LMFDB - Embedded newform 187.2.j.a.16.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(16,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("187.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.j (of order $10$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.14
Character	$\chi$	$=$	187.16
Dual form			187.2.j.a.152.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.636250 + 1.95818i) q^{2} +(1.78295 - 2.45402i) q^{3} +(-1.81160 + 1.31621i) q^{4} +(0.308808 + 0.100338i) q^{5} +(5.93981 + 1.92996i) q^{6} +(-0.911451 - 1.25450i) q^{7} +(-0.398550 - 0.289564i) q^{8} +(-1.91626 - 5.89763i) q^{9} +O(q^{10})$	\(q+(0.636250 + 1.95818i) q^{2} +(1.78295 - 2.45402i) q^{3} +(-1.81160 + 1.31621i) q^{4} +(0.308808 + 0.100338i) q^{5} +(5.93981 + 1.92996i) q^{6} +(-0.911451 - 1.25450i) q^{7} +(-0.398550 - 0.289564i) q^{8} +(-1.91626 - 5.89763i) q^{9} +0.668541i q^{10} +(-2.25299 + 2.43394i) q^{11} +6.79245i q^{12} +(0.0304646 + 0.0937603i) q^{13} +(1.87663 - 2.58296i) q^{14} +(0.796822 - 0.578925i) q^{15} +(-1.07050 + 3.29467i) q^{16} +(-0.856553 + 4.03315i) q^{17} +(10.3294 - 7.50474i) q^{18} +(1.43338 + 1.04141i) q^{19} +(-0.691504 + 0.224683i) q^{20} -4.70365 q^{21} +(-6.19954 - 2.86315i) q^{22} -0.138908i q^{23} +(-1.42119 + 0.461773i) q^{24} +(-3.95979 - 2.87696i) q^{25} +(-0.164216 + 0.119310i) q^{26} +(-9.23489 - 3.00060i) q^{27} +(3.30238 + 1.07301i) q^{28} +(1.70876 + 2.35190i) q^{29} +(1.64061 + 1.19198i) q^{30} +(-4.67478 + 1.51893i) q^{31} -8.11792 q^{32} +(1.95597 + 9.86847i) q^{33} +(-8.44260 + 0.888812i) q^{34} +(-0.155589 - 0.478854i) q^{35} +(11.2340 + 8.16199i) q^{36} +(-4.58765 - 6.31436i) q^{37} +(-1.12728 + 3.46941i) q^{38} +(0.284407 + 0.0924094i) q^{39} +(-0.0940214 - 0.129409i) q^{40} +(4.52331 - 6.22580i) q^{41} +(-2.99270 - 9.21058i) q^{42} +9.14565 q^{43} +(0.877954 - 7.37473i) q^{44} -2.01351i q^{45} +(0.272007 - 0.0883805i) q^{46} +(7.64861 + 5.55704i) q^{47} +(6.17654 + 8.50127i) q^{48} +(1.42008 - 4.37056i) q^{49} +(3.11417 - 9.58443i) q^{50} +(8.37025 + 9.29291i) q^{51} +(-0.178598 - 0.129759i) q^{52} +(-3.39054 - 10.4350i) q^{53} -19.9927i q^{54} +(-0.939957 + 0.525560i) q^{55} +0.763906i q^{56} +(5.11129 - 1.66076i) q^{57} +(-3.51824 + 4.84244i) q^{58} +(-4.87466 + 3.54165i) q^{59} +(-0.681540 + 2.09756i) q^{60} +(-11.4382 - 3.71649i) q^{61} +(-5.94866 - 8.18763i) q^{62} +(-5.65203 + 7.77936i) q^{63} +(-3.02402 - 9.30697i) q^{64} +0.0320107i q^{65} +(-18.0797 + 10.1089i) q^{66} +7.55263 q^{67} +(-3.75673 - 8.43388i) q^{68} +(-0.340884 - 0.247667i) q^{69} +(0.838687 - 0.609342i) q^{70} +(12.2893 + 3.99302i) q^{71} +(-0.944016 + 2.90538i) q^{72} +(6.77402 + 9.32364i) q^{73} +(9.44573 - 13.0009i) q^{74} +(-14.1202 + 4.58794i) q^{75} -3.96743 q^{76} +(5.10687 + 0.607968i) q^{77} +0.615714i q^{78} +(-10.0200 + 3.25570i) q^{79} +(-0.661160 + 0.910009i) q^{80} +(-8.77841 + 6.37789i) q^{81} +(15.0692 + 4.89626i) q^{82} +(4.13751 - 12.7339i) q^{83} +(8.52116 - 6.19098i) q^{84} +(-0.669189 + 1.15953i) q^{85} +(5.81892 + 17.9088i) q^{86} +8.81825 q^{87} +(1.60271 - 0.317663i) q^{88} -0.0685064 q^{89} +(3.94281 - 1.28110i) q^{90} +(0.0898558 - 0.123676i) q^{91} +(0.182832 + 0.251647i) q^{92} +(-4.60743 + 14.1802i) q^{93} +(-6.01524 + 18.5130i) q^{94} +(0.338146 + 0.465418i) q^{95} +(-14.4739 + 19.9216i) q^{96} +(-5.66884 + 1.84192i) q^{97} +9.46184 q^{98} +(18.6718 + 8.62324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36} - 60 q^{38} - 10 q^{42} + 32 q^{43} + 16 q^{47} - 18 q^{49} + 4 q^{50} - 2 q^{51} + 44 q^{52} - 16 q^{53} + 22 q^{55} - 50 q^{59} + 68 q^{60} - 80 q^{64} - 172 q^{66} + 40 q^{67} + 18 q^{68} + 6 q^{69} + 128 q^{70} + 186 q^{72} - 116 q^{76} - 30 q^{77} + 48 q^{81} - 12 q^{83} + 68 q^{84} - 108 q^{85} - 16 q^{86} + 92 q^{87} - 40 q^{89} - 80 q^{93} - 188 q^{94} + 72 q^{98}+O(q^{100}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	0.636250	+	1.95818i	0.449897	+	1.38464i	0.877023	+	0.480448i	$0.159526\pi$
$2$	0.636250	+	1.95818i	0.449897	+	1.38464i	−0.427127	+	0.904192i	$0.640474\pi$
$3$	1.78295	−	2.45402i	1.02939	−	1.41683i	0.123981	−	0.992285i	$-0.460434\pi$
$3$	1.78295	−	2.45402i	1.02939	−	1.41683i	0.905407	−	0.424546i	$-0.139566\pi$
$4$	−1.81160	+	1.31621i	−0.905802	+	0.658104i
$5$	0.308808	+	0.100338i	0.138103	+	0.0448725i	0.377253	−	0.926110i	$-0.376869\pi$
$5$	0.308808	+	0.100338i	0.138103	+	0.0448725i	−0.239150	+	0.970983i	$0.576869\pi$
$6$	5.93981	+	1.92996i	2.42492	+	0.787903i
$7$	−0.911451	−	1.25450i	−0.344496	−	0.474158i	0.601252	−	0.799060i	$-0.294669\pi$
$7$	−0.911451	−	1.25450i	−0.344496	−	0.474158i	−0.945748	+	0.324901i	$0.894669\pi$
$8$	−0.398550	−	0.289564i	−0.140909	−	0.102376i
$9$	−1.91626	−	5.89763i	−0.638753	−	1.96588i
$10$			0.668541i			0.211411i
$11$	−2.25299	+	2.43394i	−0.679301	+	0.733860i
$11$	−2.25299	+	2.43394i	−0.679301	+	0.733860i
$12$			6.79245i			1.96081i
$13$	0.0304646	+	0.0937603i	0.00844935	+	0.0260044i	0.955192	−	0.295986i	$-0.0956481\pi$
$13$	0.0304646	+	0.0937603i	0.00844935	+	0.0260044i	−0.946743	+	0.321990i	$0.895648\pi$
$14$	1.87663	−	2.58296i	0.501550	−	0.690325i
$15$	0.796822	−	0.578925i	0.205738	−	0.149478i
$16$	−1.07050	+	3.29467i	−0.267626	+	0.823667i
$17$	−0.856553	+	4.03315i	−0.207745	+	0.978183i
$17$	−0.856553	+	4.03315i	−0.207745	+	0.978183i
$18$	10.3294	−	7.50474i	2.43466	−	1.76888i
$19$	1.43338	+	1.04141i	0.328840	+	0.238916i	0.739938	−	0.672675i	$-0.234855\pi$
$19$	1.43338	+	1.04141i	0.328840	+	0.238916i	−0.411098	+	0.911591i	$0.634855\pi$
$20$	−0.691504	+	0.224683i	−0.154625	+	0.0502407i
$21$	−4.70365			−1.02642
$22$	−6.19954	−	2.86315i	−1.32175	−	0.610426i
$23$		−	0.138908i		−	0.0289644i	−0.999895	−	0.0144822i	$-0.995390\pi$
$23$		−	0.138908i		−	0.0289644i	0.999895	−	0.0144822i	$-0.00460999\pi$
$24$	−1.42119	+	0.461773i	−0.290100	+	0.0942590i
$25$	−3.95979	−	2.87696i	−0.791958	−	0.575391i
$26$	−0.164216	+	0.119310i	−0.0322054	+	0.0233986i
$27$	−9.23489	−	3.00060i	−1.77726	−	0.577465i
$28$	3.30238	+	1.07301i	0.624090	+	0.202779i
$29$	1.70876	+	2.35190i	0.317308	+	0.436737i	0.937643	−	0.347600i	$-0.113003\pi$
$29$	1.70876	+	2.35190i	0.317308	+	0.436737i	−0.620335	+	0.784337i	$0.713003\pi$
$30$	1.64061	+	1.19198i	0.299534	+	0.217624i
$31$	−4.67478	+	1.51893i	−0.839616	+	0.272808i	−0.697090	−	0.716983i	$-0.745522\pi$
$31$	−4.67478	+	1.51893i	−0.839616	+	0.272808i	−0.142526	+	0.989791i	$0.545522\pi$
$32$	−8.11792			−1.43506
$33$	1.95597	+	9.86847i	0.340491	+	1.71788i
$34$	−8.44260	+	0.888812i	−1.44789	+	0.152430i
$35$	−0.155589	−	0.478854i	−0.0262994	−	0.0809412i
$36$	11.2340	+	8.16199i	1.87233	+	1.36033i
$37$	−4.58765	−	6.31436i	−0.754205	−	1.03807i	−0.997674	−	0.0681654i	$-0.978285\pi$
$37$	−4.58765	−	6.31436i	−0.754205	−	1.03807i	0.243469	−	0.969909i	$-0.421715\pi$
$38$	−1.12728	+	3.46941i	−0.182869	+	0.562812i
$39$	0.284407	+	0.0924094i	0.0455415	+	0.0147973i
$40$	−0.0940214	−	0.129409i	−0.0148661	−	0.0204614i
$41$	4.52331	−	6.22580i	0.706422	−	0.972306i	−0.293445	−	0.955976i	$-0.594802\pi$
$41$	4.52331	−	6.22580i	0.706422	−	0.972306i	0.999867	−	0.0163299i	$-0.00519821\pi$
$42$	−2.99270	−	9.21058i	−0.461784	−	1.42122i
$43$	9.14565			1.39470			0.697349	−	0.716731i	$-0.254363\pi$
$43$	9.14565			1.39470			0.697349	+	0.716731i	$0.254363\pi$
$44$	0.877954	−	7.37473i	0.132357	−	1.11178i
$45$		−	2.01351i		−	0.300157i
$46$	0.272007	−	0.0883805i	0.0401053	−	0.0130310i
$47$	7.64861	+	5.55704i	1.11567	+	0.810578i	0.983546	−	0.180656i	$-0.0578220\pi$
$47$	7.64861	+	5.55704i	1.11567	+	0.810578i	0.132119	+	0.991234i	$0.457822\pi$
$48$	6.17654	+	8.50127i	0.891506	+	1.22705i
$49$	1.42008	−	4.37056i	0.202869	−	0.624365i
$50$	3.11417	−	9.58443i	0.440410	−	1.35544i
$51$	8.37025	+	9.29291i	1.17207	+	1.30127i
$52$	−0.178598	−	0.129759i	−0.0247671	−	0.0179943i
$53$	−3.39054	−	10.4350i	−0.465726	−	1.43336i	−0.858067	−	0.513538i	$-0.828335\pi$
$53$	−3.39054	−	10.4350i	−0.465726	−	1.43336i	0.392341	−	0.919820i	$-0.371665\pi$
$54$		−	19.9927i		−	2.72066i
$55$	−0.939957	+	0.525560i	−0.126744	+	0.0708665i
$56$			0.763906i			0.102081i
$57$	5.11129	−	1.66076i	0.677007	−	0.219973i
$58$	−3.51824	+	4.84244i	−0.461968	+	0.635844i
$59$	−4.87466	+	3.54165i	−0.634627	+	0.461083i	−0.858000	−	0.513650i	$-0.828293\pi$
$59$	−4.87466	+	3.54165i	−0.634627	+	0.461083i	0.223373	+	0.974733i	$0.428293\pi$
$60$	−0.681540	+	2.09756i	−0.0879864	+	0.270794i
$61$	−11.4382	−	3.71649i	−1.46451	−	0.475848i	−0.535066	−	0.844810i	$-0.679713\pi$
$61$	−11.4382	−	3.71649i	−1.46451	−	0.475848i	−0.929444	+	0.368962i	$0.879713\pi$
$62$	−5.94866	−	8.18763i	−0.755480	−	1.03983i
$63$	−5.65203	+	7.77936i	−0.712089	+	0.980107i
$64$	−3.02402	−	9.30697i	−0.378002	−	1.16337i
$65$			0.0320107i			0.00397044i
$66$	−18.0797	+	10.1089i	−2.22546	+	1.24432i
$67$	7.55263			0.922701			0.461350	−	0.887218i	$-0.347365\pi$
$67$	7.55263			0.922701			0.461350	+	0.887218i	$0.347365\pi$
$68$	−3.75673	−	8.43388i	−0.455570	−	1.02276i
$69$	−0.340884	−	0.247667i	−0.0410376	−	0.0298156i
$70$	0.838687	−	0.609342i	0.100242	−	0.0728303i
$71$	12.2893	+	3.99302i	1.45847	+	0.473885i	0.927602	−	0.373571i	$-0.121867\pi$
$71$	12.2893	+	3.99302i	1.45847	+	0.473885i	0.530866	+	0.847456i	$0.321867\pi$
$72$	−0.944016	+	2.90538i	−0.111253	+	0.342403i
$73$	6.77402	+	9.32364i	0.792840	+	1.09125i	0.993749	+	0.111640i	$0.0356104\pi$
$73$	6.77402	+	9.32364i	0.792840	+	1.09125i	−0.200909	+	0.979610i	$0.564390\pi$
$74$	9.44573	−	13.0009i	1.09804	−	1.51133i
$75$	−14.1202	+	4.58794i	−1.63046	+	0.529770i
$76$	−3.96743			−0.455095
$77$	5.10687	+	0.607968i	0.581982	+	0.0692844i
$78$			0.615714i			0.0697159i
$79$	−10.0200	+	3.25570i	−1.12734	+	0.366295i	−0.812565	−	0.582871i	$-0.801929\pi$
$79$	−10.0200	+	3.25570i	−1.12734	+	0.366295i	−0.314775	+	0.949166i	$0.601929\pi$
$80$	−0.661160	+	0.910009i	−0.0739200	+	0.101742i
$81$	−8.77841	+	6.37789i	−0.975379	+	0.708654i
$82$	15.0692	+	4.89626i	1.66411	+	0.540702i
$83$	4.13751	−	12.7339i	0.454150	−	1.39773i	−0.417980	−	0.908456i	$-0.637262\pi$
$83$	4.13751	−	12.7339i	0.454150	−	1.39773i	0.872130	−	0.489274i	$-0.162738\pi$
$84$	8.52116	−	6.19098i	0.929735	−	0.675492i
$85$	−0.669189	+	1.15953i	−0.0725837	+	0.125768i
$86$	5.81892	+	17.9088i	0.627470	+	1.93115i
$87$	8.81825			0.945416
$88$	1.60271	−	0.317663i	0.170849	−	0.0338630i
$89$	−0.0685064			−0.00726167			−0.00363083	−	0.999993i	$-0.501156\pi$
$89$	−0.0685064			−0.00726167			−0.00363083	+	0.999993i	$0.501156\pi$
$90$	3.94281	−	1.28110i	0.415609	−	0.135039i
$91$	0.0898558	−	0.123676i	0.00941945	−	0.0129648i
$92$	0.182832	+	0.251647i	0.0190616	+	0.0262360i
$93$	−4.60743	+	14.1802i	−0.477768	+	1.47042i
$94$	−6.01524	+	18.5130i	−0.620424	+	1.90947i
$95$	0.338146	+	0.465418i	0.0346931	+	0.0477509i
$96$	−14.4739	+	19.9216i	−1.47723	+	2.03324i
$97$	−5.66884	+	1.84192i	−0.575584	+	0.187018i	−0.582321	−	0.812959i	$-0.697855\pi$
$97$	−5.66884	+	1.84192i	−0.575584	+	0.187018i	0.00673757	+	0.999977i	$0.497855\pi$
$98$	9.46184			0.955791
$99$	18.6718	+	8.62324i	1.87658	+	0.866669i
$100$	10.9602			1.09602
$101$	0.602650	+	1.85477i	0.0599659	+	0.184556i	0.976552	−	0.215281i	$-0.0690667\pi$
$101$	0.602650	+	1.85477i	0.0599659	+	0.184556i	−0.916586	+	0.399837i	$0.869067\pi$
$102$	−12.8716	+	22.3030i	−1.27448	+	2.20833i
$103$	−9.91136	+	7.20103i	−0.976596	+	0.709538i	−0.956945	−	0.290269i	$-0.906255\pi$
$103$	−9.91136	+	7.20103i	−0.976596	+	0.709538i	−0.0196505	+	0.999807i	$0.506255\pi$
$104$	0.0150079	−	0.0461896i	0.00147165	−	0.00452927i
$105$	−1.45253	−	0.471955i	−0.141752	−	0.0460581i
$106$	18.2763	−	13.2785i	1.77515	−	1.28973i
$107$	−4.42618	+	6.09211i	−0.427895	+	0.588947i	−0.967468	−	0.252992i	$-0.918585\pi$
$107$	−4.42618	+	6.09211i	−0.427895	+	0.588947i	0.539574	+	0.841938i	$0.318585\pi$
$108$	20.6794	−	6.71914i	1.98987	−	0.646549i
$109$			9.05593i			0.867401i	0.901057	+	0.433700i	$0.142792\pi$
$109$			9.05593i			0.867401i	−0.901057	+	0.433700i	$0.857208\pi$
$110$	−1.62719	−	1.50621i	−0.155146	−	0.143612i
$111$	−23.6751			−2.24714
$112$	5.10889	−	1.65998i	0.482745	−	0.156853i
$113$	10.3261	−	14.2126i	0.971394	−	1.33701i	0.0300544	−	0.999548i	$-0.490432\pi$
$113$	10.3261	−	14.2126i	0.971394	−	1.33701i	0.941340	−	0.337461i	$-0.109568\pi$
$114$	6.50411	+	8.95215i	0.609166	+	0.838445i
$115$	0.0139378	−	0.0428961i	0.00129970	−	0.00400008i
$116$	−6.19118	−	2.01164i	−0.574837	−	0.186776i
$117$	0.494586	−	0.359338i	0.0457245	−	0.0332208i
$118$	−10.0367	−	7.29207i	−0.923950	−	0.671289i
$119$	5.84031	−	2.60147i	0.535381	−	0.238476i
$120$	−0.485209			−0.0442933
$121$	−0.848100	−	10.9673i	−0.0771000	−	0.997023i
$122$		−	24.7626i		−	2.24190i
$123$	−7.21341	−	22.2006i	−0.650411	−	2.00176i
$124$	6.46963	−	8.90468i	0.580990	−	0.799664i
$125$	−1.88842	−	2.59918i	−0.168905	−	0.232478i
$126$	−18.8295	−	6.11806i	−1.67746	−	0.545040i
$127$	−2.71883	+	8.36770i	−0.241257	+	0.742513i	0.754972	+	0.655757i	$0.227650\pi$
$127$	−2.71883	+	8.36770i	−0.241257	+	0.742513i	−0.996230	+	0.0867565i	$0.972350\pi$
$128$	3.16559	−	2.29993i	0.279801	−	0.203287i
$129$	16.3063	−	22.4436i	1.43569	−	1.97605i
$130$	−0.0626826	+	0.0203668i	−0.00549763	+	0.00178629i
$131$			2.87463i			0.251158i	0.992084	+	0.125579i	$0.0400788\pi$
$131$			2.87463i			0.251158i	−0.992084	+	0.125579i	$0.959921\pi$
$132$	−16.5324	−	15.3033i	−1.43896	−	1.33198i
$133$		−	2.74737i		−	0.238228i
$134$	4.80536	+	14.7894i	0.415120	+	1.27761i
$135$	−2.55074	−	1.85322i	−0.219532	−	0.159500i
$136$	1.50923	−	1.35939i	0.129416	−	0.116567i
$137$	−2.95268	+	9.08742i	−0.252265	+	0.776391i	0.742092	+	0.670298i	$0.233834\pi$
$137$	−2.95268	+	9.08742i	−0.252265	+	0.776391i	−0.994356	+	0.106092i	$0.966166\pi$
$138$	0.268088	−	0.825089i	0.0228211	−	0.0702363i
$139$	−2.65902	−	3.65983i	−0.225535	−	0.310422i	0.681221	−	0.732078i	$-0.261449\pi$
$139$	−2.65902	−	3.65983i	−0.225535	−	0.310422i	−0.906756	+	0.421655i	$0.861449\pi$
$140$	0.912138	+	0.662707i	0.0770897	+	0.0560090i
$141$	27.2742	−	8.86193i	2.29690	−	0.746309i
$142$			26.6051i			2.23265i
$143$	−0.296843	−	0.137092i	−0.0248233	−	0.0114642i
$144$	21.4821			1.79018
$145$	0.291693	+	0.897740i	0.0242238	+	0.0745532i
$146$	−13.9474	+	19.1969i	−1.15429	+	1.58875i
$147$	−8.19351	−	11.2774i	−0.675789	−	0.930144i
$148$	16.6220	+	5.40082i	1.36632	+	0.443945i
$149$	3.56026	−	10.9574i	0.291668	−	0.897662i	−0.692652	−	0.721272i	$-0.743558\pi$
$149$	3.56026	−	10.9574i	0.291668	−	0.897662i	0.984320	−	0.176391i	$-0.0564422\pi$
$150$	−17.9680	−	24.7308i	−1.46708	−	2.01926i
$151$	−0.728676	−	0.529414i	−0.0592988	−	0.0430831i	0.557741	−	0.830015i	$-0.311668\pi$
$151$	−0.728676	−	0.529414i	−0.0592988	−	0.0430831i	−0.617040	+	0.786932i	$0.711668\pi$
$152$	−0.269719	−	0.830109i	−0.0218771	−	0.0673307i
$153$	25.4274	−	2.67692i	2.05569	−	0.216416i
$154$	2.05874	+	10.3870i	0.165898	+	0.837006i
$155$	−1.59602			−0.128195
$156$	−0.636862	+	0.206929i	−0.0509898	+	0.0165676i
$157$	−2.57021	−	1.86737i	−0.205125	−	0.149032i	0.480480	−	0.877006i	$-0.340462\pi$
$157$	−2.57021	−	1.86737i	−0.205125	−	0.149032i	−0.685605	+	0.727973i	$0.740462\pi$
$158$	−12.7505	−	17.5495i	−1.01437	−	1.39616i
$159$	−31.6529	−	10.2846i	−2.51024	−	0.815625i
$160$	−2.50688	−	0.814535i	−0.198186	−	0.0643946i
$161$	−0.174261	+	0.126608i	−0.0137337	+	0.00997812i
$162$	−18.0743	−	13.1317i	−1.42005	−	1.03173i
$163$	13.8020	−	4.48453i	1.08105	−	0.351255i	0.286269	−	0.958149i	$-0.407585\pi$
$163$	13.8020	−	4.48453i	1.08105	−	0.351255i	0.794783	+	0.606894i	$0.207585\pi$
$164$			17.2323i			1.34562i
$165$	−0.386162	+	3.24372i	−0.0300627	+	0.252524i
$166$	27.5678			2.13967
$167$	5.82427	−	1.89242i	0.450696	−	0.146440i	−0.0748693	−	0.997193i	$-0.523854\pi$
$167$	5.82427	−	1.89242i	0.450696	−	0.146440i	0.525565	+	0.850753i	$0.323854\pi$
$168$	1.87464	+	1.36201i	0.144632	+	0.105081i
$169$	10.5094	−	7.63550i	0.808412	−	0.587346i
$170$	−2.69633	−	0.572640i	−0.206799	−	0.0439195i
$171$	3.39514	−	10.4492i	0.259633	−	0.799067i
$172$	−16.5683	+	12.0376i	−1.26332	+	0.917856i
$173$	−8.12432	+	11.1822i	−0.617680	+	0.850164i	−0.997181	−	0.0750271i	$-0.976096\pi$
$173$	−8.12432	+	11.1822i	−0.617680	+	0.850164i	0.379501	+	0.925191i	$0.376096\pi$
$174$	5.61061	+	17.2677i	0.425339	+	1.30906i
$175$			7.58978i			0.573733i
$176$	−5.60719	−	10.0284i	−0.422658	−	0.755918i
$177$			18.2771i			1.37379i
$178$	−0.0435872	−	0.134148i	−0.00326700	−	0.0100548i
$179$	12.5723	+	9.13430i	0.939697	+	0.682730i	0.948348	−	0.317233i	$-0.102754\pi$
$179$	12.5723	+	9.13430i	0.939697	+	0.682730i	−0.00865053	+	0.999963i	$0.502754\pi$
$180$	2.65020	+	3.64769i	0.197534	+	0.271882i
$181$	15.2311	+	4.94888i	1.13212	+	0.367847i	0.814380	−	0.580331i	$-0.197077\pi$
$181$	15.2311	+	4.94888i	1.13212	+	0.367847i	0.317737	+	0.948179i	$0.397077\pi$
$182$	0.299350	+	0.0972647i	0.0221893	+	0.00720974i
$183$	−29.5141	+	21.4432i	−2.18174	+	1.58513i
$184$	−0.0402228	+	0.0553620i	−0.00296527	+	0.00408134i
$185$	−0.783135	−	2.41024i	−0.0575772	−	0.177204i
$186$	−30.6988			−2.25094
$187$	−7.88664	−	11.1714i	−0.576728	−	0.816936i
$188$	−21.1705			−1.54402
$189$	4.65289	+	14.3201i	0.338448	+	1.04163i
$190$	−0.696226	+	0.958272i	−0.0505095	+	0.0695204i
$191$	3.62158	−	2.63123i	0.262048	−	0.190389i	−0.449001	−	0.893531i	$-0.648220\pi$
$191$	3.62158	−	2.63123i	0.262048	−	0.190389i	0.711050	+	0.703142i	$0.248220\pi$
$192$	−28.2312	−	9.17287i	−2.03741	−	0.661995i
$193$	5.11861	+	1.66314i	0.368445	+	0.119715i	0.487387	−	0.873186i	$-0.337950\pi$
$193$	5.11861	+	1.66314i	0.368445	+	0.119715i	−0.118942	+	0.992901i	$0.537950\pi$
$194$	−7.21360	−	9.92866i	−0.517906	−	0.712837i
$195$	0.0785550	+	0.0570736i	0.00562544	+	0.00408712i
$196$	3.17994	+	9.78684i	0.227138	+	0.699060i
$197$			19.1597i			1.36507i	0.730852	+	0.682536i	$0.239123\pi$
$197$			19.1597i			1.36507i	−0.730852	+	0.682536i	$0.760877\pi$
$198$	−5.00591	+	42.0492i	−0.355755	+	2.98830i
$199$		−	11.5729i		−	0.820378i	−0.912000	−	0.410189i	$-0.865463\pi$
$199$		−	11.5729i		−	0.820378i	0.912000	−	0.410189i	$-0.134537\pi$
$200$	0.745113	+	2.29322i	0.0526875	+	0.162155i
$201$	13.4660	−	18.5343i	0.949817	−	1.30731i
$202$	−3.24852	+	2.36019i	−0.228565	+	0.166062i
$203$	1.39302	−	4.28729i	0.0977711	−	0.300909i
$204$	−27.3950	−	5.81809i	−1.91803	−	0.407348i
$205$	2.02152	−	1.46872i	0.141189	−	0.102580i
$206$	−20.4070	−	14.8265i	−1.42182	−	1.03301i
$207$	−0.819231	+	0.266184i	−0.0569405	+	0.0185011i
$208$	−0.341522			−0.0236803
$209$	−5.76411	+	1.14247i	−0.398712	+	0.0790263i
$210$		−	3.14458i		−	0.216997i
$211$	−9.87824	+	3.20963i	−0.680046	+	0.220960i	−0.628615	−	0.777716i	$-0.716378\pi$
$211$	−9.87824	+	3.20963i	−0.680046	+	0.220960i	−0.0514304	+	0.998677i	$0.516378\pi$
$212$	19.8769	+	14.4414i	1.36515	+	0.991842i
$213$	31.7101	−	23.0388i	2.17274	−	1.57859i
$214$	−14.7456	−	4.79113i	−1.00799	−	0.327515i
$215$	2.82425	+	0.917655i	0.192612	+	0.0625836i
$216$	2.81170	+	3.86998i	0.191312	+	0.263319i
$217$	6.16634	+	4.48011i	0.418598	+	0.304129i
$218$	−17.7331	+	5.76184i	−1.20104	+	0.390241i
$219$	34.9582			2.36226
$220$	1.01108	−	2.18928i	0.0681673	−	0.147602i
$221$	−0.404244	+	0.0425576i	−0.0271924	+	0.00286274i
$222$	−15.0633	−	46.3601i	−1.01098	−	3.11148i
$223$	−18.6161	−	13.5254i	−1.24662	−	0.905725i	−0.248602	−	0.968606i	$-0.579971\pi$
$223$	−18.6161	−	13.5254i	−1.24662	−	0.905725i	−0.998021	+	0.0628810i	$0.979971\pi$
$224$	7.39909	+	10.1840i	0.494372	+	0.680445i
$225$	−9.37926	+	28.8664i	−0.625284	+	1.92443i
$226$	34.4007	+	11.1775i	2.28830	+	0.743514i
$227$	4.30557	+	5.92611i	0.285771	+	0.393330i	0.927635	−	0.373489i	$-0.121839\pi$
$227$	4.30557	+	5.92611i	0.285771	+	0.393330i	−0.641864	+	0.766819i	$0.721839\pi$
$228$	−7.07373	+	9.73615i	−0.468469	+	0.644793i
$229$	−2.44290	−	7.51849i	−0.161432	−	0.496836i	0.837324	−	0.546707i	$-0.184119\pi$
$229$	−2.44290	−	7.51849i	−0.161432	−	0.496836i	−0.998756	+	0.0498715i	$0.984119\pi$
$230$	0.0928659			0.00612340
$231$	10.5973	−	11.4484i	0.697249	−	0.753249i
$232$		−	1.43215i		−	0.0940250i
$233$	−18.1266	+	5.88970i	−1.18751	+	0.385847i	−0.835153	−	0.550017i	$-0.814621\pi$
$233$	−18.1266	+	5.88970i	−1.18751	+	0.385847i	−0.352361	+	0.935864i	$0.614621\pi$
$234$	1.01833	+	0.739858i	0.0665701	+	0.0483660i
$235$	1.80437	+	2.48351i	0.117704	+	0.162006i
$236$	4.16941	−	12.8321i	0.271405	−	0.835300i
$237$	−9.87564	+	30.3941i	−0.641492	+	1.97431i
$238$	8.81004	+	9.78117i	0.571070	+	0.634019i
$239$	−7.18482	−	5.22008i	−0.464747	−	0.337659i	0.330643	−	0.943756i	$-0.392734\pi$
$239$	−7.18482	−	5.22008i	−0.464747	−	0.337659i	−0.795391	+	0.606097i	$0.792734\pi$
$240$	1.05437	+	3.24500i	0.0680590	+	0.209464i
$241$		−	24.5026i		−	1.57835i	−0.614167	−	0.789176i	$-0.710508\pi$
$241$		−	24.5026i		−	1.57835i	0.614167	−	0.789176i	$-0.289492\pi$
$242$	20.9362	−	8.63864i	1.34583	−	0.555313i
$243$			3.78347i			0.242710i
$244$	25.6131	−	8.32222i	1.63971	−	0.532775i
$245$	0.877065	−	1.20718i	0.0560336	−	0.0771237i
$246$	38.8831	−	28.2502i	2.47910	−	1.80117i
$247$	−0.0539757	+	0.166120i	−0.00343439	+	0.0105700i
$248$	2.30296	+	0.748278i	0.146238	+	0.0475157i
$249$	−23.8724	−	32.8575i	−1.51285	−	2.08226i
$250$	3.88815	−	5.35159i	0.245908	−	0.338464i
$251$	2.18630	+	6.72874i	0.137998	+	0.424714i	0.996044	−	0.0888583i	$-0.0283218\pi$
$251$	2.18630	+	6.72874i	0.137998	+	0.424714i	−0.858046	+	0.513572i	$0.828322\pi$
$252$		−	21.5324i		−	1.35641i
$253$	0.338094	+	0.312959i	0.0212558	+	0.0196756i
$254$	−18.1153			−1.13665
$255$	1.65237	+	3.70958i	0.103476	+	0.232303i
$256$	−9.31619	−	6.76861i	−0.582262	−	0.423038i
$257$	0.864076	−	0.627788i	0.0538996	−	0.0391603i	−0.560509	−	0.828148i	$-0.689395\pi$
$257$	0.864076	−	0.627788i	0.0538996	−	0.0391603i	0.614409	+	0.788988i	$0.289395\pi$
$258$	54.3234	+	17.6508i	3.38203	+	1.09889i
$259$	−3.73997	+	11.5105i	−0.232391	+	0.715225i
$260$	−0.0421327	−	0.0579907i	−0.00261296	−	0.00359643i
$261$	10.5962	−	14.5845i	0.655891	−	0.902756i
$262$	−5.62903	+	1.82898i	−0.347763	+	0.112995i
$263$	−24.6145			−1.51779			−0.758897	−	0.651211i	$-0.774261\pi$
$263$	−24.6145			−1.51779			−0.758897	+	0.651211i	$0.774261\pi$
$264$	2.07800	−	4.49946i	0.127892	−	0.276923i
$265$		−	3.56261i		−	0.218850i
$266$	5.37984	−	1.74802i	0.329859	−	0.107178i
$267$	−0.122144	+	0.168116i	−0.00747507	+	0.0102885i
$268$	−13.6824	+	9.94083i	−0.835784	+	0.607233i
$269$	20.0851	+	6.52606i	1.22461	+	0.397901i	0.848760	−	0.528779i	$-0.177350\pi$
$269$	20.0851	+	6.52606i	1.22461	+	0.397901i	0.375853	+	0.926679i	$0.377350\pi$
$270$	2.00602	−	6.17390i	0.122083	−	0.375732i
$271$	0.534653	−	0.388448i	0.0324778	−	0.0235965i	−0.571428	−	0.820652i	$-0.693610\pi$
$271$	0.534653	−	0.388448i	0.0324778	−	0.0235965i	0.603906	+	0.797056i	$0.293610\pi$
$272$	−12.3710	−	7.13956i	−0.750100	−	0.432899i
$273$	−0.143295	−	0.441016i	−0.00867260	−	0.0266915i
$274$	−19.6734			−1.18851
$275$	15.9237	−	3.15614i	0.960234	−	0.190322i
$276$	0.943528			0.0567937
$277$	7.96228	−	2.58710i	0.478407	−	0.155444i	−0.0598797	−	0.998206i	$-0.519072\pi$
$277$	7.96228	−	2.58710i	0.478407	−	0.155444i	0.538287	+	0.842762i	$0.319072\pi$
$278$	5.47478	−	7.53539i	0.328356	−	0.451943i
$279$	17.9162	+	24.6595i	1.07261	+	1.47633i
$280$	−0.0766487	+	0.235901i	−0.00458064	+	0.0140978i
$281$	5.55680	−	17.1021i	0.331491	−	1.02022i	−0.636934	−	0.770918i	$-0.719798\pi$
$281$	5.55680	−	17.1021i	0.331491	−	1.02022i	0.968425	−	0.249305i	$-0.0802022\pi$
$282$	34.7064	+	47.7693i	2.06674	+	2.84462i
$283$	−17.3369	+	23.8622i	−1.03057	+	1.41846i	−0.126054	+	0.992023i	$0.540231\pi$
$283$	−17.3369	+	23.8622i	−1.03057	+	1.41846i	−0.904518	+	0.426436i	$0.859769\pi$
$284$	−27.5189	+	8.94144i	−1.63295	+	0.530577i
$285$	1.74505			0.103368
$286$	0.0795838	−	0.668496i	0.00470589	−	0.0395290i
$287$	−11.9331			−0.704386
$288$	15.5560	+	47.8765i	0.916648	+	2.82115i
$289$	−15.5326	−	6.90921i	−0.913684	−	0.406424i
$290$	−1.57234	+	1.14237i	−0.0923311	+	0.0670825i
$291$	−5.58716	+	17.1955i	−0.327525	+	1.00802i
$292$	−24.5437	−	7.97473i	−1.43631	−	0.466686i
$293$	−15.3140	+	11.1263i	−0.894653	+	0.650004i	−0.937087	−	0.349096i	$-0.886489\pi$
$293$	−15.3140	+	11.1263i	−0.894653	+	0.650004i	0.0424339	+	0.999099i	$0.486489\pi$
$294$	16.8700	−	23.2196i	0.983879	−	1.35419i
$295$	−1.86070	+	0.604577i	−0.108334	+	0.0351998i
$296$			3.84501i			0.223486i
$297$	28.1094	−	15.7168i	1.63107	−	0.911983i
$298$	23.7217			1.37416
$299$	0.0130241	−	0.00423179i	0.000753203	−	0.000244731i
$300$	19.5416	−	26.8967i	1.12823	−	1.55288i
$301$	−8.33581	−	11.4733i	−0.480468	−	0.661308i
$302$	0.573066	−	1.76372i	0.0329763	−	0.101490i
$303$	5.62613	+	1.82804i	0.323213	+	0.105018i
$304$	−4.96554	+	3.60768i	−0.284793	+	0.206914i
$305$	−3.15930	−	2.29537i	−0.180901	−	0.131432i
$306$	21.4201	+	48.0882i	1.22450	+	2.74902i
$307$	16.1049			0.919155			0.459578	−	0.888138i	$-0.348001\pi$
$307$	16.1049			0.919155			0.459578	+	0.888138i	$0.348001\pi$
$308$	−10.0518	+	5.62030i	−0.572757	+	0.320247i
$309$			37.1618i			2.11406i
$310$	−1.01547	−	3.12528i	−0.0576746	−	0.177504i
$311$	−11.8676	+	16.3344i	−0.672951	+	0.926238i	−0.999823	−	0.0188310i	$-0.994006\pi$
$311$	−11.8676	+	16.3344i	−0.672951	+	0.926238i	0.326872	+	0.945069i	$0.394006\pi$
$312$	−0.0865920	−	0.119184i	−0.00490231	−	0.00674745i
$313$	10.3244	+	3.35461i	0.583572	+	0.189614i	0.585900	−	0.810383i	$-0.300741\pi$
$313$	10.3244	+	3.35461i	0.583572	+	0.189614i	−0.00232818	+	0.999997i	$0.500741\pi$
$314$	2.02134	−	6.22105i	0.114071	−	0.351074i
$315$	−2.52596	+	1.83522i	−0.142322	+	0.103403i
$316$	13.8671	−	19.0865i	0.780087	−	1.07370i
$317$	−11.0249	+	3.58222i	−0.619223	+	0.201198i	−0.601795	−	0.798650i	$-0.705548\pi$
$317$	−11.0249	+	3.58222i	−0.619223	+	0.201198i	−0.0174276	+	0.999848i	$0.505548\pi$
$318$		−	68.5255i		−	3.84272i
$319$	−9.57419	−	1.13980i	−0.536052	−	0.0638164i
$320$		−	3.17749i		−	0.177627i
$321$	7.05852	+	21.7239i	0.393968	+	1.21251i
$322$	−0.358795	−	0.260680i	−0.0199949	−	0.0145271i
$323$	−5.42793	+	4.88901i	−0.302018	+	0.272032i
$324$	7.50838	−	23.1084i	0.417132	−	1.28380i
$325$	0.149111	−	0.458917i	0.00827119	−	0.0254561i
$326$	17.5630	+	24.1734i	0.972723	+	1.33884i
$327$	22.2235	+	16.1463i	1.22896	+	0.892892i
$328$	−3.60553	+	1.17151i	−0.199082	+	0.0646857i
$329$		−	14.6602i		−	0.808243i
$330$	−6.59748	+	1.30765i	−0.363179	+	0.0719835i
$331$	12.5506			0.689844			0.344922	−	0.938631i	$-0.387905\pi$
$331$	12.5506			0.689844			0.344922	+	0.938631i	$0.387905\pi$
$332$	9.26498	+	28.5147i	0.508482	+	1.56495i
$333$	−28.4487	+	39.1562i	−1.55898	+	2.14575i
$334$	7.41138	+	10.2009i	0.405533	+	0.558168i
$335$	2.33231	+	0.757815i	0.127428	+	0.0414039i
$336$	5.03528	−	15.4970i	0.274697	−	0.845430i
$337$	−5.51052	−	7.58458i	−0.300177	−	0.413159i	0.632109	−	0.774879i	$-0.282189\pi$
$337$	−5.51052	−	7.58458i	−0.300177	−	0.413159i	−0.932287	+	0.361721i	$0.882189\pi$
$338$	21.6382	+	15.7211i	1.17696	+	0.855114i
$339$	−16.4672	−	50.6808i	−0.894374	−	2.75260i
$340$	−0.313872	−	2.98139i	−0.0170221	−	0.161689i
$341$	6.83525	−	14.8003i	0.370149	−	0.801479i
$342$	22.6214			1.22323
$343$	−17.1005	+	5.55630i	−0.923342	+	0.300012i
$344$	−3.64500	−	2.64825i	−0.196525	−	0.142784i
$345$	−0.0804175	−	0.110685i	−0.00432953	−	0.00595909i
$346$	−27.0657	−	8.79419i	−1.45506	−	0.472779i
$347$	27.6685	+	8.99004i	1.48532	+	0.482611i	0.935698	−	0.352801i	$-0.114771\pi$
$347$	27.6685	+	8.99004i	1.48532	+	0.482611i	0.549625	+	0.835412i	$0.314771\pi$
$348$	−15.9752	+	11.6066i	−0.856359	+	0.622181i
$349$	−16.1916	−	11.7639i	−0.866714	−	0.629705i	0.0629889	−	0.998014i	$-0.479937\pi$
$349$	−16.1916	−	11.7639i	−0.866714	−	0.629705i	−0.929703	+	0.368309i	$0.879937\pi$
$350$	−14.8621	+	4.82900i	−0.794414	+	0.258121i
$351$		−	0.957278i		−	0.0510957i
$352$	18.2896	−	19.7585i	0.974837	−	1.05313i
$353$	−3.65385			−0.194475			−0.0972373	−	0.995261i	$-0.531001\pi$
$353$	−3.65385			−0.194475			−0.0972373	+	0.995261i	$0.531001\pi$
$354$	−35.7898	+	11.6288i	−1.90221	+	0.618064i
$355$	3.39437	+	2.46616i	0.180155	+	0.130890i
$356$	0.124106	−	0.0901686i	0.00657763	−	0.00477893i
$357$	4.02893	−	18.9706i	0.213233	−	1.00403i
$358$	−9.88745	+	30.4305i	−0.522568	+	1.60830i
$359$	−3.41331	+	2.47992i	−0.180148	+	0.130885i	−0.674205	−	0.738545i	$-0.735513\pi$
$359$	−3.41331	+	2.47992i	−0.180148	+	0.130885i	0.494057	+	0.869430i	$0.335513\pi$
$360$	−0.583040	+	0.802486i	−0.0307289	+	0.0422947i
$361$	−4.90128	−	15.0846i	−0.257962	−	0.793926i
$362$			32.9739i			1.73307i
$363$	−28.4260	−	17.4728i	−1.49198	−	0.917086i
$364$			0.342321i			0.0179425i
$365$	1.15636	+	3.55891i	0.0605266	+	0.186282i
$366$	−60.7680	−	44.1505i	−3.17639	−	2.30778i
$367$	−7.38523	−	10.1649i	−0.385506	−	0.530603i	0.571527	−	0.820583i	$-0.306351\pi$
$367$	−7.38523	−	10.1649i	−0.385506	−	0.530603i	−0.957033	+	0.289980i	$0.906351\pi$
$368$	0.457657	+	0.148702i	0.0238570	+	0.00775162i
$369$	−45.3853	−	14.7466i	−2.36266	−	0.767676i
$370$	4.22141	−	3.06703i	0.219460	−	0.159447i
$371$	−10.0004	+	13.7644i	−0.519197	+	0.714614i
$372$	−10.3172	−	31.7532i	−0.534924	−	1.64633i
$373$	12.4764			0.646003			0.323002	−	0.946398i	$-0.395308\pi$
$373$	12.4764			0.646003			0.323002	+	0.946398i	$0.395308\pi$
$374$	16.8578	−	22.5512i	0.871694	−	1.16610i
$375$	−9.74541			−0.503251
$376$	−1.43924	−	4.42952i	−0.0742231	−	0.228435i
$377$	−0.168459	+	0.231863i	−0.00867606	+	0.0119416i
$378$	−25.0809	+	18.2223i	−1.29002	+	0.937256i
$379$	−20.2445	−	6.57783i	−1.03989	−	0.337881i	−0.261197	−	0.965286i	$-0.584117\pi$
$379$	−20.2445	−	6.57783i	−1.03989	−	0.337881i	−0.778693	+	0.627405i	$0.784117\pi$
$380$	−1.22517	−	0.398083i	−0.0628501	−	0.0204212i
$381$	15.6870	+	21.5913i	0.803668	+	1.10615i
$382$	7.45665	+	5.41757i	0.381515	+	0.277187i
$383$	7.22591	+	22.2391i	0.369227	+	1.13636i	0.947292	+	0.320372i	$0.103808\pi$
$383$	7.22591	+	22.2391i	0.369227	+	1.13636i	−0.578065	+	0.815991i	$0.696192\pi$
$384$		−	11.8691i		−	0.605692i
$385$	1.51604	+	0.700158i	0.0772647	+	0.0356834i
$386$			11.0813i			0.564023i
$387$	−17.5254	−	53.9377i	−0.890867	−	2.74181i
$388$	7.84535	−	10.7982i	0.398287	−	0.548195i
$389$	−23.3104	+	16.9360i	−1.18188	+	0.858689i	−0.992383	−	0.123192i	$-0.960687\pi$
$389$	−23.3104	+	16.9360i	−1.18188	+	0.858689i	−0.189501	+	0.981881i	$0.560687\pi$
$390$	−0.0617794	+	0.190138i	−0.00312832	+	0.00962799i
$391$	0.560239	+	0.118982i	0.0283325	+	0.00601720i
$392$	−1.83153	+	1.33068i	−0.0925061	+	0.0672097i
$393$	7.05441	+	5.12533i	0.355848	+	0.258539i
$394$	−37.5181	+	12.1904i	−1.89013	+	0.614141i
$395$	−3.42093			−0.172126
$396$	−45.1758	+	8.95402i	−2.27017	+	0.449957i
$397$			14.8001i			0.742795i	0.928474	+	0.371398i	$0.121121\pi$
$397$			14.8001i			0.742795i	−0.928474	+	0.371398i	$0.878879\pi$
$398$	22.6617	−	7.36323i	1.13593	−	0.369085i
$399$	−6.74212	−	4.89844i	−0.337528	−	0.245229i
$400$	13.7176	−	9.96641i	0.685879	−	0.498321i
$401$	−2.15030	−	0.698675i	−0.107381	−	0.0348902i	0.254834	−	0.966985i	$-0.417979\pi$
$401$	−2.15030	−	0.698675i	−0.107381	−	0.0348902i	−0.362215	+	0.932095i	$0.617979\pi$
$402$	44.8612	+	14.5763i	2.23747	+	0.726999i
$403$	−0.284831	−	0.392036i	−0.0141884	−	0.0195287i
$404$	−3.53302	−	2.56689i	−0.175774	−	0.127708i
$405$	−3.35079	+	1.08874i	−0.166502	+	0.0540998i
$406$	9.28157			0.460637
$407$	25.7047	+	3.06012i	1.27413	+	0.151684i
$408$	−0.645076	−	6.12742i	−0.0319360	−	0.303352i
$409$	−0.0263471	−	0.0810879i	−0.00130278	−	0.00400954i	0.950403	−	0.311021i	$-0.100671\pi$
$409$	−0.0263471	−	0.0810879i	−0.00130278	−	0.00400954i	−0.951706	+	0.307012i	$0.900671\pi$
$410$	4.16220	+	3.02401i	0.205556	+	0.149345i
$411$	17.0362	+	23.4484i	0.840336	+	1.15662i
$412$	8.47742	−	26.0908i	0.417653	−	1.28540i
$413$	8.88602	+	2.88724i	0.437253	+	0.142072i
$414$	−1.04247	−	1.43484i	−0.0512347	−	0.0705185i
$415$	2.55539	−	3.51720i	0.125439	−	0.172652i
$416$	−0.247309	−	0.761139i	−0.0121253	−	0.0373179i
$417$	−13.7222			−0.671979
$418$	−5.90457	−	10.5602i	−0.288802	−	0.516519i
$419$		−	13.7468i		−	0.671574i	−0.941938	−	0.335787i	$-0.890998\pi$
$419$		−	13.7468i		−	0.671574i	0.941938	−	0.335787i	$-0.109002\pi$
$420$	3.25259	−	1.05683i	0.158710	−	0.0515681i
$421$	10.0743	+	7.31943i	0.490993	+	0.356727i	0.805566	−	0.592506i	$-0.201861\pi$
$421$	10.0743	+	7.31943i	0.490993	+	0.356727i	−0.314573	+	0.949233i	$0.601861\pi$
$422$	−12.5701	−	17.3012i	−0.611900	−	0.842209i
$423$	18.1167	−	55.7575i	0.880864	−	2.71102i
$424$	−1.67030	+	5.14065i	−0.0811169	+	0.249652i
$425$	14.9950	−	13.5062i	0.727363	−	0.655146i
$426$	65.2895	+	47.4356i	3.16329	+	2.29826i
$427$	5.76299	+	17.7367i	0.278891	+	0.858337i
$428$		−	16.8623i		−	0.815068i
$429$	−0.865683	+	0.484031i	−0.0417956	+	0.0233692i
$430$			6.11424i			0.294855i
$431$	7.63081	−	2.47940i	0.367563	−	0.119429i	−0.119411	−	0.992845i	$-0.538101\pi$
$431$	7.63081	−	2.47940i	0.367563	−	0.119429i	0.486974	+	0.873416i	$0.338101\pi$
$432$	19.7720	−	27.2138i	0.951279	−	1.30932i
$433$	−24.5203	+	17.8151i	−1.17837	+	0.856137i	−0.991987	−	0.126340i	$-0.959677\pi$
$433$	−24.5203	+	17.8151i	−1.17837	+	0.856137i	−0.186384	+	0.982477i	$0.559677\pi$
$434$	−4.84950	+	14.9252i	−0.232784	+	0.716434i
$435$	2.72315	+	0.884805i	0.130565	+	0.0424231i
$436$	−11.9195	−	16.4058i	−0.570840	−	0.785693i
$437$	0.144661	−	0.199108i	0.00692006	−	0.00952465i
$438$	22.2421	+	68.4543i	1.06277	+	3.27087i
$439$		−	7.74290i		−	0.369549i	−0.982781	−	0.184774i	$-0.940845\pi$
$439$		−	7.74290i		−	0.369549i	0.982781	−	0.184774i	$-0.0591554\pi$
$440$	0.526803	+	0.0627154i	0.0251144	+	0.00298984i
$441$	−28.4972			−1.35701
$442$	−0.340536	−	0.764504i	−0.0161976	−	0.0363637i
$443$	26.3108	+	19.1159i	1.25007	+	0.908226i	0.998226	−	0.0595427i	$-0.0189642\pi$
$443$	26.3108	+	19.1159i	1.25007	+	0.908226i	0.251840	+	0.967769i	$0.418964\pi$
$444$	42.8900	−	31.1614i	2.03547	−	1.47885i
$445$	−0.0211553	−	0.00687379i	−0.00100286	−	0.000325849i
$446$	14.6406	−	45.0590i	0.693251	−	2.13361i
$447$	−20.5418	−	28.2734i	−0.971596	−	1.33729i
$448$	−8.91940	+	12.2765i	−0.421402	+	0.580010i
$449$	16.5277	−	5.37019i	0.779993	−	0.253435i	0.108156	−	0.994134i	$-0.465506\pi$
$449$	16.5277	−	5.37019i	0.779993	−	0.253435i	0.671837	+	0.740699i	$0.265506\pi$
$450$	−62.4930			−2.94595
$451$	4.96225	+	25.0361i	0.233663	+	1.17890i
$452$			39.3388i			1.85034i
$453$	−2.59839	+	0.844268i	−0.122083	+	0.0396672i
$454$	−8.86495	+	12.2016i	−0.416053	+	0.572647i
$455$	0.0401576	−	0.0291762i	0.00188262	−	0.00136780i
$456$	−2.51800	−	0.818148i	−0.117916	−	0.0383133i
$457$	−9.25427	+	28.4817i	−0.432896	+	1.33232i	0.462331	+	0.886708i	$0.347013\pi$
$457$	−9.25427	+	28.4817i	−0.432896	+	1.33232i	−0.895227	+	0.445610i	$0.852987\pi$
$458$	13.1682	−	9.56727i	0.615310	−	0.447049i
$459$	20.0120	−	34.6756i	0.934082	−	1.61852i
$460$	0.0312104	+	0.0960557i	0.00145519	+	0.00447862i
$461$	7.30663			0.340304			0.170152	−	0.985418i	$-0.445574\pi$
$461$	7.30663			0.340304			0.170152	+	0.985418i	$0.445574\pi$
$462$	29.1605	+	13.4673i	1.35667	+	0.626554i
$463$	−2.79714			−0.129994			−0.0649972	−	0.997885i	$-0.520704\pi$
$463$	−2.79714			−0.129994			−0.0649972	+	0.997885i	$0.520704\pi$
$464$	−9.57797	+	3.11207i	−0.444646	+	0.144474i
$465$	−2.84562	+	3.91666i	−0.131963	+	0.181631i
$466$	−23.0661	−	31.7478i	−1.06852	−	1.47069i
$467$	−9.72757	+	29.9384i	−0.450138	+	1.38538i	0.426611	+	0.904435i	$0.359707\pi$
$467$	−9.72757	+	29.9384i	−0.450138	+	1.38538i	−0.876749	+	0.480948i	$0.840293\pi$
$468$	−0.423031	+	1.30196i	−0.0195546	+	0.0601829i
$469$	−6.88385	−	9.47481i	−0.317867	−	0.437506i
$470$	−3.71511	+	5.11341i	−0.171365	+	0.235864i
$471$	−9.16514	+	2.97793i	−0.422307	+	0.137216i
$472$	2.96833			0.136628
$473$	−20.6050	+	22.2599i	−0.947421	+	1.02351i
$474$	−65.8004			−3.02231
$475$	−2.67979	−	8.24754i	−0.122957	−	0.378423i
$476$	−7.15626	+	12.3999i	−0.328007	+	0.568348i
$477$	−55.0447	+	39.9923i	−2.52032	+	1.83112i
$478$	5.65049	−	17.3904i	0.258447	−	0.795419i
$479$	25.8238	+	8.39065i	1.17992	+	0.383378i	0.832336	−	0.554271i	$-0.187003\pi$
$479$	25.8238	+	8.39065i	1.17992	+	0.383378i	0.347581	+	0.937650i	$0.387003\pi$
$480$	−6.46853	+	4.69966i	−0.295247	+	0.214509i
$481$	0.452276	−	0.622504i	0.0206220	−	0.0283837i
$482$	47.9804	−	15.5898i	2.18545	−	0.710095i
$483$			0.653377i			0.0297297i
$484$	15.9716	+	18.7521i	0.725982	+	0.852366i
$485$	−1.93540			−0.0878819
$486$	−7.40870	+	2.40723i	−0.336065	+	0.109194i
$487$	20.3169	−	27.9638i	0.920646	−	1.26716i	−0.0427515	−	0.999086i	$-0.513612\pi$
$487$	20.3169	−	27.9638i	0.920646	−	1.26716i	0.963398	−	0.268075i	$-0.0863876\pi$
$488$	3.48253	+	4.79330i	0.157647	+	0.216982i
$489$	13.6031	−	41.8660i	0.615153	−	1.89325i
$490$	2.92190	+	0.949381i	0.131998	+	0.0428887i
$491$	−7.63218	+	5.54511i	−0.344436	+	0.250247i	−0.746531	−	0.665351i	$-0.768282\pi$
$491$	−7.63218	+	5.54511i	−0.344436	+	0.250247i	0.402095	+	0.915598i	$0.368282\pi$
$492$	42.2884	+	30.7243i	1.90651	+	1.38516i
$493$	−10.9492	+	4.87715i	−0.493128	+	0.219656i
$494$	−0.359635			−0.0161807
$495$	4.90076	+	4.53642i	0.220273	+	0.203897i
$496$		−	17.0279i		−	0.764575i
$497$	−6.19179	−	19.0564i	−0.277740	−	0.854796i
$498$	49.1520	−	67.6519i	2.20255	−	3.03155i
$499$	−5.31677	−	7.31791i	−0.238011	−	0.327595i	0.673256	−	0.739409i	$-0.264895\pi$
$499$	−5.31677	−	7.31791i	−0.238011	−	0.327595i	−0.911268	+	0.411815i	$0.864895\pi$
$500$	6.84213	+	2.22314i	0.305989	+	0.0994220i
$501$	5.74035	−	17.6670i	0.256460	−	0.789303i
$502$	−11.7850	+	8.56231i	−0.525991	+	0.382155i
$503$	−23.4751	+	32.3107i	−1.04670	+	1.44066i	−0.155071	+	0.987903i	$0.549561\pi$
$503$	−23.4751	+	32.3107i	−1.04670	+	1.44066i	−0.891632	+	0.452760i	$0.850439\pi$
$504$	4.50524	−	1.46384i	0.200679	−	0.0652047i
$505$			0.633236i			0.0281786i
$506$	−0.397716	+	0.861168i	−0.0176806	+	0.0382836i
$507$		−	39.4039i		−	1.74999i
$508$	−6.08818	−	18.7375i	−0.270119	−	0.831342i
$509$	−12.8199	−	9.31423i	−0.568234	−	0.412846i	0.266229	−	0.963910i	$-0.414222\pi$
$509$	−12.8199	−	9.31423i	−0.568234	−	0.412846i	−0.834463	+	0.551064i	$0.814222\pi$
$510$	−6.21269	+	5.59586i	−0.275103	+	0.247789i
$511$	5.52236	−	16.9961i	0.244295	−	0.751863i
$512$	9.74499	−	29.9920i	0.430672	−	1.32547i
$513$	−10.1122	−	13.9183i	−0.446466	−	0.614508i
$514$	1.77909	+	1.29258i	0.0784721	+	0.0570134i
$515$	−3.78325	+	1.22925i	−0.166710	+	0.0541673i
$516$			62.1214i			2.73474i
$517$	−30.7577	+	6.09630i	−1.35272	+	0.268115i
$518$	−24.9190			−1.09488
$519$	12.9560	+	39.8745i	0.568706	+	1.75030i
$520$	0.00926914	−	0.0127579i	0.000406479	−	0.000559470i
$521$	3.14464	+	4.32822i	0.137769	+	0.189623i	0.872327	−	0.488923i	$-0.162610\pi$
$521$	3.14464	+	4.32822i	0.137769	+	0.189623i	−0.734558	+	0.678546i	$0.762610\pi$
$522$	35.3008	+	11.4699i	1.54507	+	0.502025i
$523$	−2.62191	+	8.06942i	−0.114648	+	0.352851i	−0.991874	−	0.127228i	$-0.959392\pi$
$523$	−2.62191	+	8.06942i	−0.114648	+	0.352851i	0.877225	+	0.480079i	$0.159392\pi$
$524$	−3.78361	−	5.20769i	−0.165288	−	0.227499i
$525$	18.6255	+	13.5322i	0.812883	+	0.590594i
$526$	−15.6610	−	48.1995i	−0.682850	−	2.10160i
$527$	−2.12187	−	20.1552i	−0.0924303	−	0.877972i
$528$	−34.6072	−	4.11996i	−1.50609	−	0.179298i
$529$	22.9807			0.999161
$530$	6.97622	−	2.26671i	0.303028	−	0.0984597i
$531$	30.2284	+	21.9622i	1.31180	+	0.953080i
$532$	3.61611	+	4.97716i	0.156778	+	0.215787i
$533$	0.721533	+	0.234440i	0.0312531	+	0.0101547i
$534$	−0.406915	−	0.132215i	−0.0176089	−	0.00572149i
$535$	−1.97811	+	1.43718i	−0.0855212	+	0.0621348i
$536$	−3.01010	−	2.18697i	−0.130017	−	0.0944626i
$537$	44.8316	−	14.5667i	1.93463	−	0.628598i
$538$			43.4824i			1.87466i
$539$	7.43824	+	13.3032i	0.320388	+	0.573009i
$540$	7.06015			0.303820
$541$	27.8965	−	9.06413i	1.19936	−	0.389697i	0.359838	−	0.933015i	$-0.382832\pi$
$541$	27.8965	−	9.06413i	1.19936	−	0.389697i	0.839527	+	0.543318i	$0.182832\pi$
$542$	1.10082	+	0.799794i	0.0472843	+	0.0343541i
$543$	39.3010	−	28.5538i	1.68657	−	1.22536i
$544$	6.95343	−	32.7408i	0.298126	−	1.40375i
$545$	−0.908653	+	2.79655i	−0.0389224	+	0.119791i
$546$	0.772416	−	0.561193i	0.0330563	−	0.0240168i
$547$	−4.44265	+	6.11479i	−0.189954	+	0.261450i	−0.893363	−	0.449336i	$-0.851660\pi$
$547$	−4.44265	+	6.11479i	−0.189954	+	0.261450i	0.703408	+	0.710786i	$0.251660\pi$
$548$	−6.61184	−	20.3491i	−0.282444	−	0.869273i
$549$			74.5800i			3.18300i
$550$	16.3117	+	29.1733i	0.695534	+	1.24395i
$551$			5.15068i			0.219427i
$552$	0.0641442	+	0.197415i	0.00273016	+	0.00840256i
$553$	13.2170	+	9.60274i	0.562046	+	0.408350i
$554$	10.1320	+	13.9455i	0.430467	+	0.592488i
$555$	−7.31108	−	2.37551i	−0.310338	−	0.100835i
$556$	9.63418	+	3.13033i	0.408580	+	0.132756i
$557$	7.66023	−	5.56549i	0.324575	−	0.235817i	−0.413550	−	0.910481i	$-0.635711\pi$
$557$	7.66023	−	5.56549i	0.324575	−	0.235817i	0.738125	+	0.674664i	$0.235711\pi$
$558$	−36.8885	+	50.7726i	−1.56161	+	2.14938i
$559$	0.278618	+	0.857499i	0.0117843	+	0.0362684i
$560$	1.74423			0.0737070
$561$	−41.4764	−	0.564144i	−1.75114	−	0.0238182i
$562$	37.0243			1.56178
$563$	6.53978	+	20.1274i	0.275619	+	0.848268i	0.989055	+	0.147547i	$0.0471379\pi$
$563$	6.53978	+	20.1274i	0.275619	+	0.848268i	−0.713436	+	0.700720i	$0.752862\pi$
$564$	−37.7459	+	51.9528i	−1.58939	+	2.18761i
$565$	4.61484	−	3.35287i	0.194148	−	0.141056i
$566$	−57.7569	−	18.7664i	−2.42771	−	0.788809i
$567$	16.0022	+	5.19942i	0.672029	+	0.218355i
$568$	−3.74165	−	5.14995i	−0.156996	−	0.216087i
$569$	−9.59941	−	6.97438i	−0.402428	−	0.292381i	0.368101	−	0.929786i	$-0.380008\pi$
$569$	−9.59941	−	6.97438i	−0.402428	−	0.292381i	−0.770529	+	0.637405i	$0.780008\pi$
$570$	1.11028	+	3.41711i	0.0465047	+	0.143127i
$571$		−	26.1272i		−	1.09339i	−0.837332	−	0.546695i	$-0.815886\pi$
$571$		−	26.1272i		−	1.09339i	0.837332	−	0.546695i	$-0.184114\pi$
$572$	0.718203	−	0.142351i	0.0300296	−	0.00595198i
$573$		−	13.5788i		−	0.567263i
$574$	−7.59241	−	23.3670i	−0.316901	−	0.975321i
$575$	−0.399633	+	0.550048i	−0.0166659	+	0.0229386i
$576$	−49.0943	+	35.6691i	−2.04560	+	1.48621i
$577$	0.976344	−	3.00488i	0.0406457	−	0.125095i	−0.928675	−	0.370895i	$-0.879051\pi$
$577$	0.976344	−	3.00488i	0.0406457	−	0.125095i	0.969320	+	0.245801i	$0.0790509\pi$
$578$	3.64682	−	34.8116i	0.151688	−	1.44797i
$579$	13.2076	−	9.59588i	0.548889	−	0.398791i
$580$	−1.71004	−	1.24242i	−0.0710057	−	0.0515887i
$581$	−19.7459	+	6.41584i	−0.819198	+	0.266174i
$582$	−37.2267			−1.54309
$583$	33.0370	+	15.2576i	1.36825	+	0.631904i
$584$		−	5.67745i		−	0.234935i
$585$	0.188788	−	0.0613408i	0.00780540	−	0.00253613i
$586$	−31.5307	−	22.9084i	−1.30252	−	0.946337i
$587$	−6.83065	+	4.96276i	−0.281931	+	0.204835i	−0.719759	−	0.694224i	$-0.755748\pi$
$587$	−6.83065	+	4.96276i	−0.281931	+	0.204835i	0.437828	+	0.899059i	$0.355748\pi$
$588$	29.6868	+	9.64582i	1.22426	+	0.397787i
$589$	−8.28256	−	2.69117i	−0.341277	−	0.110888i
$590$	−2.36774	−	3.25891i	−0.0974781	−	0.134167i
$591$	47.0183	+	34.1608i	1.93408	+	1.40519i
$592$	25.7148	−	8.35525i	1.05687	−	0.343399i
$593$	−8.84968			−0.363413			−0.181706	−	0.983353i	$-0.558162\pi$
$593$	−8.84968			−0.363413			−0.181706	+	0.983353i	$0.558162\pi$
$594$	48.6609	+	45.0432i	1.99658	+	1.84815i
$595$	2.06456	−	0.217351i	0.0846388	−	0.00891052i
$596$	7.97238	+	24.5365i	0.326561	+	1.00505i
$597$	−28.4001	−	20.6338i	−1.16234	−	0.844487i
$598$	0.0165732	+	0.0228110i	0.000677727	+	0.000932811i
$599$	5.92064	−	18.2219i	0.241911	−	0.744525i	−0.754218	−	0.656624i	$-0.771984\pi$
$599$	5.92064	−	18.2219i	0.241911	−	0.744525i	0.996129	−	0.0879013i	$-0.0280160\pi$
$600$	6.95612	+	2.26018i	0.283982	+	0.0922715i
$601$	10.8105	+	14.8793i	0.440968	+	0.606940i	0.970427	−	0.241395i	$-0.0776050\pi$
$601$	10.8105	+	14.8793i	0.440968	+	0.606940i	−0.529459	+	0.848336i	$0.677605\pi$
$602$	17.1630	−	23.6228i	0.699512	−	0.962795i
$603$	−14.4728	−	44.5427i	−0.589377	−	1.81392i
$604$	2.01689			0.0820662
$605$	0.838531	−	3.47188i	0.0340911	−	0.141152i
$606$			12.1801i			0.494781i
$607$	21.8859	−	7.11115i	0.888320	−	0.288633i	0.170912	−	0.985286i	$-0.445328\pi$
$607$	21.8859	−	7.11115i	0.888320	−	0.288633i	0.717408	+	0.696654i	$0.245328\pi$
$608$	−11.6361	−	8.45409i	−0.471904	−	0.342859i
$609$	−8.03740	−	11.0625i	−0.325692	−	0.448277i
$610$	2.48463	−	7.64690i	0.100600	−	0.309614i
$611$	−0.288018	+	0.886430i	−0.0116520	+	0.0358611i
$612$	−42.5411	+	38.3173i	−1.71962	+	1.54888i
$613$	5.52846	+	4.01666i	0.223293	+	0.162231i	0.693808	−	0.720160i	$-0.255932\pi$
$613$	5.52846	+	4.01666i	0.223293	+	0.162231i	−0.470515	+	0.882392i	$0.655932\pi$
$614$	10.2467	+	31.5362i	0.413525	+	1.27270i
$615$		−	7.57950i		−	0.305635i
$616$	−1.85930	−	1.72107i	−0.0749133	−	0.0693439i
$617$		−	1.19972i		−	0.0482990i	−0.999708	−	0.0241495i	$-0.992312\pi$
$617$		−	1.19972i		−	0.0482990i	0.999708	−	0.0241495i	$-0.00768778\pi$
$618$	−72.7693	+	23.6442i	−2.92721	+	0.951108i
$619$	−7.42246	+	10.2161i	−0.298334	+	0.410622i	−0.931699	−	0.363232i	$-0.881673\pi$
$619$	−7.42246	+	10.2161i	−0.298334	+	0.410622i	0.633365	+	0.773853i	$0.281673\pi$
$620$	2.89135	−	2.10069i	0.116119	−	0.0843657i
$621$	−0.416808	+	1.28280i	−0.0167259	+	0.0514772i
$622$	−39.5364	−	12.8461i	−1.58526	−	0.515083i
$623$	0.0624402	+	0.0859416i	0.00250162	+	0.00344318i
$624$	−0.608917	+	0.838102i	−0.0243762	+	0.0335509i
$625$	7.24016	+	22.2829i	0.289607	+	0.891317i
$626$			22.3514i			0.893343i
$627$	−7.47349	+	16.1822i	−0.298462	+	0.646256i
$628$	7.11406			0.283882
$629$	29.3963	−	13.0941i	1.17211	−	0.522096i
$630$	−5.20082	−	3.77862i	−0.207206	−	0.150544i
$631$	16.1427	−	11.7284i	0.642632	−	0.466900i	−0.218121	−	0.975922i	$-0.569993\pi$
$631$	16.1427	−	11.7284i	0.642632	−	0.466900i	0.860754	+	0.509022i	$0.169993\pi$
$632$	4.93621	+	1.60387i	0.196352	+	0.0637986i
$633$	−9.73590	+	29.9640i	−0.386967	+	1.19096i
$634$	−14.0292	−	19.3096i	−0.557172	−	0.766882i
$635$	−1.67919	+	2.31121i	−0.0666368	+	0.0917177i
$636$	70.8792	−	23.0301i	2.81054	−	0.913201i
$637$	0.453047			0.0179504
$638$	−3.85965	−	19.4731i	−0.152805	−	0.770949i
$639$		−	80.1292i		−	3.16986i
$640$	1.20833	−	0.392610i	0.0477634	−	0.0155193i
$641$	−21.9353	+	30.1914i	−0.866393	+	1.19249i	0.113614	+	0.993525i	$0.463757\pi$
$641$	−21.9353	+	30.1914i	−0.866393	+	1.19249i	−0.980007	+	0.198963i	$0.936243\pi$
$642$	−38.0482	+	27.6436i	−1.50164	+	1.09101i
$643$	8.89230	+	2.88928i	0.350678	+	0.113942i	0.479059	−	0.877783i	$-0.340978\pi$
$643$	8.89230	+	2.88928i	0.350678	+	0.113942i	−0.128381	+	0.991725i	$0.540978\pi$
$644$	0.149050	−	0.458728i	0.00587338	−	0.0180764i
$645$	7.28745	−	5.29464i	0.286943	−	0.208476i
$646$	−13.0271	−	7.51821i	−0.512543	−	0.295800i
$647$	−4.13517	−	12.7267i	−0.162570	−	0.500340i	0.836279	−	0.548305i	$-0.184727\pi$
$647$	−4.13517	−	12.7267i	−0.162570	−	0.500340i	−0.998849	+	0.0479647i	$0.984727\pi$
$648$	5.34544			0.209989
$649$	2.36240	−	19.8439i	0.0927322	−	0.778941i
$650$	0.993511			0.0389687
$651$	21.9886	−	7.14452i	0.861800	−	0.280016i
$652$	−19.1011	+	26.2904i	−0.748057	+	1.02961i
$653$	−27.9647	−	38.4901i	−1.09434	−	1.50623i	−0.842678	−	0.538418i	$-0.819022\pi$
$653$	−27.9647	−	38.4901i	−1.09434	−	1.50623i	−0.251664	−	0.967815i	$-0.580978\pi$
$654$	−17.4776	+	53.7905i	−0.683428	+	2.10338i
$655$	−0.288434	+	0.887710i	−0.0112701	+	0.0346857i
$656$	15.6697	+	21.5675i	0.611800	+	0.842071i
$657$	42.0067	−	57.8172i	1.63884	−	2.25566i
$658$	28.7072	−	9.32755i	1.11912	−	0.363626i
$659$	−1.58255			−0.0616473			−0.0308237	−	0.999525i	$-0.509813\pi$
$659$	−1.58255			−0.0616473			−0.0308237	+	0.999525i	$0.509813\pi$
$660$	−3.56984	−	6.38461i	−0.138956	−	0.248521i
$661$	−31.9130			−1.24127			−0.620637	−	0.784098i	$-0.713126\pi$
$661$	−31.9130			−1.24127			−0.620637	+	0.784098i	$0.713126\pi$
$662$	7.98532	+	24.5763i	0.310358	+	0.955185i
$663$	−0.616310	+	1.06790i	−0.0239355	+	0.0414739i
$664$	−5.33629	+	3.87704i	−0.207088	+	0.150458i
$665$	0.275666	−	0.848412i	0.0106899	−	0.0329000i
$666$	−94.7752	−	30.7943i	−3.67246	−	1.19326i
$667$	0.326699	−	0.237361i	0.0126498	−	0.00919064i
$668$	−8.06046	+	11.0943i	−0.311868	+	0.429250i
$669$	−66.3830	+	21.5692i	−2.56652	+	0.833912i
$670$			5.04924i			0.195069i
$671$	34.8158	−	19.4666i	1.34405	−	0.751501i
$672$	38.1839			1.47298
$673$	23.2812	−	7.56453i	0.897426	−	0.291591i	0.176251	−	0.984345i	$-0.443603\pi$
$673$	23.2812	−	7.56453i	0.897426	−	0.291591i	0.721174	+	0.692754i	$0.243603\pi$
$674$	11.3459	−	15.6163i	0.437027	−	0.601516i
$675$	27.9356	+	38.4501i	1.07524	+	1.47995i
$676$	−8.98890	+	27.6650i	−0.345727	+	1.06404i
$677$	−41.6581	−	13.5355i	−1.60105	−	0.520213i	−0.633684	−	0.773592i	$-0.718458\pi$
$677$	−41.6581	−	13.5355i	−1.60105	−	0.520213i	−0.967367	+	0.253379i	$0.918458\pi$
$678$	88.7646	−	64.4912i	3.40898	−	2.47677i
$679$	7.47756	+	5.43277i	0.286963	+	0.208490i
$680$	0.602462	−	0.268357i	0.0231034	−	0.0102910i
$681$	22.2194			0.851451
$682$	33.3304	+	3.96795i	1.27629	+	0.151941i
$683$		−	0.778825i		−	0.0298009i	−0.999889	−	0.0149005i	$-0.995257\pi$
$683$		−	0.778825i		−	0.0298009i	0.999889	−	0.0149005i	$-0.00474314\pi$
$684$	7.60261	+	23.3984i	0.290693	+	0.894662i
$685$	−1.82363	+	2.51000i	−0.0696771	+	0.0959024i
$686$	−21.7604	−	29.9506i	−0.830816	−	1.14352i
$687$	−22.8061	−	7.41015i	−0.870107	−	0.282715i
$688$	−9.79045	+	30.1319i	−0.373257	+	1.14877i
$689$	0.875098	−	0.635796i	0.0333386	−	0.0242219i
$690$	0.165575	−	0.227895i	0.00630335	−	0.00867582i
$691$	30.5398	−	9.92299i	1.16179	−	0.377488i	0.336217	−	0.941784i	$-0.390852\pi$
$691$	30.5398	−	9.92299i	1.16179	−	0.377488i	0.825572	+	0.564296i	$0.190852\pi$
$692$		−	30.9509i		−	1.17658i
$693$	−6.20051	−	31.2835i	−0.235538	−	1.18836i
$694$			59.8997i			2.27376i
$695$	−0.453908	−	1.39698i	−0.0172177	−	0.0529906i
$696$	−3.51452	−	2.55345i	−0.133217	−	0.0967881i
$697$	21.2351	+	23.5759i	0.804338	+	0.893001i
$698$	12.7338	−	39.1907i	0.481982	−	1.48339i
$699$	−17.8654	+	54.9842i	−0.675733	+	2.07969i
$700$	−9.98972	−	13.7497i	−0.377576	−	0.519689i
$701$	11.5908	+	8.42122i	0.437779	+	0.318065i	0.784752	−	0.619810i	$-0.212790\pi$
$701$	11.5908	+	8.42122i	0.437779	+	0.318065i	−0.346973	+	0.937875i	$0.612790\pi$
$702$	1.87452	−	0.609068i	0.0707492	−	0.0229878i
$703$		−	13.8285i		−	0.521552i
$704$	29.4657	+	13.6082i	1.11053	+	0.512879i
$705$	9.31169			0.350699
$706$	−2.32476	−	7.15487i	−0.0874934	−	0.269277i
$707$	1.77753	−	2.44656i	0.0668508	−	0.0920122i
$708$	−24.0565	−	33.1109i	−0.904097	−	1.24438i
$709$	34.1884	+	11.1085i	1.28397	+	0.417188i	0.869977	−	0.493092i	$-0.164133\pi$
$709$	34.1884	+	11.1085i	1.28397	+	0.417188i	0.413995	+	0.910279i	$0.364133\pi$
$710$	−2.66950	+	8.21587i	−0.100185	+	0.308336i
$711$	38.4019	+	52.8556i	1.44018	+	1.98224i
$712$	0.0273033	+	0.0198370i	0.00102323	+	0.000743422i
$713$	0.210992	+	0.649367i	0.00790171	+	0.0243190i
$714$	39.7111	−	4.18066i	1.48615	−	0.156457i
$715$	−0.0779121	−	0.0721197i	−0.00291375	−	0.00269713i
$716$	−34.7987			−1.30049
$717$	−25.6204	+	8.32456i	−0.956810	+	0.310886i
$718$	−7.02784	−	5.10602i	−0.262277	−	0.190555i
$719$	15.2351	+	20.9693i	0.568172	+	0.782022i	0.992337	−	0.123563i	$-0.0394322\pi$
$719$	15.2351	+	20.9693i	0.568172	+	0.782022i	−0.424165	+	0.905585i	$0.639432\pi$
$720$	6.63386	+	2.15547i	0.247229	+	0.0803296i
$721$	18.0674	+	5.87047i	0.672867	+	0.218628i
$722$	26.4199	−	19.1952i	0.983245	−	0.714370i
$723$	−60.1299	−	43.6870i	−2.23626	−	1.62474i
$724$	−34.1065	+	11.0819i	−1.26756	+	0.411854i
$725$		−	14.2291i		−	0.528454i
$726$	16.1288	−	66.7802i	0.598597	−	2.47845i
$727$	−1.13755			−0.0421893			−0.0210946	−	0.999777i	$-0.506715\pi$
$727$	−1.13755			−0.0421893			−0.0210946	+	0.999777i	$0.506715\pi$
$728$	−0.0716241	+	0.0232721i	−0.00265457	+	0.000862521i
$729$	−17.0505	−	12.3879i	−0.631501	−	0.458812i
$730$	−6.23324	+	4.52871i	−0.230702	+	0.167615i
$731$	−7.83373	+	36.8858i	−0.289741	+	1.36427i
$732$	25.2441	−	77.6933i	0.933049	−	2.87163i
$733$	13.5151	−	9.81928i	0.499191	−	0.362683i	−0.309517	−	0.950894i	$-0.600167\pi$
$733$	13.5151	−	9.81928i	0.499191	−	0.362683i	0.808708	+	0.588211i	$0.200167\pi$
$734$	15.2058	−	20.9290i	0.561257	−	0.772503i
$735$	−1.39867	−	4.30467i	−0.0515908	−	0.158780i
$736$			1.12765i			0.0415656i
$737$	−17.0160	+	18.3826i	−0.626792	+	0.677133i
$738$		−	98.2549i		−	3.61681i
$739$	8.69384	+	26.7569i	0.319808	+	0.984268i	0.973730	+	0.227706i	$0.0731224\pi$
$739$	8.69384	+	26.7569i	0.319808	+	0.984268i	−0.653922	+	0.756562i	$0.726878\pi$
$740$	4.59111	+	3.33563i	0.168772	+	0.122620i
$741$	0.311427	+	0.428642i	0.0114405	+	0.0157466i
$742$	−33.3160	−	10.8250i	−1.22307	−	0.397399i
$743$	−26.6284	−	8.65210i	−0.976902	−	0.317415i	−0.223303	−	0.974749i	$-0.571684\pi$
$743$	−26.6284	−	8.65210i	−0.976902	−	0.317415i	−0.753599	+	0.657335i	$0.771684\pi$
$744$	5.94236	−	4.31738i	0.217858	−	0.158283i
$745$	2.19888	−	3.02650i	0.0805607	−	0.110882i
$746$	7.93811	+	24.4310i	0.290635	+	0.894482i
$747$	−83.0286			−3.03786
$748$	28.9914	+	9.85777i	1.06003	+	0.360436i
$749$	11.6768			0.426662
$750$	−6.20052	−	19.0832i	−0.226411	−	0.696821i
$751$	−14.8342	+	20.4175i	−0.541307	+	0.745045i	−0.988801	−	0.149242i	$-0.952317\pi$
$751$	−14.8342	+	20.4175i	−0.541307	+	0.745045i	0.447494	+	0.894287i	$0.352317\pi$
$752$	−26.4965	+	19.2508i	−0.966228	+	0.702005i
$753$	20.4105	+	6.63178i	0.743801	+	0.241676i
$754$	−0.561211	−	0.182348i	−0.0204381	−	0.00664074i
$755$	−0.171901	−	0.236601i	−0.00625612	−	0.00861081i
$756$	−27.2774	−	19.8182i	−0.992070	−	0.720781i
$757$	−10.8034	−	33.2494i	−0.392656	−	1.20847i	−0.930772	−	0.365600i	$-0.880864\pi$
$757$	−10.8034	−	33.2494i	−0.392656	−	1.20847i	0.538116	−	0.842871i	$-0.319136\pi$
$758$		−	43.8274i		−	1.59188i
$759$	1.37081	−	0.271701i	0.0497574	−	0.00986211i
$760$		−	0.283408i		−	0.0102803i
$761$	−4.71253	−	14.5037i	−0.170829	−	0.525758i	0.828589	−	0.559857i	$-0.189144\pi$
$761$	−4.71253	−	14.5037i	−0.170829	−	0.525758i	−0.999418	+	0.0340991i	$0.989144\pi$
$762$	−32.2987	+	44.4553i	−1.17006	+	1.61045i
$763$	11.3607	−	8.25404i	0.411285	−	0.298816i
$764$	−3.09762	+	9.53351i	−0.112068	+	0.344910i
$765$	8.12080	+	1.72468i	0.293608	+	0.0623559i
$766$	−38.9505	+	28.2992i	−1.40734	+	1.02249i
$767$	−0.480570	−	0.349155i	−0.0173524	−	0.0126073i
$768$	−33.2206	+	10.7940i	−1.19875	+	0.389496i
$769$	−10.5440			−0.380227			−0.190114	−	0.981762i	$-0.560886\pi$
$769$	−10.5440			−0.380227			−0.190114	+	0.981762i	$0.560886\pi$
$770$	−0.406452	+	3.41415i	−0.0146475	+	0.123038i
$771$		−	3.23978i		−	0.116678i
$772$	−11.4619	+	3.72420i	−0.412524	+	0.134037i
$773$	14.0747	+	10.2259i	0.506233	+	0.367800i	0.811393	−	0.584501i	$-0.198710\pi$
$773$	14.0747	+	10.2259i	0.506233	+	0.367800i	−0.305160	+	0.952301i	$0.598710\pi$
$774$	94.4690	−	68.6357i	3.39562	−	2.46706i
$775$	22.8811	+	7.43450i	0.821912	+	0.267055i
$776$	2.79267	+	0.907394i	0.100251	+	0.0325735i
$777$	21.5787	+	29.7006i	0.774132	+	1.06550i
$778$	−47.9949	−	34.8703i	−1.72070	−	1.25016i
$779$	12.9672	−	4.21331i	0.464599	−	0.150957i
$780$	−0.217431			−0.00778529
$781$	−37.4063	+	20.9151i	−1.33850	+	0.748400i
$782$	0.123463	+	1.17275i	0.00441504	+	0.0419374i
$783$	−8.72307	−	26.8469i	−0.311737	−	0.959428i
$784$	12.8793	+	9.35739i	0.459977	+	0.334193i
$785$	−0.606336	−	0.834549i	−0.0216410	−	0.0297863i
$786$	−5.54793	+	17.0748i	−0.197888	+	0.609037i
$787$	1.96720	+	0.639184i	0.0701233	+	0.0227844i	0.343869	−	0.939018i	$-0.388263\pi$
$787$	1.96720	+	0.639184i	0.0701233	+	0.0227844i	−0.273745	+	0.961802i	$0.588263\pi$
$788$	−25.2181	−	34.7098i	−0.898359	−	1.23649i
$789$	−43.8864	+	60.4045i	−1.56240	+	2.15046i
$790$	−2.17657	−	6.69879i	−0.0774388	−	0.238332i
$791$	−27.2415			−0.968595
$792$	−4.94466	−	8.84346i	−0.175701	−	0.314239i
$793$		−	1.18567i		−	0.0421044i
$794$	−28.9812	+	9.41655i	−1.02850	+	0.334181i
$795$	−8.74273	−	6.35197i	−0.310073	−	0.225281i
$796$	15.2323	+	20.9654i	0.539894	+	0.743100i
$797$	−3.22775	+	9.93400i	−0.114333	+	0.351880i	−0.991807	−	0.127743i	$-0.959227\pi$
$797$	−3.22775	+	9.93400i	−0.114333	+	0.351880i	0.877474	+	0.479623i	$0.159227\pi$
$798$	5.30233	−	16.3189i	0.187700	−	0.577682i
$799$	−28.9638	+	26.0881i	−1.02467	+	0.922932i
$800$	32.1453	+	23.3549i	1.13651	+	0.825720i
$801$	0.131276	+	0.404026i	0.00463841	+	0.0142755i
$802$		−	4.65520i		−	0.164381i
$803$	−37.9550	−	4.51850i	−1.33940	−	0.159454i
$804$			51.3009i			1.80924i
$805$	−0.0665169	+	0.0216127i	−0.00234441	+	0.000761746i
$806$	0.586451	−	0.807181i	0.0206569	−	0.0284317i
$807$	51.8259	−	37.6537i	1.82436	−	1.32547i
$808$	0.296887	−	0.913723i	0.0104444	−	0.0321447i
$809$	−33.1584	−	10.7738i	−1.16579	−	0.378787i	−0.338717	−	0.940888i	$-0.609993\pi$
$809$	−33.1584	−	10.7738i	−1.16579	−	0.378787i	−0.827068	+	0.562102i	$0.809993\pi$
$810$	−4.26388	−	5.86873i	−0.149817	−	0.206206i
$811$	4.15897	−	5.72433i	0.146041	−	0.201008i	−0.729729	−	0.683736i	$-0.760354\pi$
$811$	4.15897	−	5.72433i	0.146041	−	0.201008i	0.875770	+	0.482728i	$0.160354\pi$
$812$	3.11935	+	9.60037i	0.109468	+	0.336907i
$813$		−	2.00463i		−	0.0703056i
$814$	10.3623	+	52.2812i	0.363200	+	1.83246i
$815$	4.71212			0.165059
$816$	−39.5775	+	17.6291i	−1.38549	+	0.617143i
$817$	13.1092	+	9.52438i	0.458632	+	0.333216i
$818$	0.142021	−	0.103184i	0.00496565	−	0.00360776i
$819$	−0.901582	−	0.292942i	−0.0315038	−	0.0102362i
$820$	−1.72905	+	5.32147i	−0.0603811	+	0.185834i
$821$	−16.0491	−	22.0897i	−0.560117	−	0.770935i	0.431225	−	0.902245i	$-0.358082\pi$
$821$	−16.0491	−	22.0897i	−0.560117	−	0.770935i	−0.991341	+	0.131310i	$0.958082\pi$
$822$	−35.0767	+	48.2790i	−1.22344	+	1.68392i
$823$	−25.6902	+	8.34724i	−0.895503	+	0.290967i	−0.720380	−	0.693580i	$-0.756032\pi$
$823$	−25.6902	+	8.34724i	−0.895503	+	0.290967i	−0.175123	+	0.984546i	$0.556032\pi$
$824$	6.03533			0.210251
$825$	20.6459	−	44.7043i	0.718799	−	1.55640i
$826$			19.2374i			0.669355i
$827$	15.7652	−	5.12243i	0.548210	−	0.178124i	−0.0217995	−	0.999762i	$-0.506940\pi$
$827$	15.7652	−	5.12243i	0.548210	−	0.178124i	0.570009	+	0.821638i	$0.306940\pi$
$828$	1.13377	−	1.56050i	0.0394012	−	0.0542311i
$829$	−9.56453	+	6.94904i	−0.332190	+	0.241350i	−0.741359	−	0.671108i	$-0.765818\pi$
$829$	−9.56453	+	6.94904i	−0.332190	+	0.241350i	0.409169	+	0.912458i	$0.365818\pi$
$830$	8.51315	+	2.76609i	0.295496	+	0.0960124i
$831$	7.84756	−	24.1523i	0.272229	−	0.837834i
$832$	0.780499	−	0.567066i	0.0270590	−	0.0196595i
$833$	16.4107	+	9.47101i	0.568599	+	0.328151i
$834$	−8.73074	−	26.8705i	−0.302321	−	0.930448i
$835$	1.98847			0.0688137
$836$	8.93856	−	9.65647i	0.309147	−	0.333976i
$837$	47.7288			1.64975
$838$	26.9186	−	8.74638i	0.929887	−	0.302139i
$839$	21.9944	−	30.2727i	0.759331	−	1.04513i	−0.237938	−	0.971280i	$-0.576472\pi$
$839$	21.9944	−	30.2727i	0.759331	−	1.04513i	0.997269	−	0.0738492i	$-0.0235283\pi$
$840$	0.442244	+	0.608697i	0.0152589	+	0.0210020i
$841$	6.34990	−	19.5430i	0.218962	−	0.673896i
$842$	−7.92294	+	24.3843i	−0.273042	+	0.840338i
$843$	−32.0613	−	44.1286i	−1.10425	−	1.51987i
$844$	13.6709	−	18.8164i	0.470572	−	0.647687i
$845$	4.01151	−	1.30342i	0.138000	−	0.0448389i
$846$	120.710			4.15008
$847$	−12.9855	+	11.0601i	−0.446186	+	0.380028i
$848$	38.0095			1.30525
$849$	27.6475	+	85.0902i	0.948859	+	2.92029i
$850$	35.9880	+	20.7695i	1.23438	+	0.712387i
$851$	−0.877118	+	0.637263i	−0.0300672	+	0.0218451i
$852$	−27.1224	+	83.4742i	−0.929199	+	2.85978i
$853$	5.16692	+	1.67883i	0.176912	+	0.0574821i	0.396133	−	0.918193i	$-0.370352\pi$
$853$	5.16692	+	1.67883i	0.176912	+	0.0574821i	−0.219222	+	0.975675i	$0.570352\pi$
$854$	−31.0648	+	22.5699i	−1.06302	+	0.772326i
$855$	2.09689	−	2.88612i	0.0717122	−	0.0987034i
$856$	3.52811	−	1.14635i	0.120588	−	0.0391815i
$857$		−	47.3509i		−	1.61748i	−0.588168	−	0.808738i	$-0.700151\pi$
$857$		−	47.3509i		−	1.61748i	0.588168	−	0.808738i	$-0.299849\pi$
$858$	−1.49861	−	1.38720i	−0.0511617	−	0.0473581i
$859$	−32.6560			−1.11421			−0.557105	−	0.830442i	$-0.688088\pi$
$859$	−32.6560			−1.11421			−0.557105	+	0.830442i	$0.688088\pi$
$860$	−6.32425	+	2.05487i	−0.215655	+	0.0700706i
$861$	−21.2761	+	29.2840i	−0.725086	+	0.997996i
$862$	9.71021	+	13.3650i	0.330731	+	0.455212i
$863$	−5.53364	+	17.0308i	−0.188367	+	0.579735i	−0.999990	−	0.00444713i	$-0.998584\pi$
$863$	−5.53364	+	17.0308i	−0.188367	+	0.579735i	0.811623	+	0.584182i	$0.198584\pi$
$864$	74.9681	+	24.3586i	2.55047	+	0.828697i
$865$	−3.63085	+	2.63797i	−0.123453	+	0.0896936i
$866$	−50.4861	−	36.6803i	−1.71559	−	1.24645i
$867$	−44.6493	+	25.7986i	−1.51637	+	0.876168i
$868$	−17.0677			−0.579316
$869$	14.6508	−	31.7231i	0.496994	−	1.07613i
$870$			5.89536i			0.199871i
$871$	0.230088	+	0.708137i	0.00779623	+	0.0239943i
$872$	2.62227	−	3.60924i	0.0888013	−	0.122224i
$873$	21.7259	+	29.9032i	0.735311	+	1.01207i
$874$	0.481930	+	0.156588i	0.0163015	+	0.00529668i
$875$	−1.53949	+	4.73806i	−0.0520442	+	0.160176i
$876$	−63.3304	+	46.0122i	−2.13974	+	1.55461i
$877$	−8.62099	+	11.8658i	−0.291110	+	0.400679i	−0.929374	−	0.369139i	$-0.879653\pi$
$877$	−8.62099	+	11.8658i	−0.291110	+	0.400679i	0.638264	+	0.769817i	$0.279653\pi$
$878$	15.1620	−	4.92642i	0.511692	−	0.166259i
$879$			57.4185i			1.93668i
$880$	−0.725320	−	3.65946i	−0.0244505	−	0.123360i
$881$			6.04107i			0.203529i	0.994809	+	0.101764i	$0.0324488\pi$
$881$			6.04107i			0.203529i	−0.994809	+	0.101764i	$0.967551\pi$
$882$	−18.1313	−	55.8025i	−0.610514	−	1.87897i
$883$	16.6615	+	12.1053i	0.560704	+	0.407375i	0.831717	−	0.555200i	$-0.187358\pi$
$883$	16.6615	+	12.1053i	0.560704	+	0.407375i	−0.271012	+	0.962576i	$0.587358\pi$
$884$	0.676316	−	0.609167i	0.0227470	−	0.0204885i
$885$	−1.83389	+	5.64412i	−0.0616454	+	0.189725i
$886$	−20.6921	+	63.6838i	−0.695165	+	2.13950i
$887$	7.29965	+	10.0471i	0.245098	+	0.337349i	0.913787	−	0.406194i	$-0.133144\pi$
$887$	7.29965	+	10.0471i	0.245098	+	0.337349i	−0.668689	+	0.743542i	$0.733144\pi$
$888$	9.43573	+	6.85546i	0.316642	+	0.230054i
$889$	12.9754	−	4.21596i	0.435181	−	0.141399i
$890$		−	0.0457993i		−	0.00153520i
$891$	4.25427	−	35.7354i	0.142523	−	1.19718i
$892$	51.5271			1.72525
$893$	5.17620	+	15.9307i	0.173215	+	0.533101i
$894$	42.2946	−	58.2135i	1.41454	−	1.94695i
$895$	2.96591	+	4.08223i	0.0991395	+	0.136454i
$896$	−5.77055	−	1.87497i	−0.192781	−	0.0626382i
$897$	0.0128364	−	0.0395065i	0.000428596	−	0.00131908i
$898$	21.0316	+	28.9475i	0.701832	+	0.965989i
$899$	−11.5604	−	8.39915i	−0.385562	−	0.280127i
$900$	−21.0026	−	64.6395i	−0.700088	−	2.15465i
$901$	44.9901	−	4.73643i	1.49884	−	0.157793i
$902$	−45.8678	+	25.6461i	−1.52723	+	0.853923i
$903$	−43.0180			−1.43155
$904$	−8.23091	+	2.67438i	−0.273756	+	0.0889487i
$905$	4.20693	+	3.05651i	0.139843	+	0.101602i
$906$	−3.30645	−	4.55094i	−0.109849	−	0.151195i
$907$	18.9009	+	6.14128i	0.627594	+	0.203918i	0.605509	−	0.795838i	$-0.292970\pi$
$907$	18.9009	+	6.14128i	0.627594	+	0.203918i	0.0220851	+	0.999756i	$0.492970\pi$
$908$	−15.6000	−	5.06874i	−0.517704	−	0.168212i
$909$	9.78390	−	7.10842i	0.324512	−	0.235771i
$910$	0.0826824	+	0.0600723i	0.00274089	+	0.00199138i
$911$	29.6352	−	9.62907i	0.981859	−	0.319025i	0.226265	−	0.974066i	$-0.427348\pi$
$911$	29.6352	−	9.62907i	0.981859	−	0.319025i	0.755594	+	0.655041i	$0.227348\pi$
$912$			18.6179i			0.616499i
$913$	21.6718	+	38.7598i	0.717234	+	1.28276i
$914$	−61.6602			−2.03954
$915$	−11.2658	+	3.66047i	−0.372435	+	0.121011i
$916$	14.3215	+	10.4051i	0.473194	+	0.343796i
$917$	3.60624	−	2.62009i	0.119088	−	0.0865228i
$918$	80.6335	+	17.1248i	2.66130	+	0.565202i
$919$	14.9667	−	46.0628i	0.493706	−	1.51947i	−0.325258	−	0.945625i	$-0.605451\pi$
$919$	14.9667	−	46.0628i	0.493706	−	1.51947i	0.818964	−	0.573845i	$-0.194549\pi$
$920$	−0.0179761	+	0.0130604i	−0.000592653	+	0.000430588i
$921$	28.7143	−	39.5218i	0.946167	−	1.30229i
$922$	4.64884	+	14.3077i	0.153101	+	0.471198i
$923$			1.27389i			0.0419306i
$924$	−4.12959	+	34.6882i	−0.135854	+	1.14116i
$925$			38.2020i			1.25607i
$926$	−1.77968	−	5.47730i	−0.0584840	−	0.179995i
$927$	61.4618	+	44.6546i	2.01867	+	1.46665i
$928$	−13.8716	−	19.0926i	−0.455356	−	0.626744i
$929$	−53.8753	−	17.5051i	−1.76759	−	0.574325i	−0.769650	−	0.638466i	$-0.779569\pi$
$929$	−53.8753	−	17.5051i	−1.76759	−	0.574325i	−0.997941	+	0.0641412i	$0.979569\pi$
$930$	−9.48004	−	3.08025i	−0.310863	−	0.101005i
$931$	6.58706	−	4.78578i	0.215882	−	0.156848i
$932$	25.0862	−	34.5282i	0.821726	−	1.13101i
$933$	18.9255	+	58.2468i	0.619594	+	1.90692i
$934$	−64.8138			−2.12077
$935$	−1.31454	−	4.24116i	−0.0429901	−	0.138701i
$936$	−0.301169			−0.00984401
$937$	−17.0720	−	52.5423i	−0.557719	−	1.71648i	−0.688652	−	0.725092i	$-0.741797\pi$
$937$	−17.0720	−	52.5423i	−0.557719	−	1.71648i	0.130933	−	0.991391i	$-0.458203\pi$
$938$	14.1735	−	19.5081i	0.462781	−	0.636963i
$939$	26.6403	−	19.3553i	0.869373	−	0.631636i
$940$	−6.53762	−	2.12420i	−0.213234	−	0.0692838i
$941$	37.6703	+	12.2398i	1.22802	+	0.399006i	0.849995	−	0.526791i	$-0.176605\pi$
$941$	37.6703	+	12.2398i	1.22802	+	0.399006i	0.378021	+	0.925797i	$0.376605\pi$
$942$	−11.6626	−	16.0522i	−0.379989	−	0.523010i
$943$	−0.864815	−	0.628325i	−0.0281623	−	0.0204611i
$944$	−6.45022	−	19.8517i	−0.209937	−	0.646119i
$945$			4.88903i			0.159040i
$946$	−56.6988	−	26.1854i	−1.84344	−	0.851361i
$947$		−	14.0834i		−	0.457648i	−0.973468	−	0.228824i	$-0.926512\pi$
$947$		−	14.0834i		−	0.457648i	0.973468	−	0.228824i	$-0.0734880\pi$
$948$	−22.1142	−	68.0605i	−0.718235	−	2.21050i
$949$	−0.667820	+	0.919176i	−0.0216784	+	0.0298377i
$950$	14.4451	−	10.4950i	0.468661	−	0.340502i
$951$	−10.8661	+	33.4424i	−0.352357	+	1.08444i
$952$	−3.08095	−	0.654326i	−0.0998542	−	0.0212068i
$953$	7.61235	−	5.53070i	0.246588	−	0.179157i	−0.457625	−	0.889145i	$-0.651300\pi$
$953$	7.61235	−	5.53070i	0.246588	−	0.179157i	0.704213	+	0.709988i	$0.251300\pi$
$954$	−113.334	−	82.3420i	−3.66933	−	2.66592i
$955$	1.38239	−	0.449165i	0.0447330	−	0.0145346i
$956$	19.8867			0.643183
$957$	−19.8674	+	21.4631i	−0.642222	+	0.693802i
$958$			55.9060i			1.80624i
$959$	14.0914	−	4.57858i	0.455036	−	0.147850i
$960$	−7.79764	−	5.66532i	−0.251668	−	0.182847i
$961$	−5.53308	+	4.02002i	−0.178486	+	0.129678i
$962$	1.50673	+	0.489567i	0.0485790	+	0.0157843i
$963$	44.4107	+	14.4299i	1.43112	+	0.464998i
$964$	32.2505	+	44.3890i	1.03872	+	1.42967i
$965$	1.41379	+	1.02718i	0.0455116	+	0.0330661i
$966$	−1.27943	+	0.415711i	−0.0411649	+	0.0133753i
$967$	−20.7749			−0.668076			−0.334038	−	0.942560i	$-0.608411\pi$
$967$	−20.7749			−0.668076			−0.334038	+	0.942560i	$0.608411\pi$
$968$	−2.83771	+	4.61658i	−0.0912074	+	0.148383i
$969$	2.32000	+	22.0371i	0.0745293	+	0.707935i
$970$	−1.23140	−	3.78985i	−0.0395378	−	0.121685i
$971$	8.92921	+	6.48745i	0.286552	+	0.208192i	0.721770	−	0.692133i	$-0.243329\pi$
$971$	8.92921	+	6.48745i	0.286552	+	0.208192i	−0.435218	+	0.900325i	$0.643329\pi$
$972$	−4.97983	−	6.85415i	−0.159728	−	0.219847i
$973$	−2.16770	+	6.67150i	−0.0694933	+	0.213879i
$974$	67.6847	+	21.9921i	2.16876	+	0.704672i
$975$	−0.860334	−	1.18415i	−0.0275527	−	0.0379231i
$976$	24.4892	−	33.7065i	0.783881	−	1.07892i
$977$	8.49739	+	26.1523i	0.271856	+	0.836685i	0.990034	+	0.140827i	$0.0449760\pi$
$977$	8.49739	+	26.1523i	0.271856	+	0.836685i	−0.718179	+	0.695859i	$0.755024\pi$
$978$	90.6359			2.89822
$979$	0.154344	−	0.166740i	0.00493286	−	0.00532904i
$980$			3.34132i			0.106735i
$981$	53.4086	−	17.3535i	1.70520	−	0.554055i
$982$	−15.7143	−	11.4171i	−0.501462	−	0.364334i
$983$	−1.57705	−	2.17062i	−0.0503000	−	0.0692319i	0.783126	−	0.621863i	$-0.213624\pi$
$983$	−1.57705	−	2.17062i	−0.0503000	−	0.0692319i	−0.833426	+	0.552631i	$0.813624\pi$
$984$	−3.55358	+	10.9368i	−0.113284	+	0.348652i
$985$	−1.92244	+	5.91667i	−0.0612542	+	0.188521i
$986$	−16.5168	−	18.3374i	−0.526001	−	0.583982i
$987$	−35.9764	−	26.1384i	−1.14514	−	0.831995i
$988$	−0.120866	−	0.371987i	−0.00384526	−	0.0118345i
$989$		−	1.27041i		−	0.0403966i
$990$	−5.76499	+	12.4828i	−0.183223	+	0.396731i
$991$		−	56.6476i		−	1.79947i	−0.436437	−	0.899735i	$-0.643760\pi$
$991$		−	56.6476i		−	1.79947i	0.436437	−	0.899735i	$-0.356240\pi$
$992$	37.9495	−	12.3305i	1.20490	−	0.391495i
$993$	22.3771	−	30.7995i	0.710117	−	0.977392i
$994$	33.3762	−	24.2492i	1.05863	−	0.769139i
$995$	1.16120	−	3.57379i	0.0368124	−	0.113297i
$996$	86.4946	+	28.1038i	2.74069	+	0.890503i
$997$	9.43460	+	12.9856i	0.298797	+	0.411258i	0.931846	−	0.362853i	$-0.118197\pi$
$997$	9.43460	+	12.9856i	0.298797	+	0.411258i	−0.633050	+	0.774111i	$0.718197\pi$
$998$	10.9470	−	15.0672i	0.346520	−	0.476944i
$999$	23.4196	+	72.0781i	0.740963	+	2.28045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.j.a.16.14	yes	64
11.9	even	5	inner	187.2.j.a.152.13	yes	64
17.16	even	2	inner	187.2.j.a.16.13	✓	64
187.152	even	10	inner	187.2.j.a.152.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.j.a.16.13	✓	64	17.16	even	2	inner
187.2.j.a.16.14	yes	64	1.1	even	1	trivial
187.2.j.a.152.13	yes	64	11.9	even	5	inner
187.2.j.a.152.14	yes	64	187.152	even	10	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.636250 + 1.95818i) q^{2} +(1.78295 - 2.45402i) q^{3} +(-1.81160 + 1.31621i) q^{4} +(0.308808 + 0.100338i) q^{5} +(5.93981 + 1.92996i) q^{6} +(-0.911451 - 1.25450i) q^{7} +(-0.398550 - 0.289564i) q^{8} +(-1.91626 - 5.89763i) q^{9} +O(q^{10})\)	\(q+(0.636250 + 1.95818i) q^{2} +(1.78295 - 2.45402i) q^{3} +(-1.81160 + 1.31621i) q^{4} +(0.308808 + 0.100338i) q^{5} +(5.93981 + 1.92996i) q^{6} +(-0.911451 - 1.25450i) q^{7} +(-0.398550 - 0.289564i) q^{8} +(-1.91626 - 5.89763i) q^{9} +0.668541i q^{10} +(-2.25299 + 2.43394i) q^{11} +6.79245i q^{12} +(0.0304646 + 0.0937603i) q^{13} +(1.87663 - 2.58296i) q^{14} +(0.796822 - 0.578925i) q^{15} +(-1.07050 + 3.29467i) q^{16} +(-0.856553 + 4.03315i) q^{17} +(10.3294 - 7.50474i) q^{18} +(1.43338 + 1.04141i) q^{19} +(-0.691504 + 0.224683i) q^{20} -4.70365 q^{21} +(-6.19954 - 2.86315i) q^{22} -0.138908i q^{23} +(-1.42119 + 0.461773i) q^{24} +(-3.95979 - 2.87696i) q^{25} +(-0.164216 + 0.119310i) q^{26} +(-9.23489 - 3.00060i) q^{27} +(3.30238 + 1.07301i) q^{28} +(1.70876 + 2.35190i) q^{29} +(1.64061 + 1.19198i) q^{30} +(-4.67478 + 1.51893i) q^{31} -8.11792 q^{32} +(1.95597 + 9.86847i) q^{33} +(-8.44260 + 0.888812i) q^{34} +(-0.155589 - 0.478854i) q^{35} +(11.2340 + 8.16199i) q^{36} +(-4.58765 - 6.31436i) q^{37} +(-1.12728 + 3.46941i) q^{38} +(0.284407 + 0.0924094i) q^{39} +(-0.0940214 - 0.129409i) q^{40} +(4.52331 - 6.22580i) q^{41} +(-2.99270 - 9.21058i) q^{42} +9.14565 q^{43} +(0.877954 - 7.37473i) q^{44} -2.01351i q^{45} +(0.272007 - 0.0883805i) q^{46} +(7.64861 + 5.55704i) q^{47} +(6.17654 + 8.50127i) q^{48} +(1.42008 - 4.37056i) q^{49} +(3.11417 - 9.58443i) q^{50} +(8.37025 + 9.29291i) q^{51} +(-0.178598 - 0.129759i) q^{52} +(-3.39054 - 10.4350i) q^{53} -19.9927i q^{54} +(-0.939957 + 0.525560i) q^{55} +0.763906i q^{56} +(5.11129 - 1.66076i) q^{57} +(-3.51824 + 4.84244i) q^{58} +(-4.87466 + 3.54165i) q^{59} +(-0.681540 + 2.09756i) q^{60} +(-11.4382 - 3.71649i) q^{61} +(-5.94866 - 8.18763i) q^{62} +(-5.65203 + 7.77936i) q^{63} +(-3.02402 - 9.30697i) q^{64} +0.0320107i q^{65} +(-18.0797 + 10.1089i) q^{66} +7.55263 q^{67} +(-3.75673 - 8.43388i) q^{68} +(-0.340884 - 0.247667i) q^{69} +(0.838687 - 0.609342i) q^{70} +(12.2893 + 3.99302i) q^{71} +(-0.944016 + 2.90538i) q^{72} +(6.77402 + 9.32364i) q^{73} +(9.44573 - 13.0009i) q^{74} +(-14.1202 + 4.58794i) q^{75} -3.96743 q^{76} +(5.10687 + 0.607968i) q^{77} +0.615714i q^{78} +(-10.0200 + 3.25570i) q^{79} +(-0.661160 + 0.910009i) q^{80} +(-8.77841 + 6.37789i) q^{81} +(15.0692 + 4.89626i) q^{82} +(4.13751 - 12.7339i) q^{83} +(8.52116 - 6.19098i) q^{84} +(-0.669189 + 1.15953i) q^{85} +(5.81892 + 17.9088i) q^{86} +8.81825 q^{87} +(1.60271 - 0.317663i) q^{88} -0.0685064 q^{89} +(3.94281 - 1.28110i) q^{90} +(0.0898558 - 0.123676i) q^{91} +(0.182832 + 0.251647i) q^{92} +(-4.60743 + 14.1802i) q^{93} +(-6.01524 + 18.5130i) q^{94} +(0.338146 + 0.465418i) q^{95} +(-14.4739 + 19.9216i) q^{96} +(-5.66884 + 1.84192i) q^{97} +9.46184 q^{98} +(18.6718 + 8.62324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36} - 60 q^{38} - 10 q^{42} + 32 q^{43} + 16 q^{47} - 18 q^{49} + 4 q^{50} - 2 q^{51} + 44 q^{52} - 16 q^{53} + 22 q^{55} - 50 q^{59} + 68 q^{60} - 80 q^{64} - 172 q^{66} + 40 q^{67} + 18 q^{68} + 6 q^{69} + 128 q^{70} + 186 q^{72} - 116 q^{76} - 30 q^{77} + 48 q^{81} - 12 q^{83} + 68 q^{84} - 108 q^{85} - 16 q^{86} + 92 q^{87} - 40 q^{89} - 80 q^{93} - 188 q^{94} + 72 q^{98}+O(q^{100}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Introduction

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