LMFDB - Embedded newform 189.2.ba.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (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			5.5
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98316 + 0.349685i) q^{2} +(-1.71808 - 0.219557i) q^{3} +(1.93127 - 0.702926i) q^{4} +(0.521105 - 2.95533i) q^{5} +(3.48401 - 0.165370i) q^{6} +(-1.49002 + 2.18628i) q^{7} +(-0.0963007 + 0.0555993i) q^{8} +(2.90359 + 0.754431i) q^{9} +O(q^{10})$	\(q+(-1.98316 + 0.349685i) q^{2} +(-1.71808 - 0.219557i) q^{3} +(1.93127 - 0.702926i) q^{4} +(0.521105 - 2.95533i) q^{5} +(3.48401 - 0.165370i) q^{6} +(-1.49002 + 2.18628i) q^{7} +(-0.0963007 + 0.0555993i) q^{8} +(2.90359 + 0.754431i) q^{9} +6.04313i q^{10} +(-2.48751 + 0.438614i) q^{11} +(-3.47241 + 0.783659i) q^{12} +(-0.315597 + 0.376113i) q^{13} +(2.19045 - 4.85680i) q^{14} +(-1.54416 + 4.96308i) q^{15} +(-2.97724 + 2.49820i) q^{16} -6.30061 q^{17} +(-6.02211 - 0.480817i) q^{18} +3.51943i q^{19} +(-1.07098 - 6.07385i) q^{20} +(3.03999 - 3.42906i) q^{21} +(4.77976 - 1.73969i) q^{22} +(-4.17780 + 4.97890i) q^{23} +(0.177659 - 0.0743805i) q^{24} +(-3.76397 - 1.36997i) q^{25} +(0.494358 - 0.856254i) q^{26} +(-4.82296 - 1.93367i) q^{27} +(-1.34085 + 5.26969i) q^{28} +(6.89178 + 8.21331i) q^{29} +(1.32681 - 10.3826i) q^{30} +(-0.294914 - 0.810269i) q^{31} +(5.17373 - 6.16581i) q^{32} +(4.37003 - 0.207426i) q^{33} +(12.4951 - 2.20323i) q^{34} +(5.68473 + 5.54279i) q^{35} +(6.13794 - 0.583997i) q^{36} +(0.524026 + 0.907639i) q^{37} +(-1.23069 - 6.97960i) q^{38} +(0.624798 - 0.576901i) q^{39} +(0.114131 + 0.313574i) q^{40} +(-4.22344 - 3.54389i) q^{41} +(-4.82971 + 7.86343i) q^{42} +(-1.84673 - 0.672155i) q^{43} +(-4.49574 + 2.59562i) q^{44} +(3.74267 - 8.18793i) q^{45} +(6.54421 - 11.3349i) q^{46} +(1.69363 + 0.616432i) q^{47} +(5.66363 - 3.63843i) q^{48} +(-2.55966 - 6.51522i) q^{49} +(7.94362 + 1.40068i) q^{50} +(10.8249 + 1.38334i) q^{51} +(-0.345124 + 0.948219i) q^{52} +(-10.5923 + 6.11546i) q^{53} +(10.2409 + 2.14827i) q^{54} +7.57997i q^{55} +(0.0219346 - 0.293385i) q^{56} +(0.772713 - 6.04665i) q^{57} +(-16.5396 - 13.8784i) q^{58} +(2.61962 + 2.19812i) q^{59} +(0.506481 + 10.6705i) q^{60} +(1.40721 - 3.86627i) q^{61} +(0.868201 + 1.50377i) q^{62} +(-5.97581 + 5.22395i) q^{63} +(-4.21774 + 7.30535i) q^{64} +(0.947080 + 1.12869i) q^{65} +(-8.59396 + 1.93950i) q^{66} +(-0.848137 + 4.81002i) q^{67} +(-12.1682 + 4.42887i) q^{68} +(8.27093 - 7.63689i) q^{69} +(-13.2120 - 9.00440i) q^{70} +(-8.74108 - 5.04667i) q^{71} +(-0.321564 + 0.0887852i) q^{72} +(4.62724 + 2.67154i) q^{73} +(-1.35662 - 1.61675i) q^{74} +(6.16601 + 3.18012i) q^{75} +(2.47390 + 6.79698i) q^{76} +(2.74751 - 6.09194i) q^{77} +(-1.03734 + 1.36257i) q^{78} +(-1.57575 - 8.93651i) q^{79} +(5.83156 + 10.1006i) q^{80} +(7.86167 + 4.38112i) q^{81} +(9.61502 + 5.55124i) q^{82} +(3.29602 - 2.76569i) q^{83} +(3.46068 - 8.75935i) q^{84} +(-3.28328 + 18.6204i) q^{85} +(3.89741 + 0.687219i) q^{86} +(-10.0373 - 15.6242i) q^{87} +(0.215162 - 0.180542i) q^{88} -14.4420 q^{89} +(-4.55912 + 17.5468i) q^{90} +(-0.352044 - 1.25040i) q^{91} +(-4.56867 + 12.5523i) q^{92} +(0.328785 + 1.45686i) q^{93} +(-3.57431 - 0.630247i) q^{94} +(10.4011 + 1.83399i) q^{95} +(-10.2426 + 9.45742i) q^{96} +(-0.764758 + 2.10116i) q^{97} +(7.35451 + 12.0257i) q^{98} +(-7.55360 - 0.603095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.98316	+	0.349685i	−1.40231	+	0.247265i	−0.823092	−	0.567908i	$-0.807753\pi$
$2$	−1.98316	+	0.349685i	−1.40231	+	0.247265i	−0.579217	+	0.815173i	$0.696642\pi$
$3$	−1.71808	−	0.219557i	−0.991933	−	0.126761i
$3$	−1.71808	−	0.219557i	−0.991933	−	0.126761i
$4$	1.93127	−	0.702926i	0.965637	−	0.351463i
$5$	0.521105	−	2.95533i	0.233045	−	1.32166i	−0.613647	−	0.789581i	$-0.710298\pi$
$5$	0.521105	−	2.95533i	0.233045	−	1.32166i	0.846692	−	0.532084i	$-0.178591\pi$
$6$	3.48401	−	0.165370i	1.42234	−	0.0675122i
$7$	−1.49002	+	2.18628i	−0.563176	+	0.826337i
$7$	−1.49002	+	2.18628i	−0.563176	+	0.826337i
$8$	−0.0963007	+	0.0555993i	−0.0340475	+	0.0196573i
$9$	2.90359	+	0.754431i	0.967863	+	0.251477i
$10$			6.04313i			1.91101i
$11$	−2.48751	+	0.438614i	−0.750011	+	0.132247i	−0.535571	−	0.844490i	$-0.679904\pi$
$11$	−2.48751	+	0.438614i	−0.750011	+	0.132247i	−0.214440	+	0.976737i	$0.568793\pi$
$12$	−3.47241	+	0.783659i	−1.00240	+	0.226223i
$13$	−0.315597	+	0.376113i	−0.0875307	+	0.104315i	−0.808032	−	0.589138i	$-0.799467\pi$
$13$	−0.315597	+	0.376113i	−0.0875307	+	0.104315i	0.720501	+	0.693453i	$0.243912\pi$
$14$	2.19045	−	4.85680i	0.585422	−	1.29803i
$15$	−1.54416	+	4.96308i	−0.398701	+	1.28146i
$16$	−2.97724	+	2.49820i	−0.744310	+	0.624550i
$17$	−6.30061			−1.52812			−0.764062	−	0.645143i	$-0.776798\pi$
$17$	−6.30061			−1.52812			−0.764062	+	0.645143i	$0.776798\pi$
$18$	−6.02211	−	0.480817i	−1.41942	−	0.113330i
$19$			3.51943i			0.807412i	0.914889	+	0.403706i	$0.132278\pi$
$19$			3.51943i			0.807412i	−0.914889	+	0.403706i	$0.867722\pi$
$20$	−1.07098	−	6.07385i	−0.239479	−	1.35815i
$21$	3.03999	−	3.42906i	0.663380	−	0.748283i
$22$	4.77976	−	1.73969i	1.01905	−	0.370903i
$23$	−4.17780	+	4.97890i	−0.871131	+	1.03817i	0.127793	+	0.991801i	$0.459211\pi$
$23$	−4.17780	+	4.97890i	−0.871131	+	1.03817i	−0.998924	+	0.0463724i	$0.985234\pi$
$24$	0.177659	−	0.0743805i	0.0362646	−	0.0151828i
$25$	−3.76397	−	1.36997i	−0.752793	−	0.273994i
$26$	0.494358	−	0.856254i	0.0969517	−	0.167925i
$27$	−4.82296	−	1.93367i	−0.928178	−	0.372136i
$28$	−1.34085	+	5.26969i	−0.253396	+	0.995877i
$29$	6.89178	+	8.21331i	1.27977	+	1.52517i	0.712591	+	0.701580i	$0.247522\pi$
$29$	6.89178	+	8.21331i	1.27977	+	1.52517i	0.567181	+	0.823593i	$0.308034\pi$
$30$	1.32681	−	10.3826i	0.242241	−	1.89559i
$31$	−0.294914	−	0.810269i	−0.0529681	−	0.145529i	0.910387	−	0.413758i	$-0.135784\pi$
$31$	−0.294914	−	0.810269i	−0.0529681	−	0.145529i	−0.963355	+	0.268229i	$0.913562\pi$
$32$	5.17373	−	6.16581i	0.914594	−	1.08997i
$33$	4.37003	−	0.207426i	0.760725	−	0.0361082i
$34$	12.4951	−	2.20323i	2.14290	−	0.377851i
$35$	5.68473	+	5.54279i	0.960895	+	0.936903i
$36$	6.13794	−	0.583997i	1.02299	−	0.0973329i
$37$	0.524026	+	0.907639i	0.0861493	+	0.149215i	0.905880	−	0.423534i	$-0.139210\pi$
$37$	0.524026	+	0.907639i	0.0861493	+	0.149215i	−0.819731	+	0.572749i	$0.805877\pi$
$38$	−1.23069	−	6.97960i	−0.199645	−	1.13224i
$39$	0.624798	−	0.576901i	0.100048	−	0.0923781i
$40$	0.114131	+	0.313574i	0.0180458	+	0.0495803i
$41$	−4.22344	−	3.54389i	−0.659591	−	0.553462i	0.250373	−	0.968149i	$-0.419447\pi$
$41$	−4.22344	−	3.54389i	−0.659591	−	0.553462i	−0.909964	+	0.414687i	$0.863891\pi$
$42$	−4.82971	+	7.86343i	−0.745240	+	1.21335i
$43$	−1.84673	−	0.672155i	−0.281624	−	0.102503i	0.197346	−	0.980334i	$-0.436768\pi$
$43$	−1.84673	−	0.672155i	−0.281624	−	0.102503i	−0.478970	+	0.877831i	$0.658990\pi$
$44$	−4.49574	+	2.59562i	−0.677759	+	0.391304i
$45$	3.74267	−	8.18793i	0.557924	−	1.22058i
$46$	6.54421	−	11.3349i	0.964891	−	1.67124i
$47$	1.69363	+	0.616432i	0.247042	+	0.0899158i	0.462573	−	0.886581i	$-0.346926\pi$
$47$	1.69363	+	0.616432i	0.247042	+	0.0899158i	−0.215532	+	0.976497i	$0.569148\pi$
$48$	5.66363	−	3.63843i	0.817475	−	0.525163i
$49$	−2.55966	−	6.51522i	−0.365666	−	0.930746i
$50$	7.94362	+	1.40068i	1.12340	+	0.198085i
$51$	10.8249	+	1.38334i	1.51580	+	0.193706i
$52$	−0.345124	+	0.948219i	−0.0478600	+	0.131494i
$53$	−10.5923	+	6.11546i	−1.45496	+	0.840023i	−0.998757	−	0.0498510i	$-0.984125\pi$
$53$	−10.5923	+	6.11546i	−1.45496	+	0.840023i	−0.456206	+	0.889874i	$0.650792\pi$
$54$	10.2409	+	2.14827i	1.39361	+	0.292343i
$55$			7.57997i			1.02208i
$56$	0.0219346	−	0.293385i	0.00293114	−	0.0392052i
$57$	0.772713	−	6.04665i	0.102348	−	0.800899i
$58$	−16.5396	−	13.8784i	−2.17176	−	1.82232i
$59$	2.61962	+	2.19812i	0.341045	+	0.286171i	0.797182	−	0.603739i	$-0.206323\pi$
$59$	2.61962	+	2.19812i	0.341045	+	0.286171i	−0.456137	+	0.889910i	$0.650767\pi$
$60$	0.506481	+	10.6705i	0.0653865	+	1.37756i
$61$	1.40721	−	3.86627i	0.180174	−	0.495025i	−0.816423	−	0.577455i	$-0.804046\pi$
$61$	1.40721	−	3.86627i	0.180174	−	0.495025i	0.996597	+	0.0824302i	$0.0262682\pi$
$62$	0.868201	+	1.50377i	0.110262	+	0.190979i
$63$	−5.97581	+	5.22395i	−0.752882	+	0.658156i
$64$	−4.21774	+	7.30535i	−0.527218	+	0.913168i
$65$	0.947080	+	1.12869i	0.117471	+	0.139996i
$66$	−8.59396	+	1.93950i	−1.05784	+	0.238735i
$67$	−0.848137	+	4.81002i	−0.103616	+	0.587638i	0.888148	+	0.459558i	$0.151992\pi$
$67$	−0.848137	+	4.81002i	−0.103616	+	0.587638i	−0.991764	+	0.128079i	$0.959119\pi$
$68$	−12.1682	+	4.42887i	−1.47561	+	0.537079i
$69$	8.27093	−	7.63689i	0.995704	−	0.919373i
$70$	−13.2120	−	9.00440i	−1.57913	−	1.07623i
$71$	−8.74108	−	5.04667i	−1.03738	−	0.598929i	−0.118287	−	0.992979i	$-0.537740\pi$
$71$	−8.74108	−	5.04667i	−1.03738	−	0.598929i	−0.919089	+	0.394050i	$0.871074\pi$
$72$	−0.321564	+	0.0887852i	−0.0378966	+	0.0104634i
$73$	4.62724	+	2.67154i	0.541578	+	0.312680i	0.745718	−	0.666262i	$-0.232107\pi$
$73$	4.62724	+	2.67154i	0.541578	+	0.312680i	−0.204140	+	0.978942i	$0.565440\pi$
$74$	−1.35662	−	1.61675i	−0.157704	−	0.187944i
$75$	6.16601	+	3.18012i	0.711989	+	0.367209i
$76$	2.47390	+	6.79698i	0.283776	+	0.779667i
$77$	2.74751	−	6.09194i	0.313107	−	0.694241i
$78$	−1.03734	+	1.36257i	−0.117456	+	0.154281i
$79$	−1.57575	−	8.93651i	−0.177285	−	1.00544i	−0.935473	−	0.353399i	$-0.885026\pi$
$79$	−1.57575	−	8.93651i	−0.177285	−	1.00544i	0.758187	−	0.652037i	$-0.226085\pi$
$80$	5.83156	+	10.1006i	0.651988	+	1.12928i
$81$	7.86167	+	4.38112i	0.873519	+	0.486791i
$82$	9.61502	+	5.55124i	1.06180	+	0.613032i
$83$	3.29602	−	2.76569i	0.361785	−	0.303574i	−0.443717	−	0.896167i	$-0.646340\pi$
$83$	3.29602	−	2.76569i	0.361785	−	0.303574i	0.805502	+	0.592593i	$0.201896\pi$
$84$	3.46068	−	8.75935i	0.377591	−	0.955723i
$85$	−3.28328	+	18.6204i	−0.356122	+	2.01967i
$86$	3.89741	+	0.687219i	0.420269	+	0.0741047i
$87$	−10.0373	−	15.6242i	−1.07612	−	1.67509i
$88$	0.215162	−	0.180542i	0.0229364	−	0.0192459i
$89$	−14.4420			−1.53085			−0.765423	−	0.643527i	$-0.777470\pi$
$89$	−14.4420			−1.53085			−0.765423	+	0.643527i	$0.777470\pi$
$90$	−4.55912	+	17.5468i	−0.480574	+	1.84959i
$91$	−0.352044	−	1.25040i	−0.0369042	−	0.131078i
$92$	−4.56867	+	12.5523i	−0.476317	+	1.30867i
$93$	0.328785	+	1.45686i	0.0340934	+	0.151069i
$94$	−3.57431	−	0.630247i	−0.368662	−	0.0650050i
$95$	10.4011	+	1.83399i	1.06713	+	0.188163i
$96$	−10.2426	+	9.45742i	−1.04538	+	0.965244i
$97$	−0.764758	+	2.10116i	−0.0776494	+	0.213340i	−0.972443	−	0.233139i	$-0.925100\pi$
$97$	−0.764758	+	2.10116i	−0.0776494	+	0.213340i	0.894794	+	0.446479i	$0.147322\pi$
$98$	7.35451	+	12.0257i	0.742918	+	1.21478i
$99$	−7.55360	−	0.603095i	−0.759166	−	0.0606133i
$100$	−8.23224			−0.823224
$101$	3.03416	−	2.54596i	0.301910	−	0.253333i	−0.479228	−	0.877690i	$-0.659083\pi$
$101$	3.03416	−	2.54596i	0.301910	−	0.253333i	0.781139	+	0.624357i	$0.214639\pi$
$102$	−21.9514	+	1.04193i	−2.17351	+	0.103167i
$103$	−10.4348	−	1.83994i	−1.02818	−	0.181295i	−0.365977	−	0.930624i	$-0.619265\pi$
$103$	−10.4348	−	1.83994i	−1.02818	−	0.181295i	−0.662198	+	0.749329i	$0.730376\pi$
$104$	0.00948056	−	0.0537669i	0.000929645	−	0.00527228i
$105$	−8.54986	−	10.7711i	−0.834381	−	1.05115i
$106$	18.8678	−	15.8319i	1.83260	−	1.53773i
$107$	5.05714	+	2.91974i	0.488892	+	0.282262i	0.724115	−	0.689680i	$-0.242249\pi$
$107$	5.05714	+	2.91974i	0.488892	+	0.282262i	−0.235223	+	0.971941i	$0.575582\pi$
$108$	−10.6737	−	0.344271i	−1.02708	−	0.0331275i
$109$	−3.51703	−	6.09167i	−0.336870	−	0.583476i	0.646972	−	0.762514i	$-0.276035\pi$
$109$	−3.51703	−	6.09167i	−0.336870	−	0.583476i	−0.983842	+	0.179037i	$0.942702\pi$
$110$	−2.65060	−	15.0323i	−0.252725	−	1.43328i
$111$	−0.701040	−	1.67445i	−0.0665397	−	0.158932i
$112$	−1.02562	−	10.2315i	−0.0969118	−	0.966783i
$113$	−2.56920	−	7.05881i	−0.241690	−	0.664037i	−0.999927	−	0.0120587i	$-0.996162\pi$
$113$	−2.56920	−	7.05881i	−0.241690	−	0.664037i	0.758238	−	0.651978i	$-0.226061\pi$
$114$	0.582009	+	12.2617i	0.0545101	+	1.14841i
$115$	12.5372	+	14.9413i	1.16910	+	1.39328i
$116$	19.0833	+	11.0177i	1.77184	+	1.02297i
$117$	−1.20011	+	0.853983i	−0.110951	+	0.0789508i
$118$	−5.96378	−	3.44319i	−0.549011	−	0.316972i
$119$	9.38806	−	13.7749i	0.860602	−	1.26274i
$120$	−0.127240	−	0.563802i	−0.0116153	−	0.0514679i
$121$	−4.34131	+	1.58011i	−0.394665	+	0.143646i
$122$	−1.43874	+	8.15952i	−0.130258	+	0.738728i
$123$	6.47812	+	7.01596i	0.584113	+	0.632608i
$124$	−1.13912	−	1.35755i	−0.102296	−	0.121911i
$125$	1.49216	−	2.58450i	0.133463	−	0.231165i
$126$	10.0243	−	12.4496i	0.893034	−	1.10910i
$127$	−2.80890	−	4.86515i	−0.249249	−	0.431713i	0.714068	−	0.700076i	$-0.246851\pi$
$127$	−2.80890	−	4.86515i	−0.249249	−	0.431713i	−0.963318	+	0.268363i	$0.913517\pi$
$128$	0.304141	−	0.835621i	0.0268825	−	0.0738591i
$129$	3.02525	+	1.56028i	0.266359	+	0.137375i
$130$	−2.27290	−	1.90719i	−0.199347	−	0.167272i
$131$	1.56796	+	1.31567i	0.136993	+	0.114951i	0.708709	−	0.705501i	$-0.249278\pi$
$131$	1.56796	+	1.31567i	0.136993	+	0.114951i	−0.571716	+	0.820451i	$0.693722\pi$
$132$	8.29393	−	3.47241i	0.721894	−	0.302234i
$133$	−7.69446	−	5.24403i	−0.667194	−	0.454715i
$134$		−	9.83565i		−	0.849670i
$135$	−8.22791	+	13.2458i	−0.708146	+	1.14002i
$136$	0.606754	−	0.350309i	0.0520287	−	0.0300388i
$137$	−0.0677287	+	0.186083i	−0.00578645	+	0.0158981i	−0.942552	−	0.334059i	$-0.891582\pi$
$137$	−0.0677287	+	0.186083i	−0.00578645	+	0.0158981i	0.936766	+	0.349957i	$0.113804\pi$
$138$	−13.7321	+	18.0374i	−1.16896	+	1.53545i
$139$	8.19637	+	1.44524i	0.695207	+	0.122584i	0.510075	−	0.860130i	$-0.329618\pi$
$139$	8.19637	+	1.44524i	0.695207	+	0.122584i	0.185132	+	0.982714i	$0.440729\pi$
$140$	14.8750	+	6.70871i	1.25716	+	0.566989i
$141$	−2.77445	−	1.43093i	−0.233651	−	0.120506i
$142$	19.0997	+	6.95174i	1.60282	+	0.583377i
$143$	0.620080	−	1.07401i	0.0518537	−	0.0898132i
$144$	−10.5294	+	5.00763i	−0.877451	+	0.417303i
$145$	27.8644	−	16.0875i	2.31401	−	1.33599i
$146$	−10.1108	−	3.68002i	−0.836774	−	0.304561i
$147$	2.96724	+	11.7557i	0.244734	+	0.969590i
$148$	1.65004	+	1.38455i	0.135633	+	0.113809i
$149$	5.32172	+	14.6213i	0.435972	+	1.19782i	0.942090	+	0.335359i	$0.108858\pi$
$149$	5.32172	+	14.6213i	0.435972	+	1.19782i	−0.506118	+	0.862464i	$0.668920\pi$
$150$	−13.3402	−	4.15054i	−1.08923	−	0.338891i
$151$	2.53475	+	14.3753i	0.206275	+	1.16984i	0.895421	+	0.445220i	$0.146875\pi$
$151$	2.53475	+	14.3753i	0.206275	+	1.16984i	−0.689146	+	0.724622i	$0.742014\pi$
$152$	−0.195678	−	0.338923i	−0.0158715	−	0.0274903i
$153$	−18.2944	−	4.75338i	−1.47901	−	0.384288i
$154$	−3.31849	+	13.0421i	−0.267412	+	1.05096i
$155$	−2.54829	+	0.449333i	−0.204684	+	0.0360913i
$156$	0.801137	−	1.55334i	0.0641423	−	0.124367i
$157$	14.6944	−	17.5121i	1.17274	−	1.39762i	0.272535	−	0.962146i	$-0.412138\pi$
$157$	14.6944	−	17.5121i	1.17274	−	1.39762i	0.900204	−	0.435469i	$-0.143418\pi$
$158$	6.24993	+	17.1715i	0.497218	+	1.36609i
$159$	19.5411	−	8.18124i	1.54971	−	0.648814i
$160$	−15.5259	−	18.5031i	−1.22743	−	1.46280i
$161$	−4.66028	−	16.5525i	−0.367281	−	1.30452i
$162$	−17.1230	−	5.93936i	−1.34531	−	0.466640i
$163$	3.61347	−	6.25871i	0.283029	−	0.490220i	−0.689101	−	0.724666i	$-0.741994\pi$
$163$	3.61347	−	6.25871i	0.283029	−	0.490220i	0.972129	+	0.234446i	$0.0753275\pi$
$164$	−10.6477	−	3.87545i	−0.831447	−	0.302622i
$165$	1.66423	−	13.0230i	0.129560	−	1.01384i
$166$	−5.56943	+	6.63739i	−0.432271	+	0.515161i
$167$	20.1413	−	7.33084i	1.55858	−	0.567277i	0.588170	−	0.808737i	$-0.299849\pi$
$167$	20.1413	−	7.33084i	1.55858	−	0.567277i	0.970411	+	0.241460i	$0.0776263\pi$
$168$	−0.102100	+	0.499242i	−0.00787718	+	0.0385174i
$169$	2.21557	+	12.5651i	0.170428	+	0.966546i
$170$		−	38.0754i		−	2.92025i
$171$	−2.65516	+	10.2190i	−0.203045	+	0.781464i
$172$	−4.03902			−0.307972
$173$	−10.3436	+	8.67935i	−0.786413	+	0.659878i	−0.944855	−	0.327490i	$-0.893797\pi$
$173$	−10.3436	+	8.67935i	−0.786413	+	0.659878i	0.158442	+	0.987368i	$0.449353\pi$
$174$	25.3693	+	27.4755i	1.92324	+	2.08291i
$175$	8.60354	−	6.18781i	0.650367	−	0.467754i
$176$	6.31016	−	7.52015i	0.475646	−	0.566853i
$177$	−4.01810	−	4.35170i	−0.302019	−	0.327094i
$178$	28.6408	−	5.05015i	2.14672	−	0.378524i
$179$		−	2.76245i		−	0.206475i	−0.994657	−	0.103238i	$-0.967080\pi$
$179$		−	2.76245i		−	0.206475i	0.994657	−	0.103238i	$-0.0329202\pi$
$180$	1.47260	−	18.4440i	0.109761	−	1.37473i
$181$	−17.6904	+	10.2136i	−1.31492	+	0.759169i	−0.982906	−	0.184105i	$-0.941061\pi$
$181$	−17.6904	+	10.2136i	−1.31492	+	0.759169i	−0.332013	+	0.943275i	$0.607728\pi$
$182$	1.13541	+	2.35665i	0.0841620	+	0.174686i
$183$	−3.26655	+	6.33359i	−0.241471	+	0.468192i
$184$	0.125502	−	0.711755i	0.00925210	−	0.0524712i
$185$	2.95545	−	1.07569i	0.217289	−	0.0790866i
$186$	−1.16148	−	2.77421i	−0.0851636	−	0.203415i
$187$	15.6728	−	2.76354i	1.14611	−	0.202090i
$188$	3.70418			0.270155
$189$	11.4139	−	7.66313i	0.830237	−	0.557410i
$190$	−21.2683			−1.54297
$191$	−16.1647	+	2.85027i	−1.16963	+	0.206238i	−0.724532	−	0.689241i	$-0.757944\pi$
$191$	−16.1647	+	2.85027i	−1.16963	+	0.206238i	−0.445103	+	0.895479i	$0.646833\pi$
$192$	8.85035	−	11.6251i	0.638719	−	0.838971i
$193$	17.9669	−	6.53943i	1.29329	−	0.470719i	0.398484	−	0.917175i	$-0.369537\pi$
$193$	17.9669	−	6.53943i	1.29329	−	0.470719i	0.894805	+	0.446457i	$0.147314\pi$
$194$	0.781898	−	4.43436i	0.0561370	−	0.318369i
$195$	−1.37935	−	2.14711i	−0.0987772	−	0.153758i
$196$	−9.52313	−	10.7834i	−0.680224	−	0.770245i
$197$	−2.96439	+	1.71149i	−0.211204	+	0.121939i	−0.601871	−	0.798593i	$-0.705578\pi$
$197$	−2.96439	+	1.71149i	−0.211204	+	0.121939i	0.390667	+	0.920532i	$0.372244\pi$
$198$	15.1909	−	1.44535i	1.07957	−	0.102716i
$199$		−	9.83127i		−	0.696920i	−0.937324	−	0.348460i	$-0.886705\pi$
$199$		−	9.83127i		−	0.696920i	0.937324	−	0.348460i	$-0.113295\pi$
$200$	0.438642	−	0.0773445i	0.0310167	−	0.00546908i
$201$	2.51324	−	8.07779i	0.177270	−	0.569763i
$202$	−5.12696	+	6.11007i	−0.360731	+	0.429903i
$203$	−28.2255	+	2.82937i	−1.98104	+	0.198583i
$204$	21.8783	−	4.93753i	1.53179	−	0.345696i
$205$	−12.6742	+	10.6349i	−0.885206	+	0.742776i
$206$	21.3374			1.48665
$207$	−15.8868	+	11.3048i	−1.10421	+	0.785740i
$208$		−	1.90820i		−	0.132310i
$209$	−1.54367	−	8.75460i	−0.106778	−	0.605568i
$210$	20.7223	+	18.3710i	1.42997	+	1.26772i
$211$	−17.9268	+	6.52483i	−1.23413	+	0.449188i	−0.875011	−	0.484103i	$-0.839146\pi$
$211$	−17.9268	+	6.52483i	−1.23413	+	0.449188i	−0.359122	+	0.933291i	$0.616924\pi$
$212$	−16.1579	+	19.2562i	−1.10973	+	1.32252i
$213$	13.9098	+	10.5897i	0.953087	+	0.725597i
$214$	−11.0501	−	4.02191i	−0.755371	−	0.274932i
$215$	−2.94878	+	5.10744i	−0.201105	+	0.348324i
$216$	0.571965	−	0.0819386i	0.0389173	−	0.00557521i
$217$	2.21090	+	0.562554i	0.150086	+	0.0381887i
$218$	9.10501	+	10.8509i	0.616669	+	0.734918i
$219$	−7.36341	−	5.60586i	−0.497573	−	0.378809i
$220$	5.32816	+	14.6390i	0.359224	+	0.986961i
$221$	1.98845	−	2.36974i	0.133758	−	0.159406i
$222$	1.97581	+	3.07556i	0.132607	+	0.206418i
$223$	−21.3740	+	3.76881i	−1.43131	+	0.252378i	−0.834944	−	0.550336i	$-0.814500\pi$
$223$	−21.3740	+	3.76881i	−1.43131	+	0.252378i	−0.596365	+	0.802714i	$0.703389\pi$
$224$	5.77123	+	20.4984i	0.385606	+	1.36961i
$225$	−9.89547	−	6.81749i	−0.659698	−	0.454499i
$226$	7.56350	+	13.1004i	0.503117	+	0.871424i
$227$	−0.0693362	−	0.393225i	−0.00460201	−	0.0260993i	0.982420	−	0.186683i	$-0.0597736\pi$
$227$	−0.0693362	−	0.393225i	−0.00460201	−	0.0260993i	−0.987022	+	0.160583i	$0.948662\pi$
$228$	−2.75803	−	12.2209i	−0.182655	−	0.809349i
$229$	−0.917133	−	2.51980i	−0.0606059	−	0.166513i	0.905694	−	0.423932i	$-0.139350\pi$
$229$	−0.917133	−	2.51980i	−0.0606059	−	0.166513i	−0.966300	+	0.257418i	$0.917128\pi$
$230$	−30.0882	−	25.2470i	−1.98395	−	1.66474i
$231$	−6.05796	+	9.86320i	−0.398584	+	0.648951i
$232$	−1.12034	−	0.407770i	−0.0735538	−	0.0267714i
$233$	10.8390	−	6.25788i	0.710085	−	0.409968i	−0.101008	−	0.994886i	$-0.532207\pi$
$233$	10.8390	−	6.25788i	0.710085	−	0.409968i	0.811092	+	0.584918i	$0.198873\pi$
$234$	2.08140	−	2.11325i	0.136065	−	0.138148i
$235$	2.70432	−	4.68402i	0.176410	−	0.305552i
$236$	6.60432	+	2.40378i	0.429905	+	0.156473i
$237$	0.745190	+	15.6996i	0.0484053	+	1.01980i
$238$	−13.8012	+	30.6008i	−0.894597	+	1.98355i
$239$	−14.8795	−	2.62366i	−0.962474	−	0.169710i	−0.329734	−	0.944074i	$-0.606959\pi$
$239$	−14.8795	−	2.62366i	−0.962474	−	0.169710i	−0.632741	+	0.774364i	$0.718070\pi$
$240$	−7.80144	−	18.6339i	−0.503580	−	1.20281i
$241$	−10.0424	+	27.5912i	−0.646886	+	1.77730i	−0.0179589	+	0.999839i	$0.505717\pi$
$241$	−10.0424	+	27.5912i	−0.646886	+	1.77730i	−0.628927	+	0.777465i	$0.716505\pi$
$242$	8.05700	−	4.65171i	0.517923	−	0.299023i
$243$	−12.5451	−	9.25318i	−0.804766	−	0.593592i
$244$		−	8.45598i		−	0.541339i
$245$	−20.5885	+	4.16954i	−1.31535	+	0.266382i
$246$	−15.3006	−	11.6485i	−0.975528	−	0.742681i
$247$	−1.32370	−	1.11072i	−0.0842252	−	0.0706734i
$248$	0.0734508	+	0.0616325i	0.00466413	+	0.00391367i
$249$	−6.27005	+	4.02801i	−0.397348	+	0.255265i
$250$	−2.05544	+	5.64728i	−0.129998	+	0.357165i
$251$	1.64062	+	2.84163i	0.103555	+	0.179362i	0.913147	−	0.407631i	$-0.133645\pi$
$251$	1.64062	+	2.84163i	0.103555	+	0.179362i	−0.809592	+	0.586993i	$0.800312\pi$
$252$	−7.86889	+	14.2894i	−0.495693	+	0.900150i
$253$	8.20848	−	14.2175i	0.516062	−	0.893846i
$254$	7.27178	+	8.66617i	0.456272	+	0.543764i
$255$	9.72916	−	31.2704i	0.609264	−	1.95823i
$256$	2.61866	−	14.8511i	0.163666	−	0.928196i
$257$	−5.23460	+	1.90524i	−0.326526	+	0.118846i	−0.500081	−	0.865978i	$-0.666697\pi$
$257$	−5.23460	+	1.90524i	−0.326526	+	0.118846i	0.173556	+	0.984824i	$0.444474\pi$
$258$	−6.54518	−	2.03640i	−0.407485	−	0.126781i
$259$	−2.76517	−	0.206735i	−0.171819	−	0.0128459i
$260$	2.62246	+	1.51408i	0.162638	+	0.0938990i
$261$	13.8145	+	29.0474i	0.855099	+	1.79799i
$262$	−3.56959	−	2.06090i	−0.220530	−	0.127323i
$263$	16.5524	+	19.7264i	1.02066	+	1.21638i	0.976088	+	0.217374i	$0.0697492\pi$
$263$	16.5524	+	19.7264i	1.02066	+	1.21638i	0.0445760	+	0.999006i	$0.485806\pi$
$264$	−0.409305	+	0.262946i	−0.0251910	+	0.0161832i
$265$	12.5535	+	34.4905i	0.771157	+	2.11874i
$266$	17.0931	+	7.70913i	1.04805	+	0.472677i
$267$	24.8124	+	3.17083i	1.51850	+	0.194052i
$268$	1.74311	+	9.88565i	0.106477	+	0.603862i
$269$	−1.10496	−	1.91384i	−0.0673703	−	0.116689i	0.830373	−	0.557208i	$-0.188128\pi$
$269$	−1.10496	−	1.91384i	−0.0673703	−	0.116689i	−0.897743	+	0.440520i	$0.854794\pi$
$270$	11.6854	−	29.1457i	0.711153	−	1.77375i
$271$	−7.89152	−	4.55617i	−0.479376	−	0.276768i	0.240780	−	0.970580i	$-0.422597\pi$
$271$	−7.89152	−	4.55617i	−0.479376	−	0.276768i	−0.720156	+	0.693812i	$0.755930\pi$
$272$	18.7584	−	15.7402i	1.13740	−	0.954390i
$273$	0.330306	+	2.22558i	0.0199910	+	0.134698i
$274$	0.0692466	−	0.392717i	0.00418334	−	0.0237249i
$275$	9.96378	+	1.75688i	0.600839	+	0.105944i
$276$	10.6053	−	20.5628i	0.638363	−	1.23773i
$277$	17.5654	−	14.7391i	1.05540	−	0.885587i	0.0617499	−	0.998092i	$-0.480332\pi$
$277$	17.5654	−	14.7391i	1.05540	−	0.885587i	0.993651	+	0.112505i	$0.0358874\pi$
$278$	−16.7601			−1.00521
$279$	−0.245017	−	2.57518i	−0.0146688	−	0.154172i
$280$	−0.855619	−	0.217708i	−0.0511330	−	0.0130106i
$281$	−1.64610	+	4.52262i	−0.0981980	+	0.269797i	−0.979058	−	0.203579i	$-0.934743\pi$
$281$	−1.64610	+	4.52262i	−0.0981980	+	0.269797i	0.880860	+	0.473376i	$0.156965\pi$
$282$	6.00257	+	1.86758i	0.357448	+	0.111213i
$283$	−17.9140	−	3.15871i	−1.06487	−	0.187766i	−0.386356	−	0.922350i	$-0.626266\pi$
$283$	−17.9140	−	3.15871i	−1.06487	−	0.187766i	−0.678518	+	0.734584i	$0.737377\pi$
$284$	−20.4289	−	3.60216i	−1.21223	−	0.213749i
$285$	−17.4672	−	5.43456i	−1.03467	−	0.321916i
$286$	−0.854154	+	2.34677i	−0.0505072	+	0.138767i
$287$	14.0410	−	3.95316i	0.828812	−	0.233348i
$288$	19.6741	−	13.9998i	1.15930	−	0.824944i
$289$	22.6977			1.33516
$290$	−49.6341	+	41.6479i	−2.91461	+	2.44565i
$291$	1.77524	−	3.44204i	0.104066	−	0.201776i
$292$	10.8144	+	1.90687i	0.632863	+	0.111591i
$293$	−3.38706	+	19.2090i	−0.197874	+	1.12220i	0.710391	+	0.703807i	$0.248518\pi$
$293$	−3.38706	+	19.2090i	−0.197874	+	1.12220i	−0.908266	+	0.418394i	$0.862593\pi$
$294$	−9.99531	−	22.2758i	−0.582938	−	1.29915i
$295$	7.86127	−	6.59639i	0.457701	−	0.384057i
$296$	−0.100928	−	0.0582709i	−0.00586633	−	0.00338693i
$297$	12.8453	+	2.69461i	0.745358	+	0.156357i
$298$	−15.6667	−	27.1355i	−0.907547	−	1.57192i
$299$	−0.554134	−	3.14265i	−0.0320464	−	0.181744i
$300$	14.1436	+	1.80744i	0.816584	+	0.104353i
$301$	4.22119	−	3.03595i	0.243305	−	0.174989i
$302$	−10.0536	−	27.6222i	−0.578522	−	1.58948i
$303$	−5.77191	+	3.70800i	−0.331588	+	0.213019i
$304$	−8.79224	−	10.4782i	−0.504269	−	0.600965i
$305$	−10.6928	−	6.17349i	−0.612268	−	0.353493i
$306$	37.9430	+	3.02944i	2.16906	+	0.173182i
$307$	−7.72295	−	4.45885i	−0.440772	−	0.254480i	0.263153	−	0.964754i	$-0.415238\pi$
$307$	−7.72295	−	4.45885i	−0.440772	−	0.254480i	−0.703925	+	0.710274i	$0.748571\pi$
$308$	1.02401	−	13.6965i	0.0583481	−	0.780430i
$309$	17.5239	+	5.45221i	0.996901	+	0.310165i
$310$	4.89656	−	1.78220i	0.278106	−	0.101222i
$311$	−0.152938	+	0.867353i	−0.00867230	+	0.0491831i	−0.988837	−	0.149002i	$-0.952394\pi$
$311$	−0.152938	+	0.867353i	−0.00867230	+	0.0491831i	0.980165	+	0.198186i	$0.0635049\pi$
$312$	−0.0280932	+	0.0902943i	−0.00159047	+	0.00511191i
$313$	−13.7354	−	16.3692i	−0.776369	−	0.925240i	0.222395	−	0.974957i	$-0.428613\pi$
$313$	−13.7354	−	16.3692i	−0.776369	−	0.925240i	−0.998763	+	0.0497165i	$0.984168\pi$
$314$	−23.0176	+	39.8677i	−1.29896	+	2.24986i
$315$	12.3245	+	20.3827i	0.694405	+	1.14844i
$316$	−9.32491	−	16.1512i	−0.524567	−	0.908577i
$317$	8.49523	−	23.3405i	0.477140	−	1.31093i	−0.434770	−	0.900541i	$-0.643170\pi$
$317$	8.49523	−	23.3405i	0.477140	−	1.31093i	0.911910	−	0.410390i	$-0.134607\pi$
$318$	−35.8923	+	23.0580i	−2.01274	+	1.29303i
$319$	−20.7458	−	17.4078i	−1.16154	−	0.974651i
$320$	19.3918	+	16.2717i	1.08404	+	0.909615i
$321$	−8.04751	−	6.12667i	−0.449168	−	0.341957i
$322$	15.0303	+	31.1967i	0.837604	+	1.73853i
$323$		−	22.1745i		−	1.23382i
$324$	18.2626	+	2.93496i	1.01459	+	0.163053i
$325$	1.70316	−	0.983320i	0.0944743	−	0.0545448i
$326$	−4.97752	+	13.6756i	−0.275679	+	0.757423i
$327$	4.70507	+	11.2382i	0.260191	+	0.621472i
$328$	0.603758	+	0.106459i	0.0333370	+	0.00587821i
$329$	−3.87125	+	2.78426i	−0.213429	+	0.153501i
$330$	1.25350	+	26.4087i	0.0690030	+	1.45375i
$331$	1.66029	+	0.604296i	0.0912577	+	0.0332151i	0.387246	−	0.921977i	$-0.373427\pi$
$331$	1.66029	+	0.604296i	0.0912577	+	0.0332151i	−0.295988	+	0.955192i	$0.595649\pi$
$332$	4.42144	−	7.65817i	0.242658	−	0.420296i
$333$	0.836805	+	3.03075i	0.0458566	+	0.166084i
$334$	−37.3800	+	21.5814i	−2.04534	+	1.18088i
$335$	13.7732	+	5.01305i	0.752513	+	0.273892i
$336$	−0.484293	+	17.8036i	−0.0264204	+	0.971269i
$337$	17.5667	+	14.7402i	0.956920	+	0.802951i	0.980449	−	0.196772i	$-0.0630459\pi$
$337$	17.5667	+	14.7402i	0.956920	+	0.802951i	−0.0235294	+	0.999723i	$0.507490\pi$
$338$	−8.78766	−	24.1439i	−0.477986	−	1.31326i
$339$	2.86428	+	12.6917i	0.155566	+	0.689317i
$340$	6.74786	+	38.2690i	0.365954	+	2.07543i
$341$	1.08900	+	1.88620i	0.0589724	+	0.102143i
$342$	1.69220	−	21.1944i	0.0915038	−	1.14606i
$343$	18.0581	+	4.11168i	0.975044	+	0.222010i
$344$	0.215213	−	0.0379478i	0.0116035	−	0.00204601i
$345$	−18.2595	−	28.4230i	−0.983059	−	1.53024i
$346$	17.4781	−	20.8296i	0.939628	−	1.11981i
$347$	−1.23029	−	3.38018i	−0.0660452	−	0.181458i	0.902280	−	0.431151i	$-0.141892\pi$
$347$	−1.23029	−	3.38018i	−0.0660452	−	0.181458i	−0.968325	+	0.249693i	$0.919670\pi$
$348$	−30.3676	−	23.1192i	−1.62787	−	1.23932i
$349$	2.52217	+	3.00581i	0.135009	+	0.160897i	0.829313	−	0.558785i	$-0.188732\pi$
$349$	2.52217	+	3.00581i	0.135009	+	0.160897i	−0.694304	+	0.719682i	$0.744288\pi$
$350$	−14.8985	+	15.2800i	−0.796356	+	0.816749i
$351$	2.24939	−	1.20372i	0.120063	−	0.0642497i
$352$	−10.1653	+	17.6068i	−0.541810	+	0.938443i
$353$	20.5680	+	7.48616i	1.09473	+	0.398448i	0.825370	−	0.564593i	$-0.190967\pi$
$353$	20.5680	+	7.48616i	1.09473	+	0.398448i	0.269357	+	0.963040i	$0.413189\pi$
$354$	9.49028	+	7.22506i	0.504403	+	0.384008i
$355$	−19.4696	+	23.2030i	−1.03334	+	1.23148i
$356$	−27.8914	+	10.1516i	−1.47824	+	0.538036i
$357$	−19.1538	+	21.6052i	−1.01373	+	1.14347i
$358$	0.965989	+	5.47840i	0.0510541	+	0.289542i
$359$		−	16.7099i		−	0.881913i	−0.897529	−	0.440956i	$-0.854639\pi$
$359$		−	16.7099i		−	0.881913i	0.897529	−	0.440956i	$-0.145361\pi$
$360$	0.0948214	+	0.996593i	0.00499752	+	0.0525251i
$361$	6.61363			0.348086
$362$	31.5115	−	26.4413i	1.65621	−	1.38972i
$363$	7.80564	−	1.76159i	0.409690	−	0.0924594i
$364$	−1.55883	−	2.16741i	−0.0817051	−	0.113603i
$365$	10.3066	−	12.2829i	0.539470	−	0.642915i
$366$	4.26335	−	13.7028i	0.222849	−	0.716258i
$367$	−26.4746	+	4.66818i	−1.38196	+	0.243677i	−0.814710	−	0.579868i	$-0.803104\pi$
$367$	−26.4746	+	4.66818i	−1.38196	+	0.243677i	−0.567251	+	0.823545i	$0.691993\pi$
$368$		−	25.2604i		−	1.31679i
$369$	−9.58952	−	13.4763i	−0.499211	−	0.701548i
$370$	−5.48498	+	3.16676i	−0.285151	+	0.164632i
$371$	2.41263	−	32.2699i	0.125257	−	1.67537i
$372$	1.65904	+	2.58248i	0.0860171	+	0.133895i
$373$	2.45572	−	13.9271i	0.127152	−	0.721116i	−0.852854	−	0.522149i	$-0.825130\pi$
$373$	2.45572	−	13.9271i	0.127152	−	0.721116i	0.980006	−	0.198967i	$-0.0637585\pi$
$374$	−30.1154	+	10.9611i	−1.55723	+	0.566785i
$375$	−3.13110	+	4.11276i	−0.161689	+	0.212382i
$376$	−0.197371	+	0.0348019i	−0.0101786	+	0.00179477i
$377$	−5.26416			−0.271118
$378$	−19.9559	+	19.1885i	−1.02642	+	0.986950i
$379$	1.54085			0.0791483			0.0395742	−	0.999217i	$-0.487400\pi$
$379$	1.54085			0.0791483			0.0395742	+	0.999217i	$0.487400\pi$
$380$	21.3765	−	3.76925i	1.09659	−	0.193358i
$381$	3.75773	+	8.97543i	0.192514	+	0.459825i
$382$	31.0605	−	11.3051i	1.58919	−	0.578419i
$383$	−4.08823	+	23.1855i	−0.208899	+	1.18472i	0.682287	+	0.731085i	$0.260986\pi$
$383$	−4.08823	+	23.1855i	−0.208899	+	1.18472i	−0.891186	+	0.453639i	$0.850126\pi$
$384$	−0.706004	+	1.36889i	−0.0360281	+	0.0698557i
$385$	−16.5720	−	11.2943i	−0.844585	−	0.575612i
$386$	−33.3447	+	19.2515i	−1.69720	+	0.979878i
$387$	−4.85505	−	3.34489i	−0.246796	−	0.170030i
$388$			4.59548i			0.233300i
$389$	−8.41415	+	1.48364i	−0.426614	+	0.0752236i	−0.382833	−	0.923818i	$-0.625052\pi$
$389$	−8.41415	+	1.48364i	−0.426614	+	0.0752236i	−0.0437811	+	0.999041i	$0.513940\pi$
$390$	3.48629	+	3.77573i	0.176535	+	0.191192i
$391$	26.3227	−	31.3701i	1.33120	−	1.58646i
$392$	0.608739	+	0.485105i	0.0307460	+	0.0245015i
$393$	−2.40501	−	2.60468i	−0.121317	−	0.131389i
$394$	5.28039	−	4.43077i	0.266022	−	0.223219i
$395$	−27.2315			−1.37016
$396$	−15.0120	+	4.14489i	−0.754382	+	0.208288i
$397$			24.7255i			1.24094i	0.784231	+	0.620469i	$0.213058\pi$
$397$			24.7255i			1.24094i	−0.784231	+	0.620469i	$0.786942\pi$
$398$	3.43785	+	19.4970i	0.172324	+	0.977297i
$399$	12.0683	+	10.6990i	0.604172	+	0.535621i
$400$	14.6287	−	5.32441i	0.731435	−	0.266221i
$401$	3.90125	−	4.64933i	0.194819	−	0.232177i	−0.659788	−	0.751452i	$-0.729354\pi$
$401$	3.90125	−	4.64933i	0.194819	−	0.232177i	0.854607	+	0.519276i	$0.173798\pi$
$402$	−2.15948	+	16.8984i	−0.107705	+	0.842816i
$403$	0.397827	+	0.144797i	0.0198172	+	0.00721285i
$404$	4.07017	−	7.04975i	0.202499	−	0.350738i
$405$	17.0444	−	20.9508i	0.846943	−	1.04105i
$406$	54.9865	−	15.4812i	2.72893	−	0.768317i
$407$	−1.70162	−	2.02791i	−0.0843462	−	0.100520i
$408$	−1.11936	+	0.468642i	−0.0554167	+	0.0232013i
$409$	2.38417	+	6.55045i	0.117890	+	0.323899i	0.984577	−	0.174953i	$-0.0559774\pi$
$409$	2.38417	+	6.55045i	0.117890	+	0.323899i	−0.866687	+	0.498852i	$0.833755\pi$
$410$	21.4162	−	25.5228i	1.05767	−	1.26048i
$411$	0.157219	−	0.304835i	0.00775504	−	0.0150364i
$412$	−21.4459	+	3.78149i	−1.05656	+	0.186301i
$413$	−8.70901	+	2.45198i	−0.428542	+	0.120654i
$414$	27.5531	−	27.9747i	1.35416	−	1.37488i
$415$	−6.45596	−	11.1820i	−0.316910	−	0.548905i
$416$	0.686232	+	3.89181i	0.0336453	+	0.190812i
$417$	−13.7647	−	4.28260i	−0.674060	−	0.209720i
$418$	6.12271	+	16.8220i	0.299471	+	0.822791i
$419$	−0.853896	−	0.716503i	−0.0417155	−	0.0350035i	0.621692	−	0.783262i	$-0.286446\pi$
$419$	−0.853896	−	0.716503i	−0.0417155	−	0.0350035i	−0.663407	+	0.748259i	$0.730890\pi$
$420$	−24.0834	−	14.7920i	−1.17515	−	0.721775i
$421$	15.7466	+	5.73128i	0.767441	+	0.279326i	0.695926	−	0.718114i	$-0.254994\pi$
$421$	15.7466	+	5.73128i	0.767441	+	0.279326i	0.0715154	+	0.997439i	$0.477217\pi$
$422$	33.2702	−	19.2085i	1.61957	−	0.935057i
$423$	4.45256	+	3.06759i	0.216491	+	0.149152i
$424$	0.680030	−	1.17785i	0.0330252	−	0.0572013i
$425$	23.7153	+	8.63166i	1.15036	+	0.418697i
$426$	−31.2886	−	16.1371i	−1.51594	−	0.781846i
$427$	6.35598	+	8.83738i	0.307588	+	0.427671i
$428$	11.8191	+	2.08402i	0.571297	+	0.100735i
$429$	−1.30115	+	1.70909i	−0.0628202	+	0.0825157i
$430$	4.06192	−	11.1600i	0.195883	−	0.538184i
$431$	17.9406	−	10.3580i	0.864167	−	0.498927i	−0.00123821	−	0.999999i	$-0.500394\pi$
$431$	17.9406	−	10.3580i	0.864167	−	0.498927i	0.865406	+	0.501072i	$0.167061\pi$
$432$	19.1898	−	6.29171i	0.923270	−	0.302710i
$433$			18.6305i			0.895324i	0.894203	+	0.447662i	$0.147743\pi$
$433$			18.6305i			0.895324i	−0.894203	+	0.447662i	$0.852257\pi$
$434$	−4.58130	−	0.342517i	−0.219910	−	0.0164413i
$435$	−51.4053	+	21.5218i	−2.46470	+	1.03189i
$436$	−11.0743	−	9.29248i	−0.530365	−	0.445029i
$437$	−17.5229	−	14.7034i	−0.838233	−	0.703361i
$438$	16.5631	+	8.54246i	0.791417	+	0.408174i
$439$	1.20161	−	3.30140i	0.0573497	−	0.157567i	−0.907709	−	0.419600i	$-0.862171\pi$
$439$	1.20161	−	3.30140i	0.0573497	−	0.157567i	0.965059	+	0.262032i	$0.0843927\pi$
$440$	−0.421441	−	0.729957i	−0.0200914	−	0.0347993i
$441$	−2.51693	−	20.8486i	−0.119854	−	0.992792i
$442$	−3.11476	+	5.39492i	−0.148154	+	0.256610i
$443$	23.6051	+	28.1315i	1.12151	+	1.33657i	0.935217	+	0.354075i	$0.115204\pi$
$443$	23.6051	+	28.1315i	1.12151	+	1.33657i	0.186297	+	0.982494i	$0.440351\pi$
$444$	−2.53091	−	2.74104i	−0.120112	−	0.130084i
$445$	−7.52578	+	42.6808i	−0.356756	+	2.02326i
$446$	41.0702	−	14.9483i	1.94473	−	0.707824i
$447$	−5.93293	−	26.2890i	−0.280618	−	1.24342i
$448$	−9.68702	−	20.1063i	−0.457669	−	0.949934i
$449$	1.43645	+	0.829336i	0.0677904	+	0.0391388i	0.533512	−	0.845792i	$-0.320872\pi$
$449$	1.43645	+	0.829336i	0.0677904	+	0.0391388i	−0.465722	+	0.884931i	$0.654205\pi$
$450$	22.0083	+	10.0599i	1.03748	+	0.474228i
$451$	12.0602	+	6.96298i	0.567895	+	0.327874i
$452$	−9.92365	−	11.8265i	−0.466769	−	0.556274i
$453$	−1.19871	−	25.2544i	−0.0563204	−	1.18655i
$454$	0.275010	+	0.755584i	0.0129069	+	0.0354613i
$455$	−3.87880	+	0.388817i	−0.181841	+	0.0182280i
$456$	0.261777	+	0.625259i	0.0122588	+	0.0292805i
$457$	4.22534	+	23.9631i	0.197653	+	1.12095i	0.908590	+	0.417690i	$0.137160\pi$
$457$	4.22534	+	23.9631i	0.197653	+	1.12095i	−0.710937	+	0.703256i	$0.751729\pi$
$458$	2.69996	+	4.67647i	0.126161	+	0.218517i
$459$	30.3876	+	12.1833i	1.41837	+	0.568669i
$460$	34.7155	+	20.0430i	1.61862	+	0.934509i
$461$	4.64297	−	3.89592i	0.216245	−	0.181451i	−0.528230	−	0.849101i	$-0.677144\pi$
$461$	4.64297	−	3.89592i	0.216245	−	0.181451i	0.744475	+	0.667650i	$0.232700\pi$
$462$	8.56491	−	21.6787i	0.398476	−	1.00859i
$463$	4.54433	−	25.7722i	0.211193	−	1.19773i	−0.676199	−	0.736719i	$-0.736374\pi$
$463$	4.54433	−	25.7722i	0.211193	−	1.19773i	0.887392	−	0.461015i	$-0.152515\pi$
$464$	−41.0370	−	7.23593i	−1.90509	−	0.335920i
$465$	4.47682	−	0.212495i	0.207608	−	0.00985422i
$466$	−19.3072	+	16.2006i	−0.894388	+	0.750480i
$467$	15.2497			0.705674			0.352837	−	0.935685i	$-0.385217\pi$
$467$	15.2497			0.705674			0.352837	+	0.935685i	$0.385217\pi$
$468$	−1.71746	+	2.49287i	−0.0793898	+	0.115233i
$469$	−9.25233	−	9.02131i	−0.427233	−	0.416566i
$470$	−3.72518	+	10.2348i	−0.171830	+	0.472098i
$471$	−29.0910	+	26.8609i	−1.34044	+	1.23768i
$472$	−0.374485	−	0.0660318i	−0.0172371	−	0.00303936i
$473$	4.88857	+	0.861987i	0.224777	+	0.0396342i
$474$	−6.96775	−	30.8743i	−0.320039	−	1.41810i
$475$	4.82152	−	13.2470i	0.221226	−	0.607814i
$476$	8.44816	−	33.2023i	0.387221	−	1.52182i
$477$	−35.3694	+	9.76564i	−1.61945	+	0.447138i
$478$	30.4259			1.39165
$479$	25.1953	−	21.1414i	1.15120	−	0.965976i	0.151458	−	0.988464i	$-0.451603\pi$
$479$	25.1953	−	21.1414i	1.15120	−	0.965976i	0.999747	+	0.0224882i	$0.00715881\pi$
$480$	22.6123	+	35.1986i	1.03211	+	1.60659i
$481$	−0.506756	−	0.0893547i	−0.0231061	−	0.00407423i
$482$	10.2674	−	58.2295i	0.467669	−	2.65228i
$483$	4.37251	+	29.4617i	0.198956	+	1.34056i
$484$	−7.27357	+	6.10325i	−0.330617	+	0.277420i
$485$	5.81109	+	3.35504i	0.263868	+	0.152344i
$486$	28.1146	+	13.9638i	1.27531	+	0.633409i
$487$	−8.71327	−	15.0918i	−0.394836	−	0.683876i	0.598244	−	0.801314i	$-0.295865\pi$
$487$	−8.71327	−	15.0918i	−0.394836	−	0.683876i	−0.993080	+	0.117438i	$0.962532\pi$
$488$	0.0794466	+	0.450564i	0.00359638	+	0.0203961i
$489$	−7.58236	+	9.95959i	−0.342886	+	0.450388i
$490$	39.3723	−	15.4684i	1.77866	−	0.698790i
$491$	3.91810	+	10.7649i	0.176821	+	0.485813i	0.996165	−	0.0874893i	$-0.0278844\pi$
$491$	3.91810	+	10.7649i	0.176821	+	0.485813i	−0.819344	+	0.573302i	$0.805662\pi$
$492$	17.4427	+	8.99611i	0.786379	+	0.405576i
$493$	−43.4225	−	51.7489i	−1.95565	−	2.33065i
$494$	3.01352	+	1.73986i	0.135585	+	0.0782799i
$495$	−5.71856	+	22.0091i	−0.257030	+	0.989236i
$496$	2.90224	+	1.67561i	0.130315	+	0.0752372i
$497$	24.0579	−	11.5908i	1.07914	−	0.519920i
$498$	11.0260	−	10.1807i	0.494087	−	0.456210i
$499$	−3.66396	+	1.33357i	−0.164021	+	0.0596989i	−0.422726	−	0.906258i	$-0.638927\pi$
$499$	−3.66396	+	1.33357i	−0.164021	+	0.0596989i	0.258704	+	0.965957i	$0.416704\pi$
$500$	1.06506	−	6.04026i	0.0476310	−	0.270129i
$501$	−36.2139	+	8.17280i	−1.61792	+	0.365134i
$502$	−4.24729	−	5.06172i	−0.189566	−	0.225916i
$503$	−4.19074	+	7.25858i	−0.186856	+	0.323644i	−0.944200	−	0.329372i	$-0.893163\pi$
$503$	−4.19074	+	7.25858i	−0.186856	+	0.323644i	0.757344	+	0.653016i	$0.226496\pi$
$504$	0.285028	−	0.835321i	0.0126961	−	0.0372082i
$505$	−5.94305	−	10.2937i	−0.264462	−	0.458062i
$506$	−11.3071	+	31.0660i	−0.502662	+	1.38105i
$507$	−1.04777	−	22.0743i	−0.0465330	−	0.980353i
$508$	−8.84460	−	7.42150i	−0.392416	−	0.329276i
$509$	33.9754	+	28.5087i	1.50593	+	1.26363i	0.871234	+	0.490867i	$0.163320\pi$
$509$	33.9754	+	28.5087i	1.50593	+	1.26363i	0.634698	+	0.772760i	$0.281124\pi$
$510$	−8.35970	+	65.4166i	−0.370174	+	2.89669i
$511$	−12.7354	+	6.13580i	−0.563383	+	0.271432i
$512$			32.1465i			1.42069i
$513$	6.80542	−	16.9740i	0.300467	−	0.749422i
$514$	9.71484	−	5.60887i	0.428503	−	0.247397i
$515$	−10.8753	+	29.8796i	−0.479222	+	1.31665i
$516$	6.93935	+	0.886793i	0.305488	+	0.0390389i
$517$	−4.48330	−	0.790526i	−0.197175	−	0.0347673i
$518$	5.55607	−	0.556949i	0.244120	−	0.0244709i
$519$	19.6768	−	12.6408i	0.863716	−	0.554869i
$520$	−0.153959	−	0.0560364i	−0.00675154	−	0.00245736i
$521$	−9.17120	+	15.8850i	−0.401798	+	0.695934i	−0.993943	−	0.109897i	$-0.964948\pi$
$521$	−9.17120	+	15.8850i	−0.401798	+	0.695934i	0.592145	+	0.805831i	$0.298281\pi$
$522$	−37.5540	−	52.7751i	−1.64369	−	2.30990i
$523$	−6.16402	+	3.55880i	−0.269534	+	0.155615i	−0.628676	−	0.777668i	$-0.716403\pi$
$523$	−6.16402	+	3.55880i	−0.269534	+	0.155615i	0.359142	+	0.933283i	$0.383069\pi$
$524$	3.95297	+	1.43876i	0.172686	+	0.0628527i
$525$	−16.1401	+	8.74218i	−0.704413	+	0.381540i
$526$	−39.7241	−	33.3325i	−1.73205	−	1.45337i
$527$	1.85814	+	5.10519i	0.0809417	+	0.222386i
$528$	−12.4924	+	11.5348i	−0.543664	+	0.501987i
$529$	−3.34159	−	18.9511i	−0.145287	−	0.823962i
$530$	−36.9565	−	64.0106i	−1.60529	−	2.78044i
$531$	5.94797	+	8.35876i	0.258120	+	0.362739i
$532$	−18.5463	−	4.71902i	−0.804083	−	0.204595i
$533$	2.66581	−	0.470054i	0.115469	−	0.0203603i
$534$	−50.3159	+	2.38827i	−2.17738	+	0.103351i
$535$	11.2641	−	13.4240i	0.486989	−	0.580371i
$536$	−0.185758	−	0.510365i	−0.00802350	−	0.0220444i
$537$	−0.606514	+	4.74611i	−0.0261730	+	0.204810i
$538$	2.86055	+	3.40907i	0.123327	+	0.146975i
$539$	9.22485	+	15.0840i	0.397342	+	0.649712i
$540$	−6.57954	+	31.3649i	−0.283138	+	1.34973i
$541$	−6.49394	+	11.2478i	−0.279196	+	0.483582i	−0.971185	−	0.238326i	$-0.923401\pi$
$541$	−6.49394	+	11.2478i	−0.279196	+	0.483582i	0.691989	+	0.721908i	$0.256735\pi$
$542$	17.2434	+	6.27609i	0.740668	+	0.269581i
$543$	32.6360	−	13.6637i	1.40055	−	0.586365i
$544$	−32.5976	+	38.8484i	−1.39761	+	1.66561i
$545$	−19.8356	+	7.21959i	−0.849666	+	0.309253i
$546$	−1.43330	−	4.29819i	−0.0613397	−	0.183945i
$547$	0.155111	+	0.879676i	0.00663205	+	0.0376122i	0.987944	−	0.154810i	$-0.0494767\pi$
$547$	0.155111	+	0.879676i	0.00663205	+	0.0376122i	−0.981312	+	0.192423i	$0.938366\pi$
$548$			0.406986i			0.0173856i
$549$	7.00278	−	10.1644i	0.298871	−	0.433807i
$550$	−20.3742			−0.868758
$551$	−28.9061	+	24.2551i	−1.23144	+	1.03330i
$552$	−0.371892	+	1.19530i	−0.0158288	+	0.0508752i
$553$	21.8856	+	9.87057i	0.930672	+	0.419739i
$554$	−29.6810	+	35.3724i	−1.26102	+	1.50283i
$555$	−5.31387	+	1.19924i	−0.225561	+	0.0509049i
$556$	16.8453	−	2.97029i	0.714401	−	0.125968i
$557$			39.5370i			1.67523i	0.546258	+	0.837617i	$0.316052\pi$
$557$			39.5370i			1.67523i	−0.546258	+	0.837617i	$0.683948\pi$
$558$	1.38641	+	5.02133i	0.0586915	+	0.212570i
$559$	0.835628	−	0.482450i	0.0353433	−	0.0204055i
$560$	−30.7718	−	2.30063i	−1.30035	−	0.0972192i
$561$	−27.5339	+	1.30691i	−1.16248	+	0.0551778i
$562$	1.68299	−	9.54471i	0.0709927	−	0.402619i
$563$	0.466161	−	0.169669i	0.0196464	−	0.00715069i	−0.332178	−	0.943217i	$-0.607784\pi$
$563$	0.466161	−	0.169669i	0.0196464	−	0.00715069i	0.351825	+	0.936066i	$0.385561\pi$
$564$	−6.36407	−	0.813276i	−0.267976	−	0.0342451i
$565$	−22.1999	+	3.91445i	−0.933959	+	0.164682i
$566$	36.6309			1.53971
$567$	−21.2924	+	10.6599i	−0.894198	+	0.447672i
$568$	1.12236			0.0470933
$569$	−27.9584	+	4.92982i	−1.17208	+	0.206669i	−0.725594	−	0.688123i	$-0.758435\pi$
$569$	−27.9584	+	4.92982i	−1.17208	+	0.206669i	−0.446483	+	0.894792i	$0.647324\pi$
$570$	36.5407	+	4.66960i	1.53052	+	0.195588i
$571$	12.8351	−	4.67158i	0.537131	−	0.195500i	−0.0591885	−	0.998247i	$-0.518851\pi$
$571$	12.8351	−	4.67158i	0.537131	−	0.195500i	0.596320	+	0.802747i	$0.296629\pi$
$572$	0.442594	−	2.51008i	0.0185058	−	0.104952i
$573$	28.3980	−	1.34793i	1.18634	−	0.0563104i
$574$	−26.4632	+	12.7497i	−1.10455	+	0.532162i
$575$	22.5460	−	13.0170i	0.940235	−	0.542845i
$576$	−17.7580	+	18.0297i	−0.739916	+	0.751239i
$577$			19.0746i			0.794084i	0.917800	+	0.397042i	$0.129963\pi$
$577$			19.0746i			0.794084i	−0.917800	+	0.397042i	$0.870037\pi$
$578$	−45.0133	+	7.93706i	−1.87231	+	0.330138i
$579$	−32.3044	+	7.29050i	−1.34253	+	0.302983i
$580$	42.5054	−	50.6560i	1.76494	−	2.10338i
$581$	1.13543	+	11.3270i	0.0471057	+	0.469922i
$582$	−2.31695	+	7.44691i	−0.0960409	+	0.308684i
$583$	23.6661	−	19.8582i	0.980148	−	0.822442i
$584$	−0.594142			−0.0245858
$585$	1.89842	+	3.99175i	0.0784899	+	0.165039i
$586$		−	39.2790i		−	1.62260i
$587$	5.92168	+	33.5835i	0.244414	+	1.38614i	0.821850	+	0.569704i	$0.192942\pi$
$587$	5.92168	+	33.5835i	0.244414	+	1.38614i	−0.577436	+	0.816436i	$0.695947\pi$
$588$	13.9939	+	20.6176i	0.577100	+	0.850257i
$589$	2.85168	−	1.03793i	0.117502	−	0.0427671i
$590$	−13.2835	+	15.8307i	−0.546874	+	0.651739i
$591$	5.46883	−	2.28963i	0.224958	−	0.0941827i
$592$	−3.82762	−	1.39314i	−0.157314	−	0.0572576i
$593$	−19.3036	+	33.4348i	−0.792703	+	1.37300i	0.131584	+	0.991305i	$0.457994\pi$
$593$	−19.3036	+	33.4348i	−0.792703	+	1.37300i	−0.924287	+	0.381697i	$0.875340\pi$
$594$	−26.4165	−	0.852045i	−1.08388	−	0.0349598i
$595$	−35.8173	−	34.9230i	−1.46837	−	1.43170i
$596$	20.5554	+	24.4970i	0.841982	+	1.00343i
$597$	−2.15852	+	16.8909i	−0.0883423	+	0.691298i
$598$	2.19788	+	6.03862i	0.0898779	+	0.246937i
$599$	8.57758	−	10.2224i	0.350471	−	0.417675i	−0.561793	−	0.827278i	$-0.689888\pi$
$599$	8.57758	−	10.2224i	0.350471	−	0.417675i	0.912264	+	0.409603i	$0.134333\pi$
$600$	−0.770604	+	0.0365771i	−0.0314598	+	0.00149326i
$601$	−17.6264	+	3.10801i	−0.718997	+	0.126778i	−0.521163	−	0.853457i	$-0.674502\pi$
$601$	−17.6264	+	3.10801i	−0.718997	+	0.126778i	−0.197834	+	0.980236i	$0.563391\pi$
$602$	−7.30969	+	7.49687i	−0.297921	+	0.305550i
$603$	−6.09147	+	13.3265i	−0.248064	+	0.542696i
$604$	15.0001	+	25.9809i	0.610343	+	1.05715i
$605$	2.40747	+	13.6534i	0.0978774	+	0.555090i
$606$	10.1500	−	9.37192i	0.412316	−	0.380708i
$607$	−8.84588	−	24.3038i	−0.359043	−	0.986463i	−0.979362	−	0.202113i	$-0.935219\pi$
$607$	−8.84588	−	24.3038i	−0.359043	−	0.986463i	0.620319	−	0.784349i	$-0.287003\pi$
$608$	21.7001	+	18.2086i	0.880056	+	0.738454i
$609$	49.1149	+	1.33602i	1.99024	+	0.0541382i
$610$	23.3643	+	8.50393i	0.945995	+	0.344314i
$611$	−0.766353	+	0.442454i	−0.0310033	+	0.0178998i
$612$	−38.6728	+	3.67954i	−1.56325	+	0.148737i
$613$	−1.37739	+	2.38571i	−0.0556323	+	0.0963579i	−0.892500	−	0.451047i	$-0.851051\pi$
$613$	−1.37739	+	2.38571i	−0.0556323	+	0.0963579i	0.836868	+	0.547405i	$0.184384\pi$
$614$	16.8751	+	6.14203i	0.681023	+	0.247872i
$615$	24.1103	−	15.4889i	0.972220	−	0.624575i
$616$	0.0741203	+	0.739417i	0.00298639	+	0.0297920i
$617$	−7.51530	−	1.32515i	−0.302554	−	0.0533485i	0.0203100	−	0.999794i	$-0.493535\pi$
$617$	−7.51530	−	1.32515i	−0.302554	−	0.0533485i	−0.322864	+	0.946445i	$0.604646\pi$
$618$	−36.6593	−	4.68477i	−1.47466	−	0.188449i
$619$	−2.71403	+	7.45673i	−0.109086	+	0.299711i	−0.982210	−	0.187787i	$-0.939868\pi$
$619$	−2.71403	+	7.45673i	−0.109086	+	0.299711i	0.873124	+	0.487499i	$0.162091\pi$
$620$	−4.60561	+	2.65905i	−0.184966	+	0.106790i
$621$	29.7769	−	15.9345i	1.19491	−	0.639431i
$622$		−	1.77358i		−	0.0711142i
$623$	21.5189	−	31.5742i	0.862135	−	1.26500i
$624$	−0.418959	+	3.27844i	−0.0167718	+	0.131243i
$625$	−22.2026	−	18.6302i	−0.888102	−	0.745206i
$626$	32.9635	+	27.6597i	1.31749	+	1.10550i
$627$	0.730021	+	15.3800i	0.0291542	+	0.614218i
$628$	16.0692	−	44.1497i	0.641230	−	1.76176i
$629$	−3.30168	−	5.71868i	−0.131647	−	0.228019i
$630$	−31.5690	−	36.1126i	−1.25774	−	1.43876i
$631$	11.5353	−	19.9797i	0.459213	−	0.795380i	−0.539706	−	0.841853i	$-0.681465\pi$
$631$	11.5353	−	19.9797i	0.459213	−	0.795380i	0.998920	+	0.0464728i	$0.0147981\pi$
$632$	0.648609	+	0.772982i	0.0258003	+	0.0307476i
$633$	32.2322	−	7.27422i	1.28112	−	0.289124i
$634$	−8.68562	+	49.2586i	−0.344950	+	1.95631i
$635$	−15.8419	+	5.76597i	−0.628665	+	0.228815i
$636$	31.9884	−	29.5362i	1.26842	−	1.17118i
$637$	3.25828	+	1.09346i	0.129098	+	0.0433244i
$638$	47.2296	+	27.2680i	1.86984	+	1.07955i
$639$	−21.5732	−	21.2480i	−0.853421	−	0.840558i
$640$	−2.31105	−	1.33428i	−0.0913521	−	0.0527422i
$641$	−19.1988	−	22.8802i	−0.758307	−	0.903715i	0.239432	−	0.970913i	$-0.423039\pi$
$641$	−19.1988	−	22.8802i	−0.758307	−	0.903715i	−0.997740	+	0.0671977i	$0.978594\pi$
$642$	18.1019	+	9.33609i	0.714426	+	0.368466i
$643$	5.32645	+	14.6343i	0.210055	+	0.577120i	0.999318	−	0.0369349i	$-0.0117594\pi$
$643$	5.32645	+	14.6343i	0.210055	+	0.577120i	−0.789263	+	0.614055i	$0.789537\pi$
$644$	−20.6355	−	28.6916i	−0.813152	−	1.13061i
$645$	6.18761	−	8.12756i	0.243637	−	0.320022i
$646$	7.75411	+	43.9758i	0.305082	+	1.73020i
$647$	−10.4580	−	18.1138i	−0.411148	−	0.712128i	0.583868	−	0.811849i	$-0.301539\pi$
$647$	−10.4580	−	18.1138i	−0.411148	−	0.712128i	−0.995016	+	0.0997202i	$0.968205\pi$
$648$	−1.00067	+	0.0151983i	−0.0393101	+	0.000597046i
$649$	−7.48045	−	4.31884i	−0.293633	−	0.169529i
$650$	−3.03379	+	2.54565i	−0.118995	+	0.0998488i
$651$	−3.67500	−	1.45193i	−0.144034	−	0.0569057i
$652$	2.57919	−	14.6273i	0.101009	−	0.572849i
$653$	25.7874	+	4.54701i	1.00914	+	0.177938i	0.653693	−	0.756760i	$-0.273219\pi$
$653$	25.7874	+	4.54701i	1.00914	+	0.177938i	0.355444	+	0.934698i	$0.384330\pi$
$654$	−13.2607	−	20.6418i	−0.518536	−	0.807159i
$655$	4.70531	−	3.94823i	0.183852	−	0.154270i
$656$	21.4276			0.836605
$657$	11.4201	+	11.2480i	0.445541	+	0.438826i
$658$	6.70370	−	6.87537i	0.261337	−	0.268030i
$659$	6.02259	−	16.5469i	0.234607	−	0.644577i	−0.765393	−	0.643564i	$-0.777455\pi$
$659$	6.02259	−	16.5469i	0.234607	−	0.644577i	0.999999	−	0.00101351i	$-0.000322611\pi$
$660$	−5.94011	−	26.3208i	−0.231219	−	1.02454i
$661$	−33.6531	−	5.93395i	−1.30895	−	0.230804i	−0.524723	−	0.851273i	$-0.675831\pi$
$661$	−33.6531	−	5.93395i	−1.30895	−	0.230804i	−0.784231	+	0.620469i	$0.786942\pi$
$662$	−3.50394	−	0.617839i	−0.136184	−	0.0240130i
$663$	−3.93661	+	3.63483i	−0.152885	+	0.141165i
$664$	−0.163639	+	0.449594i	−0.00635042	+	0.0174476i
$665$	−19.5075	+	20.0070i	−0.756467	+	0.775838i
$666$	−2.71933	−	5.71786i	−0.105372	−	0.221563i
$667$	−69.6857			−2.69824
$668$	33.7454	−	28.3157i	1.30565	−	1.09557i
$669$	37.5497	−	1.78232i	1.45175	−	0.0689083i
$670$	−29.0676	−	5.12540i	−1.12298	−	0.198011i
$671$	−1.80463	+	10.2346i	−0.0696671	+	0.395102i
$672$	−5.41486	−	36.4850i	−0.208883	−	1.40744i
$673$	−0.789136	+	0.662163i	−0.0304189	+	0.0255245i	−0.657870	−	0.753131i	$-0.728543\pi$
$673$	−0.789136	+	0.662163i	−0.0304189	+	0.0255245i	0.627451	+	0.778656i	$0.284098\pi$
$674$	−39.9921	−	23.0895i	−1.54044	−	0.889373i
$675$	15.5044	+	13.8856i	0.596764	+	0.534457i
$676$	13.1112	+	22.7093i	0.504277	+	0.873434i
$677$	−6.77842	−	38.4423i	−0.260516	−	1.47746i	−0.781507	−	0.623897i	$-0.785548\pi$
$677$	−6.77842	−	38.4423i	−0.260516	−	1.47746i	0.520991	−	0.853562i	$-0.325563\pi$
$678$	−10.1184	−	24.1681i	−0.388596	−	0.928170i
$679$	−3.45421	−	4.80275i	−0.132561	−	0.184313i
$680$	−0.719098	−	1.97571i	−0.0275762	−	0.0757649i
$681$	0.0327899	+	0.690815i	0.00125651	+	0.0264721i
$682$	−2.81923	−	3.35983i	−0.107954	−	0.128655i
$683$	37.7150	+	21.7748i	1.44312	+	0.833188i	0.998057	−	0.0623096i	$-0.0198466\pi$
$683$	37.7150	+	21.7748i	1.44312	+	0.833188i	0.445067	+	0.895497i	$0.353180\pi$
$684$	2.05534	+	21.6020i	0.0785877	+	0.825974i
$685$	0.514643	+	0.297129i	0.0196635	+	0.0113527i
$686$	−37.2499	−	1.83950i	−1.42221	−	0.0702325i
$687$	1.02247	+	4.53058i	0.0390096	+	0.172852i
$688$	7.17734	−	2.61234i	0.273634	−	0.0995945i
$689$	1.04278	−	5.91392i	0.0397269	−	0.225302i
$690$	46.1507	+	49.9823i	1.75693	+	1.90279i
$691$	8.36147	+	9.96481i	0.318085	+	0.379079i	0.901268	−	0.433262i	$-0.142637\pi$
$691$	8.36147	+	9.96481i	0.318085	+	0.379079i	−0.583183	+	0.812341i	$0.698193\pi$
$692$	−13.8755	+	24.0330i	−0.527466	+	0.913598i
$693$	12.5736	−	15.6157i	0.477631	−	0.593191i
$694$	3.62186	+	6.27324i	0.137484	+	0.238129i
$695$	8.54233	−	23.4699i	0.324029	−	0.890262i
$696$	1.83530	+	0.946558i	0.0695669	+	0.0358792i
$697$	26.6103	+	22.3287i	1.00794	+	0.845759i
$698$	−6.05296	−	5.07904i	−0.229108	−	0.192245i
$699$	−19.9962	+	8.37177i	−0.756325	+	0.316649i
$700$	12.2662	−	17.9980i	0.463620	−	0.680261i
$701$		−	15.3053i		−	0.578074i	−0.957318	−	0.289037i	$-0.906665\pi$
$701$		−	15.3053i		−	0.578074i	0.957318	−	0.289037i	$-0.0933351\pi$
$702$	−4.03998	+	3.17375i	−0.152479	+	0.119785i
$703$	−3.19437	+	1.84427i	−0.120478	+	0.0695580i
$704$	7.28743	−	20.0221i	0.274656	−	0.754610i
$705$	−5.67464	+	7.45376i	−0.213719	+	0.280725i
$706$	−43.4076	−	7.65393i	−1.63367	−	0.288060i
$707$	1.04523	+	10.4271i	0.0393098	+	0.392151i
$708$	−10.8190	−	5.57990i	−0.406602	−	0.209705i
$709$	22.4964	+	8.18802i	0.844870	+	0.307507i	0.727947	−	0.685634i	$-0.240475\pi$
$709$	22.4964	+	8.18802i	0.844870	+	0.307507i	0.116923	+	0.993141i	$0.462697\pi$
$710$	30.4977	−	52.8235i	1.14456	−	1.98243i
$711$	2.16665	−	27.1367i	0.0812558	−	1.01771i
$712$	1.39077	−	0.802963i	0.0521214	−	0.0300923i
$713$	5.26634	+	1.91679i	0.197226	+	0.0717844i
$714$	30.4301	−	49.5444i	1.13882	−	1.85415i
$715$	−2.85093	−	2.39221i	−0.106619	−	0.0894636i
$716$	−1.94180	−	5.33505i	−0.0725685	−	0.199380i
$717$	24.9881	+	7.77454i	0.933198	+	0.290345i
$718$	5.84319	+	33.1384i	0.218066	+	1.23671i
$719$	−18.8581	−	32.6631i	−0.703287	−	1.21813i	−0.967306	−	0.253612i	$-0.918381\pi$
$719$	−18.8581	−	32.6631i	−0.703287	−	1.21813i	0.264019	−	0.964518i	$-0.414952\pi$
$720$	9.31228	+	33.7274i	0.347048	+	1.25695i
$721$	19.5708	−	20.0720i	0.728854	−	0.747519i
$722$	−13.1159	+	2.31269i	−0.488124	+	0.0860694i
$723$	23.3114	−	45.1989i	0.866960	−	1.68097i
$724$	−26.9857	+	32.1603i	−1.00292	+	1.19523i
$725$	−14.6884	−	40.3562i	−0.545515	−	1.49879i
$726$	−14.8639	+	6.22304i	−0.551650	+	0.230959i
$727$	7.32384	+	8.72821i	0.271626	+	0.323712i	0.884563	−	0.466420i	$-0.154457\pi$
$727$	7.32384	+	8.72821i	0.271626	+	0.323712i	−0.612937	+	0.790132i	$0.710012\pi$
$728$	0.103423	+	0.100841i	0.00383313	+	0.00373742i
$729$	19.5218	+	18.6520i	0.723030	+	0.690817i
$730$	−16.1445	+	27.9630i	−0.597533	+	1.03496i
$731$	11.6355	+	4.23499i	0.430356	+	0.156637i
$732$	−1.85657	+	14.5280i	−0.0686207	+	0.536972i
$733$	18.6067	−	22.1746i	0.687255	−	0.819038i	−0.303766	−	0.952747i	$-0.598244\pi$
$733$	18.6067	−	22.1746i	0.687255	−	0.819038i	0.991021	+	0.133708i	$0.0426885\pi$
$734$	50.8710	−	18.5155i	1.87768	−	0.683421i
$735$	36.2881	−	2.64326i	1.33851	−	0.0974981i
$736$	9.08419	+	51.5190i	0.334848	+	1.89901i
$737$		−	12.3370i		−	0.454438i
$738$	23.7301	+	23.3724i	0.873516	+	0.860349i
$739$	−35.3795			−1.30146			−0.650728	−	0.759311i	$-0.725536\pi$
$739$	−35.3795			−1.30146			−0.650728	+	0.759311i	$0.725536\pi$
$740$	4.95164	−	4.15492i	0.182026	−	0.152738i
$741$	2.03036	+	2.19893i	0.0745872	+	0.0807797i
$742$	6.49968	+	64.8402i	0.238611	+	2.38036i
$743$	16.4643	−	19.6213i	0.604015	−	0.719837i	−0.374220	−	0.927340i	$-0.622089\pi$
$743$	16.4643	−	19.6213i	0.604015	−	0.719837i	0.978234	+	0.207503i	$0.0665338\pi$
$744$	−0.112662	−	0.122016i	−0.00413040	−	0.00447333i
$745$	45.9839	−	8.10821i	1.68472	−	0.297062i
$746$			28.4784i			1.04267i
$747$	11.6568	−	5.54381i	0.426500	−	0.202837i
$748$	28.3259	−	16.3540i	1.03570	−	0.597961i
$749$	−13.9186	+	6.70585i	−0.508575	+	0.245026i
$750$	4.77131	−	9.25118i	0.174223	−	0.337805i
$751$	0.185856	−	1.05404i	0.00678197	−	0.0384625i	−0.981229	−	0.192846i	$-0.938228\pi$
$751$	0.185856	−	1.05404i	0.00678197	−	0.0384625i	0.988011	+	0.154384i	$0.0493392\pi$
$752$	−6.58232	+	2.39577i	−0.240033	+	0.0873647i
$753$	−2.19481	−	5.24235i	−0.0799833	−	0.191042i
$754$	10.4397	−	1.84080i	0.380191	−	0.0670379i
$755$	43.8045			1.59421
$756$	16.6567	−	22.8227i	0.605799	−	0.830054i
$757$	−10.1445			−0.368708			−0.184354	−	0.982860i	$-0.559019\pi$
$757$	−10.1445			−0.368708			−0.184354	+	0.982860i	$0.559019\pi$
$758$	−3.05577	+	0.538814i	−0.110990	+	0.0195706i
$759$	−17.2244	+	22.6246i	−0.625204	+	0.821219i
$760$	−1.10360	+	0.401677i	−0.0400318	+	0.0145704i
$761$	−4.89427	+	27.7568i	−0.177417	+	1.00618i	0.757900	+	0.652371i	$0.226225\pi$
$761$	−4.89427	+	27.7568i	−0.177417	+	1.00618i	−0.935317	+	0.353811i	$0.884886\pi$
$762$	−10.5908	−	16.4857i	−0.383663	−	0.597215i
$763$	18.5586	+	1.38751i	0.671865	+	0.0502314i
$764$	−29.2149	+	16.8672i	−1.05696	+	0.610235i
$765$	−23.5811	+	51.5890i	−0.852576	+	1.86520i
$766$		−	47.4102i		−	1.71300i
$767$	−1.65349	+	0.291554i	−0.0597039	+	0.0105274i
$768$	−7.75972	+	24.9405i	−0.280005	+	0.899962i
$769$	7.76282	−	9.25137i	0.279934	−	0.333613i	−0.607696	−	0.794170i	$-0.707906\pi$
$769$	7.76282	−	9.25137i	0.279934	−	0.333613i	0.887630	+	0.460557i	$0.152350\pi$
$770$	36.8144	+	16.6035i	1.32670	+	0.598350i
$771$	9.41177	−	2.12406i	0.338957	−	0.0764962i
$772$	30.1024	−	25.2589i	1.08341	−	0.909087i
$773$	−8.97588			−0.322840			−0.161420	−	0.986886i	$-0.551607\pi$
$773$	−8.97588			−0.322840			−0.161420	+	0.986886i	$0.551607\pi$
$774$	10.7980	+	4.93573i	0.388127	+	0.177411i
$775$			3.45385i			0.124066i
$776$	−0.0431759	−	0.244863i	−0.00154993	−	0.00879006i
$777$	4.70538	+	0.962297i	0.168805	+	0.0345222i
$778$	16.1678	−	5.88461i	0.579645	−	0.210973i
$779$	12.4725	−	14.8641i	0.446872	−	0.532561i
$780$	−4.17316	−	3.17708i	−0.149423	−	0.113758i
$781$	23.9570	+	8.71965i	0.857250	+	0.312014i
$782$	−41.2325	+	71.4168i	−1.47447	+	2.55386i
$783$	−17.3569	−	52.9389i	−0.620285	−	1.89188i
$784$	23.8971	+	13.0028i	0.853467	+	0.464387i
$785$	−44.0967	−	52.5523i	−1.57388	−	1.87567i
$786$	5.68034	+	4.32452i	0.202611	+	0.154250i
$787$	12.1021	+	33.2502i	0.431392	+	1.18524i	0.944959	+	0.327190i	$0.106102\pi$
$787$	12.1021	+	33.2502i	0.431392	+	1.18524i	−0.513566	+	0.858050i	$0.671676\pi$
$788$	−4.52200	+	5.38911i	−0.161090	+	0.191979i
$789$	−24.1073	−	37.5257i	−0.858241	−	1.33595i
$790$	54.0045	−	9.52244i	1.92139	−	0.338793i
$791$	19.2607	+	4.90080i	0.684832	+	0.174252i
$792$	0.760949	−	0.361896i	0.0270392	−	0.0128594i
$793$	1.01004	+	1.74945i	0.0358677	+	0.0621248i
$794$	−8.64614	−	49.0347i	−0.306840	−	1.74018i
$795$	−13.9953	−	62.0136i	−0.496363	−	2.19940i
$796$	−6.91066	−	18.9869i	−0.244942	−	0.672972i
$797$	−26.9783	−	22.6375i	−0.955621	−	0.801861i	0.0246140	−	0.999697i	$-0.492164\pi$
$797$	−26.9783	−	22.6375i	−0.955621	−	0.801861i	−0.980235	+	0.197836i	$0.936609\pi$
$798$	−27.6748	−	16.9978i	−0.979676	−	0.601715i
$799$	−10.6709	−	3.88390i	−0.377510	−	0.137402i
$800$	−27.9207	+	16.1200i	−0.987147	+	0.569929i
$801$	−41.9336	−	10.8955i	−1.48165	−	0.384972i
$802$	−6.11102	+	10.5846i	−0.215788	+	0.373755i
$803$	−12.6821	−	4.61590i	−0.447541	−	0.162891i
$804$	−0.824337	−	17.3670i	−0.0290721	−	0.612488i
$805$	−51.3467	+	5.14707i	−1.80973	+	0.181410i
$806$	−0.839589	−	0.148042i	−0.0295733	−	0.00521456i
$807$	1.47820	+	3.53073i	0.0520353	+	0.124287i
$808$	−0.150638	+	0.413875i	−0.00529944	+	0.0145601i
$809$	−4.57135	+	2.63927i	−0.160720	+	0.0927917i	−0.578203	−	0.815893i	$-0.696246\pi$
$809$	−4.57135	+	2.63927i	−0.160720	+	0.0927917i	0.417483	+	0.908685i	$0.362912\pi$
$810$	−26.4756	+	47.5091i	−0.930259	+	1.66930i
$811$		−	27.2418i		−	0.956590i	−0.878199	−	0.478295i	$-0.841255\pi$
$811$		−	27.2418i		−	0.956590i	0.878199	−	0.478295i	$-0.158745\pi$
$812$	−52.5224	+	25.3048i	−1.84317	+	0.888023i
$813$	12.5579	+	9.56050i	0.440425	+	0.335301i
$814$	4.08373	+	3.42665i	0.143135	+	0.120104i
$815$	−16.6136	−	13.9404i	−0.581948	−	0.488312i
$816$	−35.6843	+	22.9244i	−1.24920	+	0.802513i
$817$	2.36560	−	6.49943i	0.0827619	−	0.227386i
$818$	−7.01879	−	12.1569i	−0.245406	−	0.425056i
$819$	−0.0788503	−	3.89624i	−0.00275525	−	0.136146i
$820$	−17.0018	+	29.4480i	−0.593729	+	1.02837i
$821$	−2.95732	−	3.52439i	−0.103211	−	0.123002i	0.711966	−	0.702214i	$-0.247805\pi$
$821$	−2.95732	−	3.52439i	−0.103211	−	0.123002i	−0.815177	+	0.579212i	$0.803360\pi$
$822$	−0.205195	+	0.659515i	−0.00715699	+	0.0230032i
$823$	−3.91915	+	22.2266i	−0.136613	+	0.774770i	0.837110	+	0.547034i	$0.184243\pi$
$823$	−3.91915	+	22.2266i	−0.136613	+	0.774770i	−0.973723	+	0.227736i	$0.926868\pi$
$824$	1.10718	−	0.402982i	0.0385705	−	0.0140385i
$825$	−16.7328	−	5.20608i	−0.582562	−	0.181252i
$826$	16.4140	−	7.90808i	0.571115	−	0.275157i
$827$	41.6840	+	24.0663i	1.44949	+	0.836866i	0.998451	−	0.0556363i	$-0.0177187\pi$
$827$	41.6840	+	24.0663i	1.44949	+	0.836866i	0.451043	+	0.892502i	$0.351052\pi$
$828$	−22.7354	+	33.0000i	−0.790109	+	1.14683i
$829$	2.79847	+	1.61570i	0.0971947	+	0.0561154i	0.547810	−	0.836603i	$-0.315462\pi$
$829$	2.79847	+	1.61570i	0.0971947	+	0.0561154i	−0.450615	+	0.892719i	$0.648795\pi$
$830$	16.7134	+	19.9183i	0.580131	+	0.691373i
$831$	−33.4148	+	21.4663i	−1.15915	+	0.744659i
$832$	−1.41653	−	3.89189i	−0.0491094	−	0.134927i
$833$	16.1274	+	41.0499i	0.558783	+	1.42229i
$834$	28.7952	+	3.67979i	0.997096	+	0.127421i
$835$	−11.1693	−	63.3444i	−0.386530	−	2.19212i
$836$	−9.13509	−	15.8224i	−0.315944	−	0.547231i
$837$	−0.144439	+	4.47816i	−0.00499256	+	0.154788i
$838$	1.94397	+	1.12235i	0.0671532	+	0.0387709i
$839$	−31.2046	+	26.1838i	−1.07730	+	0.903965i	−0.995694	−	0.0926989i	$-0.970451\pi$
$839$	−31.2046	+	26.1838i	−1.07730	+	0.903965i	−0.0816099	+	0.996664i	$0.526006\pi$
$840$	1.42222	+	0.561897i	0.0490713	+	0.0193873i
$841$	−14.9259	+	84.6492i	−0.514688	+	2.91894i
$842$	−33.2322	−	5.85973i	−1.14526	−	0.201940i
$843$	3.82110	−	7.40880i	0.131606	−	0.255173i
$844$	−30.0351	+	25.2025i	−1.03385	+	0.867504i
$845$	38.2886			1.31717
$846$	−9.90285	−	4.52655i	−0.340467	−	0.155626i
$847$	3.01409	−	11.8457i	0.103565	−	0.407024i
$848$	16.2581	−	44.6689i	0.558307	−	1.53394i
$849$	30.0841	+	9.36004i	1.03248	+	0.321236i
$850$	−50.0497	−	8.82511i	−1.71669	−	0.302699i
$851$	−6.70832	−	1.18286i	−0.229958	−	0.0405479i
$852$	34.3075	+	10.6741i	1.17536	+	0.365688i
$853$	−0.537786	+	1.47755i	−0.0184134	+	0.0505905i	−0.948559	−	0.316601i	$-0.897458\pi$
$853$	−0.537786	+	1.47755i	−0.0184134	+	0.0505905i	0.930145	+	0.367191i	$0.119681\pi$
$854$	−15.6953	−	15.3034i	−0.537081	−	0.523671i
$855$	28.8168	+	13.1720i	0.985515	+	0.450474i
$856$	−0.649341			−0.0221940
$857$	−19.4720	+	16.3389i	−0.665149	+	0.558127i	−0.911625	−	0.411022i	$-0.865172\pi$
$857$	−19.4720	+	16.3389i	−0.665149	+	0.558127i	0.246476	+	0.969149i	$0.420727\pi$
$858$	1.98275	−	3.84440i	0.0676901	−	0.131246i
$859$	50.3208	+	8.87292i	1.71692	+	0.302740i	0.943555	−	0.331216i	$-0.107459\pi$
$859$	50.3208	+	8.87292i	1.71692	+	0.302740i	0.773369	+	0.633956i	$0.218570\pi$
$860$	−2.10475	+	11.9366i	−0.0717714	+	0.407036i
$861$	−24.9914	+	3.70906i	−0.851706	+	0.126404i
$862$	−31.9571	+	26.8152i	−1.08846	+	0.913328i
$863$	−13.2036	−	7.62313i	−0.449457	−	0.259494i	0.258144	−	0.966107i	$-0.416889\pi$
$863$	−13.2036	−	7.62313i	−0.449457	−	0.259494i	−0.707601	+	0.706612i	$0.750223\pi$
$864$	−36.8753	+	19.7331i	−1.25452	+	0.671334i
$865$	20.2602	+	35.0917i	0.688868	+	1.19315i
$866$	−6.51481	−	36.9473i	−0.221382	−	1.25552i
$867$	−38.9965	−	4.98343i	−1.32439	−	0.169246i
$868$	4.66530	−	0.467656i	0.158351	−	0.0158733i
$869$	7.83936	+	21.5385i	0.265932	+	0.730643i
$870$	94.4193	−	60.6569i	3.20111	−	2.05646i
$871$	−1.54144	−	1.83702i	−0.0522299	−	0.0622451i
$872$	0.677385	+	0.391088i	0.0229391	+	0.0132439i
$873$	−3.80572	+	5.52394i	−0.128804	+	0.186957i
$874$	39.8923	+	23.0319i	1.34938	+	0.779064i
$875$	3.42709	+	7.11326i	0.115857	+	0.240472i
$876$	−18.1613	−	5.65051i	−0.613613	−	0.190913i
$877$	7.05459	−	2.56766i	0.238217	−	0.0867038i	−0.220153	−	0.975465i	$-0.570656\pi$
$877$	7.05459	−	2.56766i	0.238217	−	0.0867038i	0.458370	+	0.888762i	$0.348433\pi$
$878$	−1.22854	+	6.96740i	−0.0414612	+	0.235138i
$879$	10.0367	−	32.2589i	0.338529	−	1.08807i
$880$	−18.9363	−	22.5674i	−0.638342	−	0.760747i
$881$	0.717000	−	1.24188i	0.0241564	−	0.0418400i	−0.853695	−	0.520774i	$-0.825643\pi$
$881$	0.717000	−	1.24188i	0.0241564	−	0.0418400i	0.877851	+	0.478934i	$0.158977\pi$
$882$	12.2819	+	40.4661i	0.413554	+	1.36256i
$883$	17.3559	+	30.0612i	0.584071	+	1.01164i	0.994991	+	0.0999695i	$0.0318745\pi$
$883$	17.3559	+	30.0612i	0.584071	+	1.01164i	−0.410919	+	0.911672i	$0.634792\pi$
$884$	2.17449	−	5.97436i	0.0731360	−	0.200940i
$885$	−14.9546	+	9.60712i	−0.502692	+	0.322940i
$886$	−56.6500	−	47.5350i	−1.90320	−	1.59697i
$887$	−22.5616	−	18.9314i	−0.757544	−	0.635655i	0.179942	−	0.983677i	$-0.442409\pi$
$887$	−22.5616	−	18.9314i	−0.757544	−	0.635655i	−0.937486	+	0.348022i	$0.886853\pi$
$888$	0.160609	+	0.122273i	0.00538968	+	0.00410323i
$889$	14.8219	+	1.10815i	0.497111	+	0.0371660i
$890$		−	87.2747i		−	2.92545i
$891$	−21.4776	−	7.44981i	−0.719526	−	0.249578i
$892$	−38.6298	+	22.3030i	−1.29342	+	0.746758i
$893$	−2.16949	+	5.96062i	−0.0725991	+	0.199464i
$894$	20.9588	+	50.0606i	0.700968	+	1.67428i
$895$	−8.16396	−	1.43953i	−0.272891	−	0.0481181i
$896$	1.37373	+	1.91003i	0.0458930	+	0.0638097i
$897$	0.262057	+	5.52098i	0.00874982	+	0.184340i
$898$	−3.13873	−	1.14240i	−0.104741	−	0.0381225i
$899$	4.62251	−	8.00641i	0.154169	−	0.267029i
$900$	−23.9031	−	6.21066i	−0.796769	−	0.207022i
$901$	66.7379	−	38.5312i	2.22336	−	1.28366i
$902$	−26.3523	−	9.59145i	−0.877435	−	0.319360i
$903$	−7.91890	+	4.28921i	−0.263525	+	0.142736i
$904$	0.639880	+	0.536923i	0.0212821	+	0.0178578i
$905$	20.9659	+	57.6034i	0.696931	+	1.91480i
$906$	11.2083	+	49.6644i	0.372372	+	1.64999i
$907$	−9.70649	−	55.0483i	−0.322299	−	1.82785i	−0.528014	−	0.849235i	$-0.677063\pi$
$907$	−9.70649	−	55.0483i	−0.322299	−	1.82785i	0.205716	−	0.978612i	$-0.434048\pi$
$908$	−0.410316	−	0.710687i	−0.0136168	−	0.0235850i
$909$	10.7307	−	5.10337i	0.355915	−	0.169268i
$910$	7.55633	−	2.12745i	0.250490	−	0.0705242i
$911$	−11.8425	+	2.08816i	−0.392361	+	0.0691838i	−0.366348	−	0.930478i	$-0.619392\pi$
$911$	−11.8425	+	2.08816i	−0.392361	+	0.0691838i	−0.0260127	+	0.999662i	$0.508281\pi$
$912$	12.8052	+	19.9327i	0.424023	+	0.660039i
$913$	−6.98580	+	8.32535i	−0.231196	+	0.275529i
$914$	−16.7591	−	46.0452i	−0.554341	−	1.52304i
$915$	17.0156	+	12.9542i	0.562520	+	0.428253i
$916$	−3.54247	−	4.22175i	−0.117047	−	0.139491i
$917$	−5.21272	+	1.46761i	−0.172139	+	0.0484649i
$918$	−64.5239	−	13.5354i	−2.12961	−	0.446736i
$919$	−10.9429	+	18.9537i	−0.360973	+	0.625224i	−0.988121	−	0.153676i	$-0.950889\pi$
$919$	−10.9429	+	18.9537i	−0.360973	+	0.625224i	0.627148	+	0.778900i	$0.284222\pi$
$920$	−2.03807	−	0.741797i	−0.0671932	−	0.0244563i
$921$	12.2897	+	9.35628i	0.404959	+	0.308300i
$922$	−7.84543	+	9.34982i	−0.258376	+	0.307920i
$923$	4.65677	−	1.69493i	0.153280	−	0.0557892i
$924$	−4.76648	+	23.3068i	−0.156806	+	0.766739i
$925$	−0.728975	−	4.13423i	−0.0239686	−	0.135932i
$926$			52.6995i			1.73181i
$927$	−28.9104	−	13.2148i	−0.949542	−	0.434031i
$928$	86.2979			2.83287
$929$	27.7252	−	23.2642i	0.909635	−	0.763275i	−0.0624141	−	0.998050i	$-0.519880\pi$
$929$	27.7252	−	23.2642i	0.909635	−	0.763275i	0.972050	+	0.234776i	$0.0754355\pi$
$930$	−8.80397	+	1.98689i	−0.288693	+	0.0651527i
$931$	22.9299	−	9.00855i	0.751495	−	0.295243i
$932$	16.5342	−	19.7047i	0.541596	−	0.645449i
$933$	0.453192	−	1.45660i	0.0148368	−	0.0476870i
$934$	−30.2427	+	5.33261i	−0.989573	+	0.174488i
$935$		−	47.7584i		−	1.56187i
$936$	0.0680911	−	0.148965i	0.00222563	−	0.00486906i
$937$	10.4934	−	6.05838i	0.342805	−	0.197919i	−0.318707	−	0.947853i	$-0.603248\pi$
$937$	10.4934	−	6.05838i	0.342805	−	0.197919i	0.661512	+	0.749935i	$0.269915\pi$
$938$	21.5035	+	14.6553i	0.702114	+	0.478514i
$939$	20.0045	+	31.1392i	0.652822	+	1.01619i
$940$	1.93026	−	10.9471i	0.0629582	−	0.357054i
$941$	42.1226	−	15.3314i	1.37316	−	0.499789i	0.453061	−	0.891479i	$-0.350332\pi$
$941$	42.1226	−	15.3314i	1.37316	−	0.499789i	0.920097	+	0.391691i	$0.128110\pi$
$942$	48.2993	−	63.4422i	1.57368	−	2.06706i
$943$	35.2894	−	6.22247i	1.14918	−	0.202631i
$944$	−13.2906			−0.432572
$945$	−16.6993	−	37.7251i	−0.543227	−	1.22720i
$946$	−9.99626			−0.325007
$947$	11.6049	−	2.04625i	0.377108	−	0.0664943i	0.0181183	−	0.999836i	$-0.494232\pi$
$947$	11.6049	−	2.04625i	0.377108	−	0.0664943i	0.358990	+	0.933342i	$0.383121\pi$
$948$	12.4748	+	29.7964i	0.405163	+	0.967742i
$949$	−2.46514	+	0.897239i	−0.0800219	+	0.0291256i
$950$	−4.92957	+	27.9570i	−0.159937	+	0.907045i
$951$	−19.7200	+	38.2356i	−0.639466	+	1.23987i
$952$	−0.138202	+	1.84850i	−0.00447914	+	0.0599104i
$953$	−9.53155	+	5.50304i	−0.308757	+	0.178261i	−0.646370	−	0.763024i	$-0.723714\pi$
$953$	−9.53155	+	5.50304i	−0.308757	+	0.178261i	0.337613	+	0.941285i	$0.390381\pi$
$954$	66.7283	−	31.7350i	2.16041	−	1.02746i
$955$			49.2572i			1.59393i
$956$	−30.5806	+	5.39219i	−0.989048	+	0.174396i
$957$	31.8210	+	34.4629i	1.02863	+	1.11403i
$958$	−42.5737	+	50.7373i	−1.37549	+	1.63925i
$959$	−0.305913	−	0.425342i	−0.00987844	−	0.0137350i
$960$	−29.7441	−	32.2136i	−0.959988	−	1.03969i
$961$	23.1778	−	19.4485i	0.747671	−	0.627371i
$962$	1.03623			0.0334093
$963$	12.4811	+	12.2930i	0.402198	+	0.396136i
$964$			60.3452i			1.94359i
$965$	−9.96353	−	56.5060i	−0.320737	−	1.81899i
$966$	−18.9737	−	56.8985i	−0.610470	−	1.83068i
$967$	12.3214	−	4.48462i	0.396229	−	0.144216i	−0.136218	−	0.990679i	$-0.543495\pi$
$967$	12.3214	−	4.48462i	0.396229	−	0.144216i	0.532447	+	0.846463i	$0.321273\pi$
$968$	0.330219	−	0.393539i	0.0106136	−	0.0126488i
$969$	−4.86857	+	38.0976i	−0.156401	+	1.22387i
$970$	−12.6976	−	4.62153i	−0.407694	−	0.148388i
$971$	3.30587	−	5.72593i	0.106090	−	0.183754i	−0.808093	−	0.589055i	$-0.799500\pi$
$971$	3.30587	−	5.72593i	0.106090	−	0.183754i	0.914183	+	0.405301i	$0.132833\pi$
$972$	−30.7323	−	9.05218i	−0.985738	−	0.290349i
$973$	−15.3725	+	15.7661i	−0.492819	+	0.505439i
$974$	22.5572	+	26.8827i	0.722781	+	0.861377i
$975$	−3.14206	+	1.31548i	−0.100626	+	0.0421291i
$976$	5.46912	+	15.0263i	0.175062	+	0.480980i
$977$	−17.2636	+	20.5739i	−0.552311	+	0.658218i	−0.967900	−	0.251334i	$-0.919131\pi$
$977$	−17.2636	+	20.5739i	−0.552311	+	0.658218i	0.415590	+	0.909552i	$0.363575\pi$
$978$	11.5543	−	22.4029i	0.369467	−	0.716367i
$979$	35.9245	−	6.33446i	1.14815	−	0.202450i
$980$	−36.8311	+	22.5247i	−1.17653	+	0.719526i
$981$	−5.61626	−	20.3411i	−0.179314	−	0.649440i
$982$	−11.5346	−	19.9784i	−0.368083	−	0.637538i
$983$	0.740849	+	4.20156i	0.0236294	+	0.134009i	0.994340	−	0.106241i	$-0.0338816\pi$
$983$	0.740849	+	4.20156i	0.0236294	+	0.134009i	−0.970711	+	0.240250i	$0.922770\pi$
$984$	−1.01393	−	0.315464i	−0.0323229	−	0.0100566i
$985$	3.51327	+	9.65263i	0.111942	+	0.307558i
$986$	104.210	+	87.4423i	3.31871	+	2.78473i
$987$	7.26241	−	3.93362i	0.231165	−	0.125209i
$988$	−3.33719	−	1.21464i	−0.106170	−	0.0386428i
$989$	11.0619	−	6.38657i	0.351747	−	0.203081i
$990$	3.64458	−	45.6474i	0.115832	−	1.45077i
$991$	−22.2053	+	38.4607i	−0.705374	+	1.22174i	0.261182	+	0.965290i	$0.415888\pi$
$991$	−22.2053	+	38.4607i	−0.705374	+	1.22174i	−0.966556	+	0.256455i	$0.917446\pi$
$992$	−6.52176	−	2.37373i	−0.207066	−	0.0753659i
$993$	−2.71983	−	1.40275i	−0.0863112	−	0.0445151i
$994$	−43.6575	+	31.3992i	−1.38473	+	0.995922i
$995$	−29.0547	−	5.12312i	−0.921095	−	0.162414i
$996$	−9.27779	+	12.1866i	−0.293978	+	0.386146i
$997$	−12.0637	+	33.1447i	−0.382060	+	1.04970i	0.588427	+	0.808550i	$0.299747\pi$
$997$	−12.0637	+	33.1447i	−0.382060	+	1.04970i	−0.970487	+	0.241152i	$0.922475\pi$
$998$	6.79990	−	3.92592i	0.215247	−	0.124273i
$999$	−0.772275	−	5.39080i	−0.0244337	−	0.170557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.5	✓	132
3.2	odd	2		567.2.ba.a.530.18		132
7.3	odd	6		189.2.bd.a.59.18	yes	132
21.17	even	6		567.2.bd.a.206.5		132
27.11	odd	18		189.2.bd.a.173.18	yes	132
27.16	even	9		567.2.bd.a.278.5		132
189.38	even	18	inner	189.2.ba.a.38.5	yes	132
189.178	odd	18		567.2.ba.a.521.18		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.5	✓	132	1.1	even	1	trivial
189.2.ba.a.38.5	yes	132	189.38	even	18	inner
189.2.bd.a.59.18	yes	132	7.3	odd	6
189.2.bd.a.173.18	yes	132	27.11	odd	18
567.2.ba.a.521.18		132	189.178	odd	18
567.2.ba.a.530.18		132	3.2	odd	2
567.2.bd.a.206.5		132	21.17	even	6
567.2.bd.a.278.5		132	27.16	even	9

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.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98316 + 0.349685i) q^{2} +(-1.71808 - 0.219557i) q^{3} +(1.93127 - 0.702926i) q^{4} +(0.521105 - 2.95533i) q^{5} +(3.48401 - 0.165370i) q^{6} +(-1.49002 + 2.18628i) q^{7} +(-0.0963007 + 0.0555993i) q^{8} +(2.90359 + 0.754431i) q^{9} +O(q^{10})\)	\(q+(-1.98316 + 0.349685i) q^{2} +(-1.71808 - 0.219557i) q^{3} +(1.93127 - 0.702926i) q^{4} +(0.521105 - 2.95533i) q^{5} +(3.48401 - 0.165370i) q^{6} +(-1.49002 + 2.18628i) q^{7} +(-0.0963007 + 0.0555993i) q^{8} +(2.90359 + 0.754431i) q^{9} +6.04313i q^{10} +(-2.48751 + 0.438614i) q^{11} +(-3.47241 + 0.783659i) q^{12} +(-0.315597 + 0.376113i) q^{13} +(2.19045 - 4.85680i) q^{14} +(-1.54416 + 4.96308i) q^{15} +(-2.97724 + 2.49820i) q^{16} -6.30061 q^{17} +(-6.02211 - 0.480817i) q^{18} +3.51943i q^{19} +(-1.07098 - 6.07385i) q^{20} +(3.03999 - 3.42906i) q^{21} +(4.77976 - 1.73969i) q^{22} +(-4.17780 + 4.97890i) q^{23} +(0.177659 - 0.0743805i) q^{24} +(-3.76397 - 1.36997i) q^{25} +(0.494358 - 0.856254i) q^{26} +(-4.82296 - 1.93367i) q^{27} +(-1.34085 + 5.26969i) q^{28} +(6.89178 + 8.21331i) q^{29} +(1.32681 - 10.3826i) q^{30} +(-0.294914 - 0.810269i) q^{31} +(5.17373 - 6.16581i) q^{32} +(4.37003 - 0.207426i) q^{33} +(12.4951 - 2.20323i) q^{34} +(5.68473 + 5.54279i) q^{35} +(6.13794 - 0.583997i) q^{36} +(0.524026 + 0.907639i) q^{37} +(-1.23069 - 6.97960i) q^{38} +(0.624798 - 0.576901i) q^{39} +(0.114131 + 0.313574i) q^{40} +(-4.22344 - 3.54389i) q^{41} +(-4.82971 + 7.86343i) q^{42} +(-1.84673 - 0.672155i) q^{43} +(-4.49574 + 2.59562i) q^{44} +(3.74267 - 8.18793i) q^{45} +(6.54421 - 11.3349i) q^{46} +(1.69363 + 0.616432i) q^{47} +(5.66363 - 3.63843i) q^{48} +(-2.55966 - 6.51522i) q^{49} +(7.94362 + 1.40068i) q^{50} +(10.8249 + 1.38334i) q^{51} +(-0.345124 + 0.948219i) q^{52} +(-10.5923 + 6.11546i) q^{53} +(10.2409 + 2.14827i) q^{54} +7.57997i q^{55} +(0.0219346 - 0.293385i) q^{56} +(0.772713 - 6.04665i) q^{57} +(-16.5396 - 13.8784i) q^{58} +(2.61962 + 2.19812i) q^{59} +(0.506481 + 10.6705i) q^{60} +(1.40721 - 3.86627i) q^{61} +(0.868201 + 1.50377i) q^{62} +(-5.97581 + 5.22395i) q^{63} +(-4.21774 + 7.30535i) q^{64} +(0.947080 + 1.12869i) q^{65} +(-8.59396 + 1.93950i) q^{66} +(-0.848137 + 4.81002i) q^{67} +(-12.1682 + 4.42887i) q^{68} +(8.27093 - 7.63689i) q^{69} +(-13.2120 - 9.00440i) q^{70} +(-8.74108 - 5.04667i) q^{71} +(-0.321564 + 0.0887852i) q^{72} +(4.62724 + 2.67154i) q^{73} +(-1.35662 - 1.61675i) q^{74} +(6.16601 + 3.18012i) q^{75} +(2.47390 + 6.79698i) q^{76} +(2.74751 - 6.09194i) q^{77} +(-1.03734 + 1.36257i) q^{78} +(-1.57575 - 8.93651i) q^{79} +(5.83156 + 10.1006i) q^{80} +(7.86167 + 4.38112i) q^{81} +(9.61502 + 5.55124i) q^{82} +(3.29602 - 2.76569i) q^{83} +(3.46068 - 8.75935i) q^{84} +(-3.28328 + 18.6204i) q^{85} +(3.89741 + 0.687219i) q^{86} +(-10.0373 - 15.6242i) q^{87} +(0.215162 - 0.180542i) q^{88} -14.4420 q^{89} +(-4.55912 + 17.5468i) q^{90} +(-0.352044 - 1.25040i) q^{91} +(-4.56867 + 12.5523i) q^{92} +(0.328785 + 1.45686i) q^{93} +(-3.57431 - 0.630247i) q^{94} +(10.4011 + 1.83399i) q^{95} +(-10.2426 + 9.45742i) q^{96} +(-0.764758 + 2.10116i) q^{97} +(7.35451 + 12.0257i) q^{98} +(-7.55360 - 0.603095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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