LMFDB - Embedded newform 189.2.be.a.83.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(20,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 9]))

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

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

chi := DirichletCharacter("189.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			83.20
Character	$\chi$	$=$	189.83
Dual form			189.2.be.a.41.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.06681 + 0.364434i) q^{2} +(1.54027 - 0.792184i) q^{3} +(2.25951 + 0.822394i) q^{4} +(-2.23837 + 1.87822i) q^{5} +(3.47215 - 1.07597i) q^{6} +(-0.356385 - 2.62164i) q^{7} +(0.735222 + 0.424480i) q^{8} +(1.74489 - 2.44036i) q^{9} +O(q^{10})$	\(q+(2.06681 + 0.364434i) q^{2} +(1.54027 - 0.792184i) q^{3} +(2.25951 + 0.822394i) q^{4} +(-2.23837 + 1.87822i) q^{5} +(3.47215 - 1.07597i) q^{6} +(-0.356385 - 2.62164i) q^{7} +(0.735222 + 0.424480i) q^{8} +(1.74489 - 2.44036i) q^{9} +(-5.31078 + 3.06618i) q^{10} +(-3.51301 + 4.18664i) q^{11} +(4.13175 - 0.523234i) q^{12} +(-0.884066 + 0.155885i) q^{13} +(0.218835 - 5.54831i) q^{14} +(-1.95981 + 4.66618i) q^{15} +(-2.31907 - 1.94593i) q^{16} +(1.68770 + 2.92318i) q^{17} +(4.49571 - 4.40787i) q^{18} +(3.42780 + 1.97904i) q^{19} +(-6.60226 + 2.40303i) q^{20} +(-2.62575 - 3.75572i) q^{21} +(-8.78648 + 7.37273i) q^{22} +(2.48663 - 6.83195i) q^{23} +(1.46871 + 0.0713855i) q^{24} +(0.614371 - 3.48427i) q^{25} -1.88401 q^{26} +(0.754393 - 5.14110i) q^{27} +(1.35076 - 6.21670i) q^{28} +(-1.03707 - 0.182863i) q^{29} +(-5.75108 + 8.92988i) q^{30} +(0.950784 - 2.61226i) q^{31} +(-5.17531 - 6.16770i) q^{32} +(-2.09441 + 9.23152i) q^{33} +(2.42285 + 6.65672i) q^{34} +(5.72173 + 5.19884i) q^{35} +(5.94953 - 4.07903i) q^{36} +(2.55208 + 4.42033i) q^{37} +(6.36338 + 5.33951i) q^{38} +(-1.23821 + 0.940448i) q^{39} +(-2.44297 + 0.430761i) q^{40} +(0.529024 + 3.00024i) q^{41} +(-4.05822 - 8.71928i) q^{42} +(-1.63755 - 1.37406i) q^{43} +(-11.3807 + 6.57067i) q^{44} +(0.677817 + 8.73972i) q^{45} +(7.62918 - 13.2141i) q^{46} +(5.50750 - 2.00456i) q^{47} +(-5.11353 - 1.16014i) q^{48} +(-6.74598 + 1.86863i) q^{49} +(2.53958 - 6.97743i) q^{50} +(4.91522 + 3.16553i) q^{51} +(-2.12575 - 0.374828i) q^{52} +9.25621i q^{53} +(3.43278 - 10.3507i) q^{54} -15.9695i q^{55} +(0.850812 - 2.07876i) q^{56} +(6.84751 + 0.332818i) q^{57} +(-2.07678 - 0.755885i) q^{58} +(-7.56717 + 6.34961i) q^{59} +(-8.26565 + 8.93152i) q^{60} +(-5.01899 - 13.7896i) q^{61} +(2.91709 - 5.05254i) q^{62} +(-7.01960 - 3.70476i) q^{63} +(-5.42134 - 9.39004i) q^{64} +(1.68608 - 2.00940i) q^{65} +(-7.69303 + 18.3165i) q^{66} +(0.693812 + 3.93480i) q^{67} +(1.40937 + 7.99291i) q^{68} +(-1.58207 - 12.4929i) q^{69} +(9.93110 + 12.8302i) q^{70} +(13.9268 - 8.04064i) q^{71} +(2.31877 - 1.05353i) q^{72} +(2.86477 + 1.65398i) q^{73} +(3.66374 + 10.0661i) q^{74} +(-1.81388 - 5.85343i) q^{75} +(6.11759 + 7.29066i) q^{76} +(12.2278 + 7.71778i) q^{77} +(-2.90189 + 1.49248i) q^{78} +(-0.601523 + 3.41141i) q^{79} +8.84582 q^{80} +(-2.91072 - 8.51632i) q^{81} +6.39373i q^{82} +(-0.164783 + 0.934532i) q^{83} +(-2.84423 - 10.6455i) q^{84} +(-9.26808 - 3.37331i) q^{85} +(-2.88374 - 3.43671i) q^{86} +(-1.74223 + 0.539888i) q^{87} +(-4.35999 + 1.58691i) q^{88} +(-2.06490 + 3.57651i) q^{89} +(-1.78414 + 18.3104i) q^{90} +(0.723741 + 2.26215i) q^{91} +(11.2371 - 13.3919i) q^{92} +(-0.604920 - 4.77679i) q^{93} +(12.1135 - 2.13593i) q^{94} +(-11.3898 + 2.00832i) q^{95} +(-12.8574 - 5.40015i) q^{96} +(3.04401 - 3.62771i) q^{97} +(-14.6237 + 1.40363i) q^{98} +(4.08710 + 15.8782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	2.06681	+	0.364434i	1.46146	+	0.257694i	0.847142	−	0.531367i	$-0.178322\pi$
$2$	2.06681	+	0.364434i	1.46146	+	0.257694i	0.614314	+	0.789061i	$0.289433\pi$
$3$	1.54027	−	0.792184i	0.889278	−	0.457368i
$3$	1.54027	−	0.792184i	0.889278	−	0.457368i
$4$	2.25951	+	0.822394i	1.12975	+	0.411197i
$5$	−2.23837	+	1.87822i	−1.00103	+	0.839965i	−0.987127	−	0.159938i	$-0.948870\pi$
$5$	−2.23837	+	1.87822i	−1.00103	+	0.839965i	−0.0139041	+	0.999903i	$0.504426\pi$
$6$	3.47215	−	1.07597i	1.41750	−	0.439261i
$7$	−0.356385	−	2.62164i	−0.134701	−	0.990886i
$7$	−0.356385	−	2.62164i	−0.134701	−	0.990886i
$8$	0.735222	+	0.424480i	0.259940	+	0.150076i
$9$	1.74489	−	2.44036i	0.581630	−	0.813454i
$10$	−5.31078	+	3.06618i	−1.67942	+	0.969612i
$11$	−3.51301	+	4.18664i	−1.05921	+	1.26232i	−0.0954846	+	0.995431i	$0.530440\pi$
$11$	−3.51301	+	4.18664i	−1.05921	+	1.26232i	−0.963727	+	0.266889i	$0.914004\pi$
$12$	4.13175	−	0.523234i	1.19273	−	0.151045i
$13$	−0.884066	+	0.155885i	−0.245196	+	0.0432346i	−0.294895	−	0.955530i	$-0.595285\pi$
$13$	−0.884066	+	0.155885i	−0.245196	+	0.0432346i	0.0496994	+	0.998764i	$0.484174\pi$
$14$	0.218835	−	5.54831i	0.0584861	−	1.48285i
$15$	−1.95981	+	4.66618i	−0.506022	+	1.20480i
$16$	−2.31907	−	1.94593i	−0.579767	−	0.486482i
$17$	1.68770	+	2.92318i	0.409327	+	0.708976i	0.994815	−	0.101706i	$-0.0324300\pi$
$17$	1.68770	+	2.92318i	0.409327	+	0.708976i	−0.585487	+	0.810682i	$0.699097\pi$
$18$	4.49571	−	4.40787i	1.05965	−	1.03894i
$19$	3.42780	+	1.97904i	0.786391	+	0.454023i	0.838690	−	0.544609i	$-0.183322\pi$
$19$	3.42780	+	1.97904i	0.786391	+	0.454023i	−0.0522997	+	0.998631i	$0.516655\pi$
$20$	−6.60226	+	2.40303i	−1.47631	+	0.537333i
$21$	−2.62575	−	3.75572i	−0.572986	−	0.819565i
$22$	−8.78648	+	7.37273i	−1.87328	+	1.57187i
$23$	2.48663	−	6.83195i	0.518497	−	1.42456i	−0.353679	−	0.935367i	$-0.615069\pi$
$23$	2.48663	−	6.83195i	0.518497	−	1.42456i	0.872176	−	0.489192i	$-0.162708\pi$
$24$	1.46871	+	0.0713855i	0.299799	+	0.0145715i
$25$	0.614371	−	3.48427i	0.122874	−	0.696854i
$26$	−1.88401			−0.369484
$27$	0.754393	−	5.14110i	0.145183	−	0.989405i
$28$	1.35076	−	6.21670i	0.255270	−	1.17485i
$29$	−1.03707	−	0.182863i	−0.192578	−	0.0339568i	0.0765270	−	0.997068i	$-0.475617\pi$
$29$	−1.03707	−	0.182863i	−0.192578	−	0.0339568i	−0.269105	+	0.963111i	$0.586728\pi$
$30$	−5.75108	+	8.92988i	−1.05000	+	1.63036i
$31$	0.950784	−	2.61226i	0.170766	−	0.469175i	−0.824557	−	0.565779i	$-0.808576\pi$
$31$	0.950784	−	2.61226i	0.170766	−	0.469175i	0.995323	+	0.0966034i	$0.0307978\pi$
$32$	−5.17531	−	6.16770i	−0.914875	−	1.09031i
$33$	−2.09441	+	9.23152i	−0.364589	+	1.60700i
$34$	2.42285	+	6.65672i	0.415515	+	1.14162i
$35$	5.72173	+	5.19884i	0.967149	+	0.878764i
$36$	5.94953	−	4.07903i	0.991588	−	0.679838i
$37$	2.55208	+	4.42033i	0.419559	+	0.726698i	0.995895	−	0.0905149i	$-0.0288513\pi$
$37$	2.55208	+	4.42033i	0.419559	+	0.726698i	−0.576336	+	0.817213i	$0.695518\pi$
$38$	6.36338	+	5.33951i	1.03228	+	0.866183i
$39$	−1.23821	+	0.940448i	−0.198273	+	0.150592i
$40$	−2.44297	+	0.430761i	−0.386267	+	0.0681093i
$41$	0.529024	+	3.00024i	0.0826197	+	0.468560i	0.997845	+	0.0656168i	$0.0209015\pi$
$41$	0.529024	+	3.00024i	0.0826197	+	0.468560i	−0.915225	+	0.402943i	$0.867987\pi$
$42$	−4.05822	−	8.71928i	−0.626196	−	1.34541i
$43$	−1.63755	−	1.37406i	−0.249723	−	0.209543i	0.509330	−	0.860571i	$-0.329893\pi$
$43$	−1.63755	−	1.37406i	−0.249723	−	0.209543i	−0.759053	+	0.651029i	$0.774338\pi$
$44$	−11.3807	+	6.57067i	−1.71571	+	0.990566i
$45$	0.677817	+	8.73972i	0.101043	+	1.30284i
$46$	7.62918	−	13.2141i	1.12486	−	1.94832i
$47$	5.50750	−	2.00456i	0.803351	−	0.292396i	0.0924765	−	0.995715i	$-0.470522\pi$
$47$	5.50750	−	2.00456i	0.803351	−	0.292396i	0.710874	+	0.703319i	$0.248299\pi$
$48$	−5.11353	−	1.16014i	−0.738075	−	0.167451i
$49$	−6.74598	+	1.86863i	−0.963711	+	0.266947i
$50$	2.53958	−	6.97743i	0.359150	−	0.986758i
$51$	4.91522	+	3.16553i	0.688268	+	0.443263i
$52$	−2.12575	−	0.374828i	−0.294789	−	0.0519792i
$53$			9.25621i			1.27144i	0.771920	+	0.635719i	$0.219296\pi$
$53$			9.25621i			1.27144i	−0.771920	+	0.635719i	$0.780704\pi$
$54$	3.43278	−	10.3507i	0.467142	−	1.40856i
$55$		−	15.9695i		−	2.15332i
$56$	0.850812	−	2.07876i	0.113695	−	0.277787i
$57$	6.84751	+	0.332818i	0.906975	+	0.0440828i
$58$	−2.07678	−	0.755885i	−0.272694	−	0.0992526i
$59$	−7.56717	+	6.34961i	−0.985161	+	0.826648i	−0.984860	−	0.173352i	$-0.944540\pi$
$59$	−7.56717	+	6.34961i	−0.985161	+	0.826648i	−0.000301062		1.00000i	$0.500096\pi$
$60$	−8.26565	+	8.93152i	−1.06709	+	1.15305i
$61$	−5.01899	−	13.7896i	−0.642615	−	1.76557i	−0.643350	−	0.765572i	$-0.722456\pi$
$61$	−5.01899	−	13.7896i	−0.642615	−	1.76557i	0.000735016	−	1.00000i	$-0.499766\pi$
$62$	2.91709	−	5.05254i	0.370470	−	0.641674i
$63$	−7.01960	−	3.70476i	−0.884386	−	0.466756i
$64$	−5.42134	−	9.39004i	−0.677668	−	1.17376i
$65$	1.68608	−	2.00940i	0.209133	−	0.249235i
$66$	−7.69303	+	18.3165i	−0.946946	+	2.25461i
$67$	0.693812	+	3.93480i	0.0847626	+	0.480712i	0.997408	+	0.0719593i	$0.0229252\pi$
$67$	0.693812	+	3.93480i	0.0847626	+	0.480712i	−0.912645	+	0.408753i	$0.865964\pi$
$68$	1.40937	+	7.99291i	0.170911	+	0.969283i
$69$	−1.58207	−	12.4929i	−0.190459	−	1.50397i
$70$	9.93110	+	12.8302i	1.18699	+	1.53350i
$71$	13.9268	−	8.04064i	1.65281	−	0.954249i	0.676897	−	0.736077i	$-0.263324\pi$
$71$	13.9268	−	8.04064i	1.65281	−	0.954249i	0.975910	−	0.218172i	$-0.0700092\pi$
$72$	2.31877	−	1.05353i	0.273269	−	0.124160i
$73$	2.86477	+	1.65398i	0.335296	+	0.193583i	0.658190	−	0.752852i	$-0.271322\pi$
$73$	2.86477	+	1.65398i	0.335296	+	0.193583i	−0.322894	+	0.946435i	$0.604656\pi$
$74$	3.66374	+	10.0661i	0.425902	+	1.17016i
$75$	−1.81388	−	5.85343i	−0.209449	−	0.675896i
$76$	6.11759	+	7.29066i	0.701735	+	0.836296i
$77$	12.2278	+	7.71778i	1.39349	+	0.879523i
$78$	−2.90189	+	1.49248i	−0.328574	+	0.168990i
$79$	−0.601523	+	3.41141i	−0.0676766	+	0.383813i	0.932090	+	0.362226i	$0.117983\pi$
$79$	−0.601523	+	3.41141i	−0.0676766	+	0.383813i	−0.999767	+	0.0215873i	$0.993128\pi$
$80$	8.84582			0.988993
$81$	−2.91072	−	8.51632i	−0.323414	−	0.946258i
$82$			6.39373i			0.706070i
$83$	−0.164783	+	0.934532i	−0.0180873	+	0.102578i	−0.992515	−	0.122123i	$-0.961030\pi$
$83$	−0.164783	+	0.934532i	−0.0180873	+	0.102578i	0.974428	+	0.224702i	$0.0721407\pi$
$84$	−2.84423	−	10.6455i	−0.310330	−	1.16152i
$85$	−9.26808	−	3.37331i	−1.00526	−	0.365886i
$86$	−2.88374	−	3.43671i	−0.310962	−	0.370590i
$87$	−1.74223	+	0.539888i	−0.186786	+	0.0578821i
$88$	−4.35999	+	1.58691i	−0.464776	+	0.169165i
$89$	−2.06490	+	3.57651i	−0.218879	+	0.379110i	−0.954466	−	0.298321i	$-0.903573\pi$
$89$	−2.06490	+	3.57651i	−0.218879	+	0.379110i	0.735586	+	0.677431i	$0.236907\pi$
$90$	−1.78414	+	18.3104i	−0.188065	+	1.93008i
$91$	0.723741	+	2.26215i	0.0758687	+	0.237137i
$92$	11.2371	−	13.3919i	1.17155	−	1.39620i
$93$	−0.604920	−	4.77679i	−0.0627273	−	0.495330i
$94$	12.1135	−	2.13593i	1.24941	−	0.220305i
$95$	−11.3898	+	2.00832i	−1.16856	+	0.206050i
$96$	−12.8574	−	5.40015i	−1.31225	−	0.551150i
$97$	3.04401	−	3.62771i	0.309072	−	0.368338i	−0.589040	−	0.808104i	$-0.700494\pi$
$97$	3.04401	−	3.62771i	0.309072	−	0.368338i	0.898113	+	0.439766i	$0.144939\pi$
$98$	−14.6237	+	1.40363i	−1.47721	+	0.141788i
$99$	4.08710	+	15.8782i	0.410769	+	1.59582i
$100$	4.25362	−	7.36748i	0.425362	−	0.736748i
$101$	−11.2525	+	4.09556i	−1.11966	+	0.407523i	−0.834529	−	0.550965i	$-0.814260\pi$
$101$	−11.2525	+	4.09556i	−1.11966	+	0.407523i	−0.285133	+	0.958488i	$0.592038\pi$
$102$	9.00520	+	8.33383i	0.891648	+	0.825173i
$103$	3.70555	+	4.41610i	0.365119	+	0.435132i	0.917059	−	0.398752i	$-0.130557\pi$
$103$	3.70555	+	4.41610i	0.365119	+	0.435132i	−0.551940	+	0.833884i	$0.686112\pi$
$104$	−0.716155	−	0.260659i	−0.0702247	−	0.0255597i
$105$	12.9315	+	3.47497i	1.26198	+	0.339122i
$106$	−3.37328	+	19.1308i	−0.327642	+	1.85815i
$107$			1.72305i			0.166574i	0.996526	+	0.0832869i	$0.0265418\pi$
$107$			1.72305i			0.166574i	−0.996526	+	0.0832869i	$0.973458\pi$
$108$	5.93256	−	10.9959i	0.570861	−	1.05809i
$109$	9.80429			0.939081			0.469541	−	0.882911i	$-0.344420\pi$
$109$	9.80429			0.939081			0.469541	+	0.882911i	$0.344420\pi$
$110$	5.81982	−	33.0059i	0.554898	−	3.14699i
$111$	7.43262	+	4.78681i	0.705473	+	0.454344i
$112$	−4.27504	+	6.77326i	−0.403953	+	0.640013i
$113$	−5.74446	−	6.84598i	−0.540393	−	0.644016i	0.424882	−	0.905249i	$-0.360315\pi$
$113$	−5.74446	−	6.84598i	−0.540393	−	0.644016i	−0.965276	+	0.261233i	$0.915871\pi$
$114$	14.0312	+	3.18334i	1.31414	+	0.298147i
$115$	7.26589	+	19.9629i	0.677548	+	1.86155i
$116$	−2.19287	−	1.26606i	−0.203603	−	0.117550i
$117$	−1.16218	+	2.42944i	−0.107444	+	0.224602i
$118$	−17.9539	+	10.3657i	−1.65279	+	0.954240i
$119$	7.06206	−	5.46632i	0.647378	−	0.501097i
$120$	−3.42160	+	2.59877i	−0.312348	+	0.237234i
$121$	−3.27660	−	18.5825i	−0.297873	−	1.68932i
$122$	−5.34791	−	30.3295i	−0.484177	−	2.74590i
$123$	3.19159	+	4.20212i	0.287776	+	0.378892i
$124$	4.29661	−	5.12050i	0.385847	−	0.459834i
$125$	−2.13594	−	3.69956i	−0.191045	−	0.330899i
$126$	−13.1580	−	10.2152i	−1.17221	−	0.910044i
$127$	−2.72990	+	4.72832i	−0.242239	+	0.419570i	−0.961352	−	0.275323i	$-0.911215\pi$
$127$	−2.72990	+	4.72832i	−0.242239	+	0.419570i	0.719113	+	0.694894i	$0.244549\pi$
$128$	−2.27538	−	6.25156i	−0.201117	−	0.552565i
$129$	−3.61078	−	0.819198i	−0.317911	−	0.0721263i
$130$	4.21711	−	3.53858i	0.369865	−	0.310354i
$131$	−7.99485	−	2.90989i	−0.698513	−	0.254238i	−0.0317374	−	0.999496i	$-0.510104\pi$
$131$	−7.99485	−	2.90989i	−0.698513	−	0.254238i	−0.666776	+	0.745258i	$0.732326\pi$
$132$	−12.3243	+	19.1363i	−1.07269	+	1.66560i
$133$	3.96671	−	9.69175i	0.343957	−	0.840381i
$134$			8.38534i			0.724383i
$135$	7.96749	+	12.9246i	0.685733	+	1.11237i
$136$			2.86558i			0.245722i
$137$	4.68415	+	0.825942i	0.400194	+	0.0705650i	0.370123	−	0.928983i	$-0.379316\pi$
$137$	4.68415	+	0.825942i	0.400194	+	0.0705650i	0.0300709	+	0.999548i	$0.490427\pi$
$138$	1.28301	−	26.3971i	0.109217	−	2.24707i
$139$	−3.84869	+	10.5742i	−0.326441	+	0.896890i	0.662563	+	0.749006i	$0.269469\pi$
$139$	−3.84869	+	10.5742i	−0.326441	+	0.896890i	−0.989005	+	0.147884i	$0.952754\pi$
$140$	8.65281	+	16.4523i	0.731296	+	1.39048i
$141$	6.89507	−	7.45053i	0.580670	−	0.627448i
$142$	31.7144	−	11.5431i	2.66141	−	0.968674i
$143$	2.45310	−	4.24889i	0.205138	−	0.355310i
$144$	−8.79528	+	2.26393i	−0.732940	+	0.188661i
$145$	2.66480	−	1.53852i	0.221299	−	0.127767i
$146$	5.31817	+	4.46247i	0.440135	+	0.369317i
$147$	−8.91036	+	8.22225i	−0.734914	+	0.678160i
$148$	2.13119	+	12.0866i	0.175183	+	0.993512i
$149$	−9.59331	+	1.69156i	−0.785914	+	0.138578i	−0.552183	−	0.833723i	$-0.686205\pi$
$149$	−9.59331	+	1.69156i	−0.785914	+	0.138578i	−0.233732	+	0.972301i	$0.575094\pi$
$150$	−1.61576	−	12.7590i	−0.131927	−	1.04177i
$151$	8.82029	+	7.40111i	0.717785	+	0.602293i	0.926772	−	0.375625i	$-0.122572\pi$
$151$	8.82029	+	7.40111i	0.717785	+	0.602293i	−0.208986	+	0.977919i	$0.567016\pi$
$152$	1.68013	+	2.91007i	0.136276	+	0.236038i
$153$	10.0785	+	0.982032i	0.814796	+	0.0793926i
$154$	22.4600	+	20.4074i	1.80988	+	1.64448i
$155$	2.77818	+	7.63299i	0.223149	+	0.613096i
$156$	−3.57118	+	1.10665i	−0.285923	+	0.0886029i
$157$	−7.27937	−	8.67522i	−0.580957	−	0.692358i	0.392884	−	0.919588i	$-0.371477\pi$
$157$	−7.27937	−	8.67522i	−0.580957	−	0.692358i	−0.973841	+	0.227230i	$0.927033\pi$
$158$	−2.48647	+	6.83151i	−0.197813	+	0.543486i
$159$	7.33262	+	14.2571i	0.581515	+	1.13066i
$160$	23.1686	+	4.08524i	1.83164	+	0.322967i
$161$	−18.7971	−	4.08423i	−1.48142	−	0.321882i
$162$	−2.91227	−	18.6624i	−0.228810	−	1.46626i
$163$	−11.0414			−0.864832			−0.432416	−	0.901674i	$-0.642339\pi$
$163$	−11.0414			−0.864832			−0.432416	+	0.901674i	$0.642339\pi$
$164$	−1.27205	+	7.21414i	−0.0993303	+	0.563330i
$165$	−12.6508	−	24.5974i	−0.984860	−	1.91490i
$166$	−0.681151	+	1.87145i	−0.0528676	+	0.145253i
$167$	15.3831	−	12.9080i	1.19038	−	0.998848i	0.190528	−	0.981682i	$-0.438980\pi$
$167$	15.3831	−	12.9080i	1.19038	−	0.998848i	0.999853	−	0.0171661i	$-0.00546442\pi$
$168$	−0.336279	−	3.87587i	−0.0259445	−	0.299030i
$169$	−11.4587	+	4.17064i	−0.881441	+	0.320818i
$170$	−17.9260	−	10.3496i	−1.37486	−	0.793777i
$171$	10.8107	−	4.91186i	0.826715	−	0.375619i
$172$	−2.57003	−	4.45142i	−0.195963	−	0.339417i
$173$	−2.40291	−	2.01628i	−0.182690	−	0.153295i	0.546856	−	0.837226i	$-0.315824\pi$
$173$	−2.40291	−	2.01628i	−0.182690	−	0.153295i	−0.729547	+	0.683931i	$0.760269\pi$
$174$	−3.79761	+	0.480919i	−0.287896	+	0.0364584i
$175$	−9.35345	−	0.368916i	−0.707054	−	0.0278874i
$176$	16.2938	−	2.87304i	1.22819	−	0.216563i
$177$	−6.62545	+	15.7747i	−0.498000	+	1.18570i
$178$	−5.57116	+	6.63945i	−0.417576	+	0.497648i
$179$	−2.86918	+	1.65652i	−0.214453	+	0.123814i	−0.603379	−	0.797454i	$-0.706179\pi$
$179$	−2.86918	+	1.65652i	−0.214453	+	0.123814i	0.388926	+	0.921269i	$0.372846\pi$
$180$	−5.65596	+	20.3049i	−0.421570	+	1.51344i
$181$	4.44142	+	2.56425i	0.330128	+	0.190599i	0.655898	−	0.754850i	$-0.272290\pi$
$181$	4.44142	+	2.56425i	0.330128	+	0.190599i	−0.325770	+	0.945449i	$0.605624\pi$
$182$	0.671432	+	4.93919i	0.0497699	+	0.366117i
$183$	−18.6545	−	17.2637i	−1.37898	−	1.27617i
$184$	4.72825	−	3.96747i	0.348571	−	0.292486i
$185$	−14.0149	−	5.10099i	−1.03039	−	0.375032i
$186$	0.490571	−	10.0932i	0.0359704	−	0.740067i
$187$	−18.1672	−	3.20337i	−1.32852	−	0.234254i
$188$	14.0928			1.02782
$189$	−13.7470	−	0.145535i	−0.999944	−	0.0105861i
$190$	−24.2724			−1.76090
$191$	−13.3367	−	2.35163i	−0.965013	−	0.170158i	−0.331129	−	0.943586i	$-0.607429\pi$
$191$	−13.3367	−	2.35163i	−0.965013	−	0.170158i	−0.633884	+	0.773428i	$0.718541\pi$
$192$	−15.7890	−	10.1685i	−1.13947	−	0.733851i
$193$	4.77840	+	1.73920i	0.343957	+	0.125190i	0.508222	−	0.861226i	$-0.330303\pi$
$193$	4.77840	+	1.73920i	0.343957	+	0.125190i	−0.164265	+	0.986416i	$0.552525\pi$
$194$	7.61345	−	6.38845i	0.546614	−	0.458664i
$195$	1.00522	−	4.43071i	0.0719853	−	0.317290i
$196$	−16.7793	−	1.32567i	−1.19852	−	0.0946910i
$197$	−17.1705	−	9.91339i	−1.22335	−	0.706300i	−0.257718	−	0.966220i	$-0.582970\pi$
$197$	−17.1705	−	9.91339i	−1.22335	−	0.706300i	−0.965630	+	0.259920i	$0.916304\pi$
$198$	2.66069	+	34.3068i	0.189087	+	2.43808i
$199$	−16.8274	+	9.71530i	−1.19286	+	0.688700i	−0.958955	−	0.283559i	$-0.908485\pi$
$199$	−16.8274	+	9.71530i	−1.19286	+	0.688700i	−0.233908	+	0.972259i	$0.575151\pi$
$200$	1.93070	−	2.30092i	0.136521	−	0.162700i
$201$	4.18575	+	5.51105i	0.295240	+	0.388719i
$202$	−24.7493	+	4.36396i	−1.74135	+	0.307047i
$203$	−0.109805	+	2.78398i	−0.00770680	+	0.195397i
$204$	8.50266	+	11.1948i	0.595306	+	0.783793i
$205$	−6.81927	−	5.72205i	−0.476278	−	0.399645i
$206$	6.04929	+	10.4777i	0.421474	+	0.730015i
$207$	−12.3335	−	17.9893i	−0.857240	−	1.25034i
$208$	2.35355	+	1.35882i	0.163189	+	0.0942174i
$209$	−20.3274	+	7.39857i	−1.40608	+	0.511770i
$210$	25.4605	+	11.8948i	1.75694	+	0.820818i
$211$	14.1055	−	11.8360i	0.971066	−	0.814821i	−0.0116516	−	0.999932i	$-0.503709\pi$
$211$	14.1055	−	11.8360i	0.971066	−	0.814821i	0.982718	+	0.185111i	$0.0592645\pi$
$212$	−7.61225	+	20.9145i	−0.522812	+	1.43641i
$213$	15.0814	−	23.4174i	1.03336	−	1.60453i
$214$	−0.627940	+	3.56122i	−0.0429251	+	0.243440i
$215$	6.24623			0.425989
$216$	2.73694	−	3.45962i	0.186225	−	0.235397i
$217$	−7.18724	−	1.56164i	−0.487902	−	0.106011i
$218$	20.2636	+	3.57302i	1.37243	+	0.241996i
$219$	5.72278	+	0.278151i	0.386710	+	0.0187957i
$220$	13.1332	−	36.0831i	0.885439	−	2.43272i
$221$	−1.94772	−	2.32120i	−0.131018	−	0.156141i
$222$	13.6173	+	12.6021i	0.913936	+	0.845799i
$223$	−0.0562598	−	0.154573i	−0.00376744	−	0.0103510i	0.937795	−	0.347190i	$-0.112864\pi$
$223$	−0.0562598	−	0.154573i	−0.00376744	−	0.0103510i	−0.941562	+	0.336839i	$0.890642\pi$
$224$	−14.3251	+	15.7659i	−0.957134	+	1.05340i
$225$	−7.43087	−	7.57895i	−0.495391	−	0.505264i
$226$	−9.37780	−	16.2428i	−0.623802	−	1.08046i
$227$	19.9304	+	16.7236i	1.32283	+	1.10999i	0.985697	+	0.168529i	$0.0539018\pi$
$227$	19.9304	+	16.7236i	1.32283	+	1.10999i	0.337133	+	0.941457i	$0.390543\pi$
$228$	15.1983	+	6.38336i	1.00653	+	0.422748i
$229$	10.9980	−	1.93924i	0.726765	−	0.128148i	0.201988	−	0.979388i	$-0.435260\pi$
$229$	10.9980	−	1.93924i	0.726765	−	0.128148i	0.524777	+	0.851240i	$0.324149\pi$
$230$	7.74206	+	43.9074i	0.510496	+	2.89517i
$231$	24.9481	+	2.20080i	1.64147	+	0.144802i
$232$	−0.684852	−	0.574659i	−0.0449627	−	0.0377282i
$233$	7.13536	−	4.11960i	0.467453	−	0.269884i	−0.247720	−	0.968832i	$-0.579681\pi$
$233$	7.13536	−	4.11960i	0.467453	−	0.269884i	0.715173	+	0.698948i	$0.246348\pi$
$234$	−3.28738	+	4.59766i	−0.214903	+	0.300558i
$235$	−8.56282	+	14.8312i	−0.558577	+	0.967484i
$236$	−22.3199	+	8.12380i	−1.45290	+	0.528814i
$237$	1.77595	+	5.73102i	0.115360	+	0.372270i
$238$	16.5881	−	8.72419i	1.07524	−	0.565505i
$239$	−3.27587	+	9.00039i	−0.211899	+	0.582187i	−0.999418	−	0.0341027i	$-0.989143\pi$
$239$	−3.27587	+	9.00039i	−0.211899	+	0.582187i	0.787520	+	0.616290i	$0.211365\pi$
$240$	13.6250	−	7.00752i	0.879489	−	0.452333i
$241$	−0.579223	−	0.102133i	−0.0373111	−	0.00657895i	0.154961	−	0.987921i	$-0.450475\pi$
$241$	−0.579223	−	0.102133i	−0.0373111	−	0.00657895i	−0.192273	+	0.981342i	$0.561586\pi$
$242$		−	39.6007i		−	2.54563i
$243$	−11.2298	−	10.8116i	−0.720392	−	0.693567i
$244$		−	35.2852i		−	2.25890i
$245$	11.5903	−	16.8531i	0.740479	−	1.07671i
$246$	5.06501	+	9.84810i	0.322933	+	0.627892i
$247$	−3.33890	−	1.21526i	−0.212449	−	0.0773252i
$248$	1.80789	−	1.51700i	0.114801	−	0.0963295i
$249$	0.486510	+	1.56997i	0.0308313	+	0.0994931i
$250$	−3.06634	−	8.42471i	−0.193933	−	0.532825i
$251$	12.8053	−	22.1794i	0.808261	−	1.39995i	−0.105806	−	0.994387i	$-0.533742\pi$
$251$	12.8053	−	22.1794i	0.808261	−	1.39995i	0.914067	−	0.405563i	$-0.132924\pi$
$252$	−12.8141	−	14.1438i	−0.807210	−	0.890976i
$253$	19.8674	+	34.4113i	1.24905	+	2.16342i
$254$	−7.36534	+	8.77767i	−0.462143	+	0.550760i
$255$	−16.9477	+	2.14621i	−1.06130	+	0.134401i
$256$	1.34113	+	7.60591i	0.0838205	+	0.475369i
$257$	3.58065	+	20.3069i	0.223355	+	1.26671i	0.865805	+	0.500381i	$0.166807\pi$
$257$	3.58065	+	20.3069i	0.223355	+	1.26671i	−0.642451	+	0.766327i	$0.722082\pi$
$258$	−7.16426	−	3.00902i	−0.446027	−	0.187333i
$259$	10.6790	−	8.26597i	0.663560	−	0.513623i
$260$	5.46224	−	3.15362i	0.338754	−	0.195580i
$261$	−2.25582	+	2.21174i	−0.139632	+	0.136903i
$262$	−15.4634	−	8.92779i	−0.955331	−	0.551561i
$263$	−2.50612	−	6.88551i	−0.154534	−	0.424579i	0.838132	−	0.545467i	$-0.183648\pi$
$263$	−2.50612	−	6.88551i	−0.154534	−	0.424579i	−0.992666	+	0.120889i	$0.961426\pi$
$264$	−5.45845	+	5.89818i	−0.335945	+	0.363008i
$265$	−17.3852	−	20.7189i	−1.06796	−	1.27275i
$266$	11.7304	−	18.5854i	0.719240	−	1.13954i
$267$	−0.347257	+	7.14459i	−0.0212518	+	0.437242i
$268$	−1.66828	+	9.46130i	−0.101907	+	0.577941i
$269$	−1.75282			−0.106872			−0.0534358	−	0.998571i	$-0.517017\pi$
$269$	−1.75282			−0.106872			−0.0534358	+	0.998571i	$0.517017\pi$
$270$	11.7571	+	29.6164i	0.715516	+	1.80239i
$271$			7.35453i			0.446756i	0.974732	+	0.223378i	$0.0717084\pi$
$271$			7.35453i			0.446756i	−0.974732	+	0.223378i	$0.928292\pi$
$272$	1.77441	−	10.0632i	0.107590	−	0.610171i
$273$	2.90680	+	2.91099i	0.175927	+	0.176181i
$274$	9.38025	+	3.41413i	0.566681	+	0.206255i
$275$	12.4291	+	14.8124i	0.749503	+	0.893223i
$276$	6.69940	−	29.5290i	0.403257	−	1.77744i
$277$	−0.218507	+	0.0795299i	−0.0131288	+	0.00477849i	−0.348576	−	0.937280i	$-0.613335\pi$
$277$	−0.218507	+	0.0795299i	−0.0131288	+	0.00477849i	0.335447	+	0.942059i	$0.391113\pi$
$278$	−11.8081	+	20.4522i	−0.708203	+	1.22664i
$279$	−4.71584	−	6.87836i	−0.282330	−	0.411796i
$280$	1.99994	+	6.25106i	0.119519	+	0.373572i
$281$	−9.11248	+	10.8598i	−0.543605	+	0.647843i	−0.965992	−	0.258572i	$-0.916748\pi$
$281$	−9.11248	+	10.8598i	−0.543605	+	0.647843i	0.422387	+	0.906416i	$0.361192\pi$
$282$	16.9660	−	12.8860i	1.01031	−	0.767352i
$283$	26.6742	−	4.70338i	1.58562	−	0.279587i	0.689796	−	0.724004i	$-0.257700\pi$
$283$	26.6742	−	4.70338i	1.58562	−	0.279587i	0.895820	+	0.444417i	$0.146589\pi$
$284$	38.0803	−	6.71459i	2.25965	−	0.398437i
$285$	−15.9524	+	12.1162i	−0.944938	+	0.717699i
$286$	6.61853	−	7.88766i	0.391362	−	0.466407i
$287$	7.67702	−	2.45615i	0.453160	−	0.144982i
$288$	−24.0818	+	1.86768i	−1.41903	+	0.110054i
$289$	2.80333	−	4.85552i	0.164902	−	0.285619i
$290$	6.06832	−	2.20869i	0.356344	−	0.129699i
$291$	1.81480	−	7.99908i	0.106385	−	0.468914i
$292$	5.11275	+	6.09314i	0.299201	+	0.356574i
$293$	−12.0006	−	4.36785i	−0.701080	−	0.255172i	−0.0332081	−	0.999448i	$-0.510572\pi$
$293$	−12.0006	−	4.36785i	−0.701080	−	0.255172i	−0.667872	+	0.744276i	$0.732795\pi$
$294$	−21.4125	+	13.7466i	−1.24880	+	0.801718i
$295$	5.01220	−	28.4256i	0.291821	−	1.65500i
$296$			4.33323i			0.251864i
$297$	18.8737	+	21.2191i	1.09517	+	1.23126i
$298$	−20.4440			−1.18429
$299$	−1.13334	+	6.42752i	−0.0655430	+	0.371713i
$300$	0.715337	−	14.7176i	0.0413000	−	0.849721i
$301$	−3.01870	+	4.78275i	−0.173995	+	0.275673i
$302$	15.5327	+	18.5111i	0.893804	+	1.06519i
$303$	−14.0874	+	15.2223i	−0.809302	+	0.874498i
$304$	−4.09822	−	11.2598i	−0.235049	−	0.645792i
$305$	37.1342	+	21.4394i	2.12630	+	1.22762i
$306$	20.4724	+	5.70262i	1.17033	+	0.325997i
$307$	1.86612	−	1.07740i	0.106505	−	0.0614907i	−0.445801	−	0.895132i	$-0.647081\pi$
$307$	1.86612	−	1.07740i	0.106505	−	0.0614907i	0.552306	+	0.833641i	$0.313748\pi$
$308$	21.2819	+	27.4945i	1.21265	+	1.56664i
$309$	9.20593	+	3.86653i	0.523707	+	0.219959i
$310$	2.96025	+	16.7884i	0.168131	+	0.953517i
$311$	−3.15457	−	17.8904i	−0.178879	−	1.01447i	−0.933571	−	0.358394i	$-0.883325\pi$
$311$	−3.15457	−	17.8904i	−0.178879	−	1.01447i	0.754692	−	0.656080i	$-0.227786\pi$
$312$	−1.30956	+	0.165840i	−0.0741395	+	0.00938883i
$313$	−9.02777	+	10.7589i	−0.510280	+	0.608128i	−0.958254	−	0.285919i	$-0.907701\pi$
$313$	−9.02777	+	10.7589i	−0.510280	+	0.608128i	0.447974	+	0.894046i	$0.352146\pi$
$314$	−11.8835	−	20.5829i	−0.670627	−	1.16156i
$315$	22.6708	−	4.89170i	1.27736	−	0.275616i
$316$	−4.16466	+	7.21341i	−0.234281	+	0.405786i
$317$	−7.21221	−	19.8154i	−0.405078	−	1.11294i	−0.959745	−	0.280871i	$-0.909377\pi$
$317$	−7.21221	−	19.8154i	−0.405078	−	1.11294i	0.554667	−	0.832072i	$-0.312846\pi$
$318$	9.95936	+	32.1390i	0.558493	+	1.80227i
$319$	4.40880	−	3.69943i	0.246846	−	0.207128i
$320$	29.7715	+	10.8360i	1.66428	+	0.605748i
$321$	1.36497	+	2.65397i	0.0761854	+	0.148130i
$322$	−37.3616	−	15.2916i	−2.08208	−	0.852169i
$323$			13.3601i			0.743376i
$324$	0.426965	−	21.6365i	0.0237203	−	1.20203i
$325$			3.17610i			0.176178i
$326$	−22.8206	−	4.02388i	−1.26391	−	0.222862i
$327$	15.1013	−	7.76680i	0.835104	−	0.429505i
$328$	−0.884595	+	2.43041i	−0.0488436	+	0.134197i
$329$	−7.21803	−	13.7243i	−0.397943	−	0.756643i
$330$	−17.1826	−	55.4484i	−0.945870	−	3.05234i
$331$	10.2880	−	3.74454i	0.565481	−	0.205818i	−0.0434304	−	0.999056i	$-0.513829\pi$
$331$	10.2880	−	3.74454i	0.565481	−	0.205818i	0.608911	+	0.793238i	$0.291606\pi$
$332$	−1.14088	+	1.97607i	−0.0626141	+	0.108451i
$333$	15.2403	+	1.48499i	0.835163	+	0.0813772i
$334$	36.4981	−	21.0722i	1.99709	−	1.15302i
$335$	−8.94343	−	7.50443i	−0.488632	−	0.410011i
$336$	−1.21907	+	13.8193i	−0.0665057	+	0.753904i
$337$	−1.54659	−	8.77115i	−0.0842481	−	0.477795i	−0.997516	−	0.0704359i	$-0.977561\pi$
$337$	−1.54659	−	8.77115i	−0.0842481	−	0.477795i	0.913268	−	0.407359i	$-0.133550\pi$
$338$	−25.2030	+	4.44396i	−1.37086	+	0.241720i
$339$	−14.2713	−	5.99402i	−0.775112	−	0.325550i
$340$	−18.1671	−	15.2440i	−0.985250	−	0.826723i
$341$	7.59647	+	13.1575i	0.411372	+	0.712517i
$342$	24.1337	−	6.21209i	1.30500	−	0.335911i
$343$	7.30303	+	17.0196i	0.394327	+	0.918970i
$344$	−0.620696	−	1.70535i	−0.0334657	−	0.0919462i
$345$	27.0057	+	24.9924i	1.45394	+	1.34554i
$346$	−4.23157	−	5.04298i	−0.227490	−	0.271112i
$347$	−7.68903	+	21.1254i	−0.412769	+	1.13407i	0.542943	+	0.839769i	$0.317310\pi$
$347$	−7.68903	+	21.1254i	−0.412769	+	1.13407i	−0.955712	+	0.294303i	$0.904912\pi$
$348$	−4.38058	−	0.212915i	−0.234824	−	0.0114134i
$349$	16.7656	+	2.95623i	0.897442	+	0.158243i	0.603296	−	0.797517i	$-0.293854\pi$
$349$	16.7656	+	2.95623i	0.897442	+	0.158243i	0.294146	+	0.955761i	$0.404965\pi$
$350$	−19.1974	−	4.17120i	−1.02614	−	0.222960i
$351$	0.134485	+	4.66267i	0.00717829	+	0.248875i
$352$	44.0029			2.34536
$353$	−0.619528	+	3.51352i	−0.0329742	+	0.187006i	−0.996846	−	0.0793608i	$-0.974712\pi$
$353$	−0.619528	+	3.51352i	−0.0329742	+	0.187006i	0.963872	+	0.266367i	$0.0858232\pi$
$354$	−19.4424	+	30.1888i	−1.03335	+	1.60452i
$355$	−16.0713	+	44.1556i	−0.852976	+	2.34353i
$356$	−7.60696	+	6.38300i	−0.403168	+	0.338298i
$357$	6.54717	−	14.0141i	0.346513	−	0.741704i
$358$	−6.53376	+	2.37809i	−0.345320	+	0.125686i
$359$	5.37214	+	3.10161i	0.283531	+	0.163697i	0.635021	−	0.772495i	$-0.280992\pi$
$359$	5.37214	+	3.10161i	0.283531	+	0.163697i	−0.351490	+	0.936192i	$0.614325\pi$
$360$	−3.21150	+	6.71335i	−0.169261	+	0.353825i
$361$	−1.66680	−	2.88699i	−0.0877265	−	0.151947i
$362$	8.24506	+	6.91843i	0.433351	+	0.363625i
$363$	−19.7676	−	26.0265i	−1.03753	−	1.36604i
$364$	−0.225076	+	5.70654i	−0.0117972	+	0.299104i
$365$	−9.51895	+	1.67845i	−0.498245	+	0.0878540i
$366$	−32.2638	−	42.4792i	−1.68645	−	2.22042i
$367$	−19.3243	+	23.0298i	−1.00872	+	1.20214i	−0.0294524	+	0.999566i	$0.509376\pi$
$367$	−19.3243	+	23.0298i	−1.00872	+	1.20214i	−0.979266	+	0.202578i	$0.935068\pi$
$368$	−19.0611	+	11.0049i	−0.993630	+	0.573673i
$369$	8.24477	+	3.94409i	0.429206	+	0.205321i
$370$	−27.1071	−	15.6503i	−1.40923	−	0.813619i
$371$	24.2665	−	3.29878i	1.25985	−	0.171264i
$372$	2.56158	−	11.2907i	0.132812	−	0.585394i
$373$	10.6645	−	8.94855i	0.552185	−	0.463338i	−0.323495	−	0.946230i	$-0.604858\pi$
$373$	10.6645	−	8.94855i	0.552185	−	0.463338i	0.875680	+	0.482892i	$0.160413\pi$
$374$	−36.3808	−	13.2415i	−1.88121	−	0.684703i
$375$	−6.22067	−	4.00628i	−0.321234	−	0.206883i
$376$	4.90013	+	0.864025i	0.252705	+	0.0445587i
$377$	0.945341			0.0486875
$378$	−28.3593	−	5.31066i	−1.45865	−	0.273151i
$379$	33.7802			1.73517			0.867585	−	0.497288i	$-0.165671\pi$
$379$	33.7802			1.73517			0.867585	+	0.497288i	$0.165671\pi$
$380$	−27.3869	−	4.82905i	−1.40492	−	0.247725i
$381$	−0.459090	+	9.44549i	−0.0235199	+	0.483907i
$382$	−26.7075	−	9.72074i	−1.36648	−	0.497356i
$383$	−13.1818	+	11.0609i	−0.673561	+	0.565185i	−0.914117	−	0.405451i	$-0.867115\pi$
$383$	−13.1818	+	11.0609i	−0.673561	+	0.565185i	0.240556	+	0.970635i	$0.422670\pi$
$384$	−8.45709	−	7.82659i	−0.431574	−	0.399399i
$385$	−41.8662	+	5.69128i	−2.13370	+	0.290055i
$386$	9.24222	+	5.33600i	0.470417	+	0.271595i
$387$	−6.21055	+	1.59861i	−0.315700	+	0.0812621i
$388$	9.86137	−	5.69346i	0.500635	−	0.289042i
$389$	6.73876	−	8.03094i	0.341669	−	0.407185i	−0.567660	−	0.823263i	$-0.692151\pi$
$389$	6.73876	−	8.03094i	0.341669	−	0.407185i	0.909329	+	0.416078i	$0.136596\pi$
$390$	3.69230	−	8.79111i	0.186967	−	0.445155i
$391$	24.1677	−	4.26142i	1.22221	−	0.215509i
$392$	−5.75299	−	1.48968i	−0.290570	−	0.0752403i
$393$	−14.6194	+	1.85137i	−0.737453	+	0.0933891i
$394$	−31.8754	−	26.7466i	−1.60586	−	1.34748i
$395$	−5.06093	−	8.76579i	−0.254643	−	0.441055i
$396$	−3.82332	+	39.2382i	−0.192129	+	1.97179i
$397$	−25.1685	−	14.5310i	−1.26317	−	0.729291i	−0.289483	−	0.957183i	$-0.593483\pi$
$397$	−25.1685	−	14.5310i	−1.26317	−	0.729291i	−0.973686	+	0.227892i	$0.926817\pi$
$398$	−38.3196	+	13.9472i	−1.92079	+	0.699110i
$399$	−1.56782	−	18.0703i	−0.0784893	−	0.904647i
$400$	−8.20491	+	6.88474i	−0.410245	+	0.344237i
$401$	6.94535	−	19.0822i	0.346834	−	0.952919i	−0.636526	−	0.771255i	$-0.719629\pi$
$401$	6.94535	−	19.0822i	0.346834	−	0.952919i	0.983361	−	0.181664i	$-0.0581484\pi$
$402$	6.64273	+	12.9157i	0.331309	+	0.644178i
$403$	−0.433345	+	2.45762i	−0.0215864	+	0.122423i
$404$	−28.7932			−1.43251
$405$	22.5108	+	13.5957i	1.11857	+	0.675577i
$406$	−1.24153	+	5.71395i	−0.0616159	+	0.283578i
$407$	−27.4718	−	4.84402i	−1.36173	−	0.240109i
$408$	2.27007	+	4.41378i	0.112385	+	0.218515i
$409$	9.86562	−	27.1056i	0.487823	−	1.34028i	−0.414824	−	0.909902i	$-0.636157\pi$
$409$	9.86562	−	27.1056i	0.487823	−	1.34028i	0.902647	−	0.430382i	$-0.141621\pi$
$410$	−12.0088	−	14.3116i	−0.593074	−	0.706798i
$411$	7.86917	−	2.43853i	0.388158	−	0.120284i
$412$	4.74095	+	13.0256i	0.233570	+	0.641728i
$413$	19.3432	+	17.5755i	0.951817	+	0.864832i
$414$	−18.9352	−	41.6751i	−0.930613	−	2.04822i
$415$	−1.38641	−	2.40133i	−0.0680561	−	0.117877i
$416$	5.53677	+	4.64590i	0.271462	+	0.227784i
$417$	2.44866	+	19.3360i	0.119912	+	0.946888i
$418$	−44.7092	+	7.88344i	−2.18680	+	0.385592i
$419$	−1.55027	−	8.79202i	−0.0757357	−	0.429518i	−0.998974	−	0.0452902i	$-0.985579\pi$
$419$	−1.55027	−	8.79202i	−0.0757357	−	0.429518i	0.923238	−	0.384228i	$-0.125532\pi$
$420$	26.3610	+	18.4865i	1.28628	+	0.902048i
$421$	12.4440	+	10.4418i	0.606483	+	0.508900i	0.893522	−	0.449019i	$-0.148226\pi$
$421$	12.4440	+	10.4418i	0.606483	+	0.508900i	−0.287039	+	0.957919i	$0.592671\pi$
$422$	33.4669	−	19.3221i	1.62914	−	0.940587i
$423$	4.71811	−	16.9380i	0.229402	−	0.823555i
$424$	−3.92908	+	6.80537i	−0.190813	+	0.330498i
$425$	11.2220	−	4.08449i	0.544349	−	0.198127i
$426$	39.7046	−	42.9031i	1.92369	−	2.07866i
$427$	−34.3625	+	18.0724i	−1.66292	+	0.874583i
$428$	−1.41703	+	3.89325i	−0.0684946	+	0.188187i
$429$	0.412541	−	8.48776i	0.0199177	−	0.409793i
$430$	12.9098	+	2.27634i	0.622565	+	0.109775i
$431$		−	21.8588i		−	1.05290i	−0.850205	−	0.526452i	$-0.823522\pi$
$431$		−	21.8588i		−	1.05290i	0.850205	−	0.526452i	$-0.176478\pi$
$432$	−11.7537	+	10.4546i	−0.565500	+	0.502995i
$433$			28.8760i			1.38769i	0.720124	+	0.693845i	$0.244085\pi$
$433$			28.8760i			1.38769i	−0.720124	+	0.693845i	$0.755915\pi$
$434$	−14.2856	−	5.84690i	−0.685728	−	0.280660i
$435$	2.88573	−	4.48076i	0.138360	−	0.214836i
$436$	22.1529	+	8.06299i	1.06093	+	0.386147i
$437$	22.0443	−	18.4974i	1.05452	−	0.884851i
$438$	11.7265	+	2.66047i	0.560316	+	0.127122i
$439$	11.0078	+	30.2438i	0.525375	+	1.44346i	0.864461	+	0.502701i	$0.167660\pi$
$439$	11.0078	+	30.2438i	0.525375	+	1.44346i	−0.339086	+	0.940756i	$0.610118\pi$
$440$	6.77872	−	11.7411i	0.323163	−	0.559735i
$441$	−7.21086	+	19.7232i	−0.343374	+	0.939199i
$442$	−3.17964	−	5.50730i	−0.151240	−	0.261955i
$443$	2.00706	−	2.39192i	0.0953584	−	0.113644i	−0.716255	−	0.697839i	$-0.754145\pi$
$443$	2.00706	−	2.39192i	0.0953584	−	0.113644i	0.811613	+	0.584195i	$0.198590\pi$
$444$	12.8574	+	16.9284i	0.610186	+	0.803385i
$445$	−2.09545	−	11.8839i	−0.0993340	−	0.563351i
$446$	−0.0599468	−	0.339975i	−0.00283857	−	0.0160983i
$447$	−13.4363	+	10.2051i	−0.635515	+	0.482686i
$448$	−22.6852	+	17.5593i	−1.07178	+	0.829598i
$449$	9.03700	−	5.21751i	0.426482	−	0.246230i	−0.271365	−	0.962477i	$-0.587475\pi$
$449$	9.03700	−	5.21751i	0.426482	−	0.246230i	0.697847	+	0.716247i	$0.254142\pi$
$450$	−12.5962	−	18.3723i	−0.593789	−	0.866080i
$451$	−14.4194	−	8.32505i	−0.678984	−	0.392011i
$452$	−7.34956	−	20.1928i	−0.345694	−	0.949787i
$453$	19.4487	+	4.41244i	0.913780	+	0.207314i
$454$	35.0978	+	41.8279i	1.64722	+	1.96308i
$455$	−5.86881	−	3.70419i	−0.275134	−	0.173655i
$456$	4.89316	+	3.15133i	0.229143	+	0.147575i
$457$	−5.45091	+	30.9136i	−0.254983	+	1.44608i	0.541134	+	0.840936i	$0.317995\pi$
$457$	−5.45091	+	30.9136i	−0.254983	+	1.44608i	−0.796117	+	0.605143i	$0.793116\pi$
$458$	23.4374			1.09516
$459$	16.3016	−	6.47140i	0.760892	−	0.302059i
$460$			51.0817i			2.38170i
$461$	−0.199071	+	1.12899i	−0.00927168	+	0.0525823i	−0.989093	−	0.147295i	$-0.952943\pi$
$461$	−0.199071	+	1.12899i	−0.00927168	+	0.0525823i	0.979821	+	0.199877i	$0.0640544\pi$
$462$	50.7610	+	13.6406i	2.36162	+	0.634618i
$463$	30.0404	+	10.9338i	1.39609	+	0.508137i	0.927017	−	0.375020i	$-0.122364\pi$
$463$	30.0404	+	10.9338i	1.39609	+	0.508137i	0.469078	+	0.883157i	$0.344586\pi$
$464$	2.04919	+	2.44213i	0.0951312	+	0.113373i
$465$	10.3259	+	9.55607i	0.478852	+	0.443152i
$466$	16.2488	−	5.91406i	0.752709	−	0.273964i
$467$	16.4661	−	28.5201i	0.761961	−	1.31975i	−0.179878	−	0.983689i	$-0.557570\pi$
$467$	16.4661	−	28.5201i	0.761961	−	1.31975i	0.941839	−	0.336066i	$-0.109096\pi$
$468$	−4.62392	+	4.53357i	−0.213741	+	0.209564i
$469$	10.0684	−	3.22123i	0.464914	−	0.148743i
$470$	−23.1027	+	27.5328i	−1.06565	+	1.26999i
$471$	−18.0846	−	7.59561i	−0.833294	−	0.349987i
$472$	−8.25883	+	1.45625i	−0.380143	+	0.0670295i
$473$	11.5054	−	2.02872i	0.529020	−	0.0932805i
$474$	1.58197	+	12.4921i	0.0726624	+	0.573783i
$475$	9.00145	−	10.7275i	0.413015	−	0.492212i
$476$	20.4522	−	6.54340i	0.937427	−	0.299916i
$477$	22.5885	+	16.1511i	1.03426	+	0.739507i
$478$	−10.0507	+	17.4083i	−0.459707	+	0.796235i
$479$	−24.1903	+	8.80457i	−1.10529	+	0.402291i	−0.829262	−	0.558860i	$-0.811239\pi$
$479$	−24.1903	+	8.80457i	−1.10529	+	0.402291i	−0.276023	+	0.961151i	$0.589017\pi$
$480$	38.9222	−	12.0614i	1.77655	−	0.550524i
$481$	−2.94527	−	3.51004i	−0.134293	−	0.160044i
$482$	−1.15992	−	0.422178i	−0.0528331	−	0.0192297i
$483$	−32.1881	+	8.59992i	−1.46461	+	0.391310i
$484$	7.87865	−	44.6820i	0.358120	−	2.03100i
$485$			13.8375i			0.628328i
$486$	−19.2697	−	26.4381i	−0.874093	−	1.19926i
$487$	16.2567			0.736663			0.368331	−	0.929695i	$-0.379929\pi$
$487$	16.2567			0.736663			0.368331	+	0.929695i	$0.379929\pi$
$488$	2.16333	−	12.2688i	0.0979292	−	0.555384i
$489$	−17.0068	+	8.74685i	−0.769076	+	0.395546i
$490$	30.0969	−	30.6083i	1.35964	−	1.38274i
$491$	−6.62860	−	7.89965i	−0.299144	−	0.356506i	0.595445	−	0.803396i	$-0.296976\pi$
$491$	−6.62860	−	7.89965i	−0.299144	−	0.356506i	−0.894589	+	0.446890i	$0.852532\pi$
$492$	3.75563	+	12.1195i	0.169317	+	0.546387i
$493$	−1.21572	−	3.34015i	−0.0547531	−	0.150433i
$494$	−6.45799	−	3.72852i	−0.290559	−	0.167754i
$495$	−38.9713	−	27.8649i	−1.75163	−	1.25244i
$496$	−7.28820	+	4.20784i	−0.327250	+	0.188938i
$497$	−26.0430	−	33.6455i	−1.16819	−	1.50921i
$498$	0.433371	+	3.42214i	0.0194198	+	0.153350i
$499$	1.03851	+	5.88966i	0.0464899	+	0.263657i	0.999189	−	0.0402566i	$-0.0128175\pi$
$499$	1.03851	+	5.88966i	0.0464899	+	0.263657i	−0.952699	+	0.303914i	$0.901706\pi$
$500$	−1.78368	−	10.1158i	−0.0797688	−	0.452391i
$501$	13.4687	−	32.0680i	0.601738	−	1.43269i
$502$	34.5490	−	41.1739i	1.54200	−	1.83768i
$503$	21.2330	+	36.7766i	0.946731	+	1.63979i	0.752247	+	0.658881i	$0.228970\pi$
$503$	21.2330	+	36.7766i	0.946731	+	1.63979i	0.194484	+	0.980906i	$0.437697\pi$
$504$	−3.58836	−	5.70350i	−0.159838	−	0.254054i
$505$	17.4948	−	30.3020i	0.778511	−	1.34842i
$506$	28.5214	+	78.3620i	1.26793	+	3.48361i
$507$	−14.3457	+	15.5013i	−0.637114	+	0.688439i
$508$	−10.0568	+	8.43863i	−0.446197	+	0.374403i
$509$	10.2547	+	3.73242i	0.454533	+	0.165437i	0.559133	−	0.829078i	$-0.311134\pi$
$509$	10.2547	+	3.73242i	0.454533	+	0.165437i	−0.104600	+	0.994514i	$0.533356\pi$
$510$	−35.8098	−	1.74050i	−1.58568	−	0.0770709i
$511$	3.31516	−	8.09984i	0.146654	−	0.358316i
$512$			29.5143i			1.30436i
$513$	12.7603	−	16.1297i	0.563383	−	0.712142i
$514$			43.2754i			1.90879i
$515$	−16.5888	−	2.92506i	−0.730991	−	0.128893i
$516$	−7.48489	−	4.82047i	−0.329504	−	0.212209i
$517$	−10.9555	+	30.1000i	−0.481822	+	1.32379i
$518$	25.0839	−	13.1924i	1.10212	−	0.579641i
$519$	−5.29842	−	1.20208i	−0.232575	−	0.0527655i
$520$	2.09260	−	0.761643i	0.0917664	−	0.0334002i
$521$	12.8275	−	22.2178i	0.561981	−	0.973380i	−0.435342	−	0.900265i	$-0.643373\pi$
$521$	12.8275	−	22.2178i	0.561981	−	0.973380i	0.997324	−	0.0731148i	$-0.0232940\pi$
$522$	−5.46838	+	3.74915i	−0.239345	+	0.164096i
$523$	31.3183	−	18.0817i	1.36946	−	0.790656i	0.378597	−	0.925562i	$-0.376407\pi$
$523$	31.3183	−	18.0817i	1.36946	−	0.790656i	0.990858	+	0.134906i	$0.0430733\pi$
$524$	−15.6714	−	13.1498i	−0.684607	−	0.574453i
$525$	−14.6991	+	6.84142i	−0.641523	+	0.298584i
$526$	−2.67036	−	15.1444i	−0.116433	−	0.660326i
$527$	9.24075	−	1.62939i	0.402533	−	0.0709775i
$528$	22.8210	−	17.3330i	0.993155	−	0.754320i
$529$	−22.8732	−	19.1929i	−0.994485	−	0.834472i
$530$	−28.3812	−	49.1577i	−1.23280	−	2.13528i
$531$	2.29146	+	29.5460i	0.0994411	+	1.28219i
$532$	16.9332	−	18.6364i	0.734149	−	0.807990i
$533$	−0.935385	−	2.56995i	−0.0405160	−	0.111317i
$534$	−3.32145	+	14.6400i	−0.143733	+	0.633533i
$535$	−3.23627	−	3.85684i	−0.139916	−	0.166746i
$536$	−1.16014	+	3.18746i	−0.0501104	+	0.137677i
$537$	−3.10706	+	4.82442i	−0.134079	+	0.208189i
$538$	−3.62275	−	0.638789i	−0.156188	−	0.0275402i
$539$	15.8754	−	34.8075i	0.683803	−	1.49926i
$540$	7.37349	+	35.7557i	0.317305	+	1.53868i
$541$	−18.2893			−0.786318			−0.393159	−	0.919470i	$-0.628618\pi$
$541$	−18.2893			−0.786318			−0.393159	+	0.919470i	$0.628618\pi$
$542$	−2.68025	+	15.2004i	−0.115126	+	0.652914i
$543$	8.87236	+	0.431234i	0.380749	+	0.0185060i
$544$	9.29493	−	25.5376i	0.398517	−	1.09492i
$545$	−21.9457	+	18.4146i	−0.940049	+	0.788795i
$546$	4.94693	+	7.07580i	0.211709	+	0.302816i
$547$	−9.47460	+	3.44847i	−0.405105	+	0.147446i	−0.536532	−	0.843880i	$-0.680266\pi$
$547$	−9.47460	+	3.44847i	−0.405105	+	0.147446i	0.131428	+	0.991326i	$0.458044\pi$
$548$	9.90462	+	5.71844i	0.423105	+	0.244280i
$549$	−42.4091	−	11.8131i	−1.80997	−	0.504171i
$550$	20.2904	+	35.1441i	0.865187	+	1.49855i
$551$	−3.19296	−	2.67921i	−0.136025	−	0.114138i
$552$	4.13983	−	9.85663i	0.176203	−	0.419526i
$553$	9.15785	+	0.361201i	0.389431	+	0.0153598i
$554$	−0.480595	+	0.0847419i	−0.0204185	+	0.00360034i
$555$	−25.6276	+	3.24542i	−1.08783	+	0.137760i
$556$	−17.3923	+	20.7273i	−0.737597	+	0.879034i
$557$	−34.4610	+	19.8961i	−1.46016	+	0.843024i	−0.999018	−	0.0443013i	$-0.985894\pi$
$557$	−34.4610	+	19.8961i	−1.46016	+	0.843024i	−0.461143	+	0.887326i	$0.652561\pi$
$558$	−7.24004	−	15.9349i	−0.306495	−	0.674577i
$559$	1.66189	+	0.959495i	0.0702906	+	0.0405823i
$560$	−3.15252	−	23.1905i	−0.133218	−	0.979979i
$561$	−30.5202	+	9.45771i	−1.28856	+	0.399305i
$562$	−22.7915	+	19.1243i	−0.961400	+	0.806711i
$563$	28.7502	+	10.4642i	1.21168	+	0.441015i	0.867286	−	0.497811i	$-0.165863\pi$
$563$	28.7502	+	10.4642i	1.21168	+	0.441015i	0.344392	+	0.938826i	$0.388085\pi$
$564$	21.7067	−	11.1641i	0.914018	−	0.470092i
$565$	25.7165	+	4.53451i	1.08190	+	0.190768i
$566$	56.8446			2.38936
$567$	−21.2894	+	10.6660i	−0.894070	+	0.447928i
$568$	13.6524			0.572841
$569$	20.4130	+	3.59936i	0.855756	+	0.150893i	0.584280	−	0.811552i	$-0.301377\pi$
$569$	20.4130	+	3.59936i	0.855756	+	0.150893i	0.271476	+	0.962445i	$0.412488\pi$
$570$	−37.3861	+	19.2282i	−1.56593	+	0.805380i
$571$	15.9906	+	5.82009i	0.669185	+	0.243563i	0.654197	−	0.756324i	$-0.273007\pi$
$571$	15.9906	+	5.82009i	0.669185	+	0.243563i	0.0149879	+	0.999888i	$0.495229\pi$
$572$	9.03706	−	7.58299i	0.377858	−	0.317061i
$573$	−22.4052	+	6.94300i	−0.935989	+	0.290048i
$574$	16.7621	−	2.27863i	0.699635	−	0.0951082i
$575$	−22.2766	−	12.8614i	−0.929000	−	0.536358i
$576$	−32.3747	−	3.15455i	−1.34895	−	0.131440i
$577$	35.6270	−	20.5692i	1.48317	−	0.856309i	0.483353	−	0.875426i	$-0.339419\pi$
$577$	35.6270	−	20.5692i	1.48317	−	0.856309i	0.999817	+	0.0191170i	$0.00608550\pi$
$578$	7.56348	−	9.01381i	0.314599	−	0.374925i
$579$	8.73781	−	1.10653i	0.363131	−	0.0459860i
$580$	7.28640	−	1.28479i	0.302551	−	0.0533480i
$581$	2.50873	+	0.0989487i	0.104080	+	0.00410508i
$582$	6.66598	−	15.8712i	0.276314	−	0.657883i
$583$	−38.7524	−	32.5172i	−1.60496	−	1.34672i
$584$	1.40416	+	2.43208i	0.0581046	+	0.100640i
$585$	−1.96162	−	7.62083i	−0.0811032	−	0.315083i
$586$	−23.2111	−	13.4009i	−0.958841	−	0.553587i
$587$	26.6564	−	9.70212i	1.10023	−	0.400449i	0.272826	−	0.962063i	$-0.412042\pi$
$587$	26.6564	−	9.70212i	1.10023	−	0.400449i	0.827399	+	0.561614i	$0.189819\pi$
$588$	−26.8950	+	11.2504i	−1.10913	+	0.463960i
$589$	8.42886	−	7.07265i	0.347305	−	0.291424i
$590$	20.7185	−	56.9237i	0.852968	−	2.34351i
$591$	−34.3005	−	1.66715i	−1.41093	−	0.0685774i
$592$	2.68321	−	15.2172i	0.110279	−	0.625424i
$593$	−22.1678			−0.910324			−0.455162	−	0.890409i	$-0.650419\pi$
$593$	−22.1678			−0.910324			−0.455162	+	0.890409i	$0.650419\pi$
$594$	31.2755	+	50.7341i	1.28325	+	2.08165i
$595$	−5.54058	+	25.4998i	−0.227142	+	1.04539i
$596$	−23.0673	−	4.06738i	−0.944873	−	0.166607i
$597$	−18.2225	+	28.2946i	−0.745797	+	1.15802i
$598$	−4.68482	+	12.8714i	−0.191576	+	0.526352i
$599$	6.75443	+	8.04961i	0.275978	+	0.328898i	0.886174	−	0.463352i	$-0.153354\pi$
$599$	6.75443	+	8.04961i	0.275978	+	0.328898i	−0.610196	+	0.792251i	$0.708909\pi$
$600$	1.15106	−	5.07352i	0.0469918	−	0.207126i
$601$	1.46988	+	4.03845i	0.0599575	+	0.164732i	0.966055	−	0.258338i	$-0.0831748\pi$
$601$	1.46988	+	4.03845i	0.0599575	+	0.164732i	−0.906097	+	0.423070i	$0.860953\pi$
$602$	−7.98208	+	8.78492i	−0.325325	+	0.358046i
$603$	10.8130	+	5.17264i	0.440338	+	0.210646i
$604$	13.8429	+	23.9766i	0.563260	+	0.975595i
$605$	42.2363	+	35.4405i	1.71715	+	1.44086i
$606$	−34.6636	+	26.3277i	−1.40811	+	1.06949i
$607$	11.6458	−	2.05347i	0.472688	−	0.0833477i	0.0677708	−	0.997701i	$-0.478411\pi$
$607$	11.6458	−	2.05347i	0.472688	−	0.0833477i	0.404918	+	0.914353i	$0.367300\pi$
$608$	−5.53381	−	31.3838i	−0.224425	−	1.27278i
$609$	2.03630	+	4.37508i	0.0825149	+	0.177287i
$610$	68.9360	+	57.8442i	2.79114	+	2.34204i
$611$	−4.55651	+	2.63070i	−0.184337	+	0.106427i
$612$	21.9648	+	10.5074i	0.887873	+	0.424736i
$613$	−16.5907	+	28.7359i	−0.670090	+	1.16063i	0.307788	+	0.951455i	$0.400411\pi$
$613$	−16.5907	+	28.7359i	−0.670090	+	1.16063i	−0.977878	+	0.209175i	$0.932922\pi$
$614$	4.24956	−	1.54671i	0.171498	−	0.0624202i
$615$	−15.0365	−	3.41140i	−0.606328	−	0.137561i
$616$	5.71413	+	10.8648i	0.230229	+	0.437754i
$617$	−14.0398	+	38.5741i	−0.565223	+	1.55294i	0.246652	+	0.969104i	$0.420670\pi$
$617$	−14.0398	+	38.5741i	−0.565223	+	1.55294i	−0.811874	+	0.583832i	$0.801553\pi$
$618$	17.6178	+	11.3464i	0.708693	+	0.456417i
$619$	−17.3694	−	3.06269i	−0.698135	−	0.123100i	−0.186694	−	0.982418i	$-0.559777\pi$
$619$	−17.3694	−	3.06269i	−0.698135	−	0.123100i	−0.511441	+	0.859318i	$0.670888\pi$
$620$			19.5316i			0.784406i
$621$	−33.2478	−	17.9380i	−1.33419	−	0.719825i
$622$		−	38.1258i		−	1.52870i
$623$	10.1122	+	4.13881i	0.405138	+	0.165818i
$624$	4.70155	+	0.228515i	0.188213	+	0.00914792i
$625$	28.3529	+	10.3196i	1.13412	+	0.412784i
$626$	−22.5796	+	18.9465i	−0.902462	+	0.757255i
$627$	−25.4488	+	27.4989i	−1.01633	+	1.09820i
$628$	−9.31336	−	25.5882i	−0.371643	−	1.02108i
$629$	−8.61429	+	14.9204i	−0.343474	+	0.594915i
$630$	48.6390	−	1.84818i	1.93782	−	0.0736334i
$631$	−24.1574	−	41.8418i	−0.961689	−	1.66569i	−0.718258	−	0.695777i	$-0.755060\pi$
$631$	−24.1574	−	41.8418i	−0.961689	−	1.66569i	−0.243431	−	0.969918i	$-0.578273\pi$
$632$	−1.89033	+	2.25280i	−0.0751932	+	0.0896117i
$633$	12.3502	−	29.4048i	0.490875	−	1.16874i
$634$	−7.68487	−	43.5831i	−0.305205	−	1.73090i
$635$	−2.77029	−	15.7111i	−0.109936	−	0.623475i
$636$	4.84317	+	38.2444i	0.192044	+	1.51649i
$637$	5.67260	−	2.70358i	0.224757	−	0.107120i
$638$	10.4604	−	6.03929i	0.414130	−	0.239098i
$639$	4.67866	−	48.0165i	0.185085	−	1.89950i
$640$	16.8349	+	9.71966i	0.665459	+	0.384203i
$641$	0.948481	+	2.60593i	0.0374627	+	0.102928i	0.957014	−	0.290043i	$-0.0936696\pi$
$641$	0.948481	+	2.60593i	0.0374627	+	0.102928i	−0.919551	+	0.392971i	$0.871447\pi$
$642$	1.85394	+	5.98270i	0.0731694	+	0.236118i
$643$	−14.3961	−	17.1566i	−0.567728	−	0.676591i	0.403435	−	0.915008i	$-0.367816\pi$
$643$	−14.3961	−	17.1566i	−0.567728	−	0.676591i	−0.971163	+	0.238417i	$0.923372\pi$
$644$	−39.1133	−	24.6870i	−1.54128	−	0.972802i
$645$	9.62091	−	4.94816i	0.378823	−	0.194834i
$646$	−4.86888	+	27.6128i	−0.191564	+	1.08641i
$647$	−28.9127			−1.13668			−0.568338	−	0.822795i	$-0.692413\pi$
$647$	−28.9127			−1.13668			−0.568338	+	0.822795i	$0.692413\pi$
$648$	1.47498	−	7.49693i	0.0579428	−	0.294507i
$649$		−	53.9872i		−	2.11918i
$650$	−1.15748	+	6.56439i	−0.0454001	+	0.257477i
$651$	−12.3074	+	3.28826i	−0.482366	+	0.128877i
$652$	−24.9482	−	9.08041i	−0.977047	−	0.355616i
$653$	1.71147	+	2.03965i	0.0669751	+	0.0798178i	0.798492	−	0.602006i	$-0.205632\pi$
$653$	1.71147	+	2.03965i	0.0669751	+	0.0798178i	−0.731517	+	0.681824i	$0.761187\pi$
$654$	34.0420	−	10.5491i	1.33115	−	0.412502i
$655$	23.3609	−	8.50266i	0.912785	−	0.332226i
$656$	4.61142	−	7.98721i	0.180046	−	0.311848i
$657$	9.03500	−	4.10507i	0.352489	−	0.160154i
$658$	−9.91671	−	30.9960i	−0.386594	−	1.20835i
$659$	12.4626	−	14.8523i	0.485473	−	0.578565i	−0.466587	−	0.884475i	$-0.654516\pi$
$659$	12.4626	−	14.8523i	0.485473	−	0.578565i	0.952060	+	0.305911i	$0.0989609\pi$
$660$	−8.35577	−	65.9818i	−0.325248	−	2.56834i
$661$	−16.5131	+	2.91170i	−0.642285	+	0.113252i	−0.485298	−	0.874349i	$-0.661289\pi$
$661$	−16.5131	+	2.91170i	−0.642285	+	0.113252i	−0.156987	+	0.987601i	$0.550178\pi$
$662$	22.6280	−	3.98993i	0.879464	−	0.155073i
$663$	−4.83884	−	2.03233i	−0.187925	−	0.0789293i
$664$	−0.517843	+	0.617141i	−0.0200962	+	0.0239497i
$665$	9.32424	+	29.1441i	0.361578	+	1.13016i
$666$	30.9576	+	8.62329i	1.19958	+	0.334146i
$667$	−3.82810	+	6.63047i	−0.148225	+	0.256733i
$668$	45.3737	−	16.5147i	1.75556	−	0.638972i
$669$	−0.209106	−	0.193516i	−0.00808449	−	0.00748177i
$670$	−15.7495	−	18.7695i	−0.608456	−	0.725130i
$671$	75.3637	+	27.4301i	2.90938	+	1.05893i
$672$	−9.57506	+	35.6319i	−0.369366	+	1.37453i
$673$	3.83062	−	21.7245i	0.147660	−	0.837419i	−0.817534	−	0.575881i	$-0.804659\pi$
$673$	3.83062	−	21.7245i	0.147660	−	0.837419i	0.965193	−	0.261538i	$-0.0842297\pi$
$674$		−	18.6919i		−	0.719986i
$675$	−17.4495	−	5.78705i	−0.671632	−	0.222744i
$676$	−29.3210			−1.12773
$677$	−1.96426	+	11.1399i	−0.0754926	+	0.428140i	0.923514	+	0.383566i	$0.125304\pi$
$677$	−1.96426	+	11.1399i	−0.0754926	+	0.428140i	−0.999006	+	0.0445738i	$0.985807\pi$
$678$	−27.3117	−	17.5895i	−1.04890	−	0.675519i
$679$	−10.5954	−	6.68743i	−0.406613	−	0.256640i
$680$	−5.38219	−	6.41425i	−0.206398	−	0.245975i
$681$	43.9465	+	9.97040i	1.68404	+	0.382066i
$682$	10.9054	+	29.9624i	0.417591	+	1.14732i
$683$	−32.7715	−	18.9207i	−1.25397	−	0.723979i	−0.282073	−	0.959393i	$-0.591022\pi$
$683$	−32.7715	−	18.9207i	−1.25397	−	0.723979i	−0.971895	+	0.235414i	$0.924355\pi$
$684$	28.4663	−	2.20773i	1.08844	−	0.0844148i
$685$	−12.0362	+	6.94909i	−0.459879	+	0.265511i
$686$	8.89146	+	37.8377i	0.339478	+	1.44465i
$687$	15.4036	−	11.6994i	0.587685	−	0.446358i
$688$	1.12375	+	6.37309i	0.0428425	+	0.242972i
$689$	−1.44290	−	8.18311i	−0.0549702	−	0.311752i
$690$	46.7077	+	61.4963i	1.77813	+	2.34113i
$691$	−0.909528	+	1.08393i	−0.0346001	+	0.0412348i	−0.783067	−	0.621937i	$-0.786346\pi$
$691$	−0.909528	+	1.08393i	−0.0346001	+	0.0412348i	0.748467	+	0.663172i	$0.230790\pi$
$692$	−3.77123	−	6.53195i	−0.143360	−	0.248308i
$693$	40.1704	−	16.3737i	1.52595	−	0.621985i
$694$	−23.5906	+	40.8601i	−0.895487	+	1.55103i
$695$	−11.2458	−	30.8976i	−0.426578	−	1.17201i
$696$	−1.51010	−	0.342604i	−0.0572400	−	0.0129864i
$697$	−7.87743	+	6.60995i	−0.298379	+	0.250370i
$698$	33.5740	+	12.2199i	1.27079	+	0.462531i
$699$	7.72693	−	11.9978i	0.292259	−	0.453800i
$700$	−20.8308	−	8.52579i	−0.787330	−	0.322245i
$701$			11.8059i			0.445902i	0.974830	+	0.222951i	$0.0715690\pi$
$701$			11.8059i			0.445902i	−0.974830	+	0.222951i	$0.928431\pi$
$702$	−1.42128	+	9.68587i	−0.0536428	+	0.365569i
$703$			20.2027i			0.761958i
$704$	58.3579	+	10.2901i	2.19945	+	0.387822i
$705$	−1.44002	+	29.6275i	−0.0542344	+	1.11584i
$706$	−2.56090	+	7.03600i	−0.0963806	+	0.264803i
$707$	14.7473	+	28.0403i	0.554629	+	1.05456i
$708$	−27.9433	+	30.1944i	−1.05017	+	1.13477i
$709$	9.05383	−	3.29532i	0.340024	−	0.123758i	−0.166364	−	0.986064i	$-0.553203\pi$
$709$	9.05383	−	3.29532i	0.340024	−	0.123758i	0.506388	+	0.862306i	$0.330980\pi$
$710$	−49.3082	+	85.4042i	−1.85050	+	3.20516i
$711$	7.27547	+	7.42046i	0.272851	+	0.278289i
$712$	−3.03632	+	1.75302i	−0.113791	+	0.0656972i
$713$	−15.4826	−	12.9914i	−0.579826	−	0.486532i
$714$	18.6390	−	26.5784i	0.697546	−	0.994673i
$715$	2.48940	+	14.1181i	0.0930981	+	0.527986i
$716$	−7.84526	+	1.38333i	−0.293191	+	0.0516975i
$717$	2.08422	+	16.4582i	0.0778366	+	0.614641i
$718$	9.97287	+	8.36823i	0.372184	+	0.312300i
$719$	−12.6254	−	21.8679i	−0.470849	−	0.815535i	0.528595	−	0.848874i	$-0.322719\pi$
$719$	−12.6254	−	21.8679i	−0.470849	−	0.815535i	−0.999444	+	0.0333396i	$0.989386\pi$
$720$	15.4350	−	21.5870i	0.575228	−	0.804500i
$721$	10.2568	−	11.2885i	0.381984	−	0.420404i
$722$	−2.39285	−	6.57430i	−0.0890526	−	0.244670i
$723$	−0.973071	+	0.301539i	−0.0361889	+	0.0112144i
$724$	7.92659	+	9.44654i	0.294589	+	0.351078i
$725$	−1.27429	+	3.50107i	−0.0473258	+	0.130027i
$726$	−31.3710	−	60.9959i	−1.16429	−	2.26377i
$727$	−2.69697	−	0.475549i	−0.100025	−	0.0176371i	0.123411	−	0.992356i	$-0.460616\pi$
$727$	−2.69697	−	0.475549i	−0.100025	−	0.0176371i	−0.223437	+	0.974718i	$0.571728\pi$
$728$	−0.428127	+	1.97039i	−0.0158674	+	0.0730276i
$729$	−25.8618	−	7.75682i	−0.957844	−	0.287290i
$730$	−20.2856			−0.750802
$731$	1.25295	−	7.10585i	0.0463422	−	0.262819i
$732$	−27.9524	−	54.3489i	−1.03315	−	2.00879i
$733$	−7.72281	+	21.2182i	−0.285249	+	0.783714i	0.711466	+	0.702720i	$0.248032\pi$
$733$	−7.72281	+	21.2182i	−0.285249	+	0.783714i	−0.996715	+	0.0809935i	$0.974191\pi$
$734$	−48.3324	+	40.5557i	−1.78398	+	1.49694i
$735$	4.50153	−	35.1401i	0.166041	−	1.29616i
$736$	−55.0064	+	20.0207i	−2.02756	+	0.737973i
$737$	−18.9110	−	10.9183i	−0.696594	−	0.402179i
$738$	15.6030	+	11.1564i	0.574355	+	0.410671i
$739$	−21.0616	−	36.4798i	−0.774764	−	1.34193i	−0.934927	−	0.354840i	$-0.884535\pi$
$739$	−21.0616	−	36.4798i	−0.774764	−	1.34193i	0.160163	−	0.987091i	$-0.448798\pi$
$740$	−27.4717	−	23.0515i	−1.00988	−	0.847389i
$741$	−6.10553	+	0.773189i	−0.224292	+	0.0284038i
$742$	51.3563	+	2.02558i	1.88535	+	0.0743615i
$743$	−3.48462	+	0.614432i	−0.127838	+	0.0225413i	−0.237201	−	0.971461i	$-0.576230\pi$
$743$	−3.48462	+	0.614432i	−0.127838	+	0.0225413i	0.109363	+	0.994002i	$0.465119\pi$
$744$	1.58290	−	3.76878i	0.0580320	−	0.138170i
$745$	18.2963	−	21.8047i	0.670324	−	0.798861i
$746$	25.3026	−	14.6085i	0.926394	−	0.534854i
$747$	1.99307	+	2.03279i	0.0729225	+	0.0743757i
$748$	−38.4146	−	22.1787i	−1.40458	−	0.810932i
$749$	4.51722	−	0.614070i	0.165056	−	0.0224376i
$750$	−11.3969	−	10.5473i	−0.416157	−	0.385131i
$751$	16.7443	−	14.0502i	0.611009	−	0.512697i	−0.283954	−	0.958838i	$-0.591646\pi$
$751$	16.7443	−	14.0502i	0.611009	−	0.512697i	0.894963	+	0.446141i	$0.147202\pi$
$752$	−16.6730	−	6.06847i	−0.608002	−	0.221294i
$753$	2.15348	−	44.3064i	0.0784771	−	1.61462i
$754$	1.95384	+	0.344515i	0.0711547	+	0.0125465i
$755$	−33.6440			−1.22443
$756$	−30.9417	−	11.6342i	−1.12534	−	0.423134i
$757$	−17.2857			−0.628260			−0.314130	−	0.949380i	$-0.601713\pi$
$757$	−17.2857			−0.628260			−0.314130	+	0.949380i	$0.601713\pi$
$758$	69.8172	+	12.3107i	2.53588	+	0.447143i
$759$	57.8613	+	37.2642i	2.10023	+	1.35261i
$760$	−9.22649	−	3.35817i	−0.334680	−	0.121814i
$761$	−10.0364	+	8.42157i	−0.363820	+	0.305282i	−0.806311	−	0.591491i	$-0.798539\pi$
$761$	−10.0364	+	8.42157i	−0.363820	+	0.305282i	0.442491	+	0.896773i	$0.354095\pi$
$762$	−4.39111	+	19.3547i	−0.159073	+	0.701148i
$763$	−3.49411	−	25.7033i	−0.126495	−	0.930523i
$764$	−28.2005	−	16.2816i	−1.02026	−	0.589047i
$765$	−24.4039	+	16.7314i	−0.882323	+	0.604926i
$766$	−31.2753	+	18.0568i	−1.13002	+	0.652420i
$767$	5.70007	−	6.79308i	0.205818	−	0.245284i
$768$	8.09098	+	10.6528i	0.291958	+	0.384399i
$769$	−11.0935	+	1.95608i	−0.400041	+	0.0705381i	−0.370049	−	0.929012i	$-0.620659\pi$
$769$	−11.0935	+	1.95608i	−0.400041	+	0.0705381i	−0.0299919	+	0.999550i	$0.509548\pi$
$770$	−88.6035	−	3.49468i	−3.19305	−	0.125939i
$771$	21.6020	+	28.4416i	0.777976	+	1.02430i
$772$	9.36653	+	7.85945i	0.337109	+	0.282868i
$773$	3.99462	+	6.91888i	0.143676	+	0.248855i	0.928878	−	0.370385i	$-0.120774\pi$
$773$	3.99462	+	6.91888i	0.143676	+	0.248855i	−0.785202	+	0.619240i	$0.787441\pi$
$774$	−13.4186	+	1.04069i	−0.482322	+	0.0374069i
$775$	−8.51768	−	4.91768i	−0.305964	−	0.176648i
$776$	3.77791	−	1.37505i	0.135619	−	0.0493613i
$777$	9.90040	−	21.1916i	0.355175	−	0.760244i
$778$	16.8545	−	14.1426i	0.604263	−	0.507037i
$779$	−4.12422	+	11.3312i	−0.147765	+	0.405982i
$780$	5.91509	−	9.18454i	0.211794	−	0.328859i
$781$	−15.2617	+	86.5534i	−0.546106	+	3.09712i
$782$	51.5031			1.84175
$783$	−1.72247	+	5.19371i	−0.0615561	+	0.185608i
$784$	19.2806	+	8.79372i	0.688593	+	0.314062i
$785$	32.5879	+	5.74613i	1.16311	+	0.205088i
$786$	−30.8903	−	1.50140i	−1.10182	−	0.0535531i
$787$	1.51980	−	4.17562i	0.0541751	−	0.148845i	−0.909653	−	0.415368i	$-0.863653\pi$
$787$	1.51980	−	4.17562i	0.0541751	−	0.148845i	0.963828	+	0.266523i	$0.0858749\pi$
$788$	−30.6442	−	36.5203i	−1.09165	−	1.30098i
$789$	−9.31470	−	8.62027i	−0.331612	−	0.306890i
$790$	−7.26543	−	19.9616i	−0.258492	−	0.710202i
$791$	−15.9004	+	17.4997i	−0.565355	+	0.622218i
$792$	−3.73507	+	13.4089i	−0.132720	+	0.476465i
$793$	6.58670	+	11.4085i	0.233900	+	0.405128i
$794$	−46.7229	−	39.2051i	−1.65813	−	1.39134i
$795$	−43.1911	−	18.1405i	−1.53183	−	0.643376i
$796$	−46.0115	+	8.11306i	−1.63083	+	0.287560i
$797$	5.57839	+	31.6366i	0.197597	+	1.12063i	0.908672	+	0.417511i	$0.137097\pi$
$797$	5.57839	+	31.6366i	0.197597	+	1.12063i	−0.711075	+	0.703116i	$0.751792\pi$
$798$	3.34505	−	37.9193i	0.118414	−	1.34233i
$799$	15.1547	+	12.7163i	0.536135	+	0.449871i
$800$	−24.6695	+	14.2429i	−0.872198	+	0.503564i
$801$	5.12496	+	11.2797i	0.181082	+	0.398549i
$802$	21.3089	−	36.9081i	0.752444	−	1.30327i
$803$	−16.9886	+	6.18333i	−0.599513	+	0.218205i
$804$	4.92548	+	15.8946i	0.173708	+	0.560559i
$805$	49.7460	−	26.1630i	1.75332	−	0.922125i
$806$	−1.79128	+	4.92151i	−0.0630953	+	0.173353i
$807$	−2.69983	+	1.38856i	−0.0950384	+	0.0488796i
$808$	−10.0115	−	1.76530i	−0.352205	−	0.0621032i
$809$			43.0057i			1.51200i	0.654572	+	0.756000i	$0.272849\pi$
$809$			43.0057i			1.51200i	−0.654572	+	0.756000i	$0.727151\pi$
$810$	41.5708	+	36.3035i	1.46065	+	1.27558i
$811$			29.8103i			1.04678i	0.852093	+	0.523390i	$0.175333\pi$
$811$			29.8103i			1.04678i	−0.852093	+	0.523390i	$0.824667\pi$
$812$	−2.53764	+	6.20013i	−0.0890535	+	0.217582i
$813$	5.82614	+	11.3280i	0.204332	+	0.397290i
$814$	−55.0137	−	20.0234i	−1.92823	−	0.701818i
$815$	24.7149	−	20.7382i	0.865724	−	0.726428i
$816$	−5.23882	−	16.9058i	−0.183395	−	0.591820i
$817$	−2.89385	−	7.95078i	−0.101243	−	0.278163i
$818$	30.2686	−	52.4267i	1.05832	−	1.83306i
$819$	6.78330	+	2.18101i	0.237028	+	0.0762105i
$820$	−10.7024	−	18.5371i	−0.373745	−	0.647345i
$821$	5.68663	−	6.77706i	0.198465	−	0.236521i	−0.657629	−	0.753342i	$-0.728440\pi$
$821$	5.68663	−	6.77706i	0.198465	−	0.236521i	0.856093	+	0.516821i	$0.172885\pi$
$822$	17.1528	−	2.17218i	0.598272	−	0.0757636i
$823$	0.935749	+	5.30690i	0.0326182	+	0.184987i	0.996764	−	0.0803872i	$-0.0256157\pi$
$823$	0.935749	+	5.30690i	0.0326182	+	0.184987i	−0.964146	+	0.265374i	$0.914505\pi$
$824$	0.849852	+	4.81975i	0.0296060	+	0.167904i
$825$	30.8784	+	12.9691i	1.07505	+	0.451525i
$826$	33.5736	+	43.3745i	1.16818	+	1.50919i
$827$	−18.4580	+	10.6567i	−0.641848	+	0.370571i	−0.785326	−	0.619082i	$-0.787505\pi$
$827$	−18.4580	+	10.6567i	−0.641848	+	0.370571i	0.143478	+	0.989654i	$0.454171\pi$
$828$	−13.0735	−	50.7899i	−0.454334	−	1.76507i
$829$	19.8131	+	11.4391i	0.688139	+	0.397297i	0.802914	−	0.596094i	$-0.203282\pi$
$829$	19.8131	+	11.4391i	0.688139	+	0.397297i	−0.114776	+	0.993391i	$0.536615\pi$
$830$	−1.99032	−	5.46835i	−0.0690849	−	0.189809i
$831$	−0.273558	+	0.295595i	−0.00948961	+	0.0102541i
$832$	6.25659	+	7.45631i	0.216908	+	0.258501i
$833$	−16.8475	−	16.5660i	−0.583732	−	0.573980i
$834$	−1.98578	+	40.8562i	−0.0687621	+	1.41474i
$835$	−10.1892	+	57.7857i	−0.352611	+	1.99976i
$836$	−52.0145			−1.79896
$837$	−12.7126	−	6.85874i	−0.439412	−	0.237073i
$838$		−	18.7364i		−	0.647239i
$839$	7.06920	−	40.0914i	0.244056	−	1.38411i	−0.578619	−	0.815598i	$-0.696408\pi$
$839$	7.06920	−	40.0914i	0.244056	−	1.38411i	0.822675	−	0.568512i	$-0.192481\pi$
$840$	8.03244	+	8.04403i	0.277146	+	0.277545i
$841$	−26.2090	−	9.53930i	−0.903759	−	0.328941i
$842$	21.9140	+	26.1161i	0.755208	+	0.900022i
$843$	−5.43274	+	23.9459i	−0.187113	+	0.824740i
$844$	41.6054	−	15.1431i	1.43212	−	0.521248i
$845$	17.8156	−	30.8574i	0.612874	−	1.06153i
$846$	15.9242	−	33.2882i	0.547487	−	1.14447i
$847$	−47.5489	+	15.2126i	−1.63380	+	0.522711i
$848$	18.0119	−	21.4658i	0.618532	−	0.737138i
$849$	37.3596	−	28.3754i	1.28218	−	0.973840i
$850$	24.6823	−	4.35216i	0.846597	−	0.149278i
$851$	36.5455	−	6.44396i	1.25276	−	0.220896i
$852$	53.3349	−	40.5089i	1.82722	−	1.38781i
$853$	−8.64224	+	10.2994i	−0.295905	+	0.352645i	−0.893428	−	0.449206i	$-0.851707\pi$
$853$	−8.64224	+	10.2994i	−0.295905	+	0.352645i	0.597524	+	0.801851i	$0.296151\pi$
$854$	−77.6070	+	24.8293i	−2.65566	+	0.849640i
$855$	−14.9728	+	31.2994i	−0.512060	+	1.07042i
$856$	−0.731402	+	1.26683i	−0.0249988	+	0.0432992i
$857$	−0.0709596	+	0.0258272i	−0.00242393	+	0.000882240i	−0.343232	−	0.939251i	$-0.611522\pi$
$857$	−0.0709596	+	0.0258272i	−0.00242393	+	0.000882240i	0.340808	+	0.940133i	$0.389299\pi$
$858$	3.94588	−	17.3923i	0.134710	−	0.593762i
$859$	15.2613	+	18.1878i	0.520710	+	0.620558i	0.960749	−	0.277421i	$-0.0894796\pi$
$859$	15.2613	+	18.1878i	0.520710	+	0.620558i	−0.440038	+	0.897979i	$0.645035\pi$
$860$	14.1134	+	5.13686i	0.481263	+	0.175166i
$861$	9.87899	−	9.86476i	0.336675	−	0.336190i
$862$	7.96611	−	45.1781i	0.271327	−	1.53877i
$863$			5.19342i			0.176786i	0.996086	+	0.0883930i	$0.0281731\pi$
$863$			5.19342i			0.176786i	−0.996086	+	0.0883930i	$0.971827\pi$
$864$	−35.6130	+	21.9539i	−1.21158	+	0.746888i
$865$	9.16564			0.311641
$866$	−10.5234	+	59.6811i	−0.357600	+	2.02805i
$867$	0.471441	−	9.69959i	0.0160110	−	0.329415i
$868$	−14.9553	−	9.43929i	−0.507618	−	0.320390i
$869$	−12.1692	−	14.5027i	−0.412811	−	0.491969i
$870$	7.59719	−	8.20921i	0.257569	−	0.278318i
$871$	−1.22675	−	3.37047i	−0.0415669	−	0.114204i
$872$	7.20833	+	4.16173i	0.244105	+	0.140934i
$873$	−3.54146	−	13.7584i	−0.119860	−	0.465652i
$874$	52.3026	−	30.1969i	1.76916	−	1.02143i
$875$	−8.93770	+	6.91814i	−0.302149	+	0.233876i
$876$	12.7019	+	5.33487i	0.429158	+	0.180248i
$877$	−0.234015	−	1.32716i	−0.00790212	−	0.0448151i	0.980602	−	0.196011i	$-0.0627988\pi$
$877$	−0.234015	−	1.32716i	−0.00790212	−	0.0448151i	−0.988504	+	0.151196i	$0.951688\pi$
$878$	11.7292	+	66.5198i	0.395842	+	2.24493i
$879$	−21.9443	+	2.77897i	−0.740162	+	0.0937323i
$880$	−31.0754	+	37.0343i	−1.04755	+	1.24842i
$881$	−6.10038	−	10.5662i	−0.205527	−	0.355983i	0.744773	−	0.667317i	$-0.232558\pi$
$881$	−6.10038	−	10.5662i	−0.205527	−	0.355983i	−0.950301	+	0.311334i	$0.899224\pi$
$882$	−22.0913	+	38.1362i	−0.743853	+	1.28411i
$883$	18.8872	−	32.7135i	0.635603	−	1.10090i	−0.350784	−	0.936457i	$-0.614085\pi$
$883$	18.8872	−	32.7135i	0.635603	−	1.10090i	0.986387	−	0.164441i	$-0.0525819\pi$
$884$	−2.49194	−	6.84656i	−0.0838132	−	0.230275i
$885$	−14.7981	−	47.7538i	−0.497434	−	1.60523i
$886$	5.01991	−	4.21221i	0.168647	−	0.141512i
$887$	−31.8073	−	11.5769i	−1.06799	−	0.388715i	−0.252563	−	0.967580i	$-0.581273\pi$
$887$	−31.8073	−	11.5769i	−1.06799	−	0.388715i	−0.815423	+	0.578865i	$0.803496\pi$
$888$	3.43272	+	6.67436i	0.115194	+	0.223977i
$889$	13.3688	+	5.47170i	0.448376	+	0.183515i
$890$		−	25.3254i		−	0.848911i
$891$	45.8802	+	17.7318i	1.53704	+	0.594036i
$892$		−	0.395526i		−	0.0132432i
$893$	22.8457	+	4.02831i	0.764502	+	0.134802i
$894$	−31.4894	+	16.1954i	−1.05316	+	0.541656i
$895$	3.31099	−	9.09688i	0.110674	−	0.304075i
$896$	−15.5784	+	8.19319i	−0.520438	+	0.273715i
$897$	3.34612	+	10.7980i	0.111724	+	0.360533i
$898$	20.5792	−	7.49022i	0.686737	−	0.249952i
$899$	−1.46371	+	2.53522i	−0.0488175	+	0.0845544i
$900$	−10.5572	−	23.2358i	−0.351908	−	0.774527i
$901$	−27.0576	+	15.6217i	−0.901420	+	0.520435i
$902$	−26.7683	−	22.4612i	−0.891286	−	0.747877i
$903$	−0.860812	+	9.75811i	−0.0286460	+	0.324730i
$904$	−1.31747	−	7.47172i	−0.0438183	−	0.248506i
$905$	−14.7578	+	2.60219i	−0.490565	+	0.0864999i
$906$	38.5888	+	16.2074i	1.28203	+	0.538456i
$907$	16.9119	+	14.1908i	0.561551	+	0.471197i	0.878830	−	0.477135i	$-0.158325\pi$
$907$	16.9119	+	14.1908i	0.561551	+	0.471197i	−0.317279	+	0.948332i	$0.602769\pi$
$908$	31.2796	+	54.1779i	1.03805	+	1.79796i
$909$	−9.63965	+	34.6064i	−0.319727	+	1.14782i
$910$	−10.7798	−	9.79465i	−0.357346	−	0.324689i
$911$	−12.4795	−	34.2872i	−0.413465	−	1.13599i	−0.955335	−	0.295525i	$-0.904506\pi$
$911$	−12.4795	−	34.2872i	−0.413465	−	1.13599i	0.541870	−	0.840463i	$-0.317717\pi$
$912$	−15.2322	−	14.0966i	−0.504389	−	0.466785i
$913$	−3.33366	−	3.97291i	−0.110328	−	0.131484i
$914$	−22.5320	+	61.9061i	−0.745292	+	2.04767i
$915$	74.1808	+	3.60550i	2.45234	+	0.119194i
$916$	26.4448	+	4.66293i	0.873760	+	0.154068i
$917$	−4.77943	+	21.9967i	−0.157831	+	0.726394i
$918$	36.0506	−	7.43432i	1.18985	−	0.245369i
$919$	−31.8768			−1.05152			−0.525759	−	0.850634i	$-0.676219\pi$
$919$	−31.8768			−1.05152			−0.525759	+	0.850634i	$0.676219\pi$
$920$	−3.13181	+	17.7614i	−0.103253	+	0.585575i
$921$	2.02083	−	3.13781i	0.0665887	−	0.103394i
$922$	−0.822886	+	2.26086i	−0.0271003	+	0.0744575i
$923$	−11.0588	+	9.27944i	−0.364005	+	0.305436i
$924$	54.5606	+	25.4899i	1.79491	+	0.838557i
$925$	16.9696	−	6.17641i	0.557956	−	0.203079i
$926$	58.1031	+	33.5458i	1.90939	+	1.10238i
$927$	17.2427	−	1.33727i	0.566323	−	0.0439217i
$928$	4.23930	+	7.34268i	0.139162	+	0.241035i
$929$	6.05146	+	5.07778i	0.198542	+	0.166596i	0.736638	−	0.676287i	$-0.236412\pi$
$929$	6.05146	+	5.07778i	0.198542	+	0.166596i	−0.538097	+	0.842883i	$0.680856\pi$
$930$	17.8591	+	23.5137i	0.585623	+	0.771044i
$931$	−26.8219	−	6.94529i	−0.879053	−	0.227623i
$932$	19.5103	−	3.44020i	0.639082	−	0.112687i
$933$	−19.0314	−	25.0572i	−0.623060	−	0.820335i
$934$	44.4261	−	52.9449i	1.45366	−	1.73241i
$935$	46.6817	−	26.9517i	1.52665	−	0.881414i
$936$	−1.88571	+	1.29285i	−0.0616364	+	0.0422583i
$937$	−11.9656	−	6.90834i	−0.390899	−	0.225686i	0.291651	−	0.956525i	$-0.405796\pi$
$937$	−11.9656	−	6.90834i	−0.390899	−	0.225686i	−0.682549	+	0.730839i	$0.739129\pi$
$938$	21.9833	−	2.98841i	0.717781	−	0.0975750i
$939$	−5.38223	+	23.7233i	−0.175642	+	0.774180i
$940$	−31.5449	+	26.4693i	−1.02888	+	0.863334i
$941$	−41.4608	−	15.0905i	−1.35158	−	0.491936i	−0.438142	−	0.898906i	$-0.644363\pi$
$941$	−41.4608	−	15.0905i	−1.35158	−	0.491936i	−0.913442	+	0.406970i	$0.866585\pi$
$942$	−34.6093	−	22.2893i	−1.12763	−	0.726226i
$943$	21.8130	+	3.84622i	0.710329	+	0.125250i
$944$	29.9046			0.973313
$945$	31.0442	−	25.4940i	1.00987	−	0.829321i
$946$	24.5189			0.797177
$947$	5.42669	+	0.956873i	0.176344	+	0.0310942i	0.261123	−	0.965306i	$-0.415907\pi$
$947$	5.42669	+	0.956873i	0.176344	+	0.0310942i	−0.0847789	+	0.996400i	$0.527018\pi$
$948$	−0.700377	+	14.4098i	−0.0227472	+	0.468009i
$949$	−2.79048	−	1.01565i	−0.0905827	−	0.0329694i
$950$	22.5138	−	18.8913i	0.730443	−	0.612914i
$951$	−26.8062	−	24.8077i	−0.869251	−	0.804446i
$952$	7.51252	−	1.02125i	0.243482	−	0.0330989i
$953$	−17.4648	−	10.0833i	−0.565741	−	0.326631i	0.189706	−	0.981841i	$-0.439247\pi$
$953$	−17.4648	−	10.0833i	−0.565741	−	0.326631i	−0.755446	+	0.655210i	$0.772580\pi$
$954$	40.8002	+	41.6132i	1.32095	+	1.34728i
$955$	34.2695	−	19.7855i	1.10893	−	0.640244i
$956$	−14.8037	+	17.6424i	−0.478787	+	0.570596i
$957$	3.86014	−	9.19071i	0.124781	−	0.297094i
$958$	−53.2055	+	9.38157i	−1.71899	+	0.303105i
$959$	0.495960	−	12.5745i	0.0160154	−	0.406052i
$960$	54.4404	−	6.89419i	1.75706	−	0.222509i
$961$	17.8275	+	14.9590i	0.575080	+	0.482549i
$962$	−4.80814	−	8.32794i	−0.155021	−	0.268503i
$963$	4.20487	+	3.00654i	0.135500	+	0.0968843i
$964$	−1.22477	−	0.707119i	−0.0394471	−	0.0227748i
$965$	−13.9624	+	5.08191i	−0.449467	+	0.163592i
$966$	−69.6609	+	6.04394i	−2.24130	+	0.194461i
$967$	−38.4952	+	32.3013i	−1.23792	+	1.03874i	−0.240237	+	0.970714i	$0.577225\pi$
$967$	−38.4952	+	32.3013i	−1.23792	+	1.03874i	−0.997684	+	0.0680248i	$0.978330\pi$
$968$	5.47889	−	15.0531i	0.176098	−	0.483826i
$969$	10.5837	+	20.5782i	0.339996	+	0.661068i
$970$	−5.04286	+	28.5995i	−0.161916	+	0.918273i
$971$	10.3064			0.330749			0.165375	−	0.986231i	$-0.447117\pi$
$971$	10.3064			0.330749			0.165375	+	0.986231i	$0.447117\pi$
$972$	−16.4824	−	33.6643i	−0.528674	−	1.07978i
$973$	29.0933	+	6.32138i	0.932688	+	0.202654i
$974$	33.5996	+	5.92451i	1.07660	+	0.189834i
$975$	2.51605	+	4.89206i	0.0805782	+	0.156671i
$976$	−15.1941	+	41.7455i	−0.486352	+	1.33624i
$977$	4.31818	+	5.14621i	0.138151	+	0.164642i	0.830684	−	0.556744i	$-0.187950\pi$
$977$	4.31818	+	5.14621i	0.138151	+	0.164642i	−0.692533	+	0.721386i	$0.743505\pi$
$978$	−38.3376	+	11.8802i	−1.22590	+	0.379887i
$979$	−7.71956	−	21.2093i	−0.246718	−	0.677853i
$980$	40.0483	−	28.5479i	1.27930	−	0.911930i
$981$	17.1074	−	23.9260i	0.546198	−	0.763899i
$982$	−10.8211	−	18.7428i	−0.345317	−	0.598106i
$983$	−25.0101	−	20.9859i	−0.797697	−	0.669348i	0.149940	−	0.988695i	$-0.452092\pi$
$983$	−25.0101	−	20.9859i	−0.797697	−	0.669348i	−0.947638	+	0.319347i	$0.896536\pi$
$984$	0.562809	+	4.44425i	0.0179417	+	0.141678i
$985$	57.0535	−	10.0601i	1.81788	−	0.320541i
$986$	−1.29539	−	7.34651i	−0.0412536	−	0.233961i
$987$	−21.9899	−	15.4211i	−0.699946	−	0.490860i
$988$	−6.54485	−	5.49178i	−0.208220	−	0.174717i
$989$	−13.4595	+	7.77084i	−0.427987	+	0.247098i
$990$	−70.3913	−	71.7940i	−2.23718	−	2.28176i
$991$	−8.82289	+	15.2817i	−0.280268	+	0.485439i	−0.971451	−	0.237242i	$-0.923757\pi$
$991$	−8.82289	+	15.2817i	−0.280268	+	0.485439i	0.691183	+	0.722680i	$0.257090\pi$
$992$	−21.0322	+	7.65510i	−0.667774	+	0.243050i
$993$	12.8800	−	13.9176i	0.408735	−	0.441662i
$994$	−41.5643	−	79.0298i	−1.31834	−	2.50667i
$995$	19.4185	−	53.3520i	0.615609	−	1.69137i
$996$	−0.191864	+	3.94747i	−0.00607944	+	0.125080i
$997$	−52.8594	−	9.32054i	−1.67407	−	0.295184i	−0.745548	−	0.666452i	$-0.767812\pi$
$997$	−52.8594	−	9.32054i	−1.67407	−	0.295184i	−0.928526	+	0.371267i	$0.878923\pi$
$998$			12.5513i			0.397304i
$999$	24.6506	−	9.78582i	0.779911	−	0.309610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.83.20	yes	132
3.2	odd	2		567.2.be.a.251.4		132
7.6	odd	2	inner	189.2.be.a.83.19	yes	132
21.20	even	2		567.2.be.a.251.3		132
27.13	even	9		567.2.be.a.314.3		132
27.14	odd	18	inner	189.2.be.a.41.19	✓	132
189.13	odd	18		567.2.be.a.314.4		132
189.41	even	18	inner	189.2.be.a.41.20	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.41.19	✓	132	27.14	odd	18	inner
189.2.be.a.41.20	yes	132	189.41	even	18	inner
189.2.be.a.83.19	yes	132	7.6	odd	2	inner
189.2.be.a.83.20	yes	132	1.1	even	1	trivial
567.2.be.a.251.3		132	21.20	even	2
567.2.be.a.251.4		132	3.2	odd	2
567.2.be.a.314.3		132	27.13	even	9
567.2.be.a.314.4		132	189.13	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.06681 + 0.364434i) q^{2} +(1.54027 - 0.792184i) q^{3} +(2.25951 + 0.822394i) q^{4} +(-2.23837 + 1.87822i) q^{5} +(3.47215 - 1.07597i) q^{6} +(-0.356385 - 2.62164i) q^{7} +(0.735222 + 0.424480i) q^{8} +(1.74489 - 2.44036i) q^{9} +O(q^{10})\)	\(q+(2.06681 + 0.364434i) q^{2} +(1.54027 - 0.792184i) q^{3} +(2.25951 + 0.822394i) q^{4} +(-2.23837 + 1.87822i) q^{5} +(3.47215 - 1.07597i) q^{6} +(-0.356385 - 2.62164i) q^{7} +(0.735222 + 0.424480i) q^{8} +(1.74489 - 2.44036i) q^{9} +(-5.31078 + 3.06618i) q^{10} +(-3.51301 + 4.18664i) q^{11} +(4.13175 - 0.523234i) q^{12} +(-0.884066 + 0.155885i) q^{13} +(0.218835 - 5.54831i) q^{14} +(-1.95981 + 4.66618i) q^{15} +(-2.31907 - 1.94593i) q^{16} +(1.68770 + 2.92318i) q^{17} +(4.49571 - 4.40787i) q^{18} +(3.42780 + 1.97904i) q^{19} +(-6.60226 + 2.40303i) q^{20} +(-2.62575 - 3.75572i) q^{21} +(-8.78648 + 7.37273i) q^{22} +(2.48663 - 6.83195i) q^{23} +(1.46871 + 0.0713855i) q^{24} +(0.614371 - 3.48427i) q^{25} -1.88401 q^{26} +(0.754393 - 5.14110i) q^{27} +(1.35076 - 6.21670i) q^{28} +(-1.03707 - 0.182863i) q^{29} +(-5.75108 + 8.92988i) q^{30} +(0.950784 - 2.61226i) q^{31} +(-5.17531 - 6.16770i) q^{32} +(-2.09441 + 9.23152i) q^{33} +(2.42285 + 6.65672i) q^{34} +(5.72173 + 5.19884i) q^{35} +(5.94953 - 4.07903i) q^{36} +(2.55208 + 4.42033i) q^{37} +(6.36338 + 5.33951i) q^{38} +(-1.23821 + 0.940448i) q^{39} +(-2.44297 + 0.430761i) q^{40} +(0.529024 + 3.00024i) q^{41} +(-4.05822 - 8.71928i) q^{42} +(-1.63755 - 1.37406i) q^{43} +(-11.3807 + 6.57067i) q^{44} +(0.677817 + 8.73972i) q^{45} +(7.62918 - 13.2141i) q^{46} +(5.50750 - 2.00456i) q^{47} +(-5.11353 - 1.16014i) q^{48} +(-6.74598 + 1.86863i) q^{49} +(2.53958 - 6.97743i) q^{50} +(4.91522 + 3.16553i) q^{51} +(-2.12575 - 0.374828i) q^{52} +9.25621i q^{53} +(3.43278 - 10.3507i) q^{54} -15.9695i q^{55} +(0.850812 - 2.07876i) q^{56} +(6.84751 + 0.332818i) q^{57} +(-2.07678 - 0.755885i) q^{58} +(-7.56717 + 6.34961i) q^{59} +(-8.26565 + 8.93152i) q^{60} +(-5.01899 - 13.7896i) q^{61} +(2.91709 - 5.05254i) q^{62} +(-7.01960 - 3.70476i) q^{63} +(-5.42134 - 9.39004i) q^{64} +(1.68608 - 2.00940i) q^{65} +(-7.69303 + 18.3165i) q^{66} +(0.693812 + 3.93480i) q^{67} +(1.40937 + 7.99291i) q^{68} +(-1.58207 - 12.4929i) q^{69} +(9.93110 + 12.8302i) q^{70} +(13.9268 - 8.04064i) q^{71} +(2.31877 - 1.05353i) q^{72} +(2.86477 + 1.65398i) q^{73} +(3.66374 + 10.0661i) q^{74} +(-1.81388 - 5.85343i) q^{75} +(6.11759 + 7.29066i) q^{76} +(12.2278 + 7.71778i) q^{77} +(-2.90189 + 1.49248i) q^{78} +(-0.601523 + 3.41141i) q^{79} +8.84582 q^{80} +(-2.91072 - 8.51632i) q^{81} +6.39373i q^{82} +(-0.164783 + 0.934532i) q^{83} +(-2.84423 - 10.6455i) q^{84} +(-9.26808 - 3.37331i) q^{85} +(-2.88374 - 3.43671i) q^{86} +(-1.74223 + 0.539888i) q^{87} +(-4.35999 + 1.58691i) q^{88} +(-2.06490 + 3.57651i) q^{89} +(-1.78414 + 18.3104i) q^{90} +(0.723741 + 2.26215i) q^{91} +(11.2371 - 13.3919i) q^{92} +(-0.604920 - 4.77679i) q^{93} +(12.1135 - 2.13593i) q^{94} +(-11.3898 + 2.00832i) q^{95} +(-12.8574 - 5.40015i) q^{96} +(3.04401 - 3.62771i) q^{97} +(-14.6237 + 1.40363i) q^{98} +(4.08710 + 15.8782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

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