LMFDB - Embedded newform 490.3.f.m.393.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,3,Mod(197,490)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("490.197"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	490.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,0,0,0,0,-8,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.3515329537$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			393.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	490.393
Dual form			490.3.f.m.197.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} +(0.707107 + 0.707107i) q^{3} -2.00000i q^{4} +(3.53553 + 3.53553i) q^{5} +1.41421 q^{6} +(-2.00000 - 2.00000i) q^{8} -8.00000i q^{9} +7.07107 q^{10} +5.00000 q^{11} +(1.41421 - 1.41421i) q^{12} +(2.12132 + 2.12132i) q^{13} +5.00000i q^{15} -4.00000 q^{16} +(19.0919 - 19.0919i) q^{17} +(-8.00000 - 8.00000i) q^{18} +12.7279i q^{19} +(7.07107 - 7.07107i) q^{20} +(5.00000 - 5.00000i) q^{22} +(8.00000 + 8.00000i) q^{23} -2.82843i q^{24} +25.0000i q^{25} +4.24264 q^{26} +(12.0208 - 12.0208i) q^{27} -17.0000i q^{29} +(5.00000 + 5.00000i) q^{30} +57.9828 q^{31} +(-4.00000 + 4.00000i) q^{32} +(3.53553 + 3.53553i) q^{33} -38.1838i q^{34} -16.0000 q^{36} +(-24.0000 + 24.0000i) q^{37} +(12.7279 + 12.7279i) q^{38} +3.00000i q^{39} -14.1421i q^{40} +26.8701 q^{41} +(11.0000 + 11.0000i) q^{43} -10.0000i q^{44} +(28.2843 - 28.2843i) q^{45} +16.0000 q^{46} +(-50.2046 + 50.2046i) q^{47} +(-2.82843 - 2.82843i) q^{48} +(25.0000 + 25.0000i) q^{50} +27.0000 q^{51} +(4.24264 - 4.24264i) q^{52} +(-33.0000 - 33.0000i) q^{53} -24.0416i q^{54} +(17.6777 + 17.6777i) q^{55} +(-9.00000 + 9.00000i) q^{57} +(-17.0000 - 17.0000i) q^{58} -55.1543i q^{59} +10.0000 q^{60} -45.2548 q^{61} +(57.9828 - 57.9828i) q^{62} +8.00000i q^{64} +15.0000i q^{65} +7.07107 q^{66} +(75.0000 - 75.0000i) q^{67} +(-38.1838 - 38.1838i) q^{68} +11.3137i q^{69} -104.000 q^{71} +(-16.0000 + 16.0000i) q^{72} +(-39.5980 - 39.5980i) q^{73} +48.0000i q^{74} +(-17.6777 + 17.6777i) q^{75} +25.4558 q^{76} +(3.00000 + 3.00000i) q^{78} -115.000i q^{79} +(-14.1421 - 14.1421i) q^{80} -55.0000 q^{81} +(26.8701 - 26.8701i) q^{82} +(73.5391 + 73.5391i) q^{83} +135.000 q^{85} +22.0000 q^{86} +(12.0208 - 12.0208i) q^{87} +(-10.0000 - 10.0000i) q^{88} +113.137i q^{89} -56.5685i q^{90} +(16.0000 - 16.0000i) q^{92} +(41.0000 + 41.0000i) q^{93} +100.409i q^{94} +(-45.0000 + 45.0000i) q^{95} -5.65685 q^{96} +(-81.3173 + 81.3173i) q^{97} -40.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{8} + 20 q^{11} - 16 q^{16} - 32 q^{18} + 20 q^{22} + 32 q^{23} + 20 q^{30} - 16 q^{32} - 64 q^{36} - 96 q^{37} + 44 q^{43} + 64 q^{46} + 100 q^{50} + 108 q^{51} - 132 q^{53} - 36 q^{57}+ \cdots - 180 q^{95}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^8 + 20 * q^11 - 16 * q^16 - 32 * q^18 + 20 * q^22 + 32 * q^23 + 20 * q^30 - 16 * q^32 - 64 * q^36 - 96 * q^37 + 44 * q^43 + 64 * q^46 + 100 * q^50 + 108 * q^51 - 132 * q^53 - 36 * q^57 - 68 * q^58 + 40 * q^60 + 300 * q^67 - 416 * q^71 - 64 * q^72 + 12 * q^78 - 220 * q^81 + 540 * q^85 + 88 * q^86 - 40 * q^88 + 64 * q^92 + 164 * q^93 - 180 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	0.707107	+	0.707107i	0.235702	+	0.235702i	0.815068	−	0.579366i	$-0.196700\pi$
$3$	0.707107	+	0.707107i	0.235702	+	0.235702i	−0.579366	+	0.815068i	$0.696700\pi$
$4$		−	2.00000i		−	0.500000i
$5$	3.53553	+	3.53553i	0.707107	+	0.707107i
$5$	3.53553	+	3.53553i	0.707107	+	0.707107i
$6$	1.41421			0.235702
$7$		0			0
$7$		0			0
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		−	8.00000i		−	0.888889i
$10$	7.07107			0.707107
$11$	5.00000			0.454545			0.227273	−	0.973831i	$-0.427019\pi$
$11$	5.00000			0.454545			0.227273	+	0.973831i	$0.427019\pi$
$12$	1.41421	−	1.41421i	0.117851	−	0.117851i
$13$	2.12132	+	2.12132i	0.163178	+	0.163178i	0.783973	−	0.620795i	$-0.213190\pi$
$13$	2.12132	+	2.12132i	0.163178	+	0.163178i	−0.620795	+	0.783973i	$0.713190\pi$
$14$		0			0
$15$			5.00000i			0.333333i
$16$	−4.00000			−0.250000
$17$	19.0919	−	19.0919i	1.12305	−	1.12305i	0.131772	−	0.991280i	$-0.457933\pi$
$17$	19.0919	−	19.0919i	1.12305	−	1.12305i	0.991280	−	0.131772i	$-0.0420666\pi$
$18$	−8.00000	−	8.00000i	−0.444444	−	0.444444i
$19$			12.7279i			0.669891i	0.942238	+	0.334945i	$0.108718\pi$
$19$			12.7279i			0.669891i	−0.942238	+	0.334945i	$0.891282\pi$
$20$	7.07107	−	7.07107i	0.353553	−	0.353553i
$21$		0			0
$22$	5.00000	−	5.00000i	0.227273	−	0.227273i
$23$	8.00000	+	8.00000i	0.347826	+	0.347826i	0.859299	−	0.511473i	$-0.170900\pi$
$23$	8.00000	+	8.00000i	0.347826	+	0.347826i	−0.511473	+	0.859299i	$0.670900\pi$
$24$		−	2.82843i		−	0.117851i
$25$			25.0000i			1.00000i
$26$	4.24264			0.163178
$27$	12.0208	−	12.0208i	0.445215	−	0.445215i
$28$		0			0
$29$		−	17.0000i		−	0.586207i	−0.956081	−	0.293103i	$-0.905312\pi$
$29$		−	17.0000i		−	0.586207i	0.956081	−	0.293103i	$-0.0946880\pi$
$30$	5.00000	+	5.00000i	0.166667	+	0.166667i
$31$	57.9828			1.87041			0.935206	−	0.354105i	$-0.115214\pi$
$31$	57.9828			1.87041			0.935206	+	0.354105i	$0.115214\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	3.53553	+	3.53553i	0.107137	+	0.107137i
$34$		−	38.1838i		−	1.12305i
$35$		0			0
$36$	−16.0000			−0.444444
$37$	−24.0000	+	24.0000i	−0.648649	+	0.648649i	−0.952666	−	0.304018i	$-0.901672\pi$
$37$	−24.0000	+	24.0000i	−0.648649	+	0.648649i	0.304018	+	0.952666i	$0.401672\pi$
$38$	12.7279	+	12.7279i	0.334945	+	0.334945i
$39$			3.00000i			0.0769231i
$40$		−	14.1421i		−	0.353553i
$41$	26.8701			0.655367			0.327684	−	0.944788i	$-0.393732\pi$
$41$	26.8701			0.655367			0.327684	+	0.944788i	$0.393732\pi$
$42$		0			0
$43$	11.0000	+	11.0000i	0.255814	+	0.255814i	0.823349	−	0.567535i	$-0.192103\pi$
$43$	11.0000	+	11.0000i	0.255814	+	0.255814i	−0.567535	+	0.823349i	$0.692103\pi$
$44$		−	10.0000i		−	0.227273i
$45$	28.2843	−	28.2843i	0.628539	−	0.628539i
$46$	16.0000			0.347826
$47$	−50.2046	+	50.2046i	−1.06818	+	1.06818i	−0.0706838	+	0.997499i	$0.522518\pi$
$47$	−50.2046	+	50.2046i	−1.06818	+	1.06818i	−0.997499	+	0.0706838i	$0.977482\pi$
$48$	−2.82843	−	2.82843i	−0.0589256	−	0.0589256i
$49$		0			0
$50$	25.0000	+	25.0000i	0.500000	+	0.500000i
$51$	27.0000			0.529412
$52$	4.24264	−	4.24264i	0.0815892	−	0.0815892i
$53$	−33.0000	−	33.0000i	−0.622642	−	0.622642i	0.323565	−	0.946206i	$-0.395119\pi$
$53$	−33.0000	−	33.0000i	−0.622642	−	0.622642i	−0.946206	+	0.323565i	$0.895119\pi$
$54$		−	24.0416i		−	0.445215i
$55$	17.6777	+	17.6777i	0.321412	+	0.321412i
$56$		0			0
$57$	−9.00000	+	9.00000i	−0.157895	+	0.157895i
$58$	−17.0000	−	17.0000i	−0.293103	−	0.293103i
$59$		−	55.1543i		−	0.934819i	−0.884041	−	0.467410i	$-0.845187\pi$
$59$		−	55.1543i		−	0.934819i	0.884041	−	0.467410i	$-0.154813\pi$
$60$	10.0000			0.166667
$61$	−45.2548			−0.741883			−0.370941	−	0.928656i	$-0.620965\pi$
$61$	−45.2548			−0.741883			−0.370941	+	0.928656i	$0.620965\pi$
$62$	57.9828	−	57.9828i	0.935206	−	0.935206i
$63$		0			0
$64$			8.00000i			0.125000i
$65$			15.0000i			0.230769i
$66$	7.07107			0.107137
$67$	75.0000	−	75.0000i	1.11940	−	1.11940i	0.127574	−	0.991829i	$-0.459281\pi$
$67$	75.0000	−	75.0000i	1.11940	−	1.11940i	0.991829	−	0.127574i	$-0.0407190\pi$
$68$	−38.1838	−	38.1838i	−0.561526	−	0.561526i
$69$			11.3137i			0.163967i
$70$		0			0
$71$	−104.000			−1.46479			−0.732394	−	0.680881i	$-0.761597\pi$
$71$	−104.000			−1.46479			−0.732394	+	0.680881i	$0.761597\pi$
$72$	−16.0000	+	16.0000i	−0.222222	+	0.222222i
$73$	−39.5980	−	39.5980i	−0.542438	−	0.542438i	0.381805	−	0.924243i	$-0.375303\pi$
$73$	−39.5980	−	39.5980i	−0.542438	−	0.542438i	−0.924243	+	0.381805i	$0.875303\pi$
$74$			48.0000i			0.648649i
$75$	−17.6777	+	17.6777i	−0.235702	+	0.235702i
$76$	25.4558			0.334945
$77$		0			0
$78$	3.00000	+	3.00000i	0.0384615	+	0.0384615i
$79$		−	115.000i		−	1.45570i	−0.685738	−	0.727848i	$-0.740521\pi$
$79$		−	115.000i		−	1.45570i	0.685738	−	0.727848i	$-0.259479\pi$
$80$	−14.1421	−	14.1421i	−0.176777	−	0.176777i
$81$	−55.0000			−0.679012
$82$	26.8701	−	26.8701i	0.327684	−	0.327684i
$83$	73.5391	+	73.5391i	0.886013	+	0.886013i	0.994137	−	0.108124i	$-0.0344844\pi$
$83$	73.5391	+	73.5391i	0.886013	+	0.886013i	−0.108124	+	0.994137i	$0.534484\pi$
$84$		0			0
$85$	135.000			1.58824
$86$	22.0000			0.255814
$87$	12.0208	−	12.0208i	0.138170	−	0.138170i
$88$	−10.0000	−	10.0000i	−0.113636	−	0.113636i
$89$			113.137i			1.27120i	0.772017	+	0.635602i	$0.219248\pi$
$89$			113.137i			1.27120i	−0.772017	+	0.635602i	$0.780752\pi$
$90$		−	56.5685i		−	0.628539i
$91$		0			0
$92$	16.0000	−	16.0000i	0.173913	−	0.173913i
$93$	41.0000	+	41.0000i	0.440860	+	0.440860i
$94$			100.409i			1.06818i
$95$	−45.0000	+	45.0000i	−0.473684	+	0.473684i
$96$	−5.65685			−0.0589256
$97$	−81.3173	+	81.3173i	−0.838322	+	0.838322i	−0.988638	−	0.150316i	$-0.951971\pi$
$97$	−81.3173	+	81.3173i	−0.838322	+	0.838322i	0.150316	+	0.988638i	$0.451971\pi$
$98$		0			0
$99$		−	40.0000i		−	0.404040i
$100$	50.0000			0.500000
$101$	−97.5807			−0.966146			−0.483073	−	0.875580i	$-0.660479\pi$
$101$	−97.5807			−0.966146			−0.483073	+	0.875580i	$0.660479\pi$
$102$	27.0000	−	27.0000i	0.264706	−	0.264706i
$103$	−34.6482	−	34.6482i	−0.336391	−	0.336391i	0.518616	−	0.855007i	$-0.326447\pi$
$103$	−34.6482	−	34.6482i	−0.336391	−	0.336391i	−0.855007	+	0.518616i	$0.826447\pi$
$104$		−	8.48528i		−	0.0815892i
$105$		0			0
$106$	−66.0000			−0.622642
$107$	−75.0000	+	75.0000i	−0.700935	+	0.700935i	−0.964611	−	0.263677i	$-0.915065\pi$
$107$	−75.0000	+	75.0000i	−0.700935	+	0.700935i	0.263677	+	0.964611i	$0.415065\pi$
$108$	−24.0416	−	24.0416i	−0.222608	−	0.222608i
$109$			119.000i			1.09174i	0.837869	+	0.545872i	$0.183801\pi$
$109$			119.000i			1.09174i	−0.837869	+	0.545872i	$0.816199\pi$
$110$	35.3553			0.321412
$111$	−33.9411			−0.305776
$112$		0			0
$113$	−16.0000	−	16.0000i	−0.141593	−	0.141593i	0.632757	−	0.774350i	$-0.281923\pi$
$113$	−16.0000	−	16.0000i	−0.141593	−	0.141593i	−0.774350	+	0.632757i	$0.781923\pi$
$114$			18.0000i			0.157895i
$115$			56.5685i			0.491900i
$116$	−34.0000			−0.293103
$117$	16.9706	−	16.9706i	0.145048	−	0.145048i
$118$	−55.1543	−	55.1543i	−0.467410	−	0.467410i
$119$		0			0
$120$	10.0000	−	10.0000i	0.0833333	−	0.0833333i
$121$	−96.0000			−0.793388
$122$	−45.2548	+	45.2548i	−0.370941	+	0.370941i
$123$	19.0000	+	19.0000i	0.154472	+	0.154472i
$124$		−	115.966i		−	0.935206i
$125$	−88.3883	+	88.3883i	−0.707107	+	0.707107i
$126$		0			0
$127$	−19.0000	+	19.0000i	−0.149606	+	0.149606i	−0.777942	−	0.628336i	$-0.783736\pi$
$127$	−19.0000	+	19.0000i	−0.149606	+	0.149606i	0.628336	+	0.777942i	$0.283736\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			15.5563i			0.120592i
$130$	15.0000	+	15.0000i	0.115385	+	0.115385i
$131$	79.1960			0.604549			0.302275	−	0.953221i	$-0.402254\pi$
$131$	79.1960			0.604549			0.302275	+	0.953221i	$0.402254\pi$
$132$	7.07107	−	7.07107i	0.0535687	−	0.0535687i
$133$		0			0
$134$		−	150.000i		−	1.11940i
$135$	85.0000			0.629630
$136$	−76.3675			−0.561526
$137$	88.0000	−	88.0000i	0.642336	−	0.642336i	−0.308793	−	0.951129i	$-0.599925\pi$
$137$	88.0000	−	88.0000i	0.642336	−	0.642336i	0.951129	+	0.308793i	$0.0999252\pi$
$138$	11.3137	+	11.3137i	0.0819834	+	0.0819834i
$139$			124.451i			0.895329i	0.894201	+	0.447665i	$0.147744\pi$
$139$			124.451i			0.895329i	−0.894201	+	0.447665i	$0.852256\pi$
$140$		0			0
$141$	−71.0000			−0.503546
$142$	−104.000	+	104.000i	−0.732394	+	0.732394i
$143$	10.6066	+	10.6066i	0.0741720	+	0.0741720i
$144$			32.0000i			0.222222i
$145$	60.1041	−	60.1041i	0.414511	−	0.414511i
$146$	−79.1960			−0.542438
$147$		0			0
$148$	48.0000	+	48.0000i	0.324324	+	0.324324i
$149$		−	232.000i		−	1.55705i	−0.627615	−	0.778523i	$-0.715969\pi$
$149$		−	232.000i		−	1.55705i	0.627615	−	0.778523i	$-0.284031\pi$
$150$			35.3553i			0.235702i
$151$	−3.00000			−0.0198675			−0.00993377	−	0.999951i	$-0.503162\pi$
$151$	−3.00000			−0.0198675			−0.00993377	+	0.999951i	$0.503162\pi$
$152$	25.4558	−	25.4558i	0.167473	−	0.167473i
$153$	−152.735	−	152.735i	−0.998268	−	0.998268i
$154$		0			0
$155$	205.000	+	205.000i	1.32258	+	1.32258i
$156$	6.00000			0.0384615
$157$	−181.019	+	181.019i	−1.15299	+	1.15299i	−0.167039	+	0.985950i	$0.553421\pi$
$157$	−181.019	+	181.019i	−1.15299	+	1.15299i	−0.985950	+	0.167039i	$0.946579\pi$
$158$	−115.000	−	115.000i	−0.727848	−	0.727848i
$159$		−	46.6690i		−	0.293516i
$160$	−28.2843			−0.176777
$161$		0			0
$162$	−55.0000	+	55.0000i	−0.339506	+	0.339506i
$163$	136.000	+	136.000i	0.834356	+	0.834356i	0.988109	−	0.153753i	$-0.0491361\pi$
$163$	136.000	+	136.000i	0.834356	+	0.834356i	−0.153753	+	0.988109i	$0.549136\pi$
$164$		−	53.7401i		−	0.327684i
$165$			25.0000i			0.151515i
$166$	147.078			0.886013
$167$	−74.2462	+	74.2462i	−0.444588	+	0.444588i	−0.893551	−	0.448963i	$-0.851794\pi$
$167$	−74.2462	+	74.2462i	−0.444588	+	0.444588i	0.448963	+	0.893551i	$0.351794\pi$
$168$		0			0
$169$		−	160.000i		−	0.946746i
$170$	135.000	−	135.000i	0.794118	−	0.794118i
$171$	101.823			0.595458
$172$	22.0000	−	22.0000i	0.127907	−	0.127907i
$173$	183.141	+	183.141i	1.05862	+	1.05862i	0.998172	+	0.0604450i	$0.0192520\pi$
$173$	183.141	+	183.141i	1.05862	+	1.05862i	0.0604450	+	0.998172i	$0.480748\pi$
$174$		−	24.0416i		−	0.138170i
$175$		0			0
$176$	−20.0000			−0.113636
$177$	39.0000	−	39.0000i	0.220339	−	0.220339i
$178$	113.137	+	113.137i	0.635602	+	0.635602i
$179$		−	16.0000i		−	0.0893855i	−0.999001	−	0.0446927i	$-0.985769\pi$
$179$		−	16.0000i		−	0.0893855i	0.999001	−	0.0446927i	$-0.0142309\pi$
$180$	−56.5685	−	56.5685i	−0.314270	−	0.314270i
$181$	−207.889			−1.14856			−0.574280	−	0.818659i	$-0.694718\pi$
$181$	−207.889			−1.14856			−0.574280	+	0.818659i	$0.694718\pi$
$182$		0			0
$183$	−32.0000	−	32.0000i	−0.174863	−	0.174863i
$184$		−	32.0000i		−	0.173913i
$185$	−169.706			−0.917328
$186$	82.0000			0.440860
$187$	95.4594	−	95.4594i	0.510478	−	0.510478i
$188$	100.409	+	100.409i	0.534091	+	0.534091i
$189$		0			0
$190$			90.0000i			0.473684i
$191$	−341.000			−1.78534			−0.892670	−	0.450711i	$-0.851171\pi$
$191$	−341.000			−1.78534			−0.892670	+	0.450711i	$0.851171\pi$
$192$	−5.65685	+	5.65685i	−0.0294628	+	0.0294628i
$193$	−72.0000	−	72.0000i	−0.373057	−	0.373057i	0.495532	−	0.868589i	$-0.334973\pi$
$193$	−72.0000	−	72.0000i	−0.373057	−	0.373057i	−0.868589	+	0.495532i	$0.834973\pi$
$194$			162.635i			0.838322i
$195$	−10.6066	+	10.6066i	−0.0543928	+	0.0543928i
$196$		0			0
$197$	−169.000	+	169.000i	−0.857868	+	0.857868i	−0.991087	−	0.133219i	$-0.957469\pi$
$197$	−169.000	+	169.000i	−0.857868	+	0.857868i	0.133219	+	0.991087i	$0.457469\pi$
$198$	−40.0000	−	40.0000i	−0.202020	−	0.202020i
$199$			213.546i			1.07310i	0.843870	+	0.536548i	$0.180272\pi$
$199$			213.546i			1.07310i	−0.843870	+	0.536548i	$0.819728\pi$
$200$	50.0000	−	50.0000i	0.250000	−	0.250000i
$201$	106.066			0.527692
$202$	−97.5807	+	97.5807i	−0.483073	+	0.483073i
$203$		0			0
$204$		−	54.0000i		−	0.264706i
$205$	95.0000	+	95.0000i	0.463415	+	0.463415i
$206$	−69.2965			−0.336391
$207$	64.0000	−	64.0000i	0.309179	−	0.309179i
$208$	−8.48528	−	8.48528i	−0.0407946	−	0.0407946i
$209$			63.6396i			0.304496i
$210$		0			0
$211$	−179.000			−0.848341			−0.424171	−	0.905582i	$-0.639434\pi$
$211$	−179.000			−0.848341			−0.424171	+	0.905582i	$0.639434\pi$
$212$	−66.0000	+	66.0000i	−0.311321	+	0.311321i
$213$	−73.5391	−	73.5391i	−0.345254	−	0.345254i
$214$			150.000i			0.700935i
$215$			77.7817i			0.361776i
$216$	−48.0833			−0.222608
$217$		0			0
$218$	119.000	+	119.000i	0.545872	+	0.545872i
$219$		−	56.0000i		−	0.255708i
$220$	35.3553	−	35.3553i	0.160706	−	0.160706i
$221$	81.0000			0.366516
$222$	−33.9411	+	33.9411i	−0.152888	+	0.152888i
$223$	40.3051	+	40.3051i	0.180740	+	0.180740i	0.791678	−	0.610938i	$-0.209208\pi$
$223$	40.3051	+	40.3051i	0.180740	+	0.180740i	−0.610938	+	0.791678i	$0.709208\pi$
$224$		0			0
$225$	200.000			0.888889
$226$	−32.0000			−0.141593
$227$	129.401	−	129.401i	0.570046	−	0.570046i	−0.362095	−	0.932141i	$-0.617938\pi$
$227$	129.401	−	129.401i	0.570046	−	0.570046i	0.932141	+	0.362095i	$0.117938\pi$
$228$	18.0000	+	18.0000i	0.0789474	+	0.0789474i
$229$		−	233.345i		−	1.01897i	−0.860478	−	0.509487i	$-0.829835\pi$
$229$		−	233.345i		−	1.01897i	0.860478	−	0.509487i	$-0.170165\pi$
$230$	56.5685	+	56.5685i	0.245950	+	0.245950i
$231$		0			0
$232$	−34.0000	+	34.0000i	−0.146552	+	0.146552i
$233$	320.000	+	320.000i	1.37339	+	1.37339i	0.855365	+	0.518025i	$0.173333\pi$
$233$	320.000	+	320.000i	1.37339	+	1.37339i	0.518025	+	0.855365i	$0.326667\pi$
$234$		−	33.9411i		−	0.145048i
$235$	−355.000			−1.51064
$236$	−110.309			−0.467410
$237$	81.3173	−	81.3173i	0.343111	−	0.343111i
$238$		0			0
$239$		−	397.000i		−	1.66109i	−0.556953	−	0.830544i	$-0.688030\pi$
$239$		−	397.000i		−	1.66109i	0.556953	−	0.830544i	$-0.311970\pi$
$240$		−	20.0000i		−	0.0833333i
$241$	−248.902			−1.03279			−0.516393	−	0.856352i	$-0.672726\pi$
$241$	−248.902			−1.03279			−0.516393	+	0.856352i	$0.672726\pi$
$242$	−96.0000	+	96.0000i	−0.396694	+	0.396694i
$243$	−147.078	−	147.078i	−0.605260	−	0.605260i
$244$			90.5097i			0.370941i
$245$		0			0
$246$	38.0000			0.154472
$247$	−27.0000	+	27.0000i	−0.109312	+	0.109312i
$248$	−115.966	−	115.966i	−0.467603	−	0.467603i
$249$			104.000i			0.417671i
$250$			176.777i			0.707107i
$251$	452.548			1.80298			0.901491	−	0.432798i	$-0.142474\pi$
$251$	452.548			1.80298			0.901491	+	0.432798i	$0.142474\pi$
$252$		0			0
$253$	40.0000	+	40.0000i	0.158103	+	0.158103i
$254$			38.0000i			0.149606i
$255$	95.4594	+	95.4594i	0.374351	+	0.374351i
$256$	16.0000			0.0625000
$257$	28.2843	−	28.2843i	0.110056	−	0.110056i	−0.649935	−	0.759990i	$-0.725204\pi$
$257$	28.2843	−	28.2843i	0.110056	−	0.110056i	0.759990	+	0.649935i	$0.225204\pi$
$258$	15.5563	+	15.5563i	0.0602959	+	0.0602959i
$259$		0			0
$260$	30.0000			0.115385
$261$	−136.000			−0.521073
$262$	79.1960	−	79.1960i	0.302275	−	0.302275i
$263$	245.000	+	245.000i	0.931559	+	0.931559i	0.997803	−	0.0662445i	$-0.0211017\pi$
$263$	245.000	+	245.000i	0.931559	+	0.931559i	−0.0662445	+	0.997803i	$0.521102\pi$
$264$		−	14.1421i		−	0.0535687i
$265$		−	233.345i		−	0.880548i
$266$		0			0
$267$	−80.0000	+	80.0000i	−0.299625	+	0.299625i
$268$	−150.000	−	150.000i	−0.559701	−	0.559701i
$269$		−	305.470i		−	1.13558i	−0.823175	−	0.567788i	$-0.807799\pi$
$269$		−	305.470i		−	1.13558i	0.823175	−	0.567788i	$-0.192201\pi$
$270$	85.0000	−	85.0000i	0.314815	−	0.314815i
$271$	−463.862			−1.71167			−0.855834	−	0.517251i	$-0.826956\pi$
$271$	−463.862			−1.71167			−0.855834	+	0.517251i	$0.826956\pi$
$272$	−76.3675	+	76.3675i	−0.280763	+	0.280763i
$273$		0			0
$274$		−	176.000i		−	0.642336i
$275$			125.000i			0.454545i
$276$	22.6274			0.0819834
$277$	160.000	−	160.000i	0.577617	−	0.577617i	−0.356629	−	0.934246i	$-0.616074\pi$
$277$	160.000	−	160.000i	0.577617	−	0.577617i	0.934246	+	0.356629i	$0.116074\pi$
$278$	124.451	+	124.451i	0.447665	+	0.447665i
$279$		−	463.862i		−	1.66259i
$280$		0			0
$281$	−47.0000			−0.167260			−0.0836299	−	0.996497i	$-0.526651\pi$
$281$	−47.0000			−0.167260			−0.0836299	+	0.996497i	$0.526651\pi$
$282$	−71.0000	+	71.0000i	−0.251773	+	0.251773i
$283$	225.567	+	225.567i	0.797057	+	0.797057i	0.982630	−	0.185574i	$-0.0594143\pi$
$283$	225.567	+	225.567i	0.797057	+	0.797057i	−0.185574	+	0.982630i	$0.559414\pi$
$284$			208.000i			0.732394i
$285$	−63.6396			−0.223297
$286$	21.2132			0.0741720
$287$		0			0
$288$	32.0000	+	32.0000i	0.111111	+	0.111111i
$289$		−	440.000i		−	1.52249i
$290$		−	120.208i		−	0.414511i
$291$	−115.000			−0.395189
$292$	−79.1960	+	79.1960i	−0.271219	+	0.271219i
$293$	20.5061	+	20.5061i	0.0699867	+	0.0699867i	0.741234	−	0.671247i	$-0.234241\pi$
$293$	20.5061	+	20.5061i	0.0699867	+	0.0699867i	−0.671247	+	0.741234i	$0.734241\pi$
$294$		0			0
$295$	195.000	−	195.000i	0.661017	−	0.661017i
$296$	96.0000			0.324324
$297$	60.1041	−	60.1041i	0.202371	−	0.202371i
$298$	−232.000	−	232.000i	−0.778523	−	0.778523i
$299$			33.9411i			0.113515i
$300$	35.3553	+	35.3553i	0.117851	+	0.117851i
$301$		0			0
$302$	−3.00000	+	3.00000i	−0.00993377	+	0.00993377i
$303$	−69.0000	−	69.0000i	−0.227723	−	0.227723i
$304$		−	50.9117i		−	0.167473i
$305$	−160.000	−	160.000i	−0.524590	−	0.524590i
$306$	−305.470			−0.998268
$307$	310.420	−	310.420i	1.01114	−	1.01114i	0.0112024	−	0.999937i	$-0.496434\pi$
$307$	310.420	−	310.420i	1.01114	−	1.01114i	0.999937	−	0.0112024i	$-0.00356591\pi$
$308$		0			0
$309$		−	49.0000i		−	0.158576i
$310$	410.000			1.32258
$311$	405.879			1.30508			0.652539	−	0.757755i	$-0.273704\pi$
$311$	405.879			1.30508			0.652539	+	0.757755i	$0.273704\pi$
$312$	6.00000	−	6.00000i	0.0192308	−	0.0192308i
$313$	−195.869	−	195.869i	−0.625778	−	0.625778i	0.321225	−	0.947003i	$-0.395905\pi$
$313$	−195.869	−	195.869i	−0.625778	−	0.625778i	−0.947003	+	0.321225i	$0.895905\pi$
$314$			362.039i			1.15299i
$315$		0			0
$316$	−230.000			−0.727848
$317$	−1.00000	+	1.00000i	−0.00315457	+	0.00315457i	−0.708682	−	0.705528i	$-0.750710\pi$
$317$	−1.00000	+	1.00000i	−0.00315457	+	0.00315457i	0.705528	+	0.708682i	$0.250710\pi$
$318$	−46.6690	−	46.6690i	−0.146758	−	0.146758i
$319$		−	85.0000i		−	0.266458i
$320$	−28.2843	+	28.2843i	−0.0883883	+	0.0883883i
$321$	−106.066			−0.330424
$322$		0			0
$323$	243.000	+	243.000i	0.752322	+	0.752322i
$324$			110.000i			0.339506i
$325$	−53.0330	+	53.0330i	−0.163178	+	0.163178i
$326$	272.000			0.834356
$327$	−84.1457	+	84.1457i	−0.257326	+	0.257326i
$328$	−53.7401	−	53.7401i	−0.163842	−	0.163842i
$329$		0			0
$330$	25.0000	+	25.0000i	0.0757576	+	0.0757576i
$331$	32.0000			0.0966767			0.0483384	−	0.998831i	$-0.484607\pi$
$331$	32.0000			0.0966767			0.0483384	+	0.998831i	$0.484607\pi$
$332$	147.078	−	147.078i	0.443007	−	0.443007i
$333$	192.000	+	192.000i	0.576577	+	0.576577i
$334$			148.492i			0.444588i
$335$	530.330			1.58307
$336$		0			0
$337$	−400.000	+	400.000i	−1.18694	+	1.18694i	−0.209036	+	0.977908i	$0.567032\pi$
$337$	−400.000	+	400.000i	−1.18694	+	1.18694i	−0.977908	+	0.209036i	$0.932968\pi$
$338$	−160.000	−	160.000i	−0.473373	−	0.473373i
$339$		−	22.6274i		−	0.0667475i
$340$		−	270.000i		−	0.794118i
$341$	289.914			0.850187
$342$	101.823	−	101.823i	0.297729	−	0.297729i
$343$		0			0
$344$		−	44.0000i		−	0.127907i
$345$	−40.0000	+	40.0000i	−0.115942	+	0.115942i
$346$	366.281			1.05862
$347$	−120.000	+	120.000i	−0.345821	+	0.345821i	−0.858550	−	0.512729i	$-0.828635\pi$
$347$	−120.000	+	120.000i	−0.345821	+	0.345821i	0.512729	+	0.858550i	$0.328635\pi$
$348$	−24.0416	−	24.0416i	−0.0690851	−	0.0690851i
$349$		−	482.247i		−	1.38180i	−0.722952	−	0.690898i	$-0.757215\pi$
$349$		−	482.247i		−	1.38180i	0.722952	−	0.690898i	$-0.242785\pi$
$350$		0			0
$351$	51.0000			0.145299
$352$	−20.0000	+	20.0000i	−0.0568182	+	0.0568182i
$353$	−122.329	−	122.329i	−0.346542	−	0.346542i	0.512278	−	0.858820i	$-0.328802\pi$
$353$	−122.329	−	122.329i	−0.346542	−	0.346542i	−0.858820	+	0.512278i	$0.828802\pi$
$354$		−	78.0000i		−	0.220339i
$355$	−367.696	−	367.696i	−1.03576	−	1.03576i
$356$	226.274			0.635602
$357$		0			0
$358$	−16.0000	−	16.0000i	−0.0446927	−	0.0446927i
$359$		−	360.000i		−	1.00279i	−0.865220	−	0.501393i	$-0.832821\pi$
$359$		−	360.000i		−	1.00279i	0.865220	−	0.501393i	$-0.167179\pi$
$360$	−113.137			−0.314270
$361$	199.000			0.551247
$362$	−207.889	+	207.889i	−0.574280	+	0.574280i
$363$	−67.8823	−	67.8823i	−0.187003	−	0.187003i
$364$		0			0
$365$		−	280.000i		−	0.767123i
$366$	−64.0000			−0.174863
$367$	136.472	−	136.472i	0.371857	−	0.371857i	−0.496296	−	0.868153i	$-0.665307\pi$
$367$	136.472	−	136.472i	0.371857	−	0.371857i	0.868153	+	0.496296i	$0.165307\pi$
$368$	−32.0000	−	32.0000i	−0.0869565	−	0.0869565i
$369$		−	214.960i		−	0.582549i
$370$	−169.706	+	169.706i	−0.458664	+	0.458664i
$371$		0			0
$372$	82.0000	−	82.0000i	0.220430	−	0.220430i
$373$	−8.00000	−	8.00000i	−0.0214477	−	0.0214477i	0.696302	−	0.717749i	$-0.254828\pi$
$373$	−8.00000	−	8.00000i	−0.0214477	−	0.0214477i	−0.717749	+	0.696302i	$0.754828\pi$
$374$		−	190.919i		−	0.510478i
$375$	−125.000			−0.333333
$376$	200.818			0.534091
$377$	36.0624	−	36.0624i	0.0956564	−	0.0956564i
$378$		0			0
$379$			202.000i			0.532982i	0.963837	+	0.266491i	$0.0858642\pi$
$379$			202.000i			0.532982i	−0.963837	+	0.266491i	$0.914136\pi$
$380$	90.0000	+	90.0000i	0.236842	+	0.236842i
$381$	−26.8701			−0.0705251
$382$	−341.000	+	341.000i	−0.892670	+	0.892670i
$383$	282.843	+	282.843i	0.738493	+	0.738493i	0.972286	−	0.233794i	$-0.0751140\pi$
$383$	282.843	+	282.843i	0.738493	+	0.738493i	−0.233794	+	0.972286i	$0.575114\pi$
$384$			11.3137i			0.0294628i
$385$		0			0
$386$	−144.000			−0.373057
$387$	88.0000	−	88.0000i	0.227390	−	0.227390i
$388$	162.635	+	162.635i	0.419161	+	0.419161i
$389$		−	319.000i		−	0.820051i	−0.912074	−	0.410026i	$-0.865520\pi$
$389$		−	319.000i		−	0.820051i	0.912074	−	0.410026i	$-0.134480\pi$
$390$			21.2132i			0.0543928i
$391$	305.470			0.781254
$392$		0			0
$393$	56.0000	+	56.0000i	0.142494	+	0.142494i
$394$			338.000i			0.857868i
$395$	406.586	−	406.586i	1.02933	−	1.02933i
$396$	−80.0000			−0.202020
$397$	−3.53553	+	3.53553i	−0.00890563	+	0.00890563i	−0.711546	−	0.702640i	$-0.752004\pi$
$397$	−3.53553	+	3.53553i	−0.00890563	+	0.00890563i	0.702640	+	0.711546i	$0.252004\pi$
$398$	213.546	+	213.546i	0.536548	+	0.536548i
$399$		0			0
$400$		−	100.000i		−	0.250000i
$401$	−151.000			−0.376559			−0.188279	−	0.982116i	$-0.560291\pi$
$401$	−151.000			−0.376559			−0.188279	+	0.982116i	$0.560291\pi$
$402$	106.066	−	106.066i	0.263846	−	0.263846i
$403$	123.000	+	123.000i	0.305211	+	0.305211i
$404$			195.161i			0.483073i
$405$	−194.454	−	194.454i	−0.480134	−	0.480134i
$406$		0			0
$407$	−120.000	+	120.000i	−0.294840	+	0.294840i
$408$	−54.0000	−	54.0000i	−0.132353	−	0.132353i
$409$		−	117.380i		−	0.286992i	−0.989651	−	0.143496i	$-0.954166\pi$
$409$		−	117.380i		−	0.286992i	0.989651	−	0.143496i	$-0.0458344\pi$
$410$	190.000			0.463415
$411$	124.451			0.302800
$412$	−69.2965	+	69.2965i	−0.168195	+	0.168195i
$413$		0			0
$414$		−	128.000i		−	0.309179i
$415$			520.000i			1.25301i
$416$	−16.9706			−0.0407946
$417$	−88.0000	+	88.0000i	−0.211031	+	0.211031i
$418$	63.6396	+	63.6396i	0.152248	+	0.152248i
$419$			496.389i			1.18470i	0.805681	+	0.592350i	$0.201800\pi$
$419$			496.389i			1.18470i	−0.805681	+	0.592350i	$0.798200\pi$
$420$		0			0
$421$	425.000			1.00950			0.504751	−	0.863265i	$-0.331584\pi$
$421$	425.000			1.00950			0.504751	+	0.863265i	$0.331584\pi$
$422$	−179.000	+	179.000i	−0.424171	+	0.424171i
$423$	401.637	+	401.637i	0.949496	+	0.949496i
$424$			132.000i			0.311321i
$425$	477.297	+	477.297i	1.12305	+	1.12305i
$426$	−147.078			−0.345254
$427$		0			0
$428$	150.000	+	150.000i	0.350467	+	0.350467i
$429$			15.0000i			0.0349650i
$430$	77.7817	+	77.7817i	0.180888	+	0.180888i
$431$	171.000			0.396752			0.198376	−	0.980126i	$-0.436433\pi$
$431$	171.000			0.396752			0.198376	+	0.980126i	$0.436433\pi$
$432$	−48.0833	+	48.0833i	−0.111304	+	0.111304i
$433$	−190.919	−	190.919i	−0.440921	−	0.440921i	0.451400	−	0.892322i	$-0.350925\pi$
$433$	−190.919	−	190.919i	−0.440921	−	0.440921i	−0.892322	+	0.451400i	$0.850925\pi$
$434$		0			0
$435$	85.0000			0.195402
$436$	238.000			0.545872
$437$	−101.823	+	101.823i	−0.233005	+	0.233005i
$438$	−56.0000	−	56.0000i	−0.127854	−	0.127854i
$439$			147.078i			0.335030i	0.985870	+	0.167515i	$0.0535743\pi$
$439$			147.078i			0.335030i	−0.985870	+	0.167515i	$0.946426\pi$
$440$		−	70.7107i		−	0.160706i
$441$		0			0
$442$	81.0000	−	81.0000i	0.183258	−	0.183258i
$443$	333.000	+	333.000i	0.751693	+	0.751693i	0.974795	−	0.223102i	$-0.0716183\pi$
$443$	333.000	+	333.000i	0.751693	+	0.751693i	−0.223102	+	0.974795i	$0.571618\pi$
$444$			67.8823i			0.152888i
$445$	−400.000	+	400.000i	−0.898876	+	0.898876i
$446$	80.6102			0.180740
$447$	164.049	−	164.049i	0.366999	−	0.366999i
$448$		0			0
$449$		−	305.000i		−	0.679287i	−0.940554	−	0.339644i	$-0.889694\pi$
$449$		−	305.000i		−	0.679287i	0.940554	−	0.339644i	$-0.110306\pi$
$450$	200.000	−	200.000i	0.444444	−	0.444444i
$451$	134.350			0.297894
$452$	−32.0000	+	32.0000i	−0.0707965	+	0.0707965i
$453$	−2.12132	−	2.12132i	−0.00468283	−	0.00468283i
$454$		−	258.801i		−	0.570046i
$455$		0			0
$456$	36.0000			0.0789474
$457$	−207.000	+	207.000i	−0.452954	+	0.452954i	−0.896334	−	0.443380i	$-0.853779\pi$
$457$	−207.000	+	207.000i	−0.452954	+	0.452954i	0.443380	+	0.896334i	$0.353779\pi$
$458$	−233.345	−	233.345i	−0.509487	−	0.509487i
$459$		−	459.000i		−	1.00000i
$460$	113.137			0.245950
$461$	−305.470			−0.662625			−0.331313	−	0.943521i	$-0.607491\pi$
$461$	−305.470			−0.662625			−0.331313	+	0.943521i	$0.607491\pi$
$462$		0			0
$463$	−312.000	−	312.000i	−0.673866	−	0.673866i	0.284739	−	0.958605i	$-0.408093\pi$
$463$	−312.000	−	312.000i	−0.673866	−	0.673866i	−0.958605	+	0.284739i	$0.908093\pi$
$464$			68.0000i			0.146552i
$465$			289.914i			0.623470i
$466$	640.000			1.37339
$467$	321.734	−	321.734i	0.688937	−	0.688937i	−0.273060	−	0.961997i	$-0.588036\pi$
$467$	321.734	−	321.734i	0.688937	−	0.688937i	0.961997	+	0.273060i	$0.0880358\pi$
$468$	−33.9411	−	33.9411i	−0.0725238	−	0.0725238i
$469$		0			0
$470$	−355.000	+	355.000i	−0.755319	+	0.755319i
$471$	−256.000			−0.543524
$472$	−110.309	+	110.309i	−0.233705	+	0.233705i
$473$	55.0000	+	55.0000i	0.116279	+	0.116279i
$474$		−	162.635i		−	0.343111i
$475$	−318.198			−0.669891
$476$		0			0
$477$	−264.000	+	264.000i	−0.553459	+	0.553459i
$478$	−397.000	−	397.000i	−0.830544	−	0.830544i
$479$			610.940i			1.27545i	0.770264	+	0.637725i	$0.220124\pi$
$479$			610.940i			1.27545i	−0.770264	+	0.637725i	$0.779876\pi$
$480$	−20.0000	−	20.0000i	−0.0416667	−	0.0416667i
$481$	−101.823			−0.211691
$482$	−248.902	+	248.902i	−0.516393	+	0.516393i
$483$		0			0
$484$			192.000i			0.396694i
$485$	−575.000			−1.18557
$486$	−294.156			−0.605260
$487$	8.00000	−	8.00000i	0.0164271	−	0.0164271i	−0.698846	−	0.715273i	$-0.746303\pi$
$487$	8.00000	−	8.00000i	0.0164271	−	0.0164271i	0.715273	+	0.698846i	$0.246303\pi$
$488$	90.5097	+	90.5097i	0.185471	+	0.185471i
$489$			192.333i			0.393319i
$490$		0			0
$491$	99.0000			0.201629			0.100815	−	0.994905i	$-0.467855\pi$
$491$	99.0000			0.201629			0.100815	+	0.994905i	$0.467855\pi$
$492$	38.0000	−	38.0000i	0.0772358	−	0.0772358i
$493$	−324.562	−	324.562i	−0.658341	−	0.658341i
$494$			54.0000i			0.109312i
$495$	141.421	−	141.421i	0.285700	−	0.285700i
$496$	−231.931			−0.467603
$497$		0			0
$498$	104.000	+	104.000i	0.208835	+	0.208835i
$499$		−	195.000i		−	0.390782i	−0.980725	−	0.195391i	$-0.937402\pi$
$499$		−	195.000i		−	0.390782i	0.980725	−	0.195391i	$-0.0625975\pi$
$500$	176.777	+	176.777i	0.353553	+	0.353553i
$501$	−105.000			−0.209581
$502$	452.548	−	452.548i	0.901491	−	0.901491i
$503$	395.273	+	395.273i	0.785830	+	0.785830i	0.980808	−	0.194977i	$-0.0624633\pi$
$503$	395.273	+	395.273i	0.785830	+	0.785830i	−0.194977	+	0.980808i	$0.562463\pi$
$504$		0			0
$505$	−345.000	−	345.000i	−0.683168	−	0.683168i
$506$	80.0000			0.158103
$507$	113.137	−	113.137i	0.223150	−	0.223150i
$508$	38.0000	+	38.0000i	0.0748031	+	0.0748031i
$509$			294.156i			0.577910i	0.957343	+	0.288955i	$0.0933079\pi$
$509$			294.156i			0.577910i	−0.957343	+	0.288955i	$0.906692\pi$
$510$	190.919			0.374351
$511$		0			0
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	153.000	+	153.000i	0.298246	+	0.298246i
$514$		−	56.5685i		−	0.110056i
$515$		−	245.000i		−	0.475728i
$516$	31.1127			0.0602959
$517$	−251.023	+	251.023i	−0.485538	+	0.485538i
$518$		0			0
$519$			259.000i			0.499037i
$520$	30.0000	−	30.0000i	0.0576923	−	0.0576923i
$521$	−592.555			−1.13734			−0.568671	−	0.822565i	$-0.692542\pi$
$521$	−592.555			−1.13734			−0.568671	+	0.822565i	$0.692542\pi$
$522$	−136.000	+	136.000i	−0.260536	+	0.260536i
$523$	−502.046	−	502.046i	−0.959935	−	0.959935i	0.0392931	−	0.999228i	$-0.487489\pi$
$523$	−502.046	−	502.046i	−0.959935	−	0.959935i	−0.999228	+	0.0392931i	$0.987489\pi$
$524$		−	158.392i		−	0.302275i
$525$		0			0
$526$	490.000			0.931559
$527$	1107.00	−	1107.00i	2.10057	−	2.10057i
$528$	−14.1421	−	14.1421i	−0.0267843	−	0.0267843i
$529$		−	401.000i		−	0.758034i
$530$	−233.345	−	233.345i	−0.440274	−	0.440274i
$531$	−441.235			−0.830950
$532$		0			0
$533$	57.0000	+	57.0000i	0.106942	+	0.106942i
$534$			160.000i			0.299625i
$535$	−530.330			−0.991271
$536$	−300.000			−0.559701
$537$	11.3137	−	11.3137i	0.0210684	−	0.0210684i
$538$	−305.470	−	305.470i	−0.567788	−	0.567788i
$539$		0			0
$540$		−	170.000i		−	0.314815i
$541$	393.000			0.726433			0.363216	−	0.931705i	$-0.381679\pi$
$541$	393.000			0.726433			0.363216	+	0.931705i	$0.381679\pi$
$542$	−463.862	+	463.862i	−0.855834	+	0.855834i
$543$	−147.000	−	147.000i	−0.270718	−	0.270718i
$544$			152.735i			0.280763i
$545$	−420.729	+	420.729i	−0.771979	+	0.771979i
$546$		0			0
$547$	448.000	−	448.000i	0.819013	−	0.819013i	−0.166952	−	0.985965i	$-0.553393\pi$
$547$	448.000	−	448.000i	0.819013	−	0.819013i	0.985965	+	0.166952i	$0.0533926\pi$
$548$	−176.000	−	176.000i	−0.321168	−	0.321168i
$549$			362.039i			0.659451i
$550$	125.000	+	125.000i	0.227273	+	0.227273i
$551$	216.375			0.392695
$552$	22.6274	−	22.6274i	0.0409917	−	0.0409917i
$553$		0			0
$554$		−	320.000i		−	0.577617i
$555$	−120.000	−	120.000i	−0.216216	−	0.216216i
$556$	248.902			0.447665
$557$	−208.000	+	208.000i	−0.373429	+	0.373429i	−0.868725	−	0.495295i	$-0.835060\pi$
$557$	−208.000	+	208.000i	−0.373429	+	0.373429i	0.495295	+	0.868725i	$0.335060\pi$
$558$	−463.862	−	463.862i	−0.831294	−	0.831294i
$559$			46.6690i			0.0834867i
$560$		0			0
$561$	135.000			0.240642
$562$	−47.0000	+	47.0000i	−0.0836299	+	0.0836299i
$563$	−243.245	−	243.245i	−0.432051	−	0.432051i	0.457275	−	0.889326i	$-0.348826\pi$
$563$	−243.245	−	243.245i	−0.432051	−	0.432051i	−0.889326	+	0.457275i	$0.848826\pi$
$564$			142.000i			0.251773i
$565$		−	113.137i		−	0.200243i
$566$	451.134			0.797057
$567$		0			0
$568$	208.000	+	208.000i	0.366197	+	0.366197i
$569$			352.000i			0.618629i	0.950960	+	0.309315i	$0.100100\pi$
$569$			352.000i			0.618629i	−0.950960	+	0.309315i	$0.899900\pi$
$570$	−63.6396	+	63.6396i	−0.111648	+	0.111648i
$571$	592.000			1.03678			0.518389	−	0.855145i	$-0.326532\pi$
$571$	592.000			1.03678			0.518389	+	0.855145i	$0.326532\pi$
$572$	21.2132	−	21.2132i	0.0370860	−	0.0370860i
$573$	−241.123	−	241.123i	−0.420809	−	0.420809i
$574$		0			0
$575$	−200.000	+	200.000i	−0.347826	+	0.347826i
$576$	64.0000			0.111111
$577$	−573.464	+	573.464i	−0.993871	+	0.993871i	−0.999981	−	0.00611028i	$-0.998055\pi$
$577$	−573.464	+	573.464i	−0.993871	+	0.993871i	0.00611028	+	0.999981i	$0.498055\pi$
$578$	−440.000	−	440.000i	−0.761246	−	0.761246i
$579$		−	101.823i		−	0.175861i
$580$	−120.208	−	120.208i	−0.207255	−	0.207255i
$581$		0			0
$582$	−115.000	+	115.000i	−0.197595	+	0.197595i
$583$	−165.000	−	165.000i	−0.283019	−	0.283019i
$584$			158.392i			0.271219i
$585$	120.000			0.205128
$586$	41.0122			0.0699867
$587$	−526.087	+	526.087i	−0.896231	+	0.896231i	−0.995100	−	0.0988697i	$-0.968477\pi$
$587$	−526.087	+	526.087i	−0.896231	+	0.896231i	0.0988697	+	0.995100i	$0.468477\pi$
$588$		0			0
$589$			738.000i			1.25297i
$590$		−	390.000i		−	0.661017i
$591$	−239.002			−0.404403
$592$	96.0000	−	96.0000i	0.162162	−	0.162162i
$593$	359.917	+	359.917i	0.606943	+	0.606943i	0.942146	−	0.335203i	$-0.108805\pi$
$593$	359.917	+	359.917i	0.606943	+	0.606943i	−0.335203	+	0.942146i	$0.608805\pi$
$594$		−	120.208i		−	0.202371i
$595$		0			0
$596$	−464.000			−0.778523
$597$	−151.000	+	151.000i	−0.252931	+	0.252931i
$598$	33.9411	+	33.9411i	0.0567577	+	0.0567577i
$599$			387.000i			0.646077i	0.946386	+	0.323038i	$0.104704\pi$
$599$			387.000i			0.646077i	−0.946386	+	0.323038i	$0.895296\pi$
$600$	70.7107			0.117851
$601$	−188.090			−0.312962			−0.156481	−	0.987681i	$-0.550015\pi$
$601$	−188.090			−0.312962			−0.156481	+	0.987681i	$0.550015\pi$
$602$		0			0
$603$	−600.000	−	600.000i	−0.995025	−	0.995025i
$604$			6.00000i			0.00993377i
$605$	−339.411	−	339.411i	−0.561010	−	0.561010i
$606$	−138.000			−0.227723
$607$	−690.843	+	690.843i	−1.13813	+	1.13813i	−0.149342	+	0.988786i	$0.547715\pi$
$607$	−690.843	+	690.843i	−1.13813	+	1.13813i	−0.988786	+	0.149342i	$0.952285\pi$
$608$	−50.9117	−	50.9117i	−0.0837363	−	0.0837363i
$609$		0			0
$610$	−320.000			−0.524590
$611$	−213.000			−0.348609
$612$	−305.470	+	305.470i	−0.499134	+	0.499134i
$613$	489.000	+	489.000i	0.797716	+	0.797716i	0.982735	−	0.185019i	$-0.0592346\pi$
$613$	489.000	+	489.000i	0.797716	+	0.797716i	−0.185019	+	0.982735i	$0.559235\pi$
$614$		−	620.840i		−	1.01114i
$615$			134.350i			0.218456i
$616$		0			0
$617$	536.000	−	536.000i	0.868720	−	0.868720i	−0.123611	−	0.992331i	$-0.539448\pi$
$617$	536.000	−	536.000i	0.868720	−	0.868720i	0.992331	+	0.123611i	$0.0394475\pi$
$618$	−49.0000	−	49.0000i	−0.0792880	−	0.0792880i
$619$		−	407.294i		−	0.657986i	−0.944332	−	0.328993i	$-0.893291\pi$
$619$		−	407.294i		−	0.657986i	0.944332	−	0.328993i	$-0.106709\pi$
$620$	410.000	−	410.000i	0.661290	−	0.661290i
$621$	192.333			0.309715
$622$	405.879	−	405.879i	0.652539	−	0.652539i
$623$		0			0
$624$		−	12.0000i		−	0.0192308i
$625$	−625.000			−1.00000
$626$	−391.737			−0.625778
$627$	−45.0000	+	45.0000i	−0.0717703	+	0.0717703i
$628$	362.039	+	362.039i	0.576495	+	0.576495i
$629$			916.410i			1.45693i
$630$		0			0
$631$	67.0000			0.106181			0.0530903	−	0.998590i	$-0.483093\pi$
$631$	67.0000			0.106181			0.0530903	+	0.998590i	$0.483093\pi$
$632$	−230.000	+	230.000i	−0.363924	+	0.363924i
$633$	−126.572	−	126.572i	−0.199956	−	0.199956i
$634$			2.00000i			0.00315457i
$635$	−134.350			−0.211575
$636$	−93.3381			−0.146758
$637$		0			0
$638$	−85.0000	−	85.0000i	−0.133229	−	0.133229i
$639$			832.000i			1.30203i
$640$			56.5685i			0.0883883i
$641$	−1200.00			−1.87207			−0.936037	−	0.351900i	$-0.885536\pi$
$641$	−1200.00			−1.87207			−0.936037	+	0.351900i	$0.885536\pi$
$642$	−106.066	+	106.066i	−0.165212	+	0.165212i
$643$	310.420	+	310.420i	0.482768	+	0.482768i	0.906015	−	0.423246i	$-0.139110\pi$
$643$	310.420	+	310.420i	0.482768	+	0.482768i	−0.423246	+	0.906015i	$0.639110\pi$
$644$		0			0
$645$	−55.0000	+	55.0000i	−0.0852713	+	0.0852713i
$646$	486.000			0.752322
$647$	−352.139	+	352.139i	−0.544265	+	0.544265i	−0.924776	−	0.380512i	$-0.875748\pi$
$647$	−352.139	+	352.139i	−0.544265	+	0.544265i	0.380512	+	0.924776i	$0.375748\pi$
$648$	110.000	+	110.000i	0.169753	+	0.169753i
$649$		−	275.772i		−	0.424918i
$650$			106.066i			0.163178i
$651$		0			0
$652$	272.000	−	272.000i	0.417178	−	0.417178i
$653$	239.000	+	239.000i	0.366003	+	0.366003i	0.866017	−	0.500014i	$-0.166672\pi$
$653$	239.000	+	239.000i	0.366003	+	0.366003i	−0.500014	+	0.866017i	$0.666672\pi$
$654$			168.291i			0.257326i
$655$	280.000	+	280.000i	0.427481	+	0.427481i
$656$	−107.480			−0.163842
$657$	−316.784	+	316.784i	−0.482167	+	0.482167i
$658$		0			0
$659$			869.000i			1.31866i	0.751852	+	0.659332i	$0.229161\pi$
$659$			869.000i			1.31866i	−0.751852	+	0.659332i	$0.770839\pi$
$660$	50.0000			0.0757576
$661$	−588.313			−0.890035			−0.445017	−	0.895522i	$-0.646802\pi$
$661$	−588.313			−0.890035			−0.445017	+	0.895522i	$0.646802\pi$
$662$	32.0000	−	32.0000i	0.0483384	−	0.0483384i
$663$	57.2756	+	57.2756i	0.0863886	+	0.0863886i
$664$		−	294.156i		−	0.443007i
$665$		0			0
$666$	384.000			0.576577
$667$	136.000	−	136.000i	0.203898	−	0.203898i
$668$	148.492	+	148.492i	0.222294	+	0.222294i
$669$			57.0000i			0.0852018i
$670$	530.330	−	530.330i	0.791537	−	0.791537i
$671$	−226.274			−0.337219
$672$		0			0
$673$	32.0000	+	32.0000i	0.0475483	+	0.0475483i	0.730481	−	0.682933i	$-0.239296\pi$
$673$	32.0000	+	32.0000i	0.0475483	+	0.0475483i	−0.682933	+	0.730481i	$0.739296\pi$
$674$			800.000i			1.18694i
$675$	300.520	+	300.520i	0.445215	+	0.445215i
$676$	−320.000			−0.473373
$677$	−309.006	+	309.006i	−0.456434	+	0.456434i	−0.897483	−	0.441049i	$-0.854606\pi$
$677$	−309.006	+	309.006i	−0.456434	+	0.456434i	0.441049	+	0.897483i	$0.354606\pi$
$678$	−22.6274	−	22.6274i	−0.0333738	−	0.0333738i
$679$		0			0
$680$	−270.000	−	270.000i	−0.397059	−	0.397059i
$681$	183.000			0.268722
$682$	289.914	−	289.914i	0.425094	−	0.425094i
$683$	568.000	+	568.000i	0.831625	+	0.831625i	0.987739	−	0.156114i	$-0.0498967\pi$
$683$	568.000	+	568.000i	0.831625	+	0.831625i	−0.156114	+	0.987739i	$0.549897\pi$
$684$		−	203.647i		−	0.297729i
$685$	622.254			0.908400
$686$		0			0
$687$	165.000	−	165.000i	0.240175	−	0.240175i
$688$	−44.0000	−	44.0000i	−0.0639535	−	0.0639535i
$689$		−	140.007i		−	0.203203i
$690$			80.0000i			0.115942i
$691$	−67.8823			−0.0982377			−0.0491189	−	0.998793i	$-0.515641\pi$
$691$	−67.8823			−0.0982377			−0.0491189	+	0.998793i	$0.515641\pi$
$692$	366.281	−	366.281i	0.529308	−	0.529308i
$693$		0			0
$694$			240.000i			0.345821i
$695$	−440.000	+	440.000i	−0.633094	+	0.633094i
$696$	−48.0833			−0.0690851
$697$	513.000	−	513.000i	0.736011	−	0.736011i
$698$	−482.247	−	482.247i	−0.690898	−	0.690898i
$699$			452.548i			0.647423i
$700$		0			0
$701$	351.000			0.500713			0.250357	−	0.968154i	$-0.419452\pi$
$701$	351.000			0.500713			0.250357	+	0.968154i	$0.419452\pi$
$702$	51.0000	−	51.0000i	0.0726496	−	0.0726496i
$703$	−305.470	−	305.470i	−0.434524	−	0.434524i
$704$			40.0000i			0.0568182i
$705$	−251.023	−	251.023i	−0.356061	−	0.356061i
$706$	−244.659			−0.346542
$707$		0			0
$708$	−78.0000	−	78.0000i	−0.110169	−	0.110169i
$709$		−	127.000i		−	0.179126i	−0.995981	−	0.0895628i	$-0.971453\pi$
$709$		−	127.000i		−	0.179126i	0.995981	−	0.0895628i	$-0.0285470\pi$
$710$	−735.391			−1.03576
$711$	−920.000			−1.29395
$712$	226.274	−	226.274i	0.317801	−	0.317801i
$713$	463.862	+	463.862i	0.650578	+	0.650578i
$714$		0			0
$715$			75.0000i			0.104895i
$716$	−32.0000			−0.0446927
$717$	280.721	−	280.721i	0.391522	−	0.391522i
$718$	−360.000	−	360.000i	−0.501393	−	0.501393i
$719$			1018.23i			1.41618i	0.706122	+	0.708090i	$0.250443\pi$
$719$			1018.23i			1.41618i	−0.706122	+	0.708090i	$0.749557\pi$
$720$	−113.137	+	113.137i	−0.157135	+	0.157135i
$721$		0			0
$722$	199.000	−	199.000i	0.275623	−	0.275623i
$723$	−176.000	−	176.000i	−0.243430	−	0.243430i
$724$			415.779i			0.574280i
$725$	425.000			0.586207
$726$	−135.765			−0.187003
$727$	−56.5685	+	56.5685i	−0.0778109	+	0.0778109i	−0.744941	−	0.667130i	$-0.767522\pi$
$727$	−56.5685	+	56.5685i	−0.0778109	+	0.0778109i	0.667130	+	0.744941i	$0.267522\pi$
$728$		0			0
$729$			287.000i			0.393690i
$730$	−280.000	−	280.000i	−0.383562	−	0.383562i
$731$	420.021			0.574585
$732$	−64.0000	+	64.0000i	−0.0874317	+	0.0874317i
$733$	30.4056	+	30.4056i	0.0414810	+	0.0414810i	0.727543	−	0.686062i	$-0.240662\pi$
$733$	30.4056	+	30.4056i	0.0414810	+	0.0414810i	−0.686062	+	0.727543i	$0.740662\pi$
$734$		−	272.943i		−	0.371857i
$735$		0			0
$736$	−64.0000			−0.0869565
$737$	375.000	−	375.000i	0.508820	−	0.508820i
$738$	−214.960	−	214.960i	−0.291274	−	0.291274i
$739$		−	619.000i		−	0.837618i	−0.908074	−	0.418809i	$-0.862448\pi$
$739$		−	619.000i		−	0.837618i	0.908074	−	0.418809i	$-0.137552\pi$
$740$			339.411i			0.458664i
$741$	−38.1838			−0.0515300
$742$		0			0
$743$	−331.000	−	331.000i	−0.445491	−	0.445491i	0.448361	−	0.893852i	$-0.352008\pi$
$743$	−331.000	−	331.000i	−0.445491	−	0.445491i	−0.893852	+	0.448361i	$0.852008\pi$
$744$		−	164.000i		−	0.220430i
$745$	820.244	−	820.244i	1.10100	−	1.10100i
$746$	−16.0000			−0.0214477
$747$	588.313	−	588.313i	0.787567	−	0.787567i
$748$	−190.919	−	190.919i	−0.255239	−	0.255239i
$749$		0			0
$750$	−125.000	+	125.000i	−0.166667	+	0.166667i
$751$	197.000			0.262317			0.131158	−	0.991361i	$-0.458130\pi$
$751$	197.000			0.262317			0.131158	+	0.991361i	$0.458130\pi$
$752$	200.818	−	200.818i	0.267046	−	0.267046i
$753$	320.000	+	320.000i	0.424967	+	0.424967i
$754$		−	72.1249i		−	0.0956564i
$755$	−10.6066	−	10.6066i	−0.0140485	−	0.0140485i
$756$		0			0
$757$	264.000	−	264.000i	0.348745	−	0.348745i	−0.510897	−	0.859642i	$-0.670687\pi$
$757$	264.000	−	264.000i	0.348745	−	0.348745i	0.859642	+	0.510897i	$0.170687\pi$
$758$	202.000	+	202.000i	0.266491	+	0.266491i
$759$			56.5685i			0.0745304i
$760$	180.000			0.236842
$761$	−339.411			−0.446007			−0.223003	−	0.974818i	$-0.571586\pi$
$761$	−339.411			−0.446007			−0.223003	+	0.974818i	$0.571586\pi$
$762$	−26.8701	+	26.8701i	−0.0352625	+	0.0352625i
$763$		0			0
$764$			682.000i			0.892670i
$765$		−	1080.00i		−	1.41176i
$766$	565.685			0.738493
$767$	117.000	−	117.000i	0.152542	−	0.152542i
$768$	11.3137	+	11.3137i	0.0147314	+	0.0147314i
$769$		−	742.462i		−	0.965490i	−0.875761	−	0.482745i	$-0.839640\pi$
$769$		−	742.462i		−	0.965490i	0.875761	−	0.482745i	$-0.160360\pi$
$770$		0			0
$771$	40.0000			0.0518807
$772$	−144.000	+	144.000i	−0.186528	+	0.186528i
$773$	716.299	+	716.299i	0.926648	+	0.926648i	0.997488	−	0.0708394i	$-0.0225678\pi$
$773$	716.299	+	716.299i	0.926648	+	0.926648i	−0.0708394	+	0.997488i	$0.522568\pi$
$774$		−	176.000i		−	0.227390i
$775$			1449.57i			1.87041i
$776$	325.269			0.419161
$777$		0			0
$778$	−319.000	−	319.000i	−0.410026	−	0.410026i
$779$			342.000i			0.439024i
$780$	21.2132	+	21.2132i	0.0271964	+	0.0271964i
$781$	−520.000			−0.665813
$782$	305.470	−	305.470i	0.390627	−	0.390627i
$783$	−204.354	−	204.354i	−0.260988	−	0.260988i
$784$		0			0
$785$	−1280.00			−1.63057
$786$	112.000			0.142494
$787$	893.076	−	893.076i	1.13479	−	1.13479i	0.145414	−	0.989371i	$-0.453549\pi$
$787$	893.076	−	893.076i	1.13479	−	1.13479i	0.989371	−	0.145414i	$-0.0464515\pi$
$788$	338.000	+	338.000i	0.428934	+	0.428934i
$789$			346.482i			0.439141i
$790$		−	813.173i		−	1.02933i
$791$		0			0
$792$	−80.0000	+	80.0000i	−0.101010	+	0.101010i
$793$	−96.0000	−	96.0000i	−0.121059	−	0.121059i
$794$			7.07107i			0.00890563i
$795$	165.000	−	165.000i	0.207547	−	0.207547i
$796$	427.092			0.536548
$797$	120.915	−	120.915i	0.151713	−	0.151713i	−0.627170	−	0.778883i	$-0.715787\pi$
$797$	120.915	−	120.915i	0.151713	−	0.151713i	0.778883	+	0.627170i	$0.215787\pi$
$798$		0			0
$799$			1917.00i			2.39925i
$800$	−100.000	−	100.000i	−0.125000	−	0.125000i
$801$	905.097			1.12996
$802$	−151.000	+	151.000i	−0.188279	+	0.188279i
$803$	−197.990	−	197.990i	−0.246563	−	0.246563i
$804$		−	212.132i		−	0.263846i
$805$		0			0
$806$	246.000			0.305211
$807$	216.000	−	216.000i	0.267658	−	0.267658i
$808$	195.161	+	195.161i	0.241536	+	0.241536i
$809$		−	447.000i		−	0.552534i	−0.961081	−	0.276267i	$-0.910903\pi$
$809$		−	447.000i		−	0.552534i	0.961081	−	0.276267i	$-0.0890974\pi$
$810$	−388.909			−0.480134
$811$	305.470			0.376659			0.188329	−	0.982106i	$-0.439693\pi$
$811$	305.470			0.376659			0.188329	+	0.982106i	$0.439693\pi$
$812$		0			0
$813$	−328.000	−	328.000i	−0.403444	−	0.403444i
$814$			240.000i			0.294840i
$815$			961.665i			1.17996i
$816$	−108.000			−0.132353
$817$	−140.007	+	140.007i	−0.171367	+	0.171367i
$818$	−117.380	−	117.380i	−0.143496	−	0.143496i
$819$		0			0
$820$	190.000	−	190.000i	0.231707	−	0.231707i
$821$	447.000			0.544458			0.272229	−	0.962232i	$-0.412239\pi$
$821$	447.000			0.544458			0.272229	+	0.962232i	$0.412239\pi$
$822$	124.451	−	124.451i	0.151400	−	0.151400i
$823$	−867.000	−	867.000i	−1.05346	−	1.05346i	−0.998488	−	0.0549752i	$-0.982492\pi$
$823$	−867.000	−	867.000i	−1.05346	−	1.05346i	−0.0549752	−	0.998488i	$-0.517508\pi$
$824$			138.593i			0.168195i
$825$	−88.3883	+	88.3883i	−0.107137	+	0.107137i
$826$		0			0
$827$	912.000	−	912.000i	1.10278	−	1.10278i	0.108707	−	0.994074i	$-0.465329\pi$
$827$	912.000	−	912.000i	1.10278	−	1.10278i	0.994074	−	0.108707i	$-0.0346711\pi$
$828$	−128.000	−	128.000i	−0.154589	−	0.154589i
$829$		−	660.438i		−	0.796668i	−0.917240	−	0.398334i	$-0.869589\pi$
$829$		−	660.438i		−	0.796668i	0.917240	−	0.398334i	$-0.130411\pi$
$830$	520.000	+	520.000i	0.626506	+	0.626506i
$831$	226.274			0.272291
$832$	−16.9706	+	16.9706i	−0.0203973	+	0.0203973i
$833$		0			0
$834$			176.000i			0.211031i
$835$	−525.000			−0.628743
$836$	127.279			0.152248
$837$	697.000	−	697.000i	0.832736	−	0.832736i
$838$	496.389	+	496.389i	0.592350	+	0.592350i
$839$		−	1255.82i		−	1.49681i	−0.663243	−	0.748404i	$-0.730821\pi$
$839$		−	1255.82i		−	1.49681i	0.663243	−	0.748404i	$-0.269179\pi$
$840$		0			0
$841$	552.000			0.656361
$842$	425.000	−	425.000i	0.504751	−	0.504751i
$843$	−33.2340	−	33.2340i	−0.0394235	−	0.0394235i
$844$			358.000i			0.424171i
$845$	565.685	−	565.685i	0.669450	−	0.669450i
$846$	803.273			0.949496
$847$		0			0
$848$	132.000	+	132.000i	0.155660	+	0.155660i
$849$			319.000i			0.375736i
$850$	954.594			1.12305
$851$	−384.000			−0.451234
$852$	−147.078	+	147.078i	−0.172627	+	0.172627i
$853$	−79.1960	−	79.1960i	−0.0928440	−	0.0928440i	0.659159	−	0.752003i	$-0.270912\pi$
$853$	−79.1960	−	79.1960i	−0.0928440	−	0.0928440i	−0.752003	+	0.659159i	$0.770912\pi$
$854$		0			0
$855$	360.000	+	360.000i	0.421053	+	0.421053i
$856$	300.000			0.350467
$857$	707.107	−	707.107i	0.825095	−	0.825095i	−0.161738	−	0.986834i	$-0.551710\pi$
$857$	707.107	−	707.107i	0.825095	−	0.825095i	0.986834	+	0.161738i	$0.0517100\pi$
$858$	15.0000	+	15.0000i	0.0174825	+	0.0174825i
$859$		−	780.646i		−	0.908785i	−0.890802	−	0.454392i	$-0.849856\pi$
$859$		−	780.646i		−	0.908785i	0.890802	−	0.454392i	$-0.150144\pi$
$860$	155.563			0.180888
$861$		0			0
$862$	171.000	−	171.000i	0.198376	−	0.198376i
$863$	−3.00000	−	3.00000i	−0.00347625	−	0.00347625i	0.705367	−	0.708843i	$-0.250782\pi$
$863$	−3.00000	−	3.00000i	−0.00347625	−	0.00347625i	−0.708843	+	0.705367i	$0.750782\pi$
$864$			96.1665i			0.111304i
$865$			1295.00i			1.49711i
$866$	−381.838			−0.440921
$867$	311.127	−	311.127i	0.358855	−	0.358855i
$868$		0			0
$869$		−	575.000i		−	0.661680i
$870$	85.0000	−	85.0000i	0.0977011	−	0.0977011i
$871$	318.198			0.365325
$872$	238.000	−	238.000i	0.272936	−	0.272936i
$873$	650.538	+	650.538i	0.745176	+	0.745176i
$874$			203.647i			0.233005i
$875$		0			0
$876$	−112.000			−0.127854
$877$	−233.000	+	233.000i	−0.265678	+	0.265678i	−0.827356	−	0.561678i	$-0.810156\pi$
$877$	−233.000	+	233.000i	−0.265678	+	0.265678i	0.561678	+	0.827356i	$0.310156\pi$
$878$	147.078	+	147.078i	0.167515	+	0.167515i
$879$			29.0000i			0.0329920i
$880$	−70.7107	−	70.7107i	−0.0803530	−	0.0803530i
$881$	644.881			0.731988			0.365994	−	0.930617i	$-0.380729\pi$
$881$	644.881			0.731988			0.365994	+	0.930617i	$0.380729\pi$
$882$		0			0
$883$	−1152.00	−	1152.00i	−1.30464	−	1.30464i	−0.925225	−	0.379418i	$-0.876124\pi$
$883$	−1152.00	−	1152.00i	−1.30464	−	1.30464i	−0.379418	−	0.925225i	$-0.623876\pi$
$884$		−	162.000i		−	0.183258i
$885$	275.772			0.311606
$886$	666.000			0.751693
$887$	−339.411	+	339.411i	−0.382651	+	0.382651i	−0.872056	−	0.489406i	$-0.837214\pi$
$887$	−339.411	+	339.411i	−0.382651	+	0.382651i	0.489406	+	0.872056i	$0.337214\pi$
$888$	67.8823	+	67.8823i	0.0764440	+	0.0764440i
$889$		0			0
$890$			800.000i			0.898876i
$891$	−275.000			−0.308642
$892$	80.6102	−	80.6102i	0.0903701	−	0.0903701i
$893$	−639.000	−	639.000i	−0.715566	−	0.715566i
$894$		−	328.098i		−	0.366999i
$895$	56.5685	−	56.5685i	0.0632051	−	0.0632051i
$896$		0			0
$897$	−24.0000	+	24.0000i	−0.0267559	+	0.0267559i
$898$	−305.000	−	305.000i	−0.339644	−	0.339644i
$899$		−	985.707i		−	1.09645i
$900$		−	400.000i		−	0.444444i
$901$	−1260.06			−1.39852
$902$	134.350	−	134.350i	0.148947	−	0.148947i
$903$		0			0
$904$			64.0000i			0.0707965i
$905$	−735.000	−	735.000i	−0.812155	−	0.812155i
$906$	−4.24264			−0.00468283
$907$	−936.000	+	936.000i	−1.03197	+	1.03197i	−0.0325019	+	0.999472i	$0.510347\pi$
$907$	−936.000	+	936.000i	−1.03197	+	1.03197i	−0.999472	+	0.0325019i	$0.989653\pi$
$908$	−258.801	−	258.801i	−0.285023	−	0.285023i
$909$			780.646i			0.858796i
$910$		0			0
$911$	152.000			0.166850			0.0834248	−	0.996514i	$-0.473414\pi$
$911$	152.000			0.166850			0.0834248	+	0.996514i	$0.473414\pi$
$912$	36.0000	−	36.0000i	0.0394737	−	0.0394737i
$913$	367.696	+	367.696i	0.402733	+	0.402733i
$914$			414.000i			0.452954i
$915$		−	226.274i		−	0.247294i
$916$	−466.690			−0.509487
$917$		0			0
$918$	−459.000	−	459.000i	−0.500000	−	0.500000i
$919$			1109.00i			1.20675i	0.797459	+	0.603373i	$0.206177\pi$
$919$			1109.00i			1.20675i	−0.797459	+	0.603373i	$0.793823\pi$
$920$	113.137	−	113.137i	0.122975	−	0.122975i
$921$	439.000			0.476656
$922$	−305.470	+	305.470i	−0.331313	+	0.331313i
$923$	−220.617	−	220.617i	−0.239022	−	0.239022i
$924$		0			0
$925$	−600.000	−	600.000i	−0.648649	−	0.648649i
$926$	−624.000			−0.673866
$927$	−277.186	+	277.186i	−0.299014	+	0.299014i
$928$	68.0000	+	68.0000i	0.0732759	+	0.0732759i
$929$		−	106.066i		−	0.114172i	−0.998369	−	0.0570861i	$-0.981819\pi$
$929$		−	106.066i		−	0.114172i	0.998369	−	0.0570861i	$-0.0181810\pi$
$930$	289.914	+	289.914i	0.311735	+	0.311735i
$931$		0			0
$932$	640.000	−	640.000i	0.686695	−	0.686695i
$933$	287.000	+	287.000i	0.307610	+	0.307610i
$934$		−	643.467i		−	0.688937i
$935$	675.000			0.721925
$936$	−67.8823			−0.0725238
$937$	812.466	−	812.466i	0.867093	−	0.867093i	−0.125057	−	0.992150i	$-0.539911\pi$
$937$	812.466	−	812.466i	0.867093	−	0.867093i	0.992150	+	0.125057i	$0.0399114\pi$
$938$		0			0
$939$		−	277.000i		−	0.294995i
$940$			710.000i			0.755319i
$941$	1323.70			1.40670			0.703350	−	0.710844i	$-0.251687\pi$
$941$	1323.70			1.40670			0.703350	+	0.710844i	$0.251687\pi$
$942$	−256.000	+	256.000i	−0.271762	+	0.271762i
$943$	214.960	+	214.960i	0.227954	+	0.227954i
$944$			220.617i			0.233705i
$945$		0			0
$946$	110.000			0.116279
$947$	21.0000	−	21.0000i	0.0221753	−	0.0221753i	−0.695932	−	0.718107i	$-0.745009\pi$
$947$	21.0000	−	21.0000i	0.0221753	−	0.0221753i	0.718107	+	0.695932i	$0.245009\pi$
$948$	−162.635	−	162.635i	−0.171555	−	0.171555i
$949$		−	168.000i		−	0.177028i
$950$	−318.198	+	318.198i	−0.334945	+	0.334945i
$951$	−1.41421			−0.00148708
$952$		0			0
$953$	753.000	+	753.000i	0.790136	+	0.790136i	0.981516	−	0.191380i	$-0.0612962\pi$
$953$	753.000	+	753.000i	0.790136	+	0.790136i	−0.191380	+	0.981516i	$0.561296\pi$
$954$			528.000i			0.553459i
$955$	−1205.62	−	1205.62i	−1.26243	−	1.26243i
$956$	−794.000			−0.830544
$957$	60.1041	−	60.1041i	0.0628047	−	0.0628047i
$958$	610.940	+	610.940i	0.637725	+	0.637725i
$959$		0			0
$960$	−40.0000			−0.0416667
$961$	2401.00			2.49844
$962$	−101.823	+	101.823i	−0.105846	+	0.105846i
$963$	600.000	+	600.000i	0.623053	+	0.623053i
$964$			497.803i			0.516393i
$965$		−	509.117i		−	0.527582i
$966$		0			0
$967$	877.000	−	877.000i	0.906929	−	0.906929i	−0.0890945	−	0.996023i	$-0.528397\pi$
$967$	877.000	−	877.000i	0.906929	−	0.906929i	0.996023	+	0.0890945i	$0.0283973\pi$
$968$	192.000	+	192.000i	0.198347	+	0.198347i
$969$			343.654i			0.354648i
$970$	−575.000	+	575.000i	−0.592784	+	0.592784i
$971$	892.369			0.919020			0.459510	−	0.888173i	$-0.348025\pi$
$971$	892.369			0.919020			0.459510	+	0.888173i	$0.348025\pi$
$972$	−294.156	+	294.156i	−0.302630	+	0.302630i
$973$		0			0
$974$		−	16.0000i		−	0.0164271i
$975$	−75.0000			−0.0769231
$976$	181.019			0.185471
$977$	−9.00000	+	9.00000i	−0.00921187	+	0.00921187i	−0.711698	−	0.702486i	$-0.752073\pi$
$977$	−9.00000	+	9.00000i	−0.00921187	+	0.00921187i	0.702486	+	0.711698i	$0.252073\pi$
$978$	192.333	+	192.333i	0.196660	+	0.196660i
$979$			565.685i			0.577820i
$980$		0			0
$981$	952.000			0.970438
$982$	99.0000	−	99.0000i	0.100815	−	0.100815i
$983$	198.697	+	198.697i	0.202133	+	0.202133i	0.800913	−	0.598780i	$-0.204348\pi$
$983$	198.697	+	198.697i	0.202133	+	0.202133i	−0.598780	+	0.800913i	$0.704348\pi$
$984$		−	76.0000i		−	0.0772358i
$985$	−1195.01			−1.21321
$986$	−649.124			−0.658341
$987$		0			0
$988$	54.0000	+	54.0000i	0.0546559	+	0.0546559i
$989$			176.000i			0.177958i
$990$		−	282.843i		−	0.285700i
$991$	302.000			0.304743			0.152371	−	0.988323i	$-0.451309\pi$
$991$	302.000			0.304743			0.152371	+	0.988323i	$0.451309\pi$
$992$	−231.931	+	231.931i	−0.233801	+	0.233801i
$993$	22.6274	+	22.6274i	0.0227869	+	0.0227869i
$994$		0			0
$995$	−755.000	+	755.000i	−0.758794	+	0.758794i
$996$	208.000			0.208835
$997$	92.6310	−	92.6310i	0.0929097	−	0.0929097i	−0.659124	−	0.752034i	$-0.729073\pi$
$997$	92.6310	−	92.6310i	0.0929097	−	0.0929097i	0.752034	+	0.659124i	$0.229073\pi$
$998$	−195.000	−	195.000i	−0.195391	−	0.195391i
$999$			576.999i			0.577577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.f.m.393.2	yes	4
5.2	odd	4	inner	490.3.f.m.197.2	yes	4
7.6	odd	2	inner	490.3.f.m.393.1	yes	4
35.27	even	4	inner	490.3.f.m.197.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.3.f.m.197.1	✓	4	35.27	even	4	inner
490.3.f.m.197.2	yes	4	5.2	odd	4	inner
490.3.f.m.393.1	yes	4	7.6	odd	2	inner
490.3.f.m.393.2	yes	4	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	490.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(0.707107 + 0.707107i) q^{3} -2.00000i q^{4} +(3.53553 + 3.53553i) q^{5} +1.41421 q^{6} +(-2.00000 - 2.00000i) q^{8} -8.00000i q^{9} +7.07107 q^{10} +5.00000 q^{11} +(1.41421 - 1.41421i) q^{12} +(2.12132 + 2.12132i) q^{13} +5.00000i q^{15} -4.00000 q^{16} +(19.0919 - 19.0919i) q^{17} +(-8.00000 - 8.00000i) q^{18} +12.7279i q^{19} +(7.07107 - 7.07107i) q^{20} +(5.00000 - 5.00000i) q^{22} +(8.00000 + 8.00000i) q^{23} -2.82843i q^{24} +25.0000i q^{25} +4.24264 q^{26} +(12.0208 - 12.0208i) q^{27} -17.0000i q^{29} +(5.00000 + 5.00000i) q^{30} +57.9828 q^{31} +(-4.00000 + 4.00000i) q^{32} +(3.53553 + 3.53553i) q^{33} -38.1838i q^{34} -16.0000 q^{36} +(-24.0000 + 24.0000i) q^{37} +(12.7279 + 12.7279i) q^{38} +3.00000i q^{39} -14.1421i q^{40} +26.8701 q^{41} +(11.0000 + 11.0000i) q^{43} -10.0000i q^{44} +(28.2843 - 28.2843i) q^{45} +16.0000 q^{46} +(-50.2046 + 50.2046i) q^{47} +(-2.82843 - 2.82843i) q^{48} +(25.0000 + 25.0000i) q^{50} +27.0000 q^{51} +(4.24264 - 4.24264i) q^{52} +(-33.0000 - 33.0000i) q^{53} -24.0416i q^{54} +(17.6777 + 17.6777i) q^{55} +(-9.00000 + 9.00000i) q^{57} +(-17.0000 - 17.0000i) q^{58} -55.1543i q^{59} +10.0000 q^{60} -45.2548 q^{61} +(57.9828 - 57.9828i) q^{62} +8.00000i q^{64} +15.0000i q^{65} +7.07107 q^{66} +(75.0000 - 75.0000i) q^{67} +(-38.1838 - 38.1838i) q^{68} +11.3137i q^{69} -104.000 q^{71} +(-16.0000 + 16.0000i) q^{72} +(-39.5980 - 39.5980i) q^{73} +48.0000i q^{74} +(-17.6777 + 17.6777i) q^{75} +25.4558 q^{76} +(3.00000 + 3.00000i) q^{78} -115.000i q^{79} +(-14.1421 - 14.1421i) q^{80} -55.0000 q^{81} +(26.8701 - 26.8701i) q^{82} +(73.5391 + 73.5391i) q^{83} +135.000 q^{85} +22.0000 q^{86} +(12.0208 - 12.0208i) q^{87} +(-10.0000 - 10.0000i) q^{88} +113.137i q^{89} -56.5685i q^{90} +(16.0000 - 16.0000i) q^{92} +(41.0000 + 41.0000i) q^{93} +100.409i q^{94} +(-45.0000 + 45.0000i) q^{95} -5.65685 q^{96} +(-81.3173 + 81.3173i) q^{97} -40.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{8} + 20 q^{11} - 16 q^{16} - 32 q^{18} + 20 q^{22} + 32 q^{23} + 20 q^{30} - 16 q^{32} - 64 q^{36} - 96 q^{37} + 44 q^{43} + 64 q^{46} + 100 q^{50} + 108 q^{51} - 132 q^{53} - 36 q^{57}+ \cdots - 180 q^{95}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^8 + 20 * q^11 - 16 * q^16 - 32 * q^18 + 20 * q^22 + 32 * q^23 + 20 * q^30 - 16 * q^32 - 64 * q^36 - 96 * q^37 + 44 * q^43 + 64 * q^46 + 100 * q^50 + 108 * q^51 - 132 * q^53 - 36 * q^57 - 68 * q^58 + 40 * q^60 + 300 * q^67 - 416 * q^71 - 64 * q^72 + 12 * q^78 - 220 * q^81 + 540 * q^85 + 88 * q^86 - 40 * q^88 + 64 * q^92 + 164 * q^93 - 180 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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