LMFDB - Embedded newform 153.3.q.a.2.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(2,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 21])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.q (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$34$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			2.20
Character	$\chi$	$=$	153.2
Dual form			153.3.q.a.77.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0775060 + 0.289257i) q^{2} +(-2.82295 - 1.01536i) q^{3} +(3.38644 - 1.95516i) q^{4} +(2.93290 + 2.25049i) q^{5} +(0.0749028 - 0.895253i) q^{6} +(-2.95513 - 3.85120i) q^{7} +(1.67501 + 1.67501i) q^{8} +(6.93810 + 5.73260i) q^{9} +(-0.423652 + 1.02279i) q^{10} +(-8.57981 - 11.1814i) q^{11} +(-11.5449 + 2.08088i) q^{12} +(17.7309 - 10.2370i) q^{13} +(0.884944 - 1.15328i) q^{14} +(-5.99437 - 9.33096i) q^{15} +(7.46596 - 12.9314i) q^{16} +(16.5975 + 3.67736i) q^{17} +(-1.12045 + 2.45120i) q^{18} +(-10.6134 - 10.6134i) q^{19} +(14.3322 + 1.88686i) q^{20} +(4.43184 + 13.8723i) q^{21} +(2.56931 - 3.34839i) q^{22} +(19.4256 - 2.55743i) q^{23} +(-3.02775 - 6.42922i) q^{24} +(-2.93330 - 10.9472i) q^{25} +(4.33536 + 4.33536i) q^{26} +(-13.7653 - 23.2275i) q^{27} +(-17.5371 - 7.26410i) q^{28} +(-5.14487 + 39.0792i) q^{29} +(2.23444 - 2.45712i) q^{30} +(-5.85586 - 4.49336i) q^{31} +(13.4716 + 3.60971i) q^{32} +(12.8672 + 40.2762i) q^{33} +(0.222707 + 5.08595i) q^{34} -17.9457i q^{35} +(34.7036 + 5.84800i) q^{36} +(-43.8166 + 18.1494i) q^{37} +(2.24740 - 3.89261i) q^{38} +(-60.4477 + 10.8952i) q^{39} +(1.14304 + 8.68225i) q^{40} +(1.68353 + 12.7877i) q^{41} +(-3.66915 + 2.35712i) q^{42} +(18.9093 + 70.5703i) q^{43} +(-50.9165 - 21.0903i) q^{44} +(7.44757 + 32.4273i) q^{45} +(2.24536 + 5.42077i) q^{46} +(-33.1317 + 57.3857i) q^{47} +(-34.2061 + 28.9242i) q^{48} +(6.58318 - 24.5688i) q^{49} +(2.93921 - 1.69695i) q^{50} +(-43.1201 - 27.2334i) q^{51} +(40.0298 - 69.3337i) q^{52} +(27.5694 - 27.5694i) q^{53} +(5.65181 - 5.78197i) q^{54} -52.1028i q^{55} +(1.50093 - 11.4007i) q^{56} +(19.1848 + 40.7377i) q^{57} +(-11.7027 + 1.54068i) q^{58} +(-5.55991 + 20.7499i) q^{59} +(-38.5431 - 19.8788i) q^{60} +(-36.7955 - 47.9528i) q^{61} +(0.845869 - 2.04211i) q^{62} +(1.57441 - 43.6606i) q^{63} -55.5512i q^{64} +(75.0412 + 9.87936i) q^{65} +(-10.6529 + 6.84358i) q^{66} +(45.0944 + 78.1058i) q^{67} +(63.3963 - 19.9977i) q^{68} +(-57.4343 - 12.5044i) q^{69} +(5.19090 - 1.39090i) q^{70} +(27.6841 + 66.8352i) q^{71} +(2.01923 + 21.2236i) q^{72} +(9.76419 + 23.5728i) q^{73} +(-8.64589 - 11.2675i) q^{74} +(-2.83478 + 33.8818i) q^{75} +(-56.6928 - 15.1908i) q^{76} +(-17.7075 + 66.0851i) q^{77} +(-7.83657 - 16.6405i) q^{78} +(-9.09405 + 6.97811i) q^{79} +(50.9990 - 21.1245i) q^{80} +(15.2745 + 79.5468i) q^{81} +(-3.56844 + 1.47810i) q^{82} +(0.351254 + 1.31090i) q^{83} +(42.1307 + 38.3126i) q^{84} +(40.4029 + 48.1378i) q^{85} +(-18.9473 + 10.9393i) q^{86} +(54.2030 - 105.095i) q^{87} +(4.35774 - 33.1004i) q^{88} -117.164 q^{89} +(-8.80257 + 4.66757i) q^{90} +(-91.8218 - 38.0338i) q^{91} +(60.7835 - 46.6408i) q^{92} +(11.9684 + 18.6303i) q^{93} +(-19.1671 - 5.13581i) q^{94} +(-7.24268 - 55.0136i) q^{95} +(-34.3645 - 23.8685i) q^{96} +(182.237 + 23.9919i) q^{97} +7.61692 q^{98} +(4.57109 - 126.762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 8 q^{6} - 4 q^{7} + 16 q^{9} - 16 q^{10} - 84 q^{11} - 140 q^{12} - 12 q^{14} + 44 q^{15} + 440 q^{16} - 48 q^{18} - 16 q^{19} - 12 q^{20} - 4 q^{22} - 120 q^{23}+ \cdots - 832 q^{99}+O(q^{100}) $ 272 * q - 12 * q^2 - 8 * q^3 - 12 * q^5 - 8 * q^6 - 4 * q^7 + 16 * q^9 - 16 * q^10 - 84 * q^11 - 140 * q^12 - 12 * q^14 + 44 * q^15 + 440 * q^16 - 48 * q^18 - 16 * q^19 - 12 * q^20 - 4 * q^22 - 120 * q^23 + 112 * q^24 - 4 * q^25 + 40 * q^27 - 144 * q^28 - 12 * q^29 - 4 * q^31 - 204 * q^32 + 112 * q^33 - 28 * q^34 - 200 * q^36 - 16 * q^37 - 148 * q^39 + 60 * q^40 - 12 * q^41 - 624 * q^42 + 116 * q^43 + 44 * q^45 - 352 * q^46 - 168 * q^48 - 4 * q^49 - 24 * q^50 - 256 * q^51 - 264 * q^52 - 20 * q^54 + 708 * q^56 + 76 * q^57 - 4 * q^58 + 492 * q^59 - 656 * q^60 - 4 * q^61 + 708 * q^63 + 348 * q^65 - 508 * q^66 - 8 * q^67 - 204 * q^68 + 176 * q^69 + 12 * q^70 - 16 * q^73 + 492 * q^74 - 868 * q^75 + 92 * q^76 + 528 * q^77 + 864 * q^78 - 4 * q^79 + 176 * q^82 + 1428 * q^83 - 440 * q^84 + 188 * q^85 - 1824 * q^86 - 796 * q^87 + 156 * q^88 - 1000 * q^90 - 744 * q^91 - 12 * q^92 + 44 * q^93 + 28 * q^94 - 12 * q^95 - 1452 * q^96 - 364 * q^97 - 832 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0775060	+	0.289257i	0.0387530	+	0.144628i	0.982592	−	0.185779i	$-0.0594807\pi$
$2$	0.0775060	+	0.289257i	0.0387530	+	0.144628i	−0.943839	+	0.330407i	$0.892814\pi$
$3$	−2.82295	−	1.01536i	−0.940984	−	0.338452i
$3$	−2.82295	−	1.01536i	−0.940984	−	0.338452i
$4$	3.38644	−	1.95516i	0.846610	−	0.488790i
$5$	2.93290	+	2.25049i	0.586580	+	0.450098i	0.858925	−	0.512101i	$-0.171133\pi$
$5$	2.93290	+	2.25049i	0.586580	+	0.450098i	−0.272346	+	0.962199i	$0.587799\pi$
$6$	0.0749028	−	0.895253i	0.0124838	−	0.149209i
$7$	−2.95513	−	3.85120i	−0.422161	−	0.550171i	0.533055	−	0.846081i	$-0.321044\pi$
$7$	−2.95513	−	3.85120i	−0.422161	−	0.550171i	−0.955216	+	0.295909i	$0.904377\pi$
$8$	1.67501	+	1.67501i	0.209377	+	0.209377i
$9$	6.93810	+	5.73260i	0.770900	+	0.636956i
$10$	−0.423652	+	1.02279i	−0.0423652	+	0.102279i
$11$	−8.57981	−	11.1814i	−0.779983	−	1.01649i	−0.999167	−	0.0408096i	$-0.987006\pi$
$11$	−8.57981	−	11.1814i	−0.779983	−	1.01649i	0.219184	−	0.975683i	$-0.429660\pi$
$12$	−11.5449	+	2.08088i	−0.962078	+	0.173407i
$13$	17.7309	−	10.2370i	1.36392	−	0.787458i	0.373775	−	0.927519i	$-0.378063\pi$
$13$	17.7309	−	10.2370i	1.36392	−	0.787458i	0.990143	+	0.140061i	$0.0447299\pi$
$14$	0.884944	−	1.15328i	0.0632103	−	0.0823773i
$15$	−5.99437	−	9.33096i	−0.399625	−	0.622064i
$16$	7.46596	−	12.9314i	0.466623	−	0.808214i
$17$	16.5975	+	3.67736i	0.976324	+	0.216315i
$17$	16.5975	+	3.67736i	0.976324	+	0.216315i
$18$	−1.12045	+	2.45120i	−0.0622471	+	0.136178i
$19$	−10.6134	−	10.6134i	−0.558602	−	0.558602i	0.370307	−	0.928909i	$-0.379252\pi$
$19$	−10.6134	−	10.6134i	−0.558602	−	0.558602i	−0.928909	+	0.370307i	$0.879252\pi$
$20$	14.3322	+	1.88686i	0.716608	+	0.0943432i
$21$	4.43184	+	13.8723i	0.211040	+	0.660584i
$22$	2.56931	−	3.34839i	0.116787	−	0.152200i
$23$	19.4256	−	2.55743i	0.844592	−	0.111193i	0.304202	−	0.952607i	$-0.401610\pi$
$23$	19.4256	−	2.55743i	0.844592	−	0.111193i	0.540390	+	0.841415i	$0.318277\pi$
$24$	−3.02775	−	6.42922i	−0.126156	−	0.267884i
$25$	−2.93330	−	10.9472i	−0.117332	−	0.437889i
$26$	4.33536	+	4.33536i	0.166745	+	0.166745i
$27$	−13.7653	−	23.2275i	−0.509825	−	0.860278i
$28$	−17.5371	−	7.26410i	−0.626324	−	0.259432i
$29$	−5.14487	+	39.0792i	−0.177409	+	1.34756i	0.638609	+	0.769531i	$0.279510\pi$
$29$	−5.14487	+	39.0792i	−0.177409	+	1.34756i	−0.816019	+	0.578026i	$0.803823\pi$
$30$	2.23444	−	2.45712i	0.0744814	−	0.0819039i
$31$	−5.85586	−	4.49336i	−0.188899	−	0.144947i	0.509983	−	0.860185i	$-0.329652\pi$
$31$	−5.85586	−	4.49336i	−0.188899	−	0.144947i	−0.698881	+	0.715238i	$0.746318\pi$
$32$	13.4716	+	3.60971i	0.420988	+	0.112803i
$33$	12.8672	+	40.2762i	0.389916	+	1.22049i
$34$	0.222707	+	5.08595i	0.00655021	+	0.149587i
$35$		−	17.9457i		−	0.512733i
$36$	34.7036	+	5.84800i	0.963990	+	0.162445i
$37$	−43.8166	+	18.1494i	−1.18423	+	0.490525i	−0.885873	−	0.463929i	$-0.846439\pi$
$37$	−43.8166	+	18.1494i	−1.18423	+	0.490525i	−0.298359	+	0.954454i	$0.596439\pi$
$38$	2.24740	−	3.89261i	0.0591422	−	0.102437i
$39$	−60.4477	+	10.8952i	−1.54994	+	0.279364i
$40$	1.14304	+	8.68225i	0.0285760	+	0.217056i
$41$	1.68353	+	12.7877i	0.0410617	+	0.311895i	0.999634	+	0.0270460i	$0.00861006\pi$
$41$	1.68353	+	12.7877i	0.0410617	+	0.311895i	−0.958572	+	0.284849i	$0.908057\pi$
$42$	−3.66915	+	2.35712i	−0.0873606	+	0.0561220i
$43$	18.9093	+	70.5703i	0.439750	+	1.64117i	0.729436	+	0.684049i	$0.239782\pi$
$43$	18.9093	+	70.5703i	0.439750	+	1.64117i	−0.289686	+	0.957122i	$0.593551\pi$
$44$	−50.9165	−	21.0903i	−1.15719	−	0.479325i
$45$	7.44757	+	32.4273i	0.165501	+	0.720606i
$46$	2.24536	+	5.42077i	0.0488121	+	0.117843i
$47$	−33.1317	+	57.3857i	−0.704929	+	1.22097i	0.261788	+	0.965125i	$0.415688\pi$
$47$	−33.1317	+	57.3857i	−0.704929	+	1.22097i	−0.966717	+	0.255848i	$0.917645\pi$
$48$	−34.2061	+	28.9242i	−0.712626	+	0.602587i
$49$	6.58318	−	24.5688i	0.134351	−	0.501404i
$50$	2.93921	−	1.69695i	0.0587841	−	0.0339390i
$51$	−43.1201	−	27.2334i	−0.845492	−	0.533988i
$52$	40.0298	−	69.3337i	0.769804	−	1.33334i
$53$	27.5694	−	27.5694i	0.520178	−	0.520178i	−0.397447	−	0.917625i	$-0.630104\pi$
$53$	27.5694	−	27.5694i	0.520178	−	0.520178i	0.917625	+	0.397447i	$0.130104\pi$
$54$	5.65181	−	5.78197i	0.104663	−	0.107074i
$55$		−	52.1028i		−	0.947323i
$56$	1.50093	−	11.4007i	0.0268023	−	0.203584i
$57$	19.1848	+	40.7377i	0.336575	+	0.714696i
$58$	−11.7027	+	1.54068i	−0.201770	+	0.0265635i
$59$	−5.55991	+	20.7499i	−0.0942358	+	0.351693i	−0.996902	−	0.0786476i	$-0.974940\pi$
$59$	−5.55991	+	20.7499i	−0.0942358	+	0.351693i	0.902667	+	0.430340i	$0.141606\pi$
$60$	−38.5431	−	19.8788i	−0.642385	−	0.331313i
$61$	−36.7955	−	47.9528i	−0.603204	−	0.786111i	0.387540	−	0.921853i	$-0.373325\pi$
$61$	−36.7955	−	47.9528i	−0.603204	−	0.786111i	−0.990744	+	0.135742i	$0.956658\pi$
$62$	0.845869	−	2.04211i	0.0136431	−	0.0329372i
$63$	1.57441	−	43.6606i	0.0249907	−	0.693025i
$64$		−	55.5512i		−	0.867987i
$65$	75.0412	+	9.87936i	1.15448	+	0.151990i
$66$	−10.6529	+	6.84358i	−0.161407	+	0.103691i
$67$	45.0944	+	78.1058i	0.673050	+	1.16576i	0.977035	+	0.213080i	$0.0683496\pi$
$67$	45.0944	+	78.1058i	0.673050	+	1.16576i	−0.303984	+	0.952677i	$0.598317\pi$
$68$	63.3963	−	19.9977i	0.932298	−	0.294083i
$69$	−57.4343	−	12.5044i	−0.832381	−	0.181224i
$70$	5.19090	−	1.39090i	0.0741557	−	0.0198700i
$71$	27.6841	+	66.8352i	0.389916	+	0.941341i	0.989957	+	0.141372i	$0.0451512\pi$
$71$	27.6841	+	66.8352i	0.389916	+	0.941341i	−0.600040	+	0.799970i	$0.704849\pi$
$72$	2.01923	+	21.2236i	0.0280448	+	0.294772i
$73$	9.76419	+	23.5728i	0.133756	+	0.322916i	0.976540	−	0.215337i	$-0.0690848\pi$
$73$	9.76419	+	23.5728i	0.133756	+	0.322916i	−0.842784	+	0.538252i	$0.819085\pi$
$74$	−8.64589	−	11.2675i	−0.116836	−	0.152264i
$75$	−2.83478	+	33.8818i	−0.0377970	+	0.451758i
$76$	−56.6928	−	15.1908i	−0.745958	−	0.199879i
$77$	−17.7075	+	66.0851i	−0.229967	+	0.858248i
$78$	−7.83657	−	16.6405i	−0.100469	−	0.213339i
$79$	−9.09405	+	6.97811i	−0.115115	+	0.0883305i	−0.664715	−	0.747097i	$-0.731447\pi$
$79$	−9.09405	+	6.97811i	−0.115115	+	0.0883305i	0.549600	+	0.835428i	$0.314780\pi$
$80$	50.9990	−	21.1245i	0.637487	−	0.264056i
$81$	15.2745	+	79.5468i	0.188574	+	0.982059i
$82$	−3.56844	+	1.47810i	−0.0435175	+	0.0180256i
$83$	0.351254	+	1.31090i	0.00423197	+	0.0157939i	0.968010	−	0.250913i	$-0.0807309\pi$
$83$	0.351254	+	1.31090i	0.00423197	+	0.0157939i	−0.963778	+	0.266707i	$0.914064\pi$
$84$	42.1307	+	38.3126i	0.501556	+	0.456102i
$85$	40.4029	+	48.1378i	0.475328	+	0.566328i
$86$	−18.9473	+	10.9393i	−0.220318	+	0.127201i
$87$	54.2030	−	105.095i	0.623023	−	1.20798i
$88$	4.35774	−	33.1004i	0.0495198	−	0.376140i
$89$	−117.164			−1.31645			−0.658226	−	0.752821i	$-0.728693\pi$
$89$	−117.164			−1.31645			−0.658226	+	0.752821i	$0.728693\pi$
$90$	−8.80257	+	4.66757i	−0.0978063	+	0.0518619i
$91$	−91.8218	−	38.0338i	−1.00903	−	0.417954i
$92$	60.7835	−	46.6408i	0.660690	−	0.506965i
$93$	11.9684	+	18.6303i	0.128693	+	0.200326i
$94$	−19.1671	−	5.13581i	−0.203905	−	0.0546363i
$95$	−7.24268	−	55.0136i	−0.0762387	−	0.579091i
$96$	−34.3645	−	23.8685i	−0.357964	−	0.248630i
$97$	182.237	+	23.9919i	1.87873	+	0.247339i	0.981113	−	0.193438i	$-0.0619637\pi$
$97$	182.237	+	23.9919i	1.87873	+	0.247339i	0.897617	+	0.440777i	$0.145297\pi$
$98$	7.61692			0.0777236
$99$	4.57109	−	126.762i	0.0461726	−	1.28043i
$100$	−31.3370	−	31.3370i	−0.313370	−	0.313370i
$101$	−87.6938	−	50.6300i	−0.868255	−	0.501287i	−0.00148706	−	0.999999i	$-0.500473\pi$
$101$	−87.6938	−	50.6300i	−0.868255	−	0.501287i	−0.866768	+	0.498712i	$0.833807\pi$
$102$	4.53536	−	14.5835i	0.0444644	−	0.142976i
$103$	13.3629	+	23.1452i	0.129737	+	0.224711i	0.923575	−	0.383419i	$-0.125253\pi$
$103$	13.3629	+	23.1452i	0.129737	+	0.224711i	−0.793838	+	0.608130i	$0.791920\pi$
$104$	46.8466	+	12.5525i	0.450448	+	0.120697i
$105$	−18.2213	+	50.6597i	−0.173536	+	0.482474i
$106$	10.1114	+	5.83784i	0.0953908	+	0.0550739i
$107$	42.8540	−	17.7507i	0.400505	−	0.165894i	−0.173334	−	0.984863i	$-0.555454\pi$
$107$	42.8540	−	17.7507i	0.400505	−	0.165894i	0.573838	+	0.818969i	$0.305454\pi$
$108$	−92.0288	−	51.7452i	−0.852119	−	0.479122i
$109$	−1.60841	+	3.88305i	−0.0147561	+	0.0356243i	−0.931086	−	0.364800i	$-0.881137\pi$
$109$	−1.60841	+	3.88305i	−0.0147561	+	0.0356243i	0.916330	+	0.400424i	$0.131137\pi$
$110$	15.0711	−	4.03828i	0.137010	−	0.0367116i
$111$	142.120	−	6.74547i	1.28036	−	0.0607700i
$112$	−71.8644	+	9.46113i	−0.641646	+	0.0844743i
$113$	−131.279	+	17.2832i	−1.16176	+	0.152949i	−0.686657	−	0.726981i	$-0.740923\pi$
$113$	−131.279	+	17.2832i	−1.16176	+	0.152949i	−0.475103	+	0.879930i	$0.657589\pi$
$114$	−10.2967	+	8.70674i	−0.0903219	+	0.0763750i
$115$	62.7288	+	36.2165i	0.545468	+	0.314926i
$116$	58.9833	+	142.398i	0.508477	+	1.22757i
$117$	181.703	+	30.6193i	1.55302	+	0.261704i
$118$	−6.43296			−0.0545167
$119$	−34.8855	−	74.7874i	−0.293156	−	0.628465i
$120$	5.58884	−	25.6702i	0.0465736	−	0.213918i
$121$	−20.0940	+	74.9919i	−0.166066	+	0.619768i
$122$	11.0188	−	14.3600i	0.0903179	−	0.117705i
$123$	8.23154	−	37.8084i	0.0669231	−	0.307385i
$124$	−28.6158	−	3.76734i	−0.230772	−	0.0303818i
$125$	51.4015	−	124.094i	0.411212	−	0.992754i
$126$	12.7511	−	2.92855i	0.101200	−	0.0232425i
$127$	106.818	−	106.818i	0.841089	−	0.841089i	−0.147911	−	0.989001i	$-0.547255\pi$
$127$	106.818	−	106.818i	0.841089	−	0.841089i	0.989001	+	0.147911i	$0.0472551\pi$
$128$	69.9550	−	18.7444i	0.546523	−	0.146440i
$129$	18.2741	−	218.416i	0.141660	−	1.69315i
$130$	2.95848	+	22.4719i	0.0227575	+	0.172861i
$131$	−162.543	−	124.723i	−1.24078	−	0.952086i	−0.240953	−	0.970537i	$-0.577460\pi$
$131$	−162.543	−	124.723i	−1.24078	−	0.952086i	−0.999830	+	0.0184507i	$0.994127\pi$
$132$	122.321	+	111.235i	0.926671	+	0.842692i
$133$	−9.51039	+	72.2386i	−0.0715067	+	0.543147i
$134$	−19.0975	+	19.0975i	−0.142519	+	0.142519i
$135$	11.9011	−	99.1025i	0.0881566	−	0.734093i
$136$	21.6414	+	33.9607i	0.159128	+	0.249711i
$137$	43.2321	+	24.9601i	0.315563	+	0.182190i	0.649413	−	0.760436i	$-0.275015\pi$
$137$	43.2321	+	24.9601i	0.315563	+	0.182190i	−0.333850	+	0.942626i	$0.608348\pi$
$138$	−0.834516	−	17.5824i	−0.00604722	−	0.127409i
$139$	59.1032	+	45.3515i	0.425203	+	0.326270i	0.799097	−	0.601202i	$-0.205311\pi$
$139$	59.1032	+	45.3515i	0.425203	+	0.326270i	−0.373895	+	0.927471i	$0.621978\pi$
$140$	−35.0867	−	60.7719i	−0.250619	−	0.434085i
$141$	151.796	−	128.357i	1.07657	−	0.910331i
$142$	−17.1868	+	13.1879i	−0.121034	+	0.0928727i
$143$	−266.592	−	110.426i	−1.86428	−	0.772209i
$144$	125.930	−	46.9201i	0.874516	−	0.325834i
$145$	−103.037	+	103.037i	−0.710598	+	0.710598i
$146$	−6.06181	+	4.65139i	−0.0415193	+	0.0318589i
$147$	−43.5301	+	62.6722i	−0.296123	+	0.426341i
$148$	−112.897	+	147.130i	−0.762819	+	0.994125i
$149$	77.6639	+	134.518i	0.521234	+	0.902804i	0.999695	+	0.0246953i	$0.00786157\pi$
$149$	77.6639	+	134.518i	0.521234	+	0.902804i	−0.478461	+	0.878109i	$0.658805\pi$
$150$	−10.0202	+	1.80607i	−0.0668017	+	0.0120405i
$151$	−47.0212	+	12.5993i	−0.311399	+	0.0834391i	−0.411134	−	0.911575i	$-0.634867\pi$
$151$	−47.0212	+	12.5993i	−0.311399	+	0.0834391i	0.0997350	+	0.995014i	$0.468200\pi$
$152$		−	35.5554i		−	0.233917i
$153$	94.0743	+	120.661i	0.614865	+	0.788633i
$154$	−20.4880			−0.133039
$155$	−7.06237	−	26.3571i	−0.0455637	−	0.170046i
$156$	−183.401	+	155.081i	−1.17565	+	0.994109i
$157$	−116.928	+	67.5085i	−0.744766	+	0.429991i	−0.823800	−	0.566881i	$-0.808150\pi$
$157$	−116.928	+	67.5085i	−0.744766	+	0.429991i	0.0790338	+	0.996872i	$0.474816\pi$
$158$	−2.72331	−	2.08967i	−0.0172361	−	0.0132257i
$159$	−105.820	+	49.8343i	−0.665534	+	0.313423i
$160$	31.3872	+	40.9046i	0.196170	+	0.255654i
$161$	−67.2544	−	67.2544i	−0.417729	−	0.417729i
$162$	−21.8256	+	10.5836i	−0.134726	+	0.0653309i
$163$	−28.0428	+	67.7012i	−0.172042	+	0.415345i	−0.986257	−	0.165218i	$-0.947167\pi$
$163$	−28.0428	+	67.7012i	−0.172042	+	0.415345i	0.814216	+	0.580563i	$0.197167\pi$
$164$	30.7032	+	40.0132i	0.187214	+	0.243983i
$165$	−52.9029	+	147.084i	−0.320623	+	0.891415i
$166$	−0.351961	+	0.203205i	−0.00212025	+	0.00122412i
$167$	52.6963	−	68.6752i	0.315547	−	0.411228i	−0.608472	−	0.793575i	$-0.708217\pi$
$167$	52.6963	−	68.6752i	0.315547	−	0.411228i	0.924019	+	0.382347i	$0.124884\pi$
$168$	−15.8128	+	30.6596i	−0.0941240	+	0.182498i
$169$	125.091	−	216.663i	0.740181	−	1.28203i
$170$	−10.7927	+	15.4178i	−0.0634866	+	0.0906928i
$171$	−12.7945	−	134.480i	−0.0748216	−	0.786432i
$172$	202.011	+	202.011i	1.17449	+	1.17449i
$173$	−307.565	−	40.4917i	−1.77783	−	0.234056i	−0.831110	−	0.556108i	$-0.812294\pi$
$173$	−307.565	−	40.4917i	−1.77783	−	0.234056i	−0.946722	+	0.322052i	$0.895627\pi$
$174$	34.6004	+	7.53310i	0.198853	+	0.0432937i
$175$	−33.4917	+	43.6472i	−0.191381	+	0.249412i
$176$	−208.648	+	27.4691i	−1.18550	+	0.156074i
$177$	36.7639	−	52.9306i	0.207706	−	0.299043i
$178$	−9.08093	−	33.8905i	−0.0510165	−	0.190396i
$179$	115.575	+	115.575i	0.645671	+	0.645671i	0.951944	−	0.306273i	$-0.0990820\pi$
$179$	115.575	+	115.575i	0.645671	+	0.645671i	−0.306273	+	0.951944i	$0.599082\pi$
$180$	88.6213	+	95.2518i	0.492341	+	0.529177i
$181$	−120.420	−	49.8794i	−0.665301	−	0.275577i	0.0243661	−	0.999703i	$-0.492243\pi$
$181$	−120.420	−	49.8794i	−0.665301	−	0.275577i	−0.689667	+	0.724126i	$0.742243\pi$
$182$	3.88479	−	29.5079i	0.0213450	−	0.162131i
$183$	55.1826	+	172.729i	0.301544	+	0.943874i
$184$	36.8219	+	28.2545i	0.200119	+	0.153557i
$185$	−169.355	−	45.3785i	−0.915431	−	0.245289i
$186$	−4.46132	+	4.90591i	−0.0239856	+	0.0263759i
$187$	−101.285	−	217.135i	−0.541633	−	1.16115i
$188$			259.111i			1.37825i
$189$	−48.7756	+	121.653i	−0.258072	+	0.643667i
$190$	15.3517	−	6.35888i	0.0807984	−	0.0334678i
$191$	15.9352	−	27.6005i	0.0834301	−	0.144505i	−0.821291	−	0.570509i	$-0.806746\pi$
$191$	15.9352	−	27.6005i	0.0834301	−	0.144505i	0.904721	+	0.426004i	$0.140079\pi$
$192$	−56.4043	+	156.818i	−0.293772	+	0.816762i
$193$	46.6282	+	354.177i	0.241597	+	1.83511i	0.496370	+	0.868111i	$0.334666\pi$
$193$	46.6282	+	354.177i	0.241597	+	1.83511i	−0.254773	+	0.967001i	$0.582001\pi$
$194$	7.18463	+	54.5727i	0.0370342	+	0.281302i
$195$	−201.807	−	104.083i	−1.03491	−	0.533757i
$196$	−25.7424	−	96.0719i	−0.131339	−	0.490163i
$197$	127.660	+	52.8785i	0.648020	+	0.268419i	0.682387	−	0.730991i	$-0.260942\pi$
$197$	127.660	+	52.8785i	0.648020	+	0.268419i	−0.0343677	+	0.999409i	$0.510942\pi$
$198$	37.0212	−	8.50264i	0.186976	−	0.0429426i
$199$	75.5702	+	182.443i	0.379750	+	0.916797i	0.992012	+	0.126143i	$0.0402597\pi$
$199$	75.5702	+	182.443i	0.379750	+	0.916797i	−0.612262	+	0.790655i	$0.709740\pi$
$200$	13.4234	−	23.2501i	0.0671172	−	0.116250i
$201$	−47.9940	−	266.276i	−0.238776	−	1.32475i
$202$	7.84826	−	29.2901i	0.0388528	−	0.145001i
$203$	165.705	−	95.6700i	0.816283	−	0.471281i
$204$	−199.269	−	7.91743i	−0.976810	−	0.0388109i
$205$	−23.8410	+	41.2937i	−0.116297	+	0.201433i
$206$	−5.65920	+	5.65920i	−0.0274718	+	0.0274718i
$207$	149.438	+	93.6156i	0.721921	+	0.452250i
$208$		−	305.715i		−	1.46978i
$209$	−27.6121	+	209.735i	−0.132115	+	1.00352i
$210$	−16.0659	−	1.34418i	−0.0765044	−	0.00640086i
$211$	272.008	−	35.8105i	1.28914	−	0.169718i	0.545391	−	0.838182i	$-0.316381\pi$
$211$	272.008	−	35.8105i	1.28914	−	0.169718i	0.743745	+	0.668464i	$0.233048\pi$
$212$	39.4595	−	147.265i	0.186130	−	0.694645i
$213$	−10.2891	−	216.782i	−0.0483058	−	1.01775i
$214$	8.45595	+	11.0200i	0.0395138	+	0.0514954i
$215$	−103.359	+	249.531i	−0.480739	+	1.16061i
$216$	15.8494	−	61.9635i	0.0733767	−	0.286868i
$217$			35.8306i			0.165118i
$218$	−1.24786	−	0.164284i	−0.00572412	−	0.000753594i
$219$	−3.62899	−	76.4591i	−0.0165707	−	0.349128i
$220$	−101.869	−	176.443i	−0.463042	−	0.802013i
$221$	331.934	−	104.705i	1.50196	−	0.473778i
$222$	12.9663	+	40.5864i	0.0584070	+	0.182822i
$223$	85.9961	−	23.0426i	0.385633	−	0.103330i	−0.0607935	−	0.998150i	$-0.519363\pi$
$223$	85.9961	−	23.0426i	0.385633	−	0.103330i	0.446426	+	0.894820i	$0.352696\pi$
$224$	−25.9086	−	62.5490i	−0.115664	−	0.279237i
$225$	42.4046	−	92.7684i	0.188465	−	0.412304i
$226$	−15.1742	−	36.6337i	−0.0671424	−	0.162096i
$227$	−46.1608	−	60.1579i	−0.203352	−	0.265013i	0.680534	−	0.732717i	$-0.261748\pi$
$227$	−46.1608	−	60.1579i	−0.203352	−	0.265013i	−0.883885	+	0.467704i	$0.845081\pi$
$228$	144.617	+	100.446i	0.634285	+	0.440554i
$229$	190.378	+	51.0116i	0.831345	+	0.222758i	0.649300	−	0.760532i	$-0.275062\pi$
$229$	190.378	+	51.0116i	0.831345	+	0.222758i	0.182044	+	0.983290i	$0.441729\pi$
$230$	−5.61400	+	20.9517i	−0.0244087	+	0.0910944i
$231$	117.087	−	168.576i	0.506871	−	0.729765i
$232$	−74.0759	+	56.8404i	−0.319293	+	0.245002i
$233$	254.160	−	105.277i	1.09082	−	0.451831i	0.236525	−	0.971625i	$-0.423991\pi$
$233$	254.160	−	105.277i	1.09082	−	0.451831i	0.854291	+	0.519794i	$0.173991\pi$
$234$	5.22627	+	54.9321i	0.0223345	+	0.234753i
$235$	−226.318	+	93.7439i	−0.963055	+	0.398910i
$236$	21.7411	+	81.1387i	0.0921231	+	0.343808i
$237$	32.7573	−	10.4652i	0.138217	−	0.0441568i
$238$	18.9289	−	15.8873i	0.0795332	−	0.0667535i
$239$	−288.853	+	166.769i	−1.20859	+	0.697779i	−0.962451	−	0.271456i	$-0.912495\pi$
$239$	−288.853	+	166.769i	−1.20859	+	0.697779i	−0.246137	+	0.969235i	$0.579161\pi$
$240$	−165.416	+	7.85118i	−0.689235	+	0.0327132i
$241$	−13.6805	+	103.914i	−0.0567657	+	0.431178i	0.939338	+	0.342992i	$0.111440\pi$
$241$	−13.6805	+	103.914i	−0.0567657	+	0.431178i	−0.996104	+	0.0881863i	$0.971893\pi$
$242$	−23.2493			−0.0960715
$243$	37.6492	−	240.066i	0.154935	−	0.987925i
$244$	−218.361	−	90.4481i	−0.894923	−	0.370689i
$245$	74.5996	−	57.2423i	0.304488	−	0.233642i
$246$	11.5743	−	0.549353i	0.0470501	−	0.00223314i
$247$	−296.836	−	79.5369i	−1.20176	−	0.322012i
$248$	−2.28221	−	17.3351i	−0.00920246	−	0.0698996i
$249$	0.339456	−	4.05724i	0.00136328	−	0.0162941i
$250$	39.8790	+	5.25017i	0.159516	+	0.0210007i
$251$	−121.642			−0.484628			−0.242314	−	0.970198i	$-0.577906\pi$
$251$	−121.642			−0.484628			−0.242314	+	0.970198i	$0.577906\pi$
$252$	−80.0319	−	150.932i	−0.317587	−	0.598937i
$253$	−195.264	−	195.264i	−0.771794	−	0.771794i
$254$	39.1770	+	22.6188i	0.154240	+	0.0890505i
$255$	−65.1783	−	176.914i	−0.255601	−	0.693781i
$256$	−100.258	−	173.653i	−0.391635	−	0.678331i
$257$	273.260	+	73.2198i	1.06327	+	0.284902i	0.747725	−	0.664009i	$-0.231146\pi$
$257$	273.260	+	73.2198i	1.06327	+	0.284902i	0.315544	+	0.948911i	$0.397813\pi$
$258$	64.5947	−	11.6427i	0.250367	−	0.0451266i
$259$	199.381	+	115.113i	0.769810	+	0.444450i
$260$	273.438	−	113.262i	1.05169	−	0.435622i
$261$	−259.721	+	241.642i	−0.995099	+	0.925830i
$262$	23.4790	−	56.6833i	0.0896145	−	0.216348i
$263$	15.0616	−	4.03575i	0.0572686	−	0.0153451i	−0.230071	−	0.973174i	$-0.573896\pi$
$263$	15.0616	−	4.03575i	0.0572686	−	0.0153451i	0.287340	+	0.957829i	$0.407229\pi$
$264$	−45.9104	+	89.0160i	−0.173903	+	0.337182i
$265$	142.903	−	18.8135i	0.539257	−	0.0709945i
$266$	−21.6326	+	2.84799i	−0.0813256	+	0.0107067i
$267$	330.749	+	118.963i	1.23876	+	0.445556i
$268$	305.419	+	176.334i	1.13962	+	0.657961i
$269$	−82.1655	−	198.365i	−0.305448	−	0.737416i	−0.999841	−	0.0178207i	$-0.994327\pi$
$269$	−82.1655	−	198.365i	−0.305448	−	0.737416i	0.694393	−	0.719596i	$-0.255673\pi$
$270$	29.5885	−	4.23856i	0.109587	−	0.0156984i
$271$	215.939			0.796823			0.398412	−	0.917207i	$-0.369562\pi$
$271$	215.939			0.796823			0.398412	+	0.917207i	$0.369562\pi$
$272$	171.470	−	187.174i	0.630404	−	0.688141i
$273$	220.590	+	200.599i	0.808024	+	0.734797i
$274$	−3.86912	+	14.4397i	−0.0141209	+	0.0526998i
$275$	−97.2384	+	126.724i	−0.353594	+	0.460813i
$276$	−218.946	+	69.9478i	−0.793282	+	0.253434i
$277$	−384.695	−	50.6461i	−1.38879	−	0.182838i	−0.601231	−	0.799075i	$-0.705323\pi$
$277$	−384.695	−	50.6461i	−1.38879	−	0.182838i	−0.787561	+	0.616237i	$0.788656\pi$
$278$	−8.53736	+	20.6110i	−0.0307099	+	0.0741403i
$279$	−14.8699	−	64.7447i	−0.0532972	−	0.232060i
$280$	30.0593	−	30.0593i	0.107354	−	0.107354i
$281$	−237.035	+	63.5134i	−0.843542	+	0.226026i	−0.654613	−	0.755964i	$-0.727168\pi$
$281$	−237.035	+	63.5134i	−0.843542	+	0.226026i	−0.188929	+	0.981991i	$0.560502\pi$
$282$	48.8931	+	33.9596i	0.173380	+	0.120424i
$283$	−60.7010	−	461.070i	−0.214491	−	1.62922i	−0.672376	−	0.740210i	$-0.734726\pi$
$283$	−60.7010	−	461.070i	−0.214491	−	1.62922i	0.457885	−	0.889011i	$-0.348607\pi$
$284$	224.424	+	172.207i	0.790226	+	0.606361i
$285$	−35.4127	+	162.655i	−0.124255	+	0.570718i
$286$	11.2789	−	85.6721i	0.0394369	−	0.299553i
$287$	44.2729	−	44.2729i	0.154261	−	0.154261i
$288$	72.7744	+	102.272i	0.252689	+	0.355111i
$289$	261.954	+	122.070i	0.906416	+	0.422387i
$290$	−37.7900	−	21.8181i	−0.130310	−	0.0752347i
$291$	−490.085	−	252.763i	−1.68414	−	0.868602i
$292$	79.1545	+	60.7374i	0.271077	+	0.208005i
$293$	−12.0454	−	20.8632i	−0.0411104	−	0.0712054i	0.844738	−	0.535180i	$-0.179756\pi$
$293$	−12.0454	−	20.8632i	−0.0411104	−	0.0712054i	−0.885848	+	0.463975i	$0.846423\pi$
$294$	−21.5022	−	7.73389i	−0.0731367	−	0.0263057i
$295$	−63.0041	+	48.3447i	−0.213573	+	0.163880i
$296$	−103.794	−	42.9929i	−0.350655	−	0.145246i
$297$	−141.613	+	353.203i	−0.476812	+	1.18924i
$298$	−32.8907	+	32.8907i	−0.110372	+	0.110372i
$299$	318.254	−	244.205i	1.06439	−	0.816739i
$300$	56.6446	+	120.281i	0.188815	+	0.400937i
$301$	215.901	−	281.368i	0.717279	−	0.934777i
$302$	−7.28886	−	12.6247i	−0.0241353	−	0.0418036i
$303$	196.148	+	231.966i	0.647352	+	0.765566i
$304$	−216.487	+	58.0074i	−0.712127	+	0.190814i
$305$		−	223.449i		−	0.732618i
$306$	−27.6106	+	36.5635i	−0.0902307	+	0.119489i
$307$	31.0770			0.101228			0.0506140	−	0.998718i	$-0.483882\pi$
$307$	31.0770			0.101228			0.0506140	+	0.998718i	$0.483882\pi$
$308$	69.2419	+	258.414i	0.224811	+	0.839007i
$309$	−14.2222	−	78.9059i	−0.0460264	−	0.255359i
$310$	7.07660	−	4.08568i	0.0228277	−	0.0131796i
$311$	166.103	+	127.455i	0.534092	+	0.409823i	0.840284	−	0.542147i	$-0.182388\pi$
$311$	166.103	+	127.455i	0.534092	+	0.409823i	−0.306192	+	0.951970i	$0.599055\pi$
$312$	−119.500	−	83.0012i	−0.383014	−	0.266029i
$313$	−105.267	−	137.187i	−0.336317	−	0.438297i	0.594326	−	0.804224i	$-0.297419\pi$
$313$	−105.267	−	137.187i	−0.336317	−	0.438297i	−0.930644	+	0.365927i	$0.880752\pi$
$314$	−28.5899	−	28.5899i	−0.0910507	−	0.0910507i
$315$	102.875	−	124.509i	0.326589	−	0.395266i
$316$	−17.1531	+	41.4113i	−0.0542820	+	0.131048i
$317$	97.2513	+	126.740i	0.306786	+	0.399812i	0.921148	−	0.389213i	$-0.127253\pi$
$317$	97.2513	+	126.740i	0.306786	+	0.399812i	−0.614361	+	0.789025i	$0.710586\pi$
$318$	−22.6166	−	26.7466i	−0.0711213	−	0.0841089i
$319$	481.103	−	277.765i	1.50816	−	0.870736i
$320$	125.017	−	162.926i	0.390679	−	0.509143i
$321$	−138.998	+	6.59728i	−0.433016	+	0.0205523i
$322$	14.2411	−	24.6664i	0.0442272	−	0.0766037i
$323$	−137.127	−	215.186i	−0.424543	−	0.666211i
$324$	207.253	+	239.516i	0.639670	+	0.739248i
$325$	−164.076	−	164.076i	−0.504851	−	0.504851i
$326$	−21.7565	−	2.86430i	−0.0667377	−	0.00878619i
$327$	8.48314	−	9.32854i	0.0259423	−	0.0285276i
$328$	−18.5996	+	24.2395i	−0.0567062	+	0.0739009i
$329$	318.912	−	41.9856i	0.969338	−	0.127616i
$330$	−46.6452	−	3.90264i	−0.141349	−	0.0118262i
$331$	19.4168	+	72.4644i	0.0586610	+	0.218926i	0.989034	−	0.147689i	$-0.0471834\pi$
$331$	19.4168	+	72.4644i	0.0586610	+	0.218926i	−0.930373	+	0.366615i	$0.880517\pi$
$332$	3.75251	+	3.75251i	0.0113027	+	0.0113027i
$333$	−408.047	−	125.261i	−1.22537	−	0.376158i
$334$	23.9490	+	9.92001i	0.0717036	+	0.0297006i
$335$	−43.5191	+	330.561i	−0.129908	+	0.986748i
$336$	212.476	+	46.2597i	0.632369	+	0.137678i
$337$	101.916	+	78.2033i	0.302423	+	0.232057i	0.748813	−	0.662781i	$-0.230624\pi$
$337$	101.916	+	78.2033i	0.302423	+	0.232057i	−0.446390	+	0.894838i	$0.647291\pi$
$338$	72.3666	+	19.3906i	0.214102	+	0.0573685i
$339$	388.143	+	84.5053i	1.14496	+	0.249278i
$340$	230.939	+	84.0217i	0.679233	+	0.247123i
$341$			104.029i			0.305071i
$342$	37.9075	−	14.1239i	0.110841	−	0.0412979i
$343$	−333.829	+	138.277i	−0.973264	+	0.403139i
$344$	−86.5330	+	149.880i	−0.251550	+	0.435697i
$345$	−140.308	−	165.930i	−0.406689	−	0.480955i
$346$	−12.1257	−	92.1035i	−0.0350453	−	0.266195i
$347$	−18.3863	−	139.658i	−0.0529866	−	0.402473i	−0.997301	−	0.0734273i	$-0.976606\pi$
$347$	−18.3863	−	139.658i	−0.0529866	−	0.402473i	0.944314	−	0.329046i	$-0.106727\pi$
$348$	−21.9219	−	461.872i	−0.0629940	−	1.32722i
$349$	5.51909	+	20.5975i	0.0158140	+	0.0590187i	0.973382	−	0.229189i	$-0.0736073\pi$
$349$	5.51909	+	20.5975i	0.0158140	+	0.0590187i	−0.957568	+	0.288208i	$0.906941\pi$
$350$	−15.2210	−	6.30476i	−0.0434887	−	0.0180136i
$351$	−481.850	−	270.931i	−1.37279	−	0.771882i
$352$	−75.2221	−	181.602i	−0.213699	−	0.515916i
$353$	−21.3992	+	37.0646i	−0.0606211	+	0.104999i	−0.894743	−	0.446581i	$-0.852641\pi$
$353$	−21.3992	+	37.0646i	−0.0606211	+	0.104999i	0.834122	+	0.551580i	$0.185975\pi$
$354$	18.1599	+	6.53175i	0.0512993	+	0.0184513i
$355$	−69.2176	+	258.324i	−0.194979	+	0.727672i
$356$	−396.769	+	229.075i	−1.11452	+	0.643469i
$357$	22.5443	+	246.542i	0.0631492	+	0.690595i
$358$	−24.4731	+	42.3886i	−0.0683605	+	0.118404i
$359$	89.1192	−	89.1192i	0.248243	−	0.248243i	−0.572006	−	0.820249i	$-0.693835\pi$
$359$	89.1192	−	89.1192i	0.248243	−	0.248243i	0.820249	+	0.572006i	$0.193835\pi$
$360$	−41.8414	+	66.7909i	−0.116226	+	0.185530i
$361$		−	135.710i		−	0.375927i
$362$	5.09470	−	38.6981i	0.0140738	−	0.106901i
$363$	132.868	−	191.296i	0.366027	−	0.526986i
$364$	−385.311	+	50.7272i	−1.05855	+	0.139360i
$365$	−24.4131	+	91.1109i	−0.0668852	+	0.249619i
$366$	−45.6860	+	29.3495i	−0.124825	+	0.0801898i
$367$	−230.762	−	300.735i	−0.628779	−	0.819441i	0.364977	−	0.931017i	$-0.381077\pi$
$367$	−230.762	−	300.735i	−0.628779	−	0.819441i	−0.993756	+	0.111576i	$0.964410\pi$
$368$	111.960	−	270.295i	0.304238	−	0.734496i
$369$	−61.6262	+	98.3733i	−0.167009	+	0.266594i
$370$		−	52.5040i		−	0.141903i
$371$	−187.647	−	24.7041i	−0.505786	−	0.0665880i
$372$	76.9557	+	39.6902i	0.206870	+	0.106694i
$373$	−201.186	−	348.464i	−0.539372	−	0.934220i	−0.998938	−	0.0460759i	$-0.985328\pi$
$373$	−201.186	−	348.464i	−0.539372	−	0.934220i	0.459566	−	0.888144i	$-0.348005\pi$
$374$	54.9574	−	46.1267i	0.146945	−	0.123333i
$375$	−271.104	+	298.121i	−0.722944	+	0.794989i
$376$	−151.618	+	40.6259i	−0.403239	+	0.108048i
$377$	308.828	+	745.578i	0.819173	+	1.97766i
$378$	−38.9694	−	4.67980i	−0.103094	−	0.0123804i
$379$	185.848	+	448.676i	0.490364	+	1.18384i	0.954535	+	0.298097i	$0.0963520\pi$
$379$	185.848	+	448.676i	0.490364	+	1.18384i	−0.464172	+	0.885745i	$0.653648\pi$
$380$	−132.087	−	172.140i	−0.347598	−	0.452999i
$381$	−410.002	+	193.084i	−1.07612	+	0.506783i
$382$	9.21870	+	2.47014i	0.0241327	+	0.00646634i
$383$	−112.266	+	418.981i	−0.293121	+	1.09394i	0.649576	+	0.760296i	$0.274946\pi$
$383$	−112.266	+	418.981i	−0.293121	+	1.09394i	−0.942698	+	0.333648i	$0.891720\pi$
$384$	−216.512	−	18.1148i	−0.563832	−	0.0471739i
$385$	−200.658	+	153.970i	−0.521190	+	0.399923i
$386$	−98.8339	+	40.9384i	−0.256046	+	0.106058i
$387$	−273.357	+	598.023i	−0.706350	+	1.54528i
$388$	664.042	−	275.055i	1.71145	−	0.708905i
$389$	84.7915	+	316.446i	0.217973	+	0.813486i	0.985099	+	0.171990i	$0.0550195\pi$
$389$	84.7915	+	316.446i	0.217973	+	0.813486i	−0.767126	+	0.641497i	$0.778314\pi$
$390$	14.4653	−	66.4409i	0.0370906	−	0.170361i
$391$	331.821	+	28.9880i	0.848648	+	0.0741380i
$392$	52.1800	−	30.1261i	0.133112	−	0.0768524i
$393$	332.211	+	517.126i	0.845321	+	1.31584i
$394$	−5.40102	+	41.0249i	−0.0137082	+	0.104124i
$395$	−42.3761			−0.107281
$396$	−232.361	−	438.211i	−0.586771	−	1.10659i
$397$	408.401	+	169.165i	1.02872	+	0.426109i	0.832250	−	0.554401i	$-0.187052\pi$
$397$	408.401	+	169.165i	1.02872	+	0.426109i	0.196469	+	0.980510i	$0.437052\pi$
$398$	−46.9156	+	35.9996i	−0.117878	+	0.0904512i
$399$	100.195	−	194.270i	0.251116	−	0.486891i
$400$	−163.463	−	43.7998i	−0.408658	−	0.109500i
$401$	21.0205	+	159.666i	0.0524201	+	0.398170i	0.997461	+	0.0712175i	$0.0226884\pi$
$401$	21.0205	+	159.666i	0.0524201	+	0.398170i	−0.945041	+	0.326953i	$0.893978\pi$
$402$	73.3021	−	34.5205i	0.182344	−	0.0858720i
$403$	−149.828	−	19.7253i	−0.371782	−	0.0489461i
$404$	−395.959			−0.980098
$405$	−134.221	+	267.678i	−0.331409	+	0.660933i
$406$	40.5163	+	40.5163i	0.0997940	+	0.0997940i
$407$	578.874	+	334.213i	1.42230	+	0.821163i
$408$	−26.6105	−	117.843i	−0.0652218	−	0.288831i
$409$	−353.106	−	611.597i	−0.863339	−	1.49535i	−0.868687	−	0.495361i	$-0.835036\pi$
$409$	−353.106	−	611.597i	−0.863339	−	1.49535i	0.00534802	−	0.999986i	$-0.498298\pi$
$410$	−13.7923	−	3.69564i	−0.0336398	−	0.00901375i
$411$	−96.6988	−	114.357i	−0.235277	−	0.278241i
$412$	90.5053	+	52.2533i	0.219673	+	0.126828i
$413$	96.3422	−	39.9062i	0.233274	−	0.0966253i
$414$	−15.4966	+	50.4816i	−0.0374314	+	0.121936i
$415$	−1.91997	+	4.63522i	−0.00462643	+	0.0111692i
$416$	275.817	−	73.9048i	0.663021	−	0.177656i
$417$	−120.798	−	188.036i	−0.289682	−	0.450925i
$418$	−62.8073	+	8.26873i	−0.150257	+	0.0197817i
$419$	−75.0939	+	9.88629i	−0.179222	+	0.0235950i	−0.219603	−	0.975589i	$-0.570476\pi$
$419$	−75.0939	+	9.88629i	−0.179222	+	0.0235950i	0.0403811	+	0.999184i	$0.487143\pi$
$420$	37.3428	+	207.182i	0.0889114	+	0.493290i
$421$	125.977	+	72.7329i	0.299233	+	0.172762i	0.642098	−	0.766622i	$-0.278064\pi$
$421$	125.977	+	72.7329i	0.299233	+	0.172762i	−0.342865	+	0.939385i	$0.611397\pi$
$422$	31.4407	+	75.9045i	0.0745039	+	0.179868i
$423$	−558.841	+	208.217i	−1.32114	+	0.492240i
$424$	92.3583			0.217826
$425$	−8.42859	−	192.483i	−0.0198320	−	0.452902i
$426$	61.9081	−	19.7781i	0.145324	−	0.0464275i
$427$	−75.9404	+	283.413i	−0.177846	+	0.663732i
$428$	110.417	−	143.898i	0.257984	−	0.336211i
$429$	640.454	+	582.413i	1.49290	+	1.35761i
$430$	−80.1893	−	10.5571i	−0.186487	−	0.0245515i
$431$	−149.910	+	361.916i	−0.347820	+	0.839711i	0.649057	+	0.760740i	$0.275164\pi$
$431$	−149.910	+	361.916i	−0.347820	+	0.839711i	−0.996877	+	0.0789715i	$0.974836\pi$
$432$	−403.136	+	4.58905i	−0.933185	+	0.0106228i
$433$	−317.168	+	317.168i	−0.732489	+	0.732489i	−0.971112	−	0.238623i	$-0.923304\pi$
$433$	−317.168	+	317.168i	−0.732489	+	0.732489i	0.238623	+	0.971112i	$0.423304\pi$
$434$	−10.3642	+	2.77709i	−0.0238807	+	0.00639881i
$435$	395.486	−	186.248i	0.909164	−	0.428157i
$436$	2.14520	+	16.2944i	0.00492018	+	0.0373725i
$437$	−233.316	−	179.030i	−0.533904	−	0.409679i
$438$	21.8350	−	6.97575i	0.0498516	−	0.0159264i
$439$	−18.8608	+	143.262i	−0.0429631	+	0.326337i	0.956444	+	0.291915i	$0.0942924\pi$
$439$	−18.8608	+	143.262i	−0.0429631	+	0.326337i	−0.999407	+	0.0344221i	$0.989041\pi$
$440$	87.2729	−	87.2729i	0.198347	−	0.198347i
$441$	186.518	−	132.722i	0.422943	−	0.300957i
$442$	56.0135	+	87.8988i	0.126727	+	0.198866i
$443$	−547.612	−	316.164i	−1.23614	−	0.713688i	−0.267840	−	0.963463i	$-0.586310\pi$
$443$	−547.612	−	316.164i	−1.23614	−	0.713688i	−0.968304	+	0.249775i	$0.919643\pi$
$444$	468.093	−	300.711i	1.05426	−	0.677277i
$445$	−343.631	−	263.677i	−0.772203	−	0.592533i
$446$	13.3304	+	23.0890i	0.0298889	+	0.0517691i
$447$	−82.6578	−	458.594i	−0.184917	−	1.02594i
$448$	−213.939	+	164.161i	−0.477542	+	0.366431i
$449$	294.020	+	121.787i	0.654832	+	0.271240i	0.685262	−	0.728297i	$-0.259688\pi$
$449$	294.020	+	121.787i	0.654832	+	0.271240i	−0.0304299	+	0.999537i	$0.509688\pi$
$450$	30.1205	+	5.07568i	0.0669344	+	0.0112793i
$451$	128.540	−	128.540i	0.285011	−	0.285011i
$452$	−410.777	+	315.200i	−0.908798	+	0.697345i
$453$	145.531	+	12.1761i	0.321261	+	0.0268788i
$454$	13.8233	−	18.0149i	0.0304479	−	0.0396804i
$455$	−183.709	−	318.193i	−0.403756	−	0.699326i
$456$	−36.1014	+	100.371i	−0.0791697	+	0.220112i
$457$	84.9570	−	22.7642i	0.185901	−	0.0498122i	−0.164667	−	0.986349i	$-0.552655\pi$
$457$	84.9570	−	22.7642i	0.185901	−	0.0498122i	0.350569	+	0.936537i	$0.385988\pi$
$458$			59.0218i			0.128868i
$459$	−143.053	−	436.138i	−0.311663	−	0.950193i
$460$	283.236			0.615731
$461$	−193.412	−	721.822i	−0.419548	−	1.56578i	−0.775548	−	0.631289i	$-0.782526\pi$
$461$	−193.412	−	721.822i	−0.419548	−	1.56578i	0.356000	−	0.934486i	$-0.384140\pi$
$462$	57.8366	+	20.8026i	0.125187	+	0.0450273i
$463$	109.502	−	63.2210i	0.236505	−	0.136546i	−0.377064	−	0.926187i	$-0.623066\pi$
$463$	109.502	−	63.2210i	0.236505	−	0.136546i	0.613569	+	0.789641i	$0.289733\pi$
$464$	466.938	+	358.294i	1.00633	+	0.772185i
$465$	−6.82516	+	81.5757i	−0.0146778	+	0.175432i
$466$	50.1509	+	65.3579i	0.107620	+	0.140253i
$467$	−486.008	−	486.008i	−1.04070	−	1.04070i	−0.999136	−	0.0415673i	$-0.986765\pi$
$467$	−486.008	−	486.008i	−1.04070	−	1.04070i	−0.0415673	−	0.999136i	$-0.513235\pi$
$468$	675.194	−	251.569i	1.44272	−	0.537541i
$469$	167.541	−	404.480i	0.357231	−	0.862431i
$470$	−44.6570	−	58.1982i	−0.0950150	−	0.123826i
$471$	398.628	−	71.8494i	0.846344	−	0.152547i
$472$	−44.0693	+	25.4434i	−0.0933671	+	0.0539055i
$473$	626.839	−	816.912i	1.32524	−	1.72709i
$474$	5.56601	+	8.66416i	0.0117426	+	0.0182788i
$475$	−85.0554	+	147.320i	−0.179064	+	0.310148i
$476$	−264.359	−	185.056i	−0.555376	−	0.388773i
$477$	349.324	−	33.2349i	0.732335	−	0.0696748i
$478$	−70.6269	−	70.6269i	−0.147755	−	0.147755i
$479$	241.310	+	31.7691i	0.503779	+	0.0663237i	0.378133	−	0.925751i	$-0.376566\pi$
$479$	241.310	+	31.7691i	0.503779	+	0.0663237i	0.125646	+	0.992075i	$0.459900\pi$
$480$	−47.0718	−	147.341i	−0.0980663	−	0.306960i
$481$	−591.114	+	770.355i	−1.22893	+	1.60157i
$482$	−31.1181	+	4.09678i	−0.0645604	+	0.00849954i
$483$	121.569	+	258.143i	0.251695	+	0.534458i
$484$	78.5741	+	293.243i	0.162343	+	0.605873i
$485$	480.488	+	480.488i	0.990697	+	0.990697i
$486$	72.3586	−	7.71628i	0.148886	−	0.0158771i
$487$	403.701	+	167.218i	0.828955	+	0.343364i	0.756489	−	0.654007i	$-0.226913\pi$
$487$	403.701	+	167.218i	0.828955	+	0.343364i	0.0724659	+	0.997371i	$0.476913\pi$
$488$	18.6887	−	141.955i	0.0382965	−	0.290891i
$489$	147.904	−	162.644i	0.302463	−	0.332605i
$490$	22.3396	+	17.1418i	0.0455911	+	0.0349833i
$491$	−810.235	−	217.102i	−1.65017	−	0.442162i	−0.690512	−	0.723321i	$-0.742615\pi$
$491$	−810.235	−	217.102i	−1.65017	−	0.442162i	−0.959661	+	0.281159i	$0.909281\pi$
$492$	−46.0459	−	144.130i	−0.0935893	−	0.292947i
$493$	−229.100	+	629.697i	−0.464706	+	1.27728i
$494$		−	92.0263i		−	0.186288i
$495$	298.684	−	361.494i	0.603403	−	0.730291i
$496$	−101.825	+	42.1774i	−0.205293	+	0.0850351i
$497$	175.586	−	304.124i	0.353291	−	0.611919i
$498$	1.19989	−	0.216271i	0.00240943	−	0.000434279i
$499$	0.586592	+	4.45561i	0.00117553	+	0.00892907i	0.992023	−	0.126060i	$-0.0402333\pi$
$499$	0.586592	+	4.45561i	0.00117553	+	0.00892907i	−0.990847	+	0.134989i	$0.956900\pi$
$500$	−68.5562	−	520.736i	−0.137112	−	1.04147i
$501$	−218.489	+	140.361i	−0.436105	+	0.280162i
$502$	−9.42796	−	35.1856i	−0.0187808	−	0.0700909i
$503$	−70.1498	−	29.0570i	−0.139463	−	0.0577674i	0.311860	−	0.950128i	$-0.399048\pi$
$503$	−70.1498	−	29.0570i	−0.139463	−	0.0577674i	−0.451323	+	0.892361i	$0.649048\pi$
$504$	75.7693	−	70.4950i	0.150336	−	0.139871i
$505$	−143.254	−	345.847i	−0.283672	−	0.684845i
$506$	41.3472	−	71.6154i	0.0817138	−	0.141532i
$507$	−573.115	+	484.618i	−1.13041	+	0.955855i
$508$	152.887	−	570.581i	0.300958	−	1.12319i
$509$	−821.706	+	474.412i	−1.61435	+	0.932048i	−0.626009	+	0.779816i	$0.715313\pi$
$509$	−821.706	+	474.412i	−1.61435	+	0.932048i	−0.988345	+	0.152232i	$0.951354\pi$
$510$	46.1218	−	32.5652i	0.0904350	−	0.0638533i
$511$	61.9293	−	107.265i	0.121192	−	0.209911i
$512$	247.302	−	247.302i	0.483012	−	0.483012i
$513$	−100.427	+	392.621i	−0.195764	+	0.765343i
$514$			84.7172i			0.164820i
$515$	−12.8961	+	97.9557i	−0.0250410	+	0.190205i
$516$	−365.155	−	775.382i	−0.707664	−	1.50268i
$517$	925.918	−	121.899i	1.79094	−	0.235782i
$518$	−17.8438	+	66.5941i	−0.0344476	+	0.128560i
$519$	827.127	+	426.594i	1.59369	+	0.821954i
$520$	109.147	+	142.243i	0.209898	+	0.273545i
$521$	121.919	−	294.339i	0.234010	−	0.564950i	−0.762632	−	0.646832i	$-0.776093\pi$
$521$	121.919	−	294.339i	0.234010	−	0.564950i	0.996642	+	0.0818827i	$0.0260933\pi$
$522$	−90.0264	−	56.3973i	−0.172464	−	0.108041i
$523$			636.286i			1.21661i	0.793704	+	0.608304i	$0.208150\pi$
$523$			636.286i			1.21661i	−0.793704	+	0.608304i	$0.791850\pi$
$524$	−794.295	−	104.571i	−1.51583	−	0.199563i
$525$	138.863	−	89.2079i	0.264501	−	0.169920i
$526$	2.33473	+	4.04388i	0.00443866	+	0.00768798i
$527$	−80.6690	−	96.1127i	−0.153072	−	0.182377i
$528$	616.895	+	134.309i	1.16836	+	0.254372i
$529$	−140.161	+	37.5559i	−0.264954	+	0.0709942i
$530$	16.5178	+	39.8775i	0.0311656	+	0.0752405i
$531$	−157.526	+	112.092i	−0.296659	+	0.211096i
$532$	109.032	+	263.226i	0.204947	+	0.494786i
$533$	160.758	+	209.503i	0.301609	+	0.393065i
$534$	−8.77592	+	104.892i	−0.0164343	+	0.196426i
$535$	165.634	+	44.3815i	0.309597	+	0.0829562i
$536$	−55.2945	+	206.362i	−0.103161	+	0.385004i
$537$	−208.913	−	443.613i	−0.389037	−	0.826094i
$538$	51.0100	−	39.1414i	0.0948142	−	0.0727535i
$539$	−331.196	+	137.186i	−0.614465	+	0.254520i
$540$	−153.459	−	358.873i	−0.284183	−	0.664580i
$541$	184.646	−	76.4830i	0.341306	−	0.141373i	−0.205446	−	0.978669i	$-0.565864\pi$
$541$	184.646	−	76.4830i	0.341306	−	0.141373i	0.546751	+	0.837295i	$0.315864\pi$
$542$	16.7366	+	62.4618i	0.0308793	+	0.115243i
$543$	289.293	+	263.076i	0.532768	+	0.484486i
$544$	210.321	+	109.452i	0.386619	+	0.201199i
$545$	−13.4561	+	7.76886i	−0.0246900	+	0.0142548i
$546$	−40.9276	+	79.3549i	−0.0749590	+	0.145339i
$547$	116.060	−	881.560i	0.212175	−	1.61163i	−0.471517	−	0.881857i	$-0.656293\pi$
$547$	116.060	−	881.560i	0.212175	−	1.61163i	0.683692	−	0.729771i	$-0.260373\pi$
$548$	195.204			0.356212
$549$	19.6036	−	543.635i	0.0357079	−	0.990228i
$550$	−44.1922	−	18.3050i	−0.0803494	−	0.0332818i
$551$	469.369	−	360.160i	0.851850	−	0.653647i
$552$	−75.2581	−	117.148i	−0.136337	−	0.212225i
$553$	53.7482	+	14.4018i	0.0971939	+	0.0260430i
$554$	−15.1665	−	115.201i	−0.0273764	−	0.207944i
$555$	432.005	+	300.057i	0.778387	+	0.540642i
$556$	288.819	+	38.0237i	0.519458	+	0.0683880i
$557$	−511.810			−0.918868			−0.459434	−	0.888212i	$-0.651948\pi$
$557$	−511.810			−0.918868			−0.459434	+	0.888212i	$0.651948\pi$
$558$	17.5753	−	9.31933i	0.0314970	−	0.0167013i
$559$	1057.70	+	1057.70i	1.89214	+	1.89214i
$560$	−232.063	−	133.982i	−0.414398	−	0.239253i
$561$	65.4542	+	715.801i	0.116674	+	1.27594i
$562$	−36.7433	−	63.6413i	−0.0653796	−	0.113241i
$563$	561.314	+	150.404i	0.997005	+	0.267147i	0.720190	−	0.693777i	$-0.244055\pi$
$563$	561.314	+	150.404i	0.997005	+	0.267147i	0.276815	+	0.960923i	$0.410721\pi$
$564$	263.090	−	731.458i	0.466472	−	1.29691i
$565$	−423.923	−	244.752i	−0.750307	−	0.433190i
$566$	128.663	−	53.2938i	0.227319	−	0.0941587i
$567$	261.212	−	293.896i	0.460692	−	0.518335i
$568$	−65.5788	+	158.321i	−0.115456	+	0.278735i
$569$	684.230	−	183.339i	1.20251	−	0.322213i	0.398693	−	0.917084i	$-0.369464\pi$
$569$	684.230	−	183.339i	1.20251	−	0.322213i	0.803821	+	0.594872i	$0.202797\pi$
$570$	−49.7936	+	2.36336i	−0.0873572	+	0.00414625i
$571$	−761.489	+	100.252i	−1.33361	+	0.175573i	−0.763399	−	0.645928i	$-0.776471\pi$
$571$	−761.489	+	100.252i	−1.33361	+	0.175573i	−0.570208	+	0.821500i	$0.693137\pi$
$572$	−1118.70	+	147.279i	−1.95576	+	0.257481i
$573$	−73.0085	+	61.7350i	−0.127415	+	0.107740i
$574$	16.2376	+	9.37480i	0.0282886	+	0.0163324i
$575$	−84.9779	−	205.155i	−0.147788	−	0.356791i
$576$	318.453	−	385.420i	0.552870	−	0.669131i
$577$	−615.561			−1.06683			−0.533415	−	0.845853i	$-0.679092\pi$
$577$	−615.561			−1.06683			−0.533415	+	0.845853i	$0.679092\pi$
$578$	−15.0065	+	85.2331i	−0.0259628	+	0.147462i
$579$	227.986	−	1047.17i	0.393759	−	1.80858i
$580$	−147.474	+	550.381i	−0.254266	+	0.948932i
$581$	4.01052	−	5.22662i	0.00690279	−	0.00899590i
$582$	35.1289	−	161.351i	0.0603589	−	0.277235i
$583$	−544.806	−	71.7250i	−0.934486	−	0.123027i
$584$	−23.1297	+	55.8400i	−0.0396056	+	0.0956164i
$585$	464.009	+	498.725i	0.793178	+	0.852522i
$586$	5.10122	−	5.10122i	0.00870516	−	0.00870516i
$587$	−592.196	+	158.679i	−1.00885	+	0.270321i	−0.725150	−	0.688591i	$-0.758229\pi$
$587$	−592.196	+	158.679i	−1.00885	+	0.270321i	−0.283702	+	0.958912i	$0.591563\pi$
$588$	−24.8777	+	297.344i	−0.0423091	+	0.505687i
$589$	14.4608	+	109.841i	0.0245515	+	0.186487i
$590$	−18.8672	−	14.4773i	−0.0319784	−	0.0245379i
$591$	−306.687	−	278.894i	−0.518929	−	0.471901i
$592$	−92.4350	+	702.114i	−0.156140	+	1.18600i
$593$	764.340	−	764.340i	1.28894	−	1.28894i	0.353505	−	0.935433i	$-0.384990\pi$
$593$	764.340	−	764.340i	1.28894	−	1.28894i	0.935433	−	0.353505i	$-0.115010\pi$
$594$	−113.142	−	13.5871i	−0.190475	−	0.0228740i
$595$	65.9926	−	297.853i	0.110912	−	0.500594i
$596$	526.008	+	303.691i	0.882564	+	0.509549i
$597$	−28.0867	−	591.757i	−0.0470463	−	0.991218i
$598$	95.3045	+	73.1297i	0.159372	+	0.122290i
$599$	−326.880	−	566.173i	−0.545710	−	0.945197i	−0.998562	−	0.0536112i	$-0.982927\pi$
$599$	−326.880	−	566.173i	−0.545710	−	0.945197i	0.452852	−	0.891586i	$-0.350406\pi$
$600$	−61.5008	+	52.0043i	−0.102501	+	0.0866738i
$601$	41.4224	−	31.7845i	0.0689224	−	0.0528860i	−0.573726	−	0.819048i	$-0.694502\pi$
$601$	41.4224	−	31.7845i	0.0689224	−	0.0528860i	0.642648	+	0.766162i	$0.277836\pi$
$602$	98.1211	+	40.6431i	0.162992	+	0.0675134i
$603$	−134.880	+	800.414i	−0.223682	+	1.32739i
$604$	−134.601	+	134.601i	−0.222849	+	0.222849i
$605$	−227.702	+	174.722i	−0.376367	+	0.288797i
$606$	−51.8952	+	74.7158i	−0.0856356	+	0.123293i
$607$	255.648	−	333.167i	0.421166	−	0.548874i	−0.533792	−	0.845616i	$-0.679233\pi$
$607$	255.648	−	333.167i	0.421166	−	0.548874i	0.954958	+	0.296742i	$0.0959000\pi$
$608$	−104.669	−	181.292i	−0.172153	−	0.298177i
$609$	−564.917	+	101.822i	−0.927615	+	0.167195i
$610$	64.6339	−	17.3186i	0.105957	−	0.0283912i
$611$			1356.67i			2.22041i
$612$	554.488	+	224.680i	0.906027	+	0.367124i
$613$	−1015.02			−1.65583			−0.827914	−	0.560855i	$-0.810472\pi$
$613$	−1015.02			−1.65583			−0.827914	+	0.560855i	$0.810472\pi$
$614$	2.40866	+	8.98923i	0.00392289	+	0.0146404i
$615$	109.230	−	92.3631i	0.177609	−	0.150184i
$616$	−140.354	+	81.0333i	−0.227847	+	0.131548i
$617$	634.174	+	486.619i	1.02783	+	0.788685i	0.977689	−	0.210057i	$-0.0673650\pi$
$617$	634.174	+	486.619i	1.02783	+	0.788685i	0.0501451	+	0.998742i	$0.484032\pi$
$618$	21.7218	−	10.2295i	0.0351485	−	0.0165527i
$619$	−437.393	−	570.022i	−0.706612	−	0.920875i	0.292764	−	0.956185i	$-0.405425\pi$
$619$	−437.393	−	570.022i	−0.706612	−	0.920875i	−0.999376	+	0.0353097i	$0.988758\pi$
$620$	−75.4488	−	75.4488i	−0.121692	−	0.121692i
$621$	−326.802	−	416.005i	−0.526251	−	0.669895i
$622$	−23.9932	+	57.9248i	−0.0385743	+	0.0931267i
$623$	346.235	+	451.223i	0.555755	+	0.724274i
$624$	−310.410	+	863.018i	−0.497452	+	1.38304i
$625$	184.653	−	106.610i	0.295445	−	0.170575i
$626$	31.5234	−	41.0821i	0.0503569	−	0.0656264i
$627$	290.903	−	564.035i	0.463960	−	0.899577i
$628$	−263.980	+	457.227i	−0.420351	+	0.728069i
$629$	−793.988	+	140.106i	−1.26230	+	0.222744i
$630$	43.9885	+	20.1072i	0.0698230	+	0.0319162i
$631$	94.3715	+	94.3715i	0.149559	+	0.149559i	0.777921	−	0.628362i	$-0.216274\pi$
$631$	94.3715	+	94.3715i	0.149559	+	0.149559i	−0.628362	+	0.777921i	$0.716274\pi$
$632$	−26.9211	−	3.54423i	−0.0425967	−	0.00560796i
$633$	−804.225	−	175.094i	−1.27050	−	0.276609i
$634$	−29.1229	+	37.9537i	−0.0459352	+	0.0598639i
$635$	553.681	−	72.8935i	0.871938	−	0.114793i
$636$	−260.919	+	375.656i	−0.410249	+	0.590654i
$637$	−134.784	−	503.019i	−0.211591	−	0.789669i
$638$	117.634	+	117.634i	0.184379	+	0.184379i
$639$	−191.065	+	622.411i	−0.299006	+	0.974040i
$640$	247.355	+	102.458i	0.386492	+	0.160090i
$641$	72.9858	−	554.382i	0.113862	−	0.864870i	−0.835236	−	0.549891i	$-0.814669\pi$
$641$	72.9858	−	554.382i	0.113862	−	0.864870i	0.949099	−	0.314979i	$-0.101998\pi$
$642$	−12.6815	−	39.6948i	−0.0197531	−	0.0618298i
$643$	360.300	+	276.468i	0.560343	+	0.429966i	0.849709	−	0.527252i	$-0.176778\pi$
$643$	360.300	+	276.468i	0.560343	+	0.429966i	−0.289366	+	0.957219i	$0.593444\pi$
$644$	−359.246	−	96.2597i	−0.557836	−	0.149472i
$645$	545.140	−	599.467i	0.845178	−	0.929406i
$646$	51.6158	−	56.3432i	0.0799006	−	0.0872185i
$647$			1012.77i			1.56533i	0.622441	+	0.782666i	$0.286141\pi$
$647$			1012.77i			1.56533i	−0.622441	+	0.782666i	$0.713859\pi$
$648$	−107.657	+	158.827i	−0.166137	+	0.245103i
$649$	279.716	−	115.862i	0.430996	−	0.178524i
$650$	34.7433	−	60.1771i	0.0534512	−	0.0925801i
$651$	36.3808	−	101.148i	0.0558845	−	0.155373i
$652$	37.4017	+	284.094i	0.0573646	+	0.435727i
$653$	50.3916	+	382.763i	0.0771694	+	0.586160i	0.985721	+	0.168387i	$0.0538559\pi$
$653$	50.3916	+	382.763i	0.0771694	+	0.586160i	−0.908551	+	0.417773i	$0.862811\pi$
$654$	3.35583	+	1.73079i	0.00513125	+	0.00264646i
$655$	−196.032	−	731.601i	−0.299285	−	1.11695i
$656$	177.932	+	73.7019i	0.271238	+	0.112351i
$657$	−67.3888	+	219.525i	−0.102570	+	0.334132i
$658$	36.8622	+	88.9933i	0.0560216	+	0.135248i
$659$	372.958	−	645.982i	0.565945	−	0.980246i	−0.431016	−	0.902344i	$-0.641845\pi$
$659$	372.958	−	645.982i	0.565945	−	0.980246i	0.996961	−	0.0779013i	$-0.0248219\pi$
$660$	108.420	+	601.523i	0.164272	+	0.911399i
$661$	−37.4662	+	139.826i	−0.0566812	+	0.211537i	−0.988458	−	0.151494i	$-0.951591\pi$
$661$	−37.4662	+	139.826i	−0.0566812	+	0.211537i	0.931777	+	0.363031i	$0.118258\pi$
$662$	−19.4559	+	11.2329i	−0.0293895	+	0.0169681i
$663$	−1043.35	−	41.4546i	−1.57368	−	0.0625258i
$664$	−1.60742	+	2.78412i	−0.00242081	+	0.00419296i
$665$	−190.465	+	190.465i	−0.286414	+	0.286414i
$666$	4.60629	−	127.739i	0.00691636	−	0.191800i
$667$			772.294i			1.15786i
$668$	44.1818	−	335.594i	0.0661404	−	0.502386i
$669$	−266.159	−	22.2686i	−0.397847	−	0.0332865i
$670$	−98.9898	+	13.0323i	−0.147746	+	0.0194511i
$671$	−220.482	+	822.851i	−0.328588	+	1.22631i
$672$	9.62928	+	202.879i	0.0143293	+	0.301904i
$673$	−88.0854	−	114.795i	−0.130885	−	0.170572i	0.723314	−	0.690520i	$-0.242618\pi$
$673$	−88.0854	−	114.795i	−0.130885	−	0.170572i	−0.854198	+	0.519948i	$0.825951\pi$
$674$	−14.7217	+	35.5412i	−0.0218422	+	0.0527318i
$675$	−213.899	+	218.825i	−0.316887	+	0.324185i
$676$		−	978.290i		−	1.44717i
$677$	24.6662	+	3.24737i	0.0364346	+	0.00479671i	0.148721	−	0.988879i	$-0.452484\pi$
$677$	24.6662	+	3.24737i	0.0364346	+	0.00479671i	−0.112287	+	0.993676i	$0.535818\pi$
$678$	5.63969	+	118.822i	0.00831812	+	0.175254i
$679$	−446.135	−	772.729i	−0.657048	−	1.13804i
$680$	−12.9561	+	148.307i	−0.0190531	+	0.218099i
$681$	69.2279	+	216.693i	0.101656	+	0.318198i
$682$	−30.0911	+	8.06288i	−0.0441218	+	0.0118224i
$683$	−440.862	−	1064.33i	−0.645478	−	1.55832i	−0.819187	−	0.573526i	$-0.805575\pi$
$683$	−440.862	−	1064.33i	−0.645478	−	1.55832i	0.173709	−	0.984797i	$-0.444425\pi$
$684$	−306.258	−	430.393i	−0.447745	−	0.629229i
$685$	70.6230	+	170.499i	0.103099	+	0.248904i
$686$	−65.8712	−	85.8451i	−0.0960222	−	0.125139i
$687$	−485.633	−	337.305i	−0.706889	−	0.490982i
$688$	1053.75	+	282.352i	1.53161	+	0.410395i
$689$	206.604	−	771.058i	0.299861	−	1.11910i
$690$	37.1215	−	53.4455i	0.0537993	−	0.0774572i
$691$	665.858	−	510.931i	0.963616	−	0.739408i	−0.00183390	−	0.999998i	$-0.500584\pi$
$691$	665.858	−	510.931i	0.963616	−	0.739408i	0.965450	+	0.260590i	$0.0839171\pi$
$692$	−1120.72	+	464.217i	−1.61953	+	0.670833i
$693$	−501.696	+	356.995i	−0.723948	+	0.515145i
$694$	38.9720	−	16.1427i	0.0561556	−	0.0232604i
$695$	71.2805	+	266.023i	0.102562	+	0.382766i
$696$	266.826	−	85.2443i	0.383370	−	0.122477i
$697$	−19.0825	+	218.435i	−0.0273780	+	0.313393i
$698$	−5.53021	+	3.19287i	−0.00792293	+	0.00457431i
$699$	−824.375	+	39.1274i	−1.17936	+	0.0559763i
$700$	−28.0802	+	213.290i	−0.0401145	+	0.304700i
$701$	277.761			0.396236			0.198118	−	0.980178i	$-0.436517\pi$
$701$	277.761			0.396236			0.198118	+	0.980178i	$0.436517\pi$
$702$	41.0222	−	160.377i	0.0584361	−	0.228457i
$703$	657.673	+	272.417i	0.935523	+	0.387506i
$704$	−621.141	+	476.618i	−0.882303	+	0.677015i
$705$	734.068	−	34.8411i	1.04123	−	0.0494201i
$706$	−12.3797	−	3.31714i	−0.0175350	−	0.00469850i
$707$	64.1601	+	487.344i	0.0907498	+	0.689313i
$708$	21.0108	−	251.126i	0.0296763	−	0.354697i
$709$	−629.006	−	82.8102i	−0.887174	−	0.116799i	−0.326854	−	0.945075i	$-0.605988\pi$
$709$	−629.006	−	82.8102i	−0.887174	−	0.116799i	−0.560320	+	0.828276i	$0.689322\pi$
$710$	−80.0866			−0.112798
$711$	−103.098	−	3.71775i	−0.145005	−	0.00522890i
$712$	−196.252	−	196.252i	−0.275634	−	0.275634i
$713$	−125.245	−	72.3104i	−0.175659	−	0.101417i
$714$	−69.5666	+	25.6296i	−0.0974323	+	0.0358958i
$715$	−533.374	−	923.830i	−0.745977	−	1.29207i
$716$	617.356	+	165.420i	0.862229	+	0.231034i
$717$	984.747	−	177.493i	1.37343	−	0.247549i
$718$	32.6856	+	18.8710i	0.0455231	+	0.0262828i
$719$	837.800	−	347.028i	1.16523	−	0.482654i	0.285616	−	0.958344i	$-0.407802\pi$
$719$	837.800	−	347.028i	1.16523	−	0.482654i	0.879613	+	0.475690i	$0.157802\pi$
$720$	474.934	+	145.793i	0.659631	+	0.202491i
$721$	49.6478	−	119.860i	0.0688596	−	0.166242i
$722$	39.2549	−	10.5183i	0.0543696	−	0.0145683i
$723$	144.129	−	279.453i	0.199349	−	0.386519i
$724$	−505.316	+	66.5261i	−0.697950	+	0.0918869i
$725$	442.900	−	58.3088i	0.610896	−	0.0804260i
$726$	65.6316	+	23.6063i	0.0904017	+	0.0325156i
$727$	1066.98	+	616.023i	1.46765	+	0.847349i	0.999344	−	0.0362166i	$-0.0115306\pi$
$727$	1066.98	+	616.023i	1.46765	+	0.847349i	0.468308	+	0.883566i	$0.344864\pi$
$728$	−90.0956	−	217.510i	−0.123758	−	0.298778i
$729$	−350.034	+	639.466i	−0.480156	+	0.877183i
$730$	−28.2466			−0.0386940
$731$	54.3342	+	1240.83i	0.0743286	+	1.69744i
$732$	524.586	+	477.045i	0.716647	+	0.651701i
$733$	−152.894	+	570.609i	−0.208587	+	0.778456i	0.779739	+	0.626104i	$0.215352\pi$
$733$	−152.894	+	570.609i	−0.208587	+	0.778456i	−0.988326	+	0.152352i	$0.951315\pi$
$734$	69.1040	−	90.0581i	0.0941472	−	0.122695i
$735$	−268.712	+	85.8470i	−0.365595	+	0.116799i
$736$	270.926	+	35.6681i	0.368106	+	0.0484620i
$737$	486.432	−	1174.35i	0.660017	−	1.59342i
$738$	−33.2315	−	10.2013i	−0.0450292	−	0.0138229i
$739$	−83.5804	+	83.5804i	−0.113099	+	0.113099i	−0.761392	−	0.648292i	$-0.775483\pi$
$739$	−83.5804	+	83.5804i	−0.113099	+	0.113099i	0.648292	+	0.761392i	$0.275483\pi$
$740$	−662.232	+	177.444i	−0.894908	+	0.239790i
$741$	757.194	+	525.923i	1.02185	+	0.709747i
$742$	−7.39791	−	56.1927i	−0.00997023	−	0.0757314i
$743$	−485.928	−	372.866i	−0.654009	−	0.501838i	0.227640	−	0.973745i	$-0.426899\pi$
$743$	−485.928	−	372.866i	−0.654009	−	0.501838i	−0.881648	+	0.471907i	$0.843566\pi$
$744$	−11.1587	+	51.2534i	−0.0149983	+	0.0688890i
$745$	−74.9510	+	569.309i	−0.100605	+	0.764173i
$746$	85.2023	−	85.2023i	0.114212	−	0.114212i
$747$	−5.07781	+	11.1087i	−0.00679761	+	0.0148711i
$748$	−767.530	−	537.284i	−1.02611	−	0.718295i
$749$	−195.001	−	112.584i	−0.260348	−	0.150312i
$750$	−107.246	−	55.3124i	−0.142994	−	0.0737498i
$751$	158.465	+	121.595i	0.211006	+	0.161911i	0.708858	−	0.705352i	$-0.249211\pi$
$751$	158.465	+	121.595i	0.211006	+	0.161911i	−0.497852	+	0.867262i	$0.665878\pi$
$752$	494.720	+	856.879i	0.657872	+	1.13947i
$753$	343.388	+	123.510i	0.456027	+	0.164023i
$754$	−191.727	+	147.117i	−0.254280	+	0.195116i
$755$	−166.263	−	68.8684i	−0.220216	−	0.0912165i
$756$	72.6760	+	507.335i	0.0961323	+	0.671078i
$757$	−47.6215	+	47.6215i	−0.0629081	+	0.0629081i	−0.737861	−	0.674953i	$-0.764164\pi$
$757$	−47.6215	+	47.6215i	−0.0629081	+	0.0629081i	0.674953	+	0.737861i	$0.264164\pi$
$758$	−115.378	+	88.5328i	−0.152214	+	0.116798i
$759$	352.958	+	749.482i	0.465030	+	0.987460i
$760$	80.0170	−	104.280i	0.105286	−	0.137211i
$761$	−534.984	−	926.619i	−0.703001	−	1.21763i	−0.967408	−	0.253222i	$-0.918510\pi$
$761$	−534.984	−	926.619i	−0.703001	−	1.21763i	0.264408	−	0.964411i	$-0.414824\pi$
$762$	−87.6285	−	103.630i	−0.114998	−	0.135998i
$763$	19.7074	−	5.28059i	0.0258289	−	0.00692083i
$764$		−	124.623i		−	0.163119i
$765$	4.36430	+	565.599i	0.00570496	+	0.739345i
$766$	−129.894			−0.169575
$767$	113.833	+	424.831i	0.148414	+	0.553887i
$768$	106.705	+	592.011i	0.138939	+	0.770848i
$769$	72.4576	−	41.8334i	0.0942231	−	0.0543997i	−0.452148	−	0.891943i	$-0.649342\pi$
$769$	72.4576	−	41.8334i	0.0942231	−	0.0543997i	0.546371	+	0.837543i	$0.316009\pi$
$770$	−60.0891	−	46.1080i	−0.0780379	−	0.0598806i
$771$	−697.055	−	484.152i	−0.904093	−	0.627954i
$772$	850.376	+	1108.23i	1.10152	+	1.43553i
$773$	−843.735	−	843.735i	−1.09151	−	1.09151i	−0.995368	−	0.0961392i	$-0.969351\pi$
$773$	−843.735	−	843.735i	−1.09151	−	1.09151i	−0.0961392	−	0.995368i	$-0.530649\pi$
$774$	−194.169	−	32.7200i	−0.250864	−	0.0422738i
$775$	−32.0128	+	77.2858i	−0.0413069	+	0.0997236i
$776$	265.062	+	345.436i	0.341575	+	0.445150i
$777$	−445.962	−	527.400i	−0.573953	−	0.678764i
$778$	−84.9623	+	49.0530i	−0.109206	+	0.0630501i
$779$	117.853	−	153.589i	0.151288	−	0.197162i
$780$	−886.904	+	42.0952i	−1.13706	+	0.0539682i
$781$	509.789	−	882.981i	0.652739	−	1.13058i
$782$	17.3332	+	98.2282i	0.0221652	+	0.125612i
$783$	978.532	−	418.433i	1.24972	−	0.534397i
$784$	−268.560	−	268.560i	−0.342550	−	0.342550i
$785$	−494.866	−	65.1503i	−0.630402	−	0.0829940i
$786$	−123.834	+	136.175i	−0.157549	+	0.173250i
$787$	110.658	−	144.212i	0.140607	−	0.183243i	−0.717741	−	0.696310i	$-0.754824\pi$
$787$	110.658	−	144.212i	0.140607	−	0.183243i	0.858349	+	0.513067i	$0.171491\pi$
$788$	535.698	−	70.5260i	0.679820	−	0.0895000i
$789$	−46.6160	−	3.90020i	−0.0590823	−	0.00494322i
$790$	−3.28440	−	12.2576i	−0.00415747	−	0.0155159i
$791$	454.507	+	454.507i	0.574599	+	0.574599i
$792$	219.986	−	204.672i	0.277760	−	0.258425i
$793$	−1143.31	−	473.574i	−1.44175	−	0.597193i
$794$	−17.2786	+	131.244i	−0.0217615	+	0.165295i
$795$	−422.511	−	91.9878i	−0.531460	−	0.115708i
$796$	612.619	+	470.079i	0.769622	+	0.590552i
$797$	988.980	+	264.997i	1.24088	+	0.332493i	0.818806	−	0.574070i	$-0.194636\pi$
$797$	988.980	+	264.997i	1.24088	+	0.332493i	0.422072	+	0.906562i	$0.361303\pi$
$798$	63.9595	+	13.9251i	0.0801497	+	0.0174500i
$799$	−760.931	+	830.623i	−0.952354	+	1.03958i
$800$		−	158.065i		−	0.197581i
$801$	−812.897	−	671.656i	−1.01485	−	0.838522i
$802$	−44.5553	+	18.4554i	−0.0555552	+	0.0230117i
$803$	179.803	−	311.428i	0.223914	−	0.387831i
$804$	−683.141	−	807.890i	−0.849677	−	1.00484i
$805$	−45.8948	−	348.606i	−0.0570122	−	0.433051i
$806$	−5.90694	−	44.8676i	−0.00732870	−	0.0556670i
$807$	30.5379	+	643.402i	0.0378412	+	0.797276i
$808$	−62.0823	−	231.694i	−0.0768345	−	0.286750i
$809$	1135.92	+	470.515i	1.40411	+	0.581601i	0.950815	−	0.309761i	$-0.100249\pi$
$809$	1135.92	+	470.515i	1.40411	+	0.581601i	0.453293	+	0.891361i	$0.350249\pi$
$810$	−87.8304	−	18.0776i	−0.108433	−	0.0223180i
$811$	−391.773	−	945.824i	−0.483074	−	1.16624i	−0.958142	−	0.286295i	$-0.907576\pi$
$811$	−391.773	−	945.824i	−0.483074	−	1.16624i	0.475068	−	0.879949i	$-0.342424\pi$
$812$	374.101	−	647.962i	0.460715	−	0.797982i
$813$	−609.585	−	219.255i	−0.749797	−	0.269687i
$814$	−51.8071	+	193.347i	−0.0636451	+	0.237527i
$815$	−234.608	+	135.451i	−0.287862	+	0.166197i
$816$	−674.099	+	354.281i	−0.826102	+	0.434168i
$817$	548.302	−	949.687i	0.671116	−	1.16241i
$818$	149.541	−	149.541i	0.182812	−	0.182812i
$819$	−419.036	−	790.260i	−0.511643	−	0.964909i
$820$			186.452i			0.227380i
$821$	25.4841	−	193.571i	0.0310403	−	0.235774i	−0.968891	−	0.247487i	$-0.920395\pi$
$821$	25.4841	−	193.571i	0.0310403	−	0.235774i	0.999931	+	0.0117131i	$0.00372848\pi$
$822$	25.5838	−	36.8341i	0.0311238	−	0.0448104i
$823$	1255.81	−	165.331i	1.52590	−	0.200888i	0.679594	−	0.733589i	$-0.262156\pi$
$823$	1255.81	−	165.331i	1.52590	−	0.200888i	0.846304	+	0.532701i	$0.178823\pi$
$824$	−16.3855	+	61.1516i	−0.0198854	+	0.0742132i
$825$	403.169	−	259.003i	0.488689	−	0.313943i
$826$	19.0102	+	24.7746i	0.0230148	+	0.0299935i
$827$	−59.4069	+	143.421i	−0.0718342	+	0.173423i	−0.955718	−	0.294283i	$-0.904919\pi$
$827$	−59.4069	+	143.421i	−0.0718342	+	0.173423i	0.883884	+	0.467706i	$0.154919\pi$
$828$	689.095	+	24.8490i	0.832241	+	0.0300108i
$829$		−	1294.44i		−	1.56145i	−0.624877	−	0.780723i	$-0.714851\pi$
$829$		−	1294.44i		−	1.56145i	0.624877	−	0.780723i	$-0.285149\pi$
$830$	−1.48958	−	0.196106i	−0.00179467	−	0.000236273i
$831$	1034.55	+	533.574i	1.24495	+	0.642087i
$832$	−568.675	−	984.974i	−0.683504	−	1.18386i
$833$	199.613	−	383.572i	0.239631	−	0.460470i
$834$	45.0281	−	49.5154i	0.0539905	−	0.0593710i
$835$	309.106	−	82.8246i	0.370186	−	0.0991912i
$836$	316.559	+	764.240i	0.378659	+	0.914163i
$837$	−23.7620	+	197.869i	−0.0283895	+	0.236403i
$838$	−8.67990	−	20.9551i	−0.0103579	−	0.0250061i
$839$	823.255	+	1072.89i	0.981234	+	1.27877i	0.960294	+	0.278988i	$0.0899991\pi$
$839$	823.255	+	1072.89i	0.981234	+	1.27877i	0.0209396	+	0.999781i	$0.493334\pi$
$840$	−115.377	+	54.3349i	−0.137353	+	0.0646844i
$841$	−688.367	−	184.447i	−0.818510	−	0.219319i
$842$	−11.2745	+	42.0769i	−0.0133901	+	0.0499726i
$843$	733.628	+	61.3801i	0.870258	+	0.0728115i
$844$	851.122	−	653.089i	1.00844	−	0.773802i
$845$	854.477	−	353.936i	1.01122	−	0.418859i
$846$	−103.542	−	145.510i	−0.122390	−	0.171998i
$847$	348.189	−	144.225i	0.411085	−	0.170277i
$848$	−150.680	−	562.344i	−0.177688	−	0.663142i
$849$	−296.794	+	1363.21i	−0.349581	+	1.60567i
$850$	55.0238	−	17.3566i	0.0647339	−	0.0204196i
$851$	−804.748	+	464.622i	−0.945650	+	0.545971i
$852$	−458.687	−	714.001i	−0.538365	−	0.838030i
$853$	67.3064	−	511.243i	0.0789056	−	0.599347i	−0.905618	−	0.424095i	$-0.860592\pi$
$853$	67.3064	−	511.243i	0.0789056	−	0.599347i	0.984523	−	0.175253i	$-0.0560742\pi$
$854$	−87.8650			−0.102886
$855$	265.121	−	423.210i	0.310083	−	0.494982i
$856$	101.514	+	42.0484i	0.118591	+	0.0491219i
$857$	34.5296	−	26.4955i	0.0402912	−	0.0309165i	−0.588420	−	0.808556i	$-0.700250\pi$
$857$	34.5296	−	26.4955i	0.0402912	−	0.0309165i	0.628711	+	0.777639i	$0.283583\pi$
$858$	−118.828	+	230.396i	−0.138494	+	0.268527i
$859$	−933.639	−	250.168i	−1.08689	−	0.291231i	−0.329475	−	0.944164i	$-0.606872\pi$
$859$	−933.639	−	250.168i	−1.08689	−	0.291231i	−0.757416	+	0.652933i	$0.773538\pi$
$860$	137.854	+	1047.10i	0.160295	+	1.21756i
$861$	−169.933	+	80.0274i	−0.197367	+	0.0929470i
$862$	−116.305	−	15.3119i	−0.134925	−	0.0177632i
$863$	−128.812			−0.149261			−0.0746304	−	0.997211i	$-0.523778\pi$
$863$	−128.812			−0.149261			−0.0746304	+	0.997211i	$0.523778\pi$
$864$	−101.596	−	362.600i	−0.117588	−	0.419676i
$865$	−810.930	−	810.930i	−0.937492	−	0.937492i
$866$	−116.325	−	67.1604i	−0.134325	−	0.0775524i
$867$	−615.539	−	610.574i	−0.709964	−	0.704238i
$868$	70.0545	+	121.338i	0.0807080	+	0.139790i
$869$	156.050	+	41.8136i	0.179575	+	0.0481169i
$870$	84.5262	+	99.9616i	0.0971565	+	0.114898i
$871$	1599.13	+	923.259i	1.83597	+	1.06000i
$872$	−9.19827	+	3.81005i	−0.0105485	+	0.00436932i
$873$	1126.84	+	1211.15i	1.29077	+	1.38734i
$874$	33.7021	−	81.3640i	0.0385607	−	0.0930938i
$875$	−629.810	+	168.757i	−0.719783	+	0.192865i
$876$	−161.779	−	251.829i	−0.184679	−	0.287476i
$877$	1287.68	−	169.526i	1.46827	−	0.193302i	0.646411	−	0.762989i	$-0.276269\pi$
$877$	1287.68	−	169.526i	1.46827	−	0.193302i	0.821862	+	0.569687i	$0.192936\pi$
$878$	−42.9013	+	5.64806i	−0.0488625	+	0.00643287i
$879$	12.8199	+	71.1261i	0.0145846	+	0.0809170i
$880$	−673.763	−	388.997i	−0.765640	−	0.442042i
$881$	−56.1817	−	135.635i	−0.0637703	−	0.153955i	0.888782	−	0.458330i	$-0.151552\pi$
$881$	−56.1817	−	135.635i	−0.0637703	−	0.153955i	−0.952552	+	0.304375i	$0.901552\pi$
$882$	52.8469	+	43.6648i	0.0599172	+	0.0495065i
$883$	−1041.43			−1.17943			−0.589714	−	0.807612i	$-0.700760\pi$
$883$	−1041.43			−1.17943			−0.589714	+	0.807612i	$0.700760\pi$
$884$	919.360	−	1003.56i	1.04000	−	1.13525i
$885$	226.945	−	72.5032i	0.256435	−	0.0819245i
$886$	49.0092	−	182.905i	0.0553151	−	0.206439i
$887$	495.465	−	645.702i	0.558585	−	0.727962i	−0.425638	−	0.904893i	$-0.639950\pi$
$887$	495.465	−	645.702i	0.558585	−	0.727962i	0.984223	+	0.176931i	$0.0566171\pi$
$888$	249.352	+	226.755i	0.280802	+	0.255354i
$889$	−727.041	−	95.7167i	−0.817819	−	0.107668i
$890$	49.6368	−	119.834i	0.0557717	−	0.134645i
$891$	758.394	−	853.287i	0.851171	−	0.957673i
$892$	246.169	−	246.169i	0.275974	−	0.275974i
$893$	960.702	−	257.419i	1.07581	−	0.288263i
$894$	126.245	−	59.4531i	0.141213	−	0.0665024i
$895$	78.8691	+	599.071i	0.0881219	+	0.669353i
$896$	−278.914	−	214.018i	−0.311288	−	0.238860i
$897$	−1146.37	+	366.237i	−1.27800	+	0.408291i
$898$	−12.4394	+	94.4863i	−0.0138523	+	0.105219i
$899$	205.724	−	205.724i	0.228837	−	0.228837i
$900$	−37.7767	−	397.062i	−0.0419742	−	0.441180i
$901$	558.966	−	356.201i	0.620384	−	0.395339i
$902$	47.1437	+	27.2184i	0.0522658	+	0.0301757i
$903$	−895.167	+	575.071i	−0.991325	+	0.636845i
$904$	−248.844	−	190.945i	−0.275270	−	0.211222i
$905$	−240.925	−	417.294i	−0.266215	−	0.461099i
$906$	7.75754	+	43.0396i	0.00856241	+	0.0475051i
$907$	98.7286	−	75.7572i	0.108852	−	0.0835250i	−0.552901	−	0.833247i	$-0.686479\pi$
$907$	98.7286	−	75.7572i	0.108852	−	0.0835250i	0.661753	+	0.749722i	$0.269813\pi$
$908$	−273.939	−	113.469i	−0.301695	−	0.124966i
$909$	−318.186	−	853.990i	−0.350040	−	0.939483i
$910$	77.8010	−	77.8010i	0.0854956	−	0.0854956i
$911$	−15.3259	+	11.7600i	−0.0168231	+	0.0129088i	−0.617139	−	0.786854i	$-0.711708\pi$
$911$	−15.3259	+	11.7600i	−0.0168231	+	0.0129088i	0.600316	+	0.799763i	$0.295042\pi$
$912$	670.029	+	56.0590i	0.734681	+	0.0614682i
$913$	11.6440	−	15.1748i	0.0127536	−	0.0166208i
$914$	13.1694	+	22.8100i	0.0144085	+	0.0249562i
$915$	−226.880	+	630.784i	−0.247956	+	0.689382i
$916$	744.439	−	199.472i	0.812707	−	0.217764i
$917$			994.557i			1.08458i
$918$	115.068	−	75.1825i	0.125347	−	0.0818982i
$919$	−152.878			−0.166353			−0.0831764	−	0.996535i	$-0.526506\pi$
$919$	−152.878			−0.166353			−0.0831764	+	0.996535i	$0.526506\pi$
$920$	44.4085	+	165.735i	0.0482701	+	0.180147i
$921$	−87.7289	−	31.5543i	−0.0952539	−	0.0342609i
$922$	193.801	−	111.891i	0.210197	−	0.121357i
$923$	1175.05	+	901.650i	1.27308	+	0.976869i
$924$	66.9162	−	799.796i	0.0724201	−	0.865580i
$925$	327.213	+	426.432i	0.353744	+	0.461008i
$926$	26.7741	+	26.7741i	0.0289138	+	0.0289138i
$927$	−39.9692	+	237.188i	−0.0431167	+	0.255866i
$928$	−210.374	+	507.887i	−0.226696	+	0.547293i
$929$	−509.150	−	663.537i	−0.548062	−	0.714249i	0.434398	−	0.900721i	$-0.356961\pi$
$929$	−509.150	−	663.537i	−0.548062	−	0.714249i	−0.982460	+	0.186472i	$0.940294\pi$
$930$	−24.1253	+	4.34839i	−0.0259412	+	0.00467569i
$931$	−330.630	+	190.889i	−0.355134	+	0.205037i
$932$	654.866	−	853.437i	0.702646	−	0.915705i
$933$	−339.487	−	528.452i	−0.363866	−	0.566401i
$934$	102.912	−	178.250i	0.110185	−	0.190845i
$935$	191.600	−	864.775i	0.204920	−	0.924894i
$936$	253.068	+	355.644i	0.270372	+	0.379961i
$937$	−584.743	−	584.743i	−0.624059	−	0.624059i	0.322508	−	0.946567i	$-0.395474\pi$
$937$	−584.743	−	584.743i	−0.624059	−	0.624059i	−0.946567	+	0.322508i	$0.895474\pi$
$938$	129.984	+	17.1127i	0.138576	+	0.0182438i
$939$	157.871	+	494.156i	0.168126	+	0.526258i
$940$	−583.127	+	759.946i	−0.620348	+	0.808453i
$941$	213.295	−	28.0809i	0.226669	−	0.0298415i	−0.0163362	−	0.999867i	$-0.505200\pi$
$941$	213.295	−	28.0809i	0.226669	−	0.0298415i	0.243005	+	0.970025i	$0.421867\pi$
$942$	51.6790	+	109.737i	0.0548609	+	0.116494i
$943$	65.4073	+	244.103i	0.0693608	+	0.258858i
$944$	226.815	+	226.815i	0.240271	+	0.240271i
$945$	−416.833	+	247.027i	−0.441093	+	0.261404i
$946$	284.881	+	118.002i	0.301143	+	0.124737i
$947$	−37.8657	+	287.618i	−0.0399849	+	0.303715i	0.959754	+	0.280844i	$0.0906142\pi$
$947$	−37.8657	+	287.618i	−0.0399849	+	0.303715i	−0.999738	+	0.0228716i	$0.992719\pi$
$948$	90.4697	−	99.4855i	0.0954321	−	0.104943i
$949$	414.442	+	318.013i	0.436715	+	0.335103i
$950$	−49.2056	−	13.1846i	−0.0517954	−	0.0138785i
$951$	−145.849	−	456.526i	−0.153364	−	0.480049i
$952$	66.8362	−	183.704i	0.0702060	−	0.192966i
$953$			317.999i			0.333682i	0.985984	+	0.166841i	$0.0533566\pi$
$953$			317.999i			0.333682i	−0.985984	+	0.166841i	$0.946643\pi$
$954$	36.6881	+	98.4683i	0.0384572	+	0.103216i
$955$	108.851	−	45.0875i	0.113980	−	0.0472121i
$956$	−652.121	+	1129.51i	−0.682135	+	1.18149i
$957$	−1640.16	+	295.625i	−1.71385	+	0.308908i
$958$	9.51357	+	72.2628i	0.00993066	+	0.0754309i
$959$	−31.6303	−	240.256i	−0.0329826	−	0.250528i
$960$	−518.346	+	332.994i	−0.539944	+	0.346869i
$961$	−234.624	−	875.630i	−0.244146	−	0.911165i
$962$	−268.645	−	111.276i	−0.279257	−	0.115672i
$963$	399.083	+	122.509i	0.414417	+	0.127216i
$964$	156.840	+	378.646i	0.162697	+	0.392786i
$965$	−660.316	+	1143.70i	−0.684265	+	1.18518i
$966$	−65.2472	+	55.1722i	−0.0675437	+	0.0571140i
$967$	−267.123	+	996.917i	−0.276239	+	1.03094i	0.678768	+	0.734353i	$0.262514\pi$
$967$	−267.123	+	996.917i	−0.276239	+	1.03094i	−0.955007	+	0.296585i	$0.904152\pi$
$968$	−159.270	+	91.9548i	−0.164535	+	0.0949946i
$969$	168.613	+	746.693i	0.174007	+	0.770581i
$970$	−101.744	+	176.225i	−0.104890	+	0.181675i
$971$	−1276.33	+	1276.33i	−1.31445	+	1.31445i	−0.396357	+	0.918096i	$0.629726\pi$
$971$	−1276.33	+	1276.33i	−1.31445	+	1.31445i	−0.918096	+	0.396357i	$0.870274\pi$
$972$	−341.871	−	886.578i	−0.351719	−	0.912117i
$973$		−	361.638i		−	0.371673i
$974$	−17.0797	+	129.734i	−0.0175357	+	0.133197i
$975$	296.584	+	629.776i	0.304188	+	0.645924i
$976$	−894.812	+	117.804i	−0.916815	+	0.120701i
$977$	−394.591	+	1472.64i	−0.403881	+	1.50730i	0.402230	+	0.915539i	$0.368235\pi$
$977$	−394.591	+	1472.64i	−0.403881	+	1.50730i	−0.806111	+	0.591765i	$0.798431\pi$
$978$	58.5093	+	30.1764i	0.0598254	+	0.0308552i
$979$	1005.25	+	1310.06i	1.02681	+	1.33816i
$980$	140.709	−	339.702i	0.143581	−	0.346635i
$981$	−33.4193	+	17.7206i	−0.0340665	+	0.0180638i
$982$		−	251.192i		−	0.255797i
$983$	−1033.07	−	136.006i	−1.05094	−	0.138358i	−0.414782	−	0.909921i	$-0.636142\pi$
$983$	−1033.07	−	136.006i	−1.05094	−	0.138358i	−0.636154	+	0.771562i	$0.719476\pi$
$984$	77.1176	−	49.5417i	0.0783715	−	0.0503472i
$985$	255.411	+	442.385i	0.259300	+	0.449121i
$986$	−199.901	−	17.4633i	−0.202739	−	0.0177113i
$987$	−942.904	−	205.286i	−0.955323	−	0.207990i
$988$	−1160.72	+	311.015i	−1.17482	+	0.314792i
$989$	547.803	+	1322.51i	0.553896	+	1.33722i
$990$	127.714	+	58.3784i	0.129004	+	0.0589681i
$991$	234.150	+	565.288i	0.236276	+	0.570422i	0.996892	−	0.0787808i	$-0.0251027\pi$
$991$	234.150	+	565.288i	0.236276	+	0.570422i	−0.760616	+	0.649203i	$0.775103\pi$
$992$	−62.6682	−	81.6707i	−0.0631735	−	0.0823294i
$993$	18.7646	−	224.278i	0.0188969	−	0.225859i
$994$	101.579	+	27.2179i	0.102192	+	0.0273822i
$995$	−188.946	+	705.156i	−0.189895	+	0.708699i
$996$	−6.78302	−	14.4033i	−0.00681026	−	0.0144611i
$997$	323.058	−	247.891i	0.324030	−	0.248637i	−0.433918	−	0.900953i	$-0.642869\pi$
$997$	323.058	−	247.891i	0.324030	−	0.248637i	0.757947	+	0.652316i	$0.226202\pi$
$998$	−1.24335	+	0.515012i	−0.00124584	+	0.000516044i
$999$	1024.71	+	767.918i	1.02574	+	0.768687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.q.a.2.20	✓	272
9.5	odd	6	inner	153.3.q.a.104.20	yes	272
17.9	even	8	inner	153.3.q.a.128.20	yes	272
153.77	odd	24	inner	153.3.q.a.77.20	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.q.a.2.20	✓	272	1.1	even	1	trivial
153.3.q.a.77.20	yes	272	153.77	odd	24	inner
153.3.q.a.104.20	yes	272	9.5	odd	6	inner
153.3.q.a.128.20	yes	272	17.9	even	8	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.q (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0775060 + 0.289257i) q^{2} +(-2.82295 - 1.01536i) q^{3} +(3.38644 - 1.95516i) q^{4} +(2.93290 + 2.25049i) q^{5} +(0.0749028 - 0.895253i) q^{6} +(-2.95513 - 3.85120i) q^{7} +(1.67501 + 1.67501i) q^{8} +(6.93810 + 5.73260i) q^{9} +(-0.423652 + 1.02279i) q^{10} +(-8.57981 - 11.1814i) q^{11} +(-11.5449 + 2.08088i) q^{12} +(17.7309 - 10.2370i) q^{13} +(0.884944 - 1.15328i) q^{14} +(-5.99437 - 9.33096i) q^{15} +(7.46596 - 12.9314i) q^{16} +(16.5975 + 3.67736i) q^{17} +(-1.12045 + 2.45120i) q^{18} +(-10.6134 - 10.6134i) q^{19} +(14.3322 + 1.88686i) q^{20} +(4.43184 + 13.8723i) q^{21} +(2.56931 - 3.34839i) q^{22} +(19.4256 - 2.55743i) q^{23} +(-3.02775 - 6.42922i) q^{24} +(-2.93330 - 10.9472i) q^{25} +(4.33536 + 4.33536i) q^{26} +(-13.7653 - 23.2275i) q^{27} +(-17.5371 - 7.26410i) q^{28} +(-5.14487 + 39.0792i) q^{29} +(2.23444 - 2.45712i) q^{30} +(-5.85586 - 4.49336i) q^{31} +(13.4716 + 3.60971i) q^{32} +(12.8672 + 40.2762i) q^{33} +(0.222707 + 5.08595i) q^{34} -17.9457i q^{35} +(34.7036 + 5.84800i) q^{36} +(-43.8166 + 18.1494i) q^{37} +(2.24740 - 3.89261i) q^{38} +(-60.4477 + 10.8952i) q^{39} +(1.14304 + 8.68225i) q^{40} +(1.68353 + 12.7877i) q^{41} +(-3.66915 + 2.35712i) q^{42} +(18.9093 + 70.5703i) q^{43} +(-50.9165 - 21.0903i) q^{44} +(7.44757 + 32.4273i) q^{45} +(2.24536 + 5.42077i) q^{46} +(-33.1317 + 57.3857i) q^{47} +(-34.2061 + 28.9242i) q^{48} +(6.58318 - 24.5688i) q^{49} +(2.93921 - 1.69695i) q^{50} +(-43.1201 - 27.2334i) q^{51} +(40.0298 - 69.3337i) q^{52} +(27.5694 - 27.5694i) q^{53} +(5.65181 - 5.78197i) q^{54} -52.1028i q^{55} +(1.50093 - 11.4007i) q^{56} +(19.1848 + 40.7377i) q^{57} +(-11.7027 + 1.54068i) q^{58} +(-5.55991 + 20.7499i) q^{59} +(-38.5431 - 19.8788i) q^{60} +(-36.7955 - 47.9528i) q^{61} +(0.845869 - 2.04211i) q^{62} +(1.57441 - 43.6606i) q^{63} -55.5512i q^{64} +(75.0412 + 9.87936i) q^{65} +(-10.6529 + 6.84358i) q^{66} +(45.0944 + 78.1058i) q^{67} +(63.3963 - 19.9977i) q^{68} +(-57.4343 - 12.5044i) q^{69} +(5.19090 - 1.39090i) q^{70} +(27.6841 + 66.8352i) q^{71} +(2.01923 + 21.2236i) q^{72} +(9.76419 + 23.5728i) q^{73} +(-8.64589 - 11.2675i) q^{74} +(-2.83478 + 33.8818i) q^{75} +(-56.6928 - 15.1908i) q^{76} +(-17.7075 + 66.0851i) q^{77} +(-7.83657 - 16.6405i) q^{78} +(-9.09405 + 6.97811i) q^{79} +(50.9990 - 21.1245i) q^{80} +(15.2745 + 79.5468i) q^{81} +(-3.56844 + 1.47810i) q^{82} +(0.351254 + 1.31090i) q^{83} +(42.1307 + 38.3126i) q^{84} +(40.4029 + 48.1378i) q^{85} +(-18.9473 + 10.9393i) q^{86} +(54.2030 - 105.095i) q^{87} +(4.35774 - 33.1004i) q^{88} -117.164 q^{89} +(-8.80257 + 4.66757i) q^{90} +(-91.8218 - 38.0338i) q^{91} +(60.7835 - 46.6408i) q^{92} +(11.9684 + 18.6303i) q^{93} +(-19.1671 - 5.13581i) q^{94} +(-7.24268 - 55.0136i) q^{95} +(-34.3645 - 23.8685i) q^{96} +(182.237 + 23.9919i) q^{97} +7.61692 q^{98} +(4.57109 - 126.762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 8 q^{6} - 4 q^{7} + 16 q^{9} - 16 q^{10} - 84 q^{11} - 140 q^{12} - 12 q^{14} + 44 q^{15} + 440 q^{16} - 48 q^{18} - 16 q^{19} - 12 q^{20} - 4 q^{22} - 120 q^{23}+ \cdots - 832 q^{99}+O(q^{100}) \) 272 * q - 12 * q^2 - 8 * q^3 - 12 * q^5 - 8 * q^6 - 4 * q^7 + 16 * q^9 - 16 * q^10 - 84 * q^11 - 140 * q^12 - 12 * q^14 + 44 * q^15 + 440 * q^16 - 48 * q^18 - 16 * q^19 - 12 * q^20 - 4 * q^22 - 120 * q^23 + 112 * q^24 - 4 * q^25 + 40 * q^27 - 144 * q^28 - 12 * q^29 - 4 * q^31 - 204 * q^32 + 112 * q^33 - 28 * q^34 - 200 * q^36 - 16 * q^37 - 148 * q^39 + 60 * q^40 - 12 * q^41 - 624 * q^42 + 116 * q^43 + 44 * q^45 - 352 * q^46 - 168 * q^48 - 4 * q^49 - 24 * q^50 - 256 * q^51 - 264 * q^52 - 20 * q^54 + 708 * q^56 + 76 * q^57 - 4 * q^58 + 492 * q^59 - 656 * q^60 - 4 * q^61 + 708 * q^63 + 348 * q^65 - 508 * q^66 - 8 * q^67 - 204 * q^68 + 176 * q^69 + 12 * q^70 - 16 * q^73 + 492 * q^74 - 868 * q^75 + 92 * q^76 + 528 * q^77 + 864 * q^78 - 4 * q^79 + 176 * q^82 + 1428 * q^83 - 440 * q^84 + 188 * q^85 - 1824 * q^86 - 796 * q^87 + 156 * q^88 - 1000 * q^90 - 744 * q^91 - 12 * q^92 + 44 * q^93 + 28 * q^94 - 12 * q^95 - 1452 * q^96 - 364 * q^97 - 832 * q^99

Introduction

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