LMFDB - Embedded newform 690.2.q.a.401.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			401.4
Character	$\chi$	$=$	690.401
Dual form			690.2.q.a.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755750 + 0.654861i) q^{2} +(0.359391 + 1.69435i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.38118 - 1.04516i) q^{6} +(0.816450 - 2.78057i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-2.74168 + 1.21787i) q^{9} +O(q^{10})$	\(q+(-0.755750 + 0.654861i) q^{2} +(0.359391 + 1.69435i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.38118 - 1.04516i) q^{6} +(0.816450 - 2.78057i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-2.74168 + 1.21787i) q^{9} +(0.281733 + 0.959493i) q^{10} +(0.260973 - 0.301179i) q^{11} +(1.72826 - 0.114601i) q^{12} +(2.27633 - 0.668389i) q^{13} +(1.20386 + 2.63608i) q^{14} +(1.69054 + 0.376947i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.489750 - 3.40629i) q^{17} +(1.27448 - 2.71582i) q^{18} +(-0.0720347 - 0.0103570i) q^{19} +(-0.841254 - 0.540641i) q^{20} +(5.00470 + 0.384043i) q^{21} +0.398517i q^{22} +(4.78873 + 0.260982i) q^{23} +(-1.23108 + 1.21838i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(-1.28263 + 1.99581i) q^{26} +(-3.04884 - 4.20768i) q^{27} +(-2.63608 - 1.20386i) q^{28} +(8.24777 - 1.18585i) q^{29} +(-1.52447 + 0.822188i) q^{30} +(7.97523 - 5.12537i) q^{31} +(0.909632 - 0.415415i) q^{32} +(0.604096 + 0.333940i) q^{33} +(2.60077 + 2.25358i) q^{34} +(-2.19013 - 1.89776i) q^{35} +(0.815294 + 2.88709i) q^{36} +(-0.619026 + 0.282700i) q^{37} +(0.0612226 - 0.0393454i) q^{38} +(1.95058 + 3.61669i) q^{39} +(0.989821 - 0.142315i) q^{40} +(-3.91584 - 1.78831i) q^{41} +(-4.03379 + 2.98714i) q^{42} +(-2.36906 + 3.68633i) q^{43} +(-0.260973 - 0.301179i) q^{44} +(-0.0311182 + 2.99984i) q^{45} +(-3.78998 + 2.93871i) q^{46} +1.09098i q^{47} +(0.132522 - 1.72697i) q^{48} +(-1.17622 - 0.755909i) q^{49} +(0.989821 + 0.142315i) q^{50} +(5.59544 - 2.05400i) q^{51} +(-0.337631 - 2.34828i) q^{52} +(-7.85864 - 2.30751i) q^{53} +(5.05960 + 1.18339i) q^{54} +(-0.165550 - 0.362504i) q^{55} +(2.78057 - 0.816450i) q^{56} +(-0.00834014 - 0.125774i) q^{57} +(-5.45668 + 6.29734i) q^{58} +(2.89296 + 9.85253i) q^{59} +(0.613698 - 1.61968i) q^{60} +(5.38365 + 8.37713i) q^{61} +(-2.67087 + 9.09616i) q^{62} +(1.14794 + 8.61776i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(0.337631 - 2.34828i) q^{65} +(-0.675230 + 0.143224i) q^{66} +(-6.25421 + 5.41931i) q^{67} -3.44131 q^{68} +(1.27883 + 8.20759i) q^{69} +2.89796 q^{70} +(10.8997 - 9.44463i) q^{71} +(-2.50680 - 1.64801i) q^{72} +(-1.74133 + 12.1112i) q^{73} +(0.282700 - 0.619026i) q^{74} +(1.04516 - 1.38118i) q^{75} +(-0.0205032 + 0.0698275i) q^{76} +(-0.624379 - 0.971553i) q^{77} +(-3.84258 - 1.45595i) q^{78} +(-0.274710 - 0.935576i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(6.03358 - 6.67802i) q^{81} +(4.13049 - 1.21282i) q^{82} +(-7.05627 - 15.4511i) q^{83} +(1.09238 - 4.89911i) q^{84} +(-3.30192 - 0.969530i) q^{85} +(-0.623616 - 4.33734i) q^{86} +(4.97342 + 13.5485i) q^{87} +(0.394461 + 0.0567149i) q^{88} +(1.35490 + 0.870744i) q^{89} +(-1.94096 - 2.28750i) q^{90} -6.87519i q^{91} +(0.939832 - 4.70284i) q^{92} +(11.5504 + 11.6709i) q^{93} +(-0.714442 - 0.824510i) q^{94} +(-0.0393454 + 0.0612226i) q^{95} +(1.03077 + 1.39194i) q^{96} +(-1.94916 - 0.890152i) q^{97} +(1.38394 - 0.198981i) q^{98} +(-0.348707 + 1.14357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.755750	+	0.654861i	−0.534396	+	0.463056i
$2$	−0.755750	+	0.654861i	−0.534396	+	0.463056i
$3$	0.359391	+	1.69435i	0.207495	+	0.978236i
$3$	0.359391	+	1.69435i	0.207495	+	0.978236i
$4$	0.142315	−	0.989821i	0.0711574	−	0.494911i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	−1.38118	−	1.04516i	−0.563863	−	0.426683i
$7$	0.816450	−	2.78057i	0.308589	−	1.05096i	−0.648512	−	0.761204i	$-0.724609\pi$
$7$	0.816450	−	2.78057i	0.308589	−	1.05096i	0.957101	−	0.289753i	$-0.0935733\pi$
$8$	0.540641	+	0.841254i	0.191145	+	0.297428i
$9$	−2.74168	+	1.21787i	−0.913892	+	0.405957i
$10$	0.281733	+	0.959493i	0.0890917	+	0.303418i
$11$	0.260973	−	0.301179i	0.0786864	−	0.0908090i	−0.715041	−	0.699082i	$-0.753592\pi$
$11$	0.260973	−	0.301179i	0.0786864	−	0.0908090i	0.793728	+	0.608273i	$0.208138\pi$
$12$	1.72826	−	0.114601i	0.498904	−	0.0330825i
$13$	2.27633	−	0.668389i	0.631339	−	0.185378i	0.0496206	−	0.998768i	$-0.484199\pi$
$13$	2.27633	−	0.668389i	0.631339	−	0.185378i	0.581718	+	0.813390i	$0.302381\pi$
$14$	1.20386	+	2.63608i	0.321744	+	0.704521i
$15$	1.69054	+	0.376947i	0.436494	+	0.0973273i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	−0.489750	−	3.40629i	−0.118782	−	0.826146i	−0.958900	−	0.283743i	$-0.908424\pi$
$17$	−0.489750	−	3.40629i	−0.118782	−	0.826146i	0.840119	−	0.542403i	$-0.182485\pi$
$18$	1.27448	−	2.71582i	0.300399	−	0.640125i
$19$	−0.0720347	−	0.0103570i	−0.0165259	−	0.00237606i	0.134047	−	0.990975i	$-0.457203\pi$
$19$	−0.0720347	−	0.0103570i	−0.0165259	−	0.00237606i	−0.150573	+	0.988599i	$0.548112\pi$
$20$	−0.841254	−	0.540641i	−0.188110	−	0.120891i
$21$	5.00470	+	0.384043i	1.09212	+	0.0838050i
$22$			0.398517i			0.0849642i
$23$	4.78873	+	0.260982i	0.998518	+	0.0544185i
$23$	4.78873	+	0.260982i	0.998518	+	0.0544185i
$24$	−1.23108	+	1.21838i	−0.251293	+	0.248700i
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−1.28263	+	1.99581i	−0.251544	+	0.391411i
$27$	−3.04884	−	4.20768i	−0.586750	−	0.809768i
$28$	−2.63608	−	1.20386i	−0.498172	−	0.227507i
$29$	8.24777	−	1.18585i	1.53157	−	0.220207i	0.675615	−	0.737254i	$-0.263878\pi$
$29$	8.24777	−	1.18585i	1.53157	−	0.220207i	0.855957	+	0.517048i	$0.172969\pi$
$30$	−1.52447	+	0.822188i	−0.278329	+	0.150110i
$31$	7.97523	−	5.12537i	1.43239	−	0.920543i	0.432573	−	0.901599i	$-0.357606\pi$
$31$	7.97523	−	5.12537i	1.43239	−	0.920543i	0.999821	−	0.0189442i	$-0.00603050\pi$
$32$	0.909632	−	0.415415i	0.160802	−	0.0734357i
$33$	0.604096	+	0.333940i	0.105160	+	0.0581315i
$34$	2.60077	+	2.25358i	0.446029	+	0.386486i
$35$	−2.19013	−	1.89776i	−0.370200	−	0.320780i
$36$	0.815294	+	2.88709i	0.135882	+	0.481182i
$37$	−0.619026	+	0.282700i	−0.101767	+	0.0464755i	−0.465648	−	0.884970i	$-0.654179\pi$
$37$	−0.619026	+	0.282700i	−0.101767	+	0.0464755i	0.363881	+	0.931445i	$0.381451\pi$
$38$	0.0612226	−	0.0393454i	0.00993161	−	0.00638266i
$39$	1.95058	+	3.61669i	0.312343	+	0.579134i
$40$	0.989821	−	0.142315i	0.156505	−	0.0225020i
$41$	−3.91584	−	1.78831i	−0.611552	−	0.279286i	0.0854649	−	0.996341i	$-0.472762\pi$
$41$	−3.91584	−	1.78831i	−0.611552	−	0.279286i	−0.697017	+	0.717055i	$0.745490\pi$
$42$	−4.03379	+	2.98714i	−0.622428	+	0.460926i
$43$	−2.36906	+	3.68633i	−0.361278	+	0.562160i	−0.973546	−	0.228491i	$-0.926621\pi$
$43$	−2.36906	+	3.68633i	−0.361278	+	0.562160i	0.612268	+	0.790650i	$0.290257\pi$
$44$	−0.260973	−	0.301179i	−0.0393432	−	0.0454045i
$45$	−0.0311182	+	2.99984i	−0.00463883	+	0.447190i
$46$	−3.78998	+	2.93871i	−0.558803	+	0.433289i
$47$			1.09098i			0.159136i	0.996829	+	0.0795682i	$0.0253541\pi$
$47$			1.09098i			0.159136i	−0.996829	+	0.0795682i	$0.974646\pi$
$48$	0.132522	−	1.72697i	0.0191279	−	0.249267i
$49$	−1.17622	−	0.755909i	−0.168031	−	0.107987i
$50$	0.989821	+	0.142315i	0.139982	+	0.0201264i
$51$	5.59544	−	2.05400i	0.783519	−	0.287617i
$52$	−0.337631	−	2.34828i	−0.0468210	−	0.325647i
$53$	−7.85864	−	2.30751i	−1.07947	−	0.316960i	−0.306802	−	0.951773i	$-0.599259\pi$
$53$	−7.85864	−	2.30751i	−1.07947	−	0.316960i	−0.772666	+	0.634813i	$0.781077\pi$
$54$	5.05960	+	1.18339i	0.688525	+	0.161038i
$55$	−0.165550	−	0.362504i	−0.0223228	−	0.0488800i
$56$	2.78057	−	0.816450i	0.371570	−	0.109103i
$57$	−0.00834014	−	0.125774i	−0.00110468	−	0.0166592i
$58$	−5.45668	+	6.29734i	−0.716497	+	0.826882i
$59$	2.89296	+	9.85253i	0.376632	+	1.28269i	0.901971	+	0.431797i	$0.142120\pi$
$59$	2.89296	+	9.85253i	0.376632	+	1.28269i	−0.525339	+	0.850893i	$0.676061\pi$
$60$	0.613698	−	1.61968i	0.0792281	−	0.209100i
$61$	5.38365	+	8.37713i	0.689306	+	1.07258i	0.992804	+	0.119749i	$0.0382090\pi$
$61$	5.38365	+	8.37713i	0.689306	+	1.07258i	−0.303498	+	0.952832i	$0.598155\pi$
$62$	−2.67087	+	9.09616i	−0.339201	+	1.15521i
$63$	1.14794	+	8.61776i	0.144627	+	1.08574i
$64$	−0.415415	+	0.909632i	−0.0519269	+	0.113704i
$65$	0.337631	−	2.34828i	0.0418780	−	0.291268i
$66$	−0.675230	+	0.143224i	−0.0831150	+	0.0176296i
$67$	−6.25421	+	5.41931i	−0.764074	+	0.662074i	−0.947065	−	0.321041i	$-0.895967\pi$
$67$	−6.25421	+	5.41931i	−0.764074	+	0.662074i	0.182992	+	0.983114i	$0.441422\pi$
$68$	−3.44131			−0.417321
$69$	1.27883	+	8.20759i	0.153953	+	0.988078i
$70$	2.89796			0.346372
$71$	10.8997	−	9.44463i	1.29355	−	1.12087i	0.308023	−	0.951379i	$-0.400333\pi$
$71$	10.8997	−	9.44463i	1.29355	−	1.12087i	0.985531	−	0.169493i	$-0.0542130\pi$
$72$	−2.50680	−	1.64801i	−0.295429	−	0.194220i
$73$	−1.74133	+	12.1112i	−0.203807	+	1.41751i	0.589048	+	0.808098i	$0.299503\pi$
$73$	−1.74133	+	12.1112i	−0.203807	+	1.41751i	−0.792855	+	0.609411i	$0.791406\pi$
$74$	0.282700	−	0.619026i	0.0328632	−	0.0719603i
$75$	1.04516	−	1.38118i	0.120684	−	0.159484i
$76$	−0.0205032	+	0.0698275i	−0.00235188	+	0.00800976i
$77$	−0.624379	−	0.971553i	−0.0711546	−	0.110719i
$78$	−3.84258	−	1.45595i	−0.435086	−	0.164854i
$79$	−0.274710	−	0.935576i	−0.0309073	−	0.105260i	0.942595	−	0.333939i	$-0.108378\pi$
$79$	−0.274710	−	0.935576i	−0.0309073	−	0.105260i	−0.973502	+	0.228678i	$0.926560\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	6.03358	−	6.67802i	0.670397	−	0.742002i
$82$	4.13049	−	1.21282i	0.456136	−	0.133934i
$83$	−7.05627	−	15.4511i	−0.774526	−	1.69598i	−0.716424	−	0.697665i	$-0.754222\pi$
$83$	−7.05627	−	15.4511i	−0.774526	−	1.69598i	−0.0581018	−	0.998311i	$-0.518505\pi$
$84$	1.09238	−	4.89911i	0.119188	−	0.534536i
$85$	−3.30192	−	0.969530i	−0.358143	−	0.105160i
$86$	−0.623616	−	4.33734i	−0.0672462	−	0.467708i
$87$	4.97342	+	13.5485i	0.533207	+	1.45255i
$88$	0.394461	+	0.0567149i	0.0420497	+	0.00604583i
$89$	1.35490	+	0.870744i	0.143620	+	0.0922987i	0.610477	−	0.792034i	$-0.290978\pi$
$89$	1.35490	+	0.870744i	0.143620	+	0.0922987i	−0.466858	+	0.884332i	$0.654614\pi$
$90$	−1.94096	−	2.28750i	−0.204595	−	0.241124i
$91$		−	6.87519i		−	0.720716i
$92$	0.939832	−	4.70284i	0.0979843	−	0.490305i
$93$	11.5504	+	11.6709i	1.19772	+	1.21021i
$94$	−0.714442	−	0.824510i	−0.0736891	−	0.0850418i
$95$	−0.0393454	+	0.0612226i	−0.00403675	+	0.00628130i
$96$	1.03077	+	1.39194i	0.105203	+	0.142065i
$97$	−1.94916	−	0.890152i	−0.197907	−	0.0903813i	0.313996	−	0.949424i	$-0.398332\pi$
$97$	−1.94916	−	0.890152i	−0.197907	−	0.0903813i	−0.511903	+	0.859043i	$0.671059\pi$
$98$	1.38394	−	0.198981i	0.139799	−	0.0201001i
$99$	−0.348707	+	1.14357i	−0.0350463	+	0.114933i
$100$	−0.841254	+	0.540641i	−0.0841254	+	0.0540641i
$101$	1.29925	−	0.593348i	0.129280	−	0.0590403i	−0.349725	−	0.936853i	$-0.613725\pi$
$101$	1.29925	−	0.593348i	0.129280	−	0.0590403i	0.479005	+	0.877812i	$0.340998\pi$
$102$	−2.88367	+	5.21655i	−0.285526	+	0.516515i
$103$	−10.9267	−	9.46807i	−1.07664	−	0.932916i	−0.0786917	−	0.996899i	$-0.525074\pi$
$103$	−10.9267	−	9.46807i	−1.07664	−	0.932916i	−0.997951	+	0.0639828i	$0.979620\pi$
$104$	1.79296	+	1.55361i	0.175814	+	0.152344i
$105$	2.42837	−	4.39290i	0.236984	−	0.428703i
$106$	7.45026	−	3.40242i	0.723633	−	0.330472i
$107$	9.56528	−	6.14723i	0.924710	−	0.594275i	0.0106896	−	0.999943i	$-0.496597\pi$
$107$	9.56528	−	6.14723i	0.924710	−	0.594275i	0.914021	+	0.405668i	$0.132961\pi$
$108$	−4.59875	+	2.41899i	−0.442515	+	0.232768i
$109$	−8.51945	+	1.22491i	−0.816015	+	0.117325i	−0.537669	−	0.843156i	$-0.680695\pi$
$109$	−8.51945	+	1.22491i	−0.816015	+	0.117325i	−0.278346	+	0.960481i	$0.589786\pi$
$110$	0.362504	+	0.165550i	0.0345634	+	0.0157846i
$111$	−0.701466	−	0.947249i	−0.0665802	−	0.0899089i
$112$	−1.56676	+	2.43792i	−0.148044	+	0.230362i
$113$	−1.66529	−	1.92184i	−0.156657	−	0.180792i	0.671995	−	0.740555i	$-0.265437\pi$
$113$	−1.66529	−	1.92184i	−0.156657	−	0.180792i	−0.828652	+	0.559763i	$0.810892\pi$
$114$	0.0886678	+	0.0895924i	0.00830450	+	0.00839109i
$115$	2.22671	−	4.24756i	0.207641	−	0.396087i
$116$		−	8.33258i		−	0.773661i
$117$	−5.42693	+	4.60478i	−0.501720	+	0.425712i
$118$	−8.63839	−	5.55156i	−0.795228	−	0.511062i
$119$	−9.87128	−	1.41928i	−0.904899	−	0.130105i
$120$	0.596865	+	1.62596i	0.0544861	+	0.148429i
$121$	1.54286	+	10.7308i	0.140260	+	0.975531i
$122$	−9.55455	−	2.80547i	−0.865028	−	0.253995i
$123$	1.62271	−	7.27753i	0.146314	−	0.656193i
$124$	−3.93821	−	8.62347i	−0.353661	−	0.774410i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	−6.51099	−	5.76113i	−0.580045	−	0.513242i
$127$	6.52183	−	7.52659i	0.578719	−	0.667877i	−0.388610	−	0.921402i	$-0.627045\pi$
$127$	6.52183	−	7.52659i	0.578719	−	0.667877i	0.967329	+	0.253525i	$0.0815901\pi$
$128$	−0.281733	−	0.959493i	−0.0249019	−	0.0848080i
$129$	−7.09736	−	2.68919i	−0.624888	−	0.236770i
$130$	1.28263	+	1.99581i	0.112494	+	0.175044i
$131$	−1.18727	+	4.04347i	−0.103732	+	0.353279i	−0.994960	−	0.100277i	$-0.968027\pi$
$131$	−1.18727	+	4.04347i	−0.103732	+	0.353279i	0.891227	+	0.453557i	$0.149845\pi$
$132$	0.416513	−	0.550423i	0.0362528	−	0.0479081i
$133$	−0.0876111	+	0.191842i	−0.00759685	+	0.0166348i
$134$	1.17773	−	8.19128i	0.101740	−	0.707618i
$135$	−5.09397	+	1.02539i	−0.438420	+	0.0882515i
$136$	2.60077	−	2.25358i	0.223014	−	0.193243i
$137$	2.84078			0.242704			0.121352	−	0.992610i	$-0.461277\pi$
$137$	2.84078			0.242704			0.121352	+	0.992610i	$0.461277\pi$
$138$	−6.34131	−	5.36543i	−0.539808	−	0.456736i
$139$	0.628670			0.0533231			0.0266615	−	0.999645i	$-0.491512\pi$
$139$	0.628670			0.0533231			0.0266615	+	0.999645i	$0.491512\pi$
$140$	−2.19013	+	1.89776i	−0.185100	+	0.160390i
$141$	−1.84851	+	0.392090i	−0.155673	+	0.0330199i
$142$	−2.05251	+	14.2756i	−0.172243	+	1.19798i
$143$	0.392755	−	0.860014i	0.0328438	−	0.0719180i
$144$	2.97373	−	0.396120i	0.247811	−	0.0330100i
$145$	2.34756	−	7.99505i	0.194954	−	0.663953i
$146$	−6.61514	−	10.2934i	−0.547473	−	0.851885i
$147$	0.858056	−	2.26460i	0.0707713	−	0.186781i
$148$	0.191726	+	0.652957i	0.0157597	+	0.0536728i
$149$	−7.46190	+	8.61149i	−0.611303	+	0.705481i	−0.974031	−	0.226414i	$-0.927300\pi$
$149$	−7.46190	+	8.61149i	−0.611303	+	0.705481i	0.362728	+	0.931895i	$0.381845\pi$
$150$	0.114601	+	1.72826i	0.00935714	+	0.141111i
$151$	22.4886	−	6.60326i	1.83010	−	0.537365i	0.830298	−	0.557320i	$-0.188170\pi$
$151$	22.4886	−	6.60326i	1.83010	−	0.537365i	0.999801	+	0.0199545i	$0.00635212\pi$
$152$	−0.0302320	−	0.0661988i	−0.00245214	−	0.00536943i
$153$	5.49116	+	8.74248i	0.443934	+	0.706788i
$154$	1.10811	+	0.325369i	0.0892938	+	0.0262190i
$155$	−1.34917	−	9.38368i	−0.108368	−	0.753715i
$156$	3.85747	−	1.41602i	0.308845	−	0.113372i
$157$	−20.3150	−	2.92085i	−1.62131	−	0.233109i	−0.728994	−	0.684520i	$-0.760012\pi$
$157$	−20.3150	−	2.92085i	−1.62131	−	0.233109i	−0.892316	+	0.451411i	$0.850921\pi$
$158$	0.820284	+	0.527164i	0.0652583	+	0.0419389i
$159$	1.08541	−	14.1446i	0.0860784	−	1.12174i
$160$		−	1.00000i		−	0.0790569i
$161$	4.63543	−	13.1023i	0.365323	−	1.03261i
$162$	−0.186699	+	8.99806i	−0.0146685	+	0.706955i
$163$	1.83493	+	2.11763i	0.143723	+	0.165865i	0.823047	−	0.567973i	$-0.192272\pi$
$163$	1.83493	+	2.11763i	0.143723	+	0.165865i	−0.679324	+	0.733839i	$0.737727\pi$
$164$	−2.32739	+	3.62148i	−0.181738	+	0.282790i
$165$	0.554713	−	0.410781i	0.0431844	−	0.0319793i
$166$	15.4511	+	7.05627i	1.19924	+	0.547673i
$167$	−3.00840	+	0.432543i	−0.232797	+	0.0334712i	−0.257726	−	0.966218i	$-0.582973\pi$
$167$	−3.00840	+	0.432543i	−0.232797	+	0.0334712i	0.0249287	+	0.999689i	$0.492064\pi$
$168$	2.38267	+	4.41785i	0.183827	+	0.340845i
$169$	−6.20138	+	3.98539i	−0.477030	+	0.306568i
$170$	3.13033	−	1.42957i	0.240085	−	0.109643i
$171$	0.210109	−	0.0593334i	0.0160675	−	0.00453734i
$172$	3.31165	+	2.86956i	0.252511	+	0.218802i
$173$	2.41361	+	2.09141i	0.183504	+	0.159007i	0.741769	−	0.670656i	$-0.233987\pi$
$173$	2.41361	+	2.09141i	0.183504	+	0.159007i	−0.558265	+	0.829663i	$0.688533\pi$
$174$	−12.6310	−	6.98234i	−0.957555	−	0.529330i
$175$	−2.63608	+	1.20386i	−0.199269	+	0.0910030i
$176$	−0.335254	+	0.215455i	−0.0252707	+	0.0162405i
$177$	−15.6540	+	8.44262i	−1.17663	+	0.634586i
$178$	−1.59418	+	0.229209i	−0.119489	+	0.0171799i
$179$	0.698748	+	0.319108i	0.0522269	+	0.0238512i	0.441357	−	0.897331i	$-0.354497\pi$
$179$	0.698748	+	0.319108i	0.0522269	+	0.0238512i	−0.389130	+	0.921183i	$0.627224\pi$
$180$	2.96488	+	0.457723i	0.220989	+	0.0341167i
$181$	−8.16696	+	12.7080i	−0.607045	+	0.944581i	0.392645	+	0.919690i	$0.371560\pi$
$181$	−8.16696	+	12.7080i	−0.607045	+	0.944581i	−0.999690	+	0.0248905i	$0.992076\pi$
$182$	4.50229	+	5.19592i	0.333732	+	0.385148i
$183$	−12.2590	+	12.1325i	−0.906211	+	0.896859i
$184$	2.36943	+	4.16963i	0.174677	+	0.307389i
$185$			0.680523i			0.0500331i
$186$	−16.3720	−	1.25633i	−1.20045	−	0.0921185i
$187$	−1.15371	−	0.741447i	−0.0843680	−	0.0542200i
$188$	1.07988	+	0.155263i	0.0787583	+	0.0113237i
$189$	−14.1890	+	5.04216i	−1.03210	+	0.366763i
$190$	−0.0103570	−	0.0720347i	−0.000751377	−	0.00522594i
$191$	−19.2267	−	5.64547i	−1.39120	−	0.408492i	−0.501544	−	0.865132i	$-0.667234\pi$
$191$	−19.2267	−	5.64547i	−1.39120	−	0.408492i	−0.889651	+	0.456640i	$0.849053\pi$
$192$	−1.69054	−	0.376947i	−0.122004	−	0.0272038i
$193$	−7.35552	−	16.1063i	−0.529462	−	1.15936i	−0.965731	−	0.259543i	$-0.916428\pi$
$193$	−7.35552	−	16.1063i	−0.529462	−	1.15936i	0.436270	−	0.899816i	$-0.356299\pi$
$194$	2.05600	−	0.603697i	0.147612	−	0.0433429i
$195$	4.10016	−	0.271883i	0.293618	−	0.0194699i
$196$	−0.915608	+	1.05667i	−0.0654006	+	0.0754763i
$197$	2.39108	+	8.14327i	0.170357	+	0.580184i	0.999768	+	0.0215445i	$0.00685837\pi$
$197$	2.39108	+	8.14327i	0.170357	+	0.580184i	−0.829410	+	0.558640i	$0.811323\pi$
$198$	−0.485343	−	1.09261i	−0.0344918	−	0.0776481i
$199$	−3.08514	−	4.80058i	−0.218700	−	0.340304i	0.714516	−	0.699619i	$-0.246647\pi$
$199$	−3.08514	−	4.80058i	−0.218700	−	0.340304i	−0.933216	+	0.359315i	$0.883010\pi$
$200$	0.281733	−	0.959493i	0.0199215	−	0.0678464i
$201$	−11.4299	−	8.64920i	−0.806205	−	0.610068i
$202$	−0.593348	+	1.29925i	−0.0417478	+	0.0914150i
$203$	3.43655	−	23.9017i	0.241198	−	1.67757i
$204$	−1.23678	−	5.83081i	−0.0865917	−	0.408238i
$205$	−3.25340	+	2.81909i	−0.227227	+	0.196894i
$206$	14.4581			1.00735
$207$	−13.4470	+	5.11653i	−0.934629	+	0.355623i
$208$	−2.37242			−0.164498
$209$	−0.0219184	+	0.0189924i	−0.00151613	+	0.00131373i
$210$	1.04150	+	4.91017i	0.0718704	+	0.338834i
$211$	2.32174	−	16.1480i	0.159835	−	1.11168i	−0.739101	−	0.673595i	$-0.764749\pi$
$211$	2.32174	−	16.1480i	0.159835	−	1.11168i	0.898936	−	0.438081i	$-0.144342\pi$
$212$	−3.40242	+	7.45026i	−0.233679	+	0.511686i
$213$	19.9198	+	15.0736i	1.36488	+	1.03283i
$214$	−3.20337	+	10.9097i	−0.218978	+	0.745771i
$215$	2.36906	+	3.68633i	0.161568	+	0.251405i
$216$	1.89140	−	4.83969i	0.128693	−	0.329299i
$217$	−7.74008	−	26.3603i	−0.525431	−	1.78945i
$218$	5.63642	−	6.50478i	0.381747	−	0.440559i
$219$	−21.1465	+	1.40223i	−1.42895	+	0.0947540i
$220$	−0.382375	+	0.112275i	−0.0257797	+	0.00756960i
$221$	−3.39156	−	7.42647i	−0.228141	−	0.499558i
$222$	1.15045	+	0.256521i	0.0772131	+	0.0172166i
$223$	−11.1066	−	3.26120i	−0.743754	−	0.218386i	−0.112165	−	0.993690i	$-0.535779\pi$
$223$	−11.1066	−	3.26120i	−0.743754	−	0.218386i	−0.631589	+	0.775304i	$0.717597\pi$
$224$	−0.412423	−	2.86846i	−0.0275562	−	0.191657i
$225$	2.71582	+	1.27448i	0.181055	+	0.0849656i
$226$	2.51708	+	0.361901i	0.167434	+	0.0240733i
$227$	16.5844	+	10.6581i	1.10074	+	0.707405i	0.959257	−	0.282535i	$-0.0911754\pi$
$227$	16.5844	+	10.6581i	1.10074	+	0.707405i	0.141487	+	0.989940i	$0.454812\pi$
$228$	−0.125681	−	0.00964432i	−0.00832344	−	0.000638711i
$229$			12.4569i			0.823176i	0.911370	+	0.411588i	$0.135026\pi$
$229$			12.4569i			0.823176i	−0.911370	+	0.411588i	$0.864974\pi$
$230$	1.09873	+	4.66828i	0.0724481	+	0.307817i
$231$	1.42176	−	1.40709i	0.0935449	−	0.0925796i
$232$	5.45668	+	6.29734i	0.358249	+	0.413441i
$233$	−3.62652	+	5.64298i	−0.237581	+	0.369684i	−0.939486	−	0.342587i	$-0.888697\pi$
$233$	−3.62652	+	5.64298i	−0.237581	+	0.369684i	0.701905	+	0.712271i	$0.252333\pi$
$234$	1.08591	−	7.03395i	0.0709884	−	0.459823i
$235$	0.992394	+	0.453211i	0.0647366	+	0.0295642i
$236$	10.1640	−	1.46136i	0.661617	−	0.0951262i
$237$	1.48647	−	0.801693i	0.0965565	−	0.0520756i
$238$	8.38964	−	5.39170i	0.543820	−	0.349492i
$239$	−19.1664	+	8.75299i	−1.23977	+	0.566184i	−0.923905	−	0.382621i	$-0.875021\pi$
$239$	−19.1664	+	8.75299i	−1.23977	+	0.566184i	−0.315864	+	0.948805i	$0.602294\pi$
$240$	−1.51586	−	0.837957i	−0.0978483	−	0.0540899i
$241$	14.5992	+	12.6503i	0.940419	+	0.814878i	0.982885	−	0.184220i	$-0.0589759\pi$
$241$	14.5992	+	12.6503i	0.940419	+	0.814878i	−0.0424657	+	0.999098i	$0.513521\pi$
$242$	−8.19322	−	7.09947i	−0.526680	−	0.456371i
$243$	13.4833	+	7.82300i	0.864957	+	0.501846i
$244$	9.05803	−	4.13667i	0.579881	−	0.264823i
$245$	−1.17622	+	0.755909i	−0.0751458	+	0.0482933i
$246$	3.53941	+	6.56263i	0.225664	+	0.418418i
$247$	−0.170897	+	0.0245713i	−0.0108739	+	0.00156343i
$248$	8.62347	+	3.93821i	0.547591	+	0.250076i
$249$	23.6436	−	17.5088i	1.49835	−	1.10958i
$250$	0.540641	−	0.841254i	0.0341931	−	0.0532055i
$251$	−10.8428	−	12.5133i	−0.684394	−	0.789832i	0.302162	−	0.953256i	$-0.402292\pi$
$251$	−10.8428	−	12.5133i	−0.684394	−	0.789832i	−0.986556	+	0.163424i	$0.947746\pi$
$252$	8.69341	+	0.0901794i	0.547634	+	0.00568077i
$253$	1.32833	−	1.37416i	0.0835115	−	0.0863924i
$254$			9.95911i			0.624890i
$255$	0.456049	−	5.94306i	0.0285589	−	0.372169i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	11.9710	+	1.72117i	0.746730	+	0.107364i	0.505167	−	0.863022i	$-0.331431\pi$
$257$	11.9710	+	1.72117i	0.746730	+	0.107364i	0.241563	+	0.970385i	$0.422340\pi$
$258$	7.12488	−	2.61543i	0.443575	−	0.162830i
$259$	0.280663	+	1.95206i	0.0174396	+	0.121295i
$260$	−2.27633	−	0.668389i	−0.141172	−	0.0414517i
$261$	−21.1685	+	13.2959i	−1.31030	+	0.822998i
$262$	−1.75063	−	3.83335i	−0.108154	−	0.236825i
$263$	−7.89391	+	2.31786i	−0.486759	+	0.142925i	−0.515898	−	0.856650i	$-0.672542\pi$
$263$	−7.89391	+	2.31786i	−0.486759	+	0.142925i	0.0291389	+	0.999575i	$0.490723\pi$
$264$	0.0456705	+	0.688740i	0.00281083	+	0.0423890i
$265$	−5.36358	+	6.18990i	−0.329482	+	0.380242i
$266$	−0.0594175	−	0.202357i	−0.00364312	−	0.0124073i
$267$	−0.988409	+	2.60863i	−0.0604896	+	0.159645i
$268$	4.47408	+	6.96180i	0.273298	+	0.425260i
$269$	−1.83023	+	6.23320i	−0.111591	+	0.380045i	−0.996284	−	0.0861299i	$-0.972550\pi$
$269$	−1.83023	+	6.23320i	−0.111591	+	0.380045i	0.884693	+	0.466175i	$0.154368\pi$
$270$	3.17828	−	4.11078i	0.193424	−	0.250174i
$271$	2.77349	−	6.07310i	0.168478	−	0.368915i	−0.806494	−	0.591242i	$-0.798638\pi$
$271$	2.77349	−	6.07310i	0.168478	−	0.368915i	0.974972	+	0.222327i	$0.0713652\pi$
$272$	−0.489750	+	3.40629i	−0.0296955	+	0.206536i
$273$	11.6490	−	2.47088i	0.705031	−	0.149545i
$274$	−2.14692	+	1.86031i	−0.129700	+	0.112386i
$275$	−0.398517			−0.0240315
$276$	8.30605	−	0.0977500i	0.499965	−	0.00588386i
$277$	8.31559			0.499635			0.249818	−	0.968293i	$-0.419629\pi$
$277$	8.31559			0.499635			0.249818	+	0.968293i	$0.419629\pi$
$278$	−0.475117	+	0.411691i	−0.0284956	+	0.0246916i
$279$	−15.6235	+	23.7649i	−0.935352	+	1.42277i
$280$	0.412423	−	2.86846i	0.0246470	−	0.171423i
$281$	−4.51109	+	9.87791i	−0.269109	+	0.589267i	−0.995148	−	0.0983866i	$-0.968632\pi$
$281$	−4.51109	+	9.87791i	−0.269109	+	0.589267i	0.726039	+	0.687653i	$0.241359\pi$
$282$	1.14025	−	1.50684i	0.0679008	−	0.0897310i
$283$	−1.17168	+	3.99036i	−0.0696489	+	0.237202i	−0.986959	−	0.160971i	$-0.948537\pi$
$283$	−1.17168	+	3.99036i	−0.0696489	+	0.237202i	0.917310	+	0.398173i	$0.130356\pi$
$284$	−7.79731	−	12.1329i	−0.462685	−	0.719952i
$285$	−0.117873	−	0.0446621i	−0.00698220	−	0.00264556i
$286$	0.266365	+	0.907155i	0.0157505	+	0.0536412i
$287$	−8.16960	+	9.42822i	−0.482236	+	0.556530i
$288$	−1.98799	+	2.24675i	−0.117144	+	0.132391i
$289$	4.94845	−	1.45300i	0.291086	−	0.0854704i
$290$	3.46148	+	7.57958i	0.203265	+	0.445088i
$291$	0.807722	−	3.62248i	0.0473495	−	0.212354i
$292$	11.7401	+	3.44721i	0.687038	+	0.201733i
$293$	3.41836	+	23.7752i	0.199703	+	1.38896i	0.805147	+	0.593075i	$0.202086\pi$
$293$	3.41836	+	23.7752i	0.199703	+	1.38896i	−0.605444	+	0.795888i	$0.707004\pi$
$294$	0.834520	+	2.27338i	0.0486702	+	0.132586i
$295$	10.1640	+	1.46136i	0.591769	+	0.0850835i
$296$	−0.572493	−	0.367919i	−0.0332755	−	0.0213848i
$297$	−2.06293	−	0.179845i	−0.119703	−	0.0104356i
$298$		−	11.3946i		−	0.660074i
$299$	11.0751	−	2.60665i	0.640491	−	0.150747i
$300$	−1.21838	−	1.23108i	−0.0703430	−	0.0710765i
$301$	8.31588	+	9.59704i	0.479320	+	0.553164i
$302$	−12.6716	+	19.7173i	−0.729166	+	1.13460i
$303$	1.47228	+	1.98815i	0.0845804	+	0.114216i
$304$	0.0661988	+	0.0302320i	0.00379676	+	0.00173392i
$305$	9.85655	−	1.41716i	0.564385	−	0.0811463i
$306$	−9.87504	−	3.01118i	−0.564519	−	0.172138i
$307$	−4.63429	+	2.97828i	−0.264493	+	0.169979i	−0.666165	−	0.745804i	$-0.732065\pi$
$307$	−4.63429	+	2.97828i	−0.264493	+	0.169979i	0.401672	+	0.915783i	$0.368429\pi$
$308$	−1.05052	+	0.479758i	−0.0598591	+	0.0273367i
$309$	12.1153	−	21.9165i	0.689215	−	1.24679i
$310$	7.16464	+	6.20819i	0.406924	+	0.352602i
$311$	−0.184214	−	0.159622i	−0.0104458	−	0.00905134i	0.649622	−	0.760257i	$-0.274927\pi$
$311$	−0.184214	−	0.159622i	−0.0104458	−	0.00905134i	−0.660068	+	0.751206i	$0.729473\pi$
$312$	−1.98799	+	3.59626i	−0.112548	+	0.203598i
$313$	10.3063	−	4.70673i	0.582547	−	0.266040i	−0.102268	−	0.994757i	$-0.532610\pi$
$313$	10.3063	−	4.70673i	0.582547	−	0.266040i	0.684815	+	0.728717i	$0.259883\pi$
$314$	17.2658	−	11.0960i	0.974364	−	0.626186i
$315$	8.31586	+	2.53574i	0.468546	+	0.142873i
$316$	−0.965148	+	0.138767i	−0.0542938	+	0.00780627i
$317$	24.9179	+	11.3796i	1.39953	+	0.639142i	0.965176	−	0.261601i	$-0.0842506\pi$
$317$	24.9179	+	11.3796i	1.39953	+	0.639142i	0.434351	+	0.900744i	$0.356978\pi$
$318$	8.44246	+	11.4006i	0.473430	+	0.639313i
$319$	1.79529	−	2.79353i	0.100517	−	0.156408i
$320$	0.654861	+	0.755750i	0.0366078	+	0.0422477i
$321$	13.8533	+	13.9977i	0.773214	+	0.781276i
$322$	5.07697	+	12.9376i	0.282928	+	0.720986i
$323$			0.250443i			0.0139350i
$324$	−5.75138	−	6.92254i	−0.319521	−	0.384586i
$325$	−1.99581	−	1.28263i	−0.110708	−	0.0711475i
$326$	−2.77350	−	0.398769i	−0.153610	−	0.0220858i
$327$	−5.13725	−	13.9947i	−0.284090	−	0.773911i
$328$	−0.612646	−	4.26105i	−0.0338277	−	0.235277i
$329$	3.03356	+	0.890733i	0.167246	+	0.0491077i
$330$	−0.150220	+	0.673708i	−0.00826933	+	0.0370864i
$331$	1.72585	+	3.77908i	0.0948613	+	0.207717i	0.951114	−	0.308840i	$-0.0999407\pi$
$331$	1.72585	+	3.77908i	0.0948613	+	0.207717i	−0.856253	+	0.516557i	$0.827213\pi$
$332$	−16.2980	+	4.78553i	−0.894470	+	0.262640i
$333$	1.35288	−	1.52896i	0.0741372	−	0.0837867i
$334$	1.99034	−	2.29698i	0.108907	−	0.125685i
$335$	2.33148	+	7.94029i	0.127382	+	0.433824i
$336$	−4.69378	−	1.77847i	−0.256067	−	0.0970237i
$337$	−2.67315	−	4.15950i	−0.145616	−	0.226582i	0.760782	−	0.649007i	$-0.224815\pi$
$337$	−2.67315	−	4.15950i	−0.145616	−	0.226582i	−0.906398	+	0.422425i	$0.861179\pi$
$338$	2.07682	−	7.07300i	0.112964	−	0.384720i
$339$	2.65780	−	3.51228i	0.144352	−	0.190761i
$340$	−1.42957	+	3.13033i	−0.0775295	+	0.169766i
$341$	0.537667	−	3.73956i	0.0291163	−	0.202508i
$342$	−0.119935	+	0.182433i	−0.00648533	+	0.00986487i
$343$	12.2687	−	10.6309i	0.662450	−	0.574016i
$344$	−4.38195			−0.236259
$345$	7.99713	+	2.24629i	0.430551	+	0.120936i
$346$	−3.19367			−0.171693
$347$	−11.9780	+	10.3790i	−0.643011	+	0.557172i	−0.914154	−	0.405367i	$-0.867144\pi$
$347$	−11.9780	+	10.3790i	−0.643011	+	0.557172i	0.271143	+	0.962539i	$0.412598\pi$
$348$	14.1183	−	2.99465i	0.756823	−	0.160530i
$349$	4.89244	−	34.0277i	0.261886	−	1.82146i	−0.256765	−	0.966474i	$-0.582657\pi$
$349$	4.89244	−	34.0277i	0.261886	−	1.82146i	0.518651	−	0.854986i	$-0.326434\pi$
$350$	1.20386	−	2.63608i	0.0643488	−	0.140904i
$351$	−9.75252	−	7.54023i	−0.520551	−	0.402468i
$352$	0.112275	−	0.382375i	0.00598429	−	0.0203806i
$353$	6.02018	+	9.36758i	0.320422	+	0.498586i	0.963679	−	0.267065i	$-0.0860537\pi$
$353$	6.02018	+	9.36758i	0.320422	+	0.498586i	−0.643257	+	0.765650i	$0.722417\pi$
$354$	6.30175	−	16.6317i	0.334934	−	0.883964i
$355$	−4.06325	−	13.8381i	−0.215655	−	0.734453i
$356$	1.05470	−	1.21719i	0.0558992	−	0.0645111i
$357$	−1.14289	−	17.2355i	−0.0604883	−	0.912201i
$358$	−0.737050	+	0.216417i	−0.0389543	+	0.0114380i
$359$	10.2022	+	22.3398i	0.538454	+	1.17905i	0.961969	+	0.273160i	$0.0880689\pi$
$359$	10.2022	+	22.3398i	0.538454	+	1.17905i	−0.423515	+	0.905889i	$0.639204\pi$
$360$	−2.54045	+	1.59566i	−0.133893	+	0.0840985i
$361$	−18.2253	−	5.35143i	−0.959226	−	0.281654i
$362$	−2.14982	−	14.9523i	−0.112992	−	0.785876i
$363$	−17.6274	+	6.47072i	−0.925196	+	0.339625i
$364$	−6.80521	−	0.978442i	−0.356690	−	0.0512843i
$365$	10.2934	+	6.61514i	0.538779	+	0.346252i
$366$	1.31964	−	17.1970i	0.0689787	−	0.898904i
$367$		−	7.86407i		−	0.410501i	−0.978709	−	0.205251i	$-0.934199\pi$
$367$		−	7.86407i		−	0.410501i	0.978709	−	0.205251i	$-0.0658009\pi$
$368$	−4.52122	−	1.59955i	−0.235685	−	0.0833823i
$369$	12.9139	+	0.133960i	0.672271	+	0.00697367i
$370$	−0.445648	−	0.514305i	−0.0231681	−	0.0267375i
$371$	−12.8324	+	19.9676i	−0.666223	+	1.03666i
$372$	13.1959	−	9.77191i	0.684173	−	0.506650i
$373$	−7.75848	−	3.54318i	−0.401719	−	0.183459i	0.204301	−	0.978908i	$-0.434508\pi$
$373$	−7.75848	−	3.54318i	−0.401719	−	0.183459i	−0.606020	+	0.795449i	$0.707235\pi$
$374$	1.35746	−	0.195174i	0.0701928	−	0.0100922i
$375$	−0.822188	−	1.52447i	−0.0424576	−	0.0787233i
$376$	−0.917794	+	0.589830i	−0.0473316	+	0.0304182i
$377$	17.9820	−	8.21210i	0.926120	−	0.422945i
$378$	7.42140	−	13.1024i	0.381716	−	0.673916i
$379$	13.8543	+	12.0048i	0.711646	+	0.616645i	0.933560	−	0.358422i	$-0.116685\pi$
$379$	13.8543	+	12.0048i	0.711646	+	0.616645i	−0.221914	+	0.975066i	$0.571230\pi$
$380$	0.0550000	+	0.0476578i	0.00282144	+	0.00244479i
$381$	15.0966	+	8.34530i	0.773422	+	0.427543i
$382$	18.2276	−	8.32425i	0.932604	−	0.425906i
$383$	−29.9809	+	19.2675i	−1.53195	+	0.984525i	−0.542436	+	0.840097i	$0.682498\pi$
$383$	−29.9809	+	19.2675i	−1.53195	+	0.984525i	−0.989515	+	0.144428i	$0.953866\pi$
$384$	1.52447	−	0.822188i	0.0777953	−	0.0419571i
$385$	−1.14313	+	0.164358i	−0.0582594	+	0.00837644i
$386$	16.1063	+	7.35552i	0.819791	+	0.374386i
$387$	2.00572	−	12.9919i	0.101956	−	0.660417i
$388$	−1.15849	+	1.80264i	−0.0588132	+	0.0915152i
$389$	13.6299	+	15.7298i	0.691066	+	0.797532i	0.987516	−	0.157516i	$-0.0503485\pi$
$389$	13.6299	+	15.7298i	0.691066	+	0.797532i	−0.296451	+	0.955048i	$0.595803\pi$
$390$	−2.92065	+	2.89051i	−0.147893	+	0.146366i
$391$	−1.45630	−	16.4396i	−0.0736482	−	0.831385i
$392$		−	1.39817i		−	0.0706184i
$393$	−7.27776	−	0.558469i	−0.367115	−	0.0281710i
$394$	−7.13977	−	4.58845i	−0.359696	−	0.231163i
$395$	−0.965148	−	0.138767i	−0.0485619	−	0.00698214i
$396$	1.08230	+	0.507904i	0.0543877	+	0.0255231i
$397$	0.504598	+	3.50956i	0.0253250	+	0.176140i	0.998558	−	0.0536806i	$-0.0170953\pi$
$397$	0.504598	+	3.50956i	0.0253250	+	0.176140i	−0.973233	+	0.229820i	$0.926186\pi$
$398$	5.47531	+	1.60769i	0.274452	+	0.0805865i
$399$	−0.356534	−	0.0794982i	−0.0178490	−	0.00397989i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	−18.0117	+	5.28872i	−0.899462	+	0.264106i	−0.698599	−	0.715513i	$-0.746193\pi$
$401$	−18.0117	+	5.28872i	−0.899462	+	0.264106i	−0.200863	+	0.979619i	$0.564375\pi$
$402$	14.3022	−	0.948383i	0.713328	−	0.0473010i
$403$	14.7285	−	16.9976i	0.733677	−	0.846709i
$404$	−0.402406	−	1.37047i	−0.0200204	−	0.0681834i
$405$	−3.56810	−	8.26248i	−0.177300	−	0.410566i
$406$	13.0551	+	20.3142i	0.647915	+	1.00817i
$407$	−0.0764060	+	0.260215i	−0.00378730	+	0.0128984i
$408$	4.75306	+	3.59671i	0.235312	+	0.178064i
$409$	−10.4737	+	22.9342i	−0.517890	+	1.13402i	0.452342	+	0.891845i	$0.350589\pi$
$409$	−10.4737	+	22.9342i	−0.517890	+	1.13402i	−0.970232	+	0.242177i	$0.922139\pi$
$410$	0.612646	−	4.26105i	0.0302564	−	0.210438i
$411$	1.02095	+	4.81328i	0.0503597	+	0.237422i
$412$	−10.9267	+	9.46807i	−0.538321	+	0.466458i
$413$	29.7576			1.46428
$414$	6.81193	−	12.6727i	0.334788	−	0.622830i
$415$	−16.9861			−0.833813
$416$	1.79296	−	1.55361i	0.0879071	−	0.0761719i
$417$	0.225938	+	1.06519i	0.0110642	+	0.0521626i
$418$	0.00412745	−	0.0287071i	0.000201880	−	0.00140411i
$419$	5.75720	−	12.6065i	0.281258	−	0.615869i	−0.715296	−	0.698822i	$-0.753708\pi$
$419$	5.75720	−	12.6065i	0.281258	−	0.615869i	0.996553	+	0.0829534i	$0.0264353\pi$
$420$	−4.00259	−	3.02882i	−0.195307	−	0.147791i
$421$	−2.05202	+	6.98853i	−0.100009	+	0.340600i	−0.994263	−	0.106959i	$-0.965889\pi$
$421$	−2.05202	+	6.98853i	−0.100009	+	0.340600i	0.894254	+	0.447560i	$0.147707\pi$
$422$	8.82006	+	13.7243i	0.429354	+	0.668087i
$423$	−1.32868	−	2.99112i	−0.0646025	−	0.145433i
$424$	−2.30751	−	7.85864i	−0.112062	−	0.381649i
$425$	−2.25358	+	2.60077i	−0.109315	+	0.126156i
$426$	−24.9255	+	1.65282i	−1.20764	+	0.0800793i
$427$	27.6887	−	8.13013i	1.33995	−	0.393445i
$428$	−4.72338	−	10.3428i	−0.228313	−	0.499936i
$429$	1.59832	+	0.356385i	0.0771677	+	0.0172064i
$430$	−4.20445	−	1.23454i	−0.202756	−	0.0595347i
$431$	4.56291	+	31.7357i	0.219788	+	1.52866i	0.738820	+	0.673902i	$0.235383\pi$
$431$	4.56291	+	31.7357i	0.219788	+	1.52866i	−0.519033	+	0.854754i	$0.673708\pi$
$432$	1.73990	+	4.89620i	0.0837110	+	0.235568i
$433$	−35.9787	−	5.17295i	−1.72903	−	0.248596i	−0.795206	−	0.606340i	$-0.792637\pi$
$433$	−35.9787	−	5.17295i	−1.72903	−	0.248596i	−0.933820	+	0.357743i	$0.883546\pi$
$434$	23.1119	+	14.8531i	1.10941	+	0.712972i
$435$	14.3901	+	1.10425i	0.689955	+	0.0529446i
$436$			8.60705i			0.412203i
$437$	−0.342251	−	0.0683967i	−0.0163721	−	0.00327186i
$438$	15.0632	−	14.9077i	0.719747	−	0.712320i
$439$	16.8545	+	19.4512i	0.804423	+	0.928354i	0.998615	−	0.0526097i	$-0.0167539\pi$
$439$	16.8545	+	19.4512i	0.804423	+	0.928354i	−0.194192	+	0.980964i	$0.562208\pi$
$440$	0.215455	−	0.335254i	0.0102714	−	0.0159826i
$441$	4.14541	+	0.639976i	0.197400	+	0.0304750i
$442$	7.42647	+	3.39156i	0.353241	+	0.161320i
$443$	5.32405	−	0.765483i	0.252953	−	0.0363692i	−0.0146717	−	0.999892i	$-0.504670\pi$
$443$	5.32405	−	0.765483i	0.252953	−	0.0363692i	0.267625	+	0.963523i	$0.413761\pi$
$444$	−1.03744	+	0.559518i	−0.0492346	+	0.0265536i
$445$	1.35490	−	0.870744i	0.0642286	−	0.0412772i
$446$	10.5294	−	4.80864i	0.498584	−	0.227696i
$447$	−17.2727	−	9.54821i	−0.816969	−	0.451615i
$448$	2.19013	+	1.89776i	0.103474	+	0.0896607i
$449$	−12.6228	−	10.9377i	−0.595708	−	0.516184i	0.304002	−	0.952671i	$-0.401677\pi$
$449$	−12.6228	−	10.9377i	−0.595708	−	0.516184i	−0.899710	+	0.436487i	$0.856222\pi$
$450$	−2.88709	+	0.815294i	−0.136099	+	0.0384333i
$451$	−1.56053	+	0.712671i	−0.0734825	+	0.0335584i
$452$	−2.13928	+	1.37483i	−0.100623	+	0.0646666i
$453$	19.2705	+	35.7306i	0.905406	+	1.67877i
$454$	−19.5132	+	2.80558i	−0.915801	+	0.131672i
$455$	−6.25390	−	2.85606i	−0.293187	−	0.133894i
$456$	0.101299	−	0.0750150i	0.00474377	−	0.00351290i
$457$	−17.3640	+	27.0190i	−0.812256	+	1.26390i	0.149165	+	0.988812i	$0.452342\pi$
$457$	−17.3640	+	27.0190i	−0.812256	+	1.26390i	−0.961421	+	0.275083i	$0.911295\pi$
$458$	−8.15755	−	9.41431i	−0.381177	−	0.439902i
$459$	−12.8394	+	12.4459i	−0.599291	+	0.580926i
$460$	−3.88743	−	2.80853i	−0.181253	−	0.130948i
$461$		−	11.1460i		−	0.519119i	−0.965727	−	0.259559i	$-0.916423\pi$
$461$		−	11.1460i		−	0.519119i	0.965727	−	0.259559i	$-0.0835774\pi$
$462$	−0.153048	+	1.99446i	−0.00712042	+	0.0927907i
$463$	−30.9917	−	19.9172i	−1.44031	−	0.925629i	−0.999609	−	0.0279745i	$-0.991094\pi$
$463$	−30.9917	−	19.9172i	−1.44031	−	0.925629i	−0.440699	−	0.897655i	$-0.645269\pi$
$464$	−8.24777	−	1.18585i	−0.382893	−	0.0550517i
$465$	15.4144	−	5.65838i	0.714826	−	0.262401i
$466$	−0.954623	−	6.63955i	−0.0442221	−	0.307571i
$467$	−6.57804	−	1.93149i	−0.304395	−	0.0893785i	0.125968	−	0.992034i	$-0.459796\pi$
$467$	−6.57804	−	1.93149i	−0.304395	−	0.0893785i	−0.430363	+	0.902656i	$0.641615\pi$
$468$	3.78558	+	6.02702i	0.174988	+	0.278599i
$469$	9.96252	+	21.8149i	0.460026	+	1.00732i
$470$	−1.04679	+	0.307366i	−0.0482849	+	0.0141777i
$471$	−2.35206	−	35.4705i	−0.108377	−	1.63439i
$472$	−6.72442	+	7.76040i	−0.309517	+	0.357201i
$473$	0.491984	+	1.67554i	0.0226215	+	0.0770416i
$474$	−0.598401	+	1.57931i	−0.0274855	+	0.0725401i
$475$	0.0393454	+	0.0612226i	0.00180529	+	0.00280908i
$476$	−2.80966	+	9.56882i	−0.128781	+	0.438586i
$477$	24.3561	−	3.24439i	1.11519	−	0.148550i
$478$	8.75299	−	19.1664i	0.400352	−	0.876649i
$479$	−0.0539474	+	0.375212i	−0.00246492	+	0.0171439i	−0.991017	−	0.133738i	$-0.957302\pi$
$479$	−0.0539474	+	0.375212i	−0.00246492	+	0.0171439i	0.988552	+	0.150881i	$0.0482112\pi$
$480$	1.69435	−	0.359391i	0.0773364	−	0.0164039i
$481$	−1.22015	+	1.05727i	−0.0556341	+	0.0482072i
$482$	−19.3176			−0.879891
$483$	23.8659	+	3.14521i	1.08594	+	0.143112i
$484$	10.8412			0.492781
$485$	−1.61942	+	1.40324i	−0.0735342	+	0.0637177i
$486$	−15.3130	+	2.91749i	−0.694612	+	0.132340i
$487$	−3.46330	+	24.0878i	−0.156937	+	1.09152i	0.747299	+	0.664488i	$0.231350\pi$
$487$	−3.46330	+	24.0878i	−0.156937	+	1.09152i	−0.904236	+	0.427033i	$0.859559\pi$
$488$	−4.13667	+	9.05803i	−0.187258	+	0.410038i
$489$	−2.92855	+	3.87008i	−0.132434	+	0.175011i
$490$	0.393911	−	1.34154i	0.0177951	−	0.0606044i
$491$	7.70396	+	11.9876i	0.347675	+	0.540993i	0.970417	−	0.241434i	$-0.0776178\pi$
$491$	7.70396	+	11.9876i	0.347675	+	0.540993i	−0.622742	+	0.782427i	$0.713981\pi$
$492$	−6.97252	−	2.64189i	−0.314345	−	0.119106i
$493$	−8.07869	−	27.5135i	−0.363846	−	1.23914i
$494$	0.113064	−	0.130483i	0.00508701	−	0.00587072i
$495$	0.895368	+	0.792250i	0.0402438	+	0.0356090i
$496$	−9.09616	+	2.67087i	−0.408430	+	0.119926i
$497$	−17.3624	−	38.0184i	−0.778812	−	1.70536i
$498$	−6.40284	+	28.7156i	−0.286918	+	1.28677i
$499$	3.38386	+	0.993592i	0.151483	+	0.0444793i	0.356595	−	0.934259i	$-0.383938\pi$
$499$	3.38386	+	0.993592i	0.151483	+	0.0444793i	−0.205112	+	0.978738i	$0.565756\pi$
$500$	0.142315	+	0.989821i	0.00636451	+	0.0442662i
$501$	−1.81408	−	4.94185i	−0.0810469	−	0.220786i
$502$	16.3889	+	2.35637i	0.731474	+	0.105170i
$503$	16.1327	+	10.3678i	0.719321	+	0.462279i	0.848401	−	0.529355i	$-0.177566\pi$
$503$	16.1327	+	10.3678i	0.719321	+	0.462279i	−0.129080	+	0.991634i	$0.541202\pi$
$504$	−6.62910	+	5.62482i	−0.295283	+	0.250549i
$505$		−	1.42833i		−	0.0635597i
$506$	−0.104006	+	1.90839i	−0.00462362	+	0.0848383i
$507$	−8.98138	−	9.07503i	−0.398877	−	0.403036i
$508$	−6.52183	−	7.52659i	−0.289359	−	0.333938i
$509$	−17.0881	+	26.5896i	−0.757416	+	1.17856i	0.221672	+	0.975121i	$0.428849\pi$
$509$	−17.0881	+	26.5896i	−0.757416	+	1.17856i	−0.979087	+	0.203440i	$0.934788\pi$
$510$	3.54722	+	4.79011i	0.157073	+	0.212110i
$511$	32.2544	+	14.7301i	1.42685	+	0.651620i
$512$	−0.989821	+	0.142315i	−0.0437443	+	0.00628949i
$513$	0.176043	+	0.334676i	0.00777250	+	0.0147763i
$514$	−10.1742	+	6.53856i	−0.448765	+	0.288404i
$515$	−13.1516	+	6.00613i	−0.579528	+	0.264662i
$516$	−3.67188	+	6.64241i	−0.161646	+	0.292416i
$517$	0.328582	+	0.284718i	0.0144510	+	0.0125219i
$518$	−1.49044	−	1.29147i	−0.0654860	−	0.0567439i
$519$	−2.67616	+	4.84115i	−0.117470	+	0.212503i
$520$	2.15803	−	0.985541i	0.0946360	−	0.0432188i
$521$	25.9419	−	16.6718i	1.13653	−	0.730406i	0.169620	−	0.985510i	$-0.445746\pi$
$521$	25.9419	−	16.6718i	1.13653	−	0.730406i	0.966914	+	0.255104i	$0.0821097\pi$
$522$	7.29109	−	23.9108i	0.319122	−	1.04655i
$523$	−13.9455	+	2.00506i	−0.609793	+	0.0876749i	−0.440291	−	0.897855i	$-0.645125\pi$
$523$	−13.9455	+	2.00506i	−0.609793	+	0.0876749i	−0.169501	+	0.985530i	$0.554216\pi$
$524$	3.83335	+	1.75063i	0.167460	+	0.0764766i
$525$	−2.98714	−	4.03379i	−0.130370	−	0.176049i
$526$	4.44794	−	6.92113i	0.193939	−	0.301776i
$527$	−21.3643	−	24.6558i	−0.930645	−	1.07402i
$528$	−0.485544	−	0.490607i	−0.0211306	−	0.0213509i
$529$	22.8638	+	2.49954i	0.994077	+	0.108676i
$530$		−	8.19041i		−	0.355769i
$531$	−19.9307	−	23.4892i	−0.864918	−	1.01934i
$532$	0.177421	+	0.114021i	0.00769216	+	0.00494345i
$533$	−10.1090	−	1.45346i	−0.437870	−	0.0629562i
$534$	−0.961297	−	2.61874i	−0.0415994	−	0.113324i
$535$	−1.61816	−	11.2545i	−0.0699591	−	0.486576i
$536$	−7.94029	−	2.33148i	−0.342968	−	0.100705i
$537$	−0.289558	+	1.29861i	−0.0124953	+	0.0560392i
$538$	−2.69868	−	5.90928i	−0.116348	−	0.254767i
$539$	−0.534626	+	0.156980i	−0.0230280	+	0.00676162i
$540$	0.290005	+	5.18805i	0.0124798	+	0.223258i
$541$	−25.0730	+	28.9358i	−1.07797	+	1.24405i	−0.109750	+	0.993959i	$0.535005\pi$
$541$	−25.0730	+	28.9358i	−1.07797	+	1.24405i	−0.968223	+	0.250088i	$0.919541\pi$
$542$	1.88097	+	6.40600i	0.0807946	+	0.275161i
$543$	−24.4670	−	9.27057i	−1.04998	−	0.397838i
$544$	−1.86051	−	2.89502i	−0.0797689	−	0.124123i
$545$	−2.42489	+	8.25841i	−0.103871	+	0.353751i
$546$	−7.18565	+	9.49585i	−0.307518	+	0.406385i
$547$	−15.8710	+	34.7527i	−0.678597	+	1.48592i	0.185526	+	0.982639i	$0.440601\pi$
$547$	−15.8710	+	34.7527i	−0.678597	+	1.48592i	−0.864123	+	0.503281i	$0.832126\pi$
$548$	0.404285	−	2.81186i	0.0172702	−	0.120117i
$549$	−24.9625	−	16.4108i	−1.06537	−	0.700395i
$550$	0.301179	−	0.260973i	0.0128423	−	0.0111279i
$551$	−0.606407			−0.0258338
$552$	−6.21328	+	5.51318i	−0.264455	+	0.234657i
$553$	−2.82572			−0.120162
$554$	−6.28450	+	5.44555i	−0.267003	+	0.231359i
$555$	−1.15305	+	0.244574i	−0.0489442	+	0.0103816i
$556$	0.0894690	−	0.622271i	0.00379433	−	0.0263902i
$557$	−0.811133	+	1.77613i	−0.0343688	+	0.0752572i	−0.926038	−	0.377431i	$-0.876808\pi$
$557$	−0.811133	+	1.77613i	−0.0343688	+	0.0752572i	0.891669	+	0.452688i	$0.149535\pi$
$558$	−3.75529	−	28.1915i	−0.158974	−	1.19344i
$559$	−2.92885	+	9.97473i	−0.123877	+	0.421886i
$560$	1.56676	+	2.43792i	0.0662075	+	0.103021i
$561$	0.841640	−	2.22127i	0.0355341	−	0.0937821i
$562$	−3.05940	−	10.4194i	−0.129053	−	0.439514i
$563$	−16.2425	+	18.7448i	−0.684539	+	0.790001i	−0.986577	−	0.163295i	$-0.947788\pi$
$563$	−16.2425	+	18.7448i	−0.684539	+	0.790001i	0.302038	+	0.953296i	$0.402333\pi$
$564$	0.125028	+	1.88550i	0.00526463	+	0.0793938i
$565$	−2.43996	+	0.716436i	−0.102650	+	0.0301407i
$566$	−1.72764	−	3.78300i	−0.0726180	−	0.159011i
$567$	−13.6426	−	22.2291i	−0.572936	−	0.933533i
$568$	13.8381	+	4.06325i	0.580636	+	0.170490i
$569$	3.71564	+	25.8429i	0.155768	+	1.08339i	0.906324	+	0.422583i	$0.138877\pi$
$569$	3.71564	+	25.8429i	0.155768	+	1.08339i	−0.750556	+	0.660807i	$0.770214\pi$
$570$	0.118330	−	0.0434371i	0.00495630	−	0.00181938i
$571$	37.8829	+	5.44674i	1.58535	+	0.227939i	0.877907	−	0.478832i	$-0.158940\pi$
$571$	37.8829	+	5.44674i	1.58535	+	0.227939i	0.707443	+	0.706771i	$0.249849\pi$
$572$	−0.795365	−	0.511150i	−0.0332559	−	0.0213723i
$573$	2.65552	−	34.6058i	0.110936	−	1.44568i
$574$		−	12.4753i		−	0.520710i
$575$	−2.93871	−	3.78998i	−0.122553	−	0.158053i
$576$	0.0311182	−	2.99984i	0.00129659	−	0.124993i
$577$	19.2325	+	22.1955i	0.800659	+	0.924010i	0.998417	−	0.0562408i	$-0.0179114\pi$
$577$	19.2325	+	22.1955i	0.800659	+	0.924010i	−0.197758	+	0.980251i	$0.563366\pi$
$578$	−2.78828	+	4.33865i	−0.115977	+	0.180464i
$579$	24.6463	−	18.2513i	1.02427	−	0.758499i
$580$	−7.57958	−	3.46148i	−0.314725	−	0.143730i
$581$	−48.7239	+	7.00544i	−2.02141	+	0.290635i
$582$	1.76179	+	3.26664i	0.0730284	+	0.135406i
$583$	−2.74587	+	1.76466i	−0.113722	+	0.0730849i
$584$	−11.1300	+	5.08291i	−0.460564	+	0.210332i
$585$	1.93422	+	6.84941i	0.0799704	+	0.283188i
$586$	−18.1529	−	15.7296i	−0.749889	−	0.649782i
$587$	−9.65596	−	8.36694i	−0.398544	−	0.345341i	0.432414	−	0.901675i	$-0.357662\pi$
$587$	−9.65596	−	8.36694i	−0.398544	−	0.345341i	−0.830958	+	0.556335i	$0.812207\pi$
$588$	−2.11943	−	1.17161i	−0.0874039	−	0.0483163i
$589$	−0.627576	+	0.286605i	−0.0258588	+	0.0118093i
$590$	−8.63839	+	5.55156i	−0.355637	+	0.228554i
$591$	−12.9383	+	6.97796i	−0.532209	+	0.287035i
$592$	0.673597	−	0.0968486i	0.0276846	−	0.00398045i
$593$	−0.150557	−	0.0687573i	−0.00618265	−	0.00282352i	0.412321	−	0.911039i	$-0.364718\pi$
$593$	−0.150557	−	0.0687573i	−0.00618265	−	0.00282352i	−0.418504	+	0.908215i	$0.637445\pi$
$594$	1.67683	−	1.21502i	0.0688013	−	0.0498527i
$595$	−5.39170	+	8.38964i	−0.221038	+	0.343942i
$596$	7.46190	+	8.61149i	0.305651	+	0.352741i
$597$	7.02511	−	6.95261i	0.287519	−	0.284552i
$598$	−6.66303	+	9.22265i	−0.272472	+	0.377142i
$599$		−	31.1799i		−	1.27398i	−0.770874	−	0.636988i	$-0.780180\pi$
$599$		−	31.1799i		−	1.27398i	0.770874	−	0.636988i	$-0.219820\pi$
$600$	1.72697	+	0.132522i	0.0705034	+	0.00541018i
$601$	−34.2880	−	22.0355i	−1.39863	−	0.898848i	−0.398800	−	0.917038i	$-0.630573\pi$
$601$	−34.2880	−	22.0355i	−1.39863	−	0.898848i	−0.999835	+	0.0181899i	$0.994210\pi$
$602$	−12.5694	−	1.80721i	−0.512293	−	0.0736565i
$603$	10.5470	−	22.4748i	0.429507	−	0.915245i
$604$	−3.33558	−	23.1995i	−0.135723	−	0.943973i
$605$	10.4020	+	3.05431i	0.422903	+	0.124176i
$606$	−2.41464	−	0.538403i	−0.0980879	−	0.0218711i
$607$	−18.8225	−	41.2156i	−0.763983	−	1.67289i	−0.739470	−	0.673190i	$-0.764924\pi$
$607$	−18.8225	−	41.2156i	−0.763983	−	1.67289i	−0.0245131	−	0.999700i	$-0.507804\pi$
$608$	−0.0698275	+	0.0205032i	−0.00283188	+	0.000831515i
$609$	41.7330	−	2.76733i	1.69111	−	0.112138i
$610$	−6.52104	+	7.52569i	−0.264029	+	0.304706i
$611$	0.729202	+	2.48343i	0.0295003	+	0.100469i
$612$	9.43497	−	4.19108i	0.381386	−	0.169414i
$613$	14.2953	+	22.2440i	0.577383	+	0.898425i	0.999969	−	0.00789781i	$-0.00251398\pi$
$613$	14.2953	+	22.2440i	0.577383	+	0.898425i	−0.422586	+	0.906323i	$0.638878\pi$
$614$	1.55201	−	5.28565i	0.0626339	−	0.213311i
$615$	−5.94578	−	4.49926i	−0.239757	−	0.181428i
$616$	0.479758	−	1.05052i	0.0193300	−	0.0423268i
$617$	4.63337	−	32.2258i	0.186532	−	1.29736i	−0.654370	−	0.756175i	$-0.727066\pi$
$617$	4.63337	−	32.2258i	0.186532	−	1.29736i	0.840902	−	0.541187i	$-0.182025\pi$
$618$	5.19612	+	24.4972i	0.209019	+	0.985422i
$619$	18.6664	−	16.1745i	0.750264	−	0.650108i	−0.193359	−	0.981128i	$-0.561938\pi$
$619$	18.6664	−	16.1745i	0.750264	−	0.650108i	0.943624	+	0.331020i	$0.107393\pi$
$620$	−9.48017			−0.380733
$621$	−13.5019	−	20.9451i	−0.541814	−	0.840498i
$622$	0.243750			0.00977347
$623$	3.52738	−	3.05649i	0.141321	−	0.122456i
$624$	−0.852628	−	4.01973i	−0.0341324	−	0.160918i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−4.70673	+	10.3063i	−0.188119	+	0.411923i
$627$	−0.0400572	−	0.0303119i	−0.00159973	−	0.00121054i
$628$	−5.78224	+	19.6925i	−0.230736	+	0.785816i
$629$	1.26612	+	1.97013i	0.0504836	+	0.0785541i
$630$	−7.94527	+	3.52934i	−0.316547	+	0.140612i
$631$	−1.48402	−	5.05412i	−0.0590781	−	0.201201i	0.924665	−	0.380780i	$-0.124345\pi$
$631$	−1.48402	−	5.05412i	−0.0590781	−	0.201201i	−0.983744	+	0.179579i	$0.942526\pi$
$632$	0.638537	−	0.736911i	0.0253996	−	0.0293127i
$633$	28.1949	−	1.86961i	1.12065	−	0.0743104i
$634$	−26.2837	+	7.71760i	−1.04386	+	0.306505i
$635$	−4.13716	−	9.05912i	−0.164178	−	0.359500i
$636$	−13.8462	−	3.08735i	−0.549037	−	0.122421i
$637$	−3.18270	−	0.934524i	−0.126103	−	0.0370272i
$638$	0.472582	+	3.28688i	0.0187097	+	0.130129i
$639$	−18.3811	+	39.1685i	−0.727143	+	1.54948i
$640$	−0.989821	−	0.142315i	−0.0391261	−	0.00562549i
$641$	7.23157	+	4.64745i	0.285630	+	0.183563i	0.675608	−	0.737261i	$-0.263881\pi$
$641$	7.23157	+	4.64745i	0.285630	+	0.183563i	−0.389978	+	0.920824i	$0.627517\pi$
$642$	−19.6361	−	1.50681i	−0.774977	−	0.0594689i
$643$			29.1270i			1.14866i	0.818624	+	0.574329i	$0.194737\pi$
$643$			29.1270i			1.14866i	−0.818624	+	0.574329i	$0.805263\pi$
$644$	−12.3093	−	6.45290i	−0.485053	−	0.254280i
$645$	−5.39453	+	5.33886i	−0.212409	+	0.210217i
$646$	−0.164005	−	0.189272i	−0.00645270	−	0.00744681i
$647$	25.9096	−	40.3161i	1.01861	−	1.58499i	0.227065	−	0.973880i	$-0.427087\pi$
$647$	25.9096	−	40.3161i	1.01861	−	1.58499i	0.791546	−	0.611110i	$-0.209277\pi$
$648$	8.87991	+	1.46536i	0.348836	+	0.0575647i
$649$	3.72237	+	1.69995i	0.146116	+	0.0667288i
$650$	2.34828	−	0.337631i	0.0921070	−	0.0132430i
$651$	41.8820	−	22.5881i	1.64148	−	0.885298i
$652$	2.35721	−	1.51489i	0.0923155	−	0.0593276i
$653$	−12.4039	+	5.66468i	−0.485402	+	0.221676i	−0.643057	−	0.765818i	$-0.722334\pi$
$653$	−12.4039	+	5.66468i	−0.485402	+	0.221676i	0.157654	+	0.987494i	$0.449607\pi$
$654$	13.0471	+	7.21234i	0.510181	+	0.282025i
$655$	3.18486	+	2.75970i	0.124443	+	0.107830i
$656$	3.25340	+	2.81909i	0.127024	+	0.110067i
$657$	−9.97574	−	35.3257i	−0.389191	−	1.37819i
$658$	−2.87592	+	1.31339i	−0.112115	+	0.0512012i
$659$	30.5843	−	19.6553i	1.19140	−	0.765664i	0.213949	−	0.976845i	$-0.431367\pi$
$659$	30.5843	−	19.6553i	1.19140	−	0.765664i	0.977447	+	0.211181i	$0.0677311\pi$
$660$	−0.327656	−	0.607527i	−0.0127540	−	0.0236480i
$661$	−35.3062	+	5.07626i	−1.37325	+	0.197444i	−0.789132	−	0.614224i	$-0.789469\pi$
$661$	−35.3062	+	5.07626i	−1.37325	+	0.197444i	−0.584120	+	0.811667i	$0.698560\pi$
$662$	−3.77908	−	1.72585i	−0.146878	−	0.0670770i
$663$	11.3642	−	8.41550i	0.441348	−	0.326831i
$664$	9.18336	−	14.2896i	0.356384	−	0.554544i
$665$	0.138110	+	0.159388i	0.00535569	+	0.00618079i
$666$	−0.0211767	+	2.04146i	−0.000820580	+	0.0791050i
$667$	39.8058	−	3.52619i	1.54129	−	0.136535i
$668$			3.03934i			0.117596i
$669$	1.53401	−	19.9906i	0.0593081	−	0.772881i
$670$	−6.96180	−	4.47408i	−0.268958	−	0.172849i
$671$	3.92801	+	0.564762i	0.151639	+	0.0218024i
$672$	4.71197	−	1.72969i	0.181768	−	0.0667243i
$673$	−0.608820	−	4.23444i	−0.0234683	−	0.163226i	0.974717	−	0.223443i	$-0.0717297\pi$
$673$	−0.608820	−	4.23444i	−0.0234683	−	0.163226i	−0.998185	+	0.0602174i	$0.980821\pi$
$674$	4.74412	+	1.39300i	0.182737	+	0.0536563i
$675$	−1.18339	+	5.05960i	−0.0455486	+	0.194744i
$676$	3.06227	+	6.70544i	0.117780	+	0.257902i
$677$	20.9432	−	6.14948i	0.804913	−	0.236344i	0.146706	−	0.989180i	$-0.453133\pi$
$677$	20.9432	−	6.14948i	0.804913	−	0.236344i	0.658208	+	0.752836i	$0.271315\pi$
$678$	0.291426	+	4.39489i	0.0111922	+	0.168785i
$679$	−4.06652	+	4.69302i	−0.156059	+	0.180102i
$680$	−0.969530	−	3.30192i	−0.0371798	−	0.126623i
$681$	−12.0984	+	31.9303i	−0.463611	+	1.22357i
$682$	2.04255	+	3.17827i	0.0782132	+	0.121702i
$683$	7.96073	−	27.1118i	0.304609	−	1.03740i	−0.654898	−	0.755717i	$-0.727288\pi$
$683$	7.96073	−	27.1118i	0.304609	−	1.03740i	0.959507	−	0.281685i	$-0.0908934\pi$
$684$	−0.0288278	−	0.216415i	−0.00110226	−	0.00827482i
$685$	1.18010	−	2.58406i	0.0450893	−	0.0987319i
$686$	−2.31032	+	16.0686i	−0.0882085	+	0.613503i
$687$	−21.1064	+	4.47690i	−0.805261	+	0.170805i
$688$	3.31165	−	2.86956i	0.126256	−	0.109401i
$689$	−19.4311			−0.740267
$690$	−7.51484	+	3.53937i	−0.286085	+	0.134742i
$691$	22.8914			0.870830			0.435415	−	0.900230i	$-0.356602\pi$
$691$	22.8914			0.870830			0.435415	+	0.900230i	$0.356602\pi$
$692$	2.41361	−	2.09141i	0.0917519	−	0.0795035i
$693$	2.89507	+	1.90327i	0.109975	+	0.0722992i
$694$	2.25557	−	15.6878i	0.0856201	−	0.595501i
$695$	0.261159	−	0.571858i	0.00990632	−	0.0216918i
$696$	−8.70885	+	11.5088i	−0.330108	+	0.436238i
$697$	−4.17370	+	14.2143i	−0.158090	+	0.538405i
$698$	18.5859	+	28.9203i	0.703488	+	1.09465i
$699$	−10.8646	−	4.11658i	−0.410935	−	0.155703i
$700$	0.816450	+	2.78057i	0.0308589	+	0.105096i
$701$	−14.1950	+	16.3819i	−0.536139	+	0.618737i	−0.957597	−	0.288111i	$-0.906973\pi$
$701$	−14.1950	+	16.3819i	−0.536139	+	0.618737i	0.421459	+	0.906848i	$0.361518\pi$
$702$	12.3083	−	0.688014i	0.464546	−	0.0259674i
$703$	0.0475192	−	0.0139529i	0.00179222	−	0.000526244i
$704$	0.165550	+	0.362504i	0.00623940	+	0.0136624i
$705$	−0.411243	+	1.84435i	−0.0154883	+	0.0694621i
$706$	−10.6842	−	3.13716i	−0.402105	−	0.118069i
$707$	−0.589074	−	4.09710i	−0.0221544	−	0.154087i
$708$	6.12889	+	16.6962i	0.230338	+	0.627480i
$709$	−1.72653	−	0.248237i	−0.0648411	−	0.00932275i	0.109818	−	0.993952i	$-0.464973\pi$
$709$	−1.72653	−	0.248237i	−0.0648411	−	0.00932275i	−0.174659	+	0.984629i	$0.555882\pi$
$710$	12.1329	+	7.79731i	0.455338	+	0.292628i
$711$	1.89258	+	2.23048i	0.0709772	+	0.0836497i
$712$			1.61058i			0.0603589i
$713$	39.5288	−	22.4626i	1.48037	−	0.841231i
$714$	12.1506	+	12.2773i	0.454725	+	0.459467i
$715$	−0.619140	−	0.714525i	−0.0231545	−	0.0267217i
$716$	0.415302	−	0.646222i	0.0155206	−	0.0241505i
$717$	−21.7189	−	29.3289i	−0.811107	−	1.09531i
$718$	−22.3398	−	10.2022i	−0.833714	−	0.380744i
$719$	−14.5517	+	2.09222i	−0.542687	+	0.0780266i	−0.408207	−	0.912890i	$-0.633846\pi$
$719$	−14.5517	+	2.09222i	−0.542687	+	0.0780266i	−0.134481	+	0.990916i	$0.542937\pi$
$720$	0.875010	−	2.86956i	0.0326097	−	0.106942i
$721$	−35.2478	+	22.6524i	−1.31270	+	0.843618i
$722$	17.2782	−	7.89069i	0.643028	−	0.293661i
$723$	−16.1873	+	29.2827i	−0.602011	+	1.08903i
$724$	11.4164	+	9.89237i	0.424287	+	0.367647i
$725$	−6.29734	−	5.45668i	−0.233878	−	0.202656i
$726$	9.08444	−	16.4337i	0.337155	−	0.609912i
$727$	22.4093	−	10.2340i	0.831117	−	0.379558i	0.0460268	−	0.998940i	$-0.485344\pi$
$727$	22.4093	−	10.2340i	0.831117	−	0.379558i	0.785090	+	0.619382i	$0.212617\pi$
$728$	5.78378	−	3.71701i	0.214361	−	0.137762i
$729$	−8.40914	+	25.6571i	−0.311450	+	0.950263i
$730$	−12.1112	+	1.74133i	−0.448256	+	0.0644495i
$731$	13.7169	+	6.26431i	0.507339	+	0.231694i
$732$	10.2644	+	13.8608i	0.379381	+	0.512311i
$733$	−0.482471	+	0.750740i	−0.0178205	+	0.0277292i	−0.850050	−	0.526703i	$-0.823428\pi$
$733$	−0.482471	+	0.750740i	−0.0178205	+	0.0277292i	0.832229	+	0.554432i	$0.187064\pi$
$734$	5.14987	+	5.94327i	0.190085	+	0.219370i
$735$	−1.70350	−	1.72126i	−0.0628346	−	0.0634897i
$736$	4.46439	−	1.75191i	0.164560	−	0.0645763i
$737$			3.29793i			0.121481i
$738$	−9.84740	+	8.35557i	−0.362488	+	0.307573i
$739$	−6.34819	−	4.07973i	−0.233522	−	0.150075i	0.418647	−	0.908149i	$-0.362504\pi$
$739$	−6.34819	−	4.07973i	−0.233522	−	0.150075i	−0.652169	+	0.758074i	$0.726141\pi$
$740$	0.673597	+	0.0968486i	0.0247619	+	0.00356022i
$741$	−0.103051	−	0.280729i	−0.00378568	−	0.0103128i
$742$	−3.37791	−	23.4939i	−0.124007	−	0.862488i
$743$	−6.08347	−	1.78627i	−0.223181	−	0.0655318i	0.168230	−	0.985748i	$-0.446195\pi$
$743$	−6.08347	−	1.78627i	−0.223181	−	0.0655318i	−0.391411	+	0.920216i	$0.628013\pi$
$744$	−3.57352	+	16.0266i	−0.131012	+	0.587563i
$745$	4.73350	+	10.3649i	0.173422	+	0.379742i
$746$	8.18376	−	2.40297i	0.299629	−	0.0879789i
$747$	38.1634	+	33.7682i	1.39633	+	1.23551i
$748$	−0.898091	+	1.03645i	−0.0328375	+	0.0378965i
$749$	−9.28325	−	31.6158i	−0.339203	−	1.15522i
$750$	1.61968	+	0.613698i	0.0591425	+	0.0224091i
$751$	−0.288256	−	0.448535i	−0.0105186	−	0.0163673i	0.835954	−	0.548799i	$-0.184915\pi$
$751$	−0.288256	−	0.448535i	−0.0105186	−	0.0163673i	−0.846473	+	0.532432i	$0.821278\pi$
$752$	0.307366	−	1.04679i	0.0112085	−	0.0381725i
$753$	17.3051	−	22.8688i	0.630635	−	0.833384i
$754$	−8.21210	+	17.9820i	−0.299067	+	0.654865i
$755$	3.33558	−	23.1995i	0.121394	−	0.844315i
$756$	2.97154	+	14.7621i	0.108074	+	0.536894i
$757$	8.58371	−	7.43783i	0.311980	−	0.270333i	−0.484769	−	0.874642i	$-0.661096\pi$
$757$	8.58371	−	7.43783i	0.311980	−	0.270333i	0.796750	+	0.604310i	$0.206551\pi$
$758$	−18.3318			−0.665842
$759$	2.80570	+	1.75681i	0.101840	+	0.0637680i
$760$	−0.0727754			−0.00263984
$761$	−27.3360	+	23.6868i	−0.990928	+	0.858644i	−0.989959	−	0.141355i	$-0.954854\pi$
$761$	−27.3360	+	23.6868i	−0.990928	+	0.858644i	−0.000969211		1.00000i	$0.500309\pi$
$762$	−16.8743	+	3.57921i	−0.611290	+	0.129661i
$763$	−3.54974	+	24.6890i	−0.128509	+	0.893802i
$764$	−8.32425	+	18.2276i	−0.301161	+	0.659450i
$765$	10.2335	−	1.36317i	0.369995	−	0.0492856i
$766$	10.0405	−	34.1947i	0.362777	−	1.23551i
$767$	13.1707	+	20.4939i	0.475565	+	0.739993i
$768$	−0.613698	+	1.61968i	−0.0221449	+	0.0584453i
$769$	−10.5457	−	35.9153i	−0.380288	−	1.29514i	−0.898155	−	0.439679i	$-0.855092\pi$
$769$	−10.5457	−	35.9153i	−0.380288	−	1.29514i	0.517867	−	0.855461i	$-0.326726\pi$
$770$	0.756290	−	0.872806i	0.0272548	−	0.0314537i
$771$	1.38600	+	20.9017i	0.0499155	+	0.752756i
$772$	−16.9892	+	4.98848i	−0.611454	+	0.179539i
$773$	−7.24984	−	15.8749i	−0.260759	−	0.570982i	0.733290	−	0.679916i	$-0.237984\pi$
$773$	−7.24984	−	15.8749i	−0.260759	−	0.570982i	−0.994049	+	0.108934i	$0.965256\pi$
$774$	6.99208	+	11.1321i	0.251325	+	0.400135i
$775$	−9.09616	−	2.67087i	−0.326744	−	0.0959406i
$776$	−0.304953	−	2.12099i	−0.0109472	−	0.0761392i
$777$	−3.20661	+	1.17709i	−0.115036	+	0.0422280i
$778$	−20.6017	−	2.96207i	−0.738605	−	0.106195i
$779$	0.263555	+	0.169376i	0.00944283	+	0.00606854i
$780$	0.314398	−	4.09712i	0.0112572	−	0.146700i
$781$		−	5.74756i		−	0.205664i
$782$	11.8662	+	11.4705i	0.424336	+	0.410185i
$783$	−30.1358	−	31.0885i	−1.07697	−	1.11101i
$784$	0.915608	+	1.05667i	0.0327003	+	0.0377382i
$785$	−11.0960	+	17.2658i	−0.396035	+	0.616242i
$786$	5.86589	−	4.34386i	0.209229	−	0.154940i
$787$	−11.7446	−	5.36356i	−0.418648	−	0.191190i	0.194942	−	0.980815i	$-0.437548\pi$
$787$	−11.7446	−	5.36356i	−0.418648	−	0.191190i	−0.613590	+	0.789625i	$0.710275\pi$
$788$	8.40067	−	1.20783i	0.299262	−	0.0430273i
$789$	−6.76428	−	12.5421i	−0.240815	−	0.446509i
$790$	0.820284	−	0.527164i	0.0291844	−	0.0187557i
$791$	−6.70345	+	3.06136i	−0.238347	+	0.108850i
$792$	−1.15056	+	0.324909i	−0.0408832	+	0.0115451i
$793$	17.8541	+	15.4707i	0.634019	+	0.549380i
$794$	−2.67962	−	2.32190i	−0.0950962	−	0.0824013i
$795$	−12.4155	−	6.86321i	−0.440333	−	0.243413i
$796$	−5.19078	+	2.37055i	−0.183982	+	0.0840219i
$797$	41.3493	−	26.5736i	1.46467	−	0.941285i	0.466274	−	0.884640i	$-0.345596\pi$
$797$	41.3493	−	26.5736i	1.46467	−	0.941285i	0.998394	−	0.0566453i	$-0.0180404\pi$
$798$	0.321511	−	0.173400i	0.0113814	−	0.00613828i
$799$	3.71620	−	0.534309i	0.131470	−	0.0189025i
$800$	−0.909632	−	0.415415i	−0.0321603	−	0.0146871i
$801$	−4.77516	−	0.737198i	−0.168722	−	0.0260476i
$802$	10.1490	−	15.7921i	0.358373	−	0.557639i
$803$	3.19320	+	3.68515i	0.112686	+	0.130046i
$804$	−10.1878	+	10.0827i	−0.359297	+	0.355589i
$805$	−9.99266	−	9.65944i	−0.352195	−	0.340450i
$806$			22.4910i			0.792212i
$807$	−11.2190	−	0.860907i	−0.394928	−	0.0303054i
$808$	1.20158	+	0.772211i	0.0422716	+	0.0271663i
$809$	13.1991	+	1.89774i	0.464054	+	0.0667209i	0.370377	−	0.928882i	$-0.379229\pi$
$809$	13.1991	+	1.89774i	0.464054	+	0.0667209i	0.0936777	+	0.995603i	$0.470138\pi$
$810$	8.10737	+	3.90776i	0.284864	+	0.137305i
$811$	6.77762	+	47.1394i	0.237994	+	1.65529i	0.661908	+	0.749585i	$0.269747\pi$
$811$	6.77762	+	47.1394i	0.237994	+	1.65529i	−0.423914	+	0.905703i	$0.639344\pi$
$812$	−23.1693	−	6.80313i	−0.813085	−	0.238743i
$813$	11.2868	+	2.51666i	0.395844	+	0.0882632i
$814$	−0.112661	−	0.246692i	−0.00394875	−	0.00864657i
$815$	2.68852	−	0.789421i	0.0941747	−	0.0276522i
$816$	−5.94747	+	0.394378i	−0.208203	+	0.0138060i
$817$	0.208834	−	0.241007i	0.00730617	−	0.00843176i
$818$	−7.10320	−	24.1913i	−0.248358	−	0.845828i
$819$	8.37310	+	18.8496i	0.292580	+	0.658657i
$820$	2.32739	+	3.62148i	0.0812758	+	0.126468i
$821$	3.22359	−	10.9785i	0.112504	−	0.383154i	−0.883921	−	0.467636i	$-0.845106\pi$
$821$	3.22359	−	10.9785i	0.112504	−	0.383154i	0.996425	+	0.0844829i	$0.0269238\pi$
$822$	−3.92361	−	2.96906i	−0.136852	−	0.103558i
$823$	−21.0170	+	46.0209i	−0.732607	+	1.60419i	0.0627384	+	0.998030i	$0.480017\pi$
$823$	−21.0170	+	46.0209i	−0.732607	+	1.60419i	−0.795346	+	0.606156i	$0.792711\pi$
$824$	2.05761	−	14.3110i	0.0716801	−	0.498546i
$825$	−0.143224	−	0.675230i	−0.00498640	−	0.0235085i
$826$	−22.4893	+	19.4871i	−0.782504	+	0.678043i
$827$	−10.3830			−0.361053			−0.180527	−	0.983570i	$-0.557780\pi$
$827$	−10.3830			−0.361053			−0.180527	+	0.983570i	$0.557780\pi$
$828$	3.15074	+	14.0383i	0.109496	+	0.487863i
$829$	27.9560			0.970953			0.485477	−	0.874250i	$-0.338646\pi$
$829$	27.9560			0.970953			0.485477	+	0.874250i	$0.338646\pi$
$830$	12.8372	−	11.1235i	0.445586	−	0.386103i
$831$	2.98855	+	14.0896i	0.103672	+	0.488761i
$832$	−0.337631	+	2.34828i	−0.0117053	+	0.0814119i
$833$	−1.99879	+	4.37674i	−0.0692540	+	0.151645i
$834$	−0.868304	−	0.657058i	−0.0300669	−	0.0227521i
$835$	−0.856281	+	2.91623i	−0.0296328	+	0.100920i
$836$	0.0156798	+	0.0243983i	0.000542297	+	0.000843831i
$837$	−45.8811	−	17.9308i	−1.58588	−	0.619778i
$838$	3.90451	+	13.2975i	0.134879	+	0.459356i
$839$	22.9630	−	26.5007i	0.792770	−	0.914905i	−0.205192	−	0.978722i	$-0.565782\pi$
$839$	22.9630	−	26.5007i	0.792770	−	0.914905i	0.997962	+	0.0638165i	$0.0203272\pi$
$840$	5.00841	−	0.332110i	0.172807	−	0.0114589i
$841$	38.7941	−	11.3910i	1.33773	−	0.392793i
$842$	−3.02570	−	6.62537i	−0.104273	−	0.228325i
$843$	−18.3579	−	4.09336i	−0.632281	−	0.140983i
$844$	−15.6532	−	4.59621i	−0.538807	−	0.158208i
$845$	1.04909	+	7.29657i	0.0360897	+	0.251010i
$846$	2.96292	+	1.39044i	0.101867	+	0.0478044i
$847$	31.0975	+	4.47115i	1.06852	+	0.153631i
$848$	6.89021	+	4.42807i	0.236611	+	0.152061i
$849$	−7.18218	−	0.551134i	−0.246492	−	0.0189149i
$850$		−	3.44131i		−	0.118036i
$851$	−3.03812	+	1.19222i	−0.104146	+	0.0408686i
$852$	17.7551	−	17.5719i	0.608279	−	0.602002i
$853$	−1.85823	−	2.14451i	−0.0636244	−	0.0734265i	0.723045	−	0.690801i	$-0.242742\pi$
$853$	−1.85823	−	2.14451i	−0.0636244	−	0.0734265i	−0.786670	+	0.617374i	$0.788196\pi$
$854$	−15.6016	+	24.2766i	−0.533876	+	0.830727i
$855$	0.0333110	−	0.215770i	0.00113921	−	0.00737918i
$856$	10.3428	+	4.72338i	0.353508	+	0.161442i
$857$	−57.6061	+	8.28251i	−1.96779	+	0.282925i	−0.968341	+	0.249631i	$0.919691\pi$
$857$	−57.6061	+	8.28251i	−1.96779	+	0.282925i	−0.999446	+	0.0332937i	$0.989400\pi$
$858$	−1.44131	+	0.777340i	−0.0492056	+	0.0265379i
$859$	44.6347	−	28.6850i	1.52292	−	0.978719i	0.531633	−	0.846975i	$-0.321579\pi$
$859$	44.6347	−	28.6850i	1.52292	−	0.978719i	0.991284	−	0.131744i	$-0.0420578\pi$
$860$	3.98596	−	1.82033i	0.135920	−	0.0620726i
$861$	−18.9108	−	10.4538i	−0.644480	−	0.356264i
$862$	−24.2309	−	20.9962i	−0.825308	−	0.715133i
$863$	−1.03633	−	0.897989i	−0.0352772	−	0.0305679i	0.637044	−	0.770828i	$-0.280157\pi$
$863$	−1.03633	−	0.897989i	−0.0352772	−	0.0305679i	−0.672321	+	0.740260i	$0.734703\pi$
$864$	−4.52126	−	2.56091i	−0.153816	−	0.0871238i
$865$	2.90506	−	1.32670i	0.0987752	−	0.0451091i
$866$	30.5784	−	19.6516i	1.03910	−	0.667788i
$867$	4.24032	+	7.86224i	0.144009	+	0.267016i
$868$	−27.1935	+	3.90984i	−0.923008	+	0.132709i
$869$	−0.353468	−	0.161423i	−0.0119906	−	0.00547591i
$870$	−11.5985	+	8.58901i	−0.393225	+	0.291195i
$871$	−10.6144	+	16.5163i	−0.359656	+	0.559635i
$872$	−5.63642	−	6.50478i	−0.190873	−	0.220280i
$873$	6.42806	+	0.0666802i	0.217557	+	0.00225678i
$874$	0.303446	−	0.172436i	0.0102642	−	0.00583274i
$875$			2.89796i			0.0979689i
$876$	−1.62150	+	21.1308i	−0.0547855	+	0.713944i
$877$	39.5237	+	25.4003i	1.33462	+	0.857708i	0.996516	−	0.0834007i	$-0.0265781\pi$
$877$	39.5237	+	25.4003i	1.33462	+	0.857708i	0.338104	+	0.941109i	$0.390215\pi$
$878$	−25.4756	−	3.66284i	−0.859761	−	0.123615i
$879$	−39.0551	+	14.3365i	−1.31730	+	0.483559i
$880$	0.0567149	+	0.394461i	0.00191186	+	0.0132973i
$881$	21.3081	+	6.25661i	0.717887	+	0.210791i	0.620219	−	0.784429i	$-0.287044\pi$
$881$	21.3081	+	6.25661i	0.717887	+	0.210791i	0.0976674	+	0.995219i	$0.468862\pi$
$882$	−3.55199	+	2.23100i	−0.119602	+	0.0751218i
$883$	−3.95640	−	8.66331i	−0.133143	−	0.291544i	0.831304	−	0.555818i	$-0.187595\pi$
$883$	−3.95640	−	8.66331i	−0.133143	−	0.291544i	−0.964448	+	0.264274i	$0.914868\pi$
$884$	−7.83355	+	2.30014i	−0.263471	+	0.0773620i
$885$	1.17678	+	17.7465i	0.0395570	+	0.596544i
$886$	−3.52236	+	4.06502i	−0.118336	+	0.136567i
$887$	9.64064	+	32.8330i	0.323701	+	1.10242i	0.947211	+	0.320610i	$0.103888\pi$
$887$	9.64064	+	32.8330i	0.323701	+	1.10242i	−0.623510	+	0.781815i	$0.714294\pi$
$888$	0.417636	−	1.10223i	0.0140149	−	0.0369885i
$889$	−15.6035	−	24.2795i	−0.523324	−	0.814308i
$890$	−0.453752	+	1.54534i	−0.0152098	+	0.0517998i
$891$	−0.436679	−	3.55997i	−0.0146293	−	0.119264i
$892$	−4.80864	+	10.5294i	−0.161005	+	0.352552i
$893$	0.0112993	−	0.0785886i	0.000378118	−	0.00262987i
$894$	19.3066	−	4.09513i	0.645708	−	0.136962i
$895$	0.580541	−	0.503042i	0.0194053	−	0.0168148i
$896$	−2.89796			−0.0968141
$897$	8.39690	+	17.8284i	0.280364	+	0.595273i
$898$	16.7024			0.557366
$899$	59.6999	−	51.7303i	1.99110	−	1.72530i
$900$	1.64801	−	2.50680i	0.0549338	−	0.0835600i
$901$	−4.01125	+	27.8989i	−0.133634	+	0.929446i
$902$	0.712671	−	1.56053i	0.0237293	−	0.0519600i
$903$	−13.2721	+	17.5391i	−0.441669	+	0.583666i
$904$	0.716436	−	2.43996i	0.0238283	−	0.0811517i
$905$	8.16696	+	12.7080i	0.271479	+	0.422429i
$906$	−37.9622	−	14.3839i	−1.26121	−	0.477873i
$907$	4.18004	+	14.2359i	0.138796	+	0.472696i	0.999326	−	0.0367037i	$-0.0116858\pi$
$907$	4.18004	+	14.2359i	0.138796	+	0.472696i	−0.860530	+	0.509399i	$0.829868\pi$
$908$	12.9098	−	14.8988i	0.428428	−	0.494433i
$909$	−2.83950	+	3.20909i	−0.0941804	+	0.106439i
$910$	6.59670	−	1.93697i	0.218678	−	0.0642098i
$911$	18.4855	+	40.4775i	0.612451	+	1.34108i	0.920885	+	0.389835i	$0.127468\pi$
$911$	18.4855	+	40.4775i	0.612451	+	1.34108i	−0.308434	+	0.951246i	$0.599805\pi$
$912$	−0.0274325	+	0.123029i	−0.000908379	+	0.00407391i
$913$	−6.49504	−	1.90712i	−0.214954	−	0.0631163i
$914$	−4.57080	−	31.7906i	−0.151189	−	1.05154i
$915$	5.94353	+	16.1912i	0.196487	+	0.535264i
$916$	12.3301	+	1.77280i	0.407399	+	0.0585751i
$917$	10.2738	+	6.60258i	0.339271	+	0.218036i
$918$	1.55301	−	17.8140i	0.0512570	−	0.587950i
$919$		−	48.5905i		−	1.60285i	−0.598093	−	0.801427i	$-0.704075\pi$
$919$		−	48.5905i		−	1.60285i	0.598093	−	0.801427i	$-0.295925\pi$
$920$	4.77712	−	0.423181i	0.157497	−	0.0139519i
$921$	−6.71178	−	6.78177i	−0.221161	−	0.223467i
$922$	7.29905	+	8.42355i	0.240381	+	0.277415i
$923$	18.4985	−	28.7843i	0.608887	−	0.947446i
$924$	−1.19043	−	1.60754i	−0.0391622	−	0.0528841i
$925$	0.619026	+	0.282700i	0.0203534	+	0.00929510i
$926$	36.4650	−	5.24287i	1.19831	−	0.172291i
$927$	41.4884	+	12.6510i	1.36266	+	0.415514i
$928$	7.00981	−	4.50493i	0.230108	−	0.147882i
$929$	−14.4284	+	6.58922i	−0.473380	+	0.216185i	−0.637795	−	0.770206i	$-0.720153\pi$
$929$	−14.4284	+	6.58922i	−0.473380	+	0.216185i	0.164416	+	0.986391i	$0.447426\pi$
$930$	−7.94397	+	14.3706i	−0.260493	+	0.471231i
$931$	0.0768995	+	0.0666338i	0.00252028	+	0.00218383i
$932$	5.06944	+	4.39269i	0.166055	+	0.143887i
$933$	0.204252	−	0.369490i	0.00668690	−	0.0120966i
$934$	6.23621	−	2.84798i	0.204055	−	0.0931887i
$935$	−1.15371	+	0.741447i	−0.0377305	+	0.0242479i
$936$	−6.80781	−	2.07590i	−0.222520	−	0.0678528i
$937$	−10.5654	+	1.51907i	−0.345156	+	0.0496259i	−0.312713	−	0.949848i	$-0.601238\pi$
$937$	−10.5654	+	1.51907i	−0.345156	+	0.0496259i	−0.0324427	+	0.999474i	$0.510329\pi$
$938$	−21.8149	−	9.96252i	−0.712281	−	0.325288i
$939$	11.6789	+	15.7710i	0.381126	+	0.514667i
$940$	0.589830	−	0.917794i	0.0192381	−	0.0299351i
$941$	−37.2661	−	43.0074i	−1.21484	−	1.40200i	−0.889830	−	0.456292i	$-0.849177\pi$
$941$	−37.2661	−	43.0074i	−1.21484	−	1.40200i	−0.325011	−	0.945710i	$-0.605368\pi$
$942$	25.0058	+	25.2665i	0.814732	+	0.823228i
$943$	−18.2852	−	9.58567i	−0.595447	−	0.312152i
$944$		−	10.2685i		−	0.334210i
$945$	−1.30780	+	15.0013i	−0.0425428	+	0.487994i
$946$	−1.46907	−	0.944111i	−0.0477634	−	0.0306957i
$947$	39.1209	+	5.62474i	1.27126	+	0.182779i	0.744723	−	0.667374i	$-0.232582\pi$
$947$	39.1209	+	5.62474i	1.27126	+	0.182779i	0.526535	+	0.850153i	$0.323491\pi$
$948$	−0.581987	−	1.58543i	−0.0189020	−	0.0514924i
$949$	4.13117	+	28.7329i	0.134103	+	0.932710i
$950$	−0.0698275	−	0.0205032i	−0.00226550	−	0.000665212i
$951$	−10.3258	+	46.3094i	−0.334838	+	1.50169i
$952$	−4.14285	−	9.07157i	−0.134270	−	0.294011i
$953$	−15.6935	+	4.60803i	−0.508363	+	0.149269i	−0.525848	−	0.850578i	$-0.676252\pi$
$953$	−15.6935	+	4.60803i	−0.508363	+	0.149269i	0.0174855	+	0.999847i	$0.494434\pi$
$954$	−16.2825	+	18.4018i	−0.527165	+	0.595780i
$955$	−13.1224	+	15.1440i	−0.424630	+	0.490049i
$956$	5.93623	+	20.2170i	0.191992	+	0.653863i
$957$	5.37845	+	2.03789i	0.173861	+	0.0658758i
$958$	−0.204941	−	0.318894i	−0.00662134	−	0.0103030i
$959$	2.31935	−	7.89898i	0.0748958	−	0.255072i
$960$	−1.04516	+	1.38118i	−0.0337323	+	0.0445773i
$961$	24.4570	−	53.5534i	0.788936	−	1.72753i
$962$	0.229766	−	1.59806i	0.00740795	−	0.0515234i
$963$	−18.7384	+	28.5030i	−0.603835	+	0.918496i
$964$	14.5992	−	12.6503i	0.470210	−	0.407439i
$965$	−17.7064			−0.569990
$966$	−20.0963	+	13.2519i	−0.646589	+	0.426371i
$967$	53.5361			1.72160			0.860802	−	0.508940i	$-0.169962\pi$
$967$	53.5361			1.72160			0.860802	+	0.508940i	$0.169962\pi$
$968$	−8.19322	+	7.09947i	−0.263340	+	0.228185i
$969$	−0.424339	+	0.0900070i	−0.0136317	+	0.00289144i
$970$	0.304953	−	2.12099i	0.00979144	−	0.0681009i
$971$	−9.78797	+	21.4327i	−0.314111	+	0.687807i	−0.999172	−	0.0406784i	$-0.987048\pi$
$971$	−9.78797	+	21.4327i	−0.314111	+	0.687807i	0.685061	+	0.728485i	$0.259775\pi$
$972$	9.66225	−	12.2328i	0.309917	−	0.392367i
$973$	0.513277	−	1.74806i	0.0164549	−	0.0560403i
$974$	−13.1567	−	20.4723i	−0.421569	−	0.655974i
$975$	1.45595	−	3.84258i	0.0466278	−	0.123061i
$976$	−2.80547	−	9.55455i	−0.0898008	−	0.305834i
$977$	4.12663	−	4.76238i	0.132022	−	0.152362i	−0.685889	−	0.727706i	$-0.740586\pi$
$977$	4.12663	−	4.76238i	0.132022	−	0.152362i	0.817911	+	0.575344i	$0.195132\pi$
$978$	−0.321115	−	4.84261i	−0.0102681	−	0.154850i
$979$	0.615844	−	0.180828i	0.0196825	−	0.00577929i
$980$	0.580822	+	1.27182i	0.0185537	+	0.0406269i
$981$	21.8658	−	13.7339i	0.698121	−	0.438490i
$982$	−13.6725	−	4.01460i	−0.436306	−	0.128111i
$983$	6.50458	+	45.2404i	0.207464	+	1.44294i	0.781393	+	0.624039i	$0.214509\pi$
$983$	6.50458	+	45.2404i	0.207464	+	1.44294i	−0.573929	+	0.818905i	$0.694582\pi$
$984$	6.99955	−	2.56942i	0.223137	−	0.0819102i
$985$	8.40067	+	1.20783i	0.267668	+	0.0384848i
$986$	24.1230	+	15.5029i	0.768232	+	0.493712i
$987$	−0.418984	+	5.46005i	−0.0133364	+	0.173795i
$988$			0.172654i			0.00549286i
$989$	−12.3068	+	17.0345i	−0.391335	+	0.541666i
$990$	−1.19549	−	0.0124012i	−0.0379951	−	0.000394135i
$991$	−39.3586	−	45.4222i	−1.25027	−	1.44288i	−0.850253	−	0.526374i	$-0.823551\pi$
$991$	−39.3586	−	45.4222i	−1.25027	−	1.44288i	−0.400013	−	0.916509i	$-0.630994\pi$
$992$	5.12537	−	7.97523i	0.162731	−	0.253214i
$993$	−5.78285	+	4.28237i	−0.183513	+	0.135897i
$994$	38.0184	+	17.3624i	1.20587	+	0.550703i
$995$	−5.64837	+	0.812114i	−0.179066	+	0.0257457i
$996$	−13.9657	−	25.8947i	−0.442522	−	0.820506i
$997$	26.7830	−	17.2124i	0.848227	−	0.545123i	−0.0427941	−	0.999084i	$-0.513626\pi$
$997$	26.7830	−	17.2124i	0.848227	−	0.545123i	0.891021	+	0.453961i	$0.149990\pi$
$998$	−3.20802	+	1.46505i	−0.101548	+	0.0463754i
$999$	3.07682	+	1.74276i	0.0973463	+	0.0551384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.401.4	yes	160
3.2	odd	2		690.2.q.b.401.15	yes	160
23.7	odd	22		690.2.q.b.191.15	yes	160
69.53	even	22	inner	690.2.q.a.191.4	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.191.4	✓	160	69.53	even	22	inner
690.2.q.a.401.4	yes	160	1.1	even	1	trivial
690.2.q.b.191.15	yes	160	23.7	odd	22
690.2.q.b.401.15	yes	160	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.755750 + 0.654861i) q^{2} +(0.359391 + 1.69435i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.38118 - 1.04516i) q^{6} +(0.816450 - 2.78057i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-2.74168 + 1.21787i) q^{9} +O(q^{10})\)	\(q+(-0.755750 + 0.654861i) q^{2} +(0.359391 + 1.69435i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-1.38118 - 1.04516i) q^{6} +(0.816450 - 2.78057i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-2.74168 + 1.21787i) q^{9} +(0.281733 + 0.959493i) q^{10} +(0.260973 - 0.301179i) q^{11} +(1.72826 - 0.114601i) q^{12} +(2.27633 - 0.668389i) q^{13} +(1.20386 + 2.63608i) q^{14} +(1.69054 + 0.376947i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.489750 - 3.40629i) q^{17} +(1.27448 - 2.71582i) q^{18} +(-0.0720347 - 0.0103570i) q^{19} +(-0.841254 - 0.540641i) q^{20} +(5.00470 + 0.384043i) q^{21} +0.398517i q^{22} +(4.78873 + 0.260982i) q^{23} +(-1.23108 + 1.21838i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(-1.28263 + 1.99581i) q^{26} +(-3.04884 - 4.20768i) q^{27} +(-2.63608 - 1.20386i) q^{28} +(8.24777 - 1.18585i) q^{29} +(-1.52447 + 0.822188i) q^{30} +(7.97523 - 5.12537i) q^{31} +(0.909632 - 0.415415i) q^{32} +(0.604096 + 0.333940i) q^{33} +(2.60077 + 2.25358i) q^{34} +(-2.19013 - 1.89776i) q^{35} +(0.815294 + 2.88709i) q^{36} +(-0.619026 + 0.282700i) q^{37} +(0.0612226 - 0.0393454i) q^{38} +(1.95058 + 3.61669i) q^{39} +(0.989821 - 0.142315i) q^{40} +(-3.91584 - 1.78831i) q^{41} +(-4.03379 + 2.98714i) q^{42} +(-2.36906 + 3.68633i) q^{43} +(-0.260973 - 0.301179i) q^{44} +(-0.0311182 + 2.99984i) q^{45} +(-3.78998 + 2.93871i) q^{46} +1.09098i q^{47} +(0.132522 - 1.72697i) q^{48} +(-1.17622 - 0.755909i) q^{49} +(0.989821 + 0.142315i) q^{50} +(5.59544 - 2.05400i) q^{51} +(-0.337631 - 2.34828i) q^{52} +(-7.85864 - 2.30751i) q^{53} +(5.05960 + 1.18339i) q^{54} +(-0.165550 - 0.362504i) q^{55} +(2.78057 - 0.816450i) q^{56} +(-0.00834014 - 0.125774i) q^{57} +(-5.45668 + 6.29734i) q^{58} +(2.89296 + 9.85253i) q^{59} +(0.613698 - 1.61968i) q^{60} +(5.38365 + 8.37713i) q^{61} +(-2.67087 + 9.09616i) q^{62} +(1.14794 + 8.61776i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(0.337631 - 2.34828i) q^{65} +(-0.675230 + 0.143224i) q^{66} +(-6.25421 + 5.41931i) q^{67} -3.44131 q^{68} +(1.27883 + 8.20759i) q^{69} +2.89796 q^{70} +(10.8997 - 9.44463i) q^{71} +(-2.50680 - 1.64801i) q^{72} +(-1.74133 + 12.1112i) q^{73} +(0.282700 - 0.619026i) q^{74} +(1.04516 - 1.38118i) q^{75} +(-0.0205032 + 0.0698275i) q^{76} +(-0.624379 - 0.971553i) q^{77} +(-3.84258 - 1.45595i) q^{78} +(-0.274710 - 0.935576i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(6.03358 - 6.67802i) q^{81} +(4.13049 - 1.21282i) q^{82} +(-7.05627 - 15.4511i) q^{83} +(1.09238 - 4.89911i) q^{84} +(-3.30192 - 0.969530i) q^{85} +(-0.623616 - 4.33734i) q^{86} +(4.97342 + 13.5485i) q^{87} +(0.394461 + 0.0567149i) q^{88} +(1.35490 + 0.870744i) q^{89} +(-1.94096 - 2.28750i) q^{90} -6.87519i q^{91} +(0.939832 - 4.70284i) q^{92} +(11.5504 + 11.6709i) q^{93} +(-0.714442 - 0.824510i) q^{94} +(-0.0393454 + 0.0612226i) q^{95} +(1.03077 + 1.39194i) q^{96} +(-1.94916 - 0.890152i) q^{97} +(1.38394 - 0.198981i) q^{98} +(-0.348707 + 1.14357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

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