LMFDB - Embedded newform 370.2.l.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(11,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("370.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.l (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:	$2.95446487479$
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	$\chi$	$=$	370.11
Dual form			370.2.l.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000i q^{8} -1.00000 q^{10} +1.26795 q^{11} +(-0.866025 - 1.50000i) q^{12} +(6.23205 + 3.59808i) q^{13} -0.732051i q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.36603 - 1.36603i) q^{17} +(-6.46410 - 3.73205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.633975 + 1.09808i) q^{21} +(-1.09808 + 0.633975i) q^{22} -4.73205i q^{23} +(1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} -7.19615 q^{26} +5.19615 q^{27} +(0.366025 + 0.633975i) q^{28} -8.92820i q^{29} +(-0.866025 + 1.50000i) q^{30} +5.92820i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.09808 - 1.90192i) q^{33} +(-1.36603 + 2.36603i) q^{34} +(-0.633975 + 0.366025i) q^{35} +(-0.500000 - 6.06218i) q^{37} +7.46410 q^{38} +(10.7942 - 6.23205i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-1.23205 + 2.13397i) q^{41} +(-1.09808 - 0.633975i) q^{42} +8.46410i q^{43} +(0.633975 - 1.09808i) q^{44} +(2.36603 + 4.09808i) q^{46} -3.26795 q^{47} -1.73205 q^{48} +(3.23205 + 5.59808i) q^{49} +(-0.866025 - 0.500000i) q^{50} -4.73205i q^{51} +(6.23205 - 3.59808i) q^{52} +(3.69615 + 6.40192i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(1.09808 + 0.633975i) q^{55} +(-0.633975 - 0.366025i) q^{56} +(-11.1962 + 6.46410i) q^{57} +(4.46410 + 7.73205i) q^{58} +(-10.0981 + 5.83013i) q^{59} -1.73205i q^{60} +(-6.46410 - 3.73205i) q^{61} +(-2.96410 - 5.13397i) q^{62} -1.00000 q^{64} +(3.59808 + 6.23205i) q^{65} +2.19615i q^{66} +(-4.00000 + 6.92820i) q^{67} -2.73205i q^{68} +(-7.09808 - 4.09808i) q^{69} +(0.366025 - 0.633975i) q^{70} +(4.19615 - 7.26795i) q^{71} +11.6603 q^{73} +(3.46410 + 5.00000i) q^{74} +1.73205 q^{75} +(-6.46410 + 3.73205i) q^{76} +(-0.464102 + 0.803848i) q^{77} +(-6.23205 + 10.7942i) q^{78} +(-10.3923 - 6.00000i) q^{79} -1.00000i q^{80} +(4.50000 - 7.79423i) q^{81} -2.46410i q^{82} +(-7.73205 - 13.3923i) q^{83} +1.26795 q^{84} +2.73205 q^{85} +(-4.23205 - 7.33013i) q^{86} +(-13.3923 - 7.73205i) q^{87} +1.26795i q^{88} +(-4.26795 + 2.46410i) q^{89} +(-4.56218 + 2.63397i) q^{91} +(-4.09808 - 2.36603i) q^{92} +(8.89230 + 5.13397i) q^{93} +(2.83013 - 1.63397i) q^{94} +(-3.73205 - 6.46410i) q^{95} +(1.50000 - 0.866025i) q^{96} +6.39230i q^{97} +(-5.59808 - 3.23205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^7	$ 4 q + 2 q^{4} + 2 q^{7} - 4 q^{10} + 12 q^{11} + 18 q^{13} + 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{24} + 2 q^{25} - 8 q^{26} - 2 q^{28} - 6 q^{33} - 2 q^{34} - 6 q^{35} - 2 q^{37} + 16 q^{38} + 12 q^{39} - 2 q^{40} + 2 q^{41} + 6 q^{42} + 6 q^{44} + 6 q^{46} - 20 q^{47} + 6 q^{49} + 18 q^{52} - 6 q^{53} - 18 q^{54} - 6 q^{55} - 6 q^{56} - 24 q^{57} + 4 q^{58} - 30 q^{59} - 12 q^{61} + 2 q^{62} - 4 q^{64} + 4 q^{65} - 16 q^{67} - 18 q^{69} - 2 q^{70} - 4 q^{71} + 12 q^{73} - 12 q^{76} + 12 q^{77} - 18 q^{78} + 18 q^{81} - 24 q^{83} + 12 q^{84} + 4 q^{85} - 10 q^{86} - 12 q^{87} - 24 q^{89} + 6 q^{91} - 6 q^{92} - 6 q^{93} - 6 q^{94} - 8 q^{95} + 6 q^{96} - 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^7 - 4 * q^10 + 12 * q^11 + 18 * q^13 + 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^24 + 2 * q^25 - 8 * q^26 - 2 * q^28 - 6 * q^33 - 2 * q^34 - 6 * q^35 - 2 * q^37 + 16 * q^38 + 12 * q^39 - 2 * q^40 + 2 * q^41 + 6 * q^42 + 6 * q^44 + 6 * q^46 - 20 * q^47 + 6 * q^49 + 18 * q^52 - 6 * q^53 - 18 * q^54 - 6 * q^55 - 6 * q^56 - 24 * q^57 + 4 * q^58 - 30 * q^59 - 12 * q^61 + 2 * q^62 - 4 * q^64 + 4 * q^65 - 16 * q^67 - 18 * q^69 - 2 * q^70 - 4 * q^71 + 12 * q^73 - 12 * q^76 + 12 * q^77 - 18 * q^78 + 18 * q^81 - 24 * q^83 + 12 * q^84 + 4 * q^85 - 10 * q^86 - 12 * q^87 - 24 * q^89 + 6 * q^91 - 6 * q^92 - 6 * q^93 - 6 * q^94 - 8 * q^95 + 6 * q^96 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	1.00000			$0$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$			1.73205i			0.707107i
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	−0.926870	−	0.375382i	$-0.877511\pi$
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	0.788526	+	0.615002i	$0.210845\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	1.26795			0.382301			0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795			0.382301			0.191151	+	0.981561i	$0.438778\pi$
$12$	−0.866025	−	1.50000i	−0.250000	−	0.433013i
$13$	6.23205	+	3.59808i	1.72846	+	0.997927i	0.896410	+	0.443227i	$0.146166\pi$
$13$	6.23205	+	3.59808i	1.72846	+	0.997927i	0.832050	+	0.554700i	$0.187167\pi$
$14$		−	0.732051i		−	0.195649i
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.36603	−	1.36603i	0.573845	−	0.331310i	−0.184838	−	0.982769i	$-0.559176\pi$
$17$	2.36603	−	1.36603i	0.573845	−	0.331310i	0.758684	+	0.651459i	$0.225843\pi$
$18$		0			0
$19$	−6.46410	−	3.73205i	−1.48297	−	0.856191i	−0.483154	−	0.875536i	$-0.660509\pi$
$19$	−6.46410	−	3.73205i	−1.48297	−	0.856191i	−0.999813	+	0.0193444i	$0.993842\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	0.633975	+	1.09808i	0.138345	+	0.239620i
$22$	−1.09808	+	0.633975i	−0.234111	+	0.135164i
$23$		−	4.73205i		−	0.986701i	−0.869831	−	0.493350i	$-0.835772\pi$
$23$		−	4.73205i		−	0.986701i	0.869831	−	0.493350i	$-0.164228\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−7.19615			−1.41128
$27$	5.19615			1.00000
$28$	0.366025	+	0.633975i	0.0691723	+	0.119810i
$29$		−	8.92820i		−	1.65793i	−0.559304	−	0.828963i	$-0.688931\pi$
$29$		−	8.92820i		−	1.65793i	0.559304	−	0.828963i	$-0.311069\pi$
$30$	−0.866025	+	1.50000i	−0.158114	+	0.273861i
$31$			5.92820i			1.06474i	0.846513	+	0.532368i	$0.178698\pi$
$31$			5.92820i			1.06474i	−0.846513	+	0.532368i	$0.821302\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.09808	−	1.90192i	0.191151	−	0.331082i
$34$	−1.36603	+	2.36603i	−0.234271	+	0.405770i
$35$	−0.633975	+	0.366025i	−0.107161	+	0.0618696i
$36$		0			0
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$38$	7.46410			1.21084
$39$	10.7942	−	6.23205i	1.72846	−	0.997927i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−1.23205	+	2.13397i	−0.192414	+	0.333271i	−0.946050	−	0.324021i	$-0.894965\pi$
$41$	−1.23205	+	2.13397i	−0.192414	+	0.333271i	0.753636	+	0.657292i	$0.228298\pi$
$42$	−1.09808	−	0.633975i	−0.169437	−	0.0978244i
$43$			8.46410i			1.29076i	0.763860	+	0.645382i	$0.223302\pi$
$43$			8.46410i			1.29076i	−0.763860	+	0.645382i	$0.776698\pi$
$44$	0.633975	−	1.09808i	0.0955753	−	0.165541i
$45$		0			0
$46$	2.36603	+	4.09808i	0.348851	+	0.604228i
$47$	−3.26795			−0.476679			−0.238340	−	0.971182i	$-0.576603\pi$
$47$	−3.26795			−0.476679			−0.238340	+	0.971182i	$0.576603\pi$
$48$	−1.73205			−0.250000
$49$	3.23205	+	5.59808i	0.461722	+	0.799725i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		−	4.73205i		−	0.662620i
$52$	6.23205	−	3.59808i	0.864230	−	0.498963i
$53$	3.69615	+	6.40192i	0.507706	+	0.879372i	0.999960	+	0.00892061i	$0.00283956\pi$
$53$	3.69615	+	6.40192i	0.507706	+	0.879372i	−0.492255	+	0.870451i	$0.663827\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	1.09808	+	0.633975i	0.148065	+	0.0854851i
$56$	−0.633975	−	0.366025i	−0.0847184	−	0.0489122i
$57$	−11.1962	+	6.46410i	−1.48297	+	0.856191i
$58$	4.46410	+	7.73205i	0.586165	+	1.01527i
$59$	−10.0981	+	5.83013i	−1.31466	+	0.759018i	−0.982864	−	0.184334i	$-0.940987\pi$
$59$	−10.0981	+	5.83013i	−1.31466	+	0.759018i	−0.331794	+	0.943352i	$0.607654\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−6.46410	−	3.73205i	−0.827643	−	0.477840i	0.0254017	−	0.999677i	$-0.491914\pi$
$61$	−6.46410	−	3.73205i	−0.827643	−	0.477840i	−0.853045	+	0.521837i	$0.825247\pi$
$62$	−2.96410	−	5.13397i	−0.376441	−	0.652015i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.59808	+	6.23205i	0.446286	+	0.772991i
$66$			2.19615i			0.270328i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$		−	2.73205i		−	0.331310i
$69$	−7.09808	−	4.09808i	−0.854508	−	0.493350i
$70$	0.366025	−	0.633975i	0.0437484	−	0.0757745i
$71$	4.19615	−	7.26795i	0.497992	−	0.862547i	−0.502006	−	0.864864i	$-0.667404\pi$
$71$	4.19615	−	7.26795i	0.497992	−	0.862547i	0.999997	+	0.00231747i	$0.000737673\pi$
$72$		0			0
$73$	11.6603			1.36473			0.682365	−	0.731012i	$-0.260952\pi$
$73$	11.6603			1.36473			0.682365	+	0.731012i	$0.260952\pi$
$74$	3.46410	+	5.00000i	0.402694	+	0.581238i
$75$	1.73205			0.200000
$76$	−6.46410	+	3.73205i	−0.741483	+	0.428096i
$77$	−0.464102	+	0.803848i	−0.0528893	+	0.0916069i
$78$	−6.23205	+	10.7942i	−0.705641	+	1.22221i
$79$	−10.3923	−	6.00000i	−1.16923	−	0.675053i	−0.215728	−	0.976453i	$-0.569212\pi$
$79$	−10.3923	−	6.00000i	−1.16923	−	0.675053i	−0.953498	+	0.301401i	$0.902546\pi$
$80$		−	1.00000i		−	0.111803i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		−	2.46410i		−	0.272115i
$83$	−7.73205	−	13.3923i	−0.848703	−	1.47000i	−0.882366	−	0.470563i	$-0.844051\pi$
$83$	−7.73205	−	13.3923i	−0.848703	−	1.47000i	0.0336635	−	0.999433i	$-0.489283\pi$
$84$	1.26795			0.138345
$85$	2.73205			0.296333
$86$	−4.23205	−	7.33013i	−0.456354	−	0.790428i
$87$	−13.3923	−	7.73205i	−1.43581	−	0.828963i
$88$			1.26795i			0.135164i
$89$	−4.26795	+	2.46410i	−0.452402	+	0.261194i	−0.708844	−	0.705365i	$-0.750783\pi$
$89$	−4.26795	+	2.46410i	−0.452402	+	0.261194i	0.256442	+	0.966560i	$0.417450\pi$
$90$		0			0
$91$	−4.56218	+	2.63397i	−0.478246	+	0.276116i
$92$	−4.09808	−	2.36603i	−0.427254	−	0.246675i
$93$	8.89230	+	5.13397i	0.922089	+	0.532368i
$94$	2.83013	−	1.63397i	0.291905	−	0.168532i
$95$	−3.73205	−	6.46410i	−0.382900	−	0.663203i
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$			6.39230i			0.649040i	0.945879	+	0.324520i	$0.105203\pi$
$97$			6.39230i			0.649040i	−0.945879	+	0.324520i	$0.894797\pi$
$98$	−5.59808	−	3.23205i	−0.565491	−	0.326486i
$99$		0			0
$100$	1.00000			0.100000
$101$	−3.66025			−0.364209			−0.182104	−	0.983279i	$-0.558291\pi$
$101$	−3.66025			−0.364209			−0.182104	+	0.983279i	$0.558291\pi$
$102$	2.36603	+	4.09808i	0.234271	+	0.405770i
$103$			10.1962i			1.00466i	0.864677	+	0.502328i	$0.167523\pi$
$103$			10.1962i			1.00466i	−0.864677	+	0.502328i	$0.832477\pi$
$104$	−3.59808	+	6.23205i	−0.352820	+	0.611103i
$105$			1.26795i			0.123739i
$106$	−6.40192	−	3.69615i	−0.621810	−	0.359002i
$107$	4.06218	−	7.03590i	0.392706	−	0.680186i	−0.600100	−	0.799925i	$-0.704872\pi$
$107$	4.06218	−	7.03590i	0.392706	−	0.680186i	0.992805	+	0.119739i	$0.0382058\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	−8.66025	+	5.00000i	−0.829502	+	0.478913i	−0.853682	−	0.520794i	$-0.825636\pi$
$109$	−8.66025	+	5.00000i	−0.829502	+	0.478913i	0.0241802	+	0.999708i	$0.492302\pi$
$110$	−1.26795			−0.120894
$111$	−9.52628	−	4.50000i	−0.904194	−	0.427121i
$112$	0.732051			0.0691723
$113$	−10.7321	+	6.19615i	−1.00959	+	0.582885i	−0.911071	−	0.412250i	$-0.864743\pi$
$113$	−10.7321	+	6.19615i	−1.00959	+	0.582885i	−0.0985159	+	0.995135i	$0.531410\pi$
$114$	6.46410	−	11.1962i	0.605419	−	1.04862i
$115$	2.36603	−	4.09808i	0.220633	−	0.382148i
$116$	−7.73205	−	4.46410i	−0.717903	−	0.414481i
$117$		0			0
$118$	5.83013	−	10.0981i	0.536707	−	0.929603i
$119$			2.00000i			0.183340i
$120$	0.866025	+	1.50000i	0.0790569	+	0.136931i
$121$	−9.39230			−0.853846
$122$	7.46410			0.675768
$123$	2.13397	+	3.69615i	0.192414	+	0.333271i
$124$	5.13397	+	2.96410i	0.461045	+	0.266184i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	4.73205	+	8.19615i	0.419902	+	0.727291i	0.995929	−	0.0901394i	$-0.0287312\pi$
$127$	4.73205	+	8.19615i	0.419902	+	0.727291i	−0.576028	+	0.817430i	$0.695398\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	12.6962	+	7.33013i	1.11783	+	0.645382i
$130$	−6.23205	−	3.59808i	−0.546587	−	0.315572i
$131$	8.66025	−	5.00000i	0.756650	−	0.436852i	−0.0714417	−	0.997445i	$-0.522760\pi$
$131$	8.66025	−	5.00000i	0.756650	−	0.436852i	0.828092	+	0.560593i	$0.189427\pi$
$132$	−1.09808	−	1.90192i	−0.0955753	−	0.165541i
$133$	4.73205	−	2.73205i	0.410321	−	0.236899i
$134$		−	8.00000i		−	0.691095i
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	1.36603	+	2.36603i	0.117136	+	0.202885i
$137$	−11.6603			−0.996203			−0.498101	−	0.867119i	$-0.665969\pi$
$137$	−11.6603			−0.996203			−0.498101	+	0.867119i	$0.665969\pi$
$138$	8.19615			0.697703
$139$	2.83013	+	4.90192i	0.240048	+	0.415776i	0.960728	−	0.277493i	$-0.0895034\pi$
$139$	2.83013	+	4.90192i	0.240048	+	0.415776i	−0.720680	+	0.693268i	$0.756170\pi$
$140$			0.732051i			0.0618696i
$141$	−2.83013	+	4.90192i	−0.238340	+	0.412816i
$142$			8.39230i			0.704267i
$143$	7.90192	+	4.56218i	0.660792	+	0.381508i
$144$		0			0
$145$	4.46410	−	7.73205i	0.370723	−	0.642112i
$146$	−10.0981	+	5.83013i	−0.835723	+	0.482505i
$147$	11.1962			0.923443
$148$	−5.50000	−	2.59808i	−0.452097	−	0.213561i
$149$	−12.0000			−0.983078			−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000			−0.983078			−0.491539	+	0.870855i	$0.663566\pi$
$150$	−1.50000	+	0.866025i	−0.122474	+	0.0707107i
$151$	2.66987	−	4.62436i	0.217271	−	0.376325i	−0.736702	−	0.676218i	$-0.763618\pi$
$151$	2.66987	−	4.62436i	0.217271	−	0.376325i	0.953973	+	0.299893i	$0.0969511\pi$
$152$	3.73205	−	6.46410i	0.302709	−	0.524308i
$153$		0			0
$154$		−	0.928203i		−	0.0747967i
$155$	−2.96410	+	5.13397i	−0.238082	+	0.412371i
$156$		−	12.4641i		−	0.997927i
$157$	−1.23205	−	2.13397i	−0.0983284	−	0.170310i	0.812664	−	0.582732i	$-0.198016\pi$
$157$	−1.23205	−	2.13397i	−0.0983284	−	0.170310i	−0.910993	+	0.412422i	$0.864683\pi$
$158$	12.0000			0.954669
$159$	12.8038			1.01541
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	3.00000	+	1.73205i	0.236433	+	0.136505i
$162$			9.00000i			0.707107i
$163$	4.33013	−	2.50000i	0.339162	−	0.195815i	−0.320740	−	0.947167i	$-0.603931\pi$
$163$	4.33013	−	2.50000i	0.339162	−	0.195815i	0.659901	+	0.751352i	$0.270598\pi$
$164$	1.23205	+	2.13397i	0.0962070	+	0.166635i
$165$	1.90192	−	1.09808i	0.148065	−	0.0854851i
$166$	13.3923	+	7.73205i	1.03944	+	0.600124i
$167$	−13.7321	−	7.92820i	−1.06262	−	0.613503i	−0.136463	−	0.990645i	$-0.543573\pi$
$167$	−13.7321	−	7.92820i	−1.06262	−	0.613503i	−0.926155	+	0.377142i	$0.876907\pi$
$168$	−1.09808	+	0.633975i	−0.0847184	+	0.0489122i
$169$	19.3923	+	33.5885i	1.49172	+	2.58373i
$170$	−2.36603	+	1.36603i	−0.181466	+	0.104769i
$171$		0			0
$172$	7.33013	+	4.23205i	0.558917	+	0.322691i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	15.4641			1.17233
$175$	−0.732051			−0.0553378
$176$	−0.633975	−	1.09808i	−0.0477876	−	0.0827706i
$177$			20.1962i			1.51804i
$178$	2.46410	−	4.26795i	0.184692	−	0.319896i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$		0			0
$181$	6.83013	−	11.8301i	0.507679	−	0.879326i	−0.492281	−	0.870436i	$-0.663837\pi$
$181$	6.83013	−	11.8301i	0.507679	−	0.879326i	0.999960	−	0.00889016i	$-0.00282986\pi$
$182$	2.63397	−	4.56218i	0.195243	−	0.338171i
$183$	−11.1962	+	6.46410i	−0.827643	+	0.477840i
$184$	4.73205			0.348851
$185$	2.59808	−	5.50000i	0.191014	−	0.404368i
$186$	−10.2679			−0.752883
$187$	3.00000	−	1.73205i	0.219382	−	0.126660i
$188$	−1.63397	+	2.83013i	−0.119170	+	0.206408i
$189$	−1.90192	+	3.29423i	−0.138345	+	0.239620i
$190$	6.46410	+	3.73205i	0.468955	+	0.270751i
$191$			0.607695i			0.0439713i	0.999758	+	0.0219856i	$0.00699881\pi$
$191$			0.607695i			0.0439713i	−0.999758	+	0.0219856i	$0.993001\pi$
$192$	−0.866025	+	1.50000i	−0.0625000	+	0.108253i
$193$		−	16.5885i		−	1.19406i	−0.802218	−	0.597032i	$-0.796347\pi$
$193$		−	16.5885i		−	1.19406i	0.802218	−	0.597032i	$-0.203653\pi$
$194$	−3.19615	−	5.53590i	−0.229470	−	0.397454i
$195$	12.4641			0.892573
$196$	6.46410			0.461722
$197$	4.16025	+	7.20577i	0.296406	+	0.513390i	0.975311	−	0.220836i	$-0.0708786\pi$
$197$	4.16025	+	7.20577i	0.296406	+	0.513390i	−0.678905	+	0.734226i	$0.737545\pi$
$198$		0			0
$199$		−	1.00000i		−	0.0708881i	−0.999372	−	0.0354441i	$-0.988715\pi$
$199$		−	1.00000i		−	0.0708881i	0.999372	−	0.0354441i	$-0.0112846\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	6.92820	+	12.0000i	0.488678	+	0.846415i
$202$	3.16987	−	1.83013i	0.223031	−	0.128767i
$203$	5.66025	+	3.26795i	0.397272	+	0.229365i
$204$	−4.09808	−	2.36603i	−0.286923	−	0.165655i
$205$	−2.13397	+	1.23205i	−0.149043	+	0.0860502i
$206$	−5.09808	−	8.83013i	−0.355200	−	0.615224i
$207$		0			0
$208$		−	7.19615i		−	0.498963i
$209$	−8.19615	−	4.73205i	−0.566940	−	0.327323i
$210$	−0.633975	−	1.09808i	−0.0437484	−	0.0757745i
$211$	18.3923			1.26618			0.633089	−	0.774079i	$-0.281787\pi$
$211$	18.3923			1.26618			0.633089	+	0.774079i	$0.281787\pi$
$212$	7.39230			0.507706
$213$	−7.26795	−	12.5885i	−0.497992	−	0.862547i
$214$			8.12436i			0.555370i
$215$	−4.23205	+	7.33013i	−0.288623	+	0.499911i
$216$			5.19615i			0.353553i
$217$	−3.75833	−	2.16987i	−0.255132	−	0.147301i
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$	10.0981	−	17.4904i	0.682365	−	1.18189i
$220$	1.09808	−	0.633975i	0.0740323	−	0.0427426i
$221$	19.6603			1.32249
$222$	10.5000	−	0.866025i	0.704714	−	0.0581238i
$223$	−20.5885			−1.37871			−0.689353	−	0.724426i	$-0.742105\pi$
$223$	−20.5885			−1.37871			−0.689353	+	0.724426i	$0.742105\pi$
$224$	−0.633975	+	0.366025i	−0.0423592	+	0.0244561i
$225$		0			0
$226$	6.19615	−	10.7321i	0.412162	−	0.713885i
$227$	12.8660	+	7.42820i	0.853948	+	0.493027i	0.861981	−	0.506941i	$-0.169224\pi$
$227$	12.8660	+	7.42820i	0.853948	+	0.493027i	−0.00803291	+	0.999968i	$0.502557\pi$
$228$			12.9282i			0.856191i
$229$	−8.63397	+	14.9545i	−0.570549	+	0.988220i	0.425960	+	0.904742i	$0.359936\pi$
$229$	−8.63397	+	14.9545i	−0.570549	+	0.988220i	−0.996510	+	0.0834783i	$0.973397\pi$
$230$			4.73205i			0.312022i
$231$	0.803848	+	1.39230i	0.0528893	+	0.0916069i
$232$	8.92820			0.586165
$233$	13.2679			0.869212			0.434606	−	0.900621i	$-0.356888\pi$
$233$	13.2679			0.869212			0.434606	+	0.900621i	$0.356888\pi$
$234$		0			0
$235$	−2.83013	−	1.63397i	−0.184617	−	0.106589i
$236$			11.6603i			0.759018i
$237$	−18.0000	+	10.3923i	−1.16923	+	0.675053i
$238$	−1.00000	−	1.73205i	−0.0648204	−	0.112272i
$239$	5.07180	−	2.92820i	0.328067	−	0.189410i	−0.326915	−	0.945054i	$-0.606009\pi$
$239$	5.07180	−	2.92820i	0.328067	−	0.189410i	0.654983	+	0.755644i	$0.272676\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	−3.46410	−	2.00000i	−0.223142	−	0.128831i	0.384262	−	0.923224i	$-0.374456\pi$
$241$	−3.46410	−	2.00000i	−0.223142	−	0.128831i	−0.607404	+	0.794393i	$0.707789\pi$
$242$	8.13397	−	4.69615i	0.522872	−	0.301880i
$243$		0			0
$244$	−6.46410	+	3.73205i	−0.413822	+	0.238920i
$245$			6.46410i			0.412976i
$246$	−3.69615	−	2.13397i	−0.235658	−	0.136057i
$247$	−26.8564	−	46.5167i	−1.70883	−	2.95978i
$248$	−5.92820			−0.376441
$249$	−26.7846			−1.69741
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$			3.46410i			0.218652i	0.994006	+	0.109326i	$0.0348693\pi$
$251$			3.46410i			0.218652i	−0.994006	+	0.109326i	$0.965131\pi$
$252$		0			0
$253$		−	6.00000i		−	0.377217i
$254$	−8.19615	−	4.73205i	−0.514272	−	0.296915i
$255$	2.36603	−	4.09808i	0.148166	−	0.256631i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.83013	−	5.09808i	0.550808	−	0.318009i	−0.198640	−	0.980073i	$-0.563652\pi$
$257$	8.83013	−	5.09808i	0.550808	−	0.318009i	0.749448	+	0.662063i	$0.230319\pi$
$258$	−14.6603			−0.912708
$259$	4.02628	+	1.90192i	0.250181	+	0.118180i
$260$	7.19615			0.446286
$261$		0			0
$262$	−5.00000	+	8.66025i	−0.308901	+	0.535032i
$263$	−1.63397	+	2.83013i	−0.100755	+	0.174513i	−0.911996	−	0.410199i	$-0.865459\pi$
$263$	−1.63397	+	2.83013i	−0.100755	+	0.174513i	0.811241	+	0.584712i	$0.198793\pi$
$264$	1.90192	+	1.09808i	0.117055	+	0.0675819i
$265$			7.39230i			0.454106i
$266$	−2.73205	+	4.73205i	−0.167513	+	0.290141i
$267$			8.53590i			0.522388i
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	17.1244			1.04409			0.522045	−	0.852918i	$-0.325169\pi$
$269$	17.1244			1.04409			0.522045	+	0.852918i	$0.325169\pi$
$270$	−5.19615			−0.316228
$271$	−2.79423	−	4.83975i	−0.169737	−	0.293994i	0.768590	−	0.639741i	$-0.220959\pi$
$271$	−2.79423	−	4.83975i	−0.169737	−	0.293994i	−0.938327	+	0.345748i	$0.887625\pi$
$272$	−2.36603	−	1.36603i	−0.143461	−	0.0828275i
$273$			9.12436i			0.552231i
$274$	10.0981	−	5.83013i	0.610047	−	0.352211i
$275$	0.633975	+	1.09808i	0.0382301	+	0.0662165i
$276$	−7.09808	+	4.09808i	−0.427254	+	0.246675i
$277$	−17.5526	−	10.1340i	−1.05463	−	0.608892i	−0.130689	−	0.991423i	$-0.541719\pi$
$277$	−17.5526	−	10.1340i	−1.05463	−	0.608892i	−0.923942	+	0.382532i	$0.875052\pi$
$278$	−4.90192	−	2.83013i	−0.293998	−	0.169740i
$279$		0			0
$280$	−0.366025	−	0.633975i	−0.0218742	−	0.0378872i
$281$	−26.0885	+	15.0622i	−1.55631	+	0.898534i	−0.558702	+	0.829369i	$0.688700\pi$
$281$	−26.0885	+	15.0622i	−1.55631	+	0.898534i	−0.997605	+	0.0691655i	$0.977966\pi$
$282$		−	5.66025i		−	0.337063i
$283$	−17.7224	−	10.2321i	−1.05349	−	0.608232i	−0.129865	−	0.991532i	$-0.541454\pi$
$283$	−17.7224	−	10.2321i	−1.05349	−	0.608232i	−0.923624	+	0.383299i	$0.874788\pi$
$284$	−4.19615	−	7.26795i	−0.248996	−	0.431273i
$285$	−12.9282			−0.765801
$286$	−9.12436			−0.539534
$287$	−0.901924	−	1.56218i	−0.0532389	−	0.0922124i
$288$		0			0
$289$	−4.76795	+	8.25833i	−0.280468	+	0.485784i
$290$			8.92820i			0.524282i
$291$	9.58846	+	5.53590i	0.562085	+	0.324520i
$292$	5.83013	−	10.0981i	0.341182	−	0.590945i
$293$	10.7679	−	18.6506i	0.629070	−	1.08958i	−0.358668	−	0.933465i	$-0.616769\pi$
$293$	10.7679	−	18.6506i	0.629070	−	1.08958i	0.987739	−	0.156117i	$-0.0498976\pi$
$294$	−9.69615	+	5.59808i	−0.565491	+	0.326486i
$295$	−11.6603			−0.678886
$296$	6.06218	−	0.500000i	0.352357	−	0.0290619i
$297$	6.58846			0.382301
$298$	10.3923	−	6.00000i	0.602010	−	0.347571i
$299$	17.0263	−	29.4904i	0.984655	−	1.70547i
$300$	0.866025	−	1.50000i	0.0500000	−	0.0866025i
$301$	−5.36603	−	3.09808i	−0.309293	−	0.178570i
$302$			5.33975i			0.307268i
$303$	−3.16987	+	5.49038i	−0.182104	+	0.315414i
$304$			7.46410i			0.428096i
$305$	−3.73205	−	6.46410i	−0.213697	−	0.370133i
$306$		0			0
$307$	−2.80385			−0.160024			−0.0800120	−	0.996794i	$-0.525496\pi$
$307$	−2.80385			−0.160024			−0.0800120	+	0.996794i	$0.525496\pi$
$308$	0.464102	+	0.803848i	0.0264446	+	0.0458035i
$309$	15.2942	+	8.83013i	0.870058	+	0.502328i
$310$		−	5.92820i		−	0.336699i
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	−0.216391	−	0.976307i	$-0.569428\pi$
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	0.737311	+	0.675553i	$0.236095\pi$
$312$	6.23205	+	10.7942i	0.352820	+	0.611103i
$313$	−6.12436	+	3.53590i	−0.346169	+	0.199861i	−0.662997	−	0.748622i	$-0.730716\pi$
$313$	−6.12436	+	3.53590i	−0.346169	+	0.199861i	0.316828	+	0.948483i	$0.397382\pi$
$314$	2.13397	+	1.23205i	0.120427	+	0.0695286i
$315$		0			0
$316$	−10.3923	+	6.00000i	−0.584613	+	0.337526i
$317$	1.16025	+	2.00962i	0.0651664	+	0.112871i	0.896768	−	0.442501i	$-0.145909\pi$
$317$	1.16025	+	2.00962i	0.0651664	+	0.112871i	−0.831601	+	0.555373i	$0.812576\pi$
$318$	−11.0885	+	6.40192i	−0.621810	+	0.359002i
$319$		−	11.3205i		−	0.633827i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−7.03590	−	12.1865i	−0.392706	−	0.680186i
$322$	−3.46410			−0.193047
$323$	−20.3923			−1.13466
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$			7.19615i			0.399171i
$326$	−2.50000	+	4.33013i	−0.138462	+	0.239824i
$327$			17.3205i			0.957826i
$328$	−2.13397	−	1.23205i	−0.117829	−	0.0680286i
$329$	1.19615	−	2.07180i	0.0659460	−	0.114222i
$330$	−1.09808	+	1.90192i	−0.0604471	+	0.104697i
$331$	14.0263	−	8.09808i	0.770954	−	0.445111i	−0.0622608	−	0.998060i	$-0.519831\pi$
$331$	14.0263	−	8.09808i	0.770954	−	0.445111i	0.833215	+	0.552949i	$0.186498\pi$
$332$	−15.4641			−0.848703
$333$		0			0
$334$	15.8564			0.867624
$335$	−6.92820	+	4.00000i	−0.378528	+	0.218543i
$336$	0.633975	−	1.09808i	0.0345861	−	0.0599050i
$337$	8.12436	−	14.0718i	0.442562	−	0.766540i	−0.555317	−	0.831639i	$-0.687403\pi$
$337$	8.12436	−	14.0718i	0.442562	−	0.766540i	0.997879	+	0.0650992i	$0.0207364\pi$
$338$	−33.5885	−	19.3923i	−1.82697	−	1.05480i
$339$			21.4641i			1.16577i
$340$	1.36603	−	2.36603i	0.0740831	−	0.128316i
$341$			7.51666i			0.407050i
$342$		0			0
$343$	−9.85641			−0.532196
$344$	−8.46410			−0.456354
$345$	−4.09808	−	7.09808i	−0.220633	−	0.382148i
$346$	5.19615	+	3.00000i	0.279347	+	0.161281i
$347$			28.9282i			1.55295i	0.630150	+	0.776474i	$0.282994\pi$
$347$			28.9282i			1.55295i	−0.630150	+	0.776474i	$0.717006\pi$
$348$	−13.3923	+	7.73205i	−0.717903	+	0.414481i
$349$	0.464102	+	0.803848i	0.0248428	+	0.0430290i	0.878180	−	0.478331i	$-0.158758\pi$
$349$	0.464102	+	0.803848i	0.0248428	+	0.0430290i	−0.853337	+	0.521360i	$0.825425\pi$
$350$	0.633975	−	0.366025i	0.0338874	−	0.0195649i
$351$	32.3827	+	18.6962i	1.72846	+	0.997927i
$352$	1.09808	+	0.633975i	0.0585277	+	0.0337910i
$353$	−15.1699	+	8.75833i	−0.807411	+	0.466159i	−0.846056	−	0.533094i	$-0.821029\pi$
$353$	−15.1699	+	8.75833i	−0.807411	+	0.466159i	0.0386451	+	0.999253i	$0.487696\pi$
$354$	−10.0981	−	17.4904i	−0.536707	−	0.929603i
$355$	7.26795	−	4.19615i	0.385743	−	0.222709i
$356$			4.92820i			0.261194i
$357$	3.00000	+	1.73205i	0.158777	+	0.0916698i
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−31.7321			−1.67475			−0.837377	−	0.546626i	$-0.815912\pi$
$359$	−31.7321			−1.67475			−0.837377	+	0.546626i	$0.815912\pi$
$360$		0			0
$361$	18.3564	+	31.7942i	0.966127	+	1.67338i
$362$			13.6603i			0.717967i
$363$	−8.13397	+	14.0885i	−0.426923	+	0.739452i
$364$			5.26795i			0.276116i
$365$	10.0981	+	5.83013i	0.528557	+	0.305163i
$366$	6.46410	−	11.1962i	0.337884	−	0.585232i
$367$	8.12436	−	14.0718i	0.424088	−	0.734542i	−0.572247	−	0.820081i	$-0.693928\pi$
$367$	8.12436	−	14.0718i	0.424088	−	0.734542i	0.996335	+	0.0855396i	$0.0272614\pi$
$368$	−4.09808	+	2.36603i	−0.213627	+	0.123338i
$369$		0			0
$370$	0.500000	+	6.06218i	0.0259938	+	0.315158i
$371$	−5.41154			−0.280953
$372$	8.89230	−	5.13397i	0.461045	−	0.266184i
$373$	10.2321	−	17.7224i	0.529796	−	0.917633i	−0.469600	−	0.882879i	$-0.655602\pi$
$373$	10.2321	−	17.7224i	0.529796	−	0.917633i	0.999396	−	0.0347537i	$-0.0110647\pi$
$374$	−1.73205	+	3.00000i	−0.0895622	+	0.155126i
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$		−	3.26795i		−	0.168532i
$377$	32.1244	−	55.6410i	1.65449	−	2.86566i
$378$		−	3.80385i		−	0.195649i
$379$	5.56218	+	9.63397i	0.285710	+	0.494864i	0.972781	−	0.231726i	$-0.0744373\pi$
$379$	5.56218	+	9.63397i	0.285710	+	0.494864i	−0.687071	+	0.726590i	$0.741104\pi$
$380$	−7.46410			−0.382900
$381$	16.3923			0.839803
$382$	−0.303848	−	0.526279i	−0.0155462	−	0.0269268i
$383$	6.50962	+	3.75833i	0.332626	+	0.192042i	0.657006	−	0.753885i	$-0.271822\pi$
$383$	6.50962	+	3.75833i	0.332626	+	0.192042i	−0.324380	+	0.945927i	$0.605156\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	−0.803848	+	0.464102i	−0.0409679	+	0.0236528i
$386$	8.29423	+	14.3660i	0.422165	+	0.731211i
$387$		0			0
$388$	5.53590	+	3.19615i	0.281043	+	0.162260i
$389$	−0.928203	−	0.535898i	−0.0470618	−	0.0271711i	0.476285	−	0.879291i	$-0.341983\pi$
$389$	−0.928203	−	0.535898i	−0.0470618	−	0.0271711i	−0.523346	+	0.852120i	$0.675317\pi$
$390$	−10.7942	+	6.23205i	−0.546587	+	0.315572i
$391$	−6.46410	−	11.1962i	−0.326904	−	0.566214i
$392$	−5.59808	+	3.23205i	−0.282746	+	0.163243i
$393$		−	17.3205i		−	0.873704i
$394$	−7.20577	−	4.16025i	−0.363022	−	0.209591i
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$		0			0
$397$	10.4641			0.525178			0.262589	−	0.964908i	$-0.415424\pi$
$397$	10.4641			0.525178			0.262589	+	0.964908i	$0.415424\pi$
$398$	0.500000	+	0.866025i	0.0250627	+	0.0434099i
$399$		−	9.46410i		−	0.473798i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			8.92820i			0.445853i	0.974835	+	0.222927i	$0.0715610\pi$
$401$			8.92820i			0.445853i	−0.974835	+	0.222927i	$0.928439\pi$
$402$	−12.0000	−	6.92820i	−0.598506	−	0.345547i
$403$	−21.3301	+	36.9449i	−1.06253	+	1.84035i
$404$	−1.83013	+	3.16987i	−0.0910522	+	0.157707i
$405$	7.79423	−	4.50000i	0.387298	−	0.223607i
$406$	−6.53590			−0.324371
$407$	−0.633975	−	7.68653i	−0.0314250	−	0.381007i
$408$	4.73205			0.234271
$409$	−12.8205	+	7.40192i	−0.633933	+	0.366002i	−0.782274	−	0.622935i	$-0.785940\pi$
$409$	−12.8205	+	7.40192i	−0.633933	+	0.366002i	0.148340	+	0.988936i	$0.452607\pi$
$410$	1.23205	−	2.13397i	0.0608467	−	0.105389i
$411$	−10.0981	+	17.4904i	−0.498101	+	0.862737i
$412$	8.83013	+	5.09808i	0.435029	+	0.251164i
$413$		−	8.53590i		−	0.420024i
$414$		0			0
$415$		−	15.4641i		−	0.759103i
$416$	3.59808	+	6.23205i	0.176410	+	0.305551i
$417$	9.80385			0.480096
$418$	9.46410			0.462904
$419$	5.02628	+	8.70577i	0.245550	+	0.425305i	0.962286	−	0.272040i	$-0.0876982\pi$
$419$	5.02628	+	8.70577i	0.245550	+	0.425305i	−0.716736	+	0.697344i	$0.754365\pi$
$420$	1.09808	+	0.633975i	0.0535806	+	0.0309348i
$421$			10.5885i			0.516050i	0.966138	+	0.258025i	$0.0830717\pi$
$421$			10.5885i			0.516050i	−0.966138	+	0.258025i	$0.916928\pi$
$422$	−15.9282	+	9.19615i	−0.775373	+	0.447662i
$423$		0			0
$424$	−6.40192	+	3.69615i	−0.310905	+	0.179501i
$425$	2.36603	+	1.36603i	0.114769	+	0.0662620i
$426$	12.5885	+	7.26795i	0.609913	+	0.352133i
$427$	4.73205	−	2.73205i	0.229000	−	0.132213i
$428$	−4.06218	−	7.03590i	−0.196353	−	0.340093i
$429$	13.6865	−	7.90192i	0.660792	−	0.381508i
$430$		−	8.46410i		−	0.408175i
$431$	20.5981	+	11.8923i	0.992174	+	0.572832i	0.905924	−	0.423441i	$-0.139178\pi$
$431$	20.5981	+	11.8923i	0.992174	+	0.572832i	0.0862509	+	0.996273i	$0.472511\pi$
$432$	−2.59808	−	4.50000i	−0.125000	−	0.216506i
$433$	28.7846			1.38330			0.691650	−	0.722233i	$-0.256884\pi$
$433$	28.7846			1.38330			0.691650	+	0.722233i	$0.256884\pi$
$434$	4.33975			0.208314
$435$	−7.73205	−	13.3923i	−0.370723	−	0.642112i
$436$			10.0000i			0.478913i
$437$	−17.6603	+	30.5885i	−0.844805	+	1.46324i
$438$			20.1962i			0.965009i
$439$	−8.47372	−	4.89230i	−0.404429	−	0.233497i	0.283964	−	0.958835i	$-0.408350\pi$
$439$	−8.47372	−	4.89230i	−0.404429	−	0.233497i	−0.688393	+	0.725338i	$0.741684\pi$
$440$	−0.633975	+	1.09808i	−0.0302236	+	0.0523487i
$441$		0			0
$442$	−17.0263	+	9.83013i	−0.809858	+	0.467571i
$443$	33.7321			1.60266			0.801329	−	0.598224i	$-0.204127\pi$
$443$	33.7321			1.60266			0.801329	+	0.598224i	$0.204127\pi$
$444$	−8.66025	+	6.00000i	−0.410997	+	0.284747i
$445$	−4.92820			−0.233619
$446$	17.8301	−	10.2942i	0.844281	−	0.487446i
$447$	−10.3923	+	18.0000i	−0.491539	+	0.851371i
$448$	0.366025	−	0.633975i	0.0172931	−	0.0299525i
$449$	−24.6962	−	14.2583i	−1.16548	−	0.672892i	−0.212871	−	0.977080i	$-0.568282\pi$
$449$	−24.6962	−	14.2583i	−1.16548	−	0.672892i	−0.952612	+	0.304188i	$0.901615\pi$
$450$		0			0
$451$	−1.56218	+	2.70577i	−0.0735601	+	0.127410i
$452$			12.3923i			0.582885i
$453$	−4.62436	−	8.00962i	−0.217271	−	0.376325i
$454$	−14.8564			−0.697246
$455$	−5.26795			−0.246965
$456$	−6.46410	−	11.1962i	−0.302709	−	0.524308i
$457$	−22.3923	−	12.9282i	−1.04747	−	0.604756i	−0.125528	−	0.992090i	$-0.540063\pi$
$457$	−22.3923	−	12.9282i	−1.04747	−	0.604756i	−0.921939	+	0.387334i	$0.873396\pi$
$458$		−	17.2679i		−	0.806878i
$459$	12.2942	−	7.09808i	0.573845	−	0.331310i
$460$	−2.36603	−	4.09808i	−0.110317	−	0.191074i
$461$	27.0000	−	15.5885i	1.25752	−	0.726027i	0.284925	−	0.958550i	$-0.408031\pi$
$461$	27.0000	−	15.5885i	1.25752	−	0.726027i	0.972591	+	0.232523i	$0.0746981\pi$
$462$	−1.39230	−	0.803848i	−0.0647759	−	0.0373984i
$463$	−22.3923	−	12.9282i	−1.04066	−	0.600825i	−0.120639	−	0.992696i	$-0.538494\pi$
$463$	−22.3923	−	12.9282i	−1.04066	−	0.600825i	−0.920020	+	0.391872i	$0.871828\pi$
$464$	−7.73205	+	4.46410i	−0.358951	+	0.207241i
$465$	5.13397	+	8.89230i	0.238082	+	0.412371i
$466$	−11.4904	+	6.63397i	−0.532282	+	0.307313i
$467$			1.00000i			0.0462745i	0.999732	+	0.0231372i	$0.00736547\pi$
$467$			1.00000i			0.0462745i	−0.999732	+	0.0231372i	$0.992635\pi$
$468$		0			0
$469$	−2.92820	−	5.07180i	−0.135212	−	0.234194i
$470$	3.26795			0.150739
$471$	−4.26795			−0.196657
$472$	−5.83013	−	10.0981i	−0.268353	−	0.464802i
$473$			10.7321i			0.493460i
$474$	10.3923	−	18.0000i	0.477334	−	0.826767i
$475$		−	7.46410i		−	0.342476i
$476$	1.73205	+	1.00000i	0.0793884	+	0.0458349i
$477$		0			0
$478$	−2.92820	+	5.07180i	−0.133933	+	0.231979i
$479$	32.2583	−	18.6244i	1.47392	−	0.850969i	0.474352	−	0.880335i	$-0.342682\pi$
$479$	32.2583	−	18.6244i	1.47392	−	0.850969i	0.999569	+	0.0293667i	$0.00934906\pi$
$480$	1.73205			0.0790569
$481$	18.6962	−	39.5788i	0.852471	−	1.80464i
$482$	4.00000			0.182195
$483$	5.19615	−	3.00000i	0.236433	−	0.136505i
$484$	−4.69615	+	8.13397i	−0.213461	+	0.369726i
$485$	−3.19615	+	5.53590i	−0.145130	+	0.251372i
$486$		0			0
$487$			6.78461i			0.307440i	0.988114	+	0.153720i	$0.0491254\pi$
$487$			6.78461i			0.307440i	−0.988114	+	0.153720i	$0.950875\pi$
$488$	3.73205	−	6.46410i	0.168942	−	0.292616i
$489$		−	8.66025i		−	0.391630i
$490$	−3.23205	−	5.59808i	−0.146009	−	0.252895i
$491$	−13.2679			−0.598774			−0.299387	−	0.954132i	$-0.596782\pi$
$491$	−13.2679			−0.598774			−0.299387	+	0.954132i	$0.596782\pi$
$492$	4.26795			0.192414
$493$	−12.1962	−	21.1244i	−0.549287	−	0.951393i
$494$	46.5167	+	26.8564i	2.09288	+	1.20833i
$495$		0			0
$496$	5.13397	−	2.96410i	0.230522	−	0.133092i
$497$	3.07180	+	5.32051i	0.137789	+	0.238657i
$498$	23.1962	−	13.3923i	1.03944	−	0.600124i
$499$	−0.928203	−	0.535898i	−0.0415521	−	0.0239901i	0.479080	−	0.877771i	$-0.340970\pi$
$499$	−0.928203	−	0.535898i	−0.0415521	−	0.0239901i	−0.520632	+	0.853781i	$0.674304\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−23.7846	+	13.7321i	−1.06262	+	0.613503i
$502$	−1.73205	−	3.00000i	−0.0773052	−	0.133897i
$503$	−7.09808	+	4.09808i	−0.316488	+	0.182724i	−0.649826	−	0.760083i	$-0.725158\pi$
$503$	−7.09808	+	4.09808i	−0.316488	+	0.182724i	0.333338	+	0.942807i	$0.391825\pi$
$504$		0			0
$505$	−3.16987	−	1.83013i	−0.141057	−	0.0814396i
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$	67.1769			2.98343
$508$	9.46410			0.419902
$509$	−0.830127	−	1.43782i	−0.0367947	−	0.0637303i	0.847042	−	0.531527i	$-0.178381\pi$
$509$	−0.830127	−	1.43782i	−0.0367947	−	0.0637303i	−0.883836	+	0.467796i	$0.845048\pi$
$510$			4.73205i			0.209539i
$511$	−4.26795	+	7.39230i	−0.188803	+	0.327016i
$512$		−	1.00000i		−	0.0441942i
$513$	−33.5885	−	19.3923i	−1.48297	−	0.856191i
$514$	−5.09808	+	8.83013i	−0.224867	+	0.389480i
$515$	−5.09808	+	8.83013i	−0.224648	+	0.389102i
$516$	12.6962	−	7.33013i	0.558917	−	0.322691i
$517$	−4.14359			−0.182235
$518$	−4.43782	+	0.366025i	−0.194987	+	0.0160822i
$519$	−10.3923			−0.456172
$520$	−6.23205	+	3.59808i	−0.273294	+	0.157786i
$521$	8.69615	−	15.0622i	0.380985	−	0.659886i	−0.610218	−	0.792234i	$-0.708918\pi$
$521$	8.69615	−	15.0622i	0.380985	−	0.659886i	0.991203	+	0.132348i	$0.0422515\pi$
$522$		0			0
$523$	20.7224	+	11.9641i	0.906129	+	0.523154i	0.879184	−	0.476483i	$-0.158089\pi$
$523$	20.7224	+	11.9641i	0.906129	+	0.523154i	0.0269451	+	0.999637i	$0.491422\pi$
$524$		−	10.0000i		−	0.436852i
$525$	−0.633975	+	1.09808i	−0.0276689	+	0.0479240i
$526$		−	3.26795i		−	0.142489i
$527$	8.09808	+	14.0263i	0.352758	+	0.610994i
$528$	−2.19615			−0.0955753
$529$	0.607695			0.0264215
$530$	−3.69615	−	6.40192i	−0.160551	−	0.278082i
$531$		0			0
$532$		−	5.46410i		−	0.236899i
$533$	−15.3564	+	8.86603i	−0.665160	+	0.384030i
$534$	−4.26795	−	7.39230i	−0.184692	−	0.319896i
$535$	7.03590	−	4.06218i	0.304188	−	0.175623i
$536$	−6.92820	−	4.00000i	−0.299253	−	0.172774i
$537$	−18.0000	−	10.3923i	−0.776757	−	0.448461i
$538$	−14.8301	+	8.56218i	−0.639372	+	0.369142i
$539$	4.09808	+	7.09808i	0.176517	+	0.305736i
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$		−	40.2487i		−	1.73043i	−0.501403	−	0.865214i	$-0.667183\pi$
$541$		−	40.2487i		−	1.73043i	0.501403	−	0.865214i	$-0.332817\pi$
$542$	4.83975	+	2.79423i	0.207885	+	0.120022i
$543$	−11.8301	−	20.4904i	−0.507679	−	0.879326i
$544$	2.73205			0.117136
$545$	−10.0000			−0.428353
$546$	−4.56218	−	7.90192i	−0.195243	−	0.338171i
$547$			11.7846i			0.503874i	0.967744	+	0.251937i	$0.0810675\pi$
$547$			11.7846i			0.503874i	−0.967744	+	0.251937i	$0.918933\pi$
$548$	−5.83013	+	10.0981i	−0.249051	+	0.431368i
$549$		0			0
$550$	−1.09808	−	0.633975i	−0.0468221	−	0.0270328i
$551$	−33.3205	+	57.7128i	−1.41950	+	2.45865i
$552$	4.09808	−	7.09808i	0.174426	−	0.302114i
$553$	7.60770	−	4.39230i	0.323512	−	0.186780i
$554$	20.2679			0.861103
$555$	−6.00000	−	8.66025i	−0.254686	−	0.367607i
$556$	5.66025			0.240048
$557$	16.5000	−	9.52628i	0.699127	−	0.403641i	−0.107895	−	0.994162i	$-0.534411\pi$
$557$	16.5000	−	9.52628i	0.699127	−	0.403641i	0.807022	+	0.590521i	$0.201078\pi$
$558$		0			0
$559$	−30.4545	+	52.7487i	−1.28809	+	2.23103i
$560$	0.633975	+	0.366025i	0.0267903	+	0.0154674i
$561$		−	6.00000i		−	0.253320i
$562$	15.0622	−	26.0885i	0.635360	−	1.10048i
$563$			36.2487i			1.52770i	0.645393	+	0.763851i	$0.276694\pi$
$563$			36.2487i			1.52770i	−0.645393	+	0.763851i	$0.723306\pi$
$564$	2.83013	+	4.90192i	0.119170	+	0.206408i
$565$	−12.3923			−0.521348
$566$	20.4641			0.860170
$567$	3.29423	+	5.70577i	0.138345	+	0.239620i
$568$	7.26795	+	4.19615i	0.304956	+	0.176067i
$569$			23.9808i			1.00533i	0.864482	+	0.502663i	$0.167646\pi$
$569$			23.9808i			1.00533i	−0.864482	+	0.502663i	$0.832354\pi$
$570$	11.1962	−	6.46410i	0.468955	−	0.270751i
$571$	−8.73205	−	15.1244i	−0.365425	−	0.632935i	0.623419	−	0.781888i	$-0.285743\pi$
$571$	−8.73205	−	15.1244i	−0.365425	−	0.632935i	−0.988844	+	0.148953i	$0.952410\pi$
$572$	7.90192	−	4.56218i	0.330396	−	0.190754i
$573$	0.911543	+	0.526279i	0.0380802	+	0.0219856i
$574$	1.56218	+	0.901924i	0.0652040	+	0.0376456i
$575$	4.09808	−	2.36603i	0.170902	−	0.0986701i
$576$		0			0
$577$	25.2224	−	14.5622i	1.05002	−	0.606231i	0.127368	−	0.991856i	$-0.459347\pi$
$577$	25.2224	−	14.5622i	1.05002	−	0.606231i	0.922656	+	0.385624i	$0.126014\pi$
$578$		−	9.53590i		−	0.396641i
$579$	−24.8827	−	14.3660i	−1.03409	−	0.597032i
$580$	−4.46410	−	7.73205i	−0.185362	−	0.321056i
$581$	11.3205			0.469654
$582$	−11.0718			−0.458941
$583$	4.68653	+	8.11731i	0.194096	+	0.336185i
$584$			11.6603i			0.482505i
$585$		0			0
$586$			21.5359i			0.889640i
$587$	20.5981	+	11.8923i	0.850174	+	0.490848i	0.860709	−	0.509097i	$-0.170020\pi$
$587$	20.5981	+	11.8923i	0.850174	+	0.490848i	−0.0105358	+	0.999944i	$0.503354\pi$
$588$	5.59808	−	9.69615i	0.230861	−	0.399863i
$589$	22.1244	−	38.3205i	0.911618	−	1.57897i
$590$	10.0981	−	5.83013i	0.415731	−	0.240023i
$591$	14.4115			0.592812
$592$	−5.00000	+	3.46410i	−0.205499	+	0.142374i
$593$	38.1962			1.56853			0.784264	−	0.620427i	$-0.213041\pi$
$593$	38.1962			1.56853			0.784264	+	0.620427i	$0.213041\pi$
$594$	−5.70577	+	3.29423i	−0.234111	+	0.135164i
$595$	−1.00000	+	1.73205i	−0.0409960	+	0.0710072i
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$	−1.50000	−	0.866025i	−0.0613909	−	0.0354441i
$598$			34.0526i			1.39251i
$599$	18.2583	−	31.6244i	0.746015	−	1.29214i	−0.203704	−	0.979033i	$-0.565298\pi$
$599$	18.2583	−	31.6244i	0.746015	−	1.29214i	0.949719	−	0.313104i	$-0.101369\pi$
$600$			1.73205i			0.0707107i
$601$	−4.30385	−	7.45448i	−0.175558	−	0.304075i	0.764796	−	0.644272i	$-0.222839\pi$
$601$	−4.30385	−	7.45448i	−0.175558	−	0.304075i	−0.940354	+	0.340197i	$0.889506\pi$
$602$	6.19615			0.252536
$603$		0			0
$604$	−2.66987	−	4.62436i	−0.108636	−	0.188162i
$605$	−8.13397	−	4.69615i	−0.330693	−	0.190926i
$606$		−	6.33975i		−	0.257535i
$607$	−1.68653	+	0.973721i	−0.0684543	+	0.0395221i	−0.533836	−	0.845588i	$-0.679250\pi$
$607$	−1.68653	+	0.973721i	−0.0684543	+	0.0395221i	0.465382	+	0.885110i	$0.345917\pi$
$608$	−3.73205	−	6.46410i	−0.151355	−	0.262154i
$609$	9.80385	−	5.66025i	0.397272	−	0.229365i
$610$	6.46410	+	3.73205i	0.261724	+	0.151106i
$611$	−20.3660	−	11.7583i	−0.823921	−	0.475691i
$612$		0			0
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	0.999845	−	0.0176058i	$-0.00560439\pi$
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	−0.515170	+	0.857088i	$0.672271\pi$
$614$	2.42820	−	1.40192i	0.0979943	−	0.0565770i
$615$			4.26795i			0.172100i
$616$	−0.803848	−	0.464102i	−0.0323879	−	0.0186992i
$617$	19.0526	+	33.0000i	0.767027	+	1.32853i	0.939168	+	0.343458i	$0.111598\pi$
$617$	19.0526	+	33.0000i	0.767027	+	1.32853i	−0.172141	+	0.985072i	$0.555068\pi$
$618$	−17.6603			−0.710400
$619$	27.8564			1.11964			0.559822	−	0.828613i	$-0.310870\pi$
$619$	27.8564			1.11964			0.559822	+	0.828613i	$0.310870\pi$
$620$	2.96410	+	5.13397i	0.119041	+	0.206185i
$621$		−	24.5885i		−	0.986701i
$622$	−5.30385	+	9.18653i	−0.212665	+	0.368346i
$623$		−	3.60770i		−	0.144539i
$624$	−10.7942	−	6.23205i	−0.432115	−	0.249482i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.53590	−	6.12436i	0.141323	−	0.244778i
$627$	−14.1962	+	8.19615i	−0.566940	+	0.327323i
$628$	−2.46410			−0.0983284
$629$	−9.46410	−	13.6603i	−0.377358	−	0.544670i
$630$		0			0
$631$	−24.3109	+	14.0359i	−0.967801	+	0.558760i	−0.898565	−	0.438840i	$-0.855389\pi$
$631$	−24.3109	+	14.0359i	−0.967801	+	0.558760i	−0.0692360	+	0.997600i	$0.522056\pi$
$632$	6.00000	−	10.3923i	0.238667	−	0.413384i
$633$	15.9282	−	27.5885i	0.633089	−	1.09654i
$634$	−2.00962	−	1.16025i	−0.0798122	−	0.0460796i
$635$			9.46410i			0.375571i
$636$	6.40192	−	11.0885i	0.253853	−	0.439686i
$637$			46.5167i			1.84306i
$638$	5.66025	+	9.80385i	0.224092	+	0.388138i
$639$		0			0
$640$	1.00000			0.0395285
$641$	−9.89230	−	17.1340i	−0.390723	−	0.676751i	0.601822	−	0.798630i	$-0.294441\pi$
$641$	−9.89230	−	17.1340i	−0.390723	−	0.676751i	−0.992545	+	0.121879i	$0.961108\pi$
$642$	12.1865	+	7.03590i	0.480964	+	0.277685i
$643$		−	5.78461i		−	0.228123i	−0.993474	−	0.114061i	$-0.963614\pi$
$643$		−	5.78461i		−	0.228123i	0.993474	−	0.114061i	$-0.0363861\pi$
$644$	3.00000	−	1.73205i	0.118217	−	0.0682524i
$645$	7.33013	+	12.6962i	0.288623	+	0.499911i
$646$	17.6603	−	10.1962i	0.694833	−	0.401162i
$647$	1.60770	+	0.928203i	0.0632050	+	0.0364914i	0.531269	−	0.847203i	$-0.321715\pi$
$647$	1.60770	+	0.928203i	0.0632050	+	0.0364914i	−0.468064	+	0.883694i	$0.655049\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$	−12.8038	+	7.39230i	−0.502595	+	0.290173i
$650$	−3.59808	−	6.23205i	−0.141128	−	0.244441i
$651$	−6.50962	+	3.75833i	−0.255132	+	0.147301i
$652$		−	5.00000i		−	0.195815i
$653$	−26.5526	−	15.3301i	−1.03908	−	0.599914i	−0.119509	−	0.992833i	$-0.538132\pi$
$653$	−26.5526	−	15.3301i	−1.03908	−	0.599914i	−0.919573	+	0.392919i	$0.871465\pi$
$654$	−8.66025	−	15.0000i	−0.338643	−	0.586546i
$655$	10.0000			0.390732
$656$	2.46410			0.0962070
$657$		0			0
$658$			2.39230i			0.0932618i
$659$	−3.12436	+	5.41154i	−0.121708	+	0.210804i	−0.920441	−	0.390881i	$-0.872170\pi$
$659$	−3.12436	+	5.41154i	−0.121708	+	0.210804i	0.798734	+	0.601685i	$0.205504\pi$
$660$		−	2.19615i		−	0.0854851i
$661$	11.6147	+	6.70577i	0.451761	+	0.260824i	0.708574	−	0.705637i	$-0.249339\pi$
$661$	11.6147	+	6.70577i	0.451761	+	0.260824i	−0.256813	+	0.966461i	$0.582672\pi$
$662$	−8.09808	+	14.0263i	−0.314741	+	0.545147i
$663$	17.0263	−	29.4904i	0.661246	−	1.14531i
$664$	13.3923	−	7.73205i	0.519722	−	0.300062i
$665$	5.46410			0.211889
$666$		0			0
$667$	−42.2487			−1.63588
$668$	−13.7321	+	7.92820i	−0.531309	+	0.306751i
$669$	−17.8301	+	30.8827i	−0.689353	+	1.19399i
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	−8.19615	−	4.73205i	−0.316409	−	0.182679i
$672$			1.26795i			0.0489122i
$673$	−24.2942	+	42.0788i	−0.936474	+	1.62202i	−0.164489	+	0.986379i	$0.552597\pi$
$673$	−24.2942	+	42.0788i	−0.936474	+	1.62202i	−0.771985	+	0.635641i	$0.780736\pi$
$674$			16.2487i			0.625877i
$675$	2.59808	+	4.50000i	0.100000	+	0.173205i
$676$	38.7846			1.49172
$677$	−12.7846			−0.491352			−0.245676	−	0.969352i	$-0.579010\pi$
$677$	−12.7846			−0.491352			−0.245676	+	0.969352i	$0.579010\pi$
$678$	−10.7321	−	18.5885i	−0.412162	−	0.713885i
$679$	−4.05256	−	2.33975i	−0.155523	−	0.0897912i
$680$			2.73205i			0.104769i
$681$	22.2846	−	12.8660i	0.853948	−	0.493027i
$682$	−3.75833	−	6.50962i	−0.143914	−	0.249266i
$683$	17.2583	−	9.96410i	0.660372	−	0.381266i	−0.132047	−	0.991243i	$-0.542155\pi$
$683$	17.2583	−	9.96410i	0.660372	−	0.381266i	0.792419	+	0.609978i	$0.208822\pi$
$684$		0			0
$685$	−10.0981	−	5.83013i	−0.385828	−	0.222758i
$686$	8.53590	−	4.92820i	0.325902	−	0.188160i
$687$	14.9545	+	25.9019i	0.570549	+	0.988220i
$688$	7.33013	−	4.23205i	0.279458	−	0.161345i
$689$			53.1962i			2.02661i
$690$	7.09808	+	4.09808i	0.270219	+	0.156011i
$691$	12.7583	+	22.0981i	0.485350	+	0.840650i	0.999858	−	0.0168348i	$-0.00535894\pi$
$691$	12.7583	+	22.0981i	0.485350	+	0.840650i	−0.514509	+	0.857485i	$0.672026\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−14.4641	−	25.0526i	−0.549050	−	0.950982i
$695$			5.66025i			0.214706i
$696$	7.73205	−	13.3923i	0.293083	−	0.507634i
$697$			6.73205i			0.254995i
$698$	−0.803848	−	0.464102i	−0.0304261	−	0.0175665i
$699$	11.4904	−	19.9019i	0.434606	−	0.752760i
$700$	−0.366025	+	0.633975i	−0.0138345	+	0.0239620i
$701$	4.85641	−	2.80385i	0.183424	−	0.105900i	−0.405476	−	0.914106i	$-0.632894\pi$
$701$	4.85641	−	2.80385i	0.183424	−	0.105900i	0.588900	+	0.808206i	$0.299561\pi$
$702$	−37.3923			−1.41128
$703$	−19.3923	+	41.0526i	−0.731395	+	1.54833i
$704$	−1.26795			−0.0477876
$705$	−4.90192	+	2.83013i	−0.184617	+	0.106589i
$706$	8.75833	−	15.1699i	0.329624	−	0.570926i
$707$	1.33975	−	2.32051i	0.0503863	−	0.0872717i
$708$	17.4904	+	10.0981i	0.657329	+	0.379509i
$709$		−	11.6077i		−	0.435936i	−0.975956	−	0.217968i	$-0.930057\pi$
$709$		−	11.6077i		−	0.435936i	0.975956	−	0.217968i	$-0.0699429\pi$
$710$	−4.19615	+	7.26795i	−0.157479	+	0.272761i
$711$		0			0
$712$	−2.46410	−	4.26795i	−0.0923461	−	0.159948i
$713$	28.0526			1.05058
$714$	−3.46410			−0.129641
$715$	4.56218	+	7.90192i	0.170616	+	0.295515i
$716$	−10.3923	−	6.00000i	−0.388379	−	0.224231i
$717$		−	10.1436i		−	0.378819i
$718$	27.4808	−	15.8660i	1.02557	−	0.592115i
$719$	−13.0622	−	22.6244i	−0.487137	−	0.843746i	0.512754	−	0.858536i	$-0.328625\pi$
$719$	−13.0622	−	22.6244i	−0.487137	−	0.843746i	−0.999891	+	0.0147897i	$0.995292\pi$
$720$		0			0
$721$	−6.46410	−	3.73205i	−0.240736	−	0.138989i
$722$	−31.7942	−	18.3564i	−1.18326	−	0.683155i
$723$	−6.00000	+	3.46410i	−0.223142	+	0.128831i
$724$	−6.83013	−	11.8301i	−0.253840	−	0.439663i
$725$	7.73205	−	4.46410i	0.287161	−	0.165793i
$726$		−	16.2679i		−	0.603760i
$727$	−6.92820	−	4.00000i	−0.256953	−	0.148352i	0.365991	−	0.930618i	$-0.380730\pi$
$727$	−6.92820	−	4.00000i	−0.256953	−	0.148352i	−0.622944	+	0.782267i	$0.714063\pi$
$728$	−2.63397	−	4.56218i	−0.0976216	−	0.169086i
$729$	27.0000			1.00000
$730$	−11.6603			−0.431565
$731$	11.5622	+	20.0263i	0.427643	+	0.740699i
$732$			12.9282i			0.477840i
$733$	−11.6603	+	20.1962i	−0.430681	+	0.745962i	−0.996932	−	0.0782711i	$-0.975060\pi$
$733$	−11.6603	+	20.1962i	−0.430681	+	0.745962i	0.566251	+	0.824233i	$0.308393\pi$
$734$			16.2487i			0.599751i
$735$	9.69615	+	5.59808i	0.357648	+	0.206488i
$736$	2.36603	−	4.09808i	0.0872129	−	0.151057i
$737$	−5.07180	+	8.78461i	−0.186822	+	0.323585i
$738$		0			0
$739$	34.7321			1.27764			0.638820	−	0.769357i	$-0.279423\pi$
$739$	34.7321			1.27764			0.638820	+	0.769357i	$0.279423\pi$
$740$	−3.46410	−	5.00000i	−0.127343	−	0.183804i
$741$	−93.0333			−3.41766
$742$	4.68653	−	2.70577i	0.172048	−	0.0993320i
$743$	−12.8301	+	22.2224i	−0.470692	+	0.815262i	−0.999438	−	0.0335179i	$-0.989329\pi$
$743$	−12.8301	+	22.2224i	−0.470692	+	0.815262i	0.528746	+	0.848780i	$0.322662\pi$
$744$	−5.13397	+	8.89230i	−0.188221	+	0.326008i
$745$	−10.3923	−	6.00000i	−0.380745	−	0.219823i
$746$			20.4641i			0.749244i
$747$		0			0
$748$		−	3.46410i		−	0.126660i
$749$	2.97372	+	5.15064i	0.108657	+	0.188200i
$750$	−1.73205			−0.0632456
$751$	20.6603			0.753903			0.376952	−	0.926233i	$-0.376972\pi$
$751$	20.6603			0.753903			0.376952	+	0.926233i	$0.376972\pi$
$752$	1.63397	+	2.83013i	0.0595849	+	0.103204i
$753$	5.19615	+	3.00000i	0.189358	+	0.109326i
$754$			64.2487i			2.33980i
$755$	4.62436	−	2.66987i	0.168298	−	0.0971666i
$756$	1.90192	+	3.29423i	0.0691723	+	0.119810i
$757$	34.0359	−	19.6506i	1.23706	−	0.714214i	0.268564	−	0.963262i	$-0.413451\pi$
$757$	34.0359	−	19.6506i	1.23706	−	0.714214i	0.968491	+	0.249047i	$0.0801174\pi$
$758$	−9.63397	−	5.56218i	−0.349922	−	0.202027i
$759$	−9.00000	−	5.19615i	−0.326679	−	0.188608i
$760$	6.46410	−	3.73205i	0.234478	−	0.135376i
$761$	−14.7846	−	25.6077i	−0.535942	−	0.928278i	−0.999117	−	0.0420116i	$-0.986623\pi$
$761$	−14.7846	−	25.6077i	−0.535942	−	0.928278i	0.463175	−	0.886267i	$-0.346710\pi$
$762$	−14.1962	+	8.19615i	−0.514272	+	0.296915i
$763$		−	7.32051i		−	0.265020i
$764$	0.526279	+	0.303848i	0.0190401	+	0.0109928i
$765$		0			0
$766$	−7.51666			−0.271588
$767$	−83.9090			−3.02978
$768$	0.866025	+	1.50000i	0.0312500	+	0.0541266i
$769$		−	13.3205i		−	0.480350i	−0.970730	−	0.240175i	$-0.922795\pi$
$769$		−	13.3205i		−	0.480350i	0.970730	−	0.240175i	$-0.0772048\pi$
$770$	0.464102	−	0.803848i	0.0167251	−	0.0289687i
$771$		−	17.6603i		−	0.636019i
$772$	−14.3660	−	8.29423i	−0.517045	−	0.298516i
$773$	−8.16025	+	14.1340i	−0.293504	+	0.508364i	−0.974636	−	0.223797i	$-0.928155\pi$
$773$	−8.16025	+	14.1340i	−0.293504	+	0.508364i	0.681132	+	0.732161i	$0.261488\pi$
$774$		0			0
$775$	−5.13397	+	2.96410i	−0.184418	+	0.106474i
$776$	−6.39230			−0.229470
$777$	6.33975	−	4.39230i	0.227437	−	0.157573i
$778$	1.07180			0.0384258
$779$	15.9282	−	9.19615i	0.570687	−	0.329486i
$780$	6.23205	−	10.7942i	0.223143	−	0.386495i
$781$	5.32051	−	9.21539i	0.190383	−	0.329753i
$782$	11.1962	+	6.46410i	0.400374	+	0.231156i
$783$		−	46.3923i		−	1.65793i
$784$	3.23205	−	5.59808i	0.115430	−	0.199931i
$785$		−	2.46410i		−	0.0879476i
$786$	8.66025	+	15.0000i	0.308901	+	0.535032i
$787$	−2.94744			−0.105065			−0.0525325	−	0.998619i	$-0.516729\pi$
$787$	−2.94744			−0.105065			−0.0525325	+	0.998619i	$0.516729\pi$
$788$	8.32051			0.296406
$789$	2.83013	+	4.90192i	0.100755	+	0.174513i
$790$	10.3923	+	6.00000i	0.369742	+	0.213470i
$791$		−	9.07180i		−	0.322556i
$792$		0			0
$793$	−26.8564	−	46.5167i	−0.953699	−	1.65186i
$794$	−9.06218	+	5.23205i	−0.321605	+	0.185679i
$795$	11.0885	+	6.40192i	0.393267	+	0.227053i
$796$	−0.866025	−	0.500000i	−0.0306955	−	0.0177220i
$797$	30.3564	−	17.5263i	1.07528	−	0.620813i	0.145660	−	0.989335i	$-0.453469\pi$
$797$	30.3564	−	17.5263i	1.07528	−	0.620813i	0.929619	+	0.368522i	$0.120136\pi$
$798$	4.73205	+	8.19615i	0.167513	+	0.290141i
$799$	−7.73205	+	4.46410i	−0.273540	+	0.157929i
$800$			1.00000i			0.0353553i
$801$		0			0
$802$	−4.46410	−	7.73205i	−0.157633	−	0.273028i
$803$	14.7846			0.521738
$804$	13.8564			0.488678
$805$	1.73205	+	3.00000i	0.0610468	+	0.105736i
$806$		−	42.6603i		−	1.50264i
$807$	14.8301	−	25.6865i	0.522045	−	0.904209i
$808$		−	3.66025i		−	0.128767i
$809$	−44.4282	−	25.6506i	−1.56201	−	0.901828i	−0.997054	−	0.0767093i	$-0.975559\pi$
$809$	−44.4282	−	25.6506i	−1.56201	−	0.901828i	−0.564959	−	0.825119i	$-0.691108\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	−13.3205	+	23.0718i	−0.467746	+	0.810160i	−0.999321	−	0.0368512i	$-0.988267\pi$
$811$	−13.3205	+	23.0718i	−0.467746	+	0.810160i	0.531574	+	0.847012i	$0.321601\pi$
$812$	5.66025	−	3.26795i	0.198636	−	0.114683i
$813$	−9.67949			−0.339475
$814$	4.39230	+	6.33975i	0.153950	+	0.222208i
$815$	5.00000			0.175142
$816$	−4.09808	+	2.36603i	−0.143461	+	0.0828275i
$817$	31.5885	−	54.7128i	1.10514	−	1.91416i
$818$	7.40192	−	12.8205i	0.258802	−	0.448259i
$819$		0			0
$820$			2.46410i			0.0860502i
$821$	−27.2487	+	47.1962i	−0.950987	+	1.64716i	−0.207690	+	0.978195i	$0.566595\pi$
$821$	−27.2487	+	47.1962i	−0.950987	+	1.64716i	−0.743296	+	0.668962i	$0.766739\pi$
$822$		−	20.1962i		−	0.704422i
$823$	−8.16987	−	14.1506i	−0.284784	−	0.493260i	0.687773	−	0.725926i	$-0.258588\pi$
$823$	−8.16987	−	14.1506i	−0.284784	−	0.493260i	−0.972557	+	0.232666i	$0.925255\pi$
$824$	−10.1962			−0.355200
$825$	2.19615			0.0764602
$826$	4.26795	+	7.39230i	0.148501	+	0.257211i
$827$	23.1962	+	13.3923i	0.806609	+	0.465696i	0.845777	−	0.533537i	$-0.179137\pi$
$827$	23.1962	+	13.3923i	0.806609	+	0.465696i	−0.0391677	+	0.999233i	$0.512471\pi$
$828$		0			0
$829$	−19.9019	+	11.4904i	−0.691222	+	0.399077i	−0.804070	−	0.594535i	$-0.797336\pi$
$829$	−19.9019	+	11.4904i	−0.691222	+	0.399077i	0.112847	+	0.993612i	$0.464003\pi$
$830$	7.73205	+	13.3923i	0.268383	+	0.464854i
$831$	−30.4019	+	17.5526i	−1.05463	+	0.608892i
$832$	−6.23205	−	3.59808i	−0.216057	−	0.124741i
$833$	15.2942	+	8.83013i	0.529914	+	0.305946i
$834$	−8.49038	+	4.90192i	−0.293998	+	0.169740i
$835$	−7.92820	−	13.7321i	−0.274367	−	0.475217i
$836$	−8.19615	+	4.73205i	−0.283470	+	0.163661i
$837$			30.8038i			1.06474i
$838$	−8.70577	−	5.02628i	−0.300736	−	0.173630i
$839$	−5.47372	−	9.48076i	−0.188974	−	0.327312i	0.755935	−	0.654647i	$-0.227183\pi$
$839$	−5.47372	−	9.48076i	−0.188974	−	0.327312i	−0.944908	+	0.327335i	$0.893849\pi$
$840$	−1.26795			−0.0437484
$841$	−50.7128			−1.74872
$842$	−5.29423	−	9.16987i	−0.182451	−	0.316015i
$843$			52.1769i			1.79707i
$844$	9.19615	−	15.9282i	0.316545	−	0.548271i
$845$			38.7846i			1.33423i
$846$		0			0
$847$	3.43782	−	5.95448i	0.118125	−	0.204598i
$848$	3.69615	−	6.40192i	0.126926	−	0.219843i
$849$	−30.6962	+	17.7224i	−1.05349	+	0.608232i
$850$	−2.73205			−0.0937086
$851$	−28.6865	+	2.36603i	−0.983362	+	0.0811063i
$852$	−14.5359			−0.497992
$853$	17.2128	−	9.93782i	0.589355	−	0.340265i	−0.175487	−	0.984482i	$-0.556150\pi$
$853$	17.2128	−	9.93782i	0.589355	−	0.340265i	0.764843	+	0.644217i	$0.222817\pi$
$854$	−2.73205	+	4.73205i	−0.0934889	+	0.161927i
$855$		0			0
$856$	7.03590	+	4.06218i	0.240482	+	0.138842i
$857$			14.4449i			0.493427i	0.969088	+	0.246714i	$0.0793507\pi$
$857$			14.4449i			0.493427i	−0.969088	+	0.246714i	$0.920649\pi$
$858$	−7.90192	+	13.6865i	−0.269767	+	0.467251i
$859$			29.0718i			0.991917i	0.868346	+	0.495958i	$0.165183\pi$
$859$			29.0718i			0.991917i	−0.868346	+	0.495958i	$0.834817\pi$
$860$	4.23205	+	7.33013i	0.144312	+	0.249955i
$861$	−3.12436			−0.106478
$862$	−23.7846			−0.810107
$863$	5.80385	+	10.0526i	0.197565	+	0.342193i	0.947738	−	0.319048i	$-0.103363\pi$
$863$	5.80385	+	10.0526i	0.197565	+	0.342193i	−0.750173	+	0.661241i	$0.770030\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$		−	6.00000i		−	0.204006i
$866$	−24.9282	+	14.3923i	−0.847095	+	0.489070i
$867$	8.25833	+	14.3038i	0.280468	+	0.485784i
$868$	−3.75833	+	2.16987i	−0.127566	+	0.0736503i
$869$	−13.1769	−	7.60770i	−0.446996	−	0.258073i
$870$	13.3923	+	7.73205i	0.454042	+	0.262141i
$871$	−49.8564	+	28.7846i	−1.68932	+	0.975329i
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$		0			0
$874$		−	35.3205i		−	1.19473i
$875$	−0.633975	−	0.366025i	−0.0214323	−	0.0123739i
$876$	−10.0981	−	17.4904i	−0.341182	−	0.590945i
$877$	8.46410			0.285812			0.142906	−	0.989736i	$-0.454355\pi$
$877$	8.46410			0.285812			0.142906	+	0.989736i	$0.454355\pi$
$878$	9.78461			0.330215
$879$	−18.6506	−	32.3038i	−0.629070	−	1.08958i
$880$		−	1.26795i		−	0.0427426i
$881$	−13.4641	+	23.3205i	−0.453617	+	0.785688i	−0.998608	−	0.0527544i	$-0.983200\pi$
$881$	−13.4641	+	23.3205i	−0.453617	+	0.785688i	0.544990	+	0.838442i	$0.316533\pi$
$882$		0			0
$883$	−1.08142	−	0.624356i	−0.0363925	−	0.0210112i	0.481693	−	0.876340i	$-0.340022\pi$
$883$	−1.08142	−	0.624356i	−0.0363925	−	0.0210112i	−0.518086	+	0.855329i	$0.673355\pi$
$884$	9.83013	−	17.0263i	0.330623	−	0.572656i
$885$	−10.0981	+	17.4904i	−0.339443	+	0.587933i
$886$	−29.2128	+	16.8660i	−0.981424	+	0.566625i
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$	4.50000	−	9.52628i	0.151010	−	0.319681i
$889$	−6.92820			−0.232364
$890$	4.26795	−	2.46410i	0.143062	−	0.0825969i
$891$	5.70577	−	9.88269i	0.191151	−	0.331082i
$892$	−10.2942	+	17.8301i	−0.344676	+	0.596997i
$893$	21.1244	+	12.1962i	0.706900	+	0.408129i
$894$		−	20.7846i		−	0.695141i
$895$	6.00000	−	10.3923i	0.200558	−	0.347376i
$896$			0.732051i			0.0244561i
$897$	−29.4904	−	51.0788i	−0.984655	−	1.70547i
$898$	28.5167			0.951613
$899$	52.9282			1.76525
$900$		0			0
$901$	17.4904	+	10.0981i	0.582689	+	0.336416i
$902$		−	3.12436i		−	0.104030i
$903$	−9.29423	+	5.36603i	−0.309293	+	0.178570i
$904$	−6.19615	−	10.7321i	−0.206081	−	0.356943i
$905$	11.8301	−	6.83013i	0.393247	−	0.227041i
$906$	8.00962	+	4.62436i	0.266102	+	0.153634i
$907$	−11.1962	−	6.46410i	−0.371762	−	0.214637i	0.302466	−	0.953160i	$-0.402190\pi$
$907$	−11.1962	−	6.46410i	−0.371762	−	0.214637i	−0.674228	+	0.738523i	$0.735524\pi$
$908$	12.8660	−	7.42820i	0.426974	−	0.246514i
$909$		0			0
$910$	4.56218	−	2.63397i	0.151235	−	0.0873154i
$911$		−	4.07180i		−	0.134905i	−0.997722	−	0.0674523i	$-0.978513\pi$
$911$		−	4.07180i		−	0.134905i	0.997722	−	0.0674523i	$-0.0214871\pi$
$912$	11.1962	+	6.46410i	0.370742	+	0.214048i
$913$	−9.80385	−	16.9808i	−0.324460	−	0.561981i
$914$	25.8564			0.855254
$915$	−12.9282			−0.427393
$916$	8.63397	+	14.9545i	0.285275	+	0.494110i
$917$			7.32051i			0.241744i
$918$	−7.09808	+	12.2942i	−0.234271	+	0.405770i
$919$			48.5359i			1.60105i	0.599298	+	0.800526i	$0.295446\pi$
$919$			48.5359i			1.60105i	−0.599298	+	0.800526i	$0.704554\pi$
$920$	4.09808	+	2.36603i	0.135110	+	0.0780055i
$921$	−2.42820	+	4.20577i	−0.0800120	+	0.138585i
$922$	−15.5885	+	27.0000i	−0.513378	+	0.889198i
$923$	52.3013	−	30.1962i	1.72152	−	0.993918i
$924$	1.60770			0.0528893
$925$	5.00000	−	3.46410i	0.164399	−	0.113899i
$926$	25.8564			0.849694
$927$		0			0
$928$	4.46410	−	7.73205i	0.146541	−	0.253817i
$929$	−11.0359	+	19.1147i	−0.362076	+	0.627134i	−0.988302	−	0.152507i	$-0.951265\pi$
$929$	−11.0359	+	19.1147i	−0.362076	+	0.627134i	0.626226	+	0.779641i	$0.284599\pi$
$930$	−8.89230	−	5.13397i	−0.291590	−	0.168350i
$931$		−	48.2487i		−	1.58129i
$932$	6.63397	−	11.4904i	0.217303	−	0.376380i
$933$		−	18.3731i		−	0.601507i
$934$	−0.500000	−	0.866025i	−0.0163605	−	0.0283372i
$935$	3.46410			0.113288
$936$		0			0
$937$	−23.5885	−	40.8564i	−0.770601	−	1.33472i	−0.937234	−	0.348702i	$-0.886623\pi$
$937$	−23.5885	−	40.8564i	−0.770601	−	1.33472i	0.166633	−	0.986019i	$-0.446711\pi$
$938$	5.07180	+	2.92820i	0.165600	+	0.0956092i
$939$			12.2487i			0.399722i
$940$	−2.83013	+	1.63397i	−0.0923086	+	0.0532944i
$941$	−4.02628	−	6.97372i	−0.131253	−	0.227337i	0.792907	−	0.609343i	$-0.208567\pi$
$941$	−4.02628	−	6.97372i	−0.131253	−	0.227337i	−0.924160	+	0.382006i	$0.875233\pi$
$942$	3.69615	−	2.13397i	0.120427	−	0.0695286i
$943$	10.0981	+	5.83013i	0.328839	+	0.189855i
$944$	10.0981	+	5.83013i	0.328664	+	0.189754i
$945$	−3.29423	+	1.90192i	−0.107161	+	0.0618696i
$946$	−5.36603	−	9.29423i	−0.174465	−	0.302181i
$947$	21.8660	−	12.6244i	0.710550	−	0.410236i	−0.100714	−	0.994915i	$-0.532113\pi$
$947$	21.8660	−	12.6244i	0.710550	−	0.410236i	0.811265	+	0.584679i	$0.198780\pi$
$948$			20.7846i			0.675053i
$949$	72.6673	+	41.9545i	2.35888	+	1.36190i
$950$	3.73205	+	6.46410i	0.121084	+	0.209723i
$951$	4.01924			0.130333
$952$	−2.00000			−0.0648204
$953$	−15.6865	−	27.1699i	−0.508137	−	0.880119i	−0.999956	−	0.00942103i	$-0.997001\pi$
$953$	−15.6865	−	27.1699i	−0.508137	−	0.880119i	0.491819	−	0.870697i	$-0.336332\pi$
$954$		0			0
$955$	−0.303848	+	0.526279i	−0.00983228	+	0.0170300i
$956$		−	5.85641i		−	0.189410i
$957$	−16.9808	−	9.80385i	−0.548910	−	0.316913i
$958$	−18.6244	+	32.2583i	−0.601726	+	1.04222i
$959$	4.26795	−	7.39230i	0.137819	−	0.238710i
$960$	−1.50000	+	0.866025i	−0.0484123	+	0.0279508i
$961$	−4.14359			−0.133664
$962$	3.59808	+	43.6244i	0.116007	+	1.40651i
$963$		0			0
$964$	−3.46410	+	2.00000i	−0.111571	+	0.0644157i
$965$	8.29423	−	14.3660i	0.267001	−	0.462459i
$966$	−3.00000	+	5.19615i	−0.0965234	+	0.167183i
$967$	20.1962	+	11.6603i	0.649464	+	0.374968i	0.788251	−	0.615354i	$-0.210987\pi$
$967$	20.1962	+	11.6603i	0.649464	+	0.374968i	−0.138787	+	0.990322i	$0.544320\pi$
$968$		−	9.39230i		−	0.301880i
$969$	−17.6603	+	30.5885i	−0.567329	+	0.982643i
$970$		−	6.39230i		−	0.205245i
$971$	10.4378	+	18.0788i	0.334966	+	0.580178i	0.983478	−	0.181026i	$-0.0579419\pi$
$971$	10.4378	+	18.0788i	0.334966	+	0.580178i	−0.648513	+	0.761204i	$0.724609\pi$
$972$		0			0
$973$	−4.14359			−0.132838
$974$	−3.39230	−	5.87564i	−0.108696	−	0.188268i
$975$	10.7942	+	6.23205i	0.345692	+	0.199585i
$976$			7.46410i			0.238920i
$977$	−23.1962	+	13.3923i	−0.742111	+	0.428458i	−0.822836	−	0.568279i	$-0.807610\pi$
$977$	−23.1962	+	13.3923i	−0.742111	+	0.428458i	0.0807256	+	0.996736i	$0.474276\pi$
$978$	4.33013	+	7.50000i	0.138462	+	0.239824i
$979$	−5.41154	+	3.12436i	−0.172954	+	0.0998548i
$980$	5.59808	+	3.23205i	0.178824	+	0.103244i
$981$		0			0
$982$	11.4904	−	6.63397i	0.366673	−	0.211699i
$983$	27.5885	+	47.7846i	0.879935	+	1.52409i	0.851411	+	0.524499i	$0.175747\pi$
$983$	27.5885	+	47.7846i	0.879935	+	1.52409i	0.0285242	+	0.999593i	$0.490919\pi$
$984$	−3.69615	+	2.13397i	−0.117829	+	0.0680286i
$985$			8.32051i			0.265113i
$986$	21.1244	+	12.1962i	0.672737	+	0.388405i
$987$	−2.07180	−	3.58846i	−0.0659460	−	0.114222i
$988$	−53.7128			−1.70883
$989$	40.0526			1.27360
$990$		0			0
$991$			21.1051i			0.670426i	0.942142	+	0.335213i	$0.108808\pi$
$991$			21.1051i			0.670426i	−0.942142	+	0.335213i	$0.891192\pi$
$992$	−2.96410	+	5.13397i	−0.0941103	+	0.163004i
$993$		−	28.0526i		−	0.890221i
$994$	−5.32051	−	3.07180i	−0.168756	−	0.0974315i
$995$	0.500000	−	0.866025i	0.0158511	−	0.0274549i
$996$	−13.3923	+	23.1962i	−0.424351	+	0.734998i
$997$	−15.2321	+	8.79423i	−0.482404	+	0.278516i	−0.721418	−	0.692500i	$-0.756509\pi$
$997$	−15.2321	+	8.79423i	−0.482404	+	0.278516i	0.239014	+	0.971016i	$0.423176\pi$
$998$	1.07180			0.0339271
$999$	−2.59808	−	31.5000i	−0.0821995	−	0.996616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.a.11.1	✓	4
37.27	even	6	inner	370.2.l.a.101.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.a.11.1	✓	4	1.1	even	1	trivial
370.2.l.a.101.1	yes	4	37.27	even	6	inner

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000i q^{8} -1.00000 q^{10} +1.26795 q^{11} +(-0.866025 - 1.50000i) q^{12} +(6.23205 + 3.59808i) q^{13} -0.732051i q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.36603 - 1.36603i) q^{17} +(-6.46410 - 3.73205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.633975 + 1.09808i) q^{21} +(-1.09808 + 0.633975i) q^{22} -4.73205i q^{23} +(1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} -7.19615 q^{26} +5.19615 q^{27} +(0.366025 + 0.633975i) q^{28} -8.92820i q^{29} +(-0.866025 + 1.50000i) q^{30} +5.92820i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.09808 - 1.90192i) q^{33} +(-1.36603 + 2.36603i) q^{34} +(-0.633975 + 0.366025i) q^{35} +(-0.500000 - 6.06218i) q^{37} +7.46410 q^{38} +(10.7942 - 6.23205i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-1.23205 + 2.13397i) q^{41} +(-1.09808 - 0.633975i) q^{42} +8.46410i q^{43} +(0.633975 - 1.09808i) q^{44} +(2.36603 + 4.09808i) q^{46} -3.26795 q^{47} -1.73205 q^{48} +(3.23205 + 5.59808i) q^{49} +(-0.866025 - 0.500000i) q^{50} -4.73205i q^{51} +(6.23205 - 3.59808i) q^{52} +(3.69615 + 6.40192i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(1.09808 + 0.633975i) q^{55} +(-0.633975 - 0.366025i) q^{56} +(-11.1962 + 6.46410i) q^{57} +(4.46410 + 7.73205i) q^{58} +(-10.0981 + 5.83013i) q^{59} -1.73205i q^{60} +(-6.46410 - 3.73205i) q^{61} +(-2.96410 - 5.13397i) q^{62} -1.00000 q^{64} +(3.59808 + 6.23205i) q^{65} +2.19615i q^{66} +(-4.00000 + 6.92820i) q^{67} -2.73205i q^{68} +(-7.09808 - 4.09808i) q^{69} +(0.366025 - 0.633975i) q^{70} +(4.19615 - 7.26795i) q^{71} +11.6603 q^{73} +(3.46410 + 5.00000i) q^{74} +1.73205 q^{75} +(-6.46410 + 3.73205i) q^{76} +(-0.464102 + 0.803848i) q^{77} +(-6.23205 + 10.7942i) q^{78} +(-10.3923 - 6.00000i) q^{79} -1.00000i q^{80} +(4.50000 - 7.79423i) q^{81} -2.46410i q^{82} +(-7.73205 - 13.3923i) q^{83} +1.26795 q^{84} +2.73205 q^{85} +(-4.23205 - 7.33013i) q^{86} +(-13.3923 - 7.73205i) q^{87} +1.26795i q^{88} +(-4.26795 + 2.46410i) q^{89} +(-4.56218 + 2.63397i) q^{91} +(-4.09808 - 2.36603i) q^{92} +(8.89230 + 5.13397i) q^{93} +(2.83013 - 1.63397i) q^{94} +(-3.73205 - 6.46410i) q^{95} +(1.50000 - 0.866025i) q^{96} +6.39230i q^{97} +(-5.59808 - 3.23205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^7	\( 4 q + 2 q^{4} + 2 q^{7} - 4 q^{10} + 12 q^{11} + 18 q^{13} + 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{24} + 2 q^{25} - 8 q^{26} - 2 q^{28} - 6 q^{33} - 2 q^{34} - 6 q^{35} - 2 q^{37} + 16 q^{38} + 12 q^{39} - 2 q^{40} + 2 q^{41} + 6 q^{42} + 6 q^{44} + 6 q^{46} - 20 q^{47} + 6 q^{49} + 18 q^{52} - 6 q^{53} - 18 q^{54} - 6 q^{55} - 6 q^{56} - 24 q^{57} + 4 q^{58} - 30 q^{59} - 12 q^{61} + 2 q^{62} - 4 q^{64} + 4 q^{65} - 16 q^{67} - 18 q^{69} - 2 q^{70} - 4 q^{71} + 12 q^{73} - 12 q^{76} + 12 q^{77} - 18 q^{78} + 18 q^{81} - 24 q^{83} + 12 q^{84} + 4 q^{85} - 10 q^{86} - 12 q^{87} - 24 q^{89} + 6 q^{91} - 6 q^{92} - 6 q^{93} - 6 q^{94} - 8 q^{95} + 6 q^{96} - 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^7 - 4 * q^10 + 12 * q^11 + 18 * q^13 + 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^24 + 2 * q^25 - 8 * q^26 - 2 * q^28 - 6 * q^33 - 2 * q^34 - 6 * q^35 - 2 * q^37 + 16 * q^38 + 12 * q^39 - 2 * q^40 + 2 * q^41 + 6 * q^42 + 6 * q^44 + 6 * q^46 - 20 * q^47 + 6 * q^49 + 18 * q^52 - 6 * q^53 - 18 * q^54 - 6 * q^55 - 6 * q^56 - 24 * q^57 + 4 * q^58 - 30 * q^59 - 12 * q^61 + 2 * q^62 - 4 * q^64 + 4 * q^65 - 16 * q^67 - 18 * q^69 - 2 * q^70 - 4 * q^71 + 12 * q^73 - 12 * q^76 + 12 * q^77 - 18 * q^78 + 18 * q^81 - 24 * q^83 + 12 * q^84 + 4 * q^85 - 10 * q^86 - 12 * q^87 - 24 * q^89 + 6 * q^91 - 6 * q^92 - 6 * q^93 - 6 * q^94 - 8 * q^95 + 6 * q^96 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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