LMFDB - Embedded newform 220.3.w.a.7.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(7,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 5, 14])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89633 - 0.635566i) q^{2} +(-4.39098 + 2.23732i) q^{3} +(3.19211 + 2.41048i) q^{4} +(4.88411 - 1.07027i) q^{5} +(9.74869 - 1.45192i) q^{6} +(-1.29034 + 2.53243i) q^{7} +(-4.52126 - 6.59986i) q^{8} +(8.98505 - 12.3669i) q^{9} +(-9.94210 - 1.07459i) q^{10} +(-2.28240 - 10.7606i) q^{11} +(-19.4095 - 3.44262i) q^{12} +(0.417679 + 2.63712i) q^{13} +(4.05642 - 3.98221i) q^{14} +(-19.0515 + 15.6268i) q^{15} +(4.37914 + 15.3891i) q^{16} +(0.0707521 - 0.446711i) q^{17} +(-24.8985 + 17.7410i) q^{18} +(22.1514 + 7.19742i) q^{19} +(18.1705 + 8.35664i) q^{20} -14.0067i q^{21} +(-2.51090 + 21.8562i) q^{22} +(16.7927 + 16.7927i) q^{23} +(34.6187 + 18.8644i) q^{24} +(22.7090 - 10.4547i) q^{25} +(0.884011 - 5.26631i) q^{26} +(-4.84625 + 30.5980i) q^{27} +(-10.2233 + 4.97345i) q^{28} +(7.96480 + 24.5131i) q^{29} +(46.0597 - 17.5251i) q^{30} +(-14.9598 + 20.5904i) q^{31} +(1.47649 - 31.9659i) q^{32} +(34.0968 + 42.1431i) q^{33} +(-0.418084 + 0.802143i) q^{34} +(-3.59175 + 13.7496i) q^{35} +(58.4914 - 17.8181i) q^{36} +(-32.1050 + 63.0096i) q^{37} +(-37.4318 - 27.7273i) q^{38} +(-7.73410 - 10.6451i) q^{39} +(-29.1460 - 27.3955i) q^{40} +(9.74917 + 3.16770i) q^{41} +(-8.90220 + 26.5613i) q^{42} +(1.75161 - 1.75161i) q^{43} +(18.6526 - 39.8507i) q^{44} +(30.6480 - 70.0175i) q^{45} +(-21.1715 - 42.5172i) q^{46} +(2.71100 + 5.32065i) q^{47} +(-53.6589 - 57.7755i) q^{48} +(24.0533 + 33.1065i) q^{49} +(-49.7084 + 5.39233i) q^{50} +(0.688763 + 2.11980i) q^{51} +(-5.02346 + 9.42480i) q^{52} +(69.4310 - 10.9968i) q^{53} +(28.6372 - 54.9438i) q^{54} +(-22.6643 - 50.1132i) q^{55} +(22.5476 - 2.93373i) q^{56} +(-113.369 + 17.9559i) q^{57} +(0.475861 - 51.5471i) q^{58} +(16.7213 + 51.4628i) q^{59} +(-98.4827 + 3.95930i) q^{60} +(-64.3142 - 88.5209i) q^{61} +(41.4552 - 29.5382i) q^{62} +(19.7244 + 38.7113i) q^{63} +(-23.1164 + 59.6794i) q^{64} +(4.86243 + 12.4330i) q^{65} +(-37.8740 - 101.588i) q^{66} +(70.1944 - 70.1944i) q^{67} +(1.30264 - 1.25541i) q^{68} +(-111.307 - 36.1657i) q^{69} +(15.5500 - 23.7910i) q^{70} +(59.0181 + 81.2315i) q^{71} +(-122.243 - 3.38627i) q^{72} +(-43.4809 + 85.3361i) q^{73} +(100.928 - 99.0819i) q^{74} +(-76.3245 + 96.7134i) q^{75} +(53.3604 + 76.3705i) q^{76} +(30.1955 + 8.10477i) q^{77} +(7.90073 + 25.1021i) q^{78} +(-42.4238 + 58.3914i) q^{79} +(37.8587 + 70.4750i) q^{80} +(-4.66421 - 14.3550i) q^{81} +(-16.4743 - 12.2032i) q^{82} +(22.7200 - 143.448i) q^{83} +(33.7629 - 44.7110i) q^{84} +(-0.132542 - 2.25751i) q^{85} +(-4.43489 + 2.20836i) q^{86} +(-89.8169 - 89.8169i) q^{87} +(-60.6992 + 63.7151i) q^{88} +73.3129i q^{89} +(-102.619 + 113.297i) q^{90} +(-7.21727 - 2.34503i) q^{91} +(13.1256 + 94.0824i) q^{92} +(19.6209 - 123.882i) q^{93} +(-1.75933 - 11.8127i) q^{94} +(115.893 + 11.4450i) q^{95} +(65.0346 + 143.665i) q^{96} +(8.07153 + 50.9617i) q^{97} +(-24.5715 - 78.0682i) q^{98} +(-153.582 - 68.4584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.89633	−	0.635566i	−0.948163	−	0.317783i
$2$	−1.89633	−	0.635566i	−0.948163	−	0.317783i
$3$	−4.39098	+	2.23732i	−1.46366	+	0.745772i	−0.990796	−	0.135364i	$-0.956780\pi$
$3$	−4.39098	+	2.23732i	−1.46366	+	0.745772i	−0.472864	+	0.881136i	$0.656780\pi$
$4$	3.19211	+	2.41048i	0.798028	+	0.602621i
$5$	4.88411	−	1.07027i	0.976822	−	0.214054i
$5$	4.88411	−	1.07027i	0.976822	−	0.214054i
$6$	9.74869	−	1.45192i	1.62478	−	0.241987i
$7$	−1.29034	+	2.53243i	−0.184334	+	0.361775i	−0.964619	−	0.263649i	$-0.915074\pi$
$7$	−1.29034	+	2.53243i	−0.184334	+	0.361775i	0.780285	+	0.625424i	$0.215074\pi$
$8$	−4.52126	−	6.59986i	−0.565158	−	0.824983i
$9$	8.98505	−	12.3669i	0.998339	−	1.37410i
$10$	−9.94210	−	1.07459i	−0.994210	−	0.107459i
$11$	−2.28240	−	10.7606i	−0.207491	−	0.978237i
$11$	−2.28240	−	10.7606i	−0.207491	−	0.978237i
$12$	−19.4095	−	3.44262i	−1.61746	−	0.286885i
$13$	0.417679	+	2.63712i	0.0321292	+	0.202856i	0.998531	−	0.0541796i	$-0.0172543\pi$
$13$	0.417679	+	2.63712i	0.0321292	+	0.202856i	−0.966402	+	0.257035i	$0.917254\pi$
$14$	4.05642	−	3.98221i	0.289744	−	0.284444i
$15$	−19.0515	+	15.6268i	−1.27010	+	1.04179i
$16$	4.37914	+	15.3891i	0.273696	+	0.961816i
$17$	0.0707521	−	0.446711i	0.00416189	−	0.0262771i	−0.985520	−	0.169559i	$-0.945766\pi$
$17$	0.0707521	−	0.446711i	0.00416189	−	0.0262771i	0.989682	+	0.143282i	$0.0457656\pi$
$18$	−24.8985	+	17.7410i	−1.38325	+	0.985611i
$19$	22.1514	+	7.19742i	1.16586	+	0.378812i	0.827097	−	0.562059i	$-0.189991\pi$
$19$	22.1514	+	7.19742i	1.16586	+	0.378812i	0.338766	+	0.940871i	$0.389991\pi$
$20$	18.1705	+	8.35664i	0.908524	+	0.417832i
$21$		−	14.0067i		−	0.666986i
$22$	−2.51090	+	21.8562i	−0.114132	+	0.993466i
$23$	16.7927	+	16.7927i	0.730115	+	0.730115i	0.970642	−	0.240527i	$-0.0773203\pi$
$23$	16.7927	+	16.7927i	0.730115	+	0.730115i	−0.240527	+	0.970642i	$0.577320\pi$
$24$	34.6187	+	18.8644i	1.44245	+	0.786015i
$25$	22.7090	−	10.4547i	0.908361	−	0.418186i
$26$	0.884011	−	5.26631i	0.0340004	−	0.202550i
$27$	−4.84625	+	30.5980i	−0.179491	+	1.13326i
$28$	−10.2233	+	4.97345i	−0.365116	+	0.177623i
$29$	7.96480	+	24.5131i	0.274648	+	0.845281i	0.989312	+	0.145813i	$0.0465796\pi$
$29$	7.96480	+	24.5131i	0.274648	+	0.845281i	−0.714664	+	0.699468i	$0.753420\pi$
$30$	46.0597	−	17.5251i	1.53532	−	0.584170i
$31$	−14.9598	+	20.5904i	−0.482574	+	0.664206i	−0.978997	−	0.203875i	$-0.934646\pi$
$31$	−14.9598	+	20.5904i	−0.482574	+	0.664206i	0.496423	+	0.868081i	$0.334646\pi$
$32$	1.47649	−	31.9659i	0.0461403	−	0.998935i
$33$	34.0968	+	42.1431i	1.03324	+	1.27706i
$34$	−0.418084	+	0.802143i	−0.0122966	+	0.0235924i
$35$	−3.59175	+	13.7496i	−0.102622	+	0.392847i
$36$	58.4914	−	17.8181i	1.62476	−	0.494946i
$37$	−32.1050	+	63.0096i	−0.867702	+	1.70296i	−0.171414	+	0.985199i	$0.554834\pi$
$37$	−32.1050	+	63.0096i	−0.867702	+	1.70296i	−0.696288	+	0.717762i	$0.745166\pi$
$38$	−37.4318	−	27.7273i	−0.985048	−	0.729667i
$39$	−7.73410	−	10.6451i	−0.198310	−	0.272951i
$40$	−29.1460	−	27.3955i	−0.728650	−	0.684887i
$41$	9.74917	+	3.16770i	0.237785	+	0.0772609i	0.425485	−	0.904965i	$-0.360103\pi$
$41$	9.74917	+	3.16770i	0.237785	+	0.0772609i	−0.187701	+	0.982226i	$0.560103\pi$
$42$	−8.90220	+	26.5613i	−0.211957	+	0.632412i
$43$	1.75161	−	1.75161i	0.0407351	−	0.0407351i	−0.686446	−	0.727181i	$-0.740830\pi$
$43$	1.75161	−	1.75161i	0.0407351	−	0.0407351i	0.727181	+	0.686446i	$0.240830\pi$
$44$	18.6526	−	39.8507i	0.423922	−	0.905699i
$45$	30.6480	−	70.0175i	0.681068	−	1.55594i
$46$	−21.1715	−	42.5172i	−0.460250	−	0.924287i
$47$	2.71100	+	5.32065i	0.0576809	+	0.113205i	0.918047	−	0.396471i	$-0.129765\pi$
$47$	2.71100	+	5.32065i	0.0576809	+	0.113205i	−0.860366	+	0.509676i	$0.829765\pi$
$48$	−53.6589	−	57.7755i	−1.11789	−	1.20366i
$49$	24.0533	+	33.1065i	0.490883	+	0.675642i
$50$	−49.7084	+	5.39233i	−0.994168	+	0.107847i
$51$	0.688763	+	2.11980i	0.0135052	+	0.0415646i
$52$	−5.02346	+	9.42480i	−0.0966051	+	0.181246i
$53$	69.4310	−	10.9968i	1.31002	−	0.207487i	0.537924	−	0.842993i	$-0.319209\pi$
$53$	69.4310	−	10.9968i	1.31002	−	0.207487i	0.772095	+	0.635507i	$0.219209\pi$
$54$	28.6372	−	54.9438i	0.530318	−	1.01748i
$55$	−22.6643	−	50.1132i	−0.412078	−	0.911149i
$56$	22.5476	−	2.93373i	0.402636	−	0.0523879i
$57$	−113.369	+	17.9559i	−1.98893	+	0.315016i
$58$	0.475861	−	51.5471i	0.00820451	−	0.888743i
$59$	16.7213	+	51.4628i	0.283412	+	0.872251i	0.986870	+	0.161515i	$0.0516380\pi$
$59$	16.7213	+	51.4628i	0.283412	+	0.872251i	−0.703459	+	0.710736i	$0.748362\pi$
$60$	−98.4827	+	3.95930i	−1.64138	+	0.0659884i
$61$	−64.3142	−	88.5209i	−1.05433	−	1.45116i	−0.884993	−	0.465604i	$-0.845837\pi$
$61$	−64.3142	−	88.5209i	−1.05433	−	1.45116i	−0.169338	−	0.985558i	$-0.554163\pi$
$62$	41.4552	−	29.5382i	0.668633	−	0.476422i
$63$	19.7244	+	38.7113i	0.313086	+	0.614466i
$64$	−23.1164	+	59.6794i	−0.361193	+	0.932491i
$65$	4.86243	+	12.4330i	0.0748066	+	0.191276i
$66$	−37.8740	−	101.588i	−0.573849	−	1.53921i
$67$	70.1944	−	70.1944i	1.04768	−	1.04768i	0.0488728	−	0.998805i	$-0.484437\pi$
$67$	70.1944	−	70.1944i	1.04768	−	1.04768i	0.998805	−	0.0488728i	$-0.0155629\pi$
$68$	1.30264	−	1.25541i	0.0191565	−	0.0184618i
$69$	−111.307	−	36.1657i	−1.61314	−	0.524141i
$70$	15.5500	−	23.7910i	0.222142	−	0.339872i
$71$	59.0181	+	81.2315i	0.831241	+	1.14411i	0.987691	+	0.156419i	$0.0499952\pi$
$71$	59.0181	+	81.2315i	0.831241	+	1.14411i	−0.156450	+	0.987686i	$0.550005\pi$
$72$	−122.243	−	3.38627i	−1.69782	−	0.0470315i
$73$	−43.4809	+	85.3361i	−0.595629	+	1.16899i	0.374688	+	0.927151i	$0.377750\pi$
$73$	−43.4809	+	85.3361i	−0.595629	+	1.16899i	−0.970317	+	0.241837i	$0.922250\pi$
$74$	100.928	−	99.0819i	1.36390	−	1.33894i
$75$	−76.3245	+	96.7134i	−1.01766	+	1.28951i
$76$	53.3604	+	76.3705i	0.702111	+	1.00488i
$77$	30.1955	+	8.10477i	0.392149	+	0.105257i
$78$	7.90073	+	25.1021i	0.101291	+	0.321821i
$79$	−42.4238	+	58.3914i	−0.537010	+	0.739131i	−0.988179	−	0.153308i	$-0.951007\pi$
$79$	−42.4238	+	58.3914i	−0.537010	+	0.739131i	0.451168	+	0.892439i	$0.351007\pi$
$80$	37.8587	+	70.4750i	0.473233	+	0.880937i
$81$	−4.66421	−	14.3550i	−0.0575829	−	0.177222i
$82$	−16.4743	−	12.2032i	−0.200906	−	0.148820i
$83$	22.7200	−	143.448i	0.273734	−	1.72829i	−0.341443	−	0.939902i	$-0.610916\pi$
$83$	22.7200	−	143.448i	0.273734	−	1.72829i	0.615178	−	0.788389i	$-0.289084\pi$
$84$	33.7629	−	44.7110i	0.401940	−	0.532273i
$85$	−0.132542	−	2.25751i	−0.00155931	−	0.0265590i
$86$	−4.43489	+	2.20836i	−0.0515685	+	0.0256786i
$87$	−89.8169	−	89.8169i	−1.03238	−	1.03238i
$88$	−60.6992	+	63.7151i	−0.689763	+	0.724035i
$89$			73.3129i			0.823741i	0.911242	+	0.411870i	$0.135124\pi$
$89$			73.3129i			0.823741i	−0.911242	+	0.411870i	$0.864876\pi$
$90$	−102.619	+	113.297i	−1.14022	+	1.25886i
$91$	−7.21727	−	2.34503i	−0.0793106	−	0.0257696i
$92$	13.1256	+	94.0824i	0.142670	+	1.02264i
$93$	19.6209	−	123.882i	0.210978	−	1.33206i
$94$	−1.75933	−	11.8127i	−0.0187162	−	0.125667i
$95$	115.893	+	11.4450i	1.21993	+	0.120474i
$96$	65.0346	+	143.665i	0.677444	+	1.49651i
$97$	8.07153	+	50.9617i	0.0832117	+	0.525378i	0.993721	+	0.111889i	$0.0356900\pi$
$97$	8.07153	+	50.9617i	0.0832117	+	0.525378i	−0.910509	+	0.413489i	$0.864310\pi$
$98$	−24.5715	−	78.0682i	−0.250729	−	0.796614i
$99$	−153.582	−	68.4584i	−1.55134	−	0.691499i
$100$	97.6905	+	21.3674i	0.976905	+	0.213674i
$101$	112.892	−	155.382i	1.11774	−	1.53844i	0.308246	−	0.951307i	$-0.400258\pi$
$101$	112.892	−	155.382i	1.11774	−	1.53844i	0.809493	−	0.587129i	$-0.199742\pi$
$102$	0.0411505	−	4.45758i	0.000403437	−	0.0437018i
$103$	23.0411	−	45.2206i	0.223700	−	0.439035i	−0.751692	−	0.659514i	$-0.770762\pi$
$103$	23.0411	−	45.2206i	0.223700	−	0.439035i	0.975392	+	0.220479i	$0.0707620\pi$
$104$	15.5162	−	14.6798i	0.149194	−	0.141152i
$105$	−14.9910	−	68.4103i	−0.142771	−	0.651527i
$106$	−138.653	−	23.2745i	−1.30805	−	0.219571i
$107$	19.4107	−	9.89026i	0.181409	−	0.0924324i	−0.360928	−	0.932594i	$-0.617540\pi$
$107$	19.4107	−	9.89026i	0.181409	−	0.0924324i	0.542336	+	0.840161i	$0.317540\pi$
$108$	−89.2259	+	85.9905i	−0.826165	+	0.796209i
$109$	27.6368			0.253549			0.126774	−	0.991932i	$-0.459538\pi$
$109$	27.6368			0.253549			0.126774	+	0.991932i	$0.459538\pi$
$110$	11.1286	+	109.436i	0.101169	+	0.994869i
$111$		−	348.503i		−	3.13966i
$112$	−44.6222	−	8.76720i	−0.398412	−	0.0782785i
$113$	−14.0024	−	27.4813i	−0.123915	−	0.243197i	0.820712	−	0.571341i	$-0.193577\pi$
$113$	−14.0024	−	27.4813i	−0.123915	−	0.243197i	−0.944628	+	0.328144i	$0.893577\pi$
$114$	226.397	+	38.0034i	1.98594	+	0.333363i
$115$	99.9899	+	64.0444i	0.869477	+	0.556908i
$116$	−33.6640	+	97.4477i	−0.290207	+	0.840066i
$117$	36.3658	+	18.5293i	0.310819	+	0.158370i
$118$	0.999023	−	108.218i	0.00846629	−	0.917100i
$119$	1.03997	+	0.755582i	0.00873924	+	0.00634943i
$120$	189.272	+	55.0841i	1.57726	+	0.459034i
$121$	−110.581	+	49.1201i	−0.913895	+	0.405951i
$122$	65.6998	+	208.740i	0.538523	+	1.71099i
$123$	−49.8955	+	7.90267i	−0.405655	+	0.0642494i
$124$	−97.3861	+	29.6665i	−0.785372	+	0.239246i
$125$	99.7241	−	75.3665i	0.797793	−	0.602932i
$126$	−12.8003	−	85.9455i	−0.101590	−	0.682107i
$127$	139.388	+	22.0768i	1.09754	+	0.173833i	0.678836	−	0.734290i	$-0.262485\pi$
$127$	139.388	+	22.0768i	1.09754	+	0.173833i	0.418704	+	0.908123i	$0.362485\pi$
$128$	81.7664	−	98.4797i	0.638800	−	0.769373i
$129$	−3.77238	+	11.6102i	−0.0292433	+	0.0900015i
$130$	−1.31878	−	26.6674i	−0.0101445	−	0.205134i
$131$	−48.8749			−0.373091			−0.186546	−	0.982446i	$-0.559729\pi$
$131$	−48.8749			−0.373091			−0.186546	+	0.982446i	$0.559729\pi$
$132$	7.25558	+	216.715i	0.0549665	+	1.64178i
$133$	−46.8097	+	46.8097i	−0.351952	+	0.351952i
$134$	−177.725	+	88.4983i	−1.32630	+	0.660435i
$135$	9.07860	+	154.631i	0.0672489	+	1.14541i
$136$	−3.26812	+	1.55275i	−0.0240303	+	0.0114172i
$137$	111.318	+	17.6311i	0.812543	+	0.128694i	0.548859	−	0.835915i	$-0.315062\pi$
$137$	111.318	+	17.6311i	0.812543	+	0.128694i	0.263684	+	0.964609i	$0.415062\pi$
$138$	188.088	+	139.325i	1.36296	+	1.00960i
$139$	−64.7664	+	21.0439i	−0.465945	+	0.151395i	−0.532575	−	0.846383i	$-0.678775\pi$
$139$	−64.7664	+	21.0439i	−0.465945	+	0.151395i	0.0666294	+	0.997778i	$0.478775\pi$
$140$	−44.6086	+	35.2325i	−0.318633	+	0.251661i
$141$	−23.8079	−	17.2975i	−0.168851	−	0.122677i
$142$	−60.2897	−	191.551i	−0.424575	−	1.34895i
$143$	27.4237	−	10.5135i	0.191774	−	0.0735207i
$144$	229.661	+	84.1152i	1.59487	+	0.584133i
$145$	65.1367	+	111.200i	0.449218	+	0.766899i
$146$	136.691	−	134.190i	0.936239	−	0.919111i
$147$	−179.687	−	91.5551i	−1.22236	−	0.622824i
$148$	−254.366	+	123.745i	−1.71869	+	0.836115i
$149$	−94.8905	+	68.9420i	−0.636849	+	0.462698i	−0.858766	−	0.512367i	$-0.828769\pi$
$149$	−94.8905	+	68.9420i	−0.636849	+	0.462698i	0.221917	+	0.975066i	$0.428769\pi$
$150$	206.204	−	134.891i	1.37469	−	0.899273i
$151$	42.8179	−	131.780i	0.283562	−	0.872715i	−0.703264	−	0.710929i	$-0.748275\pi$
$151$	42.8179	−	131.780i	0.283562	−	0.872715i	0.986826	−	0.161786i	$-0.0517253\pi$
$152$	−52.6503	−	178.738i	−0.346383	−	1.17591i
$153$	−4.88870	−	4.88870i	−0.0319523	−	0.0319523i
$154$	−52.1094	−	34.5605i	−0.338373	−	0.224419i
$155$	−51.0279	+	116.577i	−0.329212	+	0.752108i
$156$	0.971674	−	52.6232i	0.00622868	−	0.337328i
$157$	−4.64721	+	2.36787i	−0.0296001	+	0.0150820i	−0.468728	−	0.883343i	$-0.655288\pi$
$157$	−4.64721	+	2.36787i	−0.0296001	+	0.0150820i	0.439128	+	0.898425i	$0.355288\pi$
$158$	117.561	−	83.7660i	0.744057	−	0.530164i
$159$	−280.267	+	203.626i	−1.76268	+	1.28067i
$160$	−27.0009	−	157.705i	−0.168756	−	0.985658i
$161$	−64.1943	+	20.8580i	−0.398722	+	0.129553i
$162$	−0.278666	+	30.1861i	−0.00172016	+	0.186334i
$163$	−9.32109	−	58.8510i	−0.0571846	−	0.361049i	−0.999643	−	0.0267253i	$-0.991492\pi$
$163$	−9.32109	−	58.8510i	−0.0571846	−	0.361049i	0.942458	−	0.334324i	$-0.108508\pi$
$164$	23.4847	+	33.6118i	0.143200	+	0.204950i
$165$	211.637	+	169.339i	1.28265	+	1.02630i
$166$	−134.255	+	257.585i	−0.808767	+	1.55171i
$167$	18.8832	+	119.224i	0.113073	+	0.713913i	0.977465	+	0.211096i	$0.0677032\pi$
$167$	18.8832	+	119.224i	0.113073	+	0.713913i	−0.864393	+	0.502818i	$0.832297\pi$
$168$	−92.4424	+	63.3280i	−0.550252	+	0.376952i
$169$	153.949	−	50.0209i	0.910938	−	0.295982i
$170$	−1.18346	+	4.36522i	−0.00696151	+	0.0256778i
$171$	288.041	−	209.274i	1.68445	−	1.22382i
$172$	9.81356	−	1.36911i	0.0570556	−	0.00795992i
$173$	−83.5284	+	42.5599i	−0.482823	+	0.246011i	−0.678421	−	0.734673i	$-0.737335\pi$
$173$	−83.5284	+	42.5599i	−0.482823	+	0.246011i	0.195598	+	0.980684i	$0.437335\pi$
$174$	113.238	+	227.407i	0.650791	+	1.30694i
$175$	−2.82664	+	70.9989i	−0.0161523	+	0.405708i
$176$	155.601	−	82.2462i	0.884095	−	0.467308i
$177$	−188.561	−	188.561i	−1.06532	−	1.06532i
$178$	46.5952	−	139.025i	0.261771	−	0.781041i
$179$	64.4920	−	198.486i	0.360291	−	1.10886i	−0.592587	−	0.805506i	$-0.701893\pi$
$179$	64.4920	−	198.486i	0.360291	−	1.10886i	0.952878	−	0.303354i	$-0.0981065\pi$
$180$	266.608	−	149.627i	1.48116	−	0.831261i
$181$	−209.871	+	152.480i	−1.15951	+	0.842432i	−0.989716	−	0.143048i	$-0.954310\pi$
$181$	−209.871	+	152.480i	−1.15951	+	0.842432i	−0.169792	+	0.985480i	$0.554310\pi$
$182$	12.1959	+	9.03400i	0.0670103	+	0.0496374i
$183$	480.451	+	244.802i	2.62542	+	1.33772i
$184$	34.9052	−	186.753i	0.189702	−	1.01496i
$185$	−89.3668	+	342.107i	−0.483064	+	1.84923i
$186$	−115.943	+	222.450i	−0.623348	+	1.19597i
$187$	−4.96837	+	0.258239i	−0.0265688	+	0.00138096i
$188$	−4.17150	+	23.5189i	−0.0221888	+	0.125101i
$189$	−71.2340	−	51.7545i	−0.376899	−	0.273833i
$190$	−212.497	−	95.3611i	−1.11841	−	0.501901i
$191$	−217.568	+	70.6921i	−1.13910	+	0.370116i	−0.817027	−	0.576599i	$-0.804379\pi$
$191$	−217.568	+	70.6921i	−1.13910	+	0.370116i	−0.322072	+	0.946715i	$0.604379\pi$
$192$	−32.0182	−	313.770i	−0.166761	−	1.63422i
$193$	57.2355	+	9.06521i	0.296557	+	0.0469700i	0.302940	−	0.953010i	$-0.402032\pi$
$193$	57.2355	+	9.06521i	0.296557	+	0.0469700i	−0.00638302	+	0.999980i	$0.502032\pi$
$194$	17.0833	−	101.770i	0.0880580	−	0.524587i
$195$	−49.1673	−	43.7141i	−0.252140	−	0.224175i
$196$	−3.02193	+	163.660i	−0.0154180	+	0.834998i
$197$	58.1945	−	58.1945i	0.295403	−	0.295403i	−0.543807	−	0.839210i	$-0.683018\pi$
$197$	58.1945	−	58.1945i	0.295403	−	0.295403i	0.839210	+	0.543807i	$0.183018\pi$
$198$	247.732	+	227.431i	1.25117	+	1.14864i
$199$	86.3561			0.433950			0.216975	−	0.976177i	$-0.430381\pi$
$199$	86.3561			0.433950			0.216975	+	0.976177i	$0.430381\pi$
$200$	−171.673	−	102.608i	−0.858364	−	0.513041i
$201$	−151.175	+	465.269i	−0.752115	+	2.31477i
$202$	−312.835	+	222.905i	−1.54869	+	1.10349i
$203$	−72.3549	−	11.4599i	−0.356428	−	0.0564527i
$204$	−2.91112	+	8.42687i	−0.0142702	+	0.0413082i
$205$	51.0063	+	5.03711i	0.248811	+	0.0245713i
$206$	−72.4341	+	71.1090i	−0.351622	+	0.345189i
$207$	358.555	−	56.7895i	1.73215	−	0.274346i
$208$	−38.7538	+	17.9760i	−0.186316	+	0.0864232i
$209$	26.8903	−	254.790i	0.128662	−	1.21909i
$210$	−15.0515	+	139.256i	−0.0716737	+	0.663124i
$211$	161.109	+	117.053i	0.763551	+	0.554753i	0.899998	−	0.435895i	$-0.143568\pi$
$211$	161.109	+	117.053i	0.763551	+	0.554753i	−0.136446	+	0.990647i	$0.543568\pi$
$212$	248.139	+	132.259i	1.17047	+	0.623865i
$213$	−440.888	−	224.644i	−2.06990	−	1.05466i
$214$	−43.0950	+	6.41836i	−0.201379	+	0.0299923i
$215$	6.68036	−	10.4298i	0.0310714	−	0.0485105i
$216$	223.854	−	106.357i	1.03636	−	0.492394i
$217$	−32.8405	−	64.4531i	−0.151339	−	0.297019i
$218$	−52.4084	−	17.5650i	−0.240406	−	0.0805736i
$219$		−	471.990i		−	2.15520i
$220$	48.4501	−	214.599i	0.220228	−	0.975448i
$221$	1.20759			0.00546419
$222$	−221.497	+	660.875i	−0.997732	+	2.97691i
$223$	−354.857	+	180.809i	−1.59129	+	0.810801i	−0.591296	+	0.806454i	$0.701384\pi$
$223$	−354.857	+	180.809i	−1.59129	+	0.810801i	−0.999991	+	0.00434663i	$0.998616\pi$
$224$	79.0461	+	44.9858i	0.352885	+	0.200830i
$225$	74.7506	−	374.775i	0.332225	−	1.66567i
$226$	9.08697	+	61.0129i	0.0402078	+	0.269969i
$227$	81.6905	−	160.327i	0.359870	−	0.706285i	−0.638101	−	0.769953i	$-0.720280\pi$
$227$	81.6905	−	160.327i	0.359870	−	0.706285i	0.997971	+	0.0636676i	$0.0202797\pi$
$228$	−405.169	−	215.957i	−1.77706	−	0.947181i
$229$	−12.9681	+	17.8490i	−0.0566291	+	0.0779433i	−0.836392	−	0.548131i	$-0.815339\pi$
$229$	−12.9681	+	17.8490i	−0.0566291	+	0.0779433i	0.779763	+	0.626075i	$0.215339\pi$
$230$	−148.909	−	184.999i	−0.647430	−	0.804345i
$231$	−150.721	+	31.9689i	−0.652471	+	0.138394i
$232$	125.772	−	163.397i	0.542122	−	0.704297i
$233$	−44.5774	−	281.451i	−0.191320	−	1.20794i	−0.877162	−	0.480194i	$-0.840566\pi$
$233$	−44.5774	−	281.451i	−0.191320	−	1.20794i	0.685843	−	0.727750i	$-0.259434\pi$
$234$	−57.1848	−	58.2505i	−0.244380	−	0.248934i
$235$	18.9354	+	23.0851i	0.0805761	+	0.0982345i
$236$	−70.6741	+	204.581i	−0.299466	+	0.866870i
$237$	55.6421	−	351.311i	0.234777	−	1.48232i
$238$	−1.49190	−	2.09380i	−0.00626848	−	0.00879748i
$239$	−274.942	−	89.3341i	−1.15039	−	0.373783i	−0.329097	−	0.944296i	$-0.606744\pi$
$239$	−274.942	−	89.3341i	−1.15039	−	0.373783i	−0.821288	+	0.570513i	$0.806744\pi$
$240$	−323.911	−	224.752i	−1.34963	−	0.936468i
$241$		−	469.847i		−	1.94957i	−0.223142	−	0.974786i	$-0.571631\pi$
$241$		−	469.847i		−	1.94957i	0.223142	−	0.974786i	$-0.428369\pi$
$242$	240.917	−	22.8659i	0.995526	−	0.0944873i
$243$	−144.555	−	144.555i	−0.594876	−	0.594876i
$244$	8.08012	−	437.597i	0.0331152	−	1.79343i
$245$	152.912	+	135.952i	0.624129	+	0.554907i
$246$	99.6409	+	16.7259i	0.405044	+	0.0679913i
$247$	−9.72832	+	61.4222i	−0.0393859	+	0.248673i
$248$	203.531	+	5.63802i	0.820689	+	0.0227340i
$249$	221.176	+	680.709i	0.888257	+	2.73377i
$250$	−237.010	+	79.5382i	−0.948039	+	0.318153i
$251$	−77.9244	+	107.254i	−0.310456	+	0.427305i	−0.935523	−	0.353265i	$-0.885071\pi$
$251$	−77.9244	+	107.254i	−0.310456	+	0.427305i	0.625068	+	0.780571i	$0.285071\pi$
$252$	−30.3505	+	171.116i	−0.120439	+	0.679033i
$253$	142.372	−	219.027i	0.562733	−	0.865718i
$254$	−250.293	−	130.455i	−0.985406	−	0.513602i
$255$	5.63275	+	9.61615i	0.0220892	+	0.0377104i
$256$	−217.646	+	134.782i	−0.850181	+	0.526491i
$257$	−114.721	+	225.152i	−0.446384	+	0.876078i	0.552704	+	0.833378i	$0.313596\pi$
$257$	−114.721	+	225.152i	−0.446384	+	0.876078i	−0.999088	+	0.0427002i	$0.986404\pi$
$258$	14.5327	−	19.6191i	0.0563283	−	0.0760431i
$259$	−118.141	−	162.607i	−0.456142	−	0.627826i
$260$	−14.4480	+	51.4082i	−0.0555694	+	0.197724i
$261$	374.715	+	121.752i	1.43569	+	0.466483i
$262$	92.6829	+	31.0633i	0.353751	+	0.118562i
$263$	−56.2727	+	56.2727i	−0.213964	+	0.213964i	−0.805949	−	0.591985i	$-0.798345\pi$
$263$	−56.2727	+	56.2727i	−0.213964	+	0.213964i	0.591985	+	0.805949i	$0.298345\pi$
$264$	123.978	−	415.575i	0.469614	−	1.57415i
$265$	327.339	−	128.020i	1.23524	−	0.483093i
$266$	118.517	−	59.0158i	0.445553	−	0.221864i
$267$	−164.024	−	321.916i	−0.614323	−	1.20568i
$268$	393.271	−	54.8659i	1.46743	−	0.204723i
$269$	−74.2831	−	102.242i	−0.276145	−	0.380081i	0.648307	−	0.761379i	$-0.275477\pi$
$269$	−74.2831	−	102.242i	−0.276145	−	0.380081i	−0.924452	+	0.381298i	$0.875477\pi$
$270$	81.0623	−	299.001i	0.300231	−	1.10741i
$271$	109.946	+	338.378i	0.405704	+	1.24863i	0.920306	+	0.391199i	$0.127940\pi$
$271$	109.946	+	338.378i	0.405704	+	1.24863i	−0.514602	+	0.857429i	$0.672060\pi$
$272$	7.18430	−	0.867403i	0.0264129	−	0.00318898i
$273$	36.9374	−	5.85032i	0.135302	−	0.0214297i
$274$	−199.890	−	104.185i	−0.729527	−	0.380236i
$275$	−164.330	−	220.501i	−0.597562	−	0.801823i
$276$	−268.126	−	383.748i	−0.971472	−	1.39039i
$277$	140.257	−	22.2146i	0.506345	−	0.0801971i	0.101964	−	0.994788i	$-0.467487\pi$
$277$	140.257	−	22.2146i	0.506345	−	0.0801971i	0.404380	+	0.914591i	$0.367487\pi$
$278$	136.193	+	1.25728i	0.489903	+	0.00452258i
$279$	120.224	+	370.011i	0.430910	+	1.32621i
$280$	106.985	−	38.4607i	0.382089	−	0.137360i
$281$	104.487	+	143.814i	0.371841	+	0.511795i	0.953400	−	0.301709i	$-0.0975571\pi$
$281$	104.487	+	143.814i	0.371841	+	0.511795i	−0.581559	+	0.813504i	$0.697557\pi$
$282$	34.1539	+	47.9332i	0.121113	+	0.169976i
$283$	83.7652	+	164.399i	0.295990	+	0.580914i	0.990330	−	0.138734i	$-0.0443033\pi$
$283$	83.7652	+	164.399i	0.295990	+	0.580914i	−0.694339	+	0.719648i	$0.744303\pi$
$284$	−7.41475	+	401.562i	−0.0261083	+	1.41395i
$285$	−534.490	+	209.035i	−1.87540	+	0.733455i
$286$	−58.6864	+	2.50735i	−0.205197	+	0.00876695i
$287$	−20.6016	+	20.6016i	−0.0717827	+	0.0717827i
$288$	−382.052	−	305.475i	−1.32657	−	1.06068i
$289$	274.661	+	89.2427i	0.950383	+	0.308798i
$290$	−52.8452	−	252.271i	−0.182225	−	0.869899i
$291$	−149.459	−	205.713i	−0.513606	−	0.706918i
$292$	−344.497	+	167.592i	−1.17979	+	0.573946i
$293$	−32.6998	+	64.1769i	−0.111603	+	0.219034i	−0.940052	−	0.341031i	$-0.889224\pi$
$293$	−32.6998	+	64.1769i	−0.111603	+	0.219034i	0.828449	+	0.560065i	$0.189224\pi$
$294$	282.556	+	287.821i	0.961075	+	0.978984i
$295$	136.748	+	233.454i	0.463552	+	0.791369i
$296$	561.010	−	72.9944i	1.89530	−	0.246603i
$297$	340.315	−	17.6884i	1.14584	−	0.0595569i
$298$	223.761	−	70.4273i	0.750875	−	0.236333i
$299$	−37.2704	+	51.2983i	−0.124650	+	0.171566i
$300$	−476.762	+	124.741i	−1.58921	+	0.415803i
$301$	2.17566	+	6.69599i	0.00722810	+	0.0222458i
$302$	−164.952	+	222.684i	−0.546197	+	0.737365i
$303$	−148.066	+	934.853i	−0.488667	+	3.08532i
$304$	−13.7575	+	372.408i	−0.0452550	+	1.22503i
$305$	−408.859	−	363.512i	−1.34052	−	1.19184i
$306$	6.16349	+	12.3777i	0.0201421	+	0.0404499i
$307$	272.518	+	272.518i	0.887682	+	0.887682i	0.994300	−	0.106618i	$-0.0340021\pi$
$307$	272.518	+	272.518i	0.887682	+	0.887682i	−0.106618	+	0.994300i	$0.534002\pi$
$308$	76.8509	+	98.6571i	0.249516	+	0.320315i
$309$			250.113i			0.809427i
$310$	170.858	−	188.636i	0.551155	−	0.608503i
$311$	263.860	+	85.7333i	0.848425	+	0.275670i	0.700786	−	0.713371i	$-0.252833\pi$
$311$	263.860	+	85.7333i	0.848425	+	0.275670i	0.147639	+	0.989041i	$0.452833\pi$
$312$	−35.2881	+	99.1732i	−0.113103	+	0.317863i
$313$	72.4747	−	457.587i	0.231549	−	1.46194i	−0.548463	−	0.836175i	$-0.684787\pi$
$313$	72.4747	−	457.587i	0.231549	−	1.46194i	0.780012	−	0.625765i	$-0.215213\pi$
$314$	10.3176	−	1.53665i	0.0328585	−	0.00489379i
$315$	137.768	+	167.960i	0.437358	+	0.533206i
$316$	−276.173	+	84.1298i	−0.873965	+	0.266234i
$317$	−41.9522	−	264.875i	−0.132341	−	0.835569i	−0.961148	−	0.276034i	$-0.910980\pi$
$317$	−41.9522	−	264.875i	−0.132341	−	0.835569i	0.828807	−	0.559535i	$-0.189020\pi$
$318$	660.895	−	208.013i	2.07829	−	0.654128i
$319$	245.597	−	141.655i	0.769898	−	0.444059i
$320$	−49.0296	+	316.222i	−0.153218	+	0.988192i
$321$	−63.1045	+	86.8559i	−0.196587	+	0.270579i
$322$	134.990	+	1.24617i	0.419224	+	0.00387010i
$323$	4.78243	−	9.38605i	0.0148063	−	0.0290590i
$324$	19.7137	−	57.0657i	0.0608449	−	0.176129i
$325$	37.0553	+	55.5199i	0.114016	+	0.170830i
$326$	−19.7279	+	117.525i	−0.0605151	+	0.360506i
$327$	−121.353	+	61.8323i	−0.371109	+	0.189090i
$328$	−23.1722	−	78.6651i	−0.0706469	−	0.239833i
$329$	−16.9722			−0.0515874
$330$	−293.708	−	455.631i	−0.890023	−	1.38070i
$331$		−	268.105i		−	0.809984i	−0.914320	−	0.404992i	$-0.867274\pi$
$331$		−	268.105i		−	0.809984i	0.914320	−	0.404992i	$-0.132726\pi$
$332$	418.304	−	403.136i	1.25995	−	1.21427i
$333$	490.766	+	963.182i	1.47377	+	2.89244i
$334$	39.9659	−	238.088i	0.119658	−	0.712839i
$335$	267.710	−	417.964i	0.799134	−	1.24765i
$336$	215.550	−	61.3374i	0.641518	−	0.182552i
$337$	−424.901	−	216.498i	−1.26083	−	0.642427i	−0.309591	−	0.950870i	$-0.600192\pi$
$337$	−424.901	−	216.498i	−1.26083	−	0.642427i	−0.951243	+	0.308443i	$0.900192\pi$
$338$	−323.728	−	2.98853i	−0.957776	−	0.00884180i
$339$	122.969	+	89.3419i	0.362739	+	0.263545i
$340$	5.01861	−	7.52572i	0.0147606	−	0.0221345i
$341$	255.709	+	113.981i	0.749881	+	0.334255i
$342$	−679.227	+	213.783i	−1.98604	+	0.625095i
$343$	−252.430	+	39.9810i	−0.735947	+	0.116563i
$344$	−19.4799	−	3.64090i	−0.0566276	−	0.0105840i
$345$	−582.341	−	57.5089i	−1.68794	−	0.166693i
$346$	185.447	−	27.6195i	0.535973	−	0.0798253i
$347$	−499.651	−	79.1370i	−1.43992	−	0.228060i	−0.612866	−	0.790187i	$-0.709983\pi$
$347$	−499.651	−	79.1370i	−1.43992	−	0.228060i	−0.827051	+	0.562126i	$0.809983\pi$
$348$	−70.2033	−	503.208i	−0.201734	−	1.44600i
$349$	56.5197	−	173.950i	0.161948	−	0.498423i	−0.836851	−	0.547431i	$-0.815606\pi$
$349$	56.5197	−	173.950i	0.161948	−	0.498423i	0.998798	+	0.0490075i	$0.0156058\pi$
$350$	50.4848	−	132.841i	0.144242	−	0.379545i
$351$	−82.7150			−0.235655
$352$	−347.343	+	57.0712i	−0.986769	+	0.162134i
$353$	114.594	−	114.594i	0.324630	−	0.324630i	−0.525910	−	0.850540i	$-0.676275\pi$
$353$	114.594	−	114.594i	0.324630	−	0.324630i	0.850540	+	0.525910i	$0.176275\pi$
$354$	237.731	+	477.417i	0.671556	+	1.34864i
$355$	375.191	+	333.578i	1.05688	+	0.939656i
$356$	−176.720	+	234.023i	−0.496403	+	0.657368i
$357$	−6.25696	−	0.991005i	−0.0175265	−	0.00277592i
$358$	−248.449	+	335.405i	−0.693992	+	0.936887i
$359$	−154.922	+	50.3371i	−0.431536	+	0.140215i	−0.516727	−	0.856150i	$-0.672850\pi$
$359$	−154.922	+	50.3371i	−0.431536	+	0.140215i	0.0851911	+	0.996365i	$0.472850\pi$
$360$	−600.674	+	114.295i	−1.66854	+	0.317485i
$361$	146.826	+	106.675i	0.406721	+	0.295500i
$362$	494.895	−	155.765i	1.36711	−	0.430291i
$363$	375.663	−	463.090i	1.03488	−	1.27573i
$364$	−17.3857	−	24.8827i	−0.0477628	−	0.0683591i
$365$	−121.033	+	463.327i	−0.331597	+	1.26939i
$366$	−755.505	−	769.584i	−2.06422	−	2.10269i
$367$	280.621	+	142.983i	0.764634	+	0.389600i	0.792390	−	0.610014i	$-0.208836\pi$
$367$	280.621	+	142.983i	0.764634	+	0.389600i	−0.0277565	+	0.999615i	$0.508836\pi$
$368$	−184.886	+	331.961i	−0.502407	+	0.902067i
$369$	126.771	−	92.1046i	0.343553	−	0.249606i
$370$	386.900	−	591.948i	1.04568	−	1.59986i
$371$	−61.7407	+	190.018i	−0.166417	+	0.512179i
$372$	361.247	−	348.148i	0.971094	−	0.935882i
$373$	451.611	+	451.611i	1.21075	+	1.21075i	0.970779	+	0.239975i	$0.0771391\pi$
$373$	451.611	+	451.611i	1.21075	+	1.21075i	0.239975	+	0.970779i	$0.422861\pi$
$374$	9.58578	+	2.66802i	0.0256304	+	0.00713375i
$375$	−269.268	+	554.047i	−0.718047	+	1.47746i
$376$	22.8584	−	41.9483i	0.0607935	−	0.111565i
$377$	−61.3174	+	31.2428i	−0.162646	+	0.0828722i
$378$	102.189	+	143.417i	0.270342	+	0.379411i
$379$	−385.283	+	279.925i	−1.01658	+	0.738588i	−0.965579	−	0.260111i	$-0.916241\pi$
$379$	−385.283	+	279.925i	−1.01658	+	0.738588i	−0.0510002	+	0.998699i	$0.516241\pi$
$380$	342.355	+	315.892i	0.900935	+	0.831294i
$381$	−661.441	+	214.915i	−1.73606	+	0.564082i
$382$	457.509	+	4.22354i	1.19767	+	0.0110564i
$383$	−44.4199	−	280.456i	−0.115979	−	0.732261i	−0.975310	−	0.220841i	$-0.929120\pi$
$383$	−44.4199	−	280.456i	−0.115979	−	0.732261i	0.859331	−	0.511420i	$-0.170880\pi$
$384$	−138.704	+	615.360i	−0.361210	+	1.60250i
$385$	156.152	+	7.26721i	0.405591	+	0.0188759i
$386$	−102.776	−	53.5676i	−0.266258	−	0.138776i
$387$	−5.92361	−	37.4002i	−0.0153065	−	0.0966414i
$388$	−97.0770	+	182.132i	−0.250198	+	0.469411i
$389$	−258.717	+	84.0624i	−0.665083	+	0.216099i	−0.622053	−	0.782975i	$-0.713701\pi$
$389$	−258.717	+	84.0624i	−0.665083	+	0.216099i	−0.0430301	+	0.999074i	$0.513701\pi$
$390$	65.4541	+	114.145i	0.167831	+	0.292680i
$391$	8.68959	−	6.31335i	0.0222240	−	0.0161467i
$392$	109.747	−	308.431i	0.279967	−	0.786815i
$393$	214.609	−	109.349i	0.546078	−	0.278241i
$394$	−147.342	+	73.3693i	−0.373965	+	0.186216i
$395$	−144.708	+	330.595i	−0.366349	+	0.836949i
$396$	−325.234	−	588.735i	−0.821298	−	1.48670i
$397$	−120.121	−	120.121i	−0.302573	−	0.302573i	0.539447	−	0.842020i	$-0.318633\pi$
$397$	−120.121	−	120.121i	−0.302573	−	0.302573i	−0.842020	+	0.539447i	$0.818633\pi$
$398$	−163.759	−	54.8851i	−0.411456	−	0.137902i
$399$	100.812	−	310.268i	0.252662	−	0.777614i
$400$	260.333	+	303.688i	0.650833	+	0.759221i
$401$	146.406	−	106.370i	0.365103	−	0.265263i	−0.390074	−	0.920783i	$-0.627551\pi$
$401$	146.406	−	106.370i	0.365103	−	0.265263i	0.755178	+	0.655520i	$0.227551\pi$
$402$	582.387	−	786.221i	1.44872	−	1.95577i
$403$	−60.5478	−	30.8507i	−0.150243	−	0.0765525i
$404$	734.908	−	223.873i	1.81908	−	0.554142i
$405$	−38.1443	−	65.1193i	−0.0941834	−	0.160788i
$406$	129.925	+	67.7181i	0.320013	+	0.166793i
$407$	751.298	+	201.656i	1.84594	+	0.495469i
$408$	10.8763	−	14.1299i	0.0266575	−	0.0346321i
$409$	−525.279	−	381.638i	−1.28430	−	0.933099i	−0.284627	−	0.958638i	$-0.591870\pi$
$409$	−525.279	−	381.638i	−1.28430	−	0.933099i	−0.999674	+	0.0255388i	$0.991870\pi$
$410$	−93.5232	−	41.9699i	−0.228105	−	0.102366i
$411$	−528.243	+	171.637i	−1.28526	+	0.417607i
$412$	182.553	−	88.8092i	0.443090	−	0.215556i
$413$	−151.902	−	24.0589i	−0.367801	−	0.0582540i
$414$	−716.031	−	120.194i	−1.72954	−	0.290324i
$415$	−42.5618	−	724.933i	−0.102559	−	1.74683i
$416$	84.9148	−	9.45782i	0.204122	−	0.0227352i
$417$	237.306	−	237.306i	0.569079	−	0.569079i
$418$	−212.929	+	466.074i	−0.509399	+	1.11501i
$419$	−170.819			−0.407683			−0.203841	−	0.979004i	$-0.565343\pi$
$419$	−170.819			−0.407683			−0.203841	+	0.979004i	$0.565343\pi$
$420$	117.049	−	254.509i	0.278688	−	0.605973i
$421$	147.671	−	454.484i	0.350762	−	1.07954i	−0.607664	−	0.794194i	$-0.707893\pi$
$421$	147.671	−	454.484i	0.350762	−	1.07954i	0.958426	−	0.285341i	$-0.0921069\pi$
$422$	−231.121	−	324.366i	−0.547680	−	0.768640i
$423$	90.1582	+	14.2796i	0.213140	+	0.0337580i
$424$	−386.493	−	408.516i	−0.911541	−	0.963481i
$425$	−3.06350	−	10.8841i	−0.00720823	−	0.0256096i
$426$	693.291	+	706.211i	1.62744	+	1.65777i
$427$	307.159	−	48.6493i	0.719343	−	0.113933i
$428$	85.8015	+	15.2184i	0.200471	+	0.0355571i
$429$	−96.8951	+	107.520i	−0.225863	+	0.250629i
$430$	−19.2969	+	15.5324i	−0.0448766	+	0.0361219i
$431$	−342.351	−	248.732i	−0.794318	−	0.577106i	0.114924	−	0.993374i	$-0.463338\pi$
$431$	−342.351	−	248.732i	−0.794318	−	0.577106i	−0.909242	+	0.416269i	$0.863338\pi$
$432$	−492.098	+	59.4138i	−1.13911	+	0.137532i
$433$	−170.245	−	86.7440i	−0.393175	−	0.200333i	0.246215	−	0.969215i	$-0.420813\pi$
$433$	−170.245	−	86.7440i	−0.393175	−	0.200333i	−0.639390	+	0.768883i	$0.720813\pi$
$434$	21.3121	+	143.096i	0.0491061	+	0.329715i
$435$	−534.804	−	342.547i	−1.22943	−	0.787464i
$436$	88.2198	+	66.6181i	0.202339	+	0.152794i
$437$	251.117	+	492.845i	0.574638	+	1.12779i
$438$	−299.981	+	895.047i	−0.684888	+	2.04349i
$439$			650.752i			1.48235i	0.671312	+	0.741175i	$0.265731\pi$
$439$			650.752i			1.48235i	−0.671312	+	0.741175i	$0.734269\pi$
$440$	−228.269	+	376.156i	−0.518793	+	0.854900i
$441$	625.543			1.41846
$442$	−2.28998	−	0.767501i	−0.00518094	−	0.00173643i
$443$	360.893	−	183.884i	0.814657	−	0.415089i	0.00355546	−	0.999994i	$-0.498868\pi$
$443$	360.893	−	183.884i	0.814657	−	0.415089i	0.811102	+	0.584905i	$0.198868\pi$
$444$	840.060	−	1112.46i	1.89203	−	2.50554i
$445$	78.4648	+	358.068i	0.176325	+	0.804648i
$446$	787.841	−	117.337i	1.76646	−	0.263088i
$447$	262.417	−	515.023i	0.587063	−	1.15218i
$448$	−121.306	−	135.547i	−0.270772	−	0.302560i
$449$	265.441	−	365.348i	0.591183	−	0.813693i	−0.403683	−	0.914899i	$-0.632270\pi$
$449$	265.441	−	365.348i	0.591183	−	0.813693i	0.994865	+	0.101206i	$0.0322701\pi$
$450$	−379.946	+	663.187i	−0.844324	+	1.47375i
$451$	11.8348	−	112.137i	0.0262413	−	0.248641i
$452$	21.5459	−	121.476i	0.0476680	−	0.268752i
$453$	106.821	+	674.440i	0.235807	+	1.48883i
$454$	−256.810	+	252.112i	−0.565661	+	0.555313i
$455$	−37.7597	−	3.72895i	−0.0829884	−	0.00819550i
$456$	631.079	+	667.038i	1.38394	+	1.46280i
$457$	−114.823	+	724.961i	−0.251253	+	1.58635i	0.462934	+	0.886393i	$0.346797\pi$
$457$	−114.823	+	724.961i	−0.251253	+	1.58635i	−0.714186	+	0.699956i	$0.753203\pi$
$458$	35.9359	−	25.6055i	0.0784627	−	0.0559072i
$459$	13.3256	+	4.32975i	0.0290318	+	0.00943302i
$460$	164.801	+	445.461i	0.358262	+	0.968393i
$461$		−	250.752i		−	0.543930i	−0.962307	−	0.271965i	$-0.912327\pi$
$461$		−	250.752i		−	0.543930i	0.962307	−	0.271965i	$-0.0876735\pi$
$462$	306.134	+	35.1694i	0.662628	+	0.0761243i
$463$	171.031	+	171.031i	0.369398	+	0.369398i	0.867257	−	0.497860i	$-0.165881\pi$
$463$	171.031	+	171.031i	0.369398	+	0.369398i	−0.497860	+	0.867257i	$0.665881\pi$
$464$	−342.355	+	229.917i	−0.737834	+	0.495511i
$465$	−36.7564	−	626.052i	−0.0790459	−	1.34635i
$466$	−94.3473	+	562.055i	−0.202462	+	1.20613i
$467$	−31.0155	+	195.824i	−0.0664143	+	0.419323i	0.931972	+	0.362531i	$0.118087\pi$
$467$	−31.0155	+	195.824i	−0.0664143	+	0.419323i	−0.998386	+	0.0567923i	$0.981913\pi$
$468$	71.4191	+	146.807i	0.152605	+	0.313690i
$469$	87.1878	+	268.336i	0.185901	+	0.572146i
$470$	−21.2356	−	55.8116i	−0.0451820	−	0.118748i
$471$	15.1081	−	20.7946i	0.0320767	−	0.0441498i
$472$	264.046	−	343.035i	0.559420	−	0.726769i
$473$	−22.8463	−	14.8505i	−0.0483008	−	0.0313964i
$474$	−328.797	+	630.836i	−0.693665	+	1.33088i
$475$	578.283	−	68.1385i	1.21744	−	0.143450i
$476$	1.49838	+	4.91873i	0.00314786	+	0.0103335i
$477$	487.845	−	957.450i	1.02274	−	2.00723i
$478$	464.602	+	344.151i	0.971971	+	0.719980i
$479$	−104.531	−	143.874i	−0.218227	−	0.300364i	0.685842	−	0.727751i	$-0.259434\pi$
$479$	−104.531	−	143.874i	−0.218227	−	0.300364i	−0.904069	+	0.427387i	$0.859434\pi$
$480$	471.397	+	632.071i	0.982077	+	1.31681i
$481$	−179.574	−	58.3470i	−0.373334	−	0.121304i
$482$	−298.619	+	890.983i	−0.619541	+	1.84851i
$483$	235.210	−	235.210i	0.486977	−	0.486977i
$484$	−471.391	−	109.758i	−0.973948	−	0.226772i
$485$	93.9651	+	240.264i	0.193742	+	0.495389i
$486$	182.249	+	365.998i	0.374998	+	0.753082i
$487$	−167.584	−	328.903i	−0.344115	−	0.675365i	0.652480	−	0.757806i	$-0.273728\pi$
$487$	−167.584	−	328.903i	−0.344115	−	0.675365i	−0.996596	+	0.0824409i	$0.973728\pi$
$488$	−293.444	+	824.691i	−0.601320	+	1.68994i
$489$	172.597	+	237.559i	0.352959	+	0.485807i
$490$	−203.564	−	354.995i	−0.415437	−	0.724480i
$491$	−180.667	−	556.035i	−0.367956	−	1.13245i	−0.948109	−	0.317945i	$-0.897007\pi$
$491$	−180.667	−	556.035i	−0.367956	−	1.13245i	0.580153	−	0.814508i	$-0.302993\pi$
$492$	−178.321	−	95.0461i	−0.362442	−	0.193183i
$493$	11.5138	−	1.82361i	0.0233546	−	0.00369901i
$494$	57.4860	−	110.294i	0.116368	−	0.223266i
$495$	−823.382	−	169.983i	−1.66340	−	0.343401i
$496$	−382.378	−	140.049i	−0.770923	−	0.282357i
$497$	−281.866	+	44.6432i	−0.567134	+	0.0898253i
$498$	13.2143	−	1431.42i	0.0265347	−	2.87434i
$499$	117.887	+	362.817i	0.236245	+	0.727089i	0.996954	+	0.0779949i	$0.0248518\pi$
$499$	117.887	+	362.817i	0.236245	+	0.727089i	−0.760708	+	0.649094i	$0.775148\pi$
$500$	500.000	−	0.194970i	1.00000	−	0.000389941i
$501$	−349.656	−	481.261i	−0.697917	−	0.960600i
$502$	215.937	−	153.862i	0.430153	−	0.306498i
$503$	85.7539	+	168.301i	0.170485	+	0.334595i	0.960402	−	0.278618i	$-0.0898765\pi$
$503$	85.7539	+	168.301i	0.170485	+	0.334595i	−0.789917	+	0.613214i	$0.789876\pi$
$504$	166.310	−	305.203i	0.329981	−	0.605561i
$505$	385.074	−	879.727i	0.762523	−	1.74203i
$506$	−409.189	+	324.860i	−0.808674	+	0.642015i
$507$	−564.072	+	564.072i	−1.11257	+	1.11257i
$508$	391.725	+	406.463i	0.771112	+	0.800124i
$509$	−500.181	−	162.519i	−0.982674	−	0.319290i	−0.226752	−	0.973952i	$-0.572811\pi$
$509$	−500.181	−	162.519i	−0.982674	−	0.319290i	−0.755921	+	0.654662i	$0.772811\pi$
$510$	−4.56984	−	21.8153i	−0.00896047	−	0.0427752i
$511$	−160.002	−	220.224i	−0.313116	−	0.430968i
$512$	498.391	−	117.261i	0.973420	−	0.229026i
$513$	−327.578	+	642.909i	−0.638554	+	1.25323i
$514$	360.647	−	354.049i	0.701648	−	0.688812i
$515$	64.1367	−	245.523i	0.124537	−	0.476743i
$516$	−40.0280	+	27.9678i	−0.0775737	+	0.0542011i
$517$	51.0658	−	41.3159i	0.0987732	−	0.0799147i
$518$	120.686	+	383.442i	0.232985	+	0.740236i
$519$	271.552	−	373.759i	0.523221	−	0.720152i
$520$	60.0716	−	88.3041i	0.115522	−	0.169816i
$521$	−35.4381	−	109.067i	−0.0680194	−	0.209342i	0.911269	−	0.411811i	$-0.135104\pi$
$521$	−35.4381	−	109.067i	−0.0680194	−	0.209342i	−0.979289	+	0.202469i	$0.935104\pi$
$522$	−633.200	−	469.038i	−1.21303	−	0.898540i
$523$	−81.7832	+	516.359i	−0.156373	+	0.987301i	0.777288	+	0.629145i	$0.216595\pi$
$523$	−81.7832	+	516.359i	−0.156373	+	0.987301i	−0.933661	+	0.358157i	$0.883405\pi$
$524$	−156.014	−	117.812i	−0.297737	−	0.224833i
$525$	−146.435	−	318.079i	−0.278924	−	0.605865i
$526$	142.476	−	70.9463i	0.270868	−	0.134879i
$527$	8.13953	+	8.13953i	0.0154450	+	0.0154450i
$528$	−499.228	+	709.269i	−0.945508	+	1.34331i
$529$			34.9864i			0.0661369i
$530$	−702.107	+	34.7213i	−1.32473	+	0.0655119i
$531$	786.675	+	255.606i	1.48150	+	0.481368i
$532$	−262.255	+	36.5877i	−0.492961	+	0.0687739i
$533$	−4.28158	+	27.0328i	−0.00803299	+	0.0507183i
$534$	106.445	+	714.705i	0.199335	+	1.33840i
$535$	84.2188	−	69.0799i	0.157418	−	0.129121i
$536$	−780.641	−	145.906i	−1.45642	−	0.272213i
$537$	160.893	+	1015.84i	0.299614	+	1.89169i
$538$	75.8835	+	241.096i	0.141047	+	0.448134i
$539$	301.347	−	334.390i	0.559085	−	0.620390i
$540$	−343.756	+	515.483i	−0.636584	+	0.954598i
$541$	367.790	−	506.220i	0.679835	−	0.935712i	−0.320097	−	0.947385i	$-0.603716\pi$
$541$	367.790	−	506.220i	0.679835	−	0.935712i	0.999932	+	0.0116727i	$0.00371561\pi$
$542$	6.56877	−	711.554i	0.0121195	−	1.31283i
$543$	580.393	−	1139.08i	1.06886	−	2.09776i
$544$	−14.1751	−	2.92122i	−0.0260571	−	0.00536989i
$545$	134.981	−	29.5789i	0.247672	−	0.0542732i
$546$	−73.7637	−	12.3821i	−0.135098	−	0.0226778i
$547$	−492.699	+	251.042i	−0.900729	+	0.458944i	−0.842091	−	0.539335i	$-0.818676\pi$
$547$	−492.699	+	251.042i	−0.900729	+	0.458944i	−0.0586375	+	0.998279i	$0.518676\pi$
$548$	312.841	+	324.612i	0.570878	+	0.592357i
$549$	−1672.59			−3.04661
$550$	171.479	+	522.585i	0.311780	+	0.950154i
$551$			600.326i			1.08952i
$552$	264.558	+	898.123i	0.479271	+	1.62703i
$553$	−93.1308	−	182.780i	−0.168410	−	0.330524i
$554$	−280.093	−	47.0168i	−0.505583	−	0.0848679i
$555$	−372.993	−	1702.12i	−0.672059	−	3.06689i
$556$	−257.467	−	88.9439i	−0.463071	−	0.159971i
$557$	−99.6041	−	50.7508i	−0.178822	−	0.0911146i	0.362288	−	0.932066i	$-0.381996\pi$
$557$	−99.6041	−	50.7508i	−0.178822	−	0.0911146i	−0.541110	+	0.840952i	$0.681996\pi$
$558$	7.18285	−	778.072i	0.0128725	−	1.39440i
$559$	5.35083	+	3.88760i	0.00957214	+	0.00695457i
$560$	−227.323	+	4.93795i	−0.405934	+	0.00881777i
$561$	21.2382	−	12.2497i	0.0378578	−	0.0218355i
$562$	−106.738	−	339.128i	−0.189926	−	0.603430i
$563$	−898.071	+	142.240i	−1.59515	+	0.252647i	−0.889848	−	0.456257i	$-0.849190\pi$
$563$	−898.071	+	142.240i	−1.59515	+	0.252647i	−0.705304	+	0.708905i	$0.749190\pi$
$564$	−34.3023	−	112.604i	−0.0608196	−	0.199653i
$565$	−97.8017	−	119.235i	−0.173100	−	0.211036i
$566$	−54.3601	−	364.992i	−0.0960425	−	0.644862i
$567$	42.3713	+	6.71095i	0.0747289	+	0.0118359i
$568$	269.280	−	756.780i	0.474085	−	1.33236i
$569$	37.2528	−	114.652i	0.0654706	−	0.201498i	−0.912970	−	0.408027i	$-0.866217\pi$
$569$	37.2528	−	114.652i	0.0654706	−	0.201498i	0.978440	+	0.206529i	$0.0662169\pi$
$570$	1146.42	−	56.6940i	2.01127	−	0.0994632i
$571$	576.201			1.00911			0.504554	−	0.863380i	$-0.331657\pi$
$571$	576.201			1.00911			0.504554	+	0.863380i	$0.331657\pi$
$572$	112.882	+	32.5443i	0.197346	+	0.0568957i
$573$	797.176	−	797.176i	1.39123	−	1.39123i
$574$	52.1612	−	25.9737i	0.0908731	−	0.0452504i
$575$	556.906	+	205.784i	0.968533	+	0.357885i
$576$	530.345	+	822.099i	0.920738	+	1.42726i
$577$	−743.797	−	117.806i	−1.28908	−	0.204170i	−0.526004	−	0.850482i	$-0.676310\pi$
$577$	−743.797	−	117.806i	−1.28908	−	0.204170i	−0.763073	+	0.646312i	$0.776310\pi$
$578$	−464.127	−	343.799i	−0.802988	−	0.594807i
$579$	−271.602	+	88.2487i	−0.469088	+	0.152416i
$580$	−60.1230	+	511.975i	−0.103660	+	0.882715i
$581$	333.955	+	242.633i	0.574794	+	0.417612i
$582$	152.679	+	485.090i	0.262336	+	0.833489i
$583$	−276.802	−	722.021i	−0.474788	−	1.23846i
$584$	759.796	−	98.8589i	1.30102	−	0.169279i
$585$	197.446	+	51.5778i	0.337514	+	0.0881672i
$586$	102.798	−	100.918i	0.175423	−	0.172214i
$587$	−518.368	−	264.121i	−0.883079	−	0.449951i	−0.0472132	−	0.998885i	$-0.515034\pi$
$587$	−518.368	−	264.121i	−0.883079	−	0.449951i	−0.835866	+	0.548933i	$0.815034\pi$
$588$	−352.889	−	725.387i	−0.600151	−	1.23365i
$589$	−479.578	+	348.434i	−0.814224	+	0.591568i
$590$	−110.943	−	529.617i	−0.188039	−	0.897656i
$591$	−125.331	+	385.730i	−0.212066	+	0.652673i
$592$	−1110.25	−	218.138i	−1.87542	−	0.368476i
$593$	−199.059	−	199.059i	−0.335682	−	0.335682i	0.519058	−	0.854739i	$-0.326283\pi$
$593$	−199.059	−	199.059i	−0.335682	−	0.335682i	−0.854739	+	0.519058i	$0.826283\pi$
$594$	−656.590	−	182.750i	−1.10537	−	0.307659i
$595$	5.88800	+	2.57729i	0.00989580	+	0.00433159i
$596$	−469.085	−	8.66153i	−0.787055	−	0.0145328i
$597$	−379.188	+	193.206i	−0.635156	+	0.323628i
$598$	103.280	−	73.5905i	0.172709	−	0.123061i
$599$	84.5661	−	61.4409i	0.141179	−	0.102572i	−0.514954	−	0.857218i	$-0.672191\pi$
$599$	84.5661	−	61.4409i	0.141179	−	0.102572i	0.656133	+	0.754645i	$0.272191\pi$
$600$	983.379	+	66.4647i	1.63896	+	0.110774i
$601$	−965.522	+	313.717i	−1.60653	+	0.521992i	−0.968710	−	0.248196i	$-0.920162\pi$
$601$	−965.522	+	313.717i	−1.60653	+	0.521992i	−0.637817	+	0.770188i	$0.720162\pi$
$602$	0.129986	−	14.0806i	0.000215923	−	0.0233896i
$603$	−237.384	−	1498.78i	−0.393672	−	2.48555i
$604$	454.333	−	317.444i	0.752207	−	0.525570i
$605$	−487.519	+	358.260i	−0.805817	+	0.592165i
$606$	874.943	−	1678.68i	1.44380	−	2.77010i
$607$	−51.1511	−	322.956i	−0.0842688	−	0.532052i	−0.993322	−	0.115373i	$-0.963194\pi$
$607$	−51.1511	−	322.956i	−0.0842688	−	0.532052i	0.909054	−	0.416679i	$-0.136806\pi$
$608$	262.779	−	697.463i	0.432202	−	1.14714i
$609$	343.348	−	111.561i	0.563790	−	0.183187i
$610$	544.294	+	949.194i	0.892285	+	1.55606i
$611$	−12.8989	+	9.37158i	−0.0211111	+	0.0153381i
$612$	−3.82115	−	27.3894i	−0.00624370	−	0.0447540i
$613$	−2.18637	+	1.11401i	−0.00356667	+	0.00181731i	−0.455773	−	0.890096i	$-0.650637\pi$
$613$	−2.18637	+	1.11401i	−0.00356667	+	0.00181731i	0.452206	+	0.891913i	$0.350637\pi$
$614$	−343.580	−	689.988i	−0.559577	−	1.12376i
$615$	−235.237	+	91.9993i	−0.382499	+	0.149592i
$616$	−83.0313	−	235.930i	−0.134791	−	0.383003i
$617$	−366.501	−	366.501i	−0.594005	−	0.594005i	0.344706	−	0.938711i	$-0.387979\pi$
$617$	−366.501	−	366.501i	−0.594005	−	0.594005i	−0.938711	+	0.344706i	$0.887979\pi$
$618$	158.963	−	474.296i	0.257222	−	0.767469i
$619$	135.121	−	415.860i	0.218289	−	0.671825i	−0.780614	−	0.625013i	$-0.785094\pi$
$619$	135.121	−	415.860i	0.218289	−	0.671825i	0.998904	−	0.0468123i	$-0.0149063\pi$
$620$	−443.893	+	249.124i	−0.715957	+	0.401813i
$621$	−595.204	+	432.441i	−0.958460	+	0.696362i
$622$	−445.876	−	330.279i	−0.716842	−	0.530995i
$623$	−185.660	−	94.5982i	−0.298009	−	0.151843i
$624$	129.949	−	165.637i	0.208252	−	0.265444i
$625$	406.401	−	474.830i	0.650241	−	0.759728i
$626$	−428.263	+	821.672i	−0.684126	+	1.31258i
$627$	451.971	+	1178.94i	0.720846	+	1.88029i
$628$	−20.5421	−	3.64351i	−0.0327104	−	0.00580178i
$629$	25.8756	+	18.7997i	0.0411377	+	0.0298883i
$630$	−154.503	−	406.068i	−0.245243	−	0.644552i
$631$	466.366	−	151.532i	0.739091	−	0.240145i	0.0848102	−	0.996397i	$-0.472972\pi$
$631$	466.366	−	151.532i	0.739091	−	0.240145i	0.654280	+	0.756252i	$0.272972\pi$
$632$	577.184	+	15.9886i	0.913266	+	0.0252984i
$633$	−969.312	−	153.524i	−1.53130	−	0.242534i
$634$	−88.7910	+	528.954i	−0.140049	+	0.834312i
$635$	704.412	−	41.3570i	1.10931	−	0.0651292i
$636$	−1385.48	−	25.5825i	−2.17843	−	0.0402241i
$637$	−77.2593	+	77.2593i	−0.121286	+	0.121286i
$638$	−555.764	+	112.531i	−0.871103	+	0.176380i
$639$	1534.86			2.40197
$640$	293.956	−	568.498i	0.459306	−	0.888278i
$641$	−146.257	+	450.134i	−0.228171	+	0.702237i	0.769784	+	0.638305i	$0.220364\pi$
$641$	−146.257	+	450.134i	−0.228171	+	0.702237i	−0.997954	+	0.0639323i	$0.979636\pi$
$642$	174.869	−	124.600i	0.272382	−	0.194081i
$643$	450.266	+	71.3152i	0.700258	+	0.110910i	0.496405	−	0.868091i	$-0.334653\pi$
$643$	450.266	+	71.3152i	0.700258	+	0.110910i	0.203854	+	0.979001i	$0.434653\pi$
$644$	−255.193	−	88.1583i	−0.396263	−	0.136892i
$645$	−5.99865	+	60.7429i	−0.00930023	+	0.0941750i
$646$	−15.0345	+	14.7595i	−0.0232732	+	0.0228475i
$647$	56.8522	−	9.00451i	0.0878706	−	0.0139173i	−0.112344	−	0.993669i	$-0.535836\pi$
$647$	56.8522	−	9.00451i	0.0878706	−	0.0139173i	0.200215	+	0.979752i	$0.435836\pi$
$648$	−73.6527	+	95.6858i	−0.113662	+	0.147663i
$649$	515.607	−	297.390i	0.794463	−	0.458228i
$650$	−34.9824	−	128.835i	−0.0538191	−	0.198208i
$651$	288.404	+	209.537i	0.443016	+	0.321870i
$652$	112.105	−	210.327i	0.171941	−	0.322588i
$653$	−374.678	−	190.908i	−0.573779	−	0.292355i	0.142924	−	0.989734i	$-0.454350\pi$
$653$	−374.678	−	190.908i	−0.573779	−	0.292355i	−0.716703	+	0.697379i	$0.754350\pi$
$654$	269.423	−	40.1265i	0.411962	−	0.0613555i
$655$	−238.711	+	52.3095i	−0.364444	+	0.0798618i
$656$	−6.05489	+	163.902i	−0.00923002	+	0.249851i
$657$	664.662	+	1304.47i	1.01166	+	1.98550i
$658$	32.1849	+	10.7870i	0.0489132	+	0.0163936i
$659$			74.8890i			0.113640i	0.998384	+	0.0568202i	$0.0180962\pi$
$659$			74.8890i			0.113640i	−0.998384	+	0.0568202i	$0.981904\pi$
$660$	267.382	+	1050.70i	0.405124	+	1.59196i
$661$	734.485			1.11117			0.555586	−	0.831459i	$-0.312494\pi$
$661$	734.485			1.11117			0.555586	+	0.831459i	$0.312494\pi$
$662$	−170.398	+	508.414i	−0.257399	+	0.767997i
$663$	−5.30248	+	2.70175i	−0.00799771	+	0.00407504i
$664$	−1049.46	+	498.618i	−1.58051	+	0.750931i
$665$	−178.524	+	278.723i	−0.268458	+	0.419132i
$666$	−318.486	−	2138.42i	−0.478207	−	3.21084i
$667$	−277.890	+	545.391i	−0.416627	+	0.817677i
$668$	−227.109	+	426.092i	−0.339984	+	0.637863i
$669$	1153.64	−	1587.85i	1.72443	−	2.37347i
$670$	−773.310	+	622.449i	−1.15419	+	0.929029i
$671$	−805.747	+	894.100i	−1.20082	+	1.33249i
$672$	−447.737	−	20.6807i	−0.666276	−	0.0307749i
$673$	156.469	+	987.908i	0.232495	+	1.46792i	0.777182	+	0.629276i	$0.216649\pi$
$673$	156.469	+	987.908i	0.232495	+	1.46792i	−0.544687	+	0.838640i	$0.683351\pi$
$674$	668.152	+	680.603i	0.991324	+	1.00980i
$675$	209.838	+	745.518i	0.310871	+	1.10447i
$676$	611.996	+	211.418i	0.905319	+	0.312749i
$677$	−135.462	+	855.274i	−0.200092	+	1.26333i	0.659248	+	0.751925i	$0.270875\pi$
$677$	−135.462	+	855.274i	−0.200092	+	1.26333i	−0.859340	+	0.511404i	$0.829125\pi$
$678$	−176.406	−	247.576i	−0.260186	−	0.365157i
$679$	−139.472	−	45.3171i	−0.205407	−	0.0667409i
$680$	−14.3000	+	11.0816i	−0.0210294	+	0.0162964i
$681$			886.759i			1.30214i
$682$	−412.466	−	378.665i	−0.604789	−	0.555228i
$683$	−757.540	−	757.540i	−1.10914	−	1.10914i	−0.993264	−	0.115871i	$-0.963034\pi$
$683$	−757.540	−	757.540i	−1.10914	−	1.10914i	−0.115871	−	0.993264i	$-0.536966\pi$
$684$	1423.91	+	26.2921i	2.08174	+	0.0384388i
$685$	562.561	−	33.0287i	0.821257	−	0.0482172i
$686$	504.100	+	84.6190i	0.734840	+	0.123351i
$687$	17.0086	−	107.388i	0.0247578	−	0.156315i
$688$	34.6262	+	19.2851i	0.0503288	+	0.0280307i
$689$	57.9998	+	178.505i	0.0841797	+	0.259079i
$690$	1067.76	+	479.172i	1.54748	+	0.694452i
$691$	−177.059	+	243.700i	−0.256235	+	0.352678i	−0.917683	−	0.397314i	$-0.869942\pi$
$691$	−177.059	+	243.700i	−0.256235	+	0.352678i	0.661447	+	0.749992i	$0.269942\pi$
$692$	−369.222	−	65.4881i	−0.533558	−	0.0946360i
$693$	371.538	−	300.602i	0.536131	−	0.433768i
$694$	897.205	+	467.631i	1.29280	+	0.673820i
$695$	−293.803	+	172.098i	−0.422739	+	0.247623i
$696$	−186.693	+	998.865i	−0.268238	+	1.43515i
$697$	2.10482	−	4.13094i	0.00301983	−	0.00592675i
$698$	−217.737	+	293.944i	−0.311943	+	0.421123i
$699$	825.433	+	1136.11i	1.18088	+	1.62534i
$700$	−180.165	+	219.823i	−0.257378	+	0.314033i
$701$	−417.882	−	135.778i	−0.596122	−	0.193692i	−0.00461206	−	0.999989i	$-0.501468\pi$
$701$	−417.882	−	135.778i	−0.596122	−	0.193692i	−0.591510	+	0.806297i	$0.701468\pi$
$702$	156.855	+	52.5709i	0.223440	+	0.0748873i
$703$	−1164.68	+	1164.68i	−1.65672	+	1.65672i
$704$	694.948	+	112.534i	0.987141	+	0.159849i
$705$	−134.793	−	59.0018i	−0.191196	−	0.0836904i
$706$	−290.141	+	144.476i	−0.410964	+	0.204640i
$707$	247.825	+	486.385i	0.350531	+	0.687955i
$708$	−147.385	−	1056.43i	−0.208171	−	1.49214i
$709$	362.299	+	498.662i	0.511000	+	0.703331i	0.984088	−	0.177684i	$-0.0568606\pi$
$709$	362.299	+	498.662i	0.511000	+	0.703331i	−0.473087	+	0.881015i	$0.656861\pi$
$710$	−499.473	−	871.031i	−0.703484	−	1.22680i
$711$	340.938	+	1049.30i	0.479519	+	1.47581i
$712$	483.855	−	331.467i	0.679572	−	0.465544i
$713$	−596.982	+	94.5526i	−0.837282	+	0.132612i
$714$	11.2354	+	5.85598i	0.0157358	+	0.00820166i
$715$	122.688	−	80.6998i	0.171592	−	0.112867i
$716$	684.313	−	478.132i	0.955744	−	0.667783i
$717$	1407.13	−	222.868i	1.96253	−	0.310834i
$718$	325.774	+	3.00742i	0.453725	+	0.00418860i
$719$	36.2624	+	111.604i	0.0504345	+	0.155221i	0.973102	−	0.230376i	$-0.0739955\pi$
$719$	36.2624	+	111.604i	0.0504345	+	0.155221i	−0.922667	+	0.385597i	$0.873996\pi$
$720$	1211.72	+	165.028i	1.68294	+	0.229206i
$721$	84.7872	+	116.700i	0.117597	+	0.161858i
$722$	−210.631	−	295.609i	−0.291733	−	0.409431i
$723$	1051.20	+	2063.09i	1.45394	+	2.85351i
$724$	−1037.48	−	19.1569i	−1.43299	−	0.0264597i
$725$	437.149	+	473.400i	0.602964	+	0.652966i
$726$	−1006.70	+	639.412i	−1.38665	+	0.880733i
$727$	−626.526	+	626.526i	−0.861797	+	0.861797i	−0.991547	−	0.129750i	$-0.958582\pi$
$727$	−626.526	+	626.526i	−0.861797	+	0.861797i	0.129750	+	0.991547i	$0.458582\pi$
$728$	17.1543	+	58.2355i	0.0235636	+	0.0799938i
$729$	1087.35	+	353.301i	1.49156	+	0.484637i
$730$	523.993	−	801.696i	0.717799	−	1.09821i
$731$	−0.658534	−	0.906395i	−0.000900868	−	0.00123994i
$732$	943.562	+	1939.56i	1.28902	+	2.64967i
$733$	142.101	−	278.888i	0.193862	−	0.380475i	−0.773530	−	0.633760i	$-0.781511\pi$
$733$	142.101	−	278.888i	0.193862	−	0.380475i	0.967392	+	0.253285i	$0.0815109\pi$
$734$	−441.273	−	449.496i	−0.601189	−	0.612393i
$735$	−975.600	−	254.851i	−1.32735	−	0.346736i
$736$	561.587	−	511.998i	0.763025	−	0.695650i
$737$	−915.546	−	595.123i	−1.24226	−	0.807493i
$738$	−298.938	+	94.0890i	−0.405065	+	0.127492i
$739$	806.430	−	1109.96i	1.09124	−	1.50197i	0.244740	−	0.969589i	$-0.421297\pi$
$739$	806.430	−	1109.96i	1.09124	−	1.50197i	0.846505	−	0.532381i	$-0.178703\pi$
$740$	−1109.91	+	876.625i	−1.49988	+	1.18463i
$741$	−94.7040	−	291.469i	−0.127806	−	0.393345i
$742$	237.850	−	321.097i	0.320552	−	0.432745i
$743$	46.2152	−	291.791i	0.0622008	−	0.392721i	−0.936872	−	0.349672i	$-0.886293\pi$
$743$	46.2152	−	291.791i	0.0622008	−	0.392721i	0.999073	−	0.0430485i	$-0.0137070\pi$
$744$	−906.314	+	430.606i	−1.21816	+	0.578772i
$745$	−389.669	+	438.279i	−0.523046	+	0.588294i
$746$	−569.373	−	1143.43i	−0.763235	−	1.53275i
$747$	−1569.86	−	1569.86i	−2.10156	−	2.10156i
$748$	−16.4821	−	11.1518i	−0.0220349	−	0.0149089i
$749$			61.9180i			0.0826675i
$750$	862.753	−	879.516i	1.15034	−	1.17269i
$751$	111.707	+	36.2957i	0.148744	+	0.0483298i	0.382443	−	0.923979i	$-0.375083\pi$
$751$	111.707	+	36.2957i	0.148744	+	0.0483298i	−0.233699	+	0.972309i	$0.575083\pi$
$752$	−70.0079	+	65.0197i	−0.0930956	+	0.0864623i
$753$	102.204	−	645.290i	0.135729	−	0.856959i
$754$	136.135	−	20.2752i	0.180550	−	0.0268902i
$755$	68.0869	−	689.454i	0.0901813	−	0.913184i
$756$	−102.633	−	336.914i	−0.135758	−	0.445654i
$757$	−51.6513	−	326.113i	−0.0682316	−	0.430797i	−0.998031	−	0.0627295i	$-0.980019\pi$
$757$	−51.6513	−	326.113i	−0.0682316	−	0.430797i	0.929799	−	0.368068i	$-0.119981\pi$
$758$	908.534	−	285.956i	1.19859	−	0.377250i
$759$	−135.119	+	1280.27i	−0.178022	+	1.68679i
$760$	−448.447	−	816.624i	−0.590062	−	1.07450i
$761$	116.789	−	160.746i	0.153467	−	0.211230i	−0.725360	−	0.688370i	$-0.758327\pi$
$761$	116.789	−	160.746i	0.153467	−	0.211230i	0.878827	+	0.477140i	$0.158327\pi$
$762$	1390.90	+	12.8402i	1.82533	+	0.0168507i
$763$	−35.6608	+	69.9882i	−0.0467376	+	0.0917276i
$764$	−864.903	−	298.787i	−1.13207	−	0.391082i
$765$	−29.1092	−	18.6447i	−0.0380513	−	0.0243722i
$766$	−94.0138	+	560.068i	−0.122733	+	0.731159i
$767$	−128.730	+	65.5911i	−0.167835	+	0.0855164i
$768$	654.131	−	1078.77i	0.851733	−	1.40464i
$769$	331.548			0.431142			0.215571	−	0.976488i	$-0.430839\pi$
$769$	331.548			0.431142			0.215571	+	0.976488i	$0.430839\pi$
$770$	−291.497	−	113.026i	−0.378568	−	0.146787i
$771$		−	1245.30i		−	1.61518i
$772$	160.851	+	166.902i	0.208356	+	0.216195i
$773$	50.0116	+	98.1532i	0.0646980	+	0.126977i	0.921091	−	0.389348i	$-0.127300\pi$
$773$	50.0116	+	98.1532i	0.0646980	+	0.126977i	−0.856393	+	0.516325i	$0.827300\pi$
$774$	−12.5372	+	74.6879i	−0.0161980	+	0.0964960i
$775$	−124.457	+	623.987i	−0.160590	+	0.805145i
$776$	299.846	−	283.682i	0.386400	−	0.365570i
$777$	882.557	+	449.685i	1.13585	+	0.578745i
$778$	544.040	+	5.02235i	0.699280	+	0.00645547i
$779$	193.158	+	140.338i	0.247957	+	0.180151i
$780$	−51.5754	−	258.057i	−0.0661223	−	0.330843i
$781$	739.397	−	820.474i	0.946731	−	1.05054i
$782$	−20.4909	+	6.44937i	−0.0262031	+	0.00824728i
$783$	−788.654	+	124.910i	−1.00722	+	0.159528i
$784$	−404.145	+	515.135i	−0.515491	+	0.657060i
$785$	−20.1632	+	16.5387i	−0.0256856	+	0.0210684i
$786$	−476.467	+	70.9626i	−0.606192	+	0.0902832i
$787$	66.5836	+	10.5458i	0.0846043	+	0.0134000i	0.198593	−	0.980082i	$-0.436363\pi$
$787$	66.5836	+	10.5458i	0.0846043	+	0.0134000i	−0.113989	+	0.993482i	$0.536363\pi$
$788$	326.040	−	45.4864i	0.413756	−	0.0577238i
$789$	121.192	−	372.992i	0.153602	−	0.472740i
$790$	484.528	−	534.944i	0.613327	−	0.677145i
$791$	87.6621			0.110824
$792$	242.570	+	1323.14i	0.306275	+	1.67063i
$793$	206.578	−	206.578i	0.260502	−	0.260502i
$794$	151.444	+	304.134i	0.190736	+	0.383041i
$795$	−1150.92	+	1294.49i	−1.44770	+	1.62829i
$796$	275.658	+	208.160i	0.346304	+	0.261508i
$797$	1181.79	+	187.177i	1.48279	+	0.234851i	0.844755	−	0.535153i	$-0.179746\pi$
$797$	1181.79	+	187.177i	1.48279	+	0.234851i	0.638038	+	0.770005i	$0.279746\pi$
$798$	−388.369	+	524.297i	−0.486678	+	0.657014i
$799$	2.56860	−	0.834590i	0.00321477	−	0.00104454i
$800$	−300.663	−	741.351i	−0.375829	−	0.926689i
$801$	906.650	+	658.720i	1.13190	+	0.822372i
$802$	−345.240	+	108.662i	−0.430474	+	0.135489i
$803$	1017.51	+	273.110i	1.26714	+	0.340112i
$804$	−1604.09	+	1120.79i	−1.99514	+	1.39401i
$805$	−291.208	+	170.578i	−0.361749	+	0.211898i
$806$	95.2108	+	96.9851i	0.118128	+	0.120329i
$807$	554.923	+	282.747i	0.687637	+	0.350368i
$808$	−1535.91	−	42.5464i	−1.90088	−	0.0526565i
$809$	1131.20	−	821.868i	1.39827	−	1.01591i	0.403375	−	0.915035i	$-0.367837\pi$
$809$	1131.20	−	821.868i	1.39827	−	1.01591i	0.994900	−	0.100871i	$-0.0321630\pi$
$810$	30.9463	+	147.731i	0.0382054	+	0.182384i
$811$	337.214	−	1037.84i	0.415800	−	1.27970i	−0.495734	−	0.868475i	$-0.665101\pi$
$811$	337.214	−	1037.84i	0.415800	−	1.27970i	0.911533	−	0.411226i	$-0.134899\pi$
$812$	−203.341	−	210.992i	−0.250420	−	0.259842i
$813$	−1239.83	−	1239.83i	−1.52500	−	1.52500i
$814$	−1296.54	−	859.905i	−1.59280	−	1.05639i
$815$	−108.512	−	277.459i	−0.133143	−	0.340440i
$816$	−29.6055	+	19.8823i	−0.0362812	+	0.0243656i
$817$	51.4077	−	26.1935i	0.0629225	−	0.0320606i
$818$	753.545	+	1057.56i	0.921204	+	1.29286i
$819$	−93.8481	+	68.1847i	−0.114589	+	0.0832536i
$820$	150.676	+	139.029i	0.183751	+	0.169547i
$821$	298.904	−	97.1199i	0.364073	−	0.118295i	−0.121267	−	0.992620i	$-0.538696\pi$
$821$	298.904	−	97.1199i	0.364073	−	0.118295i	0.485340	+	0.874325i	$0.338696\pi$
$822$	1110.81	+	10.2545i	1.35135	+	0.0124751i
$823$	58.5040	+	369.380i	0.0710863	+	0.448821i	0.997400	+	0.0720674i	$0.0229597\pi$
$823$	58.5040	+	369.380i	0.0710863	+	0.448821i	−0.926314	+	0.376754i	$0.877040\pi$
$824$	−402.625	+	52.3865i	−0.488622	+	0.0635759i
$825$	1214.90	+	600.559i	1.47260	+	0.727951i
$826$	272.764	+	142.167i	0.330223	+	0.172115i
$827$	−73.7927	−	465.909i	−0.0892293	−	0.563372i	−0.991283	−	0.131748i	$-0.957941\pi$
$827$	−73.7927	−	465.909i	−0.0892293	−	0.563372i	0.902054	−	0.431624i	$-0.142059\pi$
$828$	1281.44	+	683.013i	1.54763	+	0.824894i
$829$	−1048.83	+	340.785i	−1.26517	+	0.411079i	−0.863335	−	0.504631i	$-0.831628\pi$
$829$	−1048.83	+	340.785i	−1.26517	+	0.411079i	−0.401838	+	0.915711i	$0.631628\pi$
$830$	−380.032	+	1401.76i	−0.457870	+	1.68887i
$831$	−566.166	+	411.344i	−0.681307	+	0.494999i
$832$	−167.037	−	36.0339i	−0.200766	−	0.0433099i
$833$	16.4909	−	8.40251i	0.0197970	−	0.0100871i
$834$	−600.834	+	299.186i	−0.720424	+	0.358736i
$835$	219.829	+	562.091i	0.263268	+	0.673162i
$836$	700.003	−	748.499i	0.837325	−	0.895333i
$837$	−557.527	−	557.527i	−0.666101	−	0.666101i
$838$	323.929	+	108.567i	0.386550	+	0.129555i
$839$	333.431	−	1026.19i	0.397414	−	1.22312i	−0.529651	−	0.848216i	$-0.677677\pi$
$839$	333.431	−	1026.19i	0.397414	−	1.22312i	0.927065	−	0.374900i	$-0.122323\pi$
$840$	−383.720	+	408.239i	−0.456810	+	0.485999i
$841$	142.928	−	103.843i	0.169949	−	0.123476i
$842$	−568.887	+	767.996i	−0.675638	+	0.912110i
$843$	−780.560	−	397.715i	−0.925931	−	0.471785i
$844$	232.125	+	761.997i	0.275030	+	0.902840i
$845$	698.366	−	409.075i	0.826468	−	0.484112i
$846$	−161.894	−	84.3804i	−0.191364	−	0.0997404i
$847$	18.2940	−	343.420i	0.0215986	−	0.405455i
$848$	473.279	+	1020.32i	0.558111	+	1.20321i
$849$	−735.623	−	534.461i	−0.866458	−	0.629519i
$850$	−1.10816	+	22.5868i	−0.00130371	+	0.0265727i
$851$	−1597.23	+	518.970i	−1.87688	+	0.609836i
$852$	−865.863	−	1779.84i	−1.01627	−	2.08901i
$853$	85.2454	+	13.5016i	0.0999360	+	0.0158283i	0.206202	−	0.978509i	$-0.433890\pi$
$853$	85.2454	+	13.5016i	0.0999360	+	0.0158283i	−0.106266	+	0.994338i	$0.533890\pi$
$854$	−613.394	−	102.965i	−0.718260	−	0.120568i
$855$	1182.84	−	1330.40i	1.38344	−	1.55602i
$856$	−153.035	−	83.3917i	−0.178780	−	0.0974202i
$857$	324.392	−	324.392i	0.378521	−	0.378521i	−0.492048	−	0.870568i	$-0.663751\pi$
$857$	324.392	−	324.392i	0.378521	−	0.378521i	0.870568	+	0.492048i	$0.163751\pi$
$858$	252.081	−	142.310i	0.293801	−	0.165862i
$859$	402.374			0.468422			0.234211	−	0.972186i	$-0.424749\pi$
$859$	402.374			0.468422			0.234211	+	0.972186i	$0.424749\pi$
$860$	46.4652	−	17.1900i	0.0540293	−	0.0199884i
$861$	44.3690	−	136.554i	0.0515319	−	0.158599i
$862$	491.123	+	689.265i	0.569748	+	0.799611i
$863$	942.900	+	149.341i	1.09258	+	0.173048i	0.676620	−	0.736333i	$-0.263444\pi$
$863$	942.900	+	149.341i	1.09258	+	0.173048i	0.415964	+	0.909381i	$0.363444\pi$
$864$	970.939	+	200.093i	1.12377	+	0.231589i
$865$	−362.411	+	297.265i	−0.418973	+	0.343659i
$866$	267.708	+	272.697i	0.309132	+	0.314892i
$867$	−1405.69	+	222.640i	−1.62133	+	0.256794i
$868$	50.5326	−	284.903i	0.0582173	−	0.328229i
$869$	725.155	+	323.233i	0.834470	+	0.371960i
$870$	796.452	+	989.484i	0.915462	+	1.13734i
$871$	214.430	+	155.793i	0.246188	+	0.178866i
$872$	−124.953	−	182.399i	−0.143295	−	0.209173i
$873$	702.759	+	358.073i	0.804993	+	0.410164i
$874$	−162.964	−	1094.20i	−0.186458	−	1.25194i
$875$	62.1825	+	349.792i	0.0710658	+	0.399762i
$876$	1137.72	−	1506.64i	1.29877	−	1.71991i
$877$	171.478	+	336.544i	0.195527	+	0.383744i	0.967866	−	0.251467i	$-0.0809130\pi$
$877$	171.478	+	336.544i	0.195527	+	0.383744i	−0.772338	+	0.635211i	$0.780913\pi$
$878$	413.596	−	1234.04i	0.471066	−	1.40551i
$879$		−	354.959i		−	0.403822i
$880$	671.945	−	568.235i	0.763573	−	0.645721i
$881$	−558.318			−0.633732			−0.316866	−	0.948470i	$-0.602631\pi$
$881$	−558.318			−0.633732			−0.316866	+	0.948470i	$0.602631\pi$
$882$	−1186.23	−	397.574i	−1.34494	−	0.450764i
$883$	129.788	−	66.1305i	0.146986	−	0.0748929i	−0.378951	−	0.925417i	$-0.623715\pi$
$883$	129.788	−	66.1305i	0.146986	−	0.0748929i	0.525936	+	0.850524i	$0.323715\pi$
$884$	3.85475	+	2.91086i	0.00436057	+	0.00329283i
$885$	−1122.77	−	719.142i	−1.26866	−	0.812590i
$886$	−801.242	+	119.333i	−0.904336	+	0.134687i
$887$	85.0173	−	166.856i	0.0958482	−	0.188113i	−0.838104	−	0.545510i	$-0.816336\pi$
$887$	85.0173	−	166.856i	0.0958482	−	0.188113i	0.933952	+	0.357398i	$0.116336\pi$
$888$	−2300.07	+	1575.67i	−2.59017	+	1.77441i
$889$	−235.765	+	324.502i	−0.265202	+	0.365019i
$890$	78.7813	−	728.884i	0.0885184	−	0.818971i
$891$	−143.823	+	82.9536i	−0.161417	+	0.0931017i
$892$	−1568.58	−	278.216i	−1.75850	−	0.311901i
$893$	21.7576	+	137.372i	0.0243646	+	0.153832i
$894$	−824.960	+	809.868i	−0.922774	+	0.905893i
$895$	102.552	−	1038.45i	0.114583	−	1.16028i
$896$	143.886	+	334.139i	0.160587	+	0.372923i
$897$	48.8830	−	308.635i	0.0544961	−	0.344075i
$898$	−735.566	+	524.114i	−0.819116	+	0.583646i
$899$	−623.887	−	202.713i	−0.693979	−	0.225487i
$900$	1142.00	−	1016.14i	1.26889	−	1.12904i
$901$		−	31.7937i		−	0.0352871i
$902$	−93.7131	+	205.126i	−0.103895	+	0.227413i
$903$	−24.5343	−	24.5343i	−0.0271698	−	0.0271698i
$904$	−118.064	+	216.664i	−0.130602	+	0.239673i
$905$	−861.837	+	969.349i	−0.952307	+	1.07110i
$906$	226.084	−	1346.85i	0.249541	−	1.48659i
$907$	−113.102	+	714.095i	−0.124699	+	0.787316i	0.843499	+	0.537130i	$0.180492\pi$
$907$	−113.102	+	714.095i	−0.124699	+	0.787316i	−0.968198	+	0.250186i	$0.919508\pi$
$908$	647.230	−	314.867i	0.712809	−	0.346770i
$909$	−907.250	−	2792.23i	−0.998075	−	3.07176i
$910$	69.2348	+	31.0701i	0.0760822	+	0.0341430i
$911$	333.512	−	459.040i	0.366095	−	0.503886i	−0.585739	−	0.810499i	$-0.699196\pi$
$911$	333.512	−	459.040i	0.366095	−	0.503886i	0.951834	+	0.306613i	$0.0991958\pi$
$912$	−772.784	−	1666.01i	−0.847351	−	1.82677i
$913$	−1595.45	+	82.9259i	−1.74748	+	0.0908279i
$914$	678.502	−	1301.79i	0.742344	−	1.42427i
$915$	2608.58	+	681.427i	2.85091	+	0.744729i
$916$	−84.4203	+	25.7167i	−0.0921619	+	0.0280750i
$917$	63.0651	−	123.772i	0.0687732	−	0.134975i
$918$	−22.5179	−	16.6799i	−0.0245293	−	0.0181699i
$919$	32.1978	+	44.3165i	0.0350357	+	0.0482225i	0.826175	−	0.563413i	$-0.190512\pi$
$919$	32.1978	+	44.3165i	0.0350357	+	0.0482225i	−0.791140	+	0.611635i	$0.790512\pi$
$920$	−29.3959	−	949.481i	−0.0319521	−	1.03204i
$921$	−1806.33	−	586.913i	−1.96127	−	0.637256i
$922$	−159.369	+	475.507i	−0.172852	+	0.515734i
$923$	−189.567	+	189.567i	−0.205381	+	0.205381i
$924$	−558.178	−	261.261i	−0.604088	−	0.282750i
$925$	−70.3301	+	1766.53i	−0.0760325	+	1.90977i
$926$	−215.629	−	433.032i	−0.232861	−	0.467638i
$927$	−352.212	−	691.255i	−0.379948	−	0.745690i
$928$	795.345	−	218.409i	0.857053	−	0.235354i
$929$	892.059	+	1227.81i	0.960236	+	1.32165i	0.946828	+	0.321741i	$0.104268\pi$
$929$	892.059	+	1227.81i	0.960236	+	1.32165i	0.0134083	+	0.999910i	$0.495732\pi$
$930$	−328.195	+	1210.56i	−0.352898	+	1.30168i
$931$	294.532	+	906.476i	0.316361	+	0.973659i
$932$	536.137	−	1005.88i	0.575254	−	1.07927i
$933$	−1350.42	+	213.885i	−1.44739	+	0.229244i
$934$	183.275	−	351.634i	0.196225	−	0.376482i
$935$	−23.9897	+	6.57878i	−0.0256574	+	0.00703613i
$936$	−42.1285	−	323.785i	−0.0450091	−	0.345924i
$937$	−1318.76	+	208.871i	−1.40743	+	0.222915i	−0.813483	−	0.581589i	$-0.802431\pi$
$937$	−1318.76	+	208.871i	−1.40743	+	0.222915i	−0.593947	+	0.804504i	$0.702431\pi$
$938$	5.20908	−	564.267i	0.00555339	−	0.601564i
$939$	705.532	+	2171.40i	0.751365	+	2.31246i
$940$	4.79758	+	119.334i	0.00510380	+	0.126951i
$941$	433.808	+	597.085i	0.461007	+	0.634522i	0.974717	−	0.223442i	$-0.0717293\pi$
$941$	433.808	+	597.085i	0.461007	+	0.634522i	−0.513710	+	0.857964i	$0.671729\pi$
$942$	−41.8663	+	29.8311i	−0.0444440	+	0.0316678i
$943$	110.520	+	216.908i	0.117201	+	0.230019i
$944$	−718.740	+	482.688i	−0.761377	+	0.511322i
$945$	−403.306	−	176.535i	−0.426779	−	0.186809i
$946$	33.8855	+	42.6817i	0.0358198	+	0.0451181i
$947$	−291.906	+	291.906i	−0.308243	+	0.308243i	−0.844228	−	0.535985i	$-0.819940\pi$
$947$	−291.906	+	291.906i	−0.308243	+	0.308243i	0.535985	+	0.844228i	$0.319940\pi$
$948$	1024.44	−	987.298i	1.08064	−	1.04145i
$949$	−243.203	−	79.0215i	−0.256273	−	0.0832682i
$950$	−1139.92	−	238.325i	−1.19992	−	0.250868i
$951$	776.821	+	1069.20i	0.816846	+	1.12429i
$952$	0.284763	−	10.2798i	0.000299120	−	0.0107982i
$953$	201.614	−	395.689i	0.211557	−	0.415204i	−0.760705	−	0.649097i	$-0.775147\pi$
$953$	201.614	−	395.689i	0.211557	−	0.415204i	0.972262	+	0.233894i	$0.0751468\pi$
$954$	−1533.64	+	1505.58i	−1.60759	+	1.57818i
$955$	−986.965	+	578.125i	−1.03347	+	0.605366i
$956$	−662.307	−	947.907i	−0.692790	−	0.991535i
$957$	−761.486	+	1171.48i	−0.795701	+	1.22412i
$958$	106.783	+	339.269i	0.111464	+	0.354143i
$959$	−188.287	+	259.155i	−0.196337	+	0.270235i
$960$	−492.199	−	1498.22i	−0.512708	−	1.56064i
$961$	96.7966	+	297.909i	0.100725	+	0.309999i
$962$	303.447	+	224.776i	0.315433	+	0.233655i
$963$	52.0949	−	328.914i	0.0540965	−	0.341552i
$964$	1132.56	−	1499.80i	1.17485	−	1.55581i
$965$	289.247	−	16.9821i	0.299738	−	0.0175980i
$966$	−595.526	+	296.543i	−0.616487	+	0.306981i
$967$	−1136.75	−	1136.75i	−1.17554	−	1.17554i	−0.980868	−	0.194672i	$-0.937636\pi$
$967$	−1136.75	−	1136.75i	−1.17554	−	1.17554i	−0.194672	−	0.980868i	$-0.562364\pi$
$968$	824.153	+	507.737i	0.851397	+	0.524521i
$969$			51.9137i			0.0535746i
$970$	−25.4851	−	515.339i	−0.0262733	−	0.531278i
$971$	−1287.46	−	418.321i	−1.32591	−	0.430815i	−0.441390	−	0.897315i	$-0.645515\pi$
$971$	−1287.46	−	418.321i	−1.32591	−	0.430815i	−0.884521	+	0.466500i	$0.845515\pi$
$972$	−112.988	−	809.883i	−0.116243	−	0.833213i
$973$	30.2783	−	191.170i	0.0311185	−	0.196475i
$974$	108.755	+	730.218i	0.111658	+	0.749710i
$975$	−286.924	−	160.882i	−0.294282	−	0.165007i
$976$	1080.61	−	1377.38i	1.10718	−	1.41125i
$977$	−118.462	−	747.937i	−0.121250	−	0.765545i	−0.971127	−	0.238563i	$-0.923324\pi$
$977$	−118.462	−	747.937i	−0.121250	−	0.765545i	0.849877	−	0.526982i	$-0.176676\pi$
$978$	−176.316	−	560.187i	−0.180282	−	0.572788i
$979$	788.892	−	167.330i	0.805814	−	0.170919i
$980$	160.401	+	802.565i	0.163674	+	0.818944i
$981$	248.318	−	341.781i	0.253128	−	0.348400i
$982$	−10.7940	+	1169.25i	−0.0109919	+	1.19068i
$983$	607.461	−	1192.21i	0.617966	−	1.21283i	−0.343823	−	0.939035i	$-0.611722\pi$
$983$	607.461	−	1192.21i	0.617966	−	1.21283i	0.961789	−	0.273792i	$-0.0882781\pi$
$984$	277.747	+	293.573i	0.282263	+	0.298347i
$985$	221.944	−	346.512i	0.225324	−	0.351789i
$986$	−22.9930	−	3.85964i	−0.0233195	−	0.00391444i
$987$	74.5247	−	37.9723i	0.0755063	−	0.0384724i
$988$	−179.111	+	172.616i	−0.181286	+	0.174713i
$989$	58.8284			0.0594827
$990$	1453.37	+	845.658i	1.46805	+	0.854200i
$991$		−	699.943i		−	0.706299i	−0.935567	−	0.353150i	$-0.885111\pi$
$991$		−	699.943i		−	0.706299i	0.935567	−	0.353150i	$-0.114889\pi$
$992$	636.103	+	508.605i	0.641233	+	0.512707i
$993$	599.835	+	1177.24i	0.604063	+	1.18554i
$994$	562.883	+	94.4864i	0.566281	+	0.0950568i
$995$	421.773	−	92.4246i	0.423892	−	0.0928890i
$996$	−934.821	+	2706.04i	−0.938575	+	2.71691i
$997$	−70.8204	−	36.0848i	−0.0710335	−	0.0361934i	0.418113	−	0.908395i	$-0.362692\pi$
$997$	−70.8204	−	36.0848i	−0.0710335	−	0.0361934i	−0.489146	+	0.872202i	$0.662692\pi$
$998$	7.04320	−	762.945i	0.00705731	−	0.764474i
$999$	−1772.38	−	1287.71i	−1.77416	−	1.28900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.w.a.7.7	✓	544
4.3	odd	2	inner	220.3.w.a.7.14	yes	544
5.3	odd	4	inner	220.3.w.a.183.28	yes	544
11.8	odd	10	inner	220.3.w.a.107.48	yes	544
20.3	even	4	inner	220.3.w.a.183.48	yes	544
44.19	even	10	inner	220.3.w.a.107.28	yes	544
55.8	even	20	inner	220.3.w.a.63.14	yes	544
220.63	odd	20	inner	220.3.w.a.63.7	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.7	✓	544	1.1	even	1	trivial
220.3.w.a.7.14	yes	544	4.3	odd	2	inner
220.3.w.a.63.7	yes	544	220.63	odd	20	inner
220.3.w.a.63.14	yes	544	55.8	even	20	inner
220.3.w.a.107.28	yes	544	44.19	even	10	inner
220.3.w.a.107.48	yes	544	11.8	odd	10	inner
220.3.w.a.183.28	yes	544	5.3	odd	4	inner
220.3.w.a.183.48	yes	544	20.3	even	4	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89633 - 0.635566i) q^{2} +(-4.39098 + 2.23732i) q^{3} +(3.19211 + 2.41048i) q^{4} +(4.88411 - 1.07027i) q^{5} +(9.74869 - 1.45192i) q^{6} +(-1.29034 + 2.53243i) q^{7} +(-4.52126 - 6.59986i) q^{8} +(8.98505 - 12.3669i) q^{9} +(-9.94210 - 1.07459i) q^{10} +(-2.28240 - 10.7606i) q^{11} +(-19.4095 - 3.44262i) q^{12} +(0.417679 + 2.63712i) q^{13} +(4.05642 - 3.98221i) q^{14} +(-19.0515 + 15.6268i) q^{15} +(4.37914 + 15.3891i) q^{16} +(0.0707521 - 0.446711i) q^{17} +(-24.8985 + 17.7410i) q^{18} +(22.1514 + 7.19742i) q^{19} +(18.1705 + 8.35664i) q^{20} -14.0067i q^{21} +(-2.51090 + 21.8562i) q^{22} +(16.7927 + 16.7927i) q^{23} +(34.6187 + 18.8644i) q^{24} +(22.7090 - 10.4547i) q^{25} +(0.884011 - 5.26631i) q^{26} +(-4.84625 + 30.5980i) q^{27} +(-10.2233 + 4.97345i) q^{28} +(7.96480 + 24.5131i) q^{29} +(46.0597 - 17.5251i) q^{30} +(-14.9598 + 20.5904i) q^{31} +(1.47649 - 31.9659i) q^{32} +(34.0968 + 42.1431i) q^{33} +(-0.418084 + 0.802143i) q^{34} +(-3.59175 + 13.7496i) q^{35} +(58.4914 - 17.8181i) q^{36} +(-32.1050 + 63.0096i) q^{37} +(-37.4318 - 27.7273i) q^{38} +(-7.73410 - 10.6451i) q^{39} +(-29.1460 - 27.3955i) q^{40} +(9.74917 + 3.16770i) q^{41} +(-8.90220 + 26.5613i) q^{42} +(1.75161 - 1.75161i) q^{43} +(18.6526 - 39.8507i) q^{44} +(30.6480 - 70.0175i) q^{45} +(-21.1715 - 42.5172i) q^{46} +(2.71100 + 5.32065i) q^{47} +(-53.6589 - 57.7755i) q^{48} +(24.0533 + 33.1065i) q^{49} +(-49.7084 + 5.39233i) q^{50} +(0.688763 + 2.11980i) q^{51} +(-5.02346 + 9.42480i) q^{52} +(69.4310 - 10.9968i) q^{53} +(28.6372 - 54.9438i) q^{54} +(-22.6643 - 50.1132i) q^{55} +(22.5476 - 2.93373i) q^{56} +(-113.369 + 17.9559i) q^{57} +(0.475861 - 51.5471i) q^{58} +(16.7213 + 51.4628i) q^{59} +(-98.4827 + 3.95930i) q^{60} +(-64.3142 - 88.5209i) q^{61} +(41.4552 - 29.5382i) q^{62} +(19.7244 + 38.7113i) q^{63} +(-23.1164 + 59.6794i) q^{64} +(4.86243 + 12.4330i) q^{65} +(-37.8740 - 101.588i) q^{66} +(70.1944 - 70.1944i) q^{67} +(1.30264 - 1.25541i) q^{68} +(-111.307 - 36.1657i) q^{69} +(15.5500 - 23.7910i) q^{70} +(59.0181 + 81.2315i) q^{71} +(-122.243 - 3.38627i) q^{72} +(-43.4809 + 85.3361i) q^{73} +(100.928 - 99.0819i) q^{74} +(-76.3245 + 96.7134i) q^{75} +(53.3604 + 76.3705i) q^{76} +(30.1955 + 8.10477i) q^{77} +(7.90073 + 25.1021i) q^{78} +(-42.4238 + 58.3914i) q^{79} +(37.8587 + 70.4750i) q^{80} +(-4.66421 - 14.3550i) q^{81} +(-16.4743 - 12.2032i) q^{82} +(22.7200 - 143.448i) q^{83} +(33.7629 - 44.7110i) q^{84} +(-0.132542 - 2.25751i) q^{85} +(-4.43489 + 2.20836i) q^{86} +(-89.8169 - 89.8169i) q^{87} +(-60.6992 + 63.7151i) q^{88} +73.3129i q^{89} +(-102.619 + 113.297i) q^{90} +(-7.21727 - 2.34503i) q^{91} +(13.1256 + 94.0824i) q^{92} +(19.6209 - 123.882i) q^{93} +(-1.75933 - 11.8127i) q^{94} +(115.893 + 11.4450i) q^{95} +(65.0346 + 143.665i) q^{96} +(8.07153 + 50.9617i) q^{97} +(-24.5715 - 78.0682i) q^{98} +(-153.582 - 68.4584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

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