LMFDB - Embedded newform 69.2.g.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(5,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("69.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.g (of order $22$, degree $10$, 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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	69.14
Dual form			69.2.g.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694600 + 2.36559i) q^{2} +(-1.73202 - 0.0101732i) q^{3} +(-3.43104 + 2.20500i) q^{4} +(-0.0722440 - 0.502468i) q^{5} +(-1.17900 - 4.10432i) q^{6} +(3.47479 + 1.58688i) q^{7} +(-3.87278 - 3.35579i) q^{8} +(2.99979 + 0.0352405i) q^{9} +O(q^{10})$	\(q+(0.694600 + 2.36559i) q^{2} +(-1.73202 - 0.0101732i) q^{3} +(-3.43104 + 2.20500i) q^{4} +(-0.0722440 - 0.502468i) q^{5} +(-1.17900 - 4.10432i) q^{6} +(3.47479 + 1.58688i) q^{7} +(-3.87278 - 3.35579i) q^{8} +(2.99979 + 0.0352405i) q^{9} +(1.13845 - 0.519914i) q^{10} +(0.971385 + 0.285224i) q^{11} +(5.96507 - 3.78420i) q^{12} +(-1.96293 - 4.29821i) q^{13} +(-1.34033 + 9.32218i) q^{14} +(0.120016 + 0.871021i) q^{15} +(1.85985 - 4.07250i) q^{16} +(-5.03219 - 3.23399i) q^{17} +(2.00029 + 7.12076i) q^{18} +(1.15430 + 1.79612i) q^{19} +(1.35581 + 1.56469i) q^{20} +(-6.00227 - 2.78387i) q^{21} +2.49602i q^{22} +(3.68290 - 3.07184i) q^{23} +(6.67360 + 5.85169i) q^{24} +(4.55021 - 1.33606i) q^{25} +(8.80437 - 7.62903i) q^{26} +(-5.19535 - 0.0915549i) q^{27} +(-15.4212 + 2.21724i) q^{28} +(-0.433582 + 0.674667i) q^{29} +(-1.97711 + 0.888921i) q^{30} +(-2.11763 + 2.44388i) q^{31} +(0.781186 + 0.112318i) q^{32} +(-1.67956 - 0.503897i) q^{33} +(4.15494 - 14.1504i) q^{34} +(0.546326 - 1.86062i) q^{35} +(-10.3701 + 6.49362i) q^{36} +(-4.43544 - 0.637721i) q^{37} +(-3.44711 + 3.97818i) q^{38} +(3.35611 + 7.46457i) q^{39} +(-1.40639 + 2.18839i) q^{40} +(1.70861 - 0.245661i) q^{41} +(2.41631 - 16.1326i) q^{42} +(-4.77133 + 4.13438i) q^{43} +(-3.96178 + 1.16328i) q^{44} +(-0.199010 - 1.50985i) q^{45} +(9.82487 + 6.57854i) q^{46} +0.781750i q^{47} +(-3.26273 + 7.03474i) q^{48} +(4.97194 + 5.73793i) q^{49} +(6.32115 + 9.83590i) q^{50} +(8.68295 + 5.65253i) q^{51} +(16.2124 + 10.4191i) q^{52} +(-0.0144510 + 0.0316432i) q^{53} +(-3.39211 - 12.3537i) q^{54} +(0.0731394 - 0.508696i) q^{55} +(-8.13187 - 17.8063i) q^{56} +(-1.98099 - 3.12266i) q^{57} +(-1.89715 - 0.557054i) q^{58} +(-0.669283 + 0.305651i) q^{59} +(-2.33238 - 2.72387i) q^{60} +(-4.17444 - 3.61717i) q^{61} +(-7.25212 - 3.31193i) q^{62} +(10.3677 + 4.88278i) q^{63} +(-0.997397 - 6.93705i) q^{64} +(-2.01791 + 1.29683i) q^{65} +(0.0253925 - 4.32315i) q^{66} +(-0.413359 - 1.40777i) q^{67} +24.3966 q^{68} +(-6.41012 + 5.28303i) q^{69} +4.78093 q^{70} +(0.150561 + 0.512764i) q^{71} +(-11.4993 - 10.2031i) q^{72} +(3.76147 - 2.41735i) q^{73} +(-1.57227 - 10.9354i) q^{74} +(-7.89465 + 2.26780i) q^{75} +(-7.92087 - 3.61734i) q^{76} +(2.92274 + 2.53257i) q^{77} +(-15.3270 + 13.1241i) q^{78} +(-4.78339 + 2.18450i) q^{79} +(-2.18067 - 0.640301i) q^{80} +(8.99752 + 0.211428i) q^{81} +(1.76794 + 3.87124i) q^{82} +(1.40461 - 9.76931i) q^{83} +(26.7324 - 3.68342i) q^{84} +(-1.26143 + 2.76215i) q^{85} +(-13.0944 - 8.41527i) q^{86} +(0.757837 - 1.16413i) q^{87} +(-2.80481 - 4.36437i) q^{88} +(11.1441 + 12.8610i) q^{89} +(3.43345 - 1.51952i) q^{90} -18.0503i q^{91} +(-5.86279 + 18.6604i) q^{92} +(3.69264 - 4.21130i) q^{93} +(-1.84930 + 0.543004i) q^{94} +(0.819102 - 0.709756i) q^{95} +(-1.35189 - 0.202484i) q^{96} +(-4.01587 + 0.577395i) q^{97} +(-10.1201 + 15.7472i) q^{98} +(2.90390 + 0.889846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9}+O(q^{10}) $ 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9	$ 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} + 4 q^{12} - 22 q^{13} - 46 q^{16} + 12 q^{18} - 22 q^{19} + 22 q^{21} + 50 q^{24} + 8 q^{25} + 10 q^{27} - 22 q^{28} + 33 q^{30} - 22 q^{31} + 22 q^{36} + 22 q^{37} + 13 q^{39} + 132 q^{40} - 11 q^{42} + 22 q^{43} + 66 q^{46} - 58 q^{48} + 68 q^{49} - 11 q^{51} + 94 q^{52} - 33 q^{54} - 44 q^{57} - 8 q^{58} - 121 q^{60} - 66 q^{61} - 66 q^{63} - 20 q^{64} - 66 q^{66} - 44 q^{67} - 66 q^{69} - 132 q^{70} - 101 q^{72} - 44 q^{73} - 44 q^{75} - 110 q^{76} + 84 q^{78} - 66 q^{79} + 77 q^{81} - 132 q^{82} + 77 q^{84} - 44 q^{85} + 73 q^{87} + 66 q^{88} + 176 q^{90} + 116 q^{93} + 100 q^{94} + 85 q^{96} + 44 q^{97} + 121 q^{99}+O(q^{100}) $ 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9 - 22 * q^10 + 4 * q^12 - 22 * q^13 - 46 * q^16 + 12 * q^18 - 22 * q^19 + 22 * q^21 + 50 * q^24 + 8 * q^25 + 10 * q^27 - 22 * q^28 + 33 * q^30 - 22 * q^31 + 22 * q^36 + 22 * q^37 + 13 * q^39 + 132 * q^40 - 11 * q^42 + 22 * q^43 + 66 * q^46 - 58 * q^48 + 68 * q^49 - 11 * q^51 + 94 * q^52 - 33 * q^54 - 44 * q^57 - 8 * q^58 - 121 * q^60 - 66 * q^61 - 66 * q^63 - 20 * q^64 - 66 * q^66 - 44 * q^67 - 66 * q^69 - 132 * q^70 - 101 * q^72 - 44 * q^73 - 44 * q^75 - 110 * q^76 + 84 * q^78 - 66 * q^79 + 77 * q^81 - 132 * q^82 + 77 * q^84 - 44 * q^85 + 73 * q^87 + 66 * q^88 + 176 * q^90 + 116 * q^93 + 100 * q^94 + 85 * q^96 + 44 * q^97 + 121 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.694600	+	2.36559i	0.491156	+	1.67273i	0.715817	+	0.698288i	$0.246054\pi$
$2$	0.694600	+	2.36559i	0.491156	+	1.67273i	−0.224661	+	0.974437i	$0.572127\pi$
$3$	−1.73202	−	0.0101732i	−0.999983	−	0.00587352i
$3$	−1.73202	−	0.0101732i	−0.999983	−	0.00587352i
$4$	−3.43104	+	2.20500i	−1.71552	+	1.10250i
$5$	−0.0722440	−	0.502468i	−0.0323085	−	0.224711i	0.967270	−	0.253750i	$-0.0816642\pi$
$5$	−0.0722440	−	0.502468i	−0.0323085	−	0.224711i	−0.999578	+	0.0290397i	$0.990755\pi$
$6$	−1.17900	−	4.10432i	−0.481323	−	1.67558i
$7$	3.47479	+	1.58688i	1.31335	+	0.599786i	0.944135	−	0.329559i	$-0.106900\pi$
$7$	3.47479	+	1.58688i	1.31335	+	0.599786i	0.369213	+	0.929345i	$0.379627\pi$
$8$	−3.87278	−	3.35579i	−1.36924	−	1.18645i
$9$	2.99979	+	0.0352405i	0.999931	+	0.0117468i
$10$	1.13845	−	0.519914i	0.360011	−	0.164411i
$11$	0.971385	+	0.285224i	0.292884	+	0.0859984i	0.424874	−	0.905253i	$-0.360319\pi$
$11$	0.971385	+	0.285224i	0.292884	+	0.0859984i	−0.131990	+	0.991251i	$0.542137\pi$
$12$	5.96507	−	3.78420i	1.72197	−	1.09240i
$13$	−1.96293	−	4.29821i	−0.544419	−	1.19211i	−0.959340	−	0.282253i	$-0.908918\pi$
$13$	−1.96293	−	4.29821i	−0.544419	−	1.19211i	0.414921	−	0.909857i	$-0.363809\pi$
$14$	−1.34033	+	9.32218i	−0.358218	+	2.49146i
$15$	0.120016	+	0.871021i	0.0309881	+	0.224897i
$16$	1.85985	−	4.07250i	0.464962	−	1.01813i
$17$	−5.03219	−	3.23399i	−1.22048	−	0.784358i	−0.238102	−	0.971240i	$-0.576525\pi$
$17$	−5.03219	−	3.23399i	−1.22048	−	0.784358i	−0.982382	+	0.186882i	$0.940162\pi$
$18$	2.00029	+	7.12076i	0.471473	+	1.67838i
$19$	1.15430	+	1.79612i	0.264814	+	0.412058i	0.948041	−	0.318147i	$-0.103061\pi$
$19$	1.15430	+	1.79612i	0.264814	+	0.412058i	−0.683228	+	0.730205i	$0.739424\pi$
$20$	1.35581	+	1.56469i	0.303169	+	0.349876i
$21$	−6.00227	−	2.78387i	−1.30980	−	0.607489i
$22$			2.49602i			0.532152i
$23$	3.68290	−	3.07184i	0.767938	−	0.640524i
$23$	3.68290	−	3.07184i	0.767938	−	0.640524i
$24$	6.67360	+	5.85169i	1.36224	+	1.19447i
$25$	4.55021	−	1.33606i	0.910042	−	0.267212i
$26$	8.80437	−	7.62903i	1.72668	−	1.49618i
$27$	−5.19535	−	0.0915549i	−0.999845	−	0.0176197i
$28$	−15.4212	+	2.21724i	−2.91434	+	0.419019i
$29$	−0.433582	+	0.674667i	−0.0805142	+	0.125283i	−0.879175	−	0.476499i	$-0.841906\pi$
$29$	−0.433582	+	0.674667i	−0.0805142	+	0.125283i	0.798661	+	0.601781i	$0.205542\pi$
$30$	−1.97711	+	0.888921i	−0.360970	+	0.162294i
$31$	−2.11763	+	2.44388i	−0.380338	+	0.438933i	−0.913351	−	0.407174i	$-0.866514\pi$
$31$	−2.11763	+	2.44388i	−0.380338	+	0.438933i	0.533013	+	0.846107i	$0.321060\pi$
$32$	0.781186	+	0.112318i	0.138096	+	0.0198551i
$33$	−1.67956	−	0.503897i	−0.292373	−	0.0877172i
$34$	4.15494	−	14.1504i	0.712566	−	2.42678i
$35$	0.546326	−	1.86062i	0.0923459	−	0.314501i
$36$	−10.3701	+	6.49362i	−1.72835	+	1.08227i
$37$	−4.43544	−	0.637721i	−0.729182	−	0.104841i	−0.232282	−	0.972648i	$-0.574619\pi$
$37$	−4.43544	−	0.637721i	−0.729182	−	0.104841i	−0.496900	+	0.867808i	$0.665528\pi$
$38$	−3.44711	+	3.97818i	−0.559195	+	0.645345i
$39$	3.35611	+	7.46457i	0.537407	+	1.19529i
$40$	−1.40639	+	2.18839i	−0.222370	+	0.346014i
$41$	1.70861	−	0.245661i	0.266840	−	0.0383659i	−0.00759585	−	0.999971i	$-0.502418\pi$
$41$	1.70861	−	0.245661i	0.266840	−	0.0383659i	0.274436	+	0.961605i	$0.411509\pi$
$42$	2.41631	−	16.1326i	0.372845	−	2.48931i
$43$	−4.77133	+	4.13438i	−0.727621	+	0.630487i	−0.937800	−	0.347176i	$-0.887141\pi$
$43$	−4.77133	+	4.13438i	−0.727621	+	0.630487i	0.210179	+	0.977663i	$0.432595\pi$
$44$	−3.96178	+	1.16328i	−0.597261	+	0.175372i
$45$	−0.199010	−	1.50985i	−0.0296667	−	0.225075i
$46$	9.82487	+	6.57854i	1.44860	+	0.969953i
$47$			0.781750i			0.114030i	0.998373	+	0.0570150i	$0.0181583\pi$
$47$			0.781750i			0.114030i	−0.998373	+	0.0570150i	$0.981842\pi$
$48$	−3.26273	+	7.03474i	−0.470934	+	1.01538i
$49$	4.97194	+	5.73793i	0.710278	+	0.819704i
$50$	6.32115	+	9.83590i	0.893946	+	1.39101i
$51$	8.68295	+	5.65253i	1.21586	+	0.791513i
$52$	16.2124	+	10.4191i	2.24826	+	1.44487i
$53$	−0.0144510	+	0.0316432i	−0.00198499	+	0.00434653i	−0.910622	−	0.413241i	$-0.864397\pi$
$53$	−0.0144510	+	0.0316432i	−0.00198499	+	0.00434653i	0.908637	+	0.417587i	$0.137124\pi$
$54$	−3.39211	−	12.3537i	−0.461607	−	1.68112i
$55$	0.0731394	−	0.508696i	0.00986212	−	0.0685926i
$56$	−8.13187	−	17.8063i	−1.08667	−	2.37947i
$57$	−1.98099	−	3.12266i	−0.262389	−	0.413606i
$58$	−1.89715	−	0.557054i	−0.249108	−	0.0731448i
$59$	−0.669283	+	0.305651i	−0.0871332	+	0.0397924i	−0.458505	−	0.888692i	$-0.651615\pi$
$59$	−0.669283	+	0.305651i	−0.0871332	+	0.0397924i	0.371372	+	0.928484i	$0.378888\pi$
$60$	−2.33238	−	2.72387i	−0.301109	−	0.351650i
$61$	−4.17444	−	3.61717i	−0.534483	−	0.463132i	0.345311	−	0.938488i	$-0.387774\pi$
$61$	−4.17444	−	3.61717i	−0.534483	−	0.463132i	−0.879793	+	0.475357i	$0.842319\pi$
$62$	−7.25212	−	3.31193i	−0.921020	−	0.420616i
$63$	10.3677	+	4.88278i	1.30621	+	0.615172i
$64$	−0.997397	−	6.93705i	−0.124675	−	0.867131i
$65$	−2.01791	+	1.29683i	−0.250291	+	0.160852i
$66$	0.0253925	−	4.32315i	0.00312561	−	0.532143i
$67$	−0.413359	−	1.40777i	−0.0504998	−	0.171987i	0.930382	−	0.366592i	$-0.119476\pi$
$67$	−0.413359	−	1.40777i	−0.0504998	−	0.171987i	−0.980882	+	0.194605i	$0.937657\pi$
$68$	24.3966			2.95852
$69$	−6.41012	+	5.28303i	−0.771687	+	0.636002i
$70$	4.78093			0.571431
$71$	0.150561	+	0.512764i	0.0178683	+	0.0608539i	0.967945	−	0.251164i	$-0.0808133\pi$
$71$	0.150561	+	0.512764i	0.0178683	+	0.0608539i	−0.950076	+	0.312018i	$0.898995\pi$
$72$	−11.4993	−	10.2031i	−1.35520	−	1.20245i
$73$	3.76147	−	2.41735i	0.440247	−	0.282930i	−0.301681	−	0.953409i	$-0.597548\pi$
$73$	3.76147	−	2.41735i	0.440247	−	0.282930i	0.741928	+	0.670479i	$0.233911\pi$
$74$	−1.57227	−	10.9354i	−0.182773	−	1.27121i
$75$	−7.89465	+	2.26780i	−0.911596	+	0.261863i
$76$	−7.92087	−	3.61734i	−0.908587	−	0.414938i
$77$	2.92274	+	2.53257i	0.333077	+	0.288613i
$78$	−15.3270	+	13.1241i	−1.73544	+	1.48601i
$79$	−4.78339	+	2.18450i	−0.538173	+	0.245775i	−0.665909	−	0.746033i	$-0.731956\pi$
$79$	−4.78339	+	2.18450i	−0.538173	+	0.245775i	0.127736	+	0.991808i	$0.459229\pi$
$80$	−2.18067	−	0.640301i	−0.243806	−	0.0715879i
$81$	8.99752	+	0.211428i	0.999724	+	0.0234920i
$82$	1.76794	+	3.87124i	0.195236	+	0.427507i
$83$	1.40461	−	9.76931i	0.154176	−	1.07232i	−0.754945	−	0.655789i	$-0.772336\pi$
$83$	1.40461	−	9.76931i	0.154176	−	1.07232i	0.909121	−	0.416532i	$-0.136755\pi$
$84$	26.7324	−	3.68342i	2.91675	−	0.401894i
$85$	−1.26143	+	2.76215i	−0.136822	+	0.299597i
$86$	−13.0944	−	8.41527i	−1.41201	−	0.907442i
$87$	0.757837	−	1.16413i	0.0812487	−	0.124808i
$88$	−2.80481	−	4.36437i	−0.298994	−	0.465244i
$89$	11.1441	+	12.8610i	1.18128	+	1.36327i	0.917033	+	0.398811i	$0.130577\pi$
$89$	11.1441	+	12.8610i	1.18128	+	1.36327i	0.264244	+	0.964456i	$0.414878\pi$
$90$	3.43345	−	1.51952i	0.361917	−	0.160171i
$91$		−	18.0503i		−	1.89219i
$92$	−5.86279	+	18.6604i	−0.611238	+	1.94548i
$93$	3.69264	−	4.21130i	0.382909	−	0.436692i
$94$	−1.84930	+	0.543004i	−0.190741	+	0.0560066i
$95$	0.819102	−	0.709756i	0.0840381	−	0.0728194i
$96$	−1.35189	−	0.202484i	−0.137977	−	0.0206659i
$97$	−4.01587	+	0.577395i	−0.407750	+	0.0586256i	−0.343138	−	0.939285i	$-0.611490\pi$
$97$	−4.01587	+	0.577395i	−0.407750	+	0.0586256i	−0.0646118	+	0.997910i	$0.520581\pi$
$98$	−10.1201	+	15.7472i	−1.02228	+	1.59070i
$99$	2.90390	+	0.889846i	0.291853	+	0.0894329i
$100$	−12.6659	+	14.6173i	−1.26659	+	1.46173i
$101$	9.52259	+	1.36914i	0.947533	+	0.136235i	0.598721	−	0.800958i	$-0.295676\pi$
$101$	9.52259	+	1.36914i	0.947533	+	0.136235i	0.348812	+	0.937193i	$0.386585\pi$
$102$	−7.34040	+	24.4666i	−0.726807	+	2.42255i
$103$	−2.81231	+	9.57786i	−0.277106	+	0.943735i	0.696892	+	0.717176i	$0.254566\pi$
$103$	−2.81231	+	9.57786i	−0.277106	+	0.943735i	−0.973997	+	0.226559i	$0.927252\pi$
$104$	−6.82189	+	23.2332i	−0.668941	+	2.27820i
$105$	−0.965176	+	3.21707i	−0.0941916	+	0.313954i
$106$	−0.0848926	−	0.0122057i	−0.00824550	−	0.00118552i
$107$	−8.18985	+	9.45159i	−0.791743	+	0.913720i	−0.997898	−	0.0647993i	$-0.979359\pi$
$107$	−8.18985	+	9.45159i	−0.791743	+	0.913720i	0.206155	+	0.978519i	$0.433905\pi$
$108$	18.0273	−	11.1416i	1.73468	−	1.07210i
$109$	4.38415	−	6.82187i	0.419925	−	0.653416i	−0.565259	−	0.824913i	$-0.691224\pi$
$109$	4.38415	−	6.82187i	0.419925	−	0.653416i	0.985185	+	0.171497i	$0.0548603\pi$
$110$	1.25417	−	0.180322i	0.119580	−	0.0171931i
$111$	7.67579	+	1.14967i	0.728554	+	0.109122i
$112$	12.9252	−	11.1997i	1.22131	−	1.05827i
$113$	−13.1484	+	3.86073i	−1.23690	+	0.363187i	−0.833850	−	0.551991i	$-0.813868\pi$
$113$	−13.1484	+	3.86073i	−1.23690	+	0.363187i	−0.403050	+	0.915178i	$0.632050\pi$
$114$	6.01094	−	6.85522i	0.562976	−	0.642050i
$115$	−1.80957	−	1.62862i	−0.168743	−	0.151870i
$116$		−	3.27086i		−	0.303692i
$117$	−5.73691	−	12.9629i	−0.530377	−	1.19842i
$118$	−1.18793	−	1.37094i	−0.109358	−	0.126206i
$119$	−12.3538	−	19.2229i	−1.13247	−	1.76216i
$120$	2.45816	−	3.77602i	0.224398	−	0.344702i
$121$	−8.39155	−	5.39292i	−0.762868	−	0.490266i
$122$	5.65719	−	12.3875i	0.512178	−	1.12151i
$123$	−2.96185	+	0.408109i	−0.267061	+	0.0367979i
$124$	1.87694	−	13.0544i	0.168554	−	1.17232i
$125$	−2.05445	−	4.49862i	−0.183756	−	0.402369i
$126$	−4.34922	+	27.9174i	−0.387460	+	2.48708i
$127$	3.64209	+	1.06941i	0.323183	+	0.0948952i	0.439300	−	0.898340i	$-0.355227\pi$
$127$	3.64209	+	1.06941i	0.323183	+	0.0948952i	−0.116117	+	0.993236i	$0.537045\pi$
$128$	17.1532	−	7.83361i	1.51614	−	0.692400i
$129$	8.30611	−	7.11230i	0.731312	−	0.626203i
$130$	−4.46941	−	3.87276i	−0.391993	−	0.339664i
$131$	6.86348	+	3.13445i	0.599665	+	0.273858i	0.692032	−	0.721867i	$-0.256716\pi$
$131$	6.86348	+	3.13445i	0.599665	+	0.273858i	−0.0923664	+	0.995725i	$0.529443\pi$
$132$	6.87372	−	1.97453i	0.598281	−	0.171861i
$133$	1.16070	+	8.07287i	0.100646	+	0.700007i
$134$	3.04309	−	1.95568i	0.262883	−	0.168945i
$135$	0.329329	+	2.61711i	0.0283442	+	0.225245i
$136$	8.63599	+	29.4115i	0.740530	+	2.52201i
$137$	−18.0767			−1.54440			−0.772199	−	0.635380i	$-0.780843\pi$
$137$	−18.0767			−1.54440			−0.772199	+	0.635380i	$0.780843\pi$
$138$	−16.9500	−	11.4941i	−1.44288	−	0.978444i
$139$	−13.9156			−1.18030			−0.590152	−	0.807292i	$-0.700932\pi$
$139$	−13.9156			−1.18030			−0.590152	+	0.807292i	$0.700932\pi$
$140$	2.22818	+	7.58850i	0.188316	+	0.641345i
$141$	0.00795292	−	1.35401i	0.000669757	−	0.114028i
$142$	−1.10841	+	0.712332i	−0.0930157	+	0.0597776i
$143$	−0.680804	−	4.73510i	−0.0569317	−	0.395969i
$144$	5.72268	−	12.1511i	0.476890	−	1.01259i
$145$	0.370323	+	0.169121i	0.0307536	+	0.0140447i
$146$	8.33118	+	7.21901i	0.689494	+	0.597450i
$147$	−8.55314	−	9.98879i	−0.705451	−	0.823862i
$148$	16.6244	−	7.59209i	1.36651	−	0.624066i
$149$	7.14176	+	2.09701i	0.585076	+	0.171794i	0.560857	−	0.827913i	$-0.310472\pi$
$149$	7.14176	+	2.09701i	0.585076	+	0.171794i	0.0242193	+	0.999707i	$0.492290\pi$
$150$	−10.8483	−	17.1003i	−0.885760	−	1.39623i
$151$	5.10817	+	11.1853i	0.415697	+	0.910250i	0.995435	+	0.0954464i	$0.0304278\pi$
$151$	5.10817	+	11.1853i	0.415697	+	0.910250i	−0.579737	+	0.814803i	$0.696845\pi$
$152$	1.55705	−	10.8295i	0.126294	−	0.878392i
$153$	−14.9815	−	9.87864i	−1.21119	−	0.798640i
$154$	−3.96089	+	8.67313i	−0.319177	+	0.698901i
$155$	1.38096	+	0.887487i	0.110921	+	0.0712847i
$156$	−27.9743	−	18.2110i	−2.23974	−	1.45805i
$157$	4.82934	+	7.51459i	0.385423	+	0.599730i	0.978707	−	0.205264i	$-0.0658052\pi$
$157$	4.82934	+	7.51459i	0.385423	+	0.599730i	−0.593284	+	0.804993i	$0.702169\pi$
$158$	−8.49017	−	9.79818i	−0.675442	−	0.779502i
$159$	0.0253513	−	0.0546597i	0.00201049	−	0.00433480i
$160$		−	0.400636i		−	0.0316730i
$161$	17.6720	−	4.82967i	1.39275	−	0.380632i
$162$	5.74952	+	21.4313i	0.451725	+	1.68380i
$163$	16.8944	−	4.96065i	1.32327	−	0.388548i	0.457601	−	0.889158i	$-0.348709\pi$
$163$	16.8944	−	4.96065i	1.32327	−	0.388548i	0.865673	+	0.500609i	$0.166891\pi$
$164$	−5.32064	+	4.61036i	−0.415472	+	0.360009i
$165$	−0.131854	+	0.880328i	−0.0102648	+	0.0685335i
$166$	24.0858	−	3.46302i	1.86942	−	0.268782i
$167$	6.89402	−	10.7273i	0.533475	−	0.830103i	−0.465000	−	0.885311i	$-0.653946\pi$
$167$	6.89402	−	10.7273i	0.533475	−	0.830103i	0.998475	+	0.0552074i	$0.0175820\pi$
$168$	13.9034	+	30.9236i	1.07267	+	2.38581i
$169$	−6.10837	+	7.04944i	−0.469875	+	0.542264i
$170$	−7.41031	−	1.06544i	−0.568345	−	0.0817156i
$171$	3.39935	+	5.42866i	0.259955	+	0.415140i
$172$	7.25434	−	24.7060i	0.553138	−	1.88382i
$173$	−6.12605	+	20.8634i	−0.465755	+	1.58622i	0.307128	+	0.951668i	$0.400632\pi$
$173$	−6.12605	+	20.8634i	−0.465755	+	1.58622i	−0.772883	+	0.634548i	$0.781186\pi$
$174$	3.28024	+	0.984130i	0.248674	+	0.0746067i
$175$	17.9312	+	2.57812i	1.35547	+	0.194887i
$176$	2.96821	−	3.42549i	0.223737	−	0.258206i
$177$	1.16232	−	0.522586i	0.0873654	−	0.0392799i
$178$	−22.6832	+	35.2958i	−1.70018	+	2.64553i
$179$	−14.1843	+	2.03939i	−1.06018	+	0.152431i	−0.650278	−	0.759696i	$-0.725348\pi$
$179$	−14.1843	+	2.03939i	−1.06018	+	0.152431i	−0.409906	+	0.912128i	$0.634438\pi$
$180$	4.01202	+	4.74153i	0.299038	+	0.353413i
$181$	14.0507	−	12.1750i	1.04438	−	0.904960i	0.0487935	−	0.998809i	$-0.484462\pi$
$181$	14.0507	−	12.1750i	1.04438	−	0.904960i	0.995586	+	0.0938485i	$0.0299169\pi$
$182$	42.6997	−	12.5378i	3.16511	−	0.929361i
$183$	7.19342	+	6.30749i	0.531753	+	0.466263i
$184$	−24.5715	−	0.462452i	−1.81144	−	0.0340924i
$185$			2.27474i			0.167242i
$186$	12.5271	+	5.81011i	0.918534	+	0.426018i
$187$	−3.96578	−	4.57675i	−0.290006	−	0.334685i
$188$	−1.72376	−	2.68222i	−0.125718	−	0.195621i
$189$	−17.9075	−	8.56254i	−1.30258	−	0.622833i
$190$	2.24794	+	1.44466i	0.163083	+	0.104807i
$191$	−7.92508	+	17.3535i	−0.573438	+	1.25565i	0.371508	+	0.928430i	$0.378841\pi$
$191$	−7.92508	+	17.3535i	−0.573438	+	1.25565i	−0.944946	+	0.327225i	$0.893886\pi$
$192$	1.65694	+	12.0253i	0.119579	+	0.867848i
$193$	2.79560	−	19.4438i	0.201232	−	1.39960i	−0.599404	−	0.800446i	$-0.704596\pi$
$193$	2.79560	−	19.4438i	0.201232	−	1.39960i	0.800636	−	0.599151i	$-0.204495\pi$
$194$	−4.15531	−	9.09885i	−0.298334	−	0.653260i
$195$	3.50825	−	2.22561i	0.251231	−	0.159379i
$196$	−29.7111	−	8.72396i	−2.12222	−	0.623140i
$197$	18.3667	−	8.38781i	1.30858	−	0.597606i	0.365694	−	0.930735i	$-0.380832\pi$
$197$	18.3667	−	8.38781i	1.30858	−	0.597606i	0.942881	+	0.333129i	$0.108104\pi$
$198$	−0.0879608	+	7.48753i	−0.00625110	+	0.532116i
$199$	−5.79745	−	5.02352i	−0.410970	−	0.356108i	0.424705	−	0.905332i	$-0.360378\pi$
$199$	−5.79745	−	5.02352i	−0.410970	−	0.356108i	−0.835675	+	0.549224i	$0.814923\pi$
$200$	−22.1055	−	10.0952i	−1.56310	−	0.713842i
$201$	0.701625	+	2.44249i	0.0494888	+	0.172280i
$202$	3.37556	+	23.4776i	0.237504	+	1.65187i
$203$	−2.57723	+	1.65628i	−0.180886	+	0.116248i
$204$	−42.2554	−	0.248192i	−2.95847	−	0.0173769i
$205$	−0.246874	−	0.840776i	−0.0172424	−	0.0587224i
$206$	−24.6107			−1.71471
$207$	11.1562	−	9.08511i	0.775410	−	0.631459i
$208$	−21.1552			−1.46685
$209$	0.608969	+	2.07396i	0.0421232	+	0.143459i
$210$	−8.28067	−	0.0486375i	−0.571421	−	0.00335631i
$211$	10.8487	−	6.97201i	0.746852	−	0.479973i	−0.111031	−	0.993817i	$-0.535415\pi$
$211$	10.8487	−	6.97201i	0.746852	−	0.479973i	0.857884	+	0.513844i	$0.171779\pi$
$212$	−0.0201913	−	0.140434i	−0.00138674	−	0.00964502i
$213$	−0.255559	−	0.889650i	−0.0175106	−	0.0609578i
$214$	−28.0473	−	12.8088i	−1.91727	−	0.875589i
$215$	2.42210	+	2.09876i	0.165186	+	0.143134i
$216$	19.8132	+	17.7890i	1.34812	+	1.21039i
$217$	−11.2365	+	5.13153i	−0.762782	+	0.348351i
$218$	19.1830	+	5.63263i	1.29924	+	0.381490i
$219$	−6.53954	+	4.14864i	−0.441901	+	0.280339i
$220$	0.870729	+	1.90663i	0.0587045	+	0.128545i
$221$	−4.02256	+	27.9775i	−0.270587	+	1.88197i
$222$	2.61196	+	18.9563i	0.175303	+	1.27227i
$223$	−1.68843	+	3.69714i	−0.113066	+	0.247579i	−0.957702	−	0.287761i	$-0.907089\pi$
$223$	−1.68843	+	3.69714i	−0.113066	+	0.247579i	0.844637	+	0.535340i	$0.179816\pi$
$224$	2.53622	+	1.62993i	0.169459	+	0.108904i
$225$	13.6968	−	3.84756i	0.913118	−	0.256504i
$226$	−18.2658	−	28.4221i	−1.21502	−	1.89061i
$227$	−11.2373	−	12.9685i	−0.745846	−	0.860752i	0.248312	−	0.968680i	$-0.420124\pi$
$227$	−11.2373	−	12.9685i	−0.745846	−	0.860752i	−0.994159	+	0.107927i	$0.965579\pi$
$228$	13.6823	+	6.34589i	0.906134	+	0.420267i
$229$			25.8869i			1.71065i	0.518089	+	0.855327i	$0.326644\pi$
$229$			25.8869i			1.71065i	−0.518089	+	0.855327i	$0.673356\pi$
$230$	2.59572	−	5.41195i	0.171157	−	0.356853i
$231$	−5.03649	−	4.41620i	−0.331376	−	0.290564i
$232$	3.94321	−	1.15783i	0.258884	−	0.0760153i
$233$	10.8710	−	9.41977i	0.712183	−	0.617110i	−0.221521	−	0.975156i	$-0.571102\pi$
$233$	10.8710	−	9.41977i	0.712183	−	0.617110i	0.933704	+	0.358046i	$0.116557\pi$
$234$	26.6801	−	22.5752i	1.74413	−	1.47579i
$235$	0.392805	−	0.0564768i	0.0256238	−	0.00368414i
$236$	1.62238	−	2.52447i	0.105608	−	0.164329i
$237$	8.30715	−	3.73494i	0.539607	−	0.242610i
$238$	36.8926	−	42.5763i	2.39139	−	2.75981i
$239$	9.84741	+	1.41584i	0.636976	+	0.0915834i	0.453235	−	0.891391i	$-0.350270\pi$
$239$	9.84741	+	1.41584i	0.636976	+	0.0915834i	0.183742	+	0.982975i	$0.441179\pi$
$240$	3.77044	+	1.13120i	0.243381	+	0.0730186i
$241$	−6.24011	+	21.2519i	−0.401961	+	1.36895i	0.471417	+	0.881911i	$0.343743\pi$
$241$	−6.24011	+	21.2519i	−0.401961	+	1.36895i	−0.873378	+	0.487043i	$0.838075\pi$
$242$	6.92868	−	23.5969i	0.445392	−	1.51687i
$243$	−15.5817	−	0.457732i	−0.999569	−	0.0293635i
$244$	22.2985	+	3.20605i	1.42752	+	0.205246i
$245$	2.52393	−	2.91278i	0.161248	−	0.186090i
$246$	−3.02272	−	6.72306i	−0.192722	−	0.428646i
$247$	5.45431	−	8.48707i	0.347049	−	0.540019i
$248$	16.4023	−	2.35829i	1.04154	−	0.149751i
$249$	−2.53221	+	16.9064i	−0.160472	+	1.07140i
$250$	9.21487	−	7.98473i	0.582800	−	0.504999i
$251$	−17.4379	+	5.12023i	−1.10067	+	0.323186i	−0.781119	−	0.624382i	$-0.785351\pi$
$251$	−17.4379	+	5.12023i	−1.10067	+	0.323186i	−0.319552	+	0.947569i	$0.603533\pi$
$252$	−46.3386	+	6.10780i	−2.91906	+	0.384755i
$253$	4.45368	−	1.93349i	0.280001	−	0.121557i
$254$			9.35851i			0.587205i
$255$	2.21293	−	4.77127i	0.138579	−	0.298789i
$256$	21.2667	+	24.5431i	1.32917	+	1.53394i
$257$	−0.000255750	0	0.000397955i	−1.59533e−5	0	2.48238e-5i	0.841246	−	0.540653i	$-0.181823\pi$
$257$	−0.000255750	0	0.000397955i	−1.59533e−5	0	2.48238e-5i	−0.841262	+	0.540628i	$0.818187\pi$
$258$	22.5942	+	14.7086i	1.40665	+	0.915720i
$259$	−14.4003	−	9.25448i	−0.894788	−	0.575045i
$260$	4.06402	−	8.89896i	0.252040	−	0.551890i
$261$	−1.32443	+	2.00858i	−0.0819803	+	0.124328i
$262$	−2.64744	+	18.4134i	−0.163560	+	1.13758i
$263$	11.2396	+	24.6112i	0.693062	+	1.51759i	0.848186	+	0.529698i	$0.177695\pi$
$263$	11.2396	+	24.6112i	0.693062	+	1.51759i	−0.155124	+	0.987895i	$0.549578\pi$
$264$	4.81359	+	7.58772i	0.296256	+	0.466992i
$265$	0.0169437	+	0.00497513i	0.00104084	+	0.000305620i
$266$	−18.2909	+	8.35317i	−1.12149	+	0.512166i
$267$	−19.1711	−	22.3889i	−1.17325	−	1.37018i
$268$	4.52238	+	3.91867i	0.276248	+	0.239371i
$269$	14.2411	+	6.50369i	0.868295	+	0.396537i	0.799194	−	0.601073i	$-0.205260\pi$
$269$	14.2411	+	6.50369i	0.868295	+	0.396537i	0.0691005	+	0.997610i	$0.477987\pi$
$270$	−5.96226	+	2.59690i	−0.362852	+	0.158043i
$271$	0.920245	+	6.40044i	0.0559009	+	0.388799i	0.998494	+	0.0548564i	$0.0174701\pi$
$271$	0.920245	+	6.40044i	0.0559009	+	0.388799i	−0.942593	+	0.333943i	$0.891621\pi$
$272$	−22.5295	+	14.4788i	−1.36605	+	0.877909i
$273$	−0.183630	+	31.2636i	−0.0111138	+	1.89216i
$274$	−12.5561	−	42.7621i	−0.758541	−	2.58335i
$275$	4.80108			0.289516
$276$	10.3443	−	32.2606i	0.622655	−	1.94186i
$277$	14.2655			0.857128			0.428564	−	0.903511i	$-0.359020\pi$
$277$	14.2655			0.857128			0.428564	+	0.903511i	$0.359020\pi$
$278$	−9.66576	−	32.9186i	−0.579714	−	1.97432i
$279$	−6.43858	+	7.25650i	−0.385468	+	0.434435i
$280$	−8.35963	+	5.37241i	−0.499583	+	0.321063i
$281$	−2.43945	−	16.9668i	−0.145526	−	1.01215i	−0.923429	−	0.383769i	$-0.874626\pi$
$281$	−2.43945	−	16.9668i	−0.145526	−	1.01215i	0.777904	−	0.628384i	$-0.216283\pi$
$282$	3.20855	−	0.921680i	0.191066	−	0.0548853i
$283$	−0.470078	−	0.214677i	−0.0279432	−	0.0127613i	0.401394	−	0.915905i	$-0.368526\pi$
$283$	−0.470078	−	0.214677i	−0.0279432	−	0.0127613i	−0.429338	+	0.903144i	$0.641253\pi$
$284$	−1.64723	−	1.42733i	−0.0977448	−	0.0846964i
$285$	−1.42592	+	1.22098i	−0.0844644	+	0.0723246i
$286$	10.7284	−	4.89950i	0.634384	−	0.289714i
$287$	6.32691	+	1.85775i	0.373465	+	0.109659i
$288$	2.33944	+	0.364459i	0.137853	+	0.0214760i
$289$	7.80215	+	17.0843i	0.458950	+	1.00496i
$290$	−0.142844	+	0.993503i	−0.00838810	+	0.0583405i
$291$	6.96145	−	0.959207i	0.408087	−	0.0562297i
$292$	−7.57552	+	16.5881i	−0.443324	+	0.970743i
$293$	0.412499	+	0.265097i	0.0240985	+	0.0154871i	0.552635	−	0.833424i	$-0.313623\pi$
$293$	0.412499	+	0.265097i	0.0240985	+	0.0154871i	−0.528536	+	0.848911i	$0.677259\pi$
$294$	17.6884	−	27.1714i	1.03161	−	1.58467i
$295$	0.201932	+	0.314212i	0.0117569	+	0.0182941i
$296$	15.0375	+	17.3541i	0.874034	+	1.00869i
$297$	−5.02057	−	1.57077i	−0.291323	−	0.0911456i
$298$			18.3511i			1.06305i
$299$	−20.4327	−	9.80010i	−1.18165	−	0.566754i
$300$	22.0864	−	25.1886i	1.27516	−	1.45426i
$301$	−23.1402	+	6.79456i	−1.33378	+	0.391632i
$302$	−22.9118	+	19.8532i	−1.31843	+	1.14242i
$303$	−16.4794	−	2.46826i	−0.946717	−	0.141798i
$304$	9.46151	−	1.36036i	0.542655	−	0.0780220i
$305$	−1.51594	+	2.35884i	−0.0868023	+	0.135067i
$306$	12.9626	−	42.3019i	0.741024	−	2.41824i
$307$	−5.20221	+	6.00367i	−0.296906	+	0.342648i	−0.884527	−	0.466488i	$-0.845519\pi$
$307$	−5.20221	+	6.00367i	−0.296906	+	0.342648i	0.587622	+	0.809136i	$0.300064\pi$
$308$	−15.6124	−	2.24472i	−0.889597	−	0.127905i
$309$	4.96843	−	16.5605i	0.282644	−	0.942091i
$310$	−1.14022	+	3.88323i	−0.0647601	+	0.220553i
$311$	9.58522	−	32.6443i	0.543528	−	1.85109i	0.0187881	−	0.999823i	$-0.494019\pi$
$311$	9.58522	−	32.6443i	0.543528	−	1.85109i	0.524740	−	0.851263i	$-0.324163\pi$
$312$	12.0520	−	40.1710i	0.682311	−	2.27424i
$313$	−0.378527	−	0.0544239i	−0.0213956	−	0.00307622i	0.131609	−	0.991302i	$-0.457986\pi$
$313$	−0.378527	−	0.0544239i	−0.0213956	−	0.00307622i	−0.153004	+	0.988226i	$0.548895\pi$
$314$	−14.4220	+	16.6439i	−0.813880	+	0.939268i
$315$	1.70443	−	5.56221i	0.0960340	−	0.313395i
$316$	11.5952	−	18.0425i	0.652280	−	1.01497i
$317$	−16.9969	+	2.44378i	−0.954640	+	0.137257i	−0.601994	−	0.798500i	$-0.705627\pi$
$317$	−16.9969	+	2.44378i	−0.954640	+	0.137257i	−0.352646	+	0.935757i	$0.614718\pi$
$318$	0.146912	+	0.0220042i	0.00823839	+	0.00123393i
$319$	−0.613607	+	0.531693i	−0.0343554	+	0.0297691i
$320$	−3.41359	+	1.00232i	−0.190826	+	0.0560314i
$321$	14.2811	−	16.2870i	0.797096	−	0.909054i
$322$	23.7000	+	38.4500i	1.32075	+	2.14273i
$323$		−	12.7714i		−	0.710619i
$324$	−31.3371	+	19.1141i	−1.74095	+	1.06189i
$325$	−14.6744	−	16.9352i	−0.813990	−	0.939395i
$326$	23.4698	+	36.5196i	1.29987	+	2.02264i
$327$	−7.66284	+	11.7710i	−0.423756	+	0.650939i
$328$	−7.44147	−	4.78234i	−0.410886	−	0.264061i
$329$	−1.24055	+	2.71642i	−0.0683935	+	0.149761i
$330$	−2.17408	+	0.299563i	−0.119679	+	0.0164904i
$331$	−0.511094	+	3.55474i	−0.0280923	+	0.195386i	−0.999035	−	0.0439269i	$-0.986013\pi$
$331$	−0.511094	+	3.55474i	−0.0280923	+	0.195386i	0.970942	+	0.239313i	$0.0769222\pi$
$332$	16.7220	+	36.6161i	0.917739	+	2.00957i
$333$	−13.2829	−	2.06934i	−0.727901	−	0.113399i
$334$	30.1650	+	8.85724i	1.65055	+	0.484646i
$335$	−0.677498	+	0.309403i	−0.0370157	+	0.0169045i
$336$	−22.5006	+	19.2667i	−1.22751	+	1.05108i
$337$	−5.20943	−	4.51399i	−0.283776	−	0.245893i	0.501328	−	0.865257i	$-0.332845\pi$
$337$	−5.20943	−	4.51399i	−0.283776	−	0.245893i	−0.785104	+	0.619364i	$0.787390\pi$
$338$	−20.9190	−	9.55337i	−1.13784	−	0.519635i
$339$	22.8126	−	6.55310i	1.23901	−	0.355915i
$340$	−1.76251	−	12.2585i	−0.0955854	−	0.664811i
$341$	−2.75409	+	1.76995i	−0.149142	+	0.0958479i
$342$	−10.4808	+	11.8122i	−0.566737	+	0.638732i
$343$	0.637518	+	2.17119i	0.0344227	+	0.117233i
$344$	32.3524			1.74433
$345$	3.11765	+	2.83921i	0.167849	+	0.152858i
$346$	−53.6095			−2.88206
$347$	0.503154	+	1.71359i	0.0270107	+	0.0919901i	0.971895	−	0.235414i	$-0.0756445\pi$
$347$	0.503154	+	1.71359i	0.0270107	+	0.0919901i	−0.944885	+	0.327404i	$0.893826\pi$
$348$	−0.0332752	+	5.66520i	−0.00178374	+	0.303686i
$349$	−12.0434	+	7.73985i	−0.644671	+	0.414305i	−0.821715	−	0.569898i	$-0.806983\pi$
$349$	−12.0434	+	7.73985i	−0.644671	+	0.414305i	0.177044	+	0.984203i	$0.443346\pi$
$350$	6.35624	+	44.2086i	0.339755	+	2.36305i
$351$	9.80457	+	22.5104i	0.523329	+	1.20152i
$352$	0.726797	+	0.331917i	0.0387384	+	0.0176912i
$353$	−11.1330	−	9.64676i	−0.592547	−	0.513445i	0.306168	−	0.951977i	$-0.400953\pi$
$353$	−11.1330	−	9.64676i	−0.592547	−	0.513445i	−0.898715	+	0.438532i	$0.855498\pi$
$354$	2.04357	+	2.38659i	0.108615	+	0.126846i
$355$	0.246771	−	0.112696i	0.0130972	−	0.00598130i
$356$	−66.5946	−	19.5539i	−3.52951	−	1.03636i
$357$	21.2015	+	33.4202i	1.12210	+	1.76878i
$358$	−14.6768	−	32.1377i	−0.775692	−	1.69853i
$359$	−1.56230	+	10.8660i	−0.0824548	+	0.573486i	0.906151	+	0.422955i	$0.139007\pi$
$359$	−1.56230	+	10.8660i	−0.0824548	+	0.573486i	−0.988605	+	0.150531i	$0.951902\pi$
$360$	−4.29600	+	6.51514i	−0.226419	+	0.343378i
$361$	5.99924	−	13.1365i	0.315749	−	0.691395i
$362$	38.5607	+	24.7814i	2.02670	+	1.30248i
$363$	14.4795	+	9.42603i	0.759976	+	0.494738i
$364$	39.8009	+	61.9315i	2.08614	+	3.24609i
$365$	−1.48639	−	1.71538i	−0.0778010	−	0.0897872i
$366$	−9.92439	+	21.3979i	−0.518756	+	1.11848i
$367$		−	28.8234i		−	1.50457i	−0.658839	−	0.752284i	$-0.728952\pi$
$367$		−	28.8234i		−	1.50457i	0.658839	−	0.752284i	$-0.271048\pi$
$368$	−5.66044	−	20.7118i	−0.295071	−	1.07968i
$369$	5.13414	−	0.676721i	0.267273	−	0.0352287i
$370$	−5.38111	+	1.58004i	−0.279750	+	0.0821422i
$371$	−0.100428	+	0.0870216i	−0.00521398	+	0.00451794i
$372$	−3.38371	+	22.5914i	−0.175437	+	1.17131i
$373$	17.1106	−	2.46013i	0.885954	−	0.127381i	0.315709	−	0.948856i	$-0.397758\pi$
$373$	17.1106	−	2.46013i	0.885954	−	0.127381i	0.570244	+	0.821475i	$0.306848\pi$
$374$	8.07209	−	12.5604i	0.417398	−	0.649484i
$375$	3.51259	+	7.81261i	0.181389	+	0.403441i
$376$	2.62339	−	3.02755i	0.135291	−	0.156134i
$377$	3.75096	+	0.539306i	0.193184	+	0.0277757i
$378$	7.81695	−	48.3092i	0.402061	−	2.48476i
$379$	5.58452	−	19.0191i	0.286858	−	0.976947i	−0.682416	−	0.730964i	$-0.739071\pi$
$379$	5.58452	−	19.0191i	0.286858	−	0.976947i	0.969274	−	0.245984i	$-0.0791110\pi$
$380$	−1.24536	+	4.24132i	−0.0638858	+	0.217575i
$381$	−6.29730	−	1.88930i	−0.322620	−	0.0967918i
$382$	−46.5560	−	6.69375i	−2.38201	−	0.342482i
$383$	14.9444	−	17.2468i	0.763625	−	0.881270i	−0.232189	−	0.972671i	$-0.574589\pi$
$383$	14.9444	−	17.2468i	0.763625	−	0.881270i	0.995814	+	0.0914006i	$0.0291344\pi$
$384$	−29.7894	+	13.3935i	−1.52019	+	0.683483i
$385$	1.06139	−	1.65155i	0.0540932	−	0.0841707i
$386$	47.9380	−	6.89244i	2.43998	−	0.350816i
$387$	−14.4587	+	12.2341i	−0.734977	+	0.621897i
$388$	12.5055	−	10.8361i	0.634869	−	0.550117i
$389$	27.5163	−	8.07951i	1.39513	−	0.409647i	0.504121	−	0.863633i	$-0.331816\pi$
$389$	27.5163	−	8.07951i	1.39513	−	0.409647i	0.891009	+	0.453985i	$0.149998\pi$
$390$	7.70171	+	6.75318i	0.389991	+	0.341960i
$391$	−28.4674	+	3.54762i	−1.43966	+	0.179411i
$392$		−	38.9065i		−	1.96508i
$393$	−11.8558	−	5.49875i	−0.598046	−	0.277375i
$394$	32.5996	+	37.6220i	1.64235	+	1.89537i
$395$	1.44321	+	2.24568i	0.0726160	+	0.112993i
$396$	−11.9255	+	3.35000i	−0.599280	+	0.168344i
$397$	8.78584	+	5.64632i	0.440949	+	0.283381i	0.742218	−	0.670158i	$-0.233774\pi$
$397$	8.78584	+	5.64632i	0.440949	+	0.283381i	−0.301269	+	0.953539i	$0.597410\pi$
$398$	7.85668	−	17.2037i	0.393820	−	0.862345i
$399$	−1.92824	−	13.9942i	−0.0965325	−	0.700586i
$400$	3.02159	−	21.0156i	0.151079	−	1.05078i
$401$	−2.79982	−	6.13076i	−0.139817	−	0.306156i	0.826751	−	0.562568i	$-0.190187\pi$
$401$	−2.79982	−	6.13076i	−0.139817	−	0.306156i	−0.966567	+	0.256413i	$0.917459\pi$
$402$	−5.29059	+	3.35631i	−0.263871	+	0.167398i
$403$	14.6611	+	4.30488i	0.730320	+	0.214441i
$404$	−35.6914	+	16.2997i	−1.77571	+	0.810940i
$405$	−0.543781	−	4.53624i	−0.0270207	−	0.225408i
$406$	−5.70823	−	4.94621i	−0.283295	−	0.245476i
$407$	−4.12663	−	1.88457i	−0.204549	−	0.0934146i
$408$	−14.6585	−	51.0291i	−0.725704	−	2.52632i
$409$	−2.18939	−	15.2275i	−0.108258	−	0.752952i	−0.969559	−	0.244857i	$-0.921259\pi$
$409$	−2.18939	−	15.2275i	−0.108258	−	0.752952i	0.861301	−	0.508095i	$-0.169650\pi$
$410$	1.81745	−	1.16801i	0.0897576	−	0.0576837i
$411$	31.3093	+	0.183899i	1.54437	+	0.00907105i
$412$	−11.4700	−	39.0632i	−0.565086	−	1.92451i
$413$	−2.81065			−0.138303
$414$	29.2407	+	20.0805i	1.43710	+	0.986902i
$415$	−5.01024			−0.245943
$416$	−1.05065	−	3.57818i	−0.0515122	−	0.175435i
$417$	24.1021	+	0.141566i	1.18028	+	0.00693253i
$418$	−4.48314	+	2.88114i	−0.219278	+	0.140921i
$419$	4.83896	+	33.6557i	0.236399	+	1.64419i	0.669478	+	0.742832i	$0.266518\pi$
$419$	4.83896	+	33.6557i	0.236399	+	1.64419i	−0.433079	+	0.901356i	$0.642573\pi$
$420$	−3.78206	−	13.1661i	−0.184546	−	0.642440i
$421$	3.24035	+	1.47982i	0.157925	+	0.0721218i	0.492809	−	0.870137i	$-0.335970\pi$
$421$	3.24035	+	1.47982i	0.157925	+	0.0721218i	−0.334884	+	0.942259i	$0.608697\pi$
$422$	24.0284	+	20.8207i	1.16968	+	1.01354i
$423$	−0.0275493	+	2.34509i	−0.00133949	+	0.114022i
$424$	0.162153	−	0.0740530i	0.00787486	−	0.00359633i
$425$	−27.2183	−	7.99202i	−1.32028	−	0.387670i
$426$	1.92704	−	1.22250i	0.0933652	−	0.0592302i
$427$	−8.76528	−	19.1933i	−0.424181	−	0.928828i
$428$	7.25899	−	50.4874i	0.350877	−	2.44040i
$429$	1.13100	+	8.20821i	0.0546050	+	0.396296i
$430$	−3.28242	+	7.18749i	−0.158292	+	0.346611i
$431$	−8.80204	−	5.65673i	−0.423979	−	0.272475i	0.311204	−	0.950343i	$-0.399268\pi$
$431$	−8.80204	−	5.65673i	−0.423979	−	0.272475i	−0.735184	+	0.677868i	$0.762904\pi$
$432$	−10.0354	+	20.9878i	−0.482829	+	1.00977i
$433$	−0.666468	−	1.03704i	−0.0320284	−	0.0498371i	0.824870	−	0.565322i	$-0.191248\pi$
$433$	−0.666468	−	1.03704i	−0.0320284	−	0.0498371i	−0.856899	+	0.515485i	$0.827612\pi$
$434$	−19.9439	−	23.0165i	−0.957340	−	1.10483i
$435$	−0.639686	−	0.296688i	−0.0306706	−	0.0142251i
$436$			33.0732i			1.58392i
$437$	9.76856	+	3.06912i	0.467293	+	0.146816i
$438$	−14.3563	−	12.5882i	−0.685973	−	0.601489i
$439$	0.126589	−	0.0371699i	0.00604177	−	0.00177402i	−0.278710	−	0.960375i	$-0.589907\pi$
$439$	0.126589	−	0.0371699i	0.00604177	−	0.00177402i	0.284752	+	0.958601i	$0.408089\pi$
$440$	−1.99033	+	1.72463i	−0.0948852	+	0.0822185i
$441$	14.7126	+	17.3878i	0.700600	+	0.827991i
$442$	−68.9774	+	9.91745i	−3.28092	+	0.471725i
$443$	9.39065	−	14.6121i	0.446163	−	0.694244i	−0.543217	−	0.839592i	$-0.682794\pi$
$443$	9.39065	−	14.6121i	0.446163	−	0.694244i	0.989381	+	0.145348i	$0.0464303\pi$
$444$	−28.8710	+	12.9805i	−1.37016	+	0.616029i
$445$	5.65716	−	6.52871i	0.268175	−	0.309491i
$446$	−9.91871	−	1.42609i	−0.469664	−	0.0675275i
$447$	−12.3484	−	3.70472i	−0.584057	−	0.175227i
$448$	7.54254	−	25.6875i	0.356352	−	1.21362i
$449$	2.00936	−	6.84324i	0.0948274	−	0.322952i	−0.898394	−	0.439190i	$-0.855265\pi$
$449$	2.00936	−	6.84324i	0.0948274	−	0.322952i	0.993221	+	0.116238i	$0.0370835\pi$
$450$	18.6155	+	29.7284i	0.877544	+	1.40141i
$451$	1.72979	+	0.248706i	0.0814526	+	0.0117111i
$452$	36.5999	−	42.2385i	1.72151	−	1.98673i
$453$	−8.73367	−	19.4252i	−0.410344	−	0.912676i
$454$	22.8728	−	35.5908i	1.07348	−	1.67036i
$455$	−9.06972	+	1.30403i	−0.425195	+	0.0611338i
$456$	−2.80702	+	18.7412i	−0.131451	+	0.877635i
$457$	3.01664	−	2.61394i	0.141113	−	0.122275i	−0.581444	−	0.813586i	$-0.697512\pi$
$457$	3.01664	−	2.61394i	0.141113	−	0.122275i	0.722557	+	0.691311i	$0.242967\pi$
$458$	−61.2378	+	17.9810i	−2.86145	+	0.840199i
$459$	25.8479	+	17.2624i	1.20647	+	0.805741i
$460$	9.79982	+	1.59776i	0.456919	+	0.0744961i
$461$			4.90550i			0.228472i	0.993454	+	0.114236i	$0.0364420\pi$
$461$			4.90550i			0.228472i	−0.993454	+	0.114236i	$0.963558\pi$
$462$	6.94857	−	14.9818i	0.323277	−	0.697014i
$463$	19.9841	+	23.0629i	0.928741	+	1.07182i	0.997245	+	0.0741732i	$0.0236318\pi$
$463$	19.9841	+	23.0629i	0.928741	+	1.07182i	−0.0685046	+	0.997651i	$0.521823\pi$
$464$	1.94119	+	3.02054i	0.0901173	+	0.140225i
$465$	−2.38282	−	1.55120i	−0.110501	−	0.0719350i
$466$	29.8343	+	19.1734i	1.38205	+	0.888188i
$467$	−9.99634	+	21.8889i	−0.462576	+	1.01290i	0.524317	+	0.851523i	$0.324321\pi$
$467$	−9.99634	+	21.8889i	−0.462576	+	1.01290i	−0.986893	+	0.161376i	$0.948407\pi$
$468$	48.2668	+	31.8265i	2.23113	+	1.47118i
$469$	0.797633	−	5.54766i	0.0368313	−	0.256167i
$470$	0.406443	+	0.889986i	0.0187478	+	0.0410520i
$471$	−8.28806	−	13.0646i	−0.381894	−	0.601983i
$472$	3.61769	+	1.06225i	0.166518	+	0.0488940i
$473$	−5.81403	+	2.65518i	−0.267329	+	0.122085i
$474$	14.6055	+	17.0570i	0.670852	+	0.783455i
$475$	7.65201	+	6.63051i	0.351099	+	0.304229i
$476$	84.7730	+	38.7145i	3.88556	+	1.77448i
$477$	−0.0444651	+	0.0944139i	−0.00203592	+	0.00432291i
$478$	3.49071	+	24.2784i	0.159661	+	1.11047i
$479$	18.6898	−	12.0112i	0.853959	−	0.548806i	−0.0388479	−	0.999245i	$-0.512369\pi$
$479$	18.6898	−	12.0112i	0.853959	−	0.548806i	0.892807	+	0.450439i	$0.148732\pi$
$480$	−0.00407576	+	0.693909i	−0.000186032	+	0.0316725i
$481$	5.96540	+	20.3163i	0.271999	+	0.926343i
$482$	−54.6076			−2.48731
$483$	−30.6574	+	8.18531i	−1.39496	+	0.372445i
$484$	40.6832			1.84923
$485$	0.580246	+	1.97614i	0.0263476	+	0.0897317i
$486$	−9.74027	−	37.1779i	−0.441827	−	1.68643i
$487$	−27.8990	+	17.9296i	−1.26422	+	0.812467i	−0.988856	−	0.148872i	$-0.952436\pi$
$487$	−27.8990	+	17.9296i	−1.26422	+	0.812467i	−0.275367	+	0.961339i	$0.588799\pi$
$488$	4.02825	+	28.0171i	0.182350	+	1.26827i
$489$	−29.3120	+	8.42009i	−1.32553	+	0.380769i
$490$	8.64356	+	3.94738i	0.390476	+	0.178325i
$491$	−24.5721	−	21.2918i	−1.10892	−	0.960887i	−0.109471	−	0.993990i	$-0.534916\pi$
$491$	−24.5721	−	21.2918i	−1.10892	−	0.960887i	−0.999452	+	0.0331031i	$0.989461\pi$
$492$	9.26236	−	7.93111i	0.417579	−	0.357562i
$493$	4.36373	−	1.99285i	0.196533	−	0.0897535i
$494$	23.8655	+	7.00754i	1.07376	+	0.315284i
$495$	0.237330	−	1.52341i	0.0106672	−	0.0684720i
$496$	6.01422	+	13.1693i	0.270046	+	0.591319i
$497$	−0.290529	+	2.02067i	−0.0130320	+	0.0906395i
$498$	−41.7524	+	5.75299i	−1.87097	+	0.257798i
$499$	−4.07576	+	8.92468i	−0.182456	+	0.399523i	−0.978655	−	0.205512i	$-0.934114\pi$
$499$	−4.07576	+	8.92468i	−0.182456	+	0.399523i	0.796198	+	0.605036i	$0.206841\pi$
$500$	16.9684	+	10.9049i	0.758848	+	0.487682i
$501$	−12.0497	+	18.5098i	−0.538341	+	0.826956i
$502$	−24.2247	−	37.6944i	−1.08120	−	1.68239i
$503$	1.49505	+	1.72538i	0.0666611	+	0.0769310i	0.788101	−	0.615546i	$-0.211065\pi$
$503$	1.49505	+	1.72538i	0.0666611	+	0.0769310i	−0.721440	+	0.692477i	$0.756519\pi$
$504$	−23.7664	−	53.7018i	−1.05864	−	2.39207i
$505$		−	4.88371i		−	0.217322i
$506$	7.66737	+	9.19259i	0.340856	+	0.408660i
$507$	10.6515	−	12.1476i	0.473052	−	0.539495i
$508$	−14.8542	+	4.36159i	−0.659049	+	0.193514i
$509$	4.57584	−	3.96499i	0.202821	−	0.175745i	−0.547528	−	0.836787i	$-0.684431\pi$
$509$	4.57584	−	3.96499i	0.202821	−	0.175745i	0.750349	+	0.661042i	$0.229886\pi$
$510$	12.8240	+	1.92075i	0.567855	+	0.0850524i
$511$	16.9064	−	2.43077i	0.747894	−	0.107531i
$512$	−22.8970	+	35.6284i	−1.01191	+	1.57457i
$513$	−5.83252	−	9.43714i	−0.257512	−	0.416660i
$514$	0.000763755	0	0.000881420i	3.36878e−5	0	3.88778e-5i
$515$	5.01575	+	0.721156i	0.221020	+	0.0317779i
$516$	−12.8160	+	42.7175i	−0.564193	+	1.88053i
$517$	−0.222974	+	0.759380i	−0.00980639	+	0.0333975i
$518$	11.8899	−	40.4933i	0.522412	−	1.77917i
$519$	10.8227	−	36.0736i	0.475064	−	1.58345i
$520$	12.1668	+	1.74932i	0.533549	+	0.0767128i
$521$	2.99517	−	3.45661i	0.131221	−	0.151437i	−0.686337	−	0.727284i	$-0.740782\pi$
$521$	2.99517	−	3.45661i	0.131221	−	0.151437i	0.817557	+	0.575847i	$0.195328\pi$
$522$	−5.67143	−	1.73790i	−0.248232	−	0.0760660i
$523$	−21.8790	+	34.0443i	−0.956700	+	1.48865i	−0.0863236	+	0.996267i	$0.527512\pi$
$523$	−21.8790	+	34.0443i	−0.956700	+	1.48865i	−0.870376	+	0.492387i	$0.836124\pi$
$524$	−30.4603	+	4.37954i	−1.33067	+	0.191321i
$525$	−31.0310	−	4.64777i	−1.35430	−	0.202845i
$526$	−50.4131	+	43.6832i	−2.19811	+	1.90468i
$527$	18.5598	−	5.44965i	0.808477	−	0.237390i
$528$	−5.17584	+	5.90283i	−0.225250	+	0.256888i
$529$	4.12756	−	22.6266i	0.179459	−	0.983765i
$530$			0.0435376i			0.00189115i
$531$	−2.01848	+	0.893305i	−0.0875946	+	0.0387661i
$532$	−21.7831	−	25.1390i	−0.944416	−	1.08991i
$533$	−4.40979	−	6.86177i	−0.191009	−	0.297216i
$534$	39.6469	−	60.9022i	1.71569	−	2.63550i
$535$	5.34079	+	3.43232i	0.230903	+	0.148392i
$536$	−3.12333	+	6.83913i	−0.134907	+	0.295406i
$537$	24.5882	−	3.38797i	1.06106	−	0.146202i
$538$	−5.49320	+	38.2061i	−0.236829	+	1.64718i
$539$	3.19307	+	6.99186i	0.137535	+	0.301161i
$540$	−6.90067	−	8.25325i	−0.296957	−	0.355163i
$541$	−40.4615	−	11.8806i	−1.73958	−	0.510786i	−0.750844	−	0.660479i	$-0.770353\pi$
$541$	−40.4615	−	11.8806i	−1.73958	−	0.510786i	−0.988732	+	0.149694i	$0.952171\pi$
$542$	−14.5016	+	6.62267i	−0.622898	+	0.284468i
$543$	−24.4600	+	20.9444i	−1.04968	+	0.898811i
$544$	−3.56784	−	3.09155i	−0.152970	−	0.132549i
$545$	−3.74450	−	1.71006i	−0.160397	−	0.0732508i
$546$	−74.0843	+	21.2813i	−3.17052	+	0.910755i
$547$	−3.24034	−	22.5370i	−0.138547	−	0.963615i	−0.933917	−	0.357490i	$-0.883632\pi$
$547$	−3.24034	−	22.5370i	−0.138547	−	0.963615i	0.795370	−	0.606124i	$-0.207277\pi$
$548$	62.0220	−	39.8591i	2.64945	−	1.70270i
$549$	−12.3950	−	10.9979i	−0.529005	−	0.469378i
$550$	3.33483	+	11.3574i	0.142198	+	0.484281i
$551$	−1.71227			−0.0729450
$552$	42.5537	+	1.05095i	1.81121	+	0.0447313i
$553$	−20.0878			−0.854221
$554$	9.90879	+	33.7462i	0.420984	+	1.43374i
$555$	0.0231415	−	3.93990i	0.000982301	−	0.167239i
$556$	47.7449	−	30.6838i	2.02484	−	1.30128i
$557$	−4.06135	−	28.2473i	−0.172085	−	1.19688i	−0.874470	−	0.485079i	$-0.838791\pi$
$557$	−4.06135	−	28.2473i	−0.172085	−	1.19688i	0.702386	−	0.711797i	$-0.252118\pi$
$558$	−21.6381	−	10.1907i	−0.916016	−	0.431406i
$559$	27.1362	+	12.3927i	1.14774	+	0.524156i
$560$	−6.56127	−	5.68538i	−0.277264	−	0.240251i
$561$	6.82225	+	7.96737i	0.288036	+	0.336383i
$562$	38.4420	−	17.5559i	1.62158	−	0.740550i
$563$	24.5445	+	7.20690i	1.03443	+	0.303735i	0.754509	−	0.656290i	$-0.227875\pi$
$563$	24.5445	+	7.20690i	1.03443	+	0.303735i	0.279917	+	0.960024i	$0.409693\pi$
$564$	2.95830	+	4.66319i	0.124567	+	0.196356i
$565$	2.88979	+	6.32775i	0.121574	+	0.266211i
$566$	0.181323	−	1.26113i	0.00762156	−	0.0530091i
$567$	30.9290	+	15.0127i	1.29889	+	0.630473i
$568$	1.13764	−	2.49108i	0.0477341	−	0.104523i
$569$	−18.6986	−	12.0169i	−0.783888	−	0.503774i	0.0864337	−	0.996258i	$-0.472453\pi$
$569$	−18.6986	−	12.0169i	−0.783888	−	0.503774i	−0.870322	+	0.492483i	$0.836089\pi$
$570$	−3.87878	−	2.52506i	−0.162464	−	0.105763i
$571$	10.7314	+	16.6984i	0.449095	+	0.698806i	0.989809	−	0.142401i	$-0.0454822\pi$
$571$	10.7314	+	16.6984i	0.449095	+	0.698806i	−0.540714	+	0.841207i	$0.681846\pi$
$572$	12.7767	+	14.7451i	0.534222	+	0.616525i
$573$	13.9029	−	29.9760i	0.580804	−	1.25227i
$574$			16.2573i			0.678565i
$575$	12.6538	−	18.8981i	0.527700	−	0.788106i
$576$	−2.74752	−	20.8449i	−0.114480	−	0.868536i
$577$	15.4097	−	4.52469i	0.641513	−	0.188365i	0.0552326	−	0.998474i	$-0.482410\pi$
$577$	15.4097	−	4.52469i	0.641513	−	0.188365i	0.586280	+	0.810108i	$0.300592\pi$
$578$	−34.9951	+	30.3235i	−1.45561	+	1.26129i
$579$	−5.03984	+	33.6487i	−0.209449	+	1.39839i
$580$	−1.64350	+	0.236300i	−0.0682428	+	0.00981183i
$581$	20.3835	−	31.7173i	0.845650	−	1.31586i
$582$	7.10451	+	15.8017i	0.294492	+	0.655001i
$583$	−0.0230629	+	0.0266160i	−0.000955167	+	0.00110232i
$584$	−22.6795	−	3.26082i	−0.938483	−	0.134934i
$585$	−6.09900	+	3.81911i	−0.252163	+	0.157901i
$586$	−0.340589	+	1.15994i	−0.0140696	+	0.0479167i
$587$	−3.62649	+	12.3507i	−0.149681	+	0.509768i	−0.999860	−	0.0167264i	$-0.994676\pi$
$587$	−3.62649	+	12.3507i	−0.149681	+	0.509768i	0.850179	+	0.526494i	$0.176494\pi$
$588$	51.3714	+	15.4123i	2.11852	+	0.635594i
$589$	−6.83387	−	0.982562i	−0.281585	−	0.0404858i
$590$	−0.603035	+	0.695940i	−0.0248266	+	0.0286514i
$591$	−31.8969	+	14.3410i	−1.31206	+	0.589910i
$592$	−10.8464	+	16.8773i	−0.445783	+	0.693652i
$593$	−27.4536	+	3.94723i	−1.12738	+	0.162093i	−0.680675	−	0.732586i	$-0.738313\pi$
$593$	−27.4536	+	3.94723i	−1.12738	+	0.162093i	−0.446709	+	0.894679i	$0.647404\pi$
$594$	0.228522	−	12.9677i	0.00937639	−	0.532070i
$595$	−8.76642	+	7.59615i	−0.359388	+	0.311412i
$596$	−29.1276	+	8.55263i	−1.19311	+	0.350330i
$597$	9.99020	+	8.75982i	0.408871	+	0.358515i
$598$	8.99046	−	55.1426i	0.367647	−	2.25495i
$599$			36.5356i			1.49280i	0.665496	+	0.746401i	$0.268220\pi$
$599$			36.5356i			1.49280i	−0.665496	+	0.746401i	$0.731780\pi$
$600$	38.1845	+	17.7101i	1.55888	+	0.723010i
$601$	−25.4678	−	29.3915i	−1.03885	−	1.19890i	−0.979662	−	0.200656i	$-0.935693\pi$
$601$	−25.4678	−	29.3915i	−1.03885	−	1.19890i	−0.0591929	−	0.998247i	$-0.518853\pi$
$602$	−32.1463	−	50.0206i	−1.31019	−	2.03869i
$603$	−1.19038	−	4.23759i	−0.0484760	−	0.172568i
$604$	−42.1900	−	27.1139i	−1.71669	−	1.10325i
$605$	−2.10353	+	4.60610i	−0.0855208	+	0.187264i
$606$	−5.60770	−	40.6980i	−0.227797	−	1.65324i
$607$	−0.436033	+	3.03268i	−0.0176980	+	0.123093i	−0.996755	−	0.0804932i	$-0.974350\pi$
$607$	−0.436033	+	3.03268i	−0.0176980	+	0.123093i	0.979057	+	0.203586i	$0.0652596\pi$
$608$	0.699984	+	1.53275i	0.0283881	+	0.0621613i
$609$	4.48066	−	2.84250i	0.181565	−	0.115184i
$610$	−6.63303	−	1.94763i	−0.268564	−	0.0788574i
$611$	3.36013	−	1.53452i	0.135936	−	0.0620800i
$612$	73.1847	+	0.859747i	2.95832	+	0.0347532i
$613$	20.5367	+	17.7951i	0.829469	+	0.718739i	0.962180	−	0.272416i	$-0.0878226\pi$
$613$	20.5367	+	17.7951i	0.829469	+	0.718739i	−0.132711	+	0.991155i	$0.542368\pi$
$614$	−17.8157	−	8.13615i	−0.718982	−	0.328348i
$615$	0.419038	+	1.45875i	0.0168972	+	0.0588226i
$616$	−2.82038	−	19.6162i	−0.113636	−	0.790359i
$617$	−35.0838	+	22.5470i	−1.41242	+	0.907709i	−0.999995	−	0.00328138i	$-0.998956\pi$
$617$	−35.0838	+	22.5470i	−1.41242	+	0.907709i	−0.412428	+	0.910990i	$0.635319\pi$
$618$	42.6263	+	0.250371i	1.71468	+	0.0100714i
$619$	11.0548	+	37.6491i	0.444329	+	1.51325i	0.812206	+	0.583371i	$0.198267\pi$
$619$	11.0548	+	37.6491i	0.444329	+	1.51325i	−0.367877	+	0.929874i	$0.619915\pi$
$620$	−6.69503			−0.268879
$621$	−19.4152	+	15.6221i	−0.779105	+	0.626893i
$622$	83.8808			3.36332
$623$	18.3146	+	62.3739i	0.733760	+	2.49896i
$624$	36.6413	+	0.215217i	1.46683	+	0.00861558i
$625$	17.8354	−	11.4621i	0.713417	−	0.458485i
$626$	−0.134180	−	0.933242i	−0.00536291	−	0.0372998i
$627$	−1.03365	−	3.59833i	−0.0412799	−	0.143704i
$628$	−33.1393	−	15.1342i	−1.32240	−	0.603921i
$629$	20.2576	+	17.5533i	0.807723	+	0.699896i
$630$	14.3418	+	0.168482i	0.571391	+	0.00671250i
$631$	13.8489	−	6.32458i	0.551316	−	0.251777i	−0.120223	−	0.992747i	$-0.538361\pi$
$631$	13.8489	−	6.32458i	0.551316	−	0.251777i	0.671539	+	0.740969i	$0.265634\pi$
$632$	25.8557	+	7.59193i	1.02849	+	0.301991i
$633$	−18.8610	+	11.9653i	−0.749659	+	0.475578i
$634$	−17.5870	−	38.5102i	−0.698470	−	1.52944i
$635$	0.274227	−	1.90729i	0.0108824	−	0.0756887i
$636$	0.0335431	+	0.243439i	0.00133007	+	0.00965300i
$637$	14.9033	−	32.6336i	0.590489	−	1.29299i
$638$	−1.68398	−	1.08223i	−0.0666694	−	0.0428458i
$639$	0.433582	+	1.54349i	0.0171522	+	0.0610596i
$640$	−5.17536	−	8.05302i	−0.204574	−	0.318324i
$641$	−24.7394	−	28.5508i	−0.977147	−	1.12769i	−0.991801	−	0.127795i	$-0.959210\pi$
$641$	−24.7394	−	28.5508i	−0.977147	−	1.12769i	0.0146533	−	0.999893i	$-0.495336\pi$
$642$	48.4481	+	22.4704i	1.91210	+	0.886835i
$643$			11.3340i			0.446971i	0.974707	+	0.223486i	$0.0717436\pi$
$643$			11.3340i			0.446971i	−0.974707	+	0.223486i	$0.928256\pi$
$644$	−49.9839	+	55.5375i	−1.96964	+	2.18848i
$645$	−4.17377	−	3.65973i	−0.164342	−	0.144102i
$646$	30.2119	−	8.87101i	1.18867	−	0.349025i
$647$	−25.6571	+	22.2320i	−1.00868	+	0.874029i	−0.992051	−	0.125833i	$-0.959840\pi$
$647$	−25.6571	+	22.2320i	−1.00868	+	0.874029i	−0.0166317	+	0.999862i	$0.505294\pi$
$648$	−34.1359	−	31.0125i	−1.34099	−	1.21829i
$649$	−0.737311	+	0.106009i	−0.0289420	+	0.00416123i
$650$	29.8689	−	46.4768i	1.17155	−	1.82297i
$651$	19.5140	−	8.77360i	0.764814	−	0.343864i
$652$	−47.0273	+	54.2724i	−1.84173	+	2.12547i
$653$	15.8944	+	2.28527i	0.621997	+	0.0894297i	0.446106	−	0.894980i	$-0.352810\pi$
$653$	15.8944	+	2.28527i	0.621997	+	0.0894297i	0.175891	+	0.984410i	$0.443719\pi$
$654$	−33.1680	−	9.95099i	−1.29697	−	0.389114i
$655$	1.07912	−	3.67513i	0.0421645	−	0.143599i
$656$	2.17730	−	7.41522i	0.0850094	−	0.289516i
$657$	11.3688	−	7.11900i	0.443540	−	0.277739i
$658$	−7.28762	−	1.04780i	−0.284101	−	0.0408475i
$659$	21.4645	−	24.7713i	0.836137	−	0.964953i	−0.163631	−	0.986522i	$-0.552321\pi$
$659$	21.4645	−	24.7713i	0.836137	−	0.964953i	0.999767	+	0.0215685i	$0.00686600\pi$
$660$	−1.48872	−	3.31118i	−0.0579485	−	0.128888i
$661$	−4.76485	+	7.41425i	−0.185331	+	0.288381i	−0.921470	−	0.388450i	$-0.873011\pi$
$661$	−4.76485	+	7.41425i	−0.185331	+	0.288381i	0.736139	+	0.676831i	$0.236647\pi$
$662$	−8.76407	+	1.26008i	−0.340625	+	0.0489745i
$663$	7.25178	−	48.4167i	0.281636	−	1.88035i
$664$	−38.2235	+	33.1208i	−1.48336	+	1.28534i
$665$	3.97251	−	1.16643i	0.154047	−	0.0452324i
$666$	−4.33113	−	32.8594i	−0.167828	−	1.27327i
$667$	0.475630	+	3.81663i	0.0184165	+	0.147781i
$668$			52.0071i			2.01222i
$669$	2.96200	−	6.38635i	0.114518	−	0.246911i
$670$	−1.20251	−	1.38777i	−0.0464570	−	0.0536143i
$671$	−3.02328	−	4.70432i	−0.116713	−	0.181608i
$672$	−4.37621	−	2.84888i	−0.168816	−	0.109898i
$673$	40.0750	+	25.7546i	1.54478	+	0.992767i	0.986621	+	0.163030i	$0.0521269\pi$
$673$	40.0750	+	25.7546i	1.54478	+	0.992767i	0.558155	+	0.829737i	$0.311509\pi$
$674$	7.05979	−	15.4588i	0.271933	−	0.595450i
$675$	−23.7622	+	6.52471i	−0.914609	+	0.251136i
$676$	5.41409	−	37.6558i	0.208234	−	1.44830i
$677$	2.36184	+	5.17170i	0.0907728	+	0.198765i	0.949573	−	0.313546i	$-0.101517\pi$
$677$	2.36184	+	5.17170i	0.0907728	+	0.198765i	−0.858800	+	0.512311i	$0.828790\pi$
$678$	31.3476	+	49.4135i	1.20390	+	1.89772i
$679$	−14.8706	−	4.36640i	−0.570680	−	0.167567i
$680$	14.1544	−	6.46411i	0.542798	−	0.247887i
$681$	19.3313	+	22.5761i	0.740778	+	0.865118i
$682$	−6.09996	−	5.28564i	−0.233579	−	0.202398i
$683$	11.8468	+	5.41024i	0.453304	+	0.207017i	0.628965	−	0.777434i	$-0.283479\pi$
$683$	11.8468	+	5.41024i	0.453304	+	0.207017i	−0.175661	+	0.984451i	$0.556206\pi$
$684$	−23.6335	−	11.1304i	−0.903650	−	0.425582i
$685$	1.30594	+	9.08298i	0.0498972	+	0.347043i
$686$	−4.69332	+	3.01621i	−0.179192	+	0.115160i
$687$	0.263353	−	44.8366i	0.0100476	−	1.71062i
$688$	7.96332	+	27.1206i	0.303599	+	1.03396i
$689$	0.164376			0.00626221
$690$	−4.55090	+	9.34720i	−0.173250	+	0.355842i
$691$	−11.2268			−0.427089			−0.213545	−	0.976933i	$-0.568501\pi$
$691$	−11.2268			−0.427089			−0.213545	+	0.976933i	$0.568501\pi$
$692$	−24.9850	−	85.0912i	−0.949788	−	3.23468i
$693$	8.67837	+	7.70018i	0.329664	+	0.292506i
$694$	−3.70415	+	2.38051i	−0.140608	+	0.0903630i
$695$	1.00532	+	6.99214i	0.0381339	+	0.265227i
$696$	−6.84150	+	1.96527i	−0.259326	+	0.0744934i
$697$	−9.39252	−	4.28942i	−0.355767	−	0.162473i
$698$	−26.6747	−	23.1138i	−1.00965	−	0.874869i
$699$	−18.9246	+	16.2046i	−0.715795	+	0.612916i
$700$	−67.2074	+	30.6926i	−2.54020	+	1.16007i
$701$	1.80301	+	0.529412i	0.0680988	+	0.0199956i	0.315605	−	0.948891i	$-0.397793\pi$
$701$	1.80301	+	0.529412i	0.0680988	+	0.0199956i	−0.247506	+	0.968886i	$0.579611\pi$
$702$	−46.4402	+	38.8293i	−1.75277	+	1.46552i
$703$	−3.97439	−	8.70270i	−0.149897	−	0.328229i
$704$	1.00976	−	7.02303i	0.0380567	−	0.264690i
$705$	−0.680921	+	0.0938229i	−0.0256450	+	0.00353358i
$706$	15.0873	−	33.0366i	0.567819	−	1.24335i
$707$	30.9163	+	19.8687i	1.16273	+	0.747240i
$708$	−2.83567	+	4.35593i	−0.106571	+	0.163706i
$709$	−6.05376	−	9.41984i	−0.227354	−	0.353769i	0.708770	−	0.705439i	$-0.249250\pi$
$709$	−6.05376	−	9.41984i	−0.227354	−	0.353769i	−0.936124	+	0.351670i	$0.885614\pi$
$710$	0.438000	+	0.505479i	0.0164379	+	0.0189703i
$711$	−14.4262	+	6.38448i	−0.541023	+	0.239437i
$712$		−	87.2053i		−	3.26816i
$713$	−0.291825	+	15.5056i	−0.0109289	+	0.580689i
$714$	−64.3319	+	73.3678i	−2.40756	+	2.74572i
$715$	−2.33005	+	0.684165i	−0.0871390	+	0.0255863i
$716$	44.1700	−	38.2736i	1.65071	−	1.43035i
$717$	−17.0415	−	2.55245i	−0.636427	−	0.0953231i
$718$	−26.7897	+	3.85178i	−0.999783	+	0.143747i
$719$	7.66440	−	11.9260i	0.285834	−	0.444766i	−0.668411	−	0.743792i	$-0.733025\pi$
$719$	7.66440	−	11.9260i	0.285834	−	0.444766i	0.954245	+	0.299026i	$0.0966617\pi$
$720$	−6.51898	−	1.99762i	−0.242948	−	0.0744469i
$721$	−24.9712	+	28.8183i	−0.929975	+	1.07325i
$722$	35.2427	+	5.06713i	1.31160	+	0.188579i
$723$	11.0242	−	36.7452i	0.409995	−	1.36657i
$724$	−21.3627	+	72.7547i	−0.793938	+	2.70391i
$725$	−1.07149	+	3.64917i	−0.0397943	+	0.135527i
$726$	−12.2407	+	40.7998i	−0.454294	+	1.51422i
$727$	−3.09585	−	0.445116i	−0.114819	−	0.0165084i	0.0846659	−	0.996409i	$-0.473018\pi$
$727$	−3.09585	−	0.445116i	−0.114819	−	0.0165084i	−0.199485	+	0.979901i	$0.563927\pi$
$728$	−60.5730	+	69.9050i	−2.24499	+	2.59085i
$729$	26.9832	+	0.951318i	0.999379	+	0.0352340i
$730$	3.02545	−	4.70769i	0.111977	−	0.174239i
$731$	37.3808	−	5.37454i	1.38258	−	0.198785i
$732$	−38.5889	−	5.77979i	−1.42629	−	0.213627i
$733$	37.9189	−	32.8569i	1.40056	−	1.21360i	0.454033	−	0.890985i	$-0.349985\pi$
$733$	37.9189	−	32.8569i	1.40056	−	1.21360i	0.946531	−	0.322612i	$-0.104561\pi$
$734$	68.1843	−	20.0207i	2.51673	−	0.738978i
$735$	−4.40114	+	5.01931i	−0.162339	+	0.185140i
$736$	3.22206	−	1.98603i	0.118767	−	0.0732059i
$737$		−	1.48539i		−	0.0547150i
$738$	5.16702	+	11.6752i	0.190201	+	0.429771i
$739$	−0.0243929	−	0.0281509i	−0.000897306	−	0.00103555i	0.755301	−	0.655378i	$-0.227491\pi$
$739$	−0.0243929	−	0.0281509i	−0.000897306	−	0.00103555i	−0.756198	+	0.654343i	$0.772945\pi$
$740$	−5.01580	−	7.80474i	−0.184384	−	0.286908i
$741$	−9.53331	+	14.6443i	−0.350215	+	0.537971i
$742$	−0.275615	−	0.177127i	−0.0101181	−	0.00650253i
$743$	−18.8092	+	41.1865i	−0.690044	+	1.51099i	0.161594	+	0.986857i	$0.448336\pi$
$743$	−18.8092	+	41.1865i	−0.690044	+	1.51099i	−0.851639	+	0.524129i	$0.824391\pi$
$744$	−28.4330	+	3.91774i	−1.04241	+	0.143631i
$745$	0.537732	−	3.74001i	0.0197010	−	0.137023i
$746$	17.7047	+	38.7679i	0.648215	+	1.41939i
$747$	4.55783	−	29.2564i	0.166762	−	1.07044i
$748$	23.6985	+	6.95850i	0.866502	+	0.254428i
$749$	−43.4566	+	19.8460i	−1.58787	+	0.725156i
$750$	−16.0416	+	13.7360i	−0.585756	+	0.501567i
$751$	−34.2255	−	29.6566i	−1.24891	−	1.08218i	−0.993319	−	0.115397i	$-0.963186\pi$
$751$	−34.2255	−	29.6566i	−1.24891	−	1.08218i	−0.255587	−	0.966786i	$-0.582269\pi$
$752$	3.18368	+	1.45394i	0.116097	+	0.0530196i
$753$	30.2549	−	8.69095i	1.10255	−	0.316716i
$754$	1.32964	+	9.24783i	0.0484225	+	0.336786i
$755$	5.25124	−	3.37477i	0.191112	−	0.122820i
$756$	80.3216	−	10.1074i	2.92127	−	0.367604i
$757$	14.4534	+	49.2238i	0.525318	+	1.78907i	0.609696	+	0.792635i	$0.291292\pi$
$757$	14.4534	+	49.2238i	0.525318	+	1.78907i	−0.0843778	+	0.996434i	$0.526890\pi$
$758$	48.8705			1.77506
$759$	−7.73354	+	3.30353i	−0.280710	+	0.119911i
$760$	−5.55399			−0.201465
$761$	−5.29925	−	18.0476i	−0.192098	−	0.654224i	−0.998060	−	0.0622578i	$-0.980170\pi$
$761$	−5.29925	−	18.0476i	−0.192098	−	0.654224i	0.805962	−	0.591967i	$-0.201648\pi$
$762$	0.0952063	−	16.2091i	0.00344896	−	0.587195i
$763$	26.0595	−	16.7474i	0.943418	−	0.606298i
$764$	−11.0731	−	77.0153i	−0.400612	−	2.78632i
$765$	−3.88137	+	8.24143i	−0.140331	+	0.297969i
$766$	51.1793	+	23.3728i	1.84918	+	0.844493i
$767$	2.62751	+	2.27675i	0.0948739	+	0.0822087i
$768$	−36.5847	−	42.7255i	−1.32014	−	1.54172i
$769$	40.0153	−	18.2744i	1.44299	−	0.658990i	0.468506	−	0.883460i	$-0.344792\pi$
$769$	40.0153	−	18.2744i	1.44299	−	0.658990i	0.974481	+	0.224470i	$0.0720651\pi$
$770$	4.64413	+	1.36364i	0.167363	+	0.0491421i
$771$	0.000438916	0	0.000691869i	1.58072e−5	0	2.49170e-5i
$772$	33.2818	+	72.8769i	1.19784	+	2.62290i
$773$	2.22164	−	15.4519i	0.0799069	−	0.555765i	−0.910061	−	0.414474i	$-0.863966\pi$
$773$	2.22164	−	15.4519i	0.0799069	−	0.555765i	0.989968	−	0.141291i	$-0.0451253\pi$
$774$	−38.9840	−	25.7055i	−1.40125	−	0.923966i
$775$	−6.37050	+	13.9494i	−0.228835	+	0.501079i
$776$	17.4902	+	11.2403i	0.627862	+	0.403503i
$777$	24.8474	+	16.1754i	0.891395	+	0.580291i
$778$	38.2256	+	59.4802i	1.37045	+	2.13247i
$779$	2.41348	+	2.78531i	0.0864719	+	0.0997939i
$780$	−7.12950	+	15.3718i	−0.255277	+	0.550400i
$781$			0.541035i			0.0193598i
$782$	−28.1656	−	64.8780i	−1.00720	−	2.32003i
$783$	2.31438	−	3.46543i	0.0827092	−	0.123844i
$784$	32.6148	−	9.57656i	1.16481	−	0.342020i
$785$	3.42695	−	2.96947i	0.122313	−	0.105985i
$786$	4.77275	−	31.8654i	0.170238	−	1.13660i
$787$	15.7039	−	2.25789i	0.559785	−	0.0804849i	0.143386	−	0.989667i	$-0.454201\pi$
$787$	15.7039	−	2.25789i	0.559785	−	0.0804849i	0.416399	+	0.909182i	$0.363292\pi$
$788$	−44.5219	+	69.2775i	−1.58603	+	2.46791i
$789$	−19.2168	−	42.7415i	−0.684136	−	1.52164i
$790$	−4.30991	+	4.97390i	−0.153340	+	0.176964i
$791$	−51.8145	−	7.44981i	−1.84231	−	0.264885i
$792$	−8.26005	−	13.1911i	−0.293508	−	0.468724i
$793$	−7.35326	+	25.0429i	−0.261122	+	0.889300i
$794$	−7.25423	+	24.7056i	−0.257443	+	0.876771i
$795$	−0.0292963	−	0.00878939i	−0.00103903	−	0.000311728i
$796$	30.9681	+	4.45254i	1.09764	+	0.157816i
$797$	−4.63536	+	5.34949i	−0.164193	+	0.189489i	−0.831884	−	0.554950i	$-0.812737\pi$
$797$	−4.63536	+	5.34949i	−0.164193	+	0.189489i	0.667691	+	0.744439i	$0.267283\pi$
$798$	31.7652	−	14.2818i	1.12447	−	0.505570i
$799$	2.52817	−	3.93391i	0.0894403	−	0.139172i
$800$	3.70462	−	0.532645i	0.130978	−	0.0188318i
$801$	32.9769	+	38.9732i	1.16518	+	1.37705i
$802$	12.5581	−	10.8817i	0.443442	−	0.384245i
$803$	4.34333	−	1.27532i	0.153273	−	0.0450049i
$804$	−7.79300	−	6.83322i	−0.274838	−	0.240989i
$805$	−3.70345	−	8.53069i	−0.130530	−	0.300667i
$806$			37.6723i			1.32695i
$807$	−24.5997	−	11.4094i	−0.865951	−	0.401630i
$808$	−32.2844	−	37.2582i	−1.13576	−	1.31074i
$809$	−0.942731	−	1.46692i	−0.0331447	−	0.0515741i	0.824286	−	0.566174i	$-0.191577\pi$
$809$	−0.942731	−	1.46692i	−0.0331447	−	0.0515741i	−0.857431	+	0.514600i	$0.827941\pi$
$810$	10.3532	−	4.43724i	0.363774	−	0.155909i
$811$	−5.51336	−	3.54322i	−0.193600	−	0.124419i	0.440250	−	0.897875i	$-0.354890\pi$
$811$	−5.51336	−	3.54322i	−0.193600	−	0.124419i	−0.633850	+	0.773456i	$0.718526\pi$
$812$	5.19047	−	11.3656i	0.182150	−	0.398853i
$813$	−1.52877	−	11.0951i	−0.0536163	−	0.389121i
$814$	1.59176	−	11.0709i	0.0557912	−	0.388036i
$815$	−3.71309	−	8.13054i	−0.130064	−	0.284800i
$816$	39.1689	−	24.8485i	1.37119	−	0.869870i
$817$	−12.9334	−	3.79758i	−0.452481	−	0.132861i
$818$	34.5013	−	15.7562i	1.20631	−	0.550904i
$819$	0.636103	−	54.1473i	0.0222272	−	1.89206i
$820$	2.70094	+	2.34038i	0.0943211	+	0.0817297i
$821$	−19.5137	−	8.91162i	−0.681034	−	0.311018i	0.0446928	−	0.999001i	$-0.485769\pi$
$821$	−19.5137	−	8.91162i	−0.681034	−	0.311018i	−0.725727	+	0.687983i	$0.758496\pi$
$822$	21.3124	+	74.1926i	0.743355	+	2.58777i
$823$	−7.30134	−	50.7820i	−0.254509	−	1.77015i	−0.570414	−	0.821357i	$-0.693217\pi$
$823$	−7.30134	−	50.7820i	−0.254509	−	1.77015i	0.315906	−	0.948791i	$-0.397692\pi$
$824$	43.0327	−	27.6555i	1.49912	−	0.963424i
$825$	−8.31558	−	0.0488425i	−0.289511	−	0.00170048i
$826$	−1.95228	−	6.64885i	−0.0679284	−	0.231343i
$827$	0.393001			0.0136660			0.00683300	−	0.999977i	$-0.497825\pi$
$827$	0.393001			0.0136660			0.00683300	+	0.999977i	$0.497825\pi$
$828$	−18.2448	+	55.7708i	−0.634049	+	1.93817i
$829$	−27.5490			−0.956816			−0.478408	−	0.878138i	$-0.658786\pi$
$829$	−27.5490			−0.956816			−0.478408	+	0.878138i	$0.658786\pi$
$830$	−3.48011	−	11.8522i	−0.120797	−	0.411395i
$831$	−24.7081	−	0.145126i	−0.857114	−	0.00503436i
$832$	−27.8591	+	17.9040i	−0.965841	+	0.620708i
$833$	−6.46334	−	44.9535i	−0.223942	−	1.55755i
$834$	16.4064	+	57.1140i	0.568107	+	1.97769i
$835$	−5.88818	−	2.68904i	−0.203769	−	0.0930581i
$836$	−6.66247	−	5.77306i	−0.230426	−	0.199665i
$837$	11.2256	−	12.5029i	0.388013	−	0.432164i
$838$	−76.2544	+	34.8242i	−2.63417	+	1.20298i
$839$	−11.6409	−	3.41807i	−0.401888	−	0.118005i	0.0745410	−	0.997218i	$-0.476251\pi$
$839$	−11.6409	−	3.41807i	−0.401888	−	0.118005i	−0.476429	+	0.879213i	$0.658069\pi$
$840$	14.5337	−	9.22008i	0.501460	−	0.318123i
$841$	11.7799	+	25.7943i	0.406202	+	0.889458i
$842$	−1.24990	+	8.69321i	−0.0430742	+	0.299588i
$843$	4.05258	+	29.4116i	0.139578	+	1.01299i
$844$	−21.8489	+	47.8425i	−0.752072	+	1.64681i
$845$	3.98341	+	2.55998i	0.137034	+	0.0880661i
$846$	−5.56666	+	1.56373i	−0.191386	+	0.0537621i
$847$	−20.6009	−	32.0557i	−0.707857	−	1.10145i
$848$	0.101990	+	0.117703i	0.00350237	+	0.00404195i
$849$	0.812001	+	0.376608i	0.0278678	+	0.0129252i
$850$		−	69.9386i		−	2.39888i
$851$	−18.2943	+	11.2763i	−0.627120	+	0.386547i
$852$	2.83851	+	2.48892i	0.0972457	+	0.0852690i
$853$	−42.7516	+	12.5530i	−1.46379	+	0.429806i	−0.914074	−	0.405548i	$-0.867081\pi$
$853$	−42.7516	+	12.5530i	−1.46379	+	0.429806i	−0.549712	+	0.835354i	$0.685263\pi$
$854$	39.3151	−	34.0667i	1.34533	−	1.16574i
$855$	2.48215	−	2.10026i	0.0848877	−	0.0718272i
$856$	63.4350	−	9.12058i	2.16816	−	0.311735i
$857$	−8.10346	+	12.6092i	−0.276809	+	0.430723i	−0.951625	−	0.307263i	$-0.900587\pi$
$857$	−8.10346	+	12.6092i	−0.276809	+	0.430723i	0.674816	+	0.737986i	$0.264223\pi$
$858$	−18.6317	+	8.37690i	−0.636075	+	0.285983i
$859$	24.2105	−	27.9404i	0.826051	−	0.953313i	−0.173452	−	0.984842i	$-0.555492\pi$
$859$	24.2105	−	27.9404i	0.826051	−	0.953313i	0.999503	+	0.0315290i	$0.0100376\pi$
$860$	−12.9381	−	1.86021i	−0.441185	−	0.0634328i
$861$	−10.9394	−	3.28202i	−0.372815	−	0.111851i
$862$	7.26760	−	24.7512i	0.247536	−	0.843029i
$863$	−1.97760	+	6.73508i	−0.0673182	+	0.229265i	−0.986280	−	0.165082i	$-0.947211\pi$
$863$	−1.97760	+	6.73508i	−0.0673182	+	0.229265i	0.918962	+	0.394347i	$0.129029\pi$
$864$	−4.04825	−	0.655050i	−0.137724	−	0.0222853i
$865$	10.9258	+	1.57089i	0.371488	+	0.0534119i
$866$	1.99029	−	2.29692i	0.0676329	−	0.0780525i
$867$	−13.3397	−	29.6698i	−0.453040	−	1.00764i
$868$	27.2378	−	42.3829i	0.924512	−	1.43857i
$869$	−5.26958	+	0.757652i	−0.178758	+	0.0257016i
$870$	0.257516	−	1.71932i	0.00873062	−	0.0582902i
$871$	−5.23951	+	4.54006i	−0.177534	+	0.153834i
$872$	−39.8716	+	11.7074i	−1.35022	+	0.396461i
$873$	−12.0671	+	1.59055i	−0.408411	+	0.0538318i
$874$	−0.475037	+	25.2402i	−0.0160684	+	0.853763i
$875$		−	18.8919i		−	0.638664i
$876$	13.2897	−	28.6538i	0.449018	−	0.968123i
$877$	−12.4028	−	14.3136i	−0.418813	−	0.483336i	0.506662	−	0.862145i	$-0.330879\pi$
$877$	−12.4028	−	14.3136i	−0.418813	−	0.483336i	−0.925475	+	0.378809i	$0.876334\pi$
$878$	0.175858	+	0.273640i	0.00593491	+	0.00923490i
$879$	−0.711760	−	0.463350i	−0.0240071	−	0.0156284i
$880$	−1.93564	−	1.24396i	−0.0652503	−	0.0419338i
$881$	14.4860	−	31.7199i	0.488045	−	1.06867i	−0.492127	−	0.870523i	$-0.663781\pi$
$881$	14.4860	−	31.7199i	0.488045	−	1.06867i	0.980172	−	0.198146i	$-0.0634921\pi$
$882$	−30.9131	+	46.8816i	−1.04090	+	1.57858i
$883$	−2.09188	+	14.5493i	−0.0703973	+	0.489624i	0.923870	+	0.382705i	$0.125008\pi$
$883$	−2.09188	+	14.5493i	−0.0703973	+	0.489624i	−0.994268	+	0.106919i	$0.965902\pi$
$884$	−47.8887	−	104.862i	−1.61067	−	3.52688i
$885$	−0.346554	−	0.546276i	−0.0116493	−	0.0183629i
$886$	41.0891	+	12.0648i	1.38042	+	0.405326i
$887$	22.9096	−	10.4625i	0.769230	−	0.351296i	0.00816110	−	0.999967i	$-0.497402\pi$
$887$	22.9096	−	10.4625i	0.769230	−	0.351296i	0.761069	+	0.648671i	$0.224675\pi$
$888$	−25.8686	−	30.2107i	−0.868095	−	1.01381i
$889$	10.9585	+	9.49556i	0.367535	+	0.318471i
$890$	19.3737	+	8.84769i	0.649409	+	0.296575i
$891$	8.67975	+	2.77169i	0.290782	+	0.0928551i
$892$	−2.35912	−	16.4080i	−0.0789891	−	0.549381i
$893$	−1.40412	+	0.902371i	−0.0469870	+	0.0301967i
$894$	0.186690	−	31.7844i	0.00624384	−	1.06303i
$895$	2.04946	+	6.97982i	0.0685059	+	0.233310i
$896$	72.0349			2.40652
$897$	35.2902	+	17.1818i	1.17831	+	0.573685i
$898$	17.5840			0.586786
$899$	−0.730636	−	2.48832i	−0.0243681	−	0.0829901i
$900$	−38.5103	+	43.4025i	−1.28368	+	1.44675i
$901$	0.175054	−	0.112500i	0.00583189	−	0.00374793i
$902$	0.613175	+	4.26472i	0.0204165	+	0.142000i
$903$	40.1484	−	11.5329i	1.33605	−	0.383791i
$904$	63.8768	+	29.1715i	2.12451	+	0.970231i
$905$	−7.13263	−	6.18046i	−0.237097	−	0.205445i
$906$	39.8857	−	34.1530i	1.32511	−	1.13466i
$907$	−37.4741	+	17.1138i	−1.24431	+	0.568255i	−0.925206	−	0.379466i	$-0.876108\pi$
$907$	−37.4741	+	17.1138i	−1.24431	+	0.568255i	−0.319100	+	0.947721i	$0.603381\pi$
$908$	67.1513	+	19.7174i	2.22849	+	0.654345i
$909$	28.5175	+	4.44272i	0.945867	+	0.147356i
$910$	−9.38463	−	20.5495i	−0.311097	−	0.681208i
$911$	−1.94178	+	13.5054i	−0.0643340	+	0.447453i	0.932039	+	0.362358i	$0.118028\pi$
$911$	−1.94178	+	13.5054i	−0.0643340	+	0.447453i	−0.996373	+	0.0850944i	$0.972881\pi$
$912$	−16.4014	+	2.25992i	−0.543104	+	0.0748334i
$913$	4.15087	−	9.08913i	0.137374	−	0.300806i
$914$	8.27887	+	5.32051i	0.273841	+	0.175987i
$915$	2.64963	−	4.07015i	0.0875941	−	0.134555i
$916$	−57.0805	−	88.8190i	−1.88599	−	2.93466i
$917$	18.8752	+	21.7831i	0.623313	+	0.719341i
$918$	−22.8819	+	73.1359i	−0.755215	+	2.41385i
$919$		−	11.7592i		−	0.387902i	−0.981011	−	0.193951i	$-0.937870\pi$
$919$		−	11.7592i		−	0.387902i	0.981011	−	0.193951i	$-0.0621303\pi$
$920$	1.54278	+	12.3798i	0.0508639	+	0.408151i
$921$	9.07141	−	10.3456i	0.298913	−	0.340898i
$922$	−11.6044	+	3.40736i	−0.382171	+	0.112215i
$923$	1.90843	−	1.65366i	0.0628167	−	0.0544310i
$924$	27.0181	+	4.04673i	0.888830	+	0.133128i
$925$	−21.0342	+	3.02427i	−0.691601	+	0.0994373i
$926$	−40.6764	+	63.2937i	−1.33671	+	2.07996i
$927$	−8.77389	+	28.6325i	−0.288172	+	0.940415i
$928$	−0.414486	+	0.478342i	−0.0136062	+	0.0157023i
$929$	28.5423	+	4.10376i	0.936442	+	0.134640i	0.593607	−	0.804755i	$-0.297704\pi$
$929$	28.5423	+	4.10376i	0.936442	+	0.134640i	0.342835	+	0.939395i	$0.388613\pi$
$930$	2.01439	−	6.71423i	0.0660544	−	0.220168i
$931$	−4.56691	+	15.5535i	−0.149674	+	0.509745i
$932$	−16.5283	+	56.2901i	−0.541402	+	1.84384i
$933$	−16.9339	+	56.4430i	−0.554391	+	1.84786i
$934$	−58.7237	−	8.44320i	−1.92150	−	0.276270i
$935$	−2.01317	+	2.32332i	−0.0658377	+	0.0759807i
$936$	−21.2830	+	69.4544i	−0.695657	+	2.27019i
$937$	−3.81413	+	5.93490i	−0.124602	+	0.193885i	−0.897950	−	0.440097i	$-0.854944\pi$
$937$	−3.81413	+	5.93490i	−0.124602	+	0.193885i	0.773348	+	0.633982i	$0.218581\pi$
$938$	13.6775	−	1.96653i	0.446587	−	0.0642096i
$939$	0.655062	+	0.0981142i	0.0213772	+	0.00320184i
$940$	−1.22320	+	1.05991i	−0.0398963	+	0.0345704i
$941$	34.9446	−	10.2607i	1.13916	−	0.334488i	0.342859	−	0.939387i	$-0.388605\pi$
$941$	34.9446	−	10.2607i	1.13916	−	0.334488i	0.796302	+	0.604899i	$0.206787\pi$
$942$	25.1485	−	28.6808i	0.819383	−	0.934471i
$943$	5.53802	−	6.15334i	0.180343	−	0.200380i
$944$			3.29412i			0.107214i
$945$	−3.00870	+	9.61652i	−0.0978730	+	0.312825i
$946$	−10.3195	−	11.9093i	−0.335515	−	0.387205i
$947$	26.9615	+	41.9529i	0.876131	+	1.36329i	0.931087	+	0.364798i	$0.118862\pi$
$947$	26.9615	+	41.9529i	0.876131	+	1.36329i	−0.0549554	+	0.998489i	$0.517502\pi$
$948$	−20.2667	+	31.1320i	−0.658231	+	1.01112i
$949$	−17.7738	−	11.4225i	−0.576962	−	0.370791i
$950$	−10.3700	+	22.7071i	−0.336447	+	0.736715i
$951$	29.4638	−	4.05977i	0.955430	−	0.131647i
$952$	−16.6643	+	115.903i	−0.540094	+	3.75644i
$953$	6.39189	+	13.9963i	0.207053	+	0.453384i	0.984459	−	0.175616i	$-0.0561918\pi$
$953$	6.39189	+	13.9963i	0.207053	+	0.453384i	−0.777405	+	0.629000i	$0.783465\pi$
$954$	−0.254230	−	0.0396063i	−0.00823100	−	0.00128230i
$955$	9.29212	+	2.72841i	0.300686	+	0.0882894i
$956$	−36.9088	+	16.8557i	−1.19372	+	0.545152i
$957$	1.06819	−	0.914662i	0.0345297	−	0.0295668i
$958$	41.3956	+	35.8695i	1.33743	+	1.15889i
$959$	−62.8128	−	28.6857i	−2.02833	−	0.926308i
$960$	5.92261	−	1.70131i	0.191151	−	0.0549097i
$961$	2.92359	+	20.3340i	0.0943093	+	0.655936i
$962$	−43.9165	+	28.2234i	−1.41592	+	0.909959i
$963$	−24.9009	+	28.0642i	−0.802422	+	0.904356i
$964$	−25.4502	−	86.6755i	−0.819697	−	2.79163i
$965$	−9.97187			−0.321006
$966$	−40.6577	−	66.8373i	−1.30814	−	2.15045i
$967$	29.1748			0.938198			0.469099	−	0.883146i	$-0.344579\pi$
$967$	29.1748			0.938198			0.469099	+	0.883146i	$0.344579\pi$
$968$	14.4012	+	49.0459i	0.462871	+	1.57639i
$969$	−0.129926	+	22.1203i	−0.00417383	+	0.710607i
$970$	−4.27169	+	2.74525i	−0.137156	+	0.0881446i
$971$	4.85218	+	33.7476i	0.155714	+	1.08301i	0.906420	+	0.422377i	$0.138804\pi$
$971$	4.85218	+	33.7476i	0.155714	+	1.08301i	−0.750707	+	0.660636i	$0.770287\pi$
$972$	54.4709	−	32.7872i	1.74715	−	1.05165i
$973$	−48.3537	−	22.0824i	−1.55015	−	0.707929i
$974$	−61.7927	−	53.5437i	−1.97997	−	1.71565i
$975$	25.2441	+	29.4814i	0.808459	+	0.944160i
$976$	−22.4948	+	10.2730i	−0.720040	+	0.328831i
$977$	17.3707	+	5.10049i	0.555737	+	0.163179i	0.547528	−	0.836787i	$-0.315569\pi$
$977$	17.3707	+	5.10049i	0.555737	+	0.163179i	0.00820879	+	0.999966i	$0.497387\pi$
$978$	−40.2786	−	63.4916i	−1.28797	−	2.03024i
$979$	7.15698	+	15.6716i	0.228738	+	0.500866i
$980$	−2.23706	+	15.5591i	−0.0714604	+	0.497018i
$981$	13.3919	−	20.3097i	0.427572	−	0.648439i
$982$	33.3000	−	72.9168i	1.06265	−	2.32687i
$983$	−33.5366	−	21.5527i	−1.06965	−	0.687423i	−0.117507	−	0.993072i	$-0.537490\pi$
$983$	−33.5366	−	21.5527i	−1.06965	−	0.687423i	−0.952144	+	0.305649i	$0.901127\pi$
$984$	12.8401	+	8.35882i	0.409328	+	0.266469i
$985$	−5.54149	−	8.62273i	−0.176567	−	0.274743i
$986$	7.74532	+	8.93857i	0.246661	+	0.284662i
$987$	2.17629	−	4.69227i	0.0692720	−	0.149357i
$988$			41.1462i			1.30904i
$989$	−4.87218	+	29.8833i	−0.154926	+	0.950234i
$990$	3.76860	−	0.496732i	0.119774	−	0.0157872i
$991$	0.926775	−	0.272126i	0.0294400	−	0.00864436i	−0.266979	−	0.963702i	$-0.586026\pi$
$991$	0.926775	−	0.272126i	0.0294400	−	0.00864436i	0.296419	+	0.955058i	$0.404207\pi$
$992$	−1.92876	+	1.67128i	−0.0612380	+	0.0530631i
$993$	0.921390	−	6.15169i	0.0292394	−	0.195218i
$994$	−4.98188	+	0.716286i	−0.158016	+	0.0227192i
$995$	−2.10533	+	3.27595i	−0.0667434	+	0.103855i
$996$	−28.5903	−	63.5899i	−0.905920	−	2.01492i
$997$	25.8281	−	29.8073i	0.817985	−	0.944005i	−0.181237	−	0.983439i	$-0.558010\pi$
$997$	25.8281	−	29.8073i	0.817985	−	0.944005i	0.999222	+	0.0394343i	$0.0125556\pi$
$998$	−23.9432	−	3.44251i	−0.757907	−	0.108971i
$999$	22.9853	+	3.71927i	0.727222	+	0.117672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.g.a.14.6	yes	60
3.2	odd	2	inner	69.2.g.a.14.1	yes	60
23.5	odd	22	inner	69.2.g.a.5.1	✓	60
69.5	even	22	inner	69.2.g.a.5.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.g.a.5.1	✓	60	23.5	odd	22	inner
69.2.g.a.5.6	yes	60	69.5	even	22	inner
69.2.g.a.14.1	yes	60	3.2	odd	2	inner
69.2.g.a.14.6	yes	60	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.694600 + 2.36559i) q^{2} +(-1.73202 - 0.0101732i) q^{3} +(-3.43104 + 2.20500i) q^{4} +(-0.0722440 - 0.502468i) q^{5} +(-1.17900 - 4.10432i) q^{6} +(3.47479 + 1.58688i) q^{7} +(-3.87278 - 3.35579i) q^{8} +(2.99979 + 0.0352405i) q^{9} +O(q^{10})\)	\(q+(0.694600 + 2.36559i) q^{2} +(-1.73202 - 0.0101732i) q^{3} +(-3.43104 + 2.20500i) q^{4} +(-0.0722440 - 0.502468i) q^{5} +(-1.17900 - 4.10432i) q^{6} +(3.47479 + 1.58688i) q^{7} +(-3.87278 - 3.35579i) q^{8} +(2.99979 + 0.0352405i) q^{9} +(1.13845 - 0.519914i) q^{10} +(0.971385 + 0.285224i) q^{11} +(5.96507 - 3.78420i) q^{12} +(-1.96293 - 4.29821i) q^{13} +(-1.34033 + 9.32218i) q^{14} +(0.120016 + 0.871021i) q^{15} +(1.85985 - 4.07250i) q^{16} +(-5.03219 - 3.23399i) q^{17} +(2.00029 + 7.12076i) q^{18} +(1.15430 + 1.79612i) q^{19} +(1.35581 + 1.56469i) q^{20} +(-6.00227 - 2.78387i) q^{21} +2.49602i q^{22} +(3.68290 - 3.07184i) q^{23} +(6.67360 + 5.85169i) q^{24} +(4.55021 - 1.33606i) q^{25} +(8.80437 - 7.62903i) q^{26} +(-5.19535 - 0.0915549i) q^{27} +(-15.4212 + 2.21724i) q^{28} +(-0.433582 + 0.674667i) q^{29} +(-1.97711 + 0.888921i) q^{30} +(-2.11763 + 2.44388i) q^{31} +(0.781186 + 0.112318i) q^{32} +(-1.67956 - 0.503897i) q^{33} +(4.15494 - 14.1504i) q^{34} +(0.546326 - 1.86062i) q^{35} +(-10.3701 + 6.49362i) q^{36} +(-4.43544 - 0.637721i) q^{37} +(-3.44711 + 3.97818i) q^{38} +(3.35611 + 7.46457i) q^{39} +(-1.40639 + 2.18839i) q^{40} +(1.70861 - 0.245661i) q^{41} +(2.41631 - 16.1326i) q^{42} +(-4.77133 + 4.13438i) q^{43} +(-3.96178 + 1.16328i) q^{44} +(-0.199010 - 1.50985i) q^{45} +(9.82487 + 6.57854i) q^{46} +0.781750i q^{47} +(-3.26273 + 7.03474i) q^{48} +(4.97194 + 5.73793i) q^{49} +(6.32115 + 9.83590i) q^{50} +(8.68295 + 5.65253i) q^{51} +(16.2124 + 10.4191i) q^{52} +(-0.0144510 + 0.0316432i) q^{53} +(-3.39211 - 12.3537i) q^{54} +(0.0731394 - 0.508696i) q^{55} +(-8.13187 - 17.8063i) q^{56} +(-1.98099 - 3.12266i) q^{57} +(-1.89715 - 0.557054i) q^{58} +(-0.669283 + 0.305651i) q^{59} +(-2.33238 - 2.72387i) q^{60} +(-4.17444 - 3.61717i) q^{61} +(-7.25212 - 3.31193i) q^{62} +(10.3677 + 4.88278i) q^{63} +(-0.997397 - 6.93705i) q^{64} +(-2.01791 + 1.29683i) q^{65} +(0.0253925 - 4.32315i) q^{66} +(-0.413359 - 1.40777i) q^{67} +24.3966 q^{68} +(-6.41012 + 5.28303i) q^{69} +4.78093 q^{70} +(0.150561 + 0.512764i) q^{71} +(-11.4993 - 10.2031i) q^{72} +(3.76147 - 2.41735i) q^{73} +(-1.57227 - 10.9354i) q^{74} +(-7.89465 + 2.26780i) q^{75} +(-7.92087 - 3.61734i) q^{76} +(2.92274 + 2.53257i) q^{77} +(-15.3270 + 13.1241i) q^{78} +(-4.78339 + 2.18450i) q^{79} +(-2.18067 - 0.640301i) q^{80} +(8.99752 + 0.211428i) q^{81} +(1.76794 + 3.87124i) q^{82} +(1.40461 - 9.76931i) q^{83} +(26.7324 - 3.68342i) q^{84} +(-1.26143 + 2.76215i) q^{85} +(-13.0944 - 8.41527i) q^{86} +(0.757837 - 1.16413i) q^{87} +(-2.80481 - 4.36437i) q^{88} +(11.1441 + 12.8610i) q^{89} +(3.43345 - 1.51952i) q^{90} -18.0503i q^{91} +(-5.86279 + 18.6604i) q^{92} +(3.69264 - 4.21130i) q^{93} +(-1.84930 + 0.543004i) q^{94} +(0.819102 - 0.709756i) q^{95} +(-1.35189 - 0.202484i) q^{96} +(-4.01587 + 0.577395i) q^{97} +(-10.1201 + 15.7472i) q^{98} +(2.90390 + 0.889846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9}+O(q^{10}) \) 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9	\( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} + 4 q^{12} - 22 q^{13} - 46 q^{16} + 12 q^{18} - 22 q^{19} + 22 q^{21} + 50 q^{24} + 8 q^{25} + 10 q^{27} - 22 q^{28} + 33 q^{30} - 22 q^{31} + 22 q^{36} + 22 q^{37} + 13 q^{39} + 132 q^{40} - 11 q^{42} + 22 q^{43} + 66 q^{46} - 58 q^{48} + 68 q^{49} - 11 q^{51} + 94 q^{52} - 33 q^{54} - 44 q^{57} - 8 q^{58} - 121 q^{60} - 66 q^{61} - 66 q^{63} - 20 q^{64} - 66 q^{66} - 44 q^{67} - 66 q^{69} - 132 q^{70} - 101 q^{72} - 44 q^{73} - 44 q^{75} - 110 q^{76} + 84 q^{78} - 66 q^{79} + 77 q^{81} - 132 q^{82} + 77 q^{84} - 44 q^{85} + 73 q^{87} + 66 q^{88} + 176 q^{90} + 116 q^{93} + 100 q^{94} + 85 q^{96} + 44 q^{97} + 121 q^{99}+O(q^{100}) \) 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9 - 22 * q^10 + 4 * q^12 - 22 * q^13 - 46 * q^16 + 12 * q^18 - 22 * q^19 + 22 * q^21 + 50 * q^24 + 8 * q^25 + 10 * q^27 - 22 * q^28 + 33 * q^30 - 22 * q^31 + 22 * q^36 + 22 * q^37 + 13 * q^39 + 132 * q^40 - 11 * q^42 + 22 * q^43 + 66 * q^46 - 58 * q^48 + 68 * q^49 - 11 * q^51 + 94 * q^52 - 33 * q^54 - 44 * q^57 - 8 * q^58 - 121 * q^60 - 66 * q^61 - 66 * q^63 - 20 * q^64 - 66 * q^66 - 44 * q^67 - 66 * q^69 - 132 * q^70 - 101 * q^72 - 44 * q^73 - 44 * q^75 - 110 * q^76 + 84 * q^78 - 66 * q^79 + 77 * q^81 - 132 * q^82 + 77 * q^84 - 44 * q^85 + 73 * q^87 + 66 * q^88 + 176 * q^90 + 116 * q^93 + 100 * q^94 + 85 * q^96 + 44 * q^97 + 121 * q^99

Introduction

L-functions

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