LMFDB - Embedded newform 37.2.e.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.e (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	37.11
Dual form			37.2.e.a.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.232051 + 0.133975i) q^{5} +2.73205i q^{6} +(-1.73205 + 3.00000i) q^{7} -3.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.232051 + 0.133975i) q^{5} +2.73205i q^{6} +(-1.73205 + 3.00000i) q^{7} -3.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} -0.267949 q^{10} -4.73205 q^{11} +(1.36603 + 2.36603i) q^{12} +(3.00000 + 1.73205i) q^{13} -3.46410i q^{14} +(0.633975 - 0.366025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.23205 - 1.86603i) q^{17} +(3.86603 + 2.23205i) q^{18} +(1.09808 + 0.633975i) q^{19} +(-0.232051 + 0.133975i) q^{20} +(4.73205 + 8.19615i) q^{21} +(4.09808 - 2.36603i) q^{22} -0.732051i q^{23} +(-7.09808 - 4.09808i) q^{24} +(-2.46410 - 4.26795i) q^{25} -3.46410 q^{26} -4.00000 q^{27} +(-1.73205 - 3.00000i) q^{28} +0.267949i q^{29} +(-0.366025 + 0.633975i) q^{30} -8.19615i q^{31} +(4.33013 + 2.50000i) q^{32} +(-6.46410 + 11.1962i) q^{33} +(-1.86603 + 3.23205i) q^{34} +(-0.803848 + 0.464102i) q^{35} +4.46410 q^{36} +(0.500000 + 6.06218i) q^{37} -1.26795 q^{38} +(8.19615 - 4.73205i) q^{39} +(0.401924 - 0.696152i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-8.19615 - 4.73205i) q^{42} +3.46410i q^{43} +(2.36603 - 4.09808i) q^{44} -1.19615i q^{45} +(0.366025 + 0.633975i) q^{46} -2.19615 q^{47} +2.73205 q^{48} +(-2.50000 - 4.33013i) q^{49} +(4.26795 + 2.46410i) q^{50} -10.1962i q^{51} +(-3.00000 + 1.73205i) q^{52} +(1.26795 + 2.19615i) q^{53} +(3.46410 - 2.00000i) q^{54} +(-1.09808 - 0.633975i) q^{55} +(9.00000 + 5.19615i) q^{56} +(3.00000 - 1.73205i) q^{57} +(-0.133975 - 0.232051i) q^{58} +(-11.6603 + 6.73205i) q^{59} +0.732051i q^{60} +(3.69615 + 2.13397i) q^{61} +(4.09808 + 7.09808i) q^{62} +15.4641 q^{63} -7.00000 q^{64} +(0.464102 + 0.803848i) q^{65} -12.9282i q^{66} +(3.63397 - 6.29423i) q^{67} +3.73205i q^{68} +(-1.73205 - 1.00000i) q^{69} +(0.464102 - 0.803848i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(-11.5981 + 6.69615i) q^{72} +(-3.46410 - 5.00000i) q^{74} -13.4641 q^{75} +(-1.09808 + 0.633975i) q^{76} +(8.19615 - 14.1962i) q^{77} +(-4.73205 + 8.19615i) q^{78} +(3.29423 + 1.90192i) q^{79} +0.267949i q^{80} +(1.23205 - 2.13397i) q^{81} -3.00000i q^{82} +(4.09808 + 7.09808i) q^{83} -9.46410 q^{84} +1.00000 q^{85} +(-1.73205 - 3.00000i) q^{86} +(0.633975 + 0.366025i) q^{87} +14.1962i q^{88} +(7.96410 - 4.59808i) q^{89} +(0.598076 + 1.03590i) q^{90} +(-10.3923 + 6.00000i) q^{91} +(0.633975 + 0.366025i) q^{92} +(-19.3923 - 11.1962i) q^{93} +(1.90192 - 1.09808i) q^{94} +(0.169873 + 0.294229i) q^{95} +(11.8301 - 6.83013i) q^{96} -4.26795i q^{97} +(4.33013 + 2.50000i) q^{98} +(10.5622 + 18.2942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{9} - 8 q^{10} - 12 q^{11} + 2 q^{12} + 12 q^{13} + 6 q^{15} + 2 q^{16} + 6 q^{17} + 12 q^{18} - 6 q^{19} + 6 q^{20} + 12 q^{21} + 6 q^{22} - 18 q^{24} + 4 q^{25} - 16 q^{27} + 2 q^{30} - 12 q^{33} - 4 q^{34} - 24 q^{35} + 4 q^{36} + 2 q^{37} - 12 q^{38} + 12 q^{39} + 12 q^{40} - 6 q^{41} - 12 q^{42} + 6 q^{44} - 2 q^{46} + 12 q^{47} + 4 q^{48} - 10 q^{49} + 24 q^{50} - 12 q^{52} + 12 q^{53} + 6 q^{55} + 36 q^{56} + 12 q^{57} - 4 q^{58} - 12 q^{59} - 6 q^{61} + 6 q^{62} + 48 q^{63} - 28 q^{64} - 12 q^{65} + 18 q^{67} - 12 q^{70} - 12 q^{71} - 36 q^{72} - 40 q^{75} + 6 q^{76} + 12 q^{77} - 12 q^{78} - 18 q^{79} - 2 q^{81} + 6 q^{83} - 24 q^{84} + 4 q^{85} + 6 q^{87} + 18 q^{89} - 8 q^{90} + 6 q^{92} - 36 q^{93} + 18 q^{94} + 18 q^{95} + 30 q^{96} + 18 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^9 - 8 * q^10 - 12 * q^11 + 2 * q^12 + 12 * q^13 + 6 * q^15 + 2 * q^16 + 6 * q^17 + 12 * q^18 - 6 * q^19 + 6 * q^20 + 12 * q^21 + 6 * q^22 - 18 * q^24 + 4 * q^25 - 16 * q^27 + 2 * q^30 - 12 * q^33 - 4 * q^34 - 24 * q^35 + 4 * q^36 + 2 * q^37 - 12 * q^38 + 12 * q^39 + 12 * q^40 - 6 * q^41 - 12 * q^42 + 6 * q^44 - 2 * q^46 + 12 * q^47 + 4 * q^48 - 10 * q^49 + 24 * q^50 - 12 * q^52 + 12 * q^53 + 6 * q^55 + 36 * q^56 + 12 * q^57 - 4 * q^58 - 12 * q^59 - 6 * q^61 + 6 * q^62 + 48 * q^63 - 28 * q^64 - 12 * q^65 + 18 * q^67 - 12 * q^70 - 12 * q^71 - 36 * q^72 - 40 * q^75 + 6 * q^76 + 12 * q^77 - 12 * q^78 - 18 * q^79 - 2 * q^81 + 6 * q^83 - 24 * q^84 + 4 * q^85 + 6 * q^87 + 18 * q^89 - 8 * q^90 + 6 * q^92 - 36 * q^93 + 18 * q^94 + 18 * q^95 + 30 * q^96 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	0.161521	+	0.986869i	$0.448360\pi$
$3$	1.36603	−	2.36603i	0.788675	−	1.36603i	−0.138104	−	0.990418i	$-0.544101\pi$
$3$	1.36603	−	2.36603i	0.788675	−	1.36603i	0.926779	−	0.375608i	$-0.122566\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.232051	+	0.133975i	0.103776	+	0.0599153i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	0.232051	+	0.133975i	0.103776	+	0.0599153i	−0.447214	+	0.894427i	$0.647584\pi$
$6$			2.73205i			1.11536i
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	0.327327	+	0.944911i	$0.393852\pi$
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		−	3.00000i		−	1.06066i
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$	−0.267949			−0.0847330
$11$	−4.73205			−1.42677			−0.713384	−	0.700774i	$-0.752838\pi$
$11$	−4.73205			−1.42677			−0.713384	+	0.700774i	$0.752838\pi$
$12$	1.36603	+	2.36603i	0.394338	+	0.683013i
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$		−	3.46410i		−	0.925820i
$15$	0.633975	−	0.366025i	0.163692	−	0.0945074i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.23205	−	1.86603i	0.783887	−	0.452578i	−0.0539188	−	0.998545i	$-0.517171\pi$
$17$	3.23205	−	1.86603i	0.783887	−	0.452578i	0.837806	+	0.545968i	$0.183838\pi$
$18$	3.86603	+	2.23205i	0.911231	+	0.526099i
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	0.620641	−	0.784095i	$-0.286872\pi$
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	−0.368725	+	0.929538i	$0.620206\pi$
$20$	−0.232051	+	0.133975i	−0.0518881	+	0.0299576i
$21$	4.73205	+	8.19615i	1.03262	+	1.78855i
$22$	4.09808	−	2.36603i	0.873713	−	0.504438i
$23$		−	0.732051i		−	0.152643i	−0.997083	−	0.0763216i	$-0.975682\pi$
$23$		−	0.732051i		−	0.152643i	0.997083	−	0.0763216i	$-0.0243176\pi$
$24$	−7.09808	−	4.09808i	−1.44889	−	0.836516i
$25$	−2.46410	−	4.26795i	−0.492820	−	0.853590i
$26$	−3.46410			−0.679366
$27$	−4.00000			−0.769800
$28$	−1.73205	−	3.00000i	−0.327327	−	0.566947i
$29$			0.267949i			0.0497569i	0.999690	+	0.0248785i	$0.00791988\pi$
$29$			0.267949i			0.0497569i	−0.999690	+	0.0248785i	$0.992080\pi$
$30$	−0.366025	+	0.633975i	−0.0668268	+	0.115747i
$31$		−	8.19615i		−	1.47207i	−0.676942	−	0.736036i	$-0.736695\pi$
$31$		−	8.19615i		−	1.47207i	0.676942	−	0.736036i	$-0.263305\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$	−6.46410	+	11.1962i	−1.12526	+	1.94900i
$34$	−1.86603	+	3.23205i	−0.320021	+	0.554292i
$35$	−0.803848	+	0.464102i	−0.135875	+	0.0784475i
$36$	4.46410			0.744017
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$38$	−1.26795			−0.205689
$39$	8.19615	−	4.73205i	1.31243	−	0.757735i
$40$	0.401924	−	0.696152i	0.0635497	−	0.110071i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	−8.19615	−	4.73205i	−1.26469	−	0.730171i
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$	2.36603	−	4.09808i	0.356692	−	0.617808i
$45$		−	1.19615i		−	0.178312i
$46$	0.366025	+	0.633975i	0.0539675	+	0.0934745i
$47$	−2.19615			−0.320342			−0.160171	−	0.987089i	$-0.551205\pi$
$47$	−2.19615			−0.320342			−0.160171	+	0.987089i	$0.551205\pi$
$48$	2.73205			0.394338
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$	4.26795	+	2.46410i	0.603579	+	0.348477i
$51$		−	10.1962i		−	1.42775i
$52$	−3.00000	+	1.73205i	−0.416025	+	0.240192i
$53$	1.26795	+	2.19615i	0.174166	+	0.301665i	0.939872	−	0.341526i	$-0.110944\pi$
$53$	1.26795	+	2.19615i	0.174166	+	0.301665i	−0.765706	+	0.643191i	$0.777610\pi$
$54$	3.46410	−	2.00000i	0.471405	−	0.272166i
$55$	−1.09808	−	0.633975i	−0.148065	−	0.0854851i
$56$	9.00000	+	5.19615i	1.20268	+	0.694365i
$57$	3.00000	−	1.73205i	0.397360	−	0.229416i
$58$	−0.133975	−	0.232051i	−0.0175917	−	0.0304698i
$59$	−11.6603	+	6.73205i	−1.51804	+	0.876438i	−0.518261	+	0.855223i	$0.673420\pi$
$59$	−11.6603	+	6.73205i	−1.51804	+	0.876438i	−0.999775	+	0.0212158i	$0.993246\pi$
$60$			0.732051i			0.0945074i
$61$	3.69615	+	2.13397i	0.473244	+	0.273227i	0.717597	−	0.696459i	$-0.245242\pi$
$61$	3.69615	+	2.13397i	0.473244	+	0.273227i	−0.244353	+	0.969686i	$0.578576\pi$
$62$	4.09808	+	7.09808i	0.520456	+	0.901457i
$63$	15.4641			1.94829
$64$	−7.00000			−0.875000
$65$	0.464102	+	0.803848i	0.0575647	+	0.0997050i
$66$		−	12.9282i		−	1.59135i
$67$	3.63397	−	6.29423i	0.443961	−	0.768962i	−0.554019	−	0.832504i	$-0.686906\pi$
$67$	3.63397	−	6.29423i	0.443961	−	0.768962i	0.997979	+	0.0635419i	$0.0202397\pi$
$68$			3.73205i			0.452578i
$69$	−1.73205	−	1.00000i	−0.208514	−	0.120386i
$70$	0.464102	−	0.803848i	0.0554708	−	0.0960782i
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−11.5981	+	6.69615i	−1.36685	+	0.789149i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−3.46410	−	5.00000i	−0.402694	−	0.581238i
$75$	−13.4641			−1.55470
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$	8.19615	−	14.1962i	0.934038	−	1.61780i
$78$	−4.73205	+	8.19615i	−0.535799	+	0.928032i
$79$	3.29423	+	1.90192i	0.370630	+	0.213983i	0.673734	−	0.738974i	$-0.264690\pi$
$79$	3.29423	+	1.90192i	0.370630	+	0.213983i	−0.303104	+	0.952958i	$0.598023\pi$
$80$			0.267949i			0.0299576i
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$		−	3.00000i		−	0.331295i
$83$	4.09808	+	7.09808i	0.449822	+	0.779115i	0.998374	−	0.0570015i	$-0.0181540\pi$
$83$	4.09808	+	7.09808i	0.449822	+	0.779115i	−0.548552	+	0.836117i	$0.684821\pi$
$84$	−9.46410			−1.03262
$85$	1.00000			0.108465
$86$	−1.73205	−	3.00000i	−0.186772	−	0.323498i
$87$	0.633975	+	0.366025i	0.0679692	+	0.0392420i
$88$			14.1962i			1.51331i
$89$	7.96410	−	4.59808i	0.844193	−	0.487395i	−0.0144942	−	0.999895i	$-0.504614\pi$
$89$	7.96410	−	4.59808i	0.844193	−	0.487395i	0.858687	+	0.512500i	$0.171280\pi$
$90$	0.598076	+	1.03590i	0.0630428	+	0.109193i
$91$	−10.3923	+	6.00000i	−1.08941	+	0.628971i
$92$	0.633975	+	0.366025i	0.0660964	+	0.0381608i
$93$	−19.3923	−	11.1962i	−2.01089	−	1.16099i
$94$	1.90192	−	1.09808i	0.196168	−	0.113258i
$95$	0.169873	+	0.294229i	0.0174286	+	0.0301872i
$96$	11.8301	−	6.83013i	1.20741	−	0.697097i
$97$		−	4.26795i		−	0.433345i	−0.976244	−	0.216672i	$-0.930480\pi$
$97$		−	4.26795i		−	0.433345i	0.976244	−	0.216672i	$-0.0695203\pi$
$98$	4.33013	+	2.50000i	0.437409	+	0.252538i
$99$	10.5622	+	18.2942i	1.06154	+	1.83864i
$100$	4.92820			0.492820
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$	5.09808	+	8.83013i	0.504785	+	0.874313i
$103$		−	12.9282i		−	1.27385i	−0.770924	−	0.636927i	$-0.780205\pi$
$103$		−	12.9282i		−	1.27385i	0.770924	−	0.636927i	$-0.219795\pi$
$104$	5.19615	−	9.00000i	0.509525	−	0.882523i
$105$			2.53590i			0.247478i
$106$	−2.19615	−	1.26795i	−0.213309	−	0.123154i
$107$	6.46410	−	11.1962i	0.624908	−	1.08237i	−0.363650	−	0.931536i	$-0.618470\pi$
$107$	6.46410	−	11.1962i	0.624908	−	1.08237i	0.988559	−	0.150837i	$-0.0481970\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	−5.89230	+	3.40192i	−0.564380	+	0.325845i	−0.754902	−	0.655838i	$-0.772315\pi$
$109$	−5.89230	+	3.40192i	−0.564380	+	0.325845i	0.190521	+	0.981683i	$0.438982\pi$
$110$	1.26795			0.120894
$111$	15.0263	+	7.09808i	1.42623	+	0.673720i
$112$	−3.46410			−0.327327
$113$	−3.92820	+	2.26795i	−0.369534	+	0.213351i	−0.673255	−	0.739410i	$-0.735104\pi$
$113$	−3.92820	+	2.26795i	−0.369534	+	0.213351i	0.303721	+	0.952761i	$0.401771\pi$
$114$	−1.73205	+	3.00000i	−0.162221	+	0.280976i
$115$	0.0980762	−	0.169873i	0.00914565	−	0.0158407i
$116$	−0.232051	−	0.133975i	−0.0215454	−	0.0124392i
$117$		−	15.4641i		−	1.42966i
$118$	6.73205	−	11.6603i	0.619736	−	1.07341i
$119$			12.9282i			1.18513i
$120$	−1.09808	−	1.90192i	−0.100240	−	0.173621i
$121$	11.3923			1.03566
$122$	−4.26795			−0.386402
$123$	4.09808	+	7.09808i	0.369511	+	0.640012i
$124$	7.09808	+	4.09808i	0.637426	+	0.368018i
$125$		−	2.66025i		−	0.237940i
$126$	−13.3923	+	7.73205i	−1.19308	+	0.688826i
$127$	6.09808	+	10.5622i	0.541117	+	0.937242i	0.998840	+	0.0481471i	$0.0153316\pi$
$127$	6.09808	+	10.5622i	0.541117	+	0.937242i	−0.457723	+	0.889095i	$0.651335\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$	8.19615	+	4.73205i	0.721631	+	0.416634i
$130$	−0.803848	−	0.464102i	−0.0705021	−	0.0407044i
$131$	−9.16987	+	5.29423i	−0.801176	+	0.462559i	−0.843882	−	0.536529i	$-0.819735\pi$
$131$	−9.16987	+	5.29423i	−0.801176	+	0.462559i	0.0427065	+	0.999088i	$0.486402\pi$
$132$	−6.46410	−	11.1962i	−0.562628	−	0.974500i
$133$	−3.80385	+	2.19615i	−0.329835	+	0.190431i
$134$			7.26795i			0.627855i
$135$	−0.928203	−	0.535898i	−0.0798870	−	0.0461228i
$136$	−5.59808	−	9.69615i	−0.480031	−	0.831438i
$137$	−6.46410			−0.552265			−0.276133	−	0.961120i	$-0.589053\pi$
$137$	−6.46410			−0.552265			−0.276133	+	0.961120i	$0.589053\pi$
$138$	2.00000			0.170251
$139$	−6.29423	−	10.9019i	−0.533870	−	0.924689i	−0.999217	−	0.0395611i	$-0.987404\pi$
$139$	−6.29423	−	10.9019i	−0.533870	−	0.924689i	0.465348	−	0.885128i	$-0.345929\pi$
$140$		−	0.928203i		−	0.0784475i
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$		−	6.00000i		−	0.503509i
$143$	−14.1962	−	8.19615i	−1.18714	−	0.685397i
$144$	2.23205	−	3.86603i	0.186004	−	0.322169i
$145$	−0.0358984	+	0.0621778i	−0.00298120	+	0.00516359i
$146$		0			0
$147$	−13.6603			−1.12668
$148$	−5.50000	−	2.59808i	−0.452097	−	0.213561i
$149$	5.53590			0.453518			0.226759	−	0.973951i	$-0.427187\pi$
$149$	5.53590			0.453518			0.226759	+	0.973951i	$0.427187\pi$
$150$	11.6603	−	6.73205i	0.952056	−	0.549670i
$151$	−8.29423	+	14.3660i	−0.674975	+	1.16909i	0.301502	+	0.953466i	$0.402512\pi$
$151$	−8.29423	+	14.3660i	−0.674975	+	1.16909i	−0.976476	+	0.215625i	$0.930821\pi$
$152$	1.90192	−	3.29423i	0.154266	−	0.267197i
$153$	−14.4282	−	8.33013i	−1.16645	−	0.673451i
$154$			16.3923i			1.32093i
$155$	1.09808	−	1.90192i	0.0881996	−	0.152766i
$156$			9.46410i			0.757735i
$157$	7.16025	+	12.4019i	0.571450	+	0.989781i	0.996417	+	0.0845724i	$0.0269524\pi$
$157$	7.16025	+	12.4019i	0.571450	+	0.989781i	−0.424967	+	0.905209i	$0.639714\pi$
$158$	−3.80385			−0.302618
$159$	6.92820			0.549442
$160$	0.669873	+	1.16025i	0.0529581	+	0.0917261i
$161$	2.19615	+	1.26795i	0.173081	+	0.0999284i
$162$			2.46410i			0.193598i
$163$	19.3923	−	11.1962i	1.51892	−	0.876950i	0.519171	−	0.854671i	$-0.326241\pi$
$163$	19.3923	−	11.1962i	1.51892	−	0.876950i	0.999752	−	0.0222798i	$-0.00709247\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$	−3.00000	+	1.73205i	−0.233550	+	0.134840i
$166$	−7.09808	−	4.09808i	−0.550918	−	0.318072i
$167$	9.46410	+	5.46410i	0.732354	+	0.422825i	0.819283	−	0.573390i	$-0.194372\pi$
$167$	9.46410	+	5.46410i	0.732354	+	0.422825i	−0.0869286	+	0.996215i	$0.527705\pi$
$168$	24.5885	−	14.1962i	1.89704	−	1.09526i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−0.866025	+	0.500000i	−0.0664211	+	0.0383482i
$171$		−	5.66025i		−	0.432850i
$172$	−3.00000	−	1.73205i	−0.228748	−	0.132068i
$173$	−4.96410	−	8.59808i	−0.377414	−	0.653700i	0.613271	−	0.789872i	$-0.289853\pi$
$173$	−4.96410	−	8.59808i	−0.377414	−	0.653700i	−0.990685	+	0.136173i	$0.956520\pi$
$174$	−0.732051			−0.0554966
$175$	17.0718			1.29051
$176$	−2.36603	−	4.09808i	−0.178346	−	0.308904i
$177$			36.7846i			2.76490i
$178$	−4.59808	+	7.96410i	−0.344640	+	0.596935i
$179$			1.46410i			0.109432i	0.998502	+	0.0547160i	$0.0174254\pi$
$179$			1.46410i			0.109432i	−0.998502	+	0.0547160i	$0.982575\pi$
$180$	1.03590	+	0.598076i	0.0772113	+	0.0445780i
$181$	−4.96410	+	8.59808i	−0.368979	+	0.639090i	−0.989406	−	0.145174i	$-0.953626\pi$
$181$	−4.96410	+	8.59808i	−0.368979	+	0.639090i	0.620427	+	0.784264i	$0.286959\pi$
$182$	6.00000	−	10.3923i	0.444750	−	0.770329i
$183$	10.0981	−	5.83013i	0.746471	−	0.430975i
$184$	−2.19615			−0.161903
$185$	−0.696152	+	1.47372i	−0.0511821	+	0.108350i
$186$	22.3923			1.64188
$187$	−15.2942	+	8.83013i	−1.11842	+	0.645723i
$188$	1.09808	−	1.90192i	0.0800854	−	0.138712i
$189$	6.92820	−	12.0000i	0.503953	−	0.872872i
$190$	−0.294229	−	0.169873i	−0.0213456	−	0.0123239i
$191$		−	6.19615i		−	0.448338i	−0.974550	−	0.224169i	$-0.928033\pi$
$191$		−	6.19615i		−	0.448338i	0.974550	−	0.224169i	$-0.0719667\pi$
$192$	−9.56218	+	16.5622i	−0.690091	+	1.19527i
$193$		−	14.6603i		−	1.05527i	−0.849472	−	0.527634i	$-0.823079\pi$
$193$		−	14.6603i		−	1.05527i	0.849472	−	0.527634i	$-0.176921\pi$
$194$	2.13397	+	3.69615i	0.153210	+	0.265368i
$195$	2.53590			0.181599
$196$	5.00000			0.357143
$197$	−13.9641	−	24.1865i	−0.994901	−	1.72322i	−0.584794	−	0.811182i	$-0.698825\pi$
$197$	−13.9641	−	24.1865i	−0.994901	−	1.72322i	−0.410107	−	0.912038i	$-0.634509\pi$
$198$	−18.2942	−	10.5622i	−1.30011	−	0.750621i
$199$		−	11.0718i		−	0.784859i	−0.919782	−	0.392429i	$-0.871635\pi$
$199$		−	11.0718i		−	0.784859i	0.919782	−	0.392429i	$-0.128365\pi$
$200$	−12.8038	+	7.39230i	−0.905369	+	0.522715i
$201$	−9.92820	−	17.1962i	−0.700281	−	1.21292i
$202$	7.79423	−	4.50000i	0.548400	−	0.316619i
$203$	−0.803848	−	0.464102i	−0.0564190	−	0.0325735i
$204$	8.83013	+	5.09808i	0.618233	+	0.356937i
$205$	−0.696152	+	0.401924i	−0.0486214	+	0.0280716i
$206$	6.46410	+	11.1962i	0.450375	+	0.780073i
$207$	−2.83013	+	1.63397i	−0.196707	+	0.113569i
$208$			3.46410i			0.240192i
$209$	−5.19615	−	3.00000i	−0.359425	−	0.207514i
$210$	−1.26795	−	2.19615i	−0.0874968	−	0.151549i
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	−2.53590			−0.174166
$213$	8.19615	+	14.1962i	0.561591	+	0.972704i
$214$			12.9282i			0.883754i
$215$	−0.464102	+	0.803848i	−0.0316515	+	0.0548219i
$216$			12.0000i			0.816497i
$217$	24.5885	+	14.1962i	1.66917	+	0.963698i
$218$	3.40192	−	5.89230i	0.230407	−	0.399077i
$219$		0			0
$220$	1.09808	−	0.633975i	0.0740323	−	0.0427426i
$221$	12.9282			0.869645
$222$	−16.5622	+	1.36603i	−1.11158	+	0.0916816i
$223$	4.58846			0.307266			0.153633	−	0.988128i	$-0.450903\pi$
$223$	4.58846			0.307266			0.153633	+	0.988128i	$0.450903\pi$
$224$	−15.0000	+	8.66025i	−1.00223	+	0.578638i
$225$	−11.0000	+	19.0526i	−0.733333	+	1.27017i
$226$	2.26795	−	3.92820i	0.150862	−	0.261300i
$227$	20.0263	+	11.5622i	1.32919	+	0.767409i	0.985175	−	0.171555i	$-0.0548791\pi$
$227$	20.0263	+	11.5622i	1.32919	+	0.767409i	0.344016	+	0.938964i	$0.388212\pi$
$228$			3.46410i			0.229416i
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$			0.196152i			0.0129339i
$231$	−22.3923	−	38.7846i	−1.47331	−	2.55184i
$232$	0.803848			0.0527752
$233$	−10.8564			−0.711227			−0.355613	−	0.934633i	$-0.615728\pi$
$233$	−10.8564			−0.711227			−0.355613	+	0.934633i	$0.615728\pi$
$234$	7.73205	+	13.3923i	0.505460	+	0.875482i
$235$	−0.509619	−	0.294229i	−0.0332439	−	0.0191934i
$236$		−	13.4641i		−	0.876438i
$237$	9.00000	−	5.19615i	0.584613	−	0.337526i
$238$	−6.46410	−	11.1962i	−0.419005	−	0.725739i
$239$	14.6603	−	8.46410i	0.948293	−	0.547497i	0.0557428	−	0.998445i	$-0.482247\pi$
$239$	14.6603	−	8.46410i	0.948293	−	0.547497i	0.892550	+	0.450948i	$0.148914\pi$
$240$	0.633975	+	0.366025i	0.0409229	+	0.0236268i
$241$	−13.3923	−	7.73205i	−0.862674	−	0.498065i	0.00223270	−	0.999998i	$-0.499289\pi$
$241$	−13.3923	−	7.73205i	−0.862674	−	0.498065i	−0.864907	+	0.501932i	$0.832623\pi$
$242$	−9.86603	+	5.69615i	−0.634212	+	0.366163i
$243$	−9.36603	−	16.2224i	−0.600831	−	1.04067i
$244$	−3.69615	+	2.13397i	−0.236622	+	0.136614i
$245$		−	1.33975i		−	0.0855932i
$246$	−7.09808	−	4.09808i	−0.452557	−	0.261284i
$247$	2.19615	+	3.80385i	0.139738	+	0.242033i
$248$	−24.5885			−1.56137
$249$	22.3923			1.41905
$250$	1.33013	+	2.30385i	0.0841246	+	0.145708i
$251$			25.7128i			1.62298i	0.584367	+	0.811489i	$0.301343\pi$
$251$			25.7128i			1.62298i	−0.584367	+	0.811489i	$0.698657\pi$
$252$	−7.73205	+	13.3923i	−0.487073	+	0.843636i
$253$			3.46410i			0.217786i
$254$	−10.5622	−	6.09808i	−0.662730	−	0.382627i
$255$	1.36603	−	2.36603i	0.0855438	−	0.148166i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	16.9641	−	9.79423i	1.05819	−	0.610947i	0.133260	−	0.991081i	$-0.457455\pi$
$257$	16.9641	−	9.79423i	1.05819	−	0.610947i	0.924931	+	0.380134i	$0.124122\pi$
$258$	−9.46410			−0.589209
$259$	−19.0526	−	9.00000i	−1.18387	−	0.559233i
$260$	−0.928203			−0.0575647
$261$	1.03590	−	0.598076i	0.0641205	−	0.0370200i
$262$	5.29423	−	9.16987i	0.327079	−	0.566517i
$263$	3.80385	−	6.58846i	0.234555	−	0.406262i	−0.724588	−	0.689182i	$-0.757970\pi$
$263$	3.80385	−	6.58846i	0.234555	−	0.406262i	0.959143	+	0.282921i	$0.0913033\pi$
$264$	33.5885	+	19.3923i	2.06723	+	1.19351i
$265$			0.679492i			0.0417409i
$266$	2.19615	−	3.80385i	0.134655	−	0.233229i
$267$		−	25.1244i		−	1.53759i
$268$	3.63397	+	6.29423i	0.221980	+	0.384481i
$269$	14.5359			0.886269			0.443135	−	0.896455i	$-0.353866\pi$
$269$	14.5359			0.886269			0.443135	+	0.896455i	$0.353866\pi$
$270$	1.07180			0.0652275
$271$	5.83013	+	10.0981i	0.354155	+	0.613414i	0.986973	−	0.160886i	$-0.0514352\pi$
$271$	5.83013	+	10.0981i	0.354155	+	0.613414i	−0.632818	+	0.774301i	$0.718102\pi$
$272$	3.23205	+	1.86603i	0.195972	+	0.113144i
$273$			32.7846i			1.98421i
$274$	5.59808	−	3.23205i	0.338192	−	0.195255i
$275$	11.6603	+	20.1962i	0.703140	+	1.21787i
$276$	1.73205	−	1.00000i	0.104257	−	0.0601929i
$277$	−8.89230	−	5.13397i	−0.534287	−	0.308471i	0.208474	−	0.978028i	$-0.433150\pi$
$277$	−8.89230	−	5.13397i	−0.534287	−	0.308471i	−0.742760	+	0.669557i	$0.766484\pi$
$278$	10.9019	+	6.29423i	0.653854	+	0.377503i
$279$	−31.6865	+	18.2942i	−1.89702	+	1.09525i
$280$	1.39230	+	2.41154i	0.0832061	+	0.144117i
$281$	28.7487	−	16.5981i	1.71500	−	0.990158i	0.787526	−	0.616282i	$-0.211362\pi$
$281$	28.7487	−	16.5981i	1.71500	−	0.990158i	0.927478	−	0.373877i	$-0.121972\pi$
$282$		−	6.00000i		−	0.357295i
$283$	9.00000	+	5.19615i	0.534994	+	0.308879i	0.743048	−	0.669238i	$-0.233379\pi$
$283$	9.00000	+	5.19615i	0.534994	+	0.308879i	−0.208053	+	0.978117i	$0.566713\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	0.928203			0.0549820
$286$	16.3923			0.969297
$287$	−5.19615	−	9.00000i	−0.306719	−	0.531253i
$288$		−	22.3205i		−	1.31525i
$289$	−1.53590	+	2.66025i	−0.0903470	+	0.156486i
$290$		−	0.0717968i		−	0.00421605i
$291$	−10.0981	−	5.83013i	−0.591960	−	0.341768i
$292$		0			0
$293$	−14.4282	+	24.9904i	−0.842905	+	1.45995i	0.0445239	+	0.999008i	$0.485823\pi$
$293$	−14.4282	+	24.9904i	−0.842905	+	1.45995i	−0.887429	+	0.460945i	$0.847510\pi$
$294$	11.8301	−	6.83013i	0.689947	−	0.398341i
$295$	−3.60770			−0.210048
$296$	18.1865	−	1.50000i	1.05707	−	0.0871857i
$297$	18.9282			1.09833
$298$	−4.79423	+	2.76795i	−0.277722	+	0.160343i
$299$	1.26795	−	2.19615i	0.0733274	−	0.127007i
$300$	6.73205	−	11.6603i	0.388675	−	0.673205i
$301$	−10.3923	−	6.00000i	−0.599002	−	0.345834i
$302$		−	16.5885i		−	0.954558i
$303$	−12.2942	+	21.2942i	−0.706285	+	1.22332i
$304$			1.26795i			0.0727219i
$305$	0.571797	+	0.990381i	0.0327410	+	0.0567091i
$306$	16.6603			0.952403
$307$	−14.3923			−0.821412			−0.410706	−	0.911768i	$-0.634718\pi$
$307$	−14.3923			−0.821412			−0.410706	+	0.911768i	$0.634718\pi$
$308$	8.19615	+	14.1962i	0.467019	+	0.808901i
$309$	−30.5885	−	17.6603i	−1.74012	−	1.00466i
$310$			2.19615i			0.124733i
$311$	−26.3205	+	15.1962i	−1.49250	+	0.861695i	−0.999963	−	0.00859730i	$-0.997263\pi$
$311$	−26.3205	+	15.1962i	−1.49250	+	0.861695i	−0.492536	+	0.870292i	$0.663930\pi$
$312$	−14.1962	−	24.5885i	−0.803699	−	1.39205i
$313$	−13.5000	+	7.79423i	−0.763065	+	0.440556i	−0.830395	−	0.557175i	$-0.811885\pi$
$313$	−13.5000	+	7.79423i	−0.763065	+	0.440556i	0.0673300	+	0.997731i	$0.478552\pi$
$314$	−12.4019	−	7.16025i	−0.699881	−	0.404077i
$315$	3.58846	+	2.07180i	0.202187	+	0.116733i
$316$	−3.29423	+	1.90192i	−0.185315	+	0.106992i
$317$	7.96410	+	13.7942i	0.447309	+	0.774761i	0.998210	−	0.0598093i	$-0.0190493\pi$
$317$	7.96410	+	13.7942i	0.447309	+	0.774761i	−0.550901	+	0.834570i	$0.685716\pi$
$318$	−6.00000	+	3.46410i	−0.336463	+	0.194257i
$319$		−	1.26795i		−	0.0709915i
$320$	−1.62436	−	0.937822i	−0.0908042	−	0.0524259i
$321$	−17.6603	−	30.5885i	−0.985699	−	1.70728i
$322$	−2.53590			−0.141320
$323$	4.73205			0.263298
$324$	1.23205	+	2.13397i	0.0684473	+	0.118554i
$325$		−	17.0718i		−	0.946973i
$326$	−11.1962	+	19.3923i	−0.620098	+	1.07404i
$327$			18.5885i			1.02794i
$328$	7.79423	+	4.50000i	0.430364	+	0.248471i
$329$	3.80385	−	6.58846i	0.209713	−	0.363233i
$330$	1.73205	−	3.00000i	0.0953463	−	0.165145i
$331$	28.3923	−	16.3923i	1.56058	−	0.901003i	0.563384	−	0.826195i	$-0.309499\pi$
$331$	28.3923	−	16.3923i	1.56058	−	0.901003i	0.997198	−	0.0748075i	$-0.0238342\pi$
$332$	−8.19615			−0.449822
$333$	22.3205	−	15.4641i	1.22316	−	0.847428i
$334$	−10.9282			−0.597965
$335$	1.68653	−	0.973721i	0.0921452	−	0.0532000i
$336$	−4.73205	+	8.19615i	−0.258155	+	0.447137i
$337$	−14.6962	+	25.4545i	−0.800550	+	1.38659i	0.118704	+	0.992930i	$0.462126\pi$
$337$	−14.6962	+	25.4545i	−0.800550	+	1.38659i	−0.919254	+	0.393664i	$0.871207\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$			12.3923i			0.673058i
$340$	−0.500000	+	0.866025i	−0.0271163	+	0.0469668i
$341$			38.7846i			2.10030i
$342$	2.83013	+	4.90192i	0.153036	+	0.265066i
$343$	−6.92820			−0.374088
$344$	10.3923			0.560316
$345$	−0.267949	−	0.464102i	−0.0144259	−	0.0249864i
$346$	8.59808	+	4.96410i	0.462235	+	0.266872i
$347$			12.7321i			0.683492i	0.939792	+	0.341746i	$0.111018\pi$
$347$			12.7321i			0.683492i	−0.939792	+	0.341746i	$0.888982\pi$
$348$	−0.633975	+	0.366025i	−0.0339846	+	0.0196210i
$349$	−4.03590	−	6.99038i	−0.216037	−	0.374187i	0.737556	−	0.675286i	$-0.235980\pi$
$349$	−4.03590	−	6.99038i	−0.216037	−	0.374187i	−0.953593	+	0.301099i	$0.902646\pi$
$350$	−14.7846	+	8.53590i	−0.790271	+	0.456263i
$351$	−12.0000	−	6.92820i	−0.640513	−	0.369800i
$352$	−20.4904	−	11.8301i	−1.09214	−	0.630548i
$353$	10.6244	−	6.13397i	0.565477	−	0.326479i	−0.189864	−	0.981810i	$-0.560805\pi$
$353$	10.6244	−	6.13397i	0.565477	−	0.326479i	0.755341	+	0.655332i	$0.227471\pi$
$354$	−18.3923	−	31.8564i	−0.977540	−	1.69315i
$355$	−1.39230	+	0.803848i	−0.0738959	+	0.0426638i
$356$			9.19615i			0.487395i
$357$	30.5885	+	17.6603i	1.61891	+	0.934680i
$358$	−0.732051	−	1.26795i	−0.0386901	−	0.0670132i
$359$	16.3923			0.865153			0.432576	−	0.901597i	$-0.357605\pi$
$359$	16.3923			0.865153			0.432576	+	0.901597i	$0.357605\pi$
$360$	−3.58846			−0.189128
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$		−	9.92820i		−	0.521815i
$363$	15.5622	−	26.9545i	0.816803	−	1.41474i
$364$		−	12.0000i		−	0.628971i
$365$		0			0
$366$	−5.83013	+	10.0981i	−0.304746	+	0.527835i
$367$	10.1962	−	17.6603i	0.532235	−	0.921858i	−0.467057	−	0.884227i	$-0.654686\pi$
$367$	10.1962	−	17.6603i	0.532235	−	0.921858i	0.999292	−	0.0376305i	$-0.0119810\pi$
$368$	0.633975	−	0.366025i	0.0330482	−	0.0190804i
$369$	13.3923			0.697176
$370$	−0.133975	−	1.62436i	−0.00696501	−	0.0844462i
$371$	−8.78461			−0.456074
$372$	19.3923	−	11.1962i	1.00544	−	0.580493i
$373$	−8.76795	+	15.1865i	−0.453987	+	0.786329i	−0.998629	−	0.0523397i	$-0.983332\pi$
$373$	−8.76795	+	15.1865i	−0.453987	+	0.786329i	0.544642	+	0.838669i	$0.316665\pi$
$374$	8.83013	−	15.2942i	0.456595	−	0.790846i
$375$	−6.29423	−	3.63397i	−0.325033	−	0.187658i
$376$			6.58846i			0.339774i
$377$	−0.464102	+	0.803848i	−0.0239024	+	0.0414003i
$378$			13.8564i			0.712697i
$379$	−4.26795	−	7.39230i	−0.219230	−	0.379717i	0.735343	−	0.677695i	$-0.237021\pi$
$379$	−4.26795	−	7.39230i	−0.219230	−	0.379717i	−0.954573	+	0.297978i	$0.903688\pi$
$380$	−0.339746			−0.0174286
$381$	33.3205			1.70706
$382$	3.09808	+	5.36603i	0.158511	+	0.274550i
$383$	−13.7321	−	7.92820i	−0.701675	−	0.405112i	0.106296	−	0.994335i	$-0.466101\pi$
$383$	−13.7321	−	7.92820i	−0.701675	−	0.405112i	−0.807971	+	0.589222i	$0.799434\pi$
$384$			8.19615i			0.418258i
$385$	3.80385	−	2.19615i	0.193862	−	0.111926i
$386$	7.33013	+	12.6962i	0.373094	+	0.646217i
$387$	13.3923	−	7.73205i	0.680769	−	0.393042i
$388$	3.69615	+	2.13397i	0.187644	+	0.108336i
$389$	27.0167	+	15.5981i	1.36980	+	0.790854i	0.990902	−	0.134585i	$-0.0429701\pi$
$389$	27.0167	+	15.5981i	1.36980	+	0.790854i	0.378897	+	0.925439i	$0.376303\pi$
$390$	−2.19615	+	1.26795i	−0.111207	+	0.0642051i
$391$	−1.36603	−	2.36603i	−0.0690829	−	0.119655i
$392$	−12.9904	+	7.50000i	−0.656113	+	0.378807i
$393$			28.9282i			1.45923i
$394$	24.1865	+	13.9641i	1.21850	+	0.703501i
$395$	0.509619	+	0.882686i	0.0256417	+	0.0444127i
$396$	−21.1244			−1.06154
$397$	−21.2487			−1.06644			−0.533221	−	0.845976i	$-0.679019\pi$
$397$	−21.2487			−1.06644			−0.533221	+	0.845976i	$0.679019\pi$
$398$	5.53590	+	9.58846i	0.277490	+	0.480626i
$399$			12.0000i			0.600751i
$400$	2.46410	−	4.26795i	0.123205	−	0.213397i
$401$		−	5.60770i		−	0.280035i	−0.990149	−	0.140017i	$-0.955284\pi$
$401$		−	5.60770i		−	0.280035i	0.990149	−	0.140017i	$-0.0447159\pi$
$402$	17.1962	+	9.92820i	0.857666	+	0.495174i
$403$	14.1962	−	24.5885i	0.707161	−	1.22484i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	0.571797	−	0.330127i	0.0284128	−	0.0164041i
$406$	0.928203			0.0460660
$407$	−2.36603	−	28.6865i	−0.117280	−	1.42194i
$408$	−30.5885			−1.51435
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$	0.401924	−	0.696152i	0.0198496	−	0.0343805i
$411$	−8.83013	+	15.2942i	−0.435558	+	0.754409i
$412$	11.1962	+	6.46410i	0.551595	+	0.318463i
$413$		−	46.6410i		−	2.29505i
$414$	1.63397	−	2.83013i	0.0803055	−	0.139093i
$415$			2.19615i			0.107805i
$416$	8.66025	+	15.0000i	0.424604	+	0.735436i
$417$	−34.3923			−1.68420
$418$	6.00000			0.293470
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	0.573158	−	0.819445i	$-0.305718\pi$
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	−0.996239	+	0.0866469i	$0.972385\pi$
$420$	−2.19615	−	1.26795i	−0.107161	−	0.0618696i
$421$			16.2679i			0.792851i	0.918067	+	0.396426i	$0.129750\pi$
$421$			16.2679i			0.792851i	−0.918067	+	0.396426i	$0.870250\pi$
$422$	8.66025	−	5.00000i	0.421575	−	0.243396i
$423$	4.90192	+	8.49038i	0.238340	+	0.412816i
$424$	6.58846	−	3.80385i	0.319964	−	0.184731i
$425$	−15.9282	−	9.19615i	−0.772631	−	0.446079i
$426$	−14.1962	−	8.19615i	−0.687806	−	0.397105i
$427$	−12.8038	+	7.39230i	−0.619622	+	0.357739i
$428$	6.46410	+	11.1962i	0.312454	+	0.541186i
$429$	−38.7846	+	22.3923i	−1.87254	+	1.08111i
$430$		−	0.928203i		−	0.0447619i
$431$	−9.97372	−	5.75833i	−0.480417	−	0.277369i	0.240173	−	0.970730i	$-0.422796\pi$
$431$	−9.97372	−	5.75833i	−0.480417	−	0.277369i	−0.720590	+	0.693361i	$0.756129\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	27.0000			1.29754			0.648769	−	0.760986i	$-0.275284\pi$
$433$	27.0000			1.29754			0.648769	+	0.760986i	$0.275284\pi$
$434$	−28.3923			−1.36287
$435$	0.0980762	+	0.169873i	0.00470239	+	0.00814479i
$436$		−	6.80385i		−	0.325845i
$437$	0.464102	−	0.803848i	0.0222010	−	0.0384532i
$438$		0			0
$439$	12.5885	+	7.26795i	0.600814	+	0.346880i	0.769362	−	0.638813i	$-0.220574\pi$
$439$	12.5885	+	7.26795i	0.600814	+	0.346880i	−0.168548	+	0.985694i	$0.553908\pi$
$440$	−1.90192	+	3.29423i	−0.0906707	+	0.157046i
$441$	−11.1603	+	19.3301i	−0.531441	+	0.920482i
$442$	−11.1962	+	6.46410i	−0.532547	+	0.307466i
$443$	33.4641			1.58993			0.794964	−	0.606657i	$-0.207490\pi$
$443$	33.4641			1.58993			0.794964	+	0.606657i	$0.207490\pi$
$444$	−13.6603	+	9.46410i	−0.648287	+	0.449146i
$445$	2.46410			0.116810
$446$	−3.97372	+	2.29423i	−0.188161	+	0.108635i
$447$	7.56218	−	13.0981i	0.357679	−	0.619518i
$448$	12.1244	−	21.0000i	0.572822	−	0.992157i
$449$	−27.9282	−	16.1244i	−1.31801	−	0.760955i	−0.334605	−	0.942359i	$-0.608603\pi$
$449$	−27.9282	−	16.1244i	−1.31801	−	0.760955i	−0.983409	+	0.181403i	$0.941936\pi$
$450$		−	22.0000i		−	1.03709i
$451$	7.09808	−	12.2942i	0.334235	−	0.578913i
$452$		−	4.53590i		−	0.213351i
$453$	22.6603	+	39.2487i	1.06467	+	1.84407i
$454$	−23.1244			−1.08528
$455$	−3.21539			−0.150740
$456$	−5.19615	−	9.00000i	−0.243332	−	0.421464i
$457$	−31.2846	−	18.0622i	−1.46343	−	0.844913i	−0.464264	−	0.885697i	$-0.653681\pi$
$457$	−31.2846	−	18.0622i	−1.46343	−	0.844913i	−0.999168	+	0.0407837i	$0.987015\pi$
$458$		−	7.00000i		−	0.327089i
$459$	−12.9282	+	7.46410i	−0.603437	+	0.348394i
$460$	0.0980762	+	0.169873i	0.00457283	+	0.00792037i
$461$	−14.3205	+	8.26795i	−0.666973	+	0.385077i	−0.794929	−	0.606703i	$-0.792492\pi$
$461$	−14.3205	+	8.26795i	−0.666973	+	0.385077i	0.127956	+	0.991780i	$0.459158\pi$
$462$	38.7846	+	22.3923i	1.80442	+	1.04178i
$463$	−13.3923	−	7.73205i	−0.622393	−	0.359339i	0.155407	−	0.987851i	$-0.450331\pi$
$463$	−13.3923	−	7.73205i	−0.622393	−	0.359339i	−0.777800	+	0.628512i	$0.783664\pi$
$464$	−0.232051	+	0.133975i	−0.0107727	+	0.00621961i
$465$	−3.00000	−	5.19615i	−0.139122	−	0.240966i
$466$	9.40192	−	5.42820i	0.435536	−	0.251457i
$467$		−	3.32051i		−	0.153655i	−0.997044	−	0.0768274i	$-0.975521\pi$
$467$		−	3.32051i		−	0.153655i	0.997044	−	0.0768274i	$-0.0244790\pi$
$468$	13.3923	+	7.73205i	0.619060	+	0.357414i
$469$	12.5885	+	21.8038i	0.581281	+	1.00681i
$470$	0.588457			0.0271435
$471$	39.1244			1.80276
$472$	20.1962	+	34.9808i	0.929603	+	1.61012i
$473$		−	16.3923i		−	0.753719i
$474$	−5.19615	+	9.00000i	−0.238667	+	0.413384i
$475$		−	6.24871i		−	0.286711i
$476$	−11.1962	−	6.46410i	−0.513175	−	0.296282i
$477$	5.66025	−	9.80385i	0.259165	−	0.448887i
$478$	−8.46410	+	14.6603i	−0.387139	+	0.670544i
$479$	−34.0526	+	19.6603i	−1.55590	+	0.898300i	−0.558259	+	0.829667i	$0.688531\pi$
$479$	−34.0526	+	19.6603i	−1.55590	+	0.898300i	−0.997642	+	0.0686333i	$0.978136\pi$
$480$	3.66025			0.167067
$481$	−9.00000	+	19.0526i	−0.410365	+	0.868722i
$482$	15.4641			0.704371
$483$	6.00000	−	3.46410i	0.273009	−	0.157622i
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$	0.571797	−	0.990381i	0.0259640	−	0.0449709i
$486$	16.2224	+	9.36603i	0.735864	+	0.424852i
$487$			32.4449i			1.47022i	0.677949	+	0.735109i	$0.262869\pi$
$487$			32.4449i			1.47022i	−0.677949	+	0.735109i	$0.737131\pi$
$488$	6.40192	−	11.0885i	0.289801	−	0.501951i
$489$		−	61.1769i		−	2.76652i
$490$	0.669873	+	1.16025i	0.0302618	+	0.0524149i
$491$	31.2679			1.41110			0.705551	−	0.708659i	$-0.250699\pi$
$491$	31.2679			1.41110			0.705551	+	0.708659i	$0.250699\pi$
$492$	−8.19615			−0.369511
$493$	0.500000	+	0.866025i	0.0225189	+	0.0390038i
$494$	−3.80385	−	2.19615i	−0.171143	−	0.0988096i
$495$			5.66025i			0.254409i
$496$	7.09808	−	4.09808i	0.318713	−	0.184009i
$497$	−10.3923	−	18.0000i	−0.466159	−	0.807410i
$498$	−19.3923	+	11.1962i	−0.868990	+	0.501712i
$499$	10.9019	+	6.29423i	0.488037	+	0.281768i	0.723760	−	0.690052i	$-0.242412\pi$
$499$	10.9019	+	6.29423i	0.488037	+	0.281768i	−0.235723	+	0.971820i	$0.575746\pi$
$500$	2.30385	+	1.33013i	0.103031	+	0.0594851i
$501$	25.8564	−	14.9282i	1.15518	−	0.666943i
$502$	−12.8564	−	22.2679i	−0.573810	−	0.993867i
$503$	−7.77757	+	4.49038i	−0.346785	+	0.200216i	−0.663268	−	0.748382i	$-0.730831\pi$
$503$	−7.77757	+	4.49038i	−0.346785	+	0.200216i	0.316484	+	0.948598i	$0.397498\pi$
$504$		−	46.3923i		−	2.06648i
$505$	−2.08846	−	1.20577i	−0.0929351	−	0.0536561i
$506$	−1.73205	−	3.00000i	−0.0769991	−	0.133366i
$507$	−2.73205			−0.121335
$508$	−12.1962			−0.541117
$509$	2.89230	+	5.00962i	0.128199	+	0.222047i	0.922979	−	0.384850i	$-0.125747\pi$
$509$	2.89230	+	5.00962i	0.128199	+	0.222047i	−0.794780	+	0.606898i	$0.792414\pi$
$510$			2.73205i			0.120977i
$511$		0			0
$512$			11.0000i			0.486136i
$513$	−4.39230	−	2.53590i	−0.193925	−	0.111963i
$514$	−9.79423	+	16.9641i	−0.432005	+	0.748254i
$515$	1.73205	−	3.00000i	0.0763233	−	0.132196i
$516$	−8.19615	+	4.73205i	−0.360815	+	0.208317i
$517$	10.3923			0.457053
$518$	21.0000	−	1.73205i	0.922687	−	0.0761019i
$519$	−27.1244			−1.19063
$520$	2.41154	−	1.39230i	0.105753	−	0.0610566i
$521$	−3.46410	+	6.00000i	−0.151765	+	0.262865i	−0.931876	−	0.362776i	$-0.881829\pi$
$521$	−3.46410	+	6.00000i	−0.151765	+	0.262865i	0.780111	+	0.625641i	$0.215162\pi$
$522$	−0.598076	+	1.03590i	−0.0261771	+	0.0453400i
$523$	13.9019	+	8.02628i	0.607889	+	0.350965i	0.772139	−	0.635454i	$-0.219187\pi$
$523$	13.9019	+	8.02628i	0.607889	+	0.350965i	−0.164250	+	0.986419i	$0.552520\pi$
$524$		−	10.5885i		−	0.462559i
$525$	23.3205	−	40.3923i	1.01779	−	1.76286i
$526$			7.60770i			0.331711i
$527$	−15.2942	−	26.4904i	−0.666227	−	1.15394i
$528$	−12.9282			−0.562628
$529$	22.4641			0.976700
$530$	−0.339746	−	0.588457i	−0.0147576	−	0.0255610i
$531$	52.0526	+	30.0526i	2.25889	+	1.30417i
$532$		−	4.39230i		−	0.190431i
$533$	−9.00000	+	5.19615i	−0.389833	+	0.225070i
$534$	12.5622	+	21.7583i	0.543619	+	0.941575i
$535$	3.00000	−	1.73205i	0.129701	−	0.0748831i
$536$	−18.8827	−	10.9019i	−0.815608	−	0.470891i
$537$	3.46410	+	2.00000i	0.149487	+	0.0863064i
$538$	−12.5885	+	7.26795i	−0.542727	+	0.313344i
$539$	11.8301	+	20.4904i	0.509560	+	0.882583i
$540$	0.928203	−	0.535898i	0.0399435	−	0.0230614i
$541$		−	4.26795i		−	0.183493i	−0.995782	−	0.0917467i	$-0.970755\pi$
$541$		−	4.26795i		−	0.183493i	0.995782	−	0.0917467i	$-0.0292450\pi$
$542$	−10.0981	−	5.83013i	−0.433750	−	0.250425i
$543$	13.5622	+	23.4904i	0.582009	+	1.00807i
$544$	18.6603			0.800052
$545$	−1.82309			−0.0780924
$546$	−16.3923	−	28.3923i	−0.701526	−	1.21508i
$547$			3.80385i			0.162641i	0.996688	+	0.0813204i	$0.0259137\pi$
$547$			3.80385i			0.162641i	−0.996688	+	0.0813204i	$0.974086\pi$
$548$	3.23205	−	5.59808i	0.138066	−	0.239138i
$549$		−	19.0526i		−	0.813143i
$550$	−20.1962	−	11.6603i	−0.861167	−	0.497195i
$551$	−0.169873	+	0.294229i	−0.00723683	+	0.0125346i
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−11.4115	+	6.58846i	−0.485268	+	0.280170i
$554$	10.2679			0.436243
$555$	2.53590	+	3.66025i	0.107643	+	0.155369i
$556$	12.5885			0.533870
$557$	−15.3564	+	8.86603i	−0.650672	+	0.375666i	−0.788714	−	0.614761i	$-0.789253\pi$
$557$	−15.3564	+	8.86603i	−0.650672	+	0.375666i	0.138042	+	0.990426i	$0.455919\pi$
$558$	18.2942	−	31.6865i	0.774456	−	1.34140i
$559$	−6.00000	+	10.3923i	−0.253773	+	0.439548i
$560$	−0.803848	−	0.464102i	−0.0339688	−	0.0196119i
$561$			48.2487i			2.03706i
$562$	−16.5981	+	28.7487i	−0.700148	+	1.21269i
$563$			34.5885i			1.45773i	0.684658	+	0.728865i	$0.259952\pi$
$563$			34.5885i			1.45773i	−0.684658	+	0.728865i	$0.740048\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	−1.21539			−0.0511319
$566$	−10.3923			−0.436821
$567$	4.26795	+	7.39230i	0.179237	+	0.310448i
$568$	15.5885	+	9.00000i	0.654077	+	0.377632i
$569$		−	36.5167i		−	1.53086i	−0.643520	−	0.765429i	$-0.722527\pi$
$569$		−	36.5167i		−	1.53086i	0.643520	−	0.765429i	$-0.277473\pi$
$570$	−0.803848	+	0.464102i	−0.0336695	+	0.0194391i
$571$	15.7583	+	27.2942i	0.659466	+	1.14223i	0.980754	+	0.195247i	$0.0625507\pi$
$571$	15.7583	+	27.2942i	0.659466	+	1.14223i	−0.321289	+	0.946981i	$0.604116\pi$
$572$	14.1962	−	8.19615i	0.593571	−	0.342698i
$573$	−14.6603	−	8.46410i	−0.612441	−	0.353593i
$574$	9.00000	+	5.19615i	0.375653	+	0.216883i
$575$	−3.12436	+	1.80385i	−0.130295	+	0.0752256i
$576$	15.6244	+	27.0622i	0.651015	+	1.12759i
$577$	11.1962	−	6.46410i	0.466102	−	0.269104i	−0.248505	−	0.968631i	$-0.579939\pi$
$577$	11.1962	−	6.46410i	0.466102	−	0.269104i	0.714607	+	0.699527i	$0.246606\pi$
$578$		−	3.07180i		−	0.127770i
$579$	−34.6865	−	20.0263i	−1.44152	−	0.832264i
$580$	−0.0358984	−	0.0621778i	−0.00149060	−	0.00258179i
$581$	−28.3923			−1.17791
$582$	11.6603			0.483333
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$		0			0
$585$	2.07180	−	3.58846i	0.0856583	−	0.148364i
$586$		−	28.8564i		−	1.19205i
$587$	−14.1506	−	8.16987i	−0.584059	−	0.337207i	0.178686	−	0.983906i	$-0.442815\pi$
$587$	−14.1506	−	8.16987i	−0.584059	−	0.337207i	−0.762745	+	0.646699i	$0.776149\pi$
$588$	6.83013	−	11.8301i	0.281670	−	0.487866i
$589$	5.19615	−	9.00000i	0.214104	−	0.370839i
$590$	3.12436	−	1.80385i	0.128628	−	0.0742632i
$591$	−76.3013			−3.13861
$592$	−5.00000	+	3.46410i	−0.205499	+	0.142374i
$593$	17.7846			0.730326			0.365163	−	0.930944i	$-0.381013\pi$
$593$	17.7846			0.730326			0.365163	+	0.930944i	$0.381013\pi$
$594$	−16.3923	+	9.46410i	−0.672584	+	0.388317i
$595$	−1.73205	+	3.00000i	−0.0710072	+	0.122988i
$596$	−2.76795	+	4.79423i	−0.113380	+	0.196379i
$597$	−26.1962	−	15.1244i	−1.07214	−	0.618999i
$598$			2.53590i			0.103701i
$599$	−3.97372	+	6.88269i	−0.162362	+	0.281219i	−0.935715	−	0.352756i	$-0.885245\pi$
$599$	−3.97372	+	6.88269i	−0.162362	+	0.281219i	0.773353	+	0.633975i	$0.218578\pi$
$600$			40.3923i			1.64901i
$601$	−15.6962	−	27.1865i	−0.640259	−	1.10896i	−0.985375	−	0.170402i	$-0.945494\pi$
$601$	−15.6962	−	27.1865i	−0.640259	−	1.10896i	0.345115	−	0.938560i	$-0.387840\pi$
$602$	12.0000			0.489083
$603$	−32.4449			−1.32126
$604$	−8.29423	−	14.3660i	−0.337487	−	0.584545i
$605$	2.64359	+	1.52628i	0.107477	+	0.0620521i
$606$		−	24.5885i		−	0.998838i
$607$	4.90192	−	2.83013i	0.198963	−	0.114871i	−0.397209	−	0.917728i	$-0.630021\pi$
$607$	4.90192	−	2.83013i	0.198963	−	0.114871i	0.596172	+	0.802857i	$0.296688\pi$
$608$	3.16987	+	5.49038i	0.128555	+	0.222664i
$609$	−2.19615	+	1.26795i	−0.0889926	+	0.0513799i
$610$	−0.990381	−	0.571797i	−0.0400994	−	0.0231514i
$611$	−6.58846	−	3.80385i	−0.266540	−	0.153887i
$612$	14.4282	−	8.33013i	0.583226	−	0.336725i
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	0.829737	−	0.558154i	$-0.188490\pi$
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	−0.898244	+	0.439497i	$0.855157\pi$
$614$	12.4641	−	7.19615i	0.503010	−	0.290413i
$615$			2.19615i			0.0885574i
$616$	−42.5885	−	24.5885i	−1.71594	−	0.990697i
$617$	12.5885	+	21.8038i	0.506792	+	0.877790i	0.999969	+	0.00786080i	$0.00250220\pi$
$617$	12.5885	+	21.8038i	0.506792	+	0.877790i	−0.493177	+	0.869929i	$0.664164\pi$
$618$	35.3205			1.42080
$619$	6.78461			0.272696			0.136348	−	0.990661i	$-0.456463\pi$
$619$	6.78461			0.272696			0.136348	+	0.990661i	$0.456463\pi$
$620$	1.09808	+	1.90192i	0.0440998	+	0.0763831i
$621$			2.92820i			0.117505i
$622$	15.1962	−	26.3205i	0.609310	−	1.05536i
$623$			31.8564i			1.27630i
$624$	8.19615	+	4.73205i	0.328109	+	0.189434i
$625$	−11.9641	+	20.7224i	−0.478564	+	0.828897i
$626$	7.79423	−	13.5000i	0.311520	−	0.539569i
$627$	−14.1962	+	8.19615i	−0.566940	+	0.327323i
$628$	−14.3205			−0.571450
$629$	12.9282	+	18.6603i	0.515481	+	0.744033i
$630$	−4.14359			−0.165085
$631$	16.6865	−	9.63397i	0.664280	−	0.383522i	−0.129626	−	0.991563i	$-0.541378\pi$
$631$	16.6865	−	9.63397i	0.664280	−	0.383522i	0.793906	+	0.608041i	$0.208044\pi$
$632$	5.70577	−	9.88269i	0.226963	−	0.393112i
$633$	−13.6603	+	23.6603i	−0.542946	+	0.940411i
$634$	−13.7942	−	7.96410i	−0.547839	−	0.316295i
$635$			3.26795i			0.129685i
$636$	−3.46410	+	6.00000i	−0.137361	+	0.237915i
$637$		−	17.3205i		−	0.686264i
$638$	0.633975	+	1.09808i	0.0250993	+	0.0434733i
$639$	26.7846			1.05958
$640$	−0.803848			−0.0317749
$641$	8.89230	+	15.4019i	0.351225	+	0.608339i	0.986464	−	0.163976i	$-0.0524319\pi$
$641$	8.89230	+	15.4019i	0.351225	+	0.608339i	−0.635239	+	0.772315i	$0.719099\pi$
$642$	30.5885	+	17.6603i	1.20723	+	0.696995i
$643$			5.66025i			0.223219i	0.993752	+	0.111609i	$0.0356005\pi$
$643$			5.66025i			0.223219i	−0.993752	+	0.111609i	$0.964399\pi$
$644$	−2.19615	+	1.26795i	−0.0865405	+	0.0499642i
$645$	1.26795	+	2.19615i	0.0499255	+	0.0864734i
$646$	−4.09808	+	2.36603i	−0.161237	+	0.0930900i
$647$	37.6410	+	21.7321i	1.47982	+	0.854375i	0.999739	−	0.0228485i	$-0.00727353\pi$
$647$	37.6410	+	21.7321i	1.47982	+	0.854375i	0.480082	+	0.877224i	$0.340607\pi$
$648$	−6.40192	−	3.69615i	−0.251491	−	0.145199i
$649$	55.1769	−	31.8564i	2.16588	−	1.25047i
$650$	8.53590	+	14.7846i	0.334805	+	0.579900i
$651$	67.1769	−	38.7846i	2.63287	−	1.52009i
$652$			22.3923i			0.876950i
$653$	−2.42820	−	1.40192i	−0.0950229	−	0.0548615i	0.451736	−	0.892152i	$-0.350805\pi$
$653$	−2.42820	−	1.40192i	−0.0950229	−	0.0548615i	−0.546758	+	0.837290i	$0.684138\pi$
$654$	−9.29423	−	16.0981i	−0.363433	−	0.629485i
$655$	−2.83717			−0.110857
$656$	−3.00000			−0.117130
$657$		0			0
$658$			7.60770i			0.296579i
$659$	−4.73205	+	8.19615i	−0.184335	+	0.319277i	−0.943352	−	0.331793i	$-0.892346\pi$
$659$	−4.73205	+	8.19615i	−0.184335	+	0.319277i	0.759018	+	0.651070i	$0.225680\pi$
$660$		−	3.46410i		−	0.134840i
$661$	−11.0885	−	6.40192i	−0.431291	−	0.249006i	0.268605	−	0.963250i	$-0.413437\pi$
$661$	−11.0885	−	6.40192i	−0.431291	−	0.249006i	−0.699896	+	0.714244i	$0.746771\pi$
$662$	−16.3923	+	28.3923i	−0.637105	+	1.10350i
$663$	17.6603	−	30.5885i	0.685867	−	1.18796i
$664$	21.2942	−	12.2942i	0.826376	−	0.477109i
$665$	−1.17691			−0.0456388
$666$	−11.5981	+	24.5526i	−0.449416	+	0.951392i
$667$	0.196152			0.00759505
$668$	−9.46410	+	5.46410i	−0.366177	+	0.211412i
$669$	6.26795	−	10.8564i	0.242333	−	0.419733i
$670$	−0.973721	+	1.68653i	−0.0376181	+	0.0651565i
$671$	−17.4904	−	10.0981i	−0.675209	−	0.389832i
$672$			47.3205i			1.82543i
$673$	−7.85641	+	13.6077i	−0.302842	+	0.524538i	−0.976779	−	0.214251i	$-0.931269\pi$
$673$	−7.85641	+	13.6077i	−0.302842	+	0.524538i	0.673936	+	0.738789i	$0.264602\pi$
$674$		−	29.3923i		−	1.13215i
$675$	9.85641	+	17.0718i	0.379373	+	0.657094i
$676$	1.00000			0.0384615
$677$	−44.3205			−1.70338			−0.851688	−	0.524050i	$-0.824421\pi$
$677$	−44.3205			−1.70338			−0.851688	+	0.524050i	$0.824421\pi$
$678$	−6.19615	−	10.7321i	−0.237962	−	0.412162i
$679$	12.8038	+	7.39230i	0.491367	+	0.283691i
$680$		−	3.00000i		−	0.115045i
$681$	54.7128	−	31.5885i	2.09660	−	1.21047i
$682$	−19.3923	−	33.5885i	−0.742570	−	1.28617i
$683$	26.9090	−	15.5359i	1.02964	−	0.594465i	0.112761	−	0.993622i	$-0.464031\pi$
$683$	26.9090	−	15.5359i	1.02964	−	0.594465i	0.916882	+	0.399158i	$0.130697\pi$
$684$	4.90192	+	2.83013i	0.187430	+	0.108213i
$685$	−1.50000	−	0.866025i	−0.0573121	−	0.0330891i
$686$	6.00000	−	3.46410i	0.229081	−	0.132260i
$687$	9.56218	+	16.5622i	0.364820	+	0.631886i
$688$	−3.00000	+	1.73205i	−0.114374	+	0.0660338i
$689$			8.78461i			0.334667i
$690$	0.464102	+	0.267949i	0.0176680	+	0.0102007i
$691$	−8.02628	−	13.9019i	−0.305334	−	0.528854i	0.672002	−	0.740550i	$-0.265435\pi$
$691$	−8.02628	−	13.9019i	−0.305334	−	0.528854i	−0.977336	+	0.211696i	$0.932101\pi$
$692$	9.92820			0.377414
$693$	−73.1769			−2.77976
$694$	−6.36603	−	11.0263i	−0.241651	−	0.418552i
$695$		−	3.37307i		−	0.127948i
$696$	1.09808	−	1.90192i	0.0416225	−	0.0720922i
$697$			11.1962i			0.424085i
$698$	6.99038	+	4.03590i	0.264590	+	0.152761i
$699$	−14.8301	+	25.6865i	−0.560927	+	0.971554i
$700$	−8.53590	+	14.7846i	−0.322627	+	0.558806i
$701$	−5.07180	+	2.92820i	−0.191559	+	0.110597i	−0.592712	−	0.805414i	$-0.701943\pi$
$701$	−5.07180	+	2.92820i	−0.191559	+	0.110597i	0.401153	+	0.916011i	$0.368610\pi$
$702$	13.8564			0.522976
$703$	−3.29423	+	6.97372i	−0.124244	+	0.263019i
$704$	33.1244			1.24842
$705$	−1.39230	+	0.803848i	−0.0524372	+	0.0302747i
$706$	−6.13397	+	10.6244i	−0.230855	+	0.399853i
$707$	15.5885	−	27.0000i	0.586264	−	1.01544i
$708$	−31.8564	−	18.3923i	−1.19724	−	0.691225i
$709$		−	30.0000i		−	1.12667i	−0.826227	−	0.563337i	$-0.809517\pi$
$709$		−	30.0000i		−	1.12667i	0.826227	−	0.563337i	$-0.190483\pi$
$710$	0.803848	−	1.39230i	0.0301679	−	0.0522523i
$711$		−	16.9808i		−	0.636828i
$712$	−13.7942	−	23.8923i	−0.516961	−	0.895402i
$713$	−6.00000			−0.224702
$714$	−35.3205			−1.32184
$715$	−2.19615	−	3.80385i	−0.0821314	−	0.142256i
$716$	−1.26795	−	0.732051i	−0.0473855	−	0.0273580i
$717$		−	46.2487i		−	1.72719i
$718$	−14.1962	+	8.19615i	−0.529796	+	0.305878i
$719$	−13.2224	−	22.9019i	−0.493114	−	0.854098i	0.506855	−	0.862031i	$-0.330808\pi$
$719$	−13.2224	−	22.9019i	−0.493114	−	0.854098i	−0.999969	+	0.00793367i	$0.997475\pi$
$720$	1.03590	−	0.598076i	0.0386057	−	0.0222890i
$721$	38.7846	+	22.3923i	1.44441	+	0.833933i
$722$	15.0622	+	8.69615i	0.560556	+	0.323637i
$723$	−36.5885	+	21.1244i	−1.36074	+	0.785623i
$724$	−4.96410	−	8.59808i	−0.184489	−	0.319545i
$725$	1.14359	−	0.660254i	0.0424720	−	0.0245212i
$726$			31.1244i			1.15513i
$727$	−1.60770	−	0.928203i	−0.0596261	−	0.0344252i	0.469891	−	0.882725i	$-0.344293\pi$
$727$	−1.60770	−	0.928203i	−0.0596261	−	0.0344252i	−0.529517	+	0.848300i	$0.677627\pi$
$728$	18.0000	+	31.1769i	0.667124	+	1.15549i
$729$	−43.7846			−1.62165
$730$		0			0
$731$	6.46410	+	11.1962i	0.239083	+	0.414105i
$732$			11.6603i			0.430975i
$733$	−14.3923	+	24.9282i	−0.531592	+	0.920744i	0.467728	+	0.883872i	$0.345073\pi$
$733$	−14.3923	+	24.9282i	−0.531592	+	0.920744i	−0.999320	+	0.0368718i	$0.988261\pi$
$734$			20.3923i			0.752694i
$735$	−3.16987	−	1.83013i	−0.116923	−	0.0675053i
$736$	1.83013	−	3.16987i	0.0674594	−	0.116843i
$737$	−17.1962	+	29.7846i	−0.633428	+	1.09713i
$738$	−11.5981	+	6.69615i	−0.426931	+	0.246489i
$739$	−23.8038			−0.875639			−0.437819	−	0.899063i	$-0.644249\pi$
$739$	−23.8038			−0.875639			−0.437819	+	0.899063i	$0.644249\pi$
$740$	−0.928203	−	1.33975i	−0.0341214	−	0.0492500i
$741$	12.0000			0.440831
$742$	7.60770	−	4.39230i	0.279287	−	0.161247i
$743$	21.6340	−	37.4711i	0.793674	−	1.37468i	−0.130004	−	0.991513i	$-0.541499\pi$
$743$	21.6340	−	37.4711i	0.793674	−	1.37468i	0.923678	−	0.383170i	$-0.125167\pi$
$744$	−33.5885	+	58.1769i	−1.23141	+	2.13287i
$745$	1.28461	+	0.741670i	0.0470645	+	0.0271727i
$746$		−	17.5359i		−	0.642035i
$747$	18.2942	−	31.6865i	0.669351	−	1.15935i
$748$		−	17.6603i		−	0.645723i
$749$	22.3923	+	38.7846i	0.818197	+	1.41716i
$750$	7.26795			0.265388
$751$	−9.21539			−0.336274			−0.168137	−	0.985764i	$-0.553775\pi$
$751$	−9.21539			−0.336274			−0.168137	+	0.985764i	$0.553775\pi$
$752$	−1.09808	−	1.90192i	−0.0400427	−	0.0693560i
$753$	60.8372	+	35.1244i	2.21703	+	1.28000i
$754$		−	0.928203i		−	0.0338032i
$755$	−3.84936	+	2.22243i	−0.140093	+	0.0808826i
$756$	6.92820	+	12.0000i	0.251976	+	0.436436i
$757$	36.6962	−	21.1865i	1.33374	−	0.770038i	0.347873	−	0.937542i	$-0.386904\pi$
$757$	36.6962	−	21.1865i	1.33374	−	0.770038i	0.985871	+	0.167504i	$0.0535707\pi$
$758$	7.39230	+	4.26795i	0.268501	+	0.155019i
$759$	8.19615	+	4.73205i	0.297501	+	0.171763i
$760$	0.882686	−	0.509619i	0.0320184	−	0.0184858i
$761$	1.83975	+	3.18653i	0.0666907	+	0.115512i	0.897443	−	0.441131i	$-0.145423\pi$
$761$	1.83975	+	3.18653i	0.0666907	+	0.115512i	−0.830752	+	0.556643i	$0.812089\pi$
$762$	−28.8564	+	16.6603i	−1.04536	+	0.603537i
$763$		−	23.5692i		−	0.853263i
$764$	5.36603	+	3.09808i	0.194136	+	0.112084i
$765$	−2.23205	−	3.86603i	−0.0807000	−	0.139776i
$766$	15.8564			0.572915
$767$	−46.6410			−1.68411
$768$	−23.2224	−	40.2224i	−0.837967	−	1.45140i
$769$			20.5359i			0.740543i	0.928923	+	0.370272i	$0.120735\pi$
$769$			20.5359i			0.740543i	−0.928923	+	0.370272i	$0.879265\pi$
$770$	−2.19615	+	3.80385i	−0.0791438	+	0.137081i
$771$		−	53.5167i		−	1.92736i
$772$	12.6962	+	7.33013i	0.456945	+	0.263817i
$773$	24.0167	−	41.5981i	0.863819	−	1.49618i	−0.00439560	−	0.999990i	$-0.501399\pi$
$773$	24.0167	−	41.5981i	0.863819	−	1.49618i	0.868215	−	0.496188i	$-0.165267\pi$
$774$	−7.73205	+	13.3923i	−0.277923	+	0.481376i
$775$	−34.9808	+	20.1962i	−1.25655	+	0.725467i
$776$	−12.8038			−0.459631
$777$	−47.3205	+	32.7846i	−1.69761	+	1.17614i
$778$	−31.1962			−1.11844
$779$	−3.29423	+	1.90192i	−0.118028	+	0.0681435i
$780$	−1.26795	+	2.19615i	−0.0453999	+	0.0786349i
$781$	14.1962	−	24.5885i	0.507978	−	0.879844i
$782$	2.36603	+	1.36603i	0.0846089	+	0.0488490i
$783$		−	1.07180i		−	0.0383029i
$784$	2.50000	−	4.33013i	0.0892857	−	0.154647i
$785$			3.83717i			0.136954i
$786$	−14.4641	−	25.0526i	−0.515917	−	0.893595i
$787$	0.392305			0.0139842			0.00699208	−	0.999976i	$-0.497774\pi$
$787$	0.392305			0.0139842			0.00699208	+	0.999976i	$0.497774\pi$
$788$	27.9282			0.994901
$789$	−10.3923	−	18.0000i	−0.369976	−	0.640817i
$790$	−0.882686	−	0.509619i	−0.0314046	−	0.0181314i
$791$		−	15.7128i		−	0.558683i
$792$	54.8827	−	31.6865i	1.95017	−	1.12593i
$793$	7.39230	+	12.8038i	0.262508	+	0.454678i
$794$	18.4019	−	10.6244i	0.653060	−	0.377044i
$795$	1.60770	+	0.928203i	0.0570191	+	0.0329200i
$796$	9.58846	+	5.53590i	0.339854	+	0.196215i
$797$	−6.92820	+	4.00000i	−0.245410	+	0.141687i	−0.617661	−	0.786445i	$-0.711919\pi$
$797$	−6.92820	+	4.00000i	−0.245410	+	0.141687i	0.372251	+	0.928132i	$0.378586\pi$
$798$	−6.00000	−	10.3923i	−0.212398	−	0.367884i
$799$	−7.09808	+	4.09808i	−0.251112	+	0.144980i
$800$		−	24.6410i		−	0.871191i
$801$	−35.5526	−	20.5263i	−1.25619	−	0.725260i
$802$	2.80385	+	4.85641i	0.0990073	+	0.171486i
$803$		0			0
$804$	19.8564			0.700281
$805$	0.339746	+	0.588457i	0.0119745	+	0.0207404i
$806$			28.3923i			1.00008i
$807$	19.8564	−	34.3923i	0.698979	−	1.21067i
$808$			27.0000i			0.949857i
$809$	29.3205	+	16.9282i	1.03085	+	0.595164i	0.917229	−	0.398360i	$-0.130420\pi$
$809$	29.3205	+	16.9282i	1.03085	+	0.595164i	0.113625	+	0.993524i	$0.463754\pi$
$810$	−0.330127	+	0.571797i	−0.0115995	+	0.0200909i
$811$	−9.12436	+	15.8038i	−0.320399	+	0.554948i	−0.980570	−	0.196167i	$-0.937150\pi$
$811$	−9.12436	+	15.8038i	−0.320399	+	0.554948i	0.660171	+	0.751115i	$0.270484\pi$
$812$	0.803848	−	0.464102i	0.0282095	−	0.0162868i
$813$	31.8564			1.11725
$814$	16.3923	+	23.6603i	0.574550	+	0.829291i
$815$	6.00000			0.210171
$816$	8.83013	−	5.09808i	0.309116	−	0.178468i
$817$	−2.19615	+	3.80385i	−0.0768336	+	0.133080i
$818$	−4.33013	+	7.50000i	−0.151399	+	0.262231i
$819$	46.3923	+	26.7846i	1.62108	+	0.935930i
$820$		−	0.803848i		−	0.0280716i
$821$	−24.5885	+	42.5885i	−0.858143	+	1.48635i	0.0155551	+	0.999879i	$0.495048\pi$
$821$	−24.5885	+	42.5885i	−0.858143	+	1.48635i	−0.873698	+	0.486468i	$0.838285\pi$
$822$		−	17.6603i		−	0.615972i
$823$	1.50962	+	2.61474i	0.0526220	+	0.0911440i	0.891137	−	0.453735i	$-0.149909\pi$
$823$	1.50962	+	2.61474i	0.0526220	+	0.0911440i	−0.838515	+	0.544879i	$0.816575\pi$
$824$	−38.7846			−1.35113
$825$	63.7128			2.21820
$826$	23.3205	+	40.3923i	0.811424	+	1.40543i
$827$	−19.8564	−	11.4641i	−0.690475	−	0.398646i	0.113315	−	0.993559i	$-0.463853\pi$
$827$	−19.8564	−	11.4641i	−0.690475	−	0.398646i	−0.803790	+	0.594913i	$0.797186\pi$
$828$		−	3.26795i		−	0.113569i
$829$	−38.5692	+	22.2679i	−1.33956	+	0.773398i	−0.986743	−	0.162293i	$-0.948111\pi$
$829$	−38.5692	+	22.2679i	−1.33956	+	0.773398i	−0.352822	+	0.935691i	$0.614778\pi$
$830$	−1.09808	−	1.90192i	−0.0381148	−	0.0660167i
$831$	−24.2942	+	14.0263i	−0.842757	+	0.486566i
$832$	−21.0000	−	12.1244i	−0.728044	−	0.420336i
$833$	−16.1603	−	9.33013i	−0.559920	−	0.323270i
$834$	29.7846	−	17.1962i	1.03136	−	0.595454i
$835$	1.46410	+	2.53590i	0.0506673	+	0.0877584i
$836$	5.19615	−	3.00000i	0.179713	−	0.103757i
$837$			32.7846i			1.13320i
$838$	15.0000	+	8.66025i	0.518166	+	0.299164i
$839$	14.8301	+	25.6865i	0.511993	+	0.886798i	0.999903	+	0.0139040i	$0.00442591\pi$
$839$	14.8301	+	25.6865i	0.511993	+	0.886798i	−0.487910	+	0.872894i	$0.662241\pi$
$840$	7.60770			0.262490
$841$	28.9282			0.997524
$842$	−8.13397	−	14.0885i	−0.280315	−	0.485520i
$843$		−	90.6936i		−	3.12365i
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$		−	0.267949i		−	0.00921773i
$846$	−8.49038	−	4.90192i	−0.291905	−	0.168532i
$847$	−19.7321	+	34.1769i	−0.678001	+	1.17433i
$848$	−1.26795	+	2.19615i	−0.0435416	+	0.0754162i
$849$	24.5885	−	14.1962i	0.843874	−	0.487211i
$850$	18.3923			0.630851
$851$	4.43782	−	0.366025i	0.152127	−	0.0125472i
$852$	−16.3923			−0.561591
$853$	36.4808	−	21.0622i	1.24908	−	0.721155i	0.278152	−	0.960537i	$-0.410278\pi$
$853$	36.4808	−	21.0622i	1.24908	−	0.721155i	0.970926	+	0.239382i	$0.0769448\pi$
$854$	7.39230	−	12.8038i	0.252959	−	0.438139i
$855$	0.758330	−	1.31347i	0.0259343	−	0.0449196i
$856$	−33.5885	−	19.3923i	−1.14803	−	0.662815i
$857$			23.7321i			0.810671i	0.914168	+	0.405336i	$0.132845\pi$
$857$			23.7321i			0.810671i	−0.914168	+	0.405336i	$0.867155\pi$
$858$	22.3923	−	38.7846i	0.764461	−	1.32408i
$859$		−	8.53590i		−	0.291241i	−0.989341	−	0.145621i	$-0.953482\pi$
$859$		−	8.53590i		−	0.291241i	0.989341	−	0.145621i	$-0.0465179\pi$
$860$	−0.464102	−	0.803848i	−0.0158257	−	0.0274110i
$861$	−28.3923			−0.967607
$862$	11.5167			0.392259
$863$	−19.2679	−	33.3731i	−0.655889	−	1.13603i	−0.981670	−	0.190587i	$-0.938961\pi$
$863$	−19.2679	−	33.3731i	−0.655889	−	1.13603i	0.325782	−	0.945445i	$-0.394373\pi$
$864$	−17.3205	−	10.0000i	−0.589256	−	0.340207i
$865$		−	2.66025i		−	0.0904514i
$866$	−23.3827	+	13.5000i	−0.794576	+	0.458749i
$867$	4.19615	+	7.26795i	0.142509	+	0.246832i
$868$	−24.5885	+	14.1962i	−0.834587	+	0.481849i
$869$	−15.5885	−	9.00000i	−0.528802	−	0.305304i
$870$	−0.169873	−	0.0980762i	−0.00575923	−	0.00332509i
$871$	21.8038	−	12.5885i	0.738795	−	0.426544i
$872$	10.2058	+	17.6769i	0.345611	+	0.598616i
$873$	−16.5000	+	9.52628i	−0.558440	+	0.322416i
$874$			0.928203i			0.0313969i
$875$	7.98076	+	4.60770i	0.269799	+	0.155769i
$876$		0			0
$877$	5.78461			0.195332			0.0976662	−	0.995219i	$-0.468862\pi$
$877$	5.78461			0.195332			0.0976662	+	0.995219i	$0.468862\pi$
$878$	−14.5359			−0.490563
$879$	39.4186	+	68.2750i	1.32956	+	2.30286i
$880$		−	1.26795i		−	0.0427426i
$881$	−16.1603	+	27.9904i	−0.544453	+	0.943020i	0.454188	+	0.890906i	$0.349929\pi$
$881$	−16.1603	+	27.9904i	−0.544453	+	0.943020i	−0.998641	+	0.0521142i	$0.983404\pi$
$882$		−	22.3205i		−	0.751571i
$883$	−30.8827	−	17.8301i	−1.03929	−	0.600032i	−0.119654	−	0.992816i	$-0.538179\pi$
$883$	−30.8827	−	17.8301i	−1.03929	−	0.600032i	−0.919631	+	0.392784i	$0.871512\pi$
$884$	−6.46410	+	11.1962i	−0.217411	+	0.376567i
$885$	−4.92820	+	8.53590i	−0.165660	+	0.286931i
$886$	−28.9808	+	16.7321i	−0.973628	+	0.562124i
$887$	28.9808			0.973079			0.486539	−	0.873659i	$-0.338259\pi$
$887$	28.9808			0.973079			0.486539	+	0.873659i	$0.338259\pi$
$888$	21.2942	−	45.0788i	0.714588	−	1.51275i
$889$	−42.2487			−1.41698
$890$	−2.13397	+	1.23205i	−0.0715310	+	0.0412984i
$891$	−5.83013	+	10.0981i	−0.195317	+	0.338298i
$892$	−2.29423	+	3.97372i	−0.0768165	+	0.133050i
$893$	−2.41154	−	1.39230i	−0.0806992	−	0.0465917i
$894$			15.1244i			0.505834i
$895$	−0.196152	+	0.339746i	−0.00655665	+	0.0113565i
$896$		−	10.3923i		−	0.347183i
$897$	−3.46410	−	6.00000i	−0.115663	−	0.200334i
$898$	32.2487			1.07615
$899$	2.19615			0.0732458
$900$	−11.0000	−	19.0526i	−0.366667	−	0.635085i
$901$	8.19615	+	4.73205i	0.273053	+	0.157647i
$902$			14.1962i			0.472680i
$903$	−28.3923	+	16.3923i	−0.944837	+	0.545502i
$904$	6.80385	+	11.7846i	0.226293	+	0.391950i
$905$	−2.30385	+	1.33013i	−0.0765825	+	0.0442149i
$906$	−39.2487	−	22.6603i	−1.30395	−	0.752837i
$907$	1.09808	+	0.633975i	0.0364610	+	0.0210508i	0.518120	−	0.855308i	$-0.326632\pi$
$907$	1.09808	+	0.633975i	0.0364610	+	0.0210508i	−0.481659	+	0.876359i	$0.659965\pi$
$908$	−20.0263	+	11.5622i	−0.664595	+	0.383704i
$909$	20.0885	+	34.7942i	0.666292	+	1.15405i
$910$	2.78461	−	1.60770i	0.0923089	−	0.0532946i
$911$		−	53.5167i		−	1.77309i	−0.462646	−	0.886543i	$-0.653100\pi$
$911$		−	53.5167i		−	1.77309i	0.462646	−	0.886543i	$-0.346900\pi$
$912$	3.00000	+	1.73205i	0.0993399	+	0.0573539i
$913$	−19.3923	−	33.5885i	−0.641792	−	1.11162i
$914$	36.1244			1.19489
$915$	3.12436			0.103288
$916$	−3.50000	−	6.06218i	−0.115643	−	0.200300i
$917$		−	36.6795i		−	1.21126i
$918$	7.46410	−	12.9282i	0.246352	−	0.426694i
$919$			4.05256i			0.133682i	0.997764	+	0.0668408i	$0.0212920\pi$
$919$			4.05256i			0.133682i	−0.997764	+	0.0668408i	$0.978708\pi$
$920$	−0.509619	−	0.294229i	−0.0168016	−	0.00970043i
$921$	−19.6603	+	34.0526i	−0.647827	+	1.12207i
$922$	8.26795	−	14.3205i	0.272290	−	0.471621i
$923$	−18.0000	+	10.3923i	−0.592477	+	0.342067i
$924$	44.7846			1.47331
$925$	24.6410	−	17.0718i	0.810192	−	0.561317i
$926$	15.4641			0.508182
$927$	−49.9808	+	28.8564i	−1.64158	+	0.947769i
$928$	−0.669873	+	1.16025i	−0.0219897	+	0.0380872i
$929$	15.2321	−	26.3827i	0.499747	−	0.865588i	−0.500253	−	0.865880i	$-0.666760\pi$
$929$	15.2321	−	26.3827i	0.499747	−	0.865588i	1.00000		0.000291680i	$9.28447e-5\pi$
$930$	5.19615	+	3.00000i	0.170389	+	0.0983739i
$931$		−	6.33975i		−	0.207777i
$932$	5.42820	−	9.40192i	0.177807	−	0.307970i
$933$			83.0333i			2.71839i
$934$	1.66025	+	2.87564i	0.0543252	+	0.0940940i
$935$	−4.73205			−0.154755
$936$	−46.3923			−1.51638
$937$	6.30385	+	10.9186i	0.205938	+	0.356695i	0.950431	−	0.310935i	$-0.100642\pi$
$937$	6.30385	+	10.9186i	0.205938	+	0.356695i	−0.744493	+	0.667630i	$0.767309\pi$
$938$	−21.8038	−	12.5885i	−0.711921	−	0.411028i
$939$			42.5885i			1.38982i
$940$	0.509619	−	0.294229i	0.0166219	−	0.00959668i
$941$	2.08846	+	3.61731i	0.0680818	+	0.117921i	0.898057	−	0.439879i	$-0.144979\pi$
$941$	2.08846	+	3.61731i	0.0680818	+	0.117921i	−0.829975	+	0.557800i	$0.811645\pi$
$942$	−33.8827	+	19.5622i	−1.10396	+	0.637370i
$943$	1.90192	+	1.09808i	0.0619352	+	0.0357583i
$944$	−11.6603	−	6.73205i	−0.379509	−	0.219110i
$945$	3.21539	−	1.85641i	0.104597	−	0.0603889i
$946$	8.19615	+	14.1962i	0.266480	+	0.461557i
$947$	−23.9090	+	13.8038i	−0.776937	+	0.448565i	−0.835344	−	0.549728i	$-0.814731\pi$
$947$	−23.9090	+	13.8038i	−0.776937	+	0.448565i	0.0584067	+	0.998293i	$0.481398\pi$
$948$			10.3923i			0.337526i
$949$		0			0
$950$	3.12436	+	5.41154i	0.101367	+	0.175574i
$951$	43.5167			1.41112
$952$	38.7846			1.25702
$953$	2.07180	+	3.58846i	0.0671121	+	0.116242i	0.897629	−	0.440752i	$-0.145288\pi$
$953$	2.07180	+	3.58846i	0.0671121	+	0.116242i	−0.830517	+	0.556993i	$0.811955\pi$
$954$			11.3205i			0.366515i
$955$	0.830127	−	1.43782i	0.0268623	−	0.0465268i
$956$			16.9282i			0.547497i
$957$	−3.00000	−	1.73205i	−0.0969762	−	0.0559893i
$958$	19.6603	−	34.0526i	0.635194	−	1.10019i
$959$	11.1962	−	19.3923i	0.361543	−	0.626210i
$960$	−4.43782	+	2.56218i	−0.143230	+	0.0826939i
$961$	−36.1769			−1.16700
$962$	−1.73205	−	21.0000i	−0.0558436	−	0.677067i
$963$	−57.7128			−1.85977
$964$	13.3923	−	7.73205i	0.431337	−	0.249033i
$965$	1.96410	−	3.40192i	0.0632267	−	0.109512i
$966$	−3.46410	+	6.00000i	−0.111456	+	0.193047i
$967$	28.3923	+	16.3923i	0.913035	+	0.527141i	0.881406	−	0.472359i	$-0.156597\pi$
$967$	28.3923	+	16.3923i	0.913035	+	0.527141i	0.0316286	+	0.999500i	$0.489931\pi$
$968$		−	34.1769i		−	1.09849i
$969$	6.46410	−	11.1962i	0.207657	−	0.359672i
$970$			1.14359i			0.0367186i
$971$	4.09808	+	7.09808i	0.131514	+	0.227788i	0.924260	−	0.381763i	$-0.124683\pi$
$971$	4.09808	+	7.09808i	0.131514	+	0.227788i	−0.792747	+	0.609551i	$0.791350\pi$
$972$	18.7321			0.600831
$973$	43.6077			1.39800
$974$	−16.2224	−	28.0981i	−0.519800	−	0.900320i
$975$	−40.3923	−	23.3205i	−1.29359	−	0.746854i
$976$			4.26795i			0.136614i
$977$	−14.0718	+	8.12436i	−0.450197	+	0.259921i	−0.707913	−	0.706299i	$-0.750363\pi$
$977$	−14.0718	+	8.12436i	−0.450197	+	0.259921i	0.257717	+	0.966221i	$0.417030\pi$
$978$	30.5885	+	52.9808i	0.978111	+	1.69414i
$979$	−37.6865	+	21.7583i	−1.20447	+	0.695399i
$980$	1.16025	+	0.669873i	0.0370630	+	0.0213983i
$981$	26.3038	+	15.1865i	0.839817	+	0.484869i
$982$	−27.0788	+	15.6340i	−0.864120	+	0.498900i
$983$	−28.5622	−	49.4711i	−0.910992	−	1.57788i	−0.812666	−	0.582730i	$-0.801984\pi$
$983$	−28.5622	−	49.4711i	−0.910992	−	1.57788i	−0.0983263	−	0.995154i	$-0.531349\pi$
$984$	21.2942	−	12.2942i	0.678835	−	0.391926i
$985$		−	7.48334i		−	0.238439i
$986$	−0.866025	−	0.500000i	−0.0275799	−	0.0159232i
$987$	−10.3923	−	18.0000i	−0.330791	−	0.572946i
$988$	−4.39230			−0.139738
$989$	2.53590			0.0806369
$990$	−2.83013	−	4.90192i	−0.0899473	−	0.155793i
$991$		−	46.3923i		−	1.47370i	−0.676056	−	0.736850i	$-0.736312\pi$
$991$		−	46.3923i		−	1.47370i	0.676056	−	0.736850i	$-0.263688\pi$
$992$	20.4904	−	35.4904i	0.650570	−	1.12682i
$993$		−	89.5692i		−	2.84239i
$994$	18.0000	+	10.3923i	0.570925	+	0.329624i
$995$	1.48334	−	2.56922i	0.0470250	−	0.0814497i
$996$	−11.1962	+	19.3923i	−0.354764	+	0.614469i
$997$	17.7846	−	10.2679i	0.563244	−	0.325189i	−0.191202	−	0.981551i	$-0.561239\pi$
$997$	17.7846	−	10.2679i	0.563244	−	0.325189i	0.754447	+	0.656361i	$0.227905\pi$
$998$	−12.5885			−0.398481
$999$	−2.00000	−	24.2487i	−0.0632772	−	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.e.a.11.1	✓	4
3.2	odd	2		333.2.s.b.307.2		4
4.3	odd	2		592.2.w.c.529.1		4
5.2	odd	4		925.2.m.a.899.1		4
5.3	odd	4		925.2.m.b.899.2		4
5.4	even	2		925.2.n.a.751.2		4
37.8	odd	12		1369.2.a.g.1.2		2
37.11	even	6		1369.2.b.d.1368.3		4
37.26	even	3		1369.2.b.d.1368.1		4
37.27	even	6	inner	37.2.e.a.27.1	yes	4
37.29	odd	12		1369.2.a.h.1.2		2
111.101	odd	6		333.2.s.b.64.2		4
148.27	odd	6		592.2.w.c.545.1		4
185.27	odd	12		925.2.m.b.249.2		4
185.64	even	6		925.2.n.a.101.2		4
185.138	odd	12		925.2.m.a.249.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.e.a.11.1	✓	4	1.1	even	1	trivial
37.2.e.a.27.1	yes	4	37.27	even	6	inner
333.2.s.b.64.2		4	111.101	odd	6
333.2.s.b.307.2		4	3.2	odd	2
592.2.w.c.529.1		4	4.3	odd	2
592.2.w.c.545.1		4	148.27	odd	6
925.2.m.a.249.1		4	185.138	odd	12
925.2.m.a.899.1		4	5.2	odd	4
925.2.m.b.249.2		4	185.27	odd	12
925.2.m.b.899.2		4	5.3	odd	4
925.2.n.a.101.2		4	185.64	even	6
925.2.n.a.751.2		4	5.4	even	2
1369.2.a.g.1.2		2	37.8	odd	12
1369.2.a.h.1.2		2	37.29	odd	12
1369.2.b.d.1368.1		4	37.26	even	3
1369.2.b.d.1368.3		4	37.11	even	6

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.232051 + 0.133975i) q^{5} +2.73205i q^{6} +(-1.73205 + 3.00000i) q^{7} -3.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.232051 + 0.133975i) q^{5} +2.73205i q^{6} +(-1.73205 + 3.00000i) q^{7} -3.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} -0.267949 q^{10} -4.73205 q^{11} +(1.36603 + 2.36603i) q^{12} +(3.00000 + 1.73205i) q^{13} -3.46410i q^{14} +(0.633975 - 0.366025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.23205 - 1.86603i) q^{17} +(3.86603 + 2.23205i) q^{18} +(1.09808 + 0.633975i) q^{19} +(-0.232051 + 0.133975i) q^{20} +(4.73205 + 8.19615i) q^{21} +(4.09808 - 2.36603i) q^{22} -0.732051i q^{23} +(-7.09808 - 4.09808i) q^{24} +(-2.46410 - 4.26795i) q^{25} -3.46410 q^{26} -4.00000 q^{27} +(-1.73205 - 3.00000i) q^{28} +0.267949i q^{29} +(-0.366025 + 0.633975i) q^{30} -8.19615i q^{31} +(4.33013 + 2.50000i) q^{32} +(-6.46410 + 11.1962i) q^{33} +(-1.86603 + 3.23205i) q^{34} +(-0.803848 + 0.464102i) q^{35} +4.46410 q^{36} +(0.500000 + 6.06218i) q^{37} -1.26795 q^{38} +(8.19615 - 4.73205i) q^{39} +(0.401924 - 0.696152i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-8.19615 - 4.73205i) q^{42} +3.46410i q^{43} +(2.36603 - 4.09808i) q^{44} -1.19615i q^{45} +(0.366025 + 0.633975i) q^{46} -2.19615 q^{47} +2.73205 q^{48} +(-2.50000 - 4.33013i) q^{49} +(4.26795 + 2.46410i) q^{50} -10.1962i q^{51} +(-3.00000 + 1.73205i) q^{52} +(1.26795 + 2.19615i) q^{53} +(3.46410 - 2.00000i) q^{54} +(-1.09808 - 0.633975i) q^{55} +(9.00000 + 5.19615i) q^{56} +(3.00000 - 1.73205i) q^{57} +(-0.133975 - 0.232051i) q^{58} +(-11.6603 + 6.73205i) q^{59} +0.732051i q^{60} +(3.69615 + 2.13397i) q^{61} +(4.09808 + 7.09808i) q^{62} +15.4641 q^{63} -7.00000 q^{64} +(0.464102 + 0.803848i) q^{65} -12.9282i q^{66} +(3.63397 - 6.29423i) q^{67} +3.73205i q^{68} +(-1.73205 - 1.00000i) q^{69} +(0.464102 - 0.803848i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(-11.5981 + 6.69615i) q^{72} +(-3.46410 - 5.00000i) q^{74} -13.4641 q^{75} +(-1.09808 + 0.633975i) q^{76} +(8.19615 - 14.1962i) q^{77} +(-4.73205 + 8.19615i) q^{78} +(3.29423 + 1.90192i) q^{79} +0.267949i q^{80} +(1.23205 - 2.13397i) q^{81} -3.00000i q^{82} +(4.09808 + 7.09808i) q^{83} -9.46410 q^{84} +1.00000 q^{85} +(-1.73205 - 3.00000i) q^{86} +(0.633975 + 0.366025i) q^{87} +14.1962i q^{88} +(7.96410 - 4.59808i) q^{89} +(0.598076 + 1.03590i) q^{90} +(-10.3923 + 6.00000i) q^{91} +(0.633975 + 0.366025i) q^{92} +(-19.3923 - 11.1962i) q^{93} +(1.90192 - 1.09808i) q^{94} +(0.169873 + 0.294229i) q^{95} +(11.8301 - 6.83013i) q^{96} -4.26795i q^{97} +(4.33013 + 2.50000i) q^{98} +(10.5622 + 18.2942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{9} - 8 q^{10} - 12 q^{11} + 2 q^{12} + 12 q^{13} + 6 q^{15} + 2 q^{16} + 6 q^{17} + 12 q^{18} - 6 q^{19} + 6 q^{20} + 12 q^{21} + 6 q^{22} - 18 q^{24} + 4 q^{25} - 16 q^{27} + 2 q^{30} - 12 q^{33} - 4 q^{34} - 24 q^{35} + 4 q^{36} + 2 q^{37} - 12 q^{38} + 12 q^{39} + 12 q^{40} - 6 q^{41} - 12 q^{42} + 6 q^{44} - 2 q^{46} + 12 q^{47} + 4 q^{48} - 10 q^{49} + 24 q^{50} - 12 q^{52} + 12 q^{53} + 6 q^{55} + 36 q^{56} + 12 q^{57} - 4 q^{58} - 12 q^{59} - 6 q^{61} + 6 q^{62} + 48 q^{63} - 28 q^{64} - 12 q^{65} + 18 q^{67} - 12 q^{70} - 12 q^{71} - 36 q^{72} - 40 q^{75} + 6 q^{76} + 12 q^{77} - 12 q^{78} - 18 q^{79} - 2 q^{81} + 6 q^{83} - 24 q^{84} + 4 q^{85} + 6 q^{87} + 18 q^{89} - 8 q^{90} + 6 q^{92} - 36 q^{93} + 18 q^{94} + 18 q^{95} + 30 q^{96} + 18 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^9 - 8 * q^10 - 12 * q^11 + 2 * q^12 + 12 * q^13 + 6 * q^15 + 2 * q^16 + 6 * q^17 + 12 * q^18 - 6 * q^19 + 6 * q^20 + 12 * q^21 + 6 * q^22 - 18 * q^24 + 4 * q^25 - 16 * q^27 + 2 * q^30 - 12 * q^33 - 4 * q^34 - 24 * q^35 + 4 * q^36 + 2 * q^37 - 12 * q^38 + 12 * q^39 + 12 * q^40 - 6 * q^41 - 12 * q^42 + 6 * q^44 - 2 * q^46 + 12 * q^47 + 4 * q^48 - 10 * q^49 + 24 * q^50 - 12 * q^52 + 12 * q^53 + 6 * q^55 + 36 * q^56 + 12 * q^57 - 4 * q^58 - 12 * q^59 - 6 * q^61 + 6 * q^62 + 48 * q^63 - 28 * q^64 - 12 * q^65 + 18 * q^67 - 12 * q^70 - 12 * q^71 - 36 * q^72 - 40 * q^75 + 6 * q^76 + 12 * q^77 - 12 * q^78 - 18 * q^79 - 2 * q^81 + 6 * q^83 - 24 * q^84 + 4 * q^85 + 6 * q^87 + 18 * q^89 - 8 * q^90 + 6 * q^92 - 36 * q^93 + 18 * q^94 + 18 * q^95 + 30 * q^96 + 18 * q^99

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