LMFDB - Embedded newform 950.2.f.b.493.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (of order $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.3317760000.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 17x^{4} + 256 $ x^8 + 17*x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.1
Root			$-1.01575 + 1.72286i$ of defining polynomial
Character	$\chi$	$=$	950.493
Dual form			950.2.f.b.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000 q^{6} +(-2.73861 + 2.73861i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000 q^{6} +(-2.73861 + 2.73861i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.00000i q^{9} +(-0.707107 - 0.707107i) q^{12} +(0.707107 - 0.707107i) q^{13} +3.87298 q^{14} -1.00000 q^{16} +(-2.73861 + 2.73861i) q^{17} +(1.41421 - 1.41421i) q^{18} +(3.87298 - 2.00000i) q^{19} -3.87298i q^{21} +(-2.73861 - 2.73861i) q^{23} +1.00000i q^{24} -1.00000 q^{26} +(-3.53553 - 3.53553i) q^{27} +(-2.73861 - 2.73861i) q^{28} -3.87298 q^{29} +(0.707107 + 0.707107i) q^{32} +3.87298 q^{34} -2.00000 q^{36} +(-1.41421 - 1.41421i) q^{37} +(-4.15283 - 1.32440i) q^{38} +1.00000i q^{39} -7.74597i q^{41} +(-2.73861 + 2.73861i) q^{42} +3.87298i q^{46} +(-5.47723 + 5.47723i) q^{47} +(0.707107 - 0.707107i) q^{48} -8.00000i q^{49} -3.87298i q^{51} +(0.707107 + 0.707107i) q^{52} +(6.36396 - 6.36396i) q^{53} +5.00000i q^{54} +3.87298i q^{56} +(-1.32440 + 4.15283i) q^{57} +(2.73861 + 2.73861i) q^{58} -11.6190 q^{59} +10.0000 q^{61} +(-5.47723 - 5.47723i) q^{63} -1.00000i q^{64} +(-9.19239 - 9.19239i) q^{67} +(-2.73861 - 2.73861i) q^{68} +3.87298 q^{69} +7.74597i q^{71} +(1.41421 + 1.41421i) q^{72} +(2.73861 + 2.73861i) q^{73} +2.00000i q^{74} +(2.00000 + 3.87298i) q^{76} +(0.707107 - 0.707107i) q^{78} -15.4919 q^{79} -1.00000 q^{81} +(-5.47723 + 5.47723i) q^{82} +(-5.47723 - 5.47723i) q^{83} +3.87298 q^{84} +(2.73861 - 2.73861i) q^{87} -15.4919 q^{89} +3.87298i q^{91} +(2.73861 - 2.73861i) q^{92} +7.74597 q^{94} -1.00000 q^{96} +(5.65685 + 5.65685i) q^{97} +(-5.65685 + 5.65685i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{6}+O(q^{10}) $ 8 * q + 8 * q^6	$ 8 q + 8 q^{6} - 8 q^{16} - 8 q^{26} - 16 q^{36} + 80 q^{61} + 16 q^{76} - 8 q^{81} - 8 q^{96}+O(q^{100}) $ 8 * q + 8 * q^6 - 8 * q^16 - 8 * q^26 - 16 * q^36 + 80 * q^61 + 16 * q^76 - 8 * q^81 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i	−0.881127	−	0.472879i	$-0.843215\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i	0.472879	+	0.881127i	$0.343215\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−2.73861	+	2.73861i	−1.03510	+	1.03510i	−0.0357371	+	0.999361i	$0.511378\pi$
$7$	−2.73861	+	2.73861i	−1.03510	+	1.03510i	−0.999361	+	0.0357371i	$0.988622\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			2.00000i			0.666667i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i	−0.602217	−	0.798333i	$-0.705716\pi$
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i	0.798333	+	0.602217i	$0.205716\pi$
$14$	3.87298			1.03510
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.73861	+	2.73861i	−0.664211	+	0.664211i	−0.956370	−	0.292159i	$-0.905626\pi$
$17$	−2.73861	+	2.73861i	−0.664211	+	0.664211i	0.292159	+	0.956370i	$0.405626\pi$
$18$	1.41421	−	1.41421i	0.333333	−	0.333333i
$19$	3.87298	−	2.00000i	0.888523	−	0.458831i
$19$	3.87298	−	2.00000i	0.888523	−	0.458831i
$20$		0			0
$21$		−	3.87298i		−	0.845154i
$22$		0			0
$23$	−2.73861	−	2.73861i	−0.571040	−	0.571040i	0.361379	−	0.932419i	$-0.382306\pi$
$23$	−2.73861	−	2.73861i	−0.571040	−	0.571040i	−0.932419	+	0.361379i	$0.882306\pi$
$24$			1.00000i			0.204124i
$25$		0			0
$26$	−1.00000			−0.196116
$27$	−3.53553	−	3.53553i	−0.680414	−	0.680414i
$28$	−2.73861	−	2.73861i	−0.517549	−	0.517549i
$29$	−3.87298			−0.719195			−0.359597	−	0.933108i	$-0.617086\pi$
$29$	−3.87298			−0.719195			−0.359597	+	0.933108i	$0.617086\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	3.87298			0.664211
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−1.41421	−	1.41421i	−0.232495	−	0.232495i	0.581238	−	0.813733i	$-0.302568\pi$
$37$	−1.41421	−	1.41421i	−0.232495	−	0.232495i	−0.813733	+	0.581238i	$0.802568\pi$
$38$	−4.15283	−	1.32440i	−0.673677	−	0.214846i
$39$			1.00000i			0.160128i
$40$		0			0
$41$		−	7.74597i		−	1.20972i	−0.796333	−	0.604858i	$-0.793230\pi$
$41$		−	7.74597i		−	1.20972i	0.796333	−	0.604858i	$-0.206770\pi$
$42$	−2.73861	+	2.73861i	−0.422577	+	0.422577i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$		0			0
$46$			3.87298i			0.571040i
$47$	−5.47723	+	5.47723i	−0.798935	+	0.798935i	−0.982928	−	0.183992i	$-0.941098\pi$
$47$	−5.47723	+	5.47723i	−0.798935	+	0.798935i	0.183992	+	0.982928i	$0.441098\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		−	8.00000i		−	1.14286i
$50$		0			0
$51$		−	3.87298i		−	0.542326i
$52$	0.707107	+	0.707107i	0.0980581	+	0.0980581i
$53$	6.36396	−	6.36396i	0.874157	−	0.874157i	−0.118765	−	0.992922i	$-0.537894\pi$
$53$	6.36396	−	6.36396i	0.874157	−	0.874157i	0.992922	+	0.118765i	$0.0378935\pi$
$54$			5.00000i			0.680414i
$55$		0			0
$56$			3.87298i			0.517549i
$57$	−1.32440	+	4.15283i	−0.175421	+	0.550055i
$58$	2.73861	+	2.73861i	0.359597	+	0.359597i
$59$	−11.6190			−1.51266			−0.756329	−	0.654191i	$-0.773009\pi$
$59$	−11.6190			−1.51266			−0.756329	+	0.654191i	$0.773009\pi$
$60$		0			0
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$		0			0
$63$	−5.47723	−	5.47723i	−0.690066	−	0.690066i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−9.19239	−	9.19239i	−1.12303	−	1.12303i	−0.991284	−	0.131745i	$-0.957942\pi$
$67$	−9.19239	−	9.19239i	−1.12303	−	1.12303i	−0.131745	−	0.991284i	$-0.542058\pi$
$68$	−2.73861	−	2.73861i	−0.332106	−	0.332106i
$69$	3.87298			0.466252
$70$		0			0
$71$			7.74597i			0.919277i	0.888106	+	0.459639i	$0.152021\pi$
$71$			7.74597i			0.919277i	−0.888106	+	0.459639i	$0.847979\pi$
$72$	1.41421	+	1.41421i	0.166667	+	0.166667i
$73$	2.73861	+	2.73861i	0.320530	+	0.320530i	0.848971	−	0.528440i	$-0.177223\pi$
$73$	2.73861	+	2.73861i	0.320530	+	0.320530i	−0.528440	+	0.848971i	$0.677223\pi$
$74$			2.00000i			0.232495i
$75$		0			0
$76$	2.00000	+	3.87298i	0.229416	+	0.444262i
$77$		0			0
$78$	0.707107	−	0.707107i	0.0800641	−	0.0800641i
$79$	−15.4919			−1.74298			−0.871489	−	0.490414i	$-0.836845\pi$
$79$	−15.4919			−1.74298			−0.871489	+	0.490414i	$0.836845\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−5.47723	+	5.47723i	−0.604858	+	0.604858i
$83$	−5.47723	−	5.47723i	−0.601204	−	0.601204i	0.339428	−	0.940632i	$-0.389766\pi$
$83$	−5.47723	−	5.47723i	−0.601204	−	0.601204i	−0.940632	+	0.339428i	$0.889766\pi$
$84$	3.87298			0.422577
$85$		0			0
$86$		0			0
$87$	2.73861	−	2.73861i	0.293610	−	0.293610i
$88$		0			0
$89$	−15.4919			−1.64214			−0.821071	−	0.570826i	$-0.806623\pi$
$89$	−15.4919			−1.64214			−0.821071	+	0.570826i	$0.806623\pi$
$90$		0			0
$91$			3.87298i			0.405999i
$92$	2.73861	−	2.73861i	0.285520	−	0.285520i
$93$		0			0
$94$	7.74597			0.798935
$95$		0			0
$96$	−1.00000			−0.102062
$97$	5.65685	+	5.65685i	0.574367	+	0.574367i	0.933346	−	0.358979i	$-0.116875\pi$
$97$	5.65685	+	5.65685i	0.574367	+	0.574367i	−0.358979	+	0.933346i	$0.616875\pi$
$98$	−5.65685	+	5.65685i	−0.571429	+	0.571429i
$99$		0			0
$100$		0			0
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	−2.73861	+	2.73861i	−0.271163	+	0.271163i
$103$	−2.82843	+	2.82843i	−0.278693	+	0.278693i	−0.832587	−	0.553894i	$-0.813141\pi$
$103$	−2.82843	+	2.82843i	−0.278693	+	0.278693i	0.553894	+	0.832587i	$0.313141\pi$
$104$		−	1.00000i		−	0.0980581i
$105$		0			0
$106$	−9.00000			−0.874157
$107$	−2.12132	−	2.12132i	−0.205076	−	0.205076i	0.597095	−	0.802171i	$-0.296322\pi$
$107$	−2.12132	−	2.12132i	−0.205076	−	0.205076i	−0.802171	+	0.597095i	$0.796322\pi$
$108$	3.53553	−	3.53553i	0.340207	−	0.340207i
$109$	11.6190			1.11289			0.556447	−	0.830883i	$-0.312164\pi$
$109$	11.6190			1.11289			0.556447	+	0.830883i	$0.312164\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$	2.73861	−	2.73861i	0.258775	−	0.258775i
$113$	4.24264	−	4.24264i	0.399114	−	0.399114i	−0.478806	−	0.877920i	$-0.658930\pi$
$113$	4.24264	−	4.24264i	0.399114	−	0.399114i	0.877920	+	0.478806i	$0.158930\pi$
$114$	3.87298	−	2.00000i	0.362738	−	0.187317i
$115$		0			0
$116$		−	3.87298i		−	0.359597i
$117$	1.41421	+	1.41421i	0.130744	+	0.130744i
$118$	8.21584	+	8.21584i	0.756329	+	0.756329i
$119$		−	15.0000i		−	1.37505i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	−7.07107	−	7.07107i	−0.640184	−	0.640184i
$123$	5.47723	+	5.47723i	0.493865	+	0.493865i
$124$		0			0
$125$		0			0
$126$			7.74597i			0.690066i
$127$	5.65685	+	5.65685i	0.501965	+	0.501965i	0.912048	−	0.410083i	$-0.134500\pi$
$127$	5.65685	+	5.65685i	0.501965	+	0.501965i	−0.410083	+	0.912048i	$0.634500\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$	−5.12938	+	16.0838i	−0.444773	+	1.39464i
$134$			13.0000i			1.12303i
$135$		0			0
$136$			3.87298i			0.332106i
$137$	8.21584	−	8.21584i	0.701926	−	0.701926i	−0.262897	−	0.964824i	$-0.584678\pi$
$137$	8.21584	−	8.21584i	0.701926	−	0.701926i	0.964824	+	0.262897i	$0.0846781\pi$
$138$	−2.73861	−	2.73861i	−0.233126	−	0.233126i
$139$		−	10.0000i		−	0.848189i	−0.905618	−	0.424094i	$-0.860592\pi$
$139$		−	10.0000i		−	0.848189i	0.905618	−	0.424094i	$-0.139408\pi$
$140$		0			0
$141$		−	7.74597i		−	0.652328i
$142$	5.47723	−	5.47723i	0.459639	−	0.459639i
$143$		0			0
$144$		−	2.00000i		−	0.166667i
$145$		0			0
$146$		−	3.87298i		−	0.320530i
$147$	5.65685	+	5.65685i	0.466569	+	0.466569i
$148$	1.41421	−	1.41421i	0.116248	−	0.116248i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$			7.74597i			0.630358i	0.949032	+	0.315179i	$0.102065\pi$
$151$			7.74597i			0.630358i	−0.949032	+	0.315179i	$0.897935\pi$
$152$	1.32440	−	4.15283i	0.107423	−	0.336839i
$153$	−5.47723	−	5.47723i	−0.442807	−	0.442807i
$154$		0			0
$155$		0			0
$156$	−1.00000			−0.0800641
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$	10.9545	+	10.9545i	0.871489	+	0.871489i
$159$			9.00000i			0.713746i
$160$		0			0
$161$	15.0000			1.18217
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	10.9545	+	10.9545i	0.858019	+	0.858019i	0.991105	−	0.133086i	$-0.0424886\pi$
$163$	10.9545	+	10.9545i	0.858019	+	0.858019i	−0.133086	+	0.991105i	$0.542489\pi$
$164$	7.74597			0.604858
$165$		0			0
$166$			7.74597i			0.601204i
$167$	12.7279	+	12.7279i	0.984916	+	0.984916i	0.999888	−	0.0149717i	$-0.00476583\pi$
$167$	12.7279	+	12.7279i	0.984916	+	0.984916i	−0.0149717	+	0.999888i	$0.504766\pi$
$168$	−2.73861	−	2.73861i	−0.211289	−	0.211289i
$169$			12.0000i			0.923077i
$170$		0			0
$171$	4.00000	+	7.74597i	0.305888	+	0.592349i
$172$		0			0
$173$	4.24264	−	4.24264i	0.322562	−	0.322562i	−0.527187	−	0.849749i	$-0.676753\pi$
$173$	4.24264	−	4.24264i	0.322562	−	0.322562i	0.849749	+	0.527187i	$0.176753\pi$
$174$	−3.87298			−0.293610
$175$		0			0
$176$		0			0
$177$	8.21584	−	8.21584i	0.617540	−	0.617540i
$178$	10.9545	+	10.9545i	0.821071	+	0.821071i
$179$	−7.74597			−0.578961			−0.289480	−	0.957184i	$-0.593482\pi$
$179$	−7.74597			−0.578961			−0.289480	+	0.957184i	$0.593482\pi$
$180$		0			0
$181$		−	15.4919i		−	1.15151i	−0.817624	−	0.575753i	$-0.804709\pi$
$181$		−	15.4919i		−	1.15151i	0.817624	−	0.575753i	$-0.195291\pi$
$182$	2.73861	−	2.73861i	0.202999	−	0.202999i
$183$	−7.07107	+	7.07107i	−0.522708	+	0.522708i
$184$	−3.87298			−0.285520
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−5.47723	−	5.47723i	−0.399468	−	0.399468i
$189$	19.3649			1.40859
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−18.3848	+	18.3848i	−1.32337	+	1.32337i	−0.412331	+	0.911034i	$0.635285\pi$
$193$	−18.3848	+	18.3848i	−1.32337	+	1.32337i	−0.911034	+	0.412331i	$0.864715\pi$
$194$		−	8.00000i		−	0.574367i
$195$		0			0
$196$	8.00000			0.571429
$197$	16.4317	−	16.4317i	1.17071	−	1.17071i	0.188667	−	0.982041i	$-0.439583\pi$
$197$	16.4317	−	16.4317i	1.17071	−	1.17071i	0.982041	−	0.188667i	$-0.0604168\pi$
$198$		0			0
$199$			11.0000i			0.779769i	0.920864	+	0.389885i	$0.127485\pi$
$199$			11.0000i			0.779769i	−0.920864	+	0.389885i	$0.872515\pi$
$200$		0			0
$201$	13.0000			0.916949
$202$		0			0
$203$	10.6066	−	10.6066i	0.744438	−	0.744438i
$204$	3.87298			0.271163
$205$		0			0
$206$	4.00000			0.278693
$207$	5.47723	−	5.47723i	0.380693	−	0.380693i
$208$	−0.707107	+	0.707107i	−0.0490290	+	0.0490290i
$209$		0			0
$210$		0			0
$211$			3.87298i			0.266627i	0.991074	+	0.133314i	$0.0425617\pi$
$211$			3.87298i			0.266627i	−0.991074	+	0.133314i	$0.957438\pi$
$212$	6.36396	+	6.36396i	0.437079	+	0.437079i
$213$	−5.47723	−	5.47723i	−0.375293	−	0.375293i
$214$			3.00000i			0.205076i
$215$		0			0
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−8.21584	−	8.21584i	−0.556447	−	0.556447i
$219$	−3.87298			−0.261712
$220$		0			0
$221$			3.87298i			0.260525i
$222$	−1.41421	−	1.41421i	−0.0949158	−	0.0949158i
$223$	9.89949	−	9.89949i	0.662919	−	0.662919i	−0.293148	−	0.956067i	$-0.594703\pi$
$223$	9.89949	−	9.89949i	0.662919	−	0.662919i	0.956067	+	0.293148i	$0.0947028\pi$
$224$	−3.87298			−0.258775
$225$		0			0
$226$	−6.00000			−0.399114
$227$	−2.12132	−	2.12132i	−0.140797	−	0.140797i	0.633195	−	0.773992i	$-0.281743\pi$
$227$	−2.12132	−	2.12132i	−0.140797	−	0.140797i	−0.773992	+	0.633195i	$0.781743\pi$
$228$	−4.15283	−	1.32440i	−0.275028	−	0.0877105i
$229$			20.0000i			1.32164i	0.750546	+	0.660819i	$0.229791\pi$
$229$			20.0000i			1.32164i	−0.750546	+	0.660819i	$0.770209\pi$
$230$		0			0
$231$		0			0
$232$	−2.73861	+	2.73861i	−0.179799	+	0.179799i
$233$	10.9545	+	10.9545i	0.717650	+	0.717650i	0.968123	−	0.250473i	$-0.0805863\pi$
$233$	10.9545	+	10.9545i	0.717650	+	0.717650i	−0.250473	+	0.968123i	$0.580586\pi$
$234$		−	2.00000i		−	0.130744i
$235$		0			0
$236$		−	11.6190i		−	0.756329i
$237$	10.9545	−	10.9545i	0.711568	−	0.711568i
$238$	−10.6066	+	10.6066i	−0.687524	+	0.687524i
$239$		−	21.0000i		−	1.35838i	−0.733964	−	0.679189i	$-0.762332\pi$
$239$		−	21.0000i		−	1.35838i	0.733964	−	0.679189i	$-0.237668\pi$
$240$		0			0
$241$		−	15.4919i		−	0.997923i	−0.866624	−	0.498962i	$-0.833715\pi$
$241$		−	15.4919i		−	0.997923i	0.866624	−	0.498962i	$-0.166285\pi$
$242$	7.77817	+	7.77817i	0.500000	+	0.500000i
$243$	11.3137	−	11.3137i	0.725775	−	0.725775i
$244$			10.0000i			0.640184i
$245$		0			0
$246$		−	7.74597i		−	0.493865i
$247$	1.32440	−	4.15283i	0.0842695	−	0.264238i
$248$		0			0
$249$	7.74597			0.490881
$250$		0			0
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	5.47723	−	5.47723i	0.345033	−	0.345033i
$253$		0			0
$254$		−	8.00000i		−	0.501965i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.48528	−	8.48528i	−0.529297	−	0.529297i	0.391066	−	0.920363i	$-0.372107\pi$
$257$	−8.48528	−	8.48528i	−0.529297	−	0.529297i	−0.920363	+	0.391066i	$0.872107\pi$
$258$		0			0
$259$	7.74597			0.481311
$260$		0			0
$261$		−	7.74597i		−	0.479463i
$262$	12.7279	+	12.7279i	0.786334	+	0.786334i
$263$	−5.47723	−	5.47723i	−0.337740	−	0.337740i	0.517776	−	0.855516i	$-0.326760\pi$
$263$	−5.47723	−	5.47723i	−0.337740	−	0.337740i	−0.855516	+	0.517776i	$0.826760\pi$
$264$		0			0
$265$		0			0
$266$	15.0000	−	7.74597i	0.919709	−	0.474936i
$267$	10.9545	−	10.9545i	0.670402	−	0.670402i
$268$	9.19239	−	9.19239i	0.561514	−	0.561514i
$269$	15.4919			0.944560			0.472280	−	0.881449i	$-0.343431\pi$
$269$	15.4919			0.944560			0.472280	+	0.881449i	$0.343431\pi$
$270$		0			0
$271$	−25.0000			−1.51864			−0.759321	−	0.650716i	$-0.774469\pi$
$271$	−25.0000			−1.51864			−0.759321	+	0.650716i	$0.774469\pi$
$272$	2.73861	−	2.73861i	0.166053	−	0.166053i
$273$	−2.73861	−	2.73861i	−0.165748	−	0.165748i
$274$	−11.6190			−0.701926
$275$		0			0
$276$			3.87298i			0.233126i
$277$	−16.4317	+	16.4317i	−0.987284	+	0.987284i	−0.999920	−	0.0126364i	$-0.995978\pi$
$277$	−16.4317	+	16.4317i	−0.987284	+	0.987284i	0.0126364	+	0.999920i	$0.495978\pi$
$278$	−7.07107	+	7.07107i	−0.424094	+	0.424094i
$279$		0			0
$280$		0			0
$281$		−	7.74597i		−	0.462086i	−0.972944	−	0.231043i	$-0.925786\pi$
$281$		−	7.74597i		−	0.462086i	0.972944	−	0.231043i	$-0.0742137\pi$
$282$	−5.47723	+	5.47723i	−0.326164	+	0.326164i
$283$	16.4317	+	16.4317i	0.976762	+	0.976762i	0.999736	−	0.0229743i	$-0.00731358\pi$
$283$	16.4317	+	16.4317i	0.976762	+	0.976762i	−0.0229743	+	0.999736i	$0.507314\pi$
$284$	−7.74597			−0.459639
$285$		0			0
$286$		0			0
$287$	21.2132	+	21.2132i	1.25218	+	1.25218i
$288$	−1.41421	+	1.41421i	−0.0833333	+	0.0833333i
$289$			2.00000i			0.117647i
$290$		0			0
$291$	−8.00000			−0.468968
$292$	−2.73861	+	2.73861i	−0.160265	+	0.160265i
$293$	−14.8492	+	14.8492i	−0.867502	+	0.867502i	−0.992195	−	0.124693i	$-0.960205\pi$
$293$	−14.8492	+	14.8492i	−0.867502	+	0.867502i	0.124693	+	0.992195i	$0.460205\pi$
$294$		−	8.00000i		−	0.466569i
$295$		0			0
$296$	−2.00000			−0.116248
$297$		0			0
$298$		0			0
$299$	−3.87298			−0.223980
$300$		0			0
$301$		0			0
$302$	5.47723	−	5.47723i	0.315179	−	0.315179i
$303$		0			0
$304$	−3.87298	+	2.00000i	−0.222131	+	0.114708i
$305$		0			0
$306$			7.74597i			0.442807i
$307$	−19.7990	−	19.7990i	−1.12999	−	1.12999i	−0.990178	−	0.139810i	$-0.955351\pi$
$307$	−19.7990	−	19.7990i	−1.12999	−	1.12999i	−0.139810	−	0.990178i	$-0.544649\pi$
$308$		0			0
$309$		−	4.00000i		−	0.227552i
$310$		0			0
$311$	−15.0000			−0.850572			−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000			−0.850572			−0.425286	+	0.905059i	$0.639826\pi$
$312$	0.707107	+	0.707107i	0.0400320	+	0.0400320i
$313$	19.1703	+	19.1703i	1.08357	+	1.08357i	0.996174	+	0.0873951i	$0.0278543\pi$
$313$	19.1703	+	19.1703i	1.08357	+	1.08357i	0.0873951	+	0.996174i	$0.472146\pi$
$314$		0			0
$315$		0			0
$316$		−	15.4919i		−	0.871489i
$317$	−2.12132	−	2.12132i	−0.119145	−	0.119145i	0.645020	−	0.764165i	$-0.276849\pi$
$317$	−2.12132	−	2.12132i	−0.119145	−	0.119145i	−0.764165	+	0.645020i	$0.776849\pi$
$318$	6.36396	−	6.36396i	0.356873	−	0.356873i
$319$		0			0
$320$		0			0
$321$	3.00000			0.167444
$322$	−10.6066	−	10.6066i	−0.591083	−	0.591083i
$323$	−5.12938	+	16.0838i	−0.285406	+	0.894928i
$324$		−	1.00000i		−	0.0555556i
$325$		0			0
$326$		−	15.4919i		−	0.858019i
$327$	−8.21584	+	8.21584i	−0.454337	+	0.454337i
$328$	−5.47723	−	5.47723i	−0.302429	−	0.302429i
$329$		−	30.0000i		−	1.65395i
$330$		0			0
$331$			19.3649i			1.06439i	0.846621	+	0.532196i	$0.178633\pi$
$331$			19.3649i			1.06439i	−0.846621	+	0.532196i	$0.821367\pi$
$332$	5.47723	−	5.47723i	0.300602	−	0.300602i
$333$	2.82843	−	2.82843i	0.154997	−	0.154997i
$334$		−	18.0000i		−	0.984916i
$335$		0			0
$336$			3.87298i			0.211289i
$337$	−5.65685	−	5.65685i	−0.308148	−	0.308148i	0.536043	−	0.844191i	$-0.319919\pi$
$337$	−5.65685	−	5.65685i	−0.308148	−	0.308148i	−0.844191	+	0.536043i	$0.819919\pi$
$338$	8.48528	−	8.48528i	0.461538	−	0.461538i
$339$			6.00000i			0.325875i
$340$		0			0
$341$		0			0
$342$	2.64880	−	8.30565i	0.143231	−	0.449118i
$343$	2.73861	+	2.73861i	0.147871	+	0.147871i
$344$		0			0
$345$		0			0
$346$	−6.00000			−0.322562
$347$	−10.9545	+	10.9545i	−0.588066	+	0.588066i	−0.937107	−	0.349042i	$-0.886507\pi$
$347$	−10.9545	+	10.9545i	−0.588066	+	0.588066i	0.349042	+	0.937107i	$0.386507\pi$
$348$	2.73861	+	2.73861i	0.146805	+	0.146805i
$349$			16.0000i			0.856460i	0.903670	+	0.428230i	$0.140863\pi$
$349$			16.0000i			0.856460i	−0.903670	+	0.428230i	$0.859137\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$		0			0
$353$	−24.6475	−	24.6475i	−1.31185	−	1.31185i	−0.920047	−	0.391808i	$-0.871850\pi$
$353$	−24.6475	−	24.6475i	−1.31185	−	1.31185i	−0.391808	−	0.920047i	$-0.628150\pi$
$354$	−11.6190			−0.617540
$355$		0			0
$356$		−	15.4919i		−	0.821071i
$357$	10.6066	+	10.6066i	0.561361	+	0.561361i
$358$	5.47723	+	5.47723i	0.289480	+	0.289480i
$359$			15.0000i			0.791670i	0.918322	+	0.395835i	$0.129545\pi$
$359$			15.0000i			0.791670i	−0.918322	+	0.395835i	$0.870455\pi$
$360$		0			0
$361$	11.0000	−	15.4919i	0.578947	−	0.815365i
$362$	−10.9545	+	10.9545i	−0.575753	+	0.575753i
$363$	7.77817	−	7.77817i	0.408248	−	0.408248i
$364$	−3.87298			−0.202999
$365$		0			0
$366$	10.0000			0.522708
$367$	5.47723	−	5.47723i	0.285909	−	0.285909i	−0.549551	−	0.835460i	$-0.685201\pi$
$367$	5.47723	−	5.47723i	0.285909	−	0.285909i	0.835460	+	0.549551i	$0.185201\pi$
$368$	2.73861	+	2.73861i	0.142760	+	0.142760i
$369$	15.4919			0.806478
$370$		0			0
$371$			34.8569i			1.80968i
$372$		0			0
$373$	−21.9203	+	21.9203i	−1.13499	+	1.13499i	−0.145655	+	0.989335i	$0.546529\pi$
$373$	−21.9203	+	21.9203i	−1.13499	+	1.13499i	−0.989335	+	0.145655i	$0.953471\pi$
$374$		0			0
$375$		0			0
$376$			7.74597i			0.399468i
$377$	−2.73861	+	2.73861i	−0.141046	+	0.141046i
$378$	−13.6931	−	13.6931i	−0.704295	−	0.704295i
$379$	−19.3649			−0.994709			−0.497354	−	0.867547i	$-0.665695\pi$
$379$	−19.3649			−0.994709			−0.497354	+	0.867547i	$0.665695\pi$
$380$		0			0
$381$	−8.00000			−0.409852
$382$	−2.12132	−	2.12132i	−0.108536	−	0.108536i
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	−0.992157	−	0.125001i	$-0.960106\pi$
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	0.125001	+	0.992157i	$0.460106\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$	26.0000			1.32337
$387$		0			0
$388$	−5.65685	+	5.65685i	−0.287183	+	0.287183i
$389$			24.0000i			1.21685i	0.793612	+	0.608424i	$0.208198\pi$
$389$			24.0000i			1.21685i	−0.793612	+	0.608424i	$0.791802\pi$
$390$		0			0
$391$	15.0000			0.758583
$392$	−5.65685	−	5.65685i	−0.285714	−	0.285714i
$393$	12.7279	−	12.7279i	0.642039	−	0.642039i
$394$	−23.2379			−1.17071
$395$		0			0
$396$		0			0
$397$	−16.4317	+	16.4317i	−0.824682	+	0.824682i	−0.986775	−	0.162093i	$-0.948175\pi$
$397$	−16.4317	+	16.4317i	−0.824682	+	0.824682i	0.162093	+	0.986775i	$0.448175\pi$
$398$	7.77817	−	7.77817i	0.389885	−	0.389885i
$399$	−7.74597	−	15.0000i	−0.387783	−	0.750939i
$400$		0			0
$401$		−	7.74597i		−	0.386815i	−0.981119	−	0.193408i	$-0.938046\pi$
$401$		−	7.74597i		−	0.386815i	0.981119	−	0.193408i	$-0.0619540\pi$
$402$	−9.19239	−	9.19239i	−0.458475	−	0.458475i
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−15.0000			−0.744438
$407$		0			0
$408$	−2.73861	−	2.73861i	−0.135582	−	0.135582i
$409$	15.4919			0.766027			0.383013	−	0.923743i	$-0.374886\pi$
$409$	15.4919			0.766027			0.383013	+	0.923743i	$0.374886\pi$
$410$		0			0
$411$			11.6190i			0.573121i
$412$	−2.82843	−	2.82843i	−0.139347	−	0.139347i
$413$	31.8198	−	31.8198i	1.56575	−	1.56575i
$414$	−7.74597			−0.380693
$415$		0			0
$416$	1.00000			0.0490290
$417$	7.07107	+	7.07107i	0.346272	+	0.346272i
$418$		0			0
$419$			24.0000i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$419$			24.0000i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$420$		0			0
$421$			27.1109i			1.32130i	0.750692	+	0.660652i	$0.229720\pi$
$421$			27.1109i			1.32130i	−0.750692	+	0.660652i	$0.770280\pi$
$422$	2.73861	−	2.73861i	0.133314	−	0.133314i
$423$	−10.9545	−	10.9545i	−0.532624	−	0.532624i
$424$		−	9.00000i		−	0.437079i
$425$		0			0
$426$			7.74597i			0.375293i
$427$	−27.3861	+	27.3861i	−1.32531	+	1.32531i
$428$	2.12132	−	2.12132i	0.102538	−	0.102538i
$429$		0			0
$430$		0			0
$431$			38.7298i			1.86555i	0.360459	+	0.932775i	$0.382620\pi$
$431$			38.7298i			1.86555i	−0.360459	+	0.932775i	$0.617380\pi$
$432$	3.53553	+	3.53553i	0.170103	+	0.170103i
$433$	11.3137	−	11.3137i	0.543702	−	0.543702i	−0.380910	−	0.924612i	$-0.624389\pi$
$433$	11.3137	−	11.3137i	0.543702	−	0.543702i	0.924612	+	0.380910i	$0.124389\pi$
$434$		0			0
$435$		0			0
$436$			11.6190i			0.556447i
$437$	−16.0838	−	5.12938i	−0.769394	−	0.245371i
$438$	2.73861	+	2.73861i	0.130856	+	0.130856i
$439$	23.2379			1.10908			0.554542	−	0.832156i	$-0.312893\pi$
$439$	23.2379			1.10908			0.554542	+	0.832156i	$0.312893\pi$
$440$		0			0
$441$	16.0000			0.761905
$442$	2.73861	−	2.73861i	0.130263	−	0.130263i
$443$	−10.9545	−	10.9545i	−0.520462	−	0.520462i	0.397249	−	0.917711i	$-0.369965\pi$
$443$	−10.9545	−	10.9545i	−0.520462	−	0.520462i	−0.917711	+	0.397249i	$0.869965\pi$
$444$			2.00000i			0.0949158i
$445$		0			0
$446$	−14.0000			−0.662919
$447$		0			0
$448$	2.73861	+	2.73861i	0.129387	+	0.129387i
$449$	−23.2379			−1.09666			−0.548332	−	0.836261i	$-0.684737\pi$
$449$	−23.2379			−1.09666			−0.548332	+	0.836261i	$0.684737\pi$
$450$		0			0
$451$		0			0
$452$	4.24264	+	4.24264i	0.199557	+	0.199557i
$453$	−5.47723	−	5.47723i	−0.257343	−	0.257343i
$454$			3.00000i			0.140797i
$455$		0			0
$456$	2.00000	+	3.87298i	0.0936586	+	0.181369i
$457$	−24.6475	+	24.6475i	−1.15296	+	1.15296i	−0.167006	+	0.985956i	$0.553410\pi$
$457$	−24.6475	+	24.6475i	−1.15296	+	1.15296i	−0.985956	+	0.167006i	$0.946590\pi$
$458$	14.1421	−	14.1421i	0.660819	−	0.660819i
$459$	19.3649			0.903877
$460$		0			0
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	−5.47723	−	5.47723i	−0.254548	−	0.254548i	0.568284	−	0.822832i	$-0.307607\pi$
$463$	−5.47723	−	5.47723i	−0.254548	−	0.254548i	−0.822832	+	0.568284i	$0.807607\pi$
$464$	3.87298			0.179799
$465$		0			0
$466$		−	15.4919i		−	0.717650i
$467$	16.4317	−	16.4317i	0.760367	−	0.760367i	−0.216021	−	0.976389i	$-0.569308\pi$
$467$	16.4317	−	16.4317i	0.760367	−	0.760367i	0.976389	+	0.216021i	$0.0693081\pi$
$468$	−1.41421	+	1.41421i	−0.0653720	+	0.0653720i
$469$	50.3488			2.32489
$470$		0			0
$471$		0			0
$472$	−8.21584	+	8.21584i	−0.378165	+	0.378165i
$473$		0			0
$474$	−15.4919			−0.711568
$475$		0			0
$476$	15.0000			0.687524
$477$	12.7279	+	12.7279i	0.582772	+	0.582772i
$478$	−14.8492	+	14.8492i	−0.679189	+	0.679189i
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		0			0
$481$	−2.00000			−0.0911922
$482$	−10.9545	+	10.9545i	−0.498962	+	0.498962i
$483$	−10.6066	+	10.6066i	−0.482617	+	0.482617i
$484$		−	11.0000i		−	0.500000i
$485$		0			0
$486$	−16.0000			−0.725775
$487$	−26.8701	−	26.8701i	−1.21760	−	1.21760i	−0.968471	−	0.249128i	$-0.919856\pi$
$487$	−26.8701	−	26.8701i	−1.21760	−	1.21760i	−0.249128	−	0.968471i	$-0.580144\pi$
$488$	7.07107	−	7.07107i	0.320092	−	0.320092i
$489$	−15.4919			−0.700569
$490$		0			0
$491$	−42.0000			−1.89543			−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000			−1.89543			−0.947717	+	0.319113i	$0.896615\pi$
$492$	−5.47723	+	5.47723i	−0.246932	+	0.246932i
$493$	10.6066	−	10.6066i	0.477697	−	0.477697i
$494$	−3.87298	+	2.00000i	−0.174254	+	0.0899843i
$495$		0			0
$496$		0			0
$497$	−21.2132	−	21.2132i	−0.951542	−	0.951542i
$498$	−5.47723	−	5.47723i	−0.245440	−	0.245440i
$499$		−	20.0000i		−	0.895323i	−0.894203	−	0.447661i	$-0.852257\pi$
$499$		−	20.0000i		−	0.895323i	0.894203	−	0.447661i	$-0.147743\pi$
$500$		0			0
$501$	−18.0000			−0.804181
$502$	−12.7279	−	12.7279i	−0.568075	−	0.568075i
$503$	−24.6475	−	24.6475i	−1.09898	−	1.09898i	−0.994530	−	0.104448i	$-0.966692\pi$
$503$	−24.6475	−	24.6475i	−1.09898	−	1.09898i	−0.104448	−	0.994530i	$-0.533308\pi$
$504$	−7.74597			−0.345033
$505$		0			0
$506$		0			0
$507$	−8.48528	−	8.48528i	−0.376845	−	0.376845i
$508$	−5.65685	+	5.65685i	−0.250982	+	0.250982i
$509$	15.4919			0.686668			0.343334	−	0.939213i	$-0.388444\pi$
$509$	15.4919			0.686668			0.343334	+	0.939213i	$0.388444\pi$
$510$		0			0
$511$	−15.0000			−0.663561
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−20.7641	−	6.62200i	−0.916759	−	0.292368i
$514$			12.0000i			0.529297i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−5.47723	−	5.47723i	−0.240655	−	0.240655i
$519$			6.00000i			0.263371i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−5.47723	+	5.47723i	−0.239732	+	0.239732i
$523$	−7.77817	+	7.77817i	−0.340116	+	0.340116i	−0.856411	−	0.516295i	$-0.827311\pi$
$523$	−7.77817	+	7.77817i	−0.340116	+	0.340116i	0.516295	+	0.856411i	$0.327311\pi$
$524$		−	18.0000i		−	0.786334i
$525$		0			0
$526$			7.74597i			0.337740i
$527$		0			0
$528$		0			0
$529$		−	8.00000i		−	0.347826i
$530$		0			0
$531$		−	23.2379i		−	1.00844i
$532$	−16.0838	−	5.12938i	−0.697322	−	0.222387i
$533$	−5.47723	−	5.47723i	−0.237245	−	0.237245i
$534$	−15.4919			−0.670402
$535$		0			0
$536$	−13.0000			−0.561514
$537$	5.47723	−	5.47723i	0.236360	−	0.236360i
$538$	−10.9545	−	10.9545i	−0.472280	−	0.472280i
$539$		0			0
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	17.6777	+	17.6777i	0.759321	+	0.759321i
$543$	10.9545	+	10.9545i	0.470100	+	0.470100i
$544$	−3.87298			−0.166053
$545$		0			0
$546$			3.87298i			0.165748i
$547$	19.7990	+	19.7990i	0.846544	+	0.846544i	0.989700	−	0.143156i	$-0.0457252\pi$
$547$	19.7990	+	19.7990i	0.846544	+	0.846544i	−0.143156	+	0.989700i	$0.545725\pi$
$548$	8.21584	+	8.21584i	0.350963	+	0.350963i
$549$			20.0000i			0.853579i
$550$		0			0
$551$	−15.0000	+	7.74597i	−0.639021	+	0.329989i
$552$	2.73861	−	2.73861i	0.116563	−	0.116563i
$553$	42.4264	−	42.4264i	1.80415	−	1.80415i
$554$	23.2379			0.987284
$555$		0			0
$556$	10.0000			0.424094
$557$	−27.3861	+	27.3861i	−1.16039	+	1.16039i	−0.175997	+	0.984391i	$0.556315\pi$
$557$	−27.3861	+	27.3861i	−1.16039	+	1.16039i	−0.984391	+	0.175997i	$0.943685\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−5.47723	+	5.47723i	−0.231043	+	0.231043i
$563$	−25.4558	+	25.4558i	−1.07284	+	1.07284i	−0.0757057	+	0.997130i	$0.524121\pi$
$563$	−25.4558	+	25.4558i	−1.07284	+	1.07284i	−0.997130	+	0.0757057i	$0.975879\pi$
$564$	7.74597			0.326164
$565$		0			0
$566$		−	23.2379i		−	0.976762i
$567$	2.73861	−	2.73861i	0.115011	−	0.115011i
$568$	5.47723	+	5.47723i	0.229819	+	0.229819i
$569$	−30.9839			−1.29891			−0.649456	−	0.760399i	$-0.725003\pi$
$569$	−30.9839			−1.29891			−0.649456	+	0.760399i	$0.725003\pi$
$570$		0			0
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$		0			0
$573$	−2.12132	+	2.12132i	−0.0886194	+	0.0886194i
$574$		−	30.0000i		−	1.25218i
$575$		0			0
$576$	2.00000			0.0833333
$577$	−13.6931	+	13.6931i	−0.570050	+	0.570050i	−0.932142	−	0.362092i	$-0.882062\pi$
$577$	−13.6931	+	13.6931i	−0.570050	+	0.570050i	0.362092	+	0.932142i	$0.382062\pi$
$578$	1.41421	−	1.41421i	0.0588235	−	0.0588235i
$579$		−	26.0000i		−	1.08052i
$580$		0			0
$581$	30.0000			1.24461
$582$	5.65685	+	5.65685i	0.234484	+	0.234484i
$583$		0			0
$584$	3.87298			0.160265
$585$		0			0
$586$	21.0000			0.867502
$587$	5.47723	−	5.47723i	0.226069	−	0.226069i	−0.584979	−	0.811048i	$-0.698897\pi$
$587$	5.47723	−	5.47723i	0.226069	−	0.226069i	0.811048	+	0.584979i	$0.198897\pi$
$588$	−5.65685	+	5.65685i	−0.233285	+	0.233285i
$589$		0			0
$590$		0			0
$591$			23.2379i			0.955879i
$592$	1.41421	+	1.41421i	0.0581238	+	0.0581238i
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.77817	−	7.77817i	−0.318339	−	0.318339i
$598$	2.73861	+	2.73861i	0.111990	+	0.111990i
$599$	7.74597			0.316492			0.158246	−	0.987400i	$-0.449416\pi$
$599$	7.74597			0.316492			0.158246	+	0.987400i	$0.449416\pi$
$600$		0			0
$601$		−	46.4758i		−	1.89579i	−0.318587	−	0.947894i	$-0.603208\pi$
$601$		−	46.4758i		−	1.89579i	0.318587	−	0.947894i	$-0.396792\pi$
$602$		0			0
$603$	18.3848	−	18.3848i	0.748686	−	0.748686i
$604$	−7.74597			−0.315179
$605$		0			0
$606$		0			0
$607$	−5.65685	−	5.65685i	−0.229605	−	0.229605i	0.582923	−	0.812527i	$-0.301909\pi$
$607$	−5.65685	−	5.65685i	−0.229605	−	0.229605i	−0.812527	+	0.582923i	$0.801909\pi$
$608$	4.15283	+	1.32440i	0.168419	+	0.0537115i
$609$			15.0000i			0.607831i
$610$		0			0
$611$			7.74597i			0.313368i
$612$	5.47723	−	5.47723i	0.221404	−	0.221404i
$613$	10.9545	+	10.9545i	0.442446	+	0.442446i	0.892833	−	0.450387i	$-0.148714\pi$
$613$	10.9545	+	10.9545i	0.442446	+	0.442446i	−0.450387	+	0.892833i	$0.648714\pi$
$614$			28.0000i			1.12999i
$615$		0			0
$616$		0			0
$617$	21.9089	−	21.9089i	0.882019	−	0.882019i	−0.111720	−	0.993740i	$-0.535636\pi$
$617$	21.9089	−	21.9089i	0.882019	−	0.882019i	0.993740	+	0.111720i	$0.0356361\pi$
$618$	−2.82843	+	2.82843i	−0.113776	+	0.113776i
$619$			10.0000i			0.401934i	0.979598	+	0.200967i	$0.0644084\pi$
$619$			10.0000i			0.401934i	−0.979598	+	0.200967i	$0.935592\pi$
$620$		0			0
$621$			19.3649i			0.777087i
$622$	10.6066	+	10.6066i	0.425286	+	0.425286i
$623$	42.4264	−	42.4264i	1.69978	−	1.69978i
$624$		−	1.00000i		−	0.0400320i
$625$		0			0
$626$		−	27.1109i		−	1.08357i
$627$		0			0
$628$		0			0
$629$	7.74597			0.308852
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$	−10.9545	+	10.9545i	−0.435745	+	0.435745i
$633$	−2.73861	−	2.73861i	−0.108850	−	0.108850i
$634$			3.00000i			0.119145i
$635$		0			0
$636$	−9.00000			−0.356873
$637$	−5.65685	−	5.65685i	−0.224133	−	0.224133i
$638$		0			0
$639$	−15.4919			−0.612851
$640$		0			0
$641$		−	15.4919i		−	0.611895i	−0.952048	−	0.305947i	$-0.901027\pi$
$641$		−	15.4919i		−	0.611895i	0.952048	−	0.305947i	$-0.0989731\pi$
$642$	−2.12132	−	2.12132i	−0.0837218	−	0.0837218i
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$			15.0000i			0.591083i
$645$		0			0
$646$	15.0000	−	7.74597i	0.590167	−	0.304761i
$647$	24.6475	−	24.6475i	0.968994	−	0.968994i	−0.0305397	−	0.999534i	$-0.509723\pi$
$647$	24.6475	−	24.6475i	0.968994	−	0.968994i	0.999534	+	0.0305397i	$0.00972262\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−10.9545	+	10.9545i	−0.429009	+	0.429009i
$653$	−5.47723	−	5.47723i	−0.214340	−	0.214340i	0.591768	−	0.806108i	$-0.298430\pi$
$653$	−5.47723	−	5.47723i	−0.214340	−	0.214340i	−0.806108	+	0.591768i	$0.798430\pi$
$654$	11.6190			0.454337
$655$		0			0
$656$			7.74597i			0.302429i
$657$	−5.47723	+	5.47723i	−0.213687	+	0.213687i
$658$	−21.2132	+	21.2132i	−0.826977	+	0.826977i
$659$	19.3649			0.754350			0.377175	−	0.926142i	$-0.376896\pi$
$659$	19.3649			0.754350			0.377175	+	0.926142i	$0.376896\pi$
$660$		0			0
$661$			3.87298i			0.150642i	0.997159	+	0.0753208i	$0.0239981\pi$
$661$			3.87298i			0.150642i	−0.997159	+	0.0753208i	$0.976002\pi$
$662$	13.6931	−	13.6931i	0.532196	−	0.532196i
$663$	−2.73861	−	2.73861i	−0.106359	−	0.106359i
$664$	−7.74597			−0.300602
$665$		0			0
$666$	−4.00000			−0.154997
$667$	10.6066	+	10.6066i	0.410689	+	0.410689i
$668$	−12.7279	+	12.7279i	−0.492458	+	0.492458i
$669$			14.0000i			0.541271i
$670$		0			0
$671$		0			0
$672$	2.73861	−	2.73861i	0.105644	−	0.105644i
$673$	−31.1127	+	31.1127i	−1.19931	+	1.19931i	−0.224932	+	0.974374i	$0.572216\pi$
$673$	−31.1127	+	31.1127i	−1.19931	+	1.19931i	−0.974374	+	0.224932i	$0.927784\pi$
$674$			8.00000i			0.308148i
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−19.0919	−	19.0919i	−0.733761	−	0.733761i	0.237602	−	0.971363i	$-0.423639\pi$
$677$	−19.0919	−	19.0919i	−0.733761	−	0.733761i	−0.971363	+	0.237602i	$0.923639\pi$
$678$	4.24264	−	4.24264i	0.162938	−	0.162938i
$679$	−30.9839			−1.18905
$680$		0			0
$681$	3.00000			0.114960
$682$		0			0
$683$	−25.4558	+	25.4558i	−0.974041	+	0.974041i	−0.999671	−	0.0256307i	$-0.991841\pi$
$683$	−25.4558	+	25.4558i	−0.974041	+	0.974041i	0.0256307	+	0.999671i	$0.491841\pi$
$684$	−7.74597	+	4.00000i	−0.296174	+	0.152944i
$685$		0			0
$686$		−	3.87298i		−	0.147871i
$687$	−14.1421	−	14.1421i	−0.539556	−	0.539556i
$688$		0			0
$689$		−	9.00000i		−	0.342873i
$690$		0			0
$691$	40.0000			1.52167			0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000			1.52167			0.760836	+	0.648944i	$0.224789\pi$
$692$	4.24264	+	4.24264i	0.161281	+	0.161281i
$693$		0			0
$694$	15.4919			0.588066
$695$		0			0
$696$		−	3.87298i		−	0.146805i
$697$	21.2132	+	21.2132i	0.803507	+	0.803507i
$698$	11.3137	−	11.3137i	0.428230	−	0.428230i
$699$	−15.4919			−0.585959
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	3.53553	+	3.53553i	0.133440	+	0.133440i
$703$	−8.30565	−	2.64880i	−0.313254	−	0.0999013i
$704$		0			0
$705$		0			0
$706$			34.8569i			1.31185i
$707$		0			0
$708$	8.21584	+	8.21584i	0.308770	+	0.308770i
$709$		−	44.0000i		−	1.65245i	−0.563337	−	0.826227i	$-0.690483\pi$
$709$		−	44.0000i		−	1.65245i	0.563337	−	0.826227i	$-0.309517\pi$
$710$		0			0
$711$		−	30.9839i		−	1.16199i
$712$	−10.9545	+	10.9545i	−0.410535	+	0.410535i
$713$		0			0
$714$		−	15.0000i		−	0.561361i
$715$		0			0
$716$		−	7.74597i		−	0.289480i
$717$	14.8492	+	14.8492i	0.554555	+	0.554555i
$718$	10.6066	−	10.6066i	0.395835	−	0.395835i
$719$			15.0000i			0.559406i	0.960087	+	0.279703i	$0.0902359\pi$
$719$			15.0000i			0.559406i	−0.960087	+	0.279703i	$0.909764\pi$
$720$		0			0
$721$		−	15.4919i		−	0.576950i
$722$	−18.7326	+	3.17628i	−0.697156	+	0.118209i
$723$	10.9545	+	10.9545i	0.407400	+	0.407400i
$724$	15.4919			0.575753
$725$		0			0
$726$	−11.0000			−0.408248
$727$	−8.21584	+	8.21584i	−0.304709	+	0.304709i	−0.842853	−	0.538144i	$-0.819126\pi$
$727$	−8.21584	+	8.21584i	−0.304709	+	0.304709i	0.538144	+	0.842853i	$0.319126\pi$
$728$	2.73861	+	2.73861i	0.101500	+	0.101500i
$729$			13.0000i			0.481481i
$730$		0			0
$731$		0			0
$732$	−7.07107	−	7.07107i	−0.261354	−	0.261354i
$733$	16.4317	+	16.4317i	0.606918	+	0.606918i	0.942139	−	0.335222i	$-0.108811\pi$
$733$	16.4317	+	16.4317i	0.606918	+	0.606918i	−0.335222	+	0.942139i	$0.608811\pi$
$734$	−7.74597			−0.285909
$735$		0			0
$736$		−	3.87298i		−	0.142760i
$737$		0			0
$738$	−10.9545	−	10.9545i	−0.403239	−	0.403239i
$739$			26.0000i			0.956425i	0.878244	+	0.478213i	$0.158715\pi$
$739$			26.0000i			0.956425i	−0.878244	+	0.478213i	$0.841285\pi$
$740$		0			0
$741$	2.00000	+	3.87298i	0.0734718	+	0.142278i
$742$	24.6475	−	24.6475i	0.904839	−	0.904839i
$743$	16.9706	−	16.9706i	0.622590	−	0.622590i	−0.323603	−	0.946193i	$-0.604894\pi$
$743$	16.9706	−	16.9706i	0.622590	−	0.622590i	0.946193	+	0.323603i	$0.104894\pi$
$744$		0			0
$745$		0			0
$746$	31.0000			1.13499
$747$	10.9545	−	10.9545i	0.400802	−	0.400802i
$748$		0			0
$749$	11.6190			0.424547
$750$		0			0
$751$		−	38.7298i		−	1.41327i	−0.707577	−	0.706636i	$-0.750212\pi$
$751$		−	38.7298i		−	1.41327i	0.707577	−	0.706636i	$-0.249788\pi$
$752$	5.47723	−	5.47723i	0.199734	−	0.199734i
$753$	−12.7279	+	12.7279i	−0.463831	+	0.463831i
$754$	3.87298			0.141046
$755$		0			0
$756$			19.3649i			0.704295i
$757$	21.9089	−	21.9089i	0.796293	−	0.796293i	−0.186216	−	0.982509i	$-0.559622\pi$
$757$	21.9089	−	21.9089i	0.796293	−	0.796293i	0.982509	+	0.186216i	$0.0596225\pi$
$758$	13.6931	+	13.6931i	0.497354	+	0.497354i
$759$		0			0
$760$		0			0
$761$	−15.0000			−0.543750			−0.271875	−	0.962333i	$-0.587644\pi$
$761$	−15.0000			−0.543750			−0.271875	+	0.962333i	$0.587644\pi$
$762$	5.65685	+	5.65685i	0.204926	+	0.204926i
$763$	−31.8198	+	31.8198i	−1.15195	+	1.15195i
$764$			3.00000i			0.108536i
$765$		0			0
$766$	24.0000			0.867155
$767$	−8.21584	+	8.21584i	−0.296657	+	0.296657i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$		−	5.00000i		−	0.180305i	−0.995928	−	0.0901523i	$-0.971265\pi$
$769$		−	5.00000i		−	0.180305i	0.995928	−	0.0901523i	$-0.0287354\pi$
$770$		0			0
$771$	12.0000			0.432169
$772$	−18.3848	−	18.3848i	−0.661683	−	0.661683i
$773$	−6.36396	+	6.36396i	−0.228896	+	0.228896i	−0.812231	−	0.583336i	$-0.801747\pi$
$773$	−6.36396	+	6.36396i	−0.228896	+	0.228896i	0.583336	+	0.812231i	$0.301747\pi$
$774$		0			0
$775$		0			0
$776$	8.00000			0.287183
$777$	−5.47723	+	5.47723i	−0.196494	+	0.196494i
$778$	16.9706	−	16.9706i	0.608424	−	0.608424i
$779$	−15.4919	−	30.0000i	−0.555056	−	1.07486i
$780$		0			0
$781$		0			0
$782$	−10.6066	−	10.6066i	−0.379291	−	0.379291i
$783$	13.6931	+	13.6931i	0.489350	+	0.489350i
$784$			8.00000i			0.285714i
$785$		0			0
$786$	−18.0000			−0.642039
$787$	16.2635	+	16.2635i	0.579730	+	0.579730i	0.934829	−	0.355099i	$-0.115553\pi$
$787$	16.2635	+	16.2635i	0.579730	+	0.579730i	−0.355099	+	0.934829i	$0.615553\pi$
$788$	16.4317	+	16.4317i	0.585354	+	0.585354i
$789$	7.74597			0.275764
$790$		0			0
$791$			23.2379i			0.826245i
$792$		0			0
$793$	7.07107	−	7.07107i	0.251101	−	0.251101i
$794$	23.2379			0.824682
$795$		0			0
$796$	−11.0000			−0.389885
$797$	23.3345	+	23.3345i	0.826551	+	0.826551i	0.987038	−	0.160487i	$-0.0513064\pi$
$797$	23.3345	+	23.3345i	0.826551	+	0.826551i	−0.160487	+	0.987038i	$0.551306\pi$
$798$	−5.12938	+	16.0838i	−0.181578	+	0.569361i
$799$		−	30.0000i		−	1.06132i
$800$		0			0
$801$		−	30.9839i		−	1.09476i
$802$	−5.47723	+	5.47723i	−0.193408	+	0.193408i
$803$		0			0
$804$			13.0000i			0.458475i
$805$		0			0
$806$		0			0
$807$	−10.9545	+	10.9545i	−0.385615	+	0.385615i
$808$		0			0
$809$			21.0000i			0.738321i	0.929366	+	0.369160i	$0.120355\pi$
$809$			21.0000i			0.738321i	−0.929366	+	0.369160i	$0.879645\pi$
$810$		0			0
$811$		−	34.8569i		−	1.22399i	−0.790862	−	0.611995i	$-0.790367\pi$
$811$		−	34.8569i		−	1.22399i	0.790862	−	0.611995i	$-0.209633\pi$
$812$	10.6066	+	10.6066i	0.372219	+	0.372219i
$813$	17.6777	−	17.6777i	0.619983	−	0.619983i
$814$		0			0
$815$		0			0
$816$			3.87298i			0.135582i
$817$		0			0
$818$	−10.9545	−	10.9545i	−0.383013	−	0.383013i
$819$	−7.74597			−0.270666
$820$		0			0
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$	8.21584	−	8.21584i	0.286560	−	0.286560i
$823$	35.6020	+	35.6020i	1.24101	+	1.24101i	0.959584	+	0.281423i	$0.0908063\pi$
$823$	35.6020	+	35.6020i	1.24101	+	1.24101i	0.281423	+	0.959584i	$0.409194\pi$
$824$			4.00000i			0.139347i
$825$		0			0
$826$	−45.0000			−1.56575
$827$	2.12132	+	2.12132i	0.0737655	+	0.0737655i	0.743027	−	0.669261i	$-0.233389\pi$
$827$	2.12132	+	2.12132i	0.0737655	+	0.0737655i	−0.669261	+	0.743027i	$0.733389\pi$
$828$	5.47723	+	5.47723i	0.190347	+	0.190347i
$829$	27.1109			0.941600			0.470800	−	0.882240i	$-0.343965\pi$
$829$	27.1109			0.941600			0.470800	+	0.882240i	$0.343965\pi$
$830$		0			0
$831$		−	23.2379i		−	0.806114i
$832$	−0.707107	−	0.707107i	−0.0245145	−	0.0245145i
$833$	21.9089	+	21.9089i	0.759098	+	0.759098i
$834$		−	10.0000i		−	0.346272i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	16.9706	−	16.9706i	0.586238	−	0.586238i
$839$	7.74597			0.267420			0.133710	−	0.991020i	$-0.457311\pi$
$839$	7.74597			0.267420			0.133710	+	0.991020i	$0.457311\pi$
$840$		0			0
$841$	−14.0000			−0.482759
$842$	19.1703	−	19.1703i	0.660652	−	0.660652i
$843$	5.47723	+	5.47723i	0.188646	+	0.188646i
$844$	−3.87298			−0.133314
$845$		0			0
$846$			15.4919i			0.532624i
$847$	30.1247	−	30.1247i	1.03510	−	1.03510i
$848$	−6.36396	+	6.36396i	−0.218539	+	0.218539i
$849$	−23.2379			−0.797523
$850$		0			0
$851$			7.74597i			0.265528i
$852$	5.47723	−	5.47723i	0.187647	−	0.187647i
$853$	−38.3406	−	38.3406i	−1.31276	−	1.31276i	−0.919376	−	0.393381i	$-0.871305\pi$
$853$	−38.3406	−	38.3406i	−1.31276	−	1.31276i	−0.393381	−	0.919376i	$-0.628695\pi$
$854$	38.7298			1.32531
$855$		0			0
$856$	−3.00000			−0.102538
$857$	33.9411	+	33.9411i	1.15941	+	1.15941i	0.984603	+	0.174803i	$0.0559290\pi$
$857$	33.9411	+	33.9411i	1.15941	+	1.15941i	0.174803	+	0.984603i	$0.444071\pi$
$858$		0			0
$859$			4.00000i			0.136478i	0.997669	+	0.0682391i	$0.0217381\pi$
$859$			4.00000i			0.136478i	−0.997669	+	0.0682391i	$0.978262\pi$
$860$		0			0
$861$	−30.0000			−1.02240
$862$	27.3861	−	27.3861i	0.932775	−	0.932775i
$863$	−4.24264	+	4.24264i	−0.144421	+	0.144421i	−0.775621	−	0.631199i	$-0.782563\pi$
$863$	−4.24264	+	4.24264i	−0.144421	+	0.144421i	0.631199	+	0.775621i	$0.282563\pi$
$864$		−	5.00000i		−	0.170103i
$865$		0			0
$866$	−16.0000			−0.543702
$867$	−1.41421	−	1.41421i	−0.0480292	−	0.0480292i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−13.0000			−0.440488
$872$	8.21584	−	8.21584i	0.278223	−	0.278223i
$873$	−11.3137	+	11.3137i	−0.382911	+	0.382911i
$874$	7.74597	+	15.0000i	0.262011	+	0.507383i
$875$		0			0
$876$		−	3.87298i		−	0.130856i
$877$	−26.1630	−	26.1630i	−0.883460	−	0.883460i	0.110424	−	0.993885i	$-0.464779\pi$
$877$	−26.1630	−	26.1630i	−0.883460	−	0.883460i	−0.993885	+	0.110424i	$0.964779\pi$
$878$	−16.4317	−	16.4317i	−0.554542	−	0.554542i
$879$		−	21.0000i		−	0.708312i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	−11.3137	−	11.3137i	−0.380952	−	0.380952i
$883$	−10.9545	−	10.9545i	−0.368647	−	0.368647i	0.498337	−	0.866983i	$-0.333944\pi$
$883$	−10.9545	−	10.9545i	−0.368647	−	0.368647i	−0.866983	+	0.498337i	$0.833944\pi$
$884$	−3.87298			−0.130263
$885$		0			0
$886$			15.4919i			0.520462i
$887$	29.6985	+	29.6985i	0.997178	+	0.997178i	0.999996	−	0.00281850i	$-0.000897158\pi$
$887$	29.6985	+	29.6985i	0.997178	+	0.997178i	−0.00281850	+	0.999996i	$0.500897\pi$
$888$	1.41421	−	1.41421i	0.0474579	−	0.0474579i
$889$	−30.9839			−1.03917
$890$		0			0
$891$		0			0
$892$	9.89949	+	9.89949i	0.331460	+	0.331460i
$893$	−10.2588	+	32.1677i	−0.343296	+	1.07645i
$894$		0			0
$895$		0			0
$896$		−	3.87298i		−	0.129387i
$897$	2.73861	−	2.73861i	0.0914396	−	0.0914396i
$898$	16.4317	+	16.4317i	0.548332	+	0.548332i
$899$		0			0
$900$		0			0
$901$			34.8569i			1.16125i
$902$		0			0
$903$		0			0
$904$		−	6.00000i		−	0.199557i
$905$		0			0
$906$			7.74597i			0.257343i
$907$	12.0208	+	12.0208i	0.399145	+	0.399145i	0.877931	−	0.478787i	$-0.158923\pi$
$907$	12.0208	+	12.0208i	0.399145	+	0.399145i	−0.478787	+	0.877931i	$0.658923\pi$
$908$	2.12132	−	2.12132i	0.0703985	−	0.0703985i
$909$		0			0
$910$		0			0
$911$			23.2379i			0.769906i	0.922936	+	0.384953i	$0.125782\pi$
$911$			23.2379i			0.769906i	−0.922936	+	0.384953i	$0.874218\pi$
$912$	1.32440	−	4.15283i	0.0438552	−	0.137514i
$913$		0			0
$914$	34.8569			1.15296
$915$		0			0
$916$	−20.0000			−0.660819
$917$	49.2950	−	49.2950i	1.62787	−	1.62787i
$918$	−13.6931	−	13.6931i	−0.451938	−	0.451938i
$919$		−	1.00000i		−	0.0329870i	−0.999864	−	0.0164935i	$-0.994750\pi$
$919$		−	1.00000i		−	0.0329870i	0.999864	−	0.0164935i	$-0.00525028\pi$
$920$		0			0
$921$	28.0000			0.922631
$922$	12.7279	+	12.7279i	0.419172	+	0.419172i
$923$	5.47723	+	5.47723i	0.180285	+	0.180285i
$924$		0			0
$925$		0			0
$926$			7.74597i			0.254548i
$927$	−5.65685	−	5.65685i	−0.185795	−	0.185795i
$928$	−2.73861	−	2.73861i	−0.0898994	−	0.0898994i
$929$		−	39.0000i		−	1.27955i	−0.768563	−	0.639774i	$-0.779028\pi$
$929$		−	39.0000i		−	1.27955i	0.768563	−	0.639774i	$-0.220972\pi$
$930$		0			0
$931$	−16.0000	−	30.9839i	−0.524379	−	1.01546i
$932$	−10.9545	+	10.9545i	−0.358825	+	0.358825i
$933$	10.6066	−	10.6066i	0.347245	−	0.347245i
$934$	−23.2379			−0.760367
$935$		0			0
$936$	2.00000			0.0653720
$937$	19.1703	−	19.1703i	0.626266	−	0.626266i	−0.320860	−	0.947126i	$-0.603972\pi$
$937$	19.1703	−	19.1703i	0.626266	−	0.626266i	0.947126	+	0.320860i	$0.103972\pi$
$938$	−35.6020	−	35.6020i	−1.16245	−	1.16245i
$939$	−27.1109			−0.884730
$940$		0			0
$941$			27.1109i			0.883790i	0.897067	+	0.441895i	$0.145694\pi$
$941$			27.1109i			0.883790i	−0.897067	+	0.441895i	$0.854306\pi$
$942$		0			0
$943$	−21.2132	+	21.2132i	−0.690797	+	0.690797i
$944$	11.6190			0.378165
$945$		0			0
$946$		0			0
$947$	−27.3861	+	27.3861i	−0.889930	+	0.889930i	−0.994516	−	0.104586i	$-0.966648\pi$
$947$	−27.3861	+	27.3861i	−0.889930	+	0.889930i	0.104586	+	0.994516i	$0.466648\pi$
$948$	10.9545	+	10.9545i	0.355784	+	0.355784i
$949$	3.87298			0.125722
$950$		0			0
$951$	3.00000			0.0972817
$952$	−10.6066	−	10.6066i	−0.343762	−	0.343762i
$953$	−25.4558	+	25.4558i	−0.824596	+	0.824596i	−0.986763	−	0.162168i	$-0.948151\pi$
$953$	−25.4558	+	25.4558i	−0.824596	+	0.824596i	0.162168	+	0.986763i	$0.448151\pi$
$954$		−	18.0000i		−	0.582772i
$955$		0			0
$956$	21.0000			0.679189
$957$		0			0
$958$		0			0
$959$			45.0000i			1.45313i
$960$		0			0
$961$	31.0000			1.00000
$962$	1.41421	+	1.41421i	0.0455961	+	0.0455961i
$963$	4.24264	−	4.24264i	0.136717	−	0.136717i
$964$	15.4919			0.498962
$965$		0			0
$966$	15.0000			0.482617
$967$	38.3406	−	38.3406i	1.23295	−	1.23295i	0.270124	−	0.962825i	$-0.412935\pi$
$967$	38.3406	−	38.3406i	1.23295	−	1.23295i	0.962825	−	0.270124i	$-0.0870649\pi$
$968$	−7.77817	+	7.77817i	−0.250000	+	0.250000i
$969$	−7.74597	−	15.0000i	−0.248836	−	0.481869i
$970$		0			0
$971$			7.74597i			0.248580i	0.992246	+	0.124290i	$0.0396653\pi$
$971$			7.74597i			0.248580i	−0.992246	+	0.124290i	$0.960335\pi$
$972$	11.3137	+	11.3137i	0.362887	+	0.362887i
$973$	27.3861	+	27.3861i	0.877959	+	0.877959i
$974$			38.0000i			1.21760i
$975$		0			0
$976$	−10.0000			−0.320092
$977$	−33.9411	−	33.9411i	−1.08587	−	1.08587i	−0.995949	−	0.0899242i	$-0.971338\pi$
$977$	−33.9411	−	33.9411i	−1.08587	−	1.08587i	−0.0899242	−	0.995949i	$-0.528662\pi$
$978$	10.9545	+	10.9545i	0.350285	+	0.350285i
$979$		0			0
$980$		0			0
$981$			23.2379i			0.741929i
$982$	29.6985	+	29.6985i	0.947717	+	0.947717i
$983$	25.4558	−	25.4558i	0.811915	−	0.811915i	−0.173006	−	0.984921i	$-0.555348\pi$
$983$	25.4558	−	25.4558i	0.811915	−	0.811915i	0.984921	+	0.173006i	$0.0553478\pi$
$984$	7.74597			0.246932
$985$		0			0
$986$	−15.0000			−0.477697
$987$	21.2132	+	21.2132i	0.675224	+	0.675224i
$988$	4.15283	+	1.32440i	0.132119	+	0.0421348i
$989$		0			0
$990$		0			0
$991$			15.4919i			0.492117i	0.969255	+	0.246059i	$0.0791356\pi$
$991$			15.4919i			0.492117i	−0.969255	+	0.246059i	$0.920864\pi$
$992$		0			0
$993$	−13.6931	−	13.6931i	−0.434536	−	0.434536i
$994$			30.0000i			0.951542i
$995$		0			0
$996$			7.74597i			0.245440i
$997$	32.8634	−	32.8634i	1.04079	−	1.04079i	0.0416610	−	0.999132i	$-0.486735\pi$
$997$	32.8634	−	32.8634i	1.04079	−	1.04079i	0.999132	−	0.0416610i	$-0.0132650\pi$
$998$	−14.1421	+	14.1421i	−0.447661	+	0.447661i
$999$			10.0000i			0.316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.b.493.1	✓	8
5.2	odd	4	inner	950.2.f.b.607.3	yes	8
5.3	odd	4	inner	950.2.f.b.607.2	yes	8
5.4	even	2	inner	950.2.f.b.493.4	yes	8
19.18	odd	2	inner	950.2.f.b.493.3	yes	8
95.18	even	4	inner	950.2.f.b.607.4	yes	8
95.37	even	4	inner	950.2.f.b.607.1	yes	8
95.94	odd	2	inner	950.2.f.b.493.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.f.b.493.1	✓	8	1.1	even	1	trivial
950.2.f.b.493.2	yes	8	95.94	odd	2	inner
950.2.f.b.493.3	yes	8	19.18	odd	2	inner
950.2.f.b.493.4	yes	8	5.4	even	2	inner
950.2.f.b.607.1	yes	8	95.37	even	4	inner
950.2.f.b.607.2	yes	8	5.3	odd	4	inner
950.2.f.b.607.3	yes	8	5.2	odd	4	inner
950.2.f.b.607.4	yes	8	95.18	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000 q^{6} +(-2.73861 + 2.73861i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +1.00000 q^{6} +(-2.73861 + 2.73861i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.00000i q^{9} +(-0.707107 - 0.707107i) q^{12} +(0.707107 - 0.707107i) q^{13} +3.87298 q^{14} -1.00000 q^{16} +(-2.73861 + 2.73861i) q^{17} +(1.41421 - 1.41421i) q^{18} +(3.87298 - 2.00000i) q^{19} -3.87298i q^{21} +(-2.73861 - 2.73861i) q^{23} +1.00000i q^{24} -1.00000 q^{26} +(-3.53553 - 3.53553i) q^{27} +(-2.73861 - 2.73861i) q^{28} -3.87298 q^{29} +(0.707107 + 0.707107i) q^{32} +3.87298 q^{34} -2.00000 q^{36} +(-1.41421 - 1.41421i) q^{37} +(-4.15283 - 1.32440i) q^{38} +1.00000i q^{39} -7.74597i q^{41} +(-2.73861 + 2.73861i) q^{42} +3.87298i q^{46} +(-5.47723 + 5.47723i) q^{47} +(0.707107 - 0.707107i) q^{48} -8.00000i q^{49} -3.87298i q^{51} +(0.707107 + 0.707107i) q^{52} +(6.36396 - 6.36396i) q^{53} +5.00000i q^{54} +3.87298i q^{56} +(-1.32440 + 4.15283i) q^{57} +(2.73861 + 2.73861i) q^{58} -11.6190 q^{59} +10.0000 q^{61} +(-5.47723 - 5.47723i) q^{63} -1.00000i q^{64} +(-9.19239 - 9.19239i) q^{67} +(-2.73861 - 2.73861i) q^{68} +3.87298 q^{69} +7.74597i q^{71} +(1.41421 + 1.41421i) q^{72} +(2.73861 + 2.73861i) q^{73} +2.00000i q^{74} +(2.00000 + 3.87298i) q^{76} +(0.707107 - 0.707107i) q^{78} -15.4919 q^{79} -1.00000 q^{81} +(-5.47723 + 5.47723i) q^{82} +(-5.47723 - 5.47723i) q^{83} +3.87298 q^{84} +(2.73861 - 2.73861i) q^{87} -15.4919 q^{89} +3.87298i q^{91} +(2.73861 - 2.73861i) q^{92} +7.74597 q^{94} -1.00000 q^{96} +(5.65685 + 5.65685i) q^{97} +(-5.65685 + 5.65685i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{6}+O(q^{10}) \) 8 * q + 8 * q^6	\( 8 q + 8 q^{6} - 8 q^{16} - 8 q^{26} - 16 q^{36} + 80 q^{61} + 16 q^{76} - 8 q^{81} - 8 q^{96}+O(q^{100}) \) 8 * q + 8 * q^6 - 8 * q^16 - 8 * q^26 - 16 * q^36 + 80 * q^61 + 16 * q^76 - 8 * q^81 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more