LMFDB - Embedded newform 37.2.e.a.11.2

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			11.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	37.11
Dual form			37.2.e.a.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-3.23205 - 1.86603i) q^{5} +0.732051i q^{6} +(1.73205 - 3.00000i) q^{7} +3.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-3.23205 - 1.86603i) q^{5} +0.732051i q^{6} +(1.73205 - 3.00000i) q^{7} +3.00000i q^{8} +(1.23205 + 2.13397i) q^{9} -3.73205 q^{10} -1.26795 q^{11} +(-0.366025 - 0.633975i) q^{12} +(3.00000 + 1.73205i) q^{13} -3.46410i q^{14} +(2.36603 - 1.36603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.232051 + 0.133975i) q^{17} +(2.13397 + 1.23205i) q^{18} +(-4.09808 - 2.36603i) q^{19} +(3.23205 - 1.86603i) q^{20} +(1.26795 + 2.19615i) q^{21} +(-1.09808 + 0.633975i) q^{22} -2.73205i q^{23} +(-1.90192 - 1.09808i) q^{24} +(4.46410 + 7.73205i) q^{25} +3.46410 q^{26} -4.00000 q^{27} +(1.73205 + 3.00000i) q^{28} -3.73205i q^{29} +(1.36603 - 2.36603i) q^{30} -2.19615i q^{31} +(-4.33013 - 2.50000i) q^{32} +(0.464102 - 0.803848i) q^{33} +(-0.133975 + 0.232051i) q^{34} +(-11.1962 + 6.46410i) q^{35} -2.46410 q^{36} +(0.500000 + 6.06218i) q^{37} -4.73205 q^{38} +(-2.19615 + 1.26795i) q^{39} +(5.59808 - 9.69615i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(2.19615 + 1.26795i) q^{42} +3.46410i q^{43} +(0.633975 - 1.09808i) q^{44} -9.19615i q^{45} +(-1.36603 - 2.36603i) q^{46} +8.19615 q^{47} -0.732051 q^{48} +(-2.50000 - 4.33013i) q^{49} +(7.73205 + 4.46410i) q^{50} -0.196152i q^{51} +(-3.00000 + 1.73205i) q^{52} +(4.73205 + 8.19615i) q^{53} +(-3.46410 + 2.00000i) q^{54} +(4.09808 + 2.36603i) q^{55} +(9.00000 + 5.19615i) q^{56} +(3.00000 - 1.73205i) q^{57} +(-1.86603 - 3.23205i) q^{58} +(5.66025 - 3.26795i) q^{59} +2.73205i q^{60} +(-6.69615 - 3.86603i) q^{61} +(-1.09808 - 1.90192i) q^{62} +8.53590 q^{63} -7.00000 q^{64} +(-6.46410 - 11.1962i) q^{65} -0.928203i q^{66} +(5.36603 - 9.29423i) q^{67} -0.267949i q^{68} +(1.73205 + 1.00000i) q^{69} +(-6.46410 + 11.1962i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(-6.40192 + 3.69615i) q^{72} +(3.46410 + 5.00000i) q^{74} -6.53590 q^{75} +(4.09808 - 2.36603i) q^{76} +(-2.19615 + 3.80385i) q^{77} +(-1.26795 + 2.19615i) q^{78} +(-12.2942 - 7.09808i) q^{79} -3.73205i q^{80} +(-2.23205 + 3.86603i) q^{81} +3.00000i q^{82} +(-1.09808 - 1.90192i) q^{83} -2.53590 q^{84} +1.00000 q^{85} +(1.73205 + 3.00000i) q^{86} +(2.36603 + 1.36603i) q^{87} -3.80385i q^{88} +(1.03590 - 0.598076i) q^{89} +(-4.59808 - 7.96410i) q^{90} +(10.3923 - 6.00000i) q^{91} +(2.36603 + 1.36603i) q^{92} +(1.39230 + 0.803848i) q^{93} +(7.09808 - 4.09808i) q^{94} +(8.83013 + 15.2942i) q^{95} +(3.16987 - 1.83013i) q^{96} +7.73205i q^{97} +(-4.33013 - 2.50000i) q^{98} +(-1.56218 - 2.70577i) 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	−0.161521	−	0.986869i	$-0.551640\pi$
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	0.773893	+	0.633316i	$0.218307\pi$
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	−0.952129	−	0.305695i	$-0.901111\pi$
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	0.740805	+	0.671721i	$0.234444\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.23205	−	1.86603i	−1.44542	−	0.834512i	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−3.23205	−	1.86603i	−1.44542	−	0.834512i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$			0.732051i			0.298858i
$7$	1.73205	−	3.00000i	0.654654	−	1.13389i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	1.73205	−	3.00000i	0.654654	−	1.13389i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$			3.00000i			1.06066i
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$	−3.73205			−1.18018
$11$	−1.26795			−0.382301			−0.191151	−	0.981561i	$-0.561222\pi$
$11$	−1.26795			−0.382301			−0.191151	+	0.981561i	$0.561222\pi$
$12$	−0.366025	−	0.633975i	−0.105662	−	0.183013i
$13$	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
$15$	2.36603	−	1.36603i	0.610905	−	0.352706i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.232051	+	0.133975i	−0.0562806	+	0.0324936i	−0.527876	−	0.849321i	$-0.677012\pi$
$17$	−0.232051	+	0.133975i	−0.0562806	+	0.0324936i	0.471596	+	0.881815i	$0.343678\pi$
$18$	2.13397	+	1.23205i	0.502983	+	0.290397i
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.0501517	−	0.998742i	$-0.515970\pi$
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.890011	+	0.455938i	$0.849304\pi$
$20$	3.23205	−	1.86603i	0.722709	−	0.417256i
$21$	1.26795	+	2.19615i	0.276689	+	0.479240i
$22$	−1.09808	+	0.633975i	−0.234111	+	0.135164i
$23$		−	2.73205i		−	0.569672i	−0.958576	−	0.284836i	$-0.908061\pi$
$23$		−	2.73205i		−	0.569672i	0.958576	−	0.284836i	$-0.0919391\pi$
$24$	−1.90192	−	1.09808i	−0.388229	−	0.224144i
$25$	4.46410	+	7.73205i	0.892820	+	1.54641i
$26$	3.46410			0.679366
$27$	−4.00000			−0.769800
$28$	1.73205	+	3.00000i	0.327327	+	0.566947i
$29$		−	3.73205i		−	0.693024i	−0.938045	−	0.346512i	$-0.887366\pi$
$29$		−	3.73205i		−	0.693024i	0.938045	−	0.346512i	$-0.112634\pi$
$30$	1.36603	−	2.36603i	0.249401	−	0.431975i
$31$		−	2.19615i		−	0.394441i	−0.980359	−	0.197220i	$-0.936809\pi$
$31$		−	2.19615i		−	0.394441i	0.980359	−	0.197220i	$-0.0631914\pi$
$32$	−4.33013	−	2.50000i	−0.765466	−	0.441942i
$33$	0.464102	−	0.803848i	0.0807897	−	0.139932i
$34$	−0.133975	+	0.232051i	−0.0229765	+	0.0397964i
$35$	−11.1962	+	6.46410i	−1.89250	+	1.09263i
$36$	−2.46410			−0.410684
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$38$	−4.73205			−0.767640
$39$	−2.19615	+	1.26795i	−0.351666	+	0.203034i
$40$	5.59808	−	9.69615i	0.885134	−	1.53310i
$41$	−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	$0.241934\pi$
$42$	2.19615	+	1.26795i	0.338874	+	0.195649i
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$	0.633975	−	1.09808i	0.0955753	−	0.165541i
$45$		−	9.19615i		−	1.37088i
$46$	−1.36603	−	2.36603i	−0.201409	−	0.348851i
$47$	8.19615			1.19553			0.597766	−	0.801671i	$-0.296055\pi$
$47$	8.19615			1.19553			0.597766	+	0.801671i	$0.296055\pi$
$48$	−0.732051			−0.105662
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$	7.73205	+	4.46410i	1.09348	+	0.631319i
$51$		−	0.196152i		−	0.0274668i
$52$	−3.00000	+	1.73205i	−0.416025	+	0.240192i
$53$	4.73205	+	8.19615i	0.649997	+	1.12583i	0.983123	+	0.182946i	$0.0585633\pi$
$53$	4.73205	+	8.19615i	0.649997	+	1.12583i	−0.333126	+	0.942882i	$0.608103\pi$
$54$	−3.46410	+	2.00000i	−0.471405	+	0.272166i
$55$	4.09808	+	2.36603i	0.552584	+	0.319035i
$56$	9.00000	+	5.19615i	1.20268	+	0.694365i
$57$	3.00000	−	1.73205i	0.397360	−	0.229416i
$58$	−1.86603	−	3.23205i	−0.245021	−	0.424389i
$59$	5.66025	−	3.26795i	0.736902	−	0.425451i	−0.0840396	−	0.996462i	$-0.526782\pi$
$59$	5.66025	−	3.26795i	0.736902	−	0.425451i	0.820942	+	0.571012i	$0.193449\pi$
$60$			2.73205i			0.352706i
$61$	−6.69615	−	3.86603i	−0.857354	−	0.494994i	0.00577101	−	0.999983i	$-0.498163\pi$
$61$	−6.69615	−	3.86603i	−0.857354	−	0.494994i	−0.863125	+	0.504990i	$0.831496\pi$
$62$	−1.09808	−	1.90192i	−0.139456	−	0.241545i
$63$	8.53590			1.07542
$64$	−7.00000			−0.875000
$65$	−6.46410	−	11.1962i	−0.801773	−	1.38871i
$66$		−	0.928203i		−	0.114254i
$67$	5.36603	−	9.29423i	0.655564	−	1.13547i	−0.326188	−	0.945305i	$-0.605764\pi$
$67$	5.36603	−	9.29423i	0.655564	−	1.13547i	0.981752	−	0.190166i	$-0.0609025\pi$
$68$		−	0.267949i		−	0.0324936i
$69$	1.73205	+	1.00000i	0.208514	+	0.120386i
$70$	−6.46410	+	11.1962i	−0.772608	+	1.33820i
$71$	−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	$0.282538\pi$
$72$	−6.40192	+	3.69615i	−0.754474	+	0.435596i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	3.46410	+	5.00000i	0.402694	+	0.581238i
$75$	−6.53590			−0.754701
$76$	4.09808	−	2.36603i	0.470082	−	0.271402i
$77$	−2.19615	+	3.80385i	−0.250275	+	0.433489i
$78$	−1.26795	+	2.19615i	−0.143567	+	0.248665i
$79$	−12.2942	−	7.09808i	−1.38321	−	0.798596i	−0.390671	−	0.920531i	$-0.627757\pi$
$79$	−12.2942	−	7.09808i	−1.38321	−	0.798596i	−0.992538	+	0.121935i	$0.961090\pi$
$80$		−	3.73205i		−	0.417256i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$			3.00000i			0.331295i
$83$	−1.09808	−	1.90192i	−0.120530	−	0.208763i	0.799447	−	0.600737i	$-0.205126\pi$
$83$	−1.09808	−	1.90192i	−0.120530	−	0.208763i	−0.919977	+	0.391973i	$0.871793\pi$
$84$	−2.53590			−0.276689
$85$	1.00000			0.108465
$86$	1.73205	+	3.00000i	0.186772	+	0.323498i
$87$	2.36603	+	1.36603i	0.253665	+	0.146453i
$88$		−	3.80385i		−	0.405492i
$89$	1.03590	−	0.598076i	0.109805	−	0.0633960i	−0.444092	−	0.895981i	$-0.646474\pi$
$89$	1.03590	−	0.598076i	0.109805	−	0.0633960i	0.553897	+	0.832585i	$0.313140\pi$
$90$	−4.59808	−	7.96410i	−0.484680	−	0.839490i
$91$	10.3923	−	6.00000i	1.08941	−	0.628971i
$92$	2.36603	+	1.36603i	0.246675	+	0.142418i
$93$	1.39230	+	0.803848i	0.144375	+	0.0833551i
$94$	7.09808	−	4.09808i	0.732111	−	0.422684i
$95$	8.83013	+	15.2942i	0.905952	+	1.56915i
$96$	3.16987	−	1.83013i	0.323524	−	0.186787i
$97$			7.73205i			0.785071i	0.919737	+	0.392535i	$0.128402\pi$
$97$			7.73205i			0.785071i	−0.919737	+	0.392535i	$0.871598\pi$
$98$	−4.33013	−	2.50000i	−0.437409	−	0.252538i
$99$	−1.56218	−	2.70577i	−0.157005	−	0.271940i
$100$	−8.92820			−0.892820
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$	−0.0980762	−	0.169873i	−0.00971099	−	0.0168199i
$103$		−	0.928203i		−	0.0914586i	−0.998954	−	0.0457293i	$-0.985439\pi$
$103$		−	0.928203i		−	0.0914586i	0.998954	−	0.0457293i	$-0.0145612\pi$
$104$	−5.19615	+	9.00000i	−0.509525	+	0.882523i
$105$		−	9.46410i		−	0.923602i
$106$	8.19615	+	4.73205i	0.796081	+	0.459617i
$107$	−0.464102	+	0.803848i	−0.0448664	+	0.0777109i	−0.887587	−	0.460641i	$-0.847620\pi$
$107$	−0.464102	+	0.803848i	−0.0448664	+	0.0777109i	0.842720	+	0.538352i	$0.180953\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	14.8923	−	8.59808i	1.42642	−	0.823546i	0.429588	−	0.903025i	$-0.358659\pi$
$109$	14.8923	−	8.59808i	1.42642	−	0.823546i	0.996837	+	0.0794789i	$0.0253256\pi$
$110$	4.73205			0.451183
$111$	−4.02628	−	1.90192i	−0.382158	−	0.180523i
$112$	3.46410			0.327327
$113$	9.92820	−	5.73205i	0.933967	−	0.539226i	0.0459028	−	0.998946i	$-0.485384\pi$
$113$	9.92820	−	5.73205i	0.933967	−	0.539226i	0.888064	+	0.459720i	$0.152050\pi$
$114$	1.73205	−	3.00000i	0.162221	−	0.280976i
$115$	−5.09808	+	8.83013i	−0.475398	+	0.823414i
$116$	3.23205	+	1.86603i	0.300088	+	0.173256i
$117$			8.53590i			0.789144i
$118$	3.26795	−	5.66025i	0.300839	−	0.521069i
$119$			0.928203i			0.0850883i
$120$	4.09808	+	7.09808i	0.374101	+	0.647963i
$121$	−9.39230			−0.853846
$122$	−7.73205			−0.700027
$123$	−1.09808	−	1.90192i	−0.0990102	−	0.171491i
$124$	1.90192	+	1.09808i	0.170798	+	0.0986102i
$125$		−	14.6603i		−	1.31125i
$126$	7.39230	−	4.26795i	0.658559	−	0.380219i
$127$	0.901924	+	1.56218i	0.0800328	+	0.138621i	0.903264	−	0.429086i	$-0.141164\pi$
$127$	0.901924	+	1.56218i	0.0800328	+	0.138621i	−0.823231	+	0.567707i	$0.807831\pi$
$128$	2.59808	−	1.50000i	0.229640	−	0.132583i
$129$	−2.19615	−	1.26795i	−0.193360	−	0.111637i
$130$	−11.1962	−	6.46410i	−0.981968	−	0.566939i
$131$	−17.8301	+	10.2942i	−1.55783	+	0.899411i	−0.560361	+	0.828249i	$0.689337\pi$
$131$	−17.8301	+	10.2942i	−1.55783	+	0.899411i	−0.997465	+	0.0711622i	$0.977329\pi$
$132$	0.464102	+	0.803848i	0.0403949	+	0.0699660i
$133$	−14.1962	+	8.19615i	−1.23096	+	0.710697i
$134$		−	10.7321i		−	0.927108i
$135$	12.9282	+	7.46410i	1.11268	+	0.642408i
$136$	−0.401924	−	0.696152i	−0.0344647	−	0.0596946i
$137$	0.464102			0.0396509			0.0198254	−	0.999803i	$-0.493689\pi$
$137$	0.464102			0.0396509			0.0198254	+	0.999803i	$0.493689\pi$
$138$	2.00000			0.170251
$139$	9.29423	+	16.0981i	0.788326	+	1.36542i	0.926992	+	0.375082i	$0.122385\pi$
$139$	9.29423	+	16.0981i	0.788326	+	1.36542i	−0.138666	+	0.990339i	$0.544281\pi$
$140$		−	12.9282i		−	1.09263i
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$			6.00000i			0.503509i
$143$	−3.80385	−	2.19615i	−0.318094	−	0.183651i
$144$	−1.23205	+	2.13397i	−0.102671	+	0.177831i
$145$	−6.96410	+	12.0622i	−0.578337	+	1.00171i
$146$		0			0
$147$	3.66025			0.301893
$148$	−5.50000	−	2.59808i	−0.452097	−	0.213561i
$149$	12.4641			1.02110			0.510549	−	0.859848i	$-0.329442\pi$
$149$	12.4641			1.02110			0.510549	+	0.859848i	$0.329442\pi$
$150$	−5.66025	+	3.26795i	−0.462158	+	0.266827i
$151$	7.29423	−	12.6340i	0.593596	−	1.02814i	−0.400147	−	0.916451i	$-0.631041\pi$
$151$	7.29423	−	12.6340i	0.593596	−	1.02814i	0.993743	−	0.111688i	$-0.0356256\pi$
$152$	7.09808	−	12.2942i	0.575730	−	0.997194i
$153$	−0.571797	−	0.330127i	−0.0462270	−	0.0266892i
$154$			4.39230i			0.353942i
$155$	−4.09808	+	7.09808i	−0.329165	+	0.570131i
$156$		−	2.53590i		−	0.203034i
$157$	−10.1603	−	17.5981i	−0.810877	−	1.40448i	−0.912251	−	0.409631i	$-0.865657\pi$
$157$	−10.1603	−	17.5981i	−0.810877	−	1.40448i	0.101375	−	0.994848i	$-0.467676\pi$
$158$	−14.1962			−1.12939
$159$	−6.92820			−0.549442
$160$	9.33013	+	16.1603i	0.737611	+	1.27758i
$161$	−8.19615	−	4.73205i	−0.645947	−	0.372938i
$162$			4.46410i			0.350733i
$163$	−1.39230	+	0.803848i	−0.109054	+	0.0629622i	−0.553535	−	0.832826i	$-0.686721\pi$
$163$	−1.39230	+	0.803848i	−0.109054	+	0.0629622i	0.444481	+	0.895788i	$0.353388\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$	−3.00000	+	1.73205i	−0.233550	+	0.134840i
$166$	−1.90192	−	1.09808i	−0.147618	−	0.0852272i
$167$	2.53590	+	1.46410i	0.196234	+	0.113296i	0.594898	−	0.803802i	$-0.297193\pi$
$167$	2.53590	+	1.46410i	0.196234	+	0.113296i	−0.398664	+	0.917097i	$0.630526\pi$
$168$	−6.58846	+	3.80385i	−0.508311	+	0.293473i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.866025	−	0.500000i	0.0664211	−	0.0383482i
$171$		−	11.6603i		−	0.891682i
$172$	−3.00000	−	1.73205i	−0.228748	−	0.132068i
$173$	1.96410	+	3.40192i	0.149328	+	0.258643i	0.930979	−	0.365072i	$-0.118956\pi$
$173$	1.96410	+	3.40192i	0.149328	+	0.258643i	−0.781651	+	0.623716i	$0.785622\pi$
$174$	2.73205			0.207116
$175$	30.9282			2.33795
$176$	−0.633975	−	1.09808i	−0.0477876	−	0.0827706i
$177$			4.78461i			0.359633i
$178$	0.598076	−	1.03590i	0.0448277	−	0.0776439i
$179$			5.46410i			0.408406i	0.978929	+	0.204203i	$0.0654603\pi$
$179$			5.46410i			0.408406i	−0.978929	+	0.204203i	$0.934540\pi$
$180$	7.96410	+	4.59808i	0.593609	+	0.342720i
$181$	1.96410	−	3.40192i	0.145991	−	0.252863i	−0.783752	−	0.621074i	$-0.786696\pi$
$181$	1.96410	−	3.40192i	0.145991	−	0.252863i	0.929742	+	0.368211i	$0.120030\pi$
$182$	6.00000	−	10.3923i	0.444750	−	0.770329i
$183$	4.90192	−	2.83013i	0.362361	−	0.209209i
$184$	8.19615			0.604228
$185$	9.69615	−	20.5263i	0.712875	−	1.50912i
$186$	1.60770			0.117882
$187$	0.294229	−	0.169873i	0.0215161	−	0.0124223i
$188$	−4.09808	+	7.09808i	−0.298883	+	0.517680i
$189$	−6.92820	+	12.0000i	−0.503953	+	0.872872i
$190$	15.2942	+	8.83013i	1.10956	+	0.640605i
$191$		−	4.19615i		−	0.303623i	−0.988409	−	0.151811i	$-0.951489\pi$
$191$		−	4.19615i		−	0.303623i	0.988409	−	0.151811i	$-0.0485107\pi$
$192$	2.56218	−	4.43782i	0.184909	−	0.320272i
$193$		−	2.66025i		−	0.191489i	−0.995406	−	0.0957446i	$-0.969477\pi$
$193$		−	2.66025i		−	0.191489i	0.995406	−	0.0957446i	$-0.0305232\pi$
$194$	3.86603	+	6.69615i	0.277564	+	0.480756i
$195$	9.46410			0.677738
$196$	5.00000			0.357143
$197$	−7.03590	−	12.1865i	−0.501287	−	0.868255i	−0.999999	−	0.00148674i	$-0.999527\pi$
$197$	−7.03590	−	12.1865i	−0.501287	−	0.868255i	0.498712	−	0.866768i	$-0.333807\pi$
$198$	−2.70577	−	1.56218i	−0.192291	−	0.111019i
$199$			24.9282i			1.76711i	0.468324	+	0.883557i	$0.344858\pi$
$199$			24.9282i			1.76711i	−0.468324	+	0.883557i	$0.655142\pi$
$200$	−23.1962	+	13.3923i	−1.64022	+	0.946979i
$201$	3.92820	+	6.80385i	0.277074	+	0.479906i
$202$	−7.79423	+	4.50000i	−0.548400	+	0.316619i
$203$	−11.1962	−	6.46410i	−0.785816	−	0.453691i
$204$	0.169873	+	0.0980762i	0.0118935	+	0.00686671i
$205$	9.69615	−	5.59808i	0.677209	−	0.390987i
$206$	−0.464102	−	0.803848i	−0.0323355	−	0.0560067i
$207$	5.83013	−	3.36603i	0.405222	−	0.233955i
$208$			3.46410i			0.240192i
$209$	5.19615	+	3.00000i	0.359425	+	0.207514i
$210$	−4.73205	−	8.19615i	−0.326543	−	0.565588i
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	−9.46410			−0.649997
$213$	−2.19615	−	3.80385i	−0.150478	−	0.260635i
$214$			0.928203i			0.0634507i
$215$	6.46410	−	11.1962i	0.440848	−	0.763571i
$216$		−	12.0000i		−	0.816497i
$217$	−6.58846	−	3.80385i	−0.447254	−	0.258222i
$218$	8.59808	−	14.8923i	0.582335	−	1.00863i
$219$		0			0
$220$	−4.09808	+	2.36603i	−0.276292	+	0.159517i
$221$	−0.928203			−0.0624377
$222$	−4.43782	+	0.366025i	−0.297847	+	0.0245660i
$223$	−26.5885			−1.78049			−0.890247	−	0.455477i	$-0.849469\pi$
$223$	−26.5885			−1.78049			−0.890247	+	0.455477i	$0.849469\pi$
$224$	−15.0000	+	8.66025i	−1.00223	+	0.578638i
$225$	−11.0000	+	19.0526i	−0.733333	+	1.27017i
$226$	5.73205	−	9.92820i	0.381290	−	0.660414i
$227$	0.973721	+	0.562178i	0.0646281	+	0.0373131i	0.531966	−	0.846766i	$-0.321453\pi$
$227$	0.973721	+	0.562178i	0.0646281	+	0.0373131i	−0.467338	+	0.884079i	$0.654787\pi$
$228$			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	$0.240960\pi$
$230$			10.1962i			0.672314i
$231$	−1.60770	−	2.78461i	−0.105779	−	0.183214i
$232$	11.1962			0.735063
$233$	16.8564			1.10430			0.552150	−	0.833745i	$-0.313808\pi$
$233$	16.8564			1.10430			0.552150	+	0.833745i	$0.313808\pi$
$234$	4.26795	+	7.39230i	0.279005	+	0.483250i
$235$	−26.4904	−	15.2942i	−1.72804	−	0.997685i
$236$			6.53590i			0.425451i
$237$	9.00000	−	5.19615i	0.584613	−	0.337526i
$238$	0.464102	+	0.803848i	0.0300832	+	0.0521057i
$239$	−2.66025	+	1.53590i	−0.172078	+	0.0993490i	−0.583565	−	0.812066i	$-0.698343\pi$
$239$	−2.66025	+	1.53590i	−0.172078	+	0.0993490i	0.411488	+	0.911415i	$0.365009\pi$
$240$	2.36603	+	1.36603i	0.152726	+	0.0881766i
$241$	7.39230	+	4.26795i	0.476180	+	0.274923i	0.718823	−	0.695193i	$-0.244681\pi$
$241$	7.39230	+	4.26795i	0.476180	+	0.274923i	−0.242643	+	0.970116i	$0.578014\pi$
$242$	−8.13397	+	4.69615i	−0.522872	+	0.301880i
$243$	−7.63397	−	13.2224i	−0.489720	−	0.848219i
$244$	6.69615	−	3.86603i	0.428677	−	0.247497i
$245$			18.6603i			1.19216i
$246$	−1.90192	−	1.09808i	−0.121262	−	0.0700108i
$247$	−8.19615	−	14.1962i	−0.521509	−	0.903280i
$248$	6.58846			0.418367
$249$	1.60770			0.101884
$250$	−7.33013	−	12.6962i	−0.463598	−	0.802975i
$251$			29.7128i			1.87546i	0.347370	+	0.937728i	$0.387075\pi$
$251$			29.7128i			1.87546i	−0.347370	+	0.937728i	$0.612925\pi$
$252$	−4.26795	+	7.39230i	−0.268856	+	0.465671i
$253$			3.46410i			0.217786i
$254$	1.56218	+	0.901924i	0.0980198	+	0.0565917i
$255$	−0.366025	+	0.633975i	−0.0229214	+	0.0397010i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	10.0359	−	5.79423i	0.626022	−	0.361434i	−0.153188	−	0.988197i	$-0.548954\pi$
$257$	10.0359	−	5.79423i	0.626022	−	0.361434i	0.779210	+	0.626763i	$0.215621\pi$
$258$	−2.53590			−0.157878
$259$	19.0526	+	9.00000i	1.18387	+	0.559233i
$260$	12.9282			0.801773
$261$	7.96410	−	4.59808i	0.492966	−	0.284614i
$262$	−10.2942	+	17.8301i	−0.635980	+	1.10155i
$263$	14.1962	−	24.5885i	0.875372	−	1.51619i	0.0190066	−	0.999819i	$-0.493950\pi$
$263$	14.1962	−	24.5885i	0.875372	−	1.51619i	0.856366	−	0.516370i	$-0.172717\pi$
$264$	2.41154	+	1.39230i	0.148420	+	0.0856904i
$265$		−	35.3205i		−	2.16972i
$266$	−8.19615	+	14.1962i	−0.502538	+	0.870422i
$267$			0.875644i			0.0535886i
$268$	5.36603	+	9.29423i	0.327782	+	0.567735i
$269$	21.4641			1.30869			0.654345	−	0.756196i	$-0.272945\pi$
$269$	21.4641			1.30869			0.654345	+	0.756196i	$0.272945\pi$
$270$	14.9282			0.908502
$271$	−2.83013	−	4.90192i	−0.171918	−	0.297771i	0.767172	−	0.641441i	$-0.221663\pi$
$271$	−2.83013	−	4.90192i	−0.171918	−	0.297771i	−0.939090	+	0.343670i	$0.888330\pi$
$272$	−0.232051	−	0.133975i	−0.0140701	−	0.00812340i
$273$			8.78461i			0.531669i
$274$	0.401924	−	0.232051i	0.0242811	−	0.0140187i
$275$	−5.66025	−	9.80385i	−0.341326	−	0.591194i
$276$	−1.73205	+	1.00000i	−0.104257	+	0.0601929i
$277$	11.8923	+	6.86603i	0.714539	+	0.412539i	0.812740	−	0.582627i	$-0.197975\pi$
$277$	11.8923	+	6.86603i	0.714539	+	0.412539i	−0.0982002	+	0.995167i	$0.531309\pi$
$278$	16.0981	+	9.29423i	0.965498	+	0.557431i
$279$	4.68653	−	2.70577i	0.280575	−	0.161990i
$280$	−19.3923	−	33.5885i	−1.15891	−	2.00729i
$281$	−19.7487	+	11.4019i	−1.17811	+	0.680182i	−0.955576	−	0.294743i	$-0.904766\pi$
$281$	−19.7487	+	11.4019i	−1.17811	+	0.680182i	−0.222533	+	0.974925i	$0.571432\pi$
$282$			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
$285$	−12.9282			−0.765801
$286$	−4.39230			−0.259722
$287$	5.19615	+	9.00000i	0.306719	+	0.531253i
$288$		−	12.3205i		−	0.725993i
$289$	−8.46410	+	14.6603i	−0.497888	+	0.862368i
$290$			13.9282i			0.817892i
$291$	−4.90192	−	2.83013i	−0.287356	−	0.165905i
$292$		0			0
$293$	−0.571797	+	0.990381i	−0.0334047	+	0.0578587i	−0.882244	−	0.470792i	$-0.843968\pi$
$293$	−0.571797	+	0.990381i	−0.0334047	+	0.0578587i	0.848840	+	0.528650i	$0.177302\pi$
$294$	3.16987	−	1.83013i	0.184871	−	0.106735i
$295$	−24.3923			−1.42017
$296$	−18.1865	+	1.50000i	−1.05707	+	0.0871857i
$297$	5.07180			0.294295
$298$	10.7942	−	6.23205i	0.625293	−	0.361013i
$299$	4.73205	−	8.19615i	0.273662	−	0.473996i
$300$	3.26795	−	5.66025i	0.188675	−	0.326795i
$301$	10.3923	+	6.00000i	0.599002	+	0.345834i
$302$		−	14.5885i		−	0.839471i
$303$	3.29423	−	5.70577i	0.189248	−	0.327788i
$304$		−	4.73205i		−	0.271402i
$305$	14.4282	+	24.9904i	0.826157	+	1.43095i
$306$	−0.660254			−0.0377442
$307$	6.39230			0.364828			0.182414	−	0.983222i	$-0.441609\pi$
$307$	6.39230			0.364828			0.182414	+	0.983222i	$0.441609\pi$
$308$	−2.19615	−	3.80385i	−0.125137	−	0.216744i
$309$	0.588457	+	0.339746i	0.0334762	+	0.0193275i
$310$			8.19615i			0.465510i
$311$	8.32051	−	4.80385i	0.471813	−	0.272401i	−0.245186	−	0.969476i	$-0.578849\pi$
$311$	8.32051	−	4.80385i	0.471813	−	0.272401i	0.716998	+	0.697075i	$0.245516\pi$
$312$	−3.80385	−	6.58846i	−0.215350	−	0.372998i
$313$	−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	$0.478552\pi$
$314$	−17.5981	−	10.1603i	−0.993117	−	0.573376i
$315$	−27.5885	−	15.9282i	−1.55443	−	0.897453i
$316$	12.2942	−	7.09808i	0.691604	−	0.399298i
$317$	1.03590	+	1.79423i	0.0581818	+	0.100774i	0.893649	−	0.448766i	$-0.148136\pi$
$317$	1.03590	+	1.79423i	0.0581818	+	0.100774i	−0.835467	+	0.549540i	$0.814803\pi$
$318$	−6.00000	+	3.46410i	−0.336463	+	0.194257i
$319$			4.73205i			0.264944i
$320$	22.6244	+	13.0622i	1.26474	+	0.730198i
$321$	−0.339746	−	0.588457i	−0.0189628	−	0.0328445i
$322$	−9.46410			−0.527414
$323$	1.26795			0.0705506
$324$	−2.23205	−	3.86603i	−0.124003	−	0.214779i
$325$			30.9282i			1.71559i
$326$	−0.803848	+	1.39230i	−0.0445210	+	0.0771126i
$327$			12.5885i			0.696143i
$328$	−7.79423	−	4.50000i	−0.430364	−	0.248471i
$329$	14.1962	−	24.5885i	0.782659	−	1.35561i
$330$	−1.73205	+	3.00000i	−0.0953463	+	0.165145i
$331$	7.60770	−	4.39230i	0.418157	−	0.241423i	−0.276132	−	0.961120i	$-0.589053\pi$
$331$	7.60770	−	4.39230i	0.418157	−	0.241423i	0.694288	+	0.719697i	$0.255719\pi$
$332$	2.19615			0.120530
$333$	−12.3205	+	8.53590i	−0.675160	+	0.467764i
$334$	2.92820			0.160224
$335$	−34.6865	+	20.0263i	−1.89513	+	1.09415i
$336$	−1.26795	+	2.19615i	−0.0691723	+	0.119810i
$337$	−4.30385	+	7.45448i	−0.234446	+	0.406072i	−0.959111	−	0.283029i	$-0.908661\pi$
$337$	−4.30385	+	7.45448i	−0.234446	+	0.406072i	0.724666	+	0.689100i	$0.241994\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$			8.39230i			0.455807i
$340$	−0.500000	+	0.866025i	−0.0271163	+	0.0469668i
$341$			2.78461i			0.150795i
$342$	−5.83013	−	10.0981i	−0.315257	−	0.546041i
$343$	6.92820			0.374088
$344$	−10.3923			−0.560316
$345$	−3.73205	−	6.46410i	−0.200927	−	0.348016i
$346$	3.40192	+	1.96410i	0.182889	+	0.105591i
$347$		−	9.26795i		−	0.497530i	−0.968564	−	0.248765i	$-0.919975\pi$
$347$		−	9.26795i		−	0.497530i	0.968564	−	0.248765i	$-0.0800246\pi$
$348$	−2.36603	+	1.36603i	−0.126832	+	0.0732266i
$349$	−10.9641	−	18.9904i	−0.586895	−	1.01653i	−0.994636	−	0.103434i	$-0.967017\pi$
$349$	−10.9641	−	18.9904i	−0.586895	−	1.01653i	0.407741	−	0.913097i	$-0.366316\pi$
$350$	26.7846	−	15.4641i	1.43170	−	0.826591i
$351$	−12.0000	−	6.92820i	−0.640513	−	0.369800i
$352$	5.49038	+	3.16987i	0.292638	+	0.168955i
$353$	−13.6244	+	7.86603i	−0.725151	+	0.418666i	−0.816646	−	0.577139i	$-0.804169\pi$
$353$	−13.6244	+	7.86603i	−0.725151	+	0.418666i	0.0914944	+	0.995806i	$0.470836\pi$
$354$	2.39230	+	4.14359i	0.127150	+	0.220230i
$355$	19.3923	−	11.1962i	1.02924	−	0.594230i
$356$			1.19615i			0.0633960i
$357$	−0.588457	−	0.339746i	−0.0311445	−	0.0179813i
$358$	2.73205	+	4.73205i	0.144393	+	0.250097i
$359$	−4.39230			−0.231817			−0.115908	−	0.993260i	$-0.536978\pi$
$359$	−4.39230			−0.231817			−0.115908	+	0.993260i	$0.536978\pi$
$360$	27.5885			1.45404
$361$	1.69615	+	2.93782i	0.0892712	+	0.154622i
$362$		−	3.92820i		−	0.206462i
$363$	3.43782	−	5.95448i	0.180439	−	0.312529i
$364$			12.0000i			0.628971i
$365$		0			0
$366$	2.83013	−	4.90192i	0.147933	−	0.256228i
$367$	−0.196152	+	0.339746i	−0.0102391	+	0.0177346i	−0.871100	−	0.491106i	$-0.836593\pi$
$367$	−0.196152	+	0.339746i	−0.0102391	+	0.0177346i	0.860860	+	0.508841i	$0.169926\pi$
$368$	2.36603	−	1.36603i	0.123338	−	0.0712090i
$369$	−7.39230			−0.384828
$370$	−1.86603	−	22.6244i	−0.0970100	−	1.17618i
$371$	32.7846			1.70209
$372$	−1.39230	+	0.803848i	−0.0721876	+	0.0416776i
$373$	−12.2321	+	21.1865i	−0.633352	+	1.09700i	0.353510	+	0.935431i	$0.384988\pi$
$373$	−12.2321	+	21.1865i	−0.633352	+	1.09700i	−0.986862	+	0.161566i	$0.948345\pi$
$374$	0.169873	−	0.294229i	0.00878392	−	0.0152142i
$375$	9.29423	+	5.36603i	0.479952	+	0.277100i
$376$			24.5885i			1.26805i
$377$	6.46410	−	11.1962i	0.332918	−	0.576631i
$378$			13.8564i			0.712697i
$379$	−7.73205	−	13.3923i	−0.397169	−	0.687916i	0.596207	−	0.802831i	$-0.296674\pi$
$379$	−7.73205	−	13.3923i	−0.397169	−	0.687916i	−0.993375	+	0.114915i	$0.963341\pi$
$380$	−17.6603			−0.905952
$381$	−1.32051			−0.0676517
$382$	−2.09808	−	3.63397i	−0.107347	−	0.185930i
$383$	−10.2679	−	5.92820i	−0.524668	−	0.302917i	0.214175	−	0.976795i	$-0.431294\pi$
$383$	−10.2679	−	5.92820i	−0.524668	−	0.302917i	−0.738842	+	0.673878i	$0.764627\pi$
$384$			2.19615i			0.112072i
$385$	14.1962	−	8.19615i	0.723503	−	0.417715i
$386$	−1.33013	−	2.30385i	−0.0677017	−	0.117263i
$387$	−7.39230	+	4.26795i	−0.375772	+	0.216952i
$388$	−6.69615	−	3.86603i	−0.339946	−	0.196268i
$389$	−18.0167	−	10.4019i	−0.913481	−	0.527398i	−0.0319314	−	0.999490i	$-0.510166\pi$
$389$	−18.0167	−	10.4019i	−0.913481	−	0.527398i	−0.881550	+	0.472092i	$0.843499\pi$
$390$	8.19615	−	4.73205i	0.415028	−	0.239617i
$391$	0.366025	+	0.633975i	0.0185107	+	0.0320615i
$392$	12.9904	−	7.50000i	0.656113	−	0.378807i
$393$		−	15.0718i		−	0.760272i
$394$	−12.1865	−	7.03590i	−0.613949	−	0.354463i
$395$	26.4904	+	45.8827i	1.33288	+	2.30861i
$396$	3.12436			0.157005
$397$	27.2487			1.36757			0.683787	−	0.729682i	$-0.260332\pi$
$397$	27.2487			1.36757			0.683787	+	0.729682i	$0.260332\pi$
$398$	12.4641	+	21.5885i	0.624769	+	1.08213i
$399$		−	12.0000i		−	0.600751i
$400$	−4.46410	+	7.73205i	−0.223205	+	0.386603i
$401$			26.3923i			1.31797i	0.752157	+	0.658984i	$0.229014\pi$
$401$			26.3923i			1.31797i	−0.752157	+	0.658984i	$0.770986\pi$
$402$	6.80385	+	3.92820i	0.339345	+	0.195921i
$403$	3.80385	−	6.58846i	0.189483	−	0.328194i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	14.4282	−	8.33013i	0.716943	−	0.413927i
$406$	−12.9282			−0.641616
$407$	−0.633975	−	7.68653i	−0.0314250	−	0.381007i
$408$	0.588457			0.0291330
$409$	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	$0.264648\pi$
$410$	5.59808	−	9.69615i	0.276469	−	0.478859i
$411$	−0.169873	+	0.294229i	−0.00837922	+	0.0145132i
$412$	0.803848	+	0.464102i	0.0396027	+	0.0228646i
$413$		−	22.6410i		−	1.11409i
$414$	3.36603	−	5.83013i	0.165431	−	0.286535i
$415$			8.19615i			0.402333i
$416$	−8.66025	−	15.0000i	−0.424604	−	0.735436i
$417$	−13.6077			−0.666372
$418$	6.00000			0.293470
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	0.996239	−	0.0866469i	$-0.0276152\pi$
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	−0.573158	+	0.819445i	$0.694282\pi$
$420$	8.19615	+	4.73205i	0.399931	+	0.230900i
$421$		−	19.7321i		−	0.961681i	−0.876808	−	0.480841i	$-0.840332\pi$
$421$		−	19.7321i		−	0.961681i	0.876808	−	0.480841i	$-0.159668\pi$
$422$	−8.66025	+	5.00000i	−0.421575	+	0.243396i
$423$	10.0981	+	17.4904i	0.490985	+	0.850411i
$424$	−24.5885	+	14.1962i	−1.19412	+	0.689426i
$425$	−2.07180	−	1.19615i	−0.100497	−	0.0580219i
$426$	−3.80385	−	2.19615i	−0.184297	−	0.106404i
$427$	−23.1962	+	13.3923i	−1.12254	+	0.648099i
$428$	−0.464102	−	0.803848i	−0.0224332	−	0.0388554i
$429$	2.78461	−	1.60770i	0.134442	−	0.0776203i
$430$		−	12.9282i		−	0.623453i
$431$	−29.0263	−	16.7583i	−1.39815	−	0.807220i	−0.403948	−	0.914782i	$-0.632362\pi$
$431$	−29.0263	−	16.7583i	−1.39815	−	0.807220i	−0.994198	+	0.107561i	$0.965696\pi$
$432$	−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	$0.275284\pi$
$434$	−7.60770			−0.365181
$435$	−5.09808	−	8.83013i	−0.244434	−	0.423372i
$436$			17.1962i			0.823546i
$437$	−6.46410	+	11.1962i	−0.309220	+	0.535585i
$438$		0			0
$439$	−18.5885	−	10.7321i	−0.887179	−	0.512213i	−0.0141601	−	0.999900i	$-0.504507\pi$
$439$	−18.5885	−	10.7321i	−0.887179	−	0.512213i	−0.873019	+	0.487687i	$0.837841\pi$
$440$	−7.09808	+	12.2942i	−0.338388	+	0.586104i
$441$	6.16025	−	10.6699i	0.293345	−	0.508089i
$442$	−0.803848	+	0.464102i	−0.0382351	+	0.0220751i
$443$	26.5359			1.26076			0.630379	−	0.776287i	$-0.282899\pi$
$443$	26.5359			1.26076			0.630379	+	0.776287i	$0.282899\pi$
$444$	3.66025	−	2.53590i	0.173708	−	0.120348i
$445$	−4.46410			−0.211619
$446$	−23.0263	+	13.2942i	−1.09033	+	0.629500i
$447$	−4.56218	+	7.90192i	−0.215784	+	0.373748i
$448$	−12.1244	+	21.0000i	−0.572822	+	0.992157i
$449$	−14.0718	−	8.12436i	−0.664089	−	0.383412i	0.129744	−	0.991548i	$-0.458584\pi$
$449$	−14.0718	−	8.12436i	−0.664089	−	0.383412i	−0.793833	+	0.608135i	$0.791918\pi$
$450$			22.0000i			1.03709i
$451$	1.90192	−	3.29423i	0.0895581	−	0.155119i
$452$			11.4641i			0.539226i
$453$	5.33975	+	9.24871i	0.250883	+	0.434542i
$454$	1.12436			0.0527686
$455$	−44.7846			−2.09953
$456$	5.19615	+	9.00000i	0.243332	+	0.421464i
$457$	10.2846	+	5.93782i	0.481094	+	0.277760i	0.720872	−	0.693068i	$-0.243741\pi$
$457$	10.2846	+	5.93782i	0.481094	+	0.277760i	−0.239778	+	0.970828i	$0.577075\pi$
$458$			7.00000i			0.327089i
$459$	0.928203	−	0.535898i	0.0433248	−	0.0250136i
$460$	−5.09808	−	8.83013i	−0.237699	−	0.411707i
$461$	20.3205	−	11.7321i	0.946420	−	0.546416i	0.0544533	−	0.998516i	$-0.482658\pi$
$461$	20.3205	−	11.7321i	0.946420	−	0.546416i	0.891967	+	0.452100i	$0.149325\pi$
$462$	−2.78461	−	1.60770i	−0.129552	−	0.0747967i
$463$	7.39230	+	4.26795i	0.343550	+	0.198348i	0.661841	−	0.749645i	$-0.269776\pi$
$463$	7.39230	+	4.26795i	0.343550	+	0.198348i	−0.318291	+	0.947993i	$0.603109\pi$
$464$	3.23205	−	1.86603i	0.150044	−	0.0866281i
$465$	−3.00000	−	5.19615i	−0.139122	−	0.240966i
$466$	14.5981	−	8.42820i	0.676243	−	0.390429i
$467$		−	31.3205i		−	1.44934i	−0.689096	−	0.724670i	$-0.741992\pi$
$467$		−	31.3205i		−	1.44934i	0.689096	−	0.724670i	$-0.258008\pi$
$468$	−7.39230	−	4.26795i	−0.341709	−	0.197286i
$469$	−18.5885	−	32.1962i	−0.858335	−	1.48668i
$470$	−30.5885			−1.41094
$471$	14.8756			0.685434
$472$	9.80385	+	16.9808i	0.451259	+	0.781603i
$473$		−	4.39230i		−	0.201958i
$474$	5.19615	−	9.00000i	0.238667	−	0.413384i
$475$		−	42.2487i		−	1.93850i
$476$	−0.803848	−	0.464102i	−0.0368443	−	0.0212721i
$477$	−11.6603	+	20.1962i	−0.533886	+	0.924718i
$478$	−1.53590	+	2.66025i	−0.0702504	+	0.121677i
$479$	4.05256	−	2.33975i	0.185166	−	0.106906i	−0.404552	−	0.914515i	$-0.632572\pi$
$479$	4.05256	−	2.33975i	0.185166	−	0.106906i	0.589718	+	0.807609i	$0.299239\pi$
$480$	−13.6603			−0.623502
$481$	−9.00000	+	19.0526i	−0.410365	+	0.868722i
$482$	8.53590			0.388800
$483$	6.00000	−	3.46410i	0.273009	−	0.157622i
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	14.4282	−	24.9904i	0.655151	−	1.13475i
$486$	−13.2224	−	7.63397i	−0.599782	−	0.346284i
$487$			26.4449i			1.19833i	0.800625	+	0.599166i	$0.204501\pi$
$487$			26.4449i			1.19833i	−0.800625	+	0.599166i	$0.795499\pi$
$488$	11.5981	−	20.0885i	0.525020	−	0.909362i
$489$		−	1.17691i		−	0.0532219i
$490$	9.33013	+	16.1603i	0.421492	+	0.730046i
$491$	34.7321			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$491$	34.7321			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$492$	2.19615			0.0990102
$493$	0.500000	+	0.866025i	0.0225189	+	0.0390038i
$494$	−14.1962	−	8.19615i	−0.638715	−	0.368762i
$495$			11.6603i			0.524089i
$496$	1.90192	−	1.09808i	0.0853989	−	0.0493051i
$497$	10.3923	+	18.0000i	0.466159	+	0.807410i
$498$	1.39230	−	0.803848i	0.0623907	−	0.0360213i
$499$	16.0981	+	9.29423i	0.720649	+	0.416067i	0.814991	−	0.579473i	$-0.196742\pi$
$499$	16.0981	+	9.29423i	0.720649	+	0.416067i	−0.0943426	+	0.995540i	$0.530075\pi$
$500$	12.6962	+	7.33013i	0.567789	+	0.327813i
$501$	−1.85641	+	1.07180i	−0.0829381	+	0.0478843i
$502$	14.8564	+	25.7321i	0.663074	+	1.14848i
$503$	−37.2224	+	21.4904i	−1.65967	+	0.958209i	−0.686798	+	0.726848i	$0.740984\pi$
$503$	−37.2224	+	21.4904i	−1.65967	+	0.958209i	−0.972868	+	0.231361i	$0.925682\pi$
$504$			25.6077i			1.14066i
$505$	29.0885	+	16.7942i	1.29442	+	0.747333i
$506$	1.73205	+	3.00000i	0.0769991	+	0.133366i
$507$	0.732051			0.0325115
$508$	−1.80385			−0.0800328
$509$	−17.8923	−	30.9904i	−0.793062	−	1.37362i	−0.924062	−	0.382242i	$-0.875152\pi$
$509$	−17.8923	−	30.9904i	−0.793062	−	1.37362i	0.131000	−	0.991382i	$-0.458181\pi$
$510$			0.732051i			0.0324158i
$511$		0			0
$512$		−	11.0000i		−	0.486136i
$513$	16.3923	+	9.46410i	0.723738	+	0.417850i
$514$	5.79423	−	10.0359i	0.255572	−	0.442665i
$515$	−1.73205	+	3.00000i	−0.0763233	+	0.132196i
$516$	2.19615	−	1.26795i	0.0966802	−	0.0558184i
$517$	−10.3923			−0.457053
$518$	21.0000	−	1.73205i	0.922687	−	0.0761019i
$519$	−2.87564			−0.126227
$520$	33.5885	−	19.3923i	1.47295	−	0.850409i
$521$	3.46410	−	6.00000i	0.151765	−	0.262865i	−0.780111	−	0.625641i	$-0.784838\pi$
$521$	3.46410	−	6.00000i	0.151765	−	0.262865i	0.931876	+	0.362776i	$0.118171\pi$
$522$	4.59808	−	7.96410i	0.201252	−	0.348579i
$523$	19.0981	+	11.0263i	0.835101	+	0.482146i	0.855596	−	0.517644i	$-0.173191\pi$
$523$	19.0981	+	11.0263i	0.835101	+	0.482146i	−0.0204953	+	0.999790i	$0.506524\pi$
$524$		−	20.5885i		−	0.899411i
$525$	−11.3205	+	19.6077i	−0.494067	+	0.855750i
$526$		−	28.3923i		−	1.23796i
$527$	0.294229	+	0.509619i	0.0128168	+	0.0221993i
$528$	0.928203			0.0403949
$529$	15.5359			0.675474
$530$	−17.6603	−	30.5885i	−0.767112	−	1.32868i
$531$	13.9474	+	8.05256i	0.605267	+	0.349451i
$532$		−	16.3923i		−	0.710697i
$533$	−9.00000	+	5.19615i	−0.389833	+	0.225070i
$534$	0.437822	+	0.758330i	0.0189464	+	0.0328162i
$535$	3.00000	−	1.73205i	0.129701	−	0.0748831i
$536$	27.8827	+	16.0981i	1.20435	+	0.695331i
$537$	−3.46410	−	2.00000i	−0.149487	−	0.0863064i
$538$	18.5885	−	10.7321i	0.801405	−	0.462692i
$539$	3.16987	+	5.49038i	0.136536	+	0.236487i
$540$	−12.9282	+	7.46410i	−0.556341	+	0.321204i
$541$			7.73205i			0.332427i	0.986090	+	0.166213i	$0.0531541\pi$
$541$			7.73205i			0.332427i	−0.986090	+	0.166213i	$0.946846\pi$
$542$	−4.90192	−	2.83013i	−0.210556	−	0.121564i
$543$	1.43782	+	2.49038i	0.0617029	+	0.106872i
$544$	1.33975			0.0574411
$545$	−64.1769			−2.74904
$546$	4.39230	+	7.60770i	0.187973	+	0.325579i
$547$		−	14.1962i		−	0.606984i	−0.952834	−	0.303492i	$-0.901847\pi$
$547$		−	14.1962i		−	0.606984i	0.952834	−	0.303492i	$-0.0981525\pi$
$548$	−0.232051	+	0.401924i	−0.00991272	+	0.0171693i
$549$		−	19.0526i		−	0.813143i
$550$	−9.80385	−	5.66025i	−0.418037	−	0.241354i
$551$	−8.83013	+	15.2942i	−0.376176	+	0.651556i
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−42.5885	+	24.5885i	−1.81105	+	1.04561i
$554$	13.7321			0.583419
$555$	9.46410	+	13.6603i	0.401729	+	0.579845i
$556$	−18.5885			−0.788326
$557$	12.3564	−	7.13397i	0.523558	−	0.302276i	−0.214831	−	0.976651i	$-0.568920\pi$
$557$	12.3564	−	7.13397i	0.523558	−	0.302276i	0.738389	+	0.674375i	$0.235587\pi$
$558$	2.70577	−	4.68653i	0.114544	−	0.198397i
$559$	−6.00000	+	10.3923i	−0.253773	+	0.439548i
$560$	−11.1962	−	6.46410i	−0.473124	−	0.273158i
$561$			0.248711i			0.0105006i
$562$	−11.4019	+	19.7487i	−0.480961	+	0.833049i
$563$		−	3.41154i		−	0.143779i	−0.997413	−	0.0718897i	$-0.977097\pi$
$563$		−	3.41154i		−	0.143779i	0.997413	−	0.0718897i	$-0.0229030\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	−42.7846			−1.79996
$566$	10.3923			0.436821
$567$	7.73205	+	13.3923i	0.324716	+	0.562424i
$568$	−15.5885	−	9.00000i	−0.654077	−	0.377632i
$569$		−	8.51666i		−	0.357037i	−0.983937	−	0.178518i	$-0.942870\pi$
$569$		−	8.51666i		−	0.357037i	0.983937	−	0.178518i	$-0.0571304\pi$
$570$	−11.1962	+	6.46410i	−0.468955	+	0.270751i
$571$	−6.75833	−	11.7058i	−0.282827	−	0.489871i	0.689253	−	0.724521i	$-0.257939\pi$
$571$	−6.75833	−	11.7058i	−0.282827	−	0.489871i	−0.972080	+	0.234650i	$0.924606\pi$
$572$	3.80385	−	2.19615i	0.159047	−	0.0918257i
$573$	2.66025	+	1.53590i	0.111134	+	0.0641631i
$574$	9.00000	+	5.19615i	0.375653	+	0.216883i
$575$	21.1244	−	12.1962i	0.880947	−	0.508615i
$576$	−8.62436	−	14.9378i	−0.359348	−	0.622409i
$577$	0.803848	−	0.464102i	0.0334646	−	0.0193208i	−0.483174	−	0.875524i	$-0.660516\pi$
$577$	0.803848	−	0.464102i	0.0334646	−	0.0193208i	0.516639	+	0.856203i	$0.327183\pi$
$578$			16.9282i			0.704120i
$579$	1.68653	+	0.973721i	0.0700899	+	0.0404664i
$580$	−6.96410	−	12.0622i	−0.289169	−	0.500855i
$581$	−7.60770			−0.315620
$582$	−5.66025			−0.234625
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$		0			0
$585$	15.9282	−	27.5885i	0.658550	−	1.14064i
$586$			1.14359i			0.0472414i
$587$	29.1506	+	16.8301i	1.20318	+	0.694654i	0.961260	−	0.275644i	$-0.0888910\pi$
$587$	29.1506	+	16.8301i	1.20318	+	0.694654i	0.241916	+	0.970297i	$0.422224\pi$
$588$	−1.83013	+	3.16987i	−0.0754732	+	0.130723i
$589$	−5.19615	+	9.00000i	−0.214104	+	0.370839i
$590$	−21.1244	+	12.1962i	−0.869676	+	0.502108i
$591$	10.3013			0.423738
$592$	−5.00000	+	3.46410i	−0.205499	+	0.142374i
$593$	−23.7846			−0.976717			−0.488358	−	0.872643i	$-0.662404\pi$
$593$	−23.7846			−0.976717			−0.488358	+	0.872643i	$0.662404\pi$
$594$	4.39230	−	2.53590i	0.180218	−	0.104049i
$595$	1.73205	−	3.00000i	0.0710072	−	0.122988i
$596$	−6.23205	+	10.7942i	−0.255275	+	0.442149i
$597$	−15.8038	−	9.12436i	−0.646808	−	0.373435i
$598$		−	9.46410i		−	0.387016i
$599$	−23.0263	+	39.8827i	−0.940828	+	1.62956i	−0.176932	+	0.984223i	$0.556617\pi$
$599$	−23.0263	+	39.8827i	−0.940828	+	1.62956i	−0.763896	+	0.645339i	$0.776716\pi$
$600$		−	19.6077i		−	0.800481i
$601$	−5.30385	−	9.18653i	−0.216348	−	0.374727i	0.737340	−	0.675521i	$-0.236081\pi$
$601$	−5.30385	−	9.18653i	−0.216348	−	0.374727i	−0.953689	+	0.300795i	$0.902748\pi$
$602$	12.0000			0.489083
$603$	26.4449			1.07692
$604$	7.29423	+	12.6340i	0.296798	+	0.514069i
$605$	30.3564	+	17.5263i	1.23416	+	0.712545i
$606$		−	6.58846i		−	0.267638i
$607$	10.0981	−	5.83013i	0.409868	−	0.236638i	−0.280865	−	0.959747i	$-0.590621\pi$
$607$	10.0981	−	5.83013i	0.409868	−	0.236638i	0.690733	+	0.723110i	$0.257288\pi$
$608$	11.8301	+	20.4904i	0.479775	+	0.830995i
$609$	8.19615	−	4.73205i	0.332125	−	0.191752i
$610$	24.9904	+	14.4282i	1.01183	+	0.584181i
$611$	24.5885	+	14.1962i	0.994743	+	0.574315i
$612$	0.571797	−	0.330127i	0.0231135	−	0.0133446i
$613$	8.69615	+	15.0622i	0.351234	+	0.608356i	0.986466	−	0.163966i	$-0.0524287\pi$
$613$	8.69615	+	15.0622i	0.351234	+	0.608356i	−0.635232	+	0.772322i	$0.719095\pi$
$614$	5.53590	−	3.19615i	0.223411	−	0.128986i
$615$			8.19615i			0.330501i
$616$	−11.4115	−	6.58846i	−0.459784	−	0.265457i
$617$	−18.5885	−	32.1962i	−0.748343	−	1.29617i	−0.948616	−	0.316428i	$-0.897516\pi$
$617$	−18.5885	−	32.1962i	−0.748343	−	1.29617i	0.200273	−	0.979740i	$-0.435817\pi$
$618$	0.679492			0.0273332
$619$	−34.7846			−1.39811			−0.699056	−	0.715067i	$-0.746396\pi$
$619$	−34.7846			−1.39811			−0.699056	+	0.715067i	$0.746396\pi$
$620$	−4.09808	−	7.09808i	−0.164583	−	0.285066i
$621$			10.9282i			0.438534i
$622$	4.80385	−	8.32051i	0.192617	−	0.333622i
$623$		−	4.14359i		−	0.166010i
$624$	−2.19615	−	1.26795i	−0.0879165	−	0.0507586i
$625$	−5.03590	+	8.72243i	−0.201436	+	0.348897i
$626$	−7.79423	+	13.5000i	−0.311520	+	0.539569i
$627$	−3.80385	+	2.19615i	−0.151911	+	0.0877059i
$628$	20.3205			0.810877
$629$	−0.928203	−	1.33975i	−0.0370099	−	0.0534192i
$630$	−31.8564			−1.26919
$631$	−19.6865	+	11.3660i	−0.783709	+	0.452474i	−0.837743	−	0.546065i	$-0.816125\pi$
$631$	−19.6865	+	11.3660i	−0.783709	+	0.452474i	0.0540345	+	0.998539i	$0.482792\pi$
$632$	21.2942	−	36.8827i	0.847039	−	1.46711i
$633$	3.66025	−	6.33975i	0.145482	−	0.251982i
$634$	1.79423	+	1.03590i	0.0712579	+	0.0411408i
$635$		−	6.73205i		−	0.267153i
$636$	3.46410	−	6.00000i	0.137361	−	0.237915i
$637$		−	17.3205i		−	0.686264i
$638$	2.36603	+	4.09808i	0.0936718	+	0.162244i
$639$	−14.7846			−0.584870
$640$	−11.1962			−0.442567
$641$	−11.8923	−	20.5981i	−0.469718	−	0.813575i	0.529683	−	0.848196i	$-0.322311\pi$
$641$	−11.8923	−	20.5981i	−0.469718	−	0.813575i	−0.999401	+	0.0346208i	$0.988978\pi$
$642$	−0.588457	−	0.339746i	−0.0232246	−	0.0134087i
$643$			11.6603i			0.459836i	0.973210	+	0.229918i	$0.0738457\pi$
$643$			11.6603i			0.459836i	−0.973210	+	0.229918i	$0.926154\pi$
$644$	8.19615	−	4.73205i	0.322974	−	0.186469i
$645$	4.73205	+	8.19615i	0.186324	+	0.322723i
$646$	1.09808	−	0.633975i	0.0432032	−	0.0249434i
$647$	−31.6410	−	18.2679i	−1.24394	−	0.718187i	−0.274043	−	0.961717i	$-0.588361\pi$
$647$	−31.6410	−	18.2679i	−1.24394	−	0.718187i	−0.969893	+	0.243530i	$0.921695\pi$
$648$	−11.5981	−	6.69615i	−0.455615	−	0.263050i
$649$	−7.17691	+	4.14359i	−0.281719	+	0.162650i
$650$	15.4641	+	26.7846i	0.606552	+	1.05058i
$651$	4.82309	−	2.78461i	0.189032	−	0.109137i
$652$		−	1.60770i		−	0.0629622i
$653$	11.4282	+	6.59808i	0.447220	+	0.258203i	0.706655	−	0.707558i	$-0.250203\pi$
$653$	11.4282	+	6.59808i	0.447220	+	0.258203i	−0.259435	+	0.965760i	$0.583536\pi$
$654$	6.29423	+	10.9019i	0.246124	+	0.426299i
$655$	76.8372			3.00228
$656$	−3.00000			−0.117130
$657$		0			0
$658$		−	28.3923i		−	1.10685i
$659$	−1.26795	+	2.19615i	−0.0493923	+	0.0855500i	−0.889665	−	0.456615i	$-0.849062\pi$
$659$	−1.26795	+	2.19615i	−0.0493923	+	0.0855500i	0.840272	+	0.542165i	$0.182395\pi$
$660$		−	3.46410i		−	0.134840i
$661$	20.0885	+	11.5981i	0.781350	+	0.451113i	0.836909	−	0.547343i	$-0.184361\pi$
$661$	20.0885	+	11.5981i	0.781350	+	0.451113i	−0.0555582	+	0.998455i	$0.517694\pi$
$662$	4.39230	−	7.60770i	0.170712	−	0.295681i
$663$	0.339746	−	0.588457i	0.0131946	−	0.0228538i
$664$	5.70577	−	3.29423i	0.221427	−	0.127841i
$665$	61.1769			2.37234
$666$	−6.40192	+	13.5526i	−0.248070	+	0.525151i
$667$	−10.1962			−0.394797
$668$	−2.53590	+	1.46410i	−0.0981169	+	0.0566478i
$669$	9.73205	−	16.8564i	0.376263	−	0.651706i
$670$	−20.0263	+	34.6865i	−0.773683	+	1.34006i
$671$	8.49038	+	4.90192i	0.327768	+	0.189237i
$672$		−	12.6795i		−	0.489122i
$673$	19.8564	−	34.3923i	0.765408	−	1.32573i	−0.174622	−	0.984635i	$-0.555870\pi$
$673$	19.8564	−	34.3923i	0.765408	−	1.32573i	0.940030	−	0.341090i	$-0.110796\pi$
$674$			8.60770i			0.331556i
$675$	−17.8564	−	30.9282i	−0.687293	−	1.19043i
$676$	1.00000			0.0384615
$677$	−9.67949			−0.372013			−0.186007	−	0.982549i	$-0.559555\pi$
$677$	−9.67949			−0.372013			−0.186007	+	0.982549i	$0.559555\pi$
$678$	4.19615	+	7.26795i	0.161152	+	0.279124i
$679$	23.1962	+	13.3923i	0.890187	+	0.513949i
$680$			3.00000i			0.115045i
$681$	−0.712813	+	0.411543i	−0.0273151	+	0.0157704i
$682$	1.39230	+	2.41154i	0.0533141	+	0.0923427i
$683$	−38.9090	+	22.4641i	−1.48881	+	0.859565i	−0.999918	−	0.0127794i	$-0.995932\pi$
$683$	−38.9090	+	22.4641i	−1.48881	+	0.859565i	−0.488892	+	0.872344i	$0.662599\pi$
$684$	10.0981	+	5.83013i	0.386110	+	0.222920i
$685$	−1.50000	−	0.866025i	−0.0573121	−	0.0330891i
$686$	6.00000	−	3.46410i	0.229081	−	0.132260i
$687$	−2.56218	−	4.43782i	−0.0977532	−	0.169313i
$688$	−3.00000	+	1.73205i	−0.114374	+	0.0660338i
$689$			32.7846i			1.24899i
$690$	−6.46410	−	3.73205i	−0.246084	−	0.142077i
$691$	11.0263	+	19.0981i	0.419459	+	0.726525i	0.995885	−	0.0906245i	$-0.0288863\pi$
$691$	11.0263	+	19.0981i	0.419459	+	0.726525i	−0.576426	+	0.817150i	$0.695553\pi$
$692$	−3.92820			−0.149328
$693$	−10.8231			−0.411135
$694$	−4.63397	−	8.02628i	−0.175903	−	0.304673i
$695$		−	69.3731i		−	2.63147i
$696$	−4.09808	+	7.09808i	−0.155337	+	0.269052i
$697$		−	0.803848i		−	0.0304479i
$698$	−18.9904	−	10.9641i	−0.718797	−	0.414997i
$699$	−6.16987	+	10.6865i	−0.233366	+	0.404202i
$700$	−15.4641	+	26.7846i	−0.584488	+	1.01236i
$701$	−18.9282	+	10.9282i	−0.714908	+	0.412753i	−0.812876	−	0.582437i	$-0.802099\pi$
$701$	−18.9282	+	10.9282i	−0.714908	+	0.412753i	0.0979674	+	0.995190i	$0.468766\pi$
$702$	−13.8564			−0.522976
$703$	12.2942	−	26.0263i	0.463686	−	0.981600i
$704$	8.87564			0.334513
$705$	19.3923	−	11.1962i	0.730356	−	0.421671i
$706$	−7.86603	+	13.6244i	−0.296042	+	0.512759i
$707$	−15.5885	+	27.0000i	−0.586264	+	1.01544i
$708$	−4.14359	−	2.39230i	−0.155726	−	0.0899083i
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$	11.1962	−	19.3923i	0.420184	−	0.727780i
$711$		−	34.9808i		−	1.31188i
$712$	1.79423	+	3.10770i	0.0672416	+	0.116466i
$713$	−6.00000			−0.224702
$714$	−0.679492			−0.0254293
$715$	8.19615	+	14.1962i	0.306519	+	0.530906i
$716$	−4.73205	−	2.73205i	−0.176845	−	0.102102i
$717$		−	2.24871i		−	0.0839797i
$718$	−3.80385	+	2.19615i	−0.141958	+	0.0819597i
$719$	16.2224	+	28.0981i	0.604995	+	1.04788i	0.992052	+	0.125826i	$0.0401581\pi$
$719$	16.2224	+	28.0981i	0.604995	+	1.04788i	−0.387058	+	0.922055i	$0.626509\pi$
$720$	7.96410	−	4.59808i	0.296805	−	0.171360i
$721$	−2.78461	−	1.60770i	−0.103704	−	0.0598737i
$722$	2.93782	+	1.69615i	0.109334	+	0.0631243i
$723$	−5.41154	+	3.12436i	−0.201257	+	0.116196i
$724$	1.96410	+	3.40192i	0.0729953	+	0.126432i
$725$	28.8564	−	16.6603i	1.07170	−	0.618746i
$726$		−	6.87564i		−	0.255179i
$727$	−22.3923	−	12.9282i	−0.830485	−	0.479481i	0.0235340	−	0.999723i	$-0.492508\pi$
$727$	−22.3923	−	12.9282i	−0.830485	−	0.479481i	−0.854019	+	0.520243i	$0.825842\pi$
$728$	18.0000	+	31.1769i	0.667124	+	1.15549i
$729$	−2.21539			−0.0820515
$730$		0			0
$731$	−0.464102	−	0.803848i	−0.0171654	−	0.0297314i
$732$			5.66025i			0.209209i
$733$	6.39230	−	11.0718i	0.236105	−	0.408946i	−0.723488	−	0.690337i	$-0.757462\pi$
$733$	6.39230	−	11.0718i	0.236105	−	0.408946i	0.959593	+	0.281391i	$0.0907957\pi$
$734$			0.392305i			0.0144802i
$735$	−11.8301	−	6.83013i	−0.436361	−	0.251933i
$736$	−6.83013	+	11.8301i	−0.251762	+	0.436064i
$737$	−6.80385	+	11.7846i	−0.250623	+	0.434092i
$738$	−6.40192	+	3.69615i	−0.235658	+	0.136057i
$739$	−34.1962			−1.25793			−0.628963	−	0.777435i	$-0.716520\pi$
$739$	−34.1962			−1.25793			−0.628963	+	0.777435i	$0.716520\pi$
$740$	12.9282	+	18.6603i	0.475250	+	0.685965i
$741$	12.0000			0.440831
$742$	28.3923	−	16.3923i	1.04231	−	0.601780i
$743$	23.3660	−	40.4711i	0.857216	−	1.48474i	−0.0173572	−	0.999849i	$-0.505525\pi$
$743$	23.3660	−	40.4711i	0.857216	−	1.48474i	0.874574	−	0.484893i	$-0.161141\pi$
$744$	−2.41154	+	4.17691i	−0.0884114	+	0.153133i
$745$	−40.2846	−	23.2583i	−1.47591	−	0.852119i
$746$			24.4641i			0.895694i
$747$	2.70577	−	4.68653i	0.0989990	−	0.171471i
$748$			0.339746i			0.0124223i
$749$	1.60770	+	2.78461i	0.0587439	+	0.101747i
$750$	10.7321			0.391879
$751$	−50.7846			−1.85316			−0.926578	−	0.376102i	$-0.877264\pi$
$751$	−50.7846			−1.85316			−0.926578	+	0.376102i	$0.877264\pi$
$752$	4.09808	+	7.09808i	0.149441	+	0.258840i
$753$	−18.8372	−	10.8756i	−0.686465	−	0.396331i
$754$		−	12.9282i		−	0.470817i
$755$	−47.1506	+	27.2224i	−1.71599	+	0.990726i
$756$	−6.92820	−	12.0000i	−0.251976	−	0.436436i
$757$	26.3038	−	15.1865i	0.956030	−	0.551964i	0.0610808	−	0.998133i	$-0.480545\pi$
$757$	26.3038	−	15.1865i	0.956030	−	0.551964i	0.894949	+	0.446169i	$0.147212\pi$
$758$	−13.3923	−	7.73205i	−0.486430	−	0.280841i
$759$	−2.19615	−	1.26795i	−0.0797153	−	0.0460236i
$760$	−45.8827	+	26.4904i	−1.66434	+	0.960907i
$761$	19.1603	+	33.1865i	0.694559	+	1.20301i	0.970329	+	0.241787i	$0.0777337\pi$
$761$	19.1603	+	33.1865i	0.694559	+	1.20301i	−0.275771	+	0.961223i	$0.588933\pi$
$762$	−1.14359	+	0.660254i	−0.0414280	+	0.0239185i
$763$		−	59.5692i		−	2.15655i
$764$	3.63397	+	2.09808i	0.131473	+	0.0759057i
$765$	1.23205	+	2.13397i	0.0445449	+	0.0771540i
$766$	−11.8564			−0.428389
$767$	22.6410			0.817520
$768$	6.22243	+	10.7776i	0.224533	+	0.388902i
$769$		−	27.4641i		−	0.990381i	−0.868784	−	0.495190i	$-0.835098\pi$
$769$		−	27.4641i		−	0.990381i	0.868784	−	0.495190i	$-0.164902\pi$
$770$	8.19615	−	14.1962i	0.295369	−	0.511594i
$771$			8.48334i			0.305520i
$772$	2.30385	+	1.33013i	0.0829173	+	0.0478723i
$773$	−21.0167	+	36.4019i	−0.755917	+	1.30929i	0.189001	+	0.981977i	$0.439475\pi$
$773$	−21.0167	+	36.4019i	−0.755917	+	1.30929i	−0.944917	+	0.327309i	$0.893858\pi$
$774$	−4.26795	+	7.39230i	−0.153408	+	0.265711i
$775$	16.9808	−	9.80385i	0.609967	−	0.352165i
$776$	−23.1962			−0.832693
$777$	−12.6795	+	8.78461i	−0.454874	+	0.315146i
$778$	−20.8038			−0.745854
$779$	12.2942	−	7.09808i	0.440486	−	0.254315i
$780$	−4.73205	+	8.19615i	−0.169435	+	0.293469i
$781$	3.80385	−	6.58846i	0.136112	−	0.235754i
$782$	0.633975	+	0.366025i	0.0226709	+	0.0130890i
$783$			14.9282i			0.533490i
$784$	2.50000	−	4.33013i	0.0892857	−	0.154647i
$785$			75.8372i			2.70674i
$786$	−7.53590	−	13.0526i	−0.268797	−	0.465569i
$787$	−20.3923			−0.726907			−0.363454	−	0.931612i	$-0.618402\pi$
$787$	−20.3923			−0.726907			−0.363454	+	0.931612i	$0.618402\pi$
$788$	14.0718			0.501287
$789$	10.3923	+	18.0000i	0.369976	+	0.640817i
$790$	45.8827	+	26.4904i	1.63243	+	0.942485i
$791$		−	39.7128i		−	1.41203i
$792$	8.11731	−	4.68653i	0.288436	−	0.166529i
$793$	−13.3923	−	23.1962i	−0.475575	−	0.823720i
$794$	23.5981	−	13.6244i	0.837464	−	0.483510i
$795$	22.3923	+	12.9282i	0.794173	+	0.458516i
$796$	−21.5885	−	12.4641i	−0.765183	−	0.441778i
$797$	6.92820	−	4.00000i	0.245410	−	0.141687i	−0.372251	−	0.928132i	$-0.621414\pi$
$797$	6.92820	−	4.00000i	0.245410	−	0.141687i	0.617661	+	0.786445i	$0.288081\pi$
$798$	−6.00000	−	10.3923i	−0.212398	−	0.367884i
$799$	−1.90192	+	1.09808i	−0.0672852	+	0.0388471i
$800$		−	44.6410i		−	1.57830i
$801$	2.55256	+	1.47372i	0.0901902	+	0.0520714i
$802$	13.1962	+	22.8564i	0.465972	+	0.807088i
$803$		0			0
$804$	−7.85641			−0.277074
$805$	17.6603	+	30.5885i	0.622442	+	1.07810i
$806$		−	7.60770i		−	0.267970i
$807$	−7.85641	+	13.6077i	−0.276559	+	0.479014i
$808$		−	27.0000i		−	0.949857i
$809$	−5.32051	−	3.07180i	−0.187059	−	0.107999i	0.403546	−	0.914959i	$-0.367778\pi$
$809$	−5.32051	−	3.07180i	−0.187059	−	0.107999i	−0.590605	+	0.806961i	$0.701111\pi$
$810$	8.33013	−	14.4282i	0.292691	−	0.506955i
$811$	15.1244	−	26.1962i	0.531088	−	0.919871i	−0.468254	−	0.883594i	$-0.655117\pi$
$811$	15.1244	−	26.1962i	0.531088	−	0.919871i	0.999342	−	0.0362773i	$-0.0115500\pi$
$812$	11.1962	−	6.46410i	0.392908	−	0.226845i
$813$	4.14359			0.145322
$814$	−4.39230	−	6.33975i	−0.153950	−	0.222208i
$815$	6.00000			0.210171
$816$	0.169873	−	0.0980762i	0.00594674	−	0.00343335i
$817$	8.19615	−	14.1962i	0.286747	−	0.496661i
$818$	4.33013	−	7.50000i	0.151399	−	0.262231i
$819$	25.6077	+	14.7846i	0.894805	+	0.516616i
$820$			11.1962i			0.390987i
$821$	6.58846	−	11.4115i	0.229939	−	0.398266i	−0.727851	−	0.685735i	$-0.759481\pi$
$821$	6.58846	−	11.4115i	0.229939	−	0.398266i	0.957790	+	0.287470i	$0.0928141\pi$
$822$			0.339746i			0.0118500i
$823$	27.4904	+	47.6147i	0.958254	+	1.65975i	0.726738	+	0.686914i	$0.241035\pi$
$823$	27.4904	+	47.6147i	0.958254	+	1.65975i	0.231516	+	0.972831i	$0.425631\pi$
$824$	2.78461			0.0970065
$825$	8.28719			0.288523
$826$	−11.3205	−	19.6077i	−0.393891	−	0.682239i
$827$	7.85641	+	4.53590i	0.273194	+	0.157729i	0.630338	−	0.776321i	$-0.282916\pi$
$827$	7.85641	+	4.53590i	0.273194	+	0.157729i	−0.357144	+	0.934049i	$0.616250\pi$
$828$			6.73205i			0.233955i
$829$	44.5692	−	25.7321i	1.54795	−	0.893711i	0.549655	−	0.835392i	$-0.314759\pi$
$829$	44.5692	−	25.7321i	1.54795	−	0.893711i	0.998298	−	0.0583193i	$-0.0185742\pi$
$830$	4.09808	+	7.09808i	0.142246	+	0.246378i
$831$	−8.70577	+	5.02628i	−0.302000	+	0.174360i
$832$	−21.0000	−	12.1244i	−0.728044	−	0.420336i
$833$	1.16025	+	0.669873i	0.0402004	+	0.0232097i
$834$	−11.7846	+	6.80385i	−0.408068	+	0.235598i
$835$	−5.46410	−	9.46410i	−0.189093	−	0.327519i
$836$	−5.19615	+	3.00000i	−0.179713	+	0.103757i
$837$			8.78461i			0.303641i
$838$	15.0000	+	8.66025i	0.518166	+	0.299164i
$839$	6.16987	+	10.6865i	0.213008	+	0.368940i	0.952654	−	0.304055i	$-0.0983407\pi$
$839$	6.16987	+	10.6865i	0.213008	+	0.368940i	−0.739647	+	0.672995i	$0.765007\pi$
$840$	28.3923			0.979628
$841$	15.0718			0.519717
$842$	−9.86603	−	17.0885i	−0.340006	−	0.588907i
$843$		−	16.6936i		−	0.574957i
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$			3.73205i			0.128386i
$846$	17.4904	+	10.0981i	0.601332	+	0.347179i
$847$	−16.2679	+	28.1769i	−0.558973	+	0.968170i
$848$	−4.73205	+	8.19615i	−0.162499	+	0.281457i
$849$	−6.58846	+	3.80385i	−0.226115	+	0.130548i
$850$	−2.39230			−0.0820554
$851$	16.5622	−	1.36603i	0.567744	−	0.0468267i
$852$	4.39230			0.150478
$853$	−15.4808	+	8.93782i	−0.530051	+	0.306025i	−0.741037	−	0.671464i	$-0.765666\pi$
$853$	−15.4808	+	8.93782i	−0.530051	+	0.306025i	0.210986	+	0.977489i	$0.432333\pi$
$854$	−13.3923	+	23.1962i	−0.458275	+	0.793756i
$855$	−21.7583	+	37.6865i	−0.744119	+	1.28885i
$856$	−2.41154	−	1.39230i	−0.0824248	−	0.0475880i
$857$		−	20.2679i		−	0.692340i	−0.938172	−	0.346170i	$-0.887482\pi$
$857$		−	20.2679i		−	0.692340i	0.938172	−	0.346170i	$-0.112518\pi$
$858$	1.60770	−	2.78461i	0.0548858	−	0.0950650i
$859$			15.4641i			0.527628i	0.964574	+	0.263814i	$0.0849806\pi$
$859$			15.4641i			0.527628i	−0.964574	+	0.263814i	$0.915019\pi$
$860$	6.46410	+	11.1962i	0.220424	+	0.381786i
$861$	−7.60770			−0.259270
$862$	−33.5167			−1.14158
$863$	−22.7321	−	39.3731i	−0.773808	−	1.34027i	−0.935462	−	0.353427i	$-0.885016\pi$
$863$	−22.7321	−	39.3731i	−0.773808	−	1.34027i	0.161654	−	0.986847i	$-0.448317\pi$
$864$	17.3205	+	10.0000i	0.589256	+	0.340207i
$865$		−	14.6603i		−	0.498464i
$866$	23.3827	−	13.5000i	0.794576	−	0.458749i
$867$	−6.19615	−	10.7321i	−0.210432	−	0.364480i
$868$	6.58846	−	3.80385i	0.223627	−	0.129111i
$869$	15.5885	+	9.00000i	0.528802	+	0.305304i
$870$	−8.83013	−	5.09808i	−0.299369	−	0.172841i
$871$	32.1962	−	18.5885i	1.09093	−	0.629846i
$872$	25.7942	+	44.6769i	0.873503	+	1.51295i
$873$	−16.5000	+	9.52628i	−0.558440	+	0.322416i
$874$			12.9282i			0.437303i
$875$	−43.9808	−	25.3923i	−1.48682	−	0.858417i
$876$		0			0
$877$	−35.7846			−1.20836			−0.604180	−	0.796848i	$-0.706499\pi$
$877$	−35.7846			−1.20836			−0.604180	+	0.796848i	$0.706499\pi$
$878$	−21.4641			−0.724378
$879$	−0.418584	−	0.725009i	−0.0141185	−	0.0244540i
$880$			4.73205i			0.159517i
$881$	1.16025	−	2.00962i	0.0390900	−	0.0677058i	−0.845819	−	0.533471i	$-0.820887\pi$
$881$	1.16025	−	2.00962i	0.0390900	−	0.0677058i	0.884908	+	0.465765i	$0.154221\pi$
$882$		−	12.3205i		−	0.414853i
$883$	15.8827	+	9.16987i	0.534495	+	0.308591i	0.742845	−	0.669464i	$-0.233476\pi$
$883$	15.8827	+	9.16987i	0.534495	+	0.308591i	−0.208350	+	0.978054i	$0.566809\pi$
$884$	0.464102	−	0.803848i	0.0156094	−	0.0270363i
$885$	8.92820	−	15.4641i	0.300118	−	0.519820i
$886$	22.9808	−	13.2679i	0.772054	−	0.445745i
$887$	−22.9808			−0.771618			−0.385809	−	0.922579i	$-0.626078\pi$
$887$	−22.9808			−0.771618			−0.385809	+	0.922579i	$0.626078\pi$
$888$	5.70577	−	12.0788i	0.191473	−	0.405339i
$889$	6.24871			0.209575
$890$	−3.86603	+	2.23205i	−0.129589	+	0.0748185i
$891$	2.83013	−	4.90192i	0.0948128	−	0.164221i
$892$	13.2942	−	23.0263i	0.445124	−	0.770977i
$893$	−33.5885	−	19.3923i	−1.12399	−	0.648939i
$894$			9.12436i			0.305164i
$895$	10.1962	−	17.6603i	0.340820	−	0.590317i
$896$		−	10.3923i		−	0.347183i
$897$	3.46410	+	6.00000i	0.115663	+	0.200334i
$898$	−16.2487			−0.542227
$899$	−8.19615			−0.273357
$900$	−11.0000	−	19.0526i	−0.366667	−	0.635085i
$901$	−2.19615	−	1.26795i	−0.0731644	−	0.0422415i
$902$		−	3.80385i		−	0.126654i
$903$	−7.60770	+	4.39230i	−0.253168	+	0.146167i
$904$	17.1962	+	29.7846i	0.571936	+	0.990621i
$905$	−12.6962	+	7.33013i	−0.422034	+	0.243662i
$906$	9.24871	+	5.33975i	0.307268	+	0.177401i
$907$	−4.09808	−	2.36603i	−0.136074	−	0.0785626i	0.430417	−	0.902630i	$-0.358366\pi$
$907$	−4.09808	−	2.36603i	−0.136074	−	0.0785626i	−0.566492	+	0.824067i	$0.691700\pi$
$908$	−0.973721	+	0.562178i	−0.0323141	+	0.0186565i
$909$	−11.0885	−	19.2058i	−0.367781	−	0.637015i
$910$	−38.7846	+	22.3923i	−1.28570	+	0.742298i
$911$			8.48334i			0.281066i	0.990076	+	0.140533i	$0.0448815\pi$
$911$			8.48334i			0.281066i	−0.990076	+	0.140533i	$0.955118\pi$
$912$	3.00000	+	1.73205i	0.0993399	+	0.0573539i
$913$	1.39230	+	2.41154i	0.0460786	+	0.0798104i
$914$	11.8756			0.392811
$915$	−21.1244			−0.698350
$916$	−3.50000	−	6.06218i	−0.115643	−	0.200300i
$917$			71.3205i			2.35521i
$918$	0.535898	−	0.928203i	0.0176873	−	0.0306353i
$919$			34.0526i			1.12329i	0.827378	+	0.561645i	$0.189831\pi$
$919$			34.0526i			1.12329i	−0.827378	+	0.561645i	$0.810169\pi$
$920$	−26.4904	−	15.2942i	−0.873362	−	0.504236i
$921$	−2.33975	+	4.05256i	−0.0770973	+	0.133536i
$922$	11.7321	−	20.3205i	0.386375	−	0.669220i
$923$	−18.0000	+	10.3923i	−0.592477	+	0.342067i
$924$	3.21539			0.105779
$925$	−44.6410	+	30.9282i	−1.46779	+	1.01691i
$926$	8.53590			0.280507
$927$	1.98076	−	1.14359i	0.0650568	−	0.0375605i
$928$	−9.33013	+	16.1603i	−0.306276	+	0.530486i
$929$	11.7679	−	20.3827i	0.386094	−	0.668734i	−0.605826	−	0.795597i	$-0.707157\pi$
$929$	11.7679	−	20.3827i	0.386094	−	0.668734i	0.991920	+	0.126863i	$0.0404907\pi$
$930$	−5.19615	−	3.00000i	−0.170389	−	0.0983739i
$931$			23.6603i			0.775434i
$932$	−8.42820	+	14.5981i	−0.276075	+	0.478176i
$933$			7.03332i			0.230261i
$934$	−15.6603	−	27.1244i	−0.512419	−	0.887536i
$935$	−1.26795			−0.0414664
$936$	−25.6077			−0.837014
$937$	16.6962	+	28.9186i	0.545440	+	0.944729i	0.998579	+	0.0532894i	$0.0169706\pi$
$937$	16.6962	+	28.9186i	0.545440	+	0.944729i	−0.453140	+	0.891440i	$0.649696\pi$
$938$	−32.1962	−	18.5885i	−1.05124	−	0.606935i
$939$		−	11.4115i		−	0.372402i
$940$	26.4904	−	15.2942i	0.864021	−	0.498843i
$941$	−29.0885	−	50.3827i	−0.948257	−	1.64243i	−0.749096	−	0.662462i	$-0.769512\pi$
$941$	−29.0885	−	50.3827i	−0.948257	−	1.64243i	−0.199161	−	0.979967i	$-0.563822\pi$
$942$	12.8827	−	7.43782i	0.419741	−	0.242337i
$943$	7.09808	+	4.09808i	0.231145	+	0.133452i
$944$	5.66025	+	3.26795i	0.184226	+	0.106363i
$945$	44.7846	−	25.8564i	1.45684	−	0.841109i
$946$	−2.19615	−	3.80385i	−0.0714031	−	0.123674i
$947$	41.9090	−	24.1962i	1.36186	−	0.786269i	0.371987	−	0.928238i	$-0.378677\pi$
$947$	41.9090	−	24.1962i	1.36186	−	0.786269i	0.989871	+	0.141969i	$0.0453432\pi$
$948$			10.3923i			0.337526i
$949$		0			0
$950$	−21.1244	−	36.5885i	−0.685365	−	1.18709i
$951$	−1.51666			−0.0491811
$952$	−2.78461			−0.0902497
$953$	15.9282	+	27.5885i	0.515965	+	0.893678i	0.999828	+	0.0185341i	$0.00589992\pi$
$953$	15.9282	+	27.5885i	0.515965	+	0.893678i	−0.483863	+	0.875144i	$0.660767\pi$
$954$			23.3205i			0.755029i
$955$	−7.83013	+	13.5622i	−0.253377	+	0.438862i
$956$		−	3.07180i		−	0.0993490i
$957$	−3.00000	−	1.73205i	−0.0969762	−	0.0559893i
$958$	2.33975	−	4.05256i	0.0755938	−	0.130932i
$959$	0.803848	−	1.39230i	0.0259576	−	0.0449599i
$960$	−16.5622	+	9.56218i	−0.534542	+	0.308618i
$961$	26.1769			0.844417
$962$	1.73205	+	21.0000i	0.0558436	+	0.677067i
$963$	−2.28719			−0.0737036
$964$	−7.39230	+	4.26795i	−0.238090	+	0.137461i
$965$	−4.96410	+	8.59808i	−0.159800	+	0.276782i
$966$	3.46410	−	6.00000i	0.111456	−	0.193047i
$967$	7.60770	+	4.39230i	0.244647	+	0.141247i	0.617311	−	0.786719i	$-0.288222\pi$
$967$	7.60770	+	4.39230i	0.244647	+	0.141247i	−0.372664	+	0.927966i	$0.621555\pi$
$968$		−	28.1769i		−	0.905640i
$969$	−0.464102	+	0.803848i	−0.0149091	+	0.0258233i
$970$		−	28.8564i		−	0.926523i
$971$	−1.09808	−	1.90192i	−0.0352389	−	0.0610356i	0.847868	−	0.530207i	$-0.177886\pi$
$971$	−1.09808	−	1.90192i	−0.0352389	−	0.0610356i	−0.883107	+	0.469172i	$0.844553\pi$
$972$	15.2679			0.489720
$973$	64.3923			2.06432
$974$	13.2224	+	22.9019i	0.423674	+	0.733825i
$975$	−19.6077	−	11.3205i	−0.627949	−	0.362546i
$976$		−	7.73205i		−	0.247497i
$977$	−27.9282	+	16.1244i	−0.893502	+	0.515864i	−0.875086	−	0.483967i	$-0.839196\pi$
$977$	−27.9282	+	16.1244i	−0.893502	+	0.515864i	−0.0184159	+	0.999830i	$0.505862\pi$
$978$	−0.588457	−	1.01924i	−0.0188168	−	0.0325916i
$979$	−1.31347	+	0.758330i	−0.0419786	+	0.0242363i
$980$	−16.1603	−	9.33013i	−0.516220	−	0.298040i
$981$	36.6962	+	21.1865i	1.17162	+	0.676434i
$982$	30.0788	−	17.3660i	0.959854	−	0.554172i
$983$	−16.4378	−	28.4711i	−0.524285	−	0.908088i	−0.999600	−	0.0282728i	$-0.990999\pi$
$983$	−16.4378	−	28.4711i	−0.524285	−	0.908088i	0.475315	−	0.879816i	$-0.342334\pi$
$984$	5.70577	−	3.29423i	0.181893	−	0.105016i
$985$			52.5167i			1.67332i
$986$	0.866025	+	0.500000i	0.0275799	+	0.0159232i
$987$	10.3923	+	18.0000i	0.330791	+	0.572946i
$988$	16.3923			0.521509
$989$	9.46410			0.300941
$990$	5.83013	+	10.0981i	0.185294	+	0.320938i
$991$			25.6077i			0.813455i	0.913549	+	0.406728i	$0.133330\pi$
$991$			25.6077i			0.813455i	−0.913549	+	0.406728i	$0.866670\pi$
$992$	−5.49038	+	9.50962i	−0.174320	+	0.301931i
$993$			6.43078i			0.204075i
$994$	18.0000	+	10.3923i	0.570925	+	0.329624i
$995$	46.5167	−	80.5692i	1.47468	−	2.55422i
$996$	−0.803848	+	1.39230i	−0.0254709	+	0.0441169i
$997$	−23.7846	+	13.7321i	−0.753266	+	0.434898i	−0.826873	−	0.562389i	$-0.809882\pi$
$997$	−23.7846	+	13.7321i	−0.753266	+	0.434898i	0.0736067	+	0.997287i	$0.476549\pi$
$998$	18.5885			0.588407
$999$	−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.11.2	✓	4
3.2	odd	2		333.2.s.b.307.1		4
4.3	odd	2		592.2.w.c.529.2		4
5.2	odd	4		925.2.m.b.899.1		4
5.3	odd	4		925.2.m.a.899.2		4
5.4	even	2		925.2.n.a.751.1		4
37.8	odd	12		1369.2.a.h.1.1		2
37.11	even	6		1369.2.b.d.1368.2		4
37.26	even	3		1369.2.b.d.1368.4		4
37.27	even	6	inner	37.2.e.a.27.2	yes	4
37.29	odd	12		1369.2.a.g.1.1		2
111.101	odd	6		333.2.s.b.64.1		4
148.27	odd	6		592.2.w.c.545.2		4
185.27	odd	12		925.2.m.a.249.2		4
185.64	even	6		925.2.n.a.101.1		4
185.138	odd	12		925.2.m.b.249.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.e.a.11.2	✓	4	1.1	even	1	trivial
37.2.e.a.27.2	yes	4	37.27	even	6	inner
333.2.s.b.64.1		4	111.101	odd	6
333.2.s.b.307.1		4	3.2	odd	2
592.2.w.c.529.2		4	4.3	odd	2
592.2.w.c.545.2		4	148.27	odd	6
925.2.m.a.249.2		4	185.27	odd	12
925.2.m.a.899.2		4	5.3	odd	4
925.2.m.b.249.1		4	185.138	odd	12
925.2.m.b.899.1		4	5.2	odd	4
925.2.n.a.101.1		4	185.64	even	6
925.2.n.a.751.1		4	5.4	even	2
1369.2.a.g.1.1		2	37.29	odd	12
1369.2.a.h.1.1		2	37.8	odd	12
1369.2.b.d.1368.2		4	37.11	even	6
1369.2.b.d.1368.4		4	37.26	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-3.23205 - 1.86603i) q^{5} +0.732051i q^{6} +(1.73205 - 3.00000i) q^{7} +3.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-3.23205 - 1.86603i) q^{5} +0.732051i q^{6} +(1.73205 - 3.00000i) q^{7} +3.00000i q^{8} +(1.23205 + 2.13397i) q^{9} -3.73205 q^{10} -1.26795 q^{11} +(-0.366025 - 0.633975i) q^{12} +(3.00000 + 1.73205i) q^{13} -3.46410i q^{14} +(2.36603 - 1.36603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.232051 + 0.133975i) q^{17} +(2.13397 + 1.23205i) q^{18} +(-4.09808 - 2.36603i) q^{19} +(3.23205 - 1.86603i) q^{20} +(1.26795 + 2.19615i) q^{21} +(-1.09808 + 0.633975i) q^{22} -2.73205i q^{23} +(-1.90192 - 1.09808i) q^{24} +(4.46410 + 7.73205i) q^{25} +3.46410 q^{26} -4.00000 q^{27} +(1.73205 + 3.00000i) q^{28} -3.73205i q^{29} +(1.36603 - 2.36603i) q^{30} -2.19615i q^{31} +(-4.33013 - 2.50000i) q^{32} +(0.464102 - 0.803848i) q^{33} +(-0.133975 + 0.232051i) q^{34} +(-11.1962 + 6.46410i) q^{35} -2.46410 q^{36} +(0.500000 + 6.06218i) q^{37} -4.73205 q^{38} +(-2.19615 + 1.26795i) q^{39} +(5.59808 - 9.69615i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(2.19615 + 1.26795i) q^{42} +3.46410i q^{43} +(0.633975 - 1.09808i) q^{44} -9.19615i q^{45} +(-1.36603 - 2.36603i) q^{46} +8.19615 q^{47} -0.732051 q^{48} +(-2.50000 - 4.33013i) q^{49} +(7.73205 + 4.46410i) q^{50} -0.196152i q^{51} +(-3.00000 + 1.73205i) q^{52} +(4.73205 + 8.19615i) q^{53} +(-3.46410 + 2.00000i) q^{54} +(4.09808 + 2.36603i) q^{55} +(9.00000 + 5.19615i) q^{56} +(3.00000 - 1.73205i) q^{57} +(-1.86603 - 3.23205i) q^{58} +(5.66025 - 3.26795i) q^{59} +2.73205i q^{60} +(-6.69615 - 3.86603i) q^{61} +(-1.09808 - 1.90192i) q^{62} +8.53590 q^{63} -7.00000 q^{64} +(-6.46410 - 11.1962i) q^{65} -0.928203i q^{66} +(5.36603 - 9.29423i) q^{67} -0.267949i q^{68} +(1.73205 + 1.00000i) q^{69} +(-6.46410 + 11.1962i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(-6.40192 + 3.69615i) q^{72} +(3.46410 + 5.00000i) q^{74} -6.53590 q^{75} +(4.09808 - 2.36603i) q^{76} +(-2.19615 + 3.80385i) q^{77} +(-1.26795 + 2.19615i) q^{78} +(-12.2942 - 7.09808i) q^{79} -3.73205i q^{80} +(-2.23205 + 3.86603i) q^{81} +3.00000i q^{82} +(-1.09808 - 1.90192i) q^{83} -2.53590 q^{84} +1.00000 q^{85} +(1.73205 + 3.00000i) q^{86} +(2.36603 + 1.36603i) q^{87} -3.80385i q^{88} +(1.03590 - 0.598076i) q^{89} +(-4.59808 - 7.96410i) q^{90} +(10.3923 - 6.00000i) q^{91} +(2.36603 + 1.36603i) q^{92} +(1.39230 + 0.803848i) q^{93} +(7.09808 - 4.09808i) q^{94} +(8.83013 + 15.2942i) q^{95} +(3.16987 - 1.83013i) q^{96} +7.73205i q^{97} +(-4.33013 - 2.50000i) q^{98} +(-1.56218 - 2.70577i) 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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