LMFDB - Embedded newform 152.2.o.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(27,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("152.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	152.107
Dual form			152.2.o.a.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-2.12132 + 1.22474i) q^{5} +(-2.12132 - 1.22474i) q^{6} -2.44949i q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-2.12132 + 1.22474i) q^{5} +(-2.12132 - 1.22474i) q^{6} -2.44949i q^{7} -2.82843 q^{8} +(-3.00000 - 1.73205i) q^{10} +5.00000 q^{11} -3.46410i q^{12} +(-2.82843 + 4.89898i) q^{13} +(3.00000 - 1.73205i) q^{14} +(2.12132 - 3.67423i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 + 4.33013i) q^{19} -4.89898i q^{20} +(2.12132 + 3.67423i) q^{21} +(3.53553 + 6.12372i) q^{22} +(2.12132 + 1.22474i) q^{23} +(4.24264 - 2.44949i) q^{24} +(0.500000 - 0.866025i) q^{25} -8.00000 q^{26} -5.19615i q^{27} +(4.24264 + 2.44949i) q^{28} +(3.53553 - 6.12372i) q^{29} +6.00000 q^{30} -1.41421 q^{31} +(2.82843 - 4.89898i) q^{32} +(-7.50000 + 4.33013i) q^{33} +(-2.82843 + 4.89898i) q^{34} +(3.00000 + 5.19615i) q^{35} +1.41421 q^{37} +(-5.65685 + 2.44949i) q^{38} -9.79796i q^{39} +(6.00000 - 3.46410i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-3.00000 + 5.19615i) q^{42} +(-3.00000 - 5.19615i) q^{43} +(-5.00000 + 8.66025i) q^{44} +3.46410i q^{46} +(6.36396 + 3.67423i) q^{47} +(6.00000 + 3.46410i) q^{48} +1.00000 q^{49} +1.41421 q^{50} +(-6.00000 - 3.46410i) q^{51} +(-5.65685 - 9.79796i) q^{52} +(-4.24264 + 7.34847i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-10.6066 + 6.12372i) q^{55} +6.92820i q^{56} +(-3.00000 - 6.92820i) q^{57} +10.0000 q^{58} +(-1.50000 + 0.866025i) q^{59} +(4.24264 + 7.34847i) q^{60} +(6.36396 + 3.67423i) q^{61} +(-1.00000 - 1.73205i) q^{62} +8.00000 q^{64} -13.8564i q^{65} +(-10.6066 - 6.12372i) q^{66} +(-10.5000 - 6.06218i) q^{67} -8.00000 q^{68} -4.24264 q^{69} +(-4.24264 + 7.34847i) q^{70} +(-1.41421 - 2.44949i) q^{71} +(-1.50000 - 2.59808i) q^{73} +(1.00000 + 1.73205i) q^{74} +1.73205i q^{75} +(-7.00000 - 5.19615i) q^{76} -12.2474i q^{77} +(12.0000 - 6.92820i) q^{78} +(1.41421 + 2.44949i) q^{79} +(8.48528 + 4.89898i) q^{80} +(4.50000 + 7.79423i) q^{81} +(6.36396 + 3.67423i) q^{82} +7.00000 q^{83} -8.48528 q^{84} +(-8.48528 - 4.89898i) q^{85} +(4.24264 - 7.34847i) q^{86} +12.2474i q^{87} -14.1421 q^{88} +(3.00000 + 1.73205i) q^{89} +(12.0000 + 6.92820i) q^{91} +(-4.24264 + 2.44949i) q^{92} +(2.12132 - 1.22474i) q^{93} +10.3923i q^{94} +(-4.24264 - 9.79796i) q^{95} +9.79796i q^{96} +(-16.5000 + 9.52628i) q^{97} +(0.707107 + 1.22474i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 4 * q - 6 * q^3 - 4 * q^4	$ 4 q - 6 q^{3} - 4 q^{4} - 12 q^{10} + 20 q^{11} + 12 q^{14} - 8 q^{16} + 8 q^{17} - 2 q^{19} + 2 q^{25} - 32 q^{26} + 24 q^{30} - 30 q^{33} + 12 q^{35} + 24 q^{40} + 18 q^{41} - 12 q^{42} - 12 q^{43} - 20 q^{44} + 24 q^{48} + 4 q^{49} - 24 q^{51} - 12 q^{57} + 40 q^{58} - 6 q^{59} - 4 q^{62} + 32 q^{64} - 42 q^{67} - 32 q^{68} - 6 q^{73} + 4 q^{74} - 28 q^{76} + 48 q^{78} + 18 q^{81} + 28 q^{83} + 12 q^{89} + 48 q^{91} - 66 q^{97}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 + 20 * q^11 + 12 * q^14 - 8 * q^16 + 8 * q^17 - 2 * q^19 + 2 * q^25 - 32 * q^26 + 24 * q^30 - 30 * q^33 + 12 * q^35 + 24 * q^40 + 18 * q^41 - 12 * q^42 - 12 * q^43 - 20 * q^44 + 24 * q^48 + 4 * q^49 - 24 * q^51 - 12 * q^57 + 40 * q^58 - 6 * q^59 - 4 * q^62 + 32 * q^64 - 42 * q^67 - 32 * q^68 - 6 * q^73 + 4 * q^74 - 28 * q^76 + 48 * q^78 + 18 * q^81 + 28 * q^83 + 12 * q^89 + 48 * q^91 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.500000	+	0.866025i
$2$	0.707107	+	1.22474i	0.500000	+	0.866025i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−2.12132	+	1.22474i	−0.948683	+	0.547723i	−0.892672	−	0.450708i	$-0.851172\pi$
$5$	−2.12132	+	1.22474i	−0.948683	+	0.547723i	−0.0560116	+	0.998430i	$0.517838\pi$
$6$	−2.12132	−	1.22474i	−0.866025	−	0.500000i
$7$		−	2.44949i		−	0.925820i	−0.886405	−	0.462910i	$-0.846805\pi$
$7$		−	2.44949i		−	0.925820i	0.886405	−	0.462910i	$-0.153195\pi$
$8$	−2.82843			−1.00000
$9$		0			0
$10$	−3.00000	−	1.73205i	−0.948683	−	0.547723i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		−	3.46410i		−	1.00000i
$13$	−2.82843	+	4.89898i	−0.784465	+	1.35873i	0.144854	+	0.989453i	$0.453729\pi$
$13$	−2.82843	+	4.89898i	−0.784465	+	1.35873i	−0.929318	+	0.369279i	$0.879605\pi$
$14$	3.00000	−	1.73205i	0.801784	−	0.462910i
$15$	2.12132	−	3.67423i	0.547723	−	0.948683i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$		−	4.89898i		−	1.09545i
$21$	2.12132	+	3.67423i	0.462910	+	0.801784i
$22$	3.53553	+	6.12372i	0.753778	+	1.30558i
$23$	2.12132	+	1.22474i	0.442326	+	0.255377i	0.704584	−	0.709621i	$-0.251134\pi$
$23$	2.12132	+	1.22474i	0.442326	+	0.255377i	−0.262258	+	0.964998i	$0.584467\pi$
$24$	4.24264	−	2.44949i	0.866025	−	0.500000i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−8.00000			−1.56893
$27$		−	5.19615i		−	1.00000i
$28$	4.24264	+	2.44949i	0.801784	+	0.462910i
$29$	3.53553	−	6.12372i	0.656532	−	1.13715i	−0.324975	−	0.945723i	$-0.605356\pi$
$29$	3.53553	−	6.12372i	0.656532	−	1.13715i	0.981507	−	0.191425i	$-0.0613107\pi$
$30$	6.00000			1.09545
$31$	−1.41421			−0.254000			−0.127000	−	0.991903i	$-0.540535\pi$
$31$	−1.41421			−0.254000			−0.127000	+	0.991903i	$0.540535\pi$
$32$	2.82843	−	4.89898i	0.500000	−	0.866025i
$33$	−7.50000	+	4.33013i	−1.30558	+	0.753778i
$34$	−2.82843	+	4.89898i	−0.485071	+	0.840168i
$35$	3.00000	+	5.19615i	0.507093	+	0.878310i
$36$		0			0
$37$	1.41421			0.232495			0.116248	−	0.993220i	$-0.462913\pi$
$37$	1.41421			0.232495			0.116248	+	0.993220i	$0.462913\pi$
$38$	−5.65685	+	2.44949i	−0.917663	+	0.397360i
$39$		−	9.79796i		−	1.56893i
$40$	6.00000	−	3.46410i	0.948683	−	0.547723i
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$	−3.00000	+	5.19615i	−0.462910	+	0.801784i
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	−5.00000	+	8.66025i	−0.753778	+	1.30558i
$45$		0			0
$46$			3.46410i			0.510754i
$47$	6.36396	+	3.67423i	0.928279	+	0.535942i	0.886267	−	0.463175i	$-0.153290\pi$
$47$	6.36396	+	3.67423i	0.928279	+	0.535942i	0.0420122	+	0.999117i	$0.486623\pi$
$48$	6.00000	+	3.46410i	0.866025	+	0.500000i
$49$	1.00000			0.142857
$50$	1.41421			0.200000
$51$	−6.00000	−	3.46410i	−0.840168	−	0.485071i
$52$	−5.65685	−	9.79796i	−0.784465	−	1.35873i
$53$	−4.24264	+	7.34847i	−0.582772	+	1.00939i	0.412378	+	0.911013i	$0.364698\pi$
$53$	−4.24264	+	7.34847i	−0.582772	+	1.00939i	−0.995149	+	0.0983769i	$0.968635\pi$
$54$	6.36396	−	3.67423i	0.866025	−	0.500000i
$55$	−10.6066	+	6.12372i	−1.43019	+	0.825723i
$56$			6.92820i			0.925820i
$57$	−3.00000	−	6.92820i	−0.397360	−	0.917663i
$58$	10.0000			1.31306
$59$	−1.50000	+	0.866025i	−0.195283	+	0.112747i	−0.594454	−	0.804130i	$-0.702632\pi$
$59$	−1.50000	+	0.866025i	−0.195283	+	0.112747i	0.399170	+	0.916877i	$0.369298\pi$
$60$	4.24264	+	7.34847i	0.547723	+	0.948683i
$61$	6.36396	+	3.67423i	0.814822	+	0.470438i	0.848628	−	0.528991i	$-0.177429\pi$
$61$	6.36396	+	3.67423i	0.814822	+	0.470438i	−0.0338058	+	0.999428i	$0.510763\pi$
$62$	−1.00000	−	1.73205i	−0.127000	−	0.219971i
$63$		0			0
$64$	8.00000			1.00000
$65$		−	13.8564i		−	1.71868i
$66$	−10.6066	−	6.12372i	−1.30558	−	0.753778i
$67$	−10.5000	−	6.06218i	−1.28278	−	0.740613i	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−10.5000	−	6.06218i	−1.28278	−	0.740613i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−8.00000			−0.970143
$69$	−4.24264			−0.510754
$70$	−4.24264	+	7.34847i	−0.507093	+	0.878310i
$71$	−1.41421	−	2.44949i	−0.167836	−	0.290701i	0.769823	−	0.638258i	$-0.220345\pi$
$71$	−1.41421	−	2.44949i	−0.167836	−	0.290701i	−0.937659	+	0.347557i	$0.887011\pi$
$72$		0			0
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	0.764794	−	0.644275i	$-0.222841\pi$
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	−0.940356	+	0.340193i	$0.889507\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$			1.73205i			0.200000i
$76$	−7.00000	−	5.19615i	−0.802955	−	0.596040i
$77$		−	12.2474i		−	1.39573i
$78$	12.0000	−	6.92820i	1.35873	−	0.784465i
$79$	1.41421	+	2.44949i	0.159111	+	0.275589i	0.934549	−	0.355836i	$-0.115804\pi$
$79$	1.41421	+	2.44949i	0.159111	+	0.275589i	−0.775437	+	0.631425i	$0.782470\pi$
$80$	8.48528	+	4.89898i	0.948683	+	0.547723i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	6.36396	+	3.67423i	0.702782	+	0.405751i
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$	−8.48528			−0.925820
$85$	−8.48528	−	4.89898i	−0.920358	−	0.531369i
$86$	4.24264	−	7.34847i	0.457496	−	0.792406i
$87$			12.2474i			1.31306i
$88$	−14.1421			−1.50756
$89$	3.00000	+	1.73205i	0.317999	+	0.183597i	0.650500	−	0.759506i	$-0.274559\pi$
$89$	3.00000	+	1.73205i	0.317999	+	0.183597i	−0.332501	+	0.943103i	$0.607893\pi$
$90$		0			0
$91$	12.0000	+	6.92820i	1.25794	+	0.726273i
$92$	−4.24264	+	2.44949i	−0.442326	+	0.255377i
$93$	2.12132	−	1.22474i	0.219971	−	0.127000i
$94$			10.3923i			1.07188i
$95$	−4.24264	−	9.79796i	−0.435286	−	1.00525i
$96$			9.79796i			1.00000i
$97$	−16.5000	+	9.52628i	−1.67532	+	0.967247i	−0.710742	+	0.703452i	$0.751641\pi$
$97$	−16.5000	+	9.52628i	−1.67532	+	0.967247i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	0.707107	+	1.22474i	0.0714286	+	0.123718i
$99$		0			0
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	−6.36396	−	3.67423i	−0.633238	−	0.365600i	0.148767	−	0.988872i	$-0.452470\pi$
$101$	−6.36396	−	3.67423i	−0.633238	−	0.365600i	−0.782005	+	0.623272i	$0.785803\pi$
$102$		−	9.79796i		−	0.970143i
$103$	2.82843			0.278693			0.139347	−	0.990244i	$-0.455500\pi$
$103$	2.82843			0.278693			0.139347	+	0.990244i	$0.455500\pi$
$104$	8.00000	−	13.8564i	0.784465	−	1.35873i
$105$	−9.00000	−	5.19615i	−0.878310	−	0.507093i
$106$	−12.0000			−1.16554
$107$		−	6.92820i		−	0.669775i	−0.942258	−	0.334887i	$-0.891302\pi$
$107$		−	6.92820i		−	0.669775i	0.942258	−	0.334887i	$-0.108698\pi$
$108$	9.00000	+	5.19615i	0.866025	+	0.500000i
$109$	7.07107	+	12.2474i	0.677285	+	1.17309i	0.975795	+	0.218686i	$0.0701771\pi$
$109$	7.07107	+	12.2474i	0.677285	+	1.17309i	−0.298510	+	0.954407i	$0.596490\pi$
$110$	−15.0000	−	8.66025i	−1.43019	−	0.825723i
$111$	−2.12132	+	1.22474i	−0.201347	+	0.116248i
$112$	−8.48528	+	4.89898i	−0.801784	+	0.462910i
$113$			12.1244i			1.14056i	0.821449	+	0.570282i	$0.193166\pi$
$113$			12.1244i			1.14056i	−0.821449	+	0.570282i	$0.806834\pi$
$114$	6.36396	−	8.57321i	0.596040	−	0.802955i
$115$	−6.00000			−0.559503
$116$	7.07107	+	12.2474i	0.656532	+	1.13715i
$117$		0			0
$118$	−2.12132	−	1.22474i	−0.195283	−	0.112747i
$119$	8.48528	−	4.89898i	0.777844	−	0.449089i
$120$	−6.00000	+	10.3923i	−0.547723	+	0.948683i
$121$	14.0000			1.27273
$122$			10.3923i			0.940875i
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$	1.41421	−	2.44949i	0.127000	−	0.219971i
$125$		−	9.79796i		−	0.876356i
$126$		0			0
$127$	−1.41421	+	2.44949i	−0.125491	+	0.217357i	−0.921925	−	0.387369i	$-0.873384\pi$
$127$	−1.41421	+	2.44949i	−0.125491	+	0.217357i	0.796434	+	0.604726i	$0.206717\pi$
$128$	5.65685	+	9.79796i	0.500000	+	0.866025i
$129$	9.00000	+	5.19615i	0.792406	+	0.457496i
$130$	16.9706	−	9.79796i	1.48842	−	0.859338i
$131$	3.50000	+	6.06218i	0.305796	+	0.529655i	0.977438	−	0.211221i	$-0.0677440\pi$
$131$	3.50000	+	6.06218i	0.305796	+	0.529655i	−0.671642	+	0.740876i	$0.734411\pi$
$132$		−	17.3205i		−	1.50756i
$133$	10.6066	+	1.22474i	0.919709	+	0.106199i
$134$		−	17.1464i		−	1.48123i
$135$	6.36396	+	11.0227i	0.547723	+	0.948683i
$136$	−5.65685	−	9.79796i	−0.485071	−	0.840168i
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	−0.232273	−	0.972651i	$-0.574616\pi$
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	0.958477	−	0.285171i	$-0.0920506\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$	−12.0000			−1.01419
$141$	−12.7279			−1.07188
$142$	2.00000	−	3.46410i	0.167836	−	0.290701i
$143$	−14.1421	+	24.4949i	−1.18262	+	2.04837i
$144$		0			0
$145$			17.3205i			1.43839i
$146$	2.12132	−	3.67423i	0.175562	−	0.304082i
$147$	−1.50000	+	0.866025i	−0.123718	+	0.0714286i
$148$	−1.41421	+	2.44949i	−0.116248	+	0.201347i
$149$	14.8492	−	8.57321i	1.21650	−	0.702345i	0.252330	−	0.967641i	$-0.418803\pi$
$149$	14.8492	−	8.57321i	1.21650	−	0.702345i	0.964167	+	0.265296i	$0.0854697\pi$
$150$	−2.12132	+	1.22474i	−0.173205	+	0.100000i
$151$	15.5563			1.26596			0.632979	−	0.774169i	$-0.281832\pi$
$151$	15.5563			1.26596			0.632979	+	0.774169i	$0.281832\pi$
$152$	1.41421	−	12.2474i	0.114708	−	0.993399i
$153$		0			0
$154$	15.0000	−	8.66025i	1.20873	−	0.697863i
$155$	3.00000	−	1.73205i	0.240966	−	0.139122i
$156$	16.9706	+	9.79796i	1.35873	+	0.784465i
$157$	4.24264	−	2.44949i	0.338600	−	0.195491i	−0.321053	−	0.947061i	$-0.604037\pi$
$157$	4.24264	−	2.44949i	0.338600	−	0.195491i	0.659653	+	0.751571i	$0.270703\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$		−	14.6969i		−	1.16554i
$160$			13.8564i			1.09545i
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	−6.36396	+	11.0227i	−0.500000	+	0.866025i
$163$	3.00000			0.234978			0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000			0.234978			0.117489	+	0.993074i	$0.462515\pi$
$164$			10.3923i			0.811503i
$165$	10.6066	−	18.3712i	0.825723	−	1.43019i
$166$	4.94975	+	8.57321i	0.384175	+	0.665410i
$167$	−2.82843	+	4.89898i	−0.218870	+	0.379094i	−0.954463	−	0.298330i	$-0.903570\pi$
$167$	−2.82843	+	4.89898i	−0.218870	+	0.379094i	0.735593	+	0.677424i	$0.236904\pi$
$168$	−6.00000	−	10.3923i	−0.462910	−	0.801784i
$169$	−9.50000	−	16.4545i	−0.730769	−	1.26573i
$170$		−	13.8564i		−	1.06274i
$171$		0			0
$172$	12.0000			0.914991
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−15.0000	+	8.66025i	−1.13715	+	0.656532i
$175$	−2.12132	−	1.22474i	−0.160357	−	0.0925820i
$176$	−10.0000	−	17.3205i	−0.753778	−	1.30558i
$177$	1.50000	−	2.59808i	0.112747	−	0.195283i
$178$			4.89898i			0.367194i
$179$		−	8.66025i		−	0.647298i	−0.946177	−	0.323649i	$-0.895090\pi$
$179$		−	8.66025i		−	0.647298i	0.946177	−	0.323649i	$-0.104910\pi$
$180$		0			0
$181$	12.0208	−	20.8207i	0.893500	−	1.54759i	0.0578502	−	0.998325i	$-0.481575\pi$
$181$	12.0208	−	20.8207i	0.893500	−	1.54759i	0.835650	−	0.549262i	$-0.185091\pi$
$182$			19.5959i			1.45255i
$183$	−12.7279			−0.940875
$184$	−6.00000	−	3.46410i	−0.442326	−	0.255377i
$185$	−3.00000	+	1.73205i	−0.220564	+	0.127343i
$186$	3.00000	+	1.73205i	0.219971	+	0.127000i
$187$	10.0000	+	17.3205i	0.731272	+	1.26660i
$188$	−12.7279	+	7.34847i	−0.928279	+	0.535942i
$189$	−12.7279			−0.925820
$190$	9.00000	−	12.1244i	0.652929	−	0.879593i
$191$			19.5959i			1.41791i	0.705253	+	0.708955i	$0.250833\pi$
$191$			19.5959i			1.41791i	−0.705253	+	0.708955i	$0.749167\pi$
$192$	−12.0000	+	6.92820i	−0.866025	+	0.500000i
$193$	−3.00000	+	1.73205i	−0.215945	+	0.124676i	−0.604071	−	0.796930i	$-0.706456\pi$
$193$	−3.00000	+	1.73205i	−0.215945	+	0.124676i	0.388126	+	0.921606i	$0.373122\pi$
$194$	−23.3345	−	13.4722i	−1.67532	−	0.967247i
$195$	12.0000	+	20.7846i	0.859338	+	1.48842i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$			17.1464i			1.22163i	0.791772	+	0.610816i	$0.209159\pi$
$197$			17.1464i			1.22163i	−0.791772	+	0.610816i	$0.790841\pi$
$198$		0			0
$199$	−21.2132	−	12.2474i	−1.50376	−	0.868199i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−21.2132	−	12.2474i	−1.50376	−	0.868199i	−0.503774	−	0.863836i	$-0.668055\pi$
$200$	−1.41421	+	2.44949i	−0.100000	+	0.173205i
$201$	21.0000			1.48123
$202$		−	10.3923i		−	0.731200i
$203$	−15.0000	−	8.66025i	−1.05279	−	0.607831i
$204$	12.0000	−	6.92820i	0.840168	−	0.485071i
$205$	−6.36396	+	11.0227i	−0.444478	+	0.769859i
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$		0			0
$208$	22.6274			1.56893
$209$	−2.50000	+	21.6506i	−0.172929	+	1.49761i
$210$		−	14.6969i		−	1.01419i
$211$	−9.00000	+	5.19615i	−0.619586	+	0.357718i	−0.776708	−	0.629861i	$-0.783112\pi$
$211$	−9.00000	+	5.19615i	−0.619586	+	0.357718i	0.157122	+	0.987579i	$0.449778\pi$
$212$	−8.48528	−	14.6969i	−0.582772	−	1.00939i
$213$	4.24264	+	2.44949i	0.290701	+	0.167836i
$214$	8.48528	−	4.89898i	0.580042	−	0.334887i
$215$	12.7279	+	7.34847i	0.868037	+	0.501161i
$216$			14.6969i			1.00000i
$217$			3.46410i			0.235159i
$218$	−10.0000	+	17.3205i	−0.677285	+	1.17309i
$219$	4.50000	+	2.59808i	0.304082	+	0.175562i
$220$		−	24.4949i		−	1.65145i
$221$	−22.6274			−1.52208
$222$	−3.00000	−	1.73205i	−0.201347	−	0.116248i
$223$	−12.0208	−	20.8207i	−0.804973	−	1.39425i	−0.916309	−	0.400472i	$-0.868846\pi$
$223$	−12.0208	−	20.8207i	−0.804973	−	1.39425i	0.111336	−	0.993783i	$-0.464487\pi$
$224$	−12.0000	−	6.92820i	−0.801784	−	0.462910i
$225$		0			0
$226$	−14.8492	+	8.57321i	−0.987757	+	0.570282i
$227$		−	1.73205i		−	0.114960i	−0.998347	−	0.0574801i	$-0.981693\pi$
$227$		−	1.73205i		−	0.114960i	0.998347	−	0.0574801i	$-0.0183066\pi$
$228$	15.0000	+	1.73205i	0.993399	+	0.114708i
$229$			9.79796i			0.647467i	0.946148	+	0.323734i	$0.104938\pi$
$229$			9.79796i			0.647467i	−0.946148	+	0.323734i	$0.895062\pi$
$230$	−4.24264	−	7.34847i	−0.279751	−	0.484544i
$231$	10.6066	+	18.3712i	0.697863	+	1.20873i
$232$	−10.0000	+	17.3205i	−0.656532	+	1.13715i
$233$	−0.500000	−	0.866025i	−0.0327561	−	0.0567352i	0.849183	−	0.528099i	$-0.177095\pi$
$233$	−0.500000	−	0.866025i	−0.0327561	−	0.0567352i	−0.881939	+	0.471364i	$0.843762\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$		−	3.46410i		−	0.225494i
$237$	−4.24264	−	2.44949i	−0.275589	−	0.159111i
$238$	12.0000	+	6.92820i	0.777844	+	0.449089i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−16.9706			−1.09545
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.00239235	−	0.999997i	$-0.500762\pi$
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.867219	+	0.497927i	$0.834095\pi$
$242$	9.89949	+	17.1464i	0.636364	+	1.10221i
$243$		0			0
$244$	−12.7279	+	7.34847i	−0.814822	+	0.470438i
$245$	−2.12132	+	1.22474i	−0.135526	+	0.0782461i
$246$	−12.7279			−0.811503
$247$	−19.7990	−	14.6969i	−1.25978	−	0.935144i
$248$	4.00000			0.254000
$249$	−10.5000	+	6.06218i	−0.665410	+	0.384175i
$250$	12.0000	−	6.92820i	0.758947	−	0.438178i
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	−0.232740	−	0.972539i	$-0.574769\pi$
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	0.958613	−	0.284711i	$-0.0918976\pi$
$252$		0			0
$253$	10.6066	+	6.12372i	0.666831	+	0.384995i
$254$	−4.00000			−0.250982
$255$	16.9706			1.06274
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	13.5000	+	7.79423i	0.842107	+	0.486191i	0.857980	−	0.513683i	$-0.171719\pi$
$257$	13.5000	+	7.79423i	0.842107	+	0.486191i	−0.0158730	+	0.999874i	$0.505053\pi$
$258$			14.6969i			0.914991i
$259$		−	3.46410i		−	0.215249i
$260$	24.0000	+	13.8564i	1.48842	+	0.859338i
$261$		0			0
$262$	−4.94975	+	8.57321i	−0.305796	+	0.529655i
$263$	23.3345	−	13.4722i	1.43887	−	0.830731i	0.441097	−	0.897459i	$-0.354589\pi$
$263$	23.3345	−	13.4722i	1.43887	−	0.830731i	0.997771	+	0.0667283i	$0.0212561\pi$
$264$	21.2132	−	12.2474i	1.30558	−	0.753778i
$265$		−	20.7846i		−	1.27679i
$266$	6.00000	+	13.8564i	0.367884	+	0.849591i
$267$	−6.00000			−0.367194
$268$	21.0000	−	12.1244i	1.28278	−	0.740613i
$269$	4.24264	+	7.34847i	0.258678	+	0.448044i	0.965888	−	0.258960i	$-0.0833797\pi$
$269$	4.24264	+	7.34847i	0.258678	+	0.448044i	−0.707210	+	0.707004i	$0.750046\pi$
$270$	−9.00000	+	15.5885i	−0.547723	+	0.948683i
$271$	−2.12132	+	1.22474i	−0.128861	+	0.0743980i	−0.563045	−	0.826426i	$-0.690370\pi$
$271$	−2.12132	+	1.22474i	−0.128861	+	0.0743980i	0.434184	+	0.900824i	$0.357037\pi$
$272$	8.00000	−	13.8564i	0.485071	−	0.840168i
$273$	−24.0000			−1.45255
$274$	24.0416			1.45241
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$	4.24264	−	7.34847i	0.255377	−	0.442326i
$277$			7.34847i			0.441527i	0.975327	+	0.220763i	$0.0708548\pi$
$277$			7.34847i			0.441527i	−0.975327	+	0.220763i	$0.929145\pi$
$278$	12.7279			0.763370
$279$		0			0
$280$	−8.48528	−	14.6969i	−0.507093	−	0.878310i
$281$	1.50000	+	0.866025i	0.0894825	+	0.0516627i	0.544074	−	0.839038i	$-0.316881\pi$
$281$	1.50000	+	0.866025i	0.0894825	+	0.0516627i	−0.454591	+	0.890700i	$0.650215\pi$
$282$	−9.00000	−	15.5885i	−0.535942	−	0.928279i
$283$	−8.50000	−	14.7224i	−0.505273	−	0.875158i	−0.999981	−	0.00609896i	$-0.998059\pi$
$283$	−8.50000	−	14.7224i	−0.505273	−	0.875158i	0.494709	−	0.869059i	$-0.335275\pi$
$284$	5.65685			0.335673
$285$	14.8492	+	11.0227i	0.879593	+	0.652929i
$286$	−40.0000			−2.36525
$287$	−6.36396	−	11.0227i	−0.375653	−	0.650650i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−21.2132	+	12.2474i	−1.24568	+	0.719195i
$291$	16.5000	−	28.5788i	0.967247	−	1.67532i
$292$	6.00000			0.351123
$293$	−29.6985			−1.73500			−0.867502	−	0.497434i	$-0.834276\pi$
$293$	−29.6985			−1.73500			−0.867502	+	0.497434i	$0.834276\pi$
$294$	−2.12132	−	1.22474i	−0.123718	−	0.0714286i
$295$	2.12132	−	3.67423i	0.123508	−	0.213922i
$296$	−4.00000			−0.232495
$297$		−	25.9808i		−	1.50756i
$298$	21.0000	+	12.1244i	1.21650	+	0.702345i
$299$	−12.0000	+	6.92820i	−0.693978	+	0.400668i
$300$	−3.00000	−	1.73205i	−0.173205	−	0.100000i
$301$	−12.7279	+	7.34847i	−0.733625	+	0.423559i
$302$	11.0000	+	19.0526i	0.632979	+	1.09635i
$303$	12.7279			0.731200
$304$	16.0000	−	6.92820i	0.917663	−	0.397360i
$305$	−18.0000			−1.03068
$306$		0			0
$307$	4.50000	−	2.59808i	0.256829	−	0.148280i	−0.366058	−	0.930592i	$-0.619293\pi$
$307$	4.50000	−	2.59808i	0.256829	−	0.148280i	0.622887	+	0.782312i	$0.285960\pi$
$308$	21.2132	+	12.2474i	1.20873	+	0.697863i
$309$	−4.24264	+	2.44949i	−0.241355	+	0.139347i
$310$	4.24264	+	2.44949i	0.240966	+	0.139122i
$311$		−	12.2474i		−	0.694489i	−0.937775	−	0.347245i	$-0.887117\pi$
$311$		−	12.2474i		−	0.694489i	0.937775	−	0.347245i	$-0.112883\pi$
$312$			27.7128i			1.56893i
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	6.00000	+	3.46410i	0.338600	+	0.195491i
$315$		0			0
$316$	−5.65685			−0.318223
$317$	4.24264	−	7.34847i	0.238290	−	0.412731i	−0.721933	−	0.691963i	$-0.756746\pi$
$317$	4.24264	−	7.34847i	0.238290	−	0.412731i	0.960224	+	0.279231i	$0.0900797\pi$
$318$	18.0000	−	10.3923i	1.00939	−	0.582772i
$319$	17.6777	−	30.6186i	0.989759	−	1.71431i
$320$	−16.9706	+	9.79796i	−0.948683	+	0.547723i
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$	8.48528			0.472866
$323$	−16.0000	+	6.92820i	−0.890264	+	0.385496i
$324$	−18.0000			−1.00000
$325$	2.82843	+	4.89898i	0.156893	+	0.271746i
$326$	2.12132	+	3.67423i	0.117489	+	0.203497i
$327$	−21.2132	−	12.2474i	−1.17309	−	0.677285i
$328$	−12.7279	+	7.34847i	−0.702782	+	0.405751i
$329$	9.00000	−	15.5885i	0.496186	−	0.859419i
$330$	30.0000			1.65145
$331$			5.19615i			0.285606i	0.989751	+	0.142803i	$0.0456116\pi$
$331$			5.19615i			0.285606i	−0.989751	+	0.142803i	$0.954388\pi$
$332$	−7.00000	+	12.1244i	−0.384175	+	0.665410i
$333$		0			0
$334$	−8.00000			−0.437741
$335$	29.6985			1.62260
$336$	8.48528	−	14.6969i	0.462910	−	0.801784i
$337$	22.5000	−	12.9904i	1.22565	−	0.707631i	0.259536	−	0.965734i	$-0.416431\pi$
$337$	22.5000	−	12.9904i	1.22565	−	0.707631i	0.966118	+	0.258102i	$0.0830972\pi$
$338$	13.4350	−	23.2702i	0.730769	−	1.26573i
$339$	−10.5000	−	18.1865i	−0.570282	−	0.987757i
$340$	16.9706	−	9.79796i	0.920358	−	0.531369i
$341$	−7.07107			−0.382920
$342$		0			0
$343$		−	19.5959i		−	1.05808i
$344$	8.48528	+	14.6969i	0.457496	+	0.792406i
$345$	9.00000	−	5.19615i	0.484544	−	0.279751i
$346$		0			0
$347$	11.5000	+	19.9186i	0.617352	+	1.06929i	0.989967	+	0.141299i	$0.0451280\pi$
$347$	11.5000	+	19.9186i	0.617352	+	1.06929i	−0.372615	+	0.927986i	$0.621539\pi$
$348$	−21.2132	−	12.2474i	−1.13715	−	0.656532i
$349$			29.3939i			1.57342i	0.617324	+	0.786709i	$0.288217\pi$
$349$			29.3939i			1.57342i	−0.617324	+	0.786709i	$0.711783\pi$
$350$		−	3.46410i		−	0.185164i
$351$	25.4558	+	14.6969i	1.35873	+	0.784465i
$352$	14.1421	−	24.4949i	0.753778	−	1.30558i
$353$	−31.0000			−1.64996			−0.824982	−	0.565159i	$-0.808815\pi$
$353$	−31.0000			−1.64996			−0.824982	+	0.565159i	$0.808815\pi$
$354$	4.24264			0.225494
$355$	6.00000	+	3.46410i	0.318447	+	0.183855i
$356$	−6.00000	+	3.46410i	−0.317999	+	0.183597i
$357$	−8.48528	+	14.6969i	−0.449089	+	0.777844i
$358$	10.6066	−	6.12372i	0.560576	−	0.323649i
$359$	−14.8492	+	8.57321i	−0.783713	+	0.452477i	−0.837745	−	0.546062i	$-0.816126\pi$
$359$	−14.8492	+	8.57321i	−0.783713	+	0.452477i	0.0540315	+	0.998539i	$0.482793\pi$
$360$		0			0
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	34.0000			1.78700
$363$	−21.0000	+	12.1244i	−1.10221	+	0.636364i
$364$	−24.0000	+	13.8564i	−1.25794	+	0.726273i
$365$	6.36396	+	3.67423i	0.333105	+	0.192318i
$366$	−9.00000	−	15.5885i	−0.470438	−	0.814822i
$367$	−6.36396	−	3.67423i	−0.332196	−	0.191793i	0.324620	−	0.945845i	$-0.394764\pi$
$367$	−6.36396	−	3.67423i	−0.332196	−	0.191793i	−0.656816	+	0.754051i	$0.728097\pi$
$368$		−	9.79796i		−	0.510754i
$369$		0			0
$370$	−4.24264	−	2.44949i	−0.220564	−	0.127343i
$371$	18.0000	+	10.3923i	0.934513	+	0.539542i
$372$			4.89898i			0.254000i
$373$	11.3137			0.585802			0.292901	−	0.956143i	$-0.405379\pi$
$373$	11.3137			0.585802			0.292901	+	0.956143i	$0.405379\pi$
$374$	−14.1421	+	24.4949i	−0.731272	+	1.26660i
$375$	8.48528	+	14.6969i	0.438178	+	0.758947i
$376$	−18.0000	−	10.3923i	−0.928279	−	0.535942i
$377$	20.0000	+	34.6410i	1.03005	+	1.78410i
$378$	−9.00000	−	15.5885i	−0.462910	−	0.801784i
$379$			24.2487i			1.24557i	0.782392	+	0.622786i	$0.213999\pi$
$379$			24.2487i			1.24557i	−0.782392	+	0.622786i	$0.786001\pi$
$380$	21.2132	+	2.44949i	1.08821	+	0.125656i
$381$		−	4.89898i		−	0.250982i
$382$	−24.0000	+	13.8564i	−1.22795	+	0.708955i
$383$	−4.94975	−	8.57321i	−0.252920	−	0.438071i	0.711408	−	0.702779i	$-0.248058\pi$
$383$	−4.94975	−	8.57321i	−0.252920	−	0.438071i	−0.964329	+	0.264708i	$0.914724\pi$
$384$	−16.9706	−	9.79796i	−0.866025	−	0.500000i
$385$	15.0000	+	25.9808i	0.764471	+	1.32410i
$386$	−4.24264	−	2.44949i	−0.215945	−	0.124676i
$387$		0			0
$388$		−	38.1051i		−	1.93449i
$389$	29.6985	+	17.1464i	1.50577	+	0.869358i	0.999978	+	0.00670497i	$0.00213427\pi$
$389$	29.6985	+	17.1464i	1.50577	+	0.869358i	0.505795	+	0.862653i	$0.331199\pi$
$390$	−16.9706	+	29.3939i	−0.859338	+	1.48842i
$391$			9.79796i			0.495504i
$392$	−2.82843			−0.142857
$393$	−10.5000	−	6.06218i	−0.529655	−	0.305796i
$394$	−21.0000	+	12.1244i	−1.05796	+	0.610816i
$395$	−6.00000	−	3.46410i	−0.301893	−	0.174298i
$396$		0			0
$397$	27.5772	−	15.9217i	1.38406	−	0.799086i	0.391421	−	0.920212i	$-0.371984\pi$
$397$	27.5772	−	15.9217i	1.38406	−	0.799086i	0.992637	+	0.121125i	$0.0386503\pi$
$398$		−	34.6410i		−	1.73640i
$399$	−16.9706	+	7.34847i	−0.849591	+	0.367884i
$400$	−4.00000			−0.200000
$401$	10.5000	−	6.06218i	0.524345	−	0.302731i	−0.214366	−	0.976753i	$-0.568768\pi$
$401$	10.5000	−	6.06218i	0.524345	−	0.302731i	0.738711	+	0.674023i	$0.235435\pi$
$402$	14.8492	+	25.7196i	0.740613	+	1.28278i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	12.7279	−	7.34847i	0.633238	−	0.365600i
$405$	−19.0919	−	11.0227i	−0.948683	−	0.547723i
$406$		−	24.4949i		−	1.21566i
$407$	7.07107			0.350500
$408$	16.9706	+	9.79796i	0.840168	+	0.485071i
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$	−18.0000			−0.888957
$411$			29.4449i			1.45241i
$412$	−2.82843	+	4.89898i	−0.139347	+	0.241355i
$413$	2.12132	+	3.67423i	0.104383	+	0.180797i
$414$		0			0
$415$	−14.8492	+	8.57321i	−0.728921	+	0.420843i
$416$	16.0000	+	27.7128i	0.784465	+	1.35873i
$417$			15.5885i			0.763370i
$418$	−28.2843	+	12.2474i	−1.38343	+	0.599042i
$419$	14.0000			0.683945			0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000			0.683945			0.341972	+	0.939710i	$0.388905\pi$
$420$	18.0000	−	10.3923i	0.878310	−	0.507093i
$421$	−16.2635	−	28.1691i	−0.792632	−	1.37288i	−0.924332	−	0.381590i	$-0.875377\pi$
$421$	−16.2635	−	28.1691i	−0.792632	−	1.37288i	0.131699	−	0.991290i	$-0.457957\pi$
$422$	−12.7279	−	7.34847i	−0.619586	−	0.357718i
$423$		0			0
$424$	12.0000	−	20.7846i	0.582772	−	1.00939i
$425$	4.00000			0.194029
$426$			6.92820i			0.335673i
$427$	9.00000	−	15.5885i	0.435541	−	0.754378i
$428$	12.0000	+	6.92820i	0.580042	+	0.334887i
$429$		−	48.9898i		−	2.36525i
$430$			20.7846i			1.00232i
$431$	−4.24264	+	7.34847i	−0.204361	+	0.353963i	−0.949929	−	0.312466i	$-0.898845\pi$
$431$	−4.24264	+	7.34847i	−0.204361	+	0.353963i	0.745568	+	0.666429i	$0.232178\pi$
$432$	−18.0000	+	10.3923i	−0.866025	+	0.500000i
$433$	27.0000	+	15.5885i	1.29754	+	0.749133i	0.979978	−	0.199105i	$-0.0638035\pi$
$433$	27.0000	+	15.5885i	1.29754	+	0.749133i	0.317559	+	0.948239i	$0.397137\pi$
$434$	−4.24264	+	2.44949i	−0.203653	+	0.117579i
$435$	−15.0000	−	25.9808i	−0.719195	−	1.24568i
$436$	−28.2843			−1.35457
$437$	−6.36396	+	8.57321i	−0.304430	+	0.410112i
$438$			7.34847i			0.351123i
$439$	−4.94975	−	8.57321i	−0.236239	−	0.409177i	0.723393	−	0.690436i	$-0.242581\pi$
$439$	−4.94975	−	8.57321i	−0.236239	−	0.409177i	−0.959632	+	0.281259i	$0.909248\pi$
$440$	30.0000	−	17.3205i	1.43019	−	0.825723i
$441$		0			0
$442$	−16.0000	−	27.7128i	−0.761042	−	1.31816i
$443$	−15.5000	+	26.8468i	−0.736427	+	1.27553i	0.217667	+	0.976023i	$0.430155\pi$
$443$	−15.5000	+	26.8468i	−0.736427	+	1.27553i	−0.954094	+	0.299506i	$0.903178\pi$
$444$		−	4.89898i		−	0.232495i
$445$	−8.48528			−0.402241
$446$	17.0000	−	29.4449i	0.804973	−	1.39425i
$447$	−14.8492	+	25.7196i	−0.702345	+	1.21650i
$448$		−	19.5959i		−	0.925820i
$449$		−	12.1244i		−	0.572184i	−0.958202	−	0.286092i	$-0.907644\pi$
$449$		−	12.1244i		−	0.572184i	0.958202	−	0.286092i	$-0.0923563\pi$
$450$		0			0
$451$	22.5000	−	12.9904i	1.05948	−	0.611693i
$452$	−21.0000	−	12.1244i	−0.987757	−	0.570282i
$453$	−23.3345	+	13.4722i	−1.09635	+	0.632979i
$454$	2.12132	−	1.22474i	0.0995585	−	0.0574801i
$455$	−33.9411			−1.59118
$456$	8.48528	+	19.5959i	0.397360	+	0.917663i
$457$	−11.0000			−0.514558			−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000			−0.514558			−0.257279	+	0.966337i	$0.582826\pi$
$458$	−12.0000	+	6.92820i	−0.560723	+	0.323734i
$459$	18.0000	−	10.3923i	0.840168	−	0.485071i
$460$	6.00000	−	10.3923i	0.279751	−	0.484544i
$461$	−12.7279	+	7.34847i	−0.592798	+	0.342252i	−0.766203	−	0.642598i	$-0.777856\pi$
$461$	−12.7279	+	7.34847i	−0.592798	+	0.342252i	0.173405	+	0.984851i	$0.444523\pi$
$462$	−15.0000	+	25.9808i	−0.697863	+	1.20873i
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	−28.2843			−1.31306
$465$	−3.00000	+	5.19615i	−0.139122	+	0.240966i
$466$	0.707107	−	1.22474i	0.0327561	−	0.0567352i
$467$	13.0000			0.601568			0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000			0.601568			0.300784	+	0.953692i	$0.402752\pi$
$468$		0			0
$469$	−14.8492	+	25.7196i	−0.685674	+	1.18762i
$470$	−12.7279	−	22.0454i	−0.587095	−	1.01688i
$471$	−4.24264	+	7.34847i	−0.195491	+	0.338600i
$472$	4.24264	−	2.44949i	0.195283	−	0.112747i
$473$	−15.0000	−	25.9808i	−0.689701	−	1.19460i
$474$		−	6.92820i		−	0.318223i
$475$	3.50000	+	2.59808i	0.160591	+	0.119208i
$476$			19.5959i			0.898177i
$477$		0			0
$478$		0			0
$479$	−21.2132	−	12.2474i	−0.969256	−	0.559600i	−0.0702467	−	0.997530i	$-0.522379\pi$
$479$	−21.2132	−	12.2474i	−0.969256	−	0.559600i	−0.899009	+	0.437929i	$0.855712\pi$
$480$	−12.0000	−	20.7846i	−0.547723	−	0.948683i
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$		−	22.0454i		−	1.00414i
$483$			10.3923i			0.472866i
$484$	−14.0000	+	24.2487i	−0.636364	+	1.10221i
$485$	23.3345	−	40.4166i	1.05957	−	1.83522i
$486$		0			0
$487$	35.3553			1.60210			0.801052	−	0.598595i	$-0.204274\pi$
$487$	35.3553			1.60210			0.801052	+	0.598595i	$0.204274\pi$
$488$	−18.0000	−	10.3923i	−0.814822	−	0.470438i
$489$	−4.50000	+	2.59808i	−0.203497	+	0.117489i
$490$	−3.00000	−	1.73205i	−0.135526	−	0.0782461i
$491$	−17.0000	−	29.4449i	−0.767199	−	1.32883i	−0.939076	−	0.343710i	$-0.888316\pi$
$491$	−17.0000	−	29.4449i	−0.767199	−	1.32883i	0.171877	−	0.985118i	$-0.445017\pi$
$492$	−9.00000	−	15.5885i	−0.405751	−	0.702782i
$493$	28.2843			1.27386
$494$	4.00000	−	34.6410i	0.179969	−	1.55857i
$495$		0			0
$496$	2.82843	+	4.89898i	0.127000	+	0.219971i
$497$	−6.00000	+	3.46410i	−0.269137	+	0.155386i
$498$	−14.8492	−	8.57321i	−0.665410	−	0.384175i
$499$	−0.500000	−	0.866025i	−0.0223831	−	0.0387686i	0.854617	−	0.519259i	$-0.173792\pi$
$499$	−0.500000	−	0.866025i	−0.0223831	−	0.0387686i	−0.877000	+	0.480490i	$0.840459\pi$
$500$	16.9706	+	9.79796i	0.758947	+	0.438178i
$501$		−	9.79796i		−	0.437741i
$502$	32.5269			1.45175
$503$	−2.12132	−	1.22474i	−0.0945850	−	0.0546087i	0.451961	−	0.892037i	$-0.350724\pi$
$503$	−2.12132	−	1.22474i	−0.0945850	−	0.0546087i	−0.546546	+	0.837429i	$0.684058\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$			17.3205i			0.769991i
$507$	28.5000	+	16.4545i	1.26573	+	0.730769i
$508$	−2.82843	−	4.89898i	−0.125491	−	0.217357i
$509$	11.3137	−	19.5959i	0.501471	−	0.868574i	−0.498527	−	0.866874i	$-0.666126\pi$
$509$	11.3137	−	19.5959i	0.501471	−	0.868574i	0.999999	−	0.00169976i	$-0.000541051\pi$
$510$	12.0000	+	20.7846i	0.531369	+	0.920358i
$511$	−6.36396	+	3.67423i	−0.281525	+	0.162539i
$512$	−22.6274			−1.00000
$513$	22.5000	+	2.59808i	0.993399	+	0.114708i
$514$			22.0454i			0.972381i
$515$	−6.00000	+	3.46410i	−0.264392	+	0.152647i
$516$	−18.0000	+	10.3923i	−0.792406	+	0.457496i
$517$	31.8198	+	18.3712i	1.39943	+	0.807963i
$518$	4.24264	−	2.44949i	0.186411	−	0.107624i
$519$		0			0
$520$			39.1918i			1.71868i
$521$			22.5167i			0.986473i	0.869895	+	0.493236i	$0.164186\pi$
$521$			22.5167i			0.986473i	−0.869895	+	0.493236i	$0.835814\pi$
$522$		0			0
$523$	−18.0000	−	10.3923i	−0.787085	−	0.454424i	0.0518503	−	0.998655i	$-0.483488\pi$
$523$	−18.0000	−	10.3923i	−0.787085	−	0.454424i	−0.838935	+	0.544231i	$0.816821\pi$
$524$	−14.0000			−0.611593
$525$	4.24264			0.185164
$526$	33.0000	+	19.0526i	1.43887	+	0.830731i
$527$	−2.82843	−	4.89898i	−0.123208	−	0.213403i
$528$	30.0000	+	17.3205i	1.30558	+	0.753778i
$529$	−8.50000	−	14.7224i	−0.369565	−	0.640106i
$530$	25.4558	−	14.6969i	1.10573	−	0.638394i
$531$		0			0
$532$	−12.7279	+	17.1464i	−0.551825	+	0.743392i
$533$			29.3939i			1.27319i
$534$	−4.24264	−	7.34847i	−0.183597	−	0.317999i
$535$	8.48528	+	14.6969i	0.366851	+	0.635404i
$536$	29.6985	+	17.1464i	1.28278	+	0.740613i
$537$	7.50000	+	12.9904i	0.323649	+	0.560576i
$538$	−6.00000	+	10.3923i	−0.258678	+	0.448044i
$539$	5.00000			0.215365
$540$	−25.4558			−1.09545
$541$	−12.7279	−	7.34847i	−0.547216	−	0.315935i	0.200782	−	0.979636i	$-0.435652\pi$
$541$	−12.7279	−	7.34847i	−0.547216	−	0.315935i	−0.747998	+	0.663701i	$0.768985\pi$
$542$	−3.00000	−	1.73205i	−0.128861	−	0.0743980i
$543$			41.6413i			1.78700i
$544$	22.6274			0.970143
$545$	−30.0000	−	17.3205i	−1.28506	−	0.741929i
$546$	−16.9706	−	29.3939i	−0.726273	−	1.25794i
$547$	12.0000	+	6.92820i	0.513083	+	0.296229i	0.734100	−	0.679041i	$-0.237604\pi$
$547$	12.0000	+	6.92820i	0.513083	+	0.296229i	−0.221017	+	0.975270i	$0.570938\pi$
$548$	17.0000	+	29.4449i	0.726204	+	1.25782i
$549$		0			0
$550$	7.07107			0.301511
$551$	24.7487	+	18.3712i	1.05433	+	0.782638i
$552$	12.0000			0.510754
$553$	6.00000	−	3.46410i	0.255146	−	0.147309i
$554$	−9.00000	+	5.19615i	−0.382373	+	0.220763i
$555$	3.00000	−	5.19615i	0.127343	−	0.220564i
$556$	9.00000	+	15.5885i	0.381685	+	0.661098i
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$	33.9411			1.43556
$560$	12.0000	−	20.7846i	0.507093	−	0.878310i
$561$	−30.0000	−	17.3205i	−1.26660	−	0.731272i
$562$			2.44949i			0.103325i
$563$			22.5167i			0.948964i	0.880265	+	0.474482i	$0.157365\pi$
$563$			22.5167i			0.948964i	−0.880265	+	0.474482i	$0.842635\pi$
$564$	12.7279	−	22.0454i	0.535942	−	0.928279i
$565$	−14.8492	−	25.7196i	−0.624712	−	1.08203i
$566$	12.0208	−	20.8207i	0.505273	−	0.875158i
$567$	19.0919	−	11.0227i	0.801784	−	0.462910i
$568$	4.00000	+	6.92820i	0.167836	+	0.290701i
$569$			17.3205i			0.726113i	0.931767	+	0.363057i	$0.118267\pi$
$569$			17.3205i			0.726113i	−0.931767	+	0.363057i	$0.881733\pi$
$570$	−3.00000	+	25.9808i	−0.125656	+	1.08821i
$571$	−9.00000			−0.376638			−0.188319	−	0.982108i	$-0.560304\pi$
$571$	−9.00000			−0.376638			−0.188319	+	0.982108i	$0.560304\pi$
$572$	−28.2843	−	48.9898i	−1.18262	−	2.04837i
$573$	−16.9706	−	29.3939i	−0.708955	−	1.22795i
$574$	9.00000	−	15.5885i	0.375653	−	0.650650i
$575$	2.12132	−	1.22474i	0.0884652	−	0.0510754i
$576$		0			0
$577$	−3.00000			−0.124892			−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000			−0.124892			−0.0624458	+	0.998048i	$0.519890\pi$
$578$	1.41421			0.0588235
$579$	3.00000	−	5.19615i	0.124676	−	0.215945i
$580$	−30.0000	−	17.3205i	−1.24568	−	0.719195i
$581$		−	17.1464i		−	0.711354i
$582$	46.6690			1.93449
$583$	−21.2132	+	36.7423i	−0.878561	+	1.52171i
$584$	4.24264	+	7.34847i	0.175562	+	0.304082i
$585$		0			0
$586$	−21.0000	−	36.3731i	−0.867502	−	1.50256i
$587$	−1.00000	−	1.73205i	−0.0412744	−	0.0714894i	0.844650	−	0.535319i	$-0.179808\pi$
$587$	−1.00000	−	1.73205i	−0.0412744	−	0.0714894i	−0.885925	+	0.463829i	$0.846475\pi$
$588$		−	3.46410i		−	0.142857i
$589$	0.707107	−	6.12372i	0.0291358	−	0.252324i
$590$	6.00000			0.247016
$591$	−14.8492	−	25.7196i	−0.610816	−	1.05796i
$592$	−2.82843	−	4.89898i	−0.116248	−	0.201347i
$593$	6.50000	−	11.2583i	0.266923	−	0.462324i	−0.701143	−	0.713021i	$-0.747326\pi$
$593$	6.50000	−	11.2583i	0.266923	−	0.462324i	0.968066	+	0.250697i	$0.0806597\pi$
$594$	31.8198	−	18.3712i	1.30558	−	0.753778i
$595$	−12.0000	+	20.7846i	−0.491952	+	0.852086i
$596$			34.2929i			1.40469i
$597$	42.4264			1.73640
$598$	−16.9706	−	9.79796i	−0.693978	−	0.400668i
$599$	−9.19239	+	15.9217i	−0.375591	+	0.650542i	−0.990415	−	0.138122i	$-0.955894\pi$
$599$	−9.19239	+	15.9217i	−0.375591	+	0.650542i	0.614824	+	0.788664i	$0.289227\pi$
$600$		−	4.89898i		−	0.200000i
$601$		−	22.5167i		−	0.918474i	−0.888314	−	0.459237i	$-0.848123\pi$
$601$		−	22.5167i		−	0.918474i	0.888314	−	0.459237i	$-0.151877\pi$
$602$	−18.0000	−	10.3923i	−0.733625	−	0.423559i
$603$		0			0
$604$	−15.5563	+	26.9444i	−0.632979	+	1.09635i
$605$	−29.6985	+	17.1464i	−1.20742	+	0.697101i
$606$	9.00000	+	15.5885i	0.365600	+	0.633238i
$607$	−7.07107			−0.287006			−0.143503	−	0.989650i	$-0.545837\pi$
$607$	−7.07107			−0.287006			−0.143503	+	0.989650i	$0.545837\pi$
$608$	19.7990	+	14.6969i	0.802955	+	0.596040i
$609$	30.0000			1.21566
$610$	−12.7279	−	22.0454i	−0.515339	−	0.892592i
$611$	−36.0000	+	20.7846i	−1.45640	+	0.840855i
$612$		0			0
$613$	8.48528	−	4.89898i	0.342717	−	0.197868i	−0.318756	−	0.947837i	$-0.603265\pi$
$613$	8.48528	−	4.89898i	0.342717	−	0.197868i	0.661473	+	0.749969i	$0.269932\pi$
$614$	6.36396	+	3.67423i	0.256829	+	0.148280i
$615$		−	22.0454i		−	0.888957i
$616$			34.6410i			1.39573i
$617$	−6.50000	+	11.2583i	−0.261680	+	0.453243i	−0.966689	−	0.255956i	$-0.917610\pi$
$617$	−6.50000	+	11.2583i	−0.261680	+	0.453243i	0.705008	+	0.709199i	$0.250943\pi$
$618$	−6.00000	−	3.46410i	−0.241355	−	0.139347i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$			6.92820i			0.278243i
$621$	6.36396	−	11.0227i	0.255377	−	0.442326i
$622$	15.0000	−	8.66025i	0.601445	−	0.347245i
$623$	4.24264	−	7.34847i	0.169978	−	0.294410i
$624$	−33.9411	+	19.5959i	−1.35873	+	0.784465i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−1.41421			−0.0565233
$627$	−15.0000	−	34.6410i	−0.599042	−	1.38343i
$628$			9.79796i			0.390981i
$629$	2.82843	+	4.89898i	0.112777	+	0.195335i
$630$		0			0
$631$	−19.0919	−	11.0227i	−0.760036	−	0.438807i	0.0692728	−	0.997598i	$-0.477932\pi$
$631$	−19.0919	−	11.0227i	−0.760036	−	0.438807i	−0.829309	+	0.558791i	$0.811265\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$	9.00000	−	15.5885i	0.357718	−	0.619586i
$634$	12.0000			0.476581
$635$		−	6.92820i		−	0.274937i
$636$	25.4558	+	14.6969i	1.00939	+	0.582772i
$637$	−2.82843	+	4.89898i	−0.112066	+	0.194105i
$638$	50.0000			1.97952
$639$		0			0
$640$	−24.0000	−	13.8564i	−0.948683	−	0.547723i
$641$	7.50000	−	4.33013i	0.296232	−	0.171030i	−0.344517	−	0.938780i	$-0.611957\pi$
$641$	7.50000	−	4.33013i	0.296232	−	0.171030i	0.640749	+	0.767750i	$0.278624\pi$
$642$	−8.48528	+	14.6969i	−0.334887	+	0.580042i
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$	−25.4558			−1.00232
$646$	−19.7990	−	14.6969i	−0.778981	−	0.578243i
$647$		−	29.3939i		−	1.15559i	−0.816181	−	0.577796i	$-0.803913\pi$
$647$		−	29.3939i		−	1.15559i	0.816181	−	0.577796i	$-0.196087\pi$
$648$	−12.7279	−	22.0454i	−0.500000	−	0.866025i
$649$	−7.50000	+	4.33013i	−0.294401	+	0.169972i
$650$	−4.00000	+	6.92820i	−0.156893	+	0.271746i
$651$	−3.00000	−	5.19615i	−0.117579	−	0.203653i
$652$	−3.00000	+	5.19615i	−0.117489	+	0.203497i
$653$		−	14.6969i		−	0.575136i	−0.957760	−	0.287568i	$-0.907153\pi$
$653$		−	14.6969i		−	0.575136i	0.957760	−	0.287568i	$-0.0928467\pi$
$654$		−	34.6410i		−	1.35457i
$655$	−14.8492	−	8.57321i	−0.580208	−	0.334983i
$656$	−18.0000	−	10.3923i	−0.702782	−	0.405751i
$657$		0			0
$658$	25.4558			0.992372
$659$	−30.0000	−	17.3205i	−1.16863	−	0.674711i	−0.215276	−	0.976553i	$-0.569065\pi$
$659$	−30.0000	−	17.3205i	−1.16863	−	0.674711i	−0.953358	+	0.301842i	$0.902398\pi$
$660$	21.2132	+	36.7423i	0.825723	+	1.43019i
$661$	4.94975	−	8.57321i	0.192523	−	0.333459i	−0.753563	−	0.657376i	$-0.771666\pi$
$661$	4.94975	−	8.57321i	0.192523	−	0.333459i	0.946086	+	0.323917i	$0.105000\pi$
$662$	−6.36396	+	3.67423i	−0.247342	+	0.142803i
$663$	33.9411	−	19.5959i	1.31816	−	0.761042i
$664$	−19.7990			−0.768350
$665$	−24.0000	+	10.3923i	−0.930680	+	0.402996i
$666$		0			0
$667$	15.0000	−	8.66025i	0.580802	−	0.335326i
$668$	−5.65685	−	9.79796i	−0.218870	−	0.379094i
$669$	36.0624	+	20.8207i	1.39425	+	0.804973i
$670$	21.0000	+	36.3731i	0.811301	+	1.40521i
$671$	31.8198	+	18.3712i	1.22839	+	0.709211i
$672$	24.0000			0.925820
$673$		−	24.2487i		−	0.934719i	−0.884067	−	0.467360i	$-0.845205\pi$
$673$		−	24.2487i		−	0.934719i	0.884067	−	0.467360i	$-0.154795\pi$
$674$	31.8198	+	18.3712i	1.22565	+	0.707631i
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	38.0000			1.46154
$677$	−16.9706			−0.652232			−0.326116	−	0.945330i	$-0.605740\pi$
$677$	−16.9706			−0.652232			−0.326116	+	0.945330i	$0.605740\pi$
$678$	14.8492	−	25.7196i	0.570282	−	0.987757i
$679$	23.3345	+	40.4166i	0.895497	+	1.55105i
$680$	24.0000	+	13.8564i	0.920358	+	0.531369i
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$	−5.00000	−	8.66025i	−0.191460	−	0.331618i
$683$		−	20.7846i		−	0.795301i	−0.917537	−	0.397650i	$-0.869826\pi$
$683$		−	20.7846i		−	0.795301i	0.917537	−	0.397650i	$-0.130174\pi$
$684$		0			0
$685$			41.6413i			1.59103i
$686$	24.0000	−	13.8564i	0.916324	−	0.529040i
$687$	−8.48528	−	14.6969i	−0.323734	−	0.560723i
$688$	−12.0000	+	20.7846i	−0.457496	+	0.792406i
$689$	−24.0000	−	41.5692i	−0.914327	−	1.58366i
$690$	12.7279	+	7.34847i	0.484544	+	0.279751i
$691$	6.00000			0.228251			0.114125	−	0.993466i	$-0.463593\pi$
$691$	6.00000			0.228251			0.114125	+	0.993466i	$0.463593\pi$
$692$		0			0
$693$		0			0
$694$	−16.2635	+	28.1691i	−0.617352	+	1.06929i
$695$			22.0454i			0.836230i
$696$		−	34.6410i		−	1.31306i
$697$	18.0000	+	10.3923i	0.681799	+	0.393637i
$698$	−36.0000	+	20.7846i	−1.36262	+	0.786709i
$699$	1.50000	+	0.866025i	0.0567352	+	0.0327561i
$700$	4.24264	−	2.44949i	0.160357	−	0.0925820i
$701$	10.6066	−	6.12372i	0.400606	−	0.231290i	−0.286140	−	0.958188i	$-0.592372\pi$
$701$	10.6066	−	6.12372i	0.400606	−	0.231290i	0.686745	+	0.726898i	$0.259039\pi$
$702$			41.5692i			1.56893i
$703$	−0.707107	+	6.12372i	−0.0266690	+	0.230961i
$704$	40.0000			1.50756
$705$	27.0000	−	15.5885i	1.01688	−	0.587095i
$706$	−21.9203	−	37.9671i	−0.824982	−	1.42891i
$707$	−9.00000	+	15.5885i	−0.338480	+	0.586264i
$708$	3.00000	+	5.19615i	0.112747	+	0.195283i
$709$	−27.5772	−	15.9217i	−1.03568	−	0.597951i	−0.117075	−	0.993123i	$-0.537352\pi$
$709$	−27.5772	−	15.9217i	−1.03568	−	0.597951i	−0.918607	+	0.395172i	$0.870685\pi$
$710$			9.79796i			0.367711i
$711$		0			0
$712$	−8.48528	−	4.89898i	−0.317999	−	0.183597i
$713$	−3.00000	−	1.73205i	−0.112351	−	0.0648658i
$714$	−24.0000			−0.898177
$715$		−	69.2820i		−	2.59100i
$716$	15.0000	+	8.66025i	0.560576	+	0.323649i
$717$		0			0
$718$	−21.0000	−	12.1244i	−0.783713	−	0.452477i
$719$	−16.9706	+	9.79796i	−0.632895	+	0.365402i	−0.781872	−	0.623438i	$-0.785735\pi$
$719$	−16.9706	+	9.79796i	−0.632895	+	0.365402i	0.148977	+	0.988841i	$0.452402\pi$
$720$		0			0
$721$		−	6.92820i		−	0.258020i
$722$	−7.77817	−	25.7196i	−0.289474	−	0.957186i
$723$	27.0000			1.00414
$724$	24.0416	+	41.6413i	0.893500	+	1.54759i
$725$	−3.53553	−	6.12372i	−0.131306	−	0.227429i
$726$	−29.6985	−	17.1464i	−1.10221	−	0.636364i
$727$	−42.4264	+	24.4949i	−1.57351	+	0.908465i	−0.577774	+	0.816197i	$0.696079\pi$
$727$	−42.4264	+	24.4949i	−1.57351	+	0.908465i	−0.995734	+	0.0922688i	$0.970588\pi$
$728$	−33.9411	−	19.5959i	−1.25794	−	0.726273i
$729$	−27.0000			−1.00000
$730$			10.3923i			0.384636i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	12.7279	−	22.0454i	0.470438	−	0.814822i
$733$		−	7.34847i		−	0.271422i	−0.990748	−	0.135711i	$-0.956668\pi$
$733$		−	7.34847i		−	0.271422i	0.990748	−	0.135711i	$-0.0433318\pi$
$734$		−	10.3923i		−	0.383587i
$735$	2.12132	−	3.67423i	0.0782461	−	0.135526i
$736$	12.0000	−	6.92820i	0.442326	−	0.255377i
$737$	−52.5000	−	30.3109i	−1.93386	−	1.11652i
$738$		0			0
$739$	25.5000	+	44.1673i	0.938033	+	1.62472i	0.769135	+	0.639087i	$0.220687\pi$
$739$	25.5000	+	44.1673i	0.938033	+	1.62472i	0.168898	+	0.985634i	$0.445979\pi$
$740$		−	6.92820i		−	0.254686i
$741$	42.4264	+	4.89898i	1.55857	+	0.179969i
$742$			29.3939i			1.07908i
$743$	−6.36396	−	11.0227i	−0.233471	−	0.404384i	0.725356	−	0.688374i	$-0.241675\pi$
$743$	−6.36396	−	11.0227i	−0.233471	−	0.404384i	−0.958827	+	0.283990i	$0.908342\pi$
$744$	−6.00000	+	3.46410i	−0.219971	+	0.127000i
$745$	−21.0000	+	36.3731i	−0.769380	+	1.33261i
$746$	8.00000	+	13.8564i	0.292901	+	0.507319i
$747$		0			0
$748$	−40.0000			−1.46254
$749$	−16.9706			−0.620091
$750$	−12.0000	+	20.7846i	−0.438178	+	0.758947i
$751$	−5.65685	+	9.79796i	−0.206422	+	0.357533i	−0.950585	−	0.310465i	$-0.899515\pi$
$751$	−5.65685	+	9.79796i	−0.206422	+	0.357533i	0.744163	+	0.667998i	$0.232848\pi$
$752$		−	29.3939i		−	1.07188i
$753$			39.8372i			1.45175i
$754$	−28.2843	+	48.9898i	−1.03005	+	1.78410i
$755$	−33.0000	+	19.0526i	−1.20099	+	0.693394i
$756$	12.7279	−	22.0454i	0.462910	−	0.801784i
$757$	−33.9411	+	19.5959i	−1.23361	+	0.712226i	−0.967781	−	0.251794i	$-0.918979\pi$
$757$	−33.9411	+	19.5959i	−1.23361	+	0.712226i	−0.265830	+	0.964020i	$0.585646\pi$
$758$	−29.6985	+	17.1464i	−1.07870	+	0.622786i
$759$	−21.2132			−0.769991
$760$	12.0000	+	27.7128i	0.435286	+	1.00525i
$761$	−1.00000			−0.0362500			−0.0181250	−	0.999836i	$-0.505770\pi$
$761$	−1.00000			−0.0362500			−0.0181250	+	0.999836i	$0.505770\pi$
$762$	6.00000	−	3.46410i	0.217357	−	0.125491i
$763$	30.0000	−	17.3205i	1.08607	−	0.627044i
$764$	−33.9411	−	19.5959i	−1.22795	−	0.708955i
$765$		0			0
$766$	7.00000	−	12.1244i	0.252920	−	0.438071i
$767$		−	9.79796i		−	0.353784i
$768$		−	27.7128i		−	1.00000i
$769$	8.00000	−	13.8564i	0.288487	−	0.499675i	−0.684962	−	0.728579i	$-0.740181\pi$
$769$	8.00000	−	13.8564i	0.288487	−	0.499675i	0.973449	+	0.228904i	$0.0735143\pi$
$770$	−21.2132	+	36.7423i	−0.764471	+	1.32410i
$771$	−27.0000			−0.972381
$772$		−	6.92820i		−	0.249351i
$773$	24.7487	−	42.8661i	0.890150	−	1.54179i	0.0504557	−	0.998726i	$-0.483933\pi$
$773$	24.7487	−	42.8661i	0.890150	−	1.54179i	0.839694	−	0.543059i	$-0.182734\pi$
$774$		0			0
$775$	−0.707107	+	1.22474i	−0.0254000	+	0.0439941i
$776$	46.6690	−	26.9444i	1.67532	−	0.967247i
$777$	3.00000	+	5.19615i	0.107624	+	0.186411i
$778$			48.4974i			1.73872i
$779$	9.00000	+	20.7846i	0.322458	+	0.744686i
$780$	−48.0000			−1.71868
$781$	−7.07107	−	12.2474i	−0.253023	−	0.438248i
$782$	−12.0000	+	6.92820i	−0.429119	+	0.247752i
$783$	−31.8198	−	18.3712i	−1.13715	−	0.656532i
$784$	−2.00000	−	3.46410i	−0.0714286	−	0.123718i
$785$	−6.00000	+	10.3923i	−0.214149	+	0.370917i
$786$		−	17.1464i		−	0.611593i
$787$		−	25.9808i		−	0.926114i	−0.886328	−	0.463057i	$-0.846752\pi$
$787$		−	25.9808i		−	0.926114i	0.886328	−	0.463057i	$-0.153248\pi$
$788$	−29.6985	−	17.1464i	−1.05796	−	0.610816i
$789$	−23.3345	+	40.4166i	−0.830731	+	1.43887i
$790$		−	9.79796i		−	0.348596i
$791$	29.6985			1.05596
$792$		0			0
$793$	−36.0000	+	20.7846i	−1.27840	+	0.738083i
$794$	39.0000	+	22.5167i	1.38406	+	0.799086i
$795$	18.0000	+	31.1769i	0.638394	+	1.10573i
$796$	42.4264	−	24.4949i	1.50376	−	0.868199i
$797$	9.89949			0.350658			0.175329	−	0.984510i	$-0.443901\pi$
$797$	9.89949			0.350658			0.175329	+	0.984510i	$0.443901\pi$
$798$	−21.0000	−	15.5885i	−0.743392	−	0.551825i
$799$			29.3939i			1.03988i
$800$	−2.82843	−	4.89898i	−0.100000	−	0.173205i
$801$		0			0
$802$	14.8492	+	8.57321i	0.524345	+	0.302731i
$803$	−7.50000	−	12.9904i	−0.264669	−	0.458421i
$804$	−21.0000	+	36.3731i	−0.740613	+	1.28278i
$805$			14.6969i			0.517999i
$806$	11.3137			0.398508
$807$	−12.7279	−	7.34847i	−0.448044	−	0.258678i
$808$	18.0000	+	10.3923i	0.633238	+	0.365600i
$809$	47.0000			1.65243			0.826216	−	0.563353i	$-0.190489\pi$
$809$	47.0000			1.65243			0.826216	+	0.563353i	$0.190489\pi$
$810$		−	31.1769i		−	1.09545i
$811$	6.00000	+	3.46410i	0.210688	+	0.121641i	0.601631	−	0.798774i	$-0.294518\pi$
$811$	6.00000	+	3.46410i	0.210688	+	0.121641i	−0.390943	+	0.920415i	$0.627851\pi$
$812$	30.0000	−	17.3205i	1.05279	−	0.607831i
$813$	2.12132	−	3.67423i	0.0743980	−	0.128861i
$814$	5.00000	+	8.66025i	0.175250	+	0.303542i
$815$	−6.36396	+	3.67423i	−0.222920	+	0.128703i
$816$			27.7128i			0.970143i
$817$	24.0000	−	10.3923i	0.839654	−	0.363581i
$818$			12.2474i			0.428222i
$819$		0			0
$820$	−12.7279	−	22.0454i	−0.444478	−	0.769859i
$821$	−12.7279	−	7.34847i	−0.444208	−	0.256463i	0.261173	−	0.965292i	$-0.415891\pi$
$821$	−12.7279	−	7.34847i	−0.444208	−	0.256463i	−0.705381	+	0.708829i	$0.749224\pi$
$822$	−36.0624	+	20.8207i	−1.25782	+	0.726204i
$823$	−29.6985	−	17.1464i	−1.03522	−	0.597687i	−0.116747	−	0.993162i	$-0.537247\pi$
$823$	−29.6985	−	17.1464i	−1.03522	−	0.597687i	−0.918477	+	0.395475i	$0.870580\pi$
$824$	−8.00000			−0.278693
$825$			8.66025i			0.301511i
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	22.5000	+	12.9904i	0.782402	+	0.451720i	0.837281	−	0.546773i	$-0.184144\pi$
$827$	22.5000	+	12.9904i	0.782402	+	0.451720i	−0.0548791	+	0.998493i	$0.517477\pi$
$828$		0			0
$829$	−31.1127			−1.08059			−0.540294	−	0.841476i	$-0.681687\pi$
$829$	−31.1127			−1.08059			−0.540294	+	0.841476i	$0.681687\pi$
$830$	−21.0000	−	12.1244i	−0.728921	−	0.420843i
$831$	−6.36396	−	11.0227i	−0.220763	−	0.382373i
$832$	−22.6274	+	39.1918i	−0.784465	+	1.35873i
$833$	2.00000	+	3.46410i	0.0692959	+	0.120024i
$834$	−19.0919	+	11.0227i	−0.661098	+	0.381685i
$835$		−	13.8564i		−	0.479521i
$836$	−35.0000	−	25.9808i	−1.21050	−	0.898563i
$837$			7.34847i			0.254000i
$838$	9.89949	+	17.1464i	0.341972	+	0.592314i
$839$	−2.12132	−	3.67423i	−0.0732361	−	0.126849i	0.827082	−	0.562082i	$-0.189999\pi$
$839$	−2.12132	−	3.67423i	−0.0732361	−	0.126849i	−0.900318	+	0.435233i	$0.856666\pi$
$840$	25.4558	+	14.6969i	0.878310	+	0.507093i
$841$	−10.5000	−	18.1865i	−0.362069	−	0.627122i
$842$	23.0000	−	39.8372i	0.792632	−	1.37288i
$843$	−3.00000			−0.103325
$844$		−	20.7846i		−	0.715436i
$845$	40.3051	+	23.2702i	1.38654	+	0.800518i
$846$		0			0
$847$		−	34.2929i		−	1.17832i
$848$	33.9411			1.16554
$849$	25.5000	+	14.7224i	0.875158	+	0.505273i
$850$	2.82843	+	4.89898i	0.0970143	+	0.168034i
$851$	3.00000	+	1.73205i	0.102839	+	0.0593739i
$852$	−8.48528	+	4.89898i	−0.290701	+	0.167836i
$853$	16.9706	−	9.79796i	0.581061	−	0.335476i	−0.180494	−	0.983576i	$-0.557770\pi$
$853$	16.9706	−	9.79796i	0.581061	−	0.335476i	0.761555	+	0.648100i	$0.224436\pi$
$854$	25.4558			0.871081
$855$		0			0
$856$			19.5959i			0.669775i
$857$	19.5000	−	11.2583i	0.666107	−	0.384577i	−0.128493	−	0.991710i	$-0.541014\pi$
$857$	19.5000	−	11.2583i	0.666107	−	0.384577i	0.794600	+	0.607133i	$0.207681\pi$
$858$	60.0000	−	34.6410i	2.04837	−	1.18262i
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	−0.999982	−	0.00607046i	$-0.998068\pi$
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	0.505248	+	0.862974i	$0.331401\pi$
$860$	−25.4558	+	14.6969i	−0.868037	+	0.501161i
$861$	19.0919	+	11.0227i	0.650650	+	0.375653i
$862$	−12.0000			−0.408722
$863$	21.2132			0.722106			0.361053	−	0.932545i	$-0.382417\pi$
$863$	21.2132			0.722106			0.361053	+	0.932545i	$0.382417\pi$
$864$	−25.4558	−	14.6969i	−0.866025	−	0.500000i
$865$		0			0
$866$			44.0908i			1.49827i
$867$			1.73205i			0.0588235i
$868$	−6.00000	−	3.46410i	−0.203653	−	0.117579i
$869$	7.07107	+	12.2474i	0.239870	+	0.415466i
$870$	21.2132	−	36.7423i	0.719195	−	1.24568i
$871$	59.3970	−	34.2929i	2.01259	−	1.16197i
$872$	−20.0000	−	34.6410i	−0.677285	−	1.17309i
$873$		0			0
$874$	−15.0000	−	1.73205i	−0.507383	−	0.0585875i
$875$	−24.0000			−0.811348
$876$	−9.00000	+	5.19615i	−0.304082	+	0.175562i
$877$	−3.53553	−	6.12372i	−0.119386	−	0.206783i	0.800138	−	0.599816i	$-0.204759\pi$
$877$	−3.53553	−	6.12372i	−0.119386	−	0.206783i	−0.919525	+	0.393032i	$0.871426\pi$
$878$	7.00000	−	12.1244i	0.236239	−	0.409177i
$879$	44.5477	−	25.7196i	1.50256	−	0.867502i
$880$	42.4264	+	24.4949i	1.43019	+	0.825723i
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$		0			0
$883$	−27.5000	+	47.6314i	−0.925449	+	1.60292i	−0.134611	+	0.990899i	$0.542978\pi$
$883$	−27.5000	+	47.6314i	−0.925449	+	1.60292i	−0.790838	+	0.612026i	$0.790355\pi$
$884$	22.6274	−	39.1918i	0.761042	−	1.31816i
$885$			7.34847i			0.247016i
$886$	−43.8406			−1.47285
$887$	11.3137	−	19.5959i	0.379877	−	0.657967i	−0.611167	−	0.791502i	$-0.709300\pi$
$887$	11.3137	−	19.5959i	0.379877	−	0.657967i	0.991044	+	0.133535i	$0.0426329\pi$
$888$	6.00000	−	3.46410i	0.201347	−	0.116248i
$889$	6.00000	+	3.46410i	0.201234	+	0.116182i
$890$	−6.00000	−	10.3923i	−0.201120	−	0.348351i
$891$	22.5000	+	38.9711i	0.753778	+	1.30558i
$892$	48.0833			1.60995
$893$	−19.0919	+	25.7196i	−0.638886	+	0.860675i
$894$	−42.0000			−1.40469
$895$	10.6066	+	18.3712i	0.354540	+	0.614081i
$896$	24.0000	−	13.8564i	0.801784	−	0.462910i
$897$	12.0000	−	20.7846i	0.400668	−	0.693978i
$898$	14.8492	−	8.57321i	0.495526	−	0.286092i
$899$	−5.00000	+	8.66025i	−0.166759	+	0.288836i
$900$		0			0
$901$	−33.9411			−1.13074
$902$	31.8198	+	18.3712i	1.05948	+	0.611693i
$903$	12.7279	−	22.0454i	0.423559	−	0.733625i
$904$		−	34.2929i		−	1.14056i
$905$			58.8897i			1.95756i
$906$	−33.0000	−	19.0526i	−1.09635	−	0.632979i
$907$	−13.5000	+	7.79423i	−0.448260	+	0.258803i	−0.707095	−	0.707118i	$-0.749995\pi$
$907$	−13.5000	+	7.79423i	−0.448260	+	0.258803i	0.258835	+	0.965922i	$0.416661\pi$
$908$	3.00000	+	1.73205i	0.0995585	+	0.0574801i
$909$		0			0
$910$	−24.0000	−	41.5692i	−0.795592	−	1.37801i
$911$	24.0416			0.796535			0.398267	−	0.917269i	$-0.369612\pi$
$911$	24.0416			0.796535			0.398267	+	0.917269i	$0.369612\pi$
$912$	−18.0000	+	24.2487i	−0.596040	+	0.802955i
$913$	35.0000			1.15833
$914$	−7.77817	−	13.4722i	−0.257279	−	0.445621i
$915$	27.0000	−	15.5885i	0.892592	−	0.515339i
$916$	−16.9706	−	9.79796i	−0.560723	−	0.323734i
$917$	14.8492	−	8.57321i	0.490365	−	0.283112i
$918$	25.4558	+	14.6969i	0.840168	+	0.485071i
$919$			19.5959i			0.646410i	0.946329	+	0.323205i	$0.104760\pi$
$919$			19.5959i			0.646410i	−0.946329	+	0.323205i	$0.895240\pi$
$920$	16.9706			0.559503
$921$	−4.50000	+	7.79423i	−0.148280	+	0.256829i
$922$	−18.0000	−	10.3923i	−0.592798	−	0.342252i
$923$	16.0000			0.526646
$924$	−42.4264			−1.39573
$925$	0.707107	−	1.22474i	0.0232495	−	0.0402694i
$926$		0			0
$927$		0			0
$928$	−20.0000	−	34.6410i	−0.656532	−	1.13715i
$929$	3.50000	+	6.06218i	0.114831	+	0.198894i	0.917712	−	0.397246i	$-0.130034\pi$
$929$	3.50000	+	6.06218i	0.114831	+	0.198894i	−0.802881	+	0.596139i	$0.796701\pi$
$930$	−8.48528			−0.278243
$931$	−0.500000	+	4.33013i	−0.0163868	+	0.141914i
$932$	2.00000			0.0655122
$933$	10.6066	+	18.3712i	0.347245	+	0.601445i
$934$	9.19239	+	15.9217i	0.300784	+	0.520973i
$935$	−42.4264	−	24.4949i	−1.38749	−	0.801069i
$936$		0			0
$937$	−16.5000	+	28.5788i	−0.539032	+	0.933630i	0.459925	+	0.887958i	$0.347876\pi$
$937$	−16.5000	+	28.5788i	−0.539032	+	0.933630i	−0.998956	+	0.0456722i	$0.985457\pi$
$938$	−42.0000			−1.37135
$939$		−	1.73205i		−	0.0565233i
$940$	18.0000	−	31.1769i	0.587095	−	1.01688i
$941$	−9.89949	+	17.1464i	−0.322714	+	0.558958i	−0.981047	−	0.193769i	$-0.937929\pi$
$941$	−9.89949	+	17.1464i	−0.322714	+	0.558958i	0.658333	+	0.752727i	$0.271262\pi$
$942$	−12.0000			−0.390981
$943$	12.7279			0.414478
$944$	6.00000	+	3.46410i	0.195283	+	0.112747i
$945$	27.0000	−	15.5885i	0.878310	−	0.507093i
$946$	21.2132	−	36.7423i	0.689701	−	1.19460i
$947$	−11.0000	−	19.0526i	−0.357452	−	0.619125i	0.630082	−	0.776528i	$-0.283021\pi$
$947$	−11.0000	−	19.0526i	−0.357452	−	0.619125i	−0.987534	+	0.157403i	$0.949688\pi$
$948$	8.48528	−	4.89898i	0.275589	−	0.159111i
$949$	16.9706			0.550888
$950$	−0.707107	+	6.12372i	−0.0229416	+	0.198680i
$951$			14.6969i			0.476581i
$952$	−24.0000	+	13.8564i	−0.777844	+	0.449089i
$953$	−19.5000	+	11.2583i	−0.631667	+	0.364693i	−0.781397	−	0.624034i	$-0.785493\pi$
$953$	−19.5000	+	11.2583i	−0.631667	+	0.364693i	0.149730	+	0.988727i	$0.452159\pi$
$954$		0			0
$955$	−24.0000	−	41.5692i	−0.776622	−	1.34515i
$956$		0			0
$957$			61.2372i			1.97952i
$958$		−	34.6410i		−	1.11920i
$959$	−36.0624	−	20.8207i	−1.16452	−	0.672334i
$960$	16.9706	−	29.3939i	0.547723	−	0.948683i
$961$	−29.0000			−0.935484
$962$	−11.3137			−0.364769
$963$		0			0
$964$	27.0000	−	15.5885i	0.869611	−	0.502070i
$965$	4.24264	−	7.34847i	0.136575	−	0.236556i
$966$	−12.7279	+	7.34847i	−0.409514	+	0.236433i
$967$	25.4558	−	14.6969i	0.818605	−	0.472622i	−0.0313303	−	0.999509i	$-0.509974\pi$
$967$	25.4558	−	14.6969i	0.818605	−	0.472622i	0.849935	+	0.526887i	$0.176641\pi$
$968$	−39.5980			−1.27273
$969$	18.0000	−	24.2487i	0.578243	−	0.778981i
$970$	66.0000			2.11913
$971$	37.5000	−	21.6506i	1.20343	−	0.694802i	0.242116	−	0.970247i	$-0.422159\pi$
$971$	37.5000	−	21.6506i	1.20343	−	0.694802i	0.961317	+	0.275445i	$0.0888254\pi$
$972$		0			0
$973$	−19.0919	−	11.0227i	−0.612058	−	0.353372i
$974$	25.0000	+	43.3013i	0.801052	+	1.38746i
$975$	−8.48528	−	4.89898i	−0.271746	−	0.156893i
$976$		−	29.3939i		−	0.940875i
$977$		−	32.9090i		−	1.05285i	−0.850221	−	0.526426i	$-0.823532\pi$
$977$		−	32.9090i		−	1.05285i	0.850221	−	0.526426i	$-0.176468\pi$
$978$	−6.36396	−	3.67423i	−0.203497	−	0.117489i
$979$	15.0000	+	8.66025i	0.479402	+	0.276783i
$980$		−	4.89898i		−	0.156492i
$981$		0			0
$982$	24.0416	−	41.6413i	0.767199	−	1.32883i
$983$	4.24264	+	7.34847i	0.135319	+	0.234380i	0.925719	−	0.378211i	$-0.123461\pi$
$983$	4.24264	+	7.34847i	0.135319	+	0.234380i	−0.790400	+	0.612591i	$0.790127\pi$
$984$	12.7279	−	22.0454i	0.405751	−	0.702782i
$985$	−21.0000	−	36.3731i	−0.669116	−	1.15894i
$986$	20.0000	+	34.6410i	0.636930	+	1.10319i
$987$			31.1769i			0.992372i
$988$	45.2548	−	19.5959i	1.43975	−	0.623429i
$989$		−	14.6969i		−	0.467335i
$990$		0			0
$991$	26.8701	+	46.5403i	0.853556	+	1.47840i	0.877979	+	0.478700i	$0.158892\pi$
$991$	26.8701	+	46.5403i	0.853556	+	1.47840i	−0.0244231	+	0.999702i	$0.507775\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$	−4.50000	−	7.79423i	−0.142803	−	0.247342i
$994$	−8.48528	−	4.89898i	−0.269137	−	0.155386i
$995$	60.0000			1.90213
$996$		−	24.2487i		−	0.768350i
$997$	23.3345	+	13.4722i	0.739012	+	0.426669i	0.821710	−	0.569906i	$-0.193020\pi$
$997$	23.3345	+	13.4722i	0.739012	+	0.426669i	−0.0826981	+	0.996575i	$0.526354\pi$
$998$	0.707107	−	1.22474i	0.0223831	−	0.0387686i
$999$		−	7.34847i		−	0.232495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.a.107.2	yes	4
4.3	odd	2		608.2.s.b.335.1		4
8.3	odd	2	inner	152.2.o.a.107.1	yes	4
8.5	even	2		608.2.s.b.335.2		4
19.8	odd	6	inner	152.2.o.a.27.1	✓	4
76.27	even	6		608.2.s.b.559.2		4
152.27	even	6	inner	152.2.o.a.27.2	yes	4
152.141	odd	6		608.2.s.b.559.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.a.27.1	✓	4	19.8	odd	6	inner
152.2.o.a.27.2	yes	4	152.27	even	6	inner
152.2.o.a.107.1	yes	4	8.3	odd	2	inner
152.2.o.a.107.2	yes	4	1.1	even	1	trivial
608.2.s.b.335.1		4	4.3	odd	2
608.2.s.b.335.2		4	8.5	even	2
608.2.s.b.559.1		4	152.141	odd	6
608.2.s.b.559.2		4	76.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-2.12132 + 1.22474i) q^{5} +(-2.12132 - 1.22474i) q^{6} -2.44949i q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-2.12132 + 1.22474i) q^{5} +(-2.12132 - 1.22474i) q^{6} -2.44949i q^{7} -2.82843 q^{8} +(-3.00000 - 1.73205i) q^{10} +5.00000 q^{11} -3.46410i q^{12} +(-2.82843 + 4.89898i) q^{13} +(3.00000 - 1.73205i) q^{14} +(2.12132 - 3.67423i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 + 4.33013i) q^{19} -4.89898i q^{20} +(2.12132 + 3.67423i) q^{21} +(3.53553 + 6.12372i) q^{22} +(2.12132 + 1.22474i) q^{23} +(4.24264 - 2.44949i) q^{24} +(0.500000 - 0.866025i) q^{25} -8.00000 q^{26} -5.19615i q^{27} +(4.24264 + 2.44949i) q^{28} +(3.53553 - 6.12372i) q^{29} +6.00000 q^{30} -1.41421 q^{31} +(2.82843 - 4.89898i) q^{32} +(-7.50000 + 4.33013i) q^{33} +(-2.82843 + 4.89898i) q^{34} +(3.00000 + 5.19615i) q^{35} +1.41421 q^{37} +(-5.65685 + 2.44949i) q^{38} -9.79796i q^{39} +(6.00000 - 3.46410i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-3.00000 + 5.19615i) q^{42} +(-3.00000 - 5.19615i) q^{43} +(-5.00000 + 8.66025i) q^{44} +3.46410i q^{46} +(6.36396 + 3.67423i) q^{47} +(6.00000 + 3.46410i) q^{48} +1.00000 q^{49} +1.41421 q^{50} +(-6.00000 - 3.46410i) q^{51} +(-5.65685 - 9.79796i) q^{52} +(-4.24264 + 7.34847i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-10.6066 + 6.12372i) q^{55} +6.92820i q^{56} +(-3.00000 - 6.92820i) q^{57} +10.0000 q^{58} +(-1.50000 + 0.866025i) q^{59} +(4.24264 + 7.34847i) q^{60} +(6.36396 + 3.67423i) q^{61} +(-1.00000 - 1.73205i) q^{62} +8.00000 q^{64} -13.8564i q^{65} +(-10.6066 - 6.12372i) q^{66} +(-10.5000 - 6.06218i) q^{67} -8.00000 q^{68} -4.24264 q^{69} +(-4.24264 + 7.34847i) q^{70} +(-1.41421 - 2.44949i) q^{71} +(-1.50000 - 2.59808i) q^{73} +(1.00000 + 1.73205i) q^{74} +1.73205i q^{75} +(-7.00000 - 5.19615i) q^{76} -12.2474i q^{77} +(12.0000 - 6.92820i) q^{78} +(1.41421 + 2.44949i) q^{79} +(8.48528 + 4.89898i) q^{80} +(4.50000 + 7.79423i) q^{81} +(6.36396 + 3.67423i) q^{82} +7.00000 q^{83} -8.48528 q^{84} +(-8.48528 - 4.89898i) q^{85} +(4.24264 - 7.34847i) q^{86} +12.2474i q^{87} -14.1421 q^{88} +(3.00000 + 1.73205i) q^{89} +(12.0000 + 6.92820i) q^{91} +(-4.24264 + 2.44949i) q^{92} +(2.12132 - 1.22474i) q^{93} +10.3923i q^{94} +(-4.24264 - 9.79796i) q^{95} +9.79796i q^{96} +(-16.5000 + 9.52628i) q^{97} +(0.707107 + 1.22474i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 4 * q - 6 * q^3 - 4 * q^4	\( 4 q - 6 q^{3} - 4 q^{4} - 12 q^{10} + 20 q^{11} + 12 q^{14} - 8 q^{16} + 8 q^{17} - 2 q^{19} + 2 q^{25} - 32 q^{26} + 24 q^{30} - 30 q^{33} + 12 q^{35} + 24 q^{40} + 18 q^{41} - 12 q^{42} - 12 q^{43} - 20 q^{44} + 24 q^{48} + 4 q^{49} - 24 q^{51} - 12 q^{57} + 40 q^{58} - 6 q^{59} - 4 q^{62} + 32 q^{64} - 42 q^{67} - 32 q^{68} - 6 q^{73} + 4 q^{74} - 28 q^{76} + 48 q^{78} + 18 q^{81} + 28 q^{83} + 12 q^{89} + 48 q^{91} - 66 q^{97}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 + 20 * q^11 + 12 * q^14 - 8 * q^16 + 8 * q^17 - 2 * q^19 + 2 * q^25 - 32 * q^26 + 24 * q^30 - 30 * q^33 + 12 * q^35 + 24 * q^40 + 18 * q^41 - 12 * q^42 - 12 * q^43 - 20 * q^44 + 24 * q^48 + 4 * q^49 - 24 * q^51 - 12 * q^57 + 40 * q^58 - 6 * q^59 - 4 * q^62 + 32 * q^64 - 42 * q^67 - 32 * q^68 - 6 * q^73 + 4 * q^74 - 28 * q^76 + 48 * q^78 + 18 * q^81 + 28 * q^83 + 12 * q^89 + 48 * q^91 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more