LMFDB - Embedded newform 570.2.q.b.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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([0, 3, 4]))

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

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

chi := DirichletCharacter("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.6
Root			$0.550552 - 0.147520i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.b.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12032 - 0.710109i) q^{5} +(0.500000 + 0.866025i) q^{6} +4.67513i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12032 - 0.710109i) q^{5} +(0.500000 + 0.866025i) q^{6} +4.67513i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.19130 + 0.445186i) q^{10} -3.96239 q^{11} +1.00000i q^{12} +(-0.698071 + 0.403032i) q^{13} +(-2.33757 + 4.04878i) q^{14} +(2.19130 + 0.445186i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.01621 - 2.31876i) q^{17} +1.00000i q^{18} +(3.01270 - 3.15018i) q^{19} +(1.67513 + 1.48119i) q^{20} +(-2.33757 + 4.04878i) q^{21} +(-3.43153 - 1.98119i) q^{22} +(5.52574 - 3.19029i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.99149 - 3.01131i) q^{25} -0.806063 q^{26} +1.00000i q^{27} +(-4.04878 + 2.33757i) q^{28} +(-2.03150 - 3.51866i) q^{29} +(1.67513 + 1.48119i) q^{30} +3.35026 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.43153 - 1.98119i) q^{33} +(-2.31876 - 4.01621i) q^{34} +(3.31985 + 9.91276i) q^{35} +(-0.500000 + 0.866025i) q^{36} -2.19394i q^{37} +(4.18416 - 1.22179i) q^{38} -0.806063 q^{39} +(0.710109 + 2.12032i) q^{40} +(-2.02785 + 3.51235i) q^{41} +(-4.04878 + 2.33757i) q^{42} +(6.36551 + 3.67513i) q^{43} +(-1.98119 - 3.43153i) q^{44} +(1.67513 + 1.48119i) q^{45} +6.38058 q^{46} +(8.12382 - 4.69029i) q^{47} +(-0.866025 + 0.500000i) q^{48} -14.8568 q^{49} +(4.96239 - 0.612127i) q^{50} +(-2.31876 - 4.01621i) q^{51} +(-0.698071 - 0.403032i) q^{52} +(1.34790 - 0.778209i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-8.40152 + 2.81373i) q^{55} -4.67513 q^{56} +(4.18416 - 1.22179i) q^{57} -4.06300i q^{58} +(3.94723 - 6.83680i) q^{59} +(0.710109 + 2.12032i) q^{60} +(2.20299 + 3.81568i) q^{61} +(2.90141 + 1.67513i) q^{62} +(-4.04878 + 2.33757i) q^{63} -1.00000 q^{64} +(-1.19394 + 1.35026i) q^{65} +(-1.98119 - 3.43153i) q^{66} +(-6.42008 + 3.70663i) q^{67} -4.63752i q^{68} +6.38058 q^{69} +(-2.08130 + 10.2446i) q^{70} +(1.08427 - 1.87801i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-10.2463 - 5.91573i) q^{73} +(1.09697 - 1.90000i) q^{74} +(4.96239 - 0.612127i) q^{75} +(4.23449 + 1.03398i) q^{76} -18.5247i q^{77} +(-0.698071 - 0.403032i) q^{78} +(-4.67513 + 8.09756i) q^{79} +(-0.445186 + 2.19130i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.51235 + 2.02785i) q^{82} +9.92478i q^{83} -4.67513 q^{84} +(-10.1622 - 2.06456i) q^{85} +(3.67513 + 6.36551i) q^{86} -4.06300i q^{87} -3.96239i q^{88} +(-9.13141 - 15.8161i) q^{89} +(0.710109 + 2.12032i) q^{90} +(-1.88423 - 3.26358i) q^{91} +(5.52574 + 3.19029i) q^{92} +(2.90141 + 1.67513i) q^{93} +9.38058 q^{94} +(4.15090 - 8.81873i) q^{95} -1.00000 q^{96} +(10.7439 + 6.20299i) q^{97} +(-12.8664 - 7.42842i) q^{98} +(-1.98119 - 3.43153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9	$ 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 2 q^{15} - 6 q^{16} + 6 q^{19} - 18 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 4 q^{34} + 2 q^{35} - 6 q^{36} - 8 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} + 28 q^{46} - 56 q^{49} + 16 q^{50} + 4 q^{51} - 6 q^{54} - 8 q^{55} - 36 q^{56} + 8 q^{59} + 2 q^{60} - 28 q^{61} - 12 q^{64} - 16 q^{65} - 2 q^{66} + 28 q^{69} + 16 q^{70} + 44 q^{71} + 14 q^{74} + 16 q^{75} - 12 q^{76} - 36 q^{79} - 6 q^{81} - 36 q^{84} - 32 q^{85} + 24 q^{86} + 6 q^{89} + 2 q^{90} + 64 q^{94} - 12 q^{95} - 12 q^{96} - 2 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 2 * q^15 - 6 * q^16 + 6 * q^19 - 18 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 4 * q^34 + 2 * q^35 - 6 * q^36 - 8 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 + 28 * q^46 - 56 * q^49 + 16 * q^50 + 4 * q^51 - 6 * q^54 - 8 * q^55 - 36 * q^56 + 8 * q^59 + 2 * q^60 - 28 * q^61 - 12 * q^64 - 16 * q^65 - 2 * q^66 + 28 * q^69 + 16 * q^70 + 44 * q^71 + 14 * q^74 + 16 * q^75 - 12 * q^76 - 36 * q^79 - 6 * q^81 - 36 * q^84 - 32 * q^85 + 24 * q^86 + 6 * q^89 + 2 * q^90 + 64 * q^94 - 12 * q^95 - 12 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.12032	−	0.710109i	0.948235	−	0.317570i
$5$	2.12032	−	0.710109i	0.948235	−	0.317570i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$			4.67513i			1.76703i	0.468400	+	0.883517i	$0.344831\pi$
$7$			4.67513i			1.76703i	−0.468400	+	0.883517i	$0.655169\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.19130	+	0.445186i	0.692951	+	0.140780i
$11$	−3.96239			−1.19471			−0.597353	−	0.801979i	$-0.703781\pi$
$11$	−3.96239			−1.19471			−0.597353	+	0.801979i	$0.703781\pi$
$12$			1.00000i			0.288675i
$13$	−0.698071	+	0.403032i	−0.193610	+	0.111781i	−0.593672	−	0.804707i	$-0.702322\pi$
$13$	−0.698071	+	0.403032i	−0.193610	+	0.111781i	0.400061	+	0.916488i	$0.368989\pi$
$14$	−2.33757	+	4.04878i	−0.624741	+	1.08208i
$15$	2.19130	+	0.445186i	0.565792	+	0.114947i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.01621	−	2.31876i	−0.974074	−	0.562382i	−0.0735981	−	0.997288i	$-0.523448\pi$
$17$	−4.01621	−	2.31876i	−0.974074	−	0.562382i	−0.900476	+	0.434906i	$0.856782\pi$
$18$			1.00000i			0.235702i
$19$	3.01270	−	3.15018i	0.691160	−	0.722702i
$19$	3.01270	−	3.15018i	0.691160	−	0.722702i
$20$	1.67513	+	1.48119i	0.374571	+	0.331205i
$21$	−2.33757	+	4.04878i	−0.510099	+	0.883517i
$22$	−3.43153	−	1.98119i	−0.731604	−	0.422392i
$23$	5.52574	−	3.19029i	1.15220	−	0.665221i	0.202775	−	0.979225i	$-0.435004\pi$
$23$	5.52574	−	3.19029i	1.15220	−	0.665221i	0.949422	+	0.314004i	$0.101671\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	3.99149	−	3.01131i	0.798298	−	0.602262i
$26$	−0.806063			−0.158082
$27$			1.00000i			0.192450i
$28$	−4.04878	+	2.33757i	−0.765148	+	0.441758i
$29$	−2.03150	−	3.51866i	−0.377240	−	0.653400i	0.613419	−	0.789757i	$-0.289794\pi$
$29$	−2.03150	−	3.51866i	−0.377240	−	0.653400i	−0.990660	+	0.136358i	$0.956460\pi$
$30$	1.67513	+	1.48119i	0.305836	+	0.270428i
$31$	3.35026			0.601725			0.300862	−	0.953668i	$-0.402726\pi$
$31$	3.35026			0.601725			0.300862	+	0.953668i	$0.402726\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.43153	−	1.98119i	−0.597353	−	0.344882i
$34$	−2.31876	−	4.01621i	−0.397664	−	0.688774i
$35$	3.31985	+	9.91276i	0.561157	+	1.67556i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$		−	2.19394i		−	0.360681i	−0.983604	−	0.180340i	$-0.942280\pi$
$37$		−	2.19394i		−	0.360681i	0.983604	−	0.180340i	$-0.0577200\pi$
$38$	4.18416	−	1.22179i	0.678761	−	0.198201i
$39$	−0.806063			−0.129073
$40$	0.710109	+	2.12032i	0.112278	+	0.335252i
$41$	−2.02785	+	3.51235i	−0.316698	+	0.548537i	−0.979797	−	0.199995i	$-0.935907\pi$
$41$	−2.02785	+	3.51235i	−0.316698	+	0.548537i	0.663099	+	0.748532i	$0.269241\pi$
$42$	−4.04878	+	2.33757i	−0.624741	+	0.360694i
$43$	6.36551	+	3.67513i	0.970732	+	0.560452i	0.899459	−	0.437005i	$-0.143961\pi$
$43$	6.36551	+	3.67513i	0.970732	+	0.560452i	0.0712725	+	0.997457i	$0.477294\pi$
$44$	−1.98119	−	3.43153i	−0.298676	−	0.517322i
$45$	1.67513	+	1.48119i	0.249714	+	0.220803i
$46$	6.38058			0.940765
$47$	8.12382	−	4.69029i	1.18498	−	0.684149i	0.227819	−	0.973703i	$-0.426840\pi$
$47$	8.12382	−	4.69029i	1.18498	−	0.684149i	0.957162	+	0.289554i	$0.0935071\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−14.8568			−2.12241
$50$	4.96239	−	0.612127i	0.701788	−	0.0865678i
$51$	−2.31876	−	4.01621i	−0.324691	−	0.562382i
$52$	−0.698071	−	0.403032i	−0.0968051	−	0.0558904i
$53$	1.34790	−	0.778209i	0.185148	−	0.106895i	−0.404561	−	0.914511i	$-0.632576\pi$
$53$	1.34790	−	0.778209i	0.185148	−	0.106895i	0.589709	+	0.807616i	$0.299242\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−8.40152	+	2.81373i	−1.13286	+	0.379403i
$56$	−4.67513			−0.624741
$57$	4.18416	−	1.22179i	0.554206	−	0.161830i
$58$		−	4.06300i		−	0.533499i
$59$	3.94723	−	6.83680i	0.513886	−	0.890076i	−0.485985	−	0.873967i	$-0.661539\pi$
$59$	3.94723	−	6.83680i	0.513886	−	0.890076i	0.999870	−	0.0161086i	$-0.00512775\pi$
$60$	0.710109	+	2.12032i	0.0916746	+	0.273732i
$61$	2.20299	+	3.81568i	0.282063	+	0.488548i	0.971893	−	0.235424i	$-0.0756478\pi$
$61$	2.20299	+	3.81568i	0.282063	+	0.488548i	−0.689829	+	0.723972i	$0.742314\pi$
$62$	2.90141	+	1.67513i	0.368480	+	0.212742i
$63$	−4.04878	+	2.33757i	−0.510099	+	0.294506i
$64$	−1.00000			−0.125000
$65$	−1.19394	+	1.35026i	−0.148090	+	0.167479i
$66$	−1.98119	−	3.43153i	−0.243868	−	0.422392i
$67$	−6.42008	+	3.70663i	−0.784337	+	0.452837i	−0.837965	−	0.545724i	$-0.816255\pi$
$67$	−6.42008	+	3.70663i	−0.784337	+	0.452837i	0.0536280	+	0.998561i	$0.482921\pi$
$68$		−	4.63752i		−	0.562382i
$69$	6.38058			0.768131
$70$	−2.08130	+	10.2446i	−0.248764	+	1.22447i
$71$	1.08427	−	1.87801i	0.128679	−	0.222879i	−0.794486	−	0.607283i	$-0.792260\pi$
$71$	1.08427	−	1.87801i	0.128679	−	0.222879i	0.923165	+	0.384403i	$0.125593\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−10.2463	−	5.91573i	−1.19924	−	0.692384i	−0.238857	−	0.971055i	$-0.576773\pi$
$73$	−10.2463	−	5.91573i	−1.19924	−	0.692384i	−0.960387	+	0.278671i	$0.910106\pi$
$74$	1.09697	−	1.90000i	0.127520	−	0.220871i
$75$	4.96239	−	0.612127i	0.573007	−	0.0706823i
$76$	4.23449	+	1.03398i	0.485729	+	0.118606i
$77$		−	18.5247i		−	2.11108i
$78$	−0.698071	−	0.403032i	−0.0790410	−	0.0456344i
$79$	−4.67513	+	8.09756i	−0.525993	+	0.911047i	0.473548	+	0.880768i	$0.342973\pi$
$79$	−4.67513	+	8.09756i	−0.525993	+	0.911047i	−0.999541	+	0.0302792i	$0.990360\pi$
$80$	−0.445186	+	2.19130i	−0.0497734	+	0.244995i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.51235	+	2.02785i	−0.387874	+	0.223939i
$83$			9.92478i			1.08939i	0.838636	+	0.544693i	$0.183354\pi$
$83$			9.92478i			1.08939i	−0.838636	+	0.544693i	$0.816646\pi$
$84$	−4.67513			−0.510099
$85$	−10.1622	−	2.06456i	−1.10225	−	0.223933i
$86$	3.67513	+	6.36551i	0.396300	+	0.686411i
$87$		−	4.06300i		−	0.435600i
$88$		−	3.96239i		−	0.422392i
$89$	−9.13141	−	15.8161i	−0.967928	−	1.67650i	−0.701535	−	0.712635i	$-0.747502\pi$
$89$	−9.13141	−	15.8161i	−0.967928	−	1.67650i	−0.266393	−	0.963865i	$-0.585832\pi$
$90$	0.710109	+	2.12032i	0.0748520	+	0.223501i
$91$	−1.88423	−	3.26358i	−0.197521	−	0.342116i
$92$	5.52574	+	3.19029i	0.576099	+	0.332611i
$93$	2.90141	+	1.67513i	0.300862	+	0.173703i
$94$	9.38058			0.967533
$95$	4.15090	−	8.81873i	0.425873	−	0.904783i
$96$	−1.00000			−0.102062
$97$	10.7439	+	6.20299i	1.09088	+	0.629818i	0.933810	−	0.357770i	$-0.116463\pi$
$97$	10.7439	+	6.20299i	1.09088	+	0.629818i	0.157067	+	0.987588i	$0.449796\pi$
$98$	−12.8664	−	7.42842i	−1.29970	−	0.750384i
$99$	−1.98119	−	3.43153i	−0.199118	−	0.344882i
$100$	4.60362	+	1.95108i	0.460362	+	0.195108i
$101$	5.21933	+	9.04014i	0.519343	+	0.899528i	0.999747	+	0.0224809i	$0.00715649\pi$
$101$	5.21933	+	9.04014i	0.519343	+	0.899528i	−0.480405	+	0.877047i	$0.659510\pi$
$102$		−	4.63752i		−	0.459183i
$103$		−	2.13093i		−	0.209967i	−0.994474	−	0.104984i	$-0.966521\pi$
$103$		−	2.13093i		−	0.209967i	0.994474	−	0.104984i	$-0.0334790\pi$
$104$	−0.403032	−	0.698071i	−0.0395205	−	0.0684515i
$105$	−2.08130	+	10.2446i	−0.203115	+	0.999773i
$106$	1.55642			0.151173
$107$		−	7.95746i		−	0.769277i	−0.923067	−	0.384639i	$-0.874326\pi$
$107$		−	7.95746i		−	0.769277i	0.923067	−	0.384639i	$-0.125674\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	5.20299	−	9.01184i	0.498356	−	0.863177i	−0.501643	−	0.865075i	$-0.667271\pi$
$109$	5.20299	−	9.01184i	0.498356	−	0.863177i	0.999998	+	0.00189769i	$0.000604054\pi$
$110$	−8.68279	−	1.76400i	−0.827872	−	0.168191i
$111$	1.09697	−	1.90000i	0.104120	−	0.180340i
$112$	−4.04878	−	2.33757i	−0.382574	−	0.220879i
$113$			12.3004i			1.15713i	0.815637	+	0.578564i	$0.196387\pi$
$113$			12.3004i			1.15713i	−0.815637	+	0.578564i	$0.803613\pi$
$114$	4.23449	+	1.03398i	0.396596	+	0.0968410i
$115$	9.45088	−	10.6883i	0.881299	−	0.996690i
$116$	2.03150	−	3.51866i	0.188620	−	0.326700i
$117$	−0.698071	−	0.403032i	−0.0645367	−	0.0372603i
$118$	6.83680	−	3.94723i	0.629379	−	0.363372i
$119$	10.8405	−	18.7763i	0.993747	−	1.72122i
$120$	−0.445186	+	2.19130i	−0.0406398	+	0.200038i
$121$	4.70052			0.427320
$122$			4.40597i			0.398898i
$123$	−3.51235	+	2.02785i	−0.316698	+	0.182846i
$124$	1.67513	+	2.90141i	0.150431	+	0.260554i
$125$	6.32487	−	9.21933i	0.565713	−	0.824602i
$126$	−4.67513			−0.416494
$127$	−10.3754	+	5.99024i	−0.920668	+	0.531548i	−0.883848	−	0.467774i	$-0.845056\pi$
$127$	−10.3754	+	5.99024i	−0.920668	+	0.531548i	−0.0368202	+	0.999322i	$0.511723\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.67513	+	6.36551i	0.323577	+	0.560452i
$130$	−1.70911	+	0.572393i	−0.149899	+	0.0502022i
$131$	6.30606	−	10.9224i	0.550963	−	0.954296i	−0.447242	−	0.894413i	$-0.647594\pi$
$131$	6.30606	−	10.9224i	0.550963	−	0.954296i	0.998205	−	0.0598835i	$-0.0190729\pi$
$132$		−	3.96239i		−	0.344882i
$133$	14.7275	+	14.0847i	1.27704	+	1.22130i
$134$	−7.41327			−0.640409
$135$	0.710109	+	2.12032i	0.0611164	+	0.182488i
$136$	2.31876	−	4.01621i	0.198832	−	0.344387i
$137$	−5.53206	+	3.19394i	−0.472636	+	0.272876i	−0.717342	−	0.696721i	$-0.754642\pi$
$137$	−5.53206	+	3.19394i	−0.472636	+	0.272876i	0.244707	+	0.969597i	$0.421308\pi$
$138$	5.52574	+	3.19029i	0.470383	+	0.271575i
$139$	−6.63752	−	11.4965i	−0.562987	−	0.975122i	−0.997234	−	0.0743282i	$-0.976319\pi$
$139$	−6.63752	−	11.4965i	−0.562987	−	0.975122i	0.434247	−	0.900794i	$-0.357015\pi$
$140$	−6.92478	+	7.83146i	−0.585250	+	0.661879i
$141$	9.38058			0.789987
$142$	1.87801	−	1.08427i	0.157599	−	0.0909901i
$143$	2.76603	−	1.59697i	0.231307	−	0.133545i
$144$	−1.00000			−0.0833333
$145$	−6.80606	−	6.01810i	−0.565213	−	0.499776i
$146$	−5.91573	−	10.2463i	−0.489589	−	0.847993i
$147$	−12.8664	−	7.42842i	−1.06120	−	0.612686i
$148$	1.90000	−	1.09697i	0.156179	−	0.0901702i
$149$	0.449692	−	0.778890i	0.0368402	−	0.0638091i	−0.847017	−	0.531565i	$-0.821604\pi$
$149$	0.449692	−	0.778890i	0.0368402	−	0.0638091i	0.883858	+	0.467756i	$0.154937\pi$
$150$	4.60362	+	1.95108i	0.375884	+	0.159305i
$151$	−10.3757			−0.844359			−0.422179	−	0.906512i	$-0.638735\pi$
$151$	−10.3757			−0.844359			−0.422179	+	0.906512i	$0.638735\pi$
$152$	3.15018	+	3.01270i	0.255514	+	0.244362i
$153$		−	4.63752i		−	0.374921i
$154$	9.26234	−	16.0428i	0.746381	−	1.29277i
$155$	7.10362	−	2.37905i	0.570576	−	0.191090i
$156$	−0.403032	−	0.698071i	−0.0322684	−	0.0558904i
$157$	−12.2534	−	7.07452i	−0.977929	−	0.564608i	−0.0762850	−	0.997086i	$-0.524306\pi$
$157$	−12.2534	−	7.07452i	−0.977929	−	0.564608i	−0.901644	+	0.432478i	$0.857639\pi$
$158$	−8.09756	+	4.67513i	−0.644208	+	0.371933i
$159$	1.55642			0.123432
$160$	−1.48119	+	1.67513i	−0.117099	+	0.132431i
$161$	14.9150	+	25.8336i	1.17547	+	2.03597i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$			17.4617i			1.36770i	0.729621	+	0.683852i	$0.239697\pi$
$163$			17.4617i			1.36770i	−0.729621	+	0.683852i	$0.760303\pi$
$164$	−4.05571			−0.316698
$165$	−8.68279	−	1.76400i	−0.675955	−	0.137327i
$166$	−4.96239	+	8.59511i	−0.385156	+	0.667110i
$167$	−20.0979	+	11.6036i	−1.55523	+	0.897910i	−0.557523	+	0.830161i	$0.688248\pi$
$167$	−20.0979	+	11.6036i	−1.55523	+	0.897910i	−0.997702	+	0.0677489i	$0.978418\pi$
$168$	−4.04878	−	2.33757i	−0.312370	−	0.180347i
$169$	−6.17513	+	10.6956i	−0.475010	+	0.822742i
$170$	−7.76845	−	6.86907i	−0.595813	−	0.526833i
$171$	4.23449	+	1.03398i	0.323819	+	0.0790704i
$172$			7.35026i			0.560452i
$173$	−16.6055	−	9.58721i	−1.26250	−	0.728902i	−0.288939	−	0.957348i	$-0.593302\pi$
$173$	−16.6055	−	9.58721i	−1.26250	−	0.728902i	−0.973557	+	0.228445i	$0.926636\pi$
$174$	2.03150	−	3.51866i	0.154008	−	0.266749i
$175$	14.0783	+	18.6607i	1.06422	+	1.41062i
$176$	1.98119	−	3.43153i	0.149338	−	0.258661i
$177$	6.83680	−	3.94723i	0.513886	−	0.296692i
$178$		−	18.2628i		−	1.36886i
$179$	−18.3707			−1.37309			−0.686546	−	0.727086i	$-0.740874\pi$
$179$	−18.3707			−1.37309			−0.686546	+	0.727086i	$0.740874\pi$
$180$	−0.445186	+	2.19130i	−0.0331822	+	0.163330i
$181$	3.10966	+	5.38610i	0.231140	+	0.400345i	0.958144	−	0.286288i	$-0.0924213\pi$
$181$	3.10966	+	5.38610i	0.231140	+	0.400345i	−0.727004	+	0.686633i	$0.759088\pi$
$182$		−	3.76845i		−	0.279336i
$183$			4.40597i			0.325699i
$184$	3.19029	+	5.52574i	0.235191	+	0.407363i
$185$	−1.55793	−	4.65184i	−0.114542	−	0.342010i
$186$	1.67513	+	2.90141i	0.122827	+	0.212742i
$187$	15.9138	+	9.18783i	1.16373	+	0.671880i
$188$	8.12382	+	4.69029i	0.592490	+	0.342075i
$189$	−4.67513			−0.340066
$190$	8.00415	−	5.56180i	0.580682	−	0.403495i
$191$	3.47627			0.251534			0.125767	−	0.992060i	$-0.459861\pi$
$191$	3.47627			0.251534			0.125767	+	0.992060i	$0.459861\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−7.57171	−	4.37153i	−0.545024	−	0.314670i	0.202089	−	0.979367i	$-0.435227\pi$
$193$	−7.57171	−	4.37153i	−0.545024	−	0.314670i	−0.747112	+	0.664698i	$0.768560\pi$
$194$	6.20299	+	10.7439i	0.445348	+	0.771366i
$195$	−1.70911	+	0.572393i	−0.122392	+	0.0409899i
$196$	−7.42842	−	12.8664i	−0.530602	−	0.919029i
$197$		−	12.6448i		−	0.900906i	−0.892800	−	0.450453i	$-0.851263\pi$
$197$		−	12.6448i		−	0.900906i	0.892800	−	0.450453i	$-0.148737\pi$
$198$		−	3.96239i		−	0.281595i
$199$	−2.18783	−	3.78943i	−0.155091	−	0.268625i	0.778001	−	0.628263i	$-0.216234\pi$
$199$	−2.18783	−	3.78943i	−0.155091	−	0.268625i	−0.933092	+	0.359637i	$0.882900\pi$
$200$	3.01131	+	3.99149i	0.212932	+	0.282241i
$201$	−7.41327			−0.522891
$202$			10.4387i			0.734461i
$203$	16.4502	−	9.49754i	1.15458	−	0.666596i
$204$	2.31876	−	4.01621i	0.162346	−	0.281191i
$205$	−1.80555	+	8.88729i	−0.126105	+	0.620715i
$206$	1.06547	−	1.84544i	0.0742346	−	0.128578i
$207$	5.52574	+	3.19029i	0.384066	+	0.221740i
$208$		−	0.806063i		−	0.0558904i
$209$	−11.9375	+	12.4823i	−0.825732	+	0.863416i
$210$	−6.92478	+	7.83146i	−0.477855	+	0.540422i
$211$	6.65022	−	11.5185i	0.457820	−	0.792967i	−0.541026	−	0.841006i	$-0.681964\pi$
$211$	6.65022	−	11.5185i	0.457820	−	0.792967i	0.998845	+	0.0480390i	$0.0152972\pi$
$212$	1.34790	+	0.778209i	0.0925739	+	0.0534476i
$213$	1.87801	−	1.08427i	0.128679	−	0.0742931i
$214$	3.97873	−	6.89137i	0.271981	−	0.471084i
$215$	16.1067	+	3.27224i	1.09846	+	0.223165i
$216$	−1.00000			−0.0680414
$217$			15.6629i			1.06327i
$218$	9.01184	−	5.20299i	0.610359	−	0.352391i
$219$	−5.91573	−	10.2463i	−0.399748	−	0.692384i
$220$	−6.63752	−	5.86907i	−0.447501	−	0.395692i
$221$	3.73813			0.251454
$222$	1.90000	−	1.09697i	0.127520	−	0.0736237i
$223$	1.57468	+	0.909141i	0.105448	+	0.0608806i	0.551797	−	0.833979i	$-0.313942\pi$
$223$	1.57468	+	0.909141i	0.105448	+	0.0608806i	−0.446348	+	0.894859i	$0.647276\pi$
$224$	−2.33757	−	4.04878i	−0.156185	−	0.270521i
$225$	4.60362	+	1.95108i	0.306908	+	0.130072i
$226$	−6.15022	+	10.6525i	−0.409106	+	0.708593i
$227$			12.8691i			0.854150i	0.904216	+	0.427075i	$0.140456\pi$
$227$			12.8691i			0.854150i	−0.904216	+	0.427075i	$0.859544\pi$
$228$	3.15018	+	3.01270i	0.208626	+	0.199521i
$229$	−16.1114			−1.06467			−0.532336	−	0.846533i	$-0.678686\pi$
$229$	−16.1114			−1.06467			−0.532336	+	0.846533i	$0.678686\pi$
$230$	13.5289	−	4.53090i	0.892066	−	0.298759i
$231$	9.26234	−	16.0428i	0.609417	−	1.05554i
$232$	3.51866	−	2.03150i	0.231012	−	0.133375i
$233$	1.90632	+	1.10062i	0.124887	+	0.0721037i	0.561142	−	0.827719i	$-0.310362\pi$
$233$	1.90632	+	1.10062i	0.124887	+	0.0721037i	−0.436255	+	0.899823i	$0.643695\pi$
$234$	−0.403032	−	0.698071i	−0.0263470	−	0.0456344i
$235$	13.8945	−	15.7137i	0.906375	−	1.02505i
$236$	7.89446			0.513886
$237$	−8.09756	+	4.67513i	−0.525993	+	0.303682i
$238$	18.7763	−	10.8405i	1.21709	−	0.702686i
$239$	−4.70052			−0.304052			−0.152026	−	0.988377i	$-0.548580\pi$
$239$	−4.70052			−0.304052			−0.152026	+	0.988377i	$0.548580\pi$
$240$	−1.48119	+	1.67513i	−0.0956107	+	0.108129i
$241$	−12.6405	−	21.8939i	−0.814244	−	1.41031i	−0.909870	−	0.414894i	$-0.863819\pi$
$241$	−12.6405	−	21.8939i	−0.814244	−	1.41031i	0.0956262	−	0.995417i	$-0.469515\pi$
$242$	4.07077	+	2.35026i	0.261679	+	0.151081i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.20299	+	3.81568i	−0.141032	+	0.244274i
$245$	−31.5012	+	10.5500i	−2.01254	+	0.674013i
$246$	−4.05571			−0.258583
$247$	−0.833453	+	3.41327i	−0.0530313	+	0.217181i
$248$			3.35026i			0.212742i
$249$	−4.96239	+	8.59511i	−0.314479	+	0.544693i
$250$	10.0872	−	4.82174i	0.637968	−	0.304954i
$251$	6.21933	+	10.7722i	0.392561	+	0.679935i	0.992787	−	0.119896i	$-0.0382560\pi$
$251$	6.21933	+	10.7722i	0.392561	+	0.679935i	−0.600226	+	0.799831i	$0.704923\pi$
$252$	−4.04878	−	2.33757i	−0.255049	−	0.147253i
$253$	−21.8951	+	12.6412i	−1.37654	+	0.794743i
$254$	−11.9805			−0.751723
$255$	−7.76845	−	6.86907i	−0.486479	−	0.430158i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	22.7011	−	13.1065i	1.41606	−	0.817561i	0.420107	−	0.907475i	$-0.361992\pi$
$257$	22.7011	−	13.1065i	1.41606	−	0.817561i	0.995950	+	0.0899138i	$0.0286592\pi$
$258$			7.35026i			0.457607i
$259$	10.2569			0.637335
$260$	−1.76633	−	0.358849i	−0.109543	−	0.0222548i
$261$	2.03150	−	3.51866i	0.125747	−	0.217800i
$262$	10.9224	−	6.30606i	0.674790	−	0.389590i
$263$	5.03329	+	2.90597i	0.310366	+	0.179190i	0.647090	−	0.762413i	$-0.275986\pi$
$263$	5.03329	+	2.90597i	0.310366	+	0.179190i	−0.336724	+	0.941603i	$0.609319\pi$
$264$	1.98119	−	3.43153i	0.121934	−	0.211196i
$265$	2.30536	−	2.60720i	0.141617	−	0.160159i
$266$	5.71203	+	19.5615i	0.350227	+	1.19939i
$267$		−	18.2628i		−	1.11767i
$268$	−6.42008	−	3.70663i	−0.392169	−	0.226419i
$269$	11.7501	−	20.3518i	0.716418	−	1.24087i	−0.245992	−	0.969272i	$-0.579114\pi$
$269$	11.7501	−	20.3518i	0.716418	−	1.24087i	0.962410	−	0.271600i	$-0.0875528\pi$
$270$	−0.445186	+	2.19130i	−0.0270932	+	0.133358i
$271$	−16.3430	+	28.3069i	−0.992765	+	1.71952i	−0.392393	+	0.919798i	$0.628353\pi$
$271$	−16.3430	+	28.3069i	−0.992765	+	1.71952i	−0.600372	+	0.799721i	$0.704981\pi$
$272$	4.01621	−	2.31876i	0.243518	−	0.140595i
$273$		−	3.76845i		−	0.228077i
$274$	−6.38787			−0.385906
$275$	−15.8158	+	11.9320i	−0.953731	+	0.719526i
$276$	3.19029	+	5.52574i	0.192033	+	0.332611i
$277$			19.6688i			1.18178i	0.806751	+	0.590892i	$0.201224\pi$
$277$			19.6688i			1.18178i	−0.806751	+	0.590892i	$0.798776\pi$
$278$		−	13.2750i		−	0.796184i
$279$	1.67513	+	2.90141i	0.100287	+	0.173703i
$280$	−9.91276	+	3.31985i	−0.592401	+	0.198399i
$281$	5.79631	+	10.0395i	0.345779	+	0.598906i	0.985495	−	0.169705i	$-0.0542815\pi$
$281$	5.79631	+	10.0395i	0.345779	+	0.598906i	−0.639716	+	0.768611i	$0.720948\pi$
$282$	8.12382	+	4.69029i	0.483766	+	0.279303i
$283$	25.4621	+	14.7005i	1.51356	+	0.873855i	0.999874	+	0.0158784i	$0.00505446\pi$
$283$	25.4621	+	14.7005i	1.51356	+	0.873855i	0.513688	+	0.857977i	$0.328279\pi$
$284$	2.16854			0.128679
$285$	8.00415	−	5.56180i	0.474125	−	0.329452i
$286$	3.19394			0.188861
$287$	−16.4207	−	9.48049i	−0.969282	−	0.559615i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	2.25329	+	3.90282i	0.132547	+	0.229578i
$290$	−2.88517	−	8.61486i	−0.169423	−	0.505882i
$291$	6.20299	+	10.7439i	0.363625	+	0.629818i
$292$		−	11.8315i		−	0.692384i
$293$			22.2628i			1.30061i	0.759674	+	0.650304i	$0.225358\pi$
$293$			22.2628i			1.30061i	−0.759674	+	0.650304i	$0.774642\pi$
$294$	−7.42842	−	12.8664i	−0.433235	−	0.750384i
$295$	3.51451	−	17.2992i	0.204622	−	1.00720i
$296$	2.19394			0.127520
$297$		−	3.96239i		−	0.229921i
$298$	0.778890	−	0.449692i	0.0451199	−	0.0260500i
$299$	−2.57158	+	4.45410i	−0.148718	+	0.257587i
$300$	3.01131	+	3.99149i	0.173858	+	0.230449i
$301$	−17.1817	+	29.7596i	−0.990338	+	1.71532i
$302$	−8.98558	−	5.18783i	−0.517062	−	0.298526i
$303$			10.4387i			0.599685i
$304$	1.22179	+	4.18416i	0.0700745	+	0.239978i
$305$	7.38058	+	6.52610i	0.422611	+	0.373683i
$306$	2.31876	−	4.01621i	0.132555	−	0.229591i
$307$	27.0744	+	15.6314i	1.54522	+	0.892132i	0.998496	+	0.0548168i	$0.0174575\pi$
$307$	27.0744	+	15.6314i	1.54522	+	0.892132i	0.546721	+	0.837315i	$0.315876\pi$
$308$	16.0428	−	9.26234i	0.914126	−	0.527771i
$309$	1.06547	−	1.84544i	0.0606123	−	0.104984i
$310$	7.34144	+	1.49149i	0.416966	+	0.0847110i
$311$	−17.7889			−1.00872			−0.504359	−	0.863494i	$-0.668271\pi$
$311$	−17.7889			−1.00872			−0.504359	+	0.863494i	$0.668271\pi$
$312$		−	0.806063i		−	0.0456344i
$313$	−5.40177	+	3.11871i	−0.305326	+	0.176280i	−0.644833	−	0.764323i	$-0.723073\pi$
$313$	−5.40177	+	3.11871i	−0.305326	+	0.176280i	0.339507	+	0.940604i	$0.389740\pi$
$314$	−7.07452	−	12.2534i	−0.399238	−	0.691501i
$315$	−6.92478	+	7.83146i	−0.390167	+	0.441253i
$316$	−9.35026			−0.525993
$317$	−11.9018	+	6.87153i	−0.668474	+	0.385944i	−0.795498	−	0.605956i	$-0.792791\pi$
$317$	−11.9018	+	6.87153i	−0.668474	+	0.385944i	0.127024	+	0.991900i	$0.459457\pi$
$318$	1.34790	+	0.778209i	0.0755863	+	0.0436398i
$319$	8.04960	+	13.9423i	0.450691	+	0.780620i
$320$	−2.12032	+	0.710109i	−0.118529	+	0.0396963i
$321$	3.97873	−	6.89137i	0.222071	−	0.384639i
$322$			29.8300i			1.66236i
$323$	−19.4041	+	5.66608i	−1.07968	+	0.315269i
$324$	−1.00000			−0.0555556
$325$	−1.57269	+	3.71081i	−0.0872372	+	0.205839i
$326$	−8.73084	+	15.1223i	−0.483557	+	0.837544i
$327$	9.01184	−	5.20299i	0.498356	−	0.287726i
$328$	−3.51235	−	2.02785i	−0.193937	−	0.111970i
$329$	21.9277	+	37.9799i	1.20891	+	2.09390i
$330$	−6.63752	−	5.86907i	−0.365383	−	0.323082i
$331$	−1.56230			−0.0858716			−0.0429358	−	0.999078i	$-0.513671\pi$
$331$	−1.56230			−0.0858716			−0.0429358	+	0.999078i	$0.513671\pi$
$332$	−8.59511	+	4.96239i	−0.471718	+	0.272346i
$333$	1.90000	−	1.09697i	0.104120	−	0.0601135i
$334$	−23.2071			−1.26984
$335$	−10.9805	+	12.4182i	−0.599928	+	0.678478i
$336$	−2.33757	−	4.04878i	−0.127525	−	0.220879i
$337$	−11.2909	−	6.51881i	−0.615055	−	0.355102i	0.159886	−	0.987135i	$-0.448887\pi$
$337$	−11.2909	−	6.51881i	−0.615055	−	0.355102i	−0.774941	+	0.632033i	$0.782221\pi$
$338$	−10.6956	+	6.17513i	−0.581766	+	0.335883i
$339$	−6.15022	+	10.6525i	−0.334034	+	0.578564i
$340$	−3.29314	−	9.83301i	−0.178596	−	0.533270i
$341$	−13.2750			−0.718884
$342$	3.15018	+	3.01270i	0.170342	+	0.162908i
$343$		−	36.7318i		−	1.98333i
$344$	−3.67513	+	6.36551i	−0.198150	+	0.343205i
$345$	13.5289	−	4.53090i	0.728369	−	0.243936i
$346$	−9.58721	−	16.6055i	−0.515412	−	0.892719i
$347$	21.2610	+	12.2750i	1.14135	+	0.658959i	0.946764	−	0.321927i	$-0.104331\pi$
$347$	21.2610	+	12.2750i	1.14135	+	0.658959i	0.194585	+	0.980886i	$0.437664\pi$
$348$	3.51866	−	2.03150i	0.188620	−	0.108900i
$349$	−6.86907			−0.367693			−0.183846	−	0.982955i	$-0.558855\pi$
$349$	−6.86907			−0.367693			−0.183846	+	0.982955i	$0.558855\pi$
$350$	2.86177	+	23.1998i	0.152968	+	1.24008i
$351$	−0.403032	−	0.698071i	−0.0215122	−	0.0372603i
$352$	3.43153	−	1.98119i	0.182901	−	0.105598i
$353$			29.1368i			1.55080i	0.631473	+	0.775398i	$0.282451\pi$
$353$			29.1368i			1.55080i	−0.631473	+	0.775398i	$0.717549\pi$
$354$	7.89446			0.419586
$355$	0.965406	−	4.75194i	0.0512385	−	0.252207i
$356$	9.13141	−	15.8161i	0.483964	−	0.838250i
$357$	18.7763	−	10.8405i	0.993747	−	0.573740i
$358$	−15.9095	−	9.18536i	−0.840844	−	0.485462i
$359$	10.4223	−	18.0520i	0.550069	−	0.952747i	−0.448200	−	0.893933i	$-0.647935\pi$
$359$	10.4223	−	18.0520i	0.550069	−	0.952747i	0.998269	−	0.0588138i	$-0.0187318\pi$
$360$	−1.48119	+	1.67513i	−0.0780658	+	0.0882871i
$361$	−0.847322	−	18.9811i	−0.0445959	−	0.999005i
$362$			6.21933i			0.326881i
$363$	4.07077	+	2.35026i	0.213660	+	0.123357i
$364$	1.88423	−	3.26358i	0.0987603	−	0.171058i
$365$	−25.9263	−	5.26720i	−1.35704	−	0.275698i
$366$	−2.20299	+	3.81568i	−0.115152	+	0.199449i
$367$	23.1758	−	13.3806i	1.20977	−	0.698461i	0.247060	−	0.969000i	$-0.420535\pi$
$367$	23.1758	−	13.3806i	1.20977	−	0.698461i	0.962709	+	0.270540i	$0.0872021\pi$
$368$			6.38058i			0.332611i
$369$	−4.05571			−0.211132
$370$	0.976711	−	4.80758i	0.0507768	−	0.249934i
$371$	3.63823	+	6.30159i	0.188887	+	0.327162i
$372$			3.35026i			0.173703i
$373$		−	27.6312i		−	1.43069i	−0.698772	−	0.715344i	$-0.746270\pi$
$373$		−	27.6312i		−	1.43069i	0.698772	−	0.715344i	$-0.253730\pi$
$374$	9.18783	+	15.9138i	0.475091	+	0.822882i
$375$	10.0872	−	4.82174i	0.520899	−	0.248994i
$376$	4.69029	+	8.12382i	0.241883	+	0.418954i
$377$	2.83627	+	1.63752i	0.146075	+	0.0843365i
$378$	−4.04878	−	2.33757i	−0.208247	−	0.120231i
$379$	28.4387			1.46080			0.730398	−	0.683022i	$-0.239335\pi$
$379$	28.4387			1.46080			0.730398	+	0.683022i	$0.239335\pi$
$380$	9.71270	−	0.814582i	0.498251	−	0.0417872i
$381$	−11.9805			−0.613779
$382$	3.01054	+	1.73813i	0.154033	+	0.0889307i
$383$	−14.7601	−	8.52175i	−0.754206	−	0.435441i	0.0730058	−	0.997332i	$-0.476741\pi$
$383$	−14.7601	−	8.52175i	−0.754206	−	0.435441i	−0.827212	+	0.561891i	$0.810074\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−13.1545	−	39.2782i	−0.670417	−	2.00180i
$386$	−4.37153	−	7.57171i	−0.222505	−	0.385390i
$387$			7.35026i			0.373635i
$388$			12.4060i			0.629818i
$389$	1.28115	+	2.21901i	0.0649568	+	0.112508i	0.896675	−	0.442690i	$-0.145976\pi$
$389$	1.28115	+	2.21901i	0.0649568	+	0.112508i	−0.831718	+	0.555198i	$0.812642\pi$
$390$	−1.76633	−	0.358849i	−0.0894416	−	0.0181710i
$391$	−29.5901			−1.49643
$392$		−	14.8568i		−	0.750384i
$393$	10.9224	−	6.30606i	0.550963	−	0.318099i
$394$	6.32241	−	10.9507i	0.318518	−	0.551690i
$395$	−4.16261	+	20.4893i	−0.209444	+	1.03093i
$396$	1.98119	−	3.43153i	0.0995588	−	0.172441i
$397$	18.6367	+	10.7599i	0.935347	+	0.540023i	0.888499	−	0.458879i	$-0.151749\pi$
$397$	18.6367	+	10.7599i	0.935347	+	0.540023i	0.0468484	+	0.998902i	$0.485082\pi$
$398$		−	4.37565i		−	0.219332i
$399$	5.71203	+	19.5615i	0.285959	+	0.979301i
$400$	0.612127	+	4.96239i	0.0306063	+	0.248119i
$401$	13.9502	−	24.1624i	0.696638	−	1.20661i	−0.272987	−	0.962018i	$-0.588012\pi$
$401$	13.9502	−	24.1624i	0.696638	−	1.20661i	0.969625	−	0.244595i	$-0.0786550\pi$
$402$	−6.42008	−	3.70663i	−0.320204	−	0.184870i
$403$	−2.33872	+	1.35026i	−0.116500	+	0.0672613i
$404$	−5.21933	+	9.04014i	−0.259671	+	0.449764i
$405$	−0.445186	+	2.19130i	−0.0221215	+	0.108887i
$406$	18.9951			0.942710
$407$			8.69323i			0.430907i
$408$	4.01621	−	2.31876i	0.198832	−	0.114796i
$409$	18.6543	+	32.3103i	0.922398	+	1.59764i	0.795694	+	0.605699i	$0.207107\pi$
$409$	18.6543	+	32.3103i	0.922398	+	1.59764i	0.126704	+	0.991941i	$0.459560\pi$
$410$	−6.00729	+	6.79384i	−0.296679	+	0.335524i
$411$	−6.38787			−0.315091
$412$	1.84544	−	1.06547i	0.0909184	−	0.0524918i
$413$	31.9629	+	18.4538i	1.57279	+	0.908053i
$414$	3.19029	+	5.52574i	0.156794	+	0.271575i
$415$	7.04767	+	21.0437i	0.345957	+	1.03299i
$416$	0.403032	−	0.698071i	0.0197603	−	0.0342258i
$417$		−	13.2750i		−	0.650081i
$418$	−16.5793	+	4.84121i	−0.810919	+	0.236791i
$419$	16.5271			0.807399			0.403700	−	0.914892i	$-0.367724\pi$
$419$	16.5271			0.807399			0.403700	+	0.914892i	$0.367724\pi$
$420$	−9.91276	+	3.31985i	−0.483693	+	0.161992i
$421$	10.4902	−	18.1696i	0.511263	−	0.885534i	−0.488652	−	0.872479i	$-0.662511\pi$
$421$	10.4902	−	18.1696i	0.511263	−	0.885534i	0.999915	−	0.0130548i	$-0.00415559\pi$
$422$	11.5185	−	6.65022i	0.560712	−	0.323727i
$423$	8.12382	+	4.69029i	0.394994	+	0.228050i
$424$	0.778209	+	1.34790i	0.0377931	+	0.0654597i
$425$	−23.0132	+	2.83875i	−1.11630	+	0.137700i
$426$	2.16854			0.105066
$427$	−17.8388	+	10.2992i	−0.863281	+	0.498415i
$428$	6.89137	−	3.97873i	0.333107	−	0.192319i
$429$	3.19394			0.154205
$430$	12.3127	+	10.8872i	0.593769	+	0.525026i
$431$	8.69640	+	15.0626i	0.418891	+	0.725540i	0.995828	−	0.0912482i	$-0.0290857\pi$
$431$	8.69640	+	15.0626i	0.418891	+	0.725540i	−0.576937	+	0.816788i	$0.695752\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−0.124800	+	0.0720532i	−0.00599750	+	0.00346266i	−0.502996	−	0.864289i	$-0.667769\pi$
$433$	−0.124800	+	0.0720532i	−0.00599750	+	0.00346266i	0.496998	+	0.867752i	$0.334436\pi$
$434$	−7.83146	+	13.5645i	−0.375922	+	0.651116i
$435$	−2.88517	−	8.61486i	−0.138334	−	0.413051i
$436$	10.4060			0.498356
$437$	6.59739	−	27.0185i	0.315596	−	1.29247i
$438$		−	11.8315i		−	0.565329i
$439$	15.5381	−	26.9128i	0.741593	−	1.28448i	−0.210177	−	0.977663i	$-0.567404\pi$
$439$	15.5381	−	26.9128i	0.741593	−	1.28448i	0.951770	−	0.306813i	$-0.0992625\pi$
$440$	−2.81373	−	8.40152i	−0.134139	−	0.400527i
$441$	−7.42842	−	12.8664i	−0.353734	−	0.612686i
$442$	3.23732	+	1.86907i	0.153984	+	0.0889025i
$443$	−26.7774	+	15.4599i	−1.27223	+	0.734523i	−0.975408	−	0.220409i	$-0.929261\pi$
$443$	−26.7774	+	15.4599i	−1.27223	+	0.734523i	−0.296824	+	0.954932i	$0.595927\pi$
$444$	2.19394			0.104120
$445$	−30.5926	−	27.0508i	−1.45023	−	1.28233i
$446$	0.909141	+	1.57468i	0.0430491	+	0.0745632i
$447$	0.778890	−	0.449692i	0.0368402	−	0.0212697i
$448$		−	4.67513i		−	0.220879i
$449$	3.40009			0.160460			0.0802301	−	0.996776i	$-0.474434\pi$
$449$	3.40009			0.160460			0.0802301	+	0.996776i	$0.474434\pi$
$450$	3.01131	+	3.99149i	0.141955	+	0.188161i
$451$	8.03515	−	13.9173i	0.378360	−	0.655339i
$452$	−10.6525	+	6.15022i	−0.501051	+	0.289282i
$453$	−8.98558	−	5.18783i	−0.422179	−	0.243745i
$454$	−6.43453	+	11.1449i	−0.301988	+	0.523058i
$455$	−6.31265	−	5.58181i	−0.295942	−	0.261679i
$456$	1.22179	+	4.18416i	0.0572156	+	0.195941i
$457$			9.11634i			0.426445i	0.977004	+	0.213222i	$0.0683959\pi$
$457$			9.11634i			0.426445i	−0.977004	+	0.213222i	$0.931604\pi$
$458$	−13.9529	−	8.05571i	−0.651976	−	0.376419i
$459$	2.31876	−	4.01621i	0.108230	−	0.187461i
$460$	13.9818	+	2.84055i	0.651904	+	0.132441i
$461$	−2.13823	+	3.70352i	−0.0995871	+	0.172490i	−0.911514	−	0.411269i	$-0.865086\pi$
$461$	−2.13823	+	3.70352i	−0.0995871	+	0.172490i	0.811927	+	0.583759i	$0.198419\pi$
$462$	16.0428	−	9.26234i	0.746381	−	0.430923i
$463$		−	29.4871i		−	1.37038i	−0.728364	−	0.685190i	$-0.759719\pi$
$463$		−	29.4871i		−	1.37038i	0.728364	−	0.685190i	$-0.240281\pi$
$464$	4.06300			0.188620
$465$	7.34144	+	1.49149i	0.340451	+	0.0691662i
$466$	1.10062	+	1.90632i	0.0509850	+	0.0883087i
$467$		−	15.9575i		−	0.738423i	−0.929345	−	0.369212i	$-0.879628\pi$
$467$		−	15.9575i		−	0.738423i	0.929345	−	0.369212i	$-0.120372\pi$
$468$		−	0.806063i		−	0.0372603i
$469$	−17.3290	−	30.0147i	−0.800179	−	1.38595i
$470$	19.8898	−	6.66123i	0.917448	−	0.307260i
$471$	−7.07452	−	12.2534i	−0.325976	−	0.564608i
$472$	6.83680	+	3.94723i	0.314689	+	0.181686i
$473$	−25.2226	−	14.5623i	−1.15974	−	0.669575i
$474$	−9.35026			−0.429472
$475$	2.53896	−	21.6461i	0.116496	−	0.993191i
$476$	21.6810			0.993747
$477$	1.34790	+	0.778209i	0.0617160	+	0.0356317i
$478$	−4.07077	−	2.35026i	−0.186193	−	0.107498i
$479$	10.5410	+	18.2576i	0.481632	+	0.834211i	0.999778	−	0.0210814i	$-0.00671090\pi$
$479$	10.5410	+	18.2576i	0.481632	+	0.834211i	−0.518146	+	0.855292i	$0.673378\pi$
$480$	−2.12032	+	0.710109i	−0.0967788	+	0.0324119i
$481$	0.884226	+	1.53152i	0.0403172	+	0.0698315i
$482$		−	25.2809i		−	1.15151i
$483$			29.8300i			1.35731i
$484$	2.35026	+	4.07077i	0.106830	+	0.185035i
$485$	27.1852	+	5.52297i	1.23442	+	0.250785i
$486$	−1.00000			−0.0453609
$487$		−	10.2365i		−	0.463859i	−0.972733	−	0.231929i	$-0.925496\pi$
$487$		−	10.2365i		−	0.463859i	0.972733	−	0.231929i	$-0.0745038\pi$
$488$	−3.81568	+	2.20299i	−0.172728	+	0.0997245i
$489$	−8.73084	+	15.1223i	−0.394822	+	0.683852i
$490$	−32.5559	−	6.61407i	−1.47072	−	0.298793i
$491$	−3.68901	+	6.38956i	−0.166483	+	0.288357i	−0.937181	−	0.348844i	$-0.886574\pi$
$491$	−3.68901	+	6.38956i	−0.166483	+	0.288357i	0.770698	+	0.637200i	$0.219908\pi$
$492$	−3.51235	−	2.02785i	−0.158349	−	0.0914228i
$493$			18.8423i			0.848613i
$494$	−2.42842	+	2.53925i	−0.109260	+	0.114246i
$495$	−6.63752	−	5.86907i	−0.298334	−	0.263795i
$496$	−1.67513	+	2.90141i	−0.0752156	+	0.130277i
$497$	8.77996	+	5.06911i	0.393835	+	0.227381i
$498$	−8.59511	+	4.96239i	−0.385156	+	0.222370i
$499$	−13.1944	+	22.8534i	−0.590663	+	1.02306i	0.403480	+	0.914988i	$0.367800\pi$
$499$	−13.1944	+	22.8534i	−0.590663	+	1.02306i	−0.994143	+	0.108070i	$0.965533\pi$
$500$	11.1466	+	0.867833i	0.498491	+	0.0388107i
$501$	−23.2071			−1.03682
$502$			12.4387i			0.555164i
$503$	−27.0701	+	15.6289i	−1.20700	+	0.696860i	−0.962102	−	0.272689i	$-0.912087\pi$
$503$	−27.0701	+	15.6289i	−1.20700	+	0.696860i	−0.244895	+	0.969550i	$0.578754\pi$
$504$	−2.33757	−	4.04878i	−0.104123	−	0.180347i
$505$	17.4861	+	15.4617i	0.778122	+	0.688036i
$506$	−25.2823			−1.12394
$507$	−10.6956	+	6.17513i	−0.475010	+	0.274247i
$508$	−10.3754	−	5.99024i	−0.460334	−	0.265774i
$509$	1.79384	+	3.10703i	0.0795108	+	0.137717i	0.903039	−	0.429559i	$-0.141331\pi$
$509$	1.79384	+	3.10703i	0.0795108	+	0.137717i	−0.823528	+	0.567275i	$0.807998\pi$
$510$	−3.29314	−	9.83301i	−0.145823	−	0.435413i
$511$	27.6568	−	47.9030i	1.22346	−	2.11910i
$512$		−	1.00000i		−	0.0441942i
$513$	3.15018	+	3.01270i	0.139084	+	0.133014i
$514$	26.2130			1.15621
$515$	−1.51319	−	4.51825i	−0.0666793	−	0.199098i
$516$	−3.67513	+	6.36551i	−0.161789	+	0.280226i
$517$	−32.1897	+	18.5847i	−1.41570	+	0.817356i
$518$	8.88277	+	5.12847i	0.390287	+	0.225332i
$519$	−9.58721	−	16.6055i	−0.420832	−	0.728902i
$520$	−1.35026	−	1.19394i	−0.0592129	−	0.0523576i
$521$	1.56134			0.0684036			0.0342018	−	0.999415i	$-0.489111\pi$
$521$	1.56134			0.0684036			0.0342018	+	0.999415i	$0.489111\pi$
$522$	3.51866	−	2.03150i	0.154008	−	0.0889164i
$523$	11.2025	−	6.46779i	0.489853	−	0.282817i	−0.234660	−	0.972077i	$-0.575398\pi$
$523$	11.2025	−	6.46779i	0.489853	−	0.282817i	0.724513	+	0.689261i	$0.242065\pi$
$524$	12.6121			0.550963
$525$	2.86177	+	23.1998i	0.124898	+	1.01252i
$526$	2.90597	+	5.03329i	0.126706	+	0.219462i
$527$	−13.4554	−	7.76845i	−0.586124	−	0.338399i
$528$	3.43153	−	1.98119i	0.149338	−	0.0862204i
$529$	8.85589	−	15.3389i	0.385039	−	0.666907i
$530$	3.30010	−	1.10523i	0.143347	−	0.0480079i
$531$	7.89446			0.342590
$532$	−4.83399	+	19.7968i	−0.209580	+	0.858299i
$533$		−	3.26916i		−	0.141603i
$534$	9.13141	−	15.8161i	0.395155	−	0.684428i
$535$	−5.65066	−	16.8723i	−0.244300	−	0.729455i
$536$	−3.70663	−	6.42008i	−0.160102	−	0.277305i
$537$	−15.9095	−	9.18536i	−0.686546	−	0.396378i
$538$	20.3518	−	11.7501i	0.877429	−	0.506584i
$539$	58.8686			2.53565
$540$	−1.48119	+	1.67513i	−0.0637405	+	0.0720862i
$541$	−16.3004	−	28.2332i	−0.700810	−	1.21384i	−0.968182	−	0.250246i	$-0.919489\pi$
$541$	−16.3004	−	28.2332i	−0.700810	−	1.21384i	0.267372	−	0.963593i	$-0.413845\pi$
$542$	−28.3069	+	16.3430i	−1.21588	+	0.701991i
$543$			6.21933i			0.266897i
$544$	4.63752			0.198832
$545$	4.63260	−	22.8026i	0.198439	−	0.976758i
$546$	1.88423	−	3.26358i	0.0806374	−	0.139668i
$547$	−24.6599	+	14.2374i	−1.05438	+	0.608748i	−0.923873	−	0.382699i	$-0.874995\pi$
$547$	−24.6599	+	14.2374i	−1.05438	+	0.608748i	−0.130510	+	0.991447i	$0.541661\pi$
$548$	−5.53206	−	3.19394i	−0.236318	−	0.136438i
$549$	−2.20299	+	3.81568i	−0.0940211	+	0.162849i
$550$	−19.6629	+	2.42548i	−0.838429	+	0.103423i
$551$	−17.2047	−	4.20106i	−0.732947	−	0.178971i
$552$			6.38058i			0.271575i
$553$	−37.8572	−	21.8568i	−1.60985	−	0.929448i
$554$	−9.83440	+	17.0337i	−0.417823	+	0.723691i
$555$	0.976711	−	4.80758i	0.0414591	−	0.204070i
$556$	6.63752	−	11.4965i	0.281494	−	0.487561i
$557$	24.3934	−	14.0836i	1.03358	−	0.596740i	0.115574	−	0.993299i	$-0.463129\pi$
$557$	24.3934	−	14.0836i	1.03358	−	0.596740i	0.918009	+	0.396559i	$0.129796\pi$
$558$			3.35026i			0.141828i
$559$	−5.92478			−0.250591
$560$	−10.2446	−	2.08130i	−0.432915	−	0.0879512i
$561$	9.18783	+	15.9138i	0.387910	+	0.671880i
$562$			11.5926i			0.489005i
$563$		−	7.02776i		−	0.296185i	−0.988974	−	0.148092i	$-0.952687\pi$
$563$		−	7.02776i		−	0.296185i	0.988974	−	0.148092i	$-0.0473133\pi$
$564$	4.69029	+	8.12382i	0.197497	+	0.342075i
$565$	8.73464	+	26.0808i	0.367469	+	1.09723i
$566$	14.7005	+	25.4621i	0.617909	+	1.07025i
$567$	−4.04878	−	2.33757i	−0.170033	−	0.0981685i
$568$	1.87801	+	1.08427i	0.0787997	+	0.0454950i
$569$	−21.5320			−0.902668			−0.451334	−	0.892355i	$-0.649052\pi$
$569$	−21.5320			−0.902668			−0.451334	+	0.892355i	$0.649052\pi$
$570$	9.71270	−	0.814582i	0.406820	−	0.0341191i
$571$	14.1417			0.591813			0.295907	−	0.955217i	$-0.404378\pi$
$571$	14.1417			0.591813			0.295907	+	0.955217i	$0.404378\pi$
$572$	2.76603	+	1.59697i	0.115654	+	0.0667726i
$573$	3.01054	+	1.73813i	0.125767	+	0.0726116i
$574$	−9.48049	−	16.4207i	−0.395708	−	0.685386i
$575$	12.4490	−	29.3737i	0.519159	−	1.22497i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	4.22918i		−	0.176063i	−0.996118	−	0.0880315i	$-0.971942\pi$
$577$		−	4.22918i		−	0.176063i	0.996118	−	0.0880315i	$-0.0280576\pi$
$578$			4.50659i			0.187449i
$579$	−4.37153	−	7.57171i	−0.181675	−	0.314670i
$580$	1.80879	−	8.90327i	0.0751061	−	0.369688i
$581$	−46.3996			−1.92498
$582$			12.4060i			0.514244i
$583$	−5.34089	+	3.08356i	−0.221197	+	0.127708i
$584$	5.91573	−	10.2463i	0.244795	−	0.423997i
$585$	−1.76633	−	0.358849i	−0.0730287	−	0.0148366i
$586$	−11.1314	+	19.2802i	−0.459834	+	0.796456i
$587$	−2.11194	−	1.21933i	−0.0871691	−	0.0503271i	0.455782	−	0.890092i	$-0.349360\pi$
$587$	−2.11194	−	1.21933i	−0.0871691	−	0.0503271i	−0.542951	+	0.839764i	$0.682693\pi$
$588$		−	14.8568i		−	0.612686i
$589$	10.0933	−	10.5539i	0.415888	−	0.434868i
$590$	11.6932	−	13.2243i	0.481403	−	0.544434i
$591$	6.32241	−	10.9507i	0.260069	−	0.450453i
$592$	1.90000	+	1.09697i	0.0780897	+	0.0450851i
$593$	−2.19785	+	1.26893i	−0.0902549	+	0.0521087i	−0.544448	−	0.838794i	$-0.683261\pi$
$593$	−2.19785	+	1.26893i	−0.0902549	+	0.0521087i	0.454193	+	0.890903i	$0.349928\pi$
$594$	1.98119	−	3.43153i	0.0812894	−	0.140797i
$595$	9.65209	−	47.5097i	0.395697	−	1.94771i
$596$	0.899385			0.0368402
$597$		−	4.37565i		−	0.179084i
$598$	−4.45410	+	2.57158i	−0.182142	+	0.105160i
$599$	−14.1776	−	24.5563i	−0.579281	−	1.00334i	−0.995562	−	0.0941078i	$-0.970000\pi$
$599$	−14.1776	−	24.5563i	−0.579281	−	1.00334i	0.416281	−	0.909236i	$-0.363333\pi$
$600$	0.612127	+	4.96239i	0.0249900	+	0.202589i
$601$	23.5705			0.961463			0.480731	−	0.876868i	$-0.340371\pi$
$601$	23.5705			0.961463			0.480731	+	0.876868i	$0.340371\pi$
$602$	−29.7596	+	17.1817i	−1.21291	+	0.700275i
$603$	−6.42008	−	3.70663i	−0.261446	−	0.150946i
$604$	−5.18783	−	8.98558i	−0.211090	−	0.365618i
$605$	9.96660	−	3.33788i	0.405200	−	0.135704i
$606$	−5.21933	+	9.04014i	−0.212021	+	0.367231i
$607$		−	20.5042i		−	0.832241i	−0.909310	−	0.416120i	$-0.863390\pi$
$607$		−	20.5042i		−	0.832241i	0.909310	−	0.416120i	$-0.136610\pi$
$608$	−1.03398	+	4.23449i	−0.0419334	+	0.171731i
$609$	18.9951			0.769719
$610$	3.12872	+	9.34206i	0.126678	+	0.378249i
$611$	−3.78067	+	6.54831i	−0.152950	+	0.264916i
$612$	4.01621	−	2.31876i	0.162346	−	0.0937303i
$613$	−0.211935	−	0.122361i	−0.00855999	−	0.00494211i	0.495714	−	0.868486i	$-0.334906\pi$
$613$	−0.211935	−	0.122361i	−0.00855999	−	0.00494211i	−0.504274	+	0.863544i	$0.668240\pi$
$614$	15.6314	+	27.0744i	0.630832	+	1.09263i
$615$	−6.00729	+	6.79384i	−0.242237	+	0.273954i
$616$	18.5247			0.746381
$617$	0.401053	−	0.231548i	0.0161458	−	0.00932177i	−0.491905	−	0.870649i	$-0.663699\pi$
$617$	0.401053	−	0.231548i	0.0161458	−	0.00932177i	0.508051	+	0.861327i	$0.330366\pi$
$618$	1.84544	−	1.06547i	0.0742346	−	0.0428593i
$619$	11.1685			0.448902			0.224451	−	0.974485i	$-0.427941\pi$
$619$	11.1685			0.448902			0.224451	+	0.974485i	$0.427941\pi$
$620$	5.61213	+	4.96239i	0.225388	+	0.199294i
$621$	3.19029	+	5.52574i	0.128022	+	0.221740i
$622$	−15.4057	−	8.89446i	−0.617711	−	0.356635i
$623$	73.9422	−	42.6905i	2.96243	−	1.71036i
$624$	0.403032	−	0.698071i	0.0161342	−	0.0279452i
$625$	6.86400	−	24.0392i	0.274560	−	0.961570i
$626$	−6.23743			−0.249298
$627$	−16.5793	+	4.84121i	−0.662113	+	0.193339i
$628$		−	14.1490i		−	0.564608i
$629$	−5.08721	+	8.81131i	−0.202840	+	0.351330i
$630$	−9.91276	+	3.31985i	−0.394934	+	0.132266i
$631$	20.9695	+	36.3202i	0.834781	+	1.44588i	0.894209	+	0.447650i	$0.147739\pi$
$631$	20.9695	+	36.3202i	0.834781	+	1.44588i	−0.0594281	+	0.998233i	$0.518928\pi$
$632$	−8.09756	−	4.67513i	−0.322104	−	0.185967i
$633$	11.5185	−	6.65022i	0.457820	−	0.264322i
$634$	−13.7431			−0.545807
$635$	−17.7454	+	20.0689i	−0.704206	+	0.796409i
$636$	0.778209	+	1.34790i	0.0308580	+	0.0534476i
$637$	10.3711	−	5.98778i	0.410920	−	0.237245i
$638$			16.0992i			0.637373i
$639$	2.16854			0.0857863
$640$	−2.19130	−	0.445186i	−0.0866189	−	0.0175975i
$641$	12.5999	−	21.8237i	0.497666	−	0.861984i	−0.502330	−	0.864676i	$-0.667524\pi$
$641$	12.5999	−	21.8237i	0.497666	−	0.861984i	0.999996	+	0.00269246i	$0.000857038\pi$
$642$	6.89137	−	3.97873i	0.271981	−	0.157028i
$643$	18.4581	+	10.6568i	0.727917	+	0.420263i	0.817660	−	0.575702i	$-0.195271\pi$
$643$	18.4581	+	10.6568i	0.727917	+	0.420263i	−0.0897424	+	0.995965i	$0.528604\pi$
$644$	−14.9150	+	25.8336i	−0.587734	+	1.01799i
$645$	12.3127	+	10.8872i	0.484810	+	0.428682i
$646$	−19.6375	−	4.79510i	−0.772628	−	0.188661i
$647$			22.0132i			0.865427i	0.901531	+	0.432714i	$0.142444\pi$
$647$			22.0132i			0.865427i	−0.901531	+	0.432714i	$0.857556\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−15.6405	+	27.0901i	−0.613942	+	1.06338i
$650$	−3.21740	+	2.42731i	−0.126197	+	0.0952069i
$651$	−7.83146	+	13.5645i	−0.306939	+	0.531634i
$652$	−15.1223	+	8.73084i	−0.592233	+	0.341926i
$653$			33.6785i			1.31794i	0.752169	+	0.658970i	$0.229008\pi$
$653$			33.6785i			1.31794i	−0.752169	+	0.658970i	$0.770992\pi$
$654$	10.4060			0.406906
$655$	5.61475	−	27.6370i	0.219386	−	1.07987i
$656$	−2.02785	−	3.51235i	−0.0791744	−	0.137134i
$657$		−	11.8315i		−	0.461589i
$658$			43.8554i			1.70966i
$659$	−22.9538	−	39.7572i	−0.894154	−	1.54872i	−0.834848	−	0.550480i	$-0.814445\pi$
$659$	−22.9538	−	39.7572i	−0.894154	−	1.54872i	−0.0593053	−	0.998240i	$-0.518889\pi$
$660$	−2.81373	−	8.40152i	−0.109524	−	0.327029i
$661$	−7.24472	−	12.5482i	−0.281787	−	0.488069i	0.690038	−	0.723773i	$-0.257594\pi$
$661$	−7.24472	−	12.5482i	−0.281787	−	0.488069i	−0.971825	+	0.235704i	$0.924260\pi$
$662$	−1.35299	−	0.781148i	−0.0525854	−	0.0303602i
$663$	3.23732	+	1.86907i	0.125727	+	0.0725886i
$664$	−9.92478			−0.385156
$665$	41.2287	+	19.4060i	1.59878	+	0.752532i
$666$	2.19394			0.0850133
$667$	−22.4511	−	12.9622i	−0.869311	−	0.501897i
$668$	−20.0979	−	11.6036i	−0.777613	−	0.448955i
$669$	0.909141	+	1.57468i	0.0351494	+	0.0608806i
$670$	−15.7185	+	5.26422i	−0.607258	+	0.203375i
$671$	−8.72909	−	15.1192i	−0.336983	−	0.583671i
$672$		−	4.67513i		−	0.180347i
$673$		−	19.8397i		−	0.764764i	−0.924004	−	0.382382i	$-0.875104\pi$
$673$		−	19.8397i		−	0.764764i	0.924004	−	0.382382i	$-0.124896\pi$
$674$	−6.51881	−	11.2909i	−0.251095	−	0.434909i
$675$	3.01131	+	3.99149i	0.115905	+	0.153633i
$676$	−12.3503			−0.475010
$677$		−	10.3479i		−	0.397702i	−0.980030	−	0.198851i	$-0.936279\pi$
$677$		−	10.3479i		−	0.397702i	0.980030	−	0.198851i	$-0.0637209\pi$
$678$	−10.6525	+	6.15022i	−0.409106	+	0.236198i
$679$	−28.9998	+	50.2291i	−1.11291	+	1.92761i
$680$	2.06456	−	10.1622i	0.0791723	−	0.389703i
$681$	−6.43453	+	11.1449i	−0.246572	+	0.427075i
$682$	−11.4965	−	6.63752i	−0.440225	−	0.254164i
$683$		−	40.3307i		−	1.54321i	−0.636100	−	0.771607i	$-0.719453\pi$
$683$		−	40.3307i		−	1.54321i	0.636100	−	0.771607i	$-0.280547\pi$
$684$	1.22179	+	4.18416i	0.0467164	+	0.159985i
$685$	−9.46168	+	10.7005i	−0.361512	+	0.408846i
$686$	18.3659	−	31.8107i	0.701213	−	1.21454i
$687$	−13.9529	−	8.05571i	−0.532336	−	0.307344i
$688$	−6.36551	+	3.67513i	−0.242683	+	0.140113i
$689$	−0.627285	+	1.08649i	−0.0238977	+	0.0413920i
$690$	13.9818	+	2.84055i	0.532277	+	0.108138i
$691$	45.8202			1.74308			0.871541	−	0.490322i	$-0.163121\pi$
$691$	45.8202			1.74308			0.871541	+	0.490322i	$0.163121\pi$
$692$		−	19.1744i		−	0.728902i
$693$	16.0428	−	9.26234i	0.609417	−	0.351847i
$694$	12.2750	+	21.2610i	0.465954	+	0.807056i
$695$	−22.2374	−	19.6629i	−0.843514	−	0.745857i
$696$	4.06300			0.154008
$697$	16.2886	−	9.40422i	0.616974	−	0.356210i
$698$	−5.94879	−	3.43453i	−0.225165	−	0.129999i
$699$	1.10062	+	1.90632i	0.0416291	+	0.0721037i
$700$	−9.12154	+	21.5225i	−0.344762	+	0.813475i
$701$	18.6375	−	32.2811i	0.703929	−	1.21924i	−0.263147	−	0.964756i	$-0.584760\pi$
$701$	18.6375	−	32.2811i	0.703929	−	1.21924i	0.967077	−	0.254486i	$-0.0819062\pi$
$702$		−	0.806063i		−	0.0304229i
$703$	−6.91130	−	6.60966i	−0.260665	−	0.249288i
$704$	3.96239			0.149338
$705$	19.8898	−	6.66123i	0.749093	−	0.250876i
$706$	−14.5684	+	25.2332i	−0.548289	+	0.949665i
$707$	−42.2639	+	24.4010i	−1.58950	+	0.917696i
$708$	6.83680	+	3.94723i	0.256943	+	0.148346i
$709$	22.8356	+	39.5524i	0.857608	+	1.48542i	0.874204	+	0.485559i	$0.161384\pi$
$709$	22.8356	+	39.5524i	0.857608	+	1.48542i	−0.0165958	+	0.999862i	$0.505283\pi$
$710$	3.21203	−	3.63259i	0.120546	−	0.136329i
$711$	−9.35026			−0.350662
$712$	15.8161	−	9.13141i	0.592732	−	0.342214i
$713$	18.5127	−	10.6883i	0.693306	−	0.400280i
$714$	21.6810			0.811391
$715$	4.73084	−	5.35026i	0.176923	−	0.200088i
$716$	−9.18536	−	15.9095i	−0.343273	−	0.594567i
$717$	−4.07077	−	2.35026i	−0.152026	−	0.0877721i
$718$	18.0520	−	10.4223i	0.673694	−	0.388957i
$719$	−14.5188	+	25.1473i	−0.541460	+	0.937836i	0.457360	+	0.889281i	$0.348795\pi$
$719$	−14.5188	+	25.1473i	−0.541460	+	0.937836i	−0.998821	+	0.0485550i	$0.984538\pi$
$720$	−2.12032	+	0.710109i	−0.0790196	+	0.0264642i
$721$	9.96239			0.371019
$722$	8.75675	−	16.8618i	0.325892	−	0.627530i
$723$		−	25.2809i		−	0.940207i
$724$	−3.10966	+	5.38610i	−0.115570	+	0.200173i
$725$	−18.7045	−	7.92723i	−0.694668	−	0.294410i
$726$	2.35026	+	4.07077i	0.0872264	+	0.151081i
$727$	−11.6107	−	6.70346i	−0.430618	−	0.248618i	0.268992	−	0.963143i	$-0.413310\pi$
$727$	−11.6107	−	6.70346i	−0.430618	−	0.248618i	−0.699610	+	0.714525i	$0.746643\pi$
$728$	3.26358	−	1.88423i	0.120956	−	0.0698341i
$729$	−1.00000			−0.0370370
$730$	−19.8192	−	17.5247i	−0.733543	−	0.648618i
$731$	−17.0435	−	29.5202i	−0.630376	−	1.09184i
$732$	−3.81568	+	2.20299i	−0.141032	+	0.0814247i
$733$			8.72829i			0.322387i	0.986923	+	0.161193i	$0.0515343\pi$
$733$			8.72829i			0.322387i	−0.986923	+	0.161193i	$0.948466\pi$
$734$	26.7612			0.987772
$735$	−32.5559	−	6.61407i	−1.20084	−	0.243964i
$736$	−3.19029	+	5.52574i	−0.117596	+	0.203682i
$737$	25.4388	−	14.6871i	0.937052	−	0.541007i
$738$	−3.51235	−	2.02785i	−0.129291	−	0.0746464i
$739$	−16.1661	+	28.0005i	−0.594679	+	1.03001i	0.398913	+	0.916989i	$0.369387\pi$
$739$	−16.1661	+	28.0005i	−0.594679	+	1.03001i	−0.993592	+	0.113025i	$0.963946\pi$
$740$	3.24965	−	3.67513i	0.119459	−	0.135100i
$741$	−2.42842	+	2.53925i	−0.0892104	+	0.0932816i
$742$			7.27645i			0.267127i
$743$	−40.5255	−	23.3974i	−1.48674	−	0.858367i	−0.486850	−	0.873486i	$-0.661854\pi$
$743$	−40.5255	−	23.3974i	−1.48674	−	0.858367i	−0.999886	+	0.0151182i	$0.995188\pi$
$744$	−1.67513	+	2.90141i	−0.0614133	+	0.106371i
$745$	0.400394	−	1.97082i	0.0146693	−	0.0722054i
$746$	13.8156	−	23.9293i	0.505825	−	0.876114i
$747$	−8.59511	+	4.96239i	−0.314479	+	0.181564i
$748$			18.3757i			0.671880i
$749$	37.2022			1.35934
$750$	11.1466	+	0.867833i	0.407017	+	0.0316888i
$751$	19.6180	+	33.9794i	0.715871	+	1.23993i	0.962623	+	0.270846i	$0.0873036\pi$
$751$	19.6180	+	33.9794i	0.715871	+	1.23993i	−0.246751	+	0.969079i	$0.579363\pi$
$752$			9.38058i			0.342075i
$753$			12.4387i			0.453290i
$754$	1.63752	+	2.83627i	0.0596349	+	0.103291i
$755$	−21.9997	+	7.36784i	−0.800650	+	0.268143i
$756$	−2.33757	−	4.04878i	−0.0850164	−	0.147253i
$757$	3.30977	+	1.91090i	0.120296	+	0.0694527i	0.558940	−	0.829208i	$-0.311208\pi$
$757$	3.30977	+	1.91090i	0.120296	+	0.0694527i	−0.438645	+	0.898661i	$0.644541\pi$
$758$	24.6286	+	14.2193i	0.894551	+	0.516469i
$759$	−25.2823			−0.917691
$760$	8.81873	+	4.15090i	0.319889	+	0.150569i
$761$	−28.3928			−1.02924			−0.514619	−	0.857419i	$-0.672067\pi$
$761$	−28.3928			−1.02924			−0.514619	+	0.857419i	$0.672067\pi$
$762$	−10.3754	−	5.99024i	−0.375861	−	0.217004i
$763$	42.1315	+	24.3246i	1.52526	+	0.880611i
$764$	1.73813	+	3.01054i	0.0628835	+	0.108917i
$765$	−3.29314	−	9.83301i	−0.119064	−	0.355513i
$766$	−8.52175	−	14.7601i	−0.307903	−	0.533304i
$767$			6.36344i			0.229770i
$768$		−	1.00000i		−	0.0360844i
$769$	3.11577	+	5.39668i	0.112358	+	0.194609i	0.916720	−	0.399529i	$-0.130826\pi$
$769$	3.11577	+	5.39668i	0.112358	+	0.194609i	−0.804363	+	0.594139i	$0.797493\pi$
$770$	8.24694	−	40.5932i	0.297199	−	1.46288i
$771$	26.2130			0.944038
$772$		−	8.74306i		−	0.314670i
$773$	−21.6189	+	12.4817i	−0.777577	+	0.448935i	−0.835571	−	0.549382i	$-0.814863\pi$
$773$	−21.6189	+	12.4817i	−0.777577	+	0.448935i	0.0579936	+	0.998317i	$0.481530\pi$
$774$	−3.67513	+	6.36551i	−0.132100	+	0.228804i
$775$	13.3725	−	10.0887i	0.480356	−	0.362396i
$776$	−6.20299	+	10.7439i	−0.222674	+	0.385683i
$777$	8.88277	+	5.12847i	0.318668	+	0.183983i
$778$			2.56230i			0.0918628i
$779$	4.95523	+	16.9698i	0.177540	+	0.608005i
$780$	−1.35026	−	1.19394i	−0.0483471	−	0.0427498i
$781$	−4.29631	+	7.44142i	−0.153734	+	0.266275i
$782$	−25.6257	−	14.7950i	−0.916375	−	0.529069i
$783$	3.51866	−	2.03150i	0.125747	−	0.0726000i
$784$	7.42842	−	12.8664i	0.265301	−	0.459515i
$785$	−31.0048	−	6.29896i	−1.10661	−	0.224819i
$786$	12.6121			0.449860
$787$			42.1744i			1.50336i	0.659530	+	0.751678i	$0.270755\pi$
$787$			42.1744i			1.50336i	−0.659530	+	0.751678i	$0.729245\pi$
$788$	10.9507	−	6.32241i	0.390104	−	0.225226i
$789$	2.90597	+	5.03329i	0.103455	+	0.179190i
$790$	−13.8496	+	15.6629i	−0.492745	+	0.557261i
$791$	−57.5061			−2.04468
$792$	3.43153	−	1.98119i	0.121934	−	0.0703987i
$793$	−3.07568	−	1.77575i	−0.109221	−	0.0630586i
$794$	10.7599	+	18.6367i	0.381854	+	0.661390i
$795$	3.30010	−	1.10523i	0.117042	−	0.0391983i
$796$	2.18783	−	3.78943i	0.0775455	−	0.134313i
$797$			11.1481i			0.394885i	0.980314	+	0.197443i	$0.0632636\pi$
$797$			11.1481i			0.394885i	−0.980314	+	0.197443i	$0.936736\pi$
$798$	−4.83399	+	19.7968i	−0.171121	+	0.700799i
$799$	−43.5026			−1.53901
$800$	−1.95108	+	4.60362i	−0.0689810	+	0.162762i
$801$	9.13141	−	15.8161i	0.322643	−	0.558833i
$802$	24.1624	−	13.9502i	0.853204	−	0.492598i
$803$	40.6000	+	23.4404i	1.43274	+	0.827194i
$804$	−3.70663	−	6.42008i	−0.130723	−	0.226419i
$805$	49.9692	+	44.1841i	1.76118	+	1.55728i
$806$	−2.70052			−0.0951219
$807$	20.3518	−	11.7501i	0.716418	−	0.413624i
$808$	−9.04014	+	5.21933i	−0.318031	+	0.183615i
$809$	−13.3561			−0.469577			−0.234788	−	0.972046i	$-0.575440\pi$
$809$	−13.3561			−0.469577			−0.234788	+	0.972046i	$0.575440\pi$
$810$	−1.48119	+	1.67513i	−0.0520439	+	0.0588581i
$811$	24.3781	+	42.2241i	0.856031	+	1.48269i	0.875685	+	0.482883i	$0.160410\pi$
$811$	24.3781	+	42.2241i	0.856031	+	1.48269i	−0.0196534	+	0.999807i	$0.506256\pi$
$812$	16.4502	+	9.49754i	0.577289	+	0.333298i
$813$	−28.3069	+	16.3430i	−0.992765	+	0.573173i
$814$	−4.34661	+	7.52856i	−0.152349	+	0.263876i
$815$	12.3997	+	37.0243i	0.434342	+	1.29690i
$816$	4.63752			0.162346
$817$	30.7547	−	8.98049i	1.07597	−	0.314187i
$818$			37.3087i			1.30447i
$819$	1.88423	−	3.26358i	0.0658402	−	0.114039i
$820$	−8.59939	+	2.87999i	−0.300304	+	0.100574i
$821$	−11.6448	−	20.1694i	−0.406407	−	0.703917i	0.588077	−	0.808805i	$-0.299885\pi$
$821$	−11.6448	−	20.1694i	−0.406407	−	0.703917i	−0.994484	+	0.104888i	$0.966552\pi$
$822$	−5.53206	−	3.19394i	−0.192953	−	0.111401i
$823$	−25.2481	+	14.5770i	−0.880092	+	0.508122i	−0.870689	−	0.491834i	$-0.836327\pi$
$823$	−25.2481	+	14.5770i	−0.880092	+	0.508122i	−0.00940343	+	0.999956i	$0.502993\pi$
$824$	2.13093			0.0742346
$825$	−19.6629	+	2.42548i	−0.684575	+	0.0844445i
$826$	18.4538	+	31.9629i	0.642090	+	1.11213i
$827$	21.7954	−	12.5836i	0.757899	−	0.437573i	−0.0706416	−	0.997502i	$-0.522505\pi$
$827$	21.7954	−	12.5836i	0.757899	−	0.437573i	0.828541	+	0.559928i	$0.189171\pi$
$828$			6.38058i			0.221740i
$829$	16.7513			0.581797			0.290898	−	0.956754i	$-0.406046\pi$
$829$	16.7513			0.581797			0.290898	+	0.956754i	$0.406046\pi$
$830$	−4.41838	+	21.7482i	−0.153364	+	0.754891i
$831$	−9.83440	+	17.0337i	−0.341151	+	0.590892i
$832$	0.698071	−	0.403032i	0.0242013	−	0.0139726i
$833$	59.6682	+	34.4495i	2.06738	+	1.19360i
$834$	6.63752	−	11.4965i	0.229839	−	0.398092i
$835$	−34.3742	+	38.8749i	−1.18957	+	1.34532i
$836$	−16.7787	−	4.09703i	−0.580303	−	0.141699i
$837$			3.35026i			0.115802i
$838$	14.3128	+	8.26353i	0.494429	+	0.285459i
$839$	9.18901	−	15.9158i	0.317240	−	0.549476i	−0.662671	−	0.748910i	$-0.730577\pi$
$839$	9.18901	−	15.9158i	0.317240	−	0.549476i	0.979911	+	0.199435i	$0.0639106\pi$
$840$	−10.2446	−	2.08130i	−0.353473	−	0.0718118i
$841$	6.24600	−	10.8184i	0.215379	−	0.373048i
$842$	18.1696	−	10.4902i	0.626167	−	0.361518i
$843$			11.5926i			0.399271i
$844$	13.3004			0.457820
$845$	−5.49817	+	27.0632i	−0.189143	+	0.931001i
$846$	4.69029	+	8.12382i	0.161255	+	0.279303i
$847$			21.9756i			0.755089i
$848$			1.55642i			0.0534476i
$849$	14.7005	+	25.4621i	0.504521	+	0.873855i
$850$	−21.3494	−	9.04816i	−0.732277	−	0.310349i
$851$	−6.99929	−	12.1231i	−0.239933	−	0.415576i
$852$	1.87801	+	1.08427i	0.0643397	+	0.0371465i
$853$	13.9216	+	8.03761i	0.476665	+	0.275203i	0.719026	−	0.694984i	$-0.244588\pi$
$853$	13.9216	+	8.03761i	0.476665	+	0.275203i	−0.242361	+	0.970186i	$0.577922\pi$
$854$	−20.5985			−0.704866
$855$	9.71270	−	0.814582i	0.332167	−	0.0278581i
$856$	7.95746			0.271981
$857$	−3.85662	−	2.22662i	−0.131740	−	0.0760600i	0.432682	−	0.901547i	$-0.357567\pi$
$857$	−3.85662	−	2.22662i	−0.131740	−	0.0760600i	−0.564422	+	0.825487i	$0.690901\pi$
$858$	2.76603	+	1.59697i	0.0944307	+	0.0545196i
$859$	23.8926	+	41.3831i	0.815204	+	1.41197i	0.909181	+	0.416400i	$0.136708\pi$
$859$	23.8926	+	41.3831i	0.815204	+	1.41197i	−0.0939775	+	0.995574i	$0.529958\pi$
$860$	5.21949	+	15.5849i	0.177983	+	0.531440i
$861$	−9.48049	−	16.4207i	−0.323094	−	0.559615i
$862$			17.3928i			0.592401i
$863$		−	20.6483i		−	0.702877i	−0.936211	−	0.351439i	$-0.885693\pi$
$863$		−	20.6483i		−	0.702877i	0.936211	−	0.351439i	$-0.114307\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−42.0170	−	8.53619i	−1.42862	−	0.290239i
$866$	−0.144106			−0.00489693
$867$			4.50659i			0.153052i
$868$	−13.5645	+	7.83146i	−0.460408	+	0.265817i
$869$	18.5247	−	32.0857i	0.628407	−	1.08843i
$870$	1.80879	−	8.90327i	0.0613239	−	0.301849i
$871$	2.98778	−	5.17499i	0.101237	−	0.175348i
$872$	9.01184	+	5.20299i	0.305179	+	0.176195i
$873$			12.4060i			0.419879i
$874$	19.2227	−	20.1000i	0.650219	−	0.679893i
$875$	43.1016	+	29.5696i	1.45710	+	0.999635i
$876$	5.91573	−	10.2463i	0.199874	−	0.346192i
$877$	14.2740	+	8.24107i	0.481997	+	0.278281i	0.721248	−	0.692676i	$-0.243569\pi$
$877$	14.2740	+	8.24107i	0.481997	+	0.278281i	−0.239251	+	0.970958i	$0.576902\pi$
$878$	26.9128	−	15.5381i	0.908262	−	0.524385i
$879$	−11.1314	+	19.2802i	−0.375453	+	0.650304i
$880$	1.76400	−	8.68279i	0.0594645	−	0.292697i
$881$	31.1197			1.04845			0.524224	−	0.851580i	$-0.324355\pi$
$881$	31.1197			1.04845			0.524224	+	0.851580i	$0.324355\pi$
$882$		−	14.8568i		−	0.500256i
$883$	7.20102	−	4.15751i	0.242334	−	0.139911i	−0.373915	−	0.927463i	$-0.621985\pi$
$883$	7.20102	−	4.15751i	0.242334	−	0.139911i	0.616249	+	0.787552i	$0.288652\pi$
$884$	1.86907	+	3.23732i	0.0628635	+	0.108883i
$885$	11.6932	−	13.2243i	0.393064	−	0.444528i
$886$	−30.9199			−1.03877
$887$	−11.2435	+	6.49143i	−0.377519	+	0.217961i	−0.676738	−	0.736224i	$-0.736607\pi$
$887$	−11.2435	+	6.49143i	−0.377519	+	0.217961i	0.299219	+	0.954184i	$0.403274\pi$
$888$	1.90000	+	1.09697i	0.0637600	+	0.0368118i
$889$	−28.0052	−	48.5064i	−0.939263	−	1.62685i
$890$	−12.9686	−	38.7230i	−0.434708	−	1.29800i
$891$	1.98119	−	3.43153i	0.0663725	−	0.114961i
$892$			1.81828i			0.0608806i
$893$	9.69933	−	39.7219i	0.324576	−	1.32924i
$894$	0.899385			0.0300799
$895$	−38.9518	+	13.0452i	−1.30201	+	0.436053i
$896$	2.33757	−	4.04878i	0.0780926	−	0.135260i
$897$	−4.45410	+	2.57158i	−0.148718	+	0.0858624i
$898$	2.94457	+	1.70005i	0.0982614	+	0.0567313i
$899$	−6.80606	−	11.7884i	−0.226995	−	0.393167i
$900$	0.612127	+	4.96239i	0.0204042	+	0.165413i
$901$	−7.21791			−0.240464
$902$	13.9173	−	8.03515i	0.463395	−	0.267541i
$903$	−29.7596	+	17.1817i	−0.990338	+	0.571772i
$904$	−12.3004			−0.409106
$905$	10.4182	+	9.21203i	0.346312	+	0.306218i
$906$	−5.18783	−	8.98558i	−0.172354	−	0.298526i
$907$	−35.8857	−	20.7186i	−1.19157	−	0.687951i	−0.232904	−	0.972500i	$-0.574823\pi$
$907$	−35.8857	−	20.7186i	−1.19157	−	0.687951i	−0.958661	+	0.284549i	$0.908156\pi$
$908$	−11.1449	+	6.43453i	−0.369858	+	0.213538i
$909$	−5.21933	+	9.04014i	−0.173114	+	0.299843i
$910$	−2.67601	−	7.99031i	−0.0887089	−	0.264876i
$911$	12.4993			0.414120			0.207060	−	0.978328i	$-0.433610\pi$
$911$	12.4993			0.414120			0.207060	+	0.978328i	$0.433610\pi$
$912$	−1.03398	+	4.23449i	−0.0342385	+	0.140218i
$913$		−	39.3258i		−	1.30149i
$914$	−4.55817	+	7.89499i	−0.150771	+	0.261143i
$915$	3.12872	+	9.34206i	0.103432	+	0.308839i
$916$	−8.05571	−	13.9529i	−0.266168	−	0.461017i
$917$	51.0638	+	29.4817i	1.68627	+	0.973571i
$918$	4.01621	−	2.31876i	0.132555	−	0.0765305i
$919$	−6.08744			−0.200806			−0.100403	−	0.994947i	$-0.532013\pi$
$919$	−6.08744			−0.200806			−0.100403	+	0.994947i	$0.532013\pi$
$920$	10.6883	+	9.45088i	0.352383	+	0.311586i
$921$	15.6314	+	27.0744i	0.515072	+	0.892132i
$922$	−3.70352	+	2.13823i	−0.121969	+	0.0704187i
$923$			1.74798i			0.0575356i
$924$	18.5247			0.609417
$925$	−6.60663	−	8.75708i	−0.217225	−	0.287931i
$926$	14.7435	−	25.5366i	0.484503	−	0.839183i
$927$	1.84544	−	1.06547i	0.0606123	−	0.0349945i
$928$	3.51866	+	2.03150i	0.115506	+	0.0666873i
$929$	−14.6502	+	25.3749i	−0.480658	+	0.832524i	−0.999754	−	0.0221920i	$-0.992935\pi$
$929$	−14.6502	+	25.3749i	−0.480658	+	0.832524i	0.519096	+	0.854716i	$0.326269\pi$
$930$	5.61213	+	4.96239i	0.184029	+	0.162723i
$931$	−44.7592	+	46.8018i	−1.46692	+	1.53387i
$932$			2.20123i			0.0721037i
$933$	−15.4057	−	8.89446i	−0.504359	−	0.291192i
$934$	7.97873	−	13.8196i	0.261072	−	0.452190i
$935$	40.2666	+	8.18059i	1.31686	+	0.267534i
$936$	0.403032	−	0.698071i	0.0131735	−	0.0228172i
$937$	3.80715	−	2.19806i	0.124374	−	0.0718075i	−0.436522	−	0.899694i	$-0.643790\pi$
$937$	3.80715	−	2.19806i	0.124374	−	0.0718075i	0.560896	+	0.827886i	$0.310457\pi$
$938$		−	34.6580i		−	1.13162i
$939$	−6.23743			−0.203551
$940$	20.5557	+	4.17611i	0.670453	+	0.136210i
$941$	28.6436	+	49.6122i	0.933756	+	1.61731i	0.776838	+	0.629700i	$0.216822\pi$
$941$	28.6436	+	49.6122i	0.933756	+	1.61731i	0.156918	+	0.987612i	$0.449844\pi$
$942$		−	14.1490i		−	0.461000i
$943$			25.8778i			0.842696i
$944$	3.94723	+	6.83680i	0.128471	+	0.222519i
$945$	−9.91276	+	3.31985i	−0.322462	+	0.107995i
$946$	−14.5623	−	25.2226i	−0.473461	−	0.820059i
$947$	6.56809	+	3.79209i	0.213434	+	0.123226i	0.602906	−	0.797812i	$-0.294009\pi$
$947$	6.56809	+	3.79209i	0.213434	+	0.123226i	−0.389472	+	0.921038i	$0.627343\pi$
$948$	−8.09756	−	4.67513i	−0.262997	−	0.151841i
$949$	9.53690			0.309581
$950$	13.0219	−	17.4766i	0.422485	−	0.567015i
$951$	−13.7431			−0.445649
$952$	18.7763	+	10.8405i	0.608544	+	0.351343i
$953$	−15.4370	−	8.91256i	−0.500054	−	0.288706i	0.228682	−	0.973501i	$-0.426558\pi$
$953$	−15.4370	−	8.91256i	−0.500054	−	0.288706i	−0.728736	+	0.684795i	$0.759892\pi$
$954$	0.778209	+	1.34790i	0.0251954	+	0.0436398i
$955$	7.37079	−	2.46853i	0.238513	−	0.0798797i
$956$	−2.35026	−	4.07077i	−0.0760129	−	0.131658i
$957$			16.0992i			0.520413i
$958$			21.0821i			0.681130i
$959$	−14.9321	−	25.8631i	−0.482182	−	0.835163i
$960$	−2.19130	−	0.445186i	−0.0707240	−	0.0143683i
$961$	−19.7757			−0.637927
$962$			1.76845i			0.0570172i
$963$	6.89137	−	3.97873i	0.222071	−	0.128213i
$964$	12.6405	−	21.8939i	0.407122	−	0.705156i
$965$	−19.1587	−	3.89229i	−0.616740	−	0.125297i
$966$	−14.9150	+	25.8336i	−0.479883	+	0.831182i
$967$	−25.6974	−	14.8364i	−0.826372	−	0.477106i	0.0262371	−	0.999656i	$-0.491647\pi$
$967$	−25.6974	−	14.8364i	−0.826372	−	0.477106i	−0.852609	+	0.522550i	$0.824981\pi$
$968$			4.70052i			0.151081i
$969$	−19.6375	−	4.79510i	−0.630848	−	0.154041i
$970$	20.7816	+	18.3757i	0.667258	+	0.590007i
$971$	−24.6840	+	42.7539i	−0.792146	+	1.37204i	0.132490	+	0.991184i	$0.457703\pi$
$971$	−24.6840	+	42.7539i	−0.792146	+	1.37204i	−0.924636	+	0.380852i	$0.875631\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	53.7477	−	31.0313i	1.72307	−	0.994817i
$974$	5.11824	−	8.86505i	0.163999	−	0.284054i
$975$	−3.21740	+	2.42731i	−0.103039	+	0.0777361i
$976$	−4.40597			−0.141032
$977$		−	14.5017i		−	0.463949i	−0.972722	−	0.231975i	$-0.925481\pi$
$977$		−	14.5017i		−	0.463949i	0.972722	−	0.231975i	$-0.0745186\pi$
$978$	−15.1223	+	8.73084i	−0.483557	+	0.279181i
$979$	36.1822	+	62.6694i	1.15639	+	2.00292i
$980$	−24.8872	−	22.0059i	−0.794991	−	0.702952i
$981$	10.4060			0.332237
$982$	−6.38956	+	3.68901i	−0.203899	+	0.117721i
$983$	−5.97931	−	3.45215i	−0.190710	−	0.110107i	0.401605	−	0.915813i	$-0.368453\pi$
$983$	−5.97931	−	3.45215i	−0.190710	−	0.110107i	−0.592315	+	0.805706i	$0.701786\pi$
$984$	−2.02785	−	3.51235i	−0.0646457	−	0.111970i
$985$	−8.97919	−	26.8110i	−0.286101	−	0.854270i
$986$	−9.42113	+	16.3179i	−0.300030	+	0.519667i
$987$			43.8554i			1.39593i
$988$	−3.37270	+	0.984841i	−0.107300	+	0.0313320i
$989$	46.8989			1.49130
$990$	−2.81373	−	8.40152i	−0.0894261	−	0.267018i
$991$	5.02421	−	8.70218i	0.159599	−	0.276434i	−0.775125	−	0.631808i	$-0.782313\pi$
$991$	5.02421	−	8.70218i	0.159599	−	0.276434i	0.934724	+	0.355374i	$0.115646\pi$
$992$	−2.90141	+	1.67513i	−0.0921199	+	0.0531855i
$993$	−1.35299	−	0.781148i	−0.0429358	−	0.0247890i
$994$	5.06911	+	8.77996i	0.160783	+	0.278483i
$995$	−7.32979	−	6.48119i	−0.232370	−	0.205468i
$996$	−9.92478			−0.314479
$997$	26.0709	−	15.0521i	0.825675	−	0.476704i	−0.0266946	−	0.999644i	$-0.508498\pi$
$997$	26.0709	−	15.0521i	0.825675	−	0.476704i	0.852369	+	0.522940i	$0.175165\pi$
$998$	−22.8534	+	13.1944i	−0.723412	+	0.417662i
$999$	2.19394			0.0694131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.b.49.6	yes	12
3.2	odd	2		1710.2.t.b.1189.1		12
5.4	even	2	inner	570.2.q.b.49.2	✓	12
15.14	odd	2		1710.2.t.b.1189.5		12
19.7	even	3	inner	570.2.q.b.349.2	yes	12
57.26	odd	6		1710.2.t.b.919.5		12
95.64	even	6	inner	570.2.q.b.349.6	yes	12
285.254	odd	6		1710.2.t.b.919.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.b.49.2	✓	12	5.4	even	2	inner
570.2.q.b.49.6	yes	12	1.1	even	1	trivial
570.2.q.b.349.2	yes	12	19.7	even	3	inner
570.2.q.b.349.6	yes	12	95.64	even	6	inner
1710.2.t.b.919.1		12	285.254	odd	6
1710.2.t.b.919.5		12	57.26	odd	6
1710.2.t.b.1189.1		12	3.2	odd	2
1710.2.t.b.1189.5		12	15.14	odd	2

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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12032 - 0.710109i) q^{5} +(0.500000 + 0.866025i) q^{6} +4.67513i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12032 - 0.710109i) q^{5} +(0.500000 + 0.866025i) q^{6} +4.67513i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.19130 + 0.445186i) q^{10} -3.96239 q^{11} +1.00000i q^{12} +(-0.698071 + 0.403032i) q^{13} +(-2.33757 + 4.04878i) q^{14} +(2.19130 + 0.445186i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.01621 - 2.31876i) q^{17} +1.00000i q^{18} +(3.01270 - 3.15018i) q^{19} +(1.67513 + 1.48119i) q^{20} +(-2.33757 + 4.04878i) q^{21} +(-3.43153 - 1.98119i) q^{22} +(5.52574 - 3.19029i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.99149 - 3.01131i) q^{25} -0.806063 q^{26} +1.00000i q^{27} +(-4.04878 + 2.33757i) q^{28} +(-2.03150 - 3.51866i) q^{29} +(1.67513 + 1.48119i) q^{30} +3.35026 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.43153 - 1.98119i) q^{33} +(-2.31876 - 4.01621i) q^{34} +(3.31985 + 9.91276i) q^{35} +(-0.500000 + 0.866025i) q^{36} -2.19394i q^{37} +(4.18416 - 1.22179i) q^{38} -0.806063 q^{39} +(0.710109 + 2.12032i) q^{40} +(-2.02785 + 3.51235i) q^{41} +(-4.04878 + 2.33757i) q^{42} +(6.36551 + 3.67513i) q^{43} +(-1.98119 - 3.43153i) q^{44} +(1.67513 + 1.48119i) q^{45} +6.38058 q^{46} +(8.12382 - 4.69029i) q^{47} +(-0.866025 + 0.500000i) q^{48} -14.8568 q^{49} +(4.96239 - 0.612127i) q^{50} +(-2.31876 - 4.01621i) q^{51} +(-0.698071 - 0.403032i) q^{52} +(1.34790 - 0.778209i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-8.40152 + 2.81373i) q^{55} -4.67513 q^{56} +(4.18416 - 1.22179i) q^{57} -4.06300i q^{58} +(3.94723 - 6.83680i) q^{59} +(0.710109 + 2.12032i) q^{60} +(2.20299 + 3.81568i) q^{61} +(2.90141 + 1.67513i) q^{62} +(-4.04878 + 2.33757i) q^{63} -1.00000 q^{64} +(-1.19394 + 1.35026i) q^{65} +(-1.98119 - 3.43153i) q^{66} +(-6.42008 + 3.70663i) q^{67} -4.63752i q^{68} +6.38058 q^{69} +(-2.08130 + 10.2446i) q^{70} +(1.08427 - 1.87801i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-10.2463 - 5.91573i) q^{73} +(1.09697 - 1.90000i) q^{74} +(4.96239 - 0.612127i) q^{75} +(4.23449 + 1.03398i) q^{76} -18.5247i q^{77} +(-0.698071 - 0.403032i) q^{78} +(-4.67513 + 8.09756i) q^{79} +(-0.445186 + 2.19130i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.51235 + 2.02785i) q^{82} +9.92478i q^{83} -4.67513 q^{84} +(-10.1622 - 2.06456i) q^{85} +(3.67513 + 6.36551i) q^{86} -4.06300i q^{87} -3.96239i q^{88} +(-9.13141 - 15.8161i) q^{89} +(0.710109 + 2.12032i) q^{90} +(-1.88423 - 3.26358i) q^{91} +(5.52574 + 3.19029i) q^{92} +(2.90141 + 1.67513i) q^{93} +9.38058 q^{94} +(4.15090 - 8.81873i) q^{95} -1.00000 q^{96} +(10.7439 + 6.20299i) q^{97} +(-12.8664 - 7.42842i) q^{98} +(-1.98119 - 3.43153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9	\( 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 2 q^{15} - 6 q^{16} + 6 q^{19} - 18 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 4 q^{34} + 2 q^{35} - 6 q^{36} - 8 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} + 28 q^{46} - 56 q^{49} + 16 q^{50} + 4 q^{51} - 6 q^{54} - 8 q^{55} - 36 q^{56} + 8 q^{59} + 2 q^{60} - 28 q^{61} - 12 q^{64} - 16 q^{65} - 2 q^{66} + 28 q^{69} + 16 q^{70} + 44 q^{71} + 14 q^{74} + 16 q^{75} - 12 q^{76} - 36 q^{79} - 6 q^{81} - 36 q^{84} - 32 q^{85} + 24 q^{86} + 6 q^{89} + 2 q^{90} + 64 q^{94} - 12 q^{95} - 12 q^{96} - 2 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 2 * q^15 - 6 * q^16 + 6 * q^19 - 18 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 4 * q^34 + 2 * q^35 - 6 * q^36 - 8 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 + 28 * q^46 - 56 * q^49 + 16 * q^50 + 4 * q^51 - 6 * q^54 - 8 * q^55 - 36 * q^56 + 8 * q^59 + 2 * q^60 - 28 * q^61 - 12 * q^64 - 16 * q^65 - 2 * q^66 + 28 * q^69 + 16 * q^70 + 44 * q^71 + 14 * q^74 + 16 * q^75 - 12 * q^76 - 36 * q^79 - 6 * q^81 - 36 * q^84 - 32 * q^85 + 24 * q^86 + 6 * q^89 + 2 * q^90 + 64 * q^94 - 12 * q^95 - 12 * q^96 - 2 * q^99

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