LMFDB - Embedded newform 570.2.q.b.49.2

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			49.2
Root			$-0.147520 - 0.550552i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.b.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 - 2.19130i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.67513i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 - 2.19130i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.67513i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.710109 + 2.12032i) q^{10} -3.96239 q^{11} -1.00000i q^{12} +(0.698071 - 0.403032i) q^{13} +(-2.33757 + 4.04878i) q^{14} +(-0.710109 + 2.12032i) 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} +(-4.60362 + 1.95108i) 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} +(-10.2446 + 2.08130i) q^{35} +(-0.500000 + 0.866025i) q^{36} +2.19394i q^{37} +(-4.18416 + 1.22179i) q^{38} -0.806063 q^{39} +(-2.19130 + 0.445186i) 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} +(1.76400 + 8.68279i) q^{55} -4.67513 q^{56} +(-4.18416 + 1.22179i) q^{57} +4.06300i q^{58} +(3.94723 - 6.83680i) q^{59} +(-2.19130 + 0.445186i) 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} +(9.91276 + 3.31985i) 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} +(2.12032 + 0.710109i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.51235 - 2.02785i) q^{82} -9.92478i q^{83} -4.67513 q^{84} +(3.29314 - 9.83301i) q^{85} +(3.67513 + 6.36551i) q^{86} +4.06300i q^{87} +3.96239i q^{88} +(-9.13141 - 15.8161i) q^{89} +(-2.19130 + 0.445186i) q^{90} +(-1.88423 - 3.26358i) q^{91} +(-5.52574 - 3.19029i) q^{92} +(-2.90141 - 1.67513i) q^{93} +9.38058 q^{94} +(-8.24422 - 5.19931i) 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
$5$	−0.445186	−	2.19130i	−0.199093	−	0.979981i
$5$	−0.445186	−	2.19130i	−0.199093	−	0.979981i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$		−	4.67513i		−	1.76703i	−0.468400	−	0.883517i	$-0.655169\pi$
$7$		−	4.67513i		−	1.76703i	0.468400	−	0.883517i	$-0.344831\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.710109	+	2.12032i	−0.224556	+	0.670503i
$11$	−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	−0.400061	−	0.916488i	$-0.631011\pi$
$13$	0.698071	−	0.403032i	0.193610	−	0.111781i	0.593672	+	0.804707i	$0.297678\pi$
$14$	−2.33757	+	4.04878i	−0.624741	+	1.08208i
$15$	−0.710109	+	2.12032i	−0.183349	+	0.547464i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.01621	+	2.31876i	0.974074	+	0.562382i	0.900476	−	0.434906i	$-0.143218\pi$
$17$	4.01621	+	2.31876i	0.974074	+	0.562382i	0.0735981	+	0.997288i	$0.476552\pi$
$18$		−	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	−0.949422	−	0.314004i	$-0.898329\pi$
$23$	−5.52574	+	3.19029i	−1.15220	+	0.665221i	−0.202775	+	0.979225i	$0.564996\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.60362	+	1.95108i	−0.920724	+	0.390215i
$26$	−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
$35$	−10.2446	+	2.08130i	−1.73166	+	0.351805i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$			2.19394i			0.360681i	0.983604	+	0.180340i	$0.0577200\pi$
$37$			2.19394i			0.360681i	−0.983604	+	0.180340i	$0.942280\pi$
$38$	−4.18416	+	1.22179i	−0.678761	+	0.198201i
$39$	−0.806063			−0.129073
$40$	−2.19130	+	0.445186i	−0.346475	+	0.0703902i
$41$	−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	−0.0712725	−	0.997457i	$-0.522706\pi$
$43$	−6.36551	−	3.67513i	−0.970732	−	0.560452i	−0.899459	+	0.437005i	$0.856039\pi$
$44$	−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	−0.957162	−	0.289554i	$-0.906493\pi$
$47$	−8.12382	+	4.69029i	−1.18498	+	0.684149i	−0.227819	+	0.973703i	$0.573160\pi$
$48$	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	−0.589709	−	0.807616i	$-0.700758\pi$
$53$	−1.34790	+	0.778209i	−0.185148	+	0.106895i	0.404561	+	0.914511i	$0.367424\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	1.76400	+	8.68279i	0.237858	+	1.17079i
$56$	−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	$-0.00512775\pi$
$60$	−2.19130	+	0.445186i	−0.282896	+	0.0574733i
$61$	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	−0.0536280	−	0.998561i	$-0.517079\pi$
$67$	6.42008	−	3.70663i	0.784337	−	0.452837i	0.837965	+	0.545724i	$0.183745\pi$
$68$			4.63752i			0.562382i
$69$	6.38058			0.768131
$70$	9.91276	+	3.31985i	1.18480	+	0.396798i
$71$	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	0.960387	−	0.278671i	$-0.0898940\pi$
$73$	10.2463	+	5.91573i	1.19924	+	0.692384i	0.238857	+	0.971055i	$0.423227\pi$
$74$	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	$0.990360\pi$
$80$	2.12032	+	0.710109i	0.237059	+	0.0793926i
$81$	−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	$-0.816646\pi$
$83$		−	9.92478i		−	1.08939i	0.838636	−	0.544693i	$-0.183354\pi$
$84$	−4.67513			−0.510099
$85$	3.29314	−	9.83301i	0.357192	−	1.06654i
$86$	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	$-0.585832\pi$
$90$	−2.19130	+	0.445186i	−0.230984	+	0.0469268i
$91$	−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
$95$	−8.24422	−	5.19931i	−0.845839	−	0.533438i
$96$	−1.00000			−0.102062
$97$	−10.7439	−	6.20299i	−1.09088	−	0.629818i	−0.157067	−	0.987588i	$-0.550204\pi$
$97$	−10.7439	−	6.20299i	−1.09088	−	0.629818i	−0.933810	+	0.357770i	$0.883537\pi$
$98$	12.8664	+	7.42842i	1.29970	+	0.750384i
$99$	−1.98119	−	3.43153i	−0.199118	−	0.344882i
$100$	−3.99149	−	3.01131i	−0.399149	−	0.301131i
$101$	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	$0.0334790\pi$
$103$			2.13093i			0.209967i	−0.994474	+	0.104984i	$0.966521\pi$
$104$	−0.403032	−	0.698071i	−0.0395205	−	0.0684515i
$105$	9.91276	+	3.31985i	0.967386	+	0.323984i
$106$	1.55642			0.151173
$107$			7.95746i			0.769277i	0.923067	+	0.384639i	$0.125674\pi$
$107$			7.95746i			0.769277i	−0.923067	+	0.384639i	$0.874326\pi$
$108$	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	$0.000604054\pi$
$110$	2.81373	−	8.40152i	0.268278	−	0.801054i
$111$	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	$-0.803613\pi$
$113$		−	12.3004i		−	1.15713i	0.815637	−	0.578564i	$-0.196387\pi$
$114$	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
$120$	2.12032	+	0.710109i	0.193558	+	0.0648238i
$121$	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	0.0368202	−	0.999322i	$-0.488277\pi$
$127$	10.3754	−	5.99024i	0.920668	−	0.531548i	0.883848	+	0.467774i	$0.154944\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.67513	+	6.36551i	0.323577	+	0.560452i
$130$	0.358849	+	1.76633i	0.0314731	+	0.154917i
$131$	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
$135$	−2.19130	+	0.445186i	−0.188597	+	0.0383155i
$136$	2.31876	−	4.01621i	0.198832	−	0.344387i
$137$	5.53206	−	3.19394i	0.472636	−	0.272876i	−0.244707	−	0.969597i	$-0.578692\pi$
$137$	5.53206	−	3.19394i	0.472636	−	0.272876i	0.717342	+	0.696721i	$0.245358\pi$
$138$	−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	$0.154937\pi$
$150$	−3.99149	−	3.01131i	−0.325904	−	0.245873i
$151$	−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
$155$	−1.49149	−	7.34144i	−0.119799	−	0.589679i
$156$	−0.403032	−	0.698071i	−0.0322684	−	0.0558904i
$157$	12.2534	+	7.07452i	0.977929	+	0.564608i	0.901644	−	0.432478i	$-0.142361\pi$
$157$	12.2534	+	7.07452i	0.977929	+	0.564608i	0.0762850	+	0.997086i	$0.475694\pi$
$158$	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	$-0.760303\pi$
$163$		−	17.4617i		−	1.36770i	0.729621	−	0.683852i	$-0.239697\pi$
$164$	−4.05571			−0.316698
$165$	2.81373	−	8.40152i	0.219048	−	0.654058i
$166$	−4.96239	+	8.59511i	−0.385156	+	0.667110i
$167$	20.0979	−	11.6036i	1.55523	−	0.897910i	0.557523	−	0.830161i	$-0.311752\pi$
$167$	20.0979	−	11.6036i	1.55523	−	0.897910i	0.997702	−	0.0677489i	$-0.0215817\pi$
$168$	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	0.973557	−	0.228445i	$-0.0733642\pi$
$173$	16.6055	+	9.58721i	1.26250	+	0.728902i	0.288939	+	0.957348i	$0.406698\pi$
$174$	2.03150	−	3.51866i	0.154008	−	0.266749i
$175$	9.12154	+	21.5225i	0.689524	+	1.62695i
$176$	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	$0.740874\pi$
$180$	2.12032	+	0.710109i	0.158039	+	0.0529284i
$181$	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
$185$	4.80758	−	0.976711i	0.353460	−	0.0718092i
$186$	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
$190$	4.54005	+	8.62485i	0.329370	+	0.625712i
$191$	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	0.747112	−	0.664698i	$-0.231440\pi$
$193$	7.57171	+	4.37153i	0.545024	+	0.314670i	−0.202089	+	0.979367i	$0.564773\pi$
$194$	6.20299	+	10.7439i	0.445348	+	0.771366i
$195$	0.358849	+	1.76633i	0.0256977	+	0.126489i
$196$	−7.42842	−	12.8664i	−0.530602	−	0.919029i
$197$			12.6448i			0.900906i	0.892800	+	0.450453i	$0.148737\pi$
$197$			12.6448i			0.900906i	−0.892800	+	0.450453i	$0.851263\pi$
$198$			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	$0.882900\pi$
$200$	1.95108	+	4.60362i	0.137962	+	0.325525i
$201$	−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
$205$	8.59939	+	2.87999i	0.600608	+	0.201148i
$206$	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
$215$	−5.21949	+	15.5849i	−0.355966	+	1.06288i
$216$	−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	0.446348	−	0.894859i	$-0.352724\pi$
$223$	−1.57468	−	0.909141i	−0.105448	−	0.0608806i	−0.551797	+	0.833979i	$0.686058\pi$
$224$	−2.33757	−	4.04878i	−0.156185	−	0.270521i
$225$	−3.99149	−	3.01131i	−0.266099	−	0.200754i
$226$	−6.15022	+	10.6525i	−0.409106	+	0.708593i
$227$		−	12.8691i		−	0.854150i	−0.904216	−	0.427075i	$-0.859544\pi$
$227$		−	12.8691i		−	0.854150i	0.904216	−	0.427075i	$-0.140456\pi$
$228$	−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	$0.678686\pi$
$230$	−2.84055	−	13.9818i	−0.187300	−	0.921931i
$231$	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	0.436255	−	0.899823i	$-0.356305\pi$
$233$	−1.90632	−	1.10062i	−0.124887	−	0.0721037i	−0.561142	+	0.827719i	$0.689638\pi$
$234$	−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
$245$	6.61407	+	32.5559i	0.422557	+	2.07992i
$246$	−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
$250$	−0.867833	−	11.1466i	−0.0548866	−	0.704973i
$251$	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	−0.995950	−	0.0899138i	$-0.971341\pi$
$257$	−22.7011	+	13.1065i	−1.41606	+	0.817561i	−0.420107	+	0.907475i	$0.638008\pi$
$258$		−	7.35026i		−	0.457607i
$259$	10.2569			0.637335
$260$	0.572393	−	1.70911i	0.0354983	−	0.105995i
$261$	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	0.336724	−	0.941603i	$-0.390681\pi$
$263$	−5.03329	−	2.90597i	−0.310366	−	0.179190i	−0.647090	+	0.762413i	$0.724014\pi$
$264$	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	$-0.0875528\pi$
$270$	2.12032	+	0.710109i	0.129038	+	0.0432158i
$271$	−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
$275$	18.2413	−	7.73092i	1.09999	−	0.466192i
$276$	3.19029	+	5.52574i	0.192033	+	0.332611i
$277$		−	19.6688i		−	1.18178i	−0.806751	−	0.590892i	$-0.798776\pi$
$277$		−	19.6688i		−	1.18178i	0.806751	−	0.590892i	$-0.201224\pi$
$278$			13.2750i			0.796184i
$279$	1.67513	+	2.90141i	0.100287	+	0.173703i
$280$	2.08130	+	10.2446i	0.124382	+	0.612234i
$281$	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	$-0.994946\pi$
$283$	−25.4621	−	14.7005i	−1.51356	−	0.873855i	−0.513688	−	0.857977i	$-0.671721\pi$
$284$	2.16854			0.128679
$285$	4.54005	+	8.62485i	0.268929	+	0.510892i
$286$	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
$290$	8.90327	−	1.80879i	0.522818	−	0.106216i
$291$	6.20299	+	10.7439i	0.363625	+	0.629818i
$292$			11.8315i			0.692384i
$293$		−	22.2628i		−	1.30061i	−0.759674	−	0.650304i	$-0.774642\pi$
$293$		−	22.2628i		−	1.30061i	0.759674	−	0.650304i	$-0.225358\pi$
$294$	−7.42842	−	12.8664i	−0.433235	−	0.750384i
$295$	−16.7388	−	5.60593i	−0.974568	−	0.326390i
$296$	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
$300$	1.95108	+	4.60362i	0.112645	+	0.265790i
$301$	−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	$-0.982543\pi$
$307$	−27.0744	−	15.6314i	−1.54522	−	0.892132i	−0.546721	−	0.837315i	$-0.684124\pi$
$308$	−16.0428	+	9.26234i	−0.914126	+	0.527771i
$309$	1.06547	−	1.84544i	0.0606123	−	0.104984i
$310$	−2.37905	+	7.10362i	−0.135121	+	0.403458i
$311$	−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	−0.339507	−	0.940604i	$-0.610260\pi$
$313$	5.40177	−	3.11871i	0.305326	−	0.176280i	0.644833	+	0.764323i	$0.276927\pi$
$314$	−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	−0.127024	−	0.991900i	$-0.540543\pi$
$317$	11.9018	−	6.87153i	0.668474	−	0.385944i	0.795498	+	0.605956i	$0.207209\pi$
$318$	−1.34790	−	0.778209i	−0.0755863	−	0.0436398i
$319$	8.04960	+	13.9423i	0.450691	+	0.780620i
$320$	0.445186	+	2.19130i	0.0248867	+	0.122498i
$321$	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
$325$	−2.42731	+	3.21740i	−0.134643	+	0.178469i
$326$	−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	0.774941	−	0.632033i	$-0.217779\pi$
$337$	11.2909	+	6.51881i	0.615055	+	0.355102i	−0.159886	+	0.987135i	$0.551113\pi$
$338$	10.6956	−	6.17513i	0.581766	−	0.335883i
$339$	−6.15022	+	10.6525i	−0.334034	+	0.578564i
$340$	10.1622	−	2.06456i	0.551123	−	0.111967i
$341$	−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
$345$	−2.84055	−	13.9818i	−0.152930	−	0.752754i
$346$	−9.58721	−	16.6055i	−0.515412	−	0.892719i
$347$	−21.2610	−	12.2750i	−1.14135	−	0.658959i	−0.194585	−	0.980886i	$-0.562336\pi$
$347$	−21.2610	−	12.2750i	−1.14135	−	0.658959i	−0.946764	+	0.321927i	$0.895669\pi$
$348$	−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	$-0.717549\pi$
$353$		−	29.1368i		−	1.55080i	0.631473	−	0.775398i	$-0.282451\pi$
$354$	7.89446			0.419586
$355$	−4.59800	−	1.53990i	−0.244037	−	0.0817295i
$356$	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
$365$	8.40162	−	25.0864i	0.439761	−	1.31308i
$366$	−2.20299	+	3.81568i	−0.115152	+	0.199449i
$367$	−23.1758	+	13.3806i	−1.20977	+	0.698461i	−0.962709	−	0.270540i	$-0.912798\pi$
$367$	−23.1758	+	13.3806i	−1.20977	+	0.698461i	−0.247060	+	0.969000i	$0.579465\pi$
$368$		−	6.38058i		−	0.332611i
$369$	−4.05571			−0.211132
$370$	−4.65184	−	1.55793i	−0.241838	−	0.0809931i
$371$	3.63823	+	6.30159i	0.188887	+	0.327162i
$372$		−	3.35026i		−	0.173703i
$373$			27.6312i			1.43069i	0.698772	+	0.715344i	$0.253730\pi$
$373$			27.6312i			1.43069i	−0.698772	+	0.715344i	$0.746270\pi$
$374$	9.18783	+	15.9138i	0.475091	+	0.822882i
$375$	−0.867833	−	11.1466i	−0.0448147	−	0.575608i
$376$	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	$0.239335\pi$
$380$	0.380626	−	9.73936i	0.0195257	−	0.499619i
$381$	−11.9805			−0.613779
$382$	−3.01054	−	1.73813i	−0.154033	−	0.0889307i
$383$	14.7601	+	8.52175i	0.754206	+	0.435441i	0.827212	−	0.561891i	$-0.189926\pi$
$383$	14.7601	+	8.52175i	0.754206	+	0.435441i	−0.0730058	+	0.997332i	$0.523259\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	40.5932	−	8.24694i	2.06882	−	0.420303i
$386$	−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	$0.812642\pi$
$390$	0.572393	−	1.70911i	0.0289842	−	0.0865442i
$391$	−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
$395$	19.8255	+	6.63970i	0.997530	+	0.334080i
$396$	1.98119	−	3.43153i	0.0995588	−	0.172441i
$397$	−18.6367	−	10.7599i	−0.935347	−	0.540023i	−0.0468484	−	0.998902i	$-0.514918\pi$
$397$	−18.6367	−	10.7599i	−0.935347	−	0.540023i	−0.888499	+	0.458879i	$0.848251\pi$
$398$			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
$405$	2.12032	+	0.710109i	0.105359	+	0.0352856i
$406$	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
$415$	−21.7482	+	4.41838i	−1.06758	+	0.216890i
$416$	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	$0.367724\pi$
$420$	2.08130	+	10.2446i	0.101557	+	0.499887i
$421$	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	−0.496998	−	0.867752i	$-0.665564\pi$
$433$	0.124800	−	0.0720532i	0.00599750	−	0.00346266i	0.502996	+	0.864289i	$0.332231\pi$
$434$	−7.83146	+	13.5645i	−0.375922	+	0.651116i
$435$	8.90327	−	1.80879i	0.426879	−	0.0867251i
$436$	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	$-0.0992625\pi$
$440$	8.68279	−	1.76400i	0.413936	−	0.0840955i
$441$	−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	0.296824	−	0.954932i	$-0.404073\pi$
$443$	26.7774	−	15.4599i	1.27223	−	0.734523i	0.975408	+	0.220409i	$0.0707392\pi$
$444$	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	$0.474434\pi$
$450$	1.95108	+	4.60362i	0.0919746	+	0.217017i
$451$	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	$-0.931604\pi$
$457$		−	9.11634i		−	0.426445i	0.977004	−	0.213222i	$-0.0683959\pi$
$458$	13.9529	+	8.05571i	0.651976	+	0.376419i
$459$	2.31876	−	4.01621i	0.108230	−	0.187461i
$460$	−4.53090	+	13.5289i	−0.211255	+	0.630786i
$461$	−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	$0.240281\pi$
$463$			29.4871i			1.37038i	−0.728364	+	0.685190i	$0.759719\pi$
$464$	4.06300			0.188620
$465$	−2.37905	+	7.10362i	−0.110326	+	0.329422i
$466$	1.10062	+	1.90632i	0.0509850	+	0.0883087i
$467$			15.9575i			0.738423i	0.929345	+	0.369212i	$0.120372\pi$
$467$			15.9575i			0.738423i	−0.929345	+	0.369212i	$0.879628\pi$
$468$			0.806063i			0.0372603i
$469$	−17.3290	−	30.0147i	−0.800179	−	1.38595i
$470$	−4.17611	−	20.5557i	−0.192629	−	0.948163i
$471$	−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
$475$	−7.72305	+	20.3802i	−0.354358	+	0.935110i
$476$	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	$0.673378\pi$
$480$	0.445186	+	2.19130i	0.0203199	+	0.100019i
$481$	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
$485$	−8.80959	+	26.3046i	−0.400023	+	1.19443i
$486$	−1.00000			−0.0453609
$487$			10.2365i			0.463859i	0.972733	+	0.231929i	$0.0745038\pi$
$487$			10.2365i			0.463859i	−0.972733	+	0.231929i	$0.925496\pi$
$488$	3.81568	−	2.20299i	0.172728	−	0.0997245i
$489$	−8.73084	+	15.1223i	−0.394822	+	0.683852i
$490$	10.5500	−	31.5012i	0.476599	−	1.42308i
$491$	−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	$0.965533\pi$
$500$	−4.82174	+	10.0872i	−0.215635	+	0.451112i
$501$	−23.2071			−1.03682
$502$		−	12.4387i		−	0.555164i
$503$	27.0701	−	15.6289i	1.20700	−	0.696860i	0.244895	−	0.969550i	$-0.421246\pi$
$503$	27.0701	−	15.6289i	1.20700	−	0.696860i	0.962102	+	0.272689i	$0.0879131\pi$
$504$	−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	$0.807998\pi$
$510$	10.1622	−	2.06456i	0.449990	−	0.0914203i
$511$	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
$515$	4.66952	−	0.948662i	0.205764	−	0.0418031i
$516$	−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	−0.724513	−	0.689261i	$-0.757935\pi$
$523$	−11.2025	+	6.46779i	−0.489853	+	0.282817i	0.234660	+	0.972077i	$0.424602\pi$
$524$	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
$530$	−0.692896	−	3.41058i	−0.0300975	−	0.148146i
$531$	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
$535$	17.4372	−	3.54256i	0.753877	−	0.153158i
$536$	−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
$545$	−22.0640	−	7.38937i	−0.945116	−	0.316526i
$546$	1.88423	−	3.26358i	0.0806374	−	0.139668i
$547$	24.6599	−	14.2374i	1.05438	−	0.608748i	0.130510	−	0.991447i	$-0.458339\pi$
$547$	24.6599	−	14.2374i	1.05438	−	0.608748i	0.923873	+	0.382699i	$0.125005\pi$
$548$	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
$555$	−4.65184	−	1.55793i	−0.197460	−	0.0661306i
$556$	6.63752	−	11.4965i	0.281494	−	0.487561i
$557$	−24.3934	+	14.0836i	−1.03358	+	0.596740i	−0.918009	−	0.396559i	$-0.870204\pi$
$557$	−24.3934	+	14.0836i	−1.03358	+	0.596740i	−0.115574	+	0.993299i	$0.536871\pi$
$558$		−	3.35026i		−	0.141828i
$559$	−5.92478			−0.250591
$560$	3.31985	−	9.91276i	0.140289	−	0.418891i
$561$	9.18783	+	15.9138i	0.387910	+	0.671880i
$562$		−	11.5926i		−	0.489005i
$563$			7.02776i			0.296185i	0.988974	+	0.148092i	$0.0473133\pi$
$563$			7.02776i			0.296185i	−0.988974	+	0.148092i	$0.952687\pi$
$564$	4.69029	+	8.12382i	0.197497	+	0.342075i
$565$	−26.9540	+	5.47599i	−1.13396	+	0.230376i
$566$	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	$0.649052\pi$
$570$	0.380626	−	9.73936i	0.0159427	−	0.407937i
$571$	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
$575$	19.2139	−	25.4680i	0.801276	−	1.06209i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$			4.22918i			0.176063i	0.996118	+	0.0880315i	$0.0280576\pi$
$577$			4.22918i			0.176063i	−0.996118	+	0.0880315i	$0.971942\pi$
$578$		−	4.50659i		−	0.187449i
$579$	−4.37153	−	7.57171i	−0.181675	−	0.314670i
$580$	−8.61486	−	2.88517i	−0.357713	−	0.119800i
$581$	−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
$585$	0.572393	−	1.70911i	0.0236655	−	0.0706630i
$586$	−11.1314	+	19.2802i	−0.459834	+	0.796456i
$587$	2.11194	+	1.21933i	0.0871691	+	0.0503271i	0.542951	−	0.839764i	$-0.317307\pi$
$587$	2.11194	+	1.21933i	0.0871691	+	0.0503271i	−0.455782	+	0.890092i	$0.650640\pi$
$588$			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	−0.454193	−	0.890903i	$-0.650072\pi$
$593$	2.19785	−	1.26893i	0.0902549	−	0.0521087i	0.544448	+	0.838794i	$0.316739\pi$
$594$	1.98119	−	3.43153i	0.0812894	−	0.140797i
$595$	−45.9706	−	15.3959i	−1.88461	−	0.631169i
$596$	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
$605$	−2.09261	−	10.3003i	−0.0850767	−	0.418766i
$606$	−5.21933	+	9.04014i	−0.212021	+	0.367231i
$607$			20.5042i			0.832241i	0.909310	+	0.416120i	$0.136610\pi$
$607$			20.5042i			0.832241i	−0.909310	+	0.416120i	$0.863390\pi$
$608$	1.03398	−	4.23449i	0.0419334	−	0.171731i
$609$	18.9951			0.769719
$610$	−9.65482	+	1.96148i	−0.390912	+	0.0794180i
$611$	−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	0.504274	−	0.863544i	$-0.331760\pi$
$613$	0.211935	+	0.122361i	0.00855999	+	0.00494211i	−0.495714	+	0.868486i	$0.665094\pi$
$614$	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	−0.508051	−	0.861327i	$-0.669634\pi$
$617$	−0.401053	+	0.231548i	−0.0161458	+	0.00932177i	0.491905	+	0.870649i	$0.336301\pi$
$618$	−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
$625$	17.3866	−	17.9640i	0.695464	−	0.718561i
$626$	−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
$630$	2.08130	+	10.2446i	0.0829212	+	0.408156i
$631$	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
$640$	0.710109	−	2.12032i	0.0280695	−	0.0838129i
$641$	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	0.0897424	−	0.995965i	$-0.471396\pi$
$643$	−18.4581	−	10.6568i	−0.727917	−	0.420263i	−0.817660	+	0.575702i	$0.804729\pi$
$644$	−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	$-0.857556\pi$
$647$		−	22.0132i		−	0.865427i	0.901531	−	0.432714i	$-0.142444\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−15.6405	+	27.0901i	−0.613942	+	1.06338i
$650$	3.71081	−	1.57269i	0.145550	−	0.0616860i
$651$	−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	$-0.770992\pi$
$653$		−	33.6785i		−	1.31794i	0.752169	−	0.658970i	$-0.229008\pi$
$654$	10.4060			0.406906
$655$	−26.7417	−	8.95598i	−1.04489	−	0.349939i
$656$	−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	$-0.518889\pi$
$660$	8.68279	−	1.76400i	0.337977	−	0.0686637i
$661$	−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
$665$	−24.3075	+	38.5428i	−0.942603	+	1.49463i
$666$	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
$670$	3.30029	+	16.2447i	0.127501	+	0.627588i
$671$	−8.72909	−	15.1192i	−0.336983	−	0.583671i
$672$			4.67513i			0.180347i
$673$			19.8397i			0.764764i	0.924004	+	0.382382i	$0.124896\pi$
$673$			19.8397i			0.764764i	−0.924004	+	0.382382i	$0.875104\pi$
$674$	−6.51881	−	11.2909i	−0.251095	−	0.434909i
$675$	1.95108	+	4.60362i	0.0750970	+	0.177193i
$676$	−12.3503			−0.475010
$677$			10.3479i			0.397702i	0.980030	+	0.198851i	$0.0637209\pi$
$677$			10.3479i			0.397702i	−0.980030	+	0.198851i	$0.936279\pi$
$678$	10.6525	−	6.15022i	0.409106	−	0.236198i
$679$	−28.9998	+	50.2291i	−1.11291	+	1.92761i
$680$	−9.83301	−	3.29314i	−0.377079	−	0.126286i
$681$	−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	$0.280547\pi$
$683$			40.3307i			1.54321i	−0.636100	+	0.771607i	$0.719453\pi$
$684$	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
$690$	−4.53090	+	13.5289i	−0.172489	+	0.515035i
$691$	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
$700$	−14.0783	+	18.6607i	−0.532109	+	0.705310i
$701$	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
$705$	−4.17611	−	20.5557i	−0.157281	−	0.774172i
$706$	−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	$0.984538\pi$
$720$	0.445186	+	2.19130i	0.0165911	+	0.0816650i
$721$	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
$725$	16.2174	+	12.2350i	0.602301	+	0.454395i
$726$	2.35026	+	4.07077i	0.0872264	+	0.151081i
$727$	11.6107	+	6.70346i	0.430618	+	0.248618i	0.699610	−	0.714525i	$-0.253357\pi$
$727$	11.6107	+	6.70346i	0.430618	+	0.248618i	−0.268992	+	0.963143i	$0.586690\pi$
$728$	−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	$-0.948466\pi$
$733$		−	8.72829i		−	0.322387i	0.986923	−	0.161193i	$-0.0515343\pi$
$734$	26.7612			0.987772
$735$	10.5500	−	31.5012i	0.389142	−	1.16194i
$736$	−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	0.999886	−	0.0151182i	$-0.00481244\pi$
$743$	40.5255	+	23.3974i	1.48674	+	0.858367i	0.486850	+	0.873486i	$0.338146\pi$
$744$	−1.67513	+	2.90141i	−0.0614133	+	0.106371i
$745$	−1.90698	−	0.638661i	−0.0698664	−	0.0233987i
$746$	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
$750$	−4.82174	+	10.0872i	−0.176065	+	0.368331i
$751$	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
$755$	4.61910	+	22.7362i	0.168106	+	0.827455i
$756$	−2.33757	−	4.04878i	−0.0850164	−	0.147253i
$757$	−3.30977	−	1.91090i	−0.120296	−	0.0694527i	0.438645	−	0.898661i	$-0.355459\pi$
$757$	−3.30977	−	1.91090i	−0.120296	−	0.0694527i	−0.558940	+	0.829208i	$0.688792\pi$
$758$	−24.6286	−	14.2193i	−0.894551	−	0.516469i
$759$	−25.2823			−0.917691
$760$	−5.19931	+	8.24422i	−0.188599	+	0.299049i
$761$	−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
$765$	10.1622	−	2.06456i	0.367415	−	0.0746444i
$766$	−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	$0.797493\pi$
$770$	−39.2782	−	13.1545i	−1.41549	−	0.474057i
$771$	26.2130			0.944038
$772$			8.74306i			0.314670i
$773$	21.6189	−	12.4817i	0.777577	−	0.448935i	−0.0579936	−	0.998317i	$-0.518470\pi$
$773$	21.6189	−	12.4817i	0.777577	−	0.448935i	0.835571	+	0.549382i	$0.185137\pi$
$774$	−3.67513	+	6.36551i	−0.132100	+	0.228804i
$775$	−15.4233	+	6.53662i	−0.554022	+	0.234802i
$776$	−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
$785$	10.0474	−	30.0004i	0.358605	−	1.07076i
$786$	12.6121			0.449860
$787$		−	42.1744i		−	1.50336i	−0.659530	−	0.751678i	$-0.729245\pi$
$787$		−	42.1744i		−	1.50336i	0.659530	−	0.751678i	$-0.270755\pi$
$788$	−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
$795$	−0.692896	−	3.41058i	−0.0245745	−	0.120961i
$796$	2.18783	−	3.78943i	0.0775455	−	0.134313i
$797$		−	11.1481i		−	0.394885i	−0.980314	−	0.197443i	$-0.936736\pi$
$797$		−	11.1481i		−	0.394885i	0.980314	−	0.197443i	$-0.0632636\pi$
$798$	4.83399	−	19.7968i	0.171121	−	0.700799i
$799$	−43.5026			−1.53901
$800$	−3.01131	+	3.99149i	−0.106466	+	0.141121i
$801$	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
$815$	−38.2638	+	7.77370i	−1.34032	+	0.272301i
$816$	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
$820$	1.80555	+	8.88729i	0.0630524	+	0.310358i
$821$	−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	0.00940343	−	0.999956i	$-0.497007\pi$
$823$	25.2481	−	14.5770i	0.880092	−	0.508122i	0.870689	+	0.491834i	$0.163673\pi$
$824$	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	−0.828541	−	0.559928i	$-0.810829\pi$
$827$	−21.7954	+	12.5836i	−0.757899	+	0.437573i	0.0706416	+	0.997502i	$0.477495\pi$
$828$		−	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	$0.406046\pi$
$830$	21.0437	+	7.04767i	0.730437	+	0.244628i
$831$	−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	$0.0639106\pi$
$840$	3.31985	−	9.91276i	0.114546	−	0.342023i
$841$	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
$845$	26.1865	+	8.77003i	0.900842	+	0.301698i
$846$	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
$850$	18.5106	+	13.9650i	0.634909	+	0.478996i
$851$	−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	0.242361	−	0.970186i	$-0.422078\pi$
$853$	−13.9216	−	8.03761i	−0.476665	−	0.275203i	−0.719026	+	0.694984i	$0.755412\pi$
$854$	−20.5985			−0.704866
$855$	0.380626	−	9.73936i	0.0130171	−	0.333079i
$856$	7.95746			0.271981
$857$	3.85662	+	2.22662i	0.131740	+	0.0760600i	0.564422	−	0.825487i	$-0.309099\pi$
$857$	3.85662	+	2.22662i	0.131740	+	0.0760600i	−0.432682	+	0.901547i	$0.642433\pi$
$858$	−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	$0.529958\pi$
$860$	−16.1067	+	3.27224i	−0.549232	+	0.111582i
$861$	−9.48049	−	16.4207i	−0.323094	−	0.559615i
$862$		−	17.3928i		−	0.592401i
$863$			20.6483i			0.702877i	0.936211	+	0.351439i	$0.114307\pi$
$863$			20.6483i			0.702877i	−0.936211	+	0.351439i	$0.885693\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	13.6159	−	40.6559i	0.462955	−	1.38234i
$866$	−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
$870$	−8.61486	−	2.88517i	−0.292071	−	0.0978166i
$871$	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	0.239251	−	0.970958i	$-0.423098\pi$
$877$	−14.2740	−	8.24107i	−0.481997	−	0.278281i	−0.721248	+	0.692676i	$0.756431\pi$
$878$	−26.9128	+	15.5381i	−0.908262	+	0.524385i
$879$	−11.1314	+	19.2802i	−0.375453	+	0.650304i
$880$	−8.40152	−	2.81373i	−0.283215	−	0.0948507i
$881$	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	−0.616249	−	0.787552i	$-0.711348\pi$
$883$	−7.20102	+	4.15751i	−0.242334	+	0.139911i	0.373915	+	0.927463i	$0.378015\pi$
$884$	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	−0.299219	−	0.954184i	$-0.596726\pi$
$887$	11.2435	−	6.49143i	0.377519	−	0.217961i	0.676738	+	0.736224i	$0.263393\pi$
$888$	−1.90000	−	1.09697i	−0.0637600	−	0.0368118i
$889$	−28.0052	−	48.5064i	−0.939263	−	1.62685i
$890$	40.0194	−	8.13036i	1.34145	−	0.272530i
$891$	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
$895$	8.17840	+	40.2558i	0.273374	+	1.34560i
$896$	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	0.958661	−	0.284549i	$-0.0918439\pi$
$907$	35.8857	+	20.7186i	1.19157	+	0.687951i	0.232904	+	0.972500i	$0.425177\pi$
$908$	11.1449	−	6.43453i	0.369858	−	0.213538i
$909$	−5.21933	+	9.04014i	−0.173114	+	0.299843i
$910$	8.25782	−	1.67766i	0.273744	−	0.0556140i
$911$	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
$915$	−9.65482	+	1.96148i	−0.319178	+	0.0648445i
$916$	−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
$925$	−4.28054	−	10.1000i	−0.140743	−	0.332087i
$926$	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
$935$	−13.0487	+	38.9622i	−0.426739	+	1.27420i
$936$	0.403032	−	0.698071i	0.0131735	−	0.0228172i
$937$	−3.80715	+	2.19806i	−0.124374	+	0.0718075i	−0.560896	−	0.827886i	$-0.689543\pi$
$937$	−3.80715	+	2.19806i	−0.124374	+	0.0718075i	0.436522	+	0.899694i	$0.356210\pi$
$938$			34.6580i			1.13162i
$939$	−6.23743			−0.203551
$940$	−6.66123	+	19.8898i	−0.217265	+	0.648734i
$941$	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
$945$	2.08130	+	10.2446i	0.0677049	+	0.333258i
$946$	−14.5623	−	25.2226i	−0.473461	−	0.820059i
$947$	−6.56809	−	3.79209i	−0.213434	−	0.123226i	0.389472	−	0.921038i	$-0.372657\pi$
$947$	−6.56809	−	3.79209i	−0.213434	−	0.123226i	−0.602906	+	0.797812i	$0.705991\pi$
$948$	8.09756	+	4.67513i	0.262997	+	0.151841i
$949$	9.53690			0.309581
$950$	16.8785	−	13.7883i	0.547610	−	0.447351i
$951$	−13.7431			−0.445649
$952$	−18.7763	−	10.8405i	−0.608544	−	0.351343i
$953$	15.4370	+	8.91256i	0.500054	+	0.288706i	0.728736	−	0.684795i	$-0.240108\pi$
$953$	15.4370	+	8.91256i	0.500054	+	0.288706i	−0.228682	+	0.973501i	$0.573442\pi$
$954$	0.778209	+	1.34790i	0.0251954	+	0.0436398i
$955$	−1.54759	−	7.61756i	−0.0500788	−	0.246498i
$956$	−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
$960$	0.710109	−	2.12032i	0.0229187	−	0.0684329i
$961$	−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
$965$	6.20852	−	18.5381i	0.199859	−	0.596761i
$966$	−14.9150	+	25.8336i	−0.479883	+	0.831182i
$967$	25.6974	+	14.8364i	0.826372	+	0.477106i	0.852609	−	0.522550i	$-0.175019\pi$
$967$	25.6974	+	14.8364i	0.826372	+	0.477106i	−0.0262371	+	0.999656i	$0.508353\pi$
$968$		−	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
$975$	3.71081	−	1.57269i	0.118841	−	0.0503664i
$976$	−4.40597			−0.141032
$977$			14.5017i			0.463949i	0.972722	+	0.231975i	$0.0745186\pi$
$977$			14.5017i			0.463949i	−0.972722	+	0.231975i	$0.925481\pi$
$978$	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	0.592315	−	0.805706i	$-0.298214\pi$
$983$	5.97931	+	3.45215i	0.190710	+	0.110107i	−0.401605	+	0.915813i	$0.631547\pi$
$984$	−2.02785	−	3.51235i	−0.0646457	−	0.111970i
$985$	27.7086	−	5.62930i	0.882870	−	0.179364i
$986$	−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
$990$	8.68279	−	1.76400i	0.275957	−	0.0560637i
$991$	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	−0.852369	−	0.522940i	$-0.824835\pi$
$997$	−26.0709	+	15.0521i	−0.825675	+	0.476704i	0.0266946	+	0.999644i	$0.491502\pi$
$998$	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.49.2	✓	12
3.2	odd	2		1710.2.t.b.1189.5		12
5.4	even	2	inner	570.2.q.b.49.6	yes	12
15.14	odd	2		1710.2.t.b.1189.1		12
19.7	even	3	inner	570.2.q.b.349.6	yes	12
57.26	odd	6		1710.2.t.b.919.1		12
95.64	even	6	inner	570.2.q.b.349.2	yes	12
285.254	odd	6		1710.2.t.b.919.5		12

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 - 2.19130i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.67513i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 - 2.19130i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.67513i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.710109 + 2.12032i) q^{10} -3.96239 q^{11} -1.00000i q^{12} +(0.698071 - 0.403032i) q^{13} +(-2.33757 + 4.04878i) q^{14} +(-0.710109 + 2.12032i) 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} +(-4.60362 + 1.95108i) 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} +(-10.2446 + 2.08130i) q^{35} +(-0.500000 + 0.866025i) q^{36} +2.19394i q^{37} +(-4.18416 + 1.22179i) q^{38} -0.806063 q^{39} +(-2.19130 + 0.445186i) 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} +(1.76400 + 8.68279i) q^{55} -4.67513 q^{56} +(-4.18416 + 1.22179i) q^{57} +4.06300i q^{58} +(3.94723 - 6.83680i) q^{59} +(-2.19130 + 0.445186i) 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} +(9.91276 + 3.31985i) 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} +(2.12032 + 0.710109i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.51235 - 2.02785i) q^{82} -9.92478i q^{83} -4.67513 q^{84} +(3.29314 - 9.83301i) q^{85} +(3.67513 + 6.36551i) q^{86} +4.06300i q^{87} +3.96239i q^{88} +(-9.13141 - 15.8161i) q^{89} +(-2.19130 + 0.445186i) q^{90} +(-1.88423 - 3.26358i) q^{91} +(-5.52574 - 3.19029i) q^{92} +(-2.90141 - 1.67513i) q^{93} +9.38058 q^{94} +(-8.24422 - 5.19931i) 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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