LMFDB - Embedded newform 950.2.bb.e.143.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.6
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.e.857.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(-0.255151 + 2.91639i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.24262 + 1.88178i) q^{6} +(-0.0607618 - 0.226766i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-5.48583 - 0.967300i) q^{9} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(-0.255151 + 2.91639i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.24262 + 1.88178i) q^{6} +(-0.0607618 - 0.226766i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-5.48583 - 0.967300i) q^{9} +(-2.29289 - 3.97140i) q^{11} +(2.82778 - 0.757702i) q^{12} +(-5.34147 + 0.467318i) q^{13} +(-0.220607 - 0.0802945i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(1.59218 + 1.11486i) q^{17} +(-3.93891 + 3.93891i) q^{18} +(-4.34904 - 0.292958i) q^{19} +(0.676843 - 0.119346i) q^{21} +(-4.56833 - 0.399677i) q^{22} +(-2.61510 - 1.21944i) q^{23} +(1.00128 - 2.75098i) q^{24} +(-2.68093 + 4.64352i) q^{26} +(1.94764 - 7.26869i) q^{27} +(-0.192309 + 0.134656i) q^{28} +(-1.37415 + 7.79317i) q^{29} +(2.51399 + 1.45145i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(12.1672 - 5.67366i) q^{33} +(1.82648 - 0.664783i) q^{34} +(0.967300 + 5.48583i) q^{36} +(-6.06921 - 6.06921i) q^{37} +(-2.73449 + 3.39449i) q^{38} -15.6971i q^{39} +(-4.55557 - 5.42911i) q^{41} +(0.290459 - 0.622891i) q^{42} +(-1.57465 - 3.37684i) q^{43} +(-2.94768 + 3.51291i) q^{44} +(-2.49887 + 1.44272i) q^{46} +(1.08781 + 1.55356i) q^{47} +(-1.67916 - 2.39810i) q^{48} +(6.01445 - 3.47244i) q^{49} +(-3.65761 + 4.35897i) q^{51} +(2.26602 + 4.85950i) q^{52} +(3.59825 - 7.71648i) q^{53} +(-4.83704 - 5.76456i) q^{54} +0.234765i q^{56} +(1.96405 - 12.6088i) q^{57} +(5.59561 + 5.59561i) q^{58} +(1.92414 + 10.9123i) q^{59} +(1.74487 - 0.635082i) q^{61} +(2.63092 - 1.22682i) q^{62} +(0.113978 + 1.30277i) q^{63} +(0.866025 + 0.500000i) q^{64} +(2.33123 - 13.2211i) q^{66} +(-4.67846 + 3.27589i) q^{67} +(0.503065 - 1.87746i) q^{68} +(4.22361 - 7.31552i) q^{69} +(-4.89943 + 13.4611i) q^{71} +(5.04855 + 2.35418i) q^{72} +(6.57809 + 0.575509i) q^{73} +(-8.45276 + 1.49045i) q^{74} +(1.21217 + 4.18696i) q^{76} +(-0.761259 + 0.761259i) q^{77} +(-12.8583 - 9.00346i) q^{78} +(1.77204 - 1.48692i) q^{79} +(4.99788 + 1.81908i) q^{81} +(-7.06023 + 0.617690i) q^{82} +(-2.86471 + 0.767598i) q^{83} +(-0.343642 - 0.595205i) q^{84} +(-3.66933 - 0.647002i) q^{86} +(-22.3773 - 5.99599i) q^{87} +(1.18689 + 4.42952i) q^{88} +(-3.00747 - 2.52357i) q^{89} +(0.430529 + 1.18287i) q^{91} +(-0.251483 + 2.87446i) q^{92} +(-4.87445 + 6.96144i) q^{93} +1.89655 q^{94} -2.92753 q^{96} +(-3.03199 + 4.33012i) q^{97} +(0.605287 - 6.91846i) q^{98} +(8.73687 + 24.0043i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$3$	−0.255151	+	2.91639i	−0.147312	+	1.68378i	0.458908	+	0.888484i	$0.348241\pi$
$3$	−0.255151	+	2.91639i	−0.147312	+	1.68378i	−0.606220	+	0.795297i	$0.707315\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	2.24262	+	1.88178i	0.915546	+	0.768235i
$7$	−0.0607618	−	0.226766i	−0.0229658	−	0.0857095i	0.953492	−	0.301419i	$-0.0974603\pi$
$7$	−0.0607618	−	0.226766i	−0.0229658	−	0.0857095i	−0.976458	+	0.215709i	$0.930794\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−5.48583	−	0.967300i	−1.82861	−	0.322433i
$10$		0			0
$11$	−2.29289	−	3.97140i	−0.691332	−	1.19742i	−0.971402	−	0.237443i	$-0.923691\pi$
$11$	−2.29289	−	3.97140i	−0.691332	−	1.19742i	0.280069	−	0.959980i	$-0.409643\pi$
$12$	2.82778	−	0.757702i	0.816310	−	0.218730i
$13$	−5.34147	+	0.467318i	−1.48146	+	0.129611i	−0.799007	−	0.601322i	$-0.794641\pi$
$13$	−5.34147	+	0.467318i	−1.48146	+	0.129611i	−0.682449	+	0.730933i	$0.739085\pi$
$14$	−0.220607	−	0.0802945i	−0.0589598	−	0.0214596i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	1.59218	+	1.11486i	0.386161	+	0.270393i	0.750496	−	0.660875i	$-0.229815\pi$
$17$	1.59218	+	1.11486i	0.386161	+	0.270393i	−0.364335	+	0.931268i	$0.618704\pi$
$18$	−3.93891	+	3.93891i	−0.928410	+	0.928410i
$19$	−4.34904	−	0.292958i	−0.997739	−	0.0672092i
$19$	−4.34904	−	0.292958i	−0.997739	−	0.0672092i
$20$		0			0
$21$	0.676843	−	0.119346i	0.147699	−	0.0260433i
$22$	−4.56833	−	0.399677i	−0.973971	−	0.0852114i
$23$	−2.61510	−	1.21944i	−0.545286	−	0.254271i	0.130399	−	0.991462i	$-0.458374\pi$
$23$	−2.61510	−	1.21944i	−0.545286	−	0.254271i	−0.675685	+	0.737191i	$0.736152\pi$
$24$	1.00128	−	2.75098i	0.204385	−	0.561542i
$25$		0			0
$26$	−2.68093	+	4.64352i	−0.525775	+	0.910668i
$27$	1.94764	−	7.26869i	0.374824	−	1.39886i
$28$	−0.192309	+	0.134656i	−0.0363429	+	0.0254476i
$29$	−1.37415	+	7.79317i	−0.255173	+	1.44716i	0.540457	+	0.841372i	$0.318251\pi$
$29$	−1.37415	+	7.79317i	−0.255173	+	1.44716i	−0.795629	+	0.605784i	$0.792860\pi$
$30$		0			0
$31$	2.51399	+	1.45145i	0.451526	+	0.260688i	0.708474	−	0.705737i	$-0.249384\pi$
$31$	2.51399	+	1.45145i	0.451526	+	0.260688i	−0.256949	+	0.966425i	$0.582717\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$	12.1672	−	5.67366i	2.11804	−	0.987658i
$34$	1.82648	−	0.664783i	0.313238	−	0.114009i
$35$		0			0
$36$	0.967300	+	5.48583i	0.161217	+	0.914305i
$37$	−6.06921	−	6.06921i	−0.997771	−	0.997771i	0.00222605	−	0.999998i	$-0.499291\pi$
$37$	−6.06921	−	6.06921i	−0.997771	−	0.997771i	−0.999998	+	0.00222605i	$0.999291\pi$
$38$	−2.73449	+	3.39449i	−0.443592	+	0.550660i
$39$		−	15.6971i		−	2.51354i
$40$		0			0
$41$	−4.55557	−	5.42911i	−0.711460	−	0.847885i	0.282311	−	0.959323i	$-0.408899\pi$
$41$	−4.55557	−	5.42911i	−0.711460	−	0.847885i	−0.993771	+	0.111438i	$0.964454\pi$
$42$	0.290459	−	0.622891i	0.0448188	−	0.0961141i
$43$	−1.57465	−	3.37684i	−0.240132	−	0.514964i	0.748897	−	0.662686i	$-0.230584\pi$
$43$	−1.57465	−	3.37684i	−0.240132	−	0.514964i	−0.989029	+	0.147722i	$0.952806\pi$
$44$	−2.94768	+	3.51291i	−0.444380	+	0.529591i
$45$		0			0
$46$	−2.49887	+	1.44272i	−0.368438	+	0.212718i
$47$	1.08781	+	1.55356i	0.158674	+	0.226610i	0.890615	−	0.454758i	$-0.150274\pi$
$47$	1.08781	+	1.55356i	0.158674	+	0.226610i	−0.731941	+	0.681368i	$0.761385\pi$
$48$	−1.67916	−	2.39810i	−0.242367	−	0.346135i
$49$	6.01445	−	3.47244i	0.859207	−	0.496063i
$50$		0			0
$51$	−3.65761	+	4.35897i	−0.512168	+	0.610378i
$52$	2.26602	+	4.85950i	0.314241	+	0.673892i
$53$	3.59825	−	7.71648i	0.494258	−	1.05994i	−0.488075	−	0.872802i	$-0.662301\pi$
$53$	3.59825	−	7.71648i	0.494258	−	1.05994i	0.982333	−	0.187139i	$-0.0599214\pi$
$54$	−4.83704	−	5.76456i	−0.658238	−	0.784458i
$55$		0			0
$56$			0.234765i			0.0313719i
$57$	1.96405	−	12.6088i	0.260144	−	1.67007i
$58$	5.59561	+	5.59561i	0.734740	+	0.734740i
$59$	1.92414	+	10.9123i	0.250502	+	1.42067i	0.807360	+	0.590059i	$0.200896\pi$
$59$	1.92414	+	10.9123i	0.250502	+	1.42067i	−0.556858	+	0.830608i	$0.687993\pi$
$60$		0			0
$61$	1.74487	−	0.635082i	0.223408	−	0.0813140i	−0.227891	−	0.973687i	$-0.573183\pi$
$61$	1.74487	−	0.635082i	0.223408	−	0.0813140i	0.451299	+	0.892373i	$0.350961\pi$
$62$	2.63092	−	1.22682i	0.334128	−	0.155806i
$63$	0.113978	+	1.30277i	0.0143599	+	0.164134i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	2.33123	−	13.2211i	0.286955	−	1.62740i
$67$	−4.67846	+	3.27589i	−0.571565	+	0.400214i	−0.823320	−	0.567577i	$-0.807881\pi$
$67$	−4.67846	+	3.27589i	−0.571565	+	0.400214i	0.251756	+	0.967791i	$0.418992\pi$
$68$	0.503065	−	1.87746i	0.0610056	−	0.227676i
$69$	4.22361	−	7.31552i	0.508463	−	0.880685i
$70$		0			0
$71$	−4.89943	+	13.4611i	−0.581456	+	1.59754i	0.204238	+	0.978921i	$0.434528\pi$
$71$	−4.89943	+	13.4611i	−0.581456	+	1.59754i	−0.785694	+	0.618616i	$0.787694\pi$
$72$	5.04855	+	2.35418i	0.594977	+	0.277442i
$73$	6.57809	+	0.575509i	0.769907	+	0.0673582i	0.465339	−	0.885132i	$-0.345932\pi$
$73$	6.57809	+	0.575509i	0.769907	+	0.0673582i	0.304568	+	0.952491i	$0.401488\pi$
$74$	−8.45276	+	1.49045i	−0.982613	+	0.173261i
$75$		0			0
$76$	1.21217	+	4.18696i	0.139045	+	0.480277i
$77$	−0.761259	+	0.761259i	−0.0867535	+	0.0867535i
$78$	−12.8583	−	9.00346i	−1.45591	−	1.01944i
$79$	1.77204	−	1.48692i	0.199370	−	0.167291i	−0.537637	−	0.843176i	$-0.680683\pi$
$79$	1.77204	−	1.48692i	0.199370	−	0.167291i	0.737007	+	0.675885i	$0.236239\pi$
$80$		0			0
$81$	4.99788	+	1.81908i	0.555320	+	0.202120i
$82$	−7.06023	+	0.617690i	−0.779672	+	0.0682125i
$83$	−2.86471	+	0.767598i	−0.314443	+	0.0842548i	−0.412589	−	0.910917i	$-0.635375\pi$
$83$	−2.86471	+	0.767598i	−0.314443	+	0.0842548i	0.0981459	+	0.995172i	$0.468709\pi$
$84$	−0.343642	−	0.595205i	−0.0374944	−	0.0649422i
$85$		0			0
$86$	−3.66933	−	0.647002i	−0.395674	−	0.0697680i
$87$	−22.3773	−	5.99599i	−2.39910	−	0.642838i
$88$	1.18689	+	4.42952i	0.126523	+	0.472189i
$89$	−3.00747	−	2.52357i	−0.318792	−	0.267498i	0.469323	−	0.883027i	$-0.344498\pi$
$89$	−3.00747	−	2.52357i	−0.318792	−	0.267498i	−0.788114	+	0.615529i	$0.788942\pi$
$90$		0			0
$91$	0.430529	+	1.18287i	0.0451317	+	0.123998i
$92$	−0.251483	+	2.87446i	−0.0262189	+	0.299683i
$93$	−4.87445	+	6.96144i	−0.505457	+	0.721868i
$94$	1.89655			0.195614
$95$		0			0
$96$	−2.92753			−0.298790
$97$	−3.03199	+	4.33012i	−0.307852	+	0.439658i	−0.943030	−	0.332708i	$-0.892038\pi$
$97$	−3.03199	+	4.33012i	−0.307852	+	0.439658i	0.635178	+	0.772365i	$0.280927\pi$
$98$	0.605287	−	6.91846i	0.0611432	−	0.698870i
$99$	8.73687	+	24.0043i	0.878088	+	2.41253i
$100$		0			0
$101$	−11.7850	−	9.88883i	−1.17266	−	0.983975i	−0.172657	−	0.984982i	$-0.555235\pi$
$101$	−11.7850	−	9.88883i	−1.17266	−	0.983975i	−0.999999	+	0.00100686i	$0.999680\pi$
$102$	1.47274	+	5.49634i	0.145823	+	0.544219i
$103$	1.00869	+	0.270279i	0.0993896	+	0.0266314i	0.308171	−	0.951331i	$-0.400283\pi$
$103$	1.00869	+	0.270279i	0.0993896	+	0.0266314i	−0.208781	+	0.977962i	$0.566950\pi$
$104$	5.28041	+	0.931079i	0.517787	+	0.0912998i
$105$		0			0
$106$	−4.25710	−	7.37351i	−0.413486	−	0.716179i
$107$	0.243516	−	0.0652498i	0.0235415	−	0.00630794i	−0.247029	−	0.969008i	$-0.579454\pi$
$107$	0.243516	−	0.0652498i	0.0235415	−	0.00630794i	0.270571	+	0.962700i	$0.412788\pi$
$108$	−7.49647	+	0.655856i	−0.721348	+	0.0631098i
$109$	−0.808369	−	0.294222i	−0.0774277	−	0.0281814i	0.303016	−	0.952985i	$-0.402006\pi$
$109$	−0.808369	−	0.294222i	−0.0774277	−	0.0281814i	−0.380444	+	0.924804i	$0.624229\pi$
$110$		0			0
$111$	19.2488	−	16.1516i	1.82701	−	1.53305i
$112$	0.192309	+	0.134656i	0.0181715	+	0.0127238i
$113$	−5.64774	+	5.64774i	−0.531295	+	0.531295i	−0.920958	−	0.389663i	$-0.872591\pi$
$113$	−5.64774	+	5.64774i	−0.531295	+	0.531295i	0.389663	+	0.920958i	$0.372591\pi$
$114$	−9.20197	−	8.84095i	−0.861844	−	0.828031i
$115$		0			0
$116$	7.79317	−	1.37415i	0.723578	−	0.127586i
$117$	29.7544	+	2.60317i	2.75080	+	0.240663i
$118$	10.0425	+	4.68290i	0.924488	+	0.431096i
$119$	0.156068	−	0.428793i	0.0143067	−	0.0393074i
$120$		0			0
$121$	−5.01468	+	8.68569i	−0.455880	+	0.789608i
$122$	0.480590	−	1.79359i	0.0435106	−	0.162384i
$123$	16.9958	−	11.9006i	1.53246	−	1.07304i
$124$	0.504084	−	2.85880i	0.0452681	−	0.256728i
$125$		0			0
$126$	1.13255	+	0.653876i	0.100895	+	0.0582519i
$127$	1.20462	+	13.7689i	0.106893	+	1.22179i	0.840346	+	0.542050i	$0.182352\pi$
$127$	1.20462	+	13.7689i	0.106893	+	1.22179i	−0.733453	+	0.679740i	$0.762093\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$	10.2500	−	3.73069i	0.902460	−	0.328469i
$130$		0			0
$131$	−0.684264	−	3.88065i	−0.0597844	−	0.339054i	0.940214	−	0.340583i	$-0.110624\pi$
$131$	−0.684264	−	3.88065i	−0.0597844	−	0.339054i	−0.999999	+	0.00152891i	$0.999513\pi$
$132$	−9.49293	−	9.49293i	−0.826253	−	0.826253i
$133$	0.197823	+	1.00402i	0.0171534	+	0.0870592i
$134$			5.71135i			0.493385i
$135$		0			0
$136$	−1.24938	−	1.48896i	−0.107134	−	0.127677i
$137$	−1.32005	+	2.83085i	−0.112779	+	0.241856i	−0.954594	−	0.297911i	$-0.903710\pi$
$137$	−1.32005	+	2.83085i	−0.112779	+	0.241856i	0.841814	+	0.539767i	$0.181488\pi$
$138$	−3.56995	−	7.65579i	−0.303895	−	0.651704i
$139$	−5.20101	+	6.19833i	−0.441144	+	0.525735i	−0.940103	−	0.340890i	$-0.889271\pi$
$139$	−5.20101	+	6.19833i	−0.441144	+	0.525735i	0.498959	+	0.866626i	$0.333716\pi$
$140$		0			0
$141$	−4.80835	+	2.77610i	−0.404936	+	0.233790i
$142$	8.21647	+	11.7343i	0.689511	+	0.984724i
$143$	14.1033	+	20.1416i	1.17938	+	1.68432i
$144$	4.82416	−	2.78523i	0.402013	−	0.232102i
$145$		0			0
$146$	4.24447	−	5.05836i	0.351275	−	0.418633i
$147$	8.59242	+	18.4265i	0.708691	+	1.51979i
$148$	−3.62740	+	7.77898i	−0.298170	+	0.639428i
$149$	−13.3754	−	15.9401i	−1.09575	−	1.30587i	−0.948504	−	0.316766i	$-0.897403\pi$
$149$	−13.3754	−	15.9401i	−1.09575	−	1.30587i	−0.147248	−	0.989100i	$-0.547041\pi$
$150$		0			0
$151$			17.8535i			1.45290i	0.687220	+	0.726450i	$0.258831\pi$
$151$			17.8535i			1.45290i	−0.687220	+	0.726450i	$0.741169\pi$
$152$	4.12503	+	1.40859i	0.334584	+	0.114252i
$153$	−7.65603	−	7.65603i	−0.618954	−	0.618954i
$154$	0.186947	+	1.06023i	0.0150646	+	0.0854355i
$155$		0			0
$156$	−14.7504	+	5.36871i	−1.18098	+	0.429841i
$157$	19.7825	−	9.22473i	1.57881	−	0.736213i	0.581793	−	0.813337i	$-0.302351\pi$
$157$	19.7825	−	9.22473i	1.57881	−	0.736213i	0.997022	+	0.0771235i	$0.0245736\pi$
$158$	−0.201611	−	2.30443i	−0.0160393	−	0.183330i
$159$	21.5862	+	12.4628i	1.71190	+	0.988364i
$160$		0			0
$161$	−0.117630	+	0.667111i	−0.00927051	+	0.0525757i
$162$	4.35677	−	3.05064i	0.342300	−	0.239681i
$163$	−4.31423	+	16.1009i	−0.337917	+	1.26112i	0.562755	+	0.826623i	$0.309741\pi$
$163$	−4.31423	+	16.1009i	−0.337917	+	1.26112i	−0.900672	+	0.434499i	$0.856925\pi$
$164$	−3.54360	+	6.13770i	−0.276709	+	0.479274i
$165$		0			0
$166$	−1.01435	+	2.78691i	−0.0787291	+	0.216306i
$167$	1.54338	+	0.719688i	0.119430	+	0.0556912i	0.481415	−	0.876493i	$-0.340123\pi$
$167$	1.54338	+	0.719688i	0.119430	+	0.0556912i	−0.361985	+	0.932184i	$0.617901\pi$
$168$	−0.684669	−	0.0599008i	−0.0528233	−	0.00462144i
$169$	15.5104	−	2.73490i	1.19311	−	0.210377i
$170$		0			0
$171$	23.5747	+	5.81395i	1.80280	+	0.444604i
$172$	−2.63463	+	2.63463i	−0.200889	+	0.200889i
$173$	10.7807	+	7.54873i	0.819642	+	0.573920i	0.906454	−	0.422305i	$-0.138779\pi$
$173$	10.7807	+	7.54873i	0.819642	+	0.573920i	−0.0868116	+	0.996225i	$0.527668\pi$
$174$	−17.7467	+	14.8913i	−1.34538	+	1.12891i
$175$		0			0
$176$	4.30922	+	1.56843i	0.324820	+	0.118225i
$177$	−32.3157	+	2.82725i	−2.42899	+	0.212509i
$178$	−3.79220	+	1.01612i	−0.284238	+	0.0761612i
$179$	−8.90666	−	15.4268i	−0.665715	−	1.15305i	−0.979091	−	0.203423i	$-0.934793\pi$
$179$	−8.90666	−	15.4268i	−0.665715	−	1.15305i	0.313376	−	0.949629i	$-0.398540\pi$
$180$		0			0
$181$	19.9588	+	3.51928i	1.48353	+	0.261586i	0.855987	−	0.516997i	$-0.172950\pi$
$181$	19.9588	+	3.51928i	1.48353	+	0.261586i	0.627542	+	0.778583i	$0.284061\pi$
$182$	1.21589	+	0.325797i	0.0901278	+	0.0241497i
$183$	1.40694	+	5.25078i	0.104004	+	0.388149i
$184$	2.21038	+	1.85473i	0.162951	+	0.136732i
$185$		0			0
$186$	2.90661	+	7.98584i	0.213123	+	0.585550i
$187$	0.776850	−	8.87943i	0.0568089	−	0.649329i
$188$	1.08781	−	1.55356i	0.0793370	−	0.113305i
$189$	−1.76663			−0.128504
$190$		0			0
$191$	13.4756			0.975059			0.487529	−	0.873107i	$-0.337898\pi$
$191$	13.4756			0.975059			0.487529	+	0.873107i	$0.337898\pi$
$192$	−1.67916	+	2.39810i	−0.121183	+	0.173068i
$193$	1.83265	−	20.9472i	0.131917	−	1.50781i	−0.585216	−	0.810878i	$-0.698990\pi$
$193$	1.83265	−	20.9472i	0.131917	−	1.50781i	0.717132	−	0.696937i	$-0.245454\pi$
$194$	1.80795	+	4.96731i	0.129804	+	0.356632i
$195$		0			0
$196$	−5.32009	−	4.46409i	−0.380006	−	0.318863i
$197$	−0.979754	−	3.65649i	−0.0698046	−	0.260514i	0.922201	−	0.386712i	$-0.126389\pi$
$197$	−0.979754	−	3.65649i	−0.0698046	−	0.260514i	−0.992005	+	0.126198i	$0.959723\pi$
$198$	24.6745	+	6.61150i	1.75354	+	0.469859i
$199$	−5.20931	−	0.918543i	−0.369279	−	0.0651138i	−0.0140704	−	0.999901i	$-0.504479\pi$
$199$	−5.20931	−	0.918543i	−0.369279	−	0.0651138i	−0.355208	+	0.934787i	$0.615590\pi$
$200$		0			0
$201$	−8.36008	−	14.4801i	−0.589675	−	1.02135i
$202$	−14.8601	+	3.98175i	−1.04555	+	0.280155i
$203$	1.85072	−	0.161917i	0.129895	−	0.0113644i
$204$	5.34707	+	1.94617i	0.374370	+	0.136259i
$205$		0			0
$206$	0.799963	−	0.671249i	0.0557361	−	0.0467681i
$207$	13.1664	+	9.21923i	0.915129	+	0.640781i
$208$	3.79141	−	3.79141i	0.262887	−	0.262887i
$209$	8.80842	+	17.9435i	0.609291	+	1.24118i
$210$		0			0
$211$	−27.4246	+	4.83570i	−1.88799	+	0.332904i	−0.993467	−	0.114118i	$-0.963596\pi$
$211$	−27.4246	+	4.83570i	−1.88799	+	0.332904i	−0.894523	+	0.447022i	$0.852485\pi$
$212$	−8.48180	−	0.742061i	−0.582532	−	0.0509650i
$213$	−38.0077	−	17.7233i	−2.60425	−	1.21438i
$214$	0.0862253	−	0.236902i	0.00589424	−	0.0161943i
$215$		0			0
$216$	−3.76255	+	6.51693i	−0.256009	+	0.443421i
$217$	0.176386	−	0.658280i	0.0119738	−	0.0446870i
$218$	−0.704674	+	0.493418i	−0.0477265	+	0.0334185i
$219$	−3.35682	+	19.0375i	−0.226833	+	1.28643i
$220$		0			0
$221$	−9.02557	−	5.21092i	−0.607126	−	0.350524i
$222$	−2.19000	−	25.0319i	−0.146983	−	1.68003i
$223$	−6.08492	+	2.83744i	−0.407476	+	0.190009i	−0.615539	−	0.788106i	$-0.711062\pi$
$223$	−6.08492	+	2.83744i	−0.407476	+	0.190009i	0.208063	+	0.978115i	$0.433284\pi$
$224$	0.220607	−	0.0802945i	0.0147400	−	0.00536490i
$225$		0			0
$226$	1.38695	+	7.86577i	0.0922583	+	0.523223i
$227$	1.44946	+	1.44946i	0.0962039	+	0.0962039i	0.753571	−	0.657367i	$-0.228330\pi$
$227$	1.44946	+	1.44946i	0.0962039	+	0.0962039i	−0.657367	+	0.753571i	$0.728330\pi$
$228$	−12.5201	+	2.46686i	−0.829165	+	0.163371i
$229$			8.46638i			0.559474i	0.960077	+	0.279737i	$0.0902473\pi$
$229$			8.46638i			0.559474i	−0.960077	+	0.279737i	$0.909753\pi$
$230$		0			0
$231$	−2.02589	−	2.41437i	−0.133294	−	0.158854i
$232$	3.34434	−	7.17197i	0.219567	−	0.470863i
$233$	5.39588	+	11.5715i	0.353496	+	0.758075i	0.999988	−	0.00484580i	$-0.00154247\pi$
$233$	5.39588	+	11.5715i	0.353496	+	0.758075i	−0.646492	+	0.762921i	$0.723765\pi$
$234$	19.1988	−	22.8803i	1.25507	−	1.49573i
$235$		0			0
$236$	9.59616	−	5.54034i	0.624657	−	0.360646i
$237$	3.88429	+	5.54735i	0.252312	+	0.360339i
$238$	−0.261730	−	0.373789i	−0.0169654	−	0.0242292i
$239$	−9.19101	+	5.30643i	−0.594517	+	0.343245i	−0.766882	−	0.641789i	$-0.778193\pi$
$239$	−9.19101	+	5.30643i	−0.594517	+	0.343245i	0.172364	+	0.985033i	$0.444859\pi$
$240$		0			0
$241$	14.3138	−	17.0586i	0.922035	−	1.09884i	−0.0728018	−	0.997346i	$-0.523194\pi$
$241$	14.3138	−	17.0586i	0.922035	−	1.09884i	0.994836	−	0.101492i	$-0.0323615\pi$
$242$	4.23859	+	9.08970i	0.272467	+	0.584308i
$243$	2.96037	−	6.34854i	0.189908	−	0.407259i
$244$	−1.19356	−	1.42243i	−0.0764101	−	0.0910620i
$245$		0			0
$246$		−	20.7480i		−	1.32285i
$247$	23.3672	−	0.467558i	1.48682	−	0.0297500i
$248$	−2.05266	−	2.05266i	−0.130344	−	0.130344i
$249$	−1.50768	−	8.55049i	−0.0955455	−	0.541865i
$250$		0			0
$251$	−17.0135	+	6.19242i	−1.07388	+	0.390862i	−0.817628	−	0.575747i	$-0.804711\pi$
$251$	−17.0135	+	6.19242i	−1.07388	+	0.390862i	−0.256256	+	0.966609i	$0.582489\pi$
$252$	1.18523	−	0.552680i	0.0746622	−	0.0348155i
$253$	1.15324	+	13.1816i	0.0725039	+	0.828723i
$254$	11.9697	+	6.91073i	0.751048	+	0.433618i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−18.1127	+	12.6826i	−1.12984	+	0.791121i	−0.980276	−	0.197631i	$-0.936675\pi$
$257$	−18.1127	+	12.6826i	−1.12984	+	0.791121i	−0.149562	+	0.988752i	$0.547786\pi$
$258$	2.82315	−	10.5361i	0.175761	−	0.655951i
$259$	−1.00751	+	1.74507i	−0.0626039	+	0.108433i
$260$		0			0
$261$	15.0767	−	41.4228i	0.933222	−	2.56401i
$262$	−3.57132	−	1.66533i	−0.220637	−	0.102885i
$263$	−2.03877	−	0.178369i	−0.125716	−	0.0109987i	0.0241242	−	0.999709i	$-0.492320\pi$
$263$	−2.03877	−	0.178369i	−0.125716	−	0.0109987i	−0.149840	+	0.988710i	$0.547876\pi$
$264$	−13.2211	+	2.33123i	−0.813701	+	0.143477i
$265$		0			0
$266$	0.935908	+	0.413833i	0.0573842	+	0.0253737i
$267$	8.12709	−	8.12709i	0.497370	−	0.497370i
$268$	4.67846	+	3.27589i	0.285782	+	0.200107i
$269$	0.617235	−	0.517922i	0.0376335	−	0.0315782i	−0.623777	−	0.781602i	$-0.714403\pi$
$269$	0.617235	−	0.517922i	0.0376335	−	0.0315782i	0.661410	+	0.750024i	$0.269958\pi$
$270$		0			0
$271$	−0.0356215	−	0.0129652i	−0.00216385	−	0.000787577i	0.340938	−	0.940086i	$-0.389255\pi$
$271$	−0.0356215	−	0.0129652i	−0.00216385	−	0.000787577i	−0.343102	+	0.939298i	$0.611478\pi$
$272$	−1.93630	+	0.169404i	−0.117405	+	0.0102716i
$273$	−3.55956	+	0.953781i	−0.215434	+	0.0577255i
$274$	1.56175	+	2.70503i	0.0943488	+	0.163417i
$275$		0			0
$276$	−8.31890	−	1.46685i	−0.500739	−	0.0882938i
$277$	−3.93669	−	1.05483i	−0.236533	−	0.0633788i	0.138605	−	0.990348i	$-0.455738\pi$
$277$	−3.93669	−	1.05483i	−0.236533	−	0.0633788i	−0.375138	+	0.926969i	$0.622405\pi$
$278$	2.09419	+	7.81564i	0.125601	+	0.468751i
$279$	−12.3873	−	10.3942i	−0.741610	−	0.622284i
$280$		0			0
$281$	5.37812	+	14.7763i	0.320832	+	0.881478i	0.990338	+	0.138672i	$0.0442834\pi$
$281$	5.37812	+	14.7763i	0.320832	+	0.881478i	−0.669507	+	0.742806i	$0.733494\pi$
$282$	−0.483907	+	5.53108i	−0.0288162	+	0.329371i
$283$	12.0976	−	17.2772i	0.719130	−	1.02702i	−0.278648	−	0.960393i	$-0.589886\pi$
$283$	12.0976	−	17.2772i	0.719130	−	1.02702i	0.997778	−	0.0666302i	$-0.0212248\pi$
$284$	14.3250			0.850032
$285$		0			0
$286$	24.5883			1.45394
$287$	−0.954334	+	1.36293i	−0.0563326	+	0.0804512i
$288$	0.485497	−	5.54926i	0.0286082	−	0.326993i
$289$	−4.52221	−	12.4247i	−0.266012	−	0.730863i
$290$		0			0
$291$	−11.8547	−	9.94730i	−0.694937	−	0.583121i
$292$	−1.70904	−	6.37822i	−0.100014	−	0.373257i
$293$	−24.6711	−	6.61061i	−1.44130	−	0.386196i	−0.548313	−	0.836273i	$-0.684730\pi$
$293$	−24.6711	−	6.61061i	−1.44130	−	0.386196i	−0.892990	+	0.450077i	$0.851396\pi$
$294$	20.0225	+	3.53051i	1.16774	+	0.205903i
$295$		0			0
$296$	4.29158	+	7.43323i	0.249443	+	0.432048i
$297$	−33.3326	+	8.93145i	−1.93415	+	0.518255i
$298$	−20.7292	+	1.81357i	−1.20081	+	0.105057i
$299$	14.5383	+	5.29152i	0.840773	+	0.306016i
$300$		0			0
$301$	−0.670075	+	0.562260i	−0.0386225	+	0.0324081i
$302$	14.6248	+	10.2404i	0.841560	+	0.589267i
$303$	31.8467	−	31.8467i	1.82954	−	1.82954i
$304$	3.51987	−	2.57109i	0.201878	−	0.147462i
$305$		0			0
$306$	−10.6628	+	1.88014i	−0.609550	+	0.107480i
$307$	−7.08104	−	0.619510i	−0.404136	−	0.0353573i	−0.116724	−	0.993164i	$-0.537239\pi$
$307$	−7.08104	−	0.619510i	−0.404136	−	0.0353573i	−0.287412	+	0.957807i	$0.592795\pi$
$308$	0.975715	+	0.454983i	0.0555965	+	0.0259251i
$309$	−1.04561	+	2.87279i	−0.0594827	+	0.163427i
$310$		0			0
$311$	7.66647	−	13.2787i	0.434726	−	0.752967i	−0.562547	−	0.826765i	$-0.690179\pi$
$311$	7.66647	−	13.2787i	0.434726	−	0.752967i	0.997273	+	0.0737979i	$0.0235120\pi$
$312$	−4.06270	+	15.1622i	−0.230005	+	0.858390i
$313$	1.43667	−	1.00596i	0.0812052	−	0.0568605i	−0.532269	−	0.846575i	$-0.678660\pi$
$313$	1.43667	−	1.00596i	0.0812052	−	0.0568605i	0.613474	+	0.789715i	$0.289772\pi$
$314$	3.79032	−	21.4960i	0.213900	−	1.21309i
$315$		0			0
$316$	−2.00332	−	1.15661i	−0.112695	−	0.0650647i
$317$	−2.02148	−	23.1057i	−0.113538	−	1.29774i	−0.812659	−	0.582740i	$-0.801981\pi$
$317$	−2.02148	−	23.1057i	−0.113538	−	1.29774i	0.699121	−	0.715004i	$-0.253575\pi$
$318$	22.5903	−	10.5340i	1.26680	−	0.590718i
$319$	34.1006	−	12.4116i	1.90927	−	0.694916i
$320$		0			0
$321$	0.128161	+	0.726836i	0.00715324	+	0.0405680i
$322$	0.478996	+	0.478996i	0.0266934	+	0.0266934i
$323$	−6.59786	−	5.31500i	−0.367115	−	0.295735i
$324$		−	5.31863i		−	0.295479i
$325$		0			0
$326$	10.7146	+	12.7691i	0.593425	+	0.707217i
$327$	1.06432	−	2.28245i	0.0588573	−	0.126220i
$328$	2.99518	+	6.42319i	0.165381	+	0.354661i
$329$	0.286197	−	0.341076i	0.0157786	−	0.0188042i
$330$		0			0
$331$	10.5119	−	6.06905i	0.577786	−	0.333585i	−0.182467	−	0.983212i	$-0.558408\pi$
$331$	10.5119	−	6.06905i	0.577786	−	0.333585i	0.760253	+	0.649627i	$0.225075\pi$
$332$	1.70110	+	2.42942i	0.0933598	+	0.133332i
$333$	27.4239	+	39.1654i	1.50282	+	2.14625i
$334$	1.47478	−	0.851464i	0.0806963	−	0.0465900i
$335$		0			0
$336$	−0.441778	+	0.526490i	−0.0241009	+	0.0287224i
$337$	−2.03747	−	4.36938i	−0.110988	−	0.238015i	0.842966	−	0.537967i	$-0.180807\pi$
$337$	−2.03747	−	4.36938i	−0.110988	−	0.238015i	−0.953955	+	0.299951i	$0.903030\pi$
$338$	6.65609	−	14.2740i	0.362043	−	0.776405i
$339$	−15.0300	−	17.9121i	−0.816318	−	0.972850i
$340$		0			0
$341$		−	13.3121i		−	0.720889i
$342$	18.2844	−	15.9765i	0.988708	−	0.863913i
$343$	−2.31491	−	2.31491i	−0.124993	−	0.124993i
$344$	0.647002	+	3.66933i	0.0348840	+	0.197837i
$345$		0			0
$346$	12.3671	−	4.50126i	0.664861	−	0.241989i
$347$	−19.9934	+	9.32305i	−1.07330	+	0.500488i	−0.877214	−	0.480099i	$-0.840601\pi$
$347$	−19.9934	+	9.32305i	−1.07330	+	0.500488i	−0.196085	+	0.980587i	$0.562823\pi$
$348$	2.01911	+	23.0786i	0.108236	+	1.23714i
$349$	10.9558	+	6.32535i	0.586452	+	0.338588i	0.763693	−	0.645579i	$-0.223384\pi$
$349$	10.9558	+	6.32535i	0.586452	+	0.338588i	−0.177241	+	0.984167i	$0.556717\pi$
$350$		0			0
$351$	−7.00647	+	39.7356i	−0.373977	+	2.12093i
$352$	3.75645	−	2.63029i	0.200219	−	0.140195i
$353$	0.243869	−	0.910133i	0.0129799	−	0.0484415i	−0.959132	−	0.282958i	$-0.908684\pi$
$353$	0.243869	−	0.910133i	0.0129799	−	0.0484415i	0.972112	+	0.234517i	$0.0753508\pi$
$354$	−16.2195	+	28.0931i	−0.862059	+	1.49313i
$355$		0			0
$356$	−1.34276	+	3.68921i	−0.0711663	+	0.195528i
$357$	1.21071	+	0.564563i	0.0640775	+	0.0298798i
$358$	−17.7455	−	1.55253i	−0.937880	−	0.0820539i
$359$	−5.34936	+	0.943236i	−0.282328	+	0.0497821i	−0.313019	−	0.949747i	$-0.601340\pi$
$359$	−5.34936	+	0.943236i	−0.282328	+	0.0497821i	0.0306908	+	0.999529i	$0.490229\pi$
$360$		0			0
$361$	18.8284	+	2.54818i	0.990966	+	0.134115i
$362$	14.3307	−	14.3307i	0.753207	−	0.753207i
$363$	−24.0514	−	16.8410i	−1.26237	−	0.883921i
$364$	0.964283	−	0.809129i	0.0505422	−	0.0424099i
$365$		0			0
$366$	5.10818	+	1.85923i	0.267009	+	0.0971833i
$367$	10.2380	−	0.895708i	0.534419	−	0.0467556i	0.183247	−	0.983067i	$-0.441339\pi$
$367$	10.2380	−	0.895708i	0.534419	−	0.0467556i	0.351171	+	0.936311i	$0.385784\pi$
$368$	2.78712	−	0.746807i	0.145289	−	0.0389300i
$369$	19.7395	+	34.1898i	1.02760	+	1.77985i
$370$		0			0
$371$	−1.96847	−	0.347095i	−0.102198	−	0.0180203i
$372$	8.20878	+	2.19954i	0.425605	+	0.114041i
$373$	6.07981	+	22.6902i	0.314801	+	1.17485i	0.924175	+	0.381969i	$0.124754\pi$
$373$	6.07981	+	22.6902i	0.314801	+	1.17485i	−0.609374	+	0.792883i	$0.708579\pi$
$374$	−6.82802	−	5.72939i	−0.353069	−	0.296260i
$375$		0			0
$376$	−0.648657	−	1.78217i	−0.0334519	−	0.0919084i
$377$	3.69807	−	42.2691i	0.190460	−	2.17697i
$378$	−1.01330	+	1.44714i	−0.0521185	+	0.0744330i
$379$	−23.9869			−1.23212			−0.616062	−	0.787698i	$-0.711273\pi$
$379$	−23.9869			−1.23212			−0.616062	+	0.787698i	$0.711273\pi$
$380$		0			0
$381$	−40.4628			−2.07297
$382$	7.72928	−	11.0386i	0.395464	−	0.564781i
$383$	0.668196	−	7.63752i	0.0341432	−	0.390259i	−0.959826	−	0.280597i	$-0.909468\pi$
$383$	0.668196	−	7.63752i	0.0341432	−	0.390259i	0.993969	−	0.109662i	$-0.0349769\pi$
$384$	1.00128	+	2.75098i	0.0510961	+	0.140385i
$385$		0			0
$386$	−16.1078	−	13.5161i	−0.819866	−	0.687949i
$387$	5.37183	+	20.0479i	0.273066	+	1.01909i
$388$	5.10599	+	1.36814i	0.259217	+	0.0694570i
$389$	−18.5772	−	3.27566i	−0.941901	−	0.166083i	−0.318445	−	0.947941i	$-0.603161\pi$
$389$	−18.5772	−	3.27566i	−0.941901	−	0.166083i	−0.623456	+	0.781859i	$0.714272\pi$
$390$		0			0
$391$	−2.80421	−	4.85703i	−0.141815	−	0.245631i
$392$	−6.70824	+	1.79747i	−0.338817	+	0.0907859i
$393$	11.4921	−	1.00543i	0.579700	−	0.0507172i
$394$	−3.55719	−	1.29471i	−0.179208	−	0.0652265i
$395$		0			0
$396$	19.5685	−	16.4199i	0.983355	−	0.825133i
$397$	2.13314	+	1.49364i	0.107059	+	0.0749638i	0.625880	−	0.779919i	$-0.284740\pi$
$397$	2.13314	+	1.49364i	0.107059	+	0.0749638i	−0.518821	+	0.854883i	$0.673629\pi$
$398$	−3.74037	+	3.74037i	−0.187488	+	0.187488i
$399$	−2.97858	+	0.320753i	−0.149116	+	0.0160577i
$400$		0			0
$401$	−18.4302	+	3.24974i	−0.920361	+	0.162284i	−0.613704	−	0.789536i	$-0.710321\pi$
$401$	−18.4302	+	3.24974i	−0.920361	+	0.162284i	−0.306656	+	0.951820i	$0.599210\pi$
$402$	−16.6565	−	1.45726i	−0.830752	−	0.0726814i
$403$	−14.1067	−	6.57805i	−0.702703	−	0.327676i
$404$	−5.26174	+	14.4565i	−0.261781	+	0.719238i
$405$		0			0
$406$	0.928896	−	1.60889i	0.0461003	−	0.0798481i
$407$	−10.1872	+	38.0193i	−0.504962	+	1.88455i
$408$	4.66116	−	3.26378i	0.230762	−	0.161581i
$409$	5.78151	−	32.7886i	0.285877	−	1.62129i	−0.416258	−	0.909246i	$-0.636659\pi$
$409$	5.78151	−	32.7886i	0.285877	−	1.62129i	0.702135	−	0.712043i	$-0.252230\pi$
$410$		0			0
$411$	−7.91908	−	4.57208i	−0.390619	−	0.225524i
$412$	−0.0910148	−	1.04030i	−0.00448398	−	0.0512521i
$413$	2.35764	−	1.09938i	0.116012	−	0.0540971i
$414$	15.1039	−	5.49737i	0.742316	−	0.270181i
$415$		0			0
$416$	−0.931079	−	5.28041i	−0.0456499	−	0.258893i
$417$	−16.7497	−	16.7497i	−0.820237	−	0.820237i
$418$	19.7508	+	3.07654i	0.966042	+	0.150479i
$419$		−	39.8810i		−	1.94831i	−0.225873	−	0.974157i	$-0.572524\pi$
$419$		−	39.8810i		−	1.94831i	0.225873	−	0.974157i	$-0.427476\pi$
$420$		0			0
$421$	8.05346	+	9.59774i	0.392502	+	0.467765i	0.925718	−	0.378213i	$-0.123461\pi$
$421$	8.05346	+	9.59774i	0.392502	+	0.467765i	−0.533217	+	0.845979i	$0.679017\pi$
$422$	−11.7690	+	25.2386i	−0.572904	+	1.22860i
$423$	−4.46481	−	9.57481i	−0.217086	−	0.465543i
$424$	−5.47282	+	6.52225i	−0.265784	+	0.316749i
$425$		0			0
$426$	−36.3184	+	20.9684i	−1.75963	+	1.01592i
$427$	−0.250037	−	0.357090i	−0.0121001	−	0.0172808i
$428$	−0.144602	−	0.206513i	−0.00698960	−	0.00998218i
$429$	−62.3393	+	35.9916i	−3.00977	+	1.73769i
$430$		0			0
$431$	−5.45523	+	6.50129i	−0.262769	+	0.313156i	−0.881256	−	0.472639i	$-0.843301\pi$
$431$	−5.45523	+	6.50129i	−0.262769	+	0.313156i	0.618487	+	0.785795i	$0.287746\pi$
$432$	3.18025	+	6.82006i	0.153010	+	0.328130i
$433$	−6.38418	+	13.6909i	−0.306804	+	0.657943i	−0.997897	−	0.0648227i	$-0.979352\pi$
$433$	−6.38418	+	13.6909i	−0.306804	+	0.657943i	0.691093	+	0.722766i	$0.257130\pi$
$434$	−0.438061	−	0.522061i	−0.0210276	−	0.0250597i
$435$		0			0
$436$			0.860248i			0.0411984i
$437$	11.0159	+	6.06951i	0.526963	+	0.290344i
$438$	13.6692	+	13.6692i	0.653139	+	0.653139i
$439$	−1.37550	−	7.80082i	−0.0656488	−	0.372313i	−0.999878	−	0.0156389i	$-0.995022\pi$
$439$	−1.37550	−	7.80082i	−0.0656488	−	0.372313i	0.934229	−	0.356674i	$-0.116089\pi$
$440$		0			0
$441$	−36.3531	+	13.2315i	−1.73110	+	0.630069i
$442$	−9.44539	+	4.40446i	−0.449271	+	0.209499i
$443$	−1.42754	−	16.3169i	−0.0678246	−	0.775239i	−0.951602	−	0.307332i	$-0.900564\pi$
$443$	−1.42754	−	16.3169i	−0.0678246	−	0.775239i	0.883778	−	0.467907i	$-0.154992\pi$
$444$	−21.7610	−	12.5637i	−1.03273	−	0.596249i
$445$		0			0
$446$	−1.16587	+	6.61196i	−0.0552054	+	0.313086i
$447$	49.9004	−	34.9407i	2.36021	−	1.65264i
$448$	0.0607618	−	0.226766i	0.00287072	−	0.0107137i
$449$	−7.50696	+	13.0024i	−0.354275	+	0.613623i	−0.986994	−	0.160759i	$-0.948606\pi$
$449$	−7.50696	+	13.0024i	−0.354275	+	0.613623i	0.632718	+	0.774382i	$0.281939\pi$
$450$		0			0
$451$	−11.1158	+	30.5403i	−0.523421	+	1.43809i
$452$	7.23878	+	3.37550i	0.340483	+	0.158770i
$453$	−52.0679	−	4.55535i	−2.44636	−	0.214029i
$454$	2.01870	−	0.355952i	0.0947424	−	0.0167056i
$455$		0			0
$456$	−5.16051	+	11.6708i	−0.241663	+	0.546536i
$457$	−1.77360	+	1.77360i	−0.0829655	+	0.0829655i	−0.747372	−	0.664406i	$-0.768685\pi$
$457$	−1.77360	+	1.77360i	−0.0829655	+	0.0829655i	0.664406	+	0.747372i	$0.268685\pi$
$458$	6.93525	+	4.85612i	0.324063	+	0.226911i
$459$	11.2046	−	9.40173i	0.522984	−	0.438835i
$460$		0			0
$461$	10.5128	+	3.82636i	0.489631	+	0.178211i	0.575025	−	0.818136i	$-0.304992\pi$
$461$	10.5128	+	3.82636i	0.489631	+	0.178211i	−0.0853933	+	0.996347i	$0.527215\pi$
$462$	−3.13974	+	0.274692i	−0.146074	+	0.0127798i
$463$	19.5976	−	5.25115i	0.910775	−	0.244042i	0.227137	−	0.973863i	$-0.427063\pi$
$463$	19.5976	−	5.25115i	0.910775	−	0.244042i	0.683638	+	0.729821i	$0.260397\pi$
$464$	−3.95670	−	6.85320i	−0.183685	−	0.318152i
$465$		0			0
$466$	12.5738	+	2.21710i	0.582469	+	0.102705i
$467$	−34.7950	−	9.32329i	−1.61012	−	0.431430i	−0.662042	−	0.749467i	$-0.730310\pi$
$467$	−34.7950	−	9.32329i	−1.61012	−	0.431430i	−0.948078	+	0.318036i	$0.896977\pi$
$468$	−7.73043	−	28.8503i	−0.357339	−	1.33361i
$469$	1.02713	+	0.861867i	0.0474286	+	0.0397973i
$470$		0			0
$471$	21.8554	+	60.0472i	1.00704	+	2.76683i
$472$	0.965746	−	11.0385i	0.0444520	−	0.508089i
$473$	−9.80031	+	13.9963i	−0.450619	+	0.643550i
$474$	6.77206			0.311051
$475$		0			0
$476$	−0.456312			−0.0209150
$477$	−27.2036	+	38.8507i	−1.24557	+	1.77885i
$478$	−0.924972	+	10.5725i	−0.0423073	+	0.483574i
$479$	−0.235550	−	0.647169i	−0.0107626	−	0.0295699i	0.934195	−	0.356763i	$-0.116120\pi$
$479$	−0.235550	−	0.647169i	−0.0107626	−	0.0295699i	−0.944958	+	0.327193i	$0.893897\pi$
$480$		0			0
$481$	35.2547	+	29.5822i	1.60748	+	1.34883i
$482$	−5.76348	−	21.5096i	−0.262519	−	0.979735i
$483$	−1.91554	−	0.513269i	−0.0871603	−	0.0233545i
$484$	9.87700	+	1.74158i	0.448955	+	0.0791628i
$485$		0			0
$486$	−3.50242	−	6.06637i	−0.158873	−	0.275176i
$487$	34.4966	−	9.24332i	1.56319	−	0.418855i	0.629517	−	0.776987i	$-0.283253\pi$
$487$	34.4966	−	9.24332i	1.56319	−	0.418855i	0.933671	+	0.358132i	$0.116586\pi$
$488$	−1.84979	+	0.161836i	−0.0837361	+	0.00732596i
$489$	−45.8559	−	16.6902i	−2.07368	−	0.754756i
$490$		0			0
$491$	−26.8130	+	22.4988i	−1.21005	+	1.01535i	−0.210768	+	0.977536i	$0.567596\pi$
$491$	−26.8130	+	22.4988i	−1.21005	+	1.01535i	−0.999285	+	0.0378184i	$0.987959\pi$
$492$	−16.9958	−	11.9006i	−0.766229	−	0.536520i
$493$	−10.8762	+	10.8762i	−0.489838	+	0.489838i
$494$	13.0199	−	19.4094i	0.585791	−	0.873272i
$495$		0			0
$496$	−2.85880	+	0.504084i	−0.128364	+	0.0226340i
$497$	3.35022	+	0.293106i	0.150278	+	0.0131476i
$498$	−7.86892	−	3.66934i	−0.352615	−	0.164427i
$499$	3.82033	−	10.4963i	0.171021	−	0.469877i	−0.824339	−	0.566097i	$-0.808453\pi$
$499$	3.82033	−	10.4963i	0.171021	−	0.469877i	0.995360	+	0.0962195i	$0.0306751\pi$
$500$		0			0
$501$	−2.49269	+	4.31746i	−0.111365	+	0.192890i
$502$	−4.68603	+	17.4885i	−0.209148	+	0.780549i
$503$	−22.1201	+	15.4886i	−0.986285	+	0.690604i	−0.951134	−	0.308778i	$-0.900080\pi$
$503$	−22.1201	+	15.4886i	−0.986285	+	0.690604i	−0.0351507	+	0.999382i	$0.511191\pi$
$504$	0.227089	−	1.28788i	0.0101153	−	0.0573669i
$505$		0			0
$506$	11.4592	+	6.61600i	0.509426	+	0.294117i
$507$	4.01854	+	45.9322i	0.178470	+	2.03992i
$508$	12.5265	−	5.84121i	0.555774	−	0.259162i
$509$	−1.38127	+	0.502740i	−0.0612236	+	0.0222836i	−0.372450	−	0.928052i	$-0.621482\pi$
$509$	−1.38127	+	0.502740i	−0.0612236	+	0.0222836i	0.311227	+	0.950336i	$0.399260\pi$
$510$		0			0
$511$	−0.269191	−	1.52666i	−0.0119083	−	0.0675353i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−10.5998	+	31.0413i	−0.467992	+	1.37051i
$514$			22.1115i			0.975297i
$515$		0			0
$516$	−7.01140	−	8.35586i	−0.308660	−	0.367846i
$517$	3.67557	−	7.88229i	0.161651	−	0.346663i
$518$	0.851588	+	1.82624i	0.0374166	+	0.0802402i
$519$	−24.7658	+	29.5147i	−1.08710	+	1.29555i
$520$		0			0
$521$	7.61128	−	4.39438i	0.333456	−	0.192521i	−0.323918	−	0.946085i	$-0.605000\pi$
$521$	7.61128	−	4.39438i	0.333456	−	0.192521i	0.657375	+	0.753564i	$0.271667\pi$
$522$	−25.2839	−	36.1092i	−1.10665	−	1.58046i
$523$	−0.342609	−	0.489296i	−0.0149812	−	0.0213954i	0.811592	−	0.584225i	$-0.198602\pi$
$523$	−0.342609	−	0.489296i	−0.0149812	−	0.0213954i	−0.826573	+	0.562830i	$0.809713\pi$
$524$	−3.41259	+	1.97026i	−0.149080	+	0.0860711i
$525$		0			0
$526$	−1.31550	+	1.56775i	−0.0573585	+	0.0683572i
$527$	2.38456	+	5.11371i	0.103873	+	0.222757i
$528$	−5.67366	+	12.1672i	−0.246914	+	0.529510i
$529$	−9.43241	−	11.2411i	−0.410105	−	0.488744i
$530$		0			0
$531$		−	61.7245i		−	2.67862i
$532$	0.875807	−	0.529286i	0.0379711	−	0.0229475i
$533$	26.8705	+	26.8705i	1.16389	+	1.16389i
$534$	−1.99581	−	11.3188i	−0.0863673	−	0.489813i
$535$		0			0
$536$	5.36691	−	1.95340i	0.231815	−	0.0843738i
$537$	47.2631	−	22.0392i	2.03955	−	0.951060i
$538$	−0.0702251	−	0.802677i	−0.00302762	−	0.0346059i
$539$	−27.5809	−	15.9239i	−1.18799	−	0.685889i
$540$		0			0
$541$	−0.307614	+	1.74456i	−0.0132253	+	0.0750046i	−0.990706	−	0.136020i	$-0.956569\pi$
$541$	−0.307614	+	1.74456i	−0.0132253	+	0.0750046i	0.977481	+	0.211025i	$0.0676800\pi$
$542$	−0.0310521	+	0.0217429i	−0.00133380	+	0.000933937i
$543$	−15.3561	+	57.3099i	−0.658995	+	2.45940i
$544$	−0.971847	+	1.68329i	−0.0416676	+	0.0721704i
$545$		0			0
$546$	−1.26039	+	3.46289i	−0.0539396	+	0.148198i
$547$	35.5551	+	16.5796i	1.52023	+	0.708894i	0.990274	−	0.139132i	$-0.0444313\pi$
$547$	35.5551	+	16.5796i	1.52023	+	0.708894i	0.529954	+	0.848026i	$0.322209\pi$
$548$	3.11162	+	0.272231i	0.132922	+	0.0116291i
$549$	−10.1864	+	1.79614i	−0.434745	+	0.0766573i
$550$		0			0
$551$	8.25929	−	33.4903i	0.351858	−	1.42673i
$552$	−5.97309	+	5.97309i	−0.254232	+	0.254232i
$553$	−0.444854	−	0.311490i	−0.0189171	−	0.0132459i
$554$	−3.12206	+	2.61972i	−0.132644	+	0.111301i
$555$		0			0
$556$	7.60337	+	2.76740i	0.322455	+	0.117364i
$557$	4.93896	−	0.432103i	0.209270	−	0.0183088i	0.0179615	−	0.999839i	$-0.494282\pi$
$557$	4.93896	−	0.432103i	0.209270	−	0.0183088i	0.191309	+	0.981530i	$0.438727\pi$
$558$	−15.6195	+	4.18523i	−0.661226	+	0.177175i
$559$	9.98899	+	17.3014i	0.422489	+	0.731773i
$560$		0			0
$561$	25.6977	+	4.53120i	1.08496	+	0.191307i
$562$	15.1888	+	4.06982i	0.640700	+	0.171675i
$563$	−4.59805	−	17.1601i	−0.193785	−	0.723214i	−0.992578	−	0.121609i	$-0.961195\pi$
$563$	−4.59805	−	17.1601i	−0.193785	−	0.723214i	0.798794	−	0.601605i	$-0.205472\pi$
$564$	4.25324	+	3.56889i	0.179094	+	0.150277i
$565$		0			0
$566$	−7.21374	−	19.8196i	−0.303216	−	0.833080i
$567$	0.108825	−	1.24388i	0.00457023	−	0.0522380i
$568$	8.21647	−	11.7343i	0.344756	−	0.492362i
$569$	13.5871			0.569600			0.284800	−	0.958587i	$-0.408073\pi$
$569$	13.5871			0.569600			0.284800	+	0.958587i	$0.408073\pi$
$570$		0			0
$571$	7.00276			0.293056			0.146528	−	0.989206i	$-0.453190\pi$
$571$	7.00276			0.293056			0.146528	+	0.989206i	$0.453190\pi$
$572$	14.1033	−	20.1416i	0.589688	−	0.842162i
$573$	−3.43831	+	39.3001i	−0.143638	+	1.64179i
$574$	0.569064	+	1.56349i	0.0237523	+	0.0652588i
$575$		0			0
$576$	−4.26722	−	3.58062i	−0.177801	−	0.149193i
$577$	1.97194	+	7.35940i	0.0820931	+	0.306376i	0.994748	−	0.102356i	$-0.0326380\pi$
$577$	1.97194	+	7.35940i	0.0820931	+	0.306376i	−0.912655	+	0.408731i	$0.865971\pi$
$578$	−12.7715	−	3.42212i	−0.531225	−	0.142341i
$579$	60.6228	+	10.6894i	2.51940	+	0.444238i
$580$		0			0
$581$	0.348130	+	0.602979i	0.0144429	+	0.0250158i
$582$	−14.9480	+	4.00529i	−0.619613	+	0.166025i
$583$	−38.8956	+	3.40293i	−1.61089	+	0.140935i
$584$	−6.20500	−	2.25843i	−0.256765	−	0.0934547i
$585$		0			0
$586$	−19.5659	+	16.4177i	−0.808259	+	0.678210i
$587$	0.995551	+	0.697092i	0.0410908	+	0.0287721i	0.593941	−	0.804508i	$-0.297571\pi$
$587$	0.995551	+	0.697092i	0.0410908	+	0.0287721i	−0.552851	+	0.833280i	$0.686460\pi$
$588$	14.3765	−	14.3765i	0.592875	−	0.592875i
$589$	−10.5082	−	7.04892i	−0.432984	−	0.290446i
$590$		0			0
$591$	10.9138	−	1.92439i	0.448932	−	0.0791588i
$592$	8.55049	+	0.748071i	0.351423	+	0.0307455i
$593$	−15.3960	−	7.17929i	−0.632240	−	0.294818i	0.0799568	−	0.996798i	$-0.474522\pi$
$593$	−15.3960	−	7.17929i	−0.632240	−	0.294818i	−0.712197	+	0.701980i	$0.752300\pi$
$594$	−11.8026	+	32.4274i	−0.484266	+	1.33051i
$595$		0			0
$596$	−10.4042	+	18.0206i	−0.426172	+	0.738151i
$597$	4.00800	−	14.9580i	0.164036	−	0.612192i
$598$	12.6734	−	8.87401i	0.518254	−	0.362885i
$599$	−1.12150	+	6.36033i	−0.0458232	+	0.259876i	−0.999110	−	0.0421919i	$-0.986566\pi$
$599$	−1.12150	+	6.36033i	−0.0458232	+	0.259876i	0.953286	+	0.302068i	$0.0976770\pi$
$600$		0			0
$601$	−28.6723	−	16.5539i	−1.16957	−	0.675249i	−0.215988	−	0.976396i	$-0.569297\pi$
$601$	−28.6723	−	16.5539i	−1.16957	−	0.675249i	−0.953578	+	0.301147i	$0.902631\pi$
$602$	0.0762369	+	0.871392i	0.00310719	+	0.0355153i
$603$	28.8340	−	13.4455i	1.17421	−	0.547544i
$604$	16.7768	−	6.10627i	0.682639	−	0.248460i
$605$		0			0
$606$	−7.82077	−	44.3538i	−0.317697	−	1.80175i
$607$	−0.993607	−	0.993607i	−0.0403293	−	0.0403293i	0.686655	−	0.726984i	$-0.259079\pi$
$607$	−0.993607	−	0.993607i	−0.0403293	−	0.0403293i	−0.726984	+	0.686655i	$0.759079\pi$
$608$	−0.0872006	−	4.35803i	−0.00353645	−	0.176741i
$609$			5.43875i			0.220389i
$610$		0			0
$611$	−6.53653	−	7.78993i	−0.264440	−	0.315147i
$612$	−4.57580	+	9.81284i	−0.184966	+	0.396660i
$613$	−8.71167	−	18.6822i	−0.351861	−	0.754568i	0.648115	−	0.761543i	$-0.275558\pi$
$613$	−8.71167	−	18.6822i	−0.351861	−	0.754568i	−0.999976	+	0.00697441i	$0.997780\pi$
$614$	−4.56899	+	5.44511i	−0.184389	+	0.219747i
$615$		0			0
$616$	0.932348	−	0.538291i	0.0375654	−	0.0216884i
$617$	−13.1635	−	18.7994i	−0.529942	−	0.756836i	0.461534	−	0.887123i	$-0.347299\pi$
$617$	−13.1635	−	18.7994i	−0.529942	−	0.756836i	−0.991476	+	0.130286i	$0.958410\pi$
$618$	1.75351	+	2.50428i	0.0705367	+	0.100737i
$619$	18.4468	−	10.6502i	0.741438	−	0.428069i	−0.0811540	−	0.996702i	$-0.525861\pi$
$619$	18.4468	−	10.6502i	0.741438	−	0.428069i	0.822592	+	0.568632i	$0.192527\pi$
$620$		0			0
$621$	−13.9570	+	16.6333i	−0.560075	+	0.667472i
$622$	−6.47998	−	13.8964i	−0.259824	−	0.557194i
$623$	−0.389521	+	0.835329i	−0.0156058	+	0.0334668i
$624$	10.0899	+	12.0246i	0.403918	+	0.481371i
$625$		0			0
$626$		−	1.75385i		−	0.0700978i
$627$	−54.5778	+	21.1105i	−2.17963	+	0.843073i
$628$	−15.4344	−	15.4344i	−0.615900	−	0.615900i
$629$	−2.89698	−	16.4296i	−0.115510	−	0.655090i
$630$		0			0
$631$	−10.7466	+	3.91145i	−0.427816	+	0.155712i	−0.546949	−	0.837166i	$-0.684211\pi$
$631$	−10.7466	+	3.91145i	−0.427816	+	0.155712i	0.119133	+	0.992878i	$0.461989\pi$
$632$	−2.09650	+	0.977613i	−0.0833942	+	0.0388874i
$633$	−7.10538	−	81.2149i	−0.282414	−	3.22800i
$634$	−20.0865	−	11.5970i	−0.797738	−	0.460574i
$635$		0			0
$636$	4.32829	−	24.5469i	0.171628	−	0.973349i
$637$	−30.5032	+	21.3586i	−1.20858	+	0.846258i
$638$	9.39230	−	35.0525i	0.371845	−	1.38774i
$639$	39.8984	−	69.1060i	1.57836	−	2.73379i
$640$		0			0
$641$	16.7077	−	45.9040i	0.659914	−	1.81310i	0.0825890	−	0.996584i	$-0.473681\pi$
$641$	16.7077	−	45.9040i	0.659914	−	1.81310i	0.577325	−	0.816515i	$-0.304097\pi$
$642$	0.668899	+	0.311913i	0.0263993	+	0.0123102i
$643$	−10.3421	−	0.904815i	−0.407852	−	0.0356824i	−0.118616	−	0.992940i	$-0.537846\pi$
$643$	−10.3421	−	0.904815i	−0.407852	−	0.0356824i	−0.289236	+	0.957258i	$0.593401\pi$
$644$	0.667111	−	0.117630i	0.0262878	−	0.00463526i
$645$		0			0
$646$	−8.13817	+	2.35609i	−0.320192	+	0.0926990i
$647$	6.23110	−	6.23110i	0.244970	−	0.244970i	−0.573933	−	0.818902i	$-0.694583\pi$
$647$	6.23110	−	6.23110i	0.244970	−	0.244970i	0.818902	+	0.573933i	$0.194583\pi$
$648$	−4.35677	−	3.05064i	−0.171150	−	0.119840i
$649$	38.9255	−	32.6623i	1.52796	−	1.28211i
$650$		0			0
$651$	1.87480	+	0.682371i	0.0734792	+	0.0267442i
$652$	16.6055	−	1.45279i	0.650321	−	0.0568957i
$653$	27.7735	−	7.44189i	1.08686	−	0.291224i	0.329458	−	0.944170i	$-0.393134\pi$
$653$	27.7735	−	7.44189i	1.08686	−	0.291224i	0.757404	+	0.652947i	$0.226467\pi$
$654$	−1.25920	−	2.18100i	−0.0492387	−	0.0852840i
$655$		0			0
$656$	6.97953	+	1.23068i	0.272505	+	0.0480500i
$657$	−35.5296	−	9.52013i	−1.38614	−	0.371416i
$658$	−0.115238	−	0.430072i	−0.00449243	−	0.0167660i
$659$	25.7083	+	21.5719i	1.00145	+	0.840320i	0.987185	−	0.159578i	$-0.0510134\pi$
$659$	25.7083	+	21.5719i	1.00145	+	0.840320i	0.0142693	+	0.999898i	$0.495458\pi$
$660$		0			0
$661$	6.66083	+	18.3005i	0.259076	+	0.711806i	0.999225	+	0.0393630i	$0.0125329\pi$
$661$	6.66083	+	18.3005i	0.259076	+	0.711806i	−0.740149	+	0.672443i	$0.765245\pi$
$662$	1.05790	−	12.0919i	0.0411166	−	0.469965i
$663$	17.5000	−	24.9926i	0.679643	−	0.970631i
$664$	2.96577			0.115094
$665$		0			0
$666$	47.8121			1.85268
$667$	13.0968	−	18.7042i	0.507111	−	0.724230i
$668$	0.148420	−	1.69645i	0.00574254	−	0.0656375i
$669$	−6.72253	−	18.4700i	−0.259908	−	0.714091i
$670$		0			0
$671$	−6.52297	−	5.47342i	−0.251816	−	0.211299i
$672$	0.177882	+	0.663865i	0.00686195	+	0.0256092i
$673$	9.70117	+	2.59942i	0.373953	+	0.100200i	0.440900	−	0.897556i	$-0.354659\pi$
$673$	9.70117	+	2.59942i	0.373953	+	0.100200i	−0.0669474	+	0.997757i	$0.521326\pi$
$674$	−4.74783	−	0.837171i	−0.182880	−	0.0322466i
$675$		0			0
$676$	−7.87482	−	13.6396i	−0.302878	−	0.524600i
$677$	1.48794	−	0.398692i	0.0571862	−	0.0153230i	−0.230113	−	0.973164i	$-0.573909\pi$
$677$	1.48794	−	0.398692i	0.0571862	−	0.0153230i	0.287299	+	0.957841i	$0.407243\pi$
$678$	−23.2936	+	2.03792i	−0.894584	+	0.0782659i
$679$	1.16615	+	0.424445i	0.0447529	+	0.0162887i
$680$		0			0
$681$	−4.59702	+	3.85736i	−0.176158	+	0.147814i
$682$	−10.9046	−	7.63549i	−0.417559	−	0.292378i
$683$	6.27894	−	6.27894i	0.240257	−	0.240257i	−0.576699	−	0.816956i	$-0.695660\pi$
$683$	6.27894	−	6.27894i	0.240257	−	0.240257i	0.816956	+	0.576699i	$0.195660\pi$
$684$	−2.59971	−	24.1415i	−0.0994024	−	0.923073i
$685$		0			0
$686$	−3.22404	+	0.568486i	−0.123094	+	0.0217049i
$687$	−24.6913	−	2.16021i	−0.942032	−	0.0824171i
$688$	3.37684	+	1.57465i	0.128741	+	0.0600329i
$689$	−15.6139	+	42.8989i	−0.594842	+	1.63432i
$690$		0			0
$691$	−3.01048	+	5.21430i	−0.114524	+	0.198361i	−0.917589	−	0.397530i	$-0.869868\pi$
$691$	−3.01048	+	5.21430i	−0.114524	+	0.198361i	0.803065	+	0.595891i	$0.203201\pi$
$692$	3.40627	−	12.7124i	0.129487	−	0.483252i
$693$	4.91250	−	3.43977i	0.186611	−	0.130666i
$694$	−3.83072	+	21.7251i	−0.145412	+	0.824673i
$695$		0			0
$696$	20.0630	+	11.5834i	0.760485	+	0.439066i
$697$	−1.20060	−	13.7229i	−0.0454760	−	0.519793i
$698$	11.4654	−	5.34642i	0.433973	−	0.202365i
$699$	−35.1239	+	12.7840i	−1.32851	+	0.483537i
$700$		0			0
$701$	−1.11066	−	6.29887i	−0.0419491	−	0.237905i	0.956623	−	0.291329i	$-0.0940975\pi$
$701$	−1.11066	−	6.29887i	−0.0419491	−	0.237905i	−0.998572	+	0.0534243i	$0.982986\pi$
$702$	28.5308	+	28.5308i	1.07683	+	1.07683i
$703$	24.6172	+	28.1733i	0.928456	+	1.06257i
$704$		−	4.58578i		−	0.172833i
$705$		0			0
$706$	−0.605659	−	0.721797i	−0.0227943	−	0.0271652i
$707$	−1.52637	+	3.27331i	−0.0574051	+	0.123106i
$708$	13.7094	+	29.3998i	0.515229	+	1.10491i
$709$	−4.64880	+	5.54022i	−0.174589	+	0.208067i	−0.846242	−	0.532799i	$-0.821140\pi$
$709$	−4.64880	+	5.54022i	−0.174589	+	0.208067i	0.671653	+	0.740866i	$0.265585\pi$
$710$		0			0
$711$	−11.1594	+	6.44287i	−0.418510	+	0.241627i
$712$	2.25185	+	3.21597i	0.0843916	+	0.120524i
$713$	−4.80437	−	6.86135i	−0.179925	−	0.256959i
$714$	1.15690	−	0.667935i	0.0432958	−	0.0249968i
$715$		0			0
$716$	−11.4502	+	13.6458i	−0.427913	+	0.509967i
$717$	−13.1306	−	28.1586i	−0.490370	−	1.05160i
$718$	−2.29561	+	4.92295i	−0.0856714	+	0.183723i
$719$	17.4755	+	20.8265i	0.651726	+	0.776697i	0.986173	−	0.165718i	$-0.0529941\pi$
$719$	17.4755	+	20.8265i	0.651726	+	0.776697i	−0.334447	+	0.942414i	$0.608550\pi$
$720$		0			0
$721$		−	0.245160i		−	0.00913025i
$722$	12.8868	−	13.9617i	0.479599	−	0.519601i
$723$	46.0973	+	46.0973i	1.71438	+	1.71438i
$724$	−3.51928	−	19.9588i	−0.130793	−	0.741765i
$725$		0			0
$726$	−27.5906	+	10.0422i	−1.02398	+	0.372700i
$727$	22.5590	−	10.5194i	0.836668	−	0.390145i	0.0434298	−	0.999056i	$-0.486172\pi$
$727$	22.5590	−	10.5194i	0.836668	−	0.390145i	0.793238	+	0.608912i	$0.208394\pi$
$728$	−0.109710	−	1.25399i	−0.00406613	−	0.0464760i
$729$	31.5777	+	18.2314i	1.16955	+	0.675237i
$730$		0			0
$731$	1.25757	−	7.13205i	0.0465130	−	0.263789i
$732$	4.45292	−	3.11797i	0.164585	−	0.115243i
$733$	10.3318	−	38.5589i	0.381614	−	1.42420i	−0.461820	−	0.886973i	$-0.652804\pi$
$733$	10.3318	−	38.5589i	0.381614	−	1.42420i	0.843435	−	0.537231i	$-0.180530\pi$
$734$	5.13855	−	8.90023i	0.189667	−	0.328513i
$735$		0			0
$736$	0.986879	−	2.71143i	0.0363768	−	0.0999446i
$737$	23.7371	+	11.0688i	0.874367	+	0.407724i
$738$	39.3287	+	3.44082i	1.44771	+	0.126658i
$739$	2.79184	−	0.492276i	0.102699	−	0.0181087i	−0.122062	−	0.992522i	$-0.538951\pi$
$739$	2.79184	−	0.492276i	0.102699	−	0.0181087i	0.224762	+	0.974414i	$0.427840\pi$
$740$		0			0
$741$	−4.59858	+	68.2672i	−0.168933	+	2.50786i
$742$	−1.41339	+	1.41339i	−0.0518873	+	0.0518873i
$743$	−7.97012	−	5.58074i	−0.292395	−	0.204737i	0.418170	−	0.908369i	$-0.362672\pi$
$743$	−7.97012	−	5.58074i	−0.292395	−	0.204737i	−0.710565	+	0.703632i	$0.751561\pi$
$744$	6.51011	−	5.46263i	0.238672	−	0.200270i
$745$		0			0
$746$	22.0739	+	8.03425i	0.808184	+	0.294155i
$747$	16.4578	−	1.43987i	0.602161	−	0.0526822i
$748$	−8.60964	+	2.30695i	−0.314800	+	0.0843503i
$749$	−0.0295929	−	0.0512564i	−0.00108130	−	0.00187287i
$750$		0			0
$751$	24.2238	+	4.27130i	0.883938	+	0.155862i	0.597148	−	0.802131i	$-0.296301\pi$
$751$	24.2238	+	4.27130i	0.883938	+	0.155862i	0.286790	+	0.957993i	$0.407412\pi$
$752$	−1.83192	−	0.490862i	−0.0668034	−	0.0178999i
$753$	−13.7185	−	51.1981i	−0.499930	−	1.86576i
$754$	−32.5037	−	27.2738i	−1.18372	−	0.993255i
$755$		0			0
$756$	0.604225	+	1.66009i	0.0219754	+	0.0603770i
$757$	−2.76289	+	31.5800i	−0.100419	+	1.14779i	0.764067	+	0.645137i	$0.223200\pi$
$757$	−2.76289	+	31.5800i	−0.100419	+	1.14779i	−0.864486	+	0.502657i	$0.832356\pi$
$758$	−13.7583	+	19.6489i	−0.499724	+	0.713680i
$759$	−38.7371			−1.40607
$760$		0			0
$761$	28.1945			1.02205			0.511026	−	0.859565i	$-0.329266\pi$
$761$	28.1945			1.02205			0.511026	+	0.859565i	$0.329266\pi$
$762$	−23.2085	+	33.1452i	−0.840756	+	1.20072i
$763$	−0.0176017	+	0.201188i	−0.000637223	+	0.00728349i
$764$	−4.60892	−	12.6629i	−0.166745	−	0.458128i
$765$		0			0
$766$	−5.87303	−	4.92806i	−0.212201	−	0.178058i
$767$	−15.3773	−	57.3887i	−0.555241	−	2.07219i
$768$	2.82778	+	0.757702i	0.102039	+	0.0273412i
$769$	−47.7970	−	8.42790i	−1.72360	−	0.303918i	−0.777765	−	0.628555i	$-0.783647\pi$
$769$	−47.7970	−	8.42790i	−1.72360	−	0.303918i	−0.945839	+	0.324637i	$0.894758\pi$
$770$		0			0
$771$	−32.3661	−	56.0597i	−1.16564	−	2.01894i
$772$	−20.3108	+	5.44225i	−0.731000	+	0.195871i
$773$	11.2035	−	0.980177i	0.402961	−	0.0352545i	0.116126	−	0.993235i	$-0.462952\pi$
$773$	11.2035	−	0.980177i	0.402961	−	0.0352545i	0.286835	+	0.957980i	$0.407397\pi$
$774$	19.5035	+	7.09868i	0.701038	+	0.255157i
$775$		0			0
$776$	4.04939	−	3.39784i	0.145365	−	0.121975i
$777$	−4.83223	−	3.38356i	−0.173355	−	0.121385i
$778$	−13.3387	+	13.3387i	−0.478216	+	0.478216i
$779$	18.2219	+	24.9460i	0.652866	+	0.893784i
$780$		0			0
$781$	64.6932	−	11.4072i	2.31491	−	0.408180i
$782$	−5.58707	−	0.488806i	−0.199793	−	0.0174797i
$783$	53.9698	+	25.1665i	1.92872	+	0.899379i
$784$	−2.37529	+	6.52606i	−0.0848318	+	0.233073i
$785$		0			0
$786$	5.76800	−	9.99047i	0.205738	−	0.356348i
$787$	10.5558	−	39.3948i	0.376274	−	1.40427i	−0.475200	−	0.879878i	$-0.657624\pi$
$787$	10.5558	−	39.3948i	0.376274	−	1.40427i	0.851474	−	0.524396i	$-0.175709\pi$
$788$	−3.10088	+	2.17126i	−0.110464	+	0.0773480i
$789$	1.04039	−	5.90033i	0.0370388	−	0.210057i
$790$		0			0
$791$	1.62388	+	0.937549i	0.0577386	+	0.0333354i
$792$	−2.22638	−	25.4477i	−0.0791111	−	0.904244i
$793$	−9.02340	+	4.20768i	−0.320430	+	0.149419i
$794$	2.44704	−	0.890650i	0.0868422	−	0.0316080i
$795$		0			0
$796$	0.918543	+	5.20931i	0.0325569	+	0.184639i
$797$	1.58222	+	1.58222i	0.0560450	+	0.0560450i	0.734574	−	0.678529i	$-0.237382\pi$
$797$	1.58222	+	1.58222i	0.0560450	+	0.0560450i	−0.678529	+	0.734574i	$0.737382\pi$
$798$	−1.44570	+	2.62389i	−0.0511772	+	0.0928846i
$799$			3.68631i			0.130412i
$800$		0			0
$801$	14.0574	+	16.7530i	0.496695	+	0.591938i
$802$	−7.90910	+	16.9611i	−0.279280	+	0.598918i
$803$	−12.7973	−	27.4438i	−0.451606	−	0.968471i
$804$	−10.7475	+	12.8084i	−0.379036	+	0.451717i
$805$		0			0
$806$	−13.4797	+	7.78250i	−0.474801	+	0.274127i
$807$	1.35298	+	1.93225i	0.0476270	+	0.0680184i
$808$	8.82406	+	12.6021i	0.310429	+	0.443339i
$809$	−3.00293	+	1.73374i	−0.105577	+	0.0609551i	−0.551859	−	0.833938i	$-0.686081\pi$
$809$	−3.00293	+	1.73374i	−0.105577	+	0.0609551i	0.446282	+	0.894893i	$0.352748\pi$
$810$		0			0
$811$	−6.44595	+	7.68198i	−0.226348	+	0.269751i	−0.867251	−	0.497871i	$-0.834115\pi$
$811$	−6.44595	+	7.68198i	−0.226348	+	0.269751i	0.640903	+	0.767622i	$0.278560\pi$
$812$	−0.785136	−	1.68373i	−0.0275529	−	0.0590874i
$813$	0.0469004	−	0.100578i	0.00164487	−	0.00352743i
$814$	25.3004	+	30.1519i	0.886779	+	1.05682i
$815$		0			0
$816$		−	5.69023i		−	0.199198i
$817$	5.85894	+	15.1473i	0.204978	+	0.529938i
$818$	−23.5427	−	23.5427i	−0.823150	−	0.823150i
$819$	−1.21762	−	6.90546i	−0.0425471	−	0.241296i
$820$		0			0
$821$	0.801361	−	0.291672i	0.0279677	−	0.0101794i	−0.327998	−	0.944678i	$-0.606374\pi$
$821$	0.801361	−	0.291672i	0.0279677	−	0.0101794i	0.355966	+	0.934499i	$0.384152\pi$
$822$	−8.28742	+	3.86449i	−0.289057	+	0.134790i
$823$	4.36435	+	49.8848i	0.152132	+	1.73887i	0.562361	+	0.826892i	$0.309893\pi$
$823$	4.36435	+	49.8848i	0.152132	+	1.73887i	−0.410229	+	0.911983i	$0.634551\pi$
$824$	−0.904371	−	0.522139i	−0.0315053	−	0.0181896i
$825$		0			0
$826$	0.451722	−	2.56184i	0.0157174	−	0.0891379i
$827$	−1.08734	+	0.761364i	−0.0378105	+	0.0264752i	−0.592329	−	0.805696i	$-0.701791\pi$
$827$	−1.08734	+	0.761364i	−0.0378105	+	0.0264752i	0.554518	+	0.832171i	$0.312903\pi$
$828$	4.16006	−	15.5255i	0.144572	−	0.539550i
$829$	−8.47737	+	14.6832i	−0.294431	+	0.509970i	−0.974852	−	0.222852i	$-0.928463\pi$
$829$	−8.47737	+	14.6832i	−0.294431	+	0.509970i	0.680421	+	0.732821i	$0.261797\pi$
$830$		0			0
$831$	4.08076	−	11.2118i	0.141560	−	0.388933i
$832$	−4.85950	−	2.26602i	−0.168473	−	0.0785602i
$833$	13.4474	+	1.17649i	0.465924	+	0.0407630i
$834$	−23.3278	+	4.11332i	−0.807776	+	0.142433i
$835$		0			0
$836$	13.8487	−	14.4143i	0.478968	−	0.498527i
$837$	15.4465	−	15.4465i	0.533909	−	0.533909i
$838$	−32.6686	−	22.8748i	−1.12852	−	0.790197i
$839$	32.9921	−	27.6837i	1.13901	−	0.955746i	0.139608	−	0.990207i	$-0.455416\pi$
$839$	32.9921	−	27.6837i	1.13901	−	0.955746i	0.999406	+	0.0344607i	$0.0109714\pi$
$840$		0			0
$841$	−31.5941	−	11.4993i	−1.08945	−	0.396528i
$842$	12.4813	−	1.09197i	0.430133	−	0.0376318i
$843$	−44.4657	+	11.9145i	−1.53148	+	0.410358i
$844$	13.9239	+	24.1168i	0.479279	+	0.830135i
$845$		0			0
$846$	−10.4041	−	1.83453i	−0.357701	−	0.0630724i
$847$	2.27432	+	0.609402i	0.0781466	+	0.0209393i
$848$	2.20364	+	8.22408i	0.0756732	+	0.282416i
$849$	47.3004	+	39.6898i	1.62335	+	1.36215i
$850$		0			0
$851$	8.47054	+	23.2726i	0.290366	+	0.797775i
$852$	−3.65504	+	41.7773i	−0.125220	+	1.43127i
$853$	−7.30694	+	10.4354i	−0.250185	+	0.357301i	−0.924526	−	0.381119i	$-0.875539\pi$
$853$	−7.30694	+	10.4354i	−0.250185	+	0.357301i	0.674341	+	0.738420i	$0.264428\pi$
$854$	−0.435926			−0.0149171
$855$		0			0
$856$	−0.252106			−0.00861680
$857$	−14.5576	+	20.7903i	−0.497277	+	0.710185i	−0.986825	−	0.161791i	$-0.948273\pi$
$857$	−14.5576	+	20.7903i	−0.497277	+	0.710185i	0.489548	+	0.871976i	$0.337162\pi$
$858$	−6.27375	+	71.7093i	−0.214182	+	2.44812i
$859$	7.14159	+	19.6214i	0.243668	+	0.669472i	0.999885	+	0.0151516i	$0.00482308\pi$
$859$	7.14159	+	19.6214i	0.243668	+	0.669472i	−0.756217	+	0.654321i	$0.772955\pi$
$860$		0			0
$861$	−3.73134	−	3.13097i	−0.127164	−	0.106703i
$862$	2.19655	+	8.19765i	0.0748149	+	0.279213i
$863$	−27.8054	−	7.45044i	−0.946507	−	0.253616i	−0.247628	−	0.968855i	$-0.579651\pi$
$863$	−27.8054	−	7.45044i	−0.946507	−	0.253616i	−0.698879	+	0.715240i	$0.746318\pi$
$864$	7.41078	+	1.30672i	0.252120	+	0.0444555i
$865$		0			0
$866$	7.55313	+	13.0824i	0.256666	+	0.444558i
$867$	37.3891	−	10.0184i	1.26980	−	0.340242i
$868$	−0.678908	+	0.0593968i	−0.0230436	+	0.00201606i
$869$	−9.96822	−	3.62814i	−0.338149	−	0.123076i
$870$		0			0
$871$	23.4590	−	19.6844i	0.794876	−	0.666980i
$872$	0.704674	+	0.493418i	0.0238633	+	0.0167092i
$873$	20.8215	−	20.8215i	0.704701	−	0.704701i
$874$	11.2903	−	5.54239i	0.381901	−	0.187474i
$875$		0			0
$876$	19.0375	−	3.35682i	0.643217	−	0.113416i
$877$	−31.4505	−	2.75156i	−1.06201	−	0.0929135i	−0.457261	−	0.889332i	$-0.651170\pi$
$877$	−31.4505	−	2.75156i	−1.06201	−	0.0929135i	−0.604745	+	0.796419i	$0.706725\pi$
$878$	−7.17901	−	3.34763i	−0.242280	−	0.112977i
$879$	25.5740	−	70.2640i	0.862590	−	2.36995i
$880$		0			0
$881$	−7.57661	+	13.1231i	−0.255263	+	0.442128i	−0.964967	−	0.262372i	$-0.915495\pi$
$881$	−7.57661	+	13.1231i	−0.255263	+	0.442128i	0.709704	+	0.704500i	$0.248829\pi$
$882$	−10.0127	+	37.3680i	−0.337146	+	1.25825i
$883$	−13.9465	+	9.76547i	−0.469338	+	0.328634i	−0.784205	−	0.620502i	$-0.786929\pi$
$883$	−13.9465	+	9.76547i	−0.469338	+	0.328634i	0.314867	+	0.949136i	$0.398040\pi$
$884$	−1.80973	+	10.2635i	−0.0608679	+	0.345199i
$885$		0			0
$886$	−14.1848	−	8.18961i	−0.476548	−	0.275135i
$887$	4.04690	+	46.2563i	0.135882	+	1.55313i	0.691917	+	0.721977i	$0.256766\pi$
$887$	4.04690	+	46.2563i	0.135882	+	1.55313i	−0.556036	+	0.831158i	$0.687678\pi$
$888$	−22.7732	+	10.6193i	−0.764220	+	0.356361i
$889$	3.04912	−	1.10979i	0.102264	−	0.0372211i
$890$		0			0
$891$	−4.23529	−	24.0195i	−0.141888	−	0.804684i
$892$	4.74749	+	4.74749i	0.158958	+	0.158958i
$893$	−4.27582	−	7.07518i	−0.143085	−	0.236762i
$894$		−	60.9172i		−	2.03737i
$895$		0			0
$896$	−0.150904	−	0.179841i	−0.00504136	−	0.00600806i
$897$	−19.1416	+	41.0493i	−0.639120	+	1.37060i
$898$	6.34516	+	13.6072i	0.211741	+	0.454079i
$899$	−14.7660	+	17.5974i	−0.492474	+	0.586907i
$900$		0			0
$901$	14.3318	−	8.27450i	0.477463	−	0.275663i
$902$	18.6414	+	26.6227i	0.620692	+	0.886440i
$903$	−1.46880	−	2.09766i	−0.0488786	−	0.0698059i
$904$	6.91704	−	3.99355i	0.230057	−	0.132824i
$905$		0			0
$906$	−33.5965	+	40.0387i	−1.11617	+	1.33020i
$907$	−21.4367	−	45.9711i	−0.711794	−	1.52645i	−0.844655	−	0.535311i	$-0.820194\pi$
$907$	−21.4367	−	45.9711i	−0.711794	−	1.52645i	0.132861	−	0.991135i	$-0.457584\pi$
$908$	0.866301	−	1.85779i	0.0287492	−	0.0616529i
$909$	55.0853	+	65.6481i	1.82706	+	2.17741i
$910$		0			0
$911$		−	29.8237i		−	0.988103i	−0.869433	−	0.494052i	$-0.835515\pi$
$911$		−	29.8237i		−	0.988103i	0.869433	−	0.494052i	$-0.164485\pi$
$912$	6.60022	+	10.9213i	0.218555	+	0.361642i
$913$	9.61691	+	9.61691i	0.318273	+	0.318273i
$914$	0.435553	+	2.47014i	0.0144068	+	0.0817051i
$915$		0			0
$916$	7.95580	−	2.89567i	0.262867	−	0.0956757i
$917$	−0.838423	+	0.390963i	−0.0276872	+	0.0129107i
$918$	−1.27478	−	14.5708i	−0.0420741	−	0.480910i
$919$	48.2705	+	27.8690i	1.59230	+	0.919313i	0.992912	+	0.118852i	$0.0379213\pi$
$919$	48.2705	+	27.8690i	1.59230	+	0.919313i	0.599384	+	0.800461i	$0.295412\pi$
$920$		0			0
$921$	3.61347	−	20.4930i	0.119068	−	0.675268i
$922$	9.16428	−	6.41690i	0.301809	−	0.211329i
$923$	19.8796	−	74.1915i	0.654344	−	2.44204i
$924$	−1.57587	+	2.72948i	−0.0518422	+	0.0897933i
$925$		0			0
$926$	6.93921	−	19.0653i	0.228036	−	0.626525i
$927$	−5.27209	−	2.45841i	−0.173158	−	0.0807449i
$928$	−7.88328	−	0.689698i	−0.258781	−	0.0226404i
$929$	−26.3001	+	4.63743i	−0.862880	+	0.152149i	−0.587537	−	0.809197i	$-0.699902\pi$
$929$	−26.3001	+	4.63743i	−0.862880	+	0.152149i	−0.275343	+	0.961346i	$0.588791\pi$
$930$		0			0
$931$	−27.1744	+	13.3398i	−0.890604	+	0.437195i
$932$	9.02816	−	9.02816i	0.295727	−	0.295727i
$933$	36.7699	+	25.7465i	1.20379	+	0.842904i
$934$	−27.5948	+	23.1548i	−0.902929	+	0.757647i
$935$		0			0
$936$	−28.0668	−	10.2155i	−0.917392	−	0.333903i
$937$	15.2920	−	1.33787i	0.499566	−	0.0437064i	0.165412	−	0.986225i	$-0.447105\pi$
$937$	15.2920	−	1.33787i	0.499566	−	0.0437064i	0.334155	+	0.942518i	$0.391549\pi$
$938$	1.29514	−	0.347032i	0.0422878	−	0.0113310i
$939$	2.56722	+	4.44656i	0.0837781	+	0.145108i
$940$		0			0
$941$	−21.6963	−	3.82564i	−0.707278	−	0.124712i	−0.191573	−	0.981478i	$-0.561359\pi$
$941$	−21.6963	−	3.82564i	−0.707278	−	0.124712i	−0.515705	+	0.856766i	$0.672470\pi$
$942$	61.7236	+	16.5388i	2.01106	+	0.538863i
$943$	5.29277	+	19.7529i	0.172356	+	0.643243i
$944$	−8.48830	−	7.12253i	−0.276271	−	0.231819i
$945$		0			0
$946$	5.84386	+	16.0559i	0.190000	+	0.522022i
$947$	−2.86336	+	32.7284i	−0.0930468	+	1.06353i	0.795872	+	0.605465i	$0.207013\pi$
$947$	−2.86336	+	32.7284i	−0.0930468	+	1.06353i	−0.888919	+	0.458065i	$0.848543\pi$
$948$	3.88429	−	5.54735i	0.126156	−	0.180169i
$949$	−35.4056			−1.14931
$950$		0			0
$951$	67.9010			2.20184
$952$	−0.261730	+	0.373789i	−0.00848272	+	0.0121146i
$953$	2.01031	−	22.9779i	0.0651203	−	0.744329i	−0.891506	−	0.453010i	$-0.850350\pi$
$953$	2.01031	−	22.9779i	0.0651203	−	0.744329i	0.956626	−	0.291319i	$-0.0940941\pi$
$954$	16.2213	+	44.5677i	0.525185	+	1.44293i
$955$		0			0
$956$	8.12993	+	6.82182i	0.262941	+	0.220633i
$957$	27.4963	+	102.618i	0.888829	+	3.31715i
$958$	−0.665236	−	0.178250i	−0.0214928	−	0.00575898i
$959$	0.722150	+	0.127335i	0.0233194	+	0.00411185i
$960$		0			0
$961$	−11.2866	−	19.5489i	−0.364083	−	0.630610i
$962$	44.4536	−	11.9113i	1.43324	−	0.384036i
$963$	−1.39900	+	0.122397i	−0.0450822	+	0.00394418i
$964$	−20.9254	−	7.61623i	−0.673962	−	0.245302i
$965$		0			0
$966$	−1.51916	+	1.27472i	−0.0488781	+	0.0410136i
$967$	−10.3756	−	7.26511i	−0.333658	−	0.233630i	0.394726	−	0.918799i	$-0.370840\pi$
$967$	−10.3756	−	7.26511i	−0.333658	−	0.233630i	−0.728384	+	0.685169i	$0.759728\pi$
$968$	7.09183	−	7.09183i	0.227940	−	0.227940i
$969$	17.1841	−	17.8858i	0.552033	−	0.574575i
$970$		0			0
$971$	−36.9373	+	6.51304i	−1.18537	+	0.209013i	−0.731367	−	0.681985i	$-0.761117\pi$
$971$	−36.9373	+	6.51304i	−1.18537	+	0.209013i	−0.454007	+	0.890998i	$0.650006\pi$
$972$	−6.97819	−	0.610512i	−0.223825	−	0.0195822i
$973$	1.72159	+	0.802792i	0.0551917	+	0.0257363i
$974$	12.2147	−	33.5597i	0.391385	−	1.07532i
$975$		0			0
$976$	−0.928428	+	1.60808i	−0.0297183	+	0.0514735i
$977$	7.92594	−	29.5800i	0.253573	−	0.946349i	−0.715305	−	0.698812i	$-0.753712\pi$
$977$	7.92594	−	29.5800i	0.253573	−	0.946349i	0.968879	−	0.247537i	$-0.0796210\pi$
$978$	−39.9737	+	27.9899i	−1.27822	+	0.895017i
$979$	−3.12630	+	17.7301i	−0.0999171	+	0.566658i
$980$		0			0
$981$	4.14997	+	2.39599i	0.132498	+	0.0764980i
$982$	3.05061	+	34.8687i	0.0973489	+	1.11270i
$983$	−15.2662	+	7.11875i	−0.486916	+	0.227053i	−0.650543	−	0.759469i	$-0.725459\pi$
$983$	−15.2662	+	7.11875i	−0.486916	+	0.227053i	0.163626	+	0.986522i	$0.447681\pi$
$984$	−19.4968	+	7.09624i	−0.621534	+	0.226220i
$985$		0			0
$986$	2.67092	+	15.1475i	0.0850594	+	0.482396i
$987$	0.921690	+	0.921690i	0.0293377	+	0.0293377i
$988$	−8.43140	−	21.7980i	−0.268239	−	0.693488i
$989$			10.7510i			0.341861i
$990$		0			0
$991$	−20.9875	−	25.0119i	−0.666690	−	0.794530i	0.321639	−	0.946862i	$-0.395766\pi$
$991$	−20.9875	−	25.0119i	−0.666690	−	0.794530i	−0.988329	+	0.152332i	$0.951322\pi$
$992$	−1.22682	+	2.63092i	−0.0389516	+	0.0835319i
$993$	15.0176	+	32.2054i	0.476569	+	1.02201i
$994$	2.16170	−	2.57622i	0.0685650	−	0.0817126i
$995$		0			0
$996$	−7.51917	+	4.34120i	−0.238254	+	0.137556i
$997$	15.5937	+	22.2702i	0.493858	+	0.705303i	0.986285	−	0.165051i	$-0.0527789\pi$
$997$	15.5937	+	22.2702i	0.493858	+	0.705303i	−0.492427	+	0.870354i	$0.663890\pi$
$998$	−6.40678	−	9.14984i	−0.202803	−	0.289633i
$999$	−55.9358	+	32.2946i	−1.76973	+	1.02175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.143.6		120
5.2	odd	4	inner	950.2.bb.e.257.10		120
5.3	odd	4		190.2.r.a.67.1	✓	120
5.4	even	2		190.2.r.a.143.5	yes	120
19.2	odd	18	inner	950.2.bb.e.743.10		120
95.2	even	36	inner	950.2.bb.e.857.6		120
95.59	odd	18		190.2.r.a.173.1	yes	120
95.78	even	36		190.2.r.a.97.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.67.1	✓	120	5.3	odd	4
190.2.r.a.97.5	yes	120	95.78	even	36
190.2.r.a.143.5	yes	120	5.4	even	2
190.2.r.a.173.1	yes	120	95.59	odd	18
950.2.bb.e.143.6		120	1.1	even	1	trivial
950.2.bb.e.257.10		120	5.2	odd	4	inner
950.2.bb.e.743.10		120	19.2	odd	18	inner
950.2.bb.e.857.6		120	95.2	even	36	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.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(-0.255151 + 2.91639i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.24262 + 1.88178i) q^{6} +(-0.0607618 - 0.226766i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-5.48583 - 0.967300i) q^{9} +O(q^{10})\)	\(q+(0.573576 - 0.819152i) q^{2} +(-0.255151 + 2.91639i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.24262 + 1.88178i) q^{6} +(-0.0607618 - 0.226766i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-5.48583 - 0.967300i) q^{9} +(-2.29289 - 3.97140i) q^{11} +(2.82778 - 0.757702i) q^{12} +(-5.34147 + 0.467318i) q^{13} +(-0.220607 - 0.0802945i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(1.59218 + 1.11486i) q^{17} +(-3.93891 + 3.93891i) q^{18} +(-4.34904 - 0.292958i) q^{19} +(0.676843 - 0.119346i) q^{21} +(-4.56833 - 0.399677i) q^{22} +(-2.61510 - 1.21944i) q^{23} +(1.00128 - 2.75098i) q^{24} +(-2.68093 + 4.64352i) q^{26} +(1.94764 - 7.26869i) q^{27} +(-0.192309 + 0.134656i) q^{28} +(-1.37415 + 7.79317i) q^{29} +(2.51399 + 1.45145i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(12.1672 - 5.67366i) q^{33} +(1.82648 - 0.664783i) q^{34} +(0.967300 + 5.48583i) q^{36} +(-6.06921 - 6.06921i) q^{37} +(-2.73449 + 3.39449i) q^{38} -15.6971i q^{39} +(-4.55557 - 5.42911i) q^{41} +(0.290459 - 0.622891i) q^{42} +(-1.57465 - 3.37684i) q^{43} +(-2.94768 + 3.51291i) q^{44} +(-2.49887 + 1.44272i) q^{46} +(1.08781 + 1.55356i) q^{47} +(-1.67916 - 2.39810i) q^{48} +(6.01445 - 3.47244i) q^{49} +(-3.65761 + 4.35897i) q^{51} +(2.26602 + 4.85950i) q^{52} +(3.59825 - 7.71648i) q^{53} +(-4.83704 - 5.76456i) q^{54} +0.234765i q^{56} +(1.96405 - 12.6088i) q^{57} +(5.59561 + 5.59561i) q^{58} +(1.92414 + 10.9123i) q^{59} +(1.74487 - 0.635082i) q^{61} +(2.63092 - 1.22682i) q^{62} +(0.113978 + 1.30277i) q^{63} +(0.866025 + 0.500000i) q^{64} +(2.33123 - 13.2211i) q^{66} +(-4.67846 + 3.27589i) q^{67} +(0.503065 - 1.87746i) q^{68} +(4.22361 - 7.31552i) q^{69} +(-4.89943 + 13.4611i) q^{71} +(5.04855 + 2.35418i) q^{72} +(6.57809 + 0.575509i) q^{73} +(-8.45276 + 1.49045i) q^{74} +(1.21217 + 4.18696i) q^{76} +(-0.761259 + 0.761259i) q^{77} +(-12.8583 - 9.00346i) q^{78} +(1.77204 - 1.48692i) q^{79} +(4.99788 + 1.81908i) q^{81} +(-7.06023 + 0.617690i) q^{82} +(-2.86471 + 0.767598i) q^{83} +(-0.343642 - 0.595205i) q^{84} +(-3.66933 - 0.647002i) q^{86} +(-22.3773 - 5.99599i) q^{87} +(1.18689 + 4.42952i) q^{88} +(-3.00747 - 2.52357i) q^{89} +(0.430529 + 1.18287i) q^{91} +(-0.251483 + 2.87446i) q^{92} +(-4.87445 + 6.96144i) q^{93} +1.89655 q^{94} -2.92753 q^{96} +(-3.03199 + 4.33012i) q^{97} +(0.605287 - 6.91846i) q^{98} +(8.73687 + 24.0043i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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