2917i	−0.298977	+	0.517843i
$873$	11.3668	+	11.3668i	0.384706	+	0.384706i
$874$	28.3155	+	16.3480i	0.957787	+	0.552978i
$875$		0			0
$876$	−0.00739838	+	0.00739838i	−0.000249968	+	0.000249968i
$877$	4.81802	+	17.9811i	0.162693	+	0.607178i	0.998323	+	0.0578858i	$0.0184359\pi$
$877$	4.81802	+	17.9811i	0.162693	+	0.607178i	−0.835630	+	0.549292i	$0.814897\pi$
$878$	14.2087	−	14.2087i	0.479521	−	0.479521i
$879$	−6.34727	+	1.70075i	−0.214088	+	0.0573647i
$880$	10.7640	+	6.21458i	0.362853	+	0.209494i
$881$	4.17631	−	7.23358i	0.140703	−	0.243705i	−0.787058	−	0.616879i	$-0.788397\pi$
$881$	4.17631	−	7.23358i	0.140703	−	0.243705i	0.927762	+	0.373173i	$0.121730\pi$
$882$		0			0
$883$		−	44.6713i		−	1.50331i	−0.659557	−	0.751655i	$-0.729256\pi$
$883$		−	44.6713i		−	1.50331i	0.659557	−	0.751655i	$-0.270744\pi$
$884$	0.000817771		0.104459i	2.75046e−5		0.00351333i
$885$	5.11786	+	2.95480i	0.172035	+	0.0993244i
$886$	−16.7781	−	4.49569i	−0.563672	−	0.151036i
$887$			1.94254i			0.0652241i	0.999468	+	0.0326121i	$0.0103826\pi$
$887$			1.94254i			0.0652241i	−0.999468	+	0.0326121i	$0.989617\pi$
$888$	7.01899	+	12.1572i	0.235542	+	0.407971i
$889$		0			0
$890$	−8.65777	−	2.31984i	−0.290209	−	0.0777613i
$891$	−25.5268	+	6.83989i	−0.855181	+	0.229145i
$892$	0.0593600	+	0.221534i	0.00198752	+	0.00741752i
$893$	−33.7232			−1.12850
$894$	−7.58763			−0.253768
$895$	−0.649644	−	2.42450i	−0.0217152	−	0.0810422i
$896$		0			0
$897$	−18.4081	−	31.3151i	−0.614630	−	1.04558i
$898$	−19.4972	−	33.7701i	−0.650628	−	1.12692i
$899$	−4.43730	+	16.5602i	−0.147992	+	0.552315i
$900$	−0.127218	−	0.220347i	−0.00424059	−	0.00734492i
$901$	−1.02963	+	1.78337i	−0.0343019	+	0.0594127i
$902$	18.0823	+	18.0823i	0.602075	+	0.602075i
$903$		0			0
$904$	−0.824563	+	3.07731i	−0.0274246	+	0.102350i
$905$	−0.980283	+	3.65847i	−0.0325857	+	0.121612i
$906$			15.2466i			0.506535i
$907$	−45.1033	+	26.0404i	−1.49763	+	0.864656i	−0.999996	−	0.00273135i	$-0.999131\pi$
$907$	−45.1033	+	26.0404i	−1.49763	+	0.864656i	−0.497633	+	0.867388i	$0.665797\pi$
$908$	1.05553	−	1.05553i	0.0350291	−	0.0350291i
$909$	−10.0509			−0.333367
$910$		0			0
$911$	−48.8065			−1.61703			−0.808516	−	0.588474i	$-0.799729\pi$
$911$	−48.8065			−1.61703			−0.808516	+	0.588474i	$0.799729\pi$
$912$	−13.3933	+	13.3933i	−0.443497	+	0.443497i
$913$	68.2415	−	39.3992i	2.25846	−	1.30392i
$914$		−	24.5227i		−	0.811140i
$915$	−1.21569	+	4.53701i	−0.0401894	+	0.149989i
$916$	0.298803	−	1.11515i	0.00987273	−	0.0368455i
$917$		0			0
$918$	2.60325	+	2.60325i	0.0859200	+	0.0859200i
$919$	−3.72510	+	6.45206i	−0.122880	+	0.212834i	−0.920902	−	0.389794i	$-0.872546\pi$
$919$	−3.72510	+	6.45206i	−0.122880	+	0.212834i	0.798022	+	0.602628i	$0.205880\pi$
$920$	−6.64588	−	11.5110i	−0.219108	−	0.379507i
$921$	−6.11533	+	22.8227i	−0.201507	+	0.752035i
$922$	−3.75518	−	6.50415i	−0.123670	−	0.214203i
$923$	−11.5593	−	3.00051i	−0.380478	−	0.0987629i
$924$		0			0
$925$	−3.98173	−	14.8600i	−0.130918	−	0.488594i
$926$	38.3499			1.26026
$927$	6.73824			0.221313
$928$	0.365960	+	1.36578i	0.0120132	+	0.0448340i
$929$	−14.4466	+	3.87096i	−0.473978	+	0.127002i	−0.487897	−	0.872901i	$-0.662236\pi$
$929$	−14.4466	+	3.87096i	−0.473978	+	0.127002i	0.0139191	+	0.999903i	$0.495569\pi$
$930$	5.50567	+	1.47524i	0.180538	+	0.0483750i
$931$		0			0
$932$	−0.140021	−	0.242523i	−0.00458653	−	0.00794410i
$933$			15.7147i			0.514475i
$934$	12.9040	+	3.45762i	0.422232	+	0.113137i
$935$	−1.30064	−	0.750925i	−0.0425355	−	0.0245579i
$936$	−8.99578	+	2.48605i	−0.294036	+	0.0812591i
$937$		−	0.823290i		−	0.0268957i	−0.999910	−	0.0134479i	$-0.995719\pi$
$937$		−	0.823290i		−	0.0268957i	0.999910	−	0.0134479i	$-0.00428071\pi$
$938$		0			0
$939$	5.20525	−	9.01576i	0.169867	−	0.294218i
$940$	0.356538	+	0.205848i	0.0116290	+	0.00671401i
$941$	24.0974	−	6.45688i	0.785553	−	0.210488i	0.156321	−	0.987706i	$-0.450036\pi$
$941$	24.0974	−	6.45688i	0.785553	−	0.210488i	0.629231	+	0.777218i	$0.283370\pi$
$942$	−35.1334	+	35.1334i	−1.14471	+	1.14471i
$943$	−6.85858	−	25.5966i	−0.223346	−	0.833539i
$944$	−16.7790	+	16.7790i	−0.546111	+	0.546111i
$945$		0			0
$946$	−22.9670	−	13.2600i	−0.746722	−	0.431120i
$947$	8.72288	+	8.72288i	0.283455	+	0.283455i	0.834485	−	0.551030i	$-0.185765\pi$
$947$	8.72288	+	8.72288i	0.283455	+	0.283455i	−0.551030	+	0.834485i	$0.685765\pi$
$948$	−0.0174829	+	0.0302813i	−0.000567819	+	0.000983491i
$949$	−0.112035	−	0.405400i	−0.00363682	−	0.0131598i
$950$	18.5514	−	10.7106i	0.601886	−	0.347499i
$951$	13.2494	−	3.55016i	0.429640	−	0.115122i
$952$		0			0
$953$	−17.9140	+	10.3426i	−0.580291	+	0.335031i	−0.761249	−	0.648460i	$-0.775414\pi$
$953$	−17.9140	+	10.3426i	−0.580291	+	0.335031i	0.180958	+	0.983491i	$0.442080\pi$
$954$	−5.33673	−	1.42997i	−0.172783	−	0.0462970i
$955$	−4.31581	−	4.31581i	−0.139656	−	0.139656i
$956$	−0.691075	−	0.691075i	−0.0223510	−	0.0223510i
$957$	−27.2403	−	7.29901i	−0.880553	−	0.235943i
$958$	−37.3132	+	21.5428i	−1.20553	+	0.696016i
$959$		0			0
$960$	7.66836	−	2.05473i	0.247495	−	0.0663161i
$961$	−11.2370	+	6.48771i	−0.362485	+	0.209281i
$962$	−16.9459	+	0.132663i	−0.546357	+	0.00427723i
$963$	1.87163	−	3.24175i	0.0603123	−	0.104464i
$964$	0.331374	+	0.331374i	0.0106728	+	0.0106728i
$965$	14.6514	+	8.45899i	0.471645	+	0.272304i
$966$		0			0
$967$	6.39351	−	6.39351i	0.205601	−	0.205601i	−0.596793	−	0.802395i	$-0.703559\pi$
$967$	6.39351	−	6.39351i	0.205601	−	0.205601i	0.802395	+	0.596793i	$0.203559\pi$
$968$	9.09612	+	33.9472i	0.292360	+	1.09110i
$969$	1.61835	−	1.61835i	0.0519889	−	0.0519889i
$970$	15.9592	−	4.27624i	0.512418	−	0.137302i
$971$	−14.9575	−	8.63569i	−0.480008	−	0.277133i	0.240412	−	0.970671i	$-0.422717\pi$
$971$	−14.9575	−	8.63569i	−0.480008	−	0.277133i	−0.720420	+	0.693538i	$0.756051\pi$
$972$	0.279112	−	0.483437i	0.00895253	−	0.0155062i
$973$		0			0
$974$			7.79056i			0.249626i
$975$	−23.7981	+	0.186307i	−0.762149	+	0.00596658i
$976$	−16.3336	−	9.43018i	−0.522824	−	0.301853i
$977$	52.2660	+	14.0046i	1.67214	+	0.448048i	0.965686	−	0.259714i	$-0.0836281\pi$
$977$	52.2660	+	14.0046i	1.67214	+	0.448048i	0.706452	+	0.707761i	$0.250295\pi$
$978$			41.8684i			1.33880i
$979$	−23.3118	−	40.3773i	−0.745049	−	1.29046i
$980$		0			0
$981$	5.35800	+	1.43567i	0.171068	+	0.0458375i
$982$	−18.6505	+	4.99738i	−0.595161	+	0.159473i
$983$	−9.70939	−	36.2359i	−0.309681	−	1.15575i	−0.928840	−	0.370481i	$-0.879193\pi$
$983$	−9.70939	−	36.2359i	−0.309681	−	1.15575i	0.619159	−	0.785266i	$-0.287474\pi$
$984$	15.8423			0.505034
$985$	−0.955968			−0.0304597
$986$	0.680815	+	2.54083i	0.0216816	+	0.0809167i
$987$		0			0
$988$	0.200815	+	0.726648i	0.00638876	+	0.0231177i
$989$	13.7408	+	23.7998i	0.436933	+	0.756790i
$990$	1.04290	−	3.89216i	0.0331456	−	0.123701i
$991$	−17.4270	−	30.1845i	−0.553587	−	0.958841i	−0.998012	−	0.0630250i	$-0.979925\pi$
$991$	−17.4270	−	30.1845i	−0.553587	−	0.958841i	0.444425	−	0.895816i	$-0.353408\pi$
$992$	0.743276	−	1.28739i	0.0235990	−	0.0408748i
$993$	6.07784	+	6.07784i	0.192874	+	0.192874i
$994$		0			0
$995$	−1.89816	+	7.08404i	−0.0601758	+	0.224579i
$996$	0.379422	−	1.41602i	0.0120224	−	0.0448683i
$997$		−	15.2231i		−	0.482119i	−0.970510	−	0.241060i	$-0.922505\pi$
$997$		−	15.2231i		−	0.482119i	0.970510	−	0.241060i	$-0.0774949\pi$
$998$	−11.0233	+	6.36431i	−0.348936	+	0.201459i
$999$	13.4925	−	13.4925i	0.426884	−	0.426884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.227.2		28
7.2	even	3		91.2.w.a.19.6	✓	28
7.3	odd	6		637.2.bd.b.97.2		28
7.4	even	3		637.2.bd.a.97.2		28
7.5	odd	6		637.2.x.a.19.6		28
7.6	odd	2		91.2.ba.a.45.2	yes	28
13.11	odd	12		637.2.x.a.570.6		28
21.2	odd	6		819.2.gh.b.19.2		28
21.20	even	2		819.2.et.b.136.6		28
91.11	odd	12		637.2.bd.b.440.2		28
91.24	even	12		637.2.bd.a.440.2		28
91.37	odd	12		91.2.ba.a.89.2	yes	28
91.76	even	12		91.2.w.a.24.6	yes	28
91.89	even	12	inner	637.2.bb.a.362.2		28
273.128	even	12		819.2.et.b.271.6		28
273.167	odd	12		819.2.gh.b.388.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.6	✓	28	7.2	even	3
91.2.w.a.24.6	yes	28	91.76	even	12
91.2.ba.a.45.2	yes	28	7.6	odd	2
91.2.ba.a.89.2	yes	28	91.37	odd	12
637.2.x.a.19.6		28	7.5	odd	6
637.2.x.a.570.6		28	13.11	odd	12
637.2.bb.a.227.2		28	1.1	even	1	trivial
637.2.bb.a.362.2		28	91.89	even	12	inner
637.2.bd.a.97.2		28	7.4	even	3
637.2.bd.a.440.2		28	91.24	even	12
637.2.bd.b.97.2		28	7.3	odd	6
637.2.bd.b.440.2		28	91.11	odd	12
819.2.et.b.136.6		28	21.20	even	2
819.2.et.b.271.6		28	273.128	even	12
819.2.gh.b.19.2		28	21.2	odd	6
819.2.gh.b.388.2		28	273.167	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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984398 + 0.984398i) q^{2} +(1.25446 - 0.724265i) q^{3} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-0.521927 + 1.94786i) q^{6} +(-2.02975 - 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +O(q^{10})\)	\(q+(-0.984398 + 0.984398i) q^{2} +(1.25446 - 0.724265i) q^{3} +0.0619199i q^{4} +(0.172312 - 0.643078i) q^{5} +(-0.521927 + 1.94786i) q^{6} +(-2.02975 - 2.02975i) q^{8} +(-0.450880 + 0.780947i) q^{9} +(0.463421 + 0.802669i) q^{10} +(-1.24780 + 4.65687i) q^{11} +(0.0448464 + 0.0776763i) q^{12} +(-3.60544 + 0.0282257i) q^{13} +(-0.249600 - 0.931519i) q^{15} +3.87233 q^{16} -0.467904 q^{17} +(-0.324918 - 1.21261i) q^{18} +(-3.26172 + 0.873976i) q^{19} +(0.0398194 + 0.0106696i) q^{20} +(-3.35587 - 5.81255i) q^{22} +6.95512i q^{23} +(-4.01633 - 1.07617i) q^{24} +(3.94627 + 2.27838i) q^{25} +(3.52140 - 3.57698i) q^{26} +5.65182i q^{27} +(-2.01911 + 3.49720i) q^{29} +(1.16269 + 0.671280i) q^{30} +(4.10087 - 1.09883i) q^{31} +(0.247590 - 0.247590i) q^{32} +(1.80748 + 6.74561i) q^{33} +(0.460604 - 0.460604i) q^{34} +(-0.0483562 - 0.0279185i) q^{36} +(-2.38729 - 2.38729i) q^{37} +(2.35049 - 4.07117i) q^{38} +(-4.50245 + 2.64670i) q^{39} +(-1.65504 + 0.955538i) q^{40} +(-3.68025 + 0.986119i) q^{41} +(3.42191 - 1.97564i) q^{43} +(-0.288353 - 0.0772639i) q^{44} +(0.424518 + 0.424518i) q^{45} +(-6.84661 - 6.84661i) q^{46} +(9.64648 + 2.58477i) q^{47} +(4.85769 - 2.80459i) q^{48} +(-6.12753 + 1.64187i) q^{50} +(-0.586968 + 0.338886i) q^{51} +(-0.00174773 - 0.223249i) q^{52} +(2.20051 - 3.81140i) q^{53} +(-5.56364 - 5.56364i) q^{54} +(2.77972 + 1.60487i) q^{55} +(-3.45872 + 3.45872i) q^{57} +(-1.45503 - 5.43025i) q^{58} +(-4.33306 + 4.33306i) q^{59} +(0.0576796 - 0.0154552i) q^{60} +(-4.21802 - 2.43528i) q^{61} +(-2.95521 + 5.11858i) q^{62} +8.23211i q^{64} +(-0.603111 + 2.32344i) q^{65} +(-8.41965 - 4.86109i) q^{66} +(-9.03697 - 2.42145i) q^{67} -0.0289726i q^{68} +(5.03735 + 8.72495i) q^{69} +(3.19935 + 0.857263i) q^{71} +(2.50030 - 0.669954i) q^{72} +(0.0301918 + 0.112678i) q^{73} +4.70008 q^{74} +6.60060 q^{75} +(-0.0541165 - 0.201966i) q^{76} +(1.82680 - 7.03762i) q^{78} +(0.194920 + 0.337611i) q^{79} +(0.667250 - 2.49021i) q^{80} +(2.74077 + 4.74716i) q^{81} +(2.65209 - 4.59356i) q^{82} +(-11.5572 - 11.5572i) q^{83} +(-0.0806256 + 0.300899i) q^{85} +(-1.42371 + 5.31334i) q^{86} +5.84949i q^{87} +(11.9850 - 6.91955i) q^{88} +(-6.83819 + 6.83819i) q^{89} -0.835790 q^{90} -0.430661 q^{92} +(4.34856 - 4.34856i) q^{93} +(-12.0404 + 6.95154i) q^{94} +2.24814i q^{95} +(0.131272 - 0.489913i) q^{96} +(4.61378 - 17.2188i) q^{97} +(-3.07416 - 3.07416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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