LMFDB - Embedded newform 189.2.bd.a.47.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (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			47.20
Character	$\chi$	$=$	189.47
Dual form			189.2.bd.a.185.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.22112 + 0.391643i) q^{2} +(1.67689 + 0.433617i) q^{3} +(2.90060 + 1.05573i) q^{4} +(-3.20807 - 1.16764i) q^{5} +(3.55476 + 1.61986i) q^{6} +(-2.62457 + 0.334082i) q^{7} +(2.12267 + 1.22552i) q^{8} +(2.62395 + 1.45426i) q^{9} +O(q^{10})$	\(q+(2.22112 + 0.391643i) q^{2} +(1.67689 + 0.433617i) q^{3} +(2.90060 + 1.05573i) q^{4} +(-3.20807 - 1.16764i) q^{5} +(3.55476 + 1.61986i) q^{6} +(-2.62457 + 0.334082i) q^{7} +(2.12267 + 1.22552i) q^{8} +(2.62395 + 1.45426i) q^{9} +(-6.66821 - 3.84989i) q^{10} +(0.870169 + 2.39077i) q^{11} +(4.40622 + 3.02810i) q^{12} +(2.11236 - 5.80365i) q^{13} +(-5.96033 - 0.285861i) q^{14} +(-4.87329 - 3.34909i) q^{15} +(-0.494450 - 0.414893i) q^{16} +(-1.19927 + 2.07719i) q^{17} +(5.25856 + 4.25774i) q^{18} +(-1.07808 + 0.622427i) q^{19} +(-8.07261 - 6.77373i) q^{20} +(-4.54600 - 0.577839i) q^{21} +(0.996420 + 5.65098i) q^{22} +(-2.21485 + 0.390538i) q^{23} +(3.02808 + 2.97550i) q^{24} +(5.09811 + 4.27783i) q^{25} +(6.96475 - 12.0633i) q^{26} +(3.76950 + 3.57643i) q^{27} +(-7.96554 - 1.80181i) q^{28} +(0.685884 + 1.88445i) q^{29} +(-9.51251 - 9.34731i) q^{30} +(-0.538767 + 1.48025i) q^{31} +(-4.08675 - 4.87040i) q^{32} +(0.422504 + 4.38639i) q^{33} +(-3.47723 + 4.14400i) q^{34} +(8.80991 + 1.99281i) q^{35} +(6.07573 + 6.98842i) q^{36} +10.0245 q^{37} +(-2.63830 + 0.960264i) q^{38} +(6.05876 - 8.81616i) q^{39} +(-5.37870 - 6.41008i) q^{40} +(5.39584 + 1.96393i) q^{41} +(-9.87090 - 3.06386i) q^{42} +(-0.110284 + 0.625454i) q^{43} +7.85333i q^{44} +(-6.71977 - 7.72921i) q^{45} -5.07240 q^{46} +(-11.3454 + 4.12940i) q^{47} +(-0.649236 - 0.910134i) q^{48} +(6.77678 - 1.75365i) q^{49} +(9.64814 + 11.4982i) q^{50} +(-2.91175 + 2.96321i) q^{51} +(12.2542 - 14.6040i) q^{52} +(-4.15350 + 2.39802i) q^{53} +(6.97183 + 9.41998i) q^{54} -8.68580i q^{55} +(-5.98053 - 2.50733i) q^{56} +(-2.07772 + 0.576273i) q^{57} +(0.785398 + 4.45421i) q^{58} +(2.11297 - 1.77299i) q^{59} +(-10.5997 - 14.8593i) q^{60} +(2.52148 + 6.92772i) q^{61} +(-1.77639 + 3.07681i) q^{62} +(-7.37260 - 2.94020i) q^{63} +(-6.52423 - 11.3003i) q^{64} +(-13.5532 + 16.1520i) q^{65} +(-0.779468 + 9.90816i) q^{66} +(-1.39215 - 7.89530i) q^{67} +(-5.67155 + 4.75899i) q^{68} +(-3.88342 - 0.305506i) q^{69} +(18.7874 + 7.87660i) q^{70} +(4.45847 - 2.57410i) q^{71} +(3.78755 + 6.30263i) q^{72} -13.4098i q^{73} +(22.2655 + 3.92601i) q^{74} +(6.69406 + 9.38409i) q^{75} +(-3.78418 + 0.667254i) q^{76} +(-3.08253 - 5.98404i) q^{77} +(16.9100 - 17.2089i) q^{78} +(0.167826 - 0.951791i) q^{79} +(1.10178 + 1.90835i) q^{80} +(4.77026 + 7.63182i) q^{81} +(11.2156 + 6.47536i) q^{82} +(2.38230 - 0.867085i) q^{83} +(-12.5761 - 6.47544i) q^{84} +(6.27275 - 5.26346i) q^{85} +(-0.489910 + 1.34602i) q^{86} +(0.333026 + 3.45744i) q^{87} +(-1.08286 + 6.14122i) q^{88} +(-4.97533 - 8.61753i) q^{89} +(-11.8983 - 19.7992i) q^{90} +(-3.60514 + 15.9378i) q^{91} +(-6.83671 - 1.20550i) q^{92} +(-1.54532 + 2.24860i) q^{93} +(-26.8168 + 4.72852i) q^{94} +(4.18532 - 0.737985i) q^{95} +(-4.74116 - 9.93922i) q^{96} +(-7.93719 - 1.39954i) q^{97} +(15.7388 - 1.24098i) q^{98} +(-1.19352 + 7.53871i) 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} - 15 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 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.22112	+	0.391643i	1.57057	+	0.276934i	0.890073	−	0.455819i	$-0.150653\pi$
$2$	2.22112	+	0.391643i	1.57057	+	0.276934i	0.680496	+	0.732752i	$0.261765\pi$
$3$	1.67689	+	0.433617i	0.968156	+	0.250349i
$3$	1.67689	+	0.433617i	0.968156	+	0.250349i
$4$	2.90060	+	1.05573i	1.45030	+	0.527866i
$5$	−3.20807	−	1.16764i	−1.43469	−	0.522186i	−0.496421	−	0.868082i	$-0.665353\pi$
$5$	−3.20807	−	1.16764i	−1.43469	−	0.522186i	−0.938273	+	0.345896i	$0.887575\pi$
$6$	3.55476	+	1.61986i	1.45122	+	0.661305i
$7$	−2.62457	+	0.334082i	−0.991996	+	0.126271i
$7$	−2.62457	+	0.334082i	−0.991996	+	0.126271i
$8$	2.12267	+	1.22552i	0.750477	+	0.433288i
$9$	2.62395	+	1.45426i	0.874651	+	0.484753i
$10$	−6.66821	−	3.84989i	−2.10867	−	1.21744i
$11$	0.870169	+	2.39077i	0.262366	+	0.720844i	0.999007	+	0.0445598i	$0.0141885\pi$
$11$	0.870169	+	2.39077i	0.262366	+	0.720844i	−0.736641	+	0.676284i	$0.763589\pi$
$12$	4.40622	+	3.02810i	1.27197	+	0.874137i
$13$	2.11236	−	5.80365i	0.585862	−	1.60964i	−0.192131	−	0.981369i	$-0.561540\pi$
$13$	2.11236	−	5.80365i	0.585862	−	1.60964i	0.777993	−	0.628273i	$-0.216238\pi$
$14$	−5.96033	−	0.285861i	−1.59297	−	0.0763994i
$15$	−4.87329	−	3.34909i	−1.25828	−	0.864731i
$16$	−0.494450	−	0.414893i	−0.123613	−	0.103723i
$17$	−1.19927	+	2.07719i	−0.290865	+	0.503793i	−0.974014	−	0.226486i	$-0.927276\pi$
$17$	−1.19927	+	2.07719i	−0.290865	+	0.503793i	0.683150	+	0.730278i	$0.260610\pi$
$18$	5.25856	+	4.25774i	1.23945	+	1.00356i
$19$	−1.07808	+	0.622427i	−0.247328	+	0.142795i	−0.618540	−	0.785753i	$-0.712276\pi$
$19$	−1.07808	+	0.622427i	−0.247328	+	0.142795i	0.371212	+	0.928548i	$0.378942\pi$
$20$	−8.07261	−	6.77373i	−1.80509	−	1.51465i
$21$	−4.54600	−	0.577839i	−0.992018	−	0.126095i
$22$	0.996420	+	5.65098i	0.212437	+	1.20479i
$23$	−2.21485	+	0.390538i	−0.461829	+	0.0814329i	−0.399722	−	0.916637i	$-0.630893\pi$
$23$	−2.21485	+	0.390538i	−0.461829	+	0.0814329i	−0.0621072	+	0.998069i	$0.519782\pi$
$24$	3.02808	+	2.97550i	0.618105	+	0.607371i
$25$	5.09811	+	4.27783i	1.01962	+	0.855565i
$26$	6.96475	−	12.0633i	1.36590	−	2.36581i
$27$	3.76950	+	3.57643i	0.725441	+	0.688284i
$28$	−7.96554	−	1.80181i	−1.50535	−	0.340510i
$29$	0.685884	+	1.88445i	0.127366	+	0.349934i	0.986943	−	0.161072i	$-0.0514952\pi$
$29$	0.685884	+	1.88445i	0.127366	+	0.349934i	−0.859577	+	0.511006i	$0.829273\pi$
$30$	−9.51251	−	9.34731i	−1.73674	−	1.70658i
$31$	−0.538767	+	1.48025i	−0.0967653	+	0.265861i	−0.978626	−	0.205650i	$-0.934069\pi$
$31$	−0.538767	+	1.48025i	−0.0967653	+	0.265861i	0.881860	+	0.471511i	$0.156291\pi$
$32$	−4.08675	−	4.87040i	−0.722442	−	0.860972i
$33$	0.422504	+	4.38639i	0.0735485	+	0.763572i
$34$	−3.47723	+	4.14400i	−0.596340	+	0.710691i
$35$	8.80991	+	1.99281i	1.48915	+	0.336846i
$36$	6.07573	+	6.98842i	1.01262	+	1.16474i
$37$	10.0245			1.64801			0.824006	−	0.566581i	$-0.191734\pi$
$37$	10.0245			1.64801			0.824006	+	0.566581i	$0.191734\pi$
$38$	−2.63830	+	0.960264i	−0.427989	+	0.155775i
$39$	6.05876	−	8.81616i	0.970178	−	1.41171i
$40$	−5.37870	−	6.41008i	−0.850447	−	1.01352i
$41$	5.39584	+	1.96393i	0.842689	+	0.306714i	0.727056	−	0.686578i	$-0.240888\pi$
$41$	5.39584	+	1.96393i	0.842689	+	0.306714i	0.115633	+	0.993292i	$0.463110\pi$
$42$	−9.87090	−	3.06386i	−1.52311	−	0.472764i
$43$	−0.110284	+	0.625454i	−0.0168182	+	0.0953809i	−0.992061	−	0.125754i	$-0.959865\pi$
$43$	−0.110284	+	0.625454i	−0.0168182	+	0.0953809i	0.975243	+	0.221135i	$0.0709761\pi$
$44$			7.85333i			1.18393i
$45$	−6.71977	−	7.72921i	−1.00172	−	1.15220i
$46$	−5.07240			−0.747885
$47$	−11.3454	+	4.12940i	−1.65490	+	0.602334i	−0.989549	−	0.144197i	$-0.953940\pi$
$47$	−11.3454	+	4.12940i	−1.65490	+	0.602334i	−0.665351	+	0.746531i	$0.731718\pi$
$48$	−0.649236	−	0.910134i	−0.0937092	−	0.131366i
$49$	6.77678	−	1.75365i	0.968111	−	0.250521i
$50$	9.64814	+	11.4982i	1.36445	+	1.62609i
$51$	−2.91175	+	2.96321i	−0.407726	+	0.414932i
$52$	12.2542	−	14.6040i	1.69935	−	2.02521i
$53$	−4.15350	+	2.39802i	−0.570527	+	0.329394i	−0.757360	−	0.652998i	$-0.773511\pi$
$53$	−4.15350	+	2.39802i	−0.570527	+	0.329394i	0.186833	+	0.982392i	$0.440178\pi$
$54$	6.97183	+	9.41998i	0.948745	+	1.28190i
$55$		−	8.68580i		−	1.17119i
$56$	−5.98053	−	2.50733i	−0.799181	−	0.335056i
$57$	−2.07772	+	0.576273i	−0.275200	+	0.0763293i
$58$	0.785398	+	4.45421i	0.103128	+	0.584867i
$59$	2.11297	−	1.77299i	0.275085	−	0.230824i	−0.494799	−	0.869007i	$-0.664758\pi$
$59$	2.11297	−	1.77299i	0.275085	−	0.230824i	0.769884	+	0.638183i	$0.220314\pi$
$60$	−10.5997	−	14.8593i	−1.36842	−	1.91832i
$61$	2.52148	+	6.92772i	0.322843	+	0.887004i	0.989871	+	0.141971i	$0.0453440\pi$
$61$	2.52148	+	6.92772i	0.322843	+	0.887004i	−0.667028	+	0.745033i	$0.732434\pi$
$62$	−1.77639	+	3.07681i	−0.225602	+	0.390755i
$63$	−7.37260	−	2.94020i	−0.928860	−	0.370430i
$64$	−6.52423	−	11.3003i	−0.815529	−	1.41254i
$65$	−13.5532	+	16.1520i	−1.68106	+	2.00341i
$66$	−0.779468	+	9.90816i	−0.0959458	+	1.21961i
$67$	−1.39215	−	7.89530i	−0.170079	−	0.964564i	−0.943672	−	0.330882i	$-0.892654\pi$
$67$	−1.39215	−	7.89530i	−0.170079	−	0.964564i	0.773594	−	0.633682i	$-0.218457\pi$
$68$	−5.67155	+	4.75899i	−0.687776	+	0.577113i
$69$	−3.88342	−	0.305506i	−0.467509	−	0.0367786i
$70$	18.7874	+	7.87660i	2.24552	+	0.941434i
$71$	4.45847	−	2.57410i	0.529123	−	0.305489i	−0.211536	−	0.977370i	$-0.567847\pi$
$71$	4.45847	−	2.57410i	0.529123	−	0.305489i	0.740659	+	0.671881i	$0.234513\pi$
$72$	3.78755	+	6.30263i	0.446367	+	0.742772i
$73$		−	13.4098i		−	1.56949i	−0.619817	−	0.784747i	$-0.712793\pi$
$73$		−	13.4098i		−	1.56949i	0.619817	−	0.784747i	$-0.287207\pi$
$74$	22.2655	+	3.92601i	2.58832	+	0.456390i
$75$	6.69406	+	9.38409i	0.772964	+	1.08358i
$76$	−3.78418	+	0.667254i	−0.434076	+	0.0765392i
$77$	−3.08253	−	5.98404i	−0.351287	−	0.681945i
$78$	16.9100	−	17.2089i	1.91468	−	1.94852i
$79$	0.167826	−	0.951791i	0.0188819	−	0.107085i	−0.973910	−	0.226934i	$-0.927130\pi$
$79$	0.167826	−	0.951791i	0.0188819	−	0.107085i	0.992792	+	0.119849i	$0.0382410\pi$
$80$	1.10178	+	1.90835i	0.123183	+	0.213360i
$81$	4.77026	+	7.63182i	0.530029	+	0.847980i
$82$	11.2156	+	6.47536i	1.23856	+	0.715084i
$83$	2.38230	−	0.867085i	0.261491	−	0.0951749i	−0.207948	−	0.978140i	$-0.566678\pi$
$83$	2.38230	−	0.867085i	0.261491	−	0.0951749i	0.469439	+	0.882965i	$0.344456\pi$
$84$	−12.5761	−	6.47544i	−1.37216	−	0.706528i
$85$	6.27275	−	5.26346i	0.680375	−	0.570903i
$86$	−0.489910	+	1.34602i	−0.0528283	+	0.145145i
$87$	0.333026	+	3.45744i	0.0357041	+	0.370676i
$88$	−1.08286	+	6.14122i	−0.115434	+	0.654656i
$89$	−4.97533	−	8.61753i	−0.527384	−	0.913456i	−0.999491	−	0.0319144i	$-0.989840\pi$
$89$	−4.97533	−	8.61753i	−0.527384	−	0.913456i	0.472107	−	0.881541i	$-0.343494\pi$
$90$	−11.8983	−	19.7992i	−1.25419	−	2.08702i
$91$	−3.60514	+	15.9378i	−0.377921	+	1.67074i
$92$	−6.83671	−	1.20550i	−0.712776	−	0.125682i
$93$	−1.54532	+	2.24860i	−0.160242	+	0.233169i
$94$	−26.8168	+	4.72852i	−2.76594	+	0.487710i
$95$	4.18532	−	0.737985i	0.429405	−	0.0757156i
$96$	−4.74116	−	9.93922i	−0.483893	−	1.01442i
$97$	−7.93719	−	1.39954i	−0.805899	−	0.142102i	−0.244503	−	0.969649i	$-0.578625\pi$
$97$	−7.93719	−	1.39954i	−0.805899	−	0.142102i	−0.561397	+	0.827547i	$0.689736\pi$
$98$	15.7388	−	1.24098i	1.58986	−	0.125358i
$99$	−1.19352	+	7.53871i	−0.119953	+	0.757669i
$100$	10.2714	+	17.7905i	1.02714	+	1.77905i
$101$	0.323316	−	1.83362i	0.0321711	−	0.182452i	−0.964488	−	0.264127i	$-0.914916\pi$
$101$	0.323316	−	1.83362i	0.0321711	−	0.182452i	0.996659	+	0.0816758i	$0.0260272\pi$
$102$	−7.62786	+	5.44127i	−0.755271	+	0.538766i
$103$	−4.55222	+	12.5071i	−0.448544	+	1.23236i	0.485194	+	0.874407i	$0.338749\pi$
$103$	−4.55222	+	12.5071i	−0.448544	+	1.23236i	−0.933738	+	0.357958i	$0.883473\pi$
$104$	11.5963	−	9.73048i	1.13711	−	0.954152i
$105$	13.9092	+	7.16185i	1.35740	+	0.698925i
$106$	−10.1646	+	3.69960i	−0.987271	+	0.359337i
$107$	−8.41217	−	4.85677i	−0.813235	−	0.469521i	0.0348431	−	0.999393i	$-0.488907\pi$
$107$	−8.41217	−	4.85677i	−0.813235	−	0.469521i	−0.848078	+	0.529871i	$0.822240\pi$
$108$	7.15806	+	14.3534i	0.688785	+	1.38115i
$109$	−3.57501	−	6.19210i	−0.342424	−	0.593095i	0.642459	−	0.766320i	$-0.277914\pi$
$109$	−3.57501	−	6.19210i	−0.342424	−	0.593095i	−0.984882	+	0.173225i	$0.944581\pi$
$110$	3.40174	−	19.2922i	0.324343	−	1.83944i
$111$	16.8100	+	4.34678i	1.59553	+	0.412578i
$112$	1.43633	+	0.923730i	0.135720	+	0.0872843i
$113$	1.44663	−	0.255080i	0.136088	−	0.0239959i	−0.105189	−	0.994452i	$-0.533545\pi$
$113$	1.44663	−	0.255080i	0.136088	−	0.0239959i	0.241277	+	0.970456i	$0.422434\pi$
$114$	−4.84055	+	0.466249i	−0.453359	+	0.0436682i
$115$	7.56142	+	1.33328i	0.705106	+	0.124329i
$116$			6.19015i			0.574741i
$117$	13.9827	−	12.1566i	1.29270	−	1.12388i
$118$	5.38754	−	3.11050i	0.495963	−	0.286345i
$119$	2.45361	−	5.85239i	0.224922	−	0.536488i
$120$	−6.23999	−	13.0813i	−0.569631	−	1.19416i
$121$	3.46791	−	2.90992i	0.315264	−	0.264538i
$122$	2.88732	+	16.3748i	0.261406	+	1.48251i
$123$	8.19667	+	5.63302i	0.739069	+	0.507913i
$124$	−3.12549	+	3.72482i	−0.280678	+	0.334498i
$125$	−2.82525	−	4.89347i	−0.252698	−	0.437685i
$126$	−15.2239	−	9.41796i	−1.35625	−	0.839018i
$127$	4.42813	−	7.66974i	0.392933	−	0.680580i	−0.599902	−	0.800073i	$-0.704794\pi$
$127$	4.42813	−	7.66974i	0.392933	−	0.680580i	0.992835	+	0.119494i	$0.0381271\pi$
$128$	−5.71639	−	15.7056i	−0.505262	−	1.38820i
$129$	−0.456143	+	1.00100i	−0.0401611	+	0.0881331i
$130$	−36.4291	+	30.5676i	−3.19504	+	2.68096i
$131$	3.28712	+	18.6422i	0.287197	+	1.62877i	0.697331	+	0.716749i	$0.254371\pi$
$131$	3.28712	+	18.6422i	0.287197	+	1.62877i	−0.410134	+	0.912025i	$0.634518\pi$
$132$	−3.40533	+	13.1692i	−0.296396	+	1.14623i
$133$	2.62155	−	1.99377i	0.227317	−	0.172882i
$134$		−	18.0816i		−	1.56201i
$135$	−7.91684	−	15.8749i	−0.681373	−	1.36629i
$136$	−5.09129	+	2.93946i	−0.436575	+	0.252056i
$137$	−0.946962	+	1.12855i	−0.0809044	+	0.0964182i	−0.804978	−	0.593304i	$-0.797823\pi$
$137$	−0.946962	+	1.12855i	−0.0809044	+	0.0964182i	0.724074	+	0.689723i	$0.242268\pi$
$138$	−8.50589	−	2.19948i	−0.724069	−	0.187232i
$139$	8.68671	+	10.3524i	0.736798	+	0.878081i	0.996147	−	0.0877025i	$-0.0279525\pi$
$139$	8.68671	+	10.3524i	0.736798	+	0.878081i	−0.259349	+	0.965784i	$0.583508\pi$
$140$	23.4502	+	15.0812i	1.98190	+	1.27460i
$141$	−20.8157	+	2.00500i	−1.75299	+	0.168851i
$142$	10.9109	−	3.97125i	0.915624	−	0.333260i
$143$	15.7133			1.31401
$144$	−0.694052	−	1.80772i	−0.0578376	−	0.150643i
$145$		−	6.84633i		−	0.568556i
$146$	5.25184	−	29.7847i	0.434645	−	2.46500i
$147$	12.1244	−	0.00215530i	1.00000	−	0.000177767i
$148$	29.0770	+	10.5831i	2.39011	+	0.869929i
$149$	−9.94653	−	11.8538i	−0.814851	−	0.971102i	0.185081	−	0.982723i	$-0.440745\pi$
$149$	−9.94653	−	11.8538i	−0.814851	−	0.971102i	−0.999932	+	0.0116212i	$0.996301\pi$
$150$	11.1931	+	23.4649i	0.913913	+	1.91590i
$151$	−5.27288	+	1.91917i	−0.429101	+	0.156180i	−0.547537	−	0.836782i	$-0.684434\pi$
$151$	−5.27288	+	1.91917i	−0.429101	+	0.156180i	0.118436	+	0.992962i	$0.462212\pi$
$152$	−3.05120			−0.247485
$153$	−6.16759	+	3.70641i	−0.498620	+	0.299645i
$154$	−4.50307	−	14.4985i	−0.362868	−	1.16832i
$155$	3.45680	−	4.11966i	0.277657	−	0.330899i
$156$	26.8815	−	19.1757i	2.15224	−	1.53529i
$157$	7.00599	+	8.34941i	0.559139	+	0.666356i	0.969364	−	0.245628i	$-0.0789943\pi$
$157$	7.00599	+	8.34941i	0.559139	+	0.666356i	−0.410225	+	0.911984i	$0.634550\pi$
$158$	0.745525	−	2.04831i	0.0593108	−	0.162955i
$159$	−8.00480	+	2.22020i	−0.634822	+	0.176074i
$160$	7.42370	+	20.3964i	0.586895	+	1.61248i
$161$	5.68257	−	1.76494i	0.447850	−	0.139097i
$162$	7.60636	+	18.8194i	0.597612	+	1.47859i
$163$	−12.6009	+	21.8255i	−0.986982	+	1.70950i	−0.354206	+	0.935168i	$0.615249\pi$
$163$	−12.6009	+	21.8255i	−0.986982	+	1.70950i	−0.632776	+	0.774335i	$0.718085\pi$
$164$	13.5778	+	11.3931i	1.06025	+	0.889654i
$165$	3.76631	−	14.5652i	0.293207	−	1.13390i
$166$	5.63095	−	0.992889i	0.437047	−	0.0770631i
$167$	0.497967	+	2.82411i	0.0385338	+	0.218536i	0.997994	−	0.0633078i	$-0.0201650\pi$
$167$	0.497967	+	2.82411i	0.0385338	+	0.218536i	−0.959460	+	0.281844i	$0.909054\pi$
$168$	−8.94149	−	6.79779i	−0.689851	−	0.524461i
$169$	−19.2617	−	16.1625i	−1.48167	−	1.24327i
$170$	15.9939	−	9.23410i	1.22668	−	0.708223i
$171$	−3.73399	+	0.0654178i	−0.285545	+	0.00500262i
$172$	−0.980203	+	1.69776i	−0.0747398	+	0.129453i
$173$	−1.99872	−	1.67712i	−0.151960	−	0.127509i	0.563638	−	0.826022i	$-0.309401\pi$
$173$	−1.99872	−	1.67712i	−0.151960	−	0.127509i	−0.715598	+	0.698512i	$0.753846\pi$
$174$	−0.614392	+	7.80981i	−0.0465769	+	0.592060i
$175$	−14.8095	−	9.52428i	−1.11949	−	0.719968i
$176$	0.561658	−	1.54314i	0.0423366	−	0.116319i
$177$	4.31203	−	2.05690i	0.324112	−	0.154606i
$178$	−7.67581	−	21.0891i	−0.575326	−	1.58070i
$179$	−12.2805	−	7.09017i	−0.917890	−	0.529944i	−0.0349288	−	0.999390i	$-0.511120\pi$
$179$	−12.2805	−	7.09017i	−0.917890	−	0.529944i	−0.882961	+	0.469446i	$0.844454\pi$
$180$	−11.3314	−	29.5136i	−0.844593	−	2.19982i
$181$	−5.86603	−	3.38675i	−0.436018	−	0.251735i	0.265889	−	0.964004i	$-0.414335\pi$
$181$	−5.86603	−	3.38675i	−0.436018	−	0.251735i	−0.701907	+	0.712268i	$0.747668\pi$
$182$	−14.2494	+	33.9878i	−1.05623	+	2.51935i
$183$	1.22429	+	12.7104i	0.0905019	+	0.939581i
$184$	−5.18001	−	1.88537i	−0.381876	−	0.138991i
$185$	−32.1592	−	11.7050i	−2.36439	−	0.860568i
$186$	−4.31298	+	4.38920i	−0.316243	+	0.321832i
$187$	−6.00965	−	1.05966i	−0.439469	−	0.0774902i
$188$	−37.2681			−2.71805
$189$	−11.0882	−	8.12728i	−0.806545	−	0.591173i
$190$	9.58512			0.695377
$191$	16.4906	+	2.90774i	1.19322	+	0.210397i	0.734765	−	0.678321i	$-0.237292\pi$
$191$	16.4906	+	2.90774i	1.19322	+	0.210397i	0.458454	+	0.888718i	$0.348403\pi$
$192$	−6.04045	−	21.7784i	−0.435932	−	1.57172i
$193$	−10.7796	−	3.92347i	−0.775936	−	0.282418i	−0.0764589	−	0.997073i	$-0.524361\pi$
$193$	−10.7796	−	3.92347i	−0.775936	−	0.282418i	−0.699477	+	0.714655i	$0.746584\pi$
$194$	−17.0813	−	6.21709i	−1.22637	−	0.446361i
$195$	−29.7310	+	21.2084i	−2.12908	+	1.51876i
$196$	21.5081	+	2.06784i	1.53629	+	0.147703i
$197$	−0.880153	−	0.508156i	−0.0627083	−	0.0362046i	0.468318	−	0.883560i	$-0.344860\pi$
$197$	−0.880153	−	0.508156i	−0.0627083	−	0.0362046i	−0.531026	+	0.847355i	$0.678193\pi$
$198$	−5.60343	+	16.2769i	−0.398218	+	1.15675i
$199$	−4.74698	−	2.74067i	−0.336505	−	0.194281i	0.322221	−	0.946665i	$-0.395571\pi$
$199$	−4.74698	−	2.74067i	−0.336505	−	0.194281i	−0.658725	+	0.752384i	$0.728904\pi$
$200$	5.57903	+	15.3283i	0.394497	+	1.08387i
$201$	1.08904	−	13.8432i	0.0768148	−	0.976427i
$202$	1.43625	−	3.94605i	0.101054	−	0.277643i
$203$	−2.42972	−	4.71674i	−0.170533	−	0.331050i
$204$	−11.5742	+	5.52105i	−0.810354	+	0.386551i
$205$	−15.0171	−	12.6008i	−1.04884	−	0.880080i
$206$	−15.0094	+	25.9970i	−1.04575	+	1.81129i
$207$	−6.37961	−	2.19622i	−0.443414	−	0.152648i
$208$	−3.45235	+	1.99321i	−0.239377	+	0.138204i
$209$	−2.42619	−	2.03581i	−0.167823	−	0.140820i
$210$	28.0891	+	21.3548i	1.93833	+	1.47362i
$211$	0.299276	+	1.69728i	0.0206030	+	0.116845i	0.993375	−	0.114920i	$-0.0366611\pi$
$211$	0.299276	+	1.69728i	0.0206030	+	0.116845i	−0.972772	+	0.231765i	$0.925550\pi$
$212$	−14.5793	+	2.57072i	−1.00131	+	0.176558i
$213$	8.59256	−	2.38323i	0.588753	−	0.163296i
$214$	−16.7823	−	14.0820i	−1.14721	−	0.962627i
$215$	1.08411	−	1.87773i	0.0739355	−	0.128060i
$216$	3.61840	+	12.2112i	0.246201	+	0.830866i
$217$	0.919508	−	4.06502i	0.0624203	−	0.275951i
$218$	−5.51543	−	15.1535i	−0.373552	−	1.02633i
$219$	5.81470	−	22.4868i	0.392921	−	1.51951i
$220$	9.16988	−	25.1940i	0.618233	−	1.69858i
$221$	9.52201	+	11.3479i	0.640520	+	0.763341i
$222$	35.6346	+	16.2382i	2.39164	+	1.08984i
$223$	14.0559	−	16.7512i	0.941253	−	1.12174i	−0.0511476	−	0.998691i	$-0.516288\pi$
$223$	14.0559	−	16.7512i	0.941253	−	1.12174i	0.992400	−	0.123050i	$-0.0392677\pi$
$224$	12.3531	+	11.4174i	0.825375	+	0.762857i
$225$	7.15614	+	18.6388i	0.477076	+	1.24259i
$226$	3.31304			0.220380
$227$	12.2370	−	4.45392i	0.812201	−	0.295617i	0.0976685	−	0.995219i	$-0.468862\pi$
$227$	12.2370	−	4.45392i	0.812201	−	0.295617i	0.714533	+	0.699602i	$0.246639\pi$
$228$	−6.63501	−	0.521971i	−0.439414	−	0.0345684i
$229$	0.564899	+	0.673221i	0.0373296	+	0.0444877i	0.784386	−	0.620273i	$-0.212978\pi$
$229$	0.564899	+	0.673221i	0.0373296	+	0.0444877i	−0.747057	+	0.664760i	$0.768534\pi$
$230$	16.2726	+	5.92275i	1.07299	+	0.390535i
$231$	−2.57431	−	11.3712i	−0.169377	−	0.748173i
$232$	−0.853534	+	4.84063i	−0.0560373	+	0.317803i
$233$		−	8.08620i		−	0.529745i	−0.964284	−	0.264872i	$-0.914670\pi$
$233$		−	8.08620i		−	0.529745i	0.964284	−	0.264872i	$-0.0853298\pi$
$234$	35.8184	−	21.5250i	2.34152	−	1.40713i
$235$	41.2186			2.68880
$236$	8.00069	−	2.91201i	0.520801	−	0.189556i
$237$	0.694140	−	1.52328i	0.0450892	−	0.0989477i
$238$	7.74181	−	12.0379i	0.501827	−	0.780303i
$239$	−4.16515	−	4.96384i	−0.269421	−	0.321084i	0.614322	−	0.789055i	$-0.289430\pi$
$239$	−4.16515	−	4.96384i	−0.269421	−	0.321084i	−0.883744	+	0.467971i	$0.844985\pi$
$240$	1.02009	+	3.67785i	0.0658463	+	0.237404i
$241$	−17.2266	+	20.5299i	−1.10966	+	1.32244i	−0.168038	+	0.985781i	$0.553743\pi$
$241$	−17.2266	+	20.5299i	−1.10966	+	1.32244i	−0.941625	+	0.336664i	$0.890701\pi$
$242$	8.84229	−	5.10510i	0.568404	−	0.328168i
$243$	4.68993	+	14.8662i	0.300859	+	0.953668i
$244$			22.7566i			1.45684i
$245$	−23.7880	−	2.28703i	−1.51976	−	0.146113i
$246$	15.9996	+	15.7218i	1.02010	+	1.00238i
$247$	1.33507	+	7.57156i	0.0849485	+	0.481767i
$248$	−2.95770	+	2.48181i	−0.187814	+	0.157595i
$249$	4.37084	−	0.421007i	0.276991	−	0.0266802i
$250$	−4.35872	−	11.9755i	−0.275669	−	0.757395i
$251$	−10.0960	+	17.4868i	−0.637253	+	1.10376i	0.348780	+	0.937205i	$0.386596\pi$
$251$	−10.0960	+	17.4868i	−0.637253	+	1.10376i	−0.986033	+	0.166550i	$0.946737\pi$
$252$	−18.2809	−	16.3118i	−1.15159	−	1.02755i
$253$	−2.86098	−	4.95537i	−0.179868	−	0.311541i
$254$	12.8392	−	15.3012i	0.805603	−	0.960081i
$255$	12.8011	−	6.10630i	0.801634	−	0.382392i
$256$	−2.01408	−	11.4224i	−0.125880	−	0.713902i
$257$	3.10766	−	2.60764i	0.193851	−	0.162660i	−0.540696	−	0.841218i	$-0.681839\pi$
$257$	3.10766	−	2.60764i	0.193851	−	0.162660i	0.734547	+	0.678558i	$0.237395\pi$
$258$	−1.40518	+	2.04469i	−0.0874828	+	0.127297i
$259$	−26.3100	+	3.34899i	−1.63482	+	0.208096i
$260$	−56.3646	+	32.5421i	−3.49558	+	2.01818i
$261$	−0.940754	+	5.94217i	−0.0582312	+	0.367811i
$262$			42.6939i			2.63764i
$263$	21.2602	+	3.74874i	1.31096	+	0.231157i	0.785075	−	0.619400i	$-0.212624\pi$
$263$	21.2602	+	3.74874i	1.31096	+	0.231157i	0.525882	+	0.850557i	$0.323735\pi$
$264$	−4.47878	+	9.82863i	−0.275650	+	0.604911i
$265$	16.1247	−	2.84323i	0.990535	−	0.174658i
$266$	6.60362	−	3.40169i	0.404894	−	0.208571i
$267$	−4.60640	−	16.6081i	−0.281907	−	1.01640i
$268$	4.29724	−	24.3708i	0.262495	−	1.48869i
$269$	−1.05277	−	1.82346i	−0.0641887	−	0.111178i	0.832145	−	0.554558i	$-0.187113\pi$
$269$	−1.05277	−	1.82346i	−0.0641887	−	0.111178i	−0.896334	+	0.443380i	$0.853779\pi$
$270$	−11.3670	−	38.3606i	−0.691771	−	2.33455i
$271$	11.3643	+	6.56119i	0.690333	+	0.398564i	0.803737	−	0.594985i	$-0.202842\pi$
$271$	11.3643	+	6.56119i	0.690333	+	0.398564i	−0.113404	+	0.993549i	$0.536175\pi$
$272$	1.45479	−	0.529500i	0.0882096	−	0.0321057i
$273$	−12.9563	+	25.1628i	−0.784153	+	1.52292i
$274$	−2.54530	+	2.13576i	−0.153767	+	0.129026i
$275$	−5.79107	+	15.9108i	−0.349215	+	0.959460i
$276$	−10.9417	−	4.98600i	−0.658614	−	0.300122i
$277$	−0.564769	+	3.20296i	−0.0339337	+	0.192447i	−0.997062	−	0.0765936i	$-0.975596\pi$
$277$	−0.564769	+	3.20296i	−0.0339337	+	0.192447i	0.963129	+	0.269041i	$0.0867067\pi$
$278$	15.2398	+	26.3961i	0.914021	+	1.58313i
$279$	−3.56637	+	3.10060i	−0.213513	+	0.185628i
$280$	16.2583	+	15.0268i	0.971619	+	0.898024i
$281$	15.2603	+	2.69080i	0.910351	+	0.160519i	0.609163	−	0.793045i	$-0.291506\pi$
$281$	15.2603	+	2.69080i	0.910351	+	0.160519i	0.301188	+	0.953565i	$0.402617\pi$
$282$	−47.0193	−	3.69897i	−2.79996	−	0.220271i
$283$	6.97844	−	1.23049i	0.414825	−	0.0731449i	0.0376593	−	0.999291i	$-0.488010\pi$
$283$	6.97844	−	1.23049i	0.414825	−	0.0731449i	0.377166	+	0.926146i	$0.376899\pi$
$284$	15.6498	−	2.75948i	0.928645	−	0.163745i
$285$	7.33834	+	0.577302i	0.434686	+	0.0341964i
$286$	34.9011	+	6.15400i	2.06374	+	0.363894i
$287$	−14.8179	−	3.35181i	−0.874673	−	0.197851i
$288$	−3.64061	−	18.7229i	−0.214525	−	1.10326i
$289$	5.62352	+	9.74022i	0.330795	+	0.572954i
$290$	2.68132	−	15.2065i	0.157452	−	0.892957i
$291$	−12.7030	−	5.78858i	−0.744661	−	0.339333i
$292$	14.1571	−	38.8963i	0.828482	−	2.27624i
$293$	21.6105	−	18.1333i	1.26250	−	1.05936i	0.267085	−	0.963673i	$-0.413939\pi$
$293$	21.6105	−	18.1333i	1.26250	−	1.05936i	0.995411	−	0.0956878i	$-0.0305051\pi$
$294$	26.9305	+	4.74363i	1.57062	+	0.276654i
$295$	−8.84879	+	3.22069i	−0.515196	+	0.187516i
$296$	21.2786	+	12.2852i	1.23679	+	0.714064i
$297$	−5.27032	+	12.1241i	−0.305815	+	0.703512i
$298$	−17.4500	−	30.2242i	−1.01085	−	1.75084i
$299$	−2.41201	+	13.6792i	−0.139490	+	0.791088i
$300$	9.50971	+	34.2866i	0.549044	+	1.97954i
$301$	0.0804967	−	1.67839i	0.00463975	−	0.0967411i
$302$	−12.4633	+	2.19762i	−0.717184	+	0.126459i
$303$	1.33725	−	2.93459i	0.0768232	−	0.168588i
$304$	0.791296	+	0.139527i	0.0453839	+	0.00800241i
$305$		−	25.1688i		−	1.44116i
$306$	−15.1505	+	5.81687i	−0.866099	+	0.332528i
$307$	13.2261	−	7.63610i	0.754854	−	0.435815i	−0.0725912	−	0.997362i	$-0.523127\pi$
$307$	13.2261	−	7.63610i	0.754854	−	0.435815i	0.827445	+	0.561547i	$0.189793\pi$
$308$	−2.62366	−	20.6116i	−0.149497	−	1.17446i
$309$	−13.0569	+	18.9992i	−0.742781	+	1.08083i
$310$	9.29141	−	7.79642i	0.527717	−	0.442807i
$311$	−1.46141	−	8.28806i	−0.0828689	−	0.469973i	−0.997796	−	0.0663540i	$-0.978863\pi$
$311$	−1.46141	−	8.28806i	−0.0828689	−	0.469973i	0.914927	−	0.403619i	$-0.132248\pi$
$312$	23.6651	−	11.2886i	1.33977	−	0.639093i
$313$	8.19044	−	9.76098i	0.462951	−	0.551723i	−0.483174	−	0.875524i	$-0.660516\pi$
$313$	8.19044	−	9.76098i	0.462951	−	0.551723i	0.946125	+	0.323801i	$0.104961\pi$
$314$	12.2911	+	21.2889i	0.693630	+	1.20140i
$315$	20.2187	+	18.0409i	1.13920	+	1.01649i
$316$	1.49163	−	2.58358i	0.0839109	−	0.145338i
$317$	8.87829	+	24.3929i	0.498654	+	1.37004i	0.892576	+	0.450897i	$0.148896\pi$
$317$	8.87829	+	24.3929i	0.498654	+	1.37004i	−0.393922	+	0.919144i	$0.628882\pi$
$318$	−18.6491	+	1.79631i	−1.04579	+	0.100732i
$319$	−3.90845	+	3.27958i	−0.218831	+	0.183621i
$320$	7.73549	+	43.8702i	0.432427	+	2.45242i
$321$	−12.0003	−	11.7919i	−0.669794	−	0.658162i
$322$	13.3129	−	1.69460i	0.741899	−	0.0944363i
$323$		−	2.98583i		−	0.166136i
$324$	5.77945	+	27.1730i	0.321081	+	1.50961i
$325$	35.5960	−	20.5514i	1.97451	−	1.13999i
$326$	−36.5360	+	43.5419i	−2.02354	+	2.41156i
$327$	−3.30992	−	11.9337i	−0.183039	−	0.659934i
$328$	9.04675	+	10.7815i	0.499523	+	0.595308i
$329$	28.3973	−	14.6282i	1.56560	−	0.806479i
$330$	14.0698	−	30.8759i	0.774516	−	1.69966i
$331$	−2.77283	+	1.00923i	−0.152409	+	0.0554722i	−0.417098	−	0.908862i	$-0.636953\pi$
$331$	−2.77283	+	1.00923i	−0.152409	+	0.0554722i	0.264689	+	0.964334i	$0.414731\pi$
$332$	7.82550			0.429480
$333$	26.3037	+	14.5782i	1.44144	+	0.798879i
$334$			6.46771i			0.353898i
$335$	−4.75276	+	26.9542i	−0.259671	+	1.47267i
$336$	2.00803	+	2.17182i	0.109547	+	0.118482i
$337$	2.27089	+	0.826536i	0.123703	+	0.0450243i	0.403130	−	0.915143i	$-0.367922\pi$
$337$	2.27089	+	0.826536i	0.123703	+	0.0450243i	−0.279427	+	0.960167i	$0.590144\pi$
$338$	−36.4526	−	43.4425i	−1.98276	−	2.36296i
$339$	2.53646	+	0.199541i	0.137762	+	0.0108376i
$340$	23.7515	−	8.64485i	1.28811	−	0.468833i
$341$	−4.00775			−0.217032
$342$	−8.31926	−	1.31709i	−0.449854	−	0.0712202i
$343$	−17.2003	+	6.86657i	−0.928729	+	0.370760i
$344$	−1.00061	+	1.19248i	−0.0539490	+	0.0642940i
$345$	12.1016	+	5.51453i	0.651526	+	0.296892i
$346$	−3.78256	−	4.50788i	−0.203352	−	0.242345i
$347$	−1.09176	+	2.99960i	−0.0586090	+	0.161027i	−0.965542	−	0.260249i	$-0.916195\pi$
$347$	−1.09176	+	2.99960i	−0.0586090	+	0.161027i	0.906933	+	0.421276i	$0.138418\pi$
$348$	−2.68415	+	10.3802i	−0.143886	+	0.556439i
$349$	8.87089	+	24.3726i	0.474848	+	1.30463i	0.913815	+	0.406130i	$0.133122\pi$
$349$	8.87089	+	24.3726i	0.474848	+	1.30463i	−0.438967	+	0.898503i	$0.644656\pi$
$350$	−29.1636	−	26.9546i	−1.55886	−	1.44078i
$351$	28.7189	−	14.3222i	1.53290	−	0.764461i
$352$	8.08783	−	14.0085i	0.431083	−	0.746657i
$353$	−19.9159	−	16.7114i	−1.06001	−	0.889457i	−0.0659030	−	0.997826i	$-0.520993\pi$
$353$	−19.9159	−	16.7114i	−1.06001	−	0.889457i	−0.994111	+	0.108369i	$0.965437\pi$
$354$	10.3831	−	2.87985i	0.551856	−	0.153062i
$355$	−17.3087	+	3.05200i	−0.918652	+	0.161983i
$356$	−5.33365	−	30.2486i	−0.282683	−	1.60317i
$357$	6.65215	−	8.74992i	0.352069	−	0.463095i
$358$	−24.4997	−	20.5577i	−1.29485	−	1.08651i
$359$	16.5008	−	9.52673i	0.870878	−	0.502802i	0.00323805	−	0.999995i	$-0.498969\pi$
$359$	16.5008	−	9.52673i	0.870878	−	0.502802i	0.867640	+	0.497193i	$0.165636\pi$
$360$	−4.79153	−	24.6418i	−0.252536	−	1.29874i
$361$	−8.72517	+	15.1124i	−0.459219	+	0.795391i
$362$	−11.7027	−	9.81977i	−0.615083	−	0.516116i
$363$	7.07711	−	3.37589i	0.371452	−	0.177188i
$364$	−27.2831	+	42.4231i	−1.43002	+	2.22358i
$365$	−15.6578	+	43.0195i	−0.819567	+	2.25174i
$366$	−2.25866	+	28.7108i	−0.118062	+	1.50074i
$367$	−3.23929	−	8.89989i	−0.169090	−	0.464570i	0.825986	−	0.563691i	$-0.190619\pi$
$367$	−3.23929	−	8.89989i	−0.169090	−	0.464570i	−0.995075	+	0.0991209i	$0.968397\pi$
$368$	1.25717	+	0.725825i	0.0655343	+	0.0378362i
$369$	11.3024	+	13.0002i	0.588378	+	0.676764i
$370$	−66.8452	−	38.5931i	−3.47512	−	2.00636i
$371$	10.1000	−	7.68139i	0.524367	−	0.398798i
$372$	−6.85627	+	4.89086i	−0.355481	+	0.253579i
$373$	−18.5099	−	6.73707i	−0.958408	−	0.348832i	−0.184999	−	0.982739i	$-0.559228\pi$
$373$	−18.5099	−	6.73707i	−0.958408	−	0.348832i	−0.773409	+	0.633907i	$0.781450\pi$
$374$	−12.9331	−	4.70727i	−0.668756	−	0.243407i
$375$	−2.61575	−	9.43091i	−0.135077	−	0.487010i
$376$	−29.1432	−	5.13874i	−1.50295	−	0.265010i
$377$	12.3855			0.637887
$378$	−21.4451	−	22.3943i	−1.10302	−	1.15184i
$379$	−24.3431			−1.25042			−0.625211	−	0.780456i	$-0.714987\pi$
$379$	−24.3431			−1.25042			−0.625211	+	0.780456i	$0.714987\pi$
$380$	12.9190	+	2.27798i	0.662733	+	0.116858i
$381$	10.7512	−	10.9412i	0.550803	−	0.560537i
$382$	35.4888	+	12.9169i	1.81577	+	0.660885i
$383$	−10.2359	−	3.72556i	−0.523029	−	0.190367i	0.0669938	−	0.997753i	$-0.478659\pi$
$383$	−10.2359	−	3.72556i	−0.523029	−	0.190367i	−0.590023	+	0.807386i	$0.700881\pi$
$384$	−2.77555	−	28.8154i	−0.141639	−	1.47048i
$385$	2.90177	+	22.7965i	0.147888	+	1.16182i
$386$	−22.4063	−	12.9363i	−1.14045	−	0.658439i
$387$	−1.19895	+	1.48078i	−0.0609462	+	0.0752723i
$388$	−21.5451	−	12.4391i	−1.09379	−	0.631497i
$389$	−2.70515	−	7.43234i	−0.137157	−	0.376835i	0.852031	−	0.523492i	$-0.175371\pi$
$389$	−2.70515	−	7.43234i	−0.137157	−	0.376835i	−0.989187	+	0.146657i	$0.953149\pi$
$390$	−74.3423	+	35.4624i	−3.76447	+	1.79571i
$391$	1.84498	−	5.06903i	0.0933045	−	0.256352i
$392$	16.5340	+	4.58269i	0.835092	+	0.231461i
$393$	−2.57141	+	32.6863i	−0.129710	+	1.64881i
$394$	−1.75591	−	1.47338i	−0.0884613	−	0.0742279i
$395$	−1.64975	+	2.85745i	−0.0830079	+	0.143774i
$396$	−11.4208	+	20.6068i	−0.573916	+	1.03553i
$397$	2.88406	−	1.66511i	0.144747	−	0.0835695i	−0.425878	−	0.904781i	$-0.640035\pi$
$397$	2.88406	−	1.66511i	0.144747	−	0.0835695i	0.570624	+	0.821211i	$0.306701\pi$
$398$	−9.47024	−	7.94648i	−0.474700	−	0.398321i
$399$	5.26059	−	2.20660i	0.263359	−	0.110468i
$400$	−0.745924	−	4.23034i	−0.0372962	−	0.211517i
$401$	34.0660	−	6.00676i	1.70118	−	0.299963i	0.763071	−	0.646314i	$-0.223691\pi$
$401$	34.0660	−	6.00676i	1.70118	−	0.299963i	0.938105	+	0.346351i	$0.112579\pi$
$402$	7.84050	−	30.3210i	0.391048	−	1.51227i
$403$	7.45278	+	6.25362i	0.371249	+	0.311515i
$404$	2.87362	−	4.97725i	0.142968	−	0.247627i
$405$	−6.39209	−	30.0534i	−0.317626	−	1.49336i
$406$	−3.54941	−	11.4280i	−0.176154	−	0.567163i
$407$	8.72297	+	23.9662i	0.432382	+	1.18796i
$408$	−9.81216	+	2.72149i	−0.485774	+	0.134734i
$409$	6.17220	−	16.9580i	0.305196	−	0.838519i	−0.688380	−	0.725350i	$-0.741678\pi$
$409$	6.17220	−	16.9580i	0.305196	−	0.838519i	0.993576	−	0.113168i	$-0.0360999\pi$
$410$	−28.4197	−	33.8693i	−1.40355	−	1.67268i
$411$	−2.07731	+	1.48183i	−0.102466	+	0.0730935i
$412$	−26.4084	+	31.4722i	−1.30105	+	1.55053i
$413$	−4.95332	+	5.35926i	−0.243737	+	0.263712i
$414$	−13.3097	−	7.37659i	−0.654138	−	0.362540i
$415$	−8.65502			−0.424858
$416$	−36.8987	+	13.4300i	−1.80911	+	0.658462i
$417$	10.0777	+	21.1266i	0.493508	+	1.03458i
$418$	−4.59154	−	5.47198i	−0.224580	−	0.267643i
$419$	8.67340	+	3.15686i	0.423724	+	0.154223i	0.545076	−	0.838387i	$-0.316501\pi$
$419$	8.67340	+	3.15686i	0.423724	+	0.154223i	−0.121352	+	0.992609i	$0.538723\pi$
$420$	32.7840	+	35.4580i	1.59969	+	1.73017i
$421$	−4.17891	+	23.6998i	−0.203668	+	1.15506i	0.695855	+	0.718182i	$0.255026\pi$
$421$	−4.17891	+	23.6998i	−0.203668	+	1.15506i	−0.899523	+	0.436874i	$0.856086\pi$
$422$			3.88706i			0.189219i
$423$	−35.7751	−	5.66385i	−1.73944	−	0.275386i
$424$	−11.7553			−0.570889
$425$	−14.9999	+	5.45950i	−0.727600	+	0.264825i
$426$	20.0185	−	1.92821i	0.969898	−	0.0934221i
$427$	−8.93225	−	17.3399i	−0.432262	−	0.839138i
$428$	−19.2729	−	22.9685i	−0.931590	−	1.11023i
$429$	26.3495	+	6.81354i	1.27217	+	0.328961i
$430$	3.14333	−	3.74608i	0.151585	−	0.180652i
$431$	−19.5471	+	11.2855i	−0.941552	+	0.543605i	−0.890447	−	0.455088i	$-0.849608\pi$
$431$	−19.5471	+	11.2855i	−0.941552	+	0.543605i	−0.0511056	+	0.998693i	$0.516274\pi$
$432$	−0.379995	−	3.33231i	−0.0182825	−	0.160326i
$433$			18.7792i			0.902469i	0.892405	+	0.451234i	$0.149016\pi$
$433$			18.7792i			0.902469i	−0.892405	+	0.451234i	$0.850984\pi$
$434$	3.63437	−	8.66877i	0.174455	−	0.416114i
$435$	2.96868	−	11.4806i	0.142337	−	0.550451i
$436$	−3.83247	−	21.7350i	−0.183542	−	1.04092i
$437$	2.14470	−	1.79962i	0.102595	−	0.0860873i
$438$	21.7219	−	47.6685i	1.03791	−	2.27769i
$439$	2.26651	+	6.22718i	0.108174	+	0.297207i	0.981955	−	0.189113i	$-0.0605612\pi$
$439$	2.26651	+	6.22718i	0.108174	+	0.297207i	−0.873781	+	0.486320i	$0.838339\pi$
$440$	10.6447	−	18.4371i	0.507464	−	0.878953i
$441$	20.3322	+	5.25371i	0.968200	+	0.250177i
$442$	16.7052	+	28.9342i	0.794585	+	1.37626i
$443$	11.4331	−	13.6254i	0.543201	−	0.647362i	−0.422701	−	0.906269i	$-0.638918\pi$
$443$	11.4331	−	13.6254i	0.543201	−	0.647362i	0.965902	+	0.258907i	$0.0833624\pi$
$444$	44.1700	+	30.3551i	2.09621	+	1.44059i
$445$	5.89903	+	33.4551i	0.279641	+	1.58592i
$446$	37.7803	−	31.7014i	1.78895	−	1.50111i
$447$	−11.5393	−	24.1906i	−0.545789	−	1.14418i
$448$	20.8986	+	27.4789i	0.987365	+	1.29825i
$449$	28.0035	−	16.1678i	1.32157	−	0.763007i	0.337589	−	0.941294i	$-0.390389\pi$
$449$	28.0035	−	16.1678i	1.32157	−	0.763007i	0.983979	+	0.178286i	$0.0570554\pi$
$450$	8.59488	+	44.2016i	0.405167	+	2.08369i
$451$			14.6092i			0.687918i
$452$	4.46540	+	0.787370i	0.210035	+	0.0370348i
$453$	−9.67426	+	0.931839i	−0.454536	+	0.0437816i
$454$	28.9243	−	5.10013i	1.35748	−	0.239361i
$455$	30.1752	−	46.9201i	1.41464	−	2.19965i
$456$	−5.11654	−	1.32305i	−0.239604	−	0.0619575i
$457$	1.55794	−	8.83554i	0.0728776	−	0.413309i	−0.926442	−	0.376437i	$-0.877149\pi$
$457$	1.55794	−	8.83554i	0.0728776	−	0.413309i	0.999320	−	0.0368727i	$-0.0117396\pi$
$458$	0.991046	+	1.71654i	0.0463085	+	0.0802087i
$459$	−11.9496	+	3.54088i	−0.557758	+	0.165274i
$460$	20.5251	+	11.8501i	0.956986	+	0.552516i
$461$	−32.7872	+	11.9336i	−1.52705	+	0.555801i	−0.962897	−	0.269869i	$-0.913020\pi$
$461$	−32.7872	+	11.9336i	−1.52705	+	0.555801i	−0.564154	+	0.825670i	$0.690797\pi$
$462$	−1.26437	−	26.2651i	−0.0588237	−	1.22196i
$463$	−21.5412	+	18.0752i	−1.00111	+	0.840028i	−0.987137	−	0.159875i	$-0.948891\pi$
$463$	−21.5412	+	18.0752i	−1.00111	+	0.840028i	−0.0139685	+	0.999902i	$0.504446\pi$
$464$	0.442710	−	1.21634i	0.0205523	−	0.0564670i
$465$	7.58305	−	5.40931i	0.351656	−	0.250851i
$466$	3.16691	−	17.9604i	0.146704	−	0.832000i
$467$	−12.2865	−	21.2808i	−0.568549	−	0.984756i	−0.996710	−	0.0810534i	$-0.974172\pi$
$467$	−12.2865	−	21.2808i	−0.568549	−	0.984756i	0.428161	−	0.903703i	$-0.359162\pi$
$468$	53.3924	−	20.4994i	2.46806	−	0.947584i
$469$	6.29149	+	20.2567i	0.290514	+	0.935367i
$470$	91.5514	+	16.1430i	4.22295	+	0.744620i
$471$	8.12786	+	17.0390i	0.374512	+	0.785116i
$472$	6.65798	−	1.17398i	0.306458	−	0.0540369i
$473$	−1.59128	+	0.280586i	−0.0731672	+	0.0129014i
$474$	2.13835	−	3.11153i	0.0982176	−	0.142917i
$475$	−8.15879	−	1.43861i	−0.374351	−	0.0660082i
$476$	13.2955	−	14.3851i	0.609399	−	0.659340i
$477$	−14.3859	+	0.252035i	−0.658686	+	0.0115399i
$478$	−7.30725	−	12.6565i	−0.334226	−	0.578896i
$479$	−5.56261	+	31.5471i	−0.254162	+	1.44143i	0.544052	+	0.839051i	$0.316889\pi$
$479$	−5.56261	+	31.5471i	−0.254162	+	1.44143i	−0.798214	+	0.602374i	$0.794222\pi$
$480$	3.60452	+	37.4217i	0.164523	+	1.70806i
$481$	21.1752	−	58.1785i	0.965507	−	2.65271i
$482$	−46.3027	+	38.8526i	−2.10903	+	1.76969i
$483$	10.2944	−	0.495558i	0.468411	−	0.0225487i
$484$	13.1311	−	4.77933i	0.596869	−	0.217242i
$485$	23.8289	+	13.7576i	1.08202	+	0.624702i
$486$	4.59465	+	34.8564i	0.208418	+	1.58112i
$487$	−2.41488	−	4.18270i	−0.109429	−	0.189536i	0.806110	−	0.591765i	$-0.201569\pi$
$487$	−2.41488	−	4.18270i	−0.109429	−	0.189536i	−0.915539	+	0.402229i	$0.868235\pi$
$488$	−3.13781	+	17.7954i	−0.142042	+	0.805560i
$489$	−30.5943	+	31.1350i	−1.38352	+	1.40797i
$490$	−51.9403	−	14.3962i	−2.34643	−	0.650354i
$491$	11.4709	−	2.02263i	0.517675	−	0.0912800i	0.0912942	−	0.995824i	$-0.470900\pi$
$491$	11.4709	−	2.02263i	0.517675	−	0.0912800i	0.426380	+	0.904544i	$0.359789\pi$
$492$	17.8283	+	24.9926i	0.803761	+	1.12675i
$493$	−4.73692	−	0.835248i	−0.213340	−	0.0376177i
$494$			17.3402i			0.780173i
$495$	12.6314	−	22.7911i	0.567740	−	1.02439i
$496$	0.880538	−	0.508379i	0.0395373	−	0.0228269i
$497$	−10.8416	+	8.24541i	−0.486313	+	0.369857i
$498$	9.87305	+	0.776706i	0.442422	+	0.0348050i
$499$	8.07665	−	6.77711i	0.361561	−	0.303385i	−0.443852	−	0.896100i	$-0.646388\pi$
$499$	8.07665	−	6.77711i	0.361561	−	0.303385i	0.805412	+	0.592715i	$0.201944\pi$
$500$	−3.02872	−	17.1767i	−0.135448	−	0.768166i
$501$	−0.389544	+	4.95167i	−0.0174035	+	0.221224i
$502$	−29.2730	+	34.8862i	−1.30652	+	1.55705i
$503$	−3.57408	−	6.19049i	−0.159360	−	0.276020i	0.775278	−	0.631620i	$-0.217610\pi$
$503$	−3.57408	−	6.19049i	−0.159360	−	0.276020i	−0.934638	+	0.355600i	$0.884277\pi$
$504$	−12.0463	−	15.2764i	−0.536585	−	0.680463i
$505$	−3.17823	+	5.50485i	−0.141429	+	0.244963i
$506$	−4.41385	−	12.1269i	−0.196219	−	0.539108i
$507$	−25.2915	−	35.4550i	−1.12324	−	1.57461i
$508$	20.9414	−	17.5719i	0.929125	−	0.779629i
$509$	−3.15365	−	17.8853i	−0.139783	−	0.792750i	−0.971409	−	0.237413i	$-0.923700\pi$
$509$	−3.15365	−	17.8853i	−0.139783	−	0.792750i	0.831625	−	0.555337i	$-0.187411\pi$
$510$	30.8242	−	8.54937i	1.36492	−	0.378573i
$511$	4.47996	+	35.1949i	0.198182	+	1.55693i
$512$			7.26783i			0.321196i
$513$	−6.28988	−	1.50942i	−0.277705	−	0.0666427i
$514$	7.92375	−	4.57478i	0.349501	−	0.201785i
$515$	29.2077	−	34.8084i	1.28705	−	1.53384i
$516$	−2.37987	+	2.42193i	−0.104768	+	0.106620i
$517$	−19.7449	−	23.5310i	−0.868378	−	1.03489i
$518$	−59.7491	−	2.86560i	−2.62523	−	0.125907i
$519$	−2.62441	−	3.67904i	−0.115199	−	0.161492i
$520$	−48.5636	+	17.6757i	−2.12965	+	0.775131i
$521$	−2.90774			−0.127391			−0.0636953	−	0.997969i	$-0.520289\pi$
$521$	−2.90774			−0.127391			−0.0636953	+	0.997969i	$0.520289\pi$
$522$	−4.41674	+	12.8298i	−0.193315	+	0.561546i
$523$		−	25.8822i		−	1.13175i	−0.824491	−	0.565875i	$-0.808539\pi$
$523$		−	25.8822i		−	1.13175i	0.824491	−	0.565875i	$-0.191461\pi$
$524$	−10.1465	+	57.5438i	−0.443253	+	2.51381i
$525$	−20.7041	−	22.3929i	−0.903602	−	0.977305i
$526$	45.7532	+	16.6528i	1.99493	+	0.726096i
$527$	−2.42864	−	2.89433i	−0.105793	−	0.126079i
$528$	1.61097	−	2.34414i	0.0701086	−	0.102016i
$529$	−16.8599	+	6.13649i	−0.733038	+	0.266804i
$530$	36.9285			1.60407
$531$	8.12273	−	1.57944i	0.352496	−	0.0685419i
$532$	9.70895	−	3.01548i	0.420936	−	0.130738i
$533$	22.7959	−	27.1671i	0.987399	−	1.17674i
$534$	−3.72693	−	38.6926i	−0.161280	−	1.67439i
$535$	21.3159	+	25.4033i	0.921565	+	1.09828i
$536$	6.72079	−	18.4652i	0.290294	−	0.797576i
$537$	−17.5187	−	17.2145i	−0.755990	−	0.742861i
$538$	−1.62419	−	4.46243i	−0.0700238	−	0.192389i
$539$	10.0895	+	14.6757i	0.434586	+	0.632129i
$540$	−6.20396	−	54.4047i	−0.266976	−	2.34121i
$541$	−9.36987	+	16.2291i	−0.402842	+	0.697743i	−0.994068	−	0.108763i	$-0.965311\pi$
$541$	−9.36987	+	16.2291i	−0.402842	+	0.697743i	0.591225	+	0.806506i	$0.298644\pi$
$542$	22.6718	+	19.0239i	0.973839	+	0.817148i
$543$	−8.36816	−	8.22283i	−0.359112	−	0.352876i
$544$	15.0178	−	2.64805i	0.643885	−	0.113534i
$545$	4.23873	+	24.0390i	0.181567	+	1.02972i
$546$	−38.6324	+	50.8153i	−1.65331	+	2.17469i
$547$	33.4456	+	28.0642i	1.43003	+	1.19994i	0.945695	+	0.325055i	$0.105383\pi$
$547$	33.4456	+	28.0642i	1.43003	+	1.19994i	0.484335	+	0.874882i	$0.339061\pi$
$548$	−3.93820	+	2.27372i	−0.168232	+	0.0971285i
$549$	−3.45845	+	21.8449i	−0.147603	+	0.932318i
$550$	−19.0940	+	33.0718i	−0.814172	+	1.41019i
$551$	−1.91237	−	1.60467i	−0.0814697	−	0.0683612i
$552$	−7.86881	−	5.40771i	−0.334919	−	0.230167i
$553$	−0.122497	+	2.55411i	−0.00520908	+	0.108612i
$554$	−2.50884	+	6.89298i	−0.106590	+	0.292855i
$555$	−48.8521	−	33.5728i	−2.07366	−	1.42509i
$556$	14.2673	+	39.1991i	0.605068	+	1.66241i
$557$	−2.37342	−	1.37029i	−0.100565	−	0.0580612i	0.448874	−	0.893595i	$-0.351825\pi$
$557$	−2.37342	−	1.37029i	−0.100565	−	0.0580612i	−0.549439	+	0.835534i	$0.685159\pi$
$558$	−9.13565	+	5.49005i	−0.386743	+	0.232412i
$559$	3.39696	+	1.96123i	0.143676	+	0.0829513i
$560$	−3.52926	−	4.64051i	−0.149138	−	0.196097i
$561$	−9.61806	−	4.38283i	−0.406075	−	0.185043i
$562$	32.8410	+	11.9532i	1.38532	+	0.504214i
$563$	12.5366	+	4.56296i	0.528356	+	0.192306i	0.592404	−	0.805641i	$-0.298179\pi$
$563$	12.5366	+	4.56296i	0.528356	+	0.192306i	−0.0640481	+	0.997947i	$0.520401\pi$
$564$	−62.4946	−	16.1601i	−2.63150	−	0.680461i
$565$	−4.93875	−	0.870834i	−0.207775	−	0.0366363i
$566$	15.9819			0.671767
$567$	−15.0695	−	18.4366i	−0.632861	−	0.774265i
$568$	12.6185			0.529459
$569$	10.1383	+	1.78766i	0.425022	+	0.0749428i	0.382068	−	0.924134i	$-0.375212\pi$
$569$	10.1383	+	1.78766i	0.425022	+	0.0749428i	0.0429537	+	0.999077i	$0.486323\pi$
$570$	16.0732	+	4.15627i	0.673234	+	0.174087i
$571$	20.3597	+	7.41032i	0.852027	+	0.310112i	0.730866	−	0.682521i	$-0.239116\pi$
$571$	20.3597	+	7.41032i	0.852027	+	0.310112i	0.121160	+	0.992633i	$0.461338\pi$
$572$	45.5779	+	16.5890i	1.90571	+	0.693622i
$573$	26.3922	+	12.0266i	1.10255	+	0.502418i
$574$	−31.5996	−	13.2481i	−1.31894	−	0.552965i
$575$	−12.9622	−	7.48375i	−0.540562	−	0.312094i
$576$	−0.685704	−	39.1394i	−0.0285710	−	1.63081i
$577$	4.44885	+	2.56854i	0.185208	+	0.106930i	0.589737	−	0.807595i	$-0.299231\pi$
$577$	4.44885	+	2.56854i	0.185208	+	0.106930i	−0.404529	+	0.914525i	$0.632565\pi$
$578$	8.67581	+	23.8366i	0.360866	+	0.991472i
$579$	−16.3750	−	11.2535i	−0.680524	−	0.467679i
$580$	7.22788	−	19.8584i	0.300122	−	0.824577i
$581$	−5.96284	+	3.07161i	−0.247380	+	0.127432i
$582$	−25.9477	−	17.8322i	−1.07557	−	0.739167i
$583$	−9.34736	−	7.84336i	−0.387128	−	0.324839i
$584$	16.4340	−	28.4645i	0.680042	−	1.17787i
$585$	−59.0522	+	22.6724i	−2.44151	+	0.937387i
$586$	55.1012	−	31.8127i	2.27621	−	1.31417i
$587$	−26.0870	−	21.8896i	−1.07672	−	0.903479i	−0.0810798	−	0.996708i	$-0.525837\pi$
$587$	−26.0870	−	21.8896i	−1.07672	−	0.903479i	−0.995645	+	0.0932285i	$0.970281\pi$
$588$	35.1702	+	12.7938i	1.45039	+	0.527608i
$589$	−0.340516	−	1.93116i	−0.0140307	−	0.0795722i
$590$	−20.9156	+	3.68798i	−0.861080	+	0.151832i
$591$	−1.25558	−	1.23377i	−0.0516476	−	0.0507507i
$592$	−4.95660	−	4.15908i	−0.203715	−	0.170937i
$593$	2.84168	−	4.92193i	0.116694	−	0.202119i	−0.801762	−	0.597644i	$-0.796104\pi$
$593$	2.84168	−	4.92193i	0.116694	−	0.202119i	0.918456	+	0.395524i	$0.129437\pi$
$594$	−16.4543	+	24.8650i	−0.675129	+	1.02022i
$595$	−14.7049	+	15.9100i	−0.602841	+	0.652245i
$596$	−16.3365	−	44.8840i	−0.669167	−	1.83852i
$597$	−6.77179	−	6.65419i	−0.277151	−	0.272338i
$598$	−10.7147	+	29.4384i	−0.438157	+	1.20383i
$599$	25.1283	+	29.9467i	1.02671	+	1.22359i	0.974368	+	0.224961i	$0.0722255\pi$
$599$	25.1283	+	29.9467i	1.02671	+	1.22359i	0.0523461	+	0.998629i	$0.483330\pi$
$600$	2.70886	+	28.1230i	0.110589	+	1.14812i
$601$	14.1568	−	16.8714i	0.577468	−	0.688199i	−0.395678	−	0.918389i	$-0.629490\pi$
$601$	14.1568	−	16.8714i	0.577468	−	0.688199i	0.973146	+	0.230190i	$0.0739347\pi$
$602$	0.836124	−	3.69639i	0.0340779	−	0.150654i
$603$	7.82887	−	22.7414i	0.318816	−	0.926103i
$604$	−17.3207			−0.704767
$605$	−14.5230	+	5.28596i	−0.590446	+	0.214905i
$606$	4.11951	−	5.99434i	0.167344	−	0.243503i
$607$	15.6462	+	18.6464i	0.635060	+	0.756835i	0.983581	−	0.180466i	$-0.0577605\pi$
$607$	15.6462	+	18.6464i	0.635060	+	0.756835i	−0.348521	+	0.937301i	$0.613316\pi$
$608$	7.43729	+	2.70695i	0.301622	+	0.109781i
$609$	−2.02912	−	8.96305i	−0.0822241	−	0.363201i
$610$	9.85720	−	55.9029i	0.399106	−	2.26344i
$611$			74.5676i			3.01668i
$612$	−21.8027	+	4.23947i	−0.881322	+	0.171371i
$613$	−14.5780			−0.588802			−0.294401	−	0.955682i	$-0.595120\pi$
$613$	−14.5780			−0.588802			−0.294401	+	0.955682i	$0.595120\pi$
$614$	32.3674	−	11.7808i	1.30624	−	0.475433i
$615$	−19.7181	−	27.6419i	−0.795112	−	1.11463i
$616$	0.790382	−	16.4799i	0.0318454	−	0.663992i
$617$	−17.1824	−	20.4772i	−0.691739	−	0.824383i	0.299826	−	0.953994i	$-0.403072\pi$
$617$	−17.1824	−	20.4772i	−0.691739	−	0.824383i	−0.991565	+	0.129611i	$0.958627\pi$
$618$	−36.4418	+	37.0859i	−1.46591	+	1.49181i
$619$	11.7385	−	13.9894i	0.471812	−	0.562283i	−0.476684	−	0.879075i	$-0.658161\pi$
$619$	11.7385	−	13.9894i	0.471812	−	0.562283i	0.948495	+	0.316792i	$0.102606\pi$
$620$	14.3761	−	8.30002i	0.577357	−	0.333337i
$621$	−9.74562	−	6.44913i	−0.391078	−	0.258795i
$622$		−	18.9811i		−	0.761074i
$623$	15.9371	+	20.9552i	0.638506	+	0.839551i
$624$	−6.65351	+	1.84541i	−0.266354	+	0.0738757i
$625$	−2.42847	−	13.7726i	−0.0971389	−	0.550902i
$626$	22.0148	−	18.4726i	0.879887	−	0.738313i
$627$	−3.18570	−	4.46588i	−0.127225	−	0.178350i
$628$	11.5068	+	31.6148i	0.459173	+	1.26157i
$629$	−12.0220	+	20.8227i	−0.479349	+	0.830256i
$630$	37.8426	+	47.9896i	1.50769	+	1.91195i
$631$	−8.50860	−	14.7373i	−0.338722	−	0.586684i	0.645471	−	0.763785i	$-0.276661\pi$
$631$	−8.50860	−	14.7373i	−0.338722	−	0.586684i	−0.984193	+	0.177101i	$0.943328\pi$
$632$	1.52268	−	1.81466i	0.0605690	−	0.0721833i
$633$	−0.234114	+	2.97593i	−0.00930519	+	0.118282i
$634$	10.1664	+	57.6566i	0.403760	+	2.28984i
$635$	−23.1613	+	19.4346i	−0.919127	+	0.771239i
$636$	−25.5627	−	2.01100i	−1.01363	−	0.0797412i
$637$	4.13742	−	43.0344i	0.163930	−	1.70508i
$638$	−9.96556	+	5.75362i	−0.394540	+	0.227788i
$639$	15.4422	−	0.270541i	0.610885	−	0.0107024i
$640$			57.0595i			2.25548i
$641$	−44.5556	−	7.85636i	−1.75984	−	0.310308i	−0.801940	−	0.597404i	$-0.796199\pi$
$641$	−44.5556	−	7.85636i	−1.75984	−	0.310308i	−0.957902	+	0.287097i	$0.907310\pi$
$642$	−22.0360	−	30.8912i	−0.869690	−	1.21918i
$643$	1.26736	−	0.223470i	0.0499799	−	0.00881280i	−0.148602	−	0.988897i	$-0.547477\pi$
$643$	1.26736	−	0.223470i	0.0499799	−	0.00881280i	0.198582	+	0.980084i	$0.436366\pi$
$644$	18.3462	+	0.879892i	0.722941	+	0.0346726i
$645$	2.63215	−	2.67867i	0.103641	−	0.105472i
$646$	1.16938	−	6.63187i	0.0460086	−	0.260928i
$647$	−11.2984	−	19.5694i	−0.444185	−	0.769351i	0.553810	−	0.832643i	$-0.313173\pi$
$647$	−11.2984	−	19.5694i	−0.444185	−	0.769351i	−0.997995	+	0.0632923i	$0.979840\pi$
$648$	0.772704	+	22.0459i	0.0303547	+	0.866044i
$649$	6.07746	+	3.50882i	0.238561	+	0.137733i
$650$	87.1118	−	31.7061i	3.41681	−	1.24362i
$651$	3.30458	−	6.41789i	0.129517	−	0.251537i
$652$	−59.5921	+	50.0037i	−2.33381	+	1.95830i
$653$	−16.2043	+	44.5208i	−0.634122	+	1.74224i	0.0353255	+	0.999376i	$0.488753\pi$
$653$	−16.2043	+	44.5208i	−0.634122	+	1.74224i	−0.669447	+	0.742860i	$0.733469\pi$
$654$	−2.67797	−	27.8024i	−0.104717	−	1.08716i
$655$	11.2221	−	63.6436i	0.438483	−	2.48676i
$656$	−1.85316	−	3.20976i	−0.0723536	−	0.125320i
$657$	19.5013	−	35.1866i	0.760817	−	1.37276i
$658$	68.8029	−	21.3694i	2.68222	−	0.833064i
$659$	6.94728	+	1.22499i	0.270628	+	0.0477190i	0.307315	−	0.951608i	$-0.400569\pi$
$659$	6.94728	+	1.22499i	0.270628	+	0.0477190i	−0.0366873	+	0.999327i	$0.511681\pi$
$660$	26.3015	−	38.2715i	1.02378	−	1.48972i
$661$	19.4165	−	3.42366i	0.755216	−	0.133165i	0.217232	−	0.976120i	$-0.430297\pi$
$661$	19.4165	−	3.42366i	0.755216	−	0.133165i	0.537984	+	0.842955i	$0.319186\pi$
$662$	−6.55405	+	1.15566i	−0.254730	+	0.0449158i
$663$	11.0468	+	23.1581i	0.429021	+	0.899387i
$664$	6.11946	+	1.07903i	0.237481	+	0.0418743i
$665$	−10.7381	+	3.33513i	−0.416407	+	0.129331i
$666$	52.7143	+	42.6815i	2.04264	+	1.65388i
$667$	−2.25508	−	3.90592i	−0.0873172	−	0.151238i
$668$	−1.53710	+	8.71734i	−0.0594723	+	0.337284i
$669$	30.8339	−	21.9951i	1.19211	−	0.850379i
$670$	−21.1129	+	58.0071i	−0.815661	+	2.24101i
$671$	−14.3685	+	12.0566i	−0.554688	+	0.465439i
$672$	15.7640	+	24.5023i	0.608111	+	0.945196i
$673$	41.0196	−	14.9299i	1.58119	−	0.575506i	0.605727	−	0.795673i	$-0.292883\pi$
$673$	41.0196	−	14.9299i	1.58119	−	0.575506i	0.975462	+	0.220167i	$0.0706603\pi$
$674$	4.72021	+	2.72521i	0.181816	+	0.104971i
$675$	3.91800	+	34.3583i	0.150804	+	1.32245i
$676$	−38.8073	−	67.2161i	−1.49259	−	2.58524i
$677$	−3.65218	+	20.7125i	−0.140365	+	0.796047i	0.830608	+	0.556857i	$0.187993\pi$
$677$	−3.65218	+	20.7125i	−0.140365	+	0.796047i	−0.970973	+	0.239190i	$0.923118\pi$
$678$	5.55563	+	1.43659i	0.213363	+	0.0551720i
$679$	21.2993	+	1.02153i	0.817392	+	0.0392025i
$680$	19.7655	−	3.48518i	0.757971	−	0.133651i
$681$	22.4515	−	2.16257i	0.860345	−	0.0828698i
$682$	−8.90169	−	1.56961i	−0.340863	−	0.0601034i
$683$			15.9478i			0.610227i	0.952316	+	0.305114i	$0.0986945\pi$
$683$			15.9478i			0.610227i	−0.952316	+	0.305114i	$0.901306\pi$
$684$	−10.8999	−	3.75234i	−0.416767	−	0.143474i
$685$	4.35566	−	2.51474i	0.166421	−	0.0960834i
$686$	−40.8931	+	8.51510i	−1.56131	+	0.325108i
$687$	0.655357	+	1.37387i	0.0250034	+	0.0524164i
$688$	0.314027	−	0.263500i	0.0119722	−	0.0100458i
$689$	5.14362	+	29.1709i	0.195956	+	1.11132i
$690$	24.7193	+	16.9879i	0.941047	+	0.646719i
$691$	−8.67771	+	10.3417i	−0.330116	+	0.393416i	−0.905416	−	0.424526i	$-0.860441\pi$
$691$	−8.67771	+	10.3417i	−0.330116	+	0.393416i	0.575300	+	0.817942i	$0.304885\pi$
$692$	−4.02689	−	6.97478i	−0.153079	−	0.265141i
$693$	0.613924	−	20.1846i	0.0233211	−	0.766751i
$694$	−3.59971	+	6.23488i	−0.136643	+	0.236673i
$695$	−15.7797	−	43.3543i	−0.598557	−	1.64452i
$696$	−3.53027	+	7.74713i	−0.133814	+	0.293654i
$697$	−10.5505	+	8.85292i	−0.399629	+	0.335328i
$698$	10.1579	+	57.6086i	0.384484	+	2.18052i
$699$	3.50631	−	13.5597i	0.132621	−	0.512875i
$700$	−32.9014	−	43.2610i	−1.24356	−	1.63511i
$701$		−	5.13366i		−	0.193896i	−0.995289	−	0.0969478i	$-0.969092\pi$
$701$		−	5.13366i		−	0.193896i	0.995289	−	0.0969478i	$-0.0309080\pi$
$702$	69.3972	−	20.5637i	2.61923	−	0.776126i
$703$	−10.8071	+	6.23950i	−0.407599	+	0.235327i
$704$	21.3392	−	25.4311i	0.804253	−	0.958471i
$705$	69.1192	+	17.8731i	2.60318	+	0.673139i
$706$	−37.6906	−	44.9179i	−1.41850	−	1.69051i
$707$	−0.235988	+	4.92047i	−0.00887526	+	0.185053i
$708$	14.6790	−	1.41391i	0.551671	−	0.0531378i
$709$	17.7409	−	6.45715i	0.666272	−	0.242503i	0.0133301	−	0.999911i	$-0.495757\pi$
$709$	17.7409	−	6.45715i	0.666272	−	0.242503i	0.652942	+	0.757408i	$0.273535\pi$
$710$	−39.6400			−1.48766
$711$	1.82452	−	2.25339i	0.0684248	−	0.0845087i
$712$		−	24.3895i		−	0.914036i
$713$	0.615195	−	3.48894i	0.0230392	−	0.130662i
$714$	18.2021	−	16.8294i	0.681195	−	0.629823i
$715$	−50.4093	−	18.3475i	−1.88520	−	0.686158i
$716$	−28.1356	−	33.5307i	−1.05148	−	1.25310i
$717$	−4.83212	−	10.1299i	−0.180459	−	0.378309i
$718$	40.3813	−	14.6976i	1.50702	−	0.548509i
$719$	−4.31712			−0.161001			−0.0805007	−	0.996755i	$-0.525652\pi$
$719$	−4.31712			−0.161001			−0.0805007	+	0.996755i	$0.525652\pi$
$720$	0.115799	+	6.60969i	0.00431557	+	0.246329i
$721$	7.76924	−	34.3467i	0.289342	−	1.27914i
$722$	−25.2983	+	30.1494i	−0.941506	+	1.12204i
$723$	−37.7893	+	26.9567i	−1.40540	+	1.00253i
$724$	−13.4395	−	16.0166i	−0.499475	−	0.595251i
$725$	−4.56464	+	12.5412i	−0.169526	+	0.465770i
$726$	17.0412	−	4.72655i	0.632460	−	0.175419i
$727$	−10.4652	−	28.7528i	−0.388131	−	1.06638i	−0.967842	−	0.251560i	$-0.919056\pi$
$727$	−10.4652	−	28.7528i	−0.388131	−	1.06638i	0.579710	−	0.814823i	$-0.303166\pi$
$728$	−27.1847	+	29.4125i	−1.00753	+	1.09010i
$729$	1.41828	+	26.9627i	0.0525290	+	0.998619i
$730$	−51.6261	+	89.4191i	−1.91077	+	3.30955i
$731$	−1.16693	−	0.979168i	−0.0431604	−	0.0362158i
$732$	−9.86763	+	38.1604i	−0.364718	+	1.41045i
$733$	−18.3922	+	3.24304i	−0.679330	+	0.119784i	−0.502658	−	0.864485i	$-0.667644\pi$
$733$	−18.3922	+	3.24304i	−0.679330	+	0.119784i	−0.176672	+	0.984270i	$0.556533\pi$
$734$	−3.70928	−	21.0364i	−0.136912	−	0.776466i
$735$	−38.8983	−	14.1500i	−1.43479	−	0.521931i
$736$	10.9536	+	9.19118i	0.403756	+	0.338791i
$737$	17.6644	−	10.1986i	0.650677	−	0.375669i
$738$	20.0125	+	33.3015i	0.736670	+	1.22585i
$739$	−20.1593	+	34.9170i	−0.741573	+	1.28444i	0.210206	+	0.977657i	$0.432586\pi$
$739$	−20.1593	+	34.9170i	−0.741573	+	1.28444i	−0.951779	+	0.306784i	$0.900747\pi$
$740$	−80.9237	−	67.9030i	−2.97481	−	2.49616i
$741$	−1.04438	+	13.2756i	−0.0383664	+	0.487692i
$742$	25.4417	−	13.1057i	0.933995	−	0.481125i
$743$	9.56525	−	26.2803i	0.350915	−	0.964131i	−0.631162	−	0.775651i	$-0.717422\pi$
$743$	9.56525	−	26.2803i	0.350915	−	0.964131i	0.982077	−	0.188480i	$-0.0603562\pi$
$744$	−6.03591	+	2.87922i	−0.221287	+	0.105557i
$745$	18.0682	+	49.6419i	0.661966	+	1.81874i
$746$	−38.4742	−	22.2131i	−1.40864	−	0.813280i
$747$	7.51200	+	1.18929i	0.274850	+	0.0435138i
$748$	−16.3129	−	9.41823i	−0.596457	−	0.344365i
$749$	23.7009	+	9.93659i	0.866013	+	0.363075i
$750$	−2.11634	−	21.9716i	−0.0772779	−	0.802290i
$751$	−35.2133	−	12.8166i	−1.28495	−	0.467684i	−0.392885	−	0.919588i	$-0.628523\pi$
$751$	−35.2133	−	12.8166i	−1.28495	−	0.467684i	−0.892067	+	0.451904i	$0.850745\pi$
$752$	7.32300	+	2.66535i	0.267042	+	0.0971955i
$753$	−24.5125	+	24.9457i	−0.893284	+	0.909071i
$754$	27.5097	+	4.85071i	1.00185	+	0.176652i
$755$	19.1567			0.697184
$756$	−23.5821	−	35.2801i	−0.857672	−	1.28313i
$757$	31.2917			1.13732			0.568659	−	0.822574i	$-0.307463\pi$
$757$	31.2917			1.13732			0.568659	+	0.822574i	$0.307463\pi$
$758$	−54.0689	−	9.53381i	−1.96387	−	0.346284i
$759$	−2.64884	−	9.55020i	−0.0961466	−	0.346650i
$760$	9.78846	+	3.56271i	0.355065	+	0.129233i
$761$	−32.9687	−	11.9996i	−1.19511	−	0.434986i	−0.333597	−	0.942716i	$-0.608262\pi$
$761$	−32.9687	−	11.9996i	−1.19511	−	0.434986i	−0.861516	+	0.507730i	$0.830485\pi$
$762$	28.1648	−	20.0912i	1.02030	−	0.727826i
$763$	11.4515	+	15.0573i	0.414574	+	0.545110i
$764$	44.7629	+	25.8439i	1.61946	+	0.934998i
$765$	24.1138	−	4.68887i	0.871838	−	0.169526i
$766$	−21.2760	−	12.2837i	−0.768734	−	0.443829i
$767$	−5.82648	−	16.0081i	−0.210382	−	0.578020i
$768$	1.57555	−	20.0276i	0.0568529	−	0.722682i
$769$	−4.55125	+	12.5045i	−0.164122	+	0.450923i	−0.994305	−	0.106568i	$-0.966014\pi$
$769$	−4.55125	+	12.5045i	−0.164122	+	0.450923i	0.830183	+	0.557491i	$0.188236\pi$
$770$	−2.48293	+	51.7703i	−0.0894785	+	1.86567i
$771$	6.34194	−	3.02520i	0.228399	−	0.108950i
$772$	−27.1253	−	22.7608i	−0.976261	−	0.819180i
$773$	−8.67984	+	15.0339i	−0.312192	+	0.540733i	−0.978837	−	0.204643i	$-0.934397\pi$
$773$	−8.67984	+	15.0339i	−0.312192	+	0.540733i	0.666645	+	0.745376i	$0.267730\pi$
$774$	−3.24296	+	2.81943i	−0.116566	+	0.101342i
$775$	−9.07894	+	5.24173i	−0.326125	+	0.188288i
$776$	−15.1329	−	12.6980i	−0.543238	−	0.455831i
$777$	−45.5712	−	5.79253i	−1.63486	−	0.207806i
$778$	−3.09764	−	17.5676i	−0.111056	−	0.629828i
$779$	−7.03953	+	1.24126i	−0.252217	+	0.0444727i
$780$	−108.628	+	30.1291i	−3.88952	+	1.07879i
$781$	10.0337	+	8.41927i	0.359034	+	0.301265i
$782$	6.08316	−	10.5363i	0.217534	−	0.376779i
$783$	−4.15417	+	9.55646i	−0.148458	+	0.341520i
$784$	−4.07835	−	1.94455i	−0.145656	−	0.0694481i
$785$	−12.7266	−	34.9660i	−0.454231	−	1.24799i
$786$	−18.5128	+	71.5931i	−0.660329	+	2.55364i
$787$	5.00026	−	13.7381i	0.178240	−	0.489710i	−0.818111	−	0.575060i	$-0.804979\pi$
$787$	5.00026	−	13.7381i	0.178240	−	0.489710i	0.996351	+	0.0853500i	$0.0272008\pi$
$788$	−2.01649	−	2.40316i	−0.0718346	−	0.0856091i
$789$	34.0255	+	15.5050i	1.21134	+	0.551993i
$790$	−4.78339	+	5.70063i	−0.170185	+	0.202819i
$791$	−3.71158	+	1.15277i	−0.131969	+	0.0409878i
$792$	−11.7723	+	14.5395i	−0.418311	+	0.516639i
$793$	45.5323			1.61690
$794$	7.05796	−	2.56889i	0.250478	−	0.0911664i
$795$	28.2724	+	2.22417i	1.00272	+	0.0788831i
$796$	−10.8757	−	12.9611i	−0.385478	−	0.459395i
$797$	29.7715	+	10.8359i	1.05456	+	0.383828i	0.810382	−	0.585902i	$-0.199260\pi$
$797$	29.7715	+	10.8359i	1.05456	+	0.383828i	0.244178	+	0.969731i	$0.421482\pi$
$798$	12.5486	−	2.84084i	0.444216	−	0.100565i
$799$	5.02864	−	28.5188i	0.177901	−	1.00892i
$800$		−	42.3122i		−	1.49596i
$801$	−0.522913	−	29.8474i	−0.0184762	−	1.05461i
$802$	78.0172			2.75488
$803$	32.0596	−	11.6688i	1.13136	−	0.411781i
$804$	17.7736	−	39.0040i	0.626827	−	1.37556i
$805$	−20.2909	−	0.973163i	−0.715161	−	0.0342995i
$806$	14.1043	+	16.8089i	0.496803	+	0.592067i
$807$	−0.974709	−	3.51425i	−0.0343114	−	0.123707i
$808$	2.93343	−	3.49593i	0.103198	−	0.122986i
$809$	−40.0677	+	23.1331i	−1.40870	+	0.813316i	−0.995263	−	0.0972146i	$-0.969007\pi$
$809$	−40.0677	+	23.1331i	−1.40870	+	0.813316i	−0.413441	+	0.910531i	$0.635673\pi$
$810$	−2.42739	−	69.2555i	−0.0852900	−	2.43339i
$811$			33.8813i			1.18973i	0.803825	+	0.594866i	$0.202795\pi$
$811$			33.8813i			1.18973i	−0.803825	+	0.594866i	$0.797205\pi$
$812$	−2.06802	−	16.2465i	−0.0725732	−	0.570141i
$813$	16.2117	+	15.9302i	0.568570	+	0.558696i
$814$	9.98857	+	56.6480i	0.350099	+	1.98551i
$815$	65.9091	−	55.3043i	2.30869	−	1.93722i
$816$	2.66913	−	0.257095i	0.0934382	−	0.00900011i
$817$	−0.270405	−	0.742931i	−0.00946027	−	0.0259919i
$818$	20.3507	−	35.2484i	0.711545	−	1.23243i
$819$	−32.6374	+	36.5772i	−1.14044	+	1.27811i
$820$	−30.2555	−	52.4040i	−1.05657	−	1.83003i
$821$	30.1751	−	35.9613i	1.05312	−	1.25506i	0.0872057	−	0.996190i	$-0.472206\pi$
$821$	30.1751	−	35.9613i	1.05312	−	1.25506i	0.965913	−	0.258867i	$-0.0833493\pi$
$822$	−5.19431	+	2.47776i	−0.181172	+	0.0864219i
$823$	−5.82950	−	33.0607i	−0.203204	−	1.15243i	−0.900242	−	0.435391i	$-0.856610\pi$
$823$	−5.82950	−	33.0607i	−0.203204	−	1.15243i	0.697038	−	0.717034i	$-0.254501\pi$
$824$	−24.9906	+	20.9696i	−0.870590	+	0.730512i
$825$	−16.6102	+	24.1697i	−0.578294	+	0.841481i
$826$	−13.1008	+	9.96361i	−0.455837	+	0.346678i
$827$	9.24493	−	5.33756i	0.321478	−	0.185605i	−0.330573	−	0.943780i	$-0.607242\pi$
$827$	9.24493	−	5.33756i	0.321478	−	0.185605i	0.652051	+	0.758175i	$0.273909\pi$
$828$	−16.1861	−	13.1055i	−0.562505	−	0.455448i
$829$			34.7871i			1.20821i	0.796906	+	0.604103i	$0.206469\pi$
$829$			34.7871i			1.20821i	−0.796906	+	0.604103i	$0.793531\pi$
$830$	−19.2238	−	3.38968i	−0.667269	−	0.117658i
$831$	−2.33592	+	5.12614i	−0.0810321	+	0.177824i
$832$	−79.3645	+	13.9941i	−2.75147	+	0.485158i
$833$	−4.48451	+	16.1798i	−0.155379	+	0.560595i
$834$	14.1097	+	50.8716i	0.488580	+	1.76154i
$835$	1.70004	−	9.64140i	0.0588323	−	0.333654i
$836$	−4.88813	−	8.46648i	−0.169059	−	0.292819i
$837$	−7.32489	+	3.65294i	−0.253185	+	0.126264i
$838$	18.0283	+	10.4086i	0.622777	+	0.359561i
$839$	14.6918	−	5.34740i	0.507219	−	0.184613i	−0.0757191	−	0.997129i	$-0.524125\pi$
$839$	14.6918	−	5.34740i	0.507219	−	0.184613i	0.582938	+	0.812517i	$0.301903\pi$
$840$	20.7476	+	32.2483i	0.715859	+	1.11267i
$841$	19.1346	−	16.0558i	0.659813	−	0.553649i
$842$	−18.5637	+	51.0034i	−0.639748	+	1.75769i
$843$	24.4231	+	11.1293i	0.841176	+	0.383313i
$844$	−0.923790	+	5.23907i	−0.0317982	+	0.180336i
$845$	42.9209	+	74.3412i	1.47653	+	2.55742i
$846$	−77.2425	−	26.5911i	−2.65565	−	0.914222i
$847$	−8.12963	+	8.79587i	−0.279337	+	0.302230i
$848$	3.04862	+	0.537554i	0.104690	+	0.0184597i
$849$	12.2357	+	0.962571i	0.419927	+	0.0330354i
$850$	−35.4546	+	6.25161i	−1.21608	+	0.214428i
$851$	−22.2027	+	3.91494i	−0.761099	+	0.134202i
$852$	27.4396	+	2.15866i	0.940066	+	0.0739543i
$853$	−13.0053	−	2.29319i	−0.445294	−	0.0785174i	−0.0534951	−	0.998568i	$-0.517036\pi$
$853$	−13.0053	−	2.29319i	−0.445294	−	0.0785174i	−0.391799	+	0.920051i	$0.628147\pi$
$854$	−13.0485	−	42.0123i	−0.446511	−	1.43763i
$855$	12.0553	+	4.15010i	0.412283	+	0.141931i
$856$	−11.9042	−	20.6186i	−0.406876	−	0.704730i
$857$	6.02293	−	34.1577i	0.205739	−	1.16681i	−0.690533	−	0.723301i	$-0.742624\pi$
$857$	6.02293	−	34.1577i	0.205739	−	1.16681i	0.896272	−	0.443505i	$-0.146265\pi$
$858$	55.8570	+	25.4533i	1.90692	+	0.868962i
$859$	−0.480650	+	1.32057i	−0.0163996	+	0.0450574i	−0.947622	−	0.319393i	$-0.896521\pi$
$859$	−0.480650	+	1.32057i	−0.0163996	+	0.0450574i	0.931223	+	0.364451i	$0.118743\pi$
$860$	5.12694	−	4.30201i	0.174827	−	0.146697i
$861$	−23.3947	−	12.0459i	−0.797288	−	0.410524i
$862$	−47.8364	+	17.4110i	−1.62931	+	0.593022i
$863$	−30.4192	−	17.5625i	−1.03548	−	0.597836i	−0.116931	−	0.993140i	$-0.537306\pi$
$863$	−30.4192	−	17.5625i	−1.03548	−	0.597836i	−0.918550	+	0.395304i	$0.870639\pi$
$864$	2.01363	−	32.9749i	0.0685052	−	1.12183i
$865$	4.45375	+	7.71412i	0.151432	+	0.262288i
$866$	−7.35473	+	41.7107i	−0.249924	+	1.41739i
$867$	5.20653	+	18.7718i	0.176823	+	0.637523i
$868$	6.95869	−	10.8202i	0.236193	−	0.367263i
$869$	2.42155	−	0.426984i	0.0821454	−	0.0144844i
$870$	11.0901	−	24.3370i	0.375989	−	0.825103i
$871$	−48.7623	−	8.59810i	−1.65225	−	0.291336i
$872$		−	17.5250i		−	0.593472i
$873$	−18.7915	−	15.2151i	−0.635996	−	0.514952i
$874$	5.46844	−	3.15720i	0.184973	−	0.106794i
$875$	9.04989	+	11.8994i	0.305942	+	0.402274i
$876$	40.6061	−	59.0863i	1.37195	−	1.99634i
$877$	−32.2840	+	27.0895i	−1.09015	+	0.914748i	−0.996724	−	0.0808781i	$-0.974228\pi$
$877$	−32.2840	+	27.0895i	−1.09015	+	0.914748i	−0.0934299	+	0.995626i	$0.529783\pi$
$878$	2.59535	+	14.7190i	0.0875888	+	0.496741i
$879$	44.1014	−	21.0370i	1.48750	−	0.709561i
$880$	−3.60368	+	4.29470i	−0.121480	+	0.144774i
$881$	−28.1569	−	48.7691i	−0.948629	−	1.64307i	−0.748317	−	0.663342i	$-0.769138\pi$
$881$	−28.1569	−	48.7691i	−0.948629	−	1.64307i	−0.200313	−	0.979732i	$-0.564196\pi$
$882$	43.1027	+	19.6321i	1.45134	+	0.661047i
$883$	−17.5215	+	30.3481i	−0.589645	+	1.02130i	0.404634	+	0.914479i	$0.367399\pi$
$883$	−17.5215	+	30.3481i	−0.589645	+	1.02130i	−0.994279	+	0.106816i	$0.965934\pi$
$884$	15.6392	+	42.9684i	0.526003	+	1.44518i
$885$	−16.2350	+	1.56378i	−0.545735	+	0.0525660i
$886$	30.7305	−	25.7859i	1.03241	−	0.866296i
$887$	−7.44929	−	42.2470i	−0.250123	−	1.41852i	−0.808288	−	0.588787i	$-0.799606\pi$
$887$	−7.44929	−	42.2470i	−0.250123	−	1.41852i	0.558166	−	0.829730i	$-0.311505\pi$
$888$	30.3549	+	29.8278i	1.01864	+	1.00095i
$889$	−9.05963	+	21.6092i	−0.303850	+	0.724748i
$890$			76.6180i			2.56824i
$891$	−14.0950	+	18.0455i	−0.472200	+	0.604549i
$892$	58.4553	−	33.7492i	1.95723	−	1.13001i
$893$	9.66098	−	11.5135i	0.323292	−	0.385285i
$894$	−16.1560	−	58.2494i	−0.540338	−	1.94815i
$895$	31.1181	+	37.0850i	1.04016	+	1.23962i
$896$	20.2501	+	39.3109i	0.676507	+	1.31328i
$897$	−9.97621	+	21.8927i	−0.333096	+	0.730975i
$898$	68.5312	−	24.9433i	2.28691	−	0.832369i
$899$	−3.15899			−0.105358
$900$	1.07953	+	61.6187i	0.0359843	+	2.05396i
$901$		−	11.5035i		−	0.383236i
$902$	−5.72158	+	32.4487i	−0.190508	+	1.08042i
$903$	0.862765	−	2.77959i	0.0287110	−	0.0924988i
$904$	3.38333	+	1.23143i	0.112528	+	0.0409568i
$905$	14.8641	+	17.7144i	0.494100	+	0.588845i
$906$	−21.8526	−	1.71913i	−0.726005	−	0.0571143i
$907$	12.6541	−	4.60570i	0.420171	−	0.152930i	−0.123278	−	0.992372i	$-0.539341\pi$
$907$	12.6541	−	4.60570i	0.420171	−	0.152930i	0.543448	+	0.839443i	$0.317118\pi$
$908$	40.1969			1.33398
$909$	3.51492	−	4.34114i	0.116583	−	0.143986i
$910$	85.3987	−	92.3972i	2.83094	−	3.06294i
$911$	−36.2342	+	43.1823i	−1.20049	+	1.43069i	−0.326197	+	0.945302i	$0.605767\pi$
$911$	−36.2342	+	43.1823i	−1.20049	+	1.43069i	−0.874297	+	0.485391i	$0.838677\pi$
$912$	1.26642	+	0.577091i	0.0419353	+	0.0191094i
$913$	4.14600	+	4.94101i	0.137213	+	0.163524i
$914$	6.92076	−	19.0146i	0.228918	−	0.628948i
$915$	10.9136	−	42.2055i	0.360793	−	1.39527i
$916$	0.927806	+	2.54913i	0.0306556	+	0.0842255i
$917$	−14.8553	−	47.8296i	−0.490565	−	1.57947i
$918$	−27.9282	+	3.18475i	−0.921767	+	0.105112i
$919$	19.3698	−	33.5495i	0.638951	−	1.10670i	−0.346712	−	0.937972i	$-0.612702\pi$
$919$	19.3698	−	33.5495i	0.638951	−	1.10670i	0.985663	−	0.168725i	$-0.0539649\pi$
$920$	14.4164	+	12.0968i	0.475295	+	0.398820i
$921$	25.4899	−	7.06987i	0.839922	−	0.232960i
$922$	−77.4979	+	13.6650i	−2.55226	+	0.450032i
$923$	−5.52129	−	31.3128i	−0.181736	−	1.03067i
$924$	4.53796	−	35.7012i	0.149288	−	1.17448i
$925$	51.1059	+	42.8829i	1.68035	+	1.40998i
$926$	−54.9247	+	31.7108i	−1.80494	+	1.04208i
$927$	−30.1334	+	26.1980i	−0.989712	+	0.860455i
$928$	6.37499	−	11.0418i	0.209269	−	0.362465i
$929$	−33.3387	−	27.9745i	−1.09381	−	0.917814i	−0.0968146	−	0.995302i	$-0.530865\pi$
$929$	−33.3387	−	27.9745i	−1.09381	−	0.917814i	−0.996993	+	0.0774887i	$0.975310\pi$
$930$	18.9614	−	9.04486i	0.621768	−	0.296593i
$931$	−6.21436	+	6.10862i	−0.203668	+	0.200202i
$932$	8.53686	−	23.4548i	0.279634	−	0.768288i
$933$	1.14321	−	14.5319i	0.0374271	−	0.475753i
$934$	−18.9552	−	52.0790i	−0.620233	−	1.70408i
$935$	18.0421	+	10.4166i	0.590039	+	0.340659i
$936$	44.5789	−	8.66824i	1.45711	−	0.283330i
$937$	29.8016	+	17.2060i	0.973576	+	0.562094i	0.900324	−	0.435219i	$-0.143329\pi$
$937$	29.8016	+	17.2060i	0.973576	+	0.562094i	0.0732512	+	0.997314i	$0.476663\pi$
$938$	6.04075	+	47.4566i	0.197237	+	1.54951i
$939$	17.9670	−	12.8166i	0.586332	−	0.418255i
$940$	119.559	+	43.5158i	3.89957	+	1.41933i
$941$	52.4492	+	19.0899i	1.70979	+	0.622314i	0.996880	−	0.0789361i	$-0.0251523\pi$
$941$	52.4492	+	19.0899i	1.70979	+	0.622314i	0.712915	+	0.701250i	$0.247375\pi$
$942$	11.3797	+	41.0289i	0.370772	+	1.33679i
$943$	−12.7180	−	2.24252i	−0.414155	−	0.0730266i
$944$	−1.78036			−0.0579458
$945$	26.0818	+	39.0199i	0.848442	+	1.26932i
$946$	−3.64432			−0.118487
$947$	−5.10738	−	0.900569i	−0.165968	−	0.0292646i	0.0900468	−	0.995938i	$-0.471298\pi$
$947$	−5.10738	−	0.900569i	−0.165968	−	0.0292646i	−0.256014	+	0.966673i	$0.582409\pi$
$948$	3.62160	−	3.68560i	0.117624	−	0.119703i
$949$	−77.8255	−	28.3262i	−2.52632	−	0.919506i
$950$	−17.5582	−	6.39067i	−0.569664	−	0.207341i
$951$	4.31078	+	44.7541i	0.139787	+	1.45125i
$952$	12.3804	−	9.41573i	0.401253	−	0.305166i
$953$	−38.7728	−	22.3855i	−1.25598	−	0.725138i	−0.283686	−	0.958917i	$-0.591557\pi$
$953$	−38.7728	−	22.3855i	−1.25598	−	0.725138i	−0.972290	+	0.233779i	$0.924891\pi$
$954$	−32.0516	−	5.07435i	−1.03771	−	0.164288i
$955$	−49.5079	−	28.5834i	−1.60204	−	0.924937i
$956$	−6.84096	−	18.7954i	−0.221253	−	0.607887i
$957$	−7.97615	+	3.80474i	−0.257832	+	0.122990i
$958$	−24.7104	+	67.8914i	−0.798358	+	2.19347i
$959$	2.10835	−	3.27831i	0.0680820	−	0.105862i
$960$	−6.05123	+	76.9199i	−0.195303	+	2.48258i
$961$	21.8465	+	18.3314i	0.704726	+	0.591335i
$962$	69.8179	−	120.928i	2.25102	−	3.89888i
$963$	−15.0101	−	24.9774i	−0.483695	−	0.804886i
$964$	−71.6415	+	41.3622i	−2.30742	+	1.33219i
$965$	30.0007	+	25.1735i	0.965756	+	0.810365i
$966$	23.0591	+	2.93103i	0.741916	+	0.0943044i
$967$	3.09720	+	17.5651i	0.0995992	+	0.564855i	0.993241	+	0.116074i	$0.0370308\pi$
$967$	3.09720	+	17.5651i	0.0995992	+	0.564855i	−0.893641	+	0.448782i	$0.851858\pi$
$968$	10.9274	−	1.92679i	0.351220	−	0.0619295i
$969$	1.29470	−	5.00692i	0.0415919	−	0.160845i
$970$	47.5388	+	39.8898i	1.52638	+	1.28078i
$971$	−4.65514	+	8.06294i	−0.149391	+	0.258752i	−0.931002	−	0.365013i	$-0.881065\pi$
$971$	−4.65514	+	8.06294i	−0.149391	+	0.258752i	0.781612	+	0.623765i	$0.214398\pi$
$972$	−2.09112	+	48.0723i	−0.0670727	+	1.54192i
$973$	−26.2575	−	24.2686i	−0.841776	−	0.778016i
$974$	−3.72561	−	10.2360i	−0.119376	−	0.327984i
$975$	68.6022	−	19.0275i	2.19703	−	0.609366i
$976$	1.62751	−	4.47156i	0.0520955	−	0.143131i
$977$	2.31558	+	2.75960i	0.0740819	+	0.0882874i	0.801812	−	0.597576i	$-0.203869\pi$
$977$	2.31558	+	2.75960i	0.0740819	+	0.0882874i	−0.727731	+	0.685863i	$0.759425\pi$
$978$	−80.1475	+	57.1725i	−2.56283	+	1.82818i
$979$	16.2731	−	19.3936i	0.520092	−	0.619821i
$980$	−66.5850	−	31.7475i	−2.12698	−	1.01414i
$981$	−0.375737	−	21.4468i	−0.0119964	−	0.684742i
$982$	26.2704			0.838322
$983$	−3.60940	+	1.31372i	−0.115122	+	0.0419010i	−0.398939	−	0.916977i	$-0.630621\pi$
$983$	−3.60940	+	1.31372i	−0.115122	+	0.0419010i	0.283817	+	0.958879i	$0.408399\pi$
$984$	10.4954	+	22.0022i	0.334581	+	0.701406i
$985$	2.23025	+	2.65791i	0.0710616	+	0.0846879i
$986$	−10.1942	−	3.71037i	−0.324648	−	0.118162i
$987$	53.9624	−	12.2164i	1.71764	−	0.388852i
$988$	−4.12103	+	23.3715i	−0.131108	+	0.743548i
$989$		−	1.42836i		−	0.0454192i
$990$	36.9819	−	45.6748i	1.17536	−	1.45164i
$991$	−6.35133			−0.201757			−0.100878	−	0.994899i	$-0.532165\pi$
$991$	−6.35133			−0.201757			−0.100878	+	0.994899i	$0.532165\pi$
$992$	9.41120	−	3.42540i	0.298806	−	0.108756i
$993$	−5.08737	+	0.490023i	−0.161443	+	0.0155504i
$994$	−27.3098	+	14.0680i	−0.866214	+	0.446209i
$995$	12.0285	+	14.3350i	0.381330	+	0.454452i
$996$	13.1225	+	3.39327i	0.415804	+	0.107520i
$997$	−34.9951	+	41.7056i	−1.10831	+	1.32083i	−0.165981	+	0.986129i	$0.553079\pi$
$997$	−34.9951	+	41.7056i	−1.10831	+	1.32083i	−0.942325	+	0.334699i	$0.891365\pi$
$998$	20.5934	−	11.8896i	0.651873	−	0.376359i
$999$	37.7872	+	35.8518i	1.19554	+	1.13430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.47.20	yes	132
3.2	odd	2		567.2.bd.a.467.3		132
7.3	odd	6		189.2.ba.a.101.3	✓	132
21.17	even	6		567.2.ba.a.143.20		132
27.4	even	9		567.2.ba.a.341.20		132
27.23	odd	18		189.2.ba.a.131.3	yes	132
189.31	odd	18		567.2.bd.a.17.3		132
189.185	even	18	inner	189.2.bd.a.185.20	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.3	✓	132	7.3	odd	6
189.2.ba.a.131.3	yes	132	27.23	odd	18
189.2.bd.a.47.20	yes	132	1.1	even	1	trivial
189.2.bd.a.185.20	yes	132	189.185	even	18	inner
567.2.ba.a.143.20		132	21.17	even	6
567.2.ba.a.341.20		132	27.4	even	9
567.2.bd.a.17.3		132	189.31	odd	18
567.2.bd.a.467.3		132	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.22112 + 0.391643i) q^{2} +(1.67689 + 0.433617i) q^{3} +(2.90060 + 1.05573i) q^{4} +(-3.20807 - 1.16764i) q^{5} +(3.55476 + 1.61986i) q^{6} +(-2.62457 + 0.334082i) q^{7} +(2.12267 + 1.22552i) q^{8} +(2.62395 + 1.45426i) q^{9} +O(q^{10})\)	\(q+(2.22112 + 0.391643i) q^{2} +(1.67689 + 0.433617i) q^{3} +(2.90060 + 1.05573i) q^{4} +(-3.20807 - 1.16764i) q^{5} +(3.55476 + 1.61986i) q^{6} +(-2.62457 + 0.334082i) q^{7} +(2.12267 + 1.22552i) q^{8} +(2.62395 + 1.45426i) q^{9} +(-6.66821 - 3.84989i) q^{10} +(0.870169 + 2.39077i) q^{11} +(4.40622 + 3.02810i) q^{12} +(2.11236 - 5.80365i) q^{13} +(-5.96033 - 0.285861i) q^{14} +(-4.87329 - 3.34909i) q^{15} +(-0.494450 - 0.414893i) q^{16} +(-1.19927 + 2.07719i) q^{17} +(5.25856 + 4.25774i) q^{18} +(-1.07808 + 0.622427i) q^{19} +(-8.07261 - 6.77373i) q^{20} +(-4.54600 - 0.577839i) q^{21} +(0.996420 + 5.65098i) q^{22} +(-2.21485 + 0.390538i) q^{23} +(3.02808 + 2.97550i) q^{24} +(5.09811 + 4.27783i) q^{25} +(6.96475 - 12.0633i) q^{26} +(3.76950 + 3.57643i) q^{27} +(-7.96554 - 1.80181i) q^{28} +(0.685884 + 1.88445i) q^{29} +(-9.51251 - 9.34731i) q^{30} +(-0.538767 + 1.48025i) q^{31} +(-4.08675 - 4.87040i) q^{32} +(0.422504 + 4.38639i) q^{33} +(-3.47723 + 4.14400i) q^{34} +(8.80991 + 1.99281i) q^{35} +(6.07573 + 6.98842i) q^{36} +10.0245 q^{37} +(-2.63830 + 0.960264i) q^{38} +(6.05876 - 8.81616i) q^{39} +(-5.37870 - 6.41008i) q^{40} +(5.39584 + 1.96393i) q^{41} +(-9.87090 - 3.06386i) q^{42} +(-0.110284 + 0.625454i) q^{43} +7.85333i q^{44} +(-6.71977 - 7.72921i) q^{45} -5.07240 q^{46} +(-11.3454 + 4.12940i) q^{47} +(-0.649236 - 0.910134i) q^{48} +(6.77678 - 1.75365i) q^{49} +(9.64814 + 11.4982i) q^{50} +(-2.91175 + 2.96321i) q^{51} +(12.2542 - 14.6040i) q^{52} +(-4.15350 + 2.39802i) q^{53} +(6.97183 + 9.41998i) q^{54} -8.68580i q^{55} +(-5.98053 - 2.50733i) q^{56} +(-2.07772 + 0.576273i) q^{57} +(0.785398 + 4.45421i) q^{58} +(2.11297 - 1.77299i) q^{59} +(-10.5997 - 14.8593i) q^{60} +(2.52148 + 6.92772i) q^{61} +(-1.77639 + 3.07681i) q^{62} +(-7.37260 - 2.94020i) q^{63} +(-6.52423 - 11.3003i) q^{64} +(-13.5532 + 16.1520i) q^{65} +(-0.779468 + 9.90816i) q^{66} +(-1.39215 - 7.89530i) q^{67} +(-5.67155 + 4.75899i) q^{68} +(-3.88342 - 0.305506i) q^{69} +(18.7874 + 7.87660i) q^{70} +(4.45847 - 2.57410i) q^{71} +(3.78755 + 6.30263i) q^{72} -13.4098i q^{73} +(22.2655 + 3.92601i) q^{74} +(6.69406 + 9.38409i) q^{75} +(-3.78418 + 0.667254i) q^{76} +(-3.08253 - 5.98404i) q^{77} +(16.9100 - 17.2089i) q^{78} +(0.167826 - 0.951791i) q^{79} +(1.10178 + 1.90835i) q^{80} +(4.77026 + 7.63182i) q^{81} +(11.2156 + 6.47536i) q^{82} +(2.38230 - 0.867085i) q^{83} +(-12.5761 - 6.47544i) q^{84} +(6.27275 - 5.26346i) q^{85} +(-0.489910 + 1.34602i) q^{86} +(0.333026 + 3.45744i) q^{87} +(-1.08286 + 6.14122i) q^{88} +(-4.97533 - 8.61753i) q^{89} +(-11.8983 - 19.7992i) q^{90} +(-3.60514 + 15.9378i) q^{91} +(-6.83671 - 1.20550i) q^{92} +(-1.54532 + 2.24860i) q^{93} +(-26.8168 + 4.72852i) q^{94} +(4.18532 - 0.737985i) q^{95} +(-4.74116 - 9.93922i) q^{96} +(-7.93719 - 1.39954i) q^{97} +(15.7388 - 1.24098i) q^{98} +(-1.19352 + 7.53871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more