LMFDB - Embedded newform 108.3.j.a.103.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,3,Mod(7,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.29
Character	$\chi$	$=$	108.103
Dual form			108.3.j.a.43.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74544 - 0.976438i) q^{2} +(2.40580 - 1.79225i) q^{3} +(2.09314 - 3.40863i) q^{4} +(-7.02836 + 2.55811i) q^{5} +(2.44916 - 5.47737i) q^{6} +(8.30860 - 1.46503i) q^{7} +(0.325138 - 7.99339i) q^{8} +(2.57570 - 8.62356i) q^{9} +(-9.76976 + 11.3278i) q^{10} +(-3.00678 + 8.26105i) q^{11} +(-1.07345 - 11.9519i) q^{12} +(5.39976 + 4.53094i) q^{13} +(13.0717 - 10.6700i) q^{14} +(-12.3240 + 18.7509i) q^{15} +(-7.23754 - 14.2695i) q^{16} +(-10.7850 + 18.6801i) q^{17} +(-3.92463 - 17.5669i) q^{18} +(-22.4736 + 12.9752i) q^{19} +(-5.99167 + 29.3116i) q^{20} +(17.3631 - 18.4156i) q^{21} +(2.81824 + 17.3551i) q^{22} +(40.0360 + 7.05942i) q^{23} +(-13.5439 - 19.8132i) q^{24} +(23.7028 - 19.8890i) q^{25} +(13.8492 + 2.63596i) q^{26} +(-9.25895 - 25.3628i) q^{27} +(12.3973 - 31.3875i) q^{28} +(-6.59975 + 5.53785i) q^{29} +(-3.20183 + 44.7622i) q^{30} +(11.2381 + 1.98159i) q^{31} +(-26.5660 - 17.8396i) q^{32} +(7.57216 + 25.2633i) q^{33} +(-0.584575 + 43.1358i) q^{34} +(-54.6481 + 31.5511i) q^{35} +(-24.0032 - 26.8299i) q^{36} +(6.02300 - 10.4321i) q^{37} +(-26.5570 + 44.5915i) q^{38} +(21.1113 + 1.22280i) q^{39} +(18.1628 + 57.0122i) q^{40} +(-57.3423 - 48.1159i) q^{41} +(12.3246 - 49.0974i) q^{42} +(-5.67130 + 15.5818i) q^{43} +(21.8653 + 27.5405i) q^{44} +(3.95711 + 67.1984i) q^{45} +(76.7735 - 26.7708i) q^{46} +(10.2447 - 1.80643i) q^{47} +(-42.9865 - 21.3580i) q^{48} +(20.8416 - 7.58571i) q^{49} +(21.9515 - 57.8594i) q^{50} +(7.53295 + 64.2697i) q^{51} +(26.7468 - 8.92192i) q^{52} -6.32010 q^{53} +(-40.9262 - 35.2285i) q^{54} -65.7533i q^{55} +(-9.00912 - 66.8902i) q^{56} +(-30.8123 + 71.4939i) q^{57} +(-6.11213 + 16.1103i) q^{58} +(-16.9160 - 46.4763i) q^{59} +(38.1189 + 81.2562i) q^{60} +(0.604658 + 3.42918i) q^{61} +(21.5504 - 7.51460i) q^{62} +(8.76668 - 75.4232i) q^{63} +(-63.7886 - 5.19790i) q^{64} +(-49.5421 - 18.0319i) q^{65} +(37.8848 + 36.7019i) q^{66} +(40.3947 - 48.1405i) q^{67} +(41.0991 + 75.8619i) q^{68} +(108.971 - 54.7708i) q^{69} +(-64.5775 + 108.431i) q^{70} +(-8.73857 - 5.04521i) q^{71} +(-68.0940 - 23.3924i) q^{72} +(-13.0231 - 22.5566i) q^{73} +(0.326464 - 24.0898i) q^{74} +(21.3780 - 90.3301i) q^{75} +(-2.81290 + 103.763i) q^{76} +(-12.8794 + 73.0428i) q^{77} +(38.0425 - 18.4795i) q^{78} +(-61.6659 - 73.4906i) q^{79} +(87.3710 + 81.7766i) q^{80} +(-67.7315 - 44.4234i) q^{81} +(-147.070 - 27.9923i) q^{82} +(-2.03051 - 2.41986i) q^{83} +(-26.4287 - 97.7308i) q^{84} +(28.0147 - 158.879i) q^{85} +(5.31570 + 32.7347i) q^{86} +(-5.95246 + 25.1513i) q^{87} +(65.0562 + 26.7203i) q^{88} +(-23.2483 - 40.2672i) q^{89} +(72.5220 + 113.427i) q^{90} +(51.5024 + 29.7349i) q^{91} +(107.864 - 121.691i) q^{92} +(30.5882 - 15.3742i) q^{93} +(16.1178 - 13.1564i) q^{94} +(124.761 - 148.684i) q^{95} +(-95.8851 + 4.69447i) q^{96} +(-8.79923 - 3.20266i) q^{97} +(28.9708 - 33.5909i) q^{98} +(63.4951 + 47.2071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.74544	−	0.976438i	0.872721	−	0.488219i
$2$	1.74544	−	0.976438i	0.872721	−	0.488219i
$3$	2.40580	−	1.79225i	0.801932	−	0.597416i
$3$	2.40580	−	1.79225i	0.801932	−	0.597416i
$4$	2.09314	−	3.40863i	0.523285	−	0.852158i
$5$	−7.02836	+	2.55811i	−1.40567	+	0.511623i	−0.929857	−	0.367922i	$-0.880069\pi$
$5$	−7.02836	+	2.55811i	−1.40567	+	0.511623i	−0.475816	+	0.879545i	$0.657847\pi$
$6$	2.44916	−	5.47737i	0.408193	−	0.912896i
$7$	8.30860	−	1.46503i	1.18694	−	0.209290i	0.454896	−	0.890545i	$-0.349676\pi$
$7$	8.30860	−	1.46503i	1.18694	−	0.209290i	0.732047	+	0.681254i	$0.238565\pi$
$8$	0.325138	−	7.99339i	0.0406422	−	0.999174i
$9$	2.57570	−	8.62356i	0.286189	−	0.958173i
$10$	−9.76976	+	11.3278i	−0.976976	+	1.13278i
$11$	−3.00678	+	8.26105i	−0.273343	+	0.751004i	0.724734	+	0.689028i	$0.241962\pi$
$11$	−3.00678	+	8.26105i	−0.273343	+	0.751004i	−0.998078	+	0.0619761i	$0.980260\pi$
$12$	−1.07345	−	11.9519i	−0.0894539	−	0.995991i
$13$	5.39976	+	4.53094i	0.415366	+	0.348534i	0.826397	−	0.563088i	$-0.190387\pi$
$13$	5.39976	+	4.53094i	0.415366	+	0.348534i	−0.411031	+	0.911621i	$0.634831\pi$
$14$	13.0717	−	10.6700i	0.933691	−	0.762140i
$15$	−12.3240	+	18.7509i	−0.821601	+	1.25006i
$16$	−7.23754	−	14.2695i	−0.452346	−	0.891842i
$17$	−10.7850	+	18.6801i	−0.634409	+	1.09883i	0.352231	+	0.935913i	$0.385423\pi$
$17$	−10.7850	+	18.6801i	−0.634409	+	1.09883i	−0.986640	+	0.162915i	$0.947910\pi$
$18$	−3.92463	−	17.5669i	−0.218035	−	0.975941i
$19$	−22.4736	+	12.9752i	−1.18282	+	0.682903i	−0.956666	−	0.291188i	$-0.905949\pi$
$19$	−22.4736	+	12.9752i	−1.18282	+	0.682903i	−0.226157	+	0.974091i	$0.572616\pi$
$20$	−5.99167	+	29.3116i	−0.299583	+	1.46558i
$21$	17.3631	−	18.4156i	0.826814	−	0.876935i
$22$	2.81824	+	17.3551i	0.128102	+	0.788869i
$23$	40.0360	+	7.05942i	1.74069	+	0.306931i	0.951600	−	0.307341i	$-0.0994391\pi$
$23$	40.0360	+	7.05942i	1.74069	+	0.306931i	0.789094	+	0.614272i	$0.210550\pi$
$24$	−13.5439	−	19.8132i	−0.564330	−	0.825549i
$25$	23.7028	−	19.8890i	0.948112	−	0.795560i
$26$	13.8492	+	2.63596i	0.532660	+	0.101383i
$27$	−9.25895	−	25.3628i	−0.342924	−	0.939363i
$28$	12.3973	−	31.3875i	0.442761	−	1.12098i
$29$	−6.59975	+	5.53785i	−0.227578	+	0.190960i	−0.749446	−	0.662066i	$-0.769680\pi$
$29$	−6.59975	+	5.53785i	−0.227578	+	0.190960i	0.521868	+	0.853026i	$0.325235\pi$
$30$	−3.20183	+	44.7622i	−0.106728	+	1.49207i
$31$	11.2381	+	1.98159i	0.362521	+	0.0639222i	0.351942	−	0.936022i	$-0.385521\pi$
$31$	11.2381	+	1.98159i	0.362521	+	0.0639222i	0.0105789	+	0.999944i	$0.496633\pi$
$32$	−26.5660	−	17.8396i	−0.830186	−	0.557486i
$33$	7.57216	+	25.2633i	0.229459	+	0.765554i
$34$	−0.584575	+	43.1358i	−0.0171934	+	1.26870i
$35$	−54.6481	+	31.5511i	−1.56137	+	0.901460i
$36$	−24.0032	−	26.8299i	−0.666757	−	0.745275i
$37$	6.02300	−	10.4321i	0.162784	−	0.281950i	−0.773082	−	0.634306i	$-0.781286\pi$
$37$	6.02300	−	10.4321i	0.162784	−	0.281950i	0.935866	+	0.352356i	$0.114619\pi$
$38$	−26.5570	+	44.5915i	−0.698868	+	1.17346i
$39$	21.1113	+	1.22280i	0.541315	+	0.0313539i
$40$	18.1628	+	57.0122i	0.454070	+	1.42530i
$41$	−57.3423	−	48.1159i	−1.39859	−	1.17356i	−0.961720	−	0.274034i	$-0.911642\pi$
$41$	−57.3423	−	48.1159i	−1.39859	−	1.17356i	−0.436872	−	0.899524i	$-0.643914\pi$
$42$	12.3246	−	49.0974i	0.293442	−	1.16899i
$43$	−5.67130	+	15.5818i	−0.131891	+	0.362367i	−0.988005	−	0.154419i	$-0.950649\pi$
$43$	−5.67130	+	15.5818i	−0.131891	+	0.362367i	0.856115	+	0.516786i	$0.172872\pi$
$44$	21.8653	+	27.5405i	0.496938	+	0.625921i
$45$	3.95711	+	67.1984i	0.0879357	+	1.49330i
$46$	76.7735	−	26.7708i	1.66899	−	0.581974i
$47$	10.2447	−	1.80643i	0.217973	−	0.0384346i	−0.0635949	−	0.997976i	$-0.520257\pi$
$47$	10.2447	−	1.80643i	0.217973	−	0.0384346i	0.281568	+	0.959541i	$0.409145\pi$
$48$	−42.9865	−	21.3580i	−0.895551	−	0.444958i
$49$	20.8416	−	7.58571i	0.425338	−	0.154810i
$50$	21.9515	−	57.8594i	0.439030	−	1.15719i
$51$	7.53295	+	64.2697i	0.147705	+	1.26019i
$52$	26.7468	−	8.92192i	0.514361	−	0.171575i
$53$	−6.32010			−0.119247			−0.0596236	−	0.998221i	$-0.518990\pi$
$53$	−6.32010			−0.119247			−0.0596236	+	0.998221i	$0.518990\pi$
$54$	−40.9262	−	35.2285i	−0.757892	−	0.652380i
$55$		−	65.7533i		−	1.19551i
$56$	−9.00912	−	66.8902i	−0.160877	−	1.19447i
$57$	−30.8123	+	71.4939i	−0.540566	+	1.25428i
$58$	−6.11213	+	16.1103i	−0.105381	+	0.277763i
$59$	−16.9160	−	46.4763i	−0.286712	−	0.787734i	−0.996521	−	0.0833403i	$-0.973441\pi$
$59$	−16.9160	−	46.4763i	−0.286712	−	0.787734i	0.709809	−	0.704394i	$-0.248781\pi$
$60$	38.1189	+	81.2562i	0.635315	+	1.35427i
$61$	0.604658	+	3.42918i	0.00991242	+	0.0562161i	0.989363	−	0.145469i	$-0.0464692\pi$
$61$	0.604658	+	3.42918i	0.00991242	+	0.0562161i	−0.979450	+	0.201685i	$0.935358\pi$
$62$	21.5504	−	7.51460i	0.347588	−	0.121203i
$63$	8.76668	−	75.4232i	0.139154	−	1.19719i
$64$	−63.7886	−	5.19790i	−0.996696	−	0.0812172i
$65$	−49.5421	−	18.0319i	−0.762187	−	0.277413i
$66$	37.8848	+	36.7019i	0.574012	+	0.556089i
$67$	40.3947	−	48.1405i	0.602906	−	0.718515i	−0.375125	−	0.926974i	$-0.622400\pi$
$67$	40.3947	−	48.1405i	0.602906	−	0.718515i	0.978031	+	0.208459i	$0.0668448\pi$
$68$	41.0991	+	75.8619i	0.604399	+	1.11562i
$69$	108.971	−	54.7708i	1.57928	−	0.793780i
$70$	−64.5775	+	108.431i	−0.922535	+	1.54902i
$71$	−8.73857	−	5.04521i	−0.123078	−	0.0710593i	0.437197	−	0.899366i	$-0.355971\pi$
$71$	−8.73857	−	5.04521i	−0.123078	−	0.0710593i	−0.560275	+	0.828307i	$0.689305\pi$
$72$	−68.0940	−	23.3924i	−0.945750	−	0.324895i
$73$	−13.0231	−	22.5566i	−0.178398	−	0.308995i	0.762934	−	0.646477i	$-0.223758\pi$
$73$	−13.0231	−	22.5566i	−0.178398	−	0.308995i	−0.941332	+	0.337482i	$0.890425\pi$
$74$	0.326464	−	24.0898i	0.00441167	−	0.325538i
$75$	21.3780	−	90.3301i	0.285041	−	1.20440i
$76$	−2.81290	+	103.763i	−0.0370119	+	1.36530i
$77$	−12.8794	+	73.0428i	−0.167265	+	0.948607i
$78$	38.0425	−	18.4795i	0.487725	−	0.236917i
$79$	−61.6659	−	73.4906i	−0.780581	−	0.930261i	0.218378	−	0.975864i	$-0.429923\pi$
$79$	−61.6659	−	73.4906i	−0.780581	−	0.930261i	−0.998960	+	0.0456035i	$0.985479\pi$
$80$	87.3710	+	81.7766i	1.09214	+	1.02221i
$81$	−67.7315	−	44.4234i	−0.836192	−	0.548437i
$82$	−147.070	−	27.9923i	−1.79353	−	0.341370i
$83$	−2.03051	−	2.41986i	−0.0244639	−	0.0291550i	0.753674	−	0.657249i	$-0.228280\pi$
$83$	−2.03051	−	2.41986i	−0.0244639	−	0.0291550i	−0.778138	+	0.628094i	$0.783835\pi$
$84$	−26.4287	−	97.7308i	−0.314628	−	1.16346i
$85$	28.0147	−	158.879i	0.329585	−	1.86917i
$86$	5.31570	+	32.7347i	0.0618104	+	0.380637i
$87$	−5.95246	+	25.1513i	−0.0684190	+	0.289096i
$88$	65.0562	+	26.7203i	0.739275	+	0.303640i
$89$	−23.2483	−	40.2672i	−0.261217	−	0.452441i	0.705349	−	0.708860i	$-0.250790\pi$
$89$	−23.2483	−	40.2672i	−0.261217	−	0.452441i	−0.966566	+	0.256420i	$0.917457\pi$
$90$	72.5220	+	113.427i	0.805800	+	1.26030i
$91$	51.5024	+	29.7349i	0.565961	+	0.326758i
$92$	107.864	−	121.691i	1.17243	−	1.32273i
$93$	30.5882	−	15.3742i	0.328905	−	0.165314i
$94$	16.1178	−	13.1564i	0.171465	−	0.139961i
$95$	124.761	−	148.684i	1.31327	−	1.56510i
$96$	−95.8851	+	4.69447i	−0.998804	+	0.0489008i
$97$	−8.79923	−	3.20266i	−0.0907137	−	0.0330171i	0.296265	−	0.955106i	$-0.404259\pi$
$97$	−8.79923	−	3.20266i	−0.0907137	−	0.0330171i	−0.386978	+	0.922089i	$0.626481\pi$
$98$	28.9708	−	33.5909i	0.295620	−	0.342764i
$99$	63.4951	+	47.2071i	0.641365	+	0.476839i
$100$	−18.1810	−	122.425i	−0.181810	−	1.22425i
$101$	14.5536	+	82.5378i	0.144095	+	0.817206i	0.968089	+	0.250607i	$0.0806301\pi$
$101$	14.5536	+	82.5378i	0.144095	+	0.817206i	−0.823994	+	0.566599i	$0.808259\pi$
$102$	75.9037	+	104.824i	0.744154	+	1.02768i
$103$	60.5834	+	166.451i	0.588188	+	1.61603i	0.773814	+	0.633413i	$0.218346\pi$
$103$	60.5834	+	166.451i	0.588188	+	1.61603i	−0.185626	+	0.982620i	$0.559431\pi$
$104$	37.9732	−	41.6892i	0.365127	−	0.400858i
$105$	−74.9248	+	173.848i	−0.713569	+	1.65570i
$106$	−11.0314	+	6.17118i	−0.104069	+	0.0582187i
$107$			59.6899i			0.557849i	0.960313	+	0.278925i	$0.0899780\pi$
$107$			59.6899i			0.557849i	−0.960313	+	0.278925i	$0.910022\pi$
$108$	−105.833	−	21.5275i	−0.979933	−	0.199329i
$109$	−30.1864			−0.276939			−0.138470	−	0.990367i	$-0.544218\pi$
$109$	−30.1864			−0.276939			−0.138470	+	0.990367i	$0.544218\pi$
$110$	−64.2040	−	114.769i	−0.583673	−	1.04335i
$111$	−4.20687	−	35.8923i	−0.0378998	−	0.323354i
$112$	−81.0390	−	107.956i	−0.723563	−	0.963894i
$113$	149.245	−	54.3208i	1.32075	−	0.480715i	0.417054	−	0.908882i	$-0.363063\pi$
$113$	149.245	−	54.3208i	1.32075	−	0.480715i	0.903700	+	0.428167i	$0.140840\pi$
$114$	16.0283	+	154.875i	0.140599	+	1.35855i
$115$	−299.446	+	52.8004i	−2.60388	+	0.459134i
$116$	5.06229	+	34.0876i	0.0436404	+	0.293859i
$117$	52.9810	−	34.8948i	0.452829	−	0.298247i
$118$	−74.9071	−	64.6043i	−0.634806	−	0.547494i
$119$	−62.2410	+	171.006i	−0.523033	+	1.43702i
$120$	145.876	+	104.607i	1.21563	+	0.871728i
$121$	33.4871	+	28.0991i	0.276753	+	0.232224i
$122$	4.40378	+	5.39503i	0.0360965	+	0.0442216i
$123$	−224.189	−	12.9854i	−1.82268	−	0.105572i
$124$	30.2775	−	34.1590i	0.244173	−	0.275475i
$125$	−22.2206	+	38.4872i	−0.177765	+	0.307898i
$126$	−58.3443	−	140.207i	−0.463050	−	1.11275i
$127$	−27.1885	+	15.6973i	−0.214083	+	0.123601i	−0.603207	−	0.797584i	$-0.706111\pi$
$127$	−27.1885	+	15.6973i	−0.214083	+	0.123601i	0.389125	+	0.921185i	$0.372778\pi$
$128$	−116.415	+	53.2129i	−0.909490	+	0.415726i
$129$	14.2824	+	47.6509i	0.110716	+	0.369387i
$130$	−104.080	+	16.9012i	−0.800615	+	0.130009i
$131$	7.38921	+	1.30292i	0.0564062	+	0.00994593i	0.201780	−	0.979431i	$-0.435327\pi$
$131$	7.38921	+	1.30292i	0.0564062	+	0.00994593i	−0.145374	+	0.989377i	$0.546439\pi$
$132$	101.963	+	27.0689i	0.772445	+	0.205067i
$133$	−167.715	+	140.730i	−1.26102	+	1.05812i
$134$	23.5004	−	123.469i	0.175376	−	0.921413i
$135$	129.956	+	154.573i	0.962638	+	1.14499i
$136$	145.811	+	92.2819i	1.07214	+	0.678544i
$137$	60.1368	−	50.4607i	0.438954	−	0.368327i	−0.396363	−	0.918094i	$-0.629728\pi$
$137$	60.1368	−	50.4607i	0.438954	−	0.368327i	0.835318	+	0.549767i	$0.185284\pi$
$138$	136.722	−	202.002i	0.990736	−	1.46378i
$139$	202.028	+	35.6229i	1.45344	+	0.256280i	0.843909	−	0.536486i	$-0.180249\pi$
$139$	202.028	+	35.6229i	1.45344	+	0.256280i	0.609526	+	0.792766i	$0.291360\pi$
$140$	−6.84001	+	252.316i	−0.0488572	+	1.80226i
$141$	21.4092	−	22.7070i	0.151838	−	0.161043i
$142$	−20.1790	−	0.273465i	−0.142106	−	0.00192581i
$143$	−53.6662	+	30.9842i	−0.375288	+	0.216673i
$144$	−141.695	+	25.6595i	−0.983996	+	0.178191i
$145$	32.2190	−	55.8049i	0.222200	−	0.384862i
$146$	−44.7562	−	26.6551i	−0.306549	−	0.182569i
$147$	36.5451	−	55.6029i	0.248606	−	0.378251i
$148$	−22.9523	−	42.3661i	−0.155083	−	0.286257i
$149$	−127.452	−	106.945i	−0.855383	−	0.717752i	0.105585	−	0.994410i	$-0.466328\pi$
$149$	−127.452	−	106.945i	−0.855383	−	0.717752i	−0.960968	+	0.276659i	$0.910773\pi$
$150$	−50.8876	−	178.540i	−0.339251	−	1.19027i
$151$	30.3543	−	83.3977i	0.201022	−	0.552303i	−0.797689	−	0.603069i	$-0.793944\pi$
$151$	30.3543	−	83.3977i	0.201022	−	0.552303i	0.998711	+	0.0507665i	$0.0161664\pi$
$152$	96.4085	+	183.859i	0.634266	+	1.20960i
$153$	133.310	+	141.119i	0.871307	+	0.922346i
$154$	48.8414	+	140.068i	0.317152	+	0.909532i
$155$	−84.0549	+	14.8211i	−0.542289	+	0.0956203i
$156$	48.3569	−	69.4011i	0.309980	−	0.444879i
$157$	−224.065	+	81.5530i	−1.42717	+	0.519446i	−0.936118	−	0.351686i	$-0.885608\pi$
$157$	−224.065	+	81.5530i	−1.42717	+	0.519446i	−0.491048	+	0.871132i	$0.663386\pi$
$158$	−179.393	−	68.0607i	−1.13540	−	0.430764i
$159$	−15.2049	+	11.3272i	−0.0956280	+	0.0712401i
$160$	232.351	+	57.4240i	1.45219	+	0.358900i
$161$	342.985			2.13034
$162$	−161.598	−	11.4028i	−0.997520	−	0.0703879i
$163$			294.501i			1.80676i	0.428844	+	0.903378i	$0.358921\pi$
$163$			294.501i			1.80676i	−0.428844	+	0.903378i	$0.641079\pi$
$164$	−284.035	+	94.7454i	−1.73192	+	0.577716i
$165$	−117.846	−	158.189i	−0.714219	−	0.958721i
$166$	−5.90698	−	2.24107i	−0.0355842	−	0.0135004i
$167$	−68.8085	−	189.050i	−0.412027	−	1.13203i	−0.956111	−	0.293004i	$-0.905345\pi$
$167$	−68.8085	−	189.050i	−0.412027	−	1.13203i	0.544084	−	0.839031i	$-0.316877\pi$
$168$	−141.558	−	144.778i	−0.842607	−	0.861771i
$169$	−20.7185	−	117.501i	−0.122595	−	0.695269i
$170$	−106.238	−	304.670i	−0.624928	−	1.79217i
$171$	54.0067	+	227.223i	0.315829	+	1.32879i
$172$	41.2417	+	51.9462i	0.239777	+	0.302013i
$173$	136.977	+	49.8557i	0.791776	+	0.288183i	0.706074	−	0.708138i	$-0.250464\pi$
$173$	136.977	+	49.8557i	0.791776	+	0.288183i	0.0857022	+	0.996321i	$0.472687\pi$
$174$	14.1690	+	49.7124i	0.0814312	+	0.285703i
$175$	167.799	−	199.975i	0.958851	−	1.14271i
$176$	139.643	−	16.8845i	0.793423	−	0.0959348i
$177$	−123.993	−	81.4948i	−0.700528	−	0.460423i
$178$	−79.8970	−	47.5836i	−0.448859	−	0.267324i
$179$	34.4045	+	19.8634i	0.192204	+	0.110969i	0.593014	−	0.805192i	$-0.297938\pi$
$179$	34.4045	+	19.8634i	0.192204	+	0.110969i	−0.400810	+	0.916161i	$0.631271\pi$
$180$	237.337	+	127.167i	1.31854	+	0.706485i
$181$	70.2548	+	121.685i	0.388148	+	0.672293i	0.992201	−	0.124652i	$-0.0397815\pi$
$181$	70.2548	+	121.685i	0.388148	+	0.672293i	−0.604052	+	0.796945i	$0.706448\pi$
$182$	118.929	+	1.61172i	0.653455	+	0.00885560i
$183$	7.60063	+	7.16622i	0.0415335	+	0.0391597i
$184$	69.4459	−	317.728i	0.377423	−	1.72678i
$185$	−15.6452	+	88.7283i	−0.0845686	+	0.479613i
$186$	38.3779	−	56.7023i	0.206333	−	0.304851i
$187$	−121.889	−	145.262i	−0.651814	−	0.776801i
$188$	15.2862	−	38.7017i	0.0813098	−	0.205860i
$189$	−114.086	−	197.165i	−0.603630	−	1.04320i
$190$	72.5820	−	381.341i	0.382011	−	2.00706i
$191$	158.452	+	188.836i	0.829594	+	0.988672i	0.999995	+	0.00329666i	$0.00104936\pi$
$191$	158.452	+	188.836i	0.829594	+	0.988672i	−0.170401	+	0.985375i	$0.554506\pi$
$192$	−162.778	+	101.820i	−0.847803	+	0.530311i
$193$	−17.0768	+	96.8473i	−0.0884808	+	0.501799i	0.908070	+	0.418818i	$0.137555\pi$
$193$	−17.0768	+	96.8473i	−0.0884808	+	0.501799i	−0.996551	+	0.0829816i	$0.973556\pi$
$194$	−18.4858	+	3.00185i	−0.0952874	+	0.0154734i
$195$	−151.506	+	45.4108i	−0.776953	+	0.232876i
$196$	17.7674	−	86.9192i	0.0906501	−	0.443465i
$197$	−93.9302	−	162.692i	−0.476803	−	0.825847i	0.522844	−	0.852429i	$-0.324871\pi$
$197$	−93.9302	−	162.692i	−0.476803	−	0.825847i	−0.999647	+	0.0265817i	$0.991538\pi$
$198$	156.922	+	20.3983i	0.792534	+	0.103021i
$199$	72.0720	+	41.6108i	0.362171	+	0.209100i	0.670033	−	0.742332i	$-0.266280\pi$
$199$	72.0720	+	41.6108i	0.362171	+	0.209100i	−0.307862	+	0.951431i	$0.599613\pi$
$200$	−151.274	−	195.932i	−0.756369	−	0.979661i
$201$	10.9016	−	188.214i	0.0542370	−	0.936386i
$202$	105.996	+	129.854i	0.524730	+	0.642843i
$203$	−46.7216	+	55.6806i	−0.230156	+	0.274289i
$204$	234.839	+	108.848i	1.15117	+	0.533571i
$205$	526.108	+	191.488i	2.56638	+	0.934086i
$206$	268.274	+	231.375i	1.30230	+	1.12318i
$207$	163.998	−	327.070i	0.792260	−	1.58005i
$208$	25.5732	−	109.845i	0.122948	−	0.528099i
$209$	−39.6152	−	224.669i	−0.189547	−	1.07497i
$210$	38.9753	+	376.602i	0.185596	+	1.79334i
$211$	−80.3337	−	220.715i	−0.380728	−	1.04604i	−0.971050	−	0.238875i	$-0.923221\pi$
$211$	−80.3337	−	220.715i	−0.380728	−	1.04604i	0.590322	−	0.807168i	$-0.299001\pi$
$212$	−13.2288	+	21.5429i	−0.0624002	+	0.101617i
$213$	−30.0655	+	3.52392i	−0.141152	+	0.0165442i
$214$	58.2834	+	104.185i	0.272352	+	0.486847i
$215$		−	124.022i		−	0.576847i
$216$	−205.745	+	65.7640i	−0.952524	+	0.304463i
$217$	96.2763			0.443670
$218$	−52.6886	+	29.4751i	−0.241691	+	0.135207i
$219$	−71.7580	−	30.9261i	−0.327662	−	0.141215i
$220$	−224.129	−	137.631i	−1.01877	−	0.625595i
$221$	−142.875	+	52.0021i	−0.646491	+	0.235303i
$222$	−42.3894	−	58.5402i	−0.190943	−	0.263694i
$223$	212.644	−	37.4949i	0.953561	−	0.168138i	0.324839	−	0.945769i	$-0.394690\pi$
$223$	212.644	−	37.4949i	0.953561	−	0.168138i	0.628721	+	0.777631i	$0.283579\pi$
$224$	−246.861	−	109.302i	−1.10206	−	0.487954i
$225$	−110.463	−	255.630i	−0.490945	−	1.13614i
$226$	207.458	−	240.542i	0.917956	−	1.06435i
$227$	116.933	−	321.270i	0.515122	−	1.41529i	−0.360713	−	0.932677i	$-0.617467\pi$
$227$	116.933	−	321.270i	0.515122	−	1.41529i	0.875835	−	0.482610i	$-0.160311\pi$
$228$	179.202	+	254.674i	0.785973	+	1.11699i
$229$	125.473	+	105.284i	0.547917	+	0.459757i	0.874235	−	0.485503i	$-0.161363\pi$
$229$	125.473	+	105.284i	0.547917	+	0.459757i	−0.326318	+	0.945260i	$0.605808\pi$
$230$	−471.109	+	384.550i	−2.04830	+	1.67196i
$231$	99.9255	+	198.809i	0.432578	+	0.860645i
$232$	42.1204	+	54.5550i	0.181553	+	0.235151i
$233$	−193.676	+	335.457i	−0.831227	+	1.43973i	0.0658383	+	0.997830i	$0.479028\pi$
$233$	−193.676	+	335.457i	−0.831227	+	1.43973i	−0.897066	+	0.441898i	$0.854305\pi$
$234$	58.4026	−	112.640i	0.249584	−	0.481366i
$235$	−67.3827	+	38.9034i	−0.286735	+	0.165547i
$236$	−193.828	−	39.6210i	−0.821306	−	0.167886i
$237$	−280.069	−	66.2827i	−1.18173	−	0.279674i
$238$	58.3383	+	359.255i	0.245119	+	1.50947i
$239$	102.743	+	18.1163i	0.429886	+	0.0758006i	0.384405	−	0.923165i	$-0.374407\pi$
$239$	102.743	+	18.1163i	0.429886	+	0.0758006i	0.0454815	+	0.998965i	$0.485518\pi$
$240$	356.761	+	40.1473i	1.48650	+	0.167281i
$241$	−318.366	+	267.141i	−1.32102	+	1.10847i	−0.334934	+	0.942242i	$0.608714\pi$
$241$	−318.366	+	267.141i	−1.32102	+	1.10847i	−0.986088	+	0.166227i	$0.946842\pi$
$242$	85.8869	+	16.3472i	0.354904	+	0.0675503i
$243$	−242.566	+	14.5181i	−0.998214	+	0.0597453i
$244$	12.9545	+	5.11670i	0.0530920	+	0.0209701i
$245$	−127.077	+	106.630i	−0.518681	+	0.435225i
$246$	−403.989	+	196.242i	−1.64223	+	0.797730i
$247$	−180.142	−	31.7639i	−0.729320	−	0.128599i
$248$	19.4936	−	89.1866i	0.0786030	−	0.359623i
$249$	−9.22197	−	2.18252i	−0.0370360	−	0.00876516i
$250$	−1.20442	+	88.8742i	−0.00481768	+	0.355497i
$251$	−297.853	+	171.965i	−1.18666	+	0.685121i	−0.957547	−	0.288278i	$-0.906917\pi$
$251$	−297.853	+	171.965i	−1.18666	+	0.685121i	−0.229117	+	0.973399i	$0.573584\pi$
$252$	−238.740	−	187.754i	−0.947381	−	0.745054i
$253$	−178.697	+	309.513i	−0.706314	+	1.22337i
$254$	−32.1286	+	53.9466i	−0.126490	+	0.212388i
$255$	−217.354	−	432.441i	−0.852367	−	1.69585i
$256$	−151.236	+	206.552i	−0.590766	+	0.806843i
$257$	319.778	+	268.326i	1.24427	+	1.04407i	0.997178	+	0.0750773i	$0.0239203\pi$
$257$	319.778	+	268.326i	1.24427	+	1.04407i	0.247095	+	0.968991i	$0.420524\pi$
$258$	71.4572	+	69.2260i	0.276966	+	0.268318i
$259$	34.7593	−	95.5003i	0.134206	−	0.368727i
$260$	−165.163	+	131.128i	−0.635241	+	0.504337i
$261$	30.7570	+	71.1772i	0.117843	+	0.272710i
$262$	14.1697	−	4.94093i	0.0540826	−	0.0188585i
$263$	363.036	−	64.0131i	1.38037	−	0.243396i	0.566315	−	0.824189i	$-0.308369\pi$
$263$	363.036	−	64.0131i	1.38037	−	0.243396i	0.814051	+	0.580793i	$0.197257\pi$
$264$	204.401	−	52.3132i	0.774247	−	0.198156i
$265$	44.4199	−	16.1675i	0.167622	−	0.0610095i
$266$	−155.324	+	409.400i	−0.583923	+	1.53910i
$267$	−128.099	−	55.2080i	−0.479773	−	0.206772i
$268$	−79.5416	−	238.455i	−0.296797	−	0.889759i
$269$	25.2355			0.0938122			0.0469061	−	0.998899i	$-0.485064\pi$
$269$	25.2355			0.0938122			0.0469061	+	0.998899i	$0.485064\pi$
$270$	377.762	+	142.905i	1.39912	+	0.529278i
$271$			278.654i			1.02824i	0.857717	+	0.514121i	$0.171882\pi$
$271$			278.654i			1.02824i	−0.857717	+	0.514121i	$0.828118\pi$
$272$	344.612	+	18.6978i	1.26695	+	0.0687420i
$273$	177.197	−	20.7689i	0.649072	−	0.0760766i
$274$	55.6935	−	146.796i	0.203261	−	0.535752i
$275$	93.0350	+	255.612i	0.338309	+	0.929497i
$276$	41.3969	−	486.083i	0.149989	−	1.76117i
$277$	−50.3543	−	285.573i	−0.181784	−	1.03095i	−0.930018	−	0.367515i	$-0.880209\pi$
$277$	−50.3543	−	285.573i	−0.181784	−	1.03095i	0.748233	−	0.663436i	$-0.230902\pi$
$278$	387.411	−	135.090i	1.39356	−	0.485934i
$279$	46.0344	−	91.8088i	0.164998	−	0.329064i
$280$	234.432	+	447.082i	0.837258	+	1.59672i
$281$	223.498	+	81.3466i	0.795366	+	0.289490i	0.707565	−	0.706648i	$-0.249794\pi$
$281$	223.498	+	81.3466i	0.795366	+	0.289490i	0.0878013	+	0.996138i	$0.472016\pi$
$282$	15.1966	−	60.5385i	0.0538885	−	0.214676i
$283$	96.4218	−	114.911i	0.340713	−	0.406046i	−0.568295	−	0.822825i	$-0.692397\pi$
$283$	96.4218	−	114.911i	0.340713	−	0.406046i	0.909008	+	0.416779i	$0.136841\pi$
$284$	−35.4883	+	19.2262i	−0.124959	+	0.0676979i
$285$	33.6702	−	581.306i	0.118141	−	2.03967i
$286$	−63.4171	+	106.483i	−0.221738	+	0.372318i
$287$	−546.925	−	315.767i	−1.90566	−	1.10023i
$288$	−222.266	+	183.144i	−0.771758	+	0.635916i
$289$	−88.1303	−	152.646i	−0.304949	−	0.528188i
$290$	1.74636	−	128.864i	0.00602194	−	0.444359i
$291$	−26.9091	+	8.06546i	−0.0924712	+	0.0277164i
$292$	−104.146	−	2.82330i	−0.356666	−	0.00966882i
$293$	66.5982	−	377.697i	0.227298	−	1.28907i	−0.630946	−	0.775826i	$-0.717333\pi$
$293$	66.5982	−	377.697i	0.227298	−	1.28907i	0.858244	−	0.513242i	$-0.171556\pi$
$294$	9.49455	−	132.736i	0.0322944	−	0.451482i
$295$	237.783	+	283.379i	0.806045	+	0.960608i
$296$	−81.4298	−	51.5360i	−0.275101	−	0.174108i
$297$	237.363	−	0.228338i	0.799202	−	0.000768813i
$298$	−326.885	−	62.2173i	−1.09693	−	0.208783i
$299$	184.199	+	219.520i	0.616050	+	0.734180i
$300$	−263.155	−	261.943i	−0.877183	−	0.873145i
$301$	−24.2928	+	137.771i	−0.0807070	+	0.457712i
$302$	−28.4510	−	175.205i	−0.0942086	−	0.580149i
$303$	182.941	+	172.485i	0.603766	+	0.569258i
$304$	347.802	+	226.779i	1.14409	+	0.745983i
$305$	−13.0220	−	22.5548i	−0.0426951	−	0.0739500i
$306$	370.479	+	116.146i	1.21072	+	0.379562i
$307$	−259.824	−	150.010i	−0.846333	−	0.488631i	0.0130787	−	0.999914i	$-0.495837\pi$
$307$	−259.824	−	150.010i	−0.846333	−	0.488631i	−0.859412	+	0.511284i	$0.829170\pi$
$308$	222.017	+	196.790i	0.720836	+	0.638928i
$309$	444.073	+	291.868i	1.43713	+	0.944555i
$310$	−132.241	+	107.944i	−0.426584	+	0.348206i
$311$	91.7452	−	109.338i	0.295001	−	0.351568i	−0.598103	−	0.801419i	$-0.704079\pi$
$311$	91.7452	−	109.338i	0.295001	−	0.351568i	0.893104	+	0.449851i	$0.148523\pi$
$312$	16.6384	−	168.353i	0.0533282	−	0.539594i
$313$	−400.421	−	145.741i	−1.27930	−	0.465627i	−0.389099	−	0.921196i	$-0.627213\pi$
$313$	−400.421	−	145.741i	−1.27930	−	0.465627i	−0.890200	+	0.455569i	$0.849436\pi$
$314$	−311.461	+	361.132i	−0.991915	+	1.15010i
$315$	131.326	+	552.527i	0.416907	+	1.75406i
$316$	−379.578	+	56.3704i	−1.20120	+	0.178387i
$317$	−23.0790	−	130.888i	−0.0728044	−	0.412895i	−0.999328	−	0.0366575i	$-0.988329\pi$
$317$	−23.0790	−	130.888i	−0.0728044	−	0.412895i	0.926523	−	0.376237i	$-0.122782\pi$
$318$	−15.4789	+	34.6175i	−0.0486759	+	0.108860i
$319$	−25.9045	−	71.1720i	−0.0812053	−	0.223110i
$320$	461.626	−	126.646i	1.44258	−	0.395768i
$321$	106.979	+	143.602i	0.333268	+	0.447357i
$322$	598.661	−	334.903i	1.85919	−	1.04007i
$323$		−	559.746i		−	1.73296i
$324$	−293.195	+	137.888i	−0.904921	+	0.425579i
$325$	218.105			0.671093
$326$	287.562	+	514.035i	0.882093	+	1.57680i
$327$	−72.6222	+	54.1014i	−0.222086	+	0.165448i
$328$	−403.253	+	442.715i	−1.22943	+	1.34974i
$329$	82.4730	−	30.0177i	0.250678	−	0.0912393i
$330$	−360.155	−	161.040i	−1.09138	−	0.488001i
$331$	78.1327	−	13.7769i	0.236050	−	0.0416221i	−0.0543714	−	0.998521i	$-0.517315\pi$
$331$	78.1327	−	13.7769i	0.236050	−	0.0416221i	0.290422	+	0.956899i	$0.406204\pi$
$332$	−12.4985	+	1.85614i	−0.0376462	+	0.00559077i
$333$	−74.4487	−	78.8097i	−0.223570	−	0.236666i
$334$	−304.697	−	262.788i	−0.912265	−	0.786791i
$335$	−160.760	+	441.683i	−0.479879	+	1.31846i
$336$	−388.447	−	114.478i	−1.15609	−	0.340710i
$337$	−414.258	−	347.604i	−1.22925	−	1.03146i	−0.998287	−	0.0585028i	$-0.981367\pi$
$337$	−414.258	−	347.604i	−1.22925	−	1.03146i	−0.230965	−	0.972962i	$-0.574188\pi$
$338$	−150.895	−	184.860i	−0.446435	−	0.546923i
$339$	261.697	−	398.169i	0.771968	−	1.17454i
$340$	−482.923	−	428.049i	−1.42036	−	1.25897i
$341$	−50.1606	+	86.8807i	−0.147099	+	0.254782i
$342$	316.134	+	343.870i	0.924370	+	1.00547i
$343$	−195.966	+	113.141i	−0.571328	+	0.329856i
$344$	122.707	+	50.3991i	0.356707	+	0.146509i
$345$	−625.774	+	663.708i	−1.81384	+	1.92379i
$346$	287.767	−	46.7296i	0.831697	−	0.135057i
$347$	−104.333	−	18.3967i	−0.300670	−	0.0530163i	0.0212778	−	0.999774i	$-0.493227\pi$
$347$	−104.333	−	18.3967i	−0.300670	−	0.0530163i	−0.321948	+	0.946757i	$0.604338\pi$
$348$	73.2723	+	72.9350i	0.210553	+	0.209583i
$349$	−2.61442	+	2.19376i	−0.00749118	+	0.00628585i	−0.646526	−	0.762892i	$-0.723779\pi$
$349$	−2.61442	+	2.19376i	−0.00749118	+	0.00628585i	0.639034	+	0.769178i	$0.279334\pi$
$350$	97.6203	−	512.890i	0.278915	−	1.46540i
$351$	64.9212	−	178.905i	0.184961	−	0.509701i
$352$	227.251	−	165.823i	0.645600	−	0.471089i
$353$	256.855	−	215.527i	0.727635	−	0.610558i	−0.201851	−	0.979416i	$-0.564696\pi$
$353$	256.855	−	215.527i	0.727635	−	0.610558i	0.929486	+	0.368858i	$0.120251\pi$
$354$	−295.998	−	21.1727i	−0.836153	−	0.0598098i
$355$	74.3240	+	13.1053i	0.209363	+	0.0369164i
$356$	−185.918	−	5.04003i	−0.522242	−	0.0141574i
$357$	156.745	+	522.956i	0.439063	+	1.46486i
$358$	79.4464	+	1.07665i	0.221917	+	0.00300742i
$359$	−16.3296	+	9.42789i	−0.0454863	+	0.0262615i	−0.522571	−	0.852596i	$-0.675027\pi$
$359$	−16.3296	+	9.42789i	−0.0454863	+	0.0262615i	0.477084	+	0.878857i	$0.341694\pi$
$360$	538.430	−	9.78195i	1.49564	−	0.0271721i
$361$	156.209	−	270.562i	0.432713	−	0.749480i
$362$	241.444	+	143.795i	0.666971	+	0.397223i
$363$	130.924	+	7.58331i	0.360671	+	0.0208907i
$364$	209.157	−	113.313i	0.574608	−	0.311301i
$365$	149.233	+	125.222i	0.408859	+	0.343073i
$366$	20.2638	+	5.08668i	0.0553656	+	0.0138980i
$367$	171.350	−	470.779i	0.466893	−	1.28278i	−0.453316	−	0.891350i	$-0.649759\pi$
$367$	171.350	−	470.779i	0.466893	−	1.28278i	0.920209	−	0.391427i	$-0.128019\pi$
$368$	−189.028	−	622.385i	−0.513662	−	1.69126i
$369$	−562.627	+	370.562i	−1.52473	+	1.00423i
$370$	59.3299	+	170.147i	0.160351	+	0.459856i
$371$	−52.5111	+	9.25913i	−0.141539	+	0.0249572i
$372$	11.6202	−	136.444i	0.0312370	−	0.366786i
$373$	391.081	−	142.342i	1.04847	−	0.381613i	0.240387	−	0.970677i	$-0.422726\pi$
$373$	391.081	−	142.342i	1.04847	−	0.381613i	0.808086	+	0.589064i	$0.200503\pi$
$374$	−354.590	−	134.529i	−0.948101	−	0.359703i
$375$	15.5204	+	132.417i	0.0413877	+	0.353112i
$376$	−11.1085	−	82.4776i	−0.0295439	−	0.219355i
$377$	−60.7288			−0.161084
$378$	−391.650	−	232.742i	−1.03611	−	0.615719i
$379$			222.431i			0.586888i	0.955976	+	0.293444i	$0.0948015\pi$
$379$			222.431i			0.586888i	−0.955976	+	0.293444i	$0.905199\pi$
$380$	−245.668	−	736.480i	−0.646494	−	1.93811i
$381$	−37.2766	+	86.4930i	−0.0978387	+	0.227016i
$382$	460.956	+	174.884i	1.20669	+	0.457811i
$383$	−48.4034	−	132.987i	−0.126380	−	0.347225i	0.860326	−	0.509745i	$-0.170260\pi$
$383$	−48.4034	−	132.987i	−0.126380	−	0.347225i	−0.986705	+	0.162519i	$0.948038\pi$
$384$	−184.699	+	336.663i	−0.480988	+	0.876727i
$385$	−96.3306	−	546.318i	−0.250209	−	1.41901i
$386$	64.7588	+	185.716i	0.167769	+	0.481129i
$387$	119.763	+	89.0407i	0.309464	+	0.230079i
$388$	−29.3347	+	23.2897i	−0.0756049	+	0.0600251i
$389$	−490.191	−	178.415i	−1.26013	−	0.458651i	−0.376319	−	0.926490i	$-0.622810\pi$
$389$	−490.191	−	178.415i	−1.26013	−	0.458651i	−0.883813	+	0.467840i	$0.845032\pi$
$390$	−220.104	+	227.198i	−0.564369	+	0.582559i
$391$	−563.656	+	671.740i	−1.44158	+	1.71800i
$392$	−53.8592	−	169.061i	−0.137396	−	0.431279i
$393$	20.1121	−	10.1087i	0.0511757	−	0.0257220i
$394$	−322.808	−	192.252i	−0.819310	−	0.487950i
$395$	621.408	+	358.770i	1.57318	+	0.908278i
$396$	293.816	−	117.620i	0.741959	−	0.297021i
$397$	178.492	+	309.158i	0.449603	+	0.778735i	0.998360	−	0.0572469i	$-0.0182322\pi$
$397$	178.492	+	309.158i	0.449603	+	0.778735i	−0.548757	+	0.835982i	$0.684899\pi$
$398$	166.428	+	2.25543i	0.418161	+	0.00566690i
$399$	−151.266	+	639.155i	−0.379113	+	1.60189i
$400$	−455.356	−	194.279i	−1.13839	−	0.485698i
$401$	52.0840	−	295.383i	0.129885	−	0.736616i	−0.848400	−	0.529355i	$-0.822434\pi$
$401$	52.0840	−	295.383i	0.129885	−	0.736616i	0.978286	−	0.207261i	$-0.0664550\pi$
$402$	−164.751	−	339.161i	−0.409827	−	0.843683i
$403$	51.7049	+	61.6195i	0.128300	+	0.152902i
$404$	311.804	+	123.155i	0.771791	+	0.304839i
$405$	589.682	+	138.959i	1.45600	+	0.343108i
$406$	−27.1812	+	142.808i	−0.0669488	+	0.351744i
$407$	68.0706	+	81.1234i	0.167250	+	0.199320i
$408$	516.182	−	39.3173i	1.26515	−	0.0963659i
$409$	1.74674	−	9.90627i	0.00427077	−	0.0242207i	−0.982598	−	0.185745i	$-0.940530\pi$
$409$	1.74674	−	9.90627i	0.00427077	−	0.0242207i	0.986869	+	0.161525i	$0.0516411\pi$
$410$	1105.27	−	179.481i	2.69577	−	0.437758i
$411$	54.2386	−	229.178i	0.131967	−	0.557611i
$412$	694.181	+	141.900i	1.68491	+	0.344416i
$413$	−208.637	−	361.371i	−0.505175	−	0.874989i
$414$	−33.1141	−	731.015i	−0.0799857	−	1.76574i
$415$	20.4614	+	11.8134i	0.0493046	+	0.0284660i
$416$	−62.6200	−	216.698i	−0.150529	−	0.520909i
$417$	549.882	−	276.382i	1.31866	−	0.662786i
$418$	−288.521	−	353.465i	−0.690243	−	0.845611i
$419$	−200.584	+	239.047i	−0.478721	+	0.570517i	−0.950312	−	0.311300i	$-0.899236\pi$
$419$	−200.584	+	239.047i	−0.478721	+	0.570517i	0.471591	+	0.881818i	$0.343680\pi$
$420$	435.757	+	619.280i	1.03752	+	1.47448i
$421$	457.349	+	166.462i	1.08634	+	0.395396i	0.822264	−	0.569106i	$-0.192711\pi$
$421$	457.349	+	166.462i	1.08634	+	0.395396i	0.264077	+	0.964502i	$0.414933\pi$
$422$	−355.732	−	306.804i	−0.842967	−	0.727025i
$423$	10.8096	−	92.9990i	0.0255545	−	0.219856i
$424$	−2.05490	+	50.5190i	−0.00484646	+	0.119149i
$425$	115.895	+	657.272i	0.272694	+	1.54652i
$426$	−49.0367	+	35.5079i	−0.115110	+	0.0833518i
$427$	10.0477	+	27.6059i	0.0235309	+	0.0646507i
$428$	203.461	+	124.939i	0.475376	+	0.291914i
$429$	−73.5785	+	170.725i	−0.171512	+	0.397960i
$430$	−121.100	−	216.473i	−0.281628	−	0.503427i
$431$			241.706i			0.560803i	0.959883	+	0.280401i	$0.0904676\pi$
$431$			241.706i			0.560803i	−0.959883	+	0.280401i	$0.909532\pi$
$432$	−294.902	+	315.685i	−0.682644	+	0.730751i
$433$	−508.564			−1.17451			−0.587257	−	0.809401i	$-0.699792\pi$
$433$	−508.564			−1.17451			−0.587257	+	0.809401i	$0.699792\pi$
$434$	168.045	−	94.0078i	0.387200	−	0.216608i
$435$	−22.5040	−	192.000i	−0.0517332	−	0.441379i
$436$	−63.1843	+	102.894i	−0.144918	+	0.235996i
$437$	−991.350	+	360.822i	−2.26854	+	0.825680i
$438$	−155.447	+	16.0875i	−0.354901	+	0.0367294i
$439$	−37.5547	+	6.62190i	−0.0855459	+	0.0150841i	−0.216257	−	0.976336i	$-0.569385\pi$
$439$	−37.5547	+	6.62190i	−0.0855459	+	0.0150841i	0.130711	+	0.991420i	$0.458274\pi$
$440$	−525.592	−	21.3789i	−1.19453	−	0.0485883i
$441$	−11.7342	−	199.267i	−0.0266082	−	0.451853i
$442$	−198.602	+	230.275i	−0.449327	+	0.520983i
$443$	15.5239	−	42.6515i	0.0350426	−	0.0962787i	−0.920937	−	0.389710i	$-0.872575\pi$
$443$	15.5239	−	42.6515i	0.0350426	−	0.0962787i	0.955980	+	0.293432i	$0.0947973\pi$
$444$	−131.149	−	60.7879i	−0.295381	−	0.136910i
$445$	266.406	+	223.541i	0.598664	+	0.502339i
$446$	334.546	−	273.079i	0.750104	−	0.612284i
$447$	−498.295	−	28.8621i	−1.11475	−	0.0645684i
$448$	−537.609	+	50.2649i	−1.20002	+	0.112198i
$449$	62.3307	−	107.960i	0.138821	−	0.240445i	−0.788229	−	0.615381i	$-0.789002\pi$
$449$	62.3307	−	107.960i	0.138821	−	0.240445i	0.927051	+	0.374936i	$0.122335\pi$
$450$	−442.414	−	338.328i	−0.983141	−	0.751841i
$451$	569.903	−	329.034i	1.26364	−	0.729565i
$452$	127.231	−	622.423i	0.281485	−	1.37704i
$453$	−76.4431	−	255.040i	−0.168749	−	0.563003i
$454$	−109.601	−	674.936i	−0.241412	−	1.48664i
$455$	−438.043	−	77.2388i	−0.962732	−	0.169756i
$456$	561.460	+	269.540i	1.23127	+	0.591096i
$457$	248.812	−	208.778i	0.544447	−	0.456845i	−0.328608	−	0.944466i	$-0.606580\pi$
$457$	248.812	−	208.778i	0.544447	−	0.456845i	0.873056	+	0.487621i	$0.162135\pi$
$458$	321.810	+	61.2512i	0.702641	+	0.133736i
$459$	573.637	+	100.579i	1.24975	+	0.219126i
$460$	−446.805	+	1131.22i	−0.971315	+	2.45917i
$461$	38.5485	−	32.3460i	0.0836193	−	0.0701649i	−0.600020	−	0.799985i	$-0.704841\pi$
$461$	38.5485	−	32.3460i	0.0836193	−	0.0701649i	0.683639	+	0.729820i	$0.260396\pi$
$462$	368.539	+	249.439i	0.797703	+	0.539911i
$463$	−320.227	−	56.4647i	−0.691636	−	0.121954i	−0.183228	−	0.983070i	$-0.558655\pi$
$463$	−320.227	−	56.4647i	−0.691636	−	0.121954i	−0.508408	+	0.861116i	$0.669766\pi$
$464$	126.788	+	54.0947i	0.273251	+	0.116583i
$465$	−175.656	+	186.304i	−0.377754	+	0.400653i
$466$	−10.4978	+	774.633i	−0.0225275	+	1.66230i
$467$	242.520	−	140.019i	0.519315	−	0.299827i	−0.217339	−	0.976096i	$-0.569738\pi$
$467$	242.520	−	140.019i	0.519315	−	0.299827i	0.736654	+	0.676269i	$0.236404\pi$
$468$	−8.04708	−	253.632i	−0.0171946	−	0.541950i
$469$	265.096	−	459.160i	0.565237	−	0.979019i
$470$	−79.6259	+	133.699i	−0.169417	+	0.284465i
$471$	−392.892	+	597.780i	−0.834165	+	1.26917i
$472$	−377.003	+	120.105i	−0.798736	+	0.254460i
$473$	−111.669	−	93.7018i	−0.236088	−	0.198101i
$474$	−553.565	+	157.777i	−1.16786	+	0.332863i
$475$	−274.625	+	754.525i	−0.578157	+	1.58847i
$476$	452.616	+	570.095i	0.950874	+	1.19768i
$477$	−16.2787	+	54.5017i	−0.0341272	+	0.114259i
$478$	197.021	−	68.7010i	0.412178	−	0.143726i
$479$	−416.211	+	73.3892i	−0.868916	+	0.153213i	−0.590295	−	0.807188i	$-0.700989\pi$
$479$	−416.211	+	73.3892i	−0.868916	+	0.153213i	−0.278621	+	0.960401i	$0.589877\pi$
$480$	661.906	−	278.280i	1.37897	−	0.579749i
$481$	79.7901	−	29.0412i	0.165884	−	0.0603768i
$482$	−294.843	+	777.144i	−0.611708	+	1.61233i
$483$	825.152	−	614.714i	1.70839	−	1.27270i
$484$	165.873	−	55.3301i	0.342712	−	0.114318i
$485$	70.0370			0.144406
$486$	−409.209	+	262.191i	−0.841993	+	0.539488i
$487$		−	880.332i		−	1.80766i	−0.427889	−	0.903832i	$-0.640742\pi$
$487$		−	880.332i		−	1.80766i	0.427889	−	0.903832i	$-0.359258\pi$
$488$	27.6074	−	3.71831i	0.0565725	−	0.00761948i
$489$	527.819	+	708.510i	1.07939	+	1.44890i
$490$	−117.688	+	310.200i	−0.240179	+	0.633061i
$491$	24.4148	+	67.0791i	0.0497246	+	0.136617i	0.962069	−	0.272807i	$-0.0879519\pi$
$491$	24.4148	+	67.0791i	0.0497246	+	0.136617i	−0.912344	+	0.409424i	$0.865730\pi$
$492$	−513.522	+	736.998i	−1.04374	+	1.49796i
$493$	−32.2695	−	183.009i	−0.0654554	−	0.371216i
$494$	−345.443	+	120.455i	−0.699277	+	0.243837i
$495$	−567.027	−	169.361i	−1.14551	−	0.342143i
$496$	−53.0603	−	174.704i	−0.106976	−	0.352226i
$497$	−79.9966	−	29.1164i	−0.160959	−	0.0585843i
$498$	−18.2275	+	5.19521i	−0.0366014	+	0.0104321i
$499$	125.900	−	150.042i	0.252305	−	0.300685i	−0.624994	−	0.780629i	$-0.714899\pi$
$499$	125.900	−	150.042i	0.252305	−	0.300685i	0.877299	+	0.479944i	$0.159343\pi$
$500$	84.6779	+	156.301i	0.169356	+	0.312602i
$501$	−504.363	−	331.493i	−1.00671	−	0.661663i
$502$	−351.971	+	590.990i	−0.701138	+	1.17727i
$503$	574.162	+	331.493i	1.14148	+	0.659031i	0.946796	−	0.321836i	$-0.104300\pi$
$503$	574.162	+	331.493i	1.14148	+	0.659031i	0.194680	+	0.980867i	$0.437633\pi$
$504$	−600.036	−	94.5984i	−1.19055	−	0.187695i
$505$	−313.429	−	542.875i	−0.620652	−	1.07500i
$506$	−9.68591	+	714.724i	−0.0191421	+	1.41250i
$507$	−260.434	−	245.549i	−0.513677	−	0.484318i
$508$	−3.40304	+	125.532i	−0.00669890	+	0.247111i
$509$	−78.9247	+	447.604i	−0.155058	+	0.879379i	0.803674	+	0.595070i	$0.202876\pi$
$509$	−78.9247	+	447.604i	−0.155058	+	0.879379i	−0.958732	+	0.284310i	$0.908236\pi$
$510$	−801.630	−	542.568i	−1.57182	−	1.06386i
$511$	−141.250	−	168.335i	−0.276418	−	0.329423i
$512$	−62.2889	+	508.197i	−0.121658	+	0.992572i
$513$	537.168	+	449.858i	1.04711	+	0.876916i
$514$	820.157	+	156.104i	1.59564	+	0.303704i
$515$	−851.603	−	1014.90i	−1.65360	−	1.97068i
$516$	192.319	+	51.0565i	0.372712	+	0.0989468i
$517$	−15.8807	+	90.0639i	−0.0307170	+	0.174205i
$518$	−32.5798	−	200.631i	−0.0628954	−	0.387318i
$519$	418.893	−	125.555i	0.807116	−	0.241917i
$520$	−160.244	+	390.147i	−0.308161	+	0.750282i
$521$	−26.7799	−	46.3841i	−0.0514009	−	0.0890290i	0.839180	−	0.543854i	$-0.183035\pi$
$521$	−26.7799	−	46.3841i	−0.0514009	−	0.0890290i	−0.890581	+	0.454825i	$0.849702\pi$
$522$	123.185	+	94.2034i	0.235986	+	0.180466i
$523$	306.031	+	176.687i	0.585146	+	0.337834i	0.763176	−	0.646191i	$-0.223639\pi$
$523$	306.031	+	176.687i	0.585146	+	0.337834i	−0.178030	+	0.984025i	$0.556972\pi$
$524$	19.9078	−	22.4599i	0.0379920	−	0.0428624i
$525$	45.2852	−	781.836i	0.0862576	−	1.48921i
$526$	571.154	−	466.213i	1.08584	−	0.886337i
$527$	−158.219	+	188.558i	−0.300226	+	0.357795i
$528$	305.690	−	290.895i	0.578958	−	0.550937i
$529$	1055.95	+	384.333i	1.99612	+	0.726527i
$530$	61.7458	−	71.5928i	0.116502	−	0.135081i
$531$	−444.362	+	26.1671i	−0.836839	+	0.0492789i
$532$	128.645	+	866.247i	0.241814	+	1.62828i
$533$	−91.6246	−	519.629i	−0.171903	−	0.974913i
$534$	−277.497	+	28.7187i	−0.519658	+	0.0537804i
$535$	−152.693	−	419.522i	−0.285408	−	0.784153i
$536$	−371.672	−	338.543i	−0.693418	−	0.631610i
$537$	118.370	−	13.8740i	0.220429	−	0.0258361i
$538$	44.0471	−	24.6409i	0.0818719	−	0.0458009i
$539$			194.982i			0.361747i
$540$	798.900	−	119.429i	1.47945	−	0.221165i
$541$	236.717			0.437555			0.218778	−	0.975775i	$-0.429793\pi$
$541$	236.717			0.437555			0.218778	+	0.975775i	$0.429793\pi$
$542$	272.088	+	486.374i	0.502007	+	0.897369i
$543$	387.108	+	166.835i	0.712907	+	0.307247i
$544$	619.757	−	303.856i	1.13926	−	0.558558i
$545$	212.161	−	77.2202i	0.389286	−	0.141688i
$546$	289.007	−	209.272i	0.529317	−	0.383283i
$547$	−156.833	+	27.6540i	−0.286716	+	0.0505557i	−0.315156	−	0.949040i	$-0.602057\pi$
$547$	−156.833	+	27.6540i	−0.286716	+	0.0505557i	0.0284407	+	0.999595i	$0.490946\pi$
$548$	−46.1274	−	310.605i	−0.0841742	−	0.566798i
$549$	31.1292	+	3.61824i	0.0567016	+	0.00659061i
$550$	411.976	+	355.313i	0.749048	+	0.646023i
$551$	76.4659	−	210.088i	0.138777	−	0.381286i
$552$	−402.374	−	888.852i	−0.728939	−	1.61024i
$553$	−620.023	−	520.261i	−1.12120	−	0.940798i
$554$	−366.735	−	449.284i	−0.661976	−	0.810982i
$555$	121.384	+	241.502i	0.218710	+	0.435139i
$556$	544.297	−	614.074i	0.978951	−	1.10445i
$557$	−370.379	+	641.515i	−0.664953	+	1.15173i	0.314345	+	0.949309i	$0.398215\pi$
$557$	−370.379	+	641.515i	−0.664953	+	1.15173i	−0.979298	+	0.202424i	$0.935118\pi$
$558$	−9.29516	−	205.197i	−0.0166580	−	0.367736i
$559$	−101.224	+	58.4415i	−0.181080	+	0.104547i
$560$	845.736	+	551.448i	1.51024	+	0.984728i
$561$	−553.585	−	131.015i	−0.986783	−	0.233538i
$562$	469.533	−	76.2460i	0.835467	−	0.135669i
$563$	−31.0725	−	5.47892i	−0.0551909	−	0.00973165i	0.145985	−	0.989287i	$-0.453365\pi$
$563$	−31.0725	−	5.47892i	−0.0551909	−	0.00973165i	−0.201175	+	0.979555i	$0.564476\pi$
$564$	−32.5874	−	120.505i	−0.0577791	−	0.213661i
$565$	−909.990	+	763.572i	−1.61060	+	1.35146i
$566$	56.0952	−	294.720i	0.0991082	−	0.520707i
$567$	−627.836	−	269.867i	−1.10729	−	0.475957i
$568$	−43.1696	+	68.2104i	−0.0760028	+	0.120089i
$569$	−437.692	+	367.267i	−0.769231	+	0.645461i	−0.940512	−	0.339761i	$-0.889654\pi$
$569$	−437.692	+	367.267i	−0.769231	+	0.645461i	0.171281	+	0.985222i	$0.445209\pi$
$570$	−508.840	−	1047.51i	−0.892701	−	1.83774i
$571$	419.235	+	73.9224i	0.734212	+	0.129461i	0.528238	−	0.849096i	$-0.322853\pi$
$571$	419.235	+	73.9224i	0.734212	+	0.129461i	0.205974	+	0.978558i	$0.433964\pi$
$572$	−6.71711	+	247.783i	−0.0117432	+	0.433186i
$573$	719.645	+	170.315i	1.25593	+	0.297235i
$574$	−1262.95	−	17.1155i	−2.20027	−	0.0298179i
$575$	1089.37	−	628.947i	1.89455	−	1.09382i
$576$	−209.125	+	536.696i	−0.363064	+	0.931764i
$577$	−204.459	+	354.133i	−0.354348	+	0.613750i	−0.987006	−	0.160682i	$-0.948631\pi$
$577$	−204.459	+	354.133i	−0.354348	+	0.613750i	0.632658	+	0.774432i	$0.281964\pi$
$578$	−302.876	−	180.381i	−0.524007	−	0.312079i
$579$	132.491	+	263.601i	0.228827	+	0.455269i
$580$	−122.780	−	226.630i	−0.211689	−	0.390742i
$581$	−20.4158	−	17.1309i	−0.0351391	−	0.0294852i
$582$	−39.0929	+	40.3529i	−0.0671699	+	0.0693348i
$583$	19.0031	−	52.2106i	0.0325954	−	0.0895551i
$584$	−184.538	+	96.7646i	−0.315990	+	0.165693i
$585$	−283.105	+	380.785i	−0.483939	+	0.650914i
$586$	−252.554	−	724.278i	−0.430980	−	1.23597i
$587$	643.104	−	113.397i	1.09558	−	0.193180i	0.403483	−	0.914987i	$-0.367799\pi$
$587$	643.104	−	113.397i	1.09558	−	0.193180i	0.692094	+	0.721807i	$0.256688\pi$
$588$	−113.036	−	240.953i	−0.192238	−	0.409785i
$589$	−278.273	+	101.283i	−0.472450	+	0.171958i
$590$	691.739	+	262.441i	1.17244	+	0.444816i
$591$	−517.561	−	223.057i	−0.875737	−	0.377423i
$592$	−192.453	−	10.4420i	−0.325089	−	0.0176386i
$593$	137.532			0.231926			0.115963	−	0.993254i	$-0.463005\pi$
$593$	137.532			0.231926			0.115963	+	0.993254i	$0.463005\pi$
$594$	414.080	−	232.169i	0.697105	−	0.390856i
$595$		−	1361.11i		−	2.28758i
$596$	−631.311	+	210.586i	−1.05925	+	0.353333i
$597$	247.967	−	29.0638i	0.415356	−	0.0486831i
$598$	535.856	+	203.300i	0.896080	+	0.339967i
$599$	265.829	+	730.360i	0.443788	+	1.21930i	0.936982	+	0.349379i	$0.113607\pi$
$599$	265.829	+	730.360i	0.443788	+	1.21930i	−0.493193	+	0.869920i	$0.664170\pi$
$600$	−715.093	−	200.253i	−1.19182	−	0.333755i
$601$	−113.696	−	644.800i	−0.189177	−	1.07288i	−0.920470	−	0.390814i	$-0.872194\pi$
$601$	−113.696	−	644.800i	−0.189177	−	1.07288i	0.731292	−	0.682064i	$-0.238918\pi$
$602$	92.1234	+	264.192i	0.153029	+	0.438858i
$603$	−311.098	−	472.342i	−0.515917	−	0.783319i
$604$	−220.736	−	278.030i	−0.365458	−	0.460314i
$605$	−307.240	−	111.826i	−0.507835	−	0.184837i
$606$	487.734	+	122.432i	0.804842	+	0.202034i
$607$	−370.617	+	441.684i	−0.610572	+	0.727651i	−0.979419	−	0.201839i	$-0.935308\pi$
$607$	−370.617	+	441.684i	−0.610572	+	0.727651i	0.368847	+	0.929490i	$0.379753\pi$
$608$	828.504	+	56.2219i	1.36267	+	0.0924703i
$609$	−12.6091	+	217.693i	−0.0207046	+	0.357460i
$610$	−44.7524	−	26.6529i	−0.0733647	−	0.0436932i
$611$	63.5040	+	36.6641i	0.103935	+	0.0600067i
$612$	760.059	−	159.023i	1.24193	−	0.259842i
$613$	−129.453	−	224.220i	−0.211180	−	0.365775i	0.740904	−	0.671611i	$-0.234397\pi$
$613$	−129.453	−	224.220i	−0.211180	−	0.365775i	−0.952084	+	0.305836i	$0.901064\pi$
$614$	−599.983	−	8.13095i	−0.977172	−	0.0132426i
$615$	1608.90	−	482.236i	2.61610	−	0.784123i
$616$	579.672	+	126.699i	0.941026	+	0.205680i
$617$	7.16997	−	40.6629i	0.0116207	−	0.0659043i	−0.978446	−	0.206503i	$-0.933792\pi$
$617$	7.16997	−	40.6629i	0.0116207	−	0.0659043i	0.990067	+	0.140599i	$0.0449028\pi$
$618$	1060.09	+	75.8283i	1.71536	+	0.122700i
$619$	333.769	+	397.771i	0.539207	+	0.642602i	0.965010	−	0.262214i	$-0.0844527\pi$
$619$	333.769	+	397.771i	0.539207	+	0.642602i	−0.425803	+	0.904816i	$0.640008\pi$
$620$	−125.419	+	317.535i	−0.202288	+	0.512153i
$621$	−191.644	−	1080.79i	−0.308606	−	1.74040i
$622$	53.3746	−	280.426i	0.0858112	−	0.450846i
$623$	−252.153	−	300.505i	−0.404741	−	0.482351i
$624$	−135.345	−	310.097i	−0.216899	−	0.496951i
$625$	−76.6049	+	434.448i	−0.122568	+	0.695117i
$626$	−841.218	+	136.603i	−1.34380	+	0.218215i
$627$	−497.969	−	469.508i	−0.794208	−	0.748816i
$628$	−191.015	+	934.457i	−0.304164	+	1.48799i
$629$	129.915	+	225.020i	0.206543	+	0.357743i
$630$	768.730	+	836.173i	1.22021	+	1.32726i
$631$	280.028	+	161.674i	0.443785	+	0.256219i	0.705202	−	0.709007i	$-0.250856\pi$
$631$	280.028	+	161.674i	0.443785	+	0.256219i	−0.261417	+	0.965226i	$0.584190\pi$
$632$	−607.489	+	469.025i	−0.961217	+	0.742129i
$633$	−588.842	−	387.017i	−0.930240	−	0.611402i
$634$	−168.087	−	205.921i	−0.265121	−	0.324797i
$635$	150.935	−	179.878i	0.237693	−	0.283272i
$636$	6.78429	+	75.5371i	0.0106671	+	0.118769i
$637$	146.910	+	53.4709i	0.230628	+	0.0839417i
$638$	−114.710	−	98.9325i	−0.179796	−	0.155067i
$639$	−66.0156	+	62.3626i	−0.103311	+	0.0975940i
$640$	682.080	−	671.802i	1.06575	−	1.04969i
$641$	32.4513	+	184.041i	0.0506261	+	0.287115i	0.999601	−	0.0282358i	$-0.00898893\pi$
$641$	32.4513	+	184.041i	0.0506261	+	0.287115i	−0.948975	+	0.315351i	$0.897878\pi$
$642$	326.944	+	146.190i	0.509258	+	0.227710i
$643$	246.361	+	676.870i	0.383143	+	1.05268i	0.970025	+	0.243004i	$0.0781327\pi$
$643$	246.361	+	676.870i	0.383143	+	1.05268i	−0.586883	+	0.809672i	$0.699645\pi$
$644$	717.915	−	1169.11i	1.11478	−	1.81539i
$645$	−222.278	−	298.372i	−0.344617	−	0.462592i
$646$	−546.557	−	977.004i	−0.846063	−	1.51239i
$647$			587.092i			0.907407i	0.891153	+	0.453704i	$0.149897\pi$
$647$			587.092i			0.907407i	−0.891153	+	0.453704i	$0.850103\pi$
$648$	−377.116	+	526.961i	−0.581968	+	0.813211i
$649$	434.806			0.669963
$650$	380.690	−	212.966i	0.585677	−	0.327640i
$651$	231.621	−	172.551i	0.355793	−	0.265055i
$652$	1003.85	+	616.432i	1.53964	+	0.945448i
$653$	1192.96	−	434.201i	1.82689	−	0.664933i	0.833172	−	0.553014i	$-0.186523\pi$
$653$	1192.96	−	434.201i	1.82689	−	0.664933i	0.993717	−	0.111919i	$-0.0356997\pi$
$654$	−73.9312	+	165.342i	−0.113045	+	0.252817i
$655$	−55.2670	+	9.74506i	−0.0843771	+	0.0148780i
$656$	−271.572	+	1166.48i	−0.413981	+	1.77818i
$657$	−228.062	+	54.2062i	−0.347127	+	0.0825057i
$658$	114.642	−	132.924i	0.174227	−	0.202012i
$659$	305.078	−	838.196i	0.462942	−	1.27192i	−0.460321	−	0.887752i	$-0.652266\pi$
$659$	305.078	−	838.196i	0.462942	−	1.27192i	0.923263	−	0.384169i	$-0.125512\pi$
$660$	−785.876	+	70.5827i	−1.19072	+	0.106943i
$661$	975.618	+	818.640i	1.47597	+	1.23849i	0.910360	+	0.413816i	$0.135804\pi$
$661$	975.618	+	818.640i	1.47597	+	1.23849i	0.565612	+	0.824672i	$0.308640\pi$
$662$	122.924	−	100.339i	0.185686	−	0.151569i
$663$	−250.526	+	381.173i	−0.377868	+	0.574921i
$664$	−20.0031	+	15.4438i	−0.0301251	+	0.0232588i
$665$	818.761	−	1418.14i	1.23122	−	2.13253i
$666$	−206.899	−	64.8633i	−0.310659	−	0.0973923i
$667$	−303.322	+	175.123i	−0.454755	+	0.262553i
$668$	−788.427	−	161.165i	−1.18028	−	0.241265i
$669$	444.378	−	471.316i	0.664242	−	0.704508i
$670$	150.680	+	927.904i	0.224895	+	1.38493i
$671$	−30.1467	−	5.31568i	−0.0449280	−	0.00792203i
$672$	−789.794	+	179.479i	−1.17529	+	0.267082i
$673$	−905.630	+	759.913i	−1.34566	+	1.12914i	−0.365528	+	0.930800i	$0.619111\pi$
$673$	−905.630	+	759.913i	−1.34566	+	1.12914i	−0.980133	+	0.198343i	$0.936444\pi$
$674$	−1062.48	−	202.225i	−1.57637	−	0.300037i
$675$	−723.904	−	417.018i	−1.07245	−	0.617804i
$676$	−443.883	−	175.323i	−0.656631	−	0.259354i
$677$	−684.951	+	574.742i	−1.01174	+	0.848954i	−0.988568	−	0.150777i	$-0.951822\pi$
$677$	−684.951	+	574.742i	−1.01174	+	0.848954i	−0.0231764	+	0.999731i	$0.507378\pi$
$678$	67.9899	−	950.512i	0.100280	−	1.40193i
$679$	−77.8013	−	13.7185i	−0.114582	−	0.0202039i
$680$	−1260.88	−	275.590i	−1.85423	−	0.405280i
$681$	−294.479	−	982.483i	−0.432422	−	1.44271i
$682$	−2.71885	+	200.624i	−0.00398658	+	0.294170i
$683$	−1053.67	+	608.338i	−1.54271	+	0.890684i	−0.544044	+	0.839056i	$0.683108\pi$
$683$	−1053.67	+	608.338i	−1.54271	+	0.890684i	−0.998666	+	0.0516281i	$0.983559\pi$
$684$	887.562	+	291.520i	1.29761	+	0.426199i
$685$	−293.579	+	508.493i	−0.428582	+	0.742325i
$686$	−231.572	+	388.829i	−0.337568	+	0.566806i
$687$	490.558	+	28.4139i	0.714058	+	0.0413594i
$688$	263.390	−	31.8471i	0.382834	−	0.0462894i
$689$	−34.1270	−	28.6360i	−0.0495312	−	0.0415616i
$690$	−444.183	+	1769.49i	−0.643744	+	2.56448i
$691$	72.9278	−	200.368i	0.105540	−	0.289968i	−0.875671	−	0.482908i	$-0.839580\pi$
$691$	72.9278	−	200.368i	0.105540	−	0.289968i	0.981210	+	0.192941i	$0.0618026\pi$
$692$	456.652	−	362.550i	0.659902	−	0.523917i
$693$	596.715	+	299.203i	0.861061	+	0.431750i
$694$	−200.070	+	69.7640i	−0.288285	+	0.100524i
$695$	−1511.05	+	266.439i	−2.17417	+	0.383365i
$696$	199.109	+	55.7580i	0.286076	+	0.0801120i
$697$	1517.24	−	552.231i	2.17682	−	0.792297i
$698$	−2.42125	+	6.38190i	−0.00346884	+	0.00914313i
$699$	135.277	+	1154.15i	0.193529	+	1.65115i
$700$	−330.415	−	990.540i	−0.472021	−	1.41506i
$701$	−752.666			−1.07370			−0.536851	−	0.843677i	$-0.680386\pi$
$701$	−752.666			−1.07370			−0.536851	+	0.843677i	$0.680386\pi$
$702$	−61.3732	−	375.660i	−0.0874262	−	0.535128i
$703$			312.597i			0.444662i
$704$	234.738	−	511.332i	0.333435	−	0.726323i
$705$	−92.3845	+	214.360i	−0.131042	+	0.304057i
$706$	237.877	−	626.993i	0.336936	−	0.888092i
$707$	241.841	+	664.452i	0.342066	+	0.939819i
$708$	−537.321	+	252.068i	−0.758929	+	0.356028i
$709$	−31.4335	−	178.268i	−0.0443350	−	0.251436i	0.954583	−	0.297946i	$-0.0963014\pi$
$709$	−31.4335	−	178.268i	−0.0443350	−	0.251436i	−0.998918	+	0.0465093i	$0.985190\pi$
$710$	142.525	−	49.6982i	0.200739	−	0.0699974i
$711$	−792.583	+	342.490i	−1.11474	+	0.481702i
$712$	−329.431	+	172.740i	−0.462683	+	0.242613i
$713$	435.941	+	158.670i	0.611418	+	0.222538i
$714$	784.224	+	759.737i	1.09835	+	1.06406i
$715$	297.924	−	355.052i	0.416677	−	0.496577i
$716$	139.720	−	75.6952i	0.195140	−	0.105720i
$717$	279.647	−	140.556i	0.390024	−	0.196034i
$718$	−19.2966	+	32.4007i	−0.0268755	+	0.0451263i
$719$	−237.329	−	137.022i	−0.330082	−	0.190573i	0.325796	−	0.945440i	$-0.394368\pi$
$719$	−237.329	−	137.022i	−0.330082	−	0.190573i	−0.655877	+	0.754867i	$0.727701\pi$
$720$	930.247	−	542.817i	1.29201	−	0.753912i
$721$	747.219	+	1294.22i	1.03637	+	1.79504i
$722$	8.46699	−	624.780i	0.0117271	−	0.865346i
$723$	−287.141	+	1213.28i	−0.397152	+	1.67811i
$724$	561.832	+	15.2307i	0.776012	+	0.0210368i
$725$	−46.2902	+	262.525i	−0.0638486	+	0.362104i
$726$	235.924	−	114.603i	0.324965	−	0.157855i
$727$	861.552	+	1026.76i	1.18508	+	1.41232i	0.889458	+	0.457016i	$0.151082\pi$
$727$	861.552	+	1026.76i	1.18508	+	1.41232i	0.295620	+	0.955306i	$0.404474\pi$
$728$	254.428	−	402.011i	0.349490	−	0.552213i
$729$	−557.544	+	469.666i	−0.764806	+	0.644260i
$730$	382.750	+	72.8502i	0.524314	+	0.0997947i
$731$	−229.904	−	273.989i	−0.314506	−	0.374814i
$732$	40.3362	−	10.9078i	0.0551040	−	0.0149014i
$733$	111.781	−	633.939i	0.152497	−	0.864856i	−0.808541	−	0.588440i	$-0.799742\pi$
$733$	111.781	−	633.939i	0.152497	−	0.864856i	0.961038	−	0.276416i	$-0.0891466\pi$
$734$	−160.606	−	989.030i	−0.218809	−	1.34745i
$735$	−114.613	+	484.284i	−0.155937	+	0.658890i
$736$	−937.657	−	901.764i	−1.27399	−	1.22522i
$737$	276.233	+	478.450i	0.374808	+	0.649186i
$738$	−620.201	+	1196.17i	−0.840381	+	1.62082i
$739$	−879.867	−	507.991i	−1.19062	−	0.687404i	−0.232171	−	0.972675i	$-0.574583\pi$
$739$	−879.867	−	507.991i	−1.19062	−	0.687404i	−0.958447	+	0.285271i	$0.907916\pi$
$740$	269.695	+	239.049i	0.364452	+	0.323040i
$741$	−490.313	+	246.441i	−0.661691	+	0.332580i
$742$	−82.6142	+	67.4351i	−0.111340	+	0.0908829i
$743$	−826.037	+	984.432i	−1.11176	+	1.32494i	−0.171229	+	0.985231i	$0.554774\pi$
$743$	−826.037	+	984.432i	−1.11176	+	1.32494i	−0.940530	+	0.339711i	$0.889671\pi$
$744$	−112.947	−	249.502i	−0.151810	−	0.335352i
$745$	1169.36	+	425.611i	1.56961	+	0.571290i
$746$	543.621	−	630.315i	0.728714	−	0.844927i
$747$	−26.0978	+	11.2773i	−0.0349368	+	0.0150969i
$748$	−750.275	+	111.422i	−1.00304	+	0.148960i
$749$	87.4475	+	495.939i	0.116752	+	0.662135i
$750$	156.387	+	215.972i	0.208516	+	0.287962i
$751$	−80.9863	−	222.508i	−0.107838	−	0.296282i	0.874023	−	0.485884i	$-0.161502\pi$
$751$	−80.9863	−	222.508i	−0.107838	−	0.296282i	−0.981861	+	0.189602i	$0.939280\pi$
$752$	−99.9235	−	133.113i	−0.132877	−	0.177012i
$753$	−408.368	+	947.539i	−0.542321	+	1.25835i
$754$	−105.999	+	59.2979i	−0.140582	+	0.0786444i
$755$			663.799i			0.879204i
$756$	−910.860	−	23.8156i	−1.20484	−	0.0315021i
$757$	−1103.11			−1.45721			−0.728607	−	0.684932i	$-0.759832\pi$
$757$	−1103.11			−1.45721			−0.728607	+	0.684932i	$0.759832\pi$
$758$	217.190	+	388.240i	0.286530	+	0.512190i
$759$	124.814	+	1064.89i	0.164446	+	1.40302i
$760$	−1147.93	−	1045.60i	−1.51043	−	1.37580i
$761$	292.651	−	106.516i	0.384561	−	0.139969i	−0.142503	−	0.989794i	$-0.545515\pi$
$761$	292.651	−	106.516i	0.384561	−	0.139969i	0.527064	+	0.849826i	$0.323293\pi$
$762$	19.3910	+	187.367i	0.0254475	+	0.245888i
$763$	−250.806	+	44.2240i	−0.328711	+	0.0579606i
$764$	975.336	−	144.845i	1.27662	−	0.189588i
$765$	−1297.95	−	650.813i	−1.69667	−	0.850735i
$766$	−214.339	−	184.859i	−0.279816	−	0.241330i
$767$	119.239	−	327.606i	0.155462	−	0.427127i
$768$	6.34889	+	767.974i	0.00826679	+	0.999966i
$769$	−1069.85	−	897.707i	−1.39122	−	1.16737i	−0.964844	−	0.262822i	$-0.915347\pi$
$769$	−1069.85	−	897.707i	−1.39122	−	1.16737i	−0.426372	−	0.904548i	$-0.640209\pi$
$770$	−701.585	−	859.506i	−0.911149	−	1.11624i
$771$	1250.23	+	72.4151i	1.62156	+	0.0939237i
$772$	294.373	+	260.923i	0.381312	+	0.337984i
$773$	340.293	−	589.405i	0.440224	−	0.762490i	−0.557482	−	0.830189i	$-0.688233\pi$
$773$	340.293	−	589.405i	0.440224	−	0.762490i	0.997706	+	0.0676993i	$0.0215658\pi$
$774$	295.982	+	38.4746i	0.382405	+	0.0497088i
$775$	305.787	−	176.546i	0.394564	−	0.227802i
$776$	−28.4611	+	69.2944i	−0.0366766	+	0.0892969i
$777$	−87.5365	−	292.051i	−0.112660	−	0.375871i
$778$	−1029.81	+	167.228i	−1.32367	+	0.214946i
$779$	1913.00	+	337.313i	2.45571	+	0.433008i
$780$	−162.334	+	611.479i	−0.208121	+	0.783947i
$781$	67.9537	−	57.0199i	0.0870085	−	0.0730088i
$782$	−327.918	+	1722.86i	−0.419333	+	2.20314i
$783$	201.562	+	116.114i	0.257423	+	0.148293i
$784$	−259.086	−	242.496i	−0.330467	−	0.309307i
$785$	1366.19	−	1146.37i	1.74037	−	1.46034i
$786$	25.2339	−	37.2824i	0.0321042	−	0.0474331i
$787$	−937.426	−	165.293i	−1.19114	−	0.210030i	−0.457274	−	0.889326i	$-0.651174\pi$
$787$	−937.426	−	165.293i	−1.19114	−	0.210030i	−0.733864	+	0.679296i	$0.762285\pi$
$788$	−751.165	−	20.3633i	−0.953256	−	0.0258417i
$789$	758.664	−	804.653i	0.961551	−	1.01984i
$790$	1434.95	+	19.4464i	1.81639	+	0.0246156i
$791$	1160.44	−	669.978i	1.46705	−	0.847002i
$792$	397.989	−	492.192i	0.502512	−	0.621455i
$793$	−12.2724	+	21.2564i	−0.0154759	+	0.0268051i
$794$	613.421	+	365.330i	0.772571	+	0.460114i
$795$	77.8890	−	118.507i	0.0979736	−	0.149066i
$796$	292.693	−	158.570i	0.367704	−	0.199208i
$797$	−156.894	−	131.650i	−0.196856	−	0.165182i	0.539031	−	0.842286i	$-0.318790\pi$
$797$	−156.894	−	131.650i	−0.196856	−	0.165182i	−0.735888	+	0.677104i	$0.763235\pi$
$798$	360.069	+	1263.31i	0.451214	+	1.58309i
$799$	−76.7449	+	210.855i	−0.0960512	+	0.263899i
$800$	−984.498	+	105.523i	−1.23062	+	0.131904i
$801$	−407.127	+	96.7668i	−0.508274	+	0.120807i
$802$	−197.514	−	566.431i	−0.246276	−	0.706273i
$803$	225.499	−	39.7616i	0.280821	−	0.0495163i
$804$	−618.732	−	431.117i	−0.769567	−	0.536215i
$805$	−2410.62	+	877.395i	−2.99456	+	1.08993i
$806$	150.415	+	57.0667i	0.186620	+	0.0708023i
$807$	60.7114	−	45.2282i	0.0752309	−	0.0560449i
$808$	664.489	−	89.4968i	0.822387	−	0.110763i
$809$	565.028			0.698428			0.349214	−	0.937043i	$-0.386449\pi$
$809$	565.028			0.698428			0.349214	+	0.937043i	$0.386449\pi$
$810$	1164.94	−	333.243i	1.43820	−	0.411412i
$811$		−	742.162i		−	0.915120i	−0.889179	−	0.457560i	$-0.848724\pi$
$811$		−	742.162i		−	0.915120i	0.889179	−	0.457560i	$-0.151276\pi$
$812$	92.0000	+	275.804i	0.113300	+	0.339660i
$813$	499.416	+	670.384i	0.614288	+	0.824580i
$814$	198.025	+	75.1295i	0.243274	+	0.0922967i
$815$	−753.368	−	2069.86i	−0.924378	−	2.53971i
$816$	862.576	−	572.646i	1.05708	−	0.701772i
$817$	−74.7212	−	423.765i	−0.0914580	−	0.518684i
$818$	−6.62402	−	18.9964i	−0.00809782	−	0.0232230i
$819$	389.076	−	367.546i	0.475062	−	0.448774i
$820$	1753.93	−	1392.50i	2.13894	−	1.69817i
$821$	1020.73	+	371.514i	1.24327	+	0.452514i	0.878123	−	0.478435i	$-0.158796\pi$
$821$	1020.73	+	371.514i	1.24327	+	0.452514i	0.365150	+	0.930949i	$0.381018\pi$
$822$	−129.108	−	452.978i	−0.157065	−	0.551068i
$823$	−516.425	+	615.451i	−0.627491	+	0.747814i	−0.982339	−	0.187109i	$-0.940088\pi$
$823$	−516.425	+	615.451i	−0.627491	+	0.747814i	0.354848	+	0.934924i	$0.384533\pi$
$824$	1350.21	−	430.147i	1.63860	−	0.522023i
$825$	681.943	+	448.207i	0.826597	+	0.543282i
$826$	−717.021	−	427.030i	−0.868064	−	0.516986i
$827$	−426.666	−	246.336i	−0.515921	−	0.297867i	0.219343	−	0.975648i	$-0.429609\pi$
$827$	−426.666	−	246.336i	−0.515921	−	0.297867i	−0.735264	+	0.677781i	$0.762942\pi$
$828$	−771.589	−	1243.61i	−0.931871	−	1.50194i
$829$	−376.230	−	651.649i	−0.453836	−	0.786067i	0.544784	−	0.838576i	$-0.316611\pi$
$829$	−376.230	−	651.649i	−0.453836	−	0.786067i	−0.998620	+	0.0525092i	$0.983278\pi$
$830$	47.2493	+	0.640320i	0.0569268	+	0.000771470i
$831$	−632.960	−	596.783i	−0.761684	−	0.718151i
$832$	−320.892	−	317.090i	−0.385687	−	0.381117i
$833$	−83.0736	+	471.134i	−0.0997282	+	0.565587i
$834$	689.917	−	1019.33i	0.827239	−	1.22222i
$835$	967.222	+	1152.69i	1.15835	+	1.38047i
$836$	−848.734	−	335.230i	−1.01523	−	0.400993i
$837$	−53.7948	−	303.378i	−0.0642709	−	0.362459i
$838$	−116.694	+	613.100i	−0.139253	+	0.731623i
$839$	8.75774	+	10.4371i	0.0104383	+	0.0124399i	0.771238	−	0.636546i	$-0.219638\pi$
$839$	8.75774	+	10.4371i	0.0104383	+	0.0124399i	−0.760800	+	0.648986i	$0.775193\pi$
$840$	1365.28	+	655.428i	1.62533	+	0.780271i
$841$	−133.149	+	755.126i	−0.158322	+	0.897891i
$842$	960.817	−	156.024i	1.14111	−	0.185302i
$843$	683.483	−	204.860i	0.810775	−	0.243013i
$844$	−920.486	−	188.159i	−1.09062	−	0.222937i
$845$	446.197	+	772.836i	0.528044	+	0.914598i
$846$	−71.9402	−	172.879i	−0.0850357	−	0.204349i
$847$	319.397	+	184.404i	0.377092	+	0.217714i
$848$	45.7419	+	90.1845i	0.0539410	+	0.106350i
$849$	26.0221	−	449.264i	0.0306503	−	0.529168i
$850$	844.073	+	1034.07i	0.993027	+	1.21655i
$851$	314.781	−	375.142i	0.369896	−	0.440825i
$852$	−50.9194	+	109.858i	−0.0597646	+	0.128941i
$853$	−715.954	−	260.586i	−0.839336	−	0.305493i	−0.113651	−	0.993521i	$-0.536255\pi$
$853$	−715.954	−	260.586i	−0.839336	−	0.305493i	−0.725685	+	0.688027i	$0.758477\pi$
$854$	44.4931	+	38.3735i	0.0520997	+	0.0449338i
$855$	−960.840	−	1458.85i	−1.12379	−	1.70625i
$856$	477.124	+	19.4074i	0.557388	+	0.0226722i
$857$	−43.4809	−	246.593i	−0.0507362	−	0.287739i	0.948874	−	0.315655i	$-0.102224\pi$
$857$	−43.4809	−	246.593i	−0.0507362	−	0.287739i	−0.999610	+	0.0279155i	$0.991113\pi$
$858$	38.2749	+	369.835i	0.0446095	+	0.431043i
$859$	178.854	+	491.397i	0.208212	+	0.572057i	0.999209	−	0.0397626i	$-0.0126602\pi$
$859$	178.854	+	491.397i	0.208212	+	0.572057i	−0.790998	+	0.611819i	$0.790438\pi$
$860$	−422.746	−	259.595i	−0.491565	−	0.301855i
$861$	−1881.72	+	220.554i	−2.18551	+	0.256160i
$862$	236.011	+	421.884i	0.273795	+	0.489425i
$863$		−	12.2958i		−	0.0142478i	−0.999975	−	0.00712388i	$-0.997732\pi$
$863$		−	12.2958i		−	0.0142478i	0.999975	−	0.00712388i	$-0.00226762\pi$
$864$	−206.488	+	838.963i	−0.238991	+	0.971022i
$865$	−1090.26			−1.26042
$866$	−887.670	+	496.582i	−1.02502	+	0.573420i
$867$	−485.603	−	209.284i	−0.560096	−	0.241389i
$868$	201.520	−	328.171i	0.232166	−	0.378077i
$869$	792.525	−	288.456i	0.911997	−	0.331940i
$870$	−226.755	−	313.151i	−0.260638	−	0.359943i
$871$	436.244	−	76.9215i	0.500854	−	0.0883140i
$872$	−9.81473	+	241.291i	−0.0112554	+	0.276710i
$873$	−50.2825	+	67.6316i	−0.0575974	+	0.0774704i
$874$	−1378.02	+	1597.79i	−1.57669	+	1.82813i
$875$	−128.237	+	352.329i	−0.146557	+	0.402661i
$876$	−255.615	+	179.864i	−0.291798	+	0.205324i
$877$	844.061	+	708.252i	0.962442	+	0.807585i	0.981349	−	0.192237i	$-0.0615742\pi$
$877$	844.061	+	708.252i	0.962442	+	0.807585i	−0.0189068	+	0.999821i	$0.506019\pi$
$878$	−59.0836	+	48.2279i	−0.0672934	+	0.0549293i
$879$	−516.705	−	1028.02i	−0.587833	−	1.16954i
$880$	−938.265	+	475.892i	−1.06621	+	0.540786i
$881$	321.472	−	556.806i	0.364894	−	0.632015i	−0.623865	−	0.781532i	$-0.714438\pi$
$881$	321.472	−	556.806i	0.364894	−	0.632015i	0.988759	+	0.149517i	$0.0477718\pi$
$882$	−215.053	−	336.351i	−0.243825	−	0.381351i
$883$	1133.10	−	654.193i	1.28323	−	0.740875i	0.305796	−	0.952097i	$-0.401078\pi$
$883$	1133.10	−	654.193i	1.28323	−	0.740875i	0.977438	+	0.211222i	$0.0677442\pi$
$884$	−121.800	+	595.854i	−0.137783	+	0.674043i
$885$	1079.94	+	255.586i	1.22028	+	0.288797i
$886$	−14.5505	−	89.6038i	−0.0164227	−	0.101133i
$887$	−1190.55	−	209.926i	−1.34222	−	0.236669i	−0.544024	−	0.839069i	$-0.683100\pi$
$887$	−1190.55	−	209.926i	−1.34222	−	0.236669i	−0.798194	+	0.602400i	$0.794211\pi$
$888$	−288.269	+	21.9572i	−0.324627	+	0.0247266i
$889$	−202.902	+	170.255i	−0.228236	+	0.191512i
$890$	683.269	+	130.049i	0.767718	+	0.146123i
$891$	570.637	−	425.962i	0.640446	−	0.478072i
$892$	317.287	−	803.307i	0.355703	−	0.900568i
$893$	−206.798	+	173.524i	−0.231577	+	0.194316i
$894$	−897.928	+	436.177i	−1.00439	+	0.487894i
$895$	−292.620	−	51.5968i	−0.326950	−	0.0576500i
$896$	−889.285	+	612.676i	−0.992505	+	0.683790i
$897$	836.578	+	197.989i	0.932640	+	0.220724i
$898$	3.37850	−	249.300i	0.00376225	−	0.277617i
$899$	−85.1428	+	49.1572i	−0.0947083	+	0.0546799i
$900$	−1102.56	−	158.543i	−1.22507	−	0.176159i
$901$	68.1619	−	118.060i	0.0756514	−	0.131032i
$902$	673.452	−	1130.78i	0.746621	−	1.25364i
$903$	188.477	+	374.988i	0.208723	+	0.415269i
$904$	−385.682	−	1210.64i	−0.426640	−	1.33920i
$905$	−805.060	−	675.526i	−0.889569	−	0.746437i
$906$	−382.458	−	370.516i	−0.422139	−	0.408958i
$907$	−32.1279	+	88.2708i	−0.0354222	+	0.0973217i	−0.956143	−	0.292900i	$-0.905380\pi$
$907$	−32.1279	+	88.2708i	−0.0354222	+	0.0973217i	0.920721	+	0.390222i	$0.127602\pi$
$908$	−850.335	−	1071.04i	−0.936493	−	1.17956i
$909$	749.255	+	87.0883i	0.824263	+	0.0958067i
$910$	−839.998	+	292.906i	−0.923075	+	0.321875i
$911$	344.152	−	60.6833i	0.377774	−	0.0666117i	0.0184627	−	0.999830i	$-0.494123\pi$
$911$	344.152	−	60.6833i	0.377774	−	0.0666117i	0.359311	+	0.933218i	$0.383012\pi$
$912$	1243.19	−	77.7647i	1.36314	−	0.0852683i
$913$	26.0959	−	9.49812i	0.0285826	−	0.0104032i
$914$	230.429	−	607.360i	0.252110	−	0.664508i
$915$	−71.7519	−	30.9235i	−0.0784174	−	0.0337962i
$916$	621.508	−	207.317i	0.678502	−	0.226328i
$917$	63.3028			0.0690325
$918$	1099.46	−	384.566i	1.19767	−	0.418917i
$919$			1567.18i			1.70531i	0.522473	+	0.852656i	$0.325009\pi$
$919$			1567.18i			1.70531i	−0.522473	+	0.852656i	$0.674991\pi$
$920$	324.693	+	2410.76i	0.352927	+	2.62039i
$921$	−893.938	+	104.777i	−0.970617	+	0.113764i
$922$	35.7003	−	94.0983i	0.0387205	−	0.102059i
$923$	−24.3266	−	66.8369i	−0.0263560	−	0.0724126i
$924$	886.825	+	75.5258i	0.959767	+	0.0817378i
$925$	−64.7230	−	367.062i	−0.0699708	−	0.396824i
$926$	−614.073	+	214.126i	−0.663145	+	0.231238i
$927$	1591.45	−	93.7154i	1.71677	−	0.101095i
$928$	274.122	−	29.3817i	0.295390	−	0.0316613i
$929$	−371.699	−	135.287i	−0.400106	−	0.145627i	0.134126	−	0.990964i	$-0.457177\pi$
$929$	−371.699	−	135.287i	−0.400106	−	0.145627i	−0.534233	+	0.845337i	$0.679399\pi$
$930$	−124.683	+	496.699i	−0.134068	+	0.534085i
$931$	−369.960	+	440.901i	−0.397379	+	0.473578i
$932$	738.057	+	1362.33i	0.791907	+	1.46172i
$933$	24.7600	−	427.474i	0.0265381	−	0.458172i
$934$	286.585	−	481.201i	0.306836	−	0.515205i
$935$	1228.28	+	709.146i	1.31367	+	0.758445i
$936$	−261.702	−	434.843i	−0.279596	−	0.464576i
$937$	−776.889	−	1345.61i	−0.829124	−	1.43608i	−0.898726	−	0.438510i	$-0.855506\pi$
$937$	−776.889	−	1345.61i	−0.829124	−	1.43608i	0.0696024	−	0.997575i	$-0.477827\pi$
$938$	14.3690	−	1060.29i	0.0153187	−	1.13037i
$939$	−1224.53	+	367.029i	−1.30408	+	0.390873i
$940$	−8.43394	+	311.113i	−0.00897227	+	0.330972i
$941$	64.8850	−	367.981i	0.0689533	−	0.391054i	−0.930726	−	0.365718i	$-0.880823\pi$
$941$	64.8850	−	367.981i	0.0689533	−	0.391054i	0.999679	−	0.0253356i	$-0.00806542\pi$
$942$	−102.075	+	1427.02i	−0.108360	+	1.51489i
$943$	−1956.08	−	2331.17i	−2.07432	−	2.47208i
$944$	−540.763	+	577.757i	−0.572842	+	0.612030i
$945$	1306.21	+	1093.90i	1.38223	+	1.15757i
$946$	−286.406	−	54.5128i	−0.302755	−	0.0576245i
$947$	297.973	+	355.111i	0.314650	+	0.374985i	0.900070	−	0.435745i	$-0.143515\pi$
$947$	297.973	+	355.111i	0.314650	+	0.374985i	−0.585421	+	0.810730i	$0.699071\pi$
$948$	−812.156	+	815.913i	−0.856705	+	0.860667i
$949$	31.8812	−	180.807i	0.0335945	−	0.190524i
$950$	257.405	+	1585.13i	0.270953	+	1.66856i
$951$	−290.106	−	273.525i	−0.305054	−	0.287619i
$952$	1346.68	+	553.117i	1.41458	+	0.581005i
$953$	381.259	+	660.360i	0.400062	+	0.692927i	0.993733	−	0.111780i	$-0.0356554\pi$
$953$	381.259	+	660.360i	0.400062	+	0.692927i	−0.593671	+	0.804708i	$0.702322\pi$
$954$	24.8041	+	111.025i	0.0260001	+	0.116378i
$955$	−1596.73	−	921.870i	−1.67196	−	0.965309i
$956$	276.807	−	312.292i	0.289547	−	0.326666i
$957$	−189.879	−	124.798i	−0.198410	−	0.130405i
$958$	−654.812	+	534.500i	−0.683520	+	0.557934i
$959$	425.726	−	507.360i	0.443927	−	0.529051i
$960$	883.597	−	1132.03i	0.920413	−	1.17920i
$961$	−780.675	−	284.143i	−0.812357	−	0.295674i
$962$	110.912	−	128.600i	0.115293	−	0.133680i
$963$	514.739	+	153.743i	0.534516	+	0.159650i
$964$	244.200	+	1644.36i	0.253320	+	1.70576i
$965$	−127.725	−	724.362i	−0.132357	−	0.750634i
$966$	840.025	−	1878.66i	0.869591	−	1.94478i
$967$	92.6954	+	254.678i	0.0958587	+	0.263370i	0.978349	−	0.206960i	$-0.0663571\pi$
$967$	92.6954	+	254.678i	0.0958587	+	0.263370i	−0.882491	+	0.470330i	$0.844135\pi$
$968$	235.495	−	258.540i	0.243280	−	0.267087i
$969$	−1003.20	−	1346.63i	−1.03530	−	1.38971i
$970$	122.245	−	68.3867i	0.126026	−	0.0705018i
$971$		−	1762.48i		−	1.81511i	−0.419929	−	0.907557i	$-0.637945\pi$
$971$		−	1762.48i		−	1.81511i	0.419929	−	0.907557i	$-0.362055\pi$
$972$	−458.237	+	857.206i	−0.471438	+	0.881899i
$973$	1730.75			1.77878
$974$	−859.589	−	1536.57i	−0.882535	−	1.57759i
$975$	524.717	−	390.899i	0.538171	−	0.400922i
$976$	44.5564	−	33.4470i	0.0456521	−	0.0342695i
$977$	−518.575	+	188.746i	−0.530783	+	0.193189i	−0.593488	−	0.804843i	$-0.702250\pi$
$977$	−518.575	+	188.746i	−0.530783	+	0.193189i	0.0627048	+	0.998032i	$0.480027\pi$
$978$	1613.09	+	721.281i	1.64938	+	0.737506i
$979$	402.552	−	70.9808i	0.411187	−	0.0725033i
$980$	97.4734	+	656.350i	0.0994627	+	0.669745i
$981$	−77.7510	+	260.314i	−0.0792569	+	0.265356i
$982$	108.113	+	93.2431i	0.110095	+	0.0949523i
$983$	−226.558	+	622.463i	−0.230476	+	0.633228i	−0.999985	−	0.00540752i	$-0.998279\pi$
$983$	−226.558	+	622.463i	−0.230476	+	0.633228i	0.769509	+	0.638636i	$0.220501\pi$
$984$	−176.690	+	1787.81i	−0.179563	+	1.81688i
$985$	1076.36	+	903.173i	1.09275	+	0.916927i
$986$	−235.022	−	287.923i	−0.238359	−	0.292011i
$987$	144.614	−	220.029i	0.146519	−	0.222927i
$988$	−485.333	+	547.551i	−0.491228	+	0.554202i
$989$	−337.054	+	583.795i	−0.340803	+	0.590288i
$990$	−1155.08	+	258.058i	−1.16675	+	0.260664i
$991$	664.876	−	383.866i	0.670914	−	0.387353i	−0.125509	−	0.992093i	$-0.540056\pi$
$991$	664.876	−	383.866i	0.670914	−	0.387353i	0.796423	+	0.604740i	$0.206723\pi$
$992$	−263.202	−	253.126i	−0.265324	−	0.255168i
$993$	163.280	−	173.178i	0.164431	−	0.174398i
$994$	−168.060	+	27.2907i	−0.169074	+	0.0274555i
$995$	−612.993	−	108.087i	−0.616074	−	0.108630i
$996$	−26.7423	+	26.8660i	−0.0268497	+	0.0269739i
$997$	694.822	−	583.025i	0.696913	−	0.584779i	−0.223981	−	0.974594i	$-0.571905\pi$
$997$	694.822	−	583.025i	0.696913	−	0.584779i	0.920893	+	0.389814i	$0.127461\pi$
$998$	73.2448	−	384.823i	0.0733916	−	0.385594i
$999$	−320.355	−	56.1695i	−0.320676	−	0.0562257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.103.29	yes	204
3.2	odd	2		324.3.j.a.199.6		204
4.3	odd	2	inner	108.3.j.a.103.25	yes	204
12.11	even	2		324.3.j.a.199.10		204
27.11	odd	18		324.3.j.a.127.10		204
27.16	even	9	inner	108.3.j.a.43.25	✓	204
108.11	even	18		324.3.j.a.127.6		204
108.43	odd	18	inner	108.3.j.a.43.29	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.25	✓	204	27.16	even	9	inner
108.3.j.a.43.29	yes	204	108.43	odd	18	inner
108.3.j.a.103.25	yes	204	4.3	odd	2	inner
108.3.j.a.103.29	yes	204	1.1	even	1	trivial
324.3.j.a.127.6		204	108.11	even	18
324.3.j.a.127.10		204	27.11	odd	18
324.3.j.a.199.6		204	3.2	odd	2
324.3.j.a.199.10		204	12.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74544 - 0.976438i) q^{2} +(2.40580 - 1.79225i) q^{3} +(2.09314 - 3.40863i) q^{4} +(-7.02836 + 2.55811i) q^{5} +(2.44916 - 5.47737i) q^{6} +(8.30860 - 1.46503i) q^{7} +(0.325138 - 7.99339i) q^{8} +(2.57570 - 8.62356i) q^{9} +(-9.76976 + 11.3278i) q^{10} +(-3.00678 + 8.26105i) q^{11} +(-1.07345 - 11.9519i) q^{12} +(5.39976 + 4.53094i) q^{13} +(13.0717 - 10.6700i) q^{14} +(-12.3240 + 18.7509i) q^{15} +(-7.23754 - 14.2695i) q^{16} +(-10.7850 + 18.6801i) q^{17} +(-3.92463 - 17.5669i) q^{18} +(-22.4736 + 12.9752i) q^{19} +(-5.99167 + 29.3116i) q^{20} +(17.3631 - 18.4156i) q^{21} +(2.81824 + 17.3551i) q^{22} +(40.0360 + 7.05942i) q^{23} +(-13.5439 - 19.8132i) q^{24} +(23.7028 - 19.8890i) q^{25} +(13.8492 + 2.63596i) q^{26} +(-9.25895 - 25.3628i) q^{27} +(12.3973 - 31.3875i) q^{28} +(-6.59975 + 5.53785i) q^{29} +(-3.20183 + 44.7622i) q^{30} +(11.2381 + 1.98159i) q^{31} +(-26.5660 - 17.8396i) q^{32} +(7.57216 + 25.2633i) q^{33} +(-0.584575 + 43.1358i) q^{34} +(-54.6481 + 31.5511i) q^{35} +(-24.0032 - 26.8299i) q^{36} +(6.02300 - 10.4321i) q^{37} +(-26.5570 + 44.5915i) q^{38} +(21.1113 + 1.22280i) q^{39} +(18.1628 + 57.0122i) q^{40} +(-57.3423 - 48.1159i) q^{41} +(12.3246 - 49.0974i) q^{42} +(-5.67130 + 15.5818i) q^{43} +(21.8653 + 27.5405i) q^{44} +(3.95711 + 67.1984i) q^{45} +(76.7735 - 26.7708i) q^{46} +(10.2447 - 1.80643i) q^{47} +(-42.9865 - 21.3580i) q^{48} +(20.8416 - 7.58571i) q^{49} +(21.9515 - 57.8594i) q^{50} +(7.53295 + 64.2697i) q^{51} +(26.7468 - 8.92192i) q^{52} -6.32010 q^{53} +(-40.9262 - 35.2285i) q^{54} -65.7533i q^{55} +(-9.00912 - 66.8902i) q^{56} +(-30.8123 + 71.4939i) q^{57} +(-6.11213 + 16.1103i) q^{58} +(-16.9160 - 46.4763i) q^{59} +(38.1189 + 81.2562i) q^{60} +(0.604658 + 3.42918i) q^{61} +(21.5504 - 7.51460i) q^{62} +(8.76668 - 75.4232i) q^{63} +(-63.7886 - 5.19790i) q^{64} +(-49.5421 - 18.0319i) q^{65} +(37.8848 + 36.7019i) q^{66} +(40.3947 - 48.1405i) q^{67} +(41.0991 + 75.8619i) q^{68} +(108.971 - 54.7708i) q^{69} +(-64.5775 + 108.431i) q^{70} +(-8.73857 - 5.04521i) q^{71} +(-68.0940 - 23.3924i) q^{72} +(-13.0231 - 22.5566i) q^{73} +(0.326464 - 24.0898i) q^{74} +(21.3780 - 90.3301i) q^{75} +(-2.81290 + 103.763i) q^{76} +(-12.8794 + 73.0428i) q^{77} +(38.0425 - 18.4795i) q^{78} +(-61.6659 - 73.4906i) q^{79} +(87.3710 + 81.7766i) q^{80} +(-67.7315 - 44.4234i) q^{81} +(-147.070 - 27.9923i) q^{82} +(-2.03051 - 2.41986i) q^{83} +(-26.4287 - 97.7308i) q^{84} +(28.0147 - 158.879i) q^{85} +(5.31570 + 32.7347i) q^{86} +(-5.95246 + 25.1513i) q^{87} +(65.0562 + 26.7203i) q^{88} +(-23.2483 - 40.2672i) q^{89} +(72.5220 + 113.427i) q^{90} +(51.5024 + 29.7349i) q^{91} +(107.864 - 121.691i) q^{92} +(30.5882 - 15.3742i) q^{93} +(16.1178 - 13.1564i) q^{94} +(124.761 - 148.684i) q^{95} +(-95.8851 + 4.69447i) q^{96} +(-8.79923 - 3.20266i) q^{97} +(28.9708 - 33.5909i) q^{98} +(63.4951 + 47.2071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

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