LMFDB - Embedded newform 650.2.o.c.549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(399,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("650.399");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.o (of order $6$, degree $2$, not 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.549
Dual form			650.2.o.c.399.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.46410 + 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.46410 + 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.00000 - 3.46410i) q^{11} +(0.866025 + 3.50000i) q^{13} -4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.59808 + 1.50000i) q^{17} -3.00000i q^{18} +(3.46410 + 2.00000i) q^{22} +(-3.46410 + 2.00000i) q^{23} +(-2.50000 - 2.59808i) q^{26} +(3.46410 - 2.00000i) q^{28} +(-0.500000 - 0.866025i) q^{29} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} -3.00000 q^{34} +(1.50000 + 2.59808i) q^{36} +(-2.59808 + 1.50000i) q^{37} +(4.50000 + 7.79423i) q^{41} +(6.92820 + 4.00000i) q^{43} -4.00000 q^{44} +(2.00000 - 3.46410i) q^{46} +8.00000i q^{47} +(4.50000 + 7.79423i) q^{49} +(3.46410 + 1.00000i) q^{52} -9.00000i q^{53} +(-2.00000 + 3.46410i) q^{56} +(0.866025 + 0.500000i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-3.46410 + 2.00000i) q^{62} +(-10.3923 + 6.00000i) q^{63} -1.00000 q^{64} +(-3.46410 + 2.00000i) q^{67} +(2.59808 - 1.50000i) q^{68} +(4.00000 - 6.92820i) q^{71} +(-2.59808 - 1.50000i) q^{72} +11.0000i q^{73} +(1.50000 - 2.59808i) q^{74} -16.0000i q^{77} +4.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} +(-7.79423 - 4.50000i) q^{82} -8.00000 q^{86} +(3.46410 - 2.00000i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(-4.00000 + 13.8564i) q^{91} +4.00000i q^{92} +(-4.00000 - 6.92820i) q^{94} +(1.73205 + 1.00000i) q^{97} +(-7.79423 - 4.50000i) q^{98} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 6 * q^9	$ 4 q + 2 q^{4} - 6 q^{9} - 8 q^{11} - 16 q^{14} - 2 q^{16} - 10 q^{26} - 2 q^{29} + 16 q^{31} - 12 q^{34} + 6 q^{36} + 18 q^{41} - 16 q^{44} + 8 q^{46} + 18 q^{49} - 8 q^{56} - 8 q^{59} - 14 q^{61} - 4 q^{64} + 16 q^{71} + 6 q^{74} + 16 q^{79} - 18 q^{81} - 32 q^{86} - 12 q^{89} - 16 q^{91} - 16 q^{94} + 48 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^9 - 8 * q^11 - 16 * q^14 - 2 * q^16 - 10 * q^26 - 2 * q^29 + 16 * q^31 - 12 * q^34 + 6 * q^36 + 18 * q^41 - 16 * q^44 + 8 * q^46 + 18 * q^49 - 8 * q^56 - 8 * q^59 - 14 * q^61 - 4 * q^64 + 16 * q^71 + 6 * q^74 + 16 * q^79 - 18 * q^81 - 32 * q^86 - 12 * q^89 - 16 * q^91 - 16 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$3$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.981981	−	0.188982i	$-0.0605189\pi$
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.327327	+	0.944911i	$0.393852\pi$
$8$			1.00000i			0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$14$	−4.00000			−1.06904
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	0.780801	−	0.624780i	$-0.214811\pi$
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	−0.150675	+	0.988583i	$0.548145\pi$
$18$		−	3.00000i		−	0.707107i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$		0			0
$22$	3.46410	+	2.00000i	0.738549	+	0.426401i
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	−0.815604	−	0.578610i	$-0.803595\pi$
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	0.0932891	+	0.995639i	$0.470262\pi$
$24$		0			0
$25$		0			0
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$		0			0
$28$	3.46410	−	2.00000i	0.654654	−	0.377964i
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−3.00000			−0.514496
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	−0.698119	−	0.715981i	$-0.745980\pi$
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	0.270998	+	0.962580i	$0.412646\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	6.92820	+	4.00000i	1.05654	+	0.609994i	0.924473	−	0.381246i	$-0.124505\pi$
$43$	6.92820	+	4.00000i	1.05654	+	0.609994i	0.132068	+	0.991241i	$0.457838\pi$
$44$	−4.00000			−0.603023
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$		0			0
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$		0			0
$51$		0			0
$52$	3.46410	+	1.00000i	0.480384	+	0.138675i
$53$		−	9.00000i		−	1.23625i	−0.786082	−	0.618123i	$-0.787894\pi$
$53$		−	9.00000i		−	1.23625i	0.786082	−	0.618123i	$-0.212106\pi$
$54$		0			0
$55$		0			0
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$		0			0
$58$	0.866025	+	0.500000i	0.113715	+	0.0656532i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−3.46410	+	2.00000i	−0.439941	+	0.254000i
$63$	−10.3923	+	6.00000i	−1.30931	+	0.755929i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$	2.59808	−	1.50000i	0.315063	−	0.181902i
$69$		0			0
$70$		0			0
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	−0.524868	−	0.851184i	$-0.675885\pi$
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	0.999581	+	0.0289572i	$0.00921865\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$			11.0000i			1.28745i	0.765256	+	0.643726i	$0.222612\pi$
$73$			11.0000i			1.28745i	−0.765256	+	0.643726i	$0.777388\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$		0			0
$76$		0			0
$77$		−	16.0000i		−	1.82337i
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−7.79423	−	4.50000i	−0.860729	−	0.496942i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$	−8.00000			−0.862662
$87$		0			0
$88$	3.46410	−	2.00000i	0.369274	−	0.213201i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	−4.00000	+	13.8564i	−0.419314	+	1.45255i
$92$			4.00000i			0.417029i
$93$		0			0
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$		0			0
$96$		0			0
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	0.585348	−	0.810782i	$-0.300958\pi$
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	−0.409484	+	0.912317i	$0.634291\pi$
$98$	−7.79423	−	4.50000i	−0.787336	−	0.454569i
$99$	12.0000			1.20605
$100$		0			0
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	0.637678	−	0.770303i	$-0.279895\pi$
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	−0.985941	+	0.167094i	$0.946562\pi$
$102$		0			0
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	−0.323122	−	0.946357i	$-0.604732\pi$
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	0.658009	+	0.753010i	$0.271399\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		0			0
$112$		−	4.00000i		−	0.377964i
$113$	0.866025	+	0.500000i	0.0814688	+	0.0470360i	0.540181	−	0.841549i	$-0.318356\pi$
$113$	0.866025	+	0.500000i	0.0814688	+	0.0470360i	−0.458712	+	0.888585i	$0.651689\pi$
$114$		0			0
$115$		0			0
$116$	−1.00000			−0.0928477
$117$	−10.3923	−	3.00000i	−0.960769	−	0.277350i
$118$		−	4.00000i		−	0.368230i
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		−	7.00000i		−	0.633750i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	6.00000	−	10.3923i	0.534522	−	0.925820i
$127$	6.92820	−	4.00000i	0.614779	−	0.354943i	−0.160055	−	0.987108i	$-0.551167\pi$
$127$	6.92820	−	4.00000i	0.614779	−	0.354943i	0.774833	+	0.632166i	$0.217834\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	20.0000			1.74741			0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000			1.74741			0.873704	+	0.486458i	$0.161711\pi$
$132$		0			0
$133$		0			0
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	0.128618	−	0.991694i	$-0.458946\pi$
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	−0.794524	+	0.607233i	$0.792279\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$		0			0
$142$			8.00000i			0.671345i
$143$	10.3923	−	10.0000i	0.869048	−	0.836242i
$144$	3.00000			0.250000
$145$		0			0
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$		0			0
$148$			3.00000i			0.246598i
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$		0			0
$153$	−7.79423	+	4.50000i	−0.630126	+	0.363803i
$154$	8.00000	+	13.8564i	0.644658	+	1.11658i
$155$		0			0
$156$		0			0
$157$		−	11.0000i		−	0.877896i	−0.898513	−	0.438948i	$-0.855351\pi$
$157$		−	11.0000i		−	0.877896i	0.898513	−	0.438948i	$-0.144649\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$		0			0
$160$		0			0
$161$	−16.0000			−1.26098
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	0.203497	−	0.979076i	$-0.434769\pi$
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	−0.746156	+	0.665771i	$0.768103\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$		0			0
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	−0.844931	−	0.534875i	$-0.820359\pi$
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	0.0407502	+	0.999169i	$0.487025\pi$
$168$		0			0
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$		0			0
$171$		0			0
$172$	6.92820	−	4.00000i	0.528271	−	0.304997i
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.0375896	−	0.999293i	$-0.511968\pi$
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.884208	+	0.467093i	$0.845301\pi$
$174$		0			0
$175$		0			0
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	5.19615	+	3.00000i	0.389468	+	0.224860i
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$		0			0
$181$	−21.0000			−1.56092			−0.780459	−	0.625207i	$-0.785014\pi$
$181$	−21.0000			−1.56092			−0.780459	+	0.625207i	$0.785014\pi$
$182$	−3.46410	−	14.0000i	−0.256776	−	1.03775i
$183$		0			0
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$		0			0
$186$		0			0
$187$		−	12.0000i		−	0.877527i
$188$	6.92820	+	4.00000i	0.505291	+	0.291730i
$189$		0			0
$190$		0			0
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$		0			0
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	−0.116289	−	0.993215i	$-0.537100\pi$
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	0.802005	+	0.597317i	$0.203766\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	9.00000			0.642857
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$	−10.3923	+	6.00000i	−0.738549	+	0.426401i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$		0			0
$202$	6.06218	+	3.50000i	0.426533	+	0.246259i
$203$		−	4.00000i		−	0.280745i
$204$		0			0
$205$		0			0
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$		−	12.0000i		−	0.834058i
$208$	2.59808	−	2.50000i	0.180144	−	0.173344i
$209$		0			0
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	−7.79423	−	4.50000i	−0.535310	−	0.309061i
$213$		0			0
$214$	−2.00000	+	3.46410i	−0.136717	+	0.236801i
$215$		0			0
$216$		0			0
$217$	13.8564	+	8.00000i	0.940634	+	0.543075i
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$		0			0
$220$		0			0
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$		0			0
$223$	10.3923	−	6.00000i	0.695920	−	0.401790i	−0.109906	−	0.993942i	$-0.535055\pi$
$223$	10.3923	−	6.00000i	0.695920	−	0.401790i	0.805826	+	0.592152i	$0.201722\pi$
$224$	2.00000	+	3.46410i	0.133631	+	0.231455i
$225$		0			0
$226$	−1.00000			−0.0665190
$227$	20.7846	+	12.0000i	1.37952	+	0.796468i	0.992102	−	0.125435i	$-0.0400326\pi$
$227$	20.7846	+	12.0000i	1.37952	+	0.796468i	0.387421	+	0.921903i	$0.373366\pi$
$228$		0			0
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$		0			0
$231$		0			0
$232$	0.866025	−	0.500000i	0.0568574	−	0.0328266i
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	10.5000	−	2.59808i	0.686406	−	0.169842i
$235$		0			0
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$	−10.3923	−	6.00000i	−0.673633	−	0.388922i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−1.50000	+	2.59808i	−0.0966235	+	0.167357i	−0.910285	−	0.413982i	$-0.864138\pi$
$241$	−1.50000	+	2.59808i	−0.0966235	+	0.167357i	0.813662	+	0.581339i	$0.197471\pi$
$242$		−	5.00000i		−	0.321412i
$243$		0			0
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$		0			0
$246$		0			0
$247$		0			0
$248$			4.00000i			0.254000i
$249$		0			0
$250$		0			0
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$			12.0000i			0.755929i
$253$	13.8564	+	8.00000i	0.871145	+	0.502956i
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.9904	+	7.50000i	−0.810318	+	0.467837i	−0.847066	−	0.531487i	$-0.821633\pi$
$257$	−12.9904	+	7.50000i	−0.810318	+	0.467837i	0.0367485	+	0.999325i	$0.488300\pi$
$258$		0			0
$259$	−12.0000			−0.745644
$260$		0			0
$261$	3.00000			0.185695
$262$	−17.3205	+	10.0000i	−1.07006	+	0.617802i
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.977147	−	0.212565i	$-0.931818\pi$
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.304487	+	0.952517i	$0.598485\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$			4.00000i			0.244339i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$		−	3.00000i		−	0.181902i
$273$		0			0
$274$	9.00000			0.543710
$275$		0			0
$276$		0			0
$277$	−7.79423	−	4.50000i	−0.468310	−	0.270379i	0.247222	−	0.968959i	$-0.420482\pi$
$277$	−7.79423	−	4.50000i	−0.468310	−	0.270379i	−0.715532	+	0.698580i	$0.753816\pi$
$278$			16.0000i			0.959616i
$279$	−6.00000	+	10.3923i	−0.359211	+	0.622171i
$280$		0			0
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$		0			0
$283$	24.2487	−	14.0000i	1.44144	−	0.832214i	0.443491	−	0.896279i	$-0.353740\pi$
$283$	24.2487	−	14.0000i	1.44144	−	0.832214i	0.997946	+	0.0640654i	$0.0204066\pi$
$284$	−4.00000	−	6.92820i	−0.237356	−	0.411113i
$285$		0			0
$286$	−4.00000	+	13.8564i	−0.236525	+	0.819346i
$287$			36.0000i			2.12501i
$288$	−2.59808	+	1.50000i	−0.153093	+	0.0883883i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$		0			0
$292$	9.52628	+	5.50000i	0.557483	+	0.321863i
$293$	4.33013	+	2.50000i	0.252969	+	0.146052i	0.621123	−	0.783713i	$-0.286677\pi$
$293$	4.33013	+	2.50000i	0.252969	+	0.146052i	−0.368154	+	0.929765i	$0.620010\pi$
$294$		0			0
$295$		0			0
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$		0			0
$298$			15.0000i			0.868927i
$299$	−10.0000	−	10.3923i	−0.578315	−	0.601003i
$300$		0			0
$301$	16.0000	+	27.7128i	0.922225	+	1.59734i
$302$	−10.3923	+	6.00000i	−0.598010	+	0.345261i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	4.50000	−	7.79423i	0.257248	−	0.445566i
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$	−13.8564	−	8.00000i	−0.789542	−	0.455842i
$309$		0			0
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$		−	22.0000i		−	1.24351i	−0.783210	−	0.621757i	$-0.786419\pi$
$313$		−	22.0000i		−	1.24351i	0.783210	−	0.621757i	$-0.213581\pi$
$314$	5.50000	+	9.52628i	0.310383	+	0.537599i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$		−	3.00000i		−	0.168497i	−0.996445	−	0.0842484i	$-0.973151\pi$
$317$		−	3.00000i		−	0.168497i	0.996445	−	0.0842484i	$-0.0268489\pi$
$318$		0			0
$319$	−2.00000	+	3.46410i	−0.111979	+	0.193952i
$320$		0			0
$321$		0			0
$322$	13.8564	−	8.00000i	0.772187	−	0.445823i
$323$		0			0
$324$	−9.00000			−0.500000
$325$		0			0
$326$	8.00000			0.443079
$327$		0			0
$328$	−7.79423	+	4.50000i	−0.430364	+	0.248471i
$329$	−16.0000	+	27.7128i	−0.882109	+	1.52786i
$330$		0			0
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$		0			0
$333$		−	9.00000i		−	0.493197i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$		0			0
$336$		0			0
$337$		−	23.0000i		−	1.25289i	−0.779466	−	0.626445i	$-0.784509\pi$
$337$		−	23.0000i		−	1.25289i	0.779466	−	0.626445i	$-0.215491\pi$
$338$	6.92820	−	11.0000i	0.376845	−	0.598321i
$339$		0			0
$340$		0			0
$341$	−8.00000	−	13.8564i	−0.433224	−	0.750366i
$342$		0			0
$343$			8.00000i			0.431959i
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	14.0000			0.752645
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$		0			0
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	0.838019	−	0.545640i	$-0.183714\pi$
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	−0.891548	+	0.452926i	$0.850380\pi$
$350$		0			0
$351$		0			0
$352$		−	4.00000i		−	0.213201i
$353$	6.06218	−	3.50000i	0.322657	−	0.186286i	−0.329919	−	0.944009i	$-0.607021\pi$
$353$	6.06218	−	3.50000i	0.322657	−	0.186286i	0.652576	+	0.757723i	$0.273688\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	20.7846	+	12.0000i	1.09850	+	0.634220i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	18.1865	−	10.5000i	0.955863	−	0.551868i
$363$		0			0
$364$	10.0000	+	10.3923i	0.524142	+	0.544705i
$365$		0			0
$366$		0			0
$367$	24.2487	−	14.0000i	1.26577	−	0.730794i	0.291587	−	0.956544i	$-0.405817\pi$
$367$	24.2487	−	14.0000i	1.26577	−	0.730794i	0.974185	+	0.225750i	$0.0724833\pi$
$368$	3.46410	+	2.00000i	0.180579	+	0.104257i
$369$	−27.0000			−1.40556
$370$		0			0
$371$	18.0000	−	31.1769i	0.934513	−	1.61862i
$372$		0			0
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	0.762299	−	0.647225i	$-0.224071\pi$
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	−0.179364	+	0.983783i	$0.557404\pi$
$374$	6.00000	+	10.3923i	0.310253	+	0.537373i
$375$		0			0
$376$	−8.00000			−0.412568
$377$	2.59808	−	2.50000i	0.133808	−	0.128757i
$378$		0			0
$379$	−4.00000	−	6.92820i	−0.205466	−	0.355878i	0.744815	−	0.667271i	$-0.232538\pi$
$379$	−4.00000	−	6.92820i	−0.205466	−	0.355878i	−0.950281	+	0.311393i	$0.899204\pi$
$380$		0			0
$381$		0			0
$382$			20.0000i			1.02329i
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$		0			0
$385$		0			0
$386$	−5.50000	+	9.52628i	−0.279943	+	0.484875i
$387$	−20.7846	+	12.0000i	−1.05654	+	0.609994i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	9.00000			0.456318			0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000			0.456318			0.228159	+	0.973624i	$0.426729\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	−7.79423	+	4.50000i	−0.393668	+	0.227284i
$393$		0			0
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		0			0
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	12.1244	+	7.00000i	0.608504	+	0.351320i	0.772380	−	0.635161i	$-0.219066\pi$
$397$	12.1244	+	7.00000i	0.608504	+	0.351320i	−0.163876	+	0.986481i	$0.552400\pi$
$398$		−	4.00000i		−	0.200502i
$399$		0			0
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	3.46410	+	14.0000i	0.172559	+	0.697390i
$404$	−7.00000			−0.348263
$405$		0			0
$406$	2.00000	+	3.46410i	0.0992583	+	0.171920i
$407$	10.3923	+	6.00000i	0.515127	+	0.297409i
$408$		0			0
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	0.939490	−	0.342578i	$-0.111300\pi$
$410$		0			0
$411$		0			0
$412$	−6.92820	−	4.00000i	−0.341328	−	0.197066i
$413$	−13.8564	+	8.00000i	−0.681829	+	0.393654i
$414$	6.00000	+	10.3923i	0.294884	+	0.510754i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$		0			0
$418$		0			0
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$		0			0
$421$	−5.00000			−0.243685			−0.121843	−	0.992549i	$-0.538880\pi$
$421$	−5.00000			−0.243685			−0.121843	+	0.992549i	$0.538880\pi$
$422$	17.3205	+	10.0000i	0.843149	+	0.486792i
$423$	−20.7846	−	12.0000i	−1.01058	−	0.583460i
$424$	9.00000			0.437079
$425$		0			0
$426$		0			0
$427$	−24.2487	+	14.0000i	−1.17348	+	0.677507i
$428$		−	4.00000i		−	0.193347i
$429$		0			0
$430$		0			0
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	0.995706	+	0.0925683i	$0.0295076\pi$
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	−0.417687	+	0.908591i	$0.637159\pi$
$432$		0			0
$433$	4.33013	+	2.50000i	0.208093	+	0.120142i	0.600425	−	0.799681i	$-0.294998\pi$
$433$	4.33013	+	2.50000i	0.208093	+	0.120142i	−0.392332	+	0.919824i	$0.628332\pi$
$434$	−16.0000			−0.768025
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	−27.0000			−1.28571
$442$	−2.59808	−	10.5000i	−0.123578	−	0.499434i
$443$			24.0000i			1.14027i	0.821549	+	0.570137i	$0.193110\pi$
$443$			24.0000i			1.14027i	−0.821549	+	0.570137i	$0.806890\pi$
$444$		0			0
$445$		0			0
$446$	−6.00000	+	10.3923i	−0.284108	+	0.492090i
$447$		0			0
$448$	−3.46410	−	2.00000i	−0.163663	−	0.0944911i
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	−0.115833	−	0.993269i	$-0.536954\pi$
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	0.918112	−	0.396320i	$-0.129713\pi$
$450$		0			0
$451$	18.0000	−	31.1769i	0.847587	−	1.46806i
$452$	0.866025	−	0.500000i	0.0407344	−	0.0235180i
$453$		0			0
$454$	−24.0000			−1.12638
$455$		0			0
$456$		0			0
$457$	−26.8468	+	15.5000i	−1.25584	+	0.725059i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$	−26.8468	+	15.5000i	−1.25584	+	0.725059i	−0.283577	+	0.958950i	$0.591521\pi$
$458$	5.19615	−	3.00000i	0.242800	−	0.140181i
$459$		0			0
$460$		0			0
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	−0.169904	−	0.985461i	$-0.554346\pi$
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	0.938386	−	0.345589i	$-0.112321\pi$
$462$		0			0
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$		−	20.0000i		−	0.925490i	−0.886492	−	0.462745i	$-0.846865\pi$
$467$		−	20.0000i		−	0.925490i	0.886492	−	0.462745i	$-0.153135\pi$
$468$	−7.79423	+	7.50000i	−0.360288	+	0.346688i
$469$	−16.0000			−0.738811
$470$		0			0
$471$		0			0
$472$	−3.46410	−	2.00000i	−0.159448	−	0.0920575i
$473$		−	32.0000i		−	1.47136i
$474$		0			0
$475$		0			0
$476$	12.0000			0.550019
$477$	23.3827	+	13.5000i	1.07062	+	0.618123i
$478$	−10.3923	+	6.00000i	−0.475333	+	0.274434i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−7.50000	−	7.79423i	−0.341971	−	0.355386i
$482$		−	3.00000i		−	0.136646i
$483$		0			0
$484$	2.50000	+	4.33013i	0.113636	+	0.196824i
$485$		0			0
$486$		0			0
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$	−6.06218	−	3.50000i	−0.274422	−	0.158438i
$489$		0			0
$490$		0			0
$491$	4.00000	+	6.92820i	0.180517	+	0.312665i	0.942057	−	0.335453i	$-0.108889\pi$
$491$	4.00000	+	6.92820i	0.180517	+	0.312665i	−0.761539	+	0.648119i	$0.775556\pi$
$492$		0			0
$493$		−	3.00000i		−	0.135113i
$494$		0			0
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	27.7128	−	16.0000i	1.24309	−	0.717698i
$498$		0			0
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$		0			0
$502$			12.0000i			0.535586i
$503$	−13.8564	−	8.00000i	−0.617827	−	0.356702i	0.158196	−	0.987408i	$-0.449432\pi$
$503$	−13.8564	−	8.00000i	−0.617827	−	0.356702i	−0.776022	+	0.630705i	$0.782766\pi$
$504$	−6.00000	−	10.3923i	−0.267261	−	0.462910i
$505$		0			0
$506$	−16.0000			−0.711287
$507$		0			0
$508$		−	8.00000i		−	0.354943i
$509$	21.5000	+	37.2391i	0.952971	+	1.65059i	0.738945	+	0.673766i	$0.235324\pi$
$509$	21.5000	+	37.2391i	0.952971	+	1.65059i	0.214026	+	0.976828i	$0.431342\pi$
$510$		0			0
$511$	−22.0000	+	38.1051i	−0.973223	+	1.68567i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	7.50000	−	12.9904i	0.330811	−	0.572981i
$515$		0			0
$516$		0			0
$517$	27.7128	−	16.0000i	1.21881	−	0.703679i
$518$	10.3923	−	6.00000i	0.456612	−	0.263625i
$519$		0			0
$520$		0			0
$521$	39.0000			1.70862			0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000			1.70862			0.854311	+	0.519763i	$0.173980\pi$
$522$	−2.59808	+	1.50000i	−0.113715	+	0.0656532i
$523$	31.1769	−	18.0000i	1.36327	−	0.787085i	0.373213	−	0.927746i	$-0.378256\pi$
$523$	31.1769	−	18.0000i	1.36327	−	0.787085i	0.990058	+	0.140660i	$0.0449226\pi$
$524$	10.0000	−	17.3205i	0.436852	−	0.756650i
$525$		0			0
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	10.3923	+	6.00000i	0.452696	+	0.261364i
$528$		0			0
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$		0			0
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$		0			0
$533$	−23.3827	+	22.5000i	−1.01282	+	0.974583i
$534$		0			0
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$		−	18.0000i		−	0.776035i
$539$	18.0000	−	31.1769i	0.775315	−	1.34288i
$540$		0			0
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$	−17.3205	−	10.0000i	−0.743980	−	0.429537i
$543$		0			0
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$		0			0
$546$		0			0
$547$		−	16.0000i		−	0.684111i	−0.939680	−	0.342055i	$-0.888877\pi$
$547$		−	16.0000i		−	0.684111i	0.939680	−	0.342055i	$-0.111123\pi$
$548$	−7.79423	+	4.50000i	−0.332953	+	0.192230i
$549$	−10.5000	−	18.1865i	−0.448129	−	0.776182i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	13.8564	+	8.00000i	0.589234	+	0.340195i
$554$	9.00000			0.382373
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−33.7750	+	19.5000i	−1.43109	+	0.826242i	−0.997204	−	0.0747252i	$-0.976192\pi$
$557$	−33.7750	+	19.5000i	−1.43109	+	0.826242i	−0.433888	+	0.900967i	$0.642859\pi$
$558$		−	12.0000i		−	0.508001i
$559$	−8.00000	+	27.7128i	−0.338364	+	1.17213i
$560$		0			0
$561$		0			0
$562$	4.33013	−	2.50000i	0.182655	−	0.105456i
$563$	3.46410	+	2.00000i	0.145994	+	0.0842900i	0.571218	−	0.820798i	$-0.306471\pi$
$563$	3.46410	+	2.00000i	0.145994	+	0.0842900i	−0.425223	+	0.905088i	$0.639804\pi$
$564$		0			0
$565$		0			0
$566$	−14.0000	+	24.2487i	−0.588464	+	1.01925i
$567$		−	36.0000i		−	1.51186i
$568$	6.92820	+	4.00000i	0.290701	+	0.167836i
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	−3.46410	−	14.0000i	−0.144841	−	0.585369i
$573$		0			0
$574$	−18.0000	−	31.1769i	−0.751305	−	1.30130i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$		−	39.0000i		−	1.62359i	−0.583942	−	0.811796i	$-0.698490\pi$
$577$		−	39.0000i		−	1.62359i	0.583942	−	0.811796i	$-0.301510\pi$
$578$	6.92820	+	4.00000i	0.288175	+	0.166378i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−31.1769	+	18.0000i	−1.29122	+	0.745484i
$584$	−11.0000			−0.455183
$585$		0			0
$586$	−5.00000			−0.206548
$587$	13.8564	−	8.00000i	0.571915	−	0.330195i	−0.185999	−	0.982550i	$-0.559552\pi$
$587$	13.8564	−	8.00000i	0.571915	−	0.330195i	0.757914	+	0.652355i	$0.226219\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	2.59808	+	1.50000i	0.106780	+	0.0616496i
$593$		−	1.00000i		−	0.0410651i	−0.999789	−	0.0205325i	$-0.993464\pi$
$593$		−	1.00000i		−	0.0410651i	0.999789	−	0.0205325i	$-0.00653617\pi$
$594$		0			0
$595$		0			0
$596$	−7.50000	−	12.9904i	−0.307212	−	0.532107i
$597$		0			0
$598$	13.8564	+	4.00000i	0.566631	+	0.163572i
$599$	44.0000			1.79779			0.898896	−	0.438163i	$-0.144371\pi$
$599$	44.0000			1.79779			0.898896	+	0.438163i	$0.144371\pi$
$600$		0			0
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$	−27.7128	−	16.0000i	−1.12949	−	0.652111i
$603$		−	12.0000i		−	0.488678i
$604$	6.00000	−	10.3923i	0.244137	−	0.422857i
$605$		0			0
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−28.0000	+	6.92820i	−1.13276	+	0.280285i
$612$			9.00000i			0.363803i
$613$	9.52628	−	5.50000i	0.384763	−	0.222143i	−0.295126	−	0.955458i	$-0.595362\pi$
$613$	9.52628	−	5.50000i	0.384763	−	0.222143i	0.679888	+	0.733316i	$0.262028\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$	16.0000			0.644658
$617$	−25.1147	−	14.5000i	−1.01108	−	0.583748i	−0.0995732	−	0.995030i	$-0.531748\pi$
$617$	−25.1147	−	14.5000i	−1.01108	−	0.583748i	−0.911508	+	0.411282i	$0.865081\pi$
$618$		0			0
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$		0			0
$622$	20.7846	−	12.0000i	0.833387	−	0.481156i
$623$		−	24.0000i		−	0.961540i
$624$		0			0
$625$		0			0
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$		0			0
$628$	−9.52628	−	5.50000i	−0.380140	−	0.219474i
$629$	−9.00000			−0.358854
$630$		0			0
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	−0.775356	−	0.631524i	$-0.782430\pi$
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	0.934594	+	0.355716i	$0.115763\pi$
$632$			4.00000i			0.159111i
$633$		0			0
$634$	1.50000	+	2.59808i	0.0595726	+	0.103183i
$635$		0			0
$636$		0			0
$637$	−23.3827	+	22.5000i	−0.926456	+	0.891482i
$638$		−	4.00000i		−	0.158362i
$639$	12.0000	+	20.7846i	0.474713	+	0.822226i
$640$		0			0
$641$	−9.50000	+	16.4545i	−0.375227	+	0.649913i	−0.990361	−	0.138510i	$-0.955769\pi$
$641$	−9.50000	+	16.4545i	−0.375227	+	0.649913i	0.615134	+	0.788423i	$0.289102\pi$
$642$		0			0
$643$	−38.1051	−	22.0000i	−1.50272	−	0.867595i	−0.999995	−	0.00314839i	$-0.998998\pi$
$643$	−38.1051	−	22.0000i	−1.50272	−	0.867595i	−0.502724	−	0.864447i	$-0.667669\pi$
$644$	−8.00000	+	13.8564i	−0.315244	+	0.546019i
$645$		0			0
$646$		0			0
$647$	−24.2487	+	14.0000i	−0.953315	+	0.550397i	−0.894109	−	0.447849i	$-0.852190\pi$
$647$	−24.2487	+	14.0000i	−0.953315	+	0.550397i	−0.0592060	+	0.998246i	$0.518857\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$	16.0000			0.628055
$650$		0			0
$651$		0			0
$652$	−6.92820	+	4.00000i	−0.271329	+	0.156652i
$653$	−15.5885	+	9.00000i	−0.610023	+	0.352197i	−0.772975	−	0.634437i	$-0.781232\pi$
$653$	−15.5885	+	9.00000i	−0.610023	+	0.352197i	0.162951	+	0.986634i	$0.447899\pi$
$654$		0			0
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	−28.5788	−	16.5000i	−1.11497	−	0.643726i
$658$		−	32.0000i		−	1.24749i
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.160108	−	0.987099i	$-0.448816\pi$
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.774799	−	0.632207i	$-0.217851\pi$
$660$		0			0
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.739014	+	0.673690i	$0.235292\pi$
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.213925	+	0.976850i	$0.431375\pi$
$662$		−	8.00000i		−	0.310929i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	4.50000	+	7.79423i	0.174371	+	0.302020i
$667$	3.46410	+	2.00000i	0.134131	+	0.0774403i
$668$			12.0000i			0.464294i
$669$		0			0
$670$		0			0
$671$	28.0000			1.08093
$672$		0			0
$673$	−25.1147	+	14.5000i	−0.968102	+	0.558934i	−0.898657	−	0.438652i	$-0.855456\pi$
$673$	−25.1147	+	14.5000i	−0.968102	+	0.558934i	−0.0694449	+	0.997586i	$0.522123\pi$
$674$	11.5000	+	19.9186i	0.442963	+	0.767235i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$		−	6.00000i		−	0.230599i	−0.993331	−	0.115299i	$-0.963217\pi$
$677$		−	6.00000i		−	0.230599i	0.993331	−	0.115299i	$-0.0367827\pi$
$678$		0			0
$679$	4.00000	+	6.92820i	0.153506	+	0.265880i
$680$		0			0
$681$		0			0
$682$	13.8564	+	8.00000i	0.530589	+	0.306336i
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.998916	−	0.0465592i	$-0.0148256\pi$
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.459136	+	0.888366i	$0.348159\pi$
$684$		0			0
$685$		0			0
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$		0			0
$688$		−	8.00000i		−	0.304997i
$689$	31.5000	−	7.79423i	1.20005	−	0.296936i
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$	−12.1244	+	7.00000i	−0.460899	+	0.266100i
$693$	41.5692	+	24.0000i	1.57908	+	0.911685i
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$			27.0000i			1.02270i
$698$	1.73205	+	1.00000i	0.0655591	+	0.0378506i
$699$		0			0
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$		0			0
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$		0			0
$706$	−3.50000	+	6.06218i	−0.131724	+	0.228153i
$707$		−	28.0000i		−	1.05305i
$708$		0			0
$709$	−6.50000	+	11.2583i	−0.244113	+	0.422815i	−0.961882	−	0.273466i	$-0.911830\pi$
$709$	−6.50000	+	11.2583i	−0.244113	+	0.422815i	0.717769	+	0.696281i	$0.245163\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	5.19615	−	3.00000i	0.194734	−	0.112430i
$713$	−13.8564	+	8.00000i	−0.518927	+	0.299602i
$714$		0			0
$715$		0			0
$716$	−24.0000			−0.896922
$717$		0			0
$718$	20.7846	−	12.0000i	0.775675	−	0.447836i
$719$	−14.0000	+	24.2487i	−0.522112	+	0.904324i	0.477557	+	0.878601i	$0.341522\pi$
$719$	−14.0000	+	24.2487i	−0.522112	+	0.904324i	−0.999669	+	0.0257237i	$0.991811\pi$
$720$		0			0
$721$	16.0000	−	27.7128i	0.595871	−	1.03208i
$722$	−16.4545	−	9.50000i	−0.612372	−	0.353553i
$723$		0			0
$724$	−10.5000	+	18.1865i	−0.390229	+	0.675897i
$725$		0			0
$726$		0			0
$727$		−	28.0000i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$727$		−	28.0000i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$728$	−13.8564	−	4.00000i	−0.513553	−	0.148250i
$729$	27.0000			1.00000
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$		−	1.00000i		−	0.0369358i	−0.999829	−	0.0184679i	$-0.994121\pi$
$733$		−	1.00000i		−	0.0369358i	0.999829	−	0.0184679i	$-0.00587886\pi$
$734$	−14.0000	+	24.2487i	−0.516749	+	0.895036i
$735$		0			0
$736$	−4.00000			−0.147442
$737$	13.8564	+	8.00000i	0.510407	+	0.294684i
$738$	23.3827	−	13.5000i	0.860729	−	0.496942i
$739$	−12.0000	−	20.7846i	−0.441427	−	0.764574i	0.556369	−	0.830936i	$-0.312194\pi$
$739$	−12.0000	−	20.7846i	−0.441427	−	0.764574i	−0.997796	+	0.0663614i	$0.978861\pi$
$740$		0			0
$741$		0			0
$742$			36.0000i			1.32160i
$743$	−6.92820	+	4.00000i	−0.254171	+	0.146746i	−0.621673	−	0.783277i	$-0.713547\pi$
$743$	−6.92820	+	4.00000i	−0.254171	+	0.146746i	0.367502	+	0.930023i	$0.380213\pi$
$744$		0			0
$745$		0			0
$746$	−13.0000			−0.475964
$747$		0			0
$748$	−10.3923	−	6.00000i	−0.379980	−	0.219382i
$749$	16.0000			0.584627
$750$		0			0
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	0.559640	−	0.828736i	$-0.310939\pi$
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	−0.997526	+	0.0702946i	$0.977606\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$		0			0
$754$	−1.00000	+	3.46410i	−0.0364179	+	0.126155i
$755$		0			0
$756$		0			0
$757$	−5.19615	+	3.00000i	−0.188857	+	0.109037i	−0.591448	−	0.806343i	$-0.701443\pi$
$757$	−5.19615	+	3.00000i	−0.188857	+	0.109037i	0.402590	+	0.915380i	$0.368110\pi$
$758$	6.92820	+	4.00000i	0.251644	+	0.145287i
$759$		0			0
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$		0			0
$763$	6.92820	+	4.00000i	0.250818	+	0.144810i
$764$	−10.0000	−	17.3205i	−0.361787	−	0.626634i
$765$		0			0
$766$		0			0
$767$	−13.8564	−	4.00000i	−0.500326	−	0.144432i
$768$		0			0
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	−0.998852	−	0.0479061i	$-0.984745\pi$
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	0.457938	−	0.888984i	$-0.348588\pi$
$770$		0			0
$771$		0			0
$772$		−	11.0000i		−	0.395899i
$773$	−32.9090	−	19.0000i	−1.18365	−	0.683383i	−0.226796	−	0.973942i	$-0.572825\pi$
$773$	−32.9090	−	19.0000i	−1.18365	−	0.683383i	−0.956857	+	0.290560i	$0.906159\pi$
$774$	12.0000	−	20.7846i	0.431331	−	0.747087i
$775$		0			0
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	−7.79423	+	4.50000i	−0.279437	+	0.161333i
$779$		0			0
$780$		0			0
$781$	−32.0000			−1.14505
$782$	10.3923	−	6.00000i	0.371628	−	0.214560i
$783$		0			0
$784$	4.50000	−	7.79423i	0.160714	−	0.278365i
$785$		0			0
$786$		0			0
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	0.436987	−	0.899468i	$-0.356046\pi$
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	−0.560469	+	0.828176i	$0.689379\pi$
$788$			6.00000i			0.213741i
$789$		0			0
$790$		0			0
$791$	2.00000	+	3.46410i	0.0711118	+	0.123169i
$792$			12.0000i			0.426401i
$793$	−24.2487	−	7.00000i	−0.861097	−	0.248577i
$794$	−14.0000			−0.496841
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	25.9808	+	15.0000i	0.920286	+	0.531327i	0.883726	−	0.468004i	$-0.155027\pi$
$797$	25.9808	+	15.0000i	0.920286	+	0.531327i	0.0365596	+	0.999331i	$0.488360\pi$
$798$		0			0
$799$	−12.0000	+	20.7846i	−0.424529	+	0.735307i
$800$		0			0
$801$	18.0000			0.635999
$802$	2.59808	+	1.50000i	0.0917413	+	0.0529668i
$803$	38.1051	−	22.0000i	1.34470	−	0.776363i
$804$		0			0
$805$		0			0
$806$	−10.0000	−	10.3923i	−0.352235	−	0.366053i
$807$		0			0
$808$	6.06218	−	3.50000i	0.213267	−	0.123130i
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−3.46410	−	2.00000i	−0.121566	−	0.0701862i
$813$		0			0
$814$	−12.0000			−0.420600
$815$		0			0
$816$		0			0
$817$		0			0
$818$			31.0000i			1.08389i
$819$	−30.0000	−	31.1769i	−1.04828	−	1.08941i
$820$		0			0
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	−0.979795	−	0.200002i	$-0.935905\pi$
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	0.316691	−	0.948529i	$-0.397428\pi$
$822$		0			0
$823$	−10.3923	−	6.00000i	−0.362253	−	0.209147i	0.307816	−	0.951446i	$-0.400402\pi$
$823$	−10.3923	−	6.00000i	−0.362253	−	0.209147i	−0.670069	+	0.742299i	$0.733735\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$	8.00000	−	13.8564i	0.278356	−	0.482126i
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	−10.3923	−	6.00000i	−0.361158	−	0.208514i
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	0.920383	−	0.391018i	$-0.127877\pi$
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$		0			0
$832$	−0.866025	−	3.50000i	−0.0300240	−	0.121341i
$833$			27.0000i			0.935495i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−10.3923	−	6.00000i	−0.358996	−	0.207267i
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	0.281205	+	0.959648i	$0.409266\pi$
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	−0.971682	+	0.236293i	$0.924067\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	4.33013	−	2.50000i	0.149226	−	0.0861557i
$843$		0			0
$844$	−20.0000			−0.688428
$845$		0			0
$846$	24.0000			0.825137
$847$	−17.3205	+	10.0000i	−0.595140	+	0.343604i
$848$	−7.79423	+	4.50000i	−0.267655	+	0.154531i
$849$		0			0
$850$		0			0
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$			7.00000i			0.239675i	0.992793	+	0.119838i	$0.0382374\pi$
$853$			7.00000i			0.239675i	−0.992793	+	0.119838i	$0.961763\pi$
$854$	14.0000	−	24.2487i	0.479070	−	0.829774i
$855$		0			0
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$			17.0000i			0.580709i	0.956919	+	0.290354i	$0.0937732\pi$
$857$			17.0000i			0.580709i	−0.956919	+	0.290354i	$0.906227\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$		0			0
$861$		0			0
$862$	−20.7846	−	12.0000i	−0.707927	−	0.408722i
$863$			52.0000i			1.77010i	0.465495	+	0.885050i	$0.345876\pi$
$863$			52.0000i			1.77010i	−0.465495	+	0.885050i	$0.654124\pi$
$864$		0			0
$865$		0			0
$866$	−5.00000			−0.169907
$867$		0			0
$868$	13.8564	−	8.00000i	0.470317	−	0.271538i
$869$	−8.00000	−	13.8564i	−0.271381	−	0.470046i
$870$		0			0
$871$	−10.0000	−	10.3923i	−0.338837	−	0.352130i
$872$			2.00000i			0.0677285i
$873$	−5.19615	+	3.00000i	−0.175863	+	0.101535i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.9904	+	7.50000i	0.438654	+	0.253257i	0.703027	−	0.711164i	$-0.251832\pi$
$877$	12.9904	+	7.50000i	0.438654	+	0.253257i	−0.264373	+	0.964421i	$0.585165\pi$
$878$	−6.92820	−	4.00000i	−0.233816	−	0.134993i
$879$		0			0
$880$		0			0
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	0.931819	−	0.362923i	$-0.118221\pi$
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	−0.780210	+	0.625517i	$0.784888\pi$
$882$	23.3827	−	13.5000i	0.787336	−	0.454569i
$883$			16.0000i			0.538443i	0.963078	+	0.269221i	$0.0867663\pi$
$883$			16.0000i			0.538443i	−0.963078	+	0.269221i	$0.913234\pi$
$884$	7.50000	+	7.79423i	0.252252	+	0.262148i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	17.3205	−	10.0000i	0.581566	−	0.335767i	−0.180190	−	0.983632i	$-0.557671\pi$
$887$	17.3205	−	10.0000i	0.581566	−	0.335767i	0.761755	+	0.647865i	$0.224338\pi$
$888$		0			0
$889$	32.0000			1.07325
$890$		0			0
$891$	−18.0000	+	31.1769i	−0.603023	+	1.04447i
$892$		−	12.0000i		−	0.401790i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	4.00000			0.133631
$897$		0			0
$898$			34.0000i			1.13459i
$899$	−2.00000	−	3.46410i	−0.0667037	−	0.115534i
$900$		0			0
$901$	13.5000	−	23.3827i	0.449750	−	0.778990i
$902$			36.0000i			1.19867i
$903$		0			0
$904$	−0.500000	+	0.866025i	−0.0166298	+	0.0288036i
$905$		0			0
$906$		0			0
$907$	20.7846	−	12.0000i	0.690142	−	0.398453i	−0.113523	−	0.993535i	$-0.536214\pi$
$907$	20.7846	−	12.0000i	0.690142	−	0.398453i	0.803665	+	0.595082i	$0.202880\pi$
$908$	20.7846	−	12.0000i	0.689761	−	0.398234i
$909$	21.0000			0.696526
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$		0			0
$914$	15.5000	−	26.8468i	0.512694	−	0.888013i
$915$		0			0
$916$	−3.00000	+	5.19615i	−0.0991228	+	0.171686i
$917$	69.2820	+	40.0000i	2.28789	+	1.32092i
$918$		0			0
$919$	−24.0000	+	41.5692i	−0.791687	+	1.37124i	0.133235	+	0.991084i	$0.457464\pi$
$919$	−24.0000	+	41.5692i	−0.791687	+	1.37124i	−0.924922	+	0.380158i	$0.875870\pi$
$920$		0			0
$921$		0			0
$922$			33.0000i			1.08680i
$923$	27.7128	+	8.00000i	0.912178	+	0.263323i
$924$		0			0
$925$		0			0
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	20.7846	+	12.0000i	0.682656	+	0.394132i
$928$		−	1.00000i		−	0.0328266i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$		0			0
$932$	8.66025	+	5.00000i	0.283676	+	0.163780i
$933$		0			0
$934$	10.0000	+	17.3205i	0.327210	+	0.566744i
$935$		0			0
$936$	3.00000	−	10.3923i	0.0980581	−	0.339683i
$937$			21.0000i			0.686040i	0.939328	+	0.343020i	$0.111450\pi$
$937$			21.0000i			0.686040i	−0.939328	+	0.343020i	$0.888550\pi$
$938$	13.8564	−	8.00000i	0.452428	−	0.261209i
$939$		0			0
$940$		0			0
$941$	46.0000			1.49956			0.749779	−	0.661689i	$-0.230160\pi$
$941$	46.0000			1.49956			0.749779	+	0.661689i	$0.230160\pi$
$942$		0			0
$943$	−31.1769	−	18.0000i	−1.01526	−	0.586161i
$944$	4.00000			0.130189
$945$		0			0
$946$	16.0000	+	27.7128i	0.520205	+	0.901021i
$947$	−20.7846	+	12.0000i	−0.675409	+	0.389948i	−0.798123	−	0.602494i	$-0.794174\pi$
$947$	−20.7846	+	12.0000i	−0.675409	+	0.389948i	0.122714	+	0.992442i	$0.460840\pi$
$948$		0			0
$949$	−38.5000	+	9.52628i	−1.24976	+	0.309236i
$950$		0			0
$951$		0			0
$952$	−10.3923	+	6.00000i	−0.336817	+	0.194461i
$953$	19.0526	+	11.0000i	0.617173	+	0.356325i	0.775768	−	0.631019i	$-0.217363\pi$
$953$	19.0526	+	11.0000i	0.617173	+	0.356325i	−0.158595	+	0.987344i	$0.550696\pi$
$954$	−27.0000			−0.874157
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$		0			0
$959$	−18.0000	−	31.1769i	−0.581250	−	1.00676i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	10.3923	+	3.00000i	0.335061	+	0.0967239i
$963$			12.0000i			0.386695i
$964$	1.50000	+	2.59808i	0.0483117	+	0.0836784i
$965$		0			0
$966$		0			0
$967$			40.0000i			1.28631i	0.765735	+	0.643157i	$0.222376\pi$
$967$			40.0000i			1.28631i	−0.765735	+	0.643157i	$0.777624\pi$
$968$	−4.33013	−	2.50000i	−0.139176	−	0.0803530i
$969$		0			0
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	55.4256	−	32.0000i	1.77686	−	1.02587i
$974$	16.0000			0.512673
$975$		0			0
$976$	7.00000			0.224065
$977$	38.9711	−	22.5000i	1.24680	−	0.719839i	0.276328	−	0.961063i	$-0.410882\pi$
$977$	38.9711	−	22.5000i	1.24680	−	0.719839i	0.970469	+	0.241225i	$0.0775491\pi$
$978$		0			0
$979$	−12.0000	+	20.7846i	−0.383522	+	0.664279i
$980$		0			0
$981$	−3.00000	+	5.19615i	−0.0957826	+	0.165900i
$982$	−6.92820	−	4.00000i	−0.221088	−	0.127645i
$983$		−	52.0000i		−	1.65854i	−0.558846	−	0.829271i	$-0.688756\pi$
$983$		−	52.0000i		−	1.65854i	0.558846	−	0.829271i	$-0.311244\pi$
$984$		0			0
$985$		0			0
$986$	1.50000	+	2.59808i	0.0477697	+	0.0827396i
$987$		0			0
$988$		0			0
$989$	−32.0000			−1.01754
$990$		0			0
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	0.991233	−	0.132125i	$-0.0421802\pi$
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	−0.610040	+	0.792370i	$0.708847\pi$
$992$	3.46410	+	2.00000i	0.109985	+	0.0635001i
$993$		0			0
$994$	−16.0000	+	27.7128i	−0.507489	+	0.878997i
$995$		0			0
$996$		0			0
$997$	−21.6506	−	12.5000i	−0.685682	−	0.395879i	0.116310	−	0.993213i	$-0.462893\pi$
$997$	−21.6506	−	12.5000i	−0.685682	−	0.395879i	−0.801993	+	0.597334i	$0.796227\pi$
$998$	−27.7128	+	16.0000i	−0.877234	+	0.506471i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.o.c.549.1		4
5.2	odd	4		26.2.c.a.3.1	✓	2
5.3	odd	4		650.2.e.c.601.1		2
5.4	even	2	inner	650.2.o.c.549.2		4
13.9	even	3	inner	650.2.o.c.399.2		4
15.2	even	4		234.2.h.c.55.1		2
20.7	even	4		208.2.i.b.81.1		2
35.2	odd	12		1274.2.h.b.263.1		2
35.12	even	12		1274.2.h.a.263.1		2
35.17	even	12		1274.2.e.m.471.1		2
35.27	even	4		1274.2.g.a.393.1		2
35.32	odd	12		1274.2.e.n.471.1		2
40.27	even	4		832.2.i.f.705.1		2
40.37	odd	4		832.2.i.e.705.1		2
60.47	odd	4		1872.2.t.k.289.1		2
65.2	even	12		338.2.b.b.337.1		2
65.3	odd	12		8450.2.a.f.1.1		1
65.7	even	12		338.2.e.b.147.1		4
65.9	even	6	inner	650.2.o.c.399.1		4
65.12	odd	4		338.2.c.e.315.1		2
65.17	odd	12		338.2.c.e.191.1		2
65.22	odd	12		26.2.c.a.9.1	yes	2
65.23	odd	12		8450.2.a.s.1.1		1
65.32	even	12		338.2.e.b.147.2		4
65.37	even	12		338.2.b.b.337.2		2
65.42	odd	12		338.2.a.e.1.1		1
65.47	even	4		338.2.e.b.23.2		4
65.48	odd	12		650.2.e.c.451.1		2
65.57	even	4		338.2.e.b.23.1		4
65.62	odd	12		338.2.a.c.1.1		1
195.2	odd	12		3042.2.b.e.1351.2		2
195.62	even	12		3042.2.a.k.1.1		1
195.107	even	12		3042.2.a.e.1.1		1
195.152	even	12		234.2.h.c.217.1		2
195.167	odd	12		3042.2.b.e.1351.1		2
260.67	odd	12		2704.2.f.g.337.2		2
260.87	even	12		208.2.i.b.113.1		2
260.107	even	12		2704.2.a.h.1.1		1
260.127	even	12		2704.2.a.i.1.1		1
260.167	odd	12		2704.2.f.g.337.1		2
455.87	even	12		1274.2.h.a.373.1		2
455.152	even	12		1274.2.e.m.165.1		2
455.282	odd	12		1274.2.e.n.165.1		2
455.347	odd	12		1274.2.h.b.373.1		2
455.412	even	12		1274.2.g.a.295.1		2
520.347	even	12		832.2.i.f.321.1		2
520.477	odd	12		832.2.i.e.321.1		2
780.347	odd	12		1872.2.t.k.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.c.a.3.1	✓	2	5.2	odd	4
26.2.c.a.9.1	yes	2	65.22	odd	12
208.2.i.b.81.1		2	20.7	even	4
208.2.i.b.113.1		2	260.87	even	12
234.2.h.c.55.1		2	15.2	even	4
234.2.h.c.217.1		2	195.152	even	12
338.2.a.c.1.1		1	65.62	odd	12
338.2.a.e.1.1		1	65.42	odd	12
338.2.b.b.337.1		2	65.2	even	12
338.2.b.b.337.2		2	65.37	even	12
338.2.c.e.191.1		2	65.17	odd	12
338.2.c.e.315.1		2	65.12	odd	4
338.2.e.b.23.1		4	65.57	even	4
338.2.e.b.23.2		4	65.47	even	4
338.2.e.b.147.1		4	65.7	even	12
338.2.e.b.147.2		4	65.32	even	12
650.2.e.c.451.1		2	65.48	odd	12
650.2.e.c.601.1		2	5.3	odd	4
650.2.o.c.399.1		4	65.9	even	6	inner
650.2.o.c.399.2		4	13.9	even	3	inner
650.2.o.c.549.1		4	1.1	even	1	trivial
650.2.o.c.549.2		4	5.4	even	2	inner
832.2.i.e.321.1		2	520.477	odd	12
832.2.i.e.705.1		2	40.37	odd	4
832.2.i.f.321.1		2	520.347	even	12
832.2.i.f.705.1		2	40.27	even	4
1274.2.e.m.165.1		2	455.152	even	12
1274.2.e.m.471.1		2	35.17	even	12
1274.2.e.n.165.1		2	455.282	odd	12
1274.2.e.n.471.1		2	35.32	odd	12
1274.2.g.a.295.1		2	455.412	even	12
1274.2.g.a.393.1		2	35.27	even	4
1274.2.h.a.263.1		2	35.12	even	12
1274.2.h.a.373.1		2	455.87	even	12
1274.2.h.b.263.1		2	35.2	odd	12
1274.2.h.b.373.1		2	455.347	odd	12
1872.2.t.k.289.1		2	60.47	odd	4
1872.2.t.k.1153.1		2	780.347	odd	12
2704.2.a.h.1.1		1	260.107	even	12
2704.2.a.i.1.1		1	260.127	even	12
2704.2.f.g.337.1		2	260.167	odd	12
2704.2.f.g.337.2		2	260.67	odd	12
3042.2.a.e.1.1		1	195.107	even	12
3042.2.a.k.1.1		1	195.62	even	12
3042.2.b.e.1351.1		2	195.167	odd	12
3042.2.b.e.1351.2		2	195.2	odd	12
8450.2.a.f.1.1		1	65.3	odd	12
8450.2.a.s.1.1		1	65.23	odd	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.46410 + 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.46410 + 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.00000 - 3.46410i) q^{11} +(0.866025 + 3.50000i) q^{13} -4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.59808 + 1.50000i) q^{17} -3.00000i q^{18} +(3.46410 + 2.00000i) q^{22} +(-3.46410 + 2.00000i) q^{23} +(-2.50000 - 2.59808i) q^{26} +(3.46410 - 2.00000i) q^{28} +(-0.500000 - 0.866025i) q^{29} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} -3.00000 q^{34} +(1.50000 + 2.59808i) q^{36} +(-2.59808 + 1.50000i) q^{37} +(4.50000 + 7.79423i) q^{41} +(6.92820 + 4.00000i) q^{43} -4.00000 q^{44} +(2.00000 - 3.46410i) q^{46} +8.00000i q^{47} +(4.50000 + 7.79423i) q^{49} +(3.46410 + 1.00000i) q^{52} -9.00000i q^{53} +(-2.00000 + 3.46410i) q^{56} +(0.866025 + 0.500000i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-3.46410 + 2.00000i) q^{62} +(-10.3923 + 6.00000i) q^{63} -1.00000 q^{64} +(-3.46410 + 2.00000i) q^{67} +(2.59808 - 1.50000i) q^{68} +(4.00000 - 6.92820i) q^{71} +(-2.59808 - 1.50000i) q^{72} +11.0000i q^{73} +(1.50000 - 2.59808i) q^{74} -16.0000i q^{77} +4.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} +(-7.79423 - 4.50000i) q^{82} -8.00000 q^{86} +(3.46410 - 2.00000i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(-4.00000 + 13.8564i) q^{91} +4.00000i q^{92} +(-4.00000 - 6.92820i) q^{94} +(1.73205 + 1.00000i) q^{97} +(-7.79423 - 4.50000i) q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 6 * q^9	\( 4 q + 2 q^{4} - 6 q^{9} - 8 q^{11} - 16 q^{14} - 2 q^{16} - 10 q^{26} - 2 q^{29} + 16 q^{31} - 12 q^{34} + 6 q^{36} + 18 q^{41} - 16 q^{44} + 8 q^{46} + 18 q^{49} - 8 q^{56} - 8 q^{59} - 14 q^{61} - 4 q^{64} + 16 q^{71} + 6 q^{74} + 16 q^{79} - 18 q^{81} - 32 q^{86} - 12 q^{89} - 16 q^{91} - 16 q^{94} + 48 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^9 - 8 * q^11 - 16 * q^14 - 2 * q^16 - 10 * q^26 - 2 * q^29 + 16 * q^31 - 12 * q^34 + 6 * q^36 + 18 * q^41 - 16 * q^44 + 8 * q^46 + 18 * q^49 - 8 * q^56 - 8 * q^59 - 14 * q^61 - 4 * q^64 + 16 * q^71 + 6 * q^74 + 16 * q^79 - 18 * q^81 - 32 * q^86 - 12 * q^89 - 16 * q^91 - 16 * q^94 + 48 * q^99

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