LMFDB - Embedded newform 471.2.s.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(2,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 47]))

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

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

chi := DirichletCharacter("471.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.s (of order $52$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$50$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	471.2
Dual form			471.2.s.a.236.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87532 + 0.343664i) q^{2} +(-0.909746 - 1.47389i) q^{3} +(1.52867 - 0.579748i) q^{4} +(-0.603303 - 1.93607i) q^{5} +(2.21258 + 2.45137i) q^{6} +(-3.07153 + 1.38238i) q^{7} +(0.595672 - 0.360097i) q^{8} +(-1.34473 + 2.68174i) q^{9} +O(q^{10})$	\(q+(-1.87532 + 0.343664i) q^{2} +(-0.909746 - 1.47389i) q^{3} +(1.52867 - 0.579748i) q^{4} +(-0.603303 - 1.93607i) q^{5} +(2.21258 + 2.45137i) q^{6} +(-3.07153 + 1.38238i) q^{7} +(0.595672 - 0.360097i) q^{8} +(-1.34473 + 2.68174i) q^{9} +(1.79674 + 3.42340i) q^{10} +(-1.91150 + 1.31941i) q^{11} +(-2.24519 - 1.72567i) q^{12} +4.46047i q^{13} +(5.28500 - 3.64798i) q^{14} +(-2.30470 + 2.65053i) q^{15} +(-3.44082 + 3.04830i) q^{16} +(2.85818 - 5.44581i) q^{17} +(1.60017 - 5.49124i) q^{18} +(-0.221092 - 0.0544943i) q^{19} +(-2.04468 - 2.60984i) q^{20} +(4.83179 + 3.26949i) q^{21} +(3.13122 - 3.13122i) q^{22} +(-0.0704760 + 1.16511i) q^{23} +(-1.07265 - 0.550362i) q^{24} +(0.730541 - 0.504256i) q^{25} +(-1.53291 - 8.36479i) q^{26} +(5.17595 - 0.457715i) q^{27} +(-3.89391 + 3.89391i) q^{28} +(-2.77905 - 0.865987i) q^{29} +(3.41115 - 5.76263i) q^{30} +(-1.32106 - 0.160405i) q^{31} +(4.54649 - 5.80316i) q^{32} +(3.68364 + 1.61701i) q^{33} +(-3.48846 + 11.1949i) q^{34} +(4.52944 + 5.11268i) q^{35} +(-0.500910 + 4.87909i) q^{36} +(10.0608 - 5.28029i) q^{37} +(0.433345 + 0.0262126i) q^{38} +(6.57426 - 4.05790i) q^{39} +(-1.05654 - 0.936014i) q^{40} +(0.385384 + 6.37115i) q^{41} +(-10.1847 - 4.47081i) q^{42} +(5.84063 + 2.62866i) q^{43} +(-2.15712 + 3.12513i) q^{44} +(6.00330 + 0.985579i) q^{45} +(-0.268241 - 2.20916i) q^{46} +(-2.99640 + 5.70916i) q^{47} +(7.62314 + 2.29822i) q^{48} +(2.88144 - 3.25247i) q^{49} +(-1.19670 + 1.19670i) q^{50} +(-10.6268 + 0.741646i) q^{51} +(2.58595 + 6.81859i) q^{52} +(4.02049 - 2.43047i) q^{53} +(-9.54924 + 2.63715i) q^{54} +(3.70768 + 2.90478i) q^{55} +(-1.33183 + 1.92949i) q^{56} +(0.120819 + 0.375442i) q^{57} +(5.50920 + 0.668939i) q^{58} +(6.08120 + 3.67621i) q^{59} +(-1.98649 + 5.38793i) q^{60} +(0.944360 - 0.570885i) q^{61} +(2.53252 - 0.153190i) q^{62} +(0.423176 - 10.0959i) q^{63} +(-2.25919 + 4.30454i) q^{64} +(8.63577 - 2.69102i) q^{65} +(-7.46370 - 1.76647i) q^{66} +(4.73672 + 1.16750i) q^{67} +(1.21202 - 9.98187i) q^{68} +(1.78136 - 0.956077i) q^{69} +(-10.2512 - 8.03129i) q^{70} +(-0.880668 + 3.57301i) q^{71} +(0.164668 + 2.08167i) q^{72} +(4.74354 + 10.5397i) q^{73} +(-17.0524 + 13.3597i) q^{74} +(-1.40783 - 0.617995i) q^{75} +(-0.369570 + 0.0448739i) q^{76} +(4.04728 - 6.69502i) q^{77} +(-10.9343 + 9.86917i) q^{78} +(-1.23874 + 6.75959i) q^{79} +(7.97757 + 4.82261i) q^{80} +(-5.38343 - 7.21240i) q^{81} +(-2.91225 - 11.8155i) q^{82} +(-5.66896 - 7.23590i) q^{83} +(9.28169 + 2.19674i) q^{84} +(-12.2678 - 2.24816i) q^{85} +(-11.8564 - 2.92234i) q^{86} +(1.25186 + 4.88385i) q^{87} +(-0.663510 + 1.47426i) q^{88} +(4.29441 + 0.521436i) q^{89} +(-11.5968 + 0.214847i) q^{90} +(-6.16608 - 13.7005i) q^{91} +(0.567734 + 1.82192i) q^{92} +(0.965406 + 2.09303i) q^{93} +(3.65715 - 11.7362i) q^{94} +(0.0278809 + 0.460926i) q^{95} +(-12.6894 - 1.42164i) q^{96} +(2.56114 + 8.21900i) q^{97} +(-4.28584 + 7.08965i) q^{98} +(-0.967873 - 6.90037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9}+O(q^{10}) $ 1200 * q - 26 * q^3 - 52 * q^4 - 20 * q^6 - 40 * q^7 - 18 * q^9	$ 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9} - 52 q^{10} - 80 q^{12} - 12 q^{15} + 16 q^{16} + 12 q^{18} - 52 q^{19} - 26 q^{21} - 64 q^{22} + 18 q^{24} + 104 q^{25} - 26 q^{27} - 84 q^{28} - 34 q^{30} - 52 q^{31} - 26 q^{33} - 80 q^{34} - 26 q^{36} - 308 q^{37} + 52 q^{39} - 340 q^{40} - 26 q^{42} - 76 q^{43} - 52 q^{45} - 60 q^{46} - 130 q^{48} - 52 q^{49} - 26 q^{51} + 84 q^{52} - 246 q^{54} - 36 q^{55} - 26 q^{57} - 52 q^{58} + 14 q^{60} - 4 q^{61} - 46 q^{63} - 52 q^{64} - 22 q^{66} + 28 q^{67} - 72 q^{69} - 40 q^{70} + 46 q^{72} - 48 q^{73} - 46 q^{75} - 52 q^{76} + 146 q^{78} - 100 q^{79} + 58 q^{81} - 52 q^{82} - 156 q^{84} - 20 q^{85} + 12 q^{87} - 116 q^{88} - 26 q^{90} + 360 q^{91} - 310 q^{93} + 96 q^{94} + 176 q^{96} + 116 q^{97} - 66 q^{99}+O(q^{100}) $ 1200 * q - 26 * q^3 - 52 * q^4 - 20 * q^6 - 40 * q^7 - 18 * q^9 - 52 * q^10 - 80 * q^12 - 12 * q^15 + 16 * q^16 + 12 * q^18 - 52 * q^19 - 26 * q^21 - 64 * q^22 + 18 * q^24 + 104 * q^25 - 26 * q^27 - 84 * q^28 - 34 * q^30 - 52 * q^31 - 26 * q^33 - 80 * q^34 - 26 * q^36 - 308 * q^37 + 52 * q^39 - 340 * q^40 - 26 * q^42 - 76 * q^43 - 52 * q^45 - 60 * q^46 - 130 * q^48 - 52 * q^49 - 26 * q^51 + 84 * q^52 - 246 * q^54 - 36 * q^55 - 26 * q^57 - 52 * q^58 + 14 * q^60 - 4 * q^61 - 46 * q^63 - 52 * q^64 - 22 * q^66 + 28 * q^67 - 72 * q^69 - 40 * q^70 + 46 * q^72 - 48 * q^73 - 46 * q^75 - 52 * q^76 + 146 * q^78 - 100 * q^79 + 58 * q^81 - 52 * q^82 - 156 * q^84 - 20 * q^85 + 12 * q^87 - 116 * q^88 - 26 * q^90 + 360 * q^91 - 310 * q^93 + 96 * q^94 + 176 * q^96 + 116 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$-1$	$e\left(\frac{47}{52}\right)$

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 $

$2$	−1.87532	+	0.343664i	−1.32605	+	0.243007i	−0.796173	−	0.605069i	$-0.793146\pi$
$2$	−1.87532	+	0.343664i	−1.32605	+	0.243007i	−0.529875	+	0.848076i	$0.677761\pi$
$3$	−0.909746	−	1.47389i	−0.525242	−	0.850953i
$3$	−0.909746	−	1.47389i	−0.525242	−	0.850953i
$4$	1.52867	−	0.579748i	0.764335	−	0.289874i
$5$	−0.603303	−	1.93607i	−0.269805	−	0.865835i	−0.985828	−	0.167758i	$-0.946347\pi$
$5$	−0.603303	−	1.93607i	−0.269805	−	0.865835i	0.716023	−	0.698077i	$-0.245961\pi$
$6$	2.21258	+	2.45137i	0.903284	+	1.00077i
$7$	−3.07153	+	1.38238i	−1.16093	+	0.522491i	−0.896991	−	0.442049i	$-0.854252\pi$
$7$	−3.07153	+	1.38238i	−1.16093	+	0.522491i	−0.263937	+	0.964540i	$0.585021\pi$
$8$	0.595672	−	0.360097i	0.210602	−	0.127313i
$9$	−1.34473	+	2.68174i	−0.448242	+	0.893912i
$10$	1.79674	+	3.42340i	0.568179	+	1.08257i
$11$	−1.91150	+	1.31941i	−0.576337	+	0.397817i	−0.820271	−	0.571975i	$-0.806177\pi$
$11$	−1.91150	+	1.31941i	−0.576337	+	0.397817i	0.243934	+	0.969792i	$0.421562\pi$
$12$	−2.24519	−	1.72567i	−0.648130	−	0.498159i
$13$			4.46047i			1.23711i	0.785740	+	0.618556i	$0.212282\pi$
$13$			4.46047i			1.23711i	−0.785740	+	0.618556i	$0.787718\pi$
$14$	5.28500	−	3.64798i	1.41248	−	0.974962i
$15$	−2.30470	+	2.65053i	−0.595072	+	0.684364i
$16$	−3.44082	+	3.04830i	−0.860205	+	0.762075i
$17$	2.85818	−	5.44581i	0.693211	−	1.32080i	−0.243227	−	0.969969i	$-0.578206\pi$
$17$	2.85818	−	5.44581i	0.693211	−	1.32080i	0.936438	−	0.350834i	$-0.114102\pi$
$18$	1.60017	−	5.49124i	0.377163	−	1.29430i
$19$	−0.221092	−	0.0544943i	−0.0507220	−	0.0125019i	0.213873	−	0.976861i	$-0.431392\pi$
$19$	−0.221092	−	0.0544943i	−0.0507220	−	0.0125019i	−0.264595	+	0.964360i	$0.585238\pi$
$20$	−2.04468	−	2.60984i	−0.457204	−	0.583578i
$21$	4.83179	+	3.26949i	1.05438	+	0.713461i
$22$	3.13122	−	3.13122i	0.667579	−	0.667579i
$23$	−0.0704760	+	1.16511i	−0.0146953	+	0.242942i	0.983409	+	0.181401i	$0.0580631\pi$
$23$	−0.0704760	+	1.16511i	−0.0146953	+	0.242942i	−0.998105	+	0.0615411i	$0.980398\pi$
$24$	−1.07265	−	0.550362i	−0.218955	−	0.112342i
$25$	0.730541	−	0.504256i	0.146108	−	0.100851i
$26$	−1.53291	−	8.36479i	−0.300627	−	1.64047i
$27$	5.17595	−	0.457715i	0.996113	−	0.0880874i
$28$	−3.89391	+	3.89391i	−0.735881	+	0.735881i
$29$	−2.77905	−	0.865987i	−0.516057	−	0.160810i	0.0284033	−	0.999597i	$-0.490958\pi$
$29$	−2.77905	−	0.865987i	−0.516057	−	0.160810i	−0.544460	+	0.838787i	$0.683265\pi$
$30$	3.41115	−	5.76263i	0.622789	−	1.05211i
$31$	−1.32106	−	0.160405i	−0.237269	−	0.0288097i	0.00103840	−	0.999999i	$-0.499669\pi$
$31$	−1.32106	−	0.160405i	−0.237269	−	0.0288097i	−0.238307	+	0.971190i	$0.576593\pi$
$32$	4.54649	−	5.80316i	0.803713	−	1.02586i
$33$	3.68364	+	1.61701i	0.641240	+	0.281486i
$34$	−3.48846	+	11.1949i	−0.598266	+	1.91990i
$35$	4.52944	+	5.11268i	0.765616	+	0.864201i
$36$	−0.500910	+	4.87909i	−0.0834850	+	0.813182i
$37$	10.0608	−	5.28029i	1.65398	−	0.868074i	0.660918	−	0.750458i	$-0.270167\pi$
$37$	10.0608	−	5.28029i	1.65398	−	0.868074i	0.993059	−	0.117617i	$-0.0375254\pi$
$38$	0.433345	+	0.0262126i	0.0702979	+	0.00425224i
$39$	6.57426	−	4.05790i	1.05272	−	0.649783i
$40$	−1.05654	−	0.936014i	−0.167054	−	0.147997i
$41$	0.385384	+	6.37115i	0.0601868	+	0.995007i	0.895452	+	0.445159i	$0.146853\pi$
$41$	0.385384	+	6.37115i	0.0601868	+	0.995007i	−0.835265	+	0.549848i	$0.814686\pi$
$42$	−10.1847	−	4.47081i	−1.57154	−	0.689860i
$43$	5.84063	+	2.62866i	0.890688	+	0.400866i	0.803486	−	0.595324i	$-0.202976\pi$
$43$	5.84063	+	2.62866i	0.890688	+	0.400866i	0.0872028	+	0.996191i	$0.472207\pi$
$44$	−2.15712	+	3.12513i	−0.325198	+	0.471130i
$45$	6.00330	+	0.985579i	0.894919	+	0.146921i
$46$	−0.268241	−	2.20916i	−0.0395500	−	0.325723i
$47$	−2.99640	+	5.70916i	−0.437069	+	0.832766i	0.562911	+	0.826517i	$0.309681\pi$
$47$	−2.99640	+	5.70916i	−0.437069	+	0.832766i	−0.999980	+	0.00624862i	$0.998011\pi$
$48$	7.62314	+	2.29822i	1.10031	+	0.331720i
$49$	2.88144	−	3.25247i	0.411634	−	0.464638i
$50$	−1.19670	+	1.19670i	−0.169239	+	0.169239i
$51$	−10.6268	+	0.741646i	−1.48804	+	0.103851i
$52$	2.58595	+	6.81859i	0.358607	+	0.945568i
$53$	4.02049	−	2.43047i	0.552257	−	0.333851i	−0.213539	−	0.976935i	$-0.568499\pi$
$53$	4.02049	−	2.43047i	0.552257	−	0.333851i	0.765796	+	0.643083i	$0.222345\pi$
$54$	−9.54924	+	2.63715i	−1.29949	+	0.358871i
$55$	3.70768	+	2.90478i	0.499943	+	0.391680i
$56$	−1.33183	+	1.92949i	−0.177974	+	0.257839i
$57$	0.120819	+	0.375442i	0.0160028	+	0.0497286i
$58$	5.50920	+	0.668939i	0.723394	+	0.0878359i
$59$	6.08120	+	3.67621i	0.791704	+	0.478602i	0.854517	−	0.519423i	$-0.173853\pi$
$59$	6.08120	+	3.67621i	0.791704	+	0.478602i	−0.0628128	+	0.998025i	$0.520007\pi$
$60$	−1.98649	+	5.38793i	−0.256455	+	0.695579i
$61$	0.944360	−	0.570885i	0.120913	−	0.0730944i	−0.455589	−	0.890190i	$-0.650571\pi$
$61$	0.944360	−	0.570885i	0.120913	−	0.0730944i	0.576502	+	0.817096i	$0.304417\pi$
$62$	2.53252	−	0.153190i	0.321631	−	0.0194551i
$63$	0.423176	−	10.0959i	0.0533152	−	1.27197i
$64$	−2.25919	+	4.30454i	−0.282399	+	0.538067i
$65$	8.63577	−	2.69102i	1.07114	−	0.333779i
$66$	−7.46370	−	1.76647i	−0.918718	−	0.217438i
$67$	4.73672	+	1.16750i	0.578683	+	0.142633i	0.517784	−	0.855511i	$-0.326757\pi$
$67$	4.73672	+	1.16750i	0.578683	+	0.142633i	0.0608989	+	0.998144i	$0.480603\pi$
$68$	1.21202	−	9.98187i	0.146979	−	1.21048i
$69$	1.78136	−	0.956077i	0.214450	−	0.115098i
$70$	−10.2512	−	8.03129i	−1.22525	−	0.959922i
$71$	−0.880668	+	3.57301i	−0.104516	+	0.424038i	−0.999768	−	0.0215211i	$-0.993149\pi$
$71$	−0.880668	+	3.57301i	−0.104516	+	0.424038i	0.895252	+	0.445560i	$0.146995\pi$
$72$	0.164668	+	2.08167i	0.0194063	+	0.245327i
$73$	4.74354	+	10.5397i	0.555190	+	1.23358i	0.949258	+	0.314499i	$0.101837\pi$
$73$	4.74354	+	10.5397i	0.555190	+	1.23358i	−0.394068	+	0.919081i	$0.628933\pi$
$74$	−17.0524	+	13.3597i	−1.98231	+	1.55304i
$75$	−1.40783	−	0.617995i	−0.162562	−	0.0713599i
$76$	−0.369570	+	0.0448739i	−0.0423926	+	0.00514739i
$77$	4.04728	−	6.69502i	0.461230	−	0.762968i
$78$	−10.9343	+	9.86917i	−1.23806	+	1.11746i
$79$	−1.23874	+	6.75959i	−0.139369	+	0.760514i	0.837461	+	0.546497i	$0.184039\pi$
$79$	−1.23874	+	6.75959i	−0.139369	+	0.760514i	−0.976830	+	0.214016i	$0.931345\pi$
$80$	7.97757	+	4.82261i	0.891919	+	0.539184i
$81$	−5.38343	−	7.21240i	−0.598158	−	0.801378i
$82$	−2.91225	−	11.8155i	−0.321605	−	1.30480i
$83$	−5.66896	−	7.23590i	−0.622249	−	0.794243i	0.368546	−	0.929609i	$-0.379856\pi$
$83$	−5.66896	−	7.23590i	−0.622249	−	0.794243i	−0.990796	+	0.135367i	$0.956779\pi$
$84$	9.28169	+	2.19674i	1.01272	+	0.239685i
$85$	−12.2678	−	2.24816i	−1.33063	−	0.243847i
$86$	−11.8564	−	2.92234i	−1.27851	−	0.315124i
$87$	1.25186	+	4.88385i	0.134213	+	0.523604i
$88$	−0.663510	+	1.47426i	−0.0707304	+	0.157157i
$89$	4.29441	+	0.521436i	0.455207	+	0.0552721i	0.344929	−	0.938629i	$-0.387903\pi$
$89$	4.29441	+	0.521436i	0.455207	+	0.0552721i	0.110277	+	0.993901i	$0.464826\pi$
$90$	−11.5968	+	0.214847i	−1.22241	+	0.0226469i
$91$	−6.16608	−	13.7005i	−0.646380	−	1.43620i
$92$	0.567734	+	1.82192i	0.0591903	+	0.189948i
$93$	0.965406	+	2.09303i	0.100108	+	0.217037i
$94$	3.65715	−	11.7362i	0.377207	−	1.21050i
$95$	0.0278809	+	0.460926i	0.00286052	+	0.0472900i
$96$	−12.6894	−	1.42164i	−1.29511	−	0.145095i
$97$	2.56114	+	8.21900i	0.260045	+	0.834513i	0.988736	+	0.149671i	$0.0478213\pi$
$97$	2.56114	+	8.21900i	0.260045	+	0.834513i	−0.728691	+	0.684843i	$0.759871\pi$
$98$	−4.28584	+	7.08965i	−0.432936	+	0.716163i
$99$	−0.967873	−	6.90037i	−0.0972749	−	0.693513i
$100$	0.824414	−	1.19437i	0.0824414	−	0.119437i
$101$	−7.58132	−	5.23301i	−0.754369	−	0.520704i	0.127706	−	0.991812i	$-0.459239\pi$
$101$	−7.58132	−	5.23301i	−0.754369	−	0.520704i	−0.882075	+	0.471109i	$0.843854\pi$
$102$	19.6737	−	5.04286i	1.94798	−	0.499317i
$103$	−9.92496	−	12.6683i	−0.977935	−	1.24824i	−0.968687	−	0.248285i	$-0.920133\pi$
$103$	−9.92496	−	12.6683i	−0.977935	−	1.24824i	−0.00924831	−	0.999957i	$-0.502944\pi$
$104$	1.60620	+	2.65698i	0.157501	+	0.260538i
$105$	3.41491	−	11.3272i	0.333261	−	1.10542i
$106$	−6.70443	+	5.93960i	−0.651192	+	0.576905i
$107$	12.3990	+	12.3990i	1.19865	+	1.19865i	0.974570	+	0.224083i	$0.0719388\pi$
$107$	12.3990	+	12.3990i	1.19865	+	1.19865i	0.224083	+	0.974570i	$0.428061\pi$
$108$	7.64696	−	3.70044i	0.735829	−	0.356075i
$109$	0.880373	+	2.32135i	0.0843244	+	0.222345i	0.970546	−	0.240917i	$-0.0774481\pi$
$109$	0.880373	+	2.32135i	0.0843244	+	0.222345i	−0.886221	+	0.463262i	$0.846679\pi$
$110$	−7.95133	−	4.17318i	−0.758129	−	0.397897i
$111$	−16.9353	−	10.0248i	−1.60743	−	0.951508i
$112$	6.35465	−	14.1195i	0.600458	−	1.33416i
$113$	−9.70011	−	6.69551i	−0.912510	−	0.629860i	0.0165204	−	0.999864i	$-0.494741\pi$
$113$	−9.70011	−	6.69551i	−0.912510	−	0.629860i	−0.929030	+	0.370003i	$0.879357\pi$
$114$	−0.355599	−	0.662552i	−0.0333049	−	0.0620537i
$115$	2.29824	−	0.566466i	0.214312	−	0.0528232i
$116$	−4.75030	+	0.287340i	−0.441055	+	0.0266789i
$117$	−11.9618	−	5.99811i	−1.10587	−	0.554526i
$118$	−12.6675	−	4.80416i	−1.16614	−	0.442259i
$119$	−1.25079	+	20.6780i	−0.114660	+	1.89555i
$120$	−0.418401	+	2.40876i	−0.0381946	+	0.219889i
$121$	−1.98768	+	5.24109i	−0.180698	+	0.476462i
$122$	−1.57478	+	1.39513i	−0.142574	+	0.126309i
$123$	9.03980	−	6.36415i	0.815092	−	0.573836i
$124$	−2.11245	+	0.520673i	−0.189704	+	0.0467578i
$125$	−9.39861	−	7.36334i	−0.840637	−	0.658597i
$126$	2.67603	+	19.0785i	0.238400	+	1.69965i
$127$	12.1436	−	1.47450i	1.07757	−	0.130841i	0.437547	−	0.899196i	$-0.355847\pi$
$127$	12.1436	−	1.47450i	1.07757	−	0.130841i	0.640024	+	0.768355i	$0.278924\pi$
$128$	−1.62903	+	5.22774i	−0.143987	+	0.462072i
$129$	−1.43913	−	10.9999i	−0.126708	−	0.968486i
$130$	−15.2700	+	8.01431i	−1.33927	+	0.702901i
$131$	−10.9503	+	2.00671i	−0.956730	+	0.175327i	−0.635867	−	0.771799i	$-0.719357\pi$
$131$	−10.9503	+	2.00671i	−0.956730	+	0.175327i	−0.320863	+	0.947126i	$0.603973\pi$
$132$	6.56853	+	0.336294i	0.571717	+	0.0292706i
$133$	0.754422	−	0.138253i	0.0654167	−	0.0119881i
$134$	−9.28408	−	0.561583i	−0.802022	−	0.0485134i
$135$	−4.00883	−	9.74485i	−0.345025	−	0.838703i
$136$	−0.258477	−	4.27314i	−0.0221643	−	0.366419i
$137$	13.0984	−	10.2620i	1.11908	−	0.876740i	0.125748	−	0.992062i	$-0.459867\pi$
$137$	13.0984	−	10.2620i	1.11908	−	0.876740i	0.993328	+	0.115322i	$0.0367900\pi$
$138$	−3.01204	+	2.40514i	−0.256402	+	0.204739i
$139$	16.0571	+	9.70686i	1.36195	+	0.823325i	0.994298	−	0.106640i	$-0.0340093\pi$
$139$	16.0571	+	9.70686i	1.36195	+	0.823325i	0.367648	+	0.929965i	$0.380163\pi$
$140$	9.88809	+	5.18967i	0.835696	+	0.438607i
$141$	11.1406	−	0.777510i	0.938212	−	0.0654782i
$142$	0.423614	−	7.00318i	0.0355489	−	0.587693i
$143$	−5.88519	−	8.52617i	−0.492145	−	0.712994i
$144$	−3.54778	−	13.3265i	−0.295648	−	1.11054i
$145$			5.90288i			0.490207i
$146$	−12.5178	−	18.1351i	−1.03598	−	1.50087i
$147$	−7.41517	−	1.28801i	−0.611593	−	0.106233i
$148$	12.3183	−	13.9045i	1.01256	−	1.14294i
$149$	12.0852	+	19.9914i	0.990062	+	1.63776i	0.743618	+	0.668605i	$0.233108\pi$
$149$	12.0852	+	19.9914i	0.990062	+	1.63776i	0.246444	+	0.969157i	$0.420738\pi$
$150$	2.85250	+	0.675116i	0.232906	+	0.0551230i
$151$	−2.37338	−	0.434938i	−0.193143	−	0.0353947i	0.0828127	−	0.996565i	$-0.473610\pi$
$151$	−2.37338	−	0.434938i	−0.193143	−	0.0353947i	−0.275956	+	0.961170i	$0.588994\pi$
$152$	−0.151322	+	0.0471538i	−0.0122738	+	0.00382468i
$153$	10.7608	+	14.9880i	0.869956	+	1.21171i
$154$	−5.28909	+	13.9462i	−0.426207	+	1.12381i
$155$	0.486442	+	2.65443i	0.0390720	+	0.213209i
$156$	7.69732	−	10.0146i	0.616279	−	0.801809i
$157$	−12.0595	−	3.40133i	−0.962451	−	0.271456i
$157$	−12.0595	−	3.40133i	−0.962451	−	0.271456i
$158$		−	13.1021i		−	1.04235i
$159$	−7.23989	−	3.71467i	−0.574160	−	0.294592i
$160$	−13.9782	−	5.30124i	−1.10507	−	0.419099i
$161$	−1.39415	−	3.67608i	−0.109875	−	0.289716i
$162$	12.5743	+	11.6754i	0.987927	+	0.917309i
$163$	−4.09929	+	22.3691i	−0.321081	+	1.75208i	0.286741	+	0.958008i	$0.407428\pi$
$163$	−4.09929	+	22.3691i	−0.321081	+	1.75208i	−0.607822	+	0.794073i	$0.707957\pi$
$164$	4.28279	+	9.51596i	0.334429	+	0.743072i
$165$	0.908293	−	8.10733i	0.0707105	−	0.631155i
$166$	13.1178	+	11.6214i	1.01814	+	0.901993i
$167$	−4.87838	+	2.56037i	−0.377500	+	0.198127i	−0.642792	−	0.766041i	$-0.722224\pi$
$167$	−4.87838	+	2.56037i	−0.377500	+	0.198127i	0.265292	+	0.964168i	$0.414532\pi$
$168$	4.05550	+	0.207632i	0.312888	+	0.0160192i
$169$	−6.89582			−0.530448
$170$	23.7786			1.82374
$171$	0.443448	−	0.519631i	0.0339113	−	0.0397372i
$172$	10.4524	+	0.632251i	0.796985	+	0.0482087i
$173$	2.30010	+	2.59628i	0.174874	+	0.197392i	0.829412	−	0.558637i	$-0.188676\pi$
$173$	2.30010	+	2.59628i	0.174874	+	0.197392i	−0.654539	+	0.756029i	$0.727137\pi$
$174$	−4.02603	−	8.72855i	−0.305213	−	0.661709i
$175$	−1.54680	+	2.55872i	−0.116927	+	0.193421i
$176$	2.55515	−	10.3667i	0.192602	−	0.781417i
$177$	−0.113997	−	12.3075i	−0.00856852	−	0.925085i
$178$	−8.23257	+	0.497979i	−0.617057	+	0.0373251i
$179$	8.29680	+	8.29680i	0.620132	+	0.620132i	0.945565	−	0.325433i	$-0.105510\pi$
$179$	8.29680	+	8.29680i	0.620132	+	0.620132i	−0.325433	+	0.945565i	$0.605510\pi$
$180$	9.74844	−	1.97377i	0.726606	−	0.147116i
$181$	3.13283	+	17.0953i	0.232861	+	1.27068i	0.867329	+	0.497735i	$0.165835\pi$
$181$	3.13283	+	17.0953i	0.232861	+	1.27068i	−0.634468	+	0.772949i	$0.718781\pi$
$182$	16.2717	+	23.5736i	1.20614	+	1.74739i
$183$	−1.70055	−	0.872526i	−0.125708	−	0.0644989i
$184$	0.377570	+	0.719400i	0.0278349	+	0.0530349i
$185$	−16.2927	−	16.2927i	−1.19786	−	1.19786i
$186$	−2.52974	−	3.59331i	−0.185489	−	0.263474i
$187$	1.72186	+	14.1808i	0.125915	+	1.03700i
$188$	−1.27063	+	10.4646i	−0.0926701	+	0.763207i
$189$	−15.2653	+	8.56103i	−1.11039	+	0.622723i
$190$	−0.210689	−	0.854799i	−0.0152850	−	0.0620137i
$191$	−5.93036	−	1.84798i	−0.429106	−	0.133715i	0.0753404	−	0.997158i	$-0.475996\pi$
$191$	−5.93036	−	1.84798i	−0.429106	−	0.133715i	−0.504446	+	0.863443i	$0.668303\pi$
$192$	8.39972	−	0.586220i	0.606198	−	0.0423068i
$193$	23.7984	+	9.02554i	1.71305	+	0.649673i	0.998741	−	0.0501614i	$-0.0159736\pi$
$193$	23.7984	+	9.02554i	1.71305	+	0.649673i	0.714305	+	0.699834i	$0.246743\pi$
$194$	−7.62753	−	14.5330i	−0.547625	−	1.04341i
$195$	−11.8226	−	10.2801i	−0.846636	−	0.736171i
$196$	2.51915	−	6.64245i	0.179939	−	0.474461i
$197$	−13.0224	+	14.6992i	−0.927804	+	1.04727i	0.0709551	+	0.997480i	$0.477395\pi$
$197$	−13.0224	+	14.6992i	−0.927804	+	1.04727i	−0.998759	+	0.0497951i	$0.984143\pi$
$198$	4.18648	+	12.6077i	0.297520	+	0.895994i
$199$	−2.25717	−	9.15768i	−0.160006	−	0.649171i	−0.995084	−	0.0990384i	$-0.968423\pi$
$199$	−2.25717	−	9.15768i	−0.160006	−	0.649171i	0.835077	−	0.550133i	$-0.185423\pi$
$200$	0.253582	−	0.563437i	0.0179310	−	0.0398410i
$201$	−2.58845	−	8.04355i	−0.182575	−	0.567349i
$202$	16.0158	+	7.20811i	1.12686	+	0.507161i
$203$	9.73305	−	1.18181i	0.683126	−	0.0829466i
$204$	−15.8148	+	7.29457i	−1.10726	+	0.510722i
$205$	12.1025	−	4.58986i	0.845273	−	0.320570i
$206$	22.9661	+	20.3462i	1.60012	+	1.41758i
$207$	−3.02974	−	1.75575i	−0.210581	−	0.122033i
$208$	−13.5969	−	15.3477i	−0.942773	−	1.06417i
$209$	0.494517	−	0.187546i	0.0342065	−	0.0129728i
$210$	−2.51130	+	22.4156i	−0.173296	+	1.54682i
$211$	−19.8040	+	15.5155i	−1.36337	+	1.06813i	−0.373273	+	0.927722i	$0.621764\pi$
$211$	−19.8040	+	15.5155i	−1.36337	+	1.06813i	−0.990094	+	0.140408i	$0.955159\pi$
$212$	4.73694	−	6.04626i	0.325335	−	0.415259i
$213$	6.06742	−	1.95252i	0.415733	−	0.133784i
$214$	−27.5131	−	18.9909i	−1.88075	−	1.29819i
$215$	1.56558	−	12.8937i	0.106772	−	0.879345i
$216$	2.91835	−	2.13649i	0.198569	−	0.145370i
$217$	4.27940	−	1.33352i	0.290505	−	0.0905250i
$218$	−2.44874	−	4.05071i	−0.165850	−	0.274349i
$219$	11.2190	−	16.5799i	0.758110	−	1.12037i
$220$	7.35185	+	2.29093i	0.495661	+	0.154454i
$221$	24.2909	+	12.7488i	1.63398	+	0.857580i
$222$	35.2042	+	12.9795i	2.36275	+	0.871128i
$223$	3.86508	−	1.73953i	0.258825	−	0.116488i	−0.276847	−	0.960914i	$-0.589289\pi$
$223$	3.86508	−	1.73953i	0.258825	−	0.116488i	0.535671	+	0.844427i	$0.320059\pi$
$224$	−5.94247	+	24.1095i	−0.397048	+	1.61089i
$225$	0.369905	+	2.63720i	0.0246603	+	0.175814i
$226$	20.4918	+	9.22260i	1.36309	+	0.613478i
$227$	−5.52654	+	7.05411i	−0.366810	+	0.468198i	−0.934974	−	0.354718i	$-0.884577\pi$
$227$	−5.52654	+	7.05411i	−0.366810	+	0.468198i	0.568164	+	0.822915i	$0.307654\pi$
$228$	0.402354	+	0.503883i	0.0266465	+	0.0333705i
$229$	2.57091	−	14.0290i	0.169890	−	0.927062i	−0.782607	−	0.622516i	$-0.786111\pi$
$229$	2.57091	−	14.0290i	0.169890	−	0.927062i	0.952498	−	0.304546i	$-0.0985048\pi$
$230$	−4.11526	+	1.85213i	−0.271352	+	0.122126i
$231$	−13.5497	+	0.125503i	−0.891507	+	0.00825751i
$232$	−1.96724	+	0.484882i	−0.129156	+	0.0318341i
$233$	−2.97139	−	24.4716i	−0.194662	−	1.60319i	−0.682922	−	0.730491i	$-0.739291\pi$
$233$	−2.97139	−	24.4716i	−0.194662	−	1.60319i	0.488260	−	0.872698i	$-0.337632\pi$
$234$	24.4935	+	7.13750i	1.60119	+	0.466593i
$235$	12.8610	+	2.35687i	0.838962	+	0.153745i
$236$	11.4274	+	2.09415i	0.743861	+	0.136318i
$237$	11.0899	−	4.32374i	0.720364	−	0.280857i
$238$	−4.76068	−	39.2077i	−0.308589	−	2.54146i
$239$	3.65638	−	0.901217i	0.236512	−	0.0582949i	−0.119278	−	0.992861i	$-0.538058\pi$
$239$	3.65638	−	0.901217i	0.236512	−	0.0582949i	0.355790	+	0.934566i	$0.384212\pi$
$240$	−0.149546	−	16.1454i	−0.00965313	−	1.04218i
$241$	24.0729	−	10.8343i	1.55067	−	0.697902i	0.559300	−	0.828965i	$-0.311070\pi$
$241$	24.0729	−	10.8343i	1.55067	−	0.697902i	0.991374	+	0.131063i	$0.0418391\pi$
$242$	1.92636	−	10.5118i	0.123831	−	0.675723i
$243$	−5.73277	+	14.4960i	−0.367757	+	0.929922i
$244$	1.11264	−	1.42019i	0.0712297	−	0.0909181i
$245$	−8.03537	−	3.61643i	−0.513361	−	0.231045i
$246$	−14.7654	+	15.0414i	−0.941404	+	0.959007i
$247$	0.243071	−	0.986176i	0.0154662	−	0.0627489i
$248$	−0.844679	+	0.380159i	−0.0536372	+	0.0241401i
$249$	−5.50763	+	14.9383i	−0.349032	+	0.946675i
$250$	20.1559	+	10.5786i	1.27477	+	0.669050i
$251$	−11.2281	−	3.49882i	−0.708711	−	0.220843i	−0.0781036	−	0.996945i	$-0.524886\pi$
$251$	−11.2281	−	3.49882i	−0.708711	−	0.220843i	−0.630607	+	0.776102i	$0.717194\pi$
$252$	−5.20621	−	15.6787i	−0.327960	−	0.987665i
$253$	−1.40254	−	2.32008i	−0.0881769	−	0.145862i
$254$	−22.2664	+	6.93848i	−1.39712	+	0.435359i
$255$	7.84703	+	20.1267i	0.491400	+	1.26038i
$256$	2.43031	−	20.0154i	0.151894	−	1.25096i
$257$	13.1128	+	9.05109i	0.817952	+	0.564592i	0.901933	−	0.431876i	$-0.142148\pi$
$257$	13.1128	+	9.05109i	0.817952	+	0.564592i	−0.0839808	+	0.996467i	$0.526763\pi$
$258$	6.47909	+	20.1337i	0.403371	+	1.25347i
$259$	−23.6025	+	30.1264i	−1.46659	+	1.87196i
$260$	11.6411	−	9.12024i	0.721952	−	0.565613i
$261$	6.05941	−	6.28817i	0.375068	−	0.389228i
$262$	19.8456	−	7.52643i	1.22606	−	0.464985i
$263$	13.3397	+	15.0574i	0.822558	+	0.928477i	0.998434	−	0.0559358i	$-0.0178142\pi$
$263$	13.3397	+	15.0574i	0.822558	+	0.928477i	−0.175876	+	0.984412i	$0.556276\pi$
$264$	2.77653	−	0.363257i	0.170883	−	0.0223569i
$265$	−7.13113	−	6.31763i	−0.438062	−	0.388089i
$266$	−1.36727	+	0.518536i	−0.0838325	+	0.0317935i
$267$	−3.13828	−	6.80388i	−0.192060	−	0.416391i
$268$	7.91774	−	0.961387i	0.483653	−	0.0587261i
$269$	18.0808	+	8.13752i	1.10241	+	0.496154i	0.878154	−	0.478377i	$-0.158775\pi$
$269$	18.0808	+	8.13752i	1.10241	+	0.496154i	0.224254	+	0.974531i	$0.428006\pi$
$270$	10.8668	+	16.8970i	0.661331	+	1.02832i
$271$	−11.1723	+	24.8238i	−0.678668	+	1.50794i	0.173592	+	0.984818i	$0.444463\pi$
$271$	−11.1723	+	24.8238i	−0.678668	+	1.50794i	−0.852259	+	0.523120i	$0.824768\pi$
$272$	6.76598	+	27.4506i	0.410248	+	1.66444i
$273$	−14.5835	+	21.5521i	−0.882631	+	1.30439i
$274$	−21.0370	+	23.7459i	−1.27089	+	1.43454i
$275$	−0.731105	+	1.92777i	−0.0440873	+	0.116249i
$276$	2.16883	−	2.49426i	0.130548	−	0.150137i
$277$	−5.41608	−	10.3195i	−0.325421	−	0.620038i	0.666699	−	0.745327i	$-0.267707\pi$
$277$	−5.41608	−	10.3195i	−0.325421	−	0.620038i	−0.992120	+	0.125289i	$0.960014\pi$
$278$	−33.4480	−	12.6852i	−2.00608	−	0.760806i
$279$	2.20663	−	3.32703i	0.132107	−	0.199184i
$280$	4.53912	+	1.41445i	0.271265	+	0.0845295i
$281$	−0.912097	−	3.70052i	−0.0544111	−	0.220755i	0.937442	−	0.348142i	$-0.113187\pi$
$281$	−0.912097	−	3.70052i	−0.0544111	−	0.220755i	−0.991853	+	0.127387i	$0.959341\pi$
$282$	−20.6250	+	5.28672i	−1.22820	+	0.314820i
$283$	0.864957	−	7.12356i	0.0514163	−	0.423452i	−0.944159	−	0.329489i	$-0.893124\pi$
$283$	0.864957	−	7.12356i	0.0514163	−	0.423452i	0.995576	−	0.0939625i	$-0.0299534\pi$
$284$	0.725195	+	5.97252i	0.0430324	+	0.354404i
$285$	0.653991	−	0.460419i	0.0387391	−	0.0272728i
$286$	13.9667	+	13.9667i	0.825870	+	0.825870i
$287$	−9.99108	−	19.0364i	−0.589755	−	1.12368i
$288$	9.44877	+	19.9961i	0.556774	+	1.17828i
$289$	−11.8305	−	17.1395i	−0.695914	−	1.00821i
$290$	−2.02861	−	11.0698i	−0.119124	−	0.650039i
$291$	9.78395	−	11.2521i	0.573545	−	0.659607i
$292$	13.3617	+	13.3617i	0.781933	+	0.781933i
$293$	3.56320	−	0.215534i	0.208165	−	0.0125916i	0.0440329	−	0.999030i	$-0.485979\pi$
$293$	3.56320	−	0.215534i	0.208165	−	0.0125916i	0.164132	+	0.986438i	$0.447518\pi$
$294$	14.3484	−	0.132901i	0.836817	−	0.00775095i
$295$	3.44859	−	13.9915i	0.200784	−	0.814615i
$296$	4.09150	−	6.76817i	0.237814	−	0.393392i
$297$	−9.28990	+	7.70413i	−0.539054	+	0.447039i
$298$	−29.5340	−	33.3370i	−1.71086	−	1.93116i
$299$	−5.19693	−	0.314356i	−0.300546	−	0.0181797i
$300$	−2.51038	−	0.128526i	−0.144937	−	0.00742045i
$301$	−21.5735			−1.24347
$302$	4.60031			0.264718
$303$	−0.815824	+	15.9348i	−0.0468679	+	0.915428i
$304$	0.926853	−	0.486450i	0.0531587	−	0.0278998i
$305$	−1.67501	−	1.48393i	−0.0959106	−	0.0849694i
$306$	−25.3307	−	24.4092i	−1.44806	−	1.39538i
$307$	−9.30821	−	20.6820i	−0.531248	−	1.18038i	−0.960775	−	0.277330i	$-0.910550\pi$
$307$	−9.30821	−	20.6820i	−0.531248	−	1.18038i	0.429527	−	0.903054i	$-0.358680\pi$
$308$	2.30553	−	12.5809i	0.131370	−	0.716862i
$309$	−9.64250	+	26.1532i	−0.548543	+	1.48781i
$310$	−1.82446	−	4.81072i	−0.103623	−	0.273230i
$311$	−11.3408	−	4.30099i	−0.643077	−	0.243887i	0.0114398	−	0.999935i	$-0.496359\pi$
$311$	−11.3408	−	4.30099i	−0.643077	−	0.243887i	−0.654516	+	0.756048i	$0.727128\pi$
$312$	2.45487	−	4.78455i	0.138980	−	0.270872i
$313$		−	4.16940i		−	0.235669i	−0.993033	−	0.117834i	$-0.962405\pi$
$313$		−	4.16940i		−	0.235669i	0.993033	−	0.117834i	$-0.0375952\pi$
$314$	23.7842	+	2.23416i	1.34222	+	0.126081i
$315$	−19.8017	+	5.27162i	−1.11570	+	0.297022i
$316$	2.02523	+	11.0513i	0.113928	+	0.621686i
$317$	−9.08323	+	23.9505i	−0.510165	+	1.34519i	0.394431	+	0.918926i	$0.370942\pi$
$317$	−9.08323	+	23.9505i	−0.510165	+	1.34519i	−0.904596	+	0.426269i	$0.859828\pi$
$318$	14.8537	+	4.47808i	0.832952	+	0.251119i
$319$	6.45473	−	2.01138i	0.361396	−	0.112615i
$320$	9.69685	+	1.77701i	0.542070	+	0.0993380i
$321$	6.99485	−	29.5547i	0.390415	−	1.64958i
$322$	3.87782	+	6.41469i	0.216102	+	0.357477i
$323$	−0.928687	+	1.04827i	−0.0516735	+	0.0583274i
$324$	−12.4108	−	7.90435i	−0.689492	−	0.439130i
$325$	2.24922	+	3.25856i	0.124764	+	0.180752i
$326$		−	43.3578i		−	2.40137i
$327$	2.62051	−	3.40942i	0.144915	−	0.188541i
$328$	2.52379	+	3.65635i	0.139353	+	0.201888i
$329$	1.31128	−	21.6780i	0.0722930	−	1.19515i
$330$	1.08286	+	15.5159i	0.0596097	+	0.854125i
$331$	8.74350	+	4.58894i	0.480586	+	0.252231i	0.687577	−	0.726112i	$-0.258675\pi$
$331$	8.74350	+	4.58894i	0.480586	+	0.252231i	−0.206990	+	0.978343i	$0.566367\pi$
$332$	−12.8610	−	7.77472i	−0.705837	−	0.426693i
$333$	0.631396	+	34.0808i	0.0346003	+	1.86762i
$334$	8.26858	−	6.47802i	0.452437	−	0.354462i
$335$	−0.597325	−	9.87497i	−0.0326354	−	0.539527i
$336$	−26.5917	+	3.47903i	−1.45070	+	0.189797i
$337$	−14.0087	−	0.847371i	−0.763104	−	0.0461593i	−0.325758	−	0.945453i	$-0.605620\pi$
$337$	−14.0087	−	0.847371i	−0.763104	−	0.0461593i	−0.437345	+	0.899294i	$0.644081\pi$
$338$	12.9318	−	2.36985i	0.703399	−	0.128903i
$339$	−1.04383	+	20.3881i	−0.0566929	+	1.10733i
$340$	−20.0568	+	3.67554i	−1.08773	+	0.199334i
$341$	2.73684	−	1.43640i	0.148208	−	0.0777855i
$342$	−0.653026	+	1.12687i	−0.0353116	+	0.0609341i
$343$	2.66024	−	8.53703i	0.143640	−	0.460956i
$344$	4.42567	−	0.537374i	0.238616	−	0.0289733i
$345$	−2.92573	−	2.87203i	−0.157516	−	0.154625i
$346$	−5.20567	−	4.07838i	−0.279858	−	0.219255i
$347$	15.6035	−	3.84593i	0.837642	−	0.206460i	0.202914	−	0.979196i	$-0.434959\pi$
$347$	15.6035	−	3.84593i	0.837642	−	0.206460i	0.634727	+	0.772736i	$0.281113\pi$
$348$	4.74508	+	6.74004i	0.254363	+	0.361304i
$349$	13.5555	−	12.0091i	0.725610	−	0.642834i	−0.217215	−	0.976124i	$-0.569697\pi$
$349$	13.5555	−	12.0091i	0.725610	−	0.642834i	0.942824	+	0.333290i	$0.108159\pi$
$350$	2.02140	−	5.32999i	0.108048	−	0.284900i
$351$	2.04163	+	23.0872i	0.108974	+	1.23230i
$352$	−1.03384	+	17.0914i	−0.0551038	+	0.910974i
$353$	−4.40347	−	1.67001i	−0.234373	−	0.0888859i	0.234622	−	0.972087i	$-0.424615\pi$
$353$	−4.40347	−	1.67001i	−0.234373	−	0.0888859i	−0.468995	+	0.883201i	$0.655384\pi$
$354$	4.44341	+	23.0412i	0.236165	+	1.22462i
$355$	7.44889	−	0.450575i	0.395346	−	0.0239140i
$356$	6.86703	−	1.69257i	0.363952	−	0.0897061i
$357$	31.6151	−	16.9682i	1.67325	−	0.898054i
$358$	−18.4104	−	12.7078i	−0.973021	−	0.671628i
$359$	6.97436	−	15.4964i	0.368093	−	0.817869i	−0.631021	−	0.775766i	$-0.717364\pi$
$359$	6.97436	−	15.4964i	0.368093	−	0.817869i	0.999113	−	0.0421024i	$-0.0134056\pi$
$360$	3.93090	−	1.57468i	0.207177	−	0.0829931i
$361$	−16.7778	−	8.80564i	−0.883040	−	0.463455i
$362$	−11.7501	−	30.9824i	−0.617571	−	1.62840i
$363$	9.53309	−	1.83842i	0.500358	−	0.0964922i
$364$	−17.3687	−	17.3687i	−0.910367	−	0.910367i
$365$	17.5438	−	15.5425i	0.918285	−	0.813529i
$366$	3.48893	+	1.05184i	0.182369	+	0.0549806i
$367$	−6.60907	−	10.9327i	−0.344991	−	0.570684i	0.634314	−	0.773075i	$-0.281283\pi$
$367$	−6.60907	−	10.9327i	−0.344991	−	0.570684i	−0.979305	+	0.202391i	$0.935129\pi$
$368$	−3.30910	−	4.22376i	−0.172499	−	0.220178i
$369$	−17.6040	−	7.53396i	−0.916427	−	0.392202i
$370$	36.1531	+	24.9547i	1.87951	+	1.29733i
$371$	−8.98921	+	13.0231i	−0.466697	+	0.676127i
$372$	2.68921	+	2.63985i	0.139429	+	0.136870i
$373$	13.0491	−	21.5858i	0.675656	−	1.11767i	−0.310296	−	0.950640i	$-0.600428\pi$
$373$	13.0491	−	21.5858i	0.675656	−	1.11767i	0.985952	−	0.167031i	$-0.0534181\pi$
$374$	−8.10244	−	26.0016i	−0.418967	−	1.34451i
$375$	−2.30244	+	20.5513i	−0.118897	+	1.06127i
$376$	0.270977	+	4.47978i	0.0139746	+	0.231027i
$377$	3.86271	−	12.3959i	0.198940	−	0.638420i
$378$	25.6852	−	21.3008i	1.32110	−	1.09559i
$379$	−1.31467	−	4.21891i	−0.0675298	−	0.216711i	0.914787	−	0.403936i	$-0.132358\pi$
$379$	−1.31467	−	4.21891i	−0.0675298	−	0.216711i	−0.982317	+	0.187225i	$0.940051\pi$
$380$	0.309841	+	0.688439i	0.0158945	+	0.0353162i
$381$	−13.2209	−	16.5570i	−0.677325	−	0.848239i
$382$	11.7564	+	1.42748i	0.601509	+	0.0730364i
$383$	−0.117367	+	0.260778i	−0.00599717	+	0.0133252i	−0.914874	−	0.403739i	$-0.867710\pi$
$383$	−0.117367	+	0.260778i	−0.00599717	+	0.0133252i	0.908877	+	0.417064i	$0.136941\pi$
$384$	9.18714	−	2.35490i	0.468829	−	0.120173i
$385$	−15.4037	−	3.79668i	−0.785047	−	0.193497i
$386$	−47.7313	−	8.74708i	−2.42946	−	0.445215i
$387$	−14.9034	+	12.1282i	−0.757583	+	0.616512i
$388$	8.68009	+	11.0793i	0.440665	+	0.562467i
$389$	4.39177	+	17.8181i	0.222672	+	0.903414i	0.970806	+	0.239867i	$0.0771037\pi$
$389$	4.39177	+	17.8181i	0.222672	+	0.903414i	−0.748134	+	0.663547i	$0.769050\pi$
$390$	25.7040	+	15.2154i	1.30157	+	0.770460i
$391$	6.14352	+	3.71389i	0.310691	+	0.187819i
$392$	0.545189	−	2.97500i	0.0275362	−	0.150260i
$393$	12.9196	+	14.3139i	0.651710	+	0.722043i
$394$	19.3694	−	32.0409i	0.975818	−	1.61420i
$395$	13.8344	−	1.67979i	0.696082	−	0.0845197i
$396$	−5.48003	−	9.98726i	−0.275382	−	0.501879i
$397$	−5.75141	+	4.50594i	−0.288655	+	0.226147i	−0.750592	−	0.660766i	$-0.770232\pi$
$397$	−5.75141	+	4.50594i	−0.288655	+	0.226147i	0.461937	+	0.886913i	$0.347155\pi$
$398$	7.38007	+	16.3978i	0.369929	+	0.821949i
$399$	−0.890103	−	0.986163i	−0.0445609	−	0.0493699i
$400$	−0.976536	+	3.96196i	−0.0488268	+	0.198098i
$401$	−9.76191	−	7.64797i	−0.487487	−	0.381921i	0.342666	−	0.939457i	$-0.388670\pi$
$401$	−9.76191	−	7.64797i	−0.487487	−	0.381921i	−0.830153	+	0.557536i	$0.811747\pi$
$402$	7.61843	+	14.1946i	0.379973	+	0.707964i
$403$	0.715484	−	5.89254i	0.0356408	−	0.293528i
$404$	−14.6231	−	3.60428i	−0.727529	−	0.179320i
$405$	−10.7159	+	14.7739i	−0.532475	+	0.734122i
$406$	−17.8464	+	5.56116i	−0.885702	+	0.275996i
$407$	−12.2642	+	23.3675i	−0.607914	+	1.15828i
$408$	−6.06301	+	4.26844i	−0.300164	+	0.211319i
$409$	14.5460	−	0.879872i	0.719255	−	0.0435069i	0.303304	−	0.952894i	$-0.401910\pi$
$409$	14.5460	−	0.879872i	0.719255	−	0.0435069i	0.415951	+	0.909387i	$0.363449\pi$
$410$	−21.1186	+	12.7666i	−1.04297	+	0.630499i
$411$	−27.0413	−	9.96993i	−1.33385	−	0.491780i
$412$	−22.5164	−	13.6116i	−1.10930	−	0.670597i
$413$	−23.7605	−	2.88504i	−1.16918	−	0.141964i
$414$	6.28510	+	2.25137i	0.308896	+	0.110649i
$415$	−10.5891	+	15.3409i	−0.519797	+	0.753056i
$416$	25.8848	+	20.2795i	1.26911	+	0.994283i
$417$	−0.301003	−	32.4972i	−0.0147402	−	1.59140i
$418$	−0.862923	+	0.521655i	−0.0422069	+	0.0255150i
$419$	−5.23411	−	13.8012i	−0.255703	−	0.674234i	−0.999980	−	0.00636245i	$-0.997975\pi$
$419$	−5.23411	−	13.8012i	−0.255703	−	0.674234i	0.744277	−	0.667872i	$-0.232794\pi$
$420$	−1.34662	−	19.2953i	−0.0657085	−	0.941513i
$421$	−8.20432	+	8.20432i	−0.399854	+	0.399854i	−0.878181	−	0.478328i	$-0.841243\pi$
$421$	−8.20432	+	8.20432i	−0.399854	+	0.399854i	0.478328	+	0.878181i	$0.341243\pi$
$422$	31.8067	−	35.9023i	1.54833	−	1.74770i
$423$	−11.2811	−	15.7128i	−0.548507	−	0.763982i
$424$	1.51969	−	2.89553i	0.0738028	−	0.140619i
$425$	−0.658064	−	5.41964i	−0.0319208	−	0.262891i
$426$	−10.7073	+	5.74675i	−0.518771	+	0.278431i
$427$	−2.11144	+	3.05896i	−0.102180	+	0.148033i
$428$	26.1422	+	11.7656i	1.26363	+	0.568714i
$429$	−7.21265	+	16.4308i	−0.348230	+	0.793286i
$430$	1.49515	+	24.7178i	0.0721027	+	1.19200i
$431$	−15.1746	−	13.4435i	−0.730936	−	0.647553i	0.213238	−	0.977000i	$-0.431599\pi$
$431$	−15.1746	−	13.4435i	−0.730936	−	0.647553i	−0.944174	+	0.329448i	$0.893137\pi$
$432$	−16.4143	+	17.3528i	−0.789732	+	0.834886i
$433$	−29.4082	−	1.77887i	−1.41327	−	0.0854871i	−0.663990	−	0.747741i	$-0.731138\pi$
$433$	−29.4082	−	1.77887i	−1.41327	−	0.0854871i	−0.749279	+	0.662254i	$0.769600\pi$
$434$	−7.56695	+	3.97144i	−0.363225	+	0.190635i
$435$	8.70022	−	5.37012i	0.417143	−	0.257477i
$436$	2.69160	+	3.03819i	0.128904	+	0.145503i
$437$	0.0790734	−	0.253756i	0.00378259	−	0.0121388i
$438$	−15.3412	+	34.9482i	−0.733033	+	1.66989i
$439$	4.36312	−	5.56912i	0.208241	−	0.265799i	−0.671763	−	0.740766i	$-0.734463\pi$
$439$	4.36312	−	5.56912i	0.208241	−	0.265799i	0.880004	+	0.474966i	$0.157540\pi$
$440$	3.25456	+	0.395175i	0.155155	+	0.0188392i
$441$	4.84752	+	12.1009i	0.230835	+	0.576235i
$442$	−49.9344	−	15.5602i	−2.37514	−	0.740123i
$443$	−15.8741	+	15.8741i	−0.754202	+	0.754202i	−0.975261	−	0.221058i	$-0.929049\pi$
$443$	−15.8741	+	15.8741i	−0.754202	+	0.754202i	0.221058	+	0.975261i	$0.429049\pi$
$444$	−31.7003	−	5.50633i	−1.50443	−	0.261319i
$445$	−1.58129	−	8.62885i	−0.0749606	−	0.409047i
$446$	−6.65042	+	4.59045i	−0.314907	+	0.217364i
$447$	18.4708	−	35.9995i	0.873637	−	1.70272i
$448$	0.988664	−	16.3446i	0.0467100	−	0.772208i
$449$	−22.1971	+	22.1971i	−1.04754	+	1.04754i	−0.0487318	+	0.998812i	$0.515518\pi$
$449$	−22.1971	+	22.1971i	−1.04754	+	1.04754i	−0.998812	+	0.0487318i	$0.984482\pi$
$450$	−1.60000	−	4.81847i	−0.0754248	−	0.227145i
$451$	−9.14282	−	11.6700i	−0.430519	−	0.549517i
$452$	−18.7100	−	4.61159i	−0.880043	−	0.216911i
$453$	1.51812	+	3.89379i	0.0713275	+	0.182946i
$454$	7.93977	−	15.1280i	0.372632	−	0.709990i
$455$	−22.8050	+	20.2035i	−1.06911	+	0.947153i
$456$	0.207164	+	0.180134i	0.00970134	+	0.00843556i
$457$	33.1495	−	22.8814i	1.55067	−	1.07035i	0.584845	−	0.811145i	$-0.301155\pi$
$457$	33.1495	−	22.8814i	1.55067	−	1.07035i	0.965823	−	0.259204i	$-0.0834602\pi$
$458$			27.1923i			1.27061i
$459$	12.3012	−	29.4955i	0.574170	−	1.37673i
$460$	3.18485	−	2.19834i	0.148494	−	0.102498i
$461$	13.7911	+	26.2767i	0.642315	+	1.22383i	0.961152	+	0.276020i	$0.0890156\pi$
$461$	13.7911	+	26.2767i	0.642315	+	1.22383i	−0.318837	+	0.947810i	$0.603292\pi$
$462$	25.3669	−	4.89192i	1.18018	−	0.227593i
$463$	31.7188	−	19.1747i	1.47410	−	0.891123i	0.474154	−	0.880442i	$-0.342754\pi$
$463$	31.7188	−	19.1747i	1.47410	−	0.891123i	0.999943	−	0.0106807i	$-0.00339983\pi$
$464$	12.2020	−	5.49167i	0.566464	−	0.254945i
$465$	3.46981	−	3.13182i	0.160908	−	0.145235i
$466$	13.9823	+	44.8708i	0.647718	+	2.07860i
$467$	17.3946	−	6.59688i	0.804924	−	0.305267i	0.0823877	−	0.996600i	$-0.473745\pi$
$467$	17.3946	−	6.59688i	0.804924	−	0.305267i	0.722536	+	0.691333i	$0.242976\pi$
$468$	−21.7630	−	2.23430i	−1.00600	−	0.103280i
$469$	−16.1629	+	2.96196i	−0.746333	+	0.136771i
$470$	−24.9285			−1.14986
$471$	5.95786	+	20.8687i	0.274524	+	0.961580i
$472$	4.94619			0.227667
$473$	−14.6326	+	2.68153i	−0.672809	+	0.123297i
$474$	−19.3111	+	11.9196i	−0.886987	+	0.547483i
$475$	−0.188996	+	0.0716767i	−0.00867173	+	0.00328875i
$476$	10.0760	+	32.3350i	0.461833	+	1.48207i
$477$	1.11143	+	14.0502i	0.0508888	+	0.643316i
$478$	−6.54715	+	2.94663i	−0.299460	+	0.134776i
$479$	−17.4159	+	10.5283i	−0.795754	+	0.481050i	−0.855901	−	0.517140i	$-0.826997\pi$
$479$	−17.4159	+	10.5283i	−0.795754	+	0.481050i	0.0601473	+	0.998190i	$0.480843\pi$
$480$	4.90316	+	25.4252i	0.223797	+	1.16050i
$481$	23.5526	+	44.8757i	1.07391	+	2.04616i
$482$	−41.4210	+	28.5908i	−1.88667	+	1.30228i
$483$	−4.14983	+	5.39913i	−0.188824	+	0.245669i
$484$			9.16424i			0.416556i
$485$	14.3674	−	9.91709i	0.652389	−	0.450312i
$486$	5.76897	−	29.1548i	0.261686	−	1.32249i
$487$	−27.2707	+	24.1598i	−1.23575	+	1.09478i	−0.243586	+	0.969879i	$0.578324\pi$
$487$	−27.2707	+	24.1598i	−1.23575	+	1.09478i	−0.992169	+	0.124903i	$0.960138\pi$
$488$	0.356955	−	0.680121i	0.0161586	−	0.0307877i
$489$	36.6990	−	14.3083i	1.65958	−	0.647042i
$490$	16.3117	+	4.02047i	0.736887	+	0.181626i
$491$	19.0526	+	24.3188i	0.859830	+	1.09749i	0.994305	+	0.106574i	$0.0339883\pi$
$491$	19.0526	+	24.3188i	0.859830	+	1.09749i	−0.134475	+	0.990917i	$0.542935\pi$
$492$	10.1293	−	14.9695i	0.456663	−	0.674876i
$493$	−12.6590	+	12.6590i	−0.570134	+	0.570134i
$494$	−0.116920	+	1.93293i	−0.00526050	+	0.0869664i
$495$	−12.7757	+	6.03688i	−0.574223	+	0.271338i
$496$	5.03448	−	3.47505i	0.226055	−	0.156034i
$497$	−2.23427	−	12.1920i	−0.100221	−	0.546887i
$498$	5.19479	−	29.9067i	0.232784	−	1.34015i
$499$	14.7597	−	14.7597i	0.660735	−	0.660735i	−0.294819	−	0.955553i	$-0.595259\pi$
$499$	14.7597	−	14.7597i	0.660735	−	0.660735i	0.955553	+	0.294819i	$0.0952592\pi$
$500$	−18.6362	−	5.80729i	−0.833438	−	0.259710i
$501$	8.21179	+	4.86092i	0.366876	+	0.217170i
$502$	22.2586	+	2.70269i	0.993451	+	0.120627i
$503$	1.05534	−	1.34705i	0.0470554	−	0.0600618i	−0.763083	−	0.646301i	$-0.776315\pi$
$503$	1.05534	−	1.34705i	0.0470554	−	0.0600618i	0.810138	+	0.586239i	$0.199392\pi$
$504$	−3.38344	−	6.16626i	−0.150710	−	0.274667i
$505$	−5.55762	+	17.8350i	−0.247311	+	0.793648i
$506$	3.42753	+	3.86888i	0.152372	+	0.171993i
$507$	6.27344	+	10.1637i	0.278613	+	0.451386i
$508$	17.7087	−	9.29425i	0.785698	−	0.412366i
$509$	−2.06498	−	0.124908i	−0.0915287	−	0.00553646i	0.0145507	−	0.999894i	$-0.495368\pi$
$509$	−2.06498	−	0.124908i	−0.0915287	−	0.00553646i	−0.106079	+	0.994358i	$0.533830\pi$
$510$	−21.6325	−	35.0471i	−0.957902	−	1.55191i
$511$	−29.1398	−	25.8156i	−1.28907	−	1.14202i
$512$	1.65975	+	27.4390i	0.0733514	+	1.21264i
$513$	−1.16931	−	0.180863i	−0.0516261	−	0.00798529i
$514$	−27.7011	−	12.4673i	−1.22184	−	0.549907i
$515$	−18.5389	+	26.8582i	−0.816920	+	1.18351i
$516$	−8.57711	−	15.9808i	−0.377586	−	0.703518i
$517$	−1.80512	−	14.8665i	−0.0793891	−	0.653828i
$518$	33.9088	−	64.6077i	1.48987	−	2.83870i
$519$	1.73413	−	5.75206i	0.0761200	−	0.252488i
$520$	4.17507	−	4.71268i	0.183089	−	0.206664i
$521$	11.7520	−	11.7520i	0.514866	−	0.514866i	−0.401148	−	0.916013i	$-0.631389\pi$
$521$	11.7520	−	11.7520i	0.514866	−	0.514866i	0.916013	+	0.401148i	$0.131389\pi$
$522$	−9.20229	+	13.8747i	−0.402773	+	0.607279i
$523$	9.86899	+	26.0224i	0.431541	+	1.13788i	0.957770	+	0.287537i	$0.0928363\pi$
$523$	9.86899	+	26.0224i	0.431541	+	1.13788i	−0.526229	+	0.850343i	$0.676394\pi$
$524$	−15.5760	+	9.41599i	−0.680439	+	0.411340i
$525$	5.17848	−	0.0479652i	0.226007	−	0.00209337i
$526$	−30.1907	−	23.6529i	−1.31638	−	1.03132i
$527$	−4.64936	+	6.73576i	−0.202529	+	0.293414i
$528$	−17.6039	+	5.66500i	−0.766111	+	0.246538i
$529$	21.4798	+	2.60812i	0.933904	+	0.113396i
$530$	15.5443	+	9.39684i	0.675200	+	0.408173i
$531$	−18.0362	+	11.3647i	−0.782703	+	0.493185i
$532$	1.07311	−	0.648718i	0.0465252	−	0.0281255i
$533$	−28.4184	+	1.71899i	−1.23094	+	0.0744579i
$534$	8.22351	+	11.6809i	0.355866	+	0.505482i
$535$	16.5249	−	31.4855i	0.714433	−	1.36124i
$536$	3.24195	−	1.01023i	0.140031	−	0.0436354i
$537$	4.68062	−	19.7766i	0.201984	−	0.853422i
$538$	−36.7038	−	9.04668i	−1.58241	−	0.390030i
$539$	−1.21651	+	10.0189i	−0.0523989	+	0.431543i
$540$	−11.7777	−	12.5725i	−0.506833	−	0.541036i
$541$	24.6117	+	19.2820i	1.05814	+	0.828999i	0.985723	−	0.168376i	$-0.0538521\pi$
$541$	24.6117	+	19.2820i	1.05814	+	0.828999i	0.0724160	+	0.997375i	$0.476929\pi$
$542$	12.4205	−	50.3919i	0.533506	−	2.16452i
$543$	22.3466	−	20.1698i	0.958983	−	0.865570i
$544$	−18.6082	−	41.3458i	−0.797821	−	1.77269i
$545$	3.96316	−	3.10494i	0.169763	−	0.133001i
$546$	19.9419	−	45.4287i	0.853435	−	1.94417i
$547$	−0.327985	+	0.0398246i	−0.0140236	+	0.00170278i	−0.127545	−	0.991833i	$-0.540710\pi$
$547$	−0.327985	+	0.0398246i	−0.0140236	+	0.00170278i	0.113522	+	0.993535i	$0.463787\pi$
$548$	14.0738	−	23.2810i	0.601204	−	0.994514i
$549$	0.261059	+	3.30021i	0.0111417	+	0.140849i
$550$	0.708548	−	3.86642i	0.0302126	−	0.164865i
$551$	0.567235	+	0.342906i	0.0241650	+	0.0146083i
$552$	0.716827	−	1.21097i	0.0305102	−	0.0515423i
$553$	−5.53951	−	22.4747i	−0.235564	−	0.955721i
$554$	13.7033	+	17.4910i	0.582198	+	0.743120i
$555$	−9.19148	+	38.8358i	−0.390157	+	1.64849i
$556$	30.1735	+	5.52950i	1.27964	+	0.234503i
$557$	41.7708	+	10.2956i	1.76989	+	0.436238i	0.983412	−	0.181385i	$-0.0580581\pi$
$557$	41.7708	+	10.2956i	1.76989	+	0.436238i	0.786474	+	0.617623i	$0.211904\pi$
$558$	−2.99474	+	6.99756i	−0.126777	+	0.296230i
$559$	−11.7250	+	26.0520i	−0.495917	+	1.10188i
$560$	−31.1700	−	3.78472i	−1.31717	−	0.159934i
$561$	19.3345	−	15.4387i	0.816302	−	0.651823i
$562$	2.98221	+	6.62619i	0.125797	+	0.279509i
$563$	5.28059	+	16.9460i	0.222550	+	0.714189i	0.996699	+	0.0811852i	$0.0258705\pi$
$563$	5.28059	+	16.9460i	0.222550	+	0.714189i	−0.774149	+	0.633004i	$0.781822\pi$
$564$	16.5796	−	7.64732i	0.698127	−	0.322010i
$565$	−7.11084	+	22.8195i	−0.299155	+	0.960023i
$566$	0.826046	+	13.6562i	0.0347213	+	0.574012i
$567$	26.5056	+	14.7111i	1.11313	+	0.617809i
$568$	0.762039	+	2.44547i	0.0319745	+	0.102610i
$569$	−1.48830	+	2.46196i	−0.0623930	+	0.103211i	−0.885420	−	0.464791i	$-0.846129\pi$
$569$	−1.48830	+	2.46196i	−0.0623930	+	0.103211i	0.823027	+	0.568002i	$0.192283\pi$
$570$	−1.06821	+	1.08818i	−0.0447424	+	0.0455790i
$571$	−4.33305	+	6.27751i	−0.181333	+	0.262706i	−0.903100	−	0.429430i	$-0.858715\pi$
$571$	−4.33305	+	6.27751i	−0.181333	+	0.262706i	0.721768	+	0.692135i	$0.243330\pi$
$572$	−13.9395	−	9.62177i	−0.582841	−	0.402306i
$573$	2.67140	+	10.4219i	0.111599	+	0.435382i
$574$	25.2786	+	32.2657i	1.05511	+	1.34674i
$575$	0.536027	+	0.886696i	0.0223539	+	0.0369778i
$576$	−8.50564	−	11.8470i	−0.354402	−	0.493624i
$577$	−6.45767	+	5.72100i	−0.268836	+	0.238168i	−0.786761	−	0.617258i	$-0.788243\pi$
$577$	−6.45767	+	5.72100i	−0.268836	+	0.238168i	0.517924	+	0.855427i	$0.326705\pi$
$578$	28.0762	+	28.0762i	1.16782	+	1.16782i
$579$	−8.34780	−	43.2873i	−0.346923	−	1.79896i
$580$	3.42218	+	9.02355i	0.142098	+	0.374682i
$581$	27.4151	+	14.3886i	1.13737	+	0.596939i
$582$	−14.4811	+	24.4635i	−0.600259	+	1.01405i
$583$	−4.47837	+	9.95052i	−0.185475	+	0.412108i
$584$	6.62091	+	4.57009i	0.273975	+	0.189112i
$585$	−4.39615	+	26.7775i	−0.181758	+	1.10712i
$586$	−6.60806	+	1.62874i	−0.272976	+	0.0672826i
$587$	22.3379	−	1.35119i	0.921983	−	0.0557697i	0.407438	−	0.913233i	$-0.366422\pi$
$587$	22.3379	−	1.35119i	0.921983	−	0.0557697i	0.514545	+	0.857463i	$0.327961\pi$
$588$	−12.0821	+	2.32998i	−0.498256	+	0.0960869i
$589$	0.283334	+	0.107455i	0.0116746	+	0.00442759i
$590$	−1.65882	+	27.4236i	−0.0682925	+	1.12901i
$591$	33.5121	+	5.82103i	1.37850	+	0.239445i
$592$	−18.5213	+	48.8367i	−0.761222	+	2.00718i
$593$	0.524619	−	0.464771i	0.0215435	−	0.0190859i	−0.652282	−	0.757976i	$-0.726188\pi$
$593$	0.524619	−	0.464771i	0.0215435	−	0.0190859i	0.673826	+	0.738890i	$0.264650\pi$
$594$	14.7739	−	17.6403i	0.606178	−	0.723789i
$595$	40.7887	−	10.0535i	1.67217	−	0.412154i
$596$	30.0643	+	23.5539i	1.23148	+	0.964805i
$597$	−11.4440	+	11.6580i	−0.468372	+	0.477130i
$598$	9.85391	−	1.19648i	0.402956	−	0.0489278i
$599$	10.8366	−	34.7760i	0.442773	−	1.42091i	−0.416379	−	0.909191i	$-0.636701\pi$
$599$	10.8366	−	34.7760i	0.442773	−	1.42091i	0.859153	−	0.511719i	$-0.170991\pi$
$600$	−1.06114	+	0.138831i	−0.0433209	+	0.00566774i
$601$	34.9396	−	18.3377i	1.42522	−	0.748012i	0.436770	−	0.899573i	$-0.356123\pi$
$601$	34.9396	−	18.3377i	1.42522	−	0.748012i	0.988448	+	0.151562i	$0.0484302\pi$
$602$	40.4570	−	7.41403i	1.64891	−	0.302173i
$603$	−9.50052	+	11.1327i	−0.386891	+	0.453358i
$604$	−3.88027	+	0.711085i	−0.157886	+	0.0289336i
$605$	11.3463	+	0.686323i	0.461291	+	0.0279030i
$606$	−3.94628	−	30.1631i	−0.160307	−	1.22529i
$607$	0.138335	+	2.28694i	0.00561483	+	0.0928241i	0.999903	−	0.0139011i	$-0.00442501\pi$
$607$	0.138335	+	2.28694i	0.00561483	+	0.0928241i	−0.994289	+	0.106725i	$0.965963\pi$
$608$	−1.32143	+	1.03528i	−0.0535911	+	0.0419860i
$609$	−10.5965	−	13.2703i	−0.429390	−	0.537741i
$610$	3.65114	+	2.20719i	0.147830	+	0.0893665i
$611$	−25.4655	−	13.3653i	−1.03023	−	0.540704i
$612$	25.1389	+	16.6732i	1.01618	+	0.673974i
$613$	−1.74871	+	28.9097i	−0.0706299	+	1.16765i	0.774316	+	0.632799i	$0.218094\pi$
$613$	−1.74871	+	28.9097i	−0.0706299	+	1.16765i	−0.844946	+	0.534852i	$0.820367\pi$
$614$	24.5635	+	35.5864i	0.991302	+	1.43615i
$615$	−17.7751	−	13.6622i	−0.716763	−	0.550911i
$616$		−	5.44545i		−	0.219403i
$617$	−1.20532	−	1.74621i	−0.0485245	−	0.0702999i	0.797971	−	0.602696i	$-0.205907\pi$
$617$	−1.20532	−	1.74621i	−0.0485245	−	0.0702999i	−0.846495	+	0.532396i	$0.821292\pi$
$618$	9.09480	−	52.3594i	0.365846	−	2.10620i
$619$	22.3589	−	25.2379i	0.898679	−	1.01440i	−0.101131	−	0.994873i	$-0.532246\pi$
$619$	22.3589	−	25.2379i	0.898679	−	1.01440i	0.999809	−	0.0195254i	$-0.00621553\pi$
$620$	2.28251	+	3.77573i	0.0916677	+	0.151637i
$621$	0.168507	+	6.06280i	0.00676196	+	0.243292i
$622$	22.7456	+	4.16829i	0.912017	+	0.167133i
$623$	−13.9112	+	4.33491i	−0.557341	+	0.173675i
$624$	−10.2512	+	34.0028i	−0.410375	+	1.36120i
$625$	−7.01184	+	18.4887i	−0.280474	+	0.739548i
$626$	1.43287	+	7.81894i	0.0572692	+	0.312508i
$627$	−0.726307	−	0.558247i	−0.0290059	−	0.0222942i
$628$	−20.4069	+	1.79195i	−0.814322	+	0.0715064i
$629$		−	69.8810i		−	2.78634i
$630$	35.3228	−	16.6911i	1.40729	−	0.664989i
$631$	−4.44851	−	1.68710i	−0.177092	−	0.0671623i	0.264465	−	0.964395i	$-0.414805\pi$
$631$	−4.44851	−	1.68710i	−0.177092	−	0.0671623i	−0.441557	+	0.897233i	$0.645574\pi$
$632$	1.69622	+	4.47257i	0.0674721	+	0.177909i
$633$	40.8848	+	15.0739i	1.62503	+	0.599134i
$634$	8.80299	−	48.0363i	0.349611	−	1.90777i
$635$	−10.1810	−	22.6213i	−0.404021	−	0.897697i
$636$	−13.2210	−	1.48119i	−0.524245	−	0.0587331i
$637$	14.5076	+	12.8526i	0.574810	+	0.509237i
$638$	−11.4134	+	5.99023i	−0.451862	+	0.237155i
$639$	−8.39762	−	7.16644i	−0.332205	−	0.283500i
$640$	11.1041			0.438926
$641$	18.1117			0.715367			0.357684	−	0.933843i	$-0.383567\pi$
$641$	18.1117			0.715367			0.357684	+	0.933843i	$0.383567\pi$
$642$	−2.96067	+	57.8282i	−0.116848	+	2.28230i
$643$	−18.8824	−	1.14217i	−0.744649	−	0.0450430i	−0.316303	−	0.948658i	$-0.602442\pi$
$643$	−18.8824	−	1.14217i	−0.744649	−	0.0450430i	−0.428345	+	0.903615i	$0.640903\pi$
$644$	−4.26240	−	4.81126i	−0.167962	−	0.189590i
$645$	−20.4283	+	9.42251i	−0.804362	+	0.371011i
$646$	1.38133	−	2.28500i	0.0543476	−	0.0899020i
$647$	5.44339	−	22.0847i	0.214002	−	0.868239i	−0.761485	−	0.648182i	$-0.775530\pi$
$647$	5.44339	−	22.0847i	0.214002	−	0.868239i	0.975487	−	0.220057i	$-0.0706243\pi$
$648$	−5.80392	−	2.35768i	−0.227999	−	0.0926183i
$649$	−16.4746	+	0.996530i	−0.646685	+	0.0391172i
$650$	−5.33785	−	5.33785i	−0.209368	−	0.209368i
$651$	−5.85863	−	5.09423i	−0.229618	−	0.199658i
$652$	6.70197	+	36.5715i	0.262469	+	1.43225i
$653$	−3.26220	−	4.72612i	−0.127660	−	0.184947i	0.753942	−	0.656941i	$-0.228150\pi$
$653$	−3.26220	−	4.72612i	−0.127660	−	0.184947i	−0.881602	+	0.471994i	$0.843535\pi$
$654$	−3.74259	+	7.29431i	−0.146347	+	0.285230i
$655$	10.4915	+	19.9898i	0.409935	+	0.781066i
$656$	−20.7472	−	20.7472i	−0.810043	−	0.810043i
$657$	−34.6435	−	1.45210i	−1.35157	−	0.0566518i
$658$	4.99089	+	41.1037i	0.194565	+	1.60239i
$659$	5.68964	−	46.8584i	0.221637	−	1.82534i	−0.279695	−	0.960089i	$-0.590233\pi$
$659$	5.68964	−	46.8584i	0.221637	−	1.82534i	0.501332	−	0.865255i	$-0.332844\pi$
$660$	−3.31173	−	12.9200i	−0.128909	−	0.502910i
$661$	0.446267	+	1.81058i	0.0173578	+	0.0704232i	0.978982	−	0.203947i	$-0.0653769\pi$
$661$	0.446267	+	1.81058i	0.0173578	+	0.0704232i	−0.961624	+	0.274370i	$0.911531\pi$
$662$	−17.9739	−	5.60089i	−0.698574	−	0.217685i
$663$	−3.30809	−	47.4004i	−0.128476	−	1.84088i
$664$	−5.98247	−	2.26885i	−0.232165	−	0.0880485i
$665$	−0.722812	−	1.37720i	−0.0280295	−	0.0534057i
$666$	−12.8964	−	63.6953i	−0.499727	−	2.46814i
$667$	1.20482	−	3.17686i	0.0466510	−	0.123009i
$668$	−5.97305	+	6.74218i	−0.231104	+	0.260863i
$669$	−6.08012	−	4.11418i	−0.235071	−	0.159063i
$670$	4.51385	+	18.3134i	0.174385	+	0.707508i
$671$	−1.05191	+	2.33724i	−0.0406084	+	0.0902282i
$672$	40.9410	−	13.1750i	1.57933	−	0.508236i
$673$	−3.24964	−	1.46255i	−0.125265	−	0.0563770i	0.346811	−	0.937935i	$-0.387264\pi$
$673$	−3.24964	−	1.46255i	−0.125265	−	0.0563770i	−0.472076	+	0.881558i	$0.656495\pi$
$674$	26.5620	−	3.22521i	1.02313	−	0.124230i
$675$	3.55044	−	2.94439i	0.136656	−	0.113329i
$676$	−10.5414	+	3.99784i	−0.405440	+	0.153763i
$677$	−2.49444	−	2.20988i	−0.0958691	−	0.0849326i	0.613827	−	0.789441i	$-0.289629\pi$
$677$	−2.49444	−	2.20988i	−0.0958691	−	0.0849326i	−0.709696	+	0.704508i	$0.751168\pi$
$678$	−5.04917	−	38.5929i	−0.193912	−	1.48215i
$679$	−19.2284	−	21.7044i	−0.737919	−	0.832938i
$680$	−8.11714	+	3.07843i	−0.311278	+	0.118052i
$681$	15.4248	+	1.72809i	0.591078	+	0.0662206i
$682$	−4.63879	+	3.63426i	−0.177628	+	0.139163i
$683$	−9.09832	+	11.6131i	−0.348138	+	0.444365i	−0.929246	−	0.369461i	$-0.879542\pi$
$683$	−9.09832	+	11.6131i	−0.348138	+	0.444365i	0.581109	+	0.813826i	$0.302619\pi$
$684$	0.376630	−	1.05143i	0.0144008	−	0.0402025i
$685$	−27.7702	−	19.1684i	−1.06104	−	0.732386i
$686$	−2.05493	+	16.9238i	−0.0784575	+	0.646155i
$687$	−23.0161	+	8.97357i	−0.878120	+	0.342363i
$688$	−28.1095	+	8.75927i	−1.07166	+	0.333944i
$689$	10.8411	+	17.9333i	0.413012	+	0.683205i
$690$	6.47367	+	4.38049i	0.246449	+	0.166762i
$691$	−28.7033	−	8.94431i	−1.09193	−	0.340258i	−0.301905	−	0.953338i	$-0.597622\pi$
$691$	−28.7033	−	8.94431i	−1.09193	−	0.340258i	−0.790021	+	0.613080i	$0.789930\pi$
$692$	5.02129	+	2.63537i	0.190881	+	0.100182i
$693$	12.5118	+	19.8567i	0.475284	+	0.754294i
$694$	−27.9398	+	12.5747i	−1.06058	+	0.477329i
$695$	9.10583	−	36.9438i	0.345404	−	1.40136i
$696$	2.50436	+	2.45839i	0.0949273	+	0.0931850i
$697$	35.7976	+	16.1112i	1.35593	+	0.610255i
$698$	−21.2937	+	27.1795i	−0.805980	+	1.02876i
$699$	−33.3654	+	26.6425i	−1.26199	+	1.00771i
$700$	−0.881134	+	4.80819i	−0.0333037	+	0.181733i
$701$	−48.1578	+	21.6741i	−1.81889	+	0.818618i	−0.879369	+	0.476142i	$0.842035\pi$
$701$	−48.1578	+	21.6741i	−1.81889	+	0.818618i	−0.939526	+	0.342476i	$0.888734\pi$
$702$	−11.7629	−	42.5941i	−0.443964	−	1.60761i
$703$	−2.51210	+	0.619177i	−0.0947456	+	0.0233527i
$704$	−1.36101	−	11.2089i	−0.0512949	−	0.422451i
$705$	−8.22649	−	21.1000i	−0.309828	−	0.794670i
$706$	8.83181	+	1.61849i	0.332390	+	0.0609126i
$707$	30.5202	+	5.59304i	1.14783	+	0.210348i
$708$	−7.30948	−	18.7479i	−0.274707	−	0.704590i
$709$	−1.88521	−	15.5261i	−0.0708005	−	0.583095i	−0.984332	−	0.176326i	$-0.943579\pi$
$709$	−1.88521	−	15.5261i	−0.0708005	−	0.583095i	0.913531	−	0.406769i	$-0.133344\pi$
$710$	−13.8142	+	3.40489i	−0.518437	+	0.127783i
$711$	−16.4617	−	12.4118i	−0.617361	−	0.465478i
$712$	2.74583	−	1.23580i	0.102904	−	0.0463135i
$713$	0.279992	−	1.52787i	0.0104858	−	0.0572191i
$714$	−53.4570	+	42.6858i	−2.00058	+	1.59747i
$715$	−12.9567	+	16.5380i	−0.484552	+	0.618486i
$716$	17.4931	+	7.87301i	0.653748	+	0.294228i
$717$	−4.65467	−	4.56924i	−0.173832	−	0.170641i
$718$	−7.75357	+	31.4575i	−0.289361	+	1.17398i
$719$	−14.8159	+	6.66811i	−0.552541	+	0.248678i	−0.667395	−	0.744704i	$-0.732591\pi$
$719$	−14.8159	+	6.66811i	−0.552541	+	0.248678i	0.114854	+	0.993382i	$0.463360\pi$
$720$	−23.6606	+	14.9086i	−0.881779	+	0.555613i
$721$	47.9972	+	25.1909i	1.78751	+	0.938157i
$722$	34.4898	+	10.7474i	1.28358	+	0.399978i
$723$	−37.8689	−	25.6245i	−1.40836	−	0.952984i
$724$	14.7000	+	24.3168i	0.546322	+	0.903727i
$725$	−2.46689	+	0.768714i	−0.0916180	+	0.0285493i
$726$	−17.2457	+	6.72381i	−0.640050	+	0.249544i
$727$	2.41617	−	19.8990i	0.0896110	−	0.738013i	−0.876772	−	0.480906i	$-0.840308\pi$
$727$	2.41617	−	19.8990i	0.0896110	−	0.738013i	0.966383	−	0.257107i	$-0.0827691\pi$
$728$	−8.60645	−	5.94060i	−0.318976	−	0.220173i
$729$	26.5810	−	4.73823i	0.984481	−	0.175490i
$730$	−27.5588	+	35.1762i	−1.02000	+	1.30193i
$731$	31.0088	−	24.2938i	1.14690	−	0.898539i
$732$	−3.10543	−	0.347912i	−0.114780	−	0.0128592i
$733$	−22.8540	+	8.66739i	−0.844133	+	0.320137i	−0.738488	−	0.674267i	$-0.764460\pi$
$733$	−22.8540	+	8.66739i	−0.844133	+	0.320137i	−0.105645	+	0.994404i	$0.533691\pi$
$734$	16.1513	+	18.2310i	0.596154	+	0.672919i
$735$	1.97992	+	15.1333i	0.0730303	+	0.558201i
$736$	6.44089	+	5.70613i	0.237414	+	0.210331i
$737$	−10.5946	+	4.01801i	−0.390258	+	0.148005i
$738$	35.6022	+	8.07868i	1.31053	+	0.297380i
$739$	−2.68736	+	0.326304i	−0.0988560	+	0.0120033i	−0.169815	−	0.985476i	$-0.554317\pi$
$739$	−2.68736	+	0.326304i	−0.0988560	+	0.0120033i	0.0709592	+	0.997479i	$0.477394\pi$
$740$	−34.3517	−	15.4605i	−1.26280	−	0.568338i
$741$	−1.67465	+	0.538909i	−0.0615198	+	0.0197973i
$742$	12.3820	−	27.5117i	0.454558	−	1.00999i
$743$	−8.70838	−	35.3313i	−0.319479	−	1.29618i	−0.882725	−	0.469890i	$-0.844294\pi$
$743$	−8.70838	−	35.3313i	−0.319479	−	1.29618i	0.563246	−	0.826289i	$-0.309552\pi$
$744$	1.32876	+	0.899119i	0.0487146	+	0.0329633i
$745$	31.4137	−	35.4587i	1.15091	−	1.29911i
$746$	−17.0529	+	44.9647i	−0.624350	+	1.64628i
$747$	27.0280	−	5.47237i	0.988902	−	0.200224i
$748$	10.8534	+	20.6794i	0.396840	+	0.756115i
$749$	−55.2239	−	20.9436i	−2.01784	−	0.765264i
$750$	−2.74496	−	39.3315i	−0.100232	−	1.43618i
$751$	8.29721	+	2.58551i	0.302769	+	0.0943468i	0.445124	−	0.895469i	$-0.353160\pi$
$751$	8.29721	+	2.58551i	0.302769	+	0.0943468i	−0.142355	+	0.989816i	$0.545467\pi$
$752$	−7.09316	−	28.7781i	−0.258661	−	1.04943i
$753$	5.05783	+	19.7320i	0.184317	+	0.719076i
$754$	−2.98378	+	24.5737i	−0.108663	+	0.894920i
$755$	0.589797	+	4.85742i	0.0214649	+	0.176780i
$756$	−18.3724	+	21.9370i	−0.668198	+	0.797842i
$757$	−4.16979	−	4.16979i	−0.151553	−	0.151553i	0.627258	−	0.778812i	$-0.284177\pi$
$757$	−4.16979	−	4.16979i	−0.151553	−	0.151553i	−0.778812	+	0.627258i	$0.784177\pi$
$758$	3.91530	+	7.45998i	0.142210	+	0.270959i
$759$	−2.14360	+	4.17788i	−0.0778078	+	0.151647i
$760$	0.182586	+	0.264521i	0.00662308	+	0.00959518i
$761$	6.12143	+	33.4036i	0.221902	+	1.21088i	0.886161	+	0.463377i	$0.153362\pi$
$761$	6.12143	+	33.4036i	0.221902	+	1.21088i	−0.664259	+	0.747502i	$0.731253\pi$
$762$	30.4833	+	26.5060i	1.10429	+	0.960211i
$763$	−5.91308	−	5.91308i	−0.214068	−	0.214068i
$764$	−10.1369	+	0.613171i	−0.366741	+	0.0221837i
$765$	22.5258	−	29.8758i	0.814422	−	1.08016i
$766$	0.130480	−	0.529377i	0.00471442	−	0.0191272i
$767$	−16.3976	+	27.1250i	−0.592084	+	0.979427i
$768$	−31.7115	+	14.6269i	−1.14429	+	0.527802i
$769$	8.81120	+	9.94579i	0.317740	+	0.358654i	0.885582	−	0.464483i	$-0.153760\pi$
$769$	8.81120	+	9.94579i	0.317740	+	0.358654i	−0.567842	+	0.823138i	$0.692222\pi$
$770$	30.1916	+	1.82626i	1.08803	+	0.0658138i
$771$	1.41106	−	27.5610i	0.0508182	−	0.992586i
$772$	41.6124			1.49766
$773$	−18.8778			−0.678988			−0.339494	−	0.940608i	$-0.610256\pi$
$773$	−18.8778			−0.678988			−0.339494	+	0.940608i	$0.610256\pi$
$774$	23.7806	−	27.8660i	0.854775	−	1.00162i
$775$	−1.04597	+	0.548968i	−0.0375724	+	0.0197195i
$776$	4.48524	+	3.97357i	0.161011	+	0.142643i
$777$	65.8753	+	7.38024i	2.36326	+	0.264765i
$778$	−14.3594	−	31.9053i	−0.514809	−	1.14386i
$779$	0.261986	−	1.42961i	0.00938664	−	0.0512212i
$780$	−24.0327	−	8.86069i	−0.860510	−	0.317263i
$781$	−3.03087	−	7.99176i	−0.108453	−	0.285967i
$782$	−12.7974	−	4.85340i	−0.457633	−	0.173557i
$783$	−14.7806	−	3.21030i	−0.528216	−	0.114727i
$784$			19.9746i			0.713380i
$785$	0.690313	+	25.4000i	0.0246383	+	0.906564i
$786$	−29.1476	−	22.4031i	−1.03966	−	0.799093i
$787$	−0.428967	−	2.34080i	−0.0152910	−	0.0834404i	0.975089	−	0.221813i	$-0.0711975\pi$
$787$	−0.428967	−	2.34080i	−0.0152910	−	0.0834404i	−0.990380	+	0.138373i	$0.955813\pi$
$788$	−11.3850	+	30.0199i	−0.405575	+	1.06941i
$789$	10.0573	−	33.3596i	0.358048	−	1.18763i
$790$	−25.3665	+	7.90452i	−0.902499	+	0.281230i
$791$	39.0499	+	7.15616i	1.38845	+	0.254444i
$792$	−3.06134	−	3.76183i	−0.108780	−	0.133671i
$793$	2.54642	+	4.21229i	0.0904260	+	0.149583i
$794$	9.23718	−	10.4266i	0.327815	−	0.370027i
$795$	−2.82400	+	16.2580i	−0.100157	+	0.576611i
$796$	−8.75961	−	12.6905i	−0.310476	−	0.449802i
$797$			42.8003i			1.51606i	0.652217	+	0.758032i	$0.273839\pi$
$797$			42.8003i			1.51606i	−0.652217	+	0.758032i	$0.726161\pi$
$798$	2.00813	+	1.54347i	0.0710871	+	0.0546383i
$799$	22.5267	+	32.6356i	0.796939	+	1.15456i
$800$	0.395116	−	6.53204i	0.0139694	−	0.230942i
$801$	−7.17316	+	10.8153i	−0.253451	+	0.382139i
$802$	20.9350	+	10.9875i	0.739240	+	0.387983i
$803$	−22.9735	−	13.8879i	−0.810716	−	0.490095i
$804$	−8.62011	−	10.7953i	−0.304008	−	0.380720i
$805$	−6.27604	+	4.91696i	−0.221201	+	0.173300i
$806$	0.683298	+	11.2963i	0.0240681	+	0.397894i
$807$	−4.45512	−	34.0523i	−0.156828	−	1.19870i
$808$	−6.40037	−	0.387151i	−0.225164	−	0.0136199i
$809$	−3.24982	+	0.595551i	−0.114257	+	0.0209385i	−0.237079	−	0.971490i	$-0.576190\pi$
$809$	−3.24982	+	0.595551i	−0.114257	+	0.0209385i	0.122822	+	0.992429i	$0.460806\pi$
$810$	15.0183	−	31.3884i	0.527690	−	1.10288i
$811$	−24.1900	+	4.43299i	−0.849427	+	0.155663i	−0.587299	−	0.809370i	$-0.699809\pi$
$811$	−24.1900	+	4.43299i	−0.849427	+	0.155663i	−0.262128	+	0.965033i	$0.584424\pi$
$812$	14.1935	−	7.44931i	0.498093	−	0.261419i
$813$	46.7515	−	6.11658i	1.63965	−	0.214518i
$814$	14.9687	−	48.0362i	0.524652	−	1.68367i
$815$	45.7811	−	5.55884i	1.60364	−	0.194718i
$816$	34.3040	−	34.9454i	1.20088	−	1.22333i
$817$	−1.14807	−	0.899457i	−0.0401659	−	0.0314680i
$818$	−26.9760	+	6.64899i	−0.943194	+	0.232476i
$819$	45.0327	+	1.88757i	1.57357	+	0.0659569i
$820$	15.8397	−	14.0328i	0.553147	−	0.490045i
$821$	−4.87276	+	12.8484i	−0.170061	+	0.448413i	−0.992768	−	0.120053i	$-0.961694\pi$
$821$	−4.87276	+	12.8484i	−0.170061	+	0.448413i	0.822707	+	0.568466i	$0.192463\pi$
$822$	54.1373	+	9.40363i	1.88826	+	0.327989i
$823$	−0.0856165	+	1.41541i	−0.00298440	+	0.0493381i	−0.999363	−	0.0356910i	$-0.988637\pi$
$823$	−0.0856165	+	1.41541i	−0.00298440	+	0.0493381i	0.996378	+	0.0850291i	$0.0270983\pi$
$824$	−10.4738	−	3.97220i	−0.364873	−	0.138378i
$825$	3.50644	−	0.676205i	0.122079	−	0.0235424i
$826$	45.5499	−	2.75526i	1.58488	−	0.0958677i
$827$	−4.03781	+	0.995230i	−0.140408	+	0.0346075i	−0.308893	−	0.951097i	$-0.599959\pi$
$827$	−4.03781	+	0.995230i	−0.140408	+	0.0346075i	0.168485	+	0.985704i	$0.446112\pi$
$828$	−5.64936	−	0.927472i	−0.196329	−	0.0322319i
$829$	−8.72258	−	6.02076i	−0.302948	−	0.209110i	0.406886	−	0.913479i	$-0.366615\pi$
$829$	−8.72258	−	6.02076i	−0.302948	−	0.209110i	−0.709834	+	0.704369i	$0.751230\pi$
$830$	14.5857	−	32.4081i	0.506278	−	1.12490i
$831$	−10.2826	+	17.3708i	−0.356698	+	0.602588i
$832$	−19.2003	−	10.0771i	−0.665650	−	0.349360i
$833$	−9.47666	−	24.9879i	−0.328347	−	0.865779i
$834$	11.7326	+	60.8391i	0.406267	+	2.10669i
$835$	7.90018	+	7.90018i	0.273397	+	0.273397i
$836$	0.647224	−	0.573390i	0.0223847	−	0.0198311i
$837$	−6.91115	−	0.225583i	−0.238884	−	0.00779727i
$838$	14.5586	+	24.0829i	0.502919	+	0.831929i
$839$	6.97745	+	8.90606i	0.240888	+	0.307471i	0.892470	−	0.451108i	$-0.148971\pi$
$839$	6.97745	+	8.90606i	0.240888	+	0.307471i	−0.651581	+	0.758579i	$0.725894\pi$
$840$	−2.04470	−	7.97698i	−0.0705489	−	0.275232i
$841$	−16.8933	−	11.6606i	−0.582529	−	0.402091i
$842$	12.5661	−	18.2052i	0.433058	−	0.627393i
$843$	−4.62440	+	4.71087i	−0.159273	+	0.162251i
$844$	−21.2788	+	35.1994i	−0.732445	+	1.21161i
$845$	4.16027	+	13.3508i	0.143118	+	0.459280i
$846$	26.5556	+	25.5895i	0.913000	+	0.879786i
$847$	−1.13997	−	18.8459i	−0.0391697	−	0.647552i
$848$	−6.42498	+	20.6185i	−0.220635	+	0.708042i
$849$	−11.2863	+	5.20577i	−0.387343	+	0.178662i
$850$	3.09661	+	9.93738i	0.106213	+	0.340849i
$851$	5.44306	+	12.0940i	0.186586	+	0.414577i
$852$	8.14311	−	6.50233i	0.278978	−	0.222766i
$853$	−39.6577	−	4.81531i	−1.35785	−	0.164873i	−0.590987	−	0.806681i	$-0.701262\pi$
$853$	−39.6577	−	4.81531i	−1.35785	−	0.164873i	−0.766866	+	0.641808i	$0.778185\pi$
$854$	2.90837	−	6.46213i	0.0995224	−	0.221130i
$855$	−1.27357	−	0.545050i	−0.0435553	−	0.0186403i
$856$	11.8505	+	2.92090i	0.405043	+	0.0998342i
$857$	−30.1687	−	5.52862i	−1.03054	−	0.188854i	−0.361729	−	0.932283i	$-0.617814\pi$
$857$	−30.1687	−	5.52862i	−1.03054	−	0.188854i	−0.668815	+	0.743429i	$0.733198\pi$
$858$	7.87931	−	33.2916i	0.268995	−	1.13656i
$859$	31.0599	+	39.6450i	1.05975	+	1.35267i	0.932651	+	0.360780i	$0.117490\pi$
$859$	31.0599	+	39.6450i	1.05975	+	1.35267i	0.127099	+	0.991890i	$0.459433\pi$
$860$	−5.08185	−	20.6179i	−0.173290	−	0.703064i
$861$	−18.9683	+	32.0441i	−0.646439	+	1.09206i
$862$	33.0773	+	19.9959i	1.12662	+	0.681063i
$863$	2.84245	−	15.5108i	0.0967582	−	0.527992i	−0.899151	−	0.437638i	$-0.855815\pi$
$863$	2.84245	−	15.5108i	0.0967582	−	0.527992i	0.995910	−	0.0903548i	$-0.0288001\pi$
$864$	20.8762	−	32.1179i	0.710223	−	1.09267i
$865$	3.63891	−	6.01950i	0.123727	−	0.204669i
$866$	55.7611	−	6.77062i	1.89484	−	0.230075i
$867$	−14.4990	+	33.0295i	−0.492412	+	1.12174i
$868$	5.76869	−	4.51948i	0.195802	−	0.153401i
$869$	−6.55083	−	14.5553i	−0.222222	−	0.493756i
$870$	−14.4701	+	13.0606i	−0.490583	+	0.442796i
$871$	−5.20759	+	21.1280i	−0.176453	+	0.715896i
$872$	1.36033	+	1.06575i	0.0460664	+	0.0360907i
$873$	−25.4852	−	4.18399i	−0.862545	−	0.141607i
$874$	−0.0610809	+	0.503046i	−0.00206609	+	0.0170158i
$875$	39.0470	+	9.62422i	1.32003	+	0.325358i
$876$	7.53797	−	31.8494i	0.254684	−	1.07609i
$877$	−44.3014	+	13.8049i	−1.49595	+	0.466157i	−0.932861	−	0.360237i	$-0.882696\pi$
$877$	−44.3014	+	13.8049i	−1.49595	+	0.466157i	−0.563091	+	0.826395i	$0.690388\pi$
$878$	−6.26833	+	11.9433i	−0.211546	+	0.403067i
$879$	−3.55928	−	5.05570i	−0.120052	−	0.170525i
$880$	−21.6121	+	1.30729i	−0.728543	+	0.0440687i
$881$	−8.07957	+	4.88427i	−0.272208	+	0.164555i	−0.646857	−	0.762611i	$-0.723917\pi$
$881$	−8.07957	+	4.88427i	−0.272208	+	0.164555i	0.374649	+	0.927167i	$0.377763\pi$
$882$	−13.2493	−	21.0271i	−0.446127	−	0.708021i
$883$	36.1433	+	21.8494i	1.21632	+	0.735290i	0.972131	−	0.234437i	$-0.0753248\pi$
$883$	36.1433	+	21.8494i	1.21632	+	0.735290i	0.244188	+	0.969728i	$0.421479\pi$
$884$	44.5238	+	5.40617i	1.49750	+	0.181829i
$885$	−23.7593	+	7.64582i	−0.798659	+	0.257012i
$886$	24.3136	−	35.2243i	0.816832	−	1.18338i
$887$	−5.16031	−	4.04284i	−0.173266	−	0.135745i	0.526340	−	0.850274i	$-0.323564\pi$
$887$	−5.16031	−	4.04284i	−0.173266	−	0.135745i	−0.699606	+	0.714529i	$0.746641\pi$
$888$	−13.6978	+	0.126875i	−0.459667	+	0.00425763i
$889$	−35.2611	+	21.3161i	−1.18262	+	0.714918i
$890$	5.93085	+	15.6384i	0.198803	+	0.524199i
$891$	19.8065	+	6.68353i	0.663543	+	0.223907i
$892$	4.89993	−	4.89993i	0.164062	−	0.164062i
$893$	0.973597	−	1.09896i	0.0325802	−	0.0367754i
$894$	−22.2667	+	73.8581i	−0.744711	+	2.47018i
$895$	11.0577	−	21.0686i	0.369617	−	0.704246i
$896$	−2.22313	−	18.3091i	−0.0742695	−	0.611664i
$897$	4.26456	+	7.94571i	0.142389	+	0.265299i
$898$	33.9981	−	49.2548i	1.13453	−	1.64365i
$899$	3.53238	+	1.58979i	0.117811	+	0.0530226i
$900$	2.09438	+	3.81696i	0.0698125	+	0.127232i
$901$	−1.74459	−	28.8416i	−0.0581209	−	0.960853i
$902$	21.1562	+	18.7428i	0.704425	+	0.624066i
$903$	19.6264	+	31.7970i	0.653125	+	1.05814i
$904$	−8.18912	−	0.495350i	−0.272366	−	0.0164751i
$905$	31.2076	−	16.3790i	1.03738	−	0.544457i
$906$	−4.18511	−	6.78036i	−0.139041	−	0.225262i
$907$	−29.7545	−	33.5859i	−0.987984	−	1.11520i	−0.993340	−	0.115217i	$-0.963244\pi$
$907$	−29.7545	−	33.5859i	−0.987984	−	1.11520i	0.00535675	−	0.999986i	$-0.498295\pi$
$908$	−4.35865	+	13.9874i	−0.144647	+	0.464188i
$909$	24.2283	−	13.2941i	0.803603	−	0.440939i
$910$	35.8233	−	45.7251i	1.18753	−	1.51577i
$911$	−40.0015	−	4.85706i	−1.32531	−	0.160921i	−0.572903	−	0.819623i	$-0.694183\pi$
$911$	−40.0015	−	4.85706i	−1.32531	−	0.160921i	−0.752404	+	0.658701i	$0.771106\pi$
$912$	−1.56018	−	0.923538i	−0.0516626	−	0.0305814i
$913$	20.3833	+	6.35169i	0.674589	+	0.210210i
$914$	−54.3022	+	54.3022i	−1.79616	+	1.79616i
$915$	−0.663320	+	3.81878i	−0.0219287	+	0.126245i
$916$	−4.20321	−	22.9362i	−0.138878	−	0.757833i
$917$	30.8600	−	21.3011i	1.01909	−	0.703425i
$918$	−12.9320	+	59.5408i	−0.426821	+	1.96514i
$919$	−3.63076	+	60.0236i	−0.119768	+	1.98000i	0.0676206	+	0.997711i	$0.478459\pi$
$919$	−3.63076	+	60.0236i	−0.119768	+	1.98000i	−0.187388	+	0.982286i	$0.560002\pi$
$920$	1.16502	−	1.16502i	0.0384095	−	0.0384095i
$921$	−22.0150	+	32.5347i	−0.725418	+	1.07205i
$922$	−34.8930	−	44.5377i	−1.14914	−	1.46677i
$923$	−15.9373	−	3.92820i	−0.524583	−	0.129298i
$924$	−20.6403	+	8.04728i	−0.679016	+	0.264736i
$925$	4.68717	−	8.93066i	0.154113	−	0.293638i
$926$	−52.8931	+	46.8592i	−1.73817	+	1.53989i
$927$	47.3193	−	9.58077i	1.55417	−	0.314674i
$928$	−17.6604	+	12.1901i	−0.579730	+	0.400159i
$929$			22.0262i			0.722656i	0.932439	+	0.361328i	$0.117677\pi$
$929$			22.0262i			0.722656i	−0.932439	+	0.361328i	$0.882323\pi$
$930$	−5.43069	+	7.06559i	−0.178079	+	0.231690i
$931$	−0.814304	+	0.562074i	−0.0266877	+	0.0184212i
$932$	−18.7296	−	35.6864i	−0.613510	−	1.16895i
$933$	3.97802	+	20.6279i	0.130235	+	0.675328i
$934$	−30.3532	+	18.3491i	−0.993186	+	0.600402i
$935$	26.4161	−	11.8889i	0.863898	−	0.388809i
$936$	−9.28522	+	0.734498i	−0.303497	+	0.0240078i
$937$	8.71195	+	27.9576i	0.284607	+	0.913336i	0.980722	+	0.195406i	$0.0626025\pi$
$937$	8.71195	+	27.9576i	0.284607	+	0.913336i	−0.696115	+	0.717930i	$0.745090\pi$
$938$	29.2926	−	11.1092i	0.956438	−	0.362729i
$939$	−6.14526	+	3.79310i	−0.200543	+	0.123783i
$940$	21.0267	−	3.85328i	0.685814	−	0.125680i
$941$	−32.7192			−1.06661			−0.533307	−	0.845921i	$-0.679051\pi$
$941$	−32.7192			−1.06661			−0.533307	+	0.845921i	$0.679051\pi$
$942$	−18.3447	−	37.0879i	−0.597702	−	1.20839i
$943$	−7.45024			−0.242613
$944$	−32.1305	+	5.88813i	−1.04576	+	0.191642i
$945$	25.7843	+	24.3898i	0.838765	+	0.793401i
$946$	26.5192	−	10.0574i	0.862214	−	0.326995i
$947$	1.07017	+	3.43429i	0.0347758	+	0.111599i	0.970477	−	0.241195i	$-0.0775393\pi$
$947$	1.07017	+	3.43429i	0.0347758	+	0.111599i	−0.935701	+	0.352794i	$0.885232\pi$
$948$	14.4461	−	13.0389i	0.469186	−	0.423483i
$949$	−47.0121	+	21.1584i	−1.52608	+	0.686832i
$950$	0.329794	−	0.199368i	0.0106999	−	0.00646834i
$951$	43.5639	−	8.40116i	1.41266	−	0.272426i
$952$	6.70103	+	12.7677i	0.217182	+	0.413805i
$953$	12.9768	−	8.95725i	0.420360	−	0.290154i	−0.339047	−	0.940770i	$-0.610104\pi$
$953$	12.9768	−	8.95725i	0.420360	−	0.290154i	0.759407	+	0.650616i	$0.225489\pi$
$954$	−6.91284	−	25.9666i	−0.223811	−	0.840701i
$955$			12.5965i			0.407612i
$956$	5.06692	−	3.49744i	0.163876	−	0.113115i
$957$	−8.83672	−	7.68375i	−0.285651	−	0.248380i
$958$	29.0421	−	25.7291i	0.938309	−	0.831269i
$959$	−26.0463	+	49.6270i	−0.841078	+	1.60254i
$960$	−6.20253	−	15.9088i	−0.200186	−	0.513453i
$961$	−28.3797	−	6.99498i	−0.915475	−	0.225644i
$962$	−59.5907	−	76.0619i	−1.92128	−	2.45233i
$963$	−49.9240	+	16.5776i	−1.60878	+	0.534204i
$964$	30.5184	−	30.5184i	0.982930	−	0.982930i
$965$	3.11641	−	51.5204i	0.100321	−	1.65850i
$966$	5.92675	−	11.5512i	0.190690	−	0.371655i
$967$	32.9822	−	22.7659i	1.06063	−	0.732103i	0.0959171	−	0.995389i	$-0.469422\pi$
$967$	32.9822	−	22.7659i	1.06063	−	0.732103i	0.964718	+	0.263286i	$0.0848062\pi$
$968$	0.703290	+	3.83773i	0.0226046	+	0.123349i
$969$	2.38991	+	0.415126i	0.0767750	+	0.0133358i
$970$	−23.5352	+	23.5352i	−0.755671	+	0.755671i
$971$	14.7781	+	4.60504i	0.474252	+	0.147783i	0.525307	−	0.850913i	$-0.323951\pi$
$971$	14.7781	+	4.60504i	0.474252	+	0.147783i	−0.0510547	+	0.998696i	$0.516258\pi$
$972$	−0.359451	+	25.4832i	−0.0115294	+	0.817375i
$973$	−62.7384	−	7.61782i	−2.01130	−	0.244216i
$974$	42.8384	−	54.6791i	1.37263	−	1.75203i
$975$	2.75655	−	6.27957i	0.0882803	−	0.201107i
$976$	−1.50914	+	4.84301i	−0.0483064	+	0.155021i
$977$	−4.84881	−	5.47317i	−0.155127	−	0.175102i	0.665809	−	0.746122i	$-0.268086\pi$
$977$	−4.84881	−	5.47317i	−0.155127	−	0.175102i	−0.820936	+	0.571020i	$0.806548\pi$
$978$	−63.9049	+	39.4446i	−2.04345	+	1.26130i
$979$	−8.89673	+	4.66936i	−0.284341	+	0.149234i
$980$	−14.3800	−	0.869832i	−0.459354	−	0.0277858i
$981$	−7.40912	−	0.760654i	−0.236555	−	0.0242858i
$982$	−44.0870	−	39.0577i	−1.40687	−	1.24638i
$983$	−1.97452	−	32.6427i	−0.0629773	−	1.04114i	−0.883170	−	0.469052i	$-0.844596\pi$
$983$	−1.97452	−	32.6427i	−0.0629773	−	1.04114i	0.820193	−	0.572087i	$-0.193866\pi$
$984$	3.09306	−	7.04615i	0.0986030	−	0.224623i
$985$	36.3150	+	16.3441i	1.15709	+	0.520766i
$986$	19.3892	−	28.0901i	0.617479	−	0.894572i
$987$	−33.1440	+	17.7888i	−1.05498	+	0.566223i
$988$	−0.200159	−	1.64846i	−0.00636790	−	0.0524444i
$989$	−3.47429	+	6.61971i	−0.110476	+	0.210494i
$990$	21.8837	−	15.7116i	0.695510	−	0.499347i
$991$	4.32702	−	4.88419i	0.137452	−	0.155151i	−0.675754	−	0.737127i	$-0.736182\pi$
$991$	4.32702	−	4.88419i	0.137452	−	0.155151i	0.813206	+	0.581976i	$0.197720\pi$
$992$	−6.93703	+	6.93703i	−0.220251	+	0.220251i
$993$	−1.19075	−	17.0618i	−0.0377872	−	0.541439i
$994$	8.37992	+	22.0960i	0.265795	+	0.700844i
$995$	−16.3681	+	9.89488i	−0.518904	+	0.313689i
$996$	0.241089	+	26.0287i	0.00763919	+	0.824751i
$997$	−6.34282	−	4.96928i	−0.200879	−	0.157379i	0.511239	−	0.859439i	$-0.329187\pi$
$997$	−6.34282	−	4.96928i	−0.200879	−	0.157379i	−0.712118	+	0.702060i	$0.752264\pi$
$998$	−22.6067	+	32.7515i	−0.715603	+	1.03673i
$999$	49.6571	−	31.9355i	1.57108	−	1.01039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.s.a.2.10	✓	1200
3.2	odd	2	inner	471.2.s.a.2.41	yes	1200
157.79	odd	52	inner	471.2.s.a.236.41	yes	1200
471.236	even	52	inner	471.2.s.a.236.10	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.s.a.2.10	✓	1200	1.1	even	1	trivial
471.2.s.a.2.41	yes	1200	3.2	odd	2	inner
471.2.s.a.236.10	yes	1200	471.236	even	52	inner
471.2.s.a.236.41	yes	1200	157.79	odd	52	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87532 + 0.343664i) q^{2} +(-0.909746 - 1.47389i) q^{3} +(1.52867 - 0.579748i) q^{4} +(-0.603303 - 1.93607i) q^{5} +(2.21258 + 2.45137i) q^{6} +(-3.07153 + 1.38238i) q^{7} +(0.595672 - 0.360097i) q^{8} +(-1.34473 + 2.68174i) q^{9} +O(q^{10})\)	\(q+(-1.87532 + 0.343664i) q^{2} +(-0.909746 - 1.47389i) q^{3} +(1.52867 - 0.579748i) q^{4} +(-0.603303 - 1.93607i) q^{5} +(2.21258 + 2.45137i) q^{6} +(-3.07153 + 1.38238i) q^{7} +(0.595672 - 0.360097i) q^{8} +(-1.34473 + 2.68174i) q^{9} +(1.79674 + 3.42340i) q^{10} +(-1.91150 + 1.31941i) q^{11} +(-2.24519 - 1.72567i) q^{12} +4.46047i q^{13} +(5.28500 - 3.64798i) q^{14} +(-2.30470 + 2.65053i) q^{15} +(-3.44082 + 3.04830i) q^{16} +(2.85818 - 5.44581i) q^{17} +(1.60017 - 5.49124i) q^{18} +(-0.221092 - 0.0544943i) q^{19} +(-2.04468 - 2.60984i) q^{20} +(4.83179 + 3.26949i) q^{21} +(3.13122 - 3.13122i) q^{22} +(-0.0704760 + 1.16511i) q^{23} +(-1.07265 - 0.550362i) q^{24} +(0.730541 - 0.504256i) q^{25} +(-1.53291 - 8.36479i) q^{26} +(5.17595 - 0.457715i) q^{27} +(-3.89391 + 3.89391i) q^{28} +(-2.77905 - 0.865987i) q^{29} +(3.41115 - 5.76263i) q^{30} +(-1.32106 - 0.160405i) q^{31} +(4.54649 - 5.80316i) q^{32} +(3.68364 + 1.61701i) q^{33} +(-3.48846 + 11.1949i) q^{34} +(4.52944 + 5.11268i) q^{35} +(-0.500910 + 4.87909i) q^{36} +(10.0608 - 5.28029i) q^{37} +(0.433345 + 0.0262126i) q^{38} +(6.57426 - 4.05790i) q^{39} +(-1.05654 - 0.936014i) q^{40} +(0.385384 + 6.37115i) q^{41} +(-10.1847 - 4.47081i) q^{42} +(5.84063 + 2.62866i) q^{43} +(-2.15712 + 3.12513i) q^{44} +(6.00330 + 0.985579i) q^{45} +(-0.268241 - 2.20916i) q^{46} +(-2.99640 + 5.70916i) q^{47} +(7.62314 + 2.29822i) q^{48} +(2.88144 - 3.25247i) q^{49} +(-1.19670 + 1.19670i) q^{50} +(-10.6268 + 0.741646i) q^{51} +(2.58595 + 6.81859i) q^{52} +(4.02049 - 2.43047i) q^{53} +(-9.54924 + 2.63715i) q^{54} +(3.70768 + 2.90478i) q^{55} +(-1.33183 + 1.92949i) q^{56} +(0.120819 + 0.375442i) q^{57} +(5.50920 + 0.668939i) q^{58} +(6.08120 + 3.67621i) q^{59} +(-1.98649 + 5.38793i) q^{60} +(0.944360 - 0.570885i) q^{61} +(2.53252 - 0.153190i) q^{62} +(0.423176 - 10.0959i) q^{63} +(-2.25919 + 4.30454i) q^{64} +(8.63577 - 2.69102i) q^{65} +(-7.46370 - 1.76647i) q^{66} +(4.73672 + 1.16750i) q^{67} +(1.21202 - 9.98187i) q^{68} +(1.78136 - 0.956077i) q^{69} +(-10.2512 - 8.03129i) q^{70} +(-0.880668 + 3.57301i) q^{71} +(0.164668 + 2.08167i) q^{72} +(4.74354 + 10.5397i) q^{73} +(-17.0524 + 13.3597i) q^{74} +(-1.40783 - 0.617995i) q^{75} +(-0.369570 + 0.0448739i) q^{76} +(4.04728 - 6.69502i) q^{77} +(-10.9343 + 9.86917i) q^{78} +(-1.23874 + 6.75959i) q^{79} +(7.97757 + 4.82261i) q^{80} +(-5.38343 - 7.21240i) q^{81} +(-2.91225 - 11.8155i) q^{82} +(-5.66896 - 7.23590i) q^{83} +(9.28169 + 2.19674i) q^{84} +(-12.2678 - 2.24816i) q^{85} +(-11.8564 - 2.92234i) q^{86} +(1.25186 + 4.88385i) q^{87} +(-0.663510 + 1.47426i) q^{88} +(4.29441 + 0.521436i) q^{89} +(-11.5968 + 0.214847i) q^{90} +(-6.16608 - 13.7005i) q^{91} +(0.567734 + 1.82192i) q^{92} +(0.965406 + 2.09303i) q^{93} +(3.65715 - 11.7362i) q^{94} +(0.0278809 + 0.460926i) q^{95} +(-12.6894 - 1.42164i) q^{96} +(2.56114 + 8.21900i) q^{97} +(-4.28584 + 7.08965i) q^{98} +(-0.967873 - 6.90037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9}+O(q^{10}) \) 1200 * q - 26 * q^3 - 52 * q^4 - 20 * q^6 - 40 * q^7 - 18 * q^9	\( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9} - 52 q^{10} - 80 q^{12} - 12 q^{15} + 16 q^{16} + 12 q^{18} - 52 q^{19} - 26 q^{21} - 64 q^{22} + 18 q^{24} + 104 q^{25} - 26 q^{27} - 84 q^{28} - 34 q^{30} - 52 q^{31} - 26 q^{33} - 80 q^{34} - 26 q^{36} - 308 q^{37} + 52 q^{39} - 340 q^{40} - 26 q^{42} - 76 q^{43} - 52 q^{45} - 60 q^{46} - 130 q^{48} - 52 q^{49} - 26 q^{51} + 84 q^{52} - 246 q^{54} - 36 q^{55} - 26 q^{57} - 52 q^{58} + 14 q^{60} - 4 q^{61} - 46 q^{63} - 52 q^{64} - 22 q^{66} + 28 q^{67} - 72 q^{69} - 40 q^{70} + 46 q^{72} - 48 q^{73} - 46 q^{75} - 52 q^{76} + 146 q^{78} - 100 q^{79} + 58 q^{81} - 52 q^{82} - 156 q^{84} - 20 q^{85} + 12 q^{87} - 116 q^{88} - 26 q^{90} + 360 q^{91} - 310 q^{93} + 96 q^{94} + 176 q^{96} + 116 q^{97} - 66 q^{99}+O(q^{100}) \) 1200 * q - 26 * q^3 - 52 * q^4 - 20 * q^6 - 40 * q^7 - 18 * q^9 - 52 * q^10 - 80 * q^12 - 12 * q^15 + 16 * q^16 + 12 * q^18 - 52 * q^19 - 26 * q^21 - 64 * q^22 + 18 * q^24 + 104 * q^25 - 26 * q^27 - 84 * q^28 - 34 * q^30 - 52 * q^31 - 26 * q^33 - 80 * q^34 - 26 * q^36 - 308 * q^37 + 52 * q^39 - 340 * q^40 - 26 * q^42 - 76 * q^43 - 52 * q^45 - 60 * q^46 - 130 * q^48 - 52 * q^49 - 26 * q^51 + 84 * q^52 - 246 * q^54 - 36 * q^55 - 26 * q^57 - 52 * q^58 + 14 * q^60 - 4 * q^61 - 46 * q^63 - 52 * q^64 - 22 * q^66 + 28 * q^67 - 72 * q^69 - 40 * q^70 + 46 * q^72 - 48 * q^73 - 46 * q^75 - 52 * q^76 + 146 * q^78 - 100 * q^79 + 58 * q^81 - 52 * q^82 - 156 * q^84 - 20 * q^85 + 12 * q^87 - 116 * q^88 - 26 * q^90 + 360 * q^91 - 310 * q^93 + 96 * q^94 + 176 * q^96 + 116 * q^97 - 66 * q^99

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