LMFDB - Embedded newform 574.2.s.a.387.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(37,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 24]))

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

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

chi := DirichletCharacter("574.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.s (of order $15$, degree $8$, 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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			387.8
Character	$\chi$	$=$	574.387
Dual form			574.2.s.a.221.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(0.176856 + 0.306324i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.438674 + 4.17371i) q^{5} +(0.109303 + 0.336401i) q^{6} +(-2.31354 + 1.28355i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43744 - 2.48973i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(0.176856 + 0.306324i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.438674 + 4.17371i) q^{5} +(0.109303 + 0.336401i) q^{6} +(-2.31354 + 1.28355i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43744 - 2.48973i) q^{9} +(-0.438674 + 4.17371i) q^{10} +(-0.0845303 + 0.804252i) q^{11} +(0.0369731 + 0.351775i) q^{12} +(-1.03444 - 3.18369i) q^{13} +(-2.52985 + 0.774492i) q^{14} +(-1.20093 + 0.872523i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.436167 + 4.14985i) q^{17} +(1.92368 - 2.13646i) q^{18} +(2.68447 + 2.98140i) q^{19} +(-1.29685 + 3.99130i) q^{20} +(-0.802349 - 0.481690i) q^{21} +(-0.249897 + 0.769103i) q^{22} +(-5.82407 - 1.23795i) q^{23} +(-0.0369731 + 0.351775i) q^{24} +(-12.3367 + 2.62224i) q^{25} +(-0.349912 - 3.32919i) q^{26} +2.07802 q^{27} +(-2.63560 + 0.231581i) q^{28} +(8.63869 - 6.27637i) q^{29} +(-1.35609 + 0.603770i) q^{30} +(-0.548579 + 5.21938i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.261312 + 0.116343i) q^{33} +(-1.28944 + 3.96848i) q^{34} +(-6.37207 - 9.09300i) q^{35} +(2.32583 - 1.68982i) q^{36} +(-0.402978 - 3.83408i) q^{37} +(2.00594 + 3.47438i) q^{38} +(0.792292 - 0.879930i) q^{39} +(-2.09835 + 3.63445i) q^{40} +(4.38385 - 4.66710i) q^{41} +(-0.684667 - 0.637982i) q^{42} +(3.37287 + 10.3806i) q^{43} +(-0.404341 + 0.700340i) q^{44} +(11.0220 + 4.90729i) q^{45} +(-5.43942 - 2.42179i) q^{46} +(8.20405 + 1.74382i) q^{47} +(-0.109303 + 0.336401i) q^{48} +(3.70498 - 5.93912i) q^{49} -12.6123 q^{50} +(-1.34834 + 0.600319i) q^{51} +(0.349912 - 3.32919i) q^{52} +(4.74110 + 2.11087i) q^{53} +(2.03261 + 0.432045i) q^{54} -3.39380 q^{55} +(-2.62615 - 0.321451i) q^{56} +(-0.438510 + 1.34960i) q^{57} +(9.75484 - 4.34314i) q^{58} +(1.99481 - 2.21546i) q^{59} +(-1.45199 + 0.308629i) q^{60} +(-7.35265 - 8.16594i) q^{61} +(-1.62176 + 4.99127i) q^{62} +(-0.129894 + 7.60513i) q^{63} +(0.309017 + 0.951057i) q^{64} +(12.8340 - 5.71406i) q^{65} +(-0.279791 + 0.0594713i) q^{66} +(10.9745 + 4.88617i) q^{67} +(-2.08635 + 3.61367i) q^{68} +(-0.650812 - 2.00299i) q^{69} +(-4.34228 - 10.2191i) q^{70} +(-7.36776 - 5.35299i) q^{71} +(2.62634 - 1.16932i) q^{72} +(-0.250865 - 0.434511i) q^{73} +(0.402978 - 3.83408i) q^{74} +(-2.98507 - 3.31526i) q^{75} +(1.23974 + 3.81552i) q^{76} +(-0.836736 - 1.96917i) q^{77} +(0.957927 - 0.695975i) q^{78} +(3.21052 - 5.56078i) q^{79} +(-2.80814 + 3.11875i) q^{80} +(-3.94482 - 6.83263i) q^{81} +(5.25840 - 3.65366i) q^{82} +3.20683 q^{83} +(-0.537061 - 0.766391i) q^{84} -17.5116 q^{85} +(1.14091 + 10.8551i) q^{86} +(3.45041 + 1.53622i) q^{87} +(-0.541114 + 0.600968i) q^{88} +(6.82221 + 7.57683i) q^{89} +(9.76081 + 7.09165i) q^{90} +(6.47966 + 6.03784i) q^{91} +(-4.81704 - 3.49978i) q^{92} +(-1.69584 + 0.755038i) q^{93} +(7.66221 + 3.41144i) q^{94} +(-11.2659 + 12.5120i) q^{95} +(-0.176856 + 0.306324i) q^{96} +(-0.368507 + 0.267736i) q^{97} +(4.85883 - 5.03903i) q^{98} +(1.88086 + 1.36652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) $ 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	0.176856	+	0.306324i	0.102108	+	0.176856i	0.912553	−	0.408958i	$-0.134108\pi$
$3$	0.176856	+	0.306324i	0.102108	+	0.176856i	−0.810445	+	0.585815i	$0.800775\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	0.438674	+	4.17371i	0.196181	+	1.86654i	0.441722	+	0.897152i	$0.354368\pi$
$5$	0.438674	+	4.17371i	0.196181	+	1.86654i	−0.245541	+	0.969386i	$0.578965\pi$
$6$	0.109303	+	0.336401i	0.0446229	+	0.137335i
$7$	−2.31354	+	1.28355i	−0.874438	+	0.485138i
$7$	−2.31354	+	1.28355i	−0.874438	+	0.485138i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.43744	−	2.48973i	0.479148	−	0.829908i
$10$	−0.438674	+	4.17371i	−0.138721	+	1.31984i
$11$	−0.0845303	+	0.804252i	−0.0254869	+	0.242491i	0.974360	+	0.224994i	$0.0722364\pi$
$11$	−0.0845303	+	0.804252i	−0.0254869	+	0.242491i	−0.999847	+	0.0174969i	$0.994430\pi$
$12$	0.0369731	+	0.351775i	0.0106732	+	0.101549i
$13$	−1.03444	−	3.18369i	−0.286903	−	0.882996i	−0.985822	−	0.167795i	$-0.946335\pi$
$13$	−1.03444	−	3.18369i	−0.286903	−	0.882996i	0.698919	−	0.715201i	$-0.253665\pi$
$14$	−2.52985	+	0.774492i	−0.676132	+	0.206992i
$15$	−1.20093	+	0.872523i	−0.310078	+	0.225285i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.436167	+	4.14985i	−0.105786	+	1.00649i	0.804906	+	0.593402i	$0.202215\pi$
$17$	−0.436167	+	4.14985i	−0.105786	+	1.00649i	−0.910692	+	0.413085i	$0.864451\pi$
$18$	1.92368	−	2.13646i	0.453415	−	0.503568i
$19$	2.68447	+	2.98140i	0.615859	+	0.683980i	0.967707	−	0.252077i	$-0.0811135\pi$
$19$	2.68447	+	2.98140i	0.615859	+	0.683980i	−0.351849	+	0.936057i	$0.614447\pi$
$20$	−1.29685	+	3.99130i	−0.289985	+	0.892481i
$21$	−0.802349	−	0.481690i	−0.175087	−	0.105113i
$22$	−0.249897	+	0.769103i	−0.0532781	+	0.163973i
$23$	−5.82407	−	1.23795i	−1.21440	−	0.258129i	−0.444200	−	0.895928i	$-0.646512\pi$
$23$	−5.82407	−	1.23795i	−1.21440	−	0.258129i	−0.770203	+	0.637798i	$0.779845\pi$
$24$	−0.0369731	+	0.351775i	−0.00754709	+	0.0718058i
$25$	−12.3367	+	2.62224i	−2.46733	+	0.524447i
$26$	−0.349912	−	3.32919i	−0.0686233	−	0.652907i
$27$	2.07802			0.399916
$28$	−2.63560	+	0.231581i	−0.498081	+	0.0437647i
$29$	8.63869	−	6.27637i	1.60416	−	1.16549i	0.725284	−	0.688450i	$-0.241709\pi$
$29$	8.63869	−	6.27637i	1.60416	−	1.16549i	0.878880	−	0.477043i	$-0.158291\pi$
$30$	−1.35609	+	0.603770i	−0.247587	+	0.110233i
$31$	−0.548579	+	5.21938i	−0.0985277	+	0.937428i	0.827880	+	0.560906i	$0.189547\pi$
$31$	−0.548579	+	5.21938i	−0.0985277	+	0.937428i	−0.926407	+	0.376523i	$0.877120\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.261312	+	0.116343i	−0.0454885	+	0.0202528i
$34$	−1.28944	+	3.96848i	−0.221137	+	0.680589i
$35$	−6.37207	−	9.09300i	−1.07708	−	1.53700i
$36$	2.32583	−	1.68982i	0.387639	−	0.281636i
$37$	−0.402978	−	3.83408i	−0.0662492	−	0.630319i	−0.976389	−	0.216018i	$-0.930693\pi$
$37$	−0.402978	−	3.83408i	−0.0662492	−	0.630319i	0.910140	−	0.414301i	$-0.135974\pi$
$38$	2.00594	+	3.47438i	0.325406	+	0.563619i
$39$	0.792292	−	0.879930i	0.126868	−	0.140902i
$40$	−2.09835	+	3.63445i	−0.331778	+	0.574656i
$41$	4.38385	−	4.66710i	0.684642	−	0.728879i
$41$	4.38385	−	4.66710i	0.684642	−	0.728879i
$42$	−0.684667	−	0.637982i	−0.105646	−	0.0984427i
$43$	3.37287	+	10.3806i	0.514358	+	1.58303i	0.784447	+	0.620196i	$0.212947\pi$
$43$	3.37287	+	10.3806i	0.514358	+	1.58303i	−0.270088	+	0.962836i	$0.587053\pi$
$44$	−0.404341	+	0.700340i	−0.0609567	+	0.105580i
$45$	11.0220	+	4.90729i	1.64306	+	0.731536i
$46$	−5.43942	−	2.42179i	−0.801999	−	0.357073i
$47$	8.20405	+	1.74382i	1.19668	+	0.254363i	0.762817	−	0.646614i	$-0.223816\pi$
$47$	8.20405	+	1.74382i	1.19668	+	0.254363i	0.433866	+	0.900977i	$0.357149\pi$
$48$	−0.109303	+	0.336401i	−0.0157766	+	0.0485553i
$49$	3.70498	−	5.93912i	0.529283	−	0.848445i
$50$	−12.6123			−1.78364
$51$	−1.34834	+	0.600319i	−0.188805	+	0.0840615i
$52$	0.349912	−	3.32919i	0.0485240	−	0.461675i
$53$	4.74110	+	2.11087i	0.651240	+	0.289951i	0.705642	−	0.708568i	$-0.250659\pi$
$53$	4.74110	+	2.11087i	0.651240	+	0.289951i	−0.0544021	+	0.998519i	$0.517325\pi$
$54$	2.03261	+	0.432045i	0.276604	+	0.0587939i
$55$	−3.39380			−0.457619
$56$	−2.62615	−	0.321451i	−0.350934	−	0.0429557i
$57$	−0.438510	+	1.34960i	−0.0580821	+	0.178758i
$58$	9.75484	−	4.34314i	1.28087	−	0.570282i
$59$	1.99481	−	2.21546i	0.259702	−	0.288428i	−0.599167	−	0.800624i	$-0.704501\pi$
$59$	1.99481	−	2.21546i	0.259702	−	0.288428i	0.858868	+	0.512196i	$0.171168\pi$
$60$	−1.45199	+	0.308629i	−0.187451	+	0.0398439i
$61$	−7.35265	−	8.16594i	−0.941410	−	1.04554i	−0.998886	−	0.0471947i	$-0.984972\pi$
$61$	−7.35265	−	8.16594i	−0.941410	−	1.04554i	0.0574758	−	0.998347i	$-0.481695\pi$
$62$	−1.62176	+	4.99127i	−0.205964	+	0.633892i
$63$	−0.129894	+	7.60513i	−0.0163651	+	0.958156i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	12.8340	−	5.71406i	1.59186	−	0.708742i
$66$	−0.279791	+	0.0594713i	−0.0344398	+	0.00732042i
$67$	10.9745	+	4.88617i	1.34075	+	0.596941i	0.946691	−	0.322144i	$-0.104403\pi$
$67$	10.9745	+	4.88617i	1.34075	+	0.596941i	0.394060	+	0.919085i	$0.371070\pi$
$68$	−2.08635	+	3.61367i	−0.253008	+	0.438222i
$69$	−0.650812	−	2.00299i	−0.0783486	−	0.241132i
$70$	−4.34228	−	10.2191i	−0.519002	−	1.22142i
$71$	−7.36776	−	5.35299i	−0.874392	−	0.635283i	0.0573696	−	0.998353i	$-0.481729\pi$
$71$	−7.36776	−	5.35299i	−0.874392	−	0.635283i	−0.931762	+	0.363070i	$0.881729\pi$
$72$	2.62634	−	1.16932i	0.309517	−	0.137806i
$73$	−0.250865	−	0.434511i	−0.0293616	−	0.0508557i	0.850971	−	0.525212i	$-0.176014\pi$
$73$	−0.250865	−	0.434511i	−0.0293616	−	0.0508557i	−0.880333	+	0.474357i	$0.842681\pi$
$74$	0.402978	−	3.83408i	0.0468452	−	0.445703i
$75$	−2.98507	−	3.31526i	−0.344686	−	0.382813i
$76$	1.23974	+	3.81552i	0.142207	+	0.437670i
$77$	−0.836736	−	1.96917i	−0.0953550	−	0.224408i
$78$	0.957927	−	0.695975i	0.108464	−	0.0788036i
$79$	3.21052	−	5.56078i	0.361211	−	0.625636i	−0.626949	−	0.779060i	$-0.715697\pi$
$79$	3.21052	−	5.56078i	0.361211	−	0.625636i	0.988160	+	0.153424i	$0.0490300\pi$
$80$	−2.80814	+	3.11875i	−0.313959	+	0.348687i
$81$	−3.94482	−	6.83263i	−0.438313	−	0.759181i
$82$	5.25840	−	3.65366i	0.580693	−	0.403479i
$83$	3.20683			0.351996			0.175998	−	0.984391i	$-0.443685\pi$
$83$	3.20683			0.351996			0.175998	+	0.984391i	$0.443685\pi$
$84$	−0.537061	−	0.766391i	−0.0585982	−	0.0836201i
$85$	−17.5116			−1.89940
$86$	1.14091	+	10.8551i	0.123028	+	1.17053i
$87$	3.45041	+	1.53622i	0.369923	+	0.164700i
$88$	−0.541114	+	0.600968i	−0.0576830	+	0.0640634i
$89$	6.82221	+	7.57683i	0.723152	+	0.803142i	0.986880	−	0.161455i	$-0.0516187\pi$
$89$	6.82221	+	7.57683i	0.723152	+	0.803142i	−0.263728	+	0.964597i	$0.584952\pi$
$90$	9.76081	+	7.09165i	1.02888	+	0.747525i
$91$	6.47966	+	6.03784i	0.679253	+	0.632937i
$92$	−4.81704	−	3.49978i	−0.502211	−	0.364878i
$93$	−1.69584	+	0.755038i	−0.175851	+	0.0782938i
$94$	7.66221	+	3.41144i	0.790297	+	0.351863i
$95$	−11.2659	+	12.5120i	−1.15586	+	1.28371i
$96$	−0.176856	+	0.306324i	−0.0180503	+	0.0312641i
$97$	−0.368507	+	0.267736i	−0.0374163	+	0.0271845i	−0.606336	−	0.795208i	$-0.707361\pi$
$97$	−0.368507	+	0.267736i	−0.0374163	+	0.0271845i	0.568920	+	0.822393i	$0.307361\pi$
$98$	4.85883	−	5.03903i	0.490816	−	0.509018i
$99$	1.88086	+	1.36652i	0.189034	+	0.137341i
$100$	−12.3367	−	2.62224i	−1.23367	−	0.262224i
$101$	−1.15543	+	0.245594i	−0.114969	+	0.0244375i	−0.265037	−	0.964238i	$-0.585384\pi$
$101$	−1.15543	+	0.245594i	−0.114969	+	0.0244375i	0.150068	+	0.988676i	$0.452051\pi$
$102$	−1.44369	+	0.306865i	−0.142946	+	0.0303842i
$103$	−6.72085	−	7.46427i	−0.662225	−	0.735476i	0.314668	−	0.949202i	$-0.398107\pi$
$103$	−6.72085	−	7.46427i	−0.662225	−	0.735476i	−0.976894	+	0.213726i	$0.931440\pi$
$104$	1.03444	−	3.18369i	0.101435	−	0.312186i
$105$	1.65846	−	3.56007i	0.161850	−	0.347428i
$106$	4.19862	+	3.05048i	0.407806	+	0.296288i
$107$	−7.42677	−	8.24826i	−0.717973	−	0.797390i	0.268155	−	0.963376i	$-0.413586\pi$
$107$	−7.42677	−	8.24826i	−0.717973	−	0.797390i	−0.986128	+	0.165986i	$0.946919\pi$
$108$	1.89837	+	0.845208i	0.182671	+	0.0813302i
$109$	−2.13447	−	3.69701i	−0.204445	−	0.354110i	0.745511	−	0.666494i	$-0.232206\pi$
$109$	−2.13447	−	3.69701i	−0.204445	−	0.354110i	−0.949956	+	0.312384i	$0.898872\pi$
$110$	−3.31963	−	0.705610i	−0.316515	−	0.0672772i
$111$	1.10320	−	0.801523i	0.104711	−	0.0760772i
$112$	−2.50193	−	0.860434i	−0.236410	−	0.0813034i
$113$	−9.20521	−	6.68797i	−0.865953	−	0.629152i	0.0635450	−	0.997979i	$-0.479759\pi$
$113$	−9.20521	−	6.68797i	−0.865953	−	0.629152i	−0.929498	+	0.368827i	$0.879759\pi$
$114$	−0.709525	+	1.22893i	−0.0664531	+	0.115100i
$115$	2.61195	−	24.8510i	0.243565	−	2.31737i
$116$	10.4447	−	2.22008i	0.969763	−	0.206129i
$117$	−9.41346	−	2.00089i	−0.870274	−	0.184983i
$118$	2.41183	−	1.75230i	0.222027	−	0.161312i
$119$	−4.31747	−	10.1607i	−0.395781	−	0.931431i
$120$	−1.48443			−0.135509
$121$	10.1199	+	2.15106i	0.919995	+	0.195551i
$122$	−5.49418	−	9.51620i	−0.497420	−	0.861556i
$123$	2.20496	+	0.517473i	0.198814	+	0.0466589i
$124$	−2.62407	+	4.54501i	−0.235648	+	0.408154i
$125$	−9.87197	−	30.3828i	−0.882976	−	2.71752i
$126$	−1.70825	+	7.41193i	−0.152183	+	0.660307i
$127$	−1.07132	+	0.778357i	−0.0950640	+	0.0690680i	−0.634302	−	0.773085i	$-0.718712\pi$
$127$	−1.07132	+	0.778357i	−0.0950640	+	0.0690680i	0.539238	+	0.842153i	$0.318712\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−2.58333	+	2.86907i	−0.227449	+	0.252608i
$130$	13.7416	−	2.92086i	1.20521	−	0.256176i
$131$	12.4472	−	5.54184i	1.08752	−	0.484193i	0.216918	−	0.976190i	$-0.430399\pi$
$131$	12.4472	−	5.54184i	1.08752	−	0.484193i	0.870597	+	0.491997i	$0.163733\pi$
$132$	−0.286041			−0.0248967
$133$	−10.0374	−	3.45195i	−0.870355	−	0.299322i
$134$	9.71881	+	7.06113i	0.839577	+	0.609989i
$135$	0.911575	+	8.67306i	0.0784559	+	0.746458i
$136$	−2.79209	+	3.10093i	−0.239420	+	0.265902i
$137$	2.18086	+	3.77736i	0.186324	+	0.322722i	0.944022	−	0.329883i	$-0.107009\pi$
$137$	2.18086	+	3.77736i	0.186324	+	0.322722i	−0.757698	+	0.652605i	$0.773676\pi$
$138$	−0.220144	−	2.09453i	−0.0187399	−	0.178299i
$139$	−4.08902	+	12.5847i	−0.346826	+	1.06742i	0.613773	+	0.789482i	$0.289651\pi$
$139$	−4.08902	+	12.5847i	−0.346826	+	1.06742i	−0.960599	+	0.277938i	$0.910349\pi$
$140$	−2.12272	−	10.8986i	−0.179403	−	0.921101i
$141$	0.916763	+	2.82151i	0.0772054	+	0.237614i
$142$	−6.09381	−	6.76786i	−0.511381	−	0.567946i
$143$	2.64793	−	0.562835i	0.221431	−	0.0470666i
$144$	2.81206	−	0.597723i	0.234339	−	0.0498102i
$145$	29.9853	+	33.3021i	2.49014	+	2.76559i
$146$	−0.155043	−	0.477174i	−0.0128315	−	0.0394912i
$147$	2.47455	+	0.0845542i	0.204097	+	0.00697391i
$148$	1.19132	−	3.66651i	0.0979261	−	0.301385i
$149$	−0.722248	−	6.87173i	−0.0591689	−	0.562954i	−0.983442	−	0.181223i	$-0.941995\pi$
$149$	−0.722248	−	6.87173i	−0.0591689	−	0.562954i	0.924273	−	0.381732i	$-0.124672\pi$
$150$	−2.23056	−	3.86344i	−0.182124	−	0.315449i
$151$	−9.43106	+	10.4742i	−0.767489	+	0.852382i	−0.992534	−	0.121966i	$-0.961080\pi$
$151$	−9.43106	+	10.4742i	−0.767489	+	0.852382i	0.225046	+	0.974348i	$0.427747\pi$
$152$	0.419355	+	3.98989i	0.0340142	+	0.323623i
$153$	9.70503	+	7.05111i	0.784605	+	0.570049i
$154$	−0.409038	−	2.10011i	−0.0329612	−	0.169232i
$155$	−22.0248			−1.76908
$156$	1.08169	−	0.481602i	0.0866049	−	0.0385590i
$157$	2.35582	−	0.500745i	0.188015	−	0.0399638i	−0.112942	−	0.993602i	$-0.536027\pi$
$157$	2.35582	−	0.500745i	0.188015	−	0.0399638i	0.300957	+	0.953638i	$0.402694\pi$
$158$	4.29651	−	4.77176i	0.341812	−	0.379621i
$159$	0.191882	+	1.82563i	0.0152172	+	0.144782i
$160$	−3.39520	+	2.46676i	−0.268414	+	0.195014i
$161$	15.0632	−	4.61147i	1.18715	−	0.363435i
$162$	−2.43803	−	7.50349i	−0.191550	−	0.589530i
$163$	−6.75765	+	11.7046i	−0.529300	+	0.916775i	0.470116	+	0.882605i	$0.344212\pi$
$163$	−6.75765	+	11.7046i	−0.529300	+	0.916775i	−0.999416	+	0.0341700i	$0.989121\pi$
$164$	5.90313	−	2.48054i	0.460957	−	0.193698i
$165$	−0.600214	−	1.03960i	−0.0467266	−	0.0809329i
$166$	3.13676	+	0.666738i	0.243460	+	0.0517489i
$167$	15.2920			1.18333			0.591664	−	0.806184i	$-0.298471\pi$
$167$	15.2920			1.18333			0.591664	+	0.806184i	$0.298471\pi$
$168$	−0.365983	−	0.861304i	−0.0282362	−	0.0664511i
$169$	1.45144	−	1.05453i	0.111649	−	0.0811177i
$170$	−17.1289	−	3.64087i	−1.31373	−	0.279242i
$171$	11.2816	−	2.39799i	0.862728	−	0.183379i
$172$	−1.14091	+	10.8551i	−0.0869937	+	0.827690i
$173$	−6.09240	+	10.5523i	−0.463197	+	0.802280i	−0.999118	−	0.0419877i	$-0.986631\pi$
$173$	−6.09240	+	10.5523i	−0.463197	+	0.802280i	0.535921	+	0.844268i	$0.319964\pi$
$174$	3.05561	+	2.22003i	0.231645	+	0.168300i
$175$	25.1756	−	21.9014i	1.90310	−	1.65559i
$176$	−0.654238	+	0.475332i	−0.0493150	+	0.0358295i
$177$	1.03144	+	0.219240i	0.0775280	+	0.0164791i
$178$	5.09781	+	8.82967i	0.382097	+	0.661812i
$179$	−18.7300	−	8.33914i	−1.39995	−	0.623296i	−0.438611	−	0.898677i	$-0.644530\pi$
$179$	−18.7300	−	8.33914i	−1.39995	−	0.623296i	−0.961335	+	0.275380i	$0.911196\pi$
$180$	8.07308	+	8.96606i	0.601732	+	0.668291i
$181$	−3.12740	−	2.27219i	−0.232458	−	0.168890i	0.465459	−	0.885070i	$-0.345889\pi$
$181$	−3.12740	−	2.27219i	−0.232458	−	0.168890i	−0.697917	+	0.716179i	$0.745889\pi$
$182$	5.08273	+	7.25309i	0.376757	+	0.537635i
$183$	1.20106	−	3.69649i	0.0887852	−	0.273253i
$184$	−3.98413	−	4.42482i	−0.293714	−	0.326202i
$185$	15.8255	−	3.36382i	1.16352	−	0.247313i
$186$	−1.81577	+	0.385953i	−0.133138	+	0.0282994i
$187$	−3.30066	−	0.701577i	−0.241368	−	0.0513044i
$188$	6.78550	+	4.92995i	0.494883	+	0.359554i
$189$	−4.80760	+	2.66725i	−0.349701	+	0.194014i
$190$	−13.6211	+	9.89631i	−0.988178	+	0.717954i
$191$	4.06048	−	7.03296i	0.293806	−	0.508887i	−0.680900	−	0.732376i	$-0.738411\pi$
$191$	4.06048	−	7.03296i	0.293806	−	0.508887i	0.974706	+	0.223489i	$0.0717446\pi$
$192$	−0.236680	+	0.262860i	−0.0170809	+	0.0189703i
$193$	17.9948	+	8.01180i	1.29529	+	0.576702i	0.934506	−	0.355946i	$-0.115841\pi$
$193$	17.9948	+	8.01180i	1.29529	+	0.576702i	0.360787	+	0.932648i	$0.382508\pi$
$194$	−0.416120	+	0.185269i	−0.0298757	+	0.0133015i
$195$	4.02013	+	2.92079i	0.287887	+	0.209162i
$196$	5.80032	−	3.91870i	0.414309	−	0.279907i
$197$	−18.8944	−	13.7276i	−1.34617	−	0.978048i	−0.999193	−	0.0401733i	$-0.987209\pi$
$197$	−18.8944	−	13.7276i	−1.34617	−	0.978048i	−0.346975	−	0.937875i	$-0.612791\pi$
$198$	1.55564	+	1.72772i	0.110555	+	0.122783i
$199$	−5.13773	+	5.70603i	−0.364204	+	0.404489i	−0.897197	−	0.441630i	$-0.854400\pi$
$199$	−5.13773	+	5.70603i	−0.364204	+	0.404489i	0.532993	+	0.846119i	$0.321067\pi$
$200$	−11.5219	−	5.12987i	−0.814720	−	0.362737i
$201$	0.444161	+	4.22591i	0.0313287	+	0.298073i
$202$	−1.18124			−0.0831118
$203$	−11.9299	+	25.6089i	−0.837317	+	1.79739i
$204$	−1.47594			−0.103337
$205$	21.4022	+	16.2496i	1.49479	+	1.13492i
$206$	−5.02208	−	8.69850i	−0.349905	−	0.606053i
$207$	−11.4539	+	12.7209i	−0.796103	+	0.884162i
$208$	1.67376	−	2.89904i	0.116055	−	0.201012i
$209$	−2.62472	+	1.90697i	−0.181555	+	0.131908i
$210$	2.36240	−	3.13746i	0.163021	−	0.216506i
$211$	−7.52535	−	23.1606i	−0.518066	−	1.59444i	−0.777633	−	0.628719i	$-0.783580\pi$
$211$	−7.52535	−	23.1606i	−0.518066	−	1.59444i	0.259566	−	0.965725i	$-0.416420\pi$
$212$	3.47264	+	3.85676i	0.238502	+	0.264883i
$213$	0.336716	−	3.20363i	0.0230714	−	0.219509i
$214$	−5.54957	−	9.61213i	−0.379361	−	0.657072i
$215$	−41.8461	+	18.6311i	−2.85388	+	1.27063i
$216$	1.68116	+	1.22143i	0.114388	+	0.0831079i
$217$	−5.43019	−	12.7794i	−0.368626	−	0.867522i
$218$	−1.31918	−	4.06001i	−0.0893459	−	0.274978i
$219$	0.0887343	−	0.153692i	0.00599611	−	0.0103856i
$220$	−3.10039	−	1.38038i	−0.209028	−	0.0930653i
$221$	13.6630	−	2.90416i	0.919074	−	0.195355i
$222$	1.24574	−	0.554640i	0.0836086	−	0.0372250i
$223$	−3.45124	−	10.6218i	−0.231112	−	0.711291i	−0.997613	−	0.0690476i	$-0.978004\pi$
$223$	−3.45124	−	10.6218i	−0.231112	−	0.711291i	0.766501	−	0.642243i	$-0.221996\pi$
$224$	−2.26836	−	1.36181i	−0.151561	−	0.0909899i
$225$	−11.2046	+	34.4842i	−0.746973	+	2.29895i
$226$	−7.61354	−	8.45570i	−0.506445	−	0.562465i
$227$	−10.8062	+	2.29693i	−0.717232	+	0.152452i	−0.552051	−	0.833811i	$-0.686154\pi$
$227$	−10.8062	+	2.29693i	−0.717232	+	0.152452i	−0.165182	+	0.986263i	$0.552821\pi$
$228$	−0.949530	+	1.05456i	−0.0628841	+	0.0698399i
$229$	7.40383	−	3.29640i	0.489259	−	0.217832i	−0.147253	−	0.989099i	$-0.547043\pi$
$229$	7.40383	−	3.29640i	0.489259	−	0.217832i	0.636512	+	0.771267i	$0.280376\pi$
$230$	7.72169	−	23.7649i	0.509153	−	1.56701i
$231$	0.455223	−	0.604574i	0.0299515	−	0.0397780i
$232$	10.6780			0.701045
$233$	−2.23776	−	0.475651i	−0.146601	−	0.0311610i	0.134027	−	0.990978i	$-0.457209\pi$
$233$	−2.23776	−	0.475651i	−0.146601	−	0.0311610i	−0.280627	+	0.959817i	$0.590543\pi$
$234$	−8.79174	−	3.91434i	−0.574734	−	0.255888i
$235$	−3.67931	+	35.0063i	−0.240012	+	2.28356i
$236$	2.72345	−	1.21256i	0.177282	−	0.0789309i
$237$	2.27120			0.147530
$238$	−2.11059	−	10.8363i	−0.136809	−	0.702415i
$239$	−2.33293	+	7.18003i	−0.150905	+	0.464437i	−0.997723	−	0.0674451i	$-0.978515\pi$
$239$	−2.33293	+	7.18003i	−0.150905	+	0.464437i	0.846818	+	0.531883i	$0.178515\pi$
$240$	−1.45199	−	0.308629i	−0.0937254	−	0.0199219i
$241$	8.60428	+	3.83087i	0.554251	+	0.246768i	0.664696	−	0.747114i	$-0.268561\pi$
$241$	8.60428	+	3.83087i	0.554251	+	0.246768i	−0.110445	+	0.993882i	$0.535228\pi$
$242$	9.45157	+	4.20811i	0.607570	+	0.270508i
$243$	4.51237	−	7.81565i	0.289468	−	0.501374i
$244$	−3.39559	−	10.4505i	−0.217380	−	0.669028i
$245$	26.4134	+	12.8582i	1.68749	+	0.821478i
$246$	2.04919	+	0.964601i	0.130651	+	0.0615007i
$247$	6.71492	−	11.6306i	0.427260	−	0.740036i
$248$	−3.51168	+	3.90012i	−0.222992	+	0.247658i
$249$	0.567149	+	0.982331i	0.0359416	+	0.0622527i
$250$	−3.33930	−	31.7714i	−0.211196	−	2.00940i
$251$	−2.09402	+	1.52139i	−0.132173	+	0.0960294i	−0.651907	−	0.758299i	$-0.726031\pi$
$251$	−2.09402	+	1.52139i	−0.132173	+	0.0960294i	0.519734	+	0.854328i	$0.326031\pi$
$252$	−3.21195	+	6.89480i	−0.202334	+	0.434331i
$253$	1.48793	−	4.57938i	0.0935454	−	0.287903i
$254$	−1.20974	+	0.538609i	−0.0759056	+	0.0337953i
$255$	−3.09704	−	5.36423i	−0.193944	−	0.335921i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−15.9837	+	7.11640i	−0.997036	+	0.443909i	−0.839356	−	0.543582i	$-0.817068\pi$
$257$	−15.9837	+	7.11640i	−0.997036	+	0.443909i	−0.157679	+	0.987490i	$0.550401\pi$
$258$	−3.12339	+	2.26927i	−0.194454	+	0.141279i
$259$	5.85355	+	8.35307i	0.363722	+	0.519035i
$260$	14.0485			0.871254
$261$	−3.20882	−	30.5299i	−0.198621	−	1.88975i
$262$	13.3274	−	2.83283i	0.823369	−	0.175013i
$263$	1.66679	−	15.8584i	0.102779	−	0.977872i	−0.814645	−	0.579960i	$-0.803068\pi$
$263$	1.66679	−	15.8584i	0.102779	−	0.977872i	0.917423	−	0.397912i	$-0.130265\pi$
$264$	−0.279791	−	0.0594713i	−0.0172199	−	0.00366021i
$265$	−6.73037	+	20.7139i	−0.413443	+	1.27245i
$266$	−9.10038	−	5.46341i	−0.557980	−	0.334983i
$267$	−1.11442	+	3.42982i	−0.0682011	+	0.209901i
$268$	8.03834	+	8.92748i	0.491020	+	0.545333i
$269$	−12.8012	+	14.2172i	−0.780503	+	0.866837i	−0.993918	−	0.110125i	$-0.964875\pi$
$269$	−12.8012	+	14.2172i	−0.780503	+	0.866837i	0.213415	+	0.976962i	$0.431541\pi$
$270$	−0.911575	+	8.67306i	−0.0554767	+	0.527825i
$271$	−12.8699	−	14.2934i	−0.781788	−	0.868264i	0.212259	−	0.977213i	$-0.431918\pi$
$271$	−12.8699	−	14.2934i	−0.781788	−	0.868264i	−0.994047	+	0.108949i	$0.965251\pi$
$272$	−3.37579	+	2.45266i	−0.204688	+	0.148714i
$273$	−0.703567	+	3.05271i	−0.0425818	+	0.184758i
$274$	1.34785	+	4.14825i	0.0814264	+	0.250605i
$275$	−1.06612	−	10.1434i	−0.0642894	−	0.611673i
$276$	0.220144	−	2.09453i	0.0132511	−	0.126076i
$277$	−0.330394	+	3.14349i	−0.0198515	+	0.188874i	−0.999954	−	0.00961907i	$-0.996938\pi$
$277$	−0.330394	+	3.14349i	−0.0198515	+	0.188874i	0.980102	+	0.198493i	$0.0636048\pi$
$278$	−6.61617	+	11.4595i	−0.396811	+	0.687298i
$279$	12.2063	+	8.86838i	0.730770	+	0.530936i
$280$	0.189617	−	11.1018i	0.0113318	−	0.663459i
$281$	7.29235	+	22.4436i	0.435025	+	1.33887i	0.893061	+	0.449936i	$0.148553\pi$
$281$	7.29235	+	22.4436i	0.435025	+	1.33887i	−0.458035	+	0.888934i	$0.651447\pi$
$282$	0.310105	+	2.95045i	0.0184665	+	0.175697i
$283$	−6.51176	−	2.89922i	−0.387084	−	0.172341i	0.203962	−	0.978979i	$-0.434618\pi$
$283$	−6.51176	−	2.89922i	−0.387084	−	0.172341i	−0.591046	+	0.806638i	$0.701285\pi$
$284$	−4.55353	−	7.88694i	−0.270202	−	0.468004i
$285$	−5.82518	−	1.23818i	−0.345054	−	0.0733435i
$286$	2.70709			0.160073
$287$	−4.15176	+	16.4245i	−0.245070	+	0.969505i
$288$	2.87489			0.169404
$289$	−0.402516	−	0.0855575i	−0.0236774	−	0.00503279i
$290$	22.4062	+	38.8086i	1.31574	+	2.27892i
$291$	−0.147187	−	0.0655319i	−0.00862826	−	0.00384155i
$292$	−0.0524451	−	0.498982i	−0.00306912	−	0.0292007i
$293$	−3.97080	−	12.2209i	−0.231977	−	0.713951i	−0.997508	−	0.0705526i	$-0.977524\pi$
$293$	−3.97080	−	12.2209i	−0.231977	−	0.713951i	0.765531	−	0.643399i	$-0.222476\pi$
$294$	2.40289	+	0.597193i	0.140139	+	0.0348290i
$295$	10.1217	+	7.35387i	0.589310	+	0.428159i
$296$	1.92760	−	3.33870i	0.112039	−	0.194058i
$297$	−0.175656	+	1.67125i	−0.0101926	+	0.0969760i
$298$	0.722248	−	6.87173i	0.0418387	−	0.398069i
$299$	2.08344	+	19.8226i	0.120488	+	1.14637i
$300$	−1.37856	−	4.24278i	−0.0795913	−	0.244957i
$301$	−21.1274	−	19.6868i	−1.21776	−	1.13473i
$302$	−11.4027	+	8.28454i	−0.656151	+	0.476721i
$303$	−0.279576	−	0.310501i	−0.0160612	−	0.0178378i
$304$	−0.419355	+	3.98989i	−0.0240516	+	0.228836i
$305$	30.8568	−	34.2700i	1.76686	−	1.96229i
$306$	8.02694	+	8.91482i	0.458870	+	0.509626i
$307$	0.519242	−	1.59806i	0.0296347	−	0.0912063i	−0.935145	−	0.354265i	$-0.884731\pi$
$307$	0.519242	−	1.59806i	0.0296347	−	0.0912063i	0.964780	+	0.263058i	$0.0847312\pi$
$308$	0.0365382	−	2.13926i	0.00208196	−	0.121896i
$309$	1.09786	−	3.37886i	0.0624550	−	0.192217i
$310$	−21.5435	−	4.57922i	−1.22359	−	0.260082i
$311$	2.67098	−	25.4127i	0.151457	−	1.44102i	−0.609792	−	0.792562i	$-0.708747\pi$
$311$	2.67098	−	25.4127i	0.151457	−	1.44102i	0.761249	−	0.648460i	$-0.224586\pi$
$312$	1.15819	−	0.246180i	0.0655695	−	0.0139372i
$313$	−1.13534	−	10.8020i	−0.0641731	−	0.610566i	−0.978594	−	0.205801i	$-0.934020\pi$
$313$	−1.13534	−	10.8020i	−0.0641731	−	0.610566i	0.914421	−	0.404765i	$-0.132647\pi$
$314$	2.40845			0.135917
$315$	−31.7986	+	2.79403i	−1.79165	+	0.157426i
$316$	5.19472	−	3.77419i	0.292226	−	0.212315i
$317$	15.6068	−	6.94862i	0.876568	−	0.390273i	0.0814136	−	0.996680i	$-0.474057\pi$
$317$	15.6068	−	6.94862i	0.876568	−	0.390273i	0.795154	+	0.606407i	$0.207390\pi$
$318$	−0.191882	+	1.82563i	−0.0107602	+	0.102377i
$319$	4.31756	+	7.47823i	0.241737	+	0.418700i
$320$	−3.83387	+	1.70695i	−0.214320	+	0.0954214i
$321$	1.21317	−	3.73376i	0.0677126	−	0.208398i
$322$	15.6928	−	1.37888i	0.874528	−	0.0768418i
$323$	−13.5432	+	9.83974i	−0.753566	+	0.547498i
$324$	−0.824692	−	7.84642i	−0.0458162	−	0.435912i
$325$	21.1099	+	36.5635i	1.17097	+	2.02818i
$326$	−9.04350	+	10.0438i	−0.500873	+	0.556276i
$327$	0.754990	−	1.30768i	0.0417510	−	0.0723149i
$328$	6.28986	−	1.19900i	0.347300	−	0.0662039i
$329$	−21.2187	+	6.49592i	−1.16983	+	0.358132i
$330$	−0.370953	−	1.14168i	−0.0204203	−	0.0628472i
$331$	−8.90204	+	15.4188i	−0.489301	+	0.847493i	−0.999924	−	0.0123109i	$-0.996081\pi$
$331$	−8.90204	+	15.4188i	−0.489301	+	0.847493i	0.510624	+	0.859804i	$0.329415\pi$
$332$	2.92959	+	1.30434i	0.160782	+	0.0715848i
$333$	−10.1251	−	4.50797i	−0.554850	−	0.247035i
$334$	14.9578	+	3.17938i	0.818455	+	0.173968i
$335$	−15.5792	+	47.9479i	−0.851183	+	2.61967i
$336$	−0.178911	−	0.918575i	−0.00976037	−	0.0501124i
$337$	6.30344			0.343370			0.171685	−	0.985152i	$-0.445079\pi$
$337$	6.30344			0.343370			0.171685	+	0.985152i	$0.445079\pi$
$338$	1.63897	−	0.729715i	0.0891480	−	0.0396913i
$339$	0.420689	−	4.00259i	0.0228487	−	0.217391i
$340$	−15.9976	−	7.12261i	−0.867594	−	0.386278i
$341$	−4.15133	−	0.882392i	−0.224807	−	0.0477842i
$342$	11.5337			0.623670
$343$	−0.948460	+	18.4960i	−0.0512120	+	0.998688i
$344$	−3.37287	+	10.3806i	−0.181853	+	0.559686i
$345$	8.07441	−	3.59496i	0.434712	−	0.193546i
$346$	−8.15322	+	9.05507i	−0.438320	+	0.486804i
$347$	5.78440	−	1.22951i	0.310523	−	0.0660037i	−0.0500143	−	0.998748i	$-0.515927\pi$
$347$	5.78440	−	1.22951i	0.310523	−	0.0660037i	0.360537	+	0.932745i	$0.382593\pi$
$348$	2.52727	+	2.80682i	0.135476	+	0.150461i
$349$	−8.17588	+	25.1628i	−0.437645	+	1.34693i	0.452707	+	0.891659i	$0.350458\pi$
$349$	−8.17588	+	25.1628i	−0.437645	+	1.34693i	−0.890352	+	0.455273i	$0.849542\pi$
$350$	29.1790	−	16.1885i	1.55969	−	0.865313i
$351$	−2.14959	−	6.61577i	−0.114737	−	0.353124i
$352$	−0.738768	+	0.328921i	−0.0393765	+	0.0175315i
$353$	−23.0736	+	4.90444i	−1.22808	+	0.261037i	−0.775881	−	0.630879i	$-0.782694\pi$
$353$	−23.0736	+	4.90444i	−1.22808	+	0.261037i	−0.452201	+	0.891916i	$0.649361\pi$
$354$	0.963321	+	0.428898i	0.0511999	+	0.0227957i
$355$	19.1098	−	33.0991i	1.01424	−	1.75672i
$356$	3.15062	+	9.69662i	0.166983	+	0.513920i
$357$	2.34890	−	3.11953i	0.124317	−	0.165103i
$358$	−16.5869	−	12.0511i	−0.876645	−	0.636920i
$359$	1.58929	−	0.707595i	0.0838793	−	0.0373455i	−0.364368	−	0.931255i	$-0.618715\pi$
$359$	1.58929	−	0.707595i	0.0838793	−	0.0373455i	0.448247	+	0.893910i	$0.352048\pi$
$360$	6.03252	+	10.4486i	0.317941	+	0.550691i
$361$	0.303645	−	2.88899i	0.0159813	−	0.152052i
$362$	−2.58664	−	2.87276i	−0.135951	−	0.150989i
$363$	1.13086	+	3.48041i	0.0593545	+	0.182674i
$364$	3.46365	+	8.15136i	0.181545	+	0.427247i
$365$	1.70348	−	1.23765i	0.0891640	−	0.0647814i
$366$	1.94336	−	3.36600i	0.101581	−	0.175944i
$367$	−15.2351	+	16.9203i	−0.795267	+	0.883234i	−0.995328	−	0.0965498i	$-0.969219\pi$
$367$	−15.2351	+	16.9203i	−0.795267	+	0.883234i	0.200061	+	0.979783i	$0.435886\pi$
$368$	−2.97709	−	5.15648i	−0.155192	−	0.268800i
$369$	−5.31827	−	17.6233i	−0.276858	−	0.917431i
$370$	16.1791			0.841111
$371$	−13.6782	+	1.20186i	−0.710135	+	0.0623972i
$372$	−1.85633			−0.0962463
$373$	2.79859	+	26.6268i	0.144905	+	1.37868i	0.789309	+	0.613997i	$0.210439\pi$
$373$	2.79859	+	26.6268i	0.144905	+	1.37868i	−0.644403	+	0.764686i	$0.722894\pi$
$374$	−3.08267	−	1.37249i	−0.159401	−	0.0709698i
$375$	7.56107	−	8.39742i	0.390452	−	0.433641i
$376$	5.61222	+	6.23300i	0.289428	+	0.321443i
$377$	−28.9182	−	21.0103i	−1.48936	−	1.08209i
$378$	−5.25709	+	1.60941i	−0.270396	+	0.0827792i
$379$	10.6923	+	7.76838i	0.549224	+	0.399035i	0.827499	−	0.561467i	$-0.189763\pi$
$379$	10.6923	+	7.76838i	0.549224	+	0.399035i	−0.278275	+	0.960501i	$0.589763\pi$
$380$	−15.3810	+	6.84806i	−0.789029	+	0.351298i
$381$	−0.427899	−	0.190513i	−0.0219219	−	0.00976027i
$382$	5.43399	−	6.03505i	0.278027	−	0.308780i
$383$	−11.9278	+	20.6595i	−0.609481	+	1.05565i	0.381845	+	0.924226i	$0.375289\pi$
$383$	−11.9278	+	20.6595i	−0.609481	+	1.05565i	−0.991326	+	0.131425i	$0.958045\pi$
$384$	−0.286160	+	0.207907i	−0.0146030	+	0.0106097i
$385$	7.85170	−	4.35612i	0.400160	−	0.222008i
$386$	15.9358	+	11.5781i	0.811112	+	0.589307i
$387$	30.6932	+	6.52405i	1.56023	+	0.331636i
$388$	−0.445547	+	0.0947038i	−0.0226192	+	0.00480786i
$389$	30.1156	−	6.40127i	1.52692	−	0.324557i	0.633488	−	0.773753i	$-0.281623\pi$
$389$	30.1156	−	6.40127i	1.52692	−	0.324557i	0.893433	+	0.449196i	$0.148289\pi$
$390$	3.32501	+	3.69280i	0.168368	+	0.186992i
$391$	7.67756	−	23.6291i	0.388271	−	1.19497i
$392$	6.48832	−	2.62711i	0.327710	−	0.132689i
$393$	3.89896	+	2.83276i	0.196677	+	0.142894i
$394$	−15.6274	−	17.3559i	−0.787295	−	0.874379i
$395$	24.6174	+	10.9604i	1.23864	+	0.551477i
$396$	1.16244	+	2.01340i	0.0584146	+	0.101177i
$397$	−3.92011	−	0.833245i	−0.196745	−	0.0418194i	0.108485	−	0.994098i	$-0.465400\pi$
$397$	−3.92011	−	0.833245i	−0.196745	−	0.0418194i	−0.305230	+	0.952279i	$0.598733\pi$
$398$	−6.21181	+	4.51314i	−0.311370	+	0.226223i
$399$	−0.717766	−	3.68520i	−0.0359332	−	0.184491i
$400$	−10.2035	−	7.41330i	−0.510177	−	0.370665i
$401$	14.9216	−	25.8449i	0.745148	−	1.29063i	−0.204978	−	0.978767i	$-0.565712\pi$
$401$	14.9216	−	25.8449i	0.745148	−	1.29063i	0.950126	−	0.311868i	$-0.100955\pi$
$402$	−0.444161	+	4.22591i	−0.0221528	+	0.210769i
$403$	17.1843	−	3.65264i	0.856013	−	0.181951i
$404$	−1.15543	−	0.245594i	−0.0574847	−	0.0122187i
$405$	26.7869	−	19.4618i	1.33105	−	0.967065i
$406$	−16.9936	+	22.5689i	−0.843379	+	1.12008i
$407$	3.11763			0.154535
$408$	−1.44369	−	0.306865i	−0.0714732	−	0.0151921i
$409$	15.4817	+	26.8150i	0.765519	+	1.32592i	0.939972	+	0.341252i	$0.110851\pi$
$409$	15.4817	+	26.8150i	0.765519	+	1.32592i	−0.174453	+	0.984665i	$0.555816\pi$
$410$	17.5560	+	20.3442i	0.867031	+	1.00473i
$411$	−0.771399	+	1.33610i	−0.0380503	+	0.0659050i
$412$	−3.10382	−	9.55256i	−0.152914	−	0.470621i
$413$	−1.77142	+	7.68600i	−0.0871657	+	0.378203i
$414$	−13.8484	+	10.0615i	−0.680614	+	0.494495i
$415$	1.40676	+	13.3844i	0.0690549	+	0.657014i
$416$	2.23993	−	2.48770i	0.109822	−	0.121969i
$417$	−4.57817	+	0.973120i	−0.224194	+	0.0476539i
$418$	−2.96384	+	1.31959i	−0.144966	+	0.0645431i
$419$	−10.6897			−0.522224			−0.261112	−	0.965309i	$-0.584089\pi$
$419$	−10.6897			−0.522224			−0.261112	+	0.965309i	$0.584089\pi$
$420$	2.96309	−	2.57773i	0.144584	−	0.125780i
$421$	−3.27523	−	2.37959i	−0.159625	−	0.115974i	0.505106	−	0.863058i	$-0.331454\pi$
$421$	−3.27523	−	2.37959i	−0.159625	−	0.115974i	−0.664730	+	0.747083i	$0.731454\pi$
$422$	−2.54553	−	24.2191i	−0.123915	−	1.17897i
$423$	16.1345	−	17.9192i	0.784486	−	0.871260i
$424$	2.59489	+	4.49448i	0.126019	+	0.218271i
$425$	−5.50105	−	52.3390i	−0.266840	−	2.53882i
$426$	0.995431	−	3.06362i	0.0482288	−	0.148433i
$427$	27.4921	+	9.45476i	1.33044	+	0.457548i
$428$	−3.42982	−	10.5559i	−0.165787	−	0.510239i
$429$	0.640713	+	0.711584i	0.0309339	+	0.0343556i
$430$	−44.8053	+	9.52366i	−2.16070	+	0.459272i
$431$	−28.3920	+	6.03490i	−1.36759	+	0.290691i	−0.832464	−	0.554080i	$-0.813070\pi$
$431$	−28.3920	+	6.03490i	−1.36759	+	0.290691i	−0.535129	+	0.844770i	$0.679737\pi$
$432$	1.39047	+	1.54427i	0.0668990	+	0.0742988i
$433$	−4.67784	−	14.3969i	−0.224803	−	0.691872i	−0.998312	−	0.0580861i	$-0.981500\pi$
$433$	−4.67784	−	14.3969i	−0.224803	−	0.691872i	0.773509	−	0.633785i	$-0.218500\pi$
$434$	−2.65454	−	13.6291i	−0.127422	−	0.654220i
$435$	−4.89813	+	15.0749i	−0.234848	+	0.722787i
$436$	−0.446226	−	4.24556i	−0.0213704	−	0.203325i
$437$	−11.9437	−	20.6871i	−0.571345	−	0.989599i
$438$	0.118750	−	0.131885i	0.00567408	−	0.00630170i
$439$	3.08619	+	29.3632i	0.147296	+	1.40143i	0.779391	+	0.626537i	$0.215528\pi$
$439$	3.08619	+	29.3632i	0.147296	+	1.40143i	−0.632095	+	0.774891i	$0.717805\pi$
$440$	−2.74564	−	1.99482i	−0.130893	−	0.0950994i
$441$	−9.46107	−	17.7615i	−0.450527	−	0.845787i
$442$	13.9683			0.664402
$443$	5.30979	−	2.36407i	0.252276	−	0.112320i	−0.276703	−	0.960955i	$-0.589242\pi$
$443$	5.30979	−	2.36407i	0.252276	−	0.112320i	0.528979	+	0.848635i	$0.322575\pi$
$444$	1.33383	−	0.283515i	0.0633010	−	0.0134550i
$445$	−28.6307	+	31.7976i	−1.35723	+	1.50735i
$446$	−1.16742	−	11.1073i	−0.0552790	−	0.525945i
$447$	1.97724	−	1.43655i	0.0935204	−	0.0679466i
$448$	−1.93566	−	1.80367i	−0.0914512	−	0.0852155i
$449$	−2.47269	−	7.61014i	−0.116693	−	0.359145i	0.875603	−	0.483031i	$-0.160464\pi$
$449$	−2.47269	−	7.61014i	−0.116693	−	0.359145i	−0.992296	+	0.123886i	$0.960464\pi$
$450$	−18.1294	+	31.4011i	−0.854629	+	1.48026i
$451$	3.38296	+	3.92023i	0.159297	+	0.184597i
$452$	−5.68913	−	9.85386i	−0.267594	−	0.463487i
$453$	−4.87646	−	1.03652i	−0.229116	−	0.0487001i
$454$	−11.0476			−0.518490
$455$	−22.3577	+	29.6928i	−1.04815	+	1.39202i
$456$	−1.14804	+	0.834096i	−0.0537617	+	0.0390601i
$457$	8.29776	+	1.76374i	0.388153	+	0.0825044i	0.397855	−	0.917449i	$-0.369755\pi$
$457$	8.29776	+	1.76374i	0.388153	+	0.0825044i	−0.00970171	+	0.999953i	$0.503088\pi$
$458$	7.92740	−	1.68502i	0.370423	−	0.0787359i
$459$	−0.906365	+	8.62349i	−0.0423055	+	0.402510i
$460$	12.4940	−	21.6402i	0.582534	−	1.00898i
$461$	−15.7776	−	11.4631i	−0.734836	−	0.533890i	0.156254	−	0.987717i	$-0.450058\pi$
$461$	−15.7776	−	11.4631i	−0.734836	−	0.533890i	−0.891090	+	0.453827i	$0.850058\pi$
$462$	0.570974	−	0.496716i	0.0265641	−	0.0231093i
$463$	7.19554	−	5.22787i	0.334405	−	0.242960i	−0.407892	−	0.913030i	$-0.633736\pi$
$463$	7.19554	−	5.22787i	0.334405	−	0.242960i	0.742298	+	0.670070i	$0.233736\pi$
$464$	10.4447	+	2.22008i	0.484881	+	0.103065i
$465$	−3.89523	−	6.74673i	−0.180637	−	0.312872i
$466$	−2.08997	−	0.930515i	−0.0968160	−	0.0431053i
$467$	−11.9353	−	13.2555i	−0.552302	−	0.613394i	0.400755	−	0.916185i	$-0.368748\pi$
$467$	−11.9353	−	13.2555i	−0.552302	−	0.613394i	−0.953057	+	0.302792i	$0.902081\pi$
$468$	−7.78578	−	5.65670i	−0.359898	−	0.261481i
$469$	−31.6617	+	2.78201i	−1.46200	+	0.128461i
$470$	−10.8771	+	33.4763i	−0.501724	+	1.54415i
$471$	0.570032	+	0.633085i	0.0262657	+	0.0291710i
$472$	2.91605	−	0.619825i	0.134222	−	0.0285297i
$473$	−8.63376	+	1.83516i	−0.396981	+	0.0843809i
$474$	2.22157	+	0.472209i	0.102040	+	0.0216893i
$475$	−40.9353	−	29.7412i	−1.87824	−	1.36462i
$476$	0.188533	−	11.0383i	0.00864139	−	0.505942i
$477$	12.0706	−	8.76977i	0.552673	−	0.401540i
$478$	−3.77476	+	6.53808i	−0.172654	+	0.299045i
$479$	10.1509	−	11.2738i	0.463808	−	0.515111i	−0.465182	−	0.885215i	$-0.654011\pi$
$479$	10.1509	−	11.2738i	0.463808	−	0.515111i	0.928990	+	0.370104i	$0.120678\pi$
$480$	−1.35609	−	0.603770i	−0.0618968	−	0.0275582i
$481$	−11.7896	+	5.24909i	−0.537562	+	0.239338i
$482$	7.61977	+	5.53609i	0.347071	+	0.252162i
$483$	4.07663	+	3.79866i	0.185493	+	0.172845i
$484$	8.37012	+	6.08125i	0.380460	+	0.276420i
$485$	−1.27911	−	1.42059i	−0.0580813	−	0.0645058i
$486$	6.03873	−	6.70668i	0.273922	−	0.304221i
$487$	−2.74940	−	1.22411i	−0.124587	−	0.0554698i	0.343496	−	0.939154i	$-0.388389\pi$
$487$	−2.74940	−	1.22411i	−0.124587	−	0.0554698i	−0.468084	+	0.883684i	$0.655055\pi$
$488$	−1.14860	−	10.9282i	−0.0519945	−	0.494695i
$489$	−4.78054			−0.216183
$490$	23.1629	+	18.0688i	1.04639	+	0.816267i
$491$	11.3133			0.510564			0.255282	−	0.966867i	$-0.417832\pi$
$491$	11.3133			0.510564			0.255282	+	0.966867i	$0.417832\pi$
$492$	1.80386	+	1.36957i	0.0813241	+	0.0617451i
$493$	22.2781	+	38.5868i	1.00336	+	1.73786i
$494$	8.98632	−	9.98031i	0.404313	−	0.449036i
$495$	−4.87839	+	8.44962i	−0.219267	+	0.379782i
$496$	−4.24583	+	3.08477i	−0.190643	+	0.138510i
$497$	23.9165	+	2.92747i	1.07280	+	0.131315i
$498$	0.350517	+	1.07878i	0.0157071	+	0.0483414i
$499$	−11.8364	−	13.1456i	−0.529869	−	0.588479i	0.417478	−	0.908687i	$-0.362914\pi$
$499$	−11.8364	−	13.1456i	−0.529869	−	0.588479i	−0.947347	+	0.320208i	$0.896247\pi$
$500$	3.33930	−	31.7714i	0.149338	−	1.42086i
$501$	2.70448	+	4.68430i	0.120827	+	0.209279i
$502$	−2.36457	+	1.05278i	−0.105536	+	0.0469877i
$503$	−0.203846	−	0.148103i	−0.00908903	−	0.00660357i	0.583231	−	0.812306i	$-0.301788\pi$
$503$	−0.203846	−	0.148103i	−0.00908903	−	0.00660357i	−0.592320	+	0.805702i	$0.701788\pi$
$504$	−4.57527	+	6.07633i	−0.203799	+	0.270661i
$505$	−1.53189	−	4.71468i	−0.0681683	−	0.209801i
$506$	2.40752	−	4.16995i	0.107027	−	0.185377i
$507$	0.579724	+	0.258110i	0.0257464	+	0.0114630i
$508$	−1.29528	+	0.275321i	−0.0574689	+	0.0122154i
$509$	−9.96483	+	4.43663i	−0.441683	+	0.196650i	−0.615515	−	0.788125i	$-0.711052\pi$
$509$	−9.96483	+	4.43663i	−0.441683	+	0.196650i	0.173831	+	0.984775i	$0.444385\pi$
$510$	−1.91407	−	5.89092i	−0.0847567	−	0.260854i
$511$	1.13811	+	0.683263i	0.0503469	+	0.0302258i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	5.57838	+	6.19542i	0.246291	+	0.273534i
$514$	−17.1140	+	3.63769i	−0.754866	+	0.160452i
$515$	28.2054	−	31.3253i	1.24288	−	1.38036i
$516$	−3.52694	+	1.57030i	−0.155265	+	0.0691284i
$517$	−2.09597	+	6.45072i	−0.0921805	+	0.283702i
$518$	3.98894	+	9.38756i	0.175264	+	0.412466i
$519$	−4.30992			−0.189185
$520$	13.7416	+	2.92086i	0.602607	+	0.128088i
$521$	5.54853	+	2.47037i	0.243086	+	0.108229i	0.524664	−	0.851310i	$-0.324191\pi$
$521$	5.54853	+	2.47037i	0.243086	+	0.108229i	−0.281578	+	0.959538i	$0.590858\pi$
$522$	3.20882	−	30.5299i	0.140446	−	1.33626i
$523$	3.34552	−	1.48952i	0.146290	−	0.0651323i	−0.332286	−	0.943179i	$-0.607820\pi$
$523$	3.34552	−	1.48952i	0.146290	−	0.0651323i	0.478576	+	0.878046i	$0.341153\pi$
$524$	13.6251			0.595217
$525$	11.1614	+	3.83850i	0.487124	+	0.167526i
$526$	4.92752	−	15.1653i	0.214850	−	0.661240i
$527$	−21.4204	−	4.55304i	−0.933087	−	0.198334i
$528$	−0.261312	−	0.116343i	−0.0113721	−	0.00506320i
$529$	11.3758	+	5.06483i	0.494599	+	0.220210i
$530$	−10.8900	+	18.8620i	−0.473030	+	0.819312i
$531$	−2.64846	−	8.15112i	−0.114933	−	0.353728i
$532$	−7.76560	−	7.23610i	−0.336682	−	0.313725i
$533$	−19.3934	−	9.12895i	−0.840023	−	0.395419i
$534$	−1.80316	+	3.12317i	−0.0780304	+	0.135153i
$535$	31.1679	−	34.6155i	1.34751	−	1.49656i
$536$	6.00656	+	10.4037i	0.259444	+	0.449370i
$537$	−0.758042	−	7.21229i	−0.0327119	−	0.311233i
$538$	−15.4774	+	11.2450i	−0.667277	+	0.484805i
$539$	4.46337	+	3.48177i	0.192251	+	0.149971i
$540$	−2.69488	+	8.29400i	−0.115969	+	0.356917i
$541$	11.3594	−	5.05752i	0.488377	−	0.217440i	−0.147748	−	0.989025i	$-0.547203\pi$
$541$	11.3594	−	5.05752i	0.488377	−	0.217440i	0.636126	+	0.771585i	$0.280536\pi$
$542$	−9.61685	−	16.6569i	−0.413079	−	0.715474i
$543$	0.142926	−	1.35985i	0.00613354	−	0.0583567i
$544$	−3.81196	+	1.69719i	−0.163436	+	0.0727666i
$545$	14.4939	−	10.5304i	0.620851	−	0.451075i
$546$	−1.32289	+	2.83972i	−0.0566143	+	0.121529i
$547$	2.09162			0.0894312			0.0447156	−	0.999000i	$-0.485762\pi$
$547$	2.09162			0.0894312			0.0447156	+	0.999000i	$0.485762\pi$
$548$	0.455924	+	4.33783i	0.0194761	+	0.185303i
$549$	−30.9000	+	6.56799i	−1.31878	+	0.280315i
$550$	1.06612	−	10.1434i	0.0454595	−	0.432518i
$551$	41.9026	+	8.90668i	1.78511	+	0.379437i
$552$	0.650812	−	2.00299i	0.0277004	−	0.0852531i
$553$	−0.290117	+	16.9860i	−0.0123370	+	0.722317i
$554$	−0.976743	+	3.00611i	−0.0414978	+	0.127717i
$555$	3.82927	+	4.25284i	0.162543	+	0.180523i
$556$	−8.85416	+	9.83354i	−0.375500	+	0.417035i
$557$	3.89032	−	37.0139i	0.164838	−	1.56833i	−0.529266	−	0.848456i	$-0.677533\pi$
$557$	3.89032	−	37.0139i	0.164838	−	1.56833i	0.694105	−	0.719874i	$-0.255801\pi$
$558$	10.0957	+	11.2124i	0.427385	+	0.474659i
$559$	29.5596	−	21.4763i	1.25024	−	0.908352i
$560$	2.49367	−	10.8198i	0.105377	−	0.457219i
$561$	−0.368833	−	1.13515i	−0.0155721	−	0.0479261i
$562$	2.46672	+	23.4693i	0.104052	+	0.989992i
$563$	0.0180811	−	0.172031i	0.000762029	−	0.00725022i	−0.994134	−	0.108153i	$-0.965506\pi$
$563$	0.0180811	−	0.172031i	0.000762029	−	0.00725022i	0.994896	+	0.100903i	$0.0321731\pi$
$564$	−0.310105	+	2.95045i	−0.0130578	+	0.124237i
$565$	23.8756	−	41.3537i	1.00445	−	1.73976i
$566$	−5.76668	−	4.18974i	−0.242392	−	0.176108i
$567$	17.8966	+	10.7442i	0.751585	+	0.451214i
$568$	−2.81423	−	8.66132i	−0.118083	−	0.363421i
$569$	1.63874	+	15.5916i	0.0686995	+	0.653632i	0.973639	+	0.228093i	$0.0732490\pi$
$569$	1.63874	+	15.5916i	0.0686995	+	0.653632i	−0.904940	+	0.425539i	$0.860084\pi$
$570$	−5.44046	−	2.42225i	−0.227876	−	0.101457i
$571$	−20.1362	−	34.8769i	−0.842673	−	1.45955i	−0.887627	−	0.460564i	$-0.847647\pi$
$571$	−20.1362	−	34.8769i	−0.842673	−	1.45955i	0.0449534	−	0.998989i	$-0.485686\pi$
$572$	2.64793	+	0.562835i	0.110715	+	0.0235333i
$573$	2.87249			0.120000
$574$	−7.47587	+	15.2023i	−0.312037	+	0.634534i
$575$	75.0958			3.13171
$576$	2.81206	+	0.597723i	0.117169	+	0.0249051i
$577$	−17.2647	−	29.9033i	−0.718737	−	1.24489i	−0.961500	−	0.274804i	$-0.911387\pi$
$577$	−17.2647	−	29.9033i	−0.718737	−	1.24489i	0.242763	−	0.970086i	$-0.421946\pi$
$578$	−0.375932	−	0.167376i	−0.0156367	−	0.00696191i
$579$	0.728286	+	6.92918i	0.0302665	+	0.287967i
$580$	13.8478	+	42.6191i	0.574998	+	1.76966i
$581$	−7.41915	+	4.11614i	−0.307798	+	0.170766i
$582$	−0.130346	−	0.0947018i	−0.00540301	−	0.00392551i
$583$	−2.09844	+	3.63461i	−0.0869086	+	0.150530i
$584$	0.0524451	−	0.498982i	0.00217019	−	0.0206480i
$585$	4.22170	−	40.1667i	0.174546	−	1.66069i
$586$	−1.34317	−	12.7794i	−0.0554858	−	0.527912i
$587$	1.49960	+	4.61528i	0.0618950	+	0.190493i	0.977223	−	0.212217i	$-0.0680683\pi$
$587$	1.49960	+	4.61528i	0.0618950	+	0.190493i	−0.915328	+	0.402710i	$0.868068\pi$
$588$	2.22622	+	1.08373i	0.0918077	+	0.0446924i
$589$	−17.0337	+	12.3757i	−0.701862	+	0.509932i
$590$	8.37160	+	9.29760i	0.344653	+	0.382776i
$591$	0.863495	−	8.21561i	0.0355194	−	0.337945i
$592$	2.57963	−	2.86497i	0.106022	−	0.117750i
$593$	2.39976	+	2.66520i	0.0985464	+	0.109447i	0.790400	−	0.612591i	$-0.209873\pi$
$593$	2.39976	+	2.66520i	0.0985464	+	0.109447i	−0.691854	+	0.722037i	$0.743206\pi$
$594$	−0.519291	+	1.59821i	−0.0213068	+	0.0655755i
$595$	40.5139	−	22.4771i	1.66091	−	0.921470i
$596$	2.13518	−	6.57140i	0.0874603	−	0.269175i
$597$	−2.65653	−	0.564664i	−0.108725	−	0.0231101i
$598$	−2.08344	+	19.8226i	−0.0851982	+	0.810607i
$599$	31.4064	−	6.67563i	1.28323	−	0.272759i	0.484682	−	0.874690i	$-0.338935\pi$
$599$	31.4064	−	6.67563i	1.28323	−	0.272759i	0.798548	+	0.601931i	$0.205602\pi$
$600$	−0.466314	−	4.43668i	−0.0190372	−	0.181127i
$601$	−0.0942275			−0.00384362			−0.00192181	−	0.999998i	$-0.500612\pi$
$601$	−0.0942275			−0.00384362			−0.00192181	+	0.999998i	$0.500612\pi$
$602$	−16.5726	−	23.6492i	−0.675449	−	0.963871i
$603$	27.9405	−	20.3000i	1.13782	−	0.826678i
$604$	−12.8760	+	5.73275i	−0.523915	+	0.233262i
$605$	−4.53854	+	43.1813i	−0.184518	+	1.75557i
$606$	−0.208910	−	0.361843i	−0.00848639	−	0.0146989i
$607$	−14.7646	+	6.57362i	−0.599277	+	0.266815i	−0.683874	−	0.729600i	$-0.739706\pi$
$607$	−14.7646	+	6.57362i	−0.599277	+	0.266815i	0.0845975	+	0.996415i	$0.473040\pi$
$608$	−1.23974	+	3.81552i	−0.0502779	+	0.154740i
$609$	−9.95451	+	0.874670i	−0.403377	+	0.0354434i
$610$	37.3077	−	27.1056i	1.51054	−	1.09747i
$611$	−2.93483	−	27.9230i	−0.118730	−	1.12964i
$612$	5.99804	+	10.3889i	0.242456	+	0.419946i
$613$	−3.98954	+	4.43083i	−0.161136	+	0.178960i	−0.818306	−	0.574783i	$-0.805087\pi$
$613$	−3.98954	+	4.43083i	−0.161136	+	0.178960i	0.657170	+	0.753742i	$0.271753\pi$
$614$	0.840152	−	1.45519i	0.0339058	−	0.0587265i
$615$	−1.19252	+	9.42985i	−0.0480871	+	0.380248i
$616$	0.480517	−	2.08492i	0.0193606	−	0.0840037i
$617$	−7.07192	−	21.7651i	−0.284705	−	0.876232i	−0.986487	−	0.163840i	$-0.947612\pi$
$617$	−7.07192	−	21.7651i	−0.284705	−	0.876232i	0.701782	−	0.712392i	$-0.252388\pi$
$618$	1.77637	−	3.07677i	0.0714562	−	0.123766i
$619$	−29.3792	−	13.0805i	−1.18085	−	0.525749i	−0.280052	−	0.959985i	$-0.590352\pi$
$619$	−29.3792	−	13.0805i	−1.18085	−	0.525749i	−0.900799	+	0.434236i	$0.857018\pi$
$620$	−20.1207	−	8.95830i	−0.808065	−	0.359774i
$621$	−12.1026	−	2.57248i	−0.485659	−	0.103230i
$622$	7.89621	−	24.3020i	0.316609	−	0.974423i
$623$	−25.5087	−	8.77266i	−1.02199	−	0.351469i
$624$	1.18406			0.0474004
$625$	64.8689	−	28.8815i	2.59476	−	1.15526i
$626$	1.13534	−	10.8020i	0.0453772	−	0.431736i
$627$	−1.04835	−	0.466755i	−0.0418670	−	0.0186404i
$628$	2.35582	+	0.500745i	0.0940075	+	0.0199819i
$629$	16.0866			0.641416
$630$	−31.6846	−	3.87831i	−1.26234	−	0.154516i
$631$	4.59926	−	14.1551i	0.183094	−	0.563504i	−0.816817	−	0.576897i	$-0.804263\pi$
$631$	4.59926	−	14.1551i	0.183094	−	0.563504i	0.999910	+	0.0133930i	$0.00426326\pi$
$632$	5.86590	−	2.61167i	0.233333	−	0.103887i
$633$	5.76376	−	6.40130i	0.229089	−	0.254429i
$634$	16.7105	−	3.55193i	0.663659	−	0.141065i
$635$	−3.71859	−	4.12992i	−0.147568	−	0.163891i
$636$	−0.567260	+	1.74585i	−0.0224933	+	0.0692273i
$637$	−22.7409	−	5.65182i	−0.901026	−	0.223933i
$638$	2.66840	+	8.21248i	0.105643	+	0.325135i
$639$	−23.9182	+	10.6491i	−0.946190	+	0.421271i
$640$	−4.10499	+	0.872542i	−0.162264	+	0.0344903i
$641$	−8.16932	−	3.63721i	−0.322669	−	0.143661i	0.239009	−	0.971017i	$-0.423177\pi$
$641$	−8.16932	−	3.63721i	−0.322669	−	0.143661i	−0.561678	+	0.827356i	$0.689844\pi$
$642$	1.96295	−	3.39993i	0.0774716	−	0.134185i
$643$	4.24235	+	13.0566i	0.167302	+	0.514903i	0.999199	−	0.0400279i	$-0.0127447\pi$
$643$	4.24235	+	13.0566i	0.167302	+	0.514903i	−0.831896	+	0.554931i	$0.812745\pi$
$644$	15.6366	+	1.91398i	0.616168	+	0.0754213i
$645$	−13.1079	−	9.52346i	−0.516124	−	0.374986i
$646$	−15.2931	+	6.80892i	−0.601699	+	0.267893i
$647$	−24.4751	−	42.3922i	−0.962217	−	1.66661i	−0.716913	−	0.697163i	$-0.754445\pi$
$647$	−24.4751	−	42.3922i	−0.962217	−	1.66661i	−0.245304	−	0.969446i	$-0.578888\pi$
$648$	0.824692	−	7.84642i	0.0323970	−	0.308236i
$649$	1.61317	+	1.79160i	0.0633223	+	0.0703265i
$650$	13.0467	+	40.1535i	0.511732	+	1.57495i
$651$	2.95428	−	3.92352i	0.115787	−	0.153775i
$652$	−10.9341	+	7.94410i	−0.428213	+	0.311115i
$653$	−14.9986	+	25.9784i	−0.586942	+	1.01661i	0.407688	+	0.913121i	$0.366335\pi$
$653$	−14.9986	+	25.9784i	−0.586942	+	1.01661i	−0.994630	+	0.103492i	$0.966998\pi$
$654$	1.01037	−	1.12213i	0.0395087	−	0.0438789i
$655$	28.5903	+	49.5198i	1.11711	+	1.93490i
$656$	6.40170	+	0.134934i	0.249944	+	0.00526829i
$657$	−1.44242			−0.0562741
$658$	−22.1056	+	1.94235i	−0.861767	+	0.0757206i
$659$	17.3808			0.677058			0.338529	−	0.940956i	$-0.390071\pi$
$659$	17.3808			0.677058			0.338529	+	0.940956i	$0.390071\pi$
$660$	−0.125479	−	1.19385i	−0.00488426	−	0.0464707i
$661$	−33.0591	−	14.7189i	−1.28585	−	0.572497i	−0.353968	−	0.935258i	$-0.615168\pi$
$661$	−33.0591	−	14.7189i	−1.28585	−	0.572497i	−0.931883	+	0.362760i	$0.881834\pi$
$662$	−11.9133	+	13.2310i	−0.463022	+	0.514238i
$663$	3.30601	+	3.67169i	0.128395	+	0.142597i
$664$	2.59438	+	1.88493i	0.100682	+	0.0731495i
$665$	10.0043	−	43.4075i	0.387949	−	1.68327i
$666$	−8.96655	−	6.51458i	−0.347447	−	0.252435i
$667$	−58.0822	+	25.8598i	−2.24895	+	1.00130i
$668$	13.9699	+	6.21981i	0.540512	+	0.240652i
$669$	2.64335	−	2.93574i	0.102198	−	0.113502i
$670$	−25.2077	+	43.6610i	−0.973858	+	1.68677i
$671$	7.18900	−	5.22311i	0.277528	−	0.201636i
$672$	0.0159816	−	0.935700i	0.000616502	−	0.0360954i
$673$	−3.71304	−	2.69768i	−0.143127	−	0.103988i	0.513918	−	0.857840i	$-0.328194\pi$
$673$	−3.71304	−	2.69768i	−0.143127	−	0.103988i	−0.657045	+	0.753852i	$0.728194\pi$
$674$	6.16569	+	1.31056i	0.237494	+	0.0504808i
$675$	−25.6358	+	5.44907i	−0.986724	+	0.209735i
$676$	1.75487	−	0.373009i	0.0674949	−	0.0143465i
$677$	24.3817	+	27.0787i	0.937066	+	1.04072i	0.999090	+	0.0426430i	$0.0135778\pi$
$677$	24.3817	+	27.0787i	0.937066	+	1.04072i	−0.0620240	+	0.998075i	$0.519756\pi$
$678$	1.24368	−	3.82766i	0.0477633	−	0.147000i
$679$	0.508905	−	1.09242i	0.0195300	−	0.0419232i
$680$	−14.1672	−	10.2931i	−0.543287	−	0.394721i
$681$	−2.61475	−	2.90397i	−0.100197	−	0.111281i
$682$	−3.87715	−	1.72622i	−0.148464	−	0.0661004i
$683$	−7.51426	−	13.0151i	−0.287525	−	0.498008i	0.685693	−	0.727891i	$-0.259499\pi$
$683$	−7.51426	−	13.0151i	−0.287525	−	0.498008i	−0.973218	+	0.229883i	$0.926166\pi$
$684$	11.2816	+	2.39799i	0.431364	+	0.0916893i
$685$	−14.8089	+	10.7593i	−0.565820	+	0.411092i
$686$	−4.77326	+	17.8946i	−0.182244	+	0.683218i
$687$	2.31918	+	1.68498i	0.0884823	+	0.0642862i
$688$	−5.45742	+	9.45253i	−0.208062	+	0.360374i
$689$	1.81596	−	17.2777i	0.0691827	−	0.658230i
$690$	8.64540	−	1.83764i	0.329125	−	0.0699576i
$691$	18.1514	+	3.85820i	0.690511	+	0.146773i	0.539785	−	0.841803i	$-0.318505\pi$
$691$	18.1514	+	3.85820i	0.690511	+	0.146773i	0.150726	+	0.988576i	$0.451839\pi$
$692$	−9.85771	+	7.16205i	−0.374734	+	0.272260i
$693$	−6.10546	−	0.747332i	−0.231927	−	0.0283888i
$694$	5.91363			0.224478
$695$	−54.3186	−	11.5458i	−2.06042	−	0.437956i
$696$	1.88847	+	3.27093i	0.0715824	+	0.123984i
$697$	17.4557	+	20.2280i	0.661182	+	0.766189i
$698$	−13.2288	+	22.9130i	−0.500719	+	0.867271i
$699$	−0.250059	−	0.769603i	−0.00945811	−	0.0291091i
$700$	31.9072	−	9.76810i	1.20598	−	0.369199i
$701$	−7.07875	+	5.14301i	−0.267361	+	0.194249i	−0.713386	−	0.700772i	$-0.752839\pi$
$701$	−7.07875	+	5.14301i	−0.267361	+	0.194249i	0.446025	+	0.895020i	$0.352839\pi$
$702$	−0.727124	−	6.91813i	−0.0274435	−	0.261108i
$703$	10.3491	−	11.4939i	0.390325	−	0.433500i
$704$	−0.791011	+	0.168135i	−0.0298123	+	0.00633681i
$705$	−11.3740	+	5.06402i	−0.428369	+	0.190722i
$706$	−23.5891			−0.887786
$707$	2.35790	−	2.05125i	0.0886780	−	0.0771451i
$708$	0.853097	+	0.619811i	0.0320613	+	0.0232939i
$709$	−3.58000	−	34.0614i	−0.134450	−	1.27920i	−0.828791	−	0.559558i	$-0.810971\pi$
$709$	−3.58000	−	34.0614i	−0.134450	−	1.27920i	0.694341	−	0.719646i	$-0.255696\pi$
$710$	25.5739	−	28.4027i	0.959770	−	1.06593i
$711$	−9.22987	−	15.9866i	−0.346147	−	0.599545i
$712$	1.06573	+	10.1398i	0.0399400	+	0.380004i
$713$	9.65627	−	29.7189i	0.361630	−	1.11298i
$714$	2.94616	−	2.56300i	0.110257	−	0.0959178i
$715$	3.51069	+	10.8048i	0.131292	+	0.404076i
$716$	−13.7189	−	15.2364i	−0.512699	−	0.569410i
$717$	−2.61201	+	0.555200i	−0.0975473	+	0.0207343i
$718$	1.70167	−	0.361702i	0.0635059	−	0.0134986i
$719$	−25.6917	−	28.5336i	−0.958140	−	1.06412i	−0.997891	−	0.0649129i	$-0.979323\pi$
$719$	−25.6917	−	28.5336i	−0.958140	−	1.06412i	0.0397508	−	0.999210i	$-0.487344\pi$
$720$	3.72830	+	11.4745i	0.138946	+	0.427630i
$721$	25.1298	+	8.64233i	0.935882	+	0.321857i
$722$	0.897663	−	2.76272i	0.0334076	−	0.102818i
$723$	0.348233	+	3.31321i	0.0129509	+	0.123220i
$724$	−1.93284	−	3.34778i	−0.0718334	−	0.124419i
$725$	−90.1144	+	100.082i	−3.34676	+	3.71696i
$726$	0.382524	+	3.63948i	0.0141968	+	0.135074i
$727$	21.2379	+	15.4303i	0.787671	+	0.572277i	0.907271	−	0.420545i	$-0.138161\pi$
$727$	21.2379	+	15.4303i	0.787671	+	0.572277i	−0.119600	+	0.992822i	$0.538161\pi$
$728$	1.69320	+	8.69336i	0.0627543	+	0.322197i
$729$	−20.4768			−0.758398
$730$	1.92357	−	0.856429i	0.0711946	−	0.0316979i
$731$	−44.5492	+	9.46923i	−1.64771	+	0.350232i
$732$	2.60073	−	2.88840i	0.0961256	−	0.106758i
$733$	3.79162	+	36.0748i	0.140047	+	1.33245i	0.808410	+	0.588619i	$0.200328\pi$
$733$	3.79162	+	36.0748i	0.140047	+	1.33245i	−0.668364	+	0.743835i	$0.733005\pi$
$734$	−18.4201	+	13.3830i	−0.679900	+	0.493976i
$735$	0.732615	+	10.3651i	0.0270229	+	0.382323i
$736$	−1.83995	−	5.66277i	−0.0678213	−	0.208732i
$737$	−4.85740	+	8.41326i	−0.178924	+	0.309906i
$738$	−1.53796	−	18.3439i	−0.0566133	−	0.675248i
$739$	−4.47327	−	7.74793i	−0.164552	−	0.285012i	0.771944	−	0.635690i	$-0.219284\pi$
$739$	−4.47327	−	7.74793i	−0.164552	−	0.285012i	−0.936496	+	0.350678i	$0.885951\pi$
$740$	15.8255	+	3.36382i	0.581759	+	0.123657i
$741$	4.75031			0.174507
$742$	−13.6291	−	1.66826i	−0.500342	−	0.0612437i
$743$	10.2279	−	7.43103i	0.375226	−	0.272618i	−0.384148	−	0.923271i	$-0.625505\pi$
$743$	10.2279	−	7.43103i	0.375226	−	0.272618i	0.759375	+	0.650653i	$0.225505\pi$
$744$	−1.81577	−	0.385953i	−0.0665692	−	0.0141497i
$745$	28.3638	−	6.02890i	1.03917	−	0.220882i
$746$	−2.79859	+	26.6268i	−0.102464	+	0.974876i
$747$	4.60964	−	7.98414i	0.168658	−	0.292124i
$748$	−2.72994	−	1.98342i	−0.0998167	−	0.0725211i
$749$	27.7693	+	9.55007i	1.01467	+	0.348952i
$750$	9.14176	−	6.64188i	0.333810	−	0.242527i
$751$	48.6343	+	10.3375i	1.77469	+	0.377222i	0.974827	−	0.222960i	$-0.0715721\pi$
$751$	48.6343	+	10.3375i	1.77469	+	0.377222i	0.799863	+	0.600183i	$0.204905\pi$
$752$	4.19367	+	7.26364i	0.152927	+	0.264878i
$753$	−0.836380	−	0.372380i	−0.0304794	−	0.0135703i
$754$	−23.9180	−	26.5636i	−0.871042	−	0.967390i
$755$	−47.8536	−	34.7677i	−1.74157	−	1.26533i
$756$	−5.47683	+	0.481231i	−0.199190	+	0.0175022i
$757$	1.43873	−	4.42794i	0.0522914	−	0.160936i	−0.921501	−	0.388377i	$-0.873036\pi$
$757$	1.43873	−	4.42794i	0.0522914	−	0.160936i	0.973792	+	0.227441i	$0.0730358\pi$
$758$	8.84347	+	9.82166i	0.321209	+	0.356739i
$759$	1.66593	−	0.354103i	0.0604693	−	0.0128531i
$760$	−16.4687	+	3.50053i	−0.597382	+	0.126977i
$761$	2.71569	+	0.577239i	0.0984439	+	0.0209249i	0.256870	−	0.966446i	$-0.417309\pi$
$761$	2.71569	+	0.577239i	0.0984439	+	0.0209249i	−0.158426	+	0.987371i	$0.550642\pi$
$762$	−0.378938	−	0.275315i	−0.0137275	−	0.00997361i
$763$	9.68351	+	5.81350i	0.350567	+	0.210463i
$764$	6.57000	−	4.77338i	0.237694	−	0.172695i
$765$	−25.1719	+	43.5991i	−0.910093	+	1.57633i
$766$	−15.9625	+	17.7281i	−0.576748	+	0.640543i
$767$	−9.11683	−	4.05908i	−0.329190	−	0.146565i
$768$	−0.323133	+	0.143868i	−0.0116600	+	0.00519139i
$769$	25.6153	+	18.6106i	0.923712	+	0.671116i	0.944445	−	0.328669i	$-0.106600\pi$
$769$	25.6153	+	18.6106i	0.923712	+	0.671116i	−0.0207334	+	0.999785i	$0.506600\pi$
$770$	8.58581	−	2.62847i	0.309411	−	0.0947234i
$771$	−5.00674	−	3.63761i	−0.180314	−	0.131005i
$772$	13.1804	+	14.6383i	0.474372	+	0.526843i
$773$	18.7204	−	20.7912i	0.673327	−	0.747806i	−0.305568	−	0.952170i	$-0.598846\pi$
$773$	18.7204	−	20.7912i	0.673327	−	0.747806i	0.978895	+	0.204365i	$0.0655128\pi$
$774$	28.6661	+	12.7630i	1.03038	+	0.458755i
$775$	−6.91882	−	65.8282i	−0.248531	−	2.36462i
$776$	−0.455500			−0.0163515
$777$	−1.52351	+	3.27038i	−0.0546556	+	0.117324i
$778$	30.7884			1.10382
$779$	25.6828	+	0.541338i	0.920182	+	0.0193955i
$780$	2.48458	+	4.30341i	0.0889621	+	0.154087i
$781$	4.92796	−	5.47305i	0.176336	−	0.195841i
$782$	12.4225	−	21.5165i	0.444229	−	0.769428i
$783$	17.9514	−	13.0424i	0.641530	−	0.466099i
$784$	6.89274	−	1.22071i	0.246169	−	0.0435968i
$785$	3.12340	+	9.61284i	0.111479	+	0.343097i
$786$	3.22480	+	3.58150i	0.115025	+	0.127748i
$787$	−0.309427	+	2.94400i	−0.0110299	+	0.104942i	−0.998652	−	0.0519117i	$-0.983469\pi$
$787$	−0.309427	+	2.94400i	−0.0110299	+	0.104942i	0.987622	+	0.156854i	$0.0501352\pi$
$788$	−11.6774	−	20.2258i	−0.415989	−	0.720513i
$789$	5.15260	−	2.29409i	0.183437	−	0.0816716i
$790$	21.8007	+	15.8391i	0.775633	+	0.563531i
$791$	29.8810	+	3.65755i	1.06245	+	0.130048i
$792$	0.718425	+	2.21108i	0.0255281	+	0.0785674i
$793$	−18.3919	+	31.8557i	−0.653116	+	1.13123i
$794$	−3.66120	−	1.63007i	−0.129931	−	0.0578491i
$795$	−7.53549	+	1.60172i	−0.267256	+	0.0568071i
$796$	−7.01440	+	3.12301i	−0.248619	+	0.110692i
$797$	7.77018	+	23.9142i	0.275234	+	0.847083i	0.989157	+	0.146859i	$0.0469164\pi$
$797$	7.77018	+	23.9142i	0.275234	+	0.847083i	−0.713924	+	0.700224i	$0.753084\pi$
$798$	0.0641160	−	3.75391i	0.00226968	−	0.132887i
$799$	−10.8149	+	33.2850i	−0.382605	+	1.17754i
$800$	−8.43925	−	9.37274i	−0.298373	−	0.331376i
$801$	28.6708	−	6.09416i	1.01303	−	0.215326i
$802$	19.9690	−	22.1778i	0.705129	−	0.783125i
$803$	0.370663	−	0.165030i	0.0130804	−	0.00582377i
$804$	−1.31307	+	4.04122i	−0.0463085	+	0.142523i
$805$	25.8548	+	60.8466i	0.911261	+	2.14456i
$806$	17.5683			0.618815
$807$	−6.61904	−	1.40692i	−0.233001	−	0.0495259i
$808$	−1.07912	−	0.480454i	−0.0379632	−	0.0169023i
$809$	−4.84149	+	46.0637i	−0.170218	+	1.61951i	0.492273	+	0.870441i	$0.336166\pi$
$809$	−4.84149	+	46.0637i	−0.170218	+	1.61951i	−0.662490	+	0.749071i	$0.730500\pi$
$810$	30.2479	−	13.4672i	1.06280	−	0.473190i
$811$	−50.5930			−1.77656			−0.888280	−	0.459302i	$-0.848100\pi$
$811$	−50.5930			−1.77656			−0.888280	+	0.459302i	$0.848100\pi$
$812$	−21.3146	+	18.5425i	−0.747996	+	0.650716i
$813$	2.10231	−	6.47024i	0.0737311	−	0.226921i
$814$	3.04950	+	0.648192i	0.106885	+	0.0227191i
$815$	−51.8160	−	23.0700i	−1.81503	−	0.808105i
$816$	−1.34834	−	0.600319i	−0.0472013	−	0.0210154i
$817$	−21.8945	+	37.9223i	−0.765991	+	1.32673i
$818$	9.56819	+	29.4479i	0.334544	+	1.02962i
$819$	24.3467	−	7.45352i	0.850743	−	0.260447i
$820$	12.9426	+	23.5498i	0.451975	+	0.822394i
$821$	−17.2913	+	29.9494i	−0.603471	+	1.04524i	0.388820	+	0.921314i	$0.372883\pi$
$821$	−17.2913	+	29.9494i	−0.603471	+	1.04524i	−0.992291	+	0.123929i	$0.960450\pi$
$822$	−1.03233	+	1.14652i	−0.0360067	+	0.0399895i
$823$	13.2393	+	22.9311i	0.461492	+	0.799328i	0.999036	−	0.0439082i	$-0.0139809\pi$
$823$	13.2393	+	22.9311i	0.461492	+	0.799328i	−0.537543	+	0.843236i	$0.680648\pi$
$824$	−1.04990	−	9.98914i	−0.0365750	−	0.347988i
$825$	2.91863	−	2.12051i	0.101614	−	0.0738267i
$826$	−3.33072	+	7.14975i	−0.115890	+	0.248771i
$827$	0.205192	−	0.631516i	0.00713523	−	0.0219600i	−0.947426	−	0.319976i	$-0.896325\pi$
$827$	0.205192	−	0.631516i	0.00713523	−	0.0219600i	0.954561	+	0.298016i	$0.0963250\pi$
$828$	−15.6377	+	6.96236i	−0.543448	+	0.241959i
$829$	−23.6978	−	41.0459i	−0.823060	−	1.42558i	−0.903393	−	0.428814i	$-0.858932\pi$
$829$	−23.6978	−	41.0459i	−0.823060	−	1.42558i	0.0803325	−	0.996768i	$-0.474402\pi$
$830$	−1.40676	+	13.3844i	−0.0488292	+	0.464579i
$831$	−1.02136	+	0.454739i	−0.0354306	+	0.0157747i
$832$	2.70821	−	1.96763i	0.0938901	−	0.0682152i
$833$	23.0305	+	17.9656i	0.797958	+	0.622470i
$834$	−4.68045			−0.162071
$835$	6.70820	+	63.8242i	0.232147	+	2.20873i
$836$	−3.17343	+	0.674534i	−0.109755	+	0.0233292i
$837$	−1.13996	+	10.8460i	−0.0394028	+	0.374892i
$838$	−10.4561	−	2.22250i	−0.361199	−	0.0767751i
$839$	2.53053	−	7.78818i	0.0873637	−	0.268878i	−0.897825	−	0.440353i	$-0.854853\pi$
$839$	2.53053	−	7.78818i	0.0873637	−	0.268878i	0.985188	+	0.171475i	$0.0548533\pi$
$840$	3.43428	−	1.90534i	0.118494	−	0.0657405i
$841$	26.2725	−	80.8586i	0.905950	−	2.78823i
$842$	−2.70891	−	3.00855i	−0.0933552	−	0.103681i
$843$	−5.58531	+	6.20311i	−0.192368	+	0.213647i
$844$	2.54553	−	24.2191i	0.0876209	−	0.833657i
$845$	5.03800	+	5.59527i	0.173313	+	0.192483i
$846$	19.5075	−	14.1731i	0.670683	−	0.487280i
$847$	−26.1740	+	8.01292i	−0.899348	+	0.275327i
$848$	1.60373	+	4.93577i	0.0550723	+	0.169495i
$849$	−0.263544	−	2.50746i	−0.00904481	−	0.0860557i
$850$	5.50105	−	52.3390i	0.188685	−	1.79521i
$851$	−2.39941	+	22.8288i	−0.0822506	+	0.782562i
$852$	1.61064	−	2.78971i	0.0551796	−	0.0955739i
$853$	7.53134	+	5.47184i	0.257868	+	0.187352i	0.709207	−	0.705001i	$-0.249053\pi$
$853$	7.53134	+	5.47184i	0.257868	+	0.187352i	−0.451339	+	0.892353i	$0.649053\pi$
$854$	24.9256	+	14.9641i	0.852936	+	0.512060i
$855$	14.9575	+	46.0343i	0.511534	+	1.57434i
$856$	−1.16018	−	11.0383i	−0.0396540	−	0.377282i
$857$	11.8418	+	5.27232i	0.404509	+	0.180099i	0.598898	−	0.800825i	$-0.295606\pi$
$857$	11.8418	+	5.27232i	0.404509	+	0.180099i	−0.194388	+	0.980925i	$0.562272\pi$
$858$	0.478765	+	0.829246i	0.0163448	+	0.0283100i
$859$	−5.33145	−	1.13323i	−0.181907	−	0.0386655i	0.116058	−	0.993242i	$-0.462974\pi$
$859$	−5.33145	−	1.13323i	−0.181907	−	0.0386655i	−0.297964	+	0.954577i	$0.596308\pi$
$860$	−45.8063			−1.56198
$861$	−5.76548	+	1.63299i	−0.196487	+	0.0556520i
$862$	−29.0263			−0.988638
$863$	16.9095	+	3.59422i	0.575605	+	0.122349i	0.486511	−	0.873675i	$-0.338269\pi$
$863$	16.9095	+	3.59422i	0.575605	+	0.122349i	0.0890941	+	0.996023i	$0.471603\pi$
$864$	1.03901	+	1.79962i	0.0353479	+	0.0612243i
$865$	−46.7150	−	20.7989i	−1.58836	−	0.707182i
$866$	−1.58233	−	15.0549i	−0.0537698	−	0.511586i
$867$	−0.0449792	−	0.138432i	−0.00152758	−	0.00470139i
$868$	0.237123	−	13.8832i	0.00804847	−	0.471227i
$869$	4.20088	+	3.05212i	0.142505	+	0.103536i
$870$	−7.92535	+	13.7271i	−0.268694	+	0.465392i
$871$	4.20353	−	39.9939i	0.142431	−	1.35514i
$872$	0.446226	−	4.24556i	0.0151111	−	0.143773i
$873$	0.136881	+	1.30234i	0.00463273	+	0.0440775i
$874$	−7.38162	−	22.7183i	−0.249687	−	0.768458i
$875$	61.8372	+	57.6208i	2.09048	+	1.94794i
$876$	0.143575	−	0.104313i	0.00485095	−	0.00352442i
$877$	4.28405	+	4.75792i	0.144662	+	0.160663i	0.811121	−	0.584878i	$-0.198858\pi$
$877$	4.28405	+	4.75792i	0.144662	+	0.160663i	−0.666459	+	0.745541i	$0.732191\pi$
$878$	−3.08619	+	29.3632i	−0.104154	+	0.990959i
$879$	3.04129	−	3.37769i	0.102580	−	0.113927i
$880$	−2.27089	−	2.52208i	−0.0765518	−	0.0850193i
$881$	−6.07793	+	18.7060i	−0.204771	+	0.630220i	0.794952	+	0.606672i	$0.207496\pi$
$881$	−6.07793	+	18.7060i	−0.204771	+	0.630220i	−0.999723	+	0.0235472i	$0.992504\pi$
$882$	−5.56150	−	19.3405i	−0.187265	−	0.651227i
$883$	8.52108	−	26.2252i	0.286757	−	0.882548i	−0.699109	−	0.715015i	$-0.746420\pi$
$883$	8.52108	−	26.2252i	0.286757	−	0.882548i	0.985866	−	0.167533i	$-0.0535802\pi$
$884$	13.6630	+	2.90416i	0.459537	+	0.0976776i
$885$	−0.462576	+	4.40111i	−0.0155493	+	0.147942i
$886$	5.68527	−	1.20844i	0.191001	−	0.0405984i
$887$	0.767316	+	7.30052i	0.0257640	+	0.245128i	0.999823	+	0.0188322i	$0.00599482\pi$
$887$	0.767316	+	7.30052i	0.0257640	+	0.245128i	−0.974059	+	0.226295i	$0.927339\pi$
$888$	1.36363			0.0457605
$889$	1.47948	−	3.17586i	0.0496200	−	0.106515i
$890$	−34.6162	+	25.1501i	−1.16034	+	0.843034i
$891$	5.82861	−	2.59507i	0.195266	−	0.0869380i
$892$	1.16742	−	11.1073i	0.0390882	−	0.371899i
$893$	16.8244	+	29.1408i	0.563009	+	0.975160i
$894$	2.23271	−	0.994067i	0.0746731	−	0.0332466i
$895$	26.5887	−	81.8317i	0.888764	−	2.73533i
$896$	−1.51835	−	2.16670i	−0.0507246	−	0.0723845i
$897$	−5.70368	+	4.14396i	−0.190440	+	0.138363i
$898$	−0.836413	−	7.95794i	−0.0279115	−	0.265560i
$899$	28.0198	+	48.5317i	0.934512	+	1.61862i
$900$	−24.2619	+	26.9456i	−0.808730	+	0.898186i
$901$	−10.8277	+	18.7542i	−0.360724	+	0.624792i
$902$	2.49397	+	4.53792i	0.0830402	+	0.151096i
$903$	2.29403	−	9.95357i	0.0763405	−	0.331234i
$904$	−3.51608	−	10.8214i	−0.116943	−	0.359913i
$905$	8.11154	−	14.0496i	0.269637	−	0.467025i
$906$	−4.55439	−	2.02775i	−0.151310	−	0.0673673i
$907$	4.21071	+	1.87473i	0.139814	+	0.0622493i	0.475451	−	0.879742i	$-0.342285\pi$
$907$	4.21071	+	1.87473i	0.139814	+	0.0622493i	−0.335637	+	0.941991i	$0.608951\pi$
$908$	−10.8062	−	2.29693i	−0.358616	−	0.0762262i
$909$	−1.04940	+	3.22973i	−0.0348065	+	0.107123i
$910$	−28.0426	+	24.3956i	−0.929604	+	0.808705i
$911$	23.7664			0.787415			0.393707	−	0.919236i	$-0.371192\pi$
$911$	23.7664			0.787415			0.393707	+	0.919236i	$0.371192\pi$
$912$	−1.29637	+	0.577180i	−0.0429270	+	0.0191123i
$913$	−0.271075	+	2.57910i	−0.00897126	+	0.0853559i
$914$	7.74973	+	3.45040i	0.256338	+	0.114129i
$915$	15.9550	+	3.39133i	0.527454	+	0.112114i
$916$	8.10451			0.267780
$917$	−21.6839	+	28.7979i	−0.716064	+	0.950991i
$918$	−2.67948	+	8.24660i	−0.0884361	+	0.272178i
$919$	−27.0238	+	12.0318i	−0.891434	+	0.396892i	−0.800758	−	0.598988i	$-0.795570\pi$
$919$	−27.0238	+	12.0318i	−0.891434	+	0.396892i	−0.0906765	+	0.995880i	$0.528903\pi$
$920$	16.7202	−	18.5696i	0.551248	−	0.612223i
$921$	0.581357	−	0.123571i	0.0191564	−	0.00407181i
$922$	−13.0495	−	14.4929i	−0.429763	−	0.477300i
$923$	−9.42072	+	28.9940i	−0.310087	+	0.954349i
$924$	0.661769	−	0.367149i	0.0217706	−	0.0120783i
$925$	15.0253	+	46.2430i	0.494028	+	1.52046i
$926$	8.12524	−	3.61759i	0.267012	−	0.118881i
$927$	−28.2448	+	6.00362i	−0.927682	+	0.197185i
$928$	9.75484	+	4.34314i	0.320218	+	0.142570i
$929$	−3.59283	+	6.22297i	−0.117877	+	0.204169i	−0.918926	−	0.394430i	$-0.870942\pi$
$929$	−3.59283	+	6.22297i	−0.117877	+	0.204169i	0.801049	+	0.598599i	$0.204276\pi$
$930$	−2.40738	−	7.40917i	−0.0789412	−	0.242956i
$931$	27.6528	−	4.89733i	0.906283	−	0.160503i
$932$	−1.85083	−	1.34471i	−0.0606261	−	0.0440474i
$933$	8.25690	−	3.67621i	0.270319	−	0.120354i
$934$	−8.91855	−	15.4474i	−0.291824	−	0.505454i
$935$	1.48026	−	14.0837i	0.0484097	−	0.460588i
$936$	−6.43955	−	7.15185i	−0.210483	−	0.233765i
$937$	10.2939	+	31.6814i	0.336287	+	1.03499i	0.966085	+	0.258226i	$0.0831379\pi$
$937$	10.2939	+	31.6814i	0.336287	+	1.03499i	−0.629797	+	0.776760i	$0.716862\pi$
$938$	−31.5482	−	3.86162i	−1.03009	−	0.126086i
$939$	3.10813	−	2.25819i	0.101430	−	0.0736932i
$940$	−17.5995	+	30.4833i	−0.574034	+	0.994256i
$941$	8.31966	−	9.23992i	0.271213	−	0.301213i	−0.592117	−	0.805852i	$-0.701708\pi$
$941$	8.31966	−	9.23992i	0.271213	−	0.301213i	0.863330	+	0.504639i	$0.168374\pi$
$942$	0.425950	+	0.737767i	0.0138782	+	0.0240378i
$943$	−31.3095	+	21.7546i	−1.01958	+	0.708427i
$944$	2.98119			0.0970295
$945$	−13.2413	−	18.8955i	−0.430740	−	0.614669i
$946$	−8.82664			−0.286979
$947$	−4.80279	−	45.6955i	−0.156070	−	1.48490i	−0.739729	−	0.672904i	$-0.765046\pi$
$947$	−4.80279	−	45.6955i	−0.156070	−	1.48490i	0.583660	−	0.811998i	$-0.301620\pi$
$948$	2.07485	+	0.923781i	0.0673878	+	0.0300030i
$949$	−1.12384	+	1.24815i	−0.0364815	+	0.0405168i
$950$	−33.8572	−	37.6022i	−1.09847	−	1.21998i
$951$	4.88870	+	3.55185i	0.158527	+	0.115177i
$952$	2.47941	−	10.7579i	0.0803583	−	0.348667i
$953$	6.80559	+	4.94455i	0.220455	+	0.160170i	0.692531	−	0.721388i	$-0.256495\pi$
$953$	6.80559	+	4.94455i	0.220455	+	0.160170i	−0.472077	+	0.881558i	$0.656495\pi$
$954$	13.6301	−	6.06852i	0.441292	−	0.196476i
$955$	31.1348	+	13.8621i	1.00750	+	0.448567i
$956$	−5.05162	+	5.61039i	−0.163381	+	0.181453i
$957$	−1.52718	+	2.64514i	−0.0493666	+	0.0855054i
$958$	12.2731	−	8.91690i	0.396525	−	0.288092i
$959$	−9.89397	−	5.93985i	−0.319493	−	0.191808i
$960$	−1.20093	−	0.872523i	−0.0387597	−	0.0281606i
$961$	3.38158	+	0.718777i	0.109083	+	0.0231863i
$962$	−12.6234	+	2.68318i	−0.406994	+	0.0865092i
$963$	−31.2115	+	6.63420i	−1.00578	+	0.213784i
$964$	6.30225	+	6.99935i	0.202982	+	0.225434i
$965$	−25.5450	+	78.6196i	−0.822324	+	2.53085i
$966$	3.19776	+	4.56323i	0.102886	+	0.146820i
$967$	2.36112	+	1.71546i	0.0759285	+	0.0551653i	0.625102	−	0.780543i	$-0.285057\pi$
$967$	2.36112	+	1.71546i	0.0759285	+	0.0551653i	−0.549173	+	0.835708i	$0.685057\pi$
$968$	6.92285	+	7.68860i	0.222509	+	0.247121i
$969$	−5.40936	−	2.40840i	−0.173774	−	0.0773690i
$970$	−0.955798	−	1.65549i	−0.0306888	−	0.0531546i
$971$	53.0677	+	11.2799i	1.70302	+	0.361989i	0.953826	−	0.300359i	$-0.0971064\pi$
$971$	53.0677	+	11.2799i	1.70302	+	0.361989i	0.749197	+	0.662347i	$0.230440\pi$
$972$	7.30116	−	5.30461i	0.234185	−	0.170145i
$973$	−6.69301	−	34.3637i	−0.214568	−	1.10165i
$974$	−2.43481	−	1.76900i	−0.0780165	−	0.0566823i
$975$	−7.46685	+	12.9330i	−0.239131	+	0.414187i
$976$	1.14860	−	10.9282i	0.0367657	−	0.349802i
$977$	8.96223	−	1.90498i	0.286727	−	0.0609457i	−0.0623028	−	0.998057i	$-0.519844\pi$
$977$	8.96223	−	1.90498i	0.286727	−	0.0609457i	0.349030	+	0.937112i	$0.386511\pi$
$978$	−4.67607	−	0.993929i	−0.149524	−	0.0317824i
$979$	−6.67037	+	4.84630i	−0.213186	+	0.154889i
$980$	18.9000	+	22.4898i	0.603737	+	0.718411i
$981$	−12.2727			−0.391838
$982$	11.0661	+	2.35218i	0.353134	+	0.0750610i
$983$	−2.97108	−	5.14605i	−0.0947626	−	0.164134i	0.814747	−	0.579817i	$-0.196876\pi$
$983$	−2.97108	−	5.14605i	−0.0947626	−	0.164134i	−0.909510	+	0.415683i	$0.863543\pi$
$984$	1.47969	+	1.71469i	0.0471707	+	0.0546622i
$985$	49.0063	−	84.8814i	1.56147	−	2.70455i
$986$	13.7686	+	42.3755i	0.438482	+	1.34951i
$987$	−5.74253	−	5.35097i	−0.182787	−	0.170323i
$988$	10.8650	−	7.89386i	0.345661	−	0.251137i
$989$	−6.79320	−	64.6330i	−0.216011	−	2.05521i
$990$	−6.52856	+	7.25070i	−0.207491	+	0.230442i
$991$	−9.48874	+	2.01689i	−0.301420	+	0.0640687i	−0.356139	−	0.934433i	$-0.615907\pi$
$991$	−9.48874	+	2.01689i	−0.301420	+	0.0640687i	0.0547192	+	0.998502i	$0.482574\pi$
$992$	−4.79441	+	2.13461i	−0.152223	+	0.0677738i
$993$	−6.29753			−0.199846
$994$	22.7852	+	7.83602i	0.722703	+	0.248543i
$995$	−26.0691	−	18.9403i	−0.826445	−	0.600447i
$996$	0.118566	+	1.12808i	0.00375692	+	0.0357447i
$997$	−15.7403	+	17.4814i	−0.498500	+	0.553640i	−0.938913	−	0.344155i	$-0.888165\pi$
$997$	−15.7403	+	17.4814i	−0.498500	+	0.553640i	0.440413	+	0.897795i	$0.354832\pi$
$998$	−8.84460	−	15.3193i	−0.279971	−	0.484924i
$999$	−0.837397	−	7.96730i	−0.0264941	−	0.252074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.s.a.387.8	yes	112
7.4	even	3	inner	574.2.s.a.305.8	yes	112
41.16	even	5	inner	574.2.s.a.303.8	yes	112
287.221	even	15	inner	574.2.s.a.221.8	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.s.a.221.8	✓	112	287.221	even	15	inner
574.2.s.a.303.8	yes	112	41.16	even	5	inner
574.2.s.a.305.8	yes	112	7.4	even	3	inner
574.2.s.a.387.8	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.s (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.176856 + 0.306324i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.438674 + 4.17371i) q^{5} +(0.109303 + 0.336401i) q^{6} +(-2.31354 + 1.28355i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43744 - 2.48973i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.176856 + 0.306324i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.438674 + 4.17371i) q^{5} +(0.109303 + 0.336401i) q^{6} +(-2.31354 + 1.28355i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.43744 - 2.48973i) q^{9} +(-0.438674 + 4.17371i) q^{10} +(-0.0845303 + 0.804252i) q^{11} +(0.0369731 + 0.351775i) q^{12} +(-1.03444 - 3.18369i) q^{13} +(-2.52985 + 0.774492i) q^{14} +(-1.20093 + 0.872523i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.436167 + 4.14985i) q^{17} +(1.92368 - 2.13646i) q^{18} +(2.68447 + 2.98140i) q^{19} +(-1.29685 + 3.99130i) q^{20} +(-0.802349 - 0.481690i) q^{21} +(-0.249897 + 0.769103i) q^{22} +(-5.82407 - 1.23795i) q^{23} +(-0.0369731 + 0.351775i) q^{24} +(-12.3367 + 2.62224i) q^{25} +(-0.349912 - 3.32919i) q^{26} +2.07802 q^{27} +(-2.63560 + 0.231581i) q^{28} +(8.63869 - 6.27637i) q^{29} +(-1.35609 + 0.603770i) q^{30} +(-0.548579 + 5.21938i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.261312 + 0.116343i) q^{33} +(-1.28944 + 3.96848i) q^{34} +(-6.37207 - 9.09300i) q^{35} +(2.32583 - 1.68982i) q^{36} +(-0.402978 - 3.83408i) q^{37} +(2.00594 + 3.47438i) q^{38} +(0.792292 - 0.879930i) q^{39} +(-2.09835 + 3.63445i) q^{40} +(4.38385 - 4.66710i) q^{41} +(-0.684667 - 0.637982i) q^{42} +(3.37287 + 10.3806i) q^{43} +(-0.404341 + 0.700340i) q^{44} +(11.0220 + 4.90729i) q^{45} +(-5.43942 - 2.42179i) q^{46} +(8.20405 + 1.74382i) q^{47} +(-0.109303 + 0.336401i) q^{48} +(3.70498 - 5.93912i) q^{49} -12.6123 q^{50} +(-1.34834 + 0.600319i) q^{51} +(0.349912 - 3.32919i) q^{52} +(4.74110 + 2.11087i) q^{53} +(2.03261 + 0.432045i) q^{54} -3.39380 q^{55} +(-2.62615 - 0.321451i) q^{56} +(-0.438510 + 1.34960i) q^{57} +(9.75484 - 4.34314i) q^{58} +(1.99481 - 2.21546i) q^{59} +(-1.45199 + 0.308629i) q^{60} +(-7.35265 - 8.16594i) q^{61} +(-1.62176 + 4.99127i) q^{62} +(-0.129894 + 7.60513i) q^{63} +(0.309017 + 0.951057i) q^{64} +(12.8340 - 5.71406i) q^{65} +(-0.279791 + 0.0594713i) q^{66} +(10.9745 + 4.88617i) q^{67} +(-2.08635 + 3.61367i) q^{68} +(-0.650812 - 2.00299i) q^{69} +(-4.34228 - 10.2191i) q^{70} +(-7.36776 - 5.35299i) q^{71} +(2.62634 - 1.16932i) q^{72} +(-0.250865 - 0.434511i) q^{73} +(0.402978 - 3.83408i) q^{74} +(-2.98507 - 3.31526i) q^{75} +(1.23974 + 3.81552i) q^{76} +(-0.836736 - 1.96917i) q^{77} +(0.957927 - 0.695975i) q^{78} +(3.21052 - 5.56078i) q^{79} +(-2.80814 + 3.11875i) q^{80} +(-3.94482 - 6.83263i) q^{81} +(5.25840 - 3.65366i) q^{82} +3.20683 q^{83} +(-0.537061 - 0.766391i) q^{84} -17.5116 q^{85} +(1.14091 + 10.8551i) q^{86} +(3.45041 + 1.53622i) q^{87} +(-0.541114 + 0.600968i) q^{88} +(6.82221 + 7.57683i) q^{89} +(9.76081 + 7.09165i) q^{90} +(6.47966 + 6.03784i) q^{91} +(-4.81704 - 3.49978i) q^{92} +(-1.69584 + 0.755038i) q^{93} +(7.66221 + 3.41144i) q^{94} +(-11.2659 + 12.5120i) q^{95} +(-0.176856 + 0.306324i) q^{96} +(-0.368507 + 0.267736i) q^{97} +(4.85883 - 5.03903i) q^{98} +(1.88086 + 1.36652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Introduction

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