LMFDB - Embedded newform 570.2.n.a.449.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(179,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("570.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.11
Character	$\chi$	$=$	570.449
Dual form			570.2.n.a.179.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.0777329 + 1.73031i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917815 - 2.03902i) q^{5} +(-0.797834 - 1.53736i) q^{6} -0.0202833i q^{7} +1.00000i q^{8} +(-2.98792 - 0.269003i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.0777329 + 1.73031i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917815 - 2.03902i) q^{5} +(-0.797834 - 1.53736i) q^{6} -0.0202833i q^{7} +1.00000i q^{8} +(-2.98792 - 0.269003i) q^{9} +(0.224660 + 2.22475i) q^{10} -3.99162i q^{11} +(1.45962 + 0.932471i) q^{12} +(0.686480 - 1.18902i) q^{13} +(0.0101416 + 0.0175658i) q^{14} +(3.45679 + 1.74660i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.52225 - 2.63661i) q^{17} +(2.72211 - 1.26099i) q^{18} +(2.10968 - 3.81435i) q^{19} +(-1.30694 - 1.81436i) q^{20} +(0.0350963 + 0.00157668i) q^{21} +(1.99581 + 3.45685i) q^{22} +(0.607462 - 1.05215i) q^{23} +(-1.73031 - 0.0777329i) q^{24} +(-3.31523 - 3.74289i) q^{25} +1.37296i q^{26} +(0.697717 - 5.14910i) q^{27} +(-0.0175658 - 0.0101416i) q^{28} +(-3.04800 + 5.27930i) q^{29} +(-3.86697 + 0.215794i) q^{30} -4.41969i q^{31} +(0.866025 + 0.500000i) q^{32} +(6.90673 + 0.310280i) q^{33} +(2.63661 + 1.52225i) q^{34} +(-0.0413581 - 0.0186163i) q^{35} +(-1.72692 + 2.45311i) q^{36} -2.82556 q^{37} +(0.0801327 + 4.35816i) q^{38} +(2.00400 + 1.28025i) q^{39} +(2.03902 + 0.917815i) q^{40} +(0.581569 + 1.00731i) q^{41} +(-0.0311826 + 0.0161827i) q^{42} +(3.23394 - 1.86712i) q^{43} +(-3.45685 - 1.99581i) q^{44} +(-3.29086 + 5.84553i) q^{45} +1.21492i q^{46} +(3.51393 - 6.08631i) q^{47} +(1.53736 - 0.797834i) q^{48} +6.99959 q^{49} +(4.74252 + 1.58383i) q^{50} +(4.68048 - 2.42901i) q^{51} +(-0.686480 - 1.18902i) q^{52} +(10.6188 + 6.13079i) q^{53} +(1.97031 + 4.80811i) q^{54} +(-8.13901 - 3.66357i) q^{55} +0.0202833 q^{56} +(6.43599 + 3.94690i) q^{57} -6.09601i q^{58} +(5.07177 + 8.78455i) q^{59} +(3.24099 - 2.12037i) q^{60} +(-1.34395 + 2.32779i) q^{61} +(2.20984 + 3.82756i) q^{62} +(-0.00545627 + 0.0606047i) q^{63} -1.00000 q^{64} +(-1.79437 - 2.49105i) q^{65} +(-6.13654 + 3.18465i) q^{66} +(1.47926 - 2.56216i) q^{67} -3.04450 q^{68} +(1.77333 + 1.13288i) q^{69} +(0.0451253 - 0.00455684i) q^{70} +(0.990840 + 1.71618i) q^{71} +(0.269003 - 2.98792i) q^{72} +(-6.30417 + 3.63971i) q^{73} +(2.44701 - 1.41278i) q^{74} +(6.73405 - 5.44542i) q^{75} +(-2.24848 - 3.73421i) q^{76} -0.0809632 q^{77} +(-2.37564 - 0.106724i) q^{78} +(8.41583 - 4.85888i) q^{79} +(-2.22475 + 0.224660i) q^{80} +(8.85527 + 1.60752i) q^{81} +(-1.00731 - 0.581569i) q^{82} -7.08504 q^{83} +(0.0189136 - 0.0296059i) q^{84} +(-6.77326 + 0.683977i) q^{85} +(-1.86712 + 3.23394i) q^{86} +(-8.89787 - 5.68435i) q^{87} +3.99162 q^{88} +(-6.40211 + 11.0888i) q^{89} +(-0.0727995 - 6.70781i) q^{90} +(-0.0241172 - 0.0139241i) q^{91} +(-0.607462 - 1.05215i) q^{92} +(7.64741 + 0.343555i) q^{93} +7.02786i q^{94} +(-5.84124 - 7.80256i) q^{95} +(-0.932471 + 1.45962i) q^{96} +(-5.81546 - 10.0727i) q^{97} +(-6.06182 + 3.49979i) q^{98} +(-1.07376 + 11.9266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4}+O(q^{10}) $ 80 * q + 40 * q^4	$ 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.0777329	+	1.73031i	−0.0448791	+	0.998992i
$3$	−0.0777329	+	1.73031i	−0.0448791	+	0.998992i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.917815	−	2.03902i	0.410460	−	0.911879i
$5$	0.917815	−	2.03902i	0.410460	−	0.911879i
$6$	−0.797834	−	1.53736i	−0.325714	−	0.627623i
$7$		−	0.0202833i		−	0.00766636i	−0.999993	−	0.00383318i	$-0.998780\pi$
$7$		−	0.0202833i		−	0.00766636i	0.999993	−	0.00383318i	$-0.00122014\pi$
$8$			1.00000i			0.353553i
$9$	−2.98792	−	0.269003i	−0.995972	−	0.0896677i
$10$	0.224660	+	2.22475i	0.0710438	+	0.703529i
$11$		−	3.99162i		−	1.20352i	−0.798677	−	0.601760i	$-0.794466\pi$
$11$		−	3.99162i		−	1.20352i	0.798677	−	0.601760i	$-0.205534\pi$
$12$	1.45962	+	0.932471i	0.421357	+	0.269181i
$13$	0.686480	−	1.18902i	0.190395	−	0.329774i	−0.754986	−	0.655741i	$-0.772356\pi$
$13$	0.686480	−	1.18902i	0.190395	−	0.329774i	0.945381	+	0.325967i	$0.105690\pi$
$14$	0.0101416	+	0.0175658i	0.00271047	+	0.00469467i
$15$	3.45679	+	1.74660i	0.892539	+	0.450970i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.52225	−	2.63661i	−0.369200	−	0.639473i	0.620241	−	0.784411i	$-0.287035\pi$
$17$	−1.52225	−	2.63661i	−0.369200	−	0.639473i	−0.989441	+	0.144939i	$0.953702\pi$
$18$	2.72211	−	1.26099i	0.641608	−	0.297219i
$19$	2.10968	−	3.81435i	0.483995	−	0.875071i
$19$	2.10968	−	3.81435i	0.483995	−	0.875071i
$20$	−1.30694	−	1.81436i	−0.292240	−	0.405704i
$21$	0.0350963	+	0.00157668i	0.00765863	+	0.000344059i
$22$	1.99581	+	3.45685i	0.425509	+	0.737003i
$23$	0.607462	−	1.05215i	0.126665	−	0.219389i	−0.795718	−	0.605668i	$-0.792906\pi$
$23$	0.607462	−	1.05215i	0.126665	−	0.219389i	0.922382	+	0.386278i	$0.126239\pi$
$24$	−1.73031	−	0.0777329i	−0.353197	−	0.0158672i
$25$	−3.31523	−	3.74289i	−0.663046	−	0.748579i
$26$			1.37296i			0.269260i
$27$	0.697717	−	5.14910i	0.134276	−	0.990944i
$28$	−0.0175658	−	0.0101416i	−0.00331963	−	0.00191659i
$29$	−3.04800	+	5.27930i	−0.566000	+	0.980341i	0.430956	+	0.902373i	$0.358177\pi$
$29$	−3.04800	+	5.27930i	−0.566000	+	0.980341i	−0.996956	+	0.0779679i	$0.975157\pi$
$30$	−3.86697	+	0.215794i	−0.706008	+	0.0393984i
$31$		−	4.41969i		−	0.793799i	−0.917862	−	0.396900i	$-0.870086\pi$
$31$		−	4.41969i		−	0.793799i	0.917862	−	0.396900i	$-0.129914\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	6.90673	+	0.310280i	1.20231	+	0.0540129i
$34$	2.63661	+	1.52225i	0.452176	+	0.261064i
$35$	−0.0413581	−	0.0186163i	−0.00699079	−	0.00314673i
$36$	−1.72692	+	2.45311i	−0.287820	+	0.408851i
$37$	−2.82556			−0.464519			−0.232260	−	0.972654i	$-0.574612\pi$
$37$	−2.82556			−0.464519			−0.232260	+	0.972654i	$0.574612\pi$
$38$	0.0801327	+	4.35816i	0.0129992	+	0.706987i
$39$	2.00400	+	1.28025i	0.320897	+	0.205004i
$40$	2.03902	+	0.917815i	0.322398	+	0.145119i
$41$	0.581569	+	1.00731i	0.0908258	+	0.157315i	0.907859	−	0.419276i	$-0.137716\pi$
$41$	0.581569	+	1.00731i	0.0908258	+	0.157315i	−0.817033	+	0.576591i	$0.804383\pi$
$42$	−0.0311826	+	0.0161827i	−0.00481158	+	0.00249704i
$43$	3.23394	−	1.86712i	0.493172	−	0.284733i	−0.232718	−	0.972544i	$-0.574762\pi$
$43$	3.23394	−	1.86712i	0.493172	−	0.284733i	0.725889	+	0.687812i	$0.241428\pi$
$44$	−3.45685	−	1.99581i	−0.521140	−	0.300880i
$45$	−3.29086	+	5.84553i	−0.490572	+	0.871401i
$46$			1.21492i			0.179131i
$47$	3.51393	−	6.08631i	0.512560	−	0.887779i	−0.487334	−	0.873216i	$-0.662031\pi$
$47$	3.51393	−	6.08631i	0.512560	−	0.887779i	0.999894	−	0.0145639i	$-0.00463601\pi$
$48$	1.53736	−	0.797834i	0.221898	−	0.115157i
$49$	6.99959			0.999941
$50$	4.74252	+	1.58383i	0.670694	+	0.223987i
$51$	4.68048	−	2.42901i	0.655398	−	0.340129i
$52$	−0.686480	−	1.18902i	−0.0951977	−	0.164887i
$53$	10.6188	+	6.13079i	1.45861	+	0.842129i	0.998943	−	0.0459626i	$-0.0146355\pi$
$53$	10.6188	+	6.13079i	1.45861	+	0.842129i	0.459667	+	0.888091i	$0.347969\pi$
$54$	1.97031	+	4.80811i	0.268125	+	0.654300i
$55$	−8.13901	−	3.66357i	−1.09746	−	0.493996i
$56$	0.0202833			0.00271047
$57$	6.43599	+	3.94690i	0.852468	+	0.522779i
$58$		−	6.09601i		−	0.800445i
$59$	5.07177	+	8.78455i	0.660288	+	1.14365i	0.980540	+	0.196319i	$0.0628989\pi$
$59$	5.07177	+	8.78455i	0.660288	+	1.14365i	−0.320252	+	0.947332i	$0.603768\pi$
$60$	3.24099	−	2.12037i	0.418411	−	0.273738i
$61$	−1.34395	+	2.32779i	−0.172075	+	0.298043i	−0.939145	−	0.343521i	$-0.888380\pi$
$61$	−1.34395	+	2.32779i	−0.172075	+	0.298043i	0.767070	+	0.641563i	$0.221714\pi$
$62$	2.20984	+	3.82756i	0.280650	+	0.486101i
$63$	−0.00545627	+	0.0606047i	−0.000687425	+	0.00763548i
$64$	−1.00000			−0.125000
$65$	−1.79437	−	2.49105i	−0.222565	−	0.308977i
$66$	−6.13654	+	3.18465i	−0.755356	+	0.392004i
$67$	1.47926	−	2.56216i	0.180721	−	0.313017i	−0.761406	−	0.648276i	$-0.775490\pi$
$67$	1.47926	−	2.56216i	0.180721	−	0.313017i	0.942126	+	0.335259i	$0.108824\pi$
$68$	−3.04450			−0.369200
$69$	1.77333	+	1.13288i	0.213484	+	0.136383i
$70$	0.0451253	−	0.00455684i	0.00539350	−	0.000544647i
$71$	0.990840	+	1.71618i	0.117591	+	0.203674i	0.918813	−	0.394694i	$-0.129149\pi$
$71$	0.990840	+	1.71618i	0.117591	+	0.203674i	−0.801221	+	0.598368i	$0.795816\pi$
$72$	0.269003	−	2.98792i	0.0317023	−	0.352129i
$73$	−6.30417	+	3.63971i	−0.737847	+	0.425996i	−0.821286	−	0.570517i	$-0.806743\pi$
$73$	−6.30417	+	3.63971i	−0.737847	+	0.425996i	0.0834387	+	0.996513i	$0.473410\pi$
$74$	2.44701	−	1.41278i	0.284459	−	0.164232i
$75$	6.73405	−	5.44542i	0.777581	−	0.628782i
$76$	−2.24848	−	3.73421i	−0.257918	−	0.428344i
$77$	−0.0809632			−0.00922662
$78$	−2.37564	−	0.106724i	−0.268988	−	0.0120841i
$79$	8.41583	−	4.85888i	0.946855	−	0.546667i	0.0547523	−	0.998500i	$-0.482563\pi$
$79$	8.41583	−	4.85888i	0.946855	−	0.546667i	0.892102	+	0.451833i	$0.149230\pi$
$80$	−2.22475	+	0.224660i	−0.248735	+	0.0251178i
$81$	8.85527	+	1.60752i	0.983919	+	0.178613i
$82$	−1.00731	−	0.581569i	−0.111238	−	0.0642236i
$83$	−7.08504			−0.777684			−0.388842	−	0.921304i	$-0.627125\pi$
$83$	−7.08504			−0.777684			−0.388842	+	0.921304i	$0.627125\pi$
$84$	0.0189136	−	0.0296059i	0.00206364	−	0.00323027i
$85$	−6.77326	+	0.683977i	−0.734663	+	0.0741878i
$86$	−1.86712	+	3.23394i	−0.201336	+	0.348725i
$87$	−8.89787	−	5.68435i	−0.953952	−	0.609427i
$88$	3.99162			0.425509
$89$	−6.40211	+	11.0888i	−0.678623	+	1.17541i	0.296773	+	0.954948i	$0.404090\pi$
$89$	−6.40211	+	11.0888i	−0.678623	+	1.17541i	−0.975396	+	0.220461i	$0.929244\pi$
$90$	−0.0727995	−	6.70781i	−0.00767374	−	0.707065i
$91$	−0.0241172	−	0.0139241i	−0.00252817	−	0.00145964i
$92$	−0.607462	−	1.05215i	−0.0633323	−	0.109695i
$93$	7.64741	+	0.343555i	0.793000	+	0.0356250i
$94$			7.02786i			0.724869i
$95$	−5.84124	−	7.80256i	−0.599298	−	0.800526i
$96$	−0.932471	+	1.45962i	−0.0951700	+	0.148972i
$97$	−5.81546	−	10.0727i	−0.590471	−	1.02273i	−0.994169	−	0.107833i	$-0.965609\pi$
$97$	−5.81546	−	10.0727i	−0.590471	−	1.02273i	0.403698	−	0.914892i	$-0.367725\pi$
$98$	−6.06182	+	3.49979i	−0.612336	+	0.353533i
$99$	−1.07376	+	11.9266i	−0.107917	+	1.19867i
$100$	−4.89906	+	0.999626i	−0.489906	+	0.0999626i
$101$	−7.98637	−	4.61093i	−0.794674	−	0.458805i	0.0469317	−	0.998898i	$-0.485056\pi$
$101$	−7.98637	−	4.61093i	−0.794674	−	0.458805i	−0.841605	+	0.540093i	$0.818389\pi$
$102$	−2.83891	+	4.44382i	−0.281094	+	0.440004i
$103$	−11.1254			−1.09621			−0.548107	−	0.836408i	$-0.684651\pi$
$103$	−11.1254			−1.09621			−0.548107	+	0.836408i	$0.684651\pi$
$104$	1.18902	+	0.686480i	0.116593	+	0.0673149i
$105$	0.0354268	−	0.0701150i	0.00345730	−	0.00684252i
$106$	−12.2616			−1.19095
$107$		−	10.6451i		−	1.02910i	−0.857461	−	0.514548i	$-0.827960\pi$
$107$		−	10.6451i		−	1.02910i	0.857461	−	0.514548i	$-0.172040\pi$
$108$	−4.11039	−	3.17879i	−0.395522	−	0.305879i
$109$	−1.79769	+	1.03789i	−0.172187	+	0.0994123i	−0.583617	−	0.812029i	$-0.698363\pi$
$109$	−1.79769	+	1.03789i	−0.172187	+	0.0994123i	0.411430	+	0.911442i	$0.365030\pi$
$110$	8.88038	−	0.896759i	0.846711	−	0.0855026i
$111$	0.219639	−	4.88908i	0.0208472	−	0.464051i
$112$	−0.0175658	+	0.0101416i	−0.00165982	+	0.000958295i
$113$		−	6.98424i		−	0.657022i	−0.944500	−	0.328511i	$-0.893453\pi$
$113$		−	6.98424i		−	0.657022i	0.944500	−	0.328511i	$-0.106547\pi$
$114$	−7.54718	−	0.200118i	−0.706858	−	0.0187428i
$115$	−1.58783	−	2.20431i	−0.148066	−	0.205553i
$116$	3.04800	+	5.27930i	0.283000	+	0.490171i
$117$	−2.37099	+	3.36802i	−0.219199	+	0.311374i
$118$	−8.78455	−	5.07177i	−0.808684	−	0.466894i
$119$	−0.0534792	+	0.0308762i	−0.00490243	+	0.00283042i
$120$	−1.74660	+	3.45679i	−0.159442	+	0.315560i
$121$	−4.93307			−0.448461
$122$		−	2.68790i		−	0.243351i
$123$	−1.78816	+	0.927992i	−0.161233	+	0.0836742i
$124$	−3.82756	−	2.20984i	−0.343725	−	0.198450i
$125$	−10.6746	+	3.32454i	−0.954767	+	0.297356i
$126$	−0.0255771	−	0.0552134i	−0.00227859	−	0.00491880i
$127$	0.312266	−	0.540860i	0.0277091	−	0.0479936i	−0.851838	−	0.523805i	$-0.824512\pi$
$127$	0.312266	−	0.540860i	0.0277091	−	0.0479936i	0.879547	+	0.475811i	$0.157845\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	2.97930	+	5.74085i	0.262313	+	0.505453i
$130$	2.79950	+	1.26012i	0.245532	+	0.110520i
$131$	15.9145	−	9.18823i	1.39046	−	0.802780i	0.397090	−	0.917780i	$-0.370020\pi$
$131$	15.9145	−	9.18823i	1.39046	−	0.802780i	0.993365	+	0.115000i	$0.0366868\pi$
$132$	3.72208	−	5.82626i	0.323965	−	0.507111i
$133$	−0.0773674	−	0.0427913i	−0.00670861	−	0.00371048i
$134$			2.95852i			0.255578i
$135$	−9.85875	−	6.14858i	−0.848506	−	0.529186i
$136$	2.63661	−	1.52225i	0.226088	−	0.130532i
$137$	−7.10557	+	12.3072i	−0.607070	+	1.05148i	0.384651	+	0.923062i	$0.374322\pi$
$137$	−7.10557	+	12.3072i	−0.607070	+	1.05148i	−0.991721	+	0.128414i	$0.959011\pi$
$138$	−2.10219	−	0.0944395i	−0.178950	−	0.00803922i
$139$	−7.37218	+	12.7690i	−0.625300	+	1.08305i	0.363183	+	0.931718i	$0.381690\pi$
$139$	−7.37218	+	12.7690i	−0.625300	+	1.08305i	−0.988483	+	0.151334i	$0.951643\pi$
$140$	−0.0368012	+	0.0265090i	−0.00311027	+	0.00224042i
$141$	10.2580	+	6.55328i	0.863882	+	0.551886i
$142$	−1.71618	−	0.990840i	−0.144019	−	0.0831494i
$143$	−4.74612	−	2.74017i	−0.396890	−	0.229145i
$144$	1.26099	+	2.72211i	0.105083	+	0.226843i
$145$	7.96710	+	11.0604i	0.661632	+	0.918514i
$146$	3.63971	−	6.30417i	0.301225	−	0.521737i
$147$	−0.544098	+	12.1114i	−0.0448764	+	0.998934i
$148$	−1.41278	+	2.44701i	−0.116130	+	0.201143i
$149$	−10.2737	+	5.93151i	−0.841652	+	0.485928i	−0.857825	−	0.513941i	$-0.828185\pi$
$149$	−10.2737	+	5.93151i	−0.841652	+	0.485928i	0.0161736	+	0.999869i	$0.494852\pi$
$150$	−3.10915	+	8.08289i	−0.253861	+	0.659966i
$151$		−	16.2219i		−	1.32012i	−0.751212	−	0.660062i	$-0.770530\pi$
$151$		−	16.2219i		−	1.32012i	0.751212	−	0.660062i	$-0.229470\pi$
$152$	3.81435	+	2.10968i	0.309384	+	0.171118i
$153$	3.83910	+	8.28747i	0.310372	+	0.670002i
$154$	0.0701162	−	0.0404816i	0.00565013	−	0.00326210i
$155$	−9.01185	−	4.05646i	−0.723849	−	0.325823i
$156$	2.11073	−	1.09539i	0.168993	−	0.0877018i
$157$	11.2338	−	6.48585i	0.896557	−	0.517627i	0.0204752	−	0.999790i	$-0.493482\pi$
$157$	11.2338	−	6.48585i	0.896557	−	0.517627i	0.876081	+	0.482163i	$0.160149\pi$
$158$	−4.85888	+	8.41583i	−0.386552	+	0.669527i
$159$	−11.4336	+	17.8973i	−0.906741	+	1.41935i
$160$	1.81436	−	1.30694i	0.143438	−	0.103323i
$161$	−0.0213411	−	0.0123213i	−0.00168192	−	0.000971056i
$162$	−8.47265	+	3.03549i	−0.665674	+	0.238490i
$163$			16.7682i			1.31338i	0.754159	+	0.656692i	$0.228045\pi$
$163$			16.7682i			1.31338i	−0.754159	+	0.656692i	$0.771955\pi$
$164$	1.16314			0.0908258
$165$	6.97177	−	13.7982i	0.542752	−	1.07419i
$166$	6.13583	−	3.54252i	0.476232	−	0.274953i
$167$	19.7487	+	11.4019i	1.52820	+	0.882305i	0.999438	+	0.0335328i	$0.0106758\pi$
$167$	19.7487	+	11.4019i	1.52820	+	0.882305i	0.528759	+	0.848772i	$0.322658\pi$
$168$	−0.00157668	+	0.0350963i	−0.000121643	+	0.00270774i
$169$	5.55749	+	9.62585i	0.427499	+	0.740450i
$170$	5.52383	−	3.97897i	0.423658	−	0.305173i
$171$	−7.32963	+	10.8294i	−0.560511	+	0.828147i
$172$		−	3.73424i		−	0.284733i
$173$	7.23298	−	4.17596i	0.549913	−	0.317493i	−0.199174	−	0.979964i	$-0.563826\pi$
$173$	7.23298	−	4.17596i	0.549913	−	0.317493i	0.749087	+	0.662472i	$0.230492\pi$
$174$	10.5480	+	0.473860i	0.799639	+	0.0359232i
$175$	−0.0759182	+	0.0672437i	−0.00573887	+	0.00508315i
$176$	−3.45685	+	1.99581i	−0.260570	+	0.150440i
$177$	−15.5942	+	8.09286i	−1.17213	+	0.608296i
$178$		−	12.8042i		−	0.959718i
$179$	−4.36389			−0.326173			−0.163086	−	0.986612i	$-0.552145\pi$
$179$	−4.36389			−0.326173			−0.163086	+	0.986612i	$0.552145\pi$
$180$	3.41695	+	5.77273i	0.254684	+	0.430274i
$181$	−21.4785	−	12.4006i	−1.59649	−	0.921732i	−0.992157	−	0.124996i	$-0.960108\pi$
$181$	−21.4785	−	12.4006i	−1.59649	−	0.921732i	−0.604329	−	0.796735i	$-0.706559\pi$
$182$	0.0278481			0.00206424
$183$	−3.92331	−	2.50639i	−0.290020	−	0.185277i
$184$	1.05215	+	0.607462i	0.0775659	+	0.0447827i
$185$	−2.59334	+	5.76138i	−0.190666	+	0.423585i
$186$	−6.79463	+	3.52618i	−0.498206	+	0.258552i
$187$	−10.5244	+	6.07625i	−0.769618	+	0.444339i
$188$	−3.51393	−	6.08631i	−0.256280	−	0.443890i
$189$	−0.104441	−	0.0141520i	−0.00759693	−	0.00102941i
$190$	8.95994	+	3.83660i	0.650022	+	0.278336i
$191$		−	10.0034i		−	0.723819i	−0.932213	−	0.361909i	$-0.882125\pi$
$191$		−	10.0034i		−	0.723819i	0.932213	−	0.361909i	$-0.117875\pi$
$192$	0.0777329	−	1.73031i	0.00560989	−	0.124874i
$193$	0.319263	+	0.552980i	0.0229811	+	0.0398044i	0.877287	−	0.479966i	$-0.159351\pi$
$193$	0.319263	+	0.552980i	0.0229811	+	0.0398044i	−0.854306	+	0.519770i	$0.826018\pi$
$194$	10.0727	+	5.81546i	0.723176	+	0.417526i
$195$	4.44976	−	2.91118i	0.318654	−	0.208474i
$196$	3.49979	−	6.06182i	0.249985	−	0.432987i
$197$	10.1393			0.722398			0.361199	−	0.932489i	$-0.382367\pi$
$197$	10.1393			0.722398			0.361199	+	0.932489i	$0.382367\pi$
$198$	−5.03341	−	10.8657i	−0.357709	−	0.772188i
$199$	4.66809	−	8.08537i	0.330912	−	0.573157i	−0.651779	−	0.758409i	$-0.725977\pi$
$199$	4.66809	−	8.08537i	0.330912	−	0.573157i	0.982691	+	0.185252i	$0.0593102\pi$
$200$	3.74289	−	3.31523i	0.264663	−	0.234422i
$201$	4.31833	+	2.75874i	0.304591	+	0.194586i
$202$	9.22187			0.648848
$203$	0.107081	+	0.0618235i	0.00751565	+	0.00433916i
$204$	0.236658	−	5.26791i	0.0165693	−	0.368828i
$205$	2.58770	−	0.261311i	0.180733	−	0.0182507i
$206$	9.63485	−	5.56268i	0.671292	−	0.387570i
$207$	−2.09808	+	2.98034i	−0.145826	+	0.207148i
$208$	−1.37296			−0.0951977
$209$	−15.2254	−	8.42107i	−1.05317	−	0.582497i
$210$	0.00437701	+	0.0784348i	0.000302043	+	0.00541251i
$211$	−22.4081	+	12.9373i	−1.54264	+	0.890641i	−0.543964	+	0.839108i	$0.683077\pi$
$211$	−22.4081	+	12.9373i	−1.54264	+	0.890641i	−0.998671	+	0.0515325i	$0.983589\pi$
$212$	10.6188	−	6.13079i	0.729305	−	0.421064i
$213$	−3.04654	+	1.58105i	−0.208746	+	0.108332i
$214$	5.32253	+	9.21889i	0.363840	+	0.630190i
$215$	−0.838934	−	8.30775i	−0.0572148	−	0.566584i
$216$	5.14910	+	0.697717i	0.350352	+	0.0474736i
$217$	−0.0896458			−0.00608555
$218$	1.03789	−	1.79769i	0.0702951	−	0.121755i
$219$	−5.80778	−	11.1911i	−0.392453	−	0.756222i
$220$	−7.24226	+	5.21681i	−0.488273	+	0.351717i
$221$	−4.17998			−0.281176
$222$	2.25433	+	4.34389i	0.151301	+	0.291543i
$223$	10.0501	+	17.4073i	0.673005	+	1.16568i	0.977048	+	0.213021i	$0.0683302\pi$
$223$	10.0501	+	17.4073i	0.673005	+	1.16568i	−0.304042	+	0.952658i	$0.598336\pi$
$224$	0.0101416	−	0.0175658i	0.000677617	−	0.00117367i
$225$	8.89878	+	12.0753i	0.593252	+	0.805017i
$226$	3.49212	+	6.04853i	0.232292	+	0.402342i
$227$		−	25.1897i		−	1.67190i	−0.548804	−	0.835951i	$-0.684917\pi$
$227$		−	25.1897i		−	1.67190i	0.548804	−	0.835951i	$-0.315083\pi$
$228$	6.63611	−	3.60028i	0.439487	−	0.238435i
$229$	27.5462			1.82030			0.910152	−	0.414273i	$-0.135964\pi$
$229$	27.5462			1.82030			0.910152	+	0.414273i	$0.135964\pi$
$230$	2.47726	+	1.11508i	0.163345	+	0.0735259i
$231$	0.00629350	−	0.140091i	0.000414082	−	0.00921732i
$232$	−5.27930	−	3.04800i	−0.346603	−	0.200111i
$233$	−0.739496	−	1.28084i	−0.0484460	−	0.0839109i	0.840786	−	0.541368i	$-0.182094\pi$
$233$	−0.739496	−	1.28084i	−0.0484460	−	0.0839109i	−0.889232	+	0.457457i	$0.848760\pi$
$234$	0.369331	−	4.10229i	0.0241439	−	0.268175i
$235$	−9.18498	−	12.7511i	−0.599162	−	0.831790i
$236$	10.1435			0.660288
$237$	7.75316	+	14.9397i	0.503622	+	0.970435i
$238$	0.0308762	−	0.0534792i	0.00200141	−	0.00346654i
$239$			9.00066i			0.582204i	0.956692	+	0.291102i	$0.0940219\pi$
$239$			9.00066i			0.582204i	−0.956692	+	0.291102i	$0.905978\pi$
$240$	−0.215794	−	3.86697i	−0.0139295	−	0.249612i
$241$	18.8017	+	10.8552i	1.21113	+	0.699244i	0.963004	−	0.269486i	$-0.0868536\pi$
$241$	18.8017	+	10.8552i	1.21113	+	0.699244i	0.248121	+	0.968729i	$0.420187\pi$
$242$	4.27216	−	2.46653i	0.274625	−	0.158555i
$243$	−3.46984	+	15.1974i	−0.222590	+	0.974912i
$244$	1.34395	+	2.32779i	0.0860375	+	0.149021i
$245$	6.42433	−	14.2723i	0.410435	−	0.911825i
$246$	1.08459	−	1.69774i	0.0691511	−	0.108244i
$247$	−3.08707	−	5.12693i	−0.196426	−	0.326219i
$248$	4.41969			0.280650
$249$	0.550740	−	12.2593i	0.0349018	−	0.776901i
$250$	7.58222	−	8.21645i	0.479541	−	0.519654i
$251$	−8.96668	−	5.17692i	−0.565972	−	0.326764i	0.189567	−	0.981868i	$-0.439292\pi$
$251$	−8.96668	−	5.17692i	−0.565972	−	0.326764i	−0.755539	+	0.655104i	$0.772625\pi$
$252$	0.0497571	+	0.0350276i	0.00313440	+	0.00220653i
$253$	−4.19981	−	2.42476i	−0.264040	−	0.152443i
$254$			0.624532i			0.0391866i
$255$	−0.656985	−	11.7730i	−0.0411420	−	0.737252i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.6197	+	7.28601i	0.787198	+	0.454489i	0.838975	−	0.544170i	$-0.183155\pi$
$257$	12.6197	+	7.28601i	0.787198	+	0.454489i	−0.0517771	+	0.998659i	$0.516489\pi$
$258$	−5.45057	−	3.48207i	−0.339338	−	0.216784i
$259$			0.0573116i			0.00356117i
$260$	−3.05450	+	0.308449i	−0.189432	+	0.0191292i
$261$	10.5273	−	14.9542i	0.651625	−	0.925640i
$262$	−9.18823	+	15.9145i	−0.567651	+	0.983200i
$263$	0.693382	+	1.20097i	0.0427557	+	0.0740551i	0.886611	−	0.462515i	$-0.153053\pi$
$263$	0.693382	+	1.20097i	0.0427557	+	0.0740551i	−0.843856	+	0.536570i	$0.819720\pi$
$264$	−0.310280	+	6.90673i	−0.0190964	+	0.425080i
$265$	22.2470	−	16.0251i	1.36662	−	0.984416i
$266$	0.0883978	−	0.00162535i	0.00542002	−	9.96569e-5i
$267$	−18.6893	−	11.9396i	−1.14377	−	0.730690i
$268$	−1.47926	−	2.56216i	−0.0903603	−	0.156509i
$269$	−10.6586	−	18.4612i	−0.649866	−	1.12560i	−0.983155	−	0.182776i	$-0.941492\pi$
$269$	−10.6586	−	18.4612i	−0.649866	−	1.12560i	0.333288	−	0.942825i	$-0.391842\pi$
$270$	11.6122	+	0.395452i	0.706697	+	0.0240664i
$271$	3.47859	+	6.02509i	0.211309	+	0.365998i	0.952124	−	0.305711i	$-0.0988940\pi$
$271$	3.47859	+	6.02509i	0.211309	+	0.365998i	−0.740815	+	0.671709i	$0.765561\pi$
$272$	−1.52225	+	2.63661i	−0.0922999	+	0.159868i
$273$	0.0259676	−	0.0406478i	0.00157163	−	0.00246011i
$274$		−	14.2111i		−	0.858527i
$275$	−14.9402	+	13.2332i	−0.900930	+	0.797989i
$276$	1.86777	−	0.969307i	0.112426	−	0.0583455i
$277$		−	18.8422i		−	1.13212i	−0.824364	−	0.566060i	$-0.808467\pi$
$277$		−	18.8422i		−	1.13212i	0.824364	−	0.566060i	$-0.191533\pi$
$278$		−	14.7444i		−	0.884308i
$279$	−1.18891	+	13.2057i	−0.0711782	+	0.790602i
$280$	0.0186163	−	0.0413581i	0.00111254	−	0.00247162i
$281$	−13.6863	+	23.7053i	−0.816454	+	1.41414i	0.0918244	+	0.995775i	$0.470730\pi$
$281$	−13.6863	+	23.7053i	−0.816454	+	1.41414i	−0.908279	+	0.418365i	$0.862603\pi$
$282$	−12.1604	−	0.546296i	−0.724139	−	0.0325315i
$283$	−10.7276	+	6.19357i	−0.637689	+	0.368170i	−0.783724	−	0.621110i	$-0.786682\pi$
$283$	−10.7276	+	6.19357i	−0.637689	+	0.368170i	0.146035	+	0.989279i	$0.453349\pi$
$284$	1.98168			0.117591
$285$	13.9549	−	9.50061i	0.826615	−	0.562768i
$286$	5.48034			0.324060
$287$	0.0204315	−	0.0117961i	0.00120603	−	0.000696303i
$288$	−2.45311	−	1.72692i	−0.144551	−	0.101760i
$289$	3.86551	−	6.69526i	0.227383	−	0.393839i
$290$	−12.4299	−	5.59501i	−0.729909	−	0.328550i
$291$	17.8809	−	9.27955i	1.04819	−	0.543977i
$292$			7.27943i			0.425996i
$293$			14.4593i			0.844722i	0.906428	+	0.422361i	$0.138799\pi$
$293$			14.4593i			0.844722i	−0.906428	+	0.422361i	$0.861201\pi$
$294$	−5.58451	−	10.7609i	−0.325695	−	0.627586i
$295$	22.5669	−	2.27885i	1.31389	−	0.132680i
$296$		−	2.82556i		−	0.164232i
$297$	−20.5533	−	2.78502i	−1.19262	−	0.161603i
$298$	5.93151	−	10.2737i	0.343603	−	0.595138i
$299$	−0.834021	−	1.44457i	−0.0482327	−	0.0835415i
$300$	−1.34884	−	8.55457i	−0.0778754	−	0.493898i
$301$	−0.0378713	−	0.0655950i	−0.00218286	−	0.00378083i
$302$	8.11097	+	14.0486i	0.466734	+	0.808407i
$303$	8.59913	−	13.4604i	0.494007	−	0.773282i
$304$	−4.35816	+	0.0801327i	−0.249958	+	0.00459593i
$305$	3.51291	+	4.87682i	0.201149	+	0.279246i
$306$	−7.46849	−	5.25761i	−0.426945	−	0.300558i
$307$	14.2128	+	24.6172i	0.811165	+	1.40498i	0.912049	+	0.410081i	$0.134500\pi$
$307$	14.2128	+	24.6172i	0.811165	+	1.40498i	−0.100884	+	0.994898i	$0.532167\pi$
$308$	−0.0404816	+	0.0701162i	−0.00230665	+	0.00399524i
$309$	0.864806	−	19.2503i	0.0491971	−	1.09511i
$310$	9.83272	−	0.992927i	0.558461	−	0.0563945i
$311$		−	7.97931i		−	0.452465i	−0.974073	−	0.226233i	$-0.927359\pi$
$311$		−	7.97931i		−	0.452465i	0.974073	−	0.226233i	$-0.0726409\pi$
$312$	−1.28025	+	2.00400i	−0.0724797	+	0.113454i
$313$	29.0368	+	16.7644i	1.64126	+	0.947579i	0.980388	+	0.197076i	$0.0631447\pi$
$313$	29.0368	+	16.7644i	1.64126	+	0.947579i	0.660867	+	0.750503i	$0.270189\pi$
$314$	−6.48585	+	11.2338i	−0.366018	+	0.633961i
$315$	0.118567	+	0.0667494i	0.00668047	+	0.00376090i
$316$		−	9.71776i		−	0.546667i
$317$	7.43608	+	4.29323i	0.417652	+	0.241132i	0.694072	−	0.719905i	$-0.255815\pi$
$317$	7.43608	+	4.29323i	0.417652	+	0.241132i	−0.276420	+	0.961037i	$0.589148\pi$
$318$	0.953128	−	21.2163i	0.0534487	−	1.18975i
$319$	21.0730	+	12.1665i	1.17986	+	0.681193i
$320$	−0.917815	+	2.03902i	−0.0513074	+	0.113985i
$321$	18.4192	+	0.827470i	1.02806	+	0.0461849i
$322$	0.0246426			0.00137328
$323$	−13.2684	+	0.243964i	−0.738275	+	0.0135745i
$324$	5.81979	−	6.86513i	0.323322	−	0.381396i
$325$	−6.72621	+	1.37245i	−0.373103	+	0.0761297i
$326$	−8.38408	−	14.5216i	−0.464351	−	0.804280i
$327$	−1.65614	−	3.19123i	−0.0915845	−	0.176475i
$328$	−1.00731	+	0.581569i	−0.0556192	+	0.0321118i
$329$	−0.123450	−	0.0712741i	−0.00680604	−	0.00392947i
$330$	0.861369	+	15.4355i	0.0474168	+	0.849695i
$331$			19.6633i			1.08080i	0.841410	+	0.540398i	$0.181726\pi$
$331$			19.6633i			1.08080i	−0.841410	+	0.540398i	$0.818274\pi$
$332$	−3.54252	+	6.13583i	−0.194421	+	0.336747i
$333$	8.44253	+	0.760085i	0.462648	+	0.0416524i
$334$	−22.8038			−1.24777
$335$	−3.86661	−	5.36784i	−0.211255	−	0.293276i
$336$	−0.0161827	−	0.0311826i	−0.000882838	−	0.00170115i
$337$	6.02018	+	10.4273i	0.327940	+	0.568009i	0.982103	−	0.188345i	$-0.0603123\pi$
$337$	6.02018	+	10.4273i	0.327940	+	0.568009i	−0.654163	+	0.756354i	$0.726979\pi$
$338$	−9.62585	−	5.55749i	−0.523577	−	0.302288i
$339$	12.0849	+	0.542905i	0.656360	+	0.0294866i
$340$	−2.79429	+	6.20780i	−0.151542	+	0.336665i
$341$	−17.6417			−0.955354
$342$	0.932930	−	13.0434i	0.0504471	−	0.705305i
$343$		−	0.283958i		−	0.0153323i
$344$	1.86712	+	3.23394i	0.100668	+	0.174363i
$345$	3.93756	−	2.57608i	0.211991	−	0.138692i
$346$	−4.17596	+	7.23298i	−0.224501	+	0.388847i
$347$	1.45338	+	2.51733i	0.0780216	+	0.135137i	0.902396	−	0.430907i	$-0.141806\pi$
$347$	1.45338	+	2.51733i	0.0780216	+	0.135137i	−0.824375	+	0.566044i	$0.808473\pi$
$348$	−9.37173	+	4.86360i	−0.502377	+	0.260717i
$349$	−21.2903			−1.13965			−0.569823	−	0.821767i	$-0.692988\pi$
$349$	−21.2903			−1.13965			−0.569823	+	0.821767i	$0.692988\pi$
$350$	0.0321252	−	0.0961939i	0.00171716	−	0.00514178i
$351$	−5.64340	−	4.36435i	−0.301223	−	0.232952i
$352$	1.99581	−	3.45685i	0.106377	−	0.184251i
$353$	−22.5734			−1.20146			−0.600730	−	0.799452i	$-0.705123\pi$
$353$	−22.5734			−1.20146			−0.600730	+	0.799452i	$0.705123\pi$
$354$	9.45855	−	14.8057i	0.502716	−	0.786915i
$355$	4.40875	−	0.445204i	0.233992	−	0.0236290i
$356$	6.40211	+	11.0888i	0.339311	+	0.587705i
$357$	−0.0492682	−	0.0949354i	−0.00260755	−	0.00502451i
$358$	3.77924	−	2.18195i	0.199739	−	0.115319i
$359$	7.32484	−	4.22900i	0.386590	−	0.223198i	−0.294091	−	0.955777i	$-0.595017\pi$
$359$	7.32484	−	4.22900i	0.386590	−	0.223198i	0.680682	+	0.732579i	$0.261684\pi$
$360$	−5.84553	−	3.29086i	−0.308087	−	0.173443i
$361$	−10.0985	−	16.0941i	−0.531498	−	0.847059i
$362$	24.8013			1.30353
$363$	0.383461	−	8.53572i	0.0201265	−	0.448009i
$364$	−0.0241172	+	0.0139241i	−0.00126408	+	0.000729820i
$365$	1.63540	+	16.1949i	0.0856006	+	0.847682i
$366$	4.65088	+	0.208938i	0.243106	+	0.0109214i
$367$	29.4740	+	17.0168i	1.53853	+	0.888272i	0.998925	+	0.0463542i	$0.0147603\pi$
$367$	29.4740	+	17.0168i	1.53853	+	0.888272i	0.539606	+	0.841917i	$0.318573\pi$
$368$	−1.21492			−0.0633323
$369$	−1.46671	−	3.16619i	−0.0763539	−	0.164825i
$370$	−0.634790	−	6.28617i	−0.0330012	−	0.326803i
$371$	0.124353	−	0.215385i	0.00645606	−	0.0111822i
$372$	4.12123	−	6.45108i	0.213676	−	0.334473i
$373$	24.4276			1.26481			0.632407	−	0.774636i	$-0.282067\pi$
$373$	24.4276			1.26481			0.632407	+	0.774636i	$0.282067\pi$
$374$	6.07625	−	10.5244i	0.314195	−	0.544202i
$375$	−4.92271	−	18.7288i	−0.254208	−	0.967150i
$376$	6.08631	+	3.51393i	0.313877	+	0.181217i
$377$	4.18479	+	7.24827i	0.215528	+	0.373305i
$378$	0.0975242	−	0.0399643i	0.00501610	−	0.00205554i
$379$		−	20.7105i		−	1.06383i	−0.846799	−	0.531913i	$-0.821473\pi$
$379$		−	20.7105i		−	1.06383i	0.846799	−	0.531913i	$-0.178527\pi$
$380$	−9.67783	+	1.15738i	−0.496462	+	0.0593724i
$381$	0.911580	+	0.582358i	0.0467017	+	0.0298351i
$382$	5.00169	+	8.66318i	0.255909	+	0.443247i
$383$	25.8063	−	14.8993i	1.31864	−	0.761317i	0.335130	−	0.942172i	$-0.391220\pi$
$383$	25.8063	−	14.8993i	1.31864	−	0.761317i	0.983510	+	0.180855i	$0.0578864\pi$
$384$	0.797834	+	1.53736i	0.0407143	+	0.0784528i
$385$	−0.0743093	+	0.165086i	−0.00378715	+	0.00841356i
$386$	−0.552980	−	0.319263i	−0.0281459	−	0.0162501i
$387$	−10.1650	+	4.70885i	−0.516716	+	0.239364i
$388$	−11.6309			−0.590471
$389$	17.9377	+	10.3563i	0.909479	+	0.525088i	0.880263	−	0.474485i	$-0.157366\pi$
$389$	17.9377	+	10.3563i	0.909479	+	0.525088i	0.0292152	+	0.999573i	$0.490699\pi$
$390$	−2.39801	+	4.74603i	−0.121428	+	0.240325i
$391$	−3.69883			−0.187058
$392$			6.99959i			0.353533i
$393$	14.6614	+	28.2512i	0.739568	+	1.42508i
$394$	−8.78093	+	5.06967i	−0.442377	+	0.255406i
$395$	−2.18319	−	21.6196i	−0.109848	−	1.08780i
$396$	9.79189	+	6.89322i	0.492061	+	0.346397i
$397$	−23.8116	+	13.7476i	−1.19507	+	0.689974i	−0.959452	−	0.281871i	$-0.909045\pi$
$397$	−23.8116	+	13.7476i	−1.19507	+	0.689974i	−0.235618	+	0.971846i	$0.575712\pi$
$398$			9.33619i			0.467981i
$399$	0.0800560	−	0.130543i	0.00400781	−	0.00653533i
$400$	−1.58383	+	4.74252i	−0.0791913	+	0.237126i
$401$	15.0652	+	26.0937i	0.752322	+	1.30306i	0.946695	+	0.322132i	$0.104399\pi$
$401$	15.0652	+	26.0937i	0.752322	+	1.30306i	−0.194373	+	0.980928i	$0.562267\pi$
$402$	−5.11915	−	0.229974i	−0.255320	−	0.0114701i
$403$	−5.25509	−	3.03403i	−0.261775	−	0.151136i
$404$	−7.98637	+	4.61093i	−0.397337	+	0.229403i
$405$	11.4053	−	16.5807i	0.566733	−	0.823902i
$406$	−0.123647			−0.00613650
$407$			11.2786i			0.559058i
$408$	2.42901	+	4.68048i	0.120254	+	0.231718i
$409$	−13.8808	−	8.01408i	−0.686361	−	0.396271i	0.115886	−	0.993262i	$-0.463029\pi$
$409$	−13.8808	−	8.01408i	−0.686361	−	0.396271i	−0.802247	+	0.596992i	$0.796362\pi$
$410$	−2.11036	+	1.52015i	−0.104223	+	0.0750748i
$411$	−20.7429	−	13.2515i	−1.02317	−	0.653648i
$412$	−5.56268	+	9.63485i	−0.274054	+	0.474675i
$413$	0.178180	−	0.102872i	0.00876764	−	0.00506200i
$414$	0.326818	−	3.63009i	0.0160622	−	0.178409i
$415$	−6.50276	+	14.4466i	−0.319208	+	0.709154i
$416$	1.18902	−	0.686480i	0.0582964	−	0.0336575i
$417$	−21.5212	−	13.7487i	−1.05390	−	0.673277i
$418$	17.3961	−	0.319860i	0.850873	−	0.0156449i
$419$		−	20.4668i		−	0.999870i	−0.866063	−	0.499935i	$-0.833357\pi$
$419$		−	20.4668i		−	0.999870i	0.866063	−	0.499935i	$-0.166643\pi$
$420$	−0.0430080	−	0.0657380i	−0.00209857	−	0.00320769i
$421$	−3.75989	+	2.17078i	−0.183246	+	0.105797i	−0.588817	−	0.808266i	$-0.700406\pi$
$421$	−3.75989	+	2.17078i	−0.183246	+	0.105797i	0.405571	+	0.914064i	$0.367073\pi$
$422$	12.9373	−	22.4081i	0.629778	−	1.09081i
$423$	−12.1366	+	17.2401i	−0.590100	+	0.838243i
$424$	−6.13079	+	10.6188i	−0.297738	+	0.515697i
$425$	−4.82196	+	14.4386i	−0.233899	+	0.700375i
$426$	1.84786	−	2.89250i	0.0895291	−	0.140142i
$427$	0.0472152	+	0.0272597i	0.00228490	+	0.00131919i
$428$	−9.21889	−	5.32253i	−0.445612	−	0.257274i
$429$	5.11026	−	7.99923i	0.246726	−	0.386207i
$430$	4.88041	+	6.77526i	0.235354	+	0.326732i
$431$	−7.60406	+	13.1706i	−0.366275	+	0.634407i	−0.988980	−	0.148050i	$-0.952700\pi$
$431$	−7.60406	+	13.1706i	−0.366275	+	0.634407i	0.622705	+	0.782457i	$0.286034\pi$
$432$	−4.80811	+	1.97031i	−0.231330	+	0.0947965i
$433$	0.703299	−	1.21815i	0.0337984	−	0.0585405i	−0.848631	−	0.528985i	$-0.822573\pi$
$433$	0.703299	−	1.21815i	0.0337984	−	0.0585405i	0.882430	+	0.470444i	$0.155906\pi$
$434$	0.0776355	−	0.0448229i	0.00372662	−	0.00215157i
$435$	−19.7571	+	12.9258i	−0.947282	+	0.619743i
$436$			2.07579i			0.0994123i
$437$	−2.73173	−	4.53678i	−0.130676	−	0.217024i
$438$	10.6252	+	6.78786i	0.507693	+	0.324337i
$439$	−17.5197	+	10.1150i	−0.836171	+	0.482763i	−0.855961	−	0.517041i	$-0.827034\pi$
$439$	−17.5197	+	10.1150i	−0.836171	+	0.482763i	0.0197901	+	0.999804i	$0.493700\pi$
$440$	3.66357	−	8.13901i	0.174654	−	0.388012i
$441$	−20.9142	−	1.88291i	−0.995913	−	0.0896625i
$442$	3.61997	−	2.08999i	0.172184	−	0.0994106i
$443$	0.106768	−	0.184928i	0.00507271	−	0.00878619i	−0.863478	−	0.504387i	$-0.831719\pi$
$443$	0.106768	−	0.184928i	0.00507271	−	0.00878619i	0.868551	+	0.495600i	$0.165052\pi$
$444$	−4.12425	−	2.63475i	−0.195728	−	0.125040i
$445$	16.7343	+	23.2315i	0.793283	+	1.10128i
$446$	−17.4073	−	10.0501i	−0.824260	−	0.475887i
$447$	−9.46472	−	18.2377i	−0.447666	−	0.862612i
$448$			0.0202833i			0.000958295i
$449$	15.8165			0.746426			0.373213	−	0.927746i	$-0.378256\pi$
$449$	15.8165			0.746426			0.373213	+	0.927746i	$0.378256\pi$
$450$	−13.7442	−	6.00809i	−0.647907	−	0.283224i
$451$	4.02079	−	2.32141i	0.189332	−	0.109311i
$452$	−6.04853	−	3.49212i	−0.284499	−	0.164256i
$453$	28.0689	+	1.26098i	1.31879	+	0.0592459i
$454$	12.5949	+	21.8150i	0.591106	+	1.02383i
$455$	−0.0505266	+	0.0363958i	−0.00236873	+	0.00170626i
$456$	−3.94690	+	6.43599i	−0.184830	+	0.301393i
$457$			15.6759i			0.733287i	0.930362	+	0.366643i	$0.119493\pi$
$457$			15.6759i			0.733287i	−0.930362	+	0.366643i	$0.880507\pi$
$458$	−23.8557	+	13.7731i	−1.11470	+	0.643575i
$459$	−14.6383	+	5.99860i	−0.683256	+	0.279991i
$460$	−2.70291	+	0.272945i	−0.126024	+	0.0127261i
$461$	−20.1979	+	11.6613i	−0.940710	+	0.543119i	−0.890183	−	0.455604i	$-0.849423\pi$
$461$	−20.1979	+	11.6613i	−0.940710	+	0.543119i	−0.0505272	+	0.998723i	$0.516090\pi$
$462$	0.0645952	+	0.124469i	0.00300524	+	0.00579083i
$463$		−	39.2341i		−	1.82336i	−0.410899	−	0.911681i	$-0.634785\pi$
$463$		−	39.2341i		−	1.82336i	0.410899	−	0.911681i	$-0.365215\pi$
$464$	6.09601			0.283000
$465$	7.71943	−	15.2779i	0.357980	−	0.708497i
$466$	1.28084	+	0.739496i	0.0593340	+	0.0342565i
$467$	24.4549			1.13164			0.565819	−	0.824530i	$-0.308560\pi$
$467$	24.4549			1.13164			0.565819	+	0.824530i	$0.308560\pi$
$468$	1.73130	+	3.73735i	0.0800291	+	0.172759i
$469$	−0.0519689	−	0.0300043i	−0.00239970	−	0.00138547i
$470$	14.3300	+	6.45028i	0.660993	+	0.297529i
$471$	10.3493	+	19.9421i	0.476869	+	0.918884i
$472$	−8.78455	+	5.07177i	−0.404342	+	0.233447i
$473$	−7.45283	−	12.9087i	−0.342682	−	0.593542i
$474$	−14.1843	−	9.06154i	−0.651505	−	0.416210i
$475$	−21.2708	+	4.74911i	−0.975970	+	0.217904i
$476$			0.0617524i			0.00283042i
$477$	−30.0790	−	21.1748i	−1.37722	−	0.969527i
$478$	−4.50033	−	7.79480i	−0.205840	−	0.356526i
$479$	27.8923	+	16.1036i	1.27443	+	0.735794i	0.975819	−	0.218580i	$-0.0701424\pi$
$479$	27.8923	+	16.1036i	1.27443	+	0.735794i	0.298614	+	0.954374i	$0.403476\pi$
$480$	2.12037	+	3.24099i	0.0967811	+	0.147930i
$481$	−1.93969	+	3.35964i	−0.0884423	+	0.153187i
$482$	−21.7104			−0.988880
$483$	0.0229785	−	0.0359689i	0.00104556	−	0.00163664i
$484$	−2.46653	+	4.27216i	−0.112115	+	0.194189i
$485$	−25.8759	+	2.61300i	−1.17497	+	0.118650i
$486$	−4.59372	−	14.8962i	−0.208375	−	0.675707i
$487$	−22.5359			−1.02120			−0.510599	−	0.859819i	$-0.670576\pi$
$487$	−22.5359			−1.02120			−0.510599	+	0.859819i	$0.670576\pi$
$488$	−2.32779	−	1.34395i	−0.105374	−	0.0608377i
$489$	−29.0140	−	1.30344i	−1.31206	−	0.0589434i
$490$	1.57253	+	15.5724i	0.0710396	+	0.703487i
$491$	25.9068	−	14.9573i	1.16916	−	0.675013i	0.215675	−	0.976465i	$-0.430805\pi$
$491$	25.9068	−	14.9573i	1.16916	−	0.675013i	0.953481	+	0.301452i	$0.0974714\pi$
$492$	−0.0904141	+	2.01258i	−0.00407618	+	0.0907343i
$493$	18.5593			0.835869
$494$	5.23695	+	2.89651i	0.235621	+	0.130320i
$495$	23.3332	+	13.1359i	1.04875	+	0.590414i
$496$	−3.82756	+	2.20984i	−0.171863	+	0.0992249i
$497$	0.0348098	−	0.0200975i	0.00156144	−	0.000901495i
$498$	5.65269	+	10.8922i	0.253303	+	0.488092i
$499$	−5.42341	−	9.39363i	−0.242785	−	0.420516i	0.718721	−	0.695298i	$-0.244728\pi$
$499$	−5.42341	−	9.39363i	−0.242785	−	0.420516i	−0.961507	+	0.274782i	$0.911394\pi$
$500$	−2.45817	+	10.9068i	−0.109933	+	0.487765i
$501$	−21.2639	+	33.2849i	−0.950000	+	1.48706i
$502$	10.3538			0.462114
$503$	1.20059	−	2.07949i	0.0535318	−	0.0927199i	−0.838018	−	0.545643i	$-0.816285\pi$
$503$	1.20059	−	2.07949i	0.0535318	−	0.0927199i	0.891550	+	0.452923i	$0.149619\pi$
$504$	−0.0606047	−	0.00545627i	−0.00269955	−	0.000243041i
$505$	−16.7318	+	12.0524i	−0.744556	+	0.536325i
$506$	4.84952			0.215587
$507$	−17.0877	+	8.86791i	−0.758890	+	0.393838i
$508$	−0.312266	−	0.540860i	−0.0138546	−	0.0239968i
$509$	17.6336	−	30.5422i	0.781594	−	1.35376i	−0.149418	−	0.988774i	$-0.547740\pi$
$509$	17.6336	−	30.5422i	0.781594	−	1.35376i	0.931013	−	0.364987i	$-0.118927\pi$
$510$	6.45545	+	9.86721i	0.285852	+	0.436927i
$511$	0.0738254	+	0.127869i	0.00326584	+	0.00565660i
$512$		−	1.00000i		−	0.0441942i
$513$	−18.1685	−	13.5243i	−0.802158	−	0.597112i
$514$	−14.5720			−0.642745
$515$	−10.2110	+	22.6849i	−0.449952	+	0.999615i
$516$	6.46137	+	0.290273i	0.284446	+	0.0127785i
$517$	−24.2943	−	14.0263i	−1.06846	−	0.616876i
$518$	−0.0286558	−	0.0496333i	−0.00125906	−	0.00218076i
$519$	6.66345	+	12.8399i	0.292493	+	0.563608i
$520$	2.49105	−	1.79437i	0.109240	−	0.0786885i
$521$	21.0405			0.921799			0.460900	−	0.887452i	$-0.347527\pi$
$521$	21.0405			0.921799			0.460900	+	0.887452i	$0.347527\pi$
$522$	−1.63985	+	18.2144i	−0.0717741	+	0.797221i
$523$	−12.7922	+	22.1567i	−0.559362	+	0.968844i	0.438187	+	0.898884i	$0.355621\pi$
$523$	−12.7922	+	22.1567i	−0.559362	+	0.968844i	−0.997550	+	0.0699605i	$0.977713\pi$
$524$		−	18.3765i		−	0.802780i
$525$	−0.110451	−	0.136589i	−0.00482047	−	0.00596122i
$526$	−1.20097	−	0.693382i	−0.0523649	−	0.0302329i
$527$	−11.6530	+	6.72787i	−0.507613	+	0.293071i
$528$	−3.18465	−	6.13654i	−0.138594	−	0.267059i
$529$	10.7620	+	18.6403i	0.467912	+	0.810448i
$530$	−11.2539	+	25.0016i	−0.488837	+	1.08600i
$531$	−12.7909	−	27.6118i	−0.555079	−	1.19825i
$532$	−0.0757421	+	0.0456065i	−0.00328384	+	0.00197729i
$533$	1.59694			0.0691713
$534$	22.1552	+	0.995309i	0.958751	+	0.0430712i
$535$	−21.7055	−	9.77020i	−0.938411	−	0.422402i
$536$	2.56216	+	1.47926i	0.110668	+	0.0638944i
$537$	0.339218	−	7.55087i	0.0146383	−	0.325844i
$538$	18.4612	+	10.6586i	0.795920	+	0.459525i
$539$		−	27.9397i		−	1.20345i
$540$	−10.2542	+	5.46364i	−0.441271	+	0.235118i
$541$	4.03165	−	6.98303i	0.173334	−	0.300224i	−0.766249	−	0.642543i	$-0.777879\pi$
$541$	4.03165	−	6.98303i	0.173334	−	0.300224i	0.939584	+	0.342320i	$0.111213\pi$
$542$	−6.02509	−	3.47859i	−0.258800	−	0.149418i
$543$	23.1265	−	36.2005i	0.992452	−	1.55351i
$544$		−	3.04450i		−	0.130532i
$545$	0.466347	+	4.61812i	0.0199761	+	0.197819i
$546$	−0.00216472	+	0.0481858i	−9.26413e−5	+	0.00206216i
$547$	18.8081	−	32.5766i	0.804176	−	1.39287i	−0.112670	−	0.993633i	$-0.535940\pi$
$547$	18.8081	−	32.5766i	0.804176	−	1.39287i	0.916846	−	0.399241i	$-0.130726\pi$
$548$	7.10557	+	12.3072i	0.303535	+	0.525738i
$549$	4.64179	−	6.59370i	0.198107	−	0.281412i
$550$	6.32204	−	18.9304i	0.269573	−	0.807193i
$551$	13.7067	+	22.7638i	0.583927	+	0.969770i
$552$	−1.13288	+	1.77333i	−0.0482186	+	0.0754779i
$553$	−0.0985540	−	0.170701i	−0.00419094	−	0.00725893i
$554$	9.42111	+	16.3178i	0.400265	+	0.693279i
$555$	−9.76736	−	4.93512i	−0.414601	−	0.209484i
$556$	7.37218	+	12.7690i	0.312650	+	0.541526i
$557$	3.23898	−	5.61008i	0.137240	−	0.237707i	−0.789211	−	0.614122i	$-0.789510\pi$
$557$	3.23898	−	5.61008i	0.137240	−	0.237707i	0.926451	+	0.376415i	$0.122843\pi$
$558$	−5.57320	−	12.0309i	−0.235932	−	0.509308i
$559$		−	5.12696i		−	0.216847i
$560$	0.00455684	+	0.0451253i	0.000192562	+	0.00190689i
$561$	−9.69568	−	18.6827i	−0.409352	−	0.788784i
$562$		−	27.3725i		−	1.15464i
$563$			23.6169i			0.995332i	0.867369	+	0.497666i	$0.165809\pi$
$563$			23.6169i			0.995332i	−0.867369	+	0.497666i	$0.834191\pi$
$564$	10.8043	−	5.60707i	0.454944	−	0.236100i
$565$	−14.2410	−	6.41025i	−0.599125	−	0.269681i
$566$	6.19357	−	10.7276i	0.260335	−	0.450914i
$567$	0.0326057	−	0.179614i	0.00136931	−	0.00754308i
$568$	−1.71618	+	0.990840i	−0.0720095	+	0.0415747i
$569$	−16.2844			−0.682676			−0.341338	−	0.939941i	$-0.610880\pi$
$569$	−16.2844			−0.682676			−0.341338	+	0.939941i	$0.610880\pi$
$570$	−7.33497	+	15.2052i	−0.307228	+	0.636876i
$571$	−4.10720			−0.171881			−0.0859405	−	0.996300i	$-0.527389\pi$
$571$	−4.10720			−0.171881			−0.0859405	+	0.996300i	$0.527389\pi$
$572$	−4.74612	+	2.74017i	−0.198445	+	0.114572i
$573$	17.3089	+	0.777591i	0.723089	+	0.0324843i
$574$	−0.0117961	+	0.0204315i	−0.000492361	+	0.000852794i
$575$	−5.95198	+	1.21447i	−0.248215	+	0.0506469i
$576$	2.98792	+	0.269003i	0.124496	+	0.0112085i
$577$		−	25.1996i		−	1.04907i	−0.851388	−	0.524537i	$-0.824239\pi$
$577$		−	25.1996i		−	1.04907i	0.851388	−	0.524537i	$-0.175761\pi$
$578$			7.73102i			0.321568i
$579$	−0.981642	+	0.509438i	−0.0407956	+	0.0211715i
$580$	13.5621	−	1.36953i	0.563136	−	0.0568666i
$581$			0.143708i			0.00596201i
$582$	−10.8455	+	16.9768i	−0.449561	+	0.703709i
$583$	24.4718	−	42.3864i	1.01352	−	1.75547i
$584$	−3.63971	−	6.30417i	−0.150612	−	0.260868i
$585$	4.69134	+	7.92574i	0.193963	+	0.327689i
$586$	−7.22966	−	12.5221i	−0.298654	−	0.517285i
$587$	0.0827925	+	0.143401i	0.00341721	+	0.00591879i	0.867729	−	0.497038i	$-0.165579\pi$
$587$	0.0827925	+	0.143401i	0.00341721	+	0.00591879i	−0.864312	+	0.502956i	$0.832246\pi$
$588$	10.2168	+	6.52692i	0.421332	+	0.269165i
$589$	−16.8582	−	9.32415i	−0.694631	−	0.384195i
$590$	−18.4040	+	13.2570i	−0.757683	+	0.545781i
$591$	−0.788160	+	17.5442i	−0.0324206	+	0.721671i
$592$	1.41278	+	2.44701i	0.0580649	+	0.100571i
$593$	0.789202	−	1.36694i	0.0324086	−	0.0561334i	−0.849366	−	0.527804i	$-0.823016\pi$
$593$	0.789202	−	1.36694i	0.0324086	−	0.0561334i	0.881775	+	0.471671i	$0.156349\pi$
$594$	19.1922	−	7.86473i	0.787464	−	0.322694i
$595$	0.0138733	+	0.137384i	0.000568750	+	0.00563219i
$596$			11.8630i			0.485928i
$597$	13.6273	+	8.70573i	0.557728	+	0.356302i
$598$	1.44457	+	0.834021i	0.0590727	+	0.0341057i
$599$	9.04236	−	15.6618i	0.369461	−	0.639925i	−0.620021	−	0.784586i	$-0.712876\pi$
$599$	9.04236	−	15.6618i	0.369461	−	0.639925i	0.989481	+	0.144661i	$0.0462091\pi$
$600$	5.44542	+	6.73405i	0.222308	+	0.274917i
$601$			11.8894i			0.484978i	0.970154	+	0.242489i	$0.0779638\pi$
$601$			11.8894i			0.484978i	−0.970154	+	0.242489i	$0.922036\pi$
$602$	0.0655950	+	0.0378713i	0.00267345	+	0.00154352i
$603$	−5.10914	+	7.25758i	−0.208060	+	0.295552i
$604$	−14.0486	−	8.11097i	−0.571630	−	0.330031i
$605$	−4.52765	+	10.0586i	−0.184075	+	0.408942i
$606$	−0.716842	+	15.9566i	−0.0291197	+	0.648195i
$607$	−6.39493			−0.259562			−0.129781	−	0.991543i	$-0.541427\pi$
$607$	−6.39493			−0.259562			−0.129781	+	0.991543i	$0.541427\pi$
$608$	3.73421	−	2.24848i	0.151442	−	0.0911878i
$609$	−0.115297	+	0.180478i	−0.00467208	+	0.00731334i
$610$	−5.48068	−	2.46699i	−0.221906	−	0.0998856i
$611$	−4.82449	−	8.35626i	−0.195178	−	0.338058i
$612$	9.09671	+	0.818980i	0.367713	+	0.0331053i
$613$	−27.7348	+	16.0127i	−1.12020	+	0.646746i	−0.941451	−	0.337150i	$-0.890537\pi$
$613$	−27.7348	+	16.0127i	−1.12020	+	0.646746i	−0.178745	+	0.983895i	$0.557204\pi$
$614$	−24.6172	−	14.2128i	−0.993470	−	0.573580i
$615$	0.250998	+	4.49782i	0.0101212	+	0.181369i
$616$		−	0.0809632i		−	0.00326210i
$617$	−1.31439	+	2.27659i	−0.0529153	+	0.0916520i	−0.891270	−	0.453473i	$-0.850185\pi$
$617$	−1.31439	+	2.27659i	−0.0529153	+	0.0916520i	0.838354	+	0.545126i	$0.183518\pi$
$618$	8.87619	+	17.1036i	0.357053	+	0.688009i
$619$	−19.3010			−0.775773			−0.387886	−	0.921707i	$-0.626795\pi$
$619$	−19.3010			−0.775773			−0.387886	+	0.921707i	$0.626795\pi$
$620$	−8.01892	+	5.77626i	−0.322048	+	0.231980i
$621$	−4.99381	−	3.86198i	−0.200395	−	0.154976i
$622$	3.98966	+	6.91029i	0.159971	+	0.277077i
$623$	0.224917	+	0.129856i	0.00901111	+	0.00520257i
$624$	0.106724	−	2.37564i	0.00427238	−	0.0951018i
$625$	−3.01850	+	24.8171i	−0.120740	+	0.992684i
$626$	−33.5288			−1.34008
$627$	15.7545	−	25.6901i	0.629176	−	1.02596i
$628$		−	12.9717i		−	0.517627i
$629$	4.30121	+	7.44991i	0.171500	+	0.297047i
$630$	−0.136056	+	0.00147661i	−0.00542061	+	5.88296e-5i
$631$	−11.7467	+	20.3459i	−0.467629	+	0.809956i	−0.999316	−	0.0369844i	$-0.988225\pi$
$631$	−11.7467	+	20.3459i	−0.467629	+	0.809956i	0.531687	+	0.846941i	$0.321558\pi$
$632$	4.85888	+	8.41583i	0.193276	+	0.334764i
$633$	−20.6437	−	39.7785i	−0.820512	−	1.58105i
$634$	−8.58645			−0.341012
$635$	−0.816224	−	1.13313i	−0.0323909	−	0.0449668i
$636$	9.78271	+	18.8504i	0.387910	+	0.747467i
$637$	4.80508	−	8.32264i	0.190384	−	0.329755i
$638$	−24.3330			−0.963352
$639$	−2.49889	−	5.39435i	−0.0988544	−	0.213397i
$640$	−0.224660	−	2.22475i	−0.00888047	−	0.0879411i
$641$	15.9663	+	27.6545i	0.630633	+	1.09229i	0.987423	+	0.158103i	$0.0505379\pi$
$641$	15.9663	+	27.6545i	0.630633	+	1.09229i	−0.356790	+	0.934185i	$0.616129\pi$
$642$	−16.3652	+	8.49299i	−0.645884	+	0.335192i
$643$	−9.38848	+	5.42044i	−0.370246	+	0.213761i	−0.673566	−	0.739127i	$-0.735238\pi$
$643$	−9.38848	+	5.42044i	−0.370246	+	0.213761i	0.303320	+	0.952889i	$0.401905\pi$
$644$	−0.0213411	+	0.0123213i	−0.000840959	+	0.000485528i
$645$	14.4402	−	0.805826i	0.568581	−	0.0317294i
$646$	11.3688	−	6.84549i	0.447300	−	0.269332i
$647$	49.7921			1.95753			0.978765	−	0.204987i	$-0.0657153\pi$
$647$	49.7921			1.95753			0.978765	+	0.204987i	$0.0657153\pi$
$648$	−1.60752	+	8.85527i	−0.0631492	+	0.347868i
$649$	35.0646	−	20.2446i	1.37641	−	0.794669i
$650$	5.13885	−	4.55168i	0.201562	−	0.178532i
$651$	0.00696842	−	0.155115i	0.000273114	−	0.00607942i
$652$	14.5216	+	8.38408i	0.568712	+	0.328346i
$653$	−18.9775			−0.742648			−0.371324	−	0.928503i	$-0.621096\pi$
$653$	−18.9775			−0.742648			−0.371324	+	0.928503i	$0.621096\pi$
$654$	3.02987	+	1.93561i	0.118477	+	0.0756885i
$655$	−4.12846	−	40.8831i	−0.161312	−	1.59744i
$656$	0.581569	−	1.00731i	0.0227065	−	0.0393287i
$657$	19.8154	−	9.17932i	0.773073	−	0.358119i
$658$	0.142548			0.00555710
$659$	−9.69407	+	16.7906i	−0.377627	+	0.654070i	−0.990717	−	0.135944i	$-0.956593\pi$
$659$	−9.69407	+	16.7906i	−0.377627	+	0.654070i	0.613089	+	0.790014i	$0.289927\pi$
$660$	−8.46371	−	12.9368i	−0.329449	−	0.503566i
$661$	14.0634	+	8.11950i	0.547002	+	0.315812i	0.747912	−	0.663798i	$-0.231056\pi$
$661$	14.0634	+	8.11950i	0.547002	+	0.315812i	−0.200910	+	0.979610i	$0.564390\pi$
$662$	−9.83167	−	17.0290i	−0.382119	−	0.661849i
$663$	0.324922	−	7.23264i	0.0126189	−	0.280892i
$664$		−	7.08504i		−	0.274953i
$665$	−0.158261	+	0.118479i	−0.00613712	+	0.00459444i
$666$	−7.69149	+	3.56301i	−0.298039	+	0.138064i
$667$	3.70309	+	6.41394i	0.143384	+	0.248349i
$668$	19.7487	−	11.4019i	0.764098	−	0.441152i
$669$	−30.9012	+	16.0366i	−1.19471	+	0.620012i
$670$	6.03250	+	2.71538i	0.233056	+	0.104904i
$671$	9.29165	+	5.36454i	0.358700	+	0.207096i
$672$	0.0296059	+	0.0189136i	0.00114207	+	0.000729607i
$673$	−23.2726			−0.897093			−0.448546	−	0.893759i	$-0.648058\pi$
$673$	−23.2726			−0.897093			−0.448546	+	0.893759i	$0.648058\pi$
$674$	−10.4273	−	6.02018i	−0.401643	−	0.231889i
$675$	−21.5856	+	14.4590i	−0.830831	+	0.556526i
$676$	11.1150			0.427499
$677$		−	29.3269i		−	1.12712i	−0.826074	−	0.563561i	$-0.809431\pi$
$677$		−	29.3269i		−	1.12712i	0.826074	−	0.563561i	$-0.190569\pi$
$678$	−10.7373	+	5.57227i	−0.412362	+	0.214002i
$679$	−0.204307	+	0.117957i	−0.00784058	+	0.00452676i
$680$	−0.683977	−	6.77326i	−0.0262293	−	0.259743i
$681$	43.5859	+	1.95807i	1.67022	+	0.0750334i
$682$	15.2782	−	8.82087i	0.585032	−	0.337769i
$683$			12.1600i			0.465290i	0.972562	+	0.232645i	$0.0747380\pi$
$683$			12.1600i			0.465290i	−0.972562	+	0.232645i	$0.925262\pi$
$684$	5.71375	+	11.7624i	0.218471	+	0.449745i
$685$	18.5731	+	25.7842i	0.709641	+	0.985163i
$686$	0.141979	+	0.245914i	0.00542077	+	0.00938906i
$687$	−2.14125	+	47.6634i	−0.0816936	+	1.81847i
$688$	−3.23394	−	1.86712i	−0.123293	−	0.0711832i
$689$	14.5793	−	8.41733i	0.555425	−	0.320675i
$690$	−2.12199	+	4.19973i	−0.0807826	+	0.159881i
$691$	29.3470			1.11641			0.558206	−	0.829702i	$-0.311490\pi$
$691$	29.3470			1.11641			0.558206	+	0.829702i	$0.311490\pi$
$692$		−	8.35192i		−	0.317493i
$693$	0.241911	+	0.0217794i	0.00918945	+	0.000827330i
$694$	−2.51733	−	1.45338i	−0.0955565	−	0.0551696i
$695$	19.2700	+	26.7516i	0.730951	+	1.01475i
$696$	5.68435	−	8.89787i	0.215465	−	0.337273i
$697$	1.77059	−	3.06675i	0.0670658	−	0.116161i
$698$	18.4380	−	10.6452i	0.697888	−	0.402926i
$699$	2.27374	−	1.17999i	0.0860006	−	0.0446313i
$700$	0.0202757	+	0.0993689i	0.000766350	+	0.00375579i
$701$	5.24529	−	3.02837i	0.198112	−	0.114380i	−0.397663	−	0.917532i	$-0.630179\pi$
$701$	5.24529	−	3.02837i	0.198112	−	0.114380i	0.595774	+	0.803152i	$0.296845\pi$
$702$	7.06951	+	0.957938i	0.266821	+	0.0361550i
$703$	−5.96104	+	10.7777i	−0.224825	+	0.406487i
$704$			3.99162i			0.150440i
$705$	22.7773	−	14.9016i	0.857842	−	0.561229i
$706$	19.5491	−	11.2867i	0.735741	−	0.424780i
$707$	−0.0935248	+	0.161990i	−0.00351736	+	0.00609225i
$708$	−0.788486	+	17.5514i	−0.0296331	+	0.659622i
$709$	8.50340	−	14.7283i	0.319352	−	0.553134i	−0.661001	−	0.750385i	$-0.729868\pi$
$709$	8.50340	−	14.7283i	0.319352	−	0.553134i	0.980353	+	0.197251i	$0.0632014\pi$
$710$	−3.59549	+	2.58993i	−0.134936	+	0.0971984i
$711$	−26.4528	+	12.2540i	−0.992059	+	0.459562i
$712$	−11.0888	−	6.40211i	−0.415570	−	0.239929i
$713$	−4.65020	−	2.68479i	−0.174151	−	0.100546i
$714$	0.0901352	+	0.0575824i	0.00337323	+	0.00215497i
$715$	−9.94333	+	7.16247i	−0.371860	+	0.267861i
$716$	−2.18195	+	3.77924i	−0.0815432	+	0.141237i
$717$	−15.5739	−	0.699647i	−0.581618	−	0.0261288i
$718$	−4.22900	+	7.32484i	−0.157825	+	0.273361i
$719$	7.31586	−	4.22381i	0.272835	−	0.157522i	−0.357340	−	0.933974i	$-0.616316\pi$
$719$	7.31586	−	4.22381i	0.272835	−	0.157522i	0.630176	+	0.776453i	$0.282983\pi$
$720$	6.70781	−	0.0727995i	0.249985	−	0.00271308i
$721$			0.225659i			0.00840397i
$722$	16.7926	+	8.88869i	0.624956	+	0.330803i
$723$	−20.2443	+	31.6889i	−0.752893	+	1.17852i
$724$	−21.4785	+	12.4006i	−0.798243	+	0.460866i
$725$	29.8647	−	6.09373i	1.10915	−	0.226315i
$726$	3.93577	+	7.58388i	0.146070	+	0.281464i
$727$	34.9928	−	20.2031i	1.29781	−	0.749291i	0.317784	−	0.948163i	$-0.397061\pi$
$727$	34.9928	−	20.2031i	1.29781	−	0.749291i	0.980025	+	0.198872i	$0.0637279\pi$
$728$	0.0139241	−	0.0241172i	0.000516060	−	0.000893843i
$729$	−26.0264	−	7.18522i	−0.963940	−	0.266119i
$730$	−9.51376	−	13.2075i	−0.352120	−	0.488833i
$731$	−9.84574	−	5.68444i	−0.364158	−	0.210247i
$732$	−4.13225	+	2.14450i	−0.152732	+	0.0792629i
$733$			11.3658i			0.419804i	0.977722	+	0.209902i	$0.0673145\pi$
$733$			11.3658i			0.419804i	−0.977722	+	0.209902i	$0.932686\pi$
$734$	−34.0337			−1.25621
$735$	24.1961	+	12.2255i	0.892487	+	0.450944i
$736$	1.05215	−	0.607462i	0.0387829	−	0.0223913i
$737$	−10.2272	−	5.90466i	−0.376723	−	0.217501i
$738$	2.85330	+	2.00865i	0.105032	+	0.0739394i
$739$	−12.1985	−	21.1285i	−0.448731	−	0.777225i	0.549573	−	0.835446i	$-0.314790\pi$
$739$	−12.1985	−	21.1285i	−0.448731	−	0.777225i	−0.998304	+	0.0582212i	$0.981457\pi$
$740$	3.69283	+	5.12659i	0.135751	+	0.188457i
$741$	9.11112	−	4.94305i	0.334705	−	0.181587i
$742$			0.248705i			0.00913025i
$743$	31.2915	−	18.0662i	1.14797	−	0.662783i	0.199581	−	0.979881i	$-0.436042\pi$
$743$	31.2915	−	18.0662i	1.14797	−	0.662783i	0.948393	+	0.317098i	$0.102709\pi$
$744$	−0.343555	+	7.64741i	−0.0125953	+	0.280368i
$745$	2.66514	+	26.3923i	0.0976433	+	0.966938i
$746$	−21.1550	+	12.2138i	−0.774538	+	0.447180i
$747$	21.1695	+	1.90590i	0.774552	+	0.0697332i
$748$			12.1525i			0.444339i
$749$	−0.215917			−0.00788942
$750$	13.6276	+	13.7582i	0.497609	+	0.502380i
$751$	23.3795	+	13.4981i	0.853129	+	0.492554i	0.861705	−	0.507409i	$-0.169397\pi$
$751$	23.3795	+	13.4981i	0.853129	+	0.492554i	−0.00857626	+	0.999963i	$0.502730\pi$
$752$	−7.02786			−0.256280
$753$	9.65466	−	15.1127i	0.351835	−	0.550737i
$754$	−7.24827	−	4.18479i	−0.263966	−	0.152401i
$755$	−33.0769	−	14.8887i	−1.20379	−	0.541857i
$756$	−0.0644763	+	0.0833722i	−0.00234498	+	0.00303222i
$757$	−43.6440	+	25.1979i	−1.58627	+	0.915833i	−0.592355	+	0.805677i	$0.701802\pi$
$757$	−43.6440	+	25.1979i	−1.58627	+	0.915833i	−0.993914	+	0.110155i	$0.964865\pi$
$758$	10.3552	+	17.9358i	0.376119	+	0.651457i
$759$	4.52204	−	7.07847i	0.164140	−	0.256932i
$760$	7.80256	−	5.84124i	0.283029	−	0.211884i
$761$		−	31.6203i		−	1.14623i	−0.819474	−	0.573117i	$-0.805734\pi$
$761$		−	31.6203i		−	1.14623i	0.819474	−	0.573117i	$-0.194266\pi$
$762$	−1.08063	−	0.0485466i	−0.0391471	−	0.00175866i
$763$	0.0210519	+	0.0364630i	0.000762130	+	0.00132005i
$764$	−8.66318	−	5.00169i	−0.313423	−	0.180955i
$765$	20.4219	−	0.221638i	0.738356	−	0.00801334i
$766$	−14.8993	+	25.8063i	−0.538333	+	0.932419i
$767$	13.9267			0.502863
$768$	−1.45962	−	0.932471i	−0.0526696	−	0.0336477i
$769$	24.8986	−	43.1256i	0.897866	−	1.55515i	0.0676486	−	0.997709i	$-0.478450\pi$
$769$	24.8986	−	43.1256i	0.897866	−	1.55515i	0.830217	−	0.557440i	$-0.188216\pi$
$770$	−0.0181892	−	0.180123i	−0.000655493	−	0.00649119i
$771$	−13.5880	+	21.2697i	−0.489360	+	0.766008i
$772$	0.638526			0.0229811
$773$	−13.3636	−	7.71548i	−0.480656	−	0.277507i	0.240034	−	0.970764i	$-0.422841\pi$
$773$	−13.3636	−	7.71548i	−0.480656	−	0.277507i	−0.720690	+	0.693258i	$0.756175\pi$
$774$	6.44873	−	9.16049i	0.231795	−	0.329267i
$775$	−16.5424	+	14.6523i	−0.594221	+	0.526326i
$776$	10.0727	−	5.81546i	0.361588	−	0.208763i
$777$	−0.0991666	−	0.00445500i	−0.00355758	−	0.000159822i
$778$	−20.7127			−0.742586
$779$	5.06915	−	0.0932055i	0.181621	−	0.00333943i
$780$	−0.296277	−	5.30919i	−0.0106084	−	0.190100i
$781$	6.85036	−	3.95506i	0.245125	−	0.141523i
$782$	3.20328	−	1.84942i	0.114549	−	0.0661350i
$783$	25.0570	+	19.3779i	0.895463	+	0.692510i
$784$	−3.49979	−	6.06182i	−0.124993	−	0.216494i
$785$	−2.91422	−	28.8588i	−0.104013	−	1.03002i
$786$	−26.8227	−	17.1355i	−0.956734	−	0.611204i
$787$	20.6176			0.734938			0.367469	−	0.930036i	$-0.380224\pi$
$787$	20.6176			0.734938			0.367469	+	0.930036i	$0.380224\pi$
$788$	5.06967	−	8.78093i	0.180600	−	0.312808i
$789$	−2.13195	+	1.10641i	−0.0758993	+	0.0393891i
$790$	12.7005	+	17.6315i	0.451864	+	0.627302i
$791$	−0.141663			−0.00503697
$792$	−11.9266	−	1.07376i	−0.423795	−	0.0381544i
$793$	1.84519	+	3.19596i	0.0655246	+	0.113492i
$794$	13.7476	−	23.8116i	0.487886	−	0.845042i
$795$	25.9990	+	39.7397i	0.922091	+	1.40942i
$796$	−4.66809	−	8.08537i	−0.165456	−	0.286578i
$797$			8.69132i			0.307862i	0.988082	+	0.153931i	$0.0491934\pi$
$797$			8.69132i			0.307862i	−0.988082	+	0.153931i	$0.950807\pi$
$798$	−0.00405905	+	0.153082i	−0.000143689	+	0.00541903i
$799$	−21.3963			−0.756948
$800$	−0.999626	−	4.89906i	−0.0353421	−	0.173208i
$801$	22.1119	−	31.4102i	0.781285	−	1.10982i
$802$	−26.0937	−	15.0652i	−0.921402	−	0.531972i
$803$	14.5284	+	25.1639i	0.512695	+	0.888014i
$804$	4.54830	−	2.36041i	0.160406	−	0.0832453i
$805$	−0.0447107	+	0.0322064i	−0.00157584	+	0.00113513i
$806$	6.06806			0.213738
$807$	32.7721	−	17.0076i	1.15363	−	0.598696i
$808$	4.61093	−	7.98637i	0.162212	−	0.280960i
$809$			17.9757i			0.631994i	0.948760	+	0.315997i	$0.102339\pi$
$809$			17.9757i			0.631994i	−0.948760	+	0.315997i	$0.897661\pi$
$810$	−1.58690	+	20.0619i	−0.0557581	+	0.704905i
$811$	−0.642549	−	0.370976i	−0.0225630	−	0.0130267i	0.488676	−	0.872465i	$-0.337480\pi$
$811$	−0.642549	−	0.370976i	−0.0225630	−	0.0130267i	−0.511239	+	0.859439i	$0.670813\pi$
$812$	0.107081	−	0.0618235i	0.00375782	−	0.00216958i
$813$	−10.6956	+	5.55067i	−0.375113	+	0.194670i
$814$	−5.63929	−	9.76753i	−0.197657	−	0.342352i
$815$	34.1906	+	15.3901i	1.19765	+	0.539091i
$816$	−4.44382	−	2.83891i	−0.155565	−	0.0993817i
$817$	−0.299235	−	16.2744i	−0.0104689	−	0.569369i
$818$	16.0282			0.560411
$819$	0.0683145	+	0.0480915i	0.00238710	+	0.00168045i
$820$	1.06755	−	2.37167i	0.0372803	−	0.0828222i
$821$	−20.8554	−	12.0409i	−0.727859	−	0.420230i	0.0897793	−	0.995962i	$-0.471384\pi$
$821$	−20.8554	−	12.0409i	−0.727859	−	0.420230i	−0.817638	+	0.575732i	$0.804717\pi$
$822$	24.5896	+	1.10467i	0.857662	+	0.0385299i
$823$	1.48098	+	0.855042i	0.0516236	+	0.0298049i	0.525590	−	0.850738i	$-0.323845\pi$
$823$	1.48098	+	0.855042i	0.0516236	+	0.0298049i	−0.473966	+	0.880543i	$0.657178\pi$
$824$		−	11.1254i		−	0.387570i
$825$	−21.7361	−	26.8798i	−0.756752	−	0.935835i
$826$	−0.102872	+	0.178180i	−0.00357938	+	0.00619966i
$827$	6.34478	+	3.66316i	0.220630	+	0.127381i	0.606242	−	0.795280i	$-0.292676\pi$
$827$	6.34478	+	3.66316i	0.220630	+	0.127381i	−0.385612	+	0.922661i	$0.626010\pi$
$828$	1.53201	+	3.30716i	0.0532411	+	0.114932i
$829$			2.81448i			0.0977508i	0.998805	+	0.0488754i	$0.0155637\pi$
$829$			2.81448i			0.0977508i	−0.998805	+	0.0488754i	$0.984436\pi$
$830$	−1.59173	−	15.7625i	−0.0552496	−	0.547123i
$831$	32.6028	+	1.46466i	1.13098	+	0.0508085i
$832$	−0.686480	+	1.18902i	−0.0237994	+	0.0412218i
$833$	−10.6551	−	18.4552i	−0.369178	−	0.639435i
$834$	25.5123	+	1.14612i	0.883417	+	0.0396869i
$835$	41.3743	−	29.8031i	1.43182	−	1.03138i
$836$	−14.9056	+	8.97508i	−0.515520	+	0.310410i
$837$	−22.7574	−	3.08369i	−0.786611	−	0.106588i
$838$	10.2334	+	17.7248i	0.353507	+	0.612293i
$839$	−16.2571	−	28.1581i	−0.561257	−	0.972126i	−0.997387	−	0.0722425i	$-0.976984\pi$
$839$	−16.2571	−	28.1581i	−0.561257	−	0.972126i	0.436130	−	0.899884i	$-0.356349\pi$
$840$	0.0701150	+	0.0354268i	0.00241920	+	0.00122234i
$841$	−4.08066	−	7.06791i	−0.140712	−	0.243721i
$842$	2.17078	−	3.75989i	0.0748099	−	0.129575i
$843$	−39.9536	−	25.5241i	−1.37607	−	0.879097i
$844$			25.8746i			0.890641i
$845$	24.7281	−	2.49709i	0.850672	−	0.0859026i
$846$	1.89052	−	20.9987i	0.0649973	−	0.721949i
$847$			0.100059i			0.00343806i
$848$		−	12.2616i		−	0.421064i
$849$	−9.88289	−	19.0434i	−0.339180	−	0.653569i
$850$	−3.04336	−	14.9152i	−0.104386	−	0.511586i
$851$	−1.71642	+	2.97293i	−0.0588381	+	0.101911i
$852$	−0.154042	+	3.42891i	−0.00527738	+	0.117473i
$853$	−31.0238	+	17.9116i	−1.06223	+	0.613282i	−0.926050	−	0.377402i	$-0.876818\pi$
$853$	−31.0238	+	17.9116i	−1.06223	+	0.613282i	−0.136185	+	0.990683i	$0.543484\pi$
$854$	−0.0545194			−0.00186561
$855$	15.3542	+	24.8847i	0.525103	+	0.851039i
$856$	10.6451			0.363840
$857$	−32.2601	+	18.6254i	−1.10199	+	0.636232i	−0.936742	−	0.350021i	$-0.886174\pi$
$857$	−32.2601	+	18.6254i	−1.10199	+	0.636232i	−0.165244	+	0.986253i	$0.552841\pi$
$858$	−0.426003	+	9.48267i	−0.0145435	+	0.323733i
$859$	17.0471	−	29.5264i	0.581639	−	1.00743i	−0.413646	−	0.910438i	$-0.635745\pi$
$859$	17.0471	−	29.5264i	0.581639	−	1.00743i	0.995285	−	0.0969905i	$-0.0309216\pi$
$860$	−7.61419	−	3.42734i	−0.259642	−	0.116871i
$861$	0.0188227	+	0.0362697i	0.000641476	+	0.00123607i
$862$		−	15.2081i		−	0.517991i
$863$			43.4280i			1.47831i	0.673537	+	0.739153i	$0.264774\pi$
$863$			43.4280i			1.47831i	−0.673537	+	0.739153i	$0.735226\pi$
$864$	3.17879	−	4.11039i	0.108145	−	0.139838i
$865$	−1.87634	−	18.5810i	−0.0637976	−	0.631772i
$866$			1.40660i			0.0477982i
$867$	11.2844	+	7.20896i	0.383237	+	0.244829i
$868$	−0.0448229	+	0.0776355i	−0.00152139	+	0.00263512i
$869$	−19.3948	−	33.5928i	−0.657925	−	1.13956i
$870$	10.6473	−	21.0726i	0.360977	−	0.714428i
$871$	−2.03097	−	3.51774i	−0.0688167	−	0.119194i
$872$	−1.03789	−	1.79769i	−0.0351476	−	0.0608774i
$873$	14.6665	+	31.6607i	0.496387	+	1.07155i
$874$	4.63414	+	2.56310i	0.156752	+	0.0866983i
$875$	0.0674327	+	0.216516i	0.00227964	+	0.00731958i
$876$	−12.5956	−	0.565851i	−0.425567	−	0.0191183i
$877$	0.220358	+	0.381672i	0.00744098	+	0.0128881i	0.869722	−	0.493542i	$-0.164298\pi$
$877$	0.220358	+	0.381672i	0.00744098	+	0.0128881i	−0.862281	+	0.506430i	$0.830965\pi$
$878$	10.1150	−	17.5197i	0.341365	−	0.591262i
$879$	−25.0190	−	1.12396i	−0.843871	−	0.0379104i
$880$	0.896759	+	8.88038i	0.0302297	+	0.299358i
$881$		−	7.27114i		−	0.244971i	−0.992470	−	0.122485i	$-0.960914\pi$
$881$		−	7.27114i		−	0.244971i	0.992470	−	0.122485i	$-0.0390865\pi$
$882$	19.0537	−	8.82644i	0.641570	−	0.297202i
$883$	−34.2175	−	19.7555i	−1.15151	−	0.664826i	−0.202257	−	0.979333i	$-0.564828\pi$
$883$	−34.2175	−	19.7555i	−1.15151	−	0.664826i	−0.949255	+	0.314507i	$0.898161\pi$
$884$	−2.08999	+	3.61997i	−0.0702939	+	0.121753i
$885$	2.18891	+	39.2247i	0.0735796	+	1.31852i
$886$			0.213536i			0.00717389i
$887$	−19.0506	−	10.9989i	−0.639657	−	0.369306i	0.144825	−	0.989457i	$-0.453738\pi$
$887$	−19.0506	−	10.9989i	−0.639657	−	0.369306i	−0.784483	+	0.620151i	$0.787071\pi$
$888$	4.88908	+	0.219639i	0.164067	+	0.00737060i
$889$	−0.0109704	−	0.00633378i	−0.000367936	−	0.000212428i
$890$	−26.1081	−	11.7519i	−0.875146	−	0.393925i
$891$	6.41661	−	35.3469i	0.214964	−	1.18417i
$892$	20.1002			0.673005
$893$	−15.8020	−	26.2435i	−0.528794	−	0.878207i
$894$	17.3155	+	11.0619i	0.579117	+	0.369966i
$895$	−4.00525	+	8.89808i	−0.133881	+	0.297430i
$896$	−0.0101416	−	0.0175658i	−0.000338808	−	0.000586833i
$897$	2.56437	−	1.33082i	0.0856219	−	0.0444348i
$898$	−13.6975	+	7.90824i	−0.457091	+	0.263901i
$899$	23.3329	+	13.4712i	0.778194	+	0.449291i
$900$	14.9069	−	1.66894i	0.496896	−	0.0556313i
$901$		−	37.3304i		−	1.24366i
$902$	−2.32141	+	4.02079i	−0.0772944	+	0.133878i
$903$	0.116443	−	0.0604300i	0.00387499	−	0.00201098i
$904$	6.98424			0.232292
$905$	−44.9985	+	32.4137i	−1.49580	+	1.07747i
$906$	−24.9389	+	12.9424i	−0.828539	+	0.429983i
$907$	19.1820	+	33.2242i	0.636928	+	1.10319i	0.986103	+	0.166134i	$0.0531285\pi$
$907$	19.1820	+	33.2242i	0.636928	+	1.10319i	−0.349175	+	0.937057i	$0.613538\pi$
$908$	−21.8150	−	12.5949i	−0.723955	−	0.417975i
$909$	22.6222	+	15.9254i	0.750332	+	0.528213i
$910$	0.0255595	−	0.0567830i	0.000847288	−	0.00188234i
$911$	−7.26657			−0.240752			−0.120376	−	0.992728i	$-0.538410\pi$
$911$	−7.26657			−0.240752			−0.120376	+	0.992728i	$0.538410\pi$
$912$	0.200118	−	7.54718i	0.00662658	−	0.249912i
$913$			28.2808i			0.935959i
$914$	−7.83794	−	13.5757i	−0.259256	−	0.449045i
$915$	−8.71146	+	5.69933i	−0.287992	+	0.188414i
$916$	13.7731	−	23.8557i	0.455076	−	0.788215i
$917$	−0.186367	−	0.322798i	−0.00615440	−	0.0106597i
$918$	9.67782	−	12.5141i	0.319416	−	0.413026i
$919$	3.88806			0.128255			0.0641277	−	0.997942i	$-0.479574\pi$
$919$	3.88806			0.128255			0.0641277	+	0.997942i	$0.479574\pi$
$920$	2.20431	−	1.58783i	0.0726740	−	0.0523492i
$921$	−43.7001	+	22.6789i	−1.43997	+	0.747294i
$922$	11.6613	−	20.1979i	0.384043	−	0.665182i
$923$	2.72077			0.0895552
$924$	−0.118176	−	0.0754959i	−0.00388770	−	0.00248363i
$925$	9.36738	+	10.5758i	0.307998	+	0.347729i
$926$	19.6170	+	33.9777i	0.644656	+	1.11658i
$927$	33.2416	+	2.99276i	1.09180	+	0.0982951i
$928$	−5.27930	+	3.04800i	−0.173301	+	0.100056i
$929$	2.63114	−	1.51909i	0.0863250	−	0.0498398i	−0.456216	−	0.889869i	$-0.650796\pi$
$929$	2.63114	−	1.51909i	0.0863250	−	0.0498398i	0.542541	+	0.840029i	$0.317462\pi$
$930$	0.953743	+	17.0908i	0.0312745	+	0.560429i
$931$	14.7669	−	26.6989i	0.483966	−	0.875019i
$932$	−1.47899			−0.0484460
$933$	13.8066	+	0.620255i	0.452009	+	0.0203062i
$934$	−21.1786	+	12.2274i	−0.692983	+	0.400094i
$935$	2.73018	+	27.0363i	0.0892865	+	0.884182i
$936$	−3.36802	−	2.37099i	−0.110087	−	0.0774984i
$937$	2.34671	+	1.35487i	0.0766636	+	0.0442618i	0.537842	−	0.843046i	$-0.319240\pi$
$937$	2.34671	+	1.35487i	0.0766636	+	0.0442618i	−0.461178	+	0.887308i	$0.652573\pi$
$938$	0.0600086			0.00195935
$939$	−31.2646	+	48.9393i	−1.02028	+	1.59708i
$940$	−15.6353	+	1.57888i	−0.509966	+	0.0514974i
$941$	15.2854	−	26.4752i	0.498291	−	0.863066i	−0.501707	−	0.865038i	$-0.667294\pi$
$941$	15.2854	−	26.4752i	0.498291	−	0.863066i	0.999998	+	0.00197191i	$0.000627678\pi$
$942$	−18.9338	−	12.0957i	−0.616896	−	0.394101i
$943$	1.41312			0.0460176
$944$	5.07177	−	8.78455i	0.165072	−	0.285913i
$945$	−0.124713	+	0.199968i	−0.00405693	+	0.00650495i
$946$	12.9087	+	7.45283i	0.419698	+	0.242313i
$947$	−6.18246	−	10.7083i	−0.200903	−	0.347974i	0.747917	−	0.663793i	$-0.231054\pi$
$947$	−6.18246	−	10.7083i	−0.200903	−	0.347974i	−0.948820	+	0.315819i	$0.897721\pi$
$948$	16.8147	+	0.755389i	0.546116	+	0.0245339i
$949$			9.99437i			0.324431i
$950$	16.0465	−	14.7482i	0.520617	−	0.478496i
$951$	−8.00662	+	12.5330i	−0.259632	+	0.406410i
$952$	−0.0308762	−	0.0534792i	−0.00100070	−	0.00173327i
$953$	−38.3044	+	22.1151i	−1.24080	+	0.716377i	−0.969257	−	0.246049i	$-0.920868\pi$
$953$	−38.3044	+	22.1151i	−1.24080	+	0.716377i	−0.271544	+	0.962426i	$0.587534\pi$
$954$	36.6366	+	3.29840i	1.18615	+	0.106790i
$955$	−20.3971	−	9.18125i	−0.660035	−	0.297098i
$956$	7.79480	+	4.50033i	0.252102	+	0.145551i
$957$	−22.6898	+	35.5170i	−0.733457	+	1.14810i
$958$	−32.2073			−1.04057
$959$	0.249631	+	0.144124i	0.00806099	+	0.00465402i
$960$	−3.45679	−	1.74660i	−0.111567	−	0.0563713i
$961$	11.4664			0.369882
$962$		−	3.87938i		−	0.125076i
$963$	−2.86355	+	31.8065i	−0.0922767	+	1.02495i
$964$	18.8017	−	10.8552i	0.605563	−	0.349622i
$965$	1.42056	−	0.143451i	0.0457296	−	0.00461786i
$966$	−0.00191554	+	0.0426393i	−6.16316e−5	+	0.00137190i
$967$	11.6150	−	6.70593i	0.373513	−	0.215648i	−0.301479	−	0.953473i	$-0.597480\pi$
$967$	11.6150	−	6.70593i	0.373513	−	0.215648i	0.674992	+	0.737825i	$0.264147\pi$
$968$		−	4.93307i		−	0.158555i
$969$	0.609260	−	22.9774i	0.0195722	−	0.738140i
$970$	21.1027	−	15.2009i	0.677568	−	0.488071i
$971$	−29.7403	−	51.5117i	−0.954412	−	1.65309i	−0.735707	−	0.677300i	$-0.763150\pi$
$971$	−29.7403	−	51.5117i	−0.954412	−	1.65309i	−0.218705	−	0.975791i	$-0.570183\pi$
$972$	11.4264	+	10.6037i	0.366502	+	0.340113i
$973$	0.258997	+	0.149532i	0.00830306	+	0.00479378i
$974$	19.5166	−	11.2679i	0.625354	−	0.361048i
$975$	−1.85191	−	11.7451i	−0.0593085	−	0.376144i
$976$	2.68790			0.0860375
$977$			9.77222i			0.312641i	0.987706	+	0.156321i	$0.0499633\pi$
$977$			9.77222i			0.312641i	−0.987706	+	0.156321i	$0.950037\pi$
$978$	25.7786	−	13.3782i	0.824309	−	0.427788i
$979$	44.2623	+	25.5548i	1.41463	+	0.816736i
$980$	−9.14803	−	12.6998i	−0.292223	−	0.405680i
$981$	5.65053	−	2.61756i	0.180408	−	0.0835722i
$982$	−14.9573	+	25.9068i	−0.477306	+	0.826719i
$983$	−19.9465	+	11.5161i	−0.636194	+	0.367307i	−0.783147	−	0.621837i	$-0.786387\pi$
$983$	−19.9465	+	11.5161i	−0.636194	+	0.367307i	0.146953	+	0.989143i	$0.453053\pi$
$984$	−0.927992	−	1.78816i	−0.0295833	−	0.0570043i
$985$	9.30605	−	20.6744i	0.296515	−	0.658740i
$986$	−16.0728	+	9.27965i	−0.511863	+	0.295524i
$987$	0.132922	−	0.208066i	0.00423096	−	0.00662283i
$988$	−5.98359	+	0.110019i	−0.190363	+	0.00350017i
$989$		−	4.53681i		−	0.144262i
$990$	−26.7751	+	0.290588i	−0.850967	+	0.00923550i
$991$	25.6000	−	14.7801i	0.813209	−	0.469507i	−0.0348598	−	0.999392i	$-0.511098\pi$
$991$	25.6000	−	14.7801i	0.813209	−	0.469507i	0.848069	+	0.529886i	$0.177765\pi$
$992$	2.20984	−	3.82756i	0.0701626	−	0.121525i
$993$	−34.0236	−	1.52849i	−1.07971	−	0.0485051i
$994$	−0.0200975	+	0.0348098i	−0.000637453	+	0.00110410i
$995$	−12.2018	−	16.9392i	−0.386824	−	0.537010i
$996$	−10.3415	−	6.60660i	−0.327682	−	0.209338i
$997$	−29.7441	−	17.1728i	−0.942005	−	0.543867i	−0.0514165	−	0.998677i	$-0.516374\pi$
$997$	−29.7441	−	17.1728i	−0.942005	−	0.543867i	−0.890588	+	0.454811i	$0.849707\pi$
$998$	9.39363	+	5.42341i	0.297350	+	0.171675i
$999$	−1.97144	+	14.5491i	−0.0623736	+	0.460313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.449.11	yes	80
3.2	odd	2	inner	570.2.n.a.449.37	yes	80
5.4	even	2	inner	570.2.n.a.449.30	yes	80
15.14	odd	2	inner	570.2.n.a.449.4	yes	80
19.8	odd	6	inner	570.2.n.a.179.4	✓	80
57.8	even	6	inner	570.2.n.a.179.30	yes	80
95.84	odd	6	inner	570.2.n.a.179.37	yes	80
285.179	even	6	inner	570.2.n.a.179.11	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.4	✓	80	19.8	odd	6	inner
570.2.n.a.179.11	yes	80	285.179	even	6	inner
570.2.n.a.179.30	yes	80	57.8	even	6	inner
570.2.n.a.179.37	yes	80	95.84	odd	6	inner
570.2.n.a.449.4	yes	80	15.14	odd	2	inner
570.2.n.a.449.11	yes	80	1.1	even	1	trivial
570.2.n.a.449.30	yes	80	5.4	even	2	inner
570.2.n.a.449.37	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.0777329 + 1.73031i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917815 - 2.03902i) q^{5} +(-0.797834 - 1.53736i) q^{6} -0.0202833i q^{7} +1.00000i q^{8} +(-2.98792 - 0.269003i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.0777329 + 1.73031i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917815 - 2.03902i) q^{5} +(-0.797834 - 1.53736i) q^{6} -0.0202833i q^{7} +1.00000i q^{8} +(-2.98792 - 0.269003i) q^{9} +(0.224660 + 2.22475i) q^{10} -3.99162i q^{11} +(1.45962 + 0.932471i) q^{12} +(0.686480 - 1.18902i) q^{13} +(0.0101416 + 0.0175658i) q^{14} +(3.45679 + 1.74660i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.52225 - 2.63661i) q^{17} +(2.72211 - 1.26099i) q^{18} +(2.10968 - 3.81435i) q^{19} +(-1.30694 - 1.81436i) q^{20} +(0.0350963 + 0.00157668i) q^{21} +(1.99581 + 3.45685i) q^{22} +(0.607462 - 1.05215i) q^{23} +(-1.73031 - 0.0777329i) q^{24} +(-3.31523 - 3.74289i) q^{25} +1.37296i q^{26} +(0.697717 - 5.14910i) q^{27} +(-0.0175658 - 0.0101416i) q^{28} +(-3.04800 + 5.27930i) q^{29} +(-3.86697 + 0.215794i) q^{30} -4.41969i q^{31} +(0.866025 + 0.500000i) q^{32} +(6.90673 + 0.310280i) q^{33} +(2.63661 + 1.52225i) q^{34} +(-0.0413581 - 0.0186163i) q^{35} +(-1.72692 + 2.45311i) q^{36} -2.82556 q^{37} +(0.0801327 + 4.35816i) q^{38} +(2.00400 + 1.28025i) q^{39} +(2.03902 + 0.917815i) q^{40} +(0.581569 + 1.00731i) q^{41} +(-0.0311826 + 0.0161827i) q^{42} +(3.23394 - 1.86712i) q^{43} +(-3.45685 - 1.99581i) q^{44} +(-3.29086 + 5.84553i) q^{45} +1.21492i q^{46} +(3.51393 - 6.08631i) q^{47} +(1.53736 - 0.797834i) q^{48} +6.99959 q^{49} +(4.74252 + 1.58383i) q^{50} +(4.68048 - 2.42901i) q^{51} +(-0.686480 - 1.18902i) q^{52} +(10.6188 + 6.13079i) q^{53} +(1.97031 + 4.80811i) q^{54} +(-8.13901 - 3.66357i) q^{55} +0.0202833 q^{56} +(6.43599 + 3.94690i) q^{57} -6.09601i q^{58} +(5.07177 + 8.78455i) q^{59} +(3.24099 - 2.12037i) q^{60} +(-1.34395 + 2.32779i) q^{61} +(2.20984 + 3.82756i) q^{62} +(-0.00545627 + 0.0606047i) q^{63} -1.00000 q^{64} +(-1.79437 - 2.49105i) q^{65} +(-6.13654 + 3.18465i) q^{66} +(1.47926 - 2.56216i) q^{67} -3.04450 q^{68} +(1.77333 + 1.13288i) q^{69} +(0.0451253 - 0.00455684i) q^{70} +(0.990840 + 1.71618i) q^{71} +(0.269003 - 2.98792i) q^{72} +(-6.30417 + 3.63971i) q^{73} +(2.44701 - 1.41278i) q^{74} +(6.73405 - 5.44542i) q^{75} +(-2.24848 - 3.73421i) q^{76} -0.0809632 q^{77} +(-2.37564 - 0.106724i) q^{78} +(8.41583 - 4.85888i) q^{79} +(-2.22475 + 0.224660i) q^{80} +(8.85527 + 1.60752i) q^{81} +(-1.00731 - 0.581569i) q^{82} -7.08504 q^{83} +(0.0189136 - 0.0296059i) q^{84} +(-6.77326 + 0.683977i) q^{85} +(-1.86712 + 3.23394i) q^{86} +(-8.89787 - 5.68435i) q^{87} +3.99162 q^{88} +(-6.40211 + 11.0888i) q^{89} +(-0.0727995 - 6.70781i) q^{90} +(-0.0241172 - 0.0139241i) q^{91} +(-0.607462 - 1.05215i) q^{92} +(7.64741 + 0.343555i) q^{93} +7.02786i q^{94} +(-5.84124 - 7.80256i) q^{95} +(-0.932471 + 1.45962i) q^{96} +(-5.81546 - 10.0727i) q^{97} +(-6.06182 + 3.49979i) q^{98} +(-1.07376 + 11.9266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4}+O(q^{10}) \) 80 * q + 40 * q^4	\( 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Introduction

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