LMFDB - Embedded newform 155.2.p.a.68.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(37,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("155.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.p (of order $12$, degree $4$, 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:	$1.23768123133$
Analytic rank:	$1$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	155.68
Dual form			155.2.p.a.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-2.36603 - 0.633975i) q^{3} +(1.23205 + 1.86603i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.36603 - 0.633975i) q^{3} +(1.23205 + 1.86603i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +(-3.09808 - 0.633975i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(-1.26795 - 4.73205i) q^{13} +(1.73205 - 1.00000i) q^{14} +(-1.73205 - 5.19615i) q^{15} +4.00000 q^{16} +(-0.633975 + 2.36603i) q^{17} +(-4.09808 + 1.09808i) q^{18} +(3.00000 + 1.73205i) q^{21} +(7.09808 - 1.90192i) q^{22} +(-3.46410 + 3.46410i) q^{23} +(3.46410 + 6.00000i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(6.00000 + 3.46410i) q^{26} -1.73205 q^{29} +(6.92820 + 3.46410i) q^{30} +(-3.50000 - 4.33013i) q^{31} +(9.00000 + 9.00000i) q^{33} +(-1.73205 - 3.00000i) q^{34} +(-1.00000 - 3.00000i) q^{35} +(1.26795 - 4.73205i) q^{37} +12.0000i q^{39} +(1.26795 - 6.19615i) q^{40} +(-3.50000 + 6.06218i) q^{41} +(-4.73205 + 1.26795i) q^{42} +(2.36603 + 0.633975i) q^{43} +(0.401924 + 6.69615i) q^{45} -6.92820i q^{46} +(-9.00000 + 9.00000i) q^{47} +(-9.46410 - 2.53590i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-2.63397 - 6.56218i) q^{50} +(3.00000 - 5.19615i) q^{51} +(1.26795 + 4.73205i) q^{53} +(-0.696152 - 11.5981i) q^{55} +(2.00000 + 3.46410i) q^{56} +(1.73205 - 1.73205i) q^{58} +(6.06218 - 3.50000i) q^{59} +5.19615i q^{61} +(7.83013 + 0.830127i) q^{62} +(-3.00000 - 3.00000i) q^{63} +8.00000i q^{64} +(7.26795 - 8.19615i) q^{65} -18.0000 q^{66} +(2.92820 + 10.9282i) q^{67} +(10.3923 - 6.00000i) q^{69} +(4.00000 + 2.00000i) q^{70} +(0.500000 - 0.866025i) q^{71} +(-2.19615 - 8.19615i) q^{72} +(-3.16987 - 11.8301i) q^{73} +(3.46410 + 6.00000i) q^{74} +(7.56218 - 9.63397i) q^{75} +(5.19615 + 5.19615i) q^{77} +(-12.0000 - 12.0000i) q^{78} +(-2.59808 - 4.50000i) q^{79} +(4.92820 + 7.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.56218 - 9.56218i) q^{82} +(-1.26795 - 4.73205i) q^{83} +(-5.19615 + 1.73205i) q^{85} +(-3.00000 + 1.73205i) q^{86} +(4.09808 + 1.09808i) q^{87} +(3.80385 + 14.1962i) q^{88} -15.5885 q^{89} +(-7.09808 - 6.29423i) q^{90} +6.92820i q^{91} +(5.53590 + 12.4641i) q^{93} -18.0000i q^{94} +(-8.00000 + 8.00000i) q^{97} +(6.83013 - 1.83013i) q^{98} +(-7.79423 - 13.5000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 12 q^{6} - 2 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 12 * q^6 - 2 * q^7 - 8 * q^8	$ 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 12 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{10} - 18 q^{11} - 12 q^{13} + 16 q^{16} - 6 q^{17} - 6 q^{18} + 12 q^{21} + 18 q^{22} + 6 q^{25} + 24 q^{26} - 14 q^{31} + 36 q^{33} - 4 q^{35} + 12 q^{37} + 12 q^{40} - 14 q^{41} - 12 q^{42} + 6 q^{43} + 12 q^{45} - 36 q^{47} - 24 q^{48} - 14 q^{50} + 12 q^{51} + 12 q^{53} + 18 q^{55} + 8 q^{56} + 14 q^{62} - 12 q^{63} + 36 q^{65} - 72 q^{66} - 16 q^{67} + 16 q^{70} + 2 q^{71} + 12 q^{72} - 30 q^{73} + 6 q^{75} - 48 q^{78} - 8 q^{80} - 18 q^{81} + 14 q^{82} - 12 q^{83} - 12 q^{86} + 6 q^{87} + 36 q^{88} - 18 q^{90} + 36 q^{93} - 32 q^{97} + 10 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 12 * q^6 - 2 * q^7 - 8 * q^8 - 2 * q^10 - 18 * q^11 - 12 * q^13 + 16 * q^16 - 6 * q^17 - 6 * q^18 + 12 * q^21 + 18 * q^22 + 6 * q^25 + 24 * q^26 - 14 * q^31 + 36 * q^33 - 4 * q^35 + 12 * q^37 + 12 * q^40 - 14 * q^41 - 12 * q^42 + 6 * q^43 + 12 * q^45 - 36 * q^47 - 24 * q^48 - 14 * q^50 + 12 * q^51 + 12 * q^53 + 18 * q^55 + 8 * q^56 + 14 * q^62 - 12 * q^63 + 36 * q^65 - 72 * q^66 - 16 * q^67 + 16 * q^70 + 2 * q^71 + 12 * q^72 - 30 * q^73 + 6 * q^75 - 48 * q^78 - 8 * q^80 - 18 * q^81 + 14 * q^82 - 12 * q^83 - 12 * q^86 + 6 * q^87 + 36 * q^88 - 18 * q^90 + 36 * q^93 - 32 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$3$	−2.36603	−	0.633975i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−2.36603	−	0.633975i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	1.23205	+	1.86603i	0.550990	+	0.834512i
$5$	1.23205	+	1.86603i	0.550990	+	0.834512i
$6$	3.00000	−	1.73205i	1.22474	−	0.707107i
$7$	−1.36603	−	0.366025i	−0.516309	−	0.138345i	−0.00875026	−	0.999962i	$-0.502785\pi$
$7$	−1.36603	−	0.366025i	−0.516309	−	0.138345i	−0.507559	+	0.861617i	$0.669452\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$	−3.09808	−	0.633975i	−0.979698	−	0.200480i
$11$	−4.50000	−	2.59808i	−1.35680	−	0.783349i	−0.367610	−	0.929980i	$-0.619824\pi$
$11$	−4.50000	−	2.59808i	−1.35680	−	0.783349i	−0.989191	+	0.146631i	$0.953157\pi$
$12$		0			0
$13$	−1.26795	−	4.73205i	−0.351666	−	1.31243i	−0.884629	−	0.466296i	$-0.845588\pi$
$13$	−1.26795	−	4.73205i	−0.351666	−	1.31243i	0.532963	−	0.846139i	$-0.321079\pi$
$14$	1.73205	−	1.00000i	0.462910	−	0.267261i
$15$	−1.73205	−	5.19615i	−0.447214	−	1.34164i
$16$	4.00000			1.00000
$17$	−0.633975	+	2.36603i	−0.153761	+	0.573845i	0.845447	+	0.534060i	$0.179334\pi$
$17$	−0.633975	+	2.36603i	−0.153761	+	0.573845i	−0.999208	+	0.0397858i	$0.987332\pi$
$18$	−4.09808	+	1.09808i	−0.965926	+	0.258819i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	3.00000	+	1.73205i	0.654654	+	0.377964i
$22$	7.09808	−	1.90192i	1.51331	−	0.405492i
$23$	−3.46410	+	3.46410i	−0.722315	+	0.722315i	−0.969076	−	0.246761i	$-0.920634\pi$
$23$	−3.46410	+	3.46410i	−0.722315	+	0.722315i	0.246761	+	0.969076i	$0.420634\pi$
$24$	3.46410	+	6.00000i	0.707107	+	1.22474i
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	6.00000	+	3.46410i	1.17670	+	0.679366i
$27$		0			0
$28$		0			0
$29$	−1.73205			−0.321634			−0.160817	−	0.986984i	$-0.551413\pi$
$29$	−1.73205			−0.321634			−0.160817	+	0.986984i	$0.551413\pi$
$30$	6.92820	+	3.46410i	1.26491	+	0.632456i
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$32$		0			0
$33$	9.00000	+	9.00000i	1.56670	+	1.56670i
$34$	−1.73205	−	3.00000i	−0.297044	−	0.514496i
$35$	−1.00000	−	3.00000i	−0.169031	−	0.507093i
$36$		0			0
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	−0.779921	−	0.625878i	$-0.784741\pi$
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	0.988370	−	0.152066i	$-0.0485927\pi$
$38$		0			0
$39$			12.0000i			1.92154i
$40$	1.26795	−	6.19615i	0.200480	−	0.979698i
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	0.451896	+	0.892071i	$0.350748\pi$
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	−0.998504	+	0.0546823i	$0.982585\pi$
$42$	−4.73205	+	1.26795i	−0.730171	+	0.195649i
$43$	2.36603	+	0.633975i	0.360815	+	0.0966802i	0.434672	−	0.900589i	$-0.356864\pi$
$43$	2.36603	+	0.633975i	0.360815	+	0.0966802i	−0.0738569	+	0.997269i	$0.523531\pi$
$44$		0			0
$45$	0.401924	+	6.69615i	0.0599153	+	0.998203i
$46$		−	6.92820i		−	1.02151i
$47$	−9.00000	+	9.00000i	−1.31278	+	1.31278i	−0.393431	+	0.919354i	$0.628712\pi$
$47$	−9.00000	+	9.00000i	−1.31278	+	1.31278i	−0.919354	+	0.393431i	$0.871288\pi$
$48$	−9.46410	−	2.53590i	−1.36603	−	0.366025i
$49$	−4.33013	−	2.50000i	−0.618590	−	0.357143i
$50$	−2.63397	−	6.56218i	−0.372500	−	0.928032i
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$		0			0
$53$	1.26795	+	4.73205i	0.174166	+	0.649997i	0.996692	+	0.0812696i	$0.0258975\pi$
$53$	1.26795	+	4.73205i	0.174166	+	0.649997i	−0.822526	+	0.568728i	$0.807436\pi$
$54$		0			0
$55$	−0.696152	−	11.5981i	−0.0938692	−	1.56388i
$56$	2.00000	+	3.46410i	0.267261	+	0.462910i
$57$		0			0
$58$	1.73205	−	1.73205i	0.227429	−	0.227429i
$59$	6.06218	−	3.50000i	0.789228	−	0.455661i	−0.0504625	−	0.998726i	$-0.516070\pi$
$59$	6.06218	−	3.50000i	0.789228	−	0.455661i	0.839691	+	0.543065i	$0.182736\pi$
$60$		0			0
$61$			5.19615i			0.665299i	0.943051	+	0.332650i	$0.107943\pi$
$61$			5.19615i			0.665299i	−0.943051	+	0.332650i	$0.892057\pi$
$62$	7.83013	+	0.830127i	0.994427	+	0.105426i
$63$	−3.00000	−	3.00000i	−0.377964	−	0.377964i
$64$			8.00000i			1.00000i
$65$	7.26795	−	8.19615i	0.901478	−	1.01661i
$66$	−18.0000			−2.21565
$67$	2.92820	+	10.9282i	0.357737	+	1.33509i	0.877005	+	0.480481i	$0.159538\pi$
$67$	2.92820	+	10.9282i	0.357737	+	1.33509i	−0.519268	+	0.854611i	$0.673795\pi$
$68$		0			0
$69$	10.3923	−	6.00000i	1.25109	−	0.722315i
$70$	4.00000	+	2.00000i	0.478091	+	0.239046i
$71$	0.500000	−	0.866025i	0.0593391	−	0.102778i	−0.834830	−	0.550508i	$-0.814434\pi$
$71$	0.500000	−	0.866025i	0.0593391	−	0.102778i	0.894169	+	0.447730i	$0.147767\pi$
$72$	−2.19615	−	8.19615i	−0.258819	−	0.965926i
$73$	−3.16987	−	11.8301i	−0.371006	−	1.38461i	−0.859094	−	0.511818i	$-0.828972\pi$
$73$	−3.16987	−	11.8301i	−0.371006	−	1.38461i	0.488089	−	0.872794i	$-0.337694\pi$
$74$	3.46410	+	6.00000i	0.402694	+	0.697486i
$75$	7.56218	−	9.63397i	0.873205	−	1.11244i
$76$		0			0
$77$	5.19615	+	5.19615i	0.592157	+	0.592157i
$78$	−12.0000	−	12.0000i	−1.35873	−	1.35873i
$79$	−2.59808	−	4.50000i	−0.292306	−	0.506290i	0.682048	−	0.731307i	$-0.261089\pi$
$79$	−2.59808	−	4.50000i	−0.292306	−	0.506290i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	4.92820	+	7.46410i	0.550990	+	0.834512i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−2.56218	−	9.56218i	−0.282945	−	1.05597i
$83$	−1.26795	−	4.73205i	−0.139176	−	0.519410i	−0.999946	−	0.0104164i	$-0.996684\pi$
$83$	−1.26795	−	4.73205i	−0.139176	−	0.519410i	0.860770	−	0.508994i	$-0.169982\pi$
$84$		0			0
$85$	−5.19615	+	1.73205i	−0.563602	+	0.187867i
$86$	−3.00000	+	1.73205i	−0.323498	+	0.186772i
$87$	4.09808	+	1.09808i	0.439360	+	0.117726i
$88$	3.80385	+	14.1962i	0.405492	+	1.51331i
$89$	−15.5885			−1.65237			−0.826187	−	0.563397i	$-0.809494\pi$
$89$	−15.5885			−1.65237			−0.826187	+	0.563397i	$0.809494\pi$
$90$	−7.09808	−	6.29423i	−0.748203	−	0.663470i
$91$			6.92820i			0.726273i
$92$		0			0
$93$	5.53590	+	12.4641i	0.574046	+	1.29247i
$94$		−	18.0000i		−	1.85656i
$95$		0			0
$96$		0			0
$97$	−8.00000	+	8.00000i	−0.812277	+	0.812277i	−0.984975	−	0.172698i	$-0.944752\pi$
$97$	−8.00000	+	8.00000i	−0.812277	+	0.812277i	0.172698	+	0.984975i	$0.444752\pi$
$98$	6.83013	−	1.83013i	0.689947	−	0.184871i
$99$	−7.79423	−	13.5000i	−0.783349	−	1.35680i
$100$		0			0
$101$	4.00000			0.398015			0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000			0.398015			0.199007	+	0.979998i	$0.436228\pi$
$102$	2.19615	+	8.19615i	0.217451	+	0.811540i
$103$	13.6603	−	3.66025i	1.34598	−	0.360656i	0.487334	−	0.873216i	$-0.337970\pi$
$103$	13.6603	−	3.66025i	1.34598	−	0.360656i	0.858651	+	0.512560i	$0.171303\pi$
$104$	−6.92820	+	12.0000i	−0.679366	+	1.17670i
$105$	0.464102	+	7.73205i	0.0452917	+	0.754571i
$106$	−6.00000	−	3.46410i	−0.582772	−	0.336463i
$107$	−4.09808	−	1.09808i	−0.396176	−	0.106155i	0.0552301	−	0.998474i	$-0.482411\pi$
$107$	−4.09808	−	1.09808i	−0.396176	−	0.106155i	−0.451406	+	0.892319i	$0.649077\pi$
$108$		0			0
$109$		−	1.00000i		−	0.0957826i	−0.998853	−	0.0478913i	$-0.984750\pi$
$109$		−	1.00000i		−	0.0957826i	0.998853	−	0.0478913i	$-0.0152501\pi$
$110$	12.2942	+	10.9019i	1.17221	+	1.03946i
$111$	−6.00000	+	10.3923i	−0.569495	+	0.986394i
$112$	−5.46410	−	1.46410i	−0.516309	−	0.138345i
$113$	16.3923	−	4.39230i	1.54206	−	0.413193i	0.615128	−	0.788427i	$-0.289104\pi$
$113$	16.3923	−	4.39230i	1.54206	−	0.413193i	0.926930	+	0.375234i	$0.122438\pi$
$114$		0			0
$115$	−10.7321	−	2.19615i	−1.00077	−	0.204792i
$116$		0			0
$117$	3.80385	−	14.1962i	0.351666	−	1.31243i
$118$	−2.56218	+	9.56218i	−0.235868	+	0.880270i
$119$	1.73205	−	3.00000i	0.158777	−	0.275010i
$120$	−6.92820	+	13.8564i	−0.632456	+	1.26491i
$121$	8.00000	+	13.8564i	0.727273	+	1.25967i
$122$	−5.19615	−	5.19615i	−0.470438	−	0.470438i
$123$	12.1244	−	12.1244i	1.09322	−	1.09322i
$124$		0			0
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	6.00000			0.534522
$127$	0.633975	−	2.36603i	0.0562561	−	0.209951i	−0.932077	−	0.362261i	$-0.882005\pi$
$127$	0.633975	−	2.36603i	0.0562561	−	0.209951i	0.988333	+	0.152311i	$0.0486714\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	−5.19615	−	3.00000i	−0.457496	−	0.264135i
$130$	0.928203	+	15.4641i	0.0814088	+	1.35629i
$131$	−8.50000	−	14.7224i	−0.742648	−	1.28630i	−0.951285	−	0.308312i	$-0.900236\pi$
$131$	−8.50000	−	14.7224i	−0.742648	−	1.28630i	0.208637	−	0.977993i	$-0.433097\pi$
$132$		0			0
$133$		0			0
$134$	−13.8564	−	8.00000i	−1.19701	−	0.691095i
$135$		0			0
$136$	6.00000	−	3.46410i	0.514496	−	0.297044i
$137$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$137$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$138$	−4.39230	+	16.3923i	−0.373898	+	1.39541i
$139$	15.5885			1.32220			0.661098	−	0.750300i	$-0.270091\pi$
$139$	15.5885			1.32220			0.661098	+	0.750300i	$0.270091\pi$
$140$		0			0
$141$	27.0000	−	15.5885i	2.27381	−	1.31278i
$142$	0.366025	+	1.36603i	0.0307162	+	0.114634i
$143$	−6.58846	+	24.5885i	−0.550954	+	2.05619i
$144$	10.3923	+	6.00000i	0.866025	+	0.500000i
$145$	−2.13397	−	3.23205i	−0.177217	−	0.268407i
$146$	15.0000	+	8.66025i	1.24141	+	0.716728i
$147$	8.66025	+	8.66025i	0.714286	+	0.714286i
$148$		0			0
$149$	9.52628	−	5.50000i	0.780423	−	0.450578i	−0.0561570	−	0.998422i	$-0.517885\pi$
$149$	9.52628	−	5.50000i	0.780423	−	0.450578i	0.836580	+	0.547844i	$0.184551\pi$
$150$	2.07180	+	17.1962i	0.169161	+	1.40406i
$151$			20.7846i			1.69143i	0.533637	+	0.845714i	$0.320825\pi$
$151$			20.7846i			1.69143i	−0.533637	+	0.845714i	$0.679175\pi$
$152$		0			0
$153$	−5.19615	+	5.19615i	−0.420084	+	0.420084i
$154$	−10.3923			−0.837436
$155$	3.76795	−	11.8660i	0.302649	−	0.953102i
$156$		0			0
$157$	−2.00000	+	2.00000i	−0.159617	+	0.159617i	−0.782397	−	0.622780i	$-0.786003\pi$
$157$	−2.00000	+	2.00000i	−0.159617	+	0.159617i	0.622780	+	0.782397i	$0.286003\pi$
$158$	7.09808	+	1.90192i	0.564693	+	0.151309i
$159$		−	12.0000i		−	0.951662i
$160$		0			0
$161$	6.00000	−	3.46410i	0.472866	−	0.273009i
$162$	12.2942	+	3.29423i	0.965926	+	0.258819i
$163$	−4.00000	−	4.00000i	−0.313304	−	0.313304i	0.532884	−	0.846188i	$-0.321108\pi$
$163$	−4.00000	−	4.00000i	−0.313304	−	0.313304i	−0.846188	+	0.532884i	$0.821108\pi$
$164$		0			0
$165$	−5.70577	+	27.8827i	−0.444194	+	2.17066i
$166$	6.00000	+	3.46410i	0.465690	+	0.268866i
$167$	5.07180	−	18.9282i	0.392467	−	1.46471i	−0.433584	−	0.901113i	$-0.642751\pi$
$167$	5.07180	−	18.9282i	0.392467	−	1.46471i	0.826051	−	0.563595i	$-0.190582\pi$
$168$	−2.53590	−	9.46410i	−0.195649	−	0.730171i
$169$	−9.52628	+	5.50000i	−0.732791	+	0.423077i
$170$	3.46410	−	6.92820i	0.265684	−	0.531369i
$171$		0			0
$172$		0			0
$173$	−16.3923	+	4.39230i	−1.24628	+	0.333941i	−0.820900	−	0.571072i	$-0.806528\pi$
$173$	−16.3923	+	4.39230i	−1.24628	+	0.333941i	−0.425384	+	0.905013i	$0.639861\pi$
$174$	−5.19615	+	3.00000i	−0.393919	+	0.227429i
$175$	4.36603	−	5.56218i	0.330040	−	0.420461i
$176$	−18.0000	−	10.3923i	−1.35680	−	0.783349i
$177$	−16.5622	+	4.43782i	−1.24489	+	0.333567i
$178$	15.5885	−	15.5885i	1.16840	−	1.16840i
$179$	6.06218	+	10.5000i	0.453108	+	0.784807i	0.998577	−	0.0533243i	$-0.0169817\pi$
$179$	6.06218	+	10.5000i	0.453108	+	0.784807i	−0.545469	+	0.838131i	$0.683648\pi$
$180$		0			0
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	0.384345	−	0.923190i	$-0.374427\pi$
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	−0.607333	+	0.794447i	$0.707761\pi$
$182$	−6.92820	−	6.92820i	−0.513553	−	0.513553i
$183$	3.29423	−	12.2942i	0.243516	−	0.908816i
$184$	13.8564			1.02151
$185$	10.3923	−	3.46410i	0.764057	−	0.254686i
$186$	−18.0000	−	6.92820i	−1.31982	−	0.508001i
$187$	9.00000	−	9.00000i	0.658145	−	0.658145i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.50000	+	6.06218i	−0.253251	+	0.438644i	−0.964419	−	0.264378i	$-0.914833\pi$
$191$	−3.50000	+	6.06218i	−0.253251	+	0.438644i	0.711168	+	0.703022i	$0.248167\pi$
$192$	5.07180	−	18.9282i	0.366025	−	1.36603i
$193$	0.732051	−	2.73205i	0.0526942	−	0.196657i	−0.934561	−	0.355803i	$-0.884207\pi$
$193$	0.732051	−	2.73205i	0.0526942	−	0.196657i	0.987255	+	0.159146i	$0.0508740\pi$
$194$		−	16.0000i		−	1.14873i
$195$	−22.3923	+	14.7846i	−1.60355	+	1.05875i
$196$		0			0
$197$	11.8301	−	3.16987i	0.842862	−	0.225844i	0.188545	−	0.982065i	$-0.439623\pi$
$197$	11.8301	−	3.16987i	0.842862	−	0.225844i	0.654317	+	0.756220i	$0.272956\pi$
$198$	21.2942	+	5.70577i	1.51331	+	0.405492i
$199$	−10.3923	+	18.0000i	−0.736691	+	1.27599i	0.217287	+	0.976108i	$0.430279\pi$
$199$	−10.3923	+	18.0000i	−0.736691	+	1.27599i	−0.953977	+	0.299878i	$0.903054\pi$
$200$	13.1244	−	5.26795i	0.928032	−	0.372500i
$201$		−	27.7128i		−	1.95471i
$202$	−4.00000	+	4.00000i	−0.281439	+	0.281439i
$203$	2.36603	+	0.633975i	0.166062	+	0.0444963i
$204$		0			0
$205$	−15.6244	+	0.937822i	−1.09125	+	0.0655003i
$206$	−10.0000	+	17.3205i	−0.696733	+	1.20678i
$207$	−14.1962	+	3.80385i	−0.986701	+	0.264386i
$208$	−5.07180	−	18.9282i	−0.351666	−	1.31243i
$209$		0			0
$210$	−8.19615	−	7.26795i	−0.565588	−	0.501536i
$211$	−1.50000	−	2.59808i	−0.103264	−	0.178859i	0.809763	−	0.586756i	$-0.199595\pi$
$211$	−1.50000	−	2.59808i	−0.103264	−	0.178859i	−0.913028	+	0.407898i	$0.866262\pi$
$212$		0			0
$213$	−1.73205	+	1.73205i	−0.118678	+	0.118678i
$214$	5.19615	−	3.00000i	0.355202	−	0.205076i
$215$	1.73205	+	5.19615i	0.118125	+	0.354375i
$216$		0			0
$217$	3.19615	+	7.19615i	0.216969	+	0.488507i
$218$	1.00000	+	1.00000i	0.0677285	+	0.0677285i
$219$			30.0000i			2.02721i
$220$		0			0
$221$	12.0000			0.807207
$222$	−4.39230	−	16.3923i	−0.294792	−	1.10018i
$223$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$223$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$224$		0			0
$225$	−12.0000	+	9.00000i	−0.800000	+	0.600000i
$226$	−12.0000	+	20.7846i	−0.798228	+	1.38257i
$227$	−2.92820	−	10.9282i	−0.194352	−	0.725330i	−0.992434	−	0.122782i	$-0.960819\pi$
$227$	−2.92820	−	10.9282i	−0.194352	−	0.725330i	0.798082	−	0.602549i	$-0.205848\pi$
$228$		0			0
$229$	−6.06218	−	10.5000i	−0.400600	−	0.693860i	0.593198	−	0.805056i	$-0.297865\pi$
$229$	−6.06218	−	10.5000i	−0.400600	−	0.693860i	−0.993798	+	0.111197i	$0.964532\pi$
$230$	12.9282	−	8.53590i	0.852460	−	0.562840i
$231$	−9.00000	−	15.5885i	−0.592157	−	1.02565i
$232$	3.46410	+	3.46410i	0.227429	+	0.227429i
$233$	−3.00000	−	3.00000i	−0.196537	−	0.196537i	0.601977	−	0.798513i	$-0.294380\pi$
$233$	−3.00000	−	3.00000i	−0.196537	−	0.196537i	−0.798513	+	0.601977i	$0.794380\pi$
$234$	10.3923	+	18.0000i	0.679366	+	1.17670i
$235$	−27.8827	−	5.70577i	−1.81887	−	0.372203i
$236$		0			0
$237$	3.29423	+	12.2942i	0.213983	+	0.798596i
$238$	1.26795	+	4.73205i	0.0821889	+	0.306733i
$239$	−0.866025	+	1.50000i	−0.0560185	+	0.0970269i	−0.892675	−	0.450701i	$-0.851174\pi$
$239$	−0.866025	+	1.50000i	−0.0560185	+	0.0970269i	0.836656	+	0.547728i	$0.184507\pi$
$240$	−6.92820	−	20.7846i	−0.447214	−	1.34164i
$241$	−12.0000	+	6.92820i	−0.772988	+	0.446285i	−0.833939	−	0.551856i	$-0.813920\pi$
$241$	−12.0000	+	6.92820i	−0.772988	+	0.446285i	0.0609515	+	0.998141i	$0.480586\pi$
$242$	−21.8564	−	5.85641i	−1.40498	−	0.376464i
$243$	5.70577	+	21.2942i	0.366025	+	1.36603i
$244$		0			0
$245$	−0.669873	−	11.1603i	−0.0427966	−	0.713002i
$246$			24.2487i			1.54604i
$247$		0			0
$248$	−1.66025	+	15.6603i	−0.105426	+	0.994427i
$249$			12.0000i			0.760469i
$250$	9.00000	−	13.0000i	0.569210	−	0.822192i
$251$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$251$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$252$		0			0
$253$	24.5885	−	6.58846i	1.54586	−	0.414213i
$254$	1.73205	+	3.00000i	0.108679	+	0.188237i
$255$	13.3923	−	0.803848i	0.838659	−	0.0503389i
$256$		0			0
$257$	−7.32051	−	27.3205i	−0.456641	−	1.70421i	−0.683219	−	0.730214i	$-0.739421\pi$
$257$	−7.32051	−	27.3205i	−0.456641	−	1.70421i	0.226578	−	0.973993i	$-0.427246\pi$
$258$	8.19615	−	2.19615i	0.510270	−	0.136726i
$259$	−3.46410	+	6.00000i	−0.215249	+	0.372822i
$260$		0			0
$261$	−4.50000	−	2.59808i	−0.278543	−	0.160817i
$262$	23.2224	+	6.22243i	1.43469	+	0.384423i
$263$	−5.19615	+	5.19615i	−0.320408	+	0.320408i	−0.848924	−	0.528515i	$-0.822749\pi$
$263$	−5.19615	+	5.19615i	−0.320408	+	0.320408i	0.528515	+	0.848924i	$0.322749\pi$
$264$		−	36.0000i		−	2.21565i
$265$	−7.26795	+	8.19615i	−0.446467	+	0.503486i
$266$		0			0
$267$	36.8827	+	9.88269i	2.25718	+	0.604811i
$268$		0			0
$269$	11.2583	−	19.5000i	0.686433	−	1.18894i	−0.286552	−	0.958065i	$-0.592509\pi$
$269$	11.2583	−	19.5000i	0.686433	−	1.18894i	0.972984	−	0.230871i	$-0.0741576\pi$
$270$		0			0
$271$			1.73205i			0.105215i	0.998615	+	0.0526073i	$0.0167532\pi$
$271$			1.73205i			0.105215i	−0.998615	+	0.0526073i	$0.983247\pi$
$272$	−2.53590	+	9.46410i	−0.153761	+	0.573845i
$273$	4.39230	−	16.3923i	0.265834	−	0.992107i
$274$		0			0
$275$	20.7846	−	15.5885i	1.25336	−	0.940019i
$276$		0			0
$277$	5.19615	+	5.19615i	0.312207	+	0.312207i	0.845764	−	0.533557i	$-0.179145\pi$
$277$	5.19615	+	5.19615i	0.312207	+	0.312207i	−0.533557	+	0.845764i	$0.679145\pi$
$278$	−15.5885	+	15.5885i	−0.934934	+	0.934934i
$279$	−2.59808	−	16.5000i	−0.155543	−	0.987829i
$280$	−4.00000	+	8.00000i	−0.239046	+	0.478091i
$281$	13.0000			0.775515			0.387757	−	0.921761i	$-0.373250\pi$
$281$	13.0000			0.775515			0.387757	+	0.921761i	$0.373250\pi$
$282$	−11.4115	+	42.5885i	−0.679547	+	2.53611i
$283$	−16.0000	−	16.0000i	−0.951101	−	0.951101i	0.0477577	−	0.998859i	$-0.484792\pi$
$283$	−16.0000	−	16.0000i	−0.951101	−	0.951101i	−0.998859	+	0.0477577i	$0.984792\pi$
$284$		0			0
$285$		0			0
$286$	−18.0000	−	31.1769i	−1.06436	−	1.84353i
$287$	7.00000	−	7.00000i	0.413197	−	0.413197i
$288$		0			0
$289$	9.52628	+	5.50000i	0.560369	+	0.323529i
$290$	5.36603	+	1.09808i	0.315104	+	0.0644813i
$291$	24.0000	−	13.8564i	1.40690	−	0.812277i
$292$		0			0
$293$	−4.02628	+	15.0263i	−0.235218	+	0.877845i	0.742833	+	0.669477i	$0.233482\pi$
$293$	−4.02628	+	15.0263i	−0.235218	+	0.877845i	−0.978051	+	0.208368i	$0.933185\pi$
$294$	−17.3205			−1.01015
$295$	14.0000	+	7.00000i	0.815112	+	0.407556i
$296$	−12.0000	+	6.92820i	−0.697486	+	0.402694i
$297$		0			0
$298$	−4.02628	+	15.0263i	−0.233236	+	0.870449i
$299$	20.7846	+	12.0000i	1.20201	+	0.693978i
$300$		0			0
$301$	−3.00000	−	1.73205i	−0.172917	−	0.0998337i
$302$	−20.7846	−	20.7846i	−1.19602	−	1.19602i
$303$	−9.46410	−	2.53590i	−0.543698	−	0.145684i
$304$		0			0
$305$	−9.69615	+	6.40192i	−0.555200	+	0.366573i
$306$		−	10.3923i		−	0.594089i
$307$	−15.0263	−	4.02628i	−0.857595	−	0.229792i	−0.196879	−	0.980428i	$-0.563081\pi$
$307$	−15.0263	−	4.02628i	−0.857595	−	0.229792i	−0.660716	+	0.750636i	$0.729747\pi$
$308$		0			0
$309$	−34.6410			−1.97066
$310$	8.09808	+	15.6340i	0.459940	+	0.887950i
$311$	−7.00000			−0.396934			−0.198467	−	0.980108i	$-0.563596\pi$
$311$	−7.00000			−0.396934			−0.198467	+	0.980108i	$0.563596\pi$
$312$	24.0000	−	24.0000i	1.35873	−	1.35873i
$313$	−23.6603	−	6.33975i	−1.33736	−	0.358344i	−0.481904	−	0.876224i	$-0.660054\pi$
$313$	−23.6603	−	6.33975i	−1.33736	−	0.358344i	−0.855453	+	0.517881i	$0.826721\pi$
$314$		−	4.00000i		−	0.225733i
$315$	1.90192	−	9.29423i	0.107161	−	0.523670i
$316$		0			0
$317$	−16.3923	−	4.39230i	−0.920684	−	0.246696i	−0.232806	−	0.972523i	$-0.574791\pi$
$317$	−16.3923	−	4.39230i	−0.920684	−	0.246696i	−0.687878	+	0.725827i	$0.741457\pi$
$318$	12.0000	+	12.0000i	0.672927	+	0.672927i
$319$	7.79423	+	4.50000i	0.436393	+	0.251952i
$320$	−14.9282	+	9.85641i	−0.834512	+	0.550990i
$321$	9.00000	+	5.19615i	0.502331	+	0.290021i
$322$	−2.53590	+	9.46410i	−0.141320	+	0.527414i
$323$		0			0
$324$		0			0
$325$	24.2487	+	3.46410i	1.34508	+	0.192154i
$326$	8.00000			0.443079
$327$	−0.633975	+	2.36603i	−0.0350589	+	0.130842i
$328$	19.1244	−	5.12436i	1.05597	−	0.282945i
$329$	15.5885	−	9.00000i	0.859419	−	0.496186i
$330$	−22.1769	−	33.5885i	−1.22080	−	1.84898i
$331$	1.50000	+	0.866025i	0.0824475	+	0.0476011i	0.540657	−	0.841243i	$-0.318176\pi$
$331$	1.50000	+	0.866025i	0.0824475	+	0.0476011i	−0.458209	+	0.888844i	$0.651509\pi$
$332$		0			0
$333$	10.3923	−	10.3923i	0.569495	−	0.569495i
$334$	13.8564	+	24.0000i	0.758189	+	1.31322i
$335$	−16.7846	+	18.9282i	−0.917041	+	1.03416i
$336$	12.0000	+	6.92820i	0.654654	+	0.377964i
$337$	19.0526	+	19.0526i	1.03786	+	1.03786i	0.999255	+	0.0386044i	$0.0122912\pi$
$337$	19.0526	+	19.0526i	1.03786	+	1.03786i	0.0386044	+	0.999255i	$0.487709\pi$
$338$	4.02628	−	15.0263i	0.219001	−	0.817322i
$339$	−41.5692			−2.25773
$340$		0			0
$341$	4.50000	+	28.5788i	0.243689	+	1.54763i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−3.46410	−	6.00000i	−0.186772	−	0.323498i
$345$	24.0000	+	12.0000i	1.29212	+	0.646058i
$346$	12.0000	−	20.7846i	0.645124	−	1.11739i
$347$	−8.87564	+	33.1244i	−0.476470	+	1.77821i	0.139265	+	0.990255i	$0.455526\pi$
$347$	−8.87564	+	33.1244i	−0.476470	+	1.77821i	−0.615735	+	0.787953i	$0.711141\pi$
$348$		0			0
$349$		−	7.00000i		−	0.374701i	−0.982293	−	0.187351i	$-0.940010\pi$
$349$		−	7.00000i		−	0.374701i	0.982293	−	0.187351i	$-0.0599901\pi$
$350$	1.19615	+	9.92820i	0.0639370	+	0.530685i
$351$		0			0
$352$		0			0
$353$	−14.1962	−	3.80385i	−0.755585	−	0.202458i	−0.139591	−	0.990209i	$-0.544579\pi$
$353$	−14.1962	−	3.80385i	−0.755585	−	0.202458i	−0.615994	+	0.787751i	$0.711245\pi$
$354$	12.1244	−	21.0000i	0.644402	−	1.11614i
$355$	2.23205	−	0.133975i	0.118465	−	0.00711063i
$356$		0			0
$357$	−6.00000	+	6.00000i	−0.317554	+	0.317554i
$358$	−16.5622	−	4.43782i	−0.875338	−	0.234546i
$359$	11.2583	+	6.50000i	0.594192	+	0.343057i	0.766753	−	0.641942i	$-0.221871\pi$
$359$	11.2583	+	6.50000i	0.594192	+	0.343057i	−0.172561	+	0.984999i	$0.555204\pi$
$360$	12.5885	−	14.1962i	0.663470	−	0.748203i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	4.73205	−	1.26795i	0.248711	−	0.0666419i
$363$	−10.1436	−	37.8564i	−0.532401	−	1.98695i
$364$		0			0
$365$	18.1699	−	20.4904i	0.951055	−	1.07252i
$366$	9.00000	+	15.5885i	0.470438	+	0.814822i
$367$	−23.6603	+	6.33975i	−1.23506	+	0.330932i	−0.816546	−	0.577280i	$-0.804114\pi$
$367$	−23.6603	+	6.33975i	−1.23506	+	0.330932i	−0.418509	+	0.908213i	$0.637447\pi$
$368$	−13.8564	+	13.8564i	−0.722315	+	0.722315i
$369$	−18.1865	+	10.5000i	−0.946753	+	0.546608i
$370$	−6.92820	+	13.8564i	−0.360180	+	0.720360i
$371$		−	6.92820i		−	0.359694i
$372$		0			0
$373$	10.0000	+	10.0000i	0.517780	+	0.517780i	0.916899	−	0.399119i	$-0.130684\pi$
$373$	10.0000	+	10.0000i	0.517780	+	0.517780i	−0.399119	+	0.916899i	$0.630684\pi$
$374$			18.0000i			0.930758i
$375$	27.2942	+	2.24167i	1.40947	+	0.115759i
$376$	36.0000			1.85656
$377$	2.19615	+	8.19615i	0.113108	+	0.422123i
$378$		0			0
$379$	5.19615	−	3.00000i	0.266908	−	0.154100i	−0.360573	−	0.932731i	$-0.617419\pi$
$379$	5.19615	−	3.00000i	0.266908	−	0.154100i	0.627482	+	0.778631i	$0.284086\pi$
$380$		0			0
$381$	−3.00000	+	5.19615i	−0.153695	+	0.266207i
$382$	−2.56218	−	9.56218i	−0.131092	−	0.489244i
$383$	−2.53590	−	9.46410i	−0.129578	−	0.483593i	0.870383	−	0.492375i	$-0.163871\pi$
$383$	−2.53590	−	9.46410i	−0.129578	−	0.483593i	−0.999961	+	0.00878215i	$0.997205\pi$
$384$	13.8564	+	24.0000i	0.707107	+	1.22474i
$385$	−3.29423	+	16.0981i	−0.167889	+	0.820434i
$386$	2.00000	+	3.46410i	0.101797	+	0.176318i
$387$	5.19615	+	5.19615i	0.264135	+	0.264135i
$388$		0			0
$389$	−9.52628	−	16.5000i	−0.483002	−	0.836583i	0.516808	−	0.856101i	$-0.327120\pi$
$389$	−9.52628	−	16.5000i	−0.483002	−	0.836583i	−0.999810	+	0.0195181i	$0.993787\pi$
$390$	7.60770	−	37.1769i	0.385231	−	1.88253i
$391$	−6.00000	−	10.3923i	−0.303433	−	0.525561i
$392$	3.66025	+	13.6603i	0.184871	+	0.689947i
$393$	10.7776	+	40.2224i	0.543656	+	2.02895i
$394$	−8.66025	+	15.0000i	−0.436297	+	0.755689i
$395$	5.19615	−	10.3923i	0.261447	−	0.522894i
$396$		0			0
$397$	5.46410	+	1.46410i	0.274235	+	0.0734812i	0.393316	−	0.919403i	$-0.371328\pi$
$397$	5.46410	+	1.46410i	0.274235	+	0.0734812i	−0.119080	+	0.992885i	$0.537995\pi$
$398$	−7.60770	−	28.3923i	−0.381339	−	1.42318i
$399$		0			0
$400$	−7.85641	+	18.3923i	−0.392820	+	0.919615i
$401$			12.1244i			0.605461i	0.953076	+	0.302731i	$0.0978983\pi$
$401$			12.1244i			0.605461i	−0.953076	+	0.302731i	$0.902102\pi$
$402$	27.7128	+	27.7128i	1.38219	+	1.38219i
$403$	−16.0526	+	22.0526i	−0.799635	+	1.09852i
$404$		0			0
$405$	9.00000	−	18.0000i	0.447214	−	0.894427i
$406$	−3.00000	+	1.73205i	−0.148888	+	0.0859602i
$407$	−18.0000	+	18.0000i	−0.892227	+	0.892227i
$408$	−16.3923	+	4.39230i	−0.811540	+	0.217451i
$409$	12.1244	+	21.0000i	0.599511	+	1.03838i	0.992893	+	0.119008i	$0.0379715\pi$
$409$	12.1244	+	21.0000i	0.599511	+	1.03838i	−0.393382	+	0.919375i	$0.628695\pi$
$410$	14.6865	−	16.5622i	0.725316	−	0.817948i
$411$		0			0
$412$		0			0
$413$	−9.56218	+	2.56218i	−0.470524	+	0.126077i
$414$	10.3923	−	18.0000i	0.510754	−	0.884652i
$415$	7.26795	−	8.19615i	0.356770	−	0.402333i
$416$		0			0
$417$	−36.8827	−	9.88269i	−1.80615	−	0.483957i
$418$		0			0
$419$			31.0000i			1.51445i	0.653155	+	0.757225i	$0.273445\pi$
$419$			31.0000i			1.51445i	−0.653155	+	0.757225i	$0.726555\pi$
$420$		0			0
$421$	7.50000	−	12.9904i	0.365528	−	0.633112i	−0.623333	−	0.781956i	$-0.714222\pi$
$421$	7.50000	−	12.9904i	0.365528	−	0.633112i	0.988861	+	0.148844i	$0.0475552\pi$
$422$	4.09808	+	1.09808i	0.199491	+	0.0534535i
$423$	−36.8827	+	9.88269i	−1.79330	+	0.480513i
$424$	6.92820	−	12.0000i	0.336463	−	0.582772i
$425$	−9.63397	−	7.56218i	−0.467316	−	0.366820i
$426$		−	3.46410i		−	0.167836i
$427$	1.90192	−	7.09808i	0.0920405	−	0.343500i
$428$		0			0
$429$	31.1769	−	54.0000i	1.50524	−	2.60714i
$430$	−6.92820	−	3.46410i	−0.334108	−	0.167054i
$431$	0.500000	+	0.866025i	0.0240842	+	0.0417150i	0.877816	−	0.478997i	$-0.159000\pi$
$431$	0.500000	+	0.866025i	0.0240842	+	0.0417150i	−0.853732	+	0.520712i	$0.825666\pi$
$432$		0			0
$433$	−1.73205	+	1.73205i	−0.0832370	+	0.0832370i	−0.747499	−	0.664262i	$-0.768746\pi$
$433$	−1.73205	+	1.73205i	−0.0832370	+	0.0832370i	0.664262	+	0.747499i	$0.268746\pi$
$434$	−10.3923	−	4.00000i	−0.498847	−	0.192006i
$435$	3.00000	+	9.00000i	0.143839	+	0.431517i
$436$		0			0
$437$		0			0
$438$	−30.0000	−	30.0000i	−1.43346	−	1.43346i
$439$	−25.1147	−	14.5000i	−1.19866	−	0.692047i	−0.238404	−	0.971166i	$-0.576624\pi$
$439$	−25.1147	−	14.5000i	−1.19866	−	0.692047i	−0.960257	+	0.279119i	$0.909958\pi$
$440$	−21.8038	+	24.5885i	−1.03946	+	1.17221i
$441$	−7.50000	−	12.9904i	−0.357143	−	0.618590i
$442$	−12.0000	+	12.0000i	−0.570782	+	0.570782i
$443$	1.36603	−	0.366025i	0.0649018	−	0.0173904i	−0.226222	−	0.974076i	$-0.572637\pi$
$443$	1.36603	−	0.366025i	0.0649018	−	0.0173904i	0.291124	+	0.956685i	$0.405971\pi$
$444$		0			0
$445$	−19.2058	−	29.0885i	−0.910441	−	1.37893i
$446$		0			0
$447$	−26.0263	+	6.97372i	−1.23100	+	0.329846i
$448$	2.92820	−	10.9282i	0.138345	−	0.516309i
$449$	−24.2487			−1.14437			−0.572184	−	0.820125i	$-0.693904\pi$
$449$	−24.2487			−1.14437			−0.572184	+	0.820125i	$0.693904\pi$
$450$	3.00000	−	21.0000i	0.141421	−	0.989949i
$451$	31.5000	−	18.1865i	1.48328	−	0.856370i
$452$		0			0
$453$	13.1769	−	49.1769i	0.619105	−	2.31053i
$454$	13.8564	+	8.00000i	0.650313	+	0.375459i
$455$	−12.9282	+	8.53590i	−0.606084	+	0.400169i
$456$		0			0
$457$	1.73205	+	1.73205i	0.0810219	+	0.0810219i	0.746456	−	0.665434i	$-0.231754\pi$
$457$	1.73205	+	1.73205i	0.0810219	+	0.0810219i	−0.665434	+	0.746456i	$0.731754\pi$
$458$	16.5622	+	4.43782i	0.773900	+	0.207366i
$459$		0			0
$460$		0			0
$461$		−	34.6410i		−	1.61339i	−0.590966	−	0.806696i	$-0.701253\pi$
$461$		−	34.6410i		−	1.61339i	0.590966	−	0.806696i	$-0.298747\pi$
$462$	24.5885	+	6.58846i	1.14396	+	0.306523i
$463$	12.1244	−	12.1244i	0.563467	−	0.563467i	−0.366824	−	0.930290i	$-0.619555\pi$
$463$	12.1244	−	12.1244i	0.563467	−	0.563467i	0.930290	+	0.366824i	$0.119555\pi$
$464$	−6.92820			−0.321634
$465$	−16.4378	+	25.6865i	−0.762286	+	1.19118i
$466$	6.00000			0.277945
$467$	3.00000	−	3.00000i	0.138823	−	0.138823i	−0.634280	−	0.773103i	$-0.718703\pi$
$467$	3.00000	−	3.00000i	0.138823	−	0.138823i	0.773103	+	0.634280i	$0.218703\pi$
$468$		0			0
$469$		−	16.0000i		−	0.738811i
$470$	33.5885	−	22.1769i	1.54932	−	1.02294i
$471$	6.00000	−	3.46410i	0.276465	−	0.159617i
$472$	−19.1244	−	5.12436i	−0.880270	−	0.235868i
$473$	−9.00000	−	9.00000i	−0.413820	−	0.413820i
$474$	−15.5885	−	9.00000i	−0.716002	−	0.413384i
$475$		0			0
$476$		0			0
$477$	−3.80385	+	14.1962i	−0.174166	+	0.649997i
$478$	−0.633975	−	2.36603i	−0.0289973	−	0.108219i
$479$	30.3109	−	17.5000i	1.38494	−	0.799595i	0.392200	−	0.919880i	$-0.371714\pi$
$479$	30.3109	−	17.5000i	1.38494	−	0.799595i	0.992739	+	0.120284i	$0.0383806\pi$
$480$		0			0
$481$	−24.0000			−1.09431
$482$	5.07180	−	18.9282i	0.231014	−	0.862156i
$483$	−16.3923	+	4.39230i	−0.745876	+	0.199857i
$484$		0			0
$485$	−24.7846	−	5.07180i	−1.12541	−	0.230298i
$486$	−27.0000	−	15.5885i	−1.22474	−	0.707107i
$487$	2.36603	−	0.633975i	0.107215	−	0.0287281i	−0.204813	−	0.978801i	$-0.565659\pi$
$487$	2.36603	−	0.633975i	0.107215	−	0.0287281i	0.312028	+	0.950073i	$0.398992\pi$
$488$	10.3923	−	10.3923i	0.470438	−	0.470438i
$489$	6.92820	+	12.0000i	0.313304	+	0.542659i
$490$	11.8301	+	10.4904i	0.534431	+	0.473907i
$491$	−16.5000	−	9.52628i	−0.744635	−	0.429915i	0.0791174	−	0.996865i	$-0.474790\pi$
$491$	−16.5000	−	9.52628i	−0.744635	−	0.429915i	−0.823752	+	0.566950i	$0.808123\pi$
$492$		0			0
$493$	1.09808	−	4.09808i	0.0494549	−	0.184568i
$494$		0			0
$495$	15.5885	−	31.1769i	0.700649	−	1.40130i
$496$	−14.0000	−	17.3205i	−0.628619	−	0.777714i
$497$	−1.00000	+	1.00000i	−0.0448561	+	0.0448561i
$498$	−12.0000	−	12.0000i	−0.537733	−	0.537733i
$499$	−4.33013	−	7.50000i	−0.193843	−	0.335746i	0.752678	−	0.658389i	$-0.228762\pi$
$499$	−4.33013	−	7.50000i	−0.193843	−	0.335746i	−0.946521	+	0.322643i	$0.895429\pi$
$500$		0			0
$501$	−24.0000	+	41.5692i	−1.07224	+	1.85718i
$502$		0			0
$503$	−7.68653	+	28.6865i	−0.342726	+	1.27907i	0.552521	+	0.833499i	$0.313666\pi$
$503$	−7.68653	+	28.6865i	−0.342726	+	1.27907i	−0.895247	+	0.445571i	$0.853001\pi$
$504$			12.0000i			0.534522i
$505$	4.92820	+	7.46410i	0.219302	+	0.332148i
$506$	−18.0000	+	31.1769i	−0.800198	+	1.38598i
$507$	26.0263	−	6.97372i	1.15587	−	0.309714i
$508$		0			0
$509$	−9.52628	+	16.5000i	−0.422245	+	0.731350i	−0.996159	−	0.0875661i	$-0.972091\pi$
$509$	−9.52628	+	16.5000i	−0.422245	+	0.731350i	0.573914	+	0.818916i	$0.305424\pi$
$510$	−12.5885	+	14.1962i	−0.557426	+	0.628616i
$511$			17.3205i			0.766214i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	34.6410	+	20.0000i	1.52795	+	0.882162i
$515$	23.6603	+	20.9808i	1.04260	+	0.924523i
$516$		0			0
$517$	63.8827	−	17.1173i	2.80956	−	0.752819i
$518$	−2.53590	−	9.46410i	−0.111421	−	0.415829i
$519$	41.5692			1.82469
$520$	−30.9282	+	1.85641i	−1.35629	+	0.0814088i
$521$	14.5000	+	25.1147i	0.635257	+	1.10030i	0.986461	+	0.163998i	$0.0524390\pi$
$521$	14.5000	+	25.1147i	0.635257	+	1.10030i	−0.351204	+	0.936299i	$0.614228\pi$
$522$	7.09808	−	1.90192i	0.310674	−	0.0832449i
$523$	−15.5885	+	15.5885i	−0.681636	+	0.681636i	−0.960369	−	0.278733i	$-0.910086\pi$
$523$	−15.5885	+	15.5885i	−0.681636	+	0.681636i	0.278733	+	0.960369i	$0.410086\pi$
$524$		0			0
$525$	−13.8564	+	10.3923i	−0.604743	+	0.453557i
$526$		−	10.3923i		−	0.453126i
$527$	12.4641	−	5.53590i	0.542945	−	0.241148i
$528$	36.0000	+	36.0000i	1.56670	+	1.56670i
$529$		−	1.00000i		−	0.0434783i
$530$	−0.928203	−	15.4641i	−0.0403186	−	0.671718i
$531$	21.0000			0.911322
$532$		0			0
$533$	33.1244	+	8.87564i	1.43478	+	0.384447i
$534$	−46.7654	+	27.0000i	−2.02374	+	1.16840i
$535$	−3.00000	−	9.00000i	−0.129701	−	0.389104i
$536$	16.0000	−	27.7128i	0.691095	−	1.19701i
$537$	−7.68653	−	28.6865i	−0.331698	−	1.23792i
$538$	8.24167	+	30.7583i	0.355324	+	1.32609i
$539$	12.9904	+	22.5000i	0.559535	+	0.969144i
$540$		0			0
$541$	−17.5000	−	30.3109i	−0.752384	−	1.30317i	−0.946664	−	0.322221i	$-0.895571\pi$
$541$	−17.5000	−	30.3109i	−0.752384	−	1.30317i	0.194281	−	0.980946i	$-0.437763\pi$
$542$	−1.73205	−	1.73205i	−0.0743980	−	0.0743980i
$543$	6.00000	+	6.00000i	0.257485	+	0.257485i
$544$		0			0
$545$	1.86603	−	1.23205i	0.0799317	−	0.0527753i
$546$	12.0000	+	20.7846i	0.513553	+	0.889499i
$547$	−5.85641	−	21.8564i	−0.250402	−	0.934512i	−0.970591	−	0.240735i	$-0.922612\pi$
$547$	−5.85641	−	21.8564i	−0.250402	−	0.934512i	0.720189	−	0.693778i	$-0.244055\pi$
$548$		0			0
$549$	−7.79423	+	13.5000i	−0.332650	+	0.576166i
$550$	−5.19615	+	36.3731i	−0.221565	+	1.55095i
$551$		0			0
$552$	−32.7846	−	8.78461i	−1.39541	−	0.373898i
$553$	1.90192	+	7.09808i	0.0808780	+	0.301841i
$554$	−10.3923			−0.441527
$555$	−26.7846	+	1.60770i	−1.13694	+	0.0682429i
$556$		0			0
$557$	−17.3205	−	17.3205i	−0.733893	−	0.733893i	0.237495	−	0.971389i	$-0.423674\pi$
$557$	−17.3205	−	17.3205i	−0.733893	−	0.733893i	−0.971389	+	0.237495i	$0.923674\pi$
$558$	19.0981	+	13.9019i	0.808486	+	0.588515i
$559$		−	12.0000i		−	0.507546i
$560$	−4.00000	−	12.0000i	−0.169031	−	0.507093i
$561$	−27.0000	+	15.5885i	−1.13994	+	0.658145i
$562$	−13.0000	+	13.0000i	−0.548372	+	0.548372i
$563$	8.19615	−	2.19615i	0.345427	−	0.0925568i	−0.0819347	−	0.996638i	$-0.526110\pi$
$563$	8.19615	−	2.19615i	0.345427	−	0.0925568i	0.427361	+	0.904081i	$0.359443\pi$
$564$		0			0
$565$	28.3923	+	25.1769i	1.19447	+	1.05920i
$566$	32.0000			1.34506
$567$	3.29423	+	12.2942i	0.138345	+	0.516309i
$568$	−2.73205	+	0.732051i	−0.114634	+	0.0307162i
$569$	11.2583	−	19.5000i	0.471974	−	0.817483i	−0.527512	−	0.849548i	$-0.676875\pi$
$569$	11.2583	−	19.5000i	0.471974	−	0.817483i	0.999486	+	0.0320650i	$0.0102084\pi$
$570$		0			0
$571$	−4.50000	−	2.59808i	−0.188319	−	0.108726i	0.402876	−	0.915254i	$-0.368010\pi$
$571$	−4.50000	−	2.59808i	−0.188319	−	0.108726i	−0.591195	+	0.806528i	$0.701344\pi$
$572$		0			0
$573$	12.1244	−	12.1244i	0.506502	−	0.506502i
$574$			14.0000i			0.584349i
$575$	−9.12436	−	22.7321i	−0.380512	−	0.947992i
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$	−21.8564	−	5.85641i	−0.909894	−	0.243805i	−0.226634	−	0.973980i	$-0.572772\pi$
$577$	−21.8564	−	5.85641i	−0.909894	−	0.243805i	−0.683261	+	0.730175i	$0.739439\pi$
$578$	−15.0263	+	4.02628i	−0.625011	+	0.167471i
$579$	−3.46410	+	6.00000i	−0.143963	+	0.249351i
$580$		0			0
$581$			6.92820i			0.287430i
$582$	−10.1436	+	37.8564i	−0.420465	+	1.56920i
$583$	6.58846	−	24.5885i	0.272866	−	1.01835i
$584$	−17.3205	+	30.0000i	−0.716728	+	1.24141i
$585$	31.1769	−	10.3923i	1.28901	−	0.429669i
$586$	−11.0000	−	19.0526i	−0.454406	−	0.787054i
$587$	−17.3205	−	17.3205i	−0.714894	−	0.714894i	0.252661	−	0.967555i	$-0.418694\pi$
$587$	−17.3205	−	17.3205i	−0.714894	−	0.714894i	−0.967555	+	0.252661i	$0.918694\pi$
$588$		0			0
$589$		0			0
$590$	−21.0000	+	7.00000i	−0.864556	+	0.288185i
$591$	−30.0000			−1.23404
$592$	5.07180	−	18.9282i	0.208450	−	0.777944i
$593$	12.0000	+	12.0000i	0.492781	+	0.492781i	0.909181	−	0.416400i	$-0.136709\pi$
$593$	12.0000	+	12.0000i	0.492781	+	0.492781i	−0.416400	+	0.909181i	$0.636709\pi$
$594$		0			0
$595$	7.73205	−	0.464102i	0.316983	−	0.0190263i
$596$		0			0
$597$	36.0000	−	36.0000i	1.47338	−	1.47338i
$598$	−32.7846	+	8.78461i	−1.34066	+	0.359229i
$599$	40.7032	+	23.5000i	1.66309	+	0.960184i	0.971228	+	0.238152i	$0.0765416\pi$
$599$	40.7032	+	23.5000i	1.66309	+	0.960184i	0.691859	+	0.722032i	$0.256792\pi$
$600$	−34.3923	+	4.14359i	−1.40406	+	0.169161i
$601$	−7.50000	+	4.33013i	−0.305931	+	0.176630i	−0.645104	−	0.764094i	$-0.723186\pi$
$601$	−7.50000	+	4.33013i	−0.305931	+	0.176630i	0.339173	+	0.940724i	$0.389853\pi$
$602$	4.73205	−	1.26795i	0.192864	−	0.0516778i
$603$	−8.78461	+	32.7846i	−0.357737	+	1.33509i
$604$		0			0
$605$	−16.0000	+	32.0000i	−0.650493	+	1.30099i
$606$	12.0000	−	6.92820i	0.487467	−	0.281439i
$607$	2.92820	+	10.9282i	0.118852	+	0.443562i	0.999546	−	0.0301234i	$-0.00959002\pi$
$607$	2.92820	+	10.9282i	0.118852	+	0.443562i	−0.880694	+	0.473685i	$0.842923\pi$
$608$		0			0
$609$	−5.19615	−	3.00000i	−0.210559	−	0.121566i
$610$	3.29423	−	16.0981i	0.133379	−	0.651792i
$611$	54.0000	+	31.1769i	2.18461	+	1.26128i
$612$		0			0
$613$	16.5622	+	4.43782i	0.668940	+	0.179242i	0.577277	−	0.816548i	$-0.304115\pi$
$613$	16.5622	+	4.43782i	0.668940	+	0.179242i	0.0916627	+	0.995790i	$0.470782\pi$
$614$	19.0526	−	11.0000i	0.768899	−	0.443924i
$615$	37.5622	+	7.68653i	1.51465	+	0.309951i
$616$		−	20.7846i		−	0.837436i
$617$	5.46410	+	1.46410i	0.219976	+	0.0589425i	0.367124	−	0.930172i	$-0.380343\pi$
$617$	5.46410	+	1.46410i	0.219976	+	0.0589425i	−0.147147	+	0.989115i	$0.547009\pi$
$618$	34.6410	−	34.6410i	1.39347	−	1.39347i
$619$	−29.4449			−1.18349			−0.591744	−	0.806126i	$-0.701561\pi$
$619$	−29.4449			−1.18349			−0.591744	+	0.806126i	$0.701561\pi$
$620$		0			0
$621$		0			0
$622$	7.00000	−	7.00000i	0.280674	−	0.280674i
$623$	21.2942	+	5.70577i	0.853135	+	0.228597i
$624$			48.0000i			1.92154i
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	30.0000	−	17.3205i	1.19904	−	0.692267i
$627$		0			0
$628$		0			0
$629$	10.3923	+	6.00000i	0.414368	+	0.239236i
$630$	7.39230	+	11.1962i	0.294516	+	0.446065i
$631$	31.5000	+	18.1865i	1.25400	+	0.723994i	0.971900	−	0.235392i	$-0.0756374\pi$
$631$	31.5000	+	18.1865i	1.25400	+	0.723994i	0.282095	+	0.959387i	$0.408971\pi$
$632$	−3.80385	+	14.1962i	−0.151309	+	0.564693i
$633$	1.90192	+	7.09808i	0.0755947	+	0.282123i
$634$	20.7846	−	12.0000i	0.825462	−	0.476581i
$635$	5.19615	−	1.73205i	0.206203	−	0.0687343i
$636$		0			0
$637$	−6.33975	+	23.6603i	−0.251190	+	0.937453i
$638$	−12.2942	+	3.29423i	−0.486733	+	0.130420i
$639$	2.59808	−	1.50000i	0.102778	−	0.0593391i
$640$	5.07180	−	24.7846i	0.200480	−	0.979698i
$641$	−39.0000	−	22.5167i	−1.54041	−	0.889355i	−0.998813	−	0.0487148i	$-0.984487\pi$
$641$	−39.0000	−	22.5167i	−1.54041	−	0.889355i	−0.541595	−	0.840640i	$-0.682179\pi$
$642$	−14.1962	+	3.80385i	−0.560277	+	0.150126i
$643$	−17.3205	+	17.3205i	−0.683054	+	0.683054i	−0.960687	−	0.277633i	$-0.910450\pi$
$643$	−17.3205	+	17.3205i	−0.683054	+	0.683054i	0.277633	+	0.960687i	$0.410450\pi$
$644$		0			0
$645$	−0.803848	−	13.3923i	−0.0316515	−	0.527321i
$646$		0			0
$647$	24.2487	+	24.2487i	0.953315	+	0.953315i	0.998958	−	0.0456426i	$-0.0145335\pi$
$647$	24.2487	+	24.2487i	0.953315	+	0.953315i	−0.0456426	+	0.998958i	$0.514534\pi$
$648$	−6.58846	+	24.5885i	−0.258819	+	0.965926i
$649$	−36.3731			−1.42777
$650$	−27.7128	+	20.7846i	−1.08699	+	0.815239i
$651$	−3.00000	−	19.0526i	−0.117579	−	0.746729i
$652$		0			0
$653$	−21.0000	−	21.0000i	−0.821794	−	0.821794i	0.164572	−	0.986365i	$-0.447376\pi$
$653$	−21.0000	−	21.0000i	−0.821794	−	0.821794i	−0.986365	+	0.164572i	$0.947376\pi$
$654$	−1.73205	−	3.00000i	−0.0677285	−	0.117309i
$655$	17.0000	−	34.0000i	0.664245	−	1.32849i
$656$	−14.0000	+	24.2487i	−0.546608	+	0.946753i
$657$	9.50962	−	35.4904i	0.371006	−	1.38461i
$658$	−6.58846	+	24.5885i	−0.256845	+	0.958558i
$659$		−	10.0000i		−	0.389545i	−0.980848	−	0.194772i	$-0.937603\pi$
$659$		−	10.0000i		−	0.389545i	0.980848	−	0.194772i	$-0.0623968\pi$
$660$		0			0
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	−0.636200	−	0.771524i	$-0.719495\pi$
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	0.986260	+	0.165203i	$0.0528281\pi$
$662$	−2.36603	+	0.633975i	−0.0919582	+	0.0246401i
$663$	−28.3923	−	7.60770i	−1.10267	−	0.295458i
$664$	−6.92820	+	12.0000i	−0.268866	+	0.465690i
$665$		0			0
$666$			20.7846i			0.805387i
$667$	6.00000	−	6.00000i	0.232321	−	0.232321i
$668$		0			0
$669$		0			0
$670$	−2.14359	−	35.7128i	−0.0828142	−	1.37971i
$671$	13.5000	−	23.3827i	0.521162	−	0.902679i
$672$		0			0
$673$	−9.50962	−	35.4904i	−0.366569	−	1.36805i	−0.865282	−	0.501286i	$-0.832860\pi$
$673$	−9.50962	−	35.4904i	−0.366569	−	1.36805i	0.498713	−	0.866767i	$-0.333806\pi$
$674$	−38.1051			−1.46775
$675$		0			0
$676$		0			0
$677$	−9.46410	+	2.53590i	−0.363735	+	0.0974625i	−0.436058	−	0.899919i	$-0.643626\pi$
$677$	−9.46410	+	2.53590i	−0.363735	+	0.0974625i	0.0723225	+	0.997381i	$0.476959\pi$
$678$	41.5692	−	41.5692i	1.59646	−	1.59646i
$679$	13.8564	−	8.00000i	0.531760	−	0.307012i
$680$	13.8564	+	6.92820i	0.531369	+	0.265684i
$681$			27.7128i			1.06196i
$682$	−33.0788	−	24.0788i	−1.26665	−	0.922026i
$683$	−29.0000	−	29.0000i	−1.10965	−	1.10965i	−0.993196	−	0.116459i	$-0.962846\pi$
$683$	−29.0000	−	29.0000i	−1.10965	−	1.10965i	−0.116459	−	0.993196i	$-0.537154\pi$
$684$		0			0
$685$		0			0
$686$	−24.0000			−0.916324
$687$	7.68653	+	28.6865i	0.293260	+	1.09446i
$688$	9.46410	+	2.53590i	0.360815	+	0.0966802i
$689$	20.7846	−	12.0000i	0.791831	−	0.457164i
$690$	−36.0000	+	12.0000i	−1.37050	+	0.456832i
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	−0.962768	−	0.270330i	$-0.912867\pi$
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	0.715496	+	0.698617i	$0.246201\pi$
$692$		0			0
$693$	5.70577	+	21.2942i	0.216744	+	0.808901i
$694$	−24.2487	−	42.0000i	−0.920468	−	1.59430i
$695$	19.2058	+	29.0885i	0.728516	+	1.10339i
$696$	−6.00000	−	10.3923i	−0.227429	−	0.393919i
$697$	−12.1244	−	12.1244i	−0.459243	−	0.459243i
$698$	7.00000	+	7.00000i	0.264954	+	0.264954i
$699$	5.19615	+	9.00000i	0.196537	+	0.340411i
$700$		0			0
$701$	0.500000	+	0.866025i	0.0188847	+	0.0327093i	0.875313	−	0.483556i	$-0.160655\pi$
$701$	0.500000	+	0.866025i	0.0188847	+	0.0327093i	−0.856429	+	0.516265i	$0.827322\pi$
$702$		0			0
$703$		0			0
$704$	20.7846	−	36.0000i	0.783349	−	1.35680i
$705$	62.3538	+	31.1769i	2.34838	+	1.17419i
$706$	18.0000	−	10.3923i	0.677439	−	0.391120i
$707$	−5.46410	−	1.46410i	−0.205499	−	0.0550632i
$708$		0			0
$709$	−17.3205			−0.650485			−0.325243	−	0.945631i	$-0.605446\pi$
$709$	−17.3205			−0.650485			−0.325243	+	0.945631i	$0.605446\pi$
$710$	−2.09808	+	2.36603i	−0.0787394	+	0.0887954i
$711$		−	15.5885i		−	0.584613i
$712$	31.1769	+	31.1769i	1.16840	+	1.16840i
$713$	27.1244	+	2.87564i	1.01582	+	0.107694i
$714$		−	12.0000i		−	0.449089i
$715$	−54.0000	+	18.0000i	−2.01949	+	0.673162i
$716$		0			0
$717$	3.00000	−	3.00000i	0.112037	−	0.112037i
$718$	−17.7583	+	4.75833i	−0.662735	+	0.177579i
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	0.604554	−	0.796564i	$-0.293351\pi$
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	−0.992122	+	0.125277i	$0.960018\pi$
$720$	1.60770	+	26.7846i	0.0599153	+	0.998203i
$721$	−20.0000			−0.744839
$722$	−6.95448	−	25.9545i	−0.258819	−	0.965926i
$723$	32.7846	−	8.78461i	1.21927	−	0.326703i
$724$		0			0
$725$	3.40192	−	7.96410i	0.126344	−	0.295779i
$726$	48.0000	+	27.7128i	1.78145	+	1.02852i
$727$	42.3468	+	11.3468i	1.57056	+	0.420829i	0.935986	−	0.352037i	$-0.114511\pi$
$727$	42.3468	+	11.3468i	1.57056	+	0.420829i	0.634569	+	0.772866i	$0.281178\pi$
$728$	13.8564	−	13.8564i	0.513553	−	0.513553i
$729$		−	27.0000i		−	1.00000i
$730$	2.32051	+	38.6603i	0.0858859	+	1.43088i
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$		0			0
$733$	−1.36603	+	0.366025i	−0.0504553	+	0.0135195i	−0.283958	−	0.958837i	$-0.591648\pi$
$733$	−1.36603	+	0.366025i	−0.0504553	+	0.0135195i	0.233503	+	0.972356i	$0.424981\pi$
$734$	17.3205	−	30.0000i	0.639312	−	1.10732i
$735$	−5.49038	+	26.8301i	−0.202516	+	0.989644i
$736$		0			0
$737$	15.2154	−	56.7846i	0.560466	−	2.09169i
$738$	7.68653	−	28.6865i	0.282945	−	1.05597i
$739$	−0.866025	+	1.50000i	−0.0318573	+	0.0551784i	−0.881514	−	0.472157i	$-0.843476\pi$
$739$	−0.866025	+	1.50000i	−0.0318573	+	0.0551784i	0.849657	+	0.527335i	$0.176809\pi$
$740$		0			0
$741$		0			0
$742$	6.92820	+	6.92820i	0.254342	+	0.254342i
$743$	15.5885	−	15.5885i	0.571885	−	0.571885i	−0.360770	−	0.932655i	$-0.617486\pi$
$743$	15.5885	−	15.5885i	0.571885	−	0.571885i	0.932655	+	0.360770i	$0.117486\pi$
$744$	13.8564	−	36.0000i	0.508001	−	1.31982i
$745$	22.0000	+	11.0000i	0.806018	+	0.403009i
$746$	−20.0000			−0.732252
$747$	3.80385	−	14.1962i	0.139176	−	0.519410i
$748$		0			0
$749$	5.19615	+	3.00000i	0.189863	+	0.109618i
$750$	−29.5359	+	25.0526i	−1.07850	+	0.914790i
$751$	5.00000	+	8.66025i	0.182453	+	0.316017i	0.942715	−	0.333599i	$-0.108263\pi$
$751$	5.00000	+	8.66025i	0.182453	+	0.316017i	−0.760263	+	0.649616i	$0.774930\pi$
$752$	−36.0000	+	36.0000i	−1.31278	+	1.31278i
$753$		0			0
$754$	−10.3923	−	6.00000i	−0.378465	−	0.218507i
$755$	−38.7846	+	25.6077i	−1.41152	+	0.931959i
$756$		0			0
$757$	−28.3923	+	7.60770i	−1.03194	+	0.276506i	−0.734768	−	0.678319i	$-0.762709\pi$
$757$	−28.3923	+	7.60770i	−1.03194	+	0.276506i	−0.297168	+	0.954825i	$0.596042\pi$
$758$	−2.19615	+	8.19615i	−0.0797678	+	0.297698i
$759$	−62.3538			−2.26330
$760$		0			0
$761$	−21.0000	+	12.1244i	−0.761249	+	0.439508i	−0.829744	−	0.558144i	$-0.811514\pi$
$761$	−21.0000	+	12.1244i	−0.761249	+	0.439508i	0.0684947	+	0.997651i	$0.478180\pi$
$762$	−2.19615	−	8.19615i	−0.0795582	−	0.296915i
$763$	−0.366025	+	1.36603i	−0.0132510	+	0.0494534i
$764$		0			0
$765$	−16.0981	−	3.29423i	−0.582027	−	0.119103i
$766$	12.0000	+	6.92820i	0.433578	+	0.250326i
$767$	−24.2487	−	24.2487i	−0.875570	−	0.875570i
$768$		0			0
$769$	0.866025	−	0.500000i	0.0312297	−	0.0180305i	−0.484304	−	0.874900i	$-0.660927\pi$
$769$	0.866025	−	0.500000i	0.0312297	−	0.0180305i	0.515534	+	0.856869i	$0.327594\pi$
$770$	−12.8038	−	19.3923i	−0.461419	−	0.698850i
$771$			69.2820i			2.49513i
$772$		0			0
$773$	25.9808	−	25.9808i	0.934463	−	0.934463i	−0.0635177	−	0.997981i	$-0.520232\pi$
$773$	25.9808	−	25.9808i	0.934463	−	0.934463i	0.997981	+	0.0635177i	$0.0202319\pi$
$774$	−10.3923			−0.373544
$775$	26.7846	−	7.58846i	0.962132	−	0.272585i
$776$	32.0000			1.14873
$777$	12.0000	−	12.0000i	0.430498	−	0.430498i
$778$	26.0263	+	6.97372i	0.933087	+	0.250020i
$779$		0			0
$780$		0			0
$781$	−4.50000	+	2.59808i	−0.161023	+	0.0929665i
$782$	16.3923	+	4.39230i	0.586188	+	0.157069i
$783$		0			0
$784$	−17.3205	−	10.0000i	−0.618590	−	0.357143i
$785$	−6.19615	−	1.26795i	−0.221150	−	0.0452550i
$786$	−51.0000	−	29.4449i	−1.81911	−	1.05026i
$787$	2.53590	−	9.46410i	0.0903950	−	0.337359i	−0.905886	−	0.423521i	$-0.860794\pi$
$787$	2.53590	−	9.46410i	0.0903950	−	0.337359i	0.996281	+	0.0861627i	$0.0274605\pi$
$788$		0			0
$789$	15.5885	−	9.00000i	0.554964	−	0.320408i
$790$	5.19615	+	15.5885i	0.184871	+	0.554612i
$791$	−24.0000			−0.853342
$792$	−11.4115	+	42.5885i	−0.405492	+	1.51331i
$793$	24.5885	−	6.58846i	0.873162	−	0.233963i
$794$	−6.92820	+	4.00000i	−0.245873	+	0.141955i
$795$	22.3923	−	14.7846i	0.794173	−	0.524356i
$796$		0			0
$797$	33.1244	−	8.87564i	1.17332	−	0.314391i	0.381049	−	0.924555i	$-0.375563\pi$
$797$	33.1244	−	8.87564i	1.17332	−	0.314391i	0.792276	+	0.610163i	$0.208896\pi$
$798$		0			0
$799$	−15.5885	−	27.0000i	−0.551480	−	0.955191i
$800$		0			0
$801$	−40.5000	−	23.3827i	−1.43100	−	0.826187i
$802$	−12.1244	−	12.1244i	−0.428126	−	0.428126i
$803$	−16.4711	+	61.4711i	−0.581254	+	2.16927i
$804$		0			0
$805$	13.8564	+	6.92820i	0.488374	+	0.244187i
$806$	−6.00000	−	38.1051i	−0.211341	−	1.34220i
$807$	−39.0000	+	39.0000i	−1.37287	+	1.37287i
$808$	−8.00000	−	8.00000i	−0.281439	−	0.281439i
$809$	13.8564	+	24.0000i	0.487165	+	0.843795i	0.999891	−	0.0147574i	$-0.00469758\pi$
$809$	13.8564	+	24.0000i	0.487165	+	0.843795i	−0.512726	+	0.858552i	$0.671364\pi$
$810$	9.00000	+	27.0000i	0.316228	+	0.948683i
$811$	4.50000	−	7.79423i	0.158016	−	0.273692i	−0.776137	−	0.630564i	$-0.782823\pi$
$811$	4.50000	−	7.79423i	0.158016	−	0.273692i	0.934153	+	0.356872i	$0.116157\pi$
$812$		0			0
$813$	1.09808	−	4.09808i	0.0385112	−	0.143726i
$814$		−	36.0000i		−	1.26180i
$815$	2.53590	−	12.3923i	0.0888286	−	0.434084i
$816$	12.0000	−	20.7846i	0.420084	−	0.727607i
$817$		0			0
$818$	−33.1244	−	8.87564i	−1.15817	−	0.310330i
$819$	−10.3923	+	18.0000i	−0.363137	+	0.628971i
$820$		0			0
$821$			15.5885i			0.544041i	0.962291	+	0.272020i	$0.0876918\pi$
$821$			15.5885i			0.544041i	−0.962291	+	0.272020i	$0.912308\pi$
$822$		0			0
$823$	−4.73205	−	1.26795i	−0.164949	−	0.0441979i	0.175399	−	0.984497i	$-0.443878\pi$
$823$	−4.73205	−	1.26795i	−0.164949	−	0.0441979i	−0.340348	+	0.940299i	$0.610545\pi$
$824$	−34.6410	−	20.0000i	−1.20678	−	0.696733i
$825$	−59.0596	+	23.7058i	−2.05619	+	0.825329i
$826$	7.00000	−	12.1244i	0.243561	−	0.421860i
$827$	−44.9545	+	12.0455i	−1.56322	+	0.418864i	−0.933681	−	0.358105i	$-0.883423\pi$
$827$	−44.9545	+	12.0455i	−1.56322	+	0.418864i	−0.629539	+	0.776969i	$0.716756\pi$
$828$		0			0
$829$	−12.1244			−0.421096			−0.210548	−	0.977583i	$-0.567525\pi$
$829$	−12.1244			−0.421096			−0.210548	+	0.977583i	$0.567525\pi$
$830$	0.928203	+	15.4641i	0.0322184	+	0.536767i
$831$	−9.00000	−	15.5885i	−0.312207	−	0.540758i
$832$	37.8564	−	10.1436i	1.31243	−	0.351666i
$833$	8.66025	−	8.66025i	0.300060	−	0.300060i
$834$	46.7654	−	27.0000i	1.61935	−	0.934934i
$835$	41.5692	−	13.8564i	1.43856	−	0.479521i
$836$		0			0
$837$		0			0
$838$	−31.0000	−	31.0000i	−1.07088	−	1.07088i
$839$		−	17.0000i		−	0.586905i	−0.955974	−	0.293453i	$-0.905196\pi$
$839$		−	17.0000i		−	0.586905i	0.955974	−	0.293453i	$-0.0948043\pi$
$840$	14.5359	−	16.3923i	0.501536	−	0.565588i
$841$	−26.0000			−0.896552
$842$	5.49038	+	20.4904i	0.189211	+	0.706145i
$843$	−30.7583	−	8.24167i	−1.05937	−	0.283858i
$844$		0			0
$845$	−22.0000	−	11.0000i	−0.756823	−	0.378412i
$846$	27.0000	−	46.7654i	0.928279	−	1.60783i
$847$	−5.85641	−	21.8564i	−0.201229	−	0.750995i
$848$	5.07180	+	18.9282i	0.174166	+	0.649997i
$849$	27.7128	+	48.0000i	0.951101	+	1.64736i
$850$	17.1962	−	2.07180i	0.589823	−	0.0710620i
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		0			0
$853$	14.0000	+	14.0000i	0.479351	+	0.479351i	0.904924	−	0.425573i	$-0.139927\pi$
$853$	14.0000	+	14.0000i	0.479351	+	0.479351i	−0.425573	+	0.904924i	$0.639927\pi$
$854$	5.19615	+	9.00000i	0.177809	+	0.307974i
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	8.41858	+	31.4186i	0.287573	+	1.07324i	0.946938	+	0.321415i	$0.104159\pi$
$857$	8.41858	+	31.4186i	0.287573	+	1.07324i	−0.659365	+	0.751823i	$0.729175\pi$
$858$	22.8231	+	85.1769i	0.779167	+	2.90789i
$859$	−25.1147	+	43.5000i	−0.856904	+	1.48420i	0.0179638	+	0.999839i	$0.494282\pi$
$859$	−25.1147	+	43.5000i	−0.856904	+	1.48420i	−0.874868	+	0.484362i	$0.839052\pi$
$860$		0			0
$861$	−21.0000	+	12.1244i	−0.715678	+	0.413197i
$862$	−1.36603	−	0.366025i	−0.0465270	−	0.0124669i
$863$	0.633975	+	2.36603i	0.0215807	+	0.0805404i	0.975876	−	0.218324i	$-0.0700589\pi$
$863$	0.633975	+	2.36603i	0.0215807	+	0.0805404i	−0.954296	+	0.298864i	$0.903392\pi$
$864$		0			0
$865$	−28.3923	−	25.1769i	−0.965367	−	0.856041i
$866$		−	3.46410i		−	0.117715i
$867$	−19.0526	−	19.0526i	−0.647059	−	0.647059i
$868$		0			0
$869$			27.0000i			0.915912i
$870$	−12.0000	−	6.00000i	−0.406838	−	0.203419i
$871$	48.0000	−	27.7128i	1.62642	−	0.939013i
$872$	−2.00000	+	2.00000i	−0.0677285	+	0.0677285i
$873$	−32.7846	+	8.78461i	−1.10959	+	0.297314i
$874$		0			0
$875$	15.7583	+	1.29423i	0.532729	+	0.0437529i
$876$		0			0
$877$	−2.56218	−	9.56218i	−0.0865186	−	0.322892i	0.909079	−	0.416624i	$-0.136787\pi$
$877$	−2.56218	−	9.56218i	−0.0865186	−	0.322892i	−0.995597	+	0.0937323i	$0.970120\pi$
$878$	39.6147	−	10.6147i	1.33693	−	0.358230i
$879$	19.0526	−	33.0000i	0.642627	−	1.11306i
$880$	−2.78461	−	46.3923i	−0.0938692	−	1.56388i
$881$	−27.0000	−	15.5885i	−0.909653	−	0.525188i	−0.0293336	−	0.999570i	$-0.509339\pi$
$881$	−27.0000	−	15.5885i	−0.909653	−	0.525188i	−0.880320	+	0.474381i	$0.842672\pi$
$882$	20.4904	+	5.49038i	0.689947	+	0.184871i
$883$	3.46410	−	3.46410i	0.116576	−	0.116576i	−0.646412	−	0.762988i	$-0.723731\pi$
$883$	3.46410	−	3.46410i	0.116576	−	0.116576i	0.762988	+	0.646412i	$0.223731\pi$
$884$		0			0
$885$	−28.6865	−	25.4378i	−0.964287	−	0.855083i
$886$	−1.00000	+	1.73205i	−0.0335957	+	0.0581894i
$887$	13.6603	+	3.66025i	0.458666	+	0.122899i	0.480752	−	0.876857i	$-0.340364\pi$
$887$	13.6603	+	3.66025i	0.458666	+	0.122899i	−0.0220852	+	0.999756i	$0.507031\pi$
$888$	32.7846	−	8.78461i	1.10018	−	0.294792i
$889$	−1.73205	+	3.00000i	−0.0580911	+	0.100617i
$890$	48.2942	+	9.88269i	1.61883	+	0.331268i
$891$			46.7654i			1.56670i
$892$		0			0
$893$		0			0
$894$	19.0526	−	33.0000i	0.637213	−	1.10369i
$895$	−12.1244	+	24.2487i	−0.405273	+	0.810545i
$896$	8.00000	+	13.8564i	0.267261	+	0.462910i
$897$	−41.5692	−	41.5692i	−1.38796	−	1.38796i
$898$	24.2487	−	24.2487i	0.809190	−	0.809190i
$899$	6.06218	+	7.50000i	0.202185	+	0.250139i
$900$		0			0
$901$	−12.0000			−0.399778
$902$	−13.3135	+	49.6865i	−0.443290	+	1.65438i
$903$	6.00000	+	6.00000i	0.199667	+	0.199667i
$904$	−41.5692	−	24.0000i	−1.38257	−	0.798228i
$905$	−0.464102	−	7.73205i	−0.0154273	−	0.257022i
$906$	36.0000	+	62.3538i	1.19602	+	2.07157i
$907$	19.0000	−	19.0000i	0.630885	−	0.630885i	−0.317405	−	0.948290i	$-0.602812\pi$
$907$	19.0000	−	19.0000i	0.630885	−	0.630885i	0.948290	+	0.317405i	$0.102812\pi$
$908$		0			0
$909$	10.3923	+	6.00000i	0.344691	+	0.199007i
$910$	4.39230	−	21.4641i	0.145603	−	0.711528i
$911$	−22.5000	+	12.9904i	−0.745458	+	0.430391i	−0.824051	−	0.566516i	$-0.808291\pi$
$911$	−22.5000	+	12.9904i	−0.745458	+	0.430391i	0.0785923	+	0.996907i	$0.474957\pi$
$912$		0			0
$913$	−6.58846	+	24.5885i	−0.218046	+	0.813759i
$914$	−3.46410			−0.114582
$915$	27.0000	−	9.00000i	0.892592	−	0.297531i
$916$		0			0
$917$	6.22243	+	23.2224i	0.205483	+	0.766872i
$918$		0			0
$919$	−12.9904	−	7.50000i	−0.428513	−	0.247402i	0.270200	−	0.962804i	$-0.412910\pi$
$919$	−12.9904	−	7.50000i	−0.428513	−	0.247402i	−0.698713	+	0.715402i	$0.746244\pi$
$920$	17.0718	+	25.8564i	0.562840	+	0.852460i
$921$	33.0000	+	19.0526i	1.08739	+	0.627803i
$922$	34.6410	+	34.6410i	1.14084	+	1.14084i
$923$	−4.73205	−	1.26795i	−0.155757	−	0.0417351i
$924$		0			0
$925$	19.2679	+	15.1244i	0.633526	+	0.497286i
$926$			24.2487i			0.796862i
$927$	40.9808	+	10.9808i	1.34598	+	0.360656i
$928$		0			0
$929$	−8.66025			−0.284134			−0.142067	−	0.989857i	$-0.545375\pi$
$929$	−8.66025			−0.284134			−0.142067	+	0.989857i	$0.545375\pi$
$930$	−9.24871	−	42.1244i	−0.303277	−	1.38131i
$931$		0			0
$932$		0			0
$933$	16.5622	+	4.43782i	0.542221	+	0.145288i
$934$			6.00000i			0.196326i
$935$	27.8827	+	5.70577i	0.911861	+	0.186599i
$936$	−36.0000	+	20.7846i	−1.17670	+	0.679366i
$937$	−9.56218	−	2.56218i	−0.312383	−	0.0837027i	0.0992216	−	0.995065i	$-0.468365\pi$
$937$	−9.56218	−	2.56218i	−0.312383	−	0.0837027i	−0.411604	+	0.911363i	$0.635031\pi$
$938$	16.0000	+	16.0000i	0.522419	+	0.522419i
$939$	51.9615	+	30.0000i	1.69570	+	0.979013i
$940$		0			0
$941$	−27.0000	−	15.5885i	−0.880175	−	0.508169i	−0.00945879	−	0.999955i	$-0.503011\pi$
$941$	−27.0000	−	15.5885i	−0.880175	−	0.508169i	−0.870716	+	0.491786i	$0.836344\pi$
$942$	−2.53590	+	9.46410i	−0.0826240	+	0.308357i
$943$	−8.87564	−	33.1244i	−0.289031	−	1.07868i
$944$	24.2487	−	14.0000i	0.789228	−	0.455661i
$945$		0			0
$946$	18.0000			0.585230
$947$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$947$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$948$		0			0
$949$	−51.9615	+	30.0000i	−1.68674	+	0.973841i
$950$		0			0
$951$	36.0000	+	20.7846i	1.16738	+	0.673987i
$952$	−9.46410	+	2.53590i	−0.306733	+	0.0821889i
$953$	3.46410	−	3.46410i	0.112213	−	0.112213i	−0.648771	−	0.760984i	$-0.724717\pi$
$953$	3.46410	−	3.46410i	0.112213	−	0.112213i	0.760984	+	0.648771i	$0.224717\pi$
$954$	−10.3923	−	18.0000i	−0.336463	−	0.582772i
$955$	−15.6244	+	0.937822i	−0.505592	+	0.0303472i
$956$		0			0
$957$	−15.5885	−	15.5885i	−0.503903	−	0.503903i
$958$	−12.8109	+	47.8109i	−0.413901	+	1.54470i
$959$		0			0
$960$	41.5692	−	13.8564i	1.34164	−	0.447214i
$961$	−6.50000	+	30.3109i	−0.209677	+	0.977771i
$962$	24.0000	−	24.0000i	0.773791	−	0.773791i
$963$	−9.00000	−	9.00000i	−0.290021	−	0.290021i
$964$		0			0
$965$	6.00000	−	2.00000i	0.193147	−	0.0643823i
$966$	12.0000	−	20.7846i	0.386094	−	0.668734i
$967$	12.6795	−	47.3205i	0.407745	−	1.52172i	−0.391191	−	0.920309i	$-0.627937\pi$
$967$	12.6795	−	47.3205i	0.407745	−	1.52172i	0.798936	−	0.601416i	$-0.205396\pi$
$968$	11.7128	−	43.7128i	0.376464	−	1.40498i
$969$		0			0
$970$	29.8564	−	19.7128i	0.958631	−	0.632940i
$971$	5.00000	−	8.66025i	0.160458	−	0.277921i	−0.774575	−	0.632482i	$-0.782036\pi$
$971$	5.00000	−	8.66025i	0.160458	−	0.277921i	0.935033	+	0.354561i	$0.115370\pi$
$972$		0			0
$973$	−21.2942	−	5.70577i	−0.682662	−	0.182919i
$974$	−1.73205	+	3.00000i	−0.0554985	+	0.0961262i
$975$	−55.1769	−	23.5692i	−1.76708	−	0.754819i
$976$			20.7846i			0.665299i
$977$	−11.0000	+	11.0000i	−0.351921	+	0.351921i	−0.860824	−	0.508903i	$-0.830051\pi$
$977$	−11.0000	+	11.0000i	−0.351921	+	0.351921i	0.508903	+	0.860824i	$0.330051\pi$
$978$	−18.9282	−	5.07180i	−0.605257	−	0.162178i
$979$	70.1481	+	40.5000i	2.24194	+	1.29439i
$980$		0			0
$981$	1.50000	−	2.59808i	0.0478913	−	0.0829502i
$982$	26.0263	−	6.97372i	0.830532	−	0.222540i
$983$	0.633975	+	2.36603i	0.0202206	+	0.0754645i	0.975299	−	0.220889i	$-0.0708959\pi$
$983$	0.633975	+	2.36603i	0.0202206	+	0.0754645i	−0.955078	+	0.296354i	$0.904229\pi$
$984$	−48.4974			−1.54604
$985$	20.4904	+	18.1699i	0.652878	+	0.578940i
$986$	3.00000	+	5.19615i	0.0955395	+	0.165479i
$987$	−42.5885	+	11.4115i	−1.35561	+	0.363233i
$988$		0			0
$989$	−10.3923	+	6.00000i	−0.330456	+	0.190789i
$990$	15.5885	+	46.7654i	0.495434	+	1.48630i
$991$		−	12.1244i		−	0.385143i	−0.981283	−	0.192571i	$-0.938317\pi$
$991$		−	12.1244i		−	0.385143i	0.981283	−	0.192571i	$-0.0616827\pi$
$992$		0			0
$993$	−3.00000	−	3.00000i	−0.0952021	−	0.0952021i
$994$		−	2.00000i		−	0.0634361i
$995$	−46.3923	+	2.78461i	−1.47073	+	0.0882781i
$996$		0			0
$997$	12.8109	+	47.8109i	0.405725	+	1.51419i	0.802715	+	0.596363i	$0.203388\pi$
$997$	12.8109	+	47.8109i	0.405725	+	1.51419i	−0.396990	+	0.917823i	$0.629945\pi$
$998$	11.8301	+	3.16987i	0.374476	+	0.100341i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.p.a.68.1	yes	4
5.2	odd	4	inner	155.2.p.a.37.1	✓	4
5.3	odd	4		775.2.bj.d.657.1		4
5.4	even	2		775.2.bj.d.68.1		4
31.26	odd	6	inner	155.2.p.a.88.1	yes	4
155.57	even	12	inner	155.2.p.a.57.1	yes	4
155.88	even	12		775.2.bj.d.57.1		4
155.119	odd	6		775.2.bj.d.243.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.p.a.37.1	✓	4	5.2	odd	4	inner
155.2.p.a.57.1	yes	4	155.57	even	12	inner
155.2.p.a.68.1	yes	4	1.1	even	1	trivial
155.2.p.a.88.1	yes	4	31.26	odd	6	inner
775.2.bj.d.57.1		4	155.88	even	12
775.2.bj.d.68.1		4	5.4	even	2
775.2.bj.d.243.1		4	155.119	odd	6
775.2.bj.d.657.1		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.36603 - 0.633975i) q^{3} +(1.23205 + 1.86603i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.36603 - 0.633975i) q^{3} +(1.23205 + 1.86603i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +(-3.09808 - 0.633975i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(-1.26795 - 4.73205i) q^{13} +(1.73205 - 1.00000i) q^{14} +(-1.73205 - 5.19615i) q^{15} +4.00000 q^{16} +(-0.633975 + 2.36603i) q^{17} +(-4.09808 + 1.09808i) q^{18} +(3.00000 + 1.73205i) q^{21} +(7.09808 - 1.90192i) q^{22} +(-3.46410 + 3.46410i) q^{23} +(3.46410 + 6.00000i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(6.00000 + 3.46410i) q^{26} -1.73205 q^{29} +(6.92820 + 3.46410i) q^{30} +(-3.50000 - 4.33013i) q^{31} +(9.00000 + 9.00000i) q^{33} +(-1.73205 - 3.00000i) q^{34} +(-1.00000 - 3.00000i) q^{35} +(1.26795 - 4.73205i) q^{37} +12.0000i q^{39} +(1.26795 - 6.19615i) q^{40} +(-3.50000 + 6.06218i) q^{41} +(-4.73205 + 1.26795i) q^{42} +(2.36603 + 0.633975i) q^{43} +(0.401924 + 6.69615i) q^{45} -6.92820i q^{46} +(-9.00000 + 9.00000i) q^{47} +(-9.46410 - 2.53590i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-2.63397 - 6.56218i) q^{50} +(3.00000 - 5.19615i) q^{51} +(1.26795 + 4.73205i) q^{53} +(-0.696152 - 11.5981i) q^{55} +(2.00000 + 3.46410i) q^{56} +(1.73205 - 1.73205i) q^{58} +(6.06218 - 3.50000i) q^{59} +5.19615i q^{61} +(7.83013 + 0.830127i) q^{62} +(-3.00000 - 3.00000i) q^{63} +8.00000i q^{64} +(7.26795 - 8.19615i) q^{65} -18.0000 q^{66} +(2.92820 + 10.9282i) q^{67} +(10.3923 - 6.00000i) q^{69} +(4.00000 + 2.00000i) q^{70} +(0.500000 - 0.866025i) q^{71} +(-2.19615 - 8.19615i) q^{72} +(-3.16987 - 11.8301i) q^{73} +(3.46410 + 6.00000i) q^{74} +(7.56218 - 9.63397i) q^{75} +(5.19615 + 5.19615i) q^{77} +(-12.0000 - 12.0000i) q^{78} +(-2.59808 - 4.50000i) q^{79} +(4.92820 + 7.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.56218 - 9.56218i) q^{82} +(-1.26795 - 4.73205i) q^{83} +(-5.19615 + 1.73205i) q^{85} +(-3.00000 + 1.73205i) q^{86} +(4.09808 + 1.09808i) q^{87} +(3.80385 + 14.1962i) q^{88} -15.5885 q^{89} +(-7.09808 - 6.29423i) q^{90} +6.92820i q^{91} +(5.53590 + 12.4641i) q^{93} -18.0000i q^{94} +(-8.00000 + 8.00000i) q^{97} +(6.83013 - 1.83013i) q^{98} +(-7.79423 - 13.5000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 12 q^{6} - 2 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 12 * q^6 - 2 * q^7 - 8 * q^8	\( 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 12 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{10} - 18 q^{11} - 12 q^{13} + 16 q^{16} - 6 q^{17} - 6 q^{18} + 12 q^{21} + 18 q^{22} + 6 q^{25} + 24 q^{26} - 14 q^{31} + 36 q^{33} - 4 q^{35} + 12 q^{37} + 12 q^{40} - 14 q^{41} - 12 q^{42} + 6 q^{43} + 12 q^{45} - 36 q^{47} - 24 q^{48} - 14 q^{50} + 12 q^{51} + 12 q^{53} + 18 q^{55} + 8 q^{56} + 14 q^{62} - 12 q^{63} + 36 q^{65} - 72 q^{66} - 16 q^{67} + 16 q^{70} + 2 q^{71} + 12 q^{72} - 30 q^{73} + 6 q^{75} - 48 q^{78} - 8 q^{80} - 18 q^{81} + 14 q^{82} - 12 q^{83} - 12 q^{86} + 6 q^{87} + 36 q^{88} - 18 q^{90} + 36 q^{93} - 32 q^{97} + 10 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 12 * q^6 - 2 * q^7 - 8 * q^8 - 2 * q^10 - 18 * q^11 - 12 * q^13 + 16 * q^16 - 6 * q^17 - 6 * q^18 + 12 * q^21 + 18 * q^22 + 6 * q^25 + 24 * q^26 - 14 * q^31 + 36 * q^33 - 4 * q^35 + 12 * q^37 + 12 * q^40 - 14 * q^41 - 12 * q^42 + 6 * q^43 + 12 * q^45 - 36 * q^47 - 24 * q^48 - 14 * q^50 + 12 * q^51 + 12 * q^53 + 18 * q^55 + 8 * q^56 + 14 * q^62 - 12 * q^63 + 36 * q^65 - 72 * q^66 - 16 * q^67 + 16 * q^70 + 2 * q^71 + 12 * q^72 - 30 * q^73 + 6 * q^75 - 48 * q^78 - 8 * q^80 - 18 * q^81 + 14 * q^82 - 12 * q^83 - 12 * q^86 + 6 * q^87 + 36 * q^88 - 18 * q^90 + 36 * q^93 - 32 * q^97 + 10 * q^98

Introduction

L-functions

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