LMFDB - Embedded newform 475.2.u.b.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			74.1
Character	$\chi$	$=$	475.74
Dual form			475.2.u.b.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18897 - 0.385975i) q^{2} +(0.666572 - 0.794389i) q^{3} +(2.76323 + 1.00573i) q^{4} +(-1.76572 + 1.48162i) q^{6} +(-1.75377 + 1.01254i) q^{7} +(-1.81055 - 1.04532i) q^{8} +(0.334208 + 1.89539i) q^{9} +O(q^{10})$	\(q+(-2.18897 - 0.385975i) q^{2} +(0.666572 - 0.794389i) q^{3} +(2.76323 + 1.00573i) q^{4} +(-1.76572 + 1.48162i) q^{6} +(-1.75377 + 1.01254i) q^{7} +(-1.81055 - 1.04532i) q^{8} +(0.334208 + 1.89539i) q^{9} +(-0.0424078 + 0.0734524i) q^{11} +(2.64084 - 1.52469i) q^{12} +(-3.67737 - 4.38252i) q^{13} +(4.22977 - 1.53951i) q^{14} +(-0.945441 - 0.793319i) q^{16} +(-2.49227 - 0.439455i) q^{17} -4.27795i q^{18} +(-3.21565 - 2.94271i) q^{19} +(-0.364663 + 2.06811i) q^{21} +(0.121180 - 0.144417i) q^{22} +(0.105714 - 0.290447i) q^{23} +(-2.03725 + 0.741500i) q^{24} +(6.35811 + 11.0126i) q^{26} +(4.42266 + 2.55342i) q^{27} +(-5.86442 + 1.03406i) q^{28} +(-0.455678 - 2.58428i) q^{29} +(-4.03639 - 6.99123i) q^{31} +(4.45102 + 5.30452i) q^{32} +(0.0300820 + 0.0826495i) q^{33} +(5.28589 + 1.92391i) q^{34} +(-0.982763 + 5.57352i) q^{36} -5.01303i q^{37} +(5.90316 + 7.68268i) q^{38} -5.93265 q^{39} +(-4.50461 - 3.77982i) q^{41} +(1.59647 - 4.38627i) q^{42} +(0.222491 + 0.611288i) q^{43} +(-0.191056 + 0.160315i) q^{44} +(-0.343511 + 0.594978i) q^{46} +(-6.79791 + 1.19865i) q^{47} +(-1.26041 + 0.222244i) q^{48} +(-1.44953 + 2.51066i) q^{49} +(-2.01037 + 1.68690i) q^{51} +(-5.75378 - 15.8084i) q^{52} +(-4.97790 + 13.6767i) q^{53} +(-8.69551 - 7.29640i) q^{54} +4.23372 q^{56} +(-4.48112 + 0.592951i) q^{57} +5.83278i q^{58} +(-1.29773 + 7.35981i) q^{59} +(-12.5139 - 4.55468i) q^{61} +(6.13710 + 16.8615i) q^{62} +(-2.50528 - 2.98568i) q^{63} +(-6.46156 - 11.1918i) q^{64} +(-0.0339479 - 0.192528i) q^{66} +(-8.74750 + 1.54242i) q^{67} +(-6.44475 - 3.72088i) q^{68} +(-0.160262 - 0.277582i) q^{69} +(13.4720 - 4.90340i) q^{71} +(1.37619 - 3.78105i) q^{72} +(6.97733 - 8.31526i) q^{73} +(-1.93490 + 10.9734i) q^{74} +(-5.92601 - 11.3655i) q^{76} -0.171758i q^{77} +(12.9864 + 2.28985i) q^{78} +(-0.0887829 - 0.0744977i) q^{79} +(-0.449247 + 0.163512i) q^{81} +(8.40155 + 10.0126i) q^{82} +(2.57688 - 1.48776i) q^{83} +(-3.08761 + 5.34790i) q^{84} +(-0.251084 - 1.42397i) q^{86} +(-2.35666 - 1.36062i) q^{87} +(0.153563 - 0.0886595i) q^{88} +(8.52291 - 7.15157i) q^{89} +(10.8867 + 3.96245i) q^{91} +(0.584226 - 0.696253i) q^{92} +(-8.24430 - 1.45369i) q^{93} +15.3431 q^{94} +7.18078 q^{96} +(-0.222471 - 0.0392276i) q^{97} +(4.14202 - 4.93627i) q^{98} +(-0.153394 - 0.0558308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49} - 90 q^{51} + 132 q^{54} - 36 q^{59} - 60 q^{61} - 72 q^{64} + 78 q^{66} - 30 q^{69} - 24 q^{71} + 30 q^{74} - 66 q^{76} + 102 q^{79} + 54 q^{81} - 96 q^{84} + 126 q^{86} + 108 q^{89} + 60 q^{91} - 60 q^{94} - 132 q^{96} + 186 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−2.18897	−	0.385975i	−1.54784	−	0.272925i	−0.666533	−	0.745476i	$-0.732222\pi$
$2$	−2.18897	−	0.385975i	−1.54784	−	0.272925i	−0.881304	+	0.472551i	$0.843333\pi$
$3$	0.666572	−	0.794389i	0.384845	−	0.458641i	−0.538492	−	0.842631i	$-0.681006\pi$
$3$	0.666572	−	0.794389i	0.384845	−	0.458641i	0.923337	+	0.383990i	$0.125450\pi$
$4$	2.76323	+	1.00573i	1.38162	+	0.502867i
$5$		0			0
$5$		0			0
$6$	−1.76572	+	1.48162i	−0.720852	+	0.604867i
$7$	−1.75377	+	1.01254i	−0.662863	+	0.382704i	−0.793367	−	0.608744i	$-0.791674\pi$
$7$	−1.75377	+	1.01254i	−0.662863	+	0.382704i	0.130504	+	0.991448i	$0.458340\pi$
$8$	−1.81055	−	1.04532i	−0.640126	−	0.369577i
$9$	0.334208	+	1.89539i	0.111403	+	0.631796i
$10$		0			0
$11$	−0.0424078	+	0.0734524i	−0.0127864	+	0.0221467i	−0.872348	−	0.488886i	$-0.837403\pi$
$11$	−0.0424078	+	0.0734524i	−0.0127864	+	0.0221467i	0.859561	+	0.511032i	$0.170737\pi$
$12$	2.64084	−	1.52469i	0.762344	−	0.440139i
$13$	−3.67737	−	4.38252i	−1.01992	−	1.21549i	−0.976295	−	0.216443i	$-0.930554\pi$
$13$	−3.67737	−	4.38252i	−1.01992	−	1.21549i	−0.0436233	−	0.999048i	$-0.513890\pi$
$14$	4.22977	−	1.53951i	1.13045	−	0.411451i
$15$		0			0
$16$	−0.945441	−	0.793319i	−0.236360	−	0.198330i
$17$	−2.49227	−	0.439455i	−0.604464	−	0.106583i	−0.136964	−	0.990576i	$-0.543734\pi$
$17$	−2.49227	−	0.439455i	−0.604464	−	0.106583i	−0.467501	+	0.883993i	$0.654845\pi$
$18$		−	4.27795i		−	1.00832i
$19$	−3.21565	−	2.94271i	−0.737722	−	0.675105i
$19$	−3.21565	−	2.94271i	−0.737722	−	0.675105i
$20$		0			0
$21$	−0.364663	+	2.06811i	−0.0795760	+	0.451298i
$22$	0.121180	−	0.144417i	0.0258357	−	0.0307898i
$23$	0.105714	−	0.290447i	0.0220429	−	0.0605624i	−0.928183	−	0.372124i	$-0.878630\pi$
$23$	0.105714	−	0.290447i	0.0220429	−	0.0605624i	0.950226	+	0.311561i	$0.100852\pi$
$24$	−2.03725	+	0.741500i	−0.415853	+	0.151358i
$25$		0			0
$26$	6.35811	+	11.0126i	1.24693	+	2.15974i
$27$	4.42266	+	2.55342i	0.851141	+	0.491406i
$28$	−5.86442	+	1.03406i	−1.10827	+	0.195418i
$29$	−0.455678	−	2.58428i	−0.0846172	−	0.479888i	−0.997439	−	0.0715288i	$-0.977212\pi$
$29$	−0.455678	−	2.58428i	−0.0846172	−	0.479888i	0.912821	−	0.408359i	$-0.133899\pi$
$30$		0			0
$31$	−4.03639	−	6.99123i	−0.724957	−	1.25566i	−0.958992	−	0.283434i	$-0.908526\pi$
$31$	−4.03639	−	6.99123i	−0.724957	−	1.25566i	0.234035	−	0.972228i	$-0.424807\pi$
$32$	4.45102	+	5.30452i	0.786837	+	0.937716i
$33$	0.0300820	+	0.0826495i	0.00523660	+	0.0143874i
$34$	5.28589	+	1.92391i	0.906523	+	0.329947i
$35$		0			0
$36$	−0.982763	+	5.57352i	−0.163794	+	0.928921i
$37$		−	5.01303i		−	0.824136i	−0.911153	−	0.412068i	$-0.864807\pi$
$37$		−	5.01303i		−	0.824136i	0.911153	−	0.412068i	$-0.135193\pi$
$38$	5.90316	+	7.68268i	0.957619	+	1.24629i
$39$	−5.93265			−0.949985
$40$		0			0
$41$	−4.50461	−	3.77982i	−0.703502	−	0.590309i	0.219265	−	0.975665i	$-0.429634\pi$
$41$	−4.50461	−	3.77982i	−0.703502	−	0.590309i	−0.922768	+	0.385357i	$0.874078\pi$
$42$	1.59647	−	4.38627i	0.246341	−	0.676817i
$43$	0.222491	+	0.611288i	0.0339295	+	0.0932205i	0.955501	−	0.294989i	$-0.0953160\pi$
$43$	0.222491	+	0.611288i	0.0339295	+	0.0932205i	−0.921571	+	0.388209i	$0.873094\pi$
$44$	−0.191056	+	0.160315i	−0.0288028	+	0.0241684i
$45$		0			0
$46$	−0.343511	+	0.594978i	−0.0506479	+	0.0877247i
$47$	−6.79791	+	1.19865i	−0.991576	+	0.174842i	−0.645826	−	0.763485i	$-0.723487\pi$
$47$	−6.79791	+	1.19865i	−0.991576	+	0.174842i	−0.345751	+	0.938326i	$0.612376\pi$
$48$	−1.26041	+	0.222244i	−0.181924	+	0.0320782i
$49$	−1.44953	+	2.51066i	−0.207075	+	0.358665i
$50$		0			0
$51$	−2.01037	+	1.68690i	−0.281509	+	0.236214i
$52$	−5.75378	−	15.8084i	−0.797905	−	2.19223i
$53$	−4.97790	+	13.6767i	−0.683767	+	1.87864i	−0.315345	+	0.948977i	$0.602120\pi$
$53$	−4.97790	+	13.6767i	−0.683767	+	1.87864i	−0.368422	+	0.929659i	$0.620102\pi$
$54$	−8.69551	−	7.29640i	−1.18331	−	0.992915i
$55$		0			0
$56$	4.23372			0.565754
$57$	−4.48112	+	0.592951i	−0.593539	+	0.0785382i
$58$			5.83278i			0.765882i
$59$	−1.29773	+	7.35981i	−0.168950	+	0.958166i	0.775947	+	0.630799i	$0.217273\pi$
$59$	−1.29773	+	7.35981i	−0.168950	+	0.958166i	−0.944897	+	0.327367i	$0.893839\pi$
$60$		0			0
$61$	−12.5139	−	4.55468i	−1.60224	−	0.583167i	−0.622355	−	0.782735i	$-0.713824\pi$
$61$	−12.5139	−	4.55468i	−1.60224	−	0.583167i	−0.979884	+	0.199567i	$0.936046\pi$
$62$	6.13710	+	16.8615i	0.779412	+	2.14142i
$63$	−2.50528	−	2.98568i	−0.315636	−	0.376160i
$64$	−6.46156	−	11.1918i	−0.807695	−	1.39897i
$65$		0			0
$66$	−0.0339479	−	0.192528i	−0.00417870	−	0.0236986i
$67$	−8.74750	+	1.54242i	−1.06868	+	0.188437i	−0.680204	−	0.733023i	$-0.738109\pi$
$67$	−8.74750	+	1.54242i	−1.06868	+	0.188437i	−0.388474	+	0.921460i	$0.626998\pi$
$68$	−6.44475	−	3.72088i	−0.781541	−	0.451223i
$69$	−0.160262	−	0.277582i	−0.0192933	−	0.0334170i
$70$		0			0
$71$	13.4720	−	4.90340i	1.59883	−	0.581926i	0.619642	−	0.784885i	$-0.287278\pi$
$71$	13.4720	−	4.90340i	1.59883	−	0.581926i	0.979187	+	0.202958i	$0.0650556\pi$
$72$	1.37619	−	3.78105i	0.162186	−	0.445601i
$73$	6.97733	−	8.31526i	0.816635	−	0.973227i	−0.183317	−	0.983054i	$-0.558684\pi$
$73$	6.97733	−	8.31526i	0.816635	−	0.973227i	0.999952	+	0.00982664i	$0.00312797\pi$
$74$	−1.93490	+	10.9734i	−0.224928	+	1.27563i
$75$		0			0
$76$	−5.92601	−	11.3655i	−0.679760	−	1.30371i
$77$		−	0.171758i		−	0.0195737i
$78$	12.9864	+	2.28985i	1.47042	+	0.259275i
$79$	−0.0887829	−	0.0744977i	−0.00998886	−	0.00838165i	0.637780	−	0.770219i	$-0.279853\pi$
$79$	−0.0887829	−	0.0744977i	−0.00998886	−	0.00838165i	−0.647768	+	0.761837i	$0.724298\pi$
$80$		0			0
$81$	−0.449247	+	0.163512i	−0.0499163	+	0.0181681i
$82$	8.40155	+	10.0126i	0.927796	+	1.10570i
$83$	2.57688	−	1.48776i	0.282849	−	0.163303i	−0.351863	−	0.936051i	$-0.614452\pi$
$83$	2.57688	−	1.48776i	0.282849	−	0.163303i	0.634713	+	0.772748i	$0.281118\pi$
$84$	−3.08761	+	5.34790i	−0.336886	+	0.583504i
$85$		0			0
$86$	−0.251084	−	1.42397i	−0.0270751	−	0.153550i
$87$	−2.35666	−	1.36062i	−0.252661	−	0.145874i
$88$	0.153563	−	0.0886595i	0.0163698	−	0.00945113i
$89$	8.52291	−	7.15157i	0.903427	−	0.758065i	−0.0674305	−	0.997724i	$-0.521480\pi$
$89$	8.52291	−	7.15157i	0.903427	−	0.758065i	0.970857	+	0.239659i	$0.0770357\pi$
$90$		0			0
$91$	10.8867	+	3.96245i	1.14124	+	0.415377i
$92$	0.584226	−	0.696253i	0.0609097	−	0.0725894i
$93$	−8.24430	−	1.45369i	−0.854894	−	0.150741i
$94$	15.3431			1.58252
$95$		0			0
$96$	7.18078			0.732885
$97$	−0.222471	−	0.0392276i	−0.0225885	−	0.00398296i	0.162343	−	0.986734i	$-0.448095\pi$
$97$	−0.222471	−	0.0392276i	−0.0225885	−	0.00398296i	−0.184931	+	0.982752i	$0.559206\pi$
$98$	4.14202	−	4.93627i	0.418408	−	0.498639i
$99$	−0.153394	−	0.0558308i	−0.0154167	−	0.00561121i
$100$		0			0
$101$	−9.65322	+	8.10001i	−0.960531	+	0.805981i	−0.981039	−	0.193808i	$-0.937916\pi$
$101$	−9.65322	+	8.10001i	−0.960531	+	0.805981i	0.0205084	+	0.999790i	$0.493472\pi$
$102$	5.05175	−	2.91663i	0.500198	−	0.288790i
$103$	15.3486	+	8.86152i	1.51234	+	0.873152i	0.999896	+	0.0144333i	$0.00459441\pi$
$103$	15.3486	+	8.86152i	1.51234	+	0.873152i	0.512447	+	0.858719i	$0.328739\pi$
$104$	2.07692	+	11.7788i	0.203659	+	1.15501i
$105$		0			0
$106$	16.1753	−	28.0165i	1.57109	−	2.72120i
$107$	4.41337	−	2.54806i	0.426657	−	0.246330i	−0.271265	−	0.962505i	$-0.587442\pi$
$107$	4.41337	−	2.54806i	0.426657	−	0.246330i	0.697921	+	0.716174i	$0.254109\pi$
$108$	9.65277	+	11.5037i	0.928838	+	1.10695i
$109$	−5.76514	+	2.09834i	−0.552200	+	0.200984i	−0.603024	−	0.797723i	$-0.706038\pi$
$109$	−5.76514	+	2.09834i	−0.552200	+	0.200984i	0.0508237	+	0.998708i	$0.483815\pi$
$110$		0			0
$111$	−3.98229	−	3.34154i	−0.377983	−	0.317165i
$112$	2.46135	+	0.434003i	0.232576	+	0.0410094i
$113$		−	11.4316i		−	1.07539i	−0.843138	−	0.537697i	$-0.819294\pi$
$113$		−	11.4316i		−	1.07539i	0.843138	−	0.537697i	$-0.180706\pi$
$114$	10.0379	+	0.431649i	0.940137	+	0.0404276i
$115$		0			0
$116$	1.33995	−	7.59925i	0.124411	−	0.705572i
$117$	7.07757	−	8.43472i	0.654321	−	0.779790i
$118$	5.68140	−	15.6095i	0.523015	−	1.43697i
$119$	4.81583	−	1.75282i	0.441467	−	0.160681i
$120$		0			0
$121$	5.49640	+	9.52005i	0.499673	+	0.865459i
$122$	25.6345	+	14.8001i	2.32084	+	1.33994i
$123$	−6.00529	+	1.05890i	−0.541479	+	0.0954774i
$124$	−4.12216	−	23.3779i	−0.370181	−	2.09940i
$125$		0			0
$126$	4.33159	+	7.50253i	0.385889	+	0.668379i
$127$	−0.925472	−	1.10293i	−0.0821224	−	0.0978696i	0.723419	−	0.690410i	$-0.242570\pi$
$127$	−0.925472	−	1.10293i	−0.0821224	−	0.0978696i	−0.805541	+	0.592540i	$0.798125\pi$
$128$	5.08776	+	13.9785i	0.449699	+	1.23554i
$129$	0.633906	+	0.230723i	0.0558123	+	0.0203140i
$130$		0			0
$131$	−0.174248	+	0.988207i	−0.0152241	+	0.0863400i	−0.991473	−	0.130311i	$-0.958402\pi$
$131$	−0.174248	+	0.988207i	−0.0152241	+	0.0863400i	0.976249	+	0.216651i	$0.0695135\pi$
$132$			0.258634i			0.0225112i
$133$	8.61913	+	1.90487i	0.747373	+	0.165173i
$134$	19.7434			1.70557
$135$		0			0
$136$	4.05301	+	3.40088i	0.347543	+	0.291623i
$137$	−3.57301	+	9.81678i	−0.305263	+	0.838704i	0.688300	+	0.725426i	$0.258357\pi$
$137$	−3.57301	+	9.81678i	−0.305263	+	0.838704i	−0.993563	+	0.113278i	$0.963865\pi$
$138$	0.243669	+	0.669476i	0.0207425	+	0.0569896i
$139$	−8.18488	+	6.86793i	−0.694233	+	0.582530i	−0.920126	−	0.391622i	$-0.871914\pi$
$139$	−8.18488	+	6.86793i	−0.694233	+	0.582530i	0.225894	+	0.974152i	$0.427470\pi$
$140$		0			0
$141$	−3.57909	+	6.19917i	−0.301414	+	0.522064i
$142$	−31.3823	+	5.53355i	−2.63355	+	0.464366i
$143$	0.477855	−	0.0842588i	0.0399603	−	0.00704607i
$144$	1.18767	−	2.05711i	0.0989729	−	0.171426i
$145$		0			0
$146$	−18.4826	+	15.5088i	−1.52963	+	1.28352i
$147$	1.02822	+	2.82502i	0.0848064	+	0.233004i
$148$	5.04177	−	13.8522i	0.414431	−	1.13864i
$149$	3.86440	+	3.24262i	0.316584	+	0.265645i	0.787207	−	0.616689i	$-0.211526\pi$
$149$	3.86440	+	3.24262i	0.316584	+	0.265645i	−0.470623	+	0.882334i	$0.655971\pi$
$150$		0			0
$151$	20.8114			1.69360			0.846802	−	0.531909i	$-0.178525\pi$
$151$	20.8114			1.69360			0.846802	+	0.531909i	$0.178525\pi$
$152$	2.74602	+	8.68933i	0.222732	+	0.704797i
$153$		−	4.87069i		−	0.393772i
$154$	−0.0662943	+	0.375974i	−0.00534214	+	0.0302968i
$155$		0			0
$156$	−16.3933	−	5.96667i	−1.31251	−	0.477716i
$157$	−8.07709	−	22.1916i	−0.644622	−	1.77108i	−0.636696	−	0.771115i	$-0.719699\pi$
$157$	−8.07709	−	22.1916i	−0.644622	−	1.77108i	−0.00792593	−	0.999969i	$-0.502523\pi$
$158$	0.165589	+	0.197341i	0.0131736	+	0.0156996i
$159$	7.54647	+	13.0709i	0.598474	+	1.03659i
$160$		0			0
$161$	0.108691	+	0.616417i	0.00856605	+	0.0485805i
$162$	1.04650	−	0.184526i	0.0822208	−	0.0144977i
$163$	−0.184925	−	0.106766i	−0.0144844	−	0.00836258i	0.492740	−	0.870176i	$-0.335995\pi$
$163$	−0.184925	−	0.106766i	−0.0144844	−	0.00836258i	−0.507225	+	0.861814i	$0.669329\pi$
$164$	−8.64580	−	14.9750i	−0.675124	−	1.16935i
$165$		0			0
$166$	−6.21495	+	2.26206i	−0.482374	+	0.175570i
$167$	6.74630	−	18.5353i	0.522045	−	1.43431i	−0.346196	−	0.938162i	$-0.612527\pi$
$167$	6.74630	−	18.5353i	0.522045	−	1.43431i	0.868240	−	0.496144i	$-0.165251\pi$
$168$	2.82208	−	3.36322i	0.217728	−	0.259478i
$169$	−3.42599	+	19.4298i	−0.263538	+	1.49460i
$170$		0			0
$171$	4.50289	−	7.07839i	0.344345	−	0.541298i
$172$			1.91290i			0.145857i
$173$	−12.3839	−	2.18361i	−0.941527	−	0.166017i	−0.318240	−	0.948010i	$-0.603092\pi$
$173$	−12.3839	−	2.18361i	−0.941527	−	0.166017i	−0.623287	+	0.781993i	$0.714203\pi$
$174$	4.63350	+	3.88797i	0.351265	+	0.294746i
$175$		0			0
$176$	0.0983652	−	0.0358020i	0.00741456	−	0.00269868i
$177$	4.98152	+	5.93675i	0.374434	+	0.446233i
$178$	−21.4167	+	12.3650i	−1.60525	+	0.926792i
$179$	−5.40914	+	9.36891i	−0.404298	+	0.700265i	−0.994240	−	0.107181i	$-0.965818\pi$
$179$	−5.40914	+	9.36891i	−0.404298	+	0.700265i	0.589941	+	0.807446i	$0.299151\pi$
$180$		0			0
$181$	−0.939769	−	5.32969i	−0.0698524	−	0.396153i	−0.999609	−	0.0279769i	$-0.991094\pi$
$181$	−0.939769	−	5.32969i	−0.0698524	−	0.396153i	0.929756	−	0.368176i	$-0.120018\pi$
$182$	−22.3013	−	12.8757i	−1.65308	−	0.954409i
$183$	−11.9596	+	6.90488i	−0.884079	+	0.510423i
$184$	−0.495012	+	0.415364i	−0.0364927	+	0.0306210i
$185$		0			0
$186$	17.4854	+	6.36418i	1.28209	+	0.466644i
$187$	0.137971	−	0.164427i	0.0100894	−	0.0120241i
$188$	−19.9897	−	3.52473i	−1.45790	−	0.257067i
$189$	−10.3418			−0.752253
$190$		0			0
$191$	4.87144			0.352485			0.176243	−	0.984347i	$-0.443606\pi$
$191$	4.87144			0.352485			0.176243	+	0.984347i	$0.443606\pi$
$192$	−13.1977	−	2.32711i	−0.952462	−	0.167945i
$193$	−0.889706	+	1.06031i	−0.0640424	+	0.0763228i	−0.797115	−	0.603828i	$-0.793641\pi$
$193$	−0.889706	+	1.06031i	−0.0640424	+	0.0763228i	0.733072	+	0.680151i	$0.238086\pi$
$194$	0.471841	+	0.171736i	0.0338762	+	0.0123299i
$195$		0			0
$196$	−6.53044	+	5.47969i	−0.466460	+	0.391406i
$197$	5.54906	−	3.20375i	0.395354	−	0.228258i	−0.289123	−	0.957292i	$-0.593364\pi$
$197$	5.54906	−	3.20375i	0.395354	−	0.228258i	0.684477	+	0.729034i	$0.260030\pi$
$198$	0.314225	+	0.181418i	0.0223310	+	0.0128928i
$199$	−2.71594	−	15.4029i	−0.192528	−	1.09188i	−0.915895	−	0.401418i	$-0.868518\pi$
$199$	−2.71594	−	15.4029i	−0.192528	−	1.09188i	0.723367	−	0.690464i	$-0.242594\pi$
$200$		0			0
$201$	−4.60555	+	7.97705i	−0.324851	+	0.562658i
$202$	24.2570	−	14.0048i	1.70672	−	0.985374i
$203$	3.41583	+	4.07083i	0.239745	+	0.285716i
$204$	−7.25171	+	2.63941i	−0.507721	+	0.184795i
$205$		0			0
$206$	−30.1773	−	25.3218i	−2.10255	−	1.76425i
$207$	0.585841	+	0.103300i	0.0407188	+	0.00717982i
$208$			7.06074i			0.489574i
$209$	0.352518	−	0.111404i	0.0243842	−	0.00770594i
$210$		0			0
$211$	1.33429	−	7.56711i	0.0918560	−	0.520941i	−0.903810	−	0.427935i	$-0.859241\pi$
$211$	1.33429	−	7.56711i	0.0918560	−	0.520941i	0.995666	−	0.0930062i	$-0.0296477\pi$
$212$	−27.5102	+	32.7854i	−1.88941	+	2.25171i
$213$	5.08483	−	13.9705i	0.348407	−	0.957240i
$214$	−10.6442	+	3.87418i	−0.727625	+	0.264834i
$215$		0			0
$216$	−5.33830	−	9.24620i	−0.363225	−	0.629124i
$217$	14.1578	+	8.17400i	0.961093	+	0.554887i
$218$	13.4296	−	2.36800i	0.909569	−	0.160382i
$219$	−1.95466	−	11.0854i	−0.132084	−	0.749084i
$220$		0			0
$221$	7.23908	+	12.5385i	0.486953	+	0.843428i
$222$	7.42737	+	8.85160i	0.498493	+	0.594080i
$223$	0.848195	+	2.33040i	0.0567993	+	0.156055i	0.964847	−	0.262812i	$-0.0846498\pi$
$223$	0.848195	+	2.33040i	0.0567993	+	0.156055i	−0.908048	+	0.418866i	$0.862428\pi$
$224$	−13.1771	−	4.79607i	−0.880432	−	0.320451i
$225$		0			0
$226$	−4.41231	+	25.0234i	−0.293502	+	1.66453i
$227$		−	0.453554i		−	0.0301034i	−0.999887	−	0.0150517i	$-0.995209\pi$
$227$		−	0.453554i		−	0.0301034i	0.999887	−	0.0150517i	$-0.00479129\pi$
$228$	−12.9787	−	2.86836i	−0.859538	−	0.189962i
$229$	−0.993282			−0.0656379			−0.0328190	−	0.999461i	$-0.510448\pi$
$229$	−0.993282			−0.0656379			−0.0328190	+	0.999461i	$0.510448\pi$
$230$		0			0
$231$	−0.136443	−	0.114489i	−0.00897727	−	0.00753283i
$232$	−1.87637	+	5.15529i	−0.123190	+	0.338461i
$233$	−1.45810	−	4.00611i	−0.0955236	−	0.262449i	0.882723	−	0.469893i	$-0.155708\pi$
$233$	−1.45810	−	4.00611i	−0.0955236	−	0.262449i	−0.978247	+	0.207444i	$0.933485\pi$
$234$	−18.7482	+	15.7316i	−1.22561	+	1.02841i
$235$		0			0
$236$	−10.9880	+	19.0317i	−0.715255	+	1.23886i
$237$	−0.118360	+	0.0208701i	−0.00768833	+	0.00135566i
$238$	−11.2183	+	1.97808i	−0.727172	+	0.128220i
$239$	12.2291	−	21.1815i	0.791037	−	1.37012i	−0.134288	−	0.990942i	$-0.542875\pi$
$239$	12.2291	−	21.1815i	0.791037	−	1.37012i	0.925325	−	0.379175i	$-0.123792\pi$
$240$		0			0
$241$	3.36665	−	2.82495i	0.216865	−	0.181971i	−0.527883	−	0.849317i	$-0.677014\pi$
$241$	3.36665	−	2.82495i	0.216865	−	0.181971i	0.744748	+	0.667346i	$0.232570\pi$
$242$	−8.35697	−	22.9606i	−0.537206	−	1.47596i
$243$	−5.40950	+	14.8625i	−0.347019	+	0.953428i
$244$	−29.9980	−	25.1713i	−1.92042	−	1.61143i
$245$		0			0
$246$	13.5541			0.864179
$247$	−1.07135	+	24.9141i	−0.0681685	+	1.58525i
$248$			16.8773i			1.07171i
$249$	0.535813	−	3.03875i	0.0339558	−	0.192573i
$250$		0			0
$251$	0.364101	+	0.132522i	0.0229818	+	0.00836471i	0.353485	−	0.935440i	$-0.384996\pi$
$251$	0.364101	+	0.132522i	0.0229818	+	0.00836471i	−0.330504	+	0.943805i	$0.607219\pi$
$252$	−3.91987	−	10.7698i	−0.246929	−	0.678431i
$253$	0.0168509	+	0.0200822i	0.00105941	+	0.00126256i
$254$	1.60013	+	2.77150i	0.100401	+	0.173899i
$255$		0			0
$256$	−1.25346	−	7.10870i	−0.0783410	−	0.444294i
$257$	2.80962	−	0.495411i	0.175259	−	0.0309029i	−0.0853298	−	0.996353i	$-0.527194\pi$
$257$	2.80962	−	0.495411i	0.175259	−	0.0309029i	0.260589	+	0.965450i	$0.416083\pi$
$258$	−1.29855	−	0.749718i	−0.0808441	−	0.0466754i
$259$	5.07589	+	8.79169i	0.315400	+	0.546289i
$260$		0			0
$261$	4.74592	−	1.72737i	0.293765	−	0.106922i
$262$	0.762846	−	2.09590i	0.0471288	−	0.129485i
$263$	−6.94691	+	8.27900i	−0.428365	+	0.510505i	−0.936450	−	0.350802i	$-0.885909\pi$
$263$	−6.94691	+	8.27900i	−0.428365	+	0.510505i	0.508085	+	0.861307i	$0.330354\pi$
$264$	0.0319304	−	0.181086i	0.00196518	−	0.0111451i
$265$		0			0
$266$	−18.1318	−	7.49647i	−1.11173	−	0.459638i
$267$		−	11.5375i		−	0.706086i
$268$	−25.7226	−	4.53560i	−1.57126	−	0.277056i
$269$	−2.12780	−	1.78544i	−0.129734	−	0.108860i	0.575612	−	0.817723i	$-0.304764\pi$
$269$	−2.12780	−	1.78544i	−0.129734	−	0.108860i	−0.705346	+	0.708863i	$0.749208\pi$
$270$		0			0
$271$	−13.9661	+	5.08325i	−0.848381	+	0.308785i	−0.729380	−	0.684109i	$-0.760191\pi$
$271$	−13.9661	+	5.08325i	−0.848381	+	0.308785i	−0.119001	+	0.992894i	$0.537969\pi$
$272$	2.00767	+	2.39264i	0.121733	+	0.145075i
$273$	10.4045	−	6.00705i	0.629709	−	0.363563i
$274$	11.6103	−	20.1095i	0.701401	−	1.21486i
$275$		0			0
$276$	−0.163668	−	0.928205i	−0.00985163	−	0.0558714i
$277$	−15.6643	−	9.04379i	−0.941177	−	0.543389i	−0.0508480	−	0.998706i	$-0.516192\pi$
$277$	−15.6643	−	9.04379i	−0.941177	−	0.543389i	−0.890329	+	0.455318i	$0.849526\pi$
$278$	20.5673	−	11.8745i	1.23355	−	0.712188i
$279$	11.9021	−	9.98705i	0.712560	−	0.597909i
$280$		0			0
$281$	3.65001	+	1.32850i	0.217741	+	0.0792514i	0.448588	−	0.893739i	$-0.351927\pi$
$281$	3.65001	+	1.32850i	0.217741	+	0.0792514i	−0.230846	+	0.972990i	$0.574149\pi$
$282$	10.2273	−	12.1884i	0.609024	−	0.725807i
$283$	21.9474	+	3.86993i	1.30464	+	0.230043i	0.782411	−	0.622762i	$-0.213990\pi$
$283$	21.9474	+	3.86993i	1.30464	+	0.230043i	0.522229	+	0.852805i	$0.325101\pi$
$284$	42.1577			2.50160
$285$		0			0
$286$	−1.07853			−0.0637750
$287$	11.7273	+	2.06783i	0.692239	+	0.122060i
$288$	−8.56656	+	10.2092i	−0.504789	+	0.601585i
$289$	−9.95648	−	3.62386i	−0.585675	−	0.213168i
$290$		0			0
$291$	−0.179455	+	0.150580i	−0.0105198	+	0.00882718i
$292$	27.6429	−	15.9596i	1.61768	−	0.933968i
$293$	−21.1755	−	12.2257i	−1.23709	−	0.714232i	−0.268589	−	0.963255i	$-0.586557\pi$
$293$	−21.1755	−	12.2257i	−1.23709	−	0.714232i	−0.968498	+	0.249023i	$0.919891\pi$
$294$	−1.16037	−	6.58076i	−0.0676739	−	0.383798i
$295$		0			0
$296$	−5.24022	+	9.07633i	−0.304582	+	0.527551i
$297$	−0.375110	+	0.216570i	−0.0217661	+	0.0125667i
$298$	−7.20749	−	8.58955i	−0.417519	−	0.497580i
$299$	−1.66164	+	0.604788i	−0.0960951	+	0.0349758i
$300$		0			0
$301$	−1.00915	−	0.846777i	−0.0581664	−	0.0488074i
$302$	−45.5554	−	8.03265i	−2.62142	−	0.462227i
$303$			13.0676i			0.750717i
$304$	0.705699	+	5.33320i	0.0404746	+	0.305880i
$305$		0			0
$306$	−1.87996	+	10.6618i	−0.107470	+	0.609495i
$307$	−4.13004	+	4.92198i	−0.235714	+	0.280913i	−0.870915	−	0.491434i	$-0.836473\pi$
$307$	−4.13004	+	4.92198i	−0.235714	+	0.280913i	0.635201	+	0.772347i	$0.280917\pi$
$308$	0.172743	−	0.474608i	0.00984295	−	0.0270433i
$309$	17.2704	−	6.28593i	0.982481	−	0.357594i
$310$		0			0
$311$	8.78200	+	15.2109i	0.497982	+	0.862529i	0.999997	−	0.00232912i	$-0.000741383\pi$
$311$	8.78200	+	15.2109i	0.497982	+	0.862529i	−0.502016	+	0.864858i	$0.667408\pi$
$312$	10.7414	+	6.20153i	0.608110	+	0.351093i
$313$	−3.58824	+	0.632703i	−0.202819	+	0.0357625i	−0.274135	−	0.961691i	$-0.588391\pi$
$313$	−3.58824	+	0.632703i	−0.202819	+	0.0357625i	0.0713155	+	0.997454i	$0.477280\pi$
$314$	9.11511	+	51.6944i	0.514395	+	2.91728i
$315$		0			0
$316$	−0.170403	−	0.295146i	−0.00958591	−	0.0166033i
$317$	2.89191	+	3.44644i	0.162426	+	0.193571i	0.841118	−	0.540851i	$-0.181898\pi$
$317$	2.89191	+	3.44644i	0.162426	+	0.193571i	−0.678693	+	0.734422i	$0.737453\pi$
$318$	−11.4740	−	31.5245i	−0.643429	−	1.76781i
$319$	0.209145	+	0.0761227i	0.0117099	+	0.00426205i
$320$		0			0
$321$	0.917676	−	5.20440i	0.0512197	−	0.290481i
$322$		−	1.39127i		−	0.0775325i
$323$	6.72109	+	8.74717i	0.373972	+	0.486706i
$324$	−1.40582			−0.0781013
$325$		0			0
$326$	0.363586	+	0.305085i	0.0201371	+	0.0168971i
$327$	−2.17598	+	5.97845i	−0.120332	+	0.330609i
$328$	4.20470	+	11.5523i	0.232166	+	0.637870i
$329$	10.7083	−	8.98531i	0.590366	−	0.495376i
$330$		0			0
$331$	−17.0501	+	29.5317i	−0.937161	+	1.62321i	−0.166426	+	0.986054i	$0.553223\pi$
$331$	−17.0501	+	29.5317i	−0.937161	+	1.62321i	−0.770735	+	0.637156i	$0.780111\pi$
$332$	8.61681	−	1.51938i	0.472909	−	0.0833866i
$333$	9.50163	−	1.67539i	0.520686	−	0.0918110i
$334$	−21.9216	+	37.9694i	−1.19950	+	2.07759i
$335$		0			0
$336$	1.98544	−	1.66598i	0.108314	−	0.0908866i
$337$	0.331394	+	0.910498i	0.0180522	+	0.0495980i	0.948391	−	0.317102i	$-0.102710\pi$
$337$	0.331394	+	0.910498i	0.0180522	+	0.0495980i	−0.930339	+	0.366700i	$0.880488\pi$
$338$	14.9988	−	41.2088i	0.815827	−	2.24146i
$339$	−9.08113	−	7.61998i	−0.493220	−	0.413860i
$340$		0			0
$341$	0.684697			0.0370784
$342$	−12.5888	+	13.7564i	−0.680723	+	0.743861i
$343$		−	20.0464i		−	1.08240i
$344$	0.236162	−	1.33934i	0.0127330	−	0.0722124i
$345$		0			0
$346$	26.2651	+	9.55971i	1.41202	+	0.513933i
$347$	8.03967	+	22.0888i	0.431592	+	1.18579i	0.944835	+	0.327546i	$0.106222\pi$
$347$	8.03967	+	22.0888i	0.431592	+	1.18579i	−0.513243	+	0.858243i	$0.671556\pi$
$348$	−5.14358	−	6.12988i	−0.275725	−	0.328596i
$349$	9.71877	+	16.8334i	0.520234	+	0.901071i	0.999723	+	0.0235237i	$0.00748852\pi$
$349$	9.71877	+	16.8334i	0.520234	+	0.901071i	−0.479490	+	0.877548i	$0.659178\pi$
$350$		0			0
$351$	−5.07332	−	28.7723i	−0.270794	−	1.53575i
$352$	−0.578388	+	0.101985i	−0.0308282	+	0.00543584i
$353$	−10.3617	−	5.98232i	−0.551497	−	0.318407i	0.198229	−	0.980156i	$-0.436481\pi$
$353$	−10.3617	−	5.98232i	−0.551497	−	0.318407i	−0.749726	+	0.661749i	$0.769815\pi$
$354$	−8.61297	−	14.9181i	−0.457774	−	0.792888i
$355$		0			0
$356$	30.7434	−	11.1897i	1.62939	−	0.593051i
$357$	1.81768	−	4.99403i	0.0962017	−	0.264312i
$358$	15.4566	−	18.4205i	0.816907	−	0.973552i
$359$	−2.98502	+	16.9289i	−0.157543	+	0.893473i	0.798880	+	0.601490i	$0.205426\pi$
$359$	−2.98502	+	16.9289i	−0.157543	+	0.893473i	−0.956424	+	0.291983i	$0.905685\pi$
$360$		0			0
$361$	1.68086	+	18.9255i	0.0884664	+	0.996079i
$362$			12.0293i			0.632244i
$363$	11.2264	+	1.97951i	0.589232	+	0.103897i
$364$	26.0974	+	21.8983i	1.36788	+	1.14778i
$365$		0			0
$366$	28.8443	−	10.4985i	1.50772	−	0.548764i
$367$	−11.3280	−	13.5002i	−0.591316	−	0.704703i	0.384542	−	0.923107i	$-0.374359\pi$
$367$	−11.3280	−	13.5002i	−0.591316	−	0.704703i	−0.975858	+	0.218404i	$0.929915\pi$
$368$	−0.330364	+	0.190736i	−0.0172214	+	0.00994279i
$369$	5.65875	−	9.80124i	0.294583	−	0.510232i
$370$		0			0
$371$	−5.11808	−	29.0261i	−0.265717	−	1.50696i
$372$	−21.3189	−	12.3085i	−1.10533	−	0.638164i
$373$	2.29909	−	1.32738i	0.119042	−	0.0687292i	−0.439296	−	0.898342i	$-0.644772\pi$
$373$	2.29909	−	1.32738i	0.119042	−	0.0687292i	0.558339	+	0.829613i	$0.311439\pi$
$374$	−0.365478	+	0.306673i	−0.0188984	+	0.0158577i
$375$		0			0
$376$	13.5609	+	4.93577i	0.699352	+	0.254543i
$377$	−9.64994	+	11.5003i	−0.496997	+	0.592298i
$378$	22.6378	+	3.99166i	1.16436	+	0.205309i
$379$	18.9795			0.974909			0.487455	−	0.873148i	$-0.337925\pi$
$379$	18.9795			0.974909			0.487455	+	0.873148i	$0.337925\pi$
$380$		0			0
$381$	−1.49305			−0.0764914
$382$	−10.6634	−	1.88025i	−0.545589	−	0.0962021i
$383$	−7.66750	+	9.13777i	−0.391791	+	0.466918i	−0.925499	−	0.378751i	$-0.876354\pi$
$383$	−7.66750	+	9.13777i	−0.391791	+	0.466918i	0.533708	+	0.845669i	$0.320798\pi$
$384$	14.4957	+	5.27601i	0.739732	+	0.269240i
$385$		0			0
$386$	2.35679	−	1.97758i	0.119958	−	0.100656i
$387$	−1.08427	+	0.626003i	−0.0551165	+	0.0318215i
$388$	−0.575286	−	0.332142i	−0.0292057	−	0.0168619i
$389$	1.69579	+	9.61728i	0.0859798	+	0.487616i	0.997141	+	0.0755652i	$0.0240761\pi$
$389$	1.69579	+	9.61728i	0.0859798	+	0.487616i	−0.911161	+	0.412050i	$0.864813\pi$
$390$		0			0
$391$	−0.391107	+	0.677417i	−0.0197791	+	0.0342584i
$392$	5.24889	−	3.03045i	0.265109	−	0.153061i
$393$	0.668872	+	0.797131i	0.0337401	+	0.0402099i
$394$	−13.3833	+	4.87112i	−0.674240	+	0.245403i
$395$		0			0
$396$	−0.367712	−	0.308547i	−0.0184782	−	0.0155051i
$397$	28.4044	+	5.00846i	1.42558	+	0.251368i	0.832610	−	0.553860i	$-0.186846\pi$
$397$	28.4044	+	5.00846i	1.42558	+	0.251368i	0.592966	+	0.805227i	$0.297957\pi$
$398$			34.7648i			1.74260i
$399$	7.25847	−	5.57721i	0.363378	−	0.279210i
$400$		0			0
$401$	1.08900	−	6.17602i	0.0543820	−	0.308416i	−0.945468	−	0.325714i	$-0.894395\pi$
$401$	1.08900	−	6.17602i	0.0543820	−	0.308416i	0.999850	+	0.0172981i	$0.00550645\pi$
$402$	13.1604	−	15.6839i	0.656379	−	0.782242i
$403$	−15.7959	+	43.3989i	−0.786849	+	2.16185i
$404$	−34.8205	+	12.6736i	−1.73239	+	0.630537i
$405$		0			0
$406$	−5.90592	−	10.2294i	−0.293106	−	0.507675i
$407$	0.368219	+	0.212591i	0.0182519	+	0.0105378i
$408$	5.40324	−	0.952737i	0.267500	−	0.0471675i
$409$	−1.94902	−	11.0534i	−0.0963726	−	0.546556i	−0.994318	−	0.106450i	$-0.966052\pi$
$409$	−1.94902	−	11.0534i	−0.0963726	−	0.546556i	0.897946	−	0.440107i	$-0.145059\pi$
$410$		0			0
$411$	5.41667	+	9.38195i	0.267185	+	0.462777i
$412$	33.4994	+	39.9231i	1.65040	+	1.96687i
$413$	−5.17617	−	14.2214i	−0.254703	−	0.699790i
$414$	−1.24252	−	0.452240i	−0.0610664	−	0.0222264i
$415$		0			0
$416$	6.87911	−	39.0134i	0.337276	−	1.91279i
$417$			11.0800i			0.542588i
$418$	−0.814651	+	0.107796i	−0.0398459	+	0.00527248i
$419$	26.0754			1.27387			0.636934	−	0.770918i	$-0.280202\pi$
$419$	26.0754			1.27387			0.636934	+	0.770918i	$0.280202\pi$
$420$		0			0
$421$	−19.3507	−	16.2372i	−0.943096	−	0.791351i	0.0350258	−	0.999386i	$-0.488849\pi$
$421$	−19.3507	−	16.2372i	−0.943096	−	0.791351i	−0.978121	+	0.208035i	$0.933293\pi$
$422$	−5.84142	+	16.0492i	−0.284356	+	0.781262i
$423$	−4.54383	−	12.4841i	−0.220929	−	0.606996i
$424$	23.3093	−	19.5588i	1.13200	−	0.949859i
$425$		0			0
$426$	−16.5228	+	28.6183i	−0.800532	+	1.38656i
$427$	26.5583	−	4.68294i	1.28525	−	0.226623i
$428$	14.7578	−	2.60221i	0.713347	−	0.125782i
$429$	0.251591	−	0.435768i	0.0121469	−	0.0210391i
$430$		0			0
$431$	29.2544	−	24.5474i	1.40914	−	1.18241i	0.452269	−	0.891881i	$-0.350615\pi$
$431$	29.2544	−	24.5474i	1.40914	−	1.18241i	0.956867	−	0.290525i	$-0.0938299\pi$
$432$	−2.15568	−	5.92269i	−0.103715	−	0.284956i
$433$	−0.896443	+	2.46296i	−0.0430803	+	0.118362i	−0.959367	−	0.282160i	$-0.908949\pi$
$433$	−0.896443	+	2.46296i	−0.0430803	+	0.118362i	0.916287	+	0.400522i	$0.131171\pi$
$434$	−27.8360	−	23.3572i	−1.33617	−	1.12118i
$435$		0			0
$436$	−18.0408			−0.863997
$437$	−1.19464	+	0.622891i	−0.0571476	+	0.0297969i
$438$			25.0201i			1.19551i
$439$	−1.16634	+	6.61462i	−0.0556662	+	0.315699i	−0.999908	−	0.0135537i	$-0.995686\pi$
$439$	−1.16634	+	6.61462i	−0.0556662	+	0.315699i	0.944242	+	0.329252i	$0.106797\pi$
$440$		0			0
$441$	−5.24311	−	1.90834i	−0.249672	−	0.0908732i
$442$	−11.0066	−	30.2404i	−0.523531	−	1.43839i
$443$	16.7163	+	19.9218i	0.794217	+	0.946511i	0.999482	−	0.0321953i	$-0.0102499\pi$
$443$	16.7163	+	19.9218i	0.794217	+	0.946511i	−0.205264	+	0.978707i	$0.565805\pi$
$444$	−7.64330	−	13.2386i	−0.362735	−	0.628275i
$445$		0			0
$446$	−0.957200	−	5.42855i	−0.0453247	−	0.257049i
$447$	5.15180	−	0.908401i	0.243672	−	0.0429659i
$448$	22.6642	+	13.0852i	1.07078	+	0.618216i
$449$	−13.7860	−	23.8781i	−0.650602	−	1.12688i	−0.982977	−	0.183728i	$-0.941183\pi$
$449$	−13.7860	−	23.8781i	−0.650602	−	1.12688i	0.332376	−	0.943147i	$-0.392150\pi$
$450$		0			0
$451$	0.468667	−	0.170581i	0.0220687	−	0.00803234i
$452$	11.4971	−	31.5882i	0.540780	−	1.48578i
$453$	13.8723	−	16.5323i	0.651775	−	0.776756i
$454$	−0.175060	+	0.992816i	−0.00821598	+	0.0465951i
$455$		0			0
$456$	8.73312	+	3.61065i	0.408966	+	0.169084i
$457$			2.22524i			0.104092i	0.998645	+	0.0520462i	$0.0165743\pi$
$457$			2.22524i			0.104092i	−0.998645	+	0.0520462i	$0.983426\pi$
$458$	2.17427	+	0.383382i	0.101597	+	0.0179143i
$459$	−9.90035	−	8.30738i	−0.462109	−	0.387755i
$460$		0			0
$461$	−19.2217	+	6.99612i	−0.895243	+	0.325842i	−0.748345	−	0.663310i	$-0.769151\pi$
$461$	−19.2217	+	6.99612i	−0.895243	+	0.325842i	−0.146898	+	0.989152i	$0.546929\pi$
$462$	0.254479	+	0.303277i	0.0118395	+	0.0141097i
$463$	28.0852	−	16.2150i	1.30523	−	0.753575i	0.323934	−	0.946080i	$-0.394994\pi$
$463$	28.0852	−	16.2150i	1.30523	−	0.753575i	0.981296	+	0.192505i	$0.0616610\pi$
$464$	−1.61934	+	2.80478i	−0.0751760	+	0.130209i
$465$		0			0
$466$	1.64549	+	9.33205i	0.0762259	+	0.432299i
$467$	5.99375	+	3.46049i	0.277357	+	0.160132i	0.632227	−	0.774784i	$-0.282141\pi$
$467$	5.99375	+	3.46049i	0.277357	+	0.160132i	−0.354869	+	0.934916i	$0.615475\pi$
$468$	28.0400	−	16.1889i	1.29615	−	0.748333i
$469$	13.7793	−	11.5622i	0.636271	−	0.533895i
$470$		0			0
$471$	−23.0127	−	8.37595i	−1.06037	−	0.385943i
$472$	10.0430	−	11.9688i	0.462266	−	0.550907i
$473$	−0.0543359	−	0.00958088i	−0.00249837	−	0.000440529i
$474$	0.267143			0.0122703
$475$		0			0
$476$	15.0701			0.690739
$477$	−27.5863	−	4.86420i	−1.26309	−	0.222717i
$478$	−34.9448	+	41.6455i	−1.59834	+	1.90482i
$479$	−18.8350	−	6.85539i	−0.860594	−	0.313231i	−0.126242	−	0.991999i	$-0.540292\pi$
$479$	−18.8350	−	6.85539i	−0.860594	−	0.313231i	−0.734352	+	0.678769i	$0.762514\pi$
$480$		0			0
$481$	−21.9697	+	18.4347i	−1.00173	+	0.840552i
$482$	−8.45985	+	4.88430i	−0.385336	+	0.222474i
$483$	0.562126	+	0.324543i	0.0255776	+	0.0147672i
$484$	5.61320	+	31.8340i	0.255145	+	1.44700i
$485$		0			0
$486$	17.5778	−	30.4456i	0.797344	−	1.38104i
$487$	6.17413	−	3.56464i	0.279777	−	0.161529i	−0.353546	−	0.935417i	$-0.615024\pi$
$487$	6.17413	−	3.56464i	0.279777	−	0.161529i	0.633322	+	0.773888i	$0.281691\pi$
$488$	17.8959	+	21.3275i	0.810110	+	0.965452i
$489$	−0.208080	+	0.0757348i	−0.00940968	+	0.00342484i
$490$		0			0
$491$	12.6437	+	10.6093i	0.570600	+	0.478790i	0.881845	−	0.471539i	$-0.156302\pi$
$491$	12.6437	+	10.6093i	0.570600	+	0.478790i	−0.311245	+	0.950330i	$0.600746\pi$
$492$	−17.6590	−	3.11376i	−0.796129	−	0.140379i
$493$			6.64096i			0.299094i
$494$	11.9614	−	54.1227i	0.538167	−	2.43510i
$495$		0			0
$496$	−1.73011	+	9.81194i	−0.0776842	+	0.440569i
$497$	−18.6619	+	22.2403i	−0.837099	+	0.997615i
$498$	−2.34576	+	6.44491i	−0.105116	+	0.288804i
$499$	−28.5296	+	10.3839i	−1.27716	+	0.464848i	−0.889491	−	0.456952i	$-0.848941\pi$
$499$	−28.5296	+	10.3839i	−1.27716	+	0.464848i	−0.387667	+	0.921800i	$0.626719\pi$
$500$		0			0
$501$	−10.2274	−	17.7143i	−0.456925	−	0.791417i
$502$	−0.745856	−	0.430620i	−0.0332892	−	0.0192195i
$503$	−5.68175	+	1.00185i	−0.253337	+	0.0446701i	−0.298874	−	0.954293i	$-0.596611\pi$
$503$	−5.68175	+	1.00185i	−0.253337	+	0.0446701i	0.0455375	+	0.998963i	$0.485500\pi$
$504$	1.41494	+	8.02454i	0.0630266	+	0.357441i
$505$		0			0
$506$	−0.0291350	−	0.0504633i	−0.00129521	−	0.00224337i
$507$	13.1511	+	15.6729i	0.584062	+	0.696058i
$508$	−1.44803	−	3.97844i	−0.0642462	−	0.176515i
$509$	−36.5216	−	13.2928i	−1.61879	−	0.589191i	−0.635638	−	0.771987i	$-0.719263\pi$
$509$	−36.5216	−	13.2928i	−1.61879	−	0.589191i	−0.983151	+	0.182796i	$0.941485\pi$
$510$		0			0
$511$	−3.81710	+	21.6479i	−0.168859	+	0.957645i
$512$		−	13.7067i		−	0.605755i
$513$	−6.70774	−	21.2255i	−0.296154	−	0.937131i
$514$	−6.34139			−0.279707
$515$		0			0
$516$	1.51958	+	1.27508i	0.0668960	+	0.0561324i
$517$	0.200240	−	0.550155i	0.00880654	−	0.0241958i
$518$	−7.71760	−	21.2039i	−0.339092	−	0.931647i
$519$	−9.98936	+	8.38207i	−0.438484	+	0.367932i
$520$		0			0
$521$	18.2553	−	31.6191i	0.799778	−	1.38526i	−0.119983	−	0.992776i	$-0.538284\pi$
$521$	18.2553	−	31.6191i	0.799778	−	1.38526i	0.919761	−	0.392480i	$-0.128383\pi$
$522$	−11.0554	+	1.94936i	−0.483881	+	0.0853214i
$523$	27.3876	−	4.82917i	1.19758	−	0.211165i	0.460925	−	0.887439i	$-0.347518\pi$
$523$	27.3876	−	4.82917i	1.19758	−	0.211165i	0.736650	+	0.676274i	$0.236407\pi$
$524$	−1.47536	+	2.55540i	−0.0644514	+	0.111633i
$525$		0			0
$526$	18.4021	−	15.4412i	0.802368	−	0.673267i
$527$	6.98744	+	19.1978i	0.304378	+	0.836271i
$528$	0.0371267	−	0.102005i	0.00161573	−	0.00443919i
$529$	17.5458	+	14.7227i	0.762863	+	0.640118i
$530$		0			0
$531$	−14.3834			−0.624187
$532$	21.9009	+	13.9321i	0.949523	+	0.604035i
$533$			33.6413i			1.45717i
$534$	−4.45320	+	25.2553i	−0.192709	+	1.09291i
$535$		0			0
$536$	17.4501	+	6.35132i	0.753730	+	0.274335i
$537$	3.83698	+	10.5420i	0.165578	+	0.454921i
$538$	3.96856	+	4.72954i	0.171097	+	0.203905i
$539$	−0.122942	−	0.212943i	−0.00529551	−	0.00917209i
$540$		0			0
$541$	−4.21069	−	23.8800i	−0.181032	−	1.02668i	−0.930949	−	0.365150i	$-0.881018\pi$
$541$	−4.21069	−	23.8800i	−0.181032	−	1.02668i	0.749917	−	0.661532i	$-0.230094\pi$
$542$	32.5334	−	5.73652i	1.39743	−	0.246405i
$543$	−4.86027	−	2.80608i	−0.208574	−	0.120420i
$544$	−8.76205	−	15.1763i	−0.375670	−	0.650679i
$545$		0			0
$546$	−25.0937	+	9.13337i	−1.07391	+	0.390872i
$547$	−0.202370	+	0.556008i	−0.00865274	+	0.0237732i	−0.943944	−	0.330106i	$-0.892915\pi$
$547$	−0.202370	+	0.556008i	−0.00865274	+	0.0237732i	0.935291	+	0.353879i	$0.115138\pi$
$548$	−19.7461	+	23.5325i	−0.843513	+	1.00526i
$549$	4.45065	−	25.2409i	0.189949	−	1.07726i
$550$		0			0
$551$	−6.13948	+	9.65107i	−0.261551	+	0.411149i
$552$			0.670102i			0.0285214i
$553$	0.231137	+	0.0407556i	0.00982893	+	0.00173311i
$554$	30.7980	+	25.8426i	1.30848	+	1.09795i
$555$		0			0
$556$	−29.5241	+	10.7459i	−1.25210	+	0.455727i
$557$	−15.8852	−	18.9312i	−0.673077	−	0.802142i	0.316122	−	0.948719i	$-0.397619\pi$
$557$	−15.8852	−	18.9312i	−0.673077	−	0.802142i	−0.989199	+	0.146576i	$0.953175\pi$
$558$	−29.9081	+	17.2675i	−1.26611	+	0.730990i
$559$	1.86080	−	3.22300i	0.0787034	−	0.136318i
$560$		0			0
$561$	−0.0386517	−	0.219205i	−0.00163188	−	0.00925483i
$562$	−7.47700	−	4.31685i	−0.315398	−	0.182095i
$563$	−10.3884	+	5.99775i	−0.437819	+	0.252775i	−0.702672	−	0.711514i	$-0.748010\pi$
$563$	−10.3884	+	5.99775i	−0.437819	+	0.252775i	0.264853	+	0.964289i	$0.414677\pi$
$564$	−16.1246	+	13.5301i	−0.678968	+	0.569721i
$565$		0			0
$566$	−46.5486	−	16.9423i	−1.95658	−	0.712138i
$567$	0.622313	−	0.741643i	0.0261347	−	0.0311461i
$568$	−29.5173	−	5.20470i	−1.23852	−	0.218384i
$569$	−33.9446			−1.42303			−0.711517	−	0.702669i	$-0.751991\pi$
$569$	−33.9446			−1.42303			−0.711517	+	0.702669i	$0.751991\pi$
$570$		0			0
$571$	−3.81177			−0.159518			−0.0797588	−	0.996814i	$-0.525415\pi$
$571$	−3.81177			−0.159518			−0.0797588	+	0.996814i	$0.525415\pi$
$572$	1.40517	+	0.247769i	0.0587530	+	0.0103597i
$573$	3.24717	−	3.86982i	0.135652	−	0.161664i
$574$	−24.8725	−	9.05286i	−1.03816	−	0.377859i
$575$		0			0
$576$	19.0532	−	15.9875i	0.793884	−	0.666148i
$577$	1.43275	−	0.827198i	0.0596461	−	0.0344367i	−0.469880	−	0.882730i	$-0.655703\pi$
$577$	1.43275	−	0.827198i	0.0596461	−	0.0344367i	0.529527	+	0.848293i	$0.322370\pi$
$578$	20.3957	+	11.7755i	0.848351	+	0.489795i
$579$	0.249246	+	1.41354i	0.0103583	+	0.0587449i
$580$		0			0
$581$	−3.01284	+	5.21838i	−0.124993	+	0.216495i
$582$	0.450941	−	0.260351i	0.0186921	−	0.0107919i
$583$	−0.793483	−	0.945636i	−0.0328627	−	0.0391642i
$584$	−21.3249	+	7.76164i	−0.882432	+	0.321179i
$585$		0			0
$586$	41.6338	+	34.9349i	1.71987	+	1.44315i
$587$	−28.9683	−	5.10789i	−1.19565	−	0.210825i	−0.459832	−	0.888006i	$-0.652091\pi$
$587$	−28.9683	−	5.10789i	−1.19565	−	0.210825i	−0.735817	+	0.677180i	$0.763202\pi$
$588$			8.84031i			0.364568i
$589$	−7.59356	+	34.3593i	−0.312887	+	1.41575i
$590$		0			0
$591$	1.15382	−	6.54364i	0.0474618	−	0.269169i
$592$	−3.97693	+	4.73952i	−0.163451	+	0.194793i
$593$	−16.0152	+	44.0015i	−0.657667	+	1.80693i	−0.0704204	+	0.997517i	$0.522434\pi$
$593$	−16.0152	+	44.0015i	−0.657667	+	1.80693i	−0.587247	+	0.809408i	$0.699788\pi$
$594$	0.904695	−	0.329282i	0.0371201	−	0.0135106i
$595$		0			0
$596$	7.41702	+	12.8467i	0.303813	+	0.526220i
$597$	−14.0463	−	8.10961i	−0.574875	−	0.331904i
$598$	3.87071	−	0.682511i	0.158285	−	0.0279100i
$599$	−2.11359	−	11.9868i	−0.0863589	−	0.489765i	−0.997055	−	0.0766887i	$-0.975565\pi$
$599$	−2.11359	−	11.9868i	−0.0863589	−	0.489765i	0.910696	−	0.413077i	$-0.135546\pi$
$600$		0			0
$601$	−5.01956	−	8.69414i	−0.204752	−	0.354641i	0.745302	−	0.666728i	$-0.232306\pi$
$601$	−5.01956	−	8.69414i	−0.204752	−	0.354641i	−0.950054	+	0.312086i	$0.898972\pi$
$602$	1.88217	+	2.24308i	0.0767113	+	0.0914210i
$603$	−5.84697	−	16.0644i	−0.238107	−	0.654194i
$604$	57.5066	+	20.9307i	2.33991	+	0.851658i
$605$		0			0
$606$	5.04378	−	28.6047i	0.204890	−	1.16199i
$607$			20.5318i			0.833358i	0.909054	+	0.416679i	$0.136806\pi$
$607$			20.5318i			0.833358i	−0.909054	+	0.416679i	$0.863194\pi$
$608$	1.29675	−	30.1556i	0.0525900	−	1.22297i
$609$	5.51072			0.223306
$610$		0			0
$611$	30.2515	+	25.3840i	1.22385	+	1.02693i
$612$	4.89862	−	13.4589i	0.198015	−	0.544042i
$613$	−12.4745	−	34.2734i	−0.503840	−	1.38429i	−0.887497	−	0.460813i	$-0.847558\pi$
$613$	−12.4745	−	34.2734i	−0.503840	−	1.38429i	0.383657	−	0.923476i	$-0.374664\pi$
$614$	10.9403	−	9.17999i	0.441514	−	0.370474i
$615$		0			0
$616$	−0.179542	+	0.310977i	−0.00723397	+	0.0125296i
$617$	−21.0816	+	3.71725i	−0.848712	+	0.149651i	−0.581056	−	0.813864i	$-0.697360\pi$
$617$	−21.0816	+	3.71725i	−0.848712	+	0.149651i	−0.267656	+	0.963514i	$0.586249\pi$
$618$	−40.2307	+	7.09376i	−1.61832	+	0.285353i
$619$	−7.68760	+	13.3153i	−0.308991	+	0.535187i	−0.978142	−	0.207939i	$-0.933324\pi$
$619$	−7.68760	+	13.3153i	−0.308991	+	0.535187i	0.669151	+	0.743126i	$0.266658\pi$
$620$		0			0
$621$	1.20917	−	1.01462i	0.0485224	−	0.0407151i
$622$	−13.3525	−	36.6858i	−0.535388	−	1.47097i
$623$	−7.70597	+	21.1720i	−0.308733	+	0.848238i
$624$	5.60897	+	4.70649i	0.224539	+	0.188410i
$625$		0			0
$626$	8.09876			0.323691
$627$	0.146481	−	0.354295i	0.00584988	−	0.0141492i
$628$		−	69.4440i		−	2.77112i
$629$	−2.20300	+	12.4938i	−0.0878392	+	0.498161i
$630$		0			0
$631$	27.9210	+	10.1624i	1.11152	+	0.404559i	0.831550	−	0.555450i	$-0.187454\pi$
$631$	27.9210	+	10.1624i	1.11152	+	0.404559i	0.279968	+	0.960009i	$0.409676\pi$
$632$	0.0828718	+	0.227689i	0.00329647	+	0.00905696i
$633$	−5.12183	−	6.10396i	−0.203575	−	0.242611i
$634$	−5.00006	−	8.66036i	−0.198578	−	0.343947i
$635$		0			0
$636$	7.70683	+	43.7076i	0.305596	+	1.73312i
$637$	16.3334	−	2.88003i	0.647154	−	0.114111i
$638$	−0.428432	−	0.247355i	−0.0169618	−	0.00979289i
$639$	13.7963	+	23.8959i	0.545773	+	0.945306i
$640$		0			0
$641$	−17.9574	+	6.53597i	−0.709275	+	0.258155i	−0.671366	−	0.741126i	$-0.734292\pi$
$641$	−17.9574	+	6.53597i	−0.709275	+	0.258155i	−0.0379095	+	0.999281i	$0.512070\pi$
$642$	−4.01753	+	11.0381i	−0.158559	+	0.435638i
$643$	10.4314	−	12.4316i	0.411374	−	0.490256i	−0.520079	−	0.854118i	$-0.674098\pi$
$643$	10.4314	−	12.4316i	0.411374	−	0.490256i	0.931453	+	0.363862i	$0.118542\pi$
$644$	−0.319614	+	1.81262i	−0.0125945	+	0.0714272i
$645$		0			0
$646$	−11.3361	−	21.7415i	−0.446012	−	0.855407i
$647$			26.6353i			1.04714i	0.851982	+	0.523571i	$0.175400\pi$
$647$			26.6353i			1.04714i	−0.851982	+	0.523571i	$0.824600\pi$
$648$	0.984307	+	0.173560i	0.0386672	+	0.00681808i
$649$	−0.485562	−	0.407435i	−0.0190600	−	0.0159932i
$650$		0			0
$651$	15.9305	−	5.79823i	0.624366	−	0.227251i
$652$	−0.403611	−	0.481005i	−0.0158066	−	0.0188376i
$653$	35.3751	−	20.4238i	1.38433	−	0.799245i	0.391664	−	0.920108i	$-0.371899\pi$
$653$	35.3751	−	20.4238i	1.38433	−	0.799245i	0.992669	+	0.120863i	$0.0385661\pi$
$654$	7.07069	−	12.2468i	0.276486	−	0.478887i
$655$		0			0
$656$	1.26024	+	7.14719i	0.0492042	+	0.279051i
$657$	18.0925	+	10.4457i	0.705857	+	0.407527i
$658$	−26.9082	+	15.5355i	−1.04899	+	0.605635i
$659$	14.0538	−	11.7926i	0.547460	−	0.459373i	−0.326620	−	0.945156i	$-0.605910\pi$
$659$	14.0538	−	11.7926i	0.547460	−	0.459373i	0.874080	+	0.485782i	$0.161465\pi$
$660$		0			0
$661$	22.8442	+	8.31460i	0.888536	+	0.323400i	0.745649	−	0.666339i	$-0.232139\pi$
$661$	22.8442	+	8.31460i	0.888536	+	0.323400i	0.142886	+	0.989739i	$0.454362\pi$
$662$	48.7208	−	58.0632i	1.89359	−	2.25669i
$663$	14.7858	+	2.60713i	0.574232	+	0.101253i
$664$	−6.22076			−0.241412
$665$		0			0
$666$	−21.4455			−0.830995
$667$	−0.798767	−	0.140844i	−0.0309284	−	0.00545351i
$668$	37.2832	−	44.4324i	1.44253	−	1.71914i
$669$	2.41662	+	0.879579i	0.0934321	+	0.0340065i
$670$		0			0
$671$	0.865238	−	0.726021i	0.0334022	−	0.0280277i
$672$	−12.5934	+	7.27082i	−0.485802	+	0.280478i
$673$	−27.3400	−	15.7847i	−1.05388	−	0.608457i	−0.130146	−	0.991495i	$-0.541545\pi$
$673$	−27.3400	−	15.7847i	−1.05388	−	0.608457i	−0.923733	+	0.383038i	$0.874878\pi$
$674$	−0.373983	−	2.12096i	−0.0144053	−	0.0816965i
$675$		0			0
$676$	−29.0080	+	50.2433i	−1.11569	+	1.93243i
$677$	−10.7607	+	6.21268i	−0.413566	+	0.238773i	−0.692321	−	0.721590i	$-0.743412\pi$
$677$	−10.7607	+	6.21268i	−0.413566	+	0.238773i	0.278755	+	0.960362i	$0.410078\pi$
$678$	16.9372	+	20.1850i	0.650470	+	0.775200i
$679$	0.429882	−	0.156464i	0.0164974	−	0.00600455i
$680$		0			0
$681$	−0.360298	−	0.302326i	−0.0138066	−	0.0115852i
$682$	−1.49878	−	0.264276i	−0.0573913	−	0.0101196i
$683$		−	9.71494i		−	0.371732i	−0.982575	−	0.185866i	$-0.940491\pi$
$683$		−	9.71494i		−	0.371732i	0.982575	−	0.185866i	$-0.0595090\pi$
$684$	19.5615	−	15.0305i	0.747953	−	0.574707i
$685$		0			0
$686$	−7.73739	+	43.8809i	−0.295415	+	1.67538i
$687$	−0.662094	+	0.789053i	−0.0252605	+	0.0301042i
$688$	0.274595	−	0.754443i	0.0104688	−	0.0287629i
$689$	78.2438	−	28.4784i	2.98085	−	1.08494i
$690$		0			0
$691$	−19.2944	−	33.4189i	−0.733994	−	1.27132i	−0.955163	−	0.296080i	$-0.904321\pi$
$691$	−19.2944	−	33.4189i	−0.733994	−	1.27132i	0.221169	−	0.975235i	$-0.429013\pi$
$692$	−32.0233	−	18.4887i	−1.21734	−	0.702834i
$693$	0.325548	−	0.0574030i	0.0123666	−	0.00218056i
$694$	−9.07288	−	51.4549i	−0.344402	−	1.95320i
$695$		0			0
$696$	2.84457	+	4.92694i	0.107823	+	0.186755i
$697$	9.56566	+	11.3999i	0.362325	+	0.431802i
$698$	−14.7768	−	40.5990i	−0.559312	−	1.53670i
$699$	−4.15434	−	1.51206i	−0.157132	−	0.0571912i
$700$		0			0
$701$	−3.17615	+	18.0129i	−0.119962	+	0.680336i	0.864212	+	0.503128i	$0.167818\pi$
$701$	−3.17615	+	18.0129i	−0.119962	+	0.680336i	−0.984173	+	0.177208i	$0.943293\pi$
$702$			64.9398i			2.45099i
$703$	−14.7519	+	16.1202i	−0.556379	+	0.607983i
$704$	1.09608			0.0413101
$705$		0			0
$706$	20.3724	+	17.0945i	0.766726	+	0.643359i
$707$	8.72794	−	23.9798i	0.328248	−	0.901854i
$708$	7.79431	+	21.4147i	0.292928	+	0.804814i
$709$	8.38460	−	7.03551i	0.314890	−	0.264224i	−0.471620	−	0.881802i	$-0.656330\pi$
$709$	8.38460	−	7.03551i	0.314890	−	0.264224i	0.786510	+	0.617578i	$0.211886\pi$
$710$		0			0
$711$	0.111530	−	0.193176i	0.00418271	−	0.00724466i
$712$	−22.9068	+	4.03910i	−0.858470	+	0.151371i
$713$	−2.45729	+	0.433286i	−0.0920261	+	0.0162267i
$714$	−5.90641	+	10.2302i	−0.221042	+	0.382856i
$715$		0			0
$716$	−24.3693	+	20.4483i	−0.910725	+	0.764189i
$717$	−8.67475	−	23.8337i	−0.323965	−	0.890085i
$718$	13.0683	−	35.9047i	0.487703	−	1.33995i
$719$	6.11975	+	5.13508i	0.228228	+	0.191506i	0.749730	−	0.661744i	$-0.230183\pi$
$719$	6.11975	+	5.13508i	0.228228	+	0.191506i	−0.521502	+	0.853250i	$0.674628\pi$
$720$		0			0
$721$	−35.8906			−1.33663
$722$	3.62541	−	42.0762i	0.134924	−	1.56591i
$723$		−	4.55746i		−	0.169494i
$724$	2.76346	−	15.6723i	0.102703	−	0.582458i
$725$		0			0
$726$	−23.8102	−	8.66619i	−0.883678	−	0.321632i
$727$	4.63222	+	12.7269i	0.171800	+	0.472016i	0.995473	−	0.0950496i	$-0.0303010\pi$
$727$	4.63222	+	12.7269i	0.171800	+	0.472016i	−0.823673	+	0.567065i	$0.808079\pi$
$728$	−15.5689	−	18.5543i	−0.577023	−	0.687670i
$729$	7.48365	+	12.9621i	0.277172	+	0.480076i
$730$		0			0
$731$	−0.285873	−	1.62127i	−0.0105734	−	0.0599648i
$732$	−39.9916	+	7.05160i	−1.47813	+	0.260635i
$733$	10.5962	+	6.11770i	0.391378	+	0.225962i	0.682757	−	0.730645i	$-0.260781\pi$
$733$	10.5962	+	6.11770i	0.391378	+	0.225962i	−0.291379	+	0.956608i	$0.594114\pi$
$734$	19.5859	+	33.9238i	0.722929	+	1.25215i
$735$		0			0
$736$	2.01122	−	0.732024i	0.0741345	−	0.0269828i
$737$	0.257667	−	0.707935i	0.00949130	−	0.0260771i
$738$	−16.1699	+	19.2705i	−0.595221	+	0.709357i
$739$	0.942774	−	5.34674i	0.0346805	−	0.196683i	−0.962545	−	0.271122i	$-0.912605\pi$
$739$	0.942774	−	5.34674i	0.0346805	−	0.196683i	0.997226	+	0.0744387i	$0.0237165\pi$
$740$		0			0
$741$	19.0774	+	17.4581i	0.700824	+	0.641339i
$742$			65.5126i			2.40505i
$743$	3.71503	+	0.655059i	0.136291	+	0.0240318i	0.241377	−	0.970431i	$-0.422401\pi$
$743$	3.71503	+	0.655059i	0.136291	+	0.0240318i	−0.105086	+	0.994463i	$0.533512\pi$
$744$	13.4071	+	11.2499i	0.491530	+	0.412442i
$745$		0			0
$746$	−5.54498	+	2.01821i	−0.203016	+	0.0738918i
$747$	3.68110	+	4.38697i	0.134684	+	0.160511i
$748$	0.546615	−	0.315588i	0.0199862	−	0.0115390i
$749$	−5.16003	+	8.93743i	−0.188543	+	0.326566i
$750$		0			0
$751$	−1.09106	−	6.18771i	−0.0398133	−	0.225793i	0.958409	−	0.285400i	$-0.0921264\pi$
$751$	−1.09106	−	6.18771i	−0.0398133	−	0.225793i	−0.998222	+	0.0596070i	$0.981015\pi$
$752$	7.37794	+	4.25965i	0.269046	+	0.155334i
$753$	0.347973	−	0.200902i	0.0126809	−	0.00732129i
$754$	25.5623	−	21.4493i	0.930923	−	0.781137i
$755$		0			0
$756$	−28.5767	−	10.4011i	−1.03932	−	0.378283i
$757$	32.6678	−	38.9320i	1.18733	−	1.41501i	0.299960	−	0.953952i	$-0.403027\pi$
$757$	32.6678	−	38.9320i	1.18733	−	1.41501i	0.887372	−	0.461055i	$-0.152529\pi$
$758$	−41.5455	−	7.32559i	−1.50900	−	0.266077i
$759$	0.0271854			0.000986768
$760$		0			0
$761$	−10.2538			−0.371701			−0.185850	−	0.982578i	$-0.559504\pi$
$761$	−10.2538			−0.371701			−0.185850	+	0.982578i	$0.559504\pi$
$762$	3.26825	+	0.576280i	0.118396	+	0.0208764i
$763$	7.98607	−	9.51743i	0.289115	−	0.344554i
$764$	13.4609	+	4.89938i	0.486999	+	0.177253i
$765$		0			0
$766$	20.3109	−	17.0429i	0.733862	−	0.615783i
$767$	37.0267	−	21.3774i	1.33696	−	0.771893i
$768$	−6.48259	−	3.74273i	−0.233920	−	0.135054i
$769$	0.261207	+	1.48138i	0.00941937	+	0.0534199i	0.989155	−	0.146874i	$-0.0469213\pi$
$769$	0.261207	+	1.48138i	0.00941937	+	0.0534199i	−0.979736	+	0.200294i	$0.935810\pi$
$770$		0			0
$771$	1.47926	−	2.56216i	0.0532743	−	0.0922738i
$772$	−3.52485	+	2.03508i	−0.126862	+	0.0732440i
$773$	−23.9903	−	28.5905i	−0.862872	−	1.02833i	−0.999290	−	0.0376792i	$-0.988003\pi$
$773$	−23.9903	−	28.5905i	−0.862872	−	1.02833i	0.136418	−	0.990651i	$-0.456441\pi$
$774$	2.61506	−	0.951803i	0.0939963	−	0.0342118i
$775$		0			0
$776$	0.361789	+	0.303577i	0.0129875	+	0.0108978i
$777$	10.3675	+	1.82806i	0.371931	+	0.0655814i
$778$		−	21.7065i		−	0.778215i
$779$	3.36235	+	25.4104i	0.120469	+	0.910421i
$780$		0			0
$781$	−0.211150	+	1.19749i	−0.00755554	+	0.0428496i
$782$	1.11759	−	1.33189i	0.0399648	−	0.0476282i
$783$	4.58344	−	12.5929i	0.163799	−	0.450034i
$784$	3.36220	−	1.22374i	0.120078	−	0.0437050i
$785$		0			0
$786$	−1.15647	−	2.00306i	−0.0412499	−	0.0714469i
$787$	−28.5177	−	16.4647i	−1.01655	−	0.586903i	−0.103444	−	0.994635i	$-0.532986\pi$
$787$	−28.5177	−	16.4647i	−1.01655	−	0.586903i	−0.913101	+	0.407732i	$0.866320\pi$
$788$	18.5555	−	3.27183i	0.661011	−	0.116554i
$789$	1.94614	+	11.0371i	0.0692844	+	0.392931i
$790$		0			0
$791$	11.5749	+	20.0484i	0.411558	+	0.712839i
$792$	0.219366	+	0.261430i	0.00779484	+	0.00928952i
$793$	26.0572	+	71.5916i	0.925318	+	2.54229i
$794$	−60.2433	−	21.9268i	−2.13795	−	0.778152i
$795$		0			0
$796$	7.98643	−	45.2933i	0.283071	−	1.60538i
$797$		−	18.1078i		−	0.641410i	−0.947179	−	0.320705i	$-0.896080\pi$
$797$		−	18.1078i		−	0.641410i	0.947179	−	0.320705i	$-0.103920\pi$
$798$	−18.0413	+	9.40677i	−0.638653	+	0.332996i
$799$	17.4690			0.618008
$800$		0			0
$801$	16.4034	+	13.7641i	0.579587	+	0.486331i
$802$	−4.76758	+	13.0988i	−0.168349	+	0.462535i
$803$	0.314883	+	0.865133i	0.0111120	+	0.0305299i
$804$	−20.7490	+	17.4105i	−0.731761	+	0.614021i
$805$		0			0
$806$	51.3276	−	88.9020i	1.80794	−	3.13144i
$807$	−2.83666	+	0.500180i	−0.0998552	+	0.0176072i
$808$	25.9448	−	4.57476i	0.912733	−	0.160939i
$809$	−3.92768	+	6.80294i	−0.138090	+	0.239179i	−0.926774	−	0.375620i	$-0.877430\pi$
$809$	−3.92768	+	6.80294i	−0.138090	+	0.239179i	0.788684	+	0.614799i	$0.210763\pi$
$810$		0			0
$811$	−14.9626	+	12.5551i	−0.525409	+	0.440870i	−0.866513	−	0.499155i	$-0.833644\pi$
$811$	−14.9626	+	12.5551i	−0.525409	+	0.440870i	0.341104	+	0.940026i	$0.389199\pi$
$812$	5.34457	+	14.6841i	0.187558	+	0.515310i
$813$	−5.27134	+	14.4829i	−0.184874	+	0.507937i
$814$	−0.723965	−	0.607479i	−0.0253750	−	0.0212921i
$815$		0			0
$816$	3.23895			0.113386
$817$	1.08339	−	2.62042i	0.0379031	−	0.0916767i
$818$			24.9479i			0.872282i
$819$	−3.87194	+	21.9589i	−0.135297	+	0.767305i
$820$		0			0
$821$	17.1492	+	6.24180i	0.598511	+	0.217840i	0.623469	−	0.781848i	$-0.285723\pi$
$821$	17.1492	+	6.24180i	0.598511	+	0.217840i	−0.0249577	+	0.999689i	$0.507945\pi$
$822$	−8.23574	−	22.6275i	−0.287254	−	0.789225i
$823$	−10.6469	−	12.6885i	−0.371128	−	0.442294i	0.547865	−	0.836567i	$-0.315441\pi$
$823$	−10.6469	−	12.6885i	−0.371128	−	0.442294i	−0.918993	+	0.394273i	$0.870996\pi$
$824$	−18.5263	−	32.0885i	−0.645394	−	1.11785i
$825$		0			0
$826$	5.84139	+	33.1282i	0.203248	+	1.15268i
$827$	−16.5046	+	2.91020i	−0.573921	+	0.101198i	−0.453073	−	0.891473i	$-0.649672\pi$
$827$	−16.5046	+	2.91020i	−0.573921	+	0.101198i	−0.120848	+	0.992671i	$0.538561\pi$
$828$	1.51492	+	0.874641i	0.0526472	+	0.0303959i
$829$	−4.99915	−	8.65878i	−0.173628	−	0.300732i	0.766058	−	0.642772i	$-0.222216\pi$
$829$	−4.99915	−	8.65878i	−0.173628	−	0.300732i	−0.939685	+	0.342040i	$0.888882\pi$
$830$		0			0
$831$	−17.6257	+	6.41522i	−0.611428	+	0.222542i
$832$	−25.2865	+	69.4741i	−0.876652	+	2.40858i
$833$	4.71593	−	5.62023i	0.163397	−	0.194730i
$834$	4.27658	−	24.2537i	0.148086	−	0.839837i
$835$		0			0
$836$	1.08613	+	0.0467056i	0.0375647	+	0.00161535i
$837$		−	41.2264i		−	1.42499i
$838$	−57.0784	−	10.0645i	−1.97174	−	0.347671i
$839$	−34.8926	−	29.2783i	−1.20463	−	1.01080i	−0.999486	−	0.0320678i	$-0.989791\pi$
$839$	−34.8926	−	29.2783i	−1.20463	−	1.01080i	−0.205139	−	0.978733i	$-0.565765\pi$
$840$		0			0
$841$	20.7802	−	7.56339i	0.716560	−	0.260807i
$842$	36.0910	+	43.0116i	1.24378	+	1.48228i
$843$	3.48834	−	2.01399i	0.120145	−	0.0693656i
$844$	11.2974	−	19.5677i	0.388874	−	0.673549i
$845$		0			0
$846$	5.12778	+	29.0811i	0.176297	+	0.999828i
$847$	−19.2789	−	11.1306i	−0.662429	−	0.382454i
$848$	15.5563	−	8.98142i	0.534205	−	0.308423i
$849$	17.7038	−	14.8552i	0.607592	−	0.509830i
$850$		0			0
$851$	−1.45602	−	0.529948i	−0.0499117	−	0.0181664i
$852$	28.1011	−	33.4896i	0.962729	−	1.14734i
$853$	−25.1133	−	4.42816i	−0.859864	−	0.151617i	−0.273706	−	0.961814i	$-0.588249\pi$
$853$	−25.1133	−	4.42816i	−0.859864	−	0.151617i	−0.586159	+	0.810196i	$0.699360\pi$
$854$	−59.9428			−2.05120
$855$		0			0
$856$	−10.6542			−0.364152
$857$	−7.13511	−	1.25811i	−0.243731	−	0.0429763i	0.0504481	−	0.998727i	$-0.483935\pi$
$857$	−7.13511	−	1.25811i	−0.243731	−	0.0429763i	−0.294179	+	0.955750i	$0.595046\pi$
$858$	−0.718920	+	0.856775i	−0.0245435	+	0.0292498i
$859$	−28.2917	−	10.2973i	−0.965300	−	0.351340i	−0.189192	−	0.981940i	$-0.560587\pi$
$859$	−28.2917	−	10.2973i	−0.965300	−	0.351340i	−0.776108	+	0.630600i	$0.782809\pi$
$860$		0			0
$861$	9.45973	−	7.93766i	0.322387	−	0.270515i
$862$	−73.5118	+	42.4421i	−2.50382	+	1.44558i
$863$	6.47754	+	3.73981i	0.220498	+	0.127305i	0.606181	−	0.795327i	$-0.292701\pi$
$863$	6.47754	+	3.73981i	0.220498	+	0.127305i	−0.385683	+	0.922631i	$0.626034\pi$
$864$	6.14066	+	34.8254i	0.208910	+	1.18478i
$865$		0			0
$866$	2.91293	−	5.04534i	0.0989853	−	0.171448i
$867$	−9.51547	+	5.49376i	−0.323162	+	0.186578i
$868$	30.9004	+	36.8256i	1.04883	+	1.24994i
$869$	0.00923712	−	0.00336204i	0.000313348	−	0.000114049i
$870$		0			0
$871$	38.9275	+	32.6640i	1.31901	+	1.10678i
$872$	12.6315	+	2.22728i	0.427757	+	0.0754251i
$873$		−	0.434779i		−	0.0147150i
$874$	2.85546	−	0.902389i	0.0965874	−	0.0305238i
$875$		0			0
$876$	5.74782	−	32.5975i	0.194201	−	1.10137i
$877$	15.8639	−	18.9058i	0.535684	−	0.638404i	−0.428530	−	0.903528i	$-0.640968\pi$
$877$	15.8639	−	18.9058i	0.535684	−	0.638404i	0.964214	+	0.265124i	$0.0854128\pi$
$878$	5.10615	−	14.0290i	0.172324	−	0.473457i
$879$	−23.8269	+	8.67230i	−0.803663	+	0.292509i
$880$		0			0
$881$	−3.65124	−	6.32413i	−0.123013	−	0.213065i	0.797941	−	0.602735i	$-0.205922\pi$
$881$	−3.65124	−	6.32413i	−0.123013	−	0.213065i	−0.920955	+	0.389670i	$0.872589\pi$
$882$	10.7405	+	6.20100i	0.361650	+	0.208799i
$883$	−43.1489	+	7.60832i	−1.45208	+	0.256040i	−0.843361	−	0.537347i	$-0.819426\pi$
$883$	−43.1489	+	7.60832i	−1.45208	+	0.256040i	−0.608717	+	0.793388i	$0.708315\pi$
$884$	7.39291	+	41.9273i	0.248650	+	1.41017i
$885$		0			0
$886$	−28.9023	−	50.0602i	−0.970991	−	1.68181i
$887$	−31.7486	−	37.8365i	−1.06601	−	1.27042i	−0.961176	−	0.275935i	$-0.911013\pi$
$887$	−31.7486	−	37.8365i	−1.06601	−	1.27042i	−0.104836	−	0.994489i	$-0.533432\pi$
$888$	3.71716	+	10.2128i	0.124740	+	0.342719i
$889$	2.73983	+	0.997216i	0.0918909	+	0.0334456i
$890$		0			0
$891$	0.00704117	−	0.0399325i	0.000235888	−	0.00133779i
$892$			7.29249i			0.244170i
$893$	25.3870	+	16.1498i	0.849544	+	0.540434i
$894$	−11.6278			−0.388890
$895$		0			0
$896$	−23.0765	−	19.3635i	−0.770933	−	0.646890i
$897$	−0.627165	+	1.72312i	−0.0209404	+	0.0575334i
$898$	20.9608	+	57.5894i	0.699472	+	1.92178i
$899$	−16.2280	+	13.6169i	−0.541233	+	0.454149i
$900$		0			0
$901$	18.4166	−	31.8984i	0.613544	−	1.06269i
$902$	−1.09174	+	0.192503i	−0.0363509	+	0.00640965i
$903$	−1.34534	+	0.237220i	−0.0447702	+	0.00789419i
$904$	−11.9497	+	20.6975i	−0.397441	+	0.688388i
$905$		0			0
$906$	−36.7470	+	30.8344i	−1.22084	+	1.02440i
$907$	3.63818	+	9.99581i	0.120804	+	0.331905i	0.985325	−	0.170692i	$-0.0546002\pi$
$907$	3.63818	+	9.99581i	0.120804	+	0.331905i	−0.864521	+	0.502597i	$0.832378\pi$
$908$	0.456154	−	1.25327i	0.0151380	−	0.0415914i
$909$	−18.5789	−	15.5895i	−0.616222	−	0.517071i
$910$		0			0
$911$	−40.5583			−1.34376			−0.671878	−	0.740662i	$-0.734512\pi$
$911$	−40.5583			−1.34376			−0.671878	+	0.740662i	$0.734512\pi$
$912$	4.70704	+	2.99436i	0.155866	+	0.0991532i
$913$			0.252371i			0.00835225i
$914$	0.858886	−	4.87099i	0.0284094	−	0.161118i
$915$		0			0
$916$	−2.74467	−	0.998978i	−0.0906864	−	0.0330072i
$917$	−0.695008	−	1.90952i	−0.0229512	−	0.0630579i
$918$	18.4651	+	22.0059i	0.609440	+	0.726303i
$919$	19.1728	+	33.2083i	0.632453	+	1.09544i	0.987049	+	0.160421i	$0.0512850\pi$
$919$	19.1728	+	33.2083i	0.632453	+	1.09544i	−0.354596	+	0.935020i	$0.615382\pi$
$920$		0			0
$921$	1.15701	+	6.56171i	0.0381247	+	0.216216i
$922$	44.7760	−	7.89522i	1.47462	−	0.260015i
$923$	−71.0306	−	41.0096i	−2.33800	−	1.34985i
$924$	−0.261877	−	0.453585i	−0.00861514	−	0.0149219i
$925$		0			0
$926$	−67.7363	+	24.6540i	−2.22595	+	0.810180i
$927$	−11.6664	+	32.0532i	−0.383175	+	1.05276i
$928$	11.6801	−	13.9198i	0.383419	−	0.456940i
$929$	−7.57843	+	42.9794i	−0.248640	+	1.41011i	0.563244	+	0.826290i	$0.309553\pi$
$929$	−7.57843	+	42.9794i	−0.248640	+	1.41011i	−0.811884	+	0.583818i	$0.801558\pi$
$930$		0			0
$931$	12.0493	−	3.80785i	0.394901	−	0.124797i
$932$		−	12.5363i		−	0.410639i
$933$	17.9372	+	3.16281i	0.587237	+	0.103546i
$934$	−11.7845	−	9.88835i	−0.385600	−	0.323557i
$935$		0			0
$936$	−21.6313	+	7.87314i	−0.707041	+	0.257342i
$937$	−23.0849	−	27.5115i	−0.754150	−	0.898760i	0.243313	−	0.969948i	$-0.421766\pi$
$937$	−23.0849	−	27.5115i	−0.754150	−	0.898760i	−0.997463	+	0.0711873i	$0.977321\pi$
$938$	−34.6253	+	19.9909i	−1.13056	+	0.652727i
$939$	−1.88921	+	3.27220i	−0.0616519	+	0.106784i
$940$		0			0
$941$	5.36936	+	30.4512i	0.175036	+	0.992680i	0.938102	+	0.346359i	$0.112582\pi$
$941$	5.36936	+	30.4512i	0.175036	+	0.992680i	−0.763066	+	0.646321i	$0.776307\pi$
$942$	47.1413	+	27.2170i	1.53595	+	0.886779i
$943$	−1.57404	+	0.908772i	−0.0512578	+	0.0295937i
$944$	7.06561	−	5.92875i	0.229966	−	0.192964i
$945$		0			0
$946$	0.115242	+	0.0419445i	0.00374683	+	0.00136373i
$947$	−7.17756	+	8.55388i	−0.233239	+	0.277964i	−0.869951	−	0.493138i	$-0.835850\pi$
$947$	−7.17756	+	8.55388i	−0.233239	+	0.277964i	0.636712	+	0.771102i	$0.280294\pi$
$948$	−0.348047	−	0.0613701i	−0.0113040	−	0.00199321i
$949$	−62.1000			−2.01585
$950$		0			0
$951$	4.66548			0.151288
$952$	−10.5516	−	1.86053i	−0.341978	−	0.0603000i
$953$	−4.75909	+	5.67166i	−0.154162	+	0.183723i	−0.837598	−	0.546288i	$-0.816041\pi$
$953$	−4.75909	+	5.67166i	−0.154162	+	0.183723i	0.683436	+	0.730011i	$0.260485\pi$
$954$	58.5081	+	21.2952i	1.89427	+	0.689458i
$955$		0			0
$956$	55.0949	−	46.2301i	1.78190	−	1.49519i
$957$	0.199882	−	0.115402i	0.00646125	−	0.00373041i
$958$	38.5833	+	22.2761i	1.24657	+	0.719708i
$959$	−3.67363	−	20.8342i	−0.118628	−	0.672771i
$960$		0			0
$961$	−17.0849	+	29.5918i	−0.551124	+	0.954575i
$962$	55.2063	−	31.8734i	1.77992	−	1.02764i
$963$	6.30455	+	7.51347i	0.203161	+	0.242118i
$964$	12.1440	−	4.42005i	0.391131	−	0.142360i
$965$		0			0
$966$	−1.10521	−	0.927382i	−0.0355596	−	0.0298380i
$967$	−17.3112	−	3.05244i	−0.556692	−	0.0981598i	−0.111778	−	0.993733i	$-0.535655\pi$
$967$	−17.3112	−	3.05244i	−0.556692	−	0.0981598i	−0.444914	+	0.895573i	$0.646766\pi$
$968$		−	22.9820i		−	0.738671i
$969$	11.4287	+	0.491457i	0.367144	+	0.0157879i
$970$		0			0
$971$	−0.922819	+	5.23357i	−0.0296147	+	0.167953i	−0.996028	−	0.0890391i	$-0.971620\pi$
$971$	−0.922819	+	5.23357i	−0.0296147	+	0.167953i	0.966413	+	0.256992i	$0.0827315\pi$
$972$	−29.8954	+	35.6279i	−0.958895	+	1.14277i
$973$	7.40035	−	20.3323i	0.237244	−	0.651823i
$974$	−14.8909	+	5.41983i	−0.477134	+	0.173662i
$975$		0			0
$976$	8.21783	+	14.2337i	0.263046	+	0.455609i
$977$	−11.8218	−	6.82533i	−0.378214	−	0.218362i	0.298827	−	0.954307i	$-0.403405\pi$
$977$	−11.8218	−	6.82533i	−0.378214	−	0.218362i	−0.677041	+	0.735946i	$0.736738\pi$
$978$	0.484712	−	0.0854678i	0.0154994	−	0.00273296i
$979$	0.163862	+	0.929310i	0.00523707	+	0.0297009i
$980$		0			0
$981$	−5.90392	−	10.2259i	−0.188498	−	0.326488i
$982$	−23.5817	−	28.1035i	−0.752521	−	0.896820i
$983$	9.83639	+	27.0252i	0.313732	+	0.861972i	0.991895	+	0.127060i	$0.0405541\pi$
$983$	9.83639	+	27.0252i	0.313732	+	0.861972i	−0.678163	+	0.734912i	$0.737224\pi$
$984$	11.9798	+	4.36028i	0.381901	+	0.139001i
$985$		0			0
$986$	2.56324	−	14.5369i	0.0816303	−	0.462949i
$987$		−	14.4959i		−	0.461409i
$988$	−28.0174	+	67.7660i	−0.891351	+	2.15592i
$989$	0.201067			0.00639357
$990$		0			0
$991$	−43.2774	−	36.3141i	−1.37475	−	1.15355i	−0.971109	−	0.238638i	$-0.923299\pi$
$991$	−43.2774	−	36.3141i	−1.37475	−	1.15355i	−0.403643	−	0.914916i	$-0.632256\pi$
$992$	19.1191	−	52.5292i	0.607031	−	1.66780i
$993$	12.0945	+	33.2295i	0.383808	+	1.05451i
$994$	49.4345	−	41.4804i	1.56797	−	1.31568i
$995$		0			0
$996$	4.53675	−	7.85787i	0.143752	−	0.248986i
$997$	13.9018	−	2.45126i	0.440274	−	0.0776323i	0.0508830	−	0.998705i	$-0.483796\pi$
$997$	13.9018	−	2.45126i	0.440274	−	0.0776323i	0.389391	+	0.921072i	$0.372685\pi$
$998$	66.4583	−	11.7184i	2.10370	−	0.370939i
$999$	12.8004	−	22.1709i	0.404986	−	0.701456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.b.74.1		36
5.2	odd	4		475.2.l.c.226.3		18
5.3	odd	4		95.2.k.a.36.1	✓	18
5.4	even	2	inner	475.2.u.b.74.6		36
15.8	even	4		855.2.bs.c.226.3		18
19.9	even	9	inner	475.2.u.b.199.6		36
95.3	even	36		1805.2.a.s.1.9		9
95.9	even	18	inner	475.2.u.b.199.1		36
95.22	even	36		9025.2.a.cf.1.1		9
95.28	odd	36		95.2.k.a.66.1	yes	18
95.47	odd	36		475.2.l.c.351.3		18
95.73	odd	36		1805.2.a.v.1.1		9
95.92	odd	36		9025.2.a.cc.1.9		9
285.218	even	36		855.2.bs.c.541.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.1	✓	18	5.3	odd	4
95.2.k.a.66.1	yes	18	95.28	odd	36
475.2.l.c.226.3		18	5.2	odd	4
475.2.l.c.351.3		18	95.47	odd	36
475.2.u.b.74.1		36	1.1	even	1	trivial
475.2.u.b.74.6		36	5.4	even	2	inner
475.2.u.b.199.1		36	95.9	even	18	inner
475.2.u.b.199.6		36	19.9	even	9	inner
855.2.bs.c.226.3		18	15.8	even	4
855.2.bs.c.541.3		18	285.218	even	36
1805.2.a.s.1.9		9	95.3	even	36
1805.2.a.v.1.1		9	95.73	odd	36
9025.2.a.cc.1.9		9	95.92	odd	36
9025.2.a.cf.1.1		9	95.22	even	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.18897 - 0.385975i) q^{2} +(0.666572 - 0.794389i) q^{3} +(2.76323 + 1.00573i) q^{4} +(-1.76572 + 1.48162i) q^{6} +(-1.75377 + 1.01254i) q^{7} +(-1.81055 - 1.04532i) q^{8} +(0.334208 + 1.89539i) q^{9} +O(q^{10})\)	\(q+(-2.18897 - 0.385975i) q^{2} +(0.666572 - 0.794389i) q^{3} +(2.76323 + 1.00573i) q^{4} +(-1.76572 + 1.48162i) q^{6} +(-1.75377 + 1.01254i) q^{7} +(-1.81055 - 1.04532i) q^{8} +(0.334208 + 1.89539i) q^{9} +(-0.0424078 + 0.0734524i) q^{11} +(2.64084 - 1.52469i) q^{12} +(-3.67737 - 4.38252i) q^{13} +(4.22977 - 1.53951i) q^{14} +(-0.945441 - 0.793319i) q^{16} +(-2.49227 - 0.439455i) q^{17} -4.27795i q^{18} +(-3.21565 - 2.94271i) q^{19} +(-0.364663 + 2.06811i) q^{21} +(0.121180 - 0.144417i) q^{22} +(0.105714 - 0.290447i) q^{23} +(-2.03725 + 0.741500i) q^{24} +(6.35811 + 11.0126i) q^{26} +(4.42266 + 2.55342i) q^{27} +(-5.86442 + 1.03406i) q^{28} +(-0.455678 - 2.58428i) q^{29} +(-4.03639 - 6.99123i) q^{31} +(4.45102 + 5.30452i) q^{32} +(0.0300820 + 0.0826495i) q^{33} +(5.28589 + 1.92391i) q^{34} +(-0.982763 + 5.57352i) q^{36} -5.01303i q^{37} +(5.90316 + 7.68268i) q^{38} -5.93265 q^{39} +(-4.50461 - 3.77982i) q^{41} +(1.59647 - 4.38627i) q^{42} +(0.222491 + 0.611288i) q^{43} +(-0.191056 + 0.160315i) q^{44} +(-0.343511 + 0.594978i) q^{46} +(-6.79791 + 1.19865i) q^{47} +(-1.26041 + 0.222244i) q^{48} +(-1.44953 + 2.51066i) q^{49} +(-2.01037 + 1.68690i) q^{51} +(-5.75378 - 15.8084i) q^{52} +(-4.97790 + 13.6767i) q^{53} +(-8.69551 - 7.29640i) q^{54} +4.23372 q^{56} +(-4.48112 + 0.592951i) q^{57} +5.83278i q^{58} +(-1.29773 + 7.35981i) q^{59} +(-12.5139 - 4.55468i) q^{61} +(6.13710 + 16.8615i) q^{62} +(-2.50528 - 2.98568i) q^{63} +(-6.46156 - 11.1918i) q^{64} +(-0.0339479 - 0.192528i) q^{66} +(-8.74750 + 1.54242i) q^{67} +(-6.44475 - 3.72088i) q^{68} +(-0.160262 - 0.277582i) q^{69} +(13.4720 - 4.90340i) q^{71} +(1.37619 - 3.78105i) q^{72} +(6.97733 - 8.31526i) q^{73} +(-1.93490 + 10.9734i) q^{74} +(-5.92601 - 11.3655i) q^{76} -0.171758i q^{77} +(12.9864 + 2.28985i) q^{78} +(-0.0887829 - 0.0744977i) q^{79} +(-0.449247 + 0.163512i) q^{81} +(8.40155 + 10.0126i) q^{82} +(2.57688 - 1.48776i) q^{83} +(-3.08761 + 5.34790i) q^{84} +(-0.251084 - 1.42397i) q^{86} +(-2.35666 - 1.36062i) q^{87} +(0.153563 - 0.0886595i) q^{88} +(8.52291 - 7.15157i) q^{89} +(10.8867 + 3.96245i) q^{91} +(0.584226 - 0.696253i) q^{92} +(-8.24430 - 1.45369i) q^{93} +15.3431 q^{94} +7.18078 q^{96} +(-0.222471 - 0.0392276i) q^{97} +(4.14202 - 4.93627i) q^{98} +(-0.153394 - 0.0558308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49} - 90 q^{51} + 132 q^{54} - 36 q^{59} - 60 q^{61} - 72 q^{64} + 78 q^{66} - 30 q^{69} - 24 q^{71} + 30 q^{74} - 66 q^{76} + 102 q^{79} + 54 q^{81} - 96 q^{84} + 126 q^{86} + 108 q^{89} + 60 q^{91} - 60 q^{94} - 132 q^{96} + 186 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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