LMFDB - Embedded newform 220.3.w.a.7.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			7.14
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60711 + 1.19046i) q^{2} +(4.39098 - 2.23732i) q^{3} +(1.16563 - 3.82640i) q^{4} +(4.88411 - 1.07027i) q^{5} +(-4.39337 + 8.82289i) q^{6} +(1.29034 - 2.53243i) q^{7} +(2.68187 + 7.53708i) q^{8} +(8.98505 - 12.3669i) q^{9} +(-6.57520 + 7.53437i) q^{10} +(2.28240 + 10.7606i) q^{11} +(-3.44262 - 19.4095i) q^{12} +(0.417679 + 2.63712i) q^{13} +(0.941028 + 5.60598i) q^{14} +(19.0515 - 15.6268i) q^{15} +(-13.2826 - 8.92029i) q^{16} +(0.0707521 - 0.446711i) q^{17} +(0.282221 + 30.5712i) q^{18} +(-22.1514 - 7.19742i) q^{19} +(1.59775 - 19.9361i) q^{20} -14.0067i q^{21} +(-16.4781 - 14.5764i) q^{22} +(-16.7927 - 16.7927i) q^{23} +(28.6389 + 27.0950i) q^{24} +(22.7090 - 10.4547i) q^{25} +(-3.81064 - 3.74093i) q^{26} +(4.84625 - 30.5980i) q^{27} +(-8.18602 - 7.88919i) q^{28} +(7.96480 + 24.5131i) q^{29} +(-12.0148 + 47.7941i) q^{30} +(14.9598 - 20.5904i) q^{31} +(31.9659 - 1.47649i) q^{32} +(34.0968 + 42.1431i) q^{33} +(0.418084 + 0.802143i) q^{34} +(3.59175 - 13.7496i) q^{35} +(-36.8473 - 48.7955i) q^{36} +(-32.1050 + 63.0096i) q^{37} +(44.1680 - 14.8032i) q^{38} +(7.73410 + 10.6451i) q^{39} +(21.1653 + 33.9416i) q^{40} +(9.74917 + 3.16770i) q^{41} +(16.6744 + 22.5104i) q^{42} +(-1.75161 + 1.75161i) q^{43} +(43.8348 + 3.80946i) q^{44} +(30.6480 - 70.0175i) q^{45} +(46.9786 + 6.99677i) q^{46} +(-2.71100 - 5.32065i) q^{47} +(-78.2813 - 9.45136i) q^{48} +(24.0533 + 33.1065i) q^{49} +(-24.0502 + 43.8359i) q^{50} +(-0.688763 - 2.11980i) q^{51} +(10.5775 + 1.47569i) 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} +(-41.9822 - 29.9136i) q^{58} +(-16.7213 - 51.4628i) q^{59} +(-37.5876 - 91.1136i) q^{60} +(-64.3142 - 88.5209i) q^{61} +(0.469889 + 50.9001i) q^{62} +(-19.7244 - 38.7113i) q^{63} +(-49.6152 + 40.4269i) q^{64} +(4.86243 + 12.4330i) q^{65} +(-104.967 - 27.1380i) q^{66} +(-70.1944 + 70.1944i) q^{67} +(-1.62683 - 0.791424i) q^{68} +(-111.307 - 36.1657i) q^{69} +(10.5960 + 26.3731i) q^{70} +(-59.0181 - 81.2315i) q^{71} +(117.307 + 34.5547i) q^{72} +(-43.4809 + 85.3361i) q^{73} +(-23.4138 - 139.483i) q^{74} +(76.3245 - 96.7134i) q^{75} +(-53.3604 + 76.3705i) q^{76} +(30.1955 + 8.10477i) q^{77} +(-25.1021 - 7.90073i) q^{78} +(42.4238 - 58.3914i) q^{79} +(-74.4210 - 29.3516i) q^{80} +(-4.66421 - 14.3550i) q^{81} +(-19.4390 + 6.51511i) q^{82} +(-22.7200 + 143.448i) q^{83} +(-53.5952 - 16.3266i) q^{84} +(-0.132542 - 2.25751i) q^{85} +(0.729820 - 4.90025i) q^{86} +(89.8169 + 89.8169i) q^{87} +(-74.9824 + 46.0612i) q^{88} +73.3129i q^{89} +(34.0980 + 149.011i) q^{90} +(7.21727 + 2.34503i) q^{91} +(-83.8293 + 44.6814i) q^{92} +(19.6209 - 123.882i) q^{93} +(10.6909 + 5.32355i) q^{94} +(-115.893 - 11.4450i) q^{95} +(137.058 - 78.0011i) q^{96} +(8.07153 + 50.9617i) q^{97} +(-78.0682 - 24.5715i) 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 $

$2$	−1.60711	+	1.19046i	−0.803557	+	0.595228i
$2$	−1.60711	+	1.19046i	−0.803557	+	0.595228i
$3$	4.39098	−	2.23732i	1.46366	−	0.745772i	0.472864	−	0.881136i	$-0.343220\pi$
$3$	4.39098	−	2.23732i	1.46366	−	0.745772i	0.990796	+	0.135364i	$0.0432203\pi$
$4$	1.16563	−	3.82640i	0.291406	−	0.956599i
$5$	4.88411	−	1.07027i	0.976822	−	0.214054i
$5$	4.88411	−	1.07027i	0.976822	−	0.214054i
$6$	−4.39337	+	8.82289i	−0.732229	+	1.47048i
$7$	1.29034	−	2.53243i	0.184334	−	0.361775i	−0.780285	−	0.625424i	$-0.784926\pi$
$7$	1.29034	−	2.53243i	0.184334	−	0.361775i	0.964619	+	0.263649i	$0.0849260\pi$
$8$	2.68187	+	7.53708i	0.335234	+	0.942135i
$9$	8.98505	−	12.3669i	0.998339	−	1.37410i
$10$	−6.57520	+	7.53437i	−0.657520	+	0.753437i
$11$	2.28240	+	10.7606i	0.207491	+	0.978237i
$11$	2.28240	+	10.7606i	0.207491	+	0.978237i
$12$	−3.44262	−	19.4095i	−0.286885	−	1.61746i
$13$	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	$0.917254\pi$
$14$	0.941028	+	5.60598i	0.0672163	+	0.400427i
$15$	19.0515	−	15.6268i	1.27010	−	1.04179i
$16$	−13.2826	−	8.92029i	−0.830165	−	0.557518i
$17$	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	$0.0457656\pi$
$18$	0.282221	+	30.5712i	0.0156790	+	1.69840i
$19$	−22.1514	−	7.19742i	−1.16586	−	0.378812i	−0.338766	−	0.940871i	$-0.610009\pi$
$19$	−22.1514	−	7.19742i	−1.16586	−	0.378812i	−0.827097	+	0.562059i	$0.810009\pi$
$20$	1.59775	−	19.9361i	0.0798877	−	0.996804i
$21$		−	14.0067i		−	0.666986i
$22$	−16.4781	−	14.5764i	−0.749005	−	0.662564i
$23$	−16.7927	−	16.7927i	−0.730115	−	0.730115i	0.240527	−	0.970642i	$-0.422680\pi$
$23$	−16.7927	−	16.7927i	−0.730115	−	0.730115i	−0.970642	+	0.240527i	$0.922680\pi$
$24$	28.6389	+	27.0950i	1.19329	+	1.12896i
$25$	22.7090	−	10.4547i	0.908361	−	0.418186i
$26$	−3.81064	−	3.74093i	−0.146563	−	0.143882i
$27$	4.84625	−	30.5980i	0.179491	−	1.13326i
$28$	−8.18602	−	7.88919i	−0.292358	−	0.281757i
$29$	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	$0.753420\pi$
$30$	−12.0148	+	47.7941i	−0.400494	+	1.59314i
$31$	14.9598	−	20.5904i	0.482574	−	0.664206i	−0.496423	−	0.868081i	$-0.665354\pi$
$31$	14.9598	−	20.5904i	0.482574	−	0.664206i	0.978997	+	0.203875i	$0.0653535\pi$
$32$	31.9659	−	1.47649i	0.998935	−	0.0461403i
$33$	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
$36$	−36.8473	−	48.7955i	−1.02354	−	1.35543i
$37$	−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	$0.745166\pi$
$38$	44.1680	−	14.8032i	1.16232	−	0.389558i
$39$	7.73410	+	10.6451i	0.198310	+	0.272951i
$40$	21.1653	+	33.9416i	0.529132	+	0.848540i
$41$	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	$0.560103\pi$
$42$	16.6744	+	22.5104i	0.397009	+	0.535961i
$43$	−1.75161	+	1.75161i	−0.0407351	+	0.0407351i	−0.727181	−	0.686446i	$-0.759170\pi$
$43$	−1.75161	+	1.75161i	−0.0407351	+	0.0407351i	0.686446	+	0.727181i	$0.259170\pi$
$44$	43.8348	+	3.80946i	0.996245	+	0.0865785i
$45$	30.6480	−	70.0175i	0.681068	−	1.55594i
$46$	46.9786	+	6.99677i	1.02127	+	0.152104i
$47$	−2.71100	−	5.32065i	−0.0576809	−	0.113205i	0.860366	−	0.509676i	$-0.170235\pi$
$47$	−2.71100	−	5.32065i	−0.0576809	−	0.113205i	−0.918047	+	0.396471i	$0.870235\pi$
$48$	−78.2813	−	9.45136i	−1.63086	−	0.196903i
$49$	24.0533	+	33.1065i	0.490883	+	0.675642i
$50$	−24.0502	+	43.8359i	−0.481004	+	0.876719i
$51$	−0.688763	−	2.11980i	−0.0135052	−	0.0415646i
$52$	10.5775	+	1.47569i	0.203414	+	0.0283787i
$53$	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
$58$	−41.9822	−	29.9136i	−0.723830	−	0.515752i
$59$	−16.7213	−	51.4628i	−0.283412	−	0.872251i	−0.986870	−	0.161515i	$-0.948362\pi$
$59$	−16.7213	−	51.4628i	−0.283412	−	0.872251i	0.703459	−	0.710736i	$-0.251638\pi$
$60$	−37.5876	−	91.1136i	−0.626460	−	1.51856i
$61$	−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	$-0.554163\pi$
$62$	0.469889	+	50.9001i	0.00757885	+	0.820969i
$63$	−19.7244	−	38.7113i	−0.313086	−	0.614466i
$64$	−49.6152	+	40.4269i	−0.775237	+	0.631671i
$65$	4.86243	+	12.4330i	0.0748066	+	0.191276i
$66$	−104.967	−	27.1380i	−1.59041	−	0.411181i
$67$	−70.1944	+	70.1944i	−1.04768	+	1.04768i	−0.0488728	+	0.998805i	$0.515563\pi$
$67$	−70.1944	+	70.1944i	−1.04768	+	1.04768i	−0.998805	+	0.0488728i	$0.984437\pi$
$68$	−1.62683	−	0.791424i	−0.0239239	−	0.0116386i
$69$	−111.307	−	36.1657i	−1.61314	−	0.524141i
$70$	10.5960	+	26.3731i	0.151372	+	0.376758i
$71$	−59.0181	−	81.2315i	−0.831241	−	1.14411i	−0.987691	−	0.156419i	$-0.950005\pi$
$71$	−59.0181	−	81.2315i	−0.831241	−	1.14411i	0.156450	−	0.987686i	$-0.449995\pi$
$72$	117.307	+	34.5547i	1.62926	+	0.479927i
$73$	−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	$0.922250\pi$
$74$	−23.4138	−	139.483i	−0.316403	−	1.88491i
$75$	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
$78$	−25.1021	−	7.90073i	−0.321821	−	0.101291i
$79$	42.4238	−	58.3914i	0.537010	−	0.739131i	−0.451168	−	0.892439i	$-0.648993\pi$
$79$	42.4238	−	58.3914i	0.537010	−	0.739131i	0.988179	+	0.153308i	$0.0489926\pi$
$80$	−74.4210	−	29.3516i	−0.930262	−	0.366895i
$81$	−4.66421	−	14.3550i	−0.0575829	−	0.177222i
$82$	−19.4390	+	6.51511i	−0.237061	+	0.0794526i
$83$	−22.7200	+	143.448i	−0.273734	+	1.72829i	0.341443	+	0.939902i	$0.389084\pi$
$83$	−22.7200	+	143.448i	−0.273734	+	1.72829i	−0.615178	+	0.788389i	$0.710916\pi$
$84$	−53.5952	−	16.3266i	−0.638039	−	0.194364i
$85$	−0.132542	−	2.25751i	−0.00155931	−	0.0265590i
$86$	0.729820	−	4.90025i	0.00848627	−	0.0569797i
$87$	89.8169	+	89.8169i	1.03238	+	1.03238i
$88$	−74.9824	+	46.0612i	−0.852073	+	0.523423i
$89$			73.3129i			0.823741i	0.911242	+	0.411870i	$0.135124\pi$
$89$			73.3129i			0.823741i	−0.911242	+	0.411870i	$0.864876\pi$
$90$	34.0980	+	149.011i	0.378866	+	1.65568i
$91$	7.21727	+	2.34503i	0.0793106	+	0.0257696i
$92$	−83.8293	+	44.6814i	−0.911188	+	0.485668i
$93$	19.6209	−	123.882i	0.210978	−	1.33206i
$94$	10.6909	+	5.32355i	0.113733	+	0.0566335i
$95$	−115.893	−	11.4450i	−1.21993	−	0.120474i
$96$	137.058	−	78.0011i	1.42769	−	0.812511i
$97$	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	$0.864310\pi$
$98$	−78.0682	−	24.5715i	−0.796614	−	0.250729i
$99$	153.582	+	68.4584i	1.55134	+	0.691499i
$100$	−13.5334	−	99.0800i	−0.135334	−	0.990800i
$101$	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	$-0.199742\pi$
$102$	3.63045	+	2.58681i	0.0355926	+	0.0253609i
$103$	−23.0411	+	45.2206i	−0.223700	+	0.439035i	−0.975392	−	0.220479i	$-0.929238\pi$
$103$	−23.0411	+	45.2206i	−0.223700	+	0.439035i	0.751692	+	0.659514i	$0.229238\pi$
$104$	−18.7561	+	10.2205i	−0.180347	+	0.0982741i
$105$	−14.9910	−	68.4103i	−0.142771	−	0.651527i
$106$	−98.4923	+	100.328i	−0.929173	+	0.946488i
$107$	−19.4107	+	9.89026i	−0.181409	+	0.0924324i	−0.542336	−	0.840161i	$-0.682460\pi$
$107$	−19.4107	+	9.89026i	−0.181409	+	0.0924324i	0.360928	+	0.932594i	$0.382460\pi$
$108$	−111.431	−	54.2096i	−1.03177	−	0.501940i
$109$	27.6368			0.253549			0.126774	−	0.991932i	$-0.459538\pi$
$109$	27.6368			0.253549			0.126774	+	0.991932i	$0.459538\pi$
$110$	−96.0816	−	53.5567i	−0.873469	−	0.486879i
$111$			348.503i			3.13966i
$112$	−39.7290	+	22.1271i	−0.354723	+	0.197564i
$113$	−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	$0.893577\pi$
$114$	160.821	−	163.818i	1.41071	−	1.43700i
$115$	−99.9899	−	64.0444i	−0.869477	−	0.556908i
$116$	103.081	−	1.90336i	0.888629	−	0.0164083i
$117$	36.3658	+	18.5293i	0.310819	+	0.158370i
$118$	88.1373	+	62.8006i	0.746926	+	0.532209i
$119$	−1.03997	−	0.755582i	−0.00873924	−	0.00634943i
$120$	168.874	+	101.683i	1.40729	+	0.847362i
$121$	−110.581	+	49.1201i	−0.913895	+	0.405951i
$122$	208.740	+	65.6998i	1.71099	+	0.538523i
$123$	49.8955	−	7.90267i	0.405655	−	0.0642494i
$124$	−61.3495	−	81.2428i	−0.494754	−	0.655184i
$125$	99.7241	−	75.3665i	0.797793	−	0.602932i
$126$	77.7835	+	38.7324i	0.617330	+	0.307400i
$127$	−139.388	−	22.0768i	−1.09754	−	0.173833i	−0.418704	−	0.908123i	$-0.637515\pi$
$127$	−139.388	−	22.0768i	−1.09754	−	0.173833i	−0.678836	+	0.734290i	$0.737515\pi$
$128$	31.6107	−	124.035i	0.246958	−	0.969026i
$129$	−3.77238	+	11.6102i	−0.0292433	+	0.0900015i
$130$	−22.6154	−	14.1927i	−0.173965	−	0.109174i
$131$	48.8749			0.373091			0.186546	−	0.982446i	$-0.440271\pi$
$131$	48.8749			0.373091			0.186546	+	0.982446i	$0.440271\pi$
$132$	201.001	−	81.3450i	1.52273	−	0.616250i
$133$	−46.8097	+	46.8097i	−0.351952	+	0.351952i
$134$	29.2469	−	196.374i	0.218261	−	1.46548i
$135$	−9.07860	−	154.631i	−0.0672489	−	1.14541i
$136$	3.55665	−	0.664757i	0.0261518	−	0.00488792i
$137$	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	$0.415062\pi$
$138$	221.936	−	74.3833i	1.60823	−	0.539010i
$139$	64.7664	−	21.0439i	0.465945	−	0.151395i	−0.0666294	−	0.997778i	$-0.521225\pi$
$139$	64.7664	−	21.0439i	0.465945	−	0.151395i	0.532575	+	0.846383i	$0.321225\pi$
$140$	−48.4250	−	29.7704i	−0.345893	−	0.212646i
$141$	−23.8079	−	17.2975i	−0.168851	−	0.122677i
$142$	191.551	+	60.2897i	1.34895	+	0.424575i
$143$	−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
$146$	−31.7102	−	188.907i	−0.217193	−	1.29388i
$147$	179.687	+	91.5551i	1.22236	+	0.622824i
$148$	203.677	+	196.292i	1.37620	+	1.32630i
$149$	−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	$0.428769\pi$
$150$	−7.52902	+	246.290i	−0.0501935	+	1.64194i
$151$	−42.8179	+	131.780i	−0.283562	+	0.872715i	0.703264	+	0.710929i	$0.251725\pi$
$151$	−42.8179	+	131.780i	−0.283562	+	0.872715i	−0.986826	+	0.161786i	$0.948275\pi$
$152$	−5.15958	−	186.259i	−0.0339446	−	1.22539i
$153$	−4.88870	−	4.88870i	−0.0319523	−	0.0319523i
$154$	−58.1760	+	22.9211i	−0.377766	+	0.148839i
$155$	51.0279	−	116.577i	0.329212	−	0.752108i
$156$	49.7474	−	17.1856i	0.318893	−	0.110164i
$157$	−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	$0.355288\pi$
$158$	1.33254	+	144.345i	0.00843377	+	0.913578i
$159$	280.267	−	203.626i	1.76268	−	1.28067i
$160$	154.545	−	41.4236i	0.965905	−	0.258897i
$161$	−64.1943	+	20.8580i	−0.398722	+	0.129553i
$162$	24.5849	+	17.5175i	0.151759	+	0.108133i
$163$	9.32109	+	58.8510i	0.0571846	+	0.361049i	0.999643	+	0.0267253i	$0.00850795\pi$
$163$	9.32109	+	58.8510i	0.0571846	+	0.361049i	−0.942458	+	0.334324i	$0.891492\pi$
$164$	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	$-0.932297\pi$
$167$	−18.8832	−	119.224i	−0.113073	−	0.713913i	0.864393	−	0.502818i	$-0.167703\pi$
$168$	105.570	−	37.5642i	0.628391	−	0.223596i
$169$	153.949	−	50.0209i	0.910938	−	0.295982i
$170$	2.90048	+	3.47029i	0.0170616	+	0.0204135i
$171$	−288.041	+	209.274i	−1.68445	+	1.22382i
$172$	4.66064	+	8.74408i	0.0270967	+	0.0508377i
$173$	−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	$0.437335\pi$
$174$	−251.269	−	37.4228i	−1.44407	−	0.215073i
$175$	2.82664	−	70.9989i	0.0161523	−	0.405708i
$176$	65.6714	−	163.289i	0.373133	−	0.927778i
$177$	−188.561	−	188.561i	−1.06532	−	1.06532i
$178$	−87.2759	−	117.822i	−0.490314	−	0.661922i
$179$	−64.4920	+	198.486i	−0.360291	+	1.10886i	0.592587	+	0.805506i	$0.298107\pi$
$179$	−64.4920	+	198.486i	−0.360291	+	1.10886i	−0.952878	+	0.303354i	$0.901893\pi$
$180$	−232.191	−	198.886i	−1.28995	−	1.10492i
$181$	−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	$0.554310\pi$
$182$	−14.3906	+	4.82311i	−0.0790693	+	0.0265006i
$183$	−480.451	−	244.802i	−2.62542	−	1.33772i
$184$	81.5319	−	171.603i	0.443108	−	0.932627i
$185$	−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
$188$	−23.5189	+	4.17150i	−0.125101	+	0.0221888i
$189$	−71.2340	−	51.7545i	−0.376899	−	0.273833i
$190$	199.878	−	119.572i	1.05199	−	0.629328i
$191$	217.568	−	70.6921i	1.13910	−	0.370116i	0.322072	−	0.946715i	$-0.395621\pi$
$191$	217.568	−	70.6921i	1.13910	−	0.370116i	0.817027	+	0.576599i	$0.195621\pi$
$192$	−127.411	+	288.519i	−0.663600	+	1.50270i
$193$	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	$0.502032\pi$
$194$	−73.6395	−	72.2923i	−0.379585	−	0.372641i
$195$	49.1673	+	43.7141i	0.252140	+	0.224175i
$196$	154.716	−	53.4476i	0.789366	−	0.272692i
$197$	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	$0.183018\pi$
$198$	−328.321	+	72.8127i	−1.65819	+	0.367741i
$199$	−86.3561			−0.433950			−0.216975	−	0.976177i	$-0.569619\pi$
$199$	−86.3561			−0.433950			−0.216975	+	0.976177i	$0.569619\pi$
$200$	139.700	+	143.122i	0.698501	+	0.715609i
$201$	−151.175	+	465.269i	−0.752115	+	2.31477i
$202$	3.54594	+	384.109i	0.0175541	+	1.90153i
$203$	72.3549	+	11.4599i	0.356428	+	0.0564527i
$204$	−8.91402	+	0.164595i	−0.0436962	+	0.000806839i
$205$	51.0063	+	5.03711i	0.248811	+	0.0245713i
$206$	−16.8036	−	100.104i	−0.0815710	−	0.485942i
$207$	−358.555	+	56.7895i	−1.73215	+	0.274346i
$208$	17.9760	−	38.7538i	0.0864232	−	0.186316i
$209$	26.8903	−	254.790i	0.128662	−	1.21909i
$210$	105.532	+	92.0970i	0.502532	+	0.438557i
$211$	−161.109	−	117.053i	−0.763551	−	0.554753i	0.136446	−	0.990647i	$-0.456432\pi$
$211$	−161.109	−	117.053i	−0.763551	−	0.554753i	−0.899998	+	0.435895i	$0.856432\pi$
$212$	38.8524	−	278.489i	0.183266	−	1.31363i
$213$	−440.888	−	224.644i	−2.06990	−	1.05466i
$214$	19.4213	−	39.0024i	0.0907538	−	0.182254i
$215$	−6.68036	+	10.4298i	−0.0310714	+	0.0485105i
$216$	243.617	−	45.5334i	1.12786	−	0.210803i
$217$	−32.8405	−	64.4531i	−0.151339	−	0.297019i
$218$	−44.4155	+	32.9004i	−0.203741	+	0.150919i
$219$			471.990i			2.15520i
$220$	218.171	−	28.3093i	0.991686	−	0.128679i
$221$	1.20759			0.00546419
$222$	−414.877	−	560.083i	−1.86882	−	2.52290i
$223$	354.857	−	180.809i	1.59129	−	0.810801i	0.591296	−	0.806454i	$-0.298616\pi$
$223$	354.857	−	180.809i	1.59129	−	0.810801i	0.999991	−	0.00434663i	$-0.00138358\pi$
$224$	37.5076	−	82.8565i	0.167445	−	0.369895i
$225$	74.7506	−	374.775i	0.332225	−	1.66567i
$226$	55.2187	+	27.4963i	0.244331	+	0.121665i
$227$	−81.6905	+	160.327i	−0.359870	+	0.706285i	−0.997971	−	0.0636676i	$-0.979720\pi$
$227$	−81.6905	+	160.327i	−0.359870	+	0.706285i	0.638101	+	0.769953i	$0.279720\pi$
$228$	−63.4395	+	454.726i	−0.278244	+	1.99441i
$229$	−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	$0.215339\pi$
$230$	236.937	−	16.1069i	1.03016	−	0.0700302i
$231$	150.721	−	31.9689i	0.652471	−	0.138394i
$232$	−163.397	+	125.772i	−0.704297	+	0.542122i
$233$	−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	$-0.259434\pi$
$234$	−80.5023	+	13.5132i	−0.344027	+	0.0577489i
$235$	−18.9354	−	23.0851i	−0.0805761	−	0.0982345i
$236$	−216.408	+	3.99592i	−0.916983	+	0.0169319i
$237$	55.6421	−	351.311i	0.234777	−	1.48232i
$238$	2.57084	−	0.0237329i	0.0108018	−	9.97181e-5i
$239$	274.942	+	89.3341i	1.15039	+	0.373783i	0.821288	−	0.570513i	$-0.193256\pi$
$239$	274.942	+	89.3341i	1.15039	+	0.373783i	0.329097	+	0.944296i	$0.393256\pi$
$240$	−392.450	+	37.6208i	−1.63521	+	0.156753i
$241$		−	469.847i		−	1.94957i	−0.223142	−	0.974786i	$-0.571631\pi$
$241$		−	469.847i		−	1.94957i	0.223142	−	0.974786i	$-0.428369\pi$
$242$	119.241	−	210.584i	0.492733	−	0.870181i
$243$	144.555	+	144.555i	0.594876	+	0.594876i
$244$	−413.682	+	142.909i	−1.69542	+	0.585694i
$245$	152.912	+	135.952i	0.624129	+	0.554907i
$246$	−70.7799	+	72.0989i	−0.287723	+	0.293085i
$247$	9.72832	−	61.4222i	0.0393859	−	0.248673i
$248$	195.312	+	57.5324i	0.787547	+	0.231986i
$249$	221.176	+	680.709i	0.888257	+	2.73377i
$250$	−70.5473	+	239.840i	−0.282189	+	0.959359i
$251$	77.9244	−	107.254i	0.310456	−	0.427305i	−0.625068	−	0.780571i	$-0.714929\pi$
$251$	77.9244	−	107.254i	0.310456	−	0.427305i	0.935523	+	0.353265i	$0.114929\pi$
$252$	−171.116	+	30.3505i	−0.679033	+	0.120439i
$253$	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
$256$	96.8568	+	236.970i	0.378347	+	0.925664i
$257$	−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	$0.986404\pi$
$258$	−7.75879	−	23.1497i	−0.0300728	−	0.0897277i
$259$	118.141	+	162.607i	0.456142	+	0.627826i
$260$	53.2413	−	4.11341i	0.204774	−	0.0158208i
$261$	374.715	+	121.752i	1.43569	+	0.466483i
$262$	−78.5476	+	58.1835i	−0.299800	+	0.222074i
$263$	56.2727	−	56.2727i	0.213964	−	0.213964i	−0.591985	−	0.805949i	$-0.701655\pi$
$263$	56.2727	−	56.2727i	0.213964	−	0.213964i	0.805949	+	0.591985i	$0.201655\pi$
$264$	−226.193	+	370.013i	−0.856791	+	1.40156i
$265$	327.339	−	128.020i	1.23524	−	0.483093i
$266$	19.5035	−	130.953i	0.0733216	−	0.492306i
$267$	164.024	+	321.916i	0.614323	+	1.20568i
$268$	186.771	+	350.412i	0.696908	+	1.30751i
$269$	−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	$0.875477\pi$
$270$	198.672	+	237.702i	0.735822	+	0.880377i
$271$	−109.946	−	338.378i	−0.405704	−	1.24863i	−0.920306	−	0.391199i	$-0.872060\pi$
$271$	−109.946	−	338.378i	−0.405704	−	1.24863i	0.514602	−	0.857429i	$-0.327940\pi$
$272$	−4.92457	+	5.30238i	−0.0181050	+	0.0194940i
$273$	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	$0.367487\pi$
$278$	−79.0351	+	110.922i	−0.284299	+	0.398998i
$279$	−120.224	−	370.011i	−0.430910	−	1.32621i
$280$	113.265	−	9.80344i	0.404517	−	0.0350123i
$281$	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	$0.697557\pi$
$282$	58.8539	−	0.543315i	0.208702	−	0.00192665i
$283$	−83.7652	−	164.399i	−0.295990	−	0.580914i	0.694339	−	0.719648i	$-0.255697\pi$
$283$	−83.7652	−	164.399i	−0.295990	−	0.580914i	−0.990330	+	0.138734i	$0.955697\pi$
$284$	−379.617	+	131.141i	−1.33668	+	0.461765i
$285$	−534.490	+	209.035i	−1.87540	+	0.733455i
$286$	31.5572	−	49.5431i	0.110340	−	0.173228i
$287$	20.6016	−	20.6016i	0.0717827	−	0.0717827i
$288$	268.956	−	408.584i	0.933874	−	1.41870i
$289$	274.661	+	89.2427i	0.950383	+	0.308798i
$290$	−237.061	−	101.169i	−0.817452	−	0.348859i
$291$	149.459	+	205.713i	0.513606	+	0.706918i
$292$	275.848	+	265.845i	0.944683	+	0.910429i
$293$	−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	$0.189224\pi$
$294$	−397.770	+	66.7702i	−1.35296	+	0.227110i
$295$	−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
$298$	70.4273	−	223.761i	0.236333	−	0.750875i
$299$	37.2704	−	51.2983i	0.124650	−	0.171566i
$300$	−281.098	−	404.780i	−0.936994	−	1.34927i
$301$	2.17566	+	6.69599i	0.00722810	+	0.0222458i
$302$	−88.0651	−	262.758i	−0.291606	−	0.870060i
$303$	148.066	−	934.853i	0.488667	−	3.08532i
$304$	230.026	+	293.198i	0.756664	+	0.964466i
$305$	−408.859	−	363.512i	−1.34052	−	1.19184i
$306$	13.6765	+	2.03691i	0.0446944	+	0.00665657i
$307$	−272.518	−	272.518i	−0.887682	−	0.887682i	0.106618	−	0.994300i	$-0.465998\pi$
$307$	−272.518	−	272.518i	−0.887682	−	0.887682i	−0.994300	+	0.106618i	$0.965998\pi$
$308$	66.2087	−	106.093i	0.214963	−	0.344457i
$309$			250.113i			0.809427i
$310$	56.7719	+	248.099i	0.183135	+	0.800318i
$311$	−263.860	−	85.7333i	−0.848425	−	0.275670i	−0.147639	−	0.989041i	$-0.547167\pi$
$311$	−263.860	−	85.7333i	−0.848425	−	0.275670i	−0.700786	+	0.713371i	$0.747167\pi$
$312$	−59.4909	+	86.8412i	−0.190676	+	0.278337i
$313$	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	$-0.215213\pi$
$314$	4.64974	−	9.33774i	0.0148081	−	0.0297380i
$315$	−137.768	−	167.960i	−0.437358	−	0.533206i
$316$	−173.978	−	230.393i	−0.550564	−	0.729091i
$317$	−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	$-0.189020\pi$
$318$	−208.013	+	660.895i	−0.654128	+	2.07829i
$319$	−245.597	+	141.655i	−0.769898	+	0.444059i
$320$	−199.058	+	250.551i	−0.622056	+	0.782973i
$321$	−63.1045	+	86.8559i	−0.196587	+	0.270579i
$322$	78.3369	−	109.942i	0.243282	−	0.341434i
$323$	−4.78243	+	9.38605i	−0.0148063	+	0.0290590i
$324$	−60.3646	+	1.11462i	−0.186310	+	0.00344018i
$325$	37.0553	+	55.5199i	0.114016	+	0.170830i
$326$	−85.0396	−	83.4839i	−0.260858	−	0.256086i
$327$	121.353	−	61.8323i	0.371109	−	0.189090i
$328$	2.27081	+	81.9756i	0.00692320	+	0.249926i
$329$	−16.9722			−0.0515874
$330$	−541.716	−	20.2014i	−1.64156	−	0.0612165i
$331$			268.105i			0.809984i	0.914320	+	0.404992i	$0.132726\pi$
$331$			268.105i			0.809984i	−0.914320	+	0.404992i	$0.867274\pi$
$332$	522.407	+	254.142i	1.57351	+	0.765489i
$333$	490.766	+	963.182i	1.47377	+	2.89244i
$334$	172.278	+	169.126i	0.515802	+	0.506366i
$335$	−267.710	+	417.964i	−0.799134	+	1.24765i
$336$	−124.944	+	186.046i	−0.371857	+	0.553708i
$337$	−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	$0.900192\pi$
$338$	−187.865	+	263.658i	−0.555814	+	0.780055i
$339$	−122.969	−	89.3419i	−0.362739	−	0.263545i
$340$	−8.79263	−	2.12426i	−0.0258607	−	0.00624781i
$341$	255.709	+	113.981i	0.749881	+	0.334255i
$342$	213.783	−	679.227i	0.625095	−	1.98604i
$343$	252.430	−	39.9810i	0.735947	−	0.116563i
$344$	−17.8996	−	8.50444i	−0.0520338	−	0.0247222i
$345$	−582.341	−	57.5089i	−1.68794	−	0.166693i
$346$	83.5740	−	167.836i	0.241543	−	0.485074i
$347$	499.651	+	79.1370i	1.43992	+	0.228060i	0.827051	−	0.562126i	$-0.190017\pi$
$347$	499.651	+	79.1370i	1.43992	+	0.228060i	0.612866	+	0.790187i	$0.290017\pi$
$348$	448.368	−	238.982i	1.28841	−	0.686731i
$349$	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	$0.0156058\pi$
$350$	79.9784	+	117.468i	0.228510	+	0.335624i
$351$	82.7150			0.235655
$352$	88.8470	+	340.603i	0.252406	+	0.967621i
$353$	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	$0.176275\pi$
$354$	527.514	+	78.5653i	1.49015	+	0.221936i
$355$	−375.191	−	333.578i	−1.05688	−	0.939656i
$356$	280.524	+	85.4554i	0.787990	+	0.240043i
$357$	−6.25696	−	0.991005i	−0.0175265	−	0.00277592i
$358$	−132.643	−	395.764i	−0.370511	−	1.10549i
$359$	154.922	−	50.3371i	0.431536	−	0.140215i	−0.0851911	−	0.996365i	$-0.527150\pi$
$359$	154.922	−	50.3371i	0.431536	−	0.140215i	0.516727	+	0.856150i	$0.327150\pi$
$360$	609.922	+	43.2189i	1.69423	+	0.120053i
$361$	146.826	+	106.675i	0.406721	+	0.295500i
$362$	155.765	−	494.895i	0.430291	−	1.36711i
$363$	−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
$366$	1063.57	−	178.532i	2.90592	−	0.487792i
$367$	−280.621	−	142.983i	−0.764634	−	0.389600i	0.0277565	−	0.999615i	$-0.491164\pi$
$367$	−280.621	−	142.983i	−0.764634	−	0.389600i	−0.792390	+	0.610014i	$0.791164\pi$
$368$	73.2554	+	372.846i	0.199063	+	1.01317i
$369$	126.771	−	92.1046i	0.343553	−	0.249606i
$370$	−263.641	−	656.191i	−0.712542	−	1.77349i
$371$	61.7407	−	190.018i	0.166417	−	0.512179i
$372$	−451.150	−	219.477i	−1.21277	−	0.589992i
$373$	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	$0.422861\pi$
$374$	−7.67731	+	6.32965i	−0.0205276	+	0.0169242i
$375$	269.268	−	554.047i	0.718047	−	1.47746i
$376$	32.8316	−	34.7023i	0.0873180	−	0.0922934i
$377$	−61.3174	+	31.2428i	−0.162646	+	0.0828722i
$378$	176.093	−	1.62561i	0.465853	−	0.00430057i
$379$	385.283	−	279.925i	1.01658	−	0.738588i	0.0510002	−	0.998699i	$-0.483759\pi$
$379$	385.283	−	279.925i	1.01658	−	0.738588i	0.965579	+	0.260111i	$0.0837591\pi$
$380$	−178.881	+	430.112i	−0.470739	+	1.13187i
$381$	−661.441	+	214.915i	−1.73606	+	0.564082i
$382$	−265.500	+	372.615i	−0.695027	+	0.975433i
$383$	44.4199	+	280.456i	0.115979	+	0.732261i	0.975310	+	0.220841i	$0.0708803\pi$
$383$	44.4199	+	280.456i	0.115979	+	0.732261i	−0.859331	+	0.511420i	$0.829120\pi$
$384$	−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
$388$	204.408	+	28.5173i	0.526825	+	0.0734982i
$389$	−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	$0.513701\pi$
$390$	−131.057	−	11.7220i	−0.336044	−	0.0300563i
$391$	−8.68959	+	6.31335i	−0.0222240	+	0.0161467i
$392$	−185.018	+	270.079i	−0.471986	+	0.688976i
$393$	214.609	−	109.349i	0.546078	−	0.278241i
$394$	−24.2471	+	162.803i	−0.0615408	+	0.413206i
$395$	144.708	−	330.595i	0.366349	−	0.836949i
$396$	440.969	−	507.870i	1.11356	−	1.28250i
$397$	−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	$0.818633\pi$
$398$	138.784	−	102.803i	0.348704	−	0.258300i
$399$	−100.812	+	310.268i	−0.252662	+	0.777614i
$400$	−394.894	−	63.7059i	−0.987236	−	0.159265i
$401$	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	$0.227551\pi$
$402$	−310.927	−	927.708i	−0.773451	−	2.30773i
$403$	60.5478	+	30.8507i	0.150243	+	0.0765525i
$404$	−462.964	−	613.086i	−1.14595	−	1.51754i
$405$	−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
$408$	14.1299	−	10.8763i	0.0346321	−	0.0266575i
$409$	−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	$0.991870\pi$
$410$	−87.9693	+	52.6256i	−0.214559	+	0.128355i
$411$	528.243	−	171.637i	1.28526	−	0.417607i
$412$	146.175	+	140.875i	0.354793	+	0.341929i
$413$	−151.902	−	24.0589i	−0.367801	−	0.0582540i
$414$	508.633	−	518.112i	1.22858	−	1.25148i
$415$	42.5618	+	724.933i	0.102559	+	1.74683i
$416$	17.2452	+	83.6814i	0.0414548	+	0.201157i
$417$	237.306	−	237.306i	0.569079	−	0.569079i
$418$	260.101	+	441.488i	0.622250	+	1.05619i
$419$	170.819			0.407683			0.203841	−	0.979004i	$-0.434657\pi$
$419$	170.819			0.407683			0.203841	+	0.979004i	$0.434657\pi$
$420$	−279.239	−	22.3793i	−0.664854	−	0.0532840i
$421$	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	$-0.0921069\pi$
$422$	398.267	−	3.67664i	0.943761	−	0.00871242i
$423$	−90.1582	−	14.2796i	−0.213140	−	0.0337580i
$424$	269.089	+	493.815i	0.634643	+	1.16466i
$425$	−3.06350	−	10.8841i	−0.00720823	−	0.0256096i
$426$	975.985	−	163.830i	2.29104	−	0.384578i
$427$	−307.159	+	48.6493i	−0.719343	+	0.113933i
$428$	15.2184	+	85.8015i	0.0355571	+	0.200471i
$429$	−96.8951	+	107.520i	−0.225863	+	0.250629i
$430$	−1.68009	−	24.7145i	−0.00390718	−	0.0574755i
$431$	342.351	+	248.732i	0.794318	+	0.577106i	0.909242	−	0.416269i	$-0.136662\pi$
$431$	342.351	+	248.732i	0.794318	+	0.577106i	−0.114924	+	0.993374i	$0.536662\pi$
$432$	−337.315	+	363.193i	−0.780821	+	0.840724i
$433$	−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	$0.720813\pi$
$434$	129.507	+	64.4882i	0.298403	+	0.148590i
$435$	534.804	+	342.547i	1.22943	+	0.787464i
$436$	32.2142	−	105.749i	0.0738857	−	0.242545i
$437$	251.117	+	492.845i	0.574638	+	1.12779i
$438$	−561.883	−	758.541i	−1.28284	−	1.73183i
$439$		−	650.752i		−	1.48235i	−0.671312	−	0.741175i	$-0.734269\pi$
$439$		−	650.752i		−	1.48235i	0.671312	−	0.741175i	$-0.265731\pi$
$440$	−316.924	+	305.219i	−0.720283	+	0.693681i
$441$	625.543			1.41846
$442$	−1.94073	+	1.43758i	−0.00439078	+	0.00325244i
$443$	−360.893	+	183.884i	−0.814657	+	0.415089i	−0.811102	−	0.584905i	$-0.801132\pi$
$443$	−360.893	+	183.884i	−0.814657	+	0.415089i	−0.00355546	+	0.999994i	$0.501132\pi$
$444$	1333.51	+	406.224i	3.00340	+	0.914918i
$445$	78.4648	+	358.068i	0.176325	+	0.804648i
$446$	−355.050	+	713.022i	−0.796077	+	1.59870i
$447$	−262.417	+	515.023i	−0.587063	+	1.15218i
$448$	38.3580	+	177.811i	0.0856205	+	0.396899i
$449$	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	$0.0322701\pi$
$450$	326.021	+	691.293i	0.724490	+	1.53621i
$451$	−11.8348	+	112.137i	−0.0262413	+	0.248641i
$452$	−121.476	+	21.5459i	−0.268752	+	0.0476680i
$453$	106.821	+	674.440i	0.235807	+	1.48883i
$454$	−59.5761	−	354.912i	−0.131225	−	0.781745i
$455$	37.7597	+	3.72895i	0.0829884	+	0.00819550i
$456$	−439.377	−	806.317i	−0.963545	−	1.76824i
$457$	−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	$0.753203\pi$
$458$	−0.407328	−	44.1233i	−0.000889363	−	0.0963391i
$459$	−13.3256	−	4.32975i	−0.0290318	−	0.00943302i
$460$	−361.610	+	307.949i	−0.786109	+	0.669455i
$461$		−	250.752i		−	0.543930i	−0.962307	−	0.271965i	$-0.912327\pi$
$461$		−	250.752i		−	0.543930i	0.962307	−	0.271965i	$-0.0876735\pi$
$462$	−204.168	+	230.804i	−0.441921	+	0.499576i
$463$	−171.031	−	171.031i	−0.369398	−	0.369398i	0.497860	−	0.867257i	$-0.334119\pi$
$463$	−171.031	−	171.031i	−0.369398	−	0.369398i	−0.867257	+	0.497860i	$0.834119\pi$
$464$	112.871	−	396.647i	0.243256	−	0.854844i
$465$	−36.7564	−	626.052i	−0.0790459	−	1.34635i
$466$	406.696	+	399.256i	0.872738	+	0.856772i
$467$	31.0155	−	195.824i	0.0664143	−	0.419323i	−0.931972	−	0.362531i	$-0.881913\pi$
$467$	31.0155	−	195.824i	0.0664143	−	0.419323i	0.998386	−	0.0567923i	$-0.0180873\pi$
$468$	113.289	−	117.552i	0.242071	−	0.251179i
$469$	87.1878	+	268.336i	0.185901	+	0.572146i
$470$	57.9131	+	14.5586i	0.123219	+	0.0309758i
$471$	−15.1081	+	20.7946i	−0.0320767	+	0.0441498i
$472$	343.035	−	264.046i	0.726769	−	0.559420i
$473$	−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
$476$	−4.10337	+	3.09861i	−0.00862053	+	0.00650969i
$477$	487.845	−	957.450i	1.02274	−	2.00723i
$478$	−548.211	+	183.737i	−1.14689	+	0.384386i
$479$	104.531	+	143.874i	0.218227	+	0.300364i	0.904069	−	0.427387i	$-0.140566\pi$
$479$	104.531	+	143.874i	0.218227	+	0.300364i	−0.685842	+	0.727751i	$0.740566\pi$
$480$	585.925	−	527.655i	1.22068	−	1.09928i
$481$	−179.574	−	58.3470i	−0.373334	−	0.121304i
$482$	559.332	+	755.097i	1.16044	+	1.56659i
$483$	−235.210	+	235.210i	−0.486977	+	0.486977i
$484$	59.0565	+	480.384i	0.122018	+	0.992528i
$485$	93.9651	+	240.264i	0.193742	+	0.495389i
$486$	−404.403	−	60.2297i	−0.832104	−	0.123930i
$487$	167.584	+	328.903i	0.344115	+	0.675365i	0.996596	−	0.0824409i	$-0.0262716\pi$
$487$	167.584	+	328.903i	0.344115	+	0.675365i	−0.652480	+	0.757806i	$0.726272\pi$
$488$	494.707	−	722.143i	1.01374	−	1.47980i
$489$	172.597	+	237.559i	0.352959	+	0.485807i
$490$	−407.592	−	36.4556i	−0.831819	−	0.0743993i
$491$	180.667	+	556.035i	0.367956	+	1.13245i	0.948109	+	0.317945i	$0.102993\pi$
$491$	180.667	+	556.035i	0.367956	+	1.13245i	−0.580153	+	0.814508i	$0.697007\pi$
$492$	27.9207	−	200.132i	0.0567494	−	0.406772i
$493$	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
$498$	−1165.81	−	830.677i	−2.34098	−	1.66803i
$499$	−117.887	−	362.817i	−0.236245	−	0.727089i	−0.996954	−	0.0779949i	$-0.975148\pi$
$499$	−117.887	−	362.817i	−0.236245	−	0.727089i	0.760708	−	0.649094i	$-0.224852\pi$
$500$	−172.141	−	469.433i	−0.344283	−	0.938866i
$501$	−349.656	−	481.261i	−0.697917	−	0.960600i
$502$	2.44761	+	265.134i	0.00487572	+	0.528156i
$503$	−85.7539	−	168.301i	−0.170485	−	0.334595i	0.789917	−	0.613214i	$-0.210124\pi$
$503$	−85.7539	−	168.301i	−0.170485	−	0.334595i	−0.960402	+	0.278618i	$0.910124\pi$
$504$	238.872	−	252.483i	0.473953	−	0.500959i
$505$	385.074	−	879.727i	0.762523	−	1.74203i
$506$	31.9347	+	521.488i	0.0631120	+	1.03061i
$507$	564.072	−	564.072i	1.11257	−	1.11257i
$508$	−246.948	+	507.619i	−0.486119	+	0.999250i
$509$	−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	$0.772811\pi$
$510$	20.5001	+	8.74869i	0.0401962	+	0.0171543i
$511$	160.002	+	220.224i	0.313116	+	0.430968i
$512$	−437.762	−	265.534i	−0.855005	−	0.518620i
$513$	−327.578	+	642.909i	−0.638554	+	1.25323i
$514$	−83.6646	−	498.415i	−0.162772	−	0.969679i
$515$	−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
$518$	−383.442	−	120.686i	−0.740236	−	0.232985i
$519$	−271.552	+	373.759i	−0.523221	+	0.720152i
$520$	−80.6679	+	69.9921i	−0.155131	+	0.134600i
$521$	−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	$0.935104\pi$
$522$	−747.149	+	250.412i	−1.43132	+	0.479716i
$523$	81.7832	−	516.359i	0.156373	−	0.987301i	−0.777288	−	0.629145i	$-0.783405\pi$
$523$	81.7832	−	516.359i	0.156373	−	0.987301i	0.933661	−	0.358157i	$-0.116595\pi$
$524$	56.9699	−	187.015i	0.108721	−	0.356899i
$525$	−146.435	−	318.079i	−0.278924	−	0.605865i
$526$	−23.4464	+	157.427i	−0.0445748	+	0.299290i
$527$	−8.13953	−	8.13953i	−0.0154450	−	0.0154450i
$528$	−76.9670	−	863.926i	−0.145771	−	1.63622i
$529$			34.9864i			0.0661369i
$530$	−373.669	+	595.425i	−0.705036	+	1.12344i
$531$	−786.675	−	255.606i	−1.48150	−	0.481368i
$532$	124.550	+	233.675i	0.234116	+	0.439238i
$533$	−4.28158	+	27.0328i	−0.00803299	+	0.0507183i
$534$	−646.832	−	322.091i	−1.21130	−	0.603167i
$535$	−84.2188	+	69.0799i	−0.157418	+	0.129121i
$536$	−717.313	−	340.809i	−1.33827	−	0.635837i
$537$	160.893	+	1015.84i	0.299614	+	1.89169i
$538$	241.096	+	75.8835i	0.448134	+	0.141047i
$539$	−301.347	+	334.390i	−0.559085	+	0.620390i
$540$	−602.262	−	145.503i	−1.11530	−	0.269451i
$541$	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	$0.00371561\pi$
$542$	579.520	+	412.926i	1.06922	+	0.761857i
$543$	−580.393	+	1139.08i	−1.06886	+	2.09776i
$544$	1.60209	−	14.3840i	0.00294502	−	0.0264412i
$545$	134.981	−	29.5789i	0.247672	−	0.0542732i
$546$	−52.3981	+	53.3745i	−0.0959672	+	0.0977556i
$547$	492.699	−	251.042i	0.900729	−	0.458944i	0.0586375	−	0.998279i	$-0.481324\pi$
$547$	492.699	−	251.042i	0.900729	−	0.458944i	0.842091	+	0.539335i	$0.181324\pi$
$548$	197.219	−	405.397i	0.359889	−	0.739776i
$549$	−1672.59			−3.04661
$550$	−526.593	−	158.743i	−0.957442	−	0.288624i
$551$		−	600.326i		−	1.08952i
$552$	−25.9260	−	935.919i	−0.0469673	−	1.69551i
$553$	−93.1308	−	182.780i	−0.168410	−	0.330524i
$554$	−198.964	+	202.672i	−0.359141	+	0.365834i
$555$	372.993	+	1702.12i	0.672059	+	3.06689i
$556$	−5.02890	−	272.351i	−0.00904478	−	0.489840i
$557$	−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	$0.681996\pi$
$558$	633.696	+	451.528i	1.13566	+	0.809191i
$559$	−5.35083	−	3.88760i	−0.00957214	−	0.00695457i
$560$	−170.359	+	150.592i	−0.304212	+	0.268914i
$561$	21.2382	−	12.2497i	0.0378578	−	0.0218355i
$562$	−339.128	−	106.738i	−0.603430	−	0.189926i
$563$	898.071	−	142.240i	1.59515	−	0.252647i	0.705304	−	0.708905i	$-0.250810\pi$
$563$	898.071	−	142.240i	1.59515	−	0.252647i	0.889848	+	0.456257i	$0.150810\pi$
$564$	−93.9381	+	70.9362i	−0.166557	+	0.125773i
$565$	−97.8017	−	119.235i	−0.173100	−	0.211036i
$566$	330.330	+	164.488i	0.583621	+	0.290615i
$567$	−42.3713	−	6.71095i	−0.0747289	−	0.0118359i
$568$	453.969	−	662.677i	0.799242	−	1.16668i
$569$	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	$0.0662169\pi$
$570$	610.139	−	972.229i	1.07042	−	1.70567i
$571$	−576.201			−1.00911			−0.504554	−	0.863380i	$-0.668343\pi$
$571$	−576.201			−1.00911			−0.504554	+	0.863380i	$0.668343\pi$
$572$	8.26288	+	117.189i	0.0144456	+	0.204876i
$573$	797.176	−	797.176i	1.39123	−	1.39123i
$574$	−8.58380	+	57.6345i	−0.0149544	+	0.100409i
$575$	−556.906	−	205.784i	−0.968533	−	0.357885i
$576$	54.1595	+	976.821i	0.0940270	+	1.69587i
$577$	−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	$0.776310\pi$
$578$	−547.651	+	183.549i	−0.947492	+	0.317558i
$579$	271.602	−	88.2487i	0.469088	−	0.152416i
$580$	501.422	−	119.621i	0.864520	−	0.206243i
$581$	333.955	+	242.633i	0.574794	+	0.417612i
$582$	−485.090	−	152.679i	−0.833489	−	0.262336i
$583$	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
$586$	−23.8476	−	142.067i	−0.0406956	−	0.242436i
$587$	518.368	+	264.121i	0.883079	+	0.449951i	0.835866	−	0.548933i	$-0.184966\pi$
$587$	518.368	+	264.121i	0.883079	+	0.449951i	0.0472132	+	0.998885i	$0.484966\pi$
$588$	559.774	−	580.835i	0.951996	−	0.987815i
$589$	−479.578	+	348.434i	−0.814224	+	0.591568i
$590$	497.686	+	212.394i	0.843535	+	0.359990i
$591$	125.331	−	385.730i	0.212066	−	0.652673i
$592$	988.503	−	550.547i	1.66977	−	0.929979i
$593$	−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	$0.826283\pi$
$594$	−525.867	+	433.557i	−0.885298	+	0.729894i
$595$	−5.88800	−	2.57729i	−0.00989580	−	0.00433159i
$596$	153.193	+	443.450i	0.257035	+	0.744043i
$597$	−379.188	+	193.206i	−0.635156	+	0.323628i
$598$	1.17067	+	126.811i	0.00195764	+	0.212058i
$599$	−84.5661	+	61.4409i	−0.141179	+	0.102572i	−0.656133	−	0.754645i	$-0.727809\pi$
$599$	−84.5661	+	61.4409i	−0.141179	+	0.102572i	0.514954	+	0.857218i	$0.327809\pi$
$600$	933.629	+	315.891i	1.55605	+	0.526486i
$601$	−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	$0.720162\pi$
$602$	−11.4678	−	8.17118i	−0.0190495	−	0.0135734i
$603$	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	$0.0368062\pi$
$607$	51.1511	+	322.956i	0.0842688	+	0.532052i	−0.909054	+	0.416679i	$0.863194\pi$
$608$	−718.717	−	197.366i	−1.18210	−	0.324615i
$609$	343.348	−	111.561i	0.563790	−	0.183187i
$610$	1089.83	+	97.4759i	1.78660	+	0.159797i
$611$	12.8989	−	9.37158i	0.0211111	−	0.0153381i
$612$	−24.4045	+	13.0077i	−0.0398767	+	0.0212545i
$613$	−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	$0.350637\pi$
$614$	762.389	+	113.547i	1.24168	+	0.184929i
$615$	235.237	−	91.9993i	0.382499	−	0.149592i
$616$	19.8940	+	249.322i	0.0322955	+	0.404743i
$617$	−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	$0.887979\pi$
$618$	−297.749	−	401.960i	−0.481794	−	0.650420i
$619$	−135.121	+	415.860i	−0.218289	+	0.671825i	0.780614	+	0.625013i	$0.214906\pi$
$619$	−135.121	+	415.860i	−0.218289	+	0.671825i	−0.998904	+	0.0468123i	$0.985094\pi$
$620$	−386.590	−	331.138i	−0.623531	−	0.534093i
$621$	−595.204	+	432.441i	−0.958460	+	0.696362i
$622$	526.115	−	176.331i	0.845844	−	0.283490i
$623$	185.660	+	94.5982i	0.298009	+	0.151843i
$624$	−7.77207	−	210.385i	−0.0124552	−	0.337156i
$625$	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
$628$	3.64351	+	20.5421i	0.00580178	+	0.0327104i
$629$	25.8756	+	18.7997i	0.0411377	+	0.0298883i
$630$	421.358	+	105.924i	0.668822	+	0.168133i
$631$	−466.366	+	151.532i	−0.739091	+	0.240145i	−0.654280	−	0.756252i	$-0.727028\pi$
$631$	−466.366	+	151.532i	−0.739091	+	0.240145i	−0.0848102	+	0.996397i	$0.527028\pi$
$632$	553.876	+	163.154i	0.876385	+	0.258154i
$633$	−969.312	−	153.524i	−1.53130	−	0.242534i
$634$	382.745	+	375.743i	0.603698	+	0.592654i
$635$	−704.412	+	41.3570i	−1.10931	+	0.0651292i
$636$	−452.467	−	1309.76i	−0.711426	−	2.05938i
$637$	−77.2593	+	77.2593i	−0.121286	+	0.121286i
$638$	226.069	−	520.028i	0.354340	−	0.815092i
$639$	−1534.86			−2.40197
$640$	21.6383	−	639.634i	0.0338098	−	0.999428i
$641$	−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	$0.979636\pi$
$642$	−1.98212	−	214.710i	−0.00308741	−	0.334440i
$643$	−450.266	−	71.3152i	−0.700258	−	0.110910i	−0.203854	−	0.979001i	$-0.565347\pi$
$643$	−450.266	−	71.3152i	−0.700258	−	0.110910i	−0.496405	+	0.868091i	$0.665347\pi$
$644$	4.98448	+	269.945i	0.00773987	+	0.419170i
$645$	−5.99865	+	60.7429i	−0.00930023	+	0.0941750i
$646$	−3.48778	−	20.7777i	−0.00539904	−	0.0321636i
$647$	−56.8522	+	9.00451i	−0.0878706	+	0.0139173i	−0.200215	−	0.979752i	$-0.564164\pi$
$647$	−56.8522	+	9.00451i	−0.0878706	+	0.0139173i	0.112344	+	0.993669i	$0.464164\pi$
$648$	95.6858	−	73.6527i	0.147663	−	0.113662i
$649$	515.607	−	297.390i	0.794463	−	0.458228i
$650$	−125.646	−	45.1139i	−0.193302	−	0.0694061i
$651$	−288.404	−	209.537i	−0.443016	−	0.321870i
$652$	236.052	+	32.9321i	0.362043	+	0.0505093i
$653$	−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	$0.754350\pi$
$654$	−121.419	+	243.837i	−0.185656	+	0.372839i
$655$	238.711	−	52.3095i	0.364444	−	0.0798618i
$656$	−101.238	−	129.041i	−0.154326	−	0.196708i
$657$	664.662	+	1304.47i	1.01166	+	1.98550i
$658$	27.2763	−	20.2047i	0.0414534	−	0.0307063i
$659$		−	74.8890i		−	0.113640i	−0.998384	−	0.0568202i	$-0.981904\pi$
$659$		−	74.8890i		−	0.113640i	0.998384	−	0.0568202i	$-0.0180962\pi$
$660$	894.647	−	612.423i	1.35553	−	0.927914i
$661$	734.485			1.11117			0.555586	−	0.831459i	$-0.312494\pi$
$661$	734.485			1.11117			0.555586	+	0.831459i	$0.312494\pi$
$662$	−319.167	−	430.875i	−0.482126	−	0.650868i
$663$	5.30248	−	2.70175i	0.00799771	−	0.00407504i
$664$	−1142.11	+	213.467i	−1.72005	+	0.321487i
$665$	−178.524	+	278.723i	−0.268458	+	0.419132i
$666$	−1935.34	−	963.707i	−2.90592	−	1.44701i
$667$	277.890	−	545.391i	0.416627	−	0.817677i
$668$	−478.207	−	66.7155i	−0.715879	−	0.0998735i
$669$	1153.64	−	1587.85i	1.72443	−	2.37347i
$670$	−67.3281	−	990.413i	−0.100490	−	1.47823i
$671$	805.747	−	894.100i	1.20082	−	1.33249i
$672$	−20.6807	−	447.737i	−0.0307749	−	0.666276i
$673$	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	$0.683351\pi$
$674$	940.595	−	157.890i	1.39554	−	0.234258i
$675$	−209.838	−	745.518i	−0.310871	−	1.10447i
$676$	−11.9536	−	647.374i	−0.0176828	−	0.957654i
$677$	−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	$0.829125\pi$
$678$	303.982	−	2.80624i	0.448351	−	0.00413899i
$679$	139.472	+	45.3171i	0.205407	+	0.0667409i
$680$	16.6596	−	7.05333i	0.0244994	−	0.0103725i
$681$			886.759i			1.30214i
$682$	−546.643	+	121.231i	−0.801530	+	0.177758i
$683$	757.540	+	757.540i	1.10914	+	1.10914i	0.993264	+	0.115871i	$0.0369661\pi$
$683$	757.540	+	757.540i	1.10914	+	1.10914i	0.115871	+	0.993264i	$0.463034\pi$
$684$	465.017	+	1346.09i	0.679850	+	1.96797i
$685$	562.561	−	33.0287i	0.821257	−	0.0482172i
$686$	−358.088	+	364.761i	−0.521994	+	0.531721i
$687$	−17.0086	+	107.388i	−0.0247578	+	0.156315i
$688$	38.8909	−	7.64113i	0.0565274	−	0.0111063i
$689$	57.9998	+	178.505i	0.0841797	+	0.259079i
$690$	1004.35	−	600.828i	1.45558	−	0.870766i
$691$	177.059	−	243.700i	0.256235	−	0.352678i	−0.661447	−	0.749992i	$-0.730058\pi$
$691$	177.059	−	243.700i	0.256235	−	0.352678i	0.917683	+	0.397314i	$0.130058\pi$
$692$	65.4881	+	369.222i	0.0946360	+	0.533558i
$693$	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
$696$	−436.080	+	917.834i	−0.626552	+	1.31873i
$697$	2.10482	−	4.13094i	0.00301983	−	0.00592675i
$698$	116.246	+	346.841i	0.166542	+	0.496907i
$699$	−825.433	−	1136.11i	−1.18088	−	1.62534i
$700$	−268.375	−	93.5740i	−0.383393	−	0.133677i
$701$	−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	$0.701468\pi$
$702$	−132.932	+	98.4687i	−0.189362	+	0.140269i
$703$	1164.68	−	1164.68i	1.65672	−	1.65672i
$704$	−548.260	−	441.619i	−0.778778	−	0.627299i
$705$	−134.793	−	59.0018i	−0.191196	−	0.0836904i
$706$	−47.7464	+	320.586i	−0.0676295	+	0.454087i
$707$	−247.825	−	486.385i	−0.350531	−	0.687955i
$708$	−941.303	+	501.719i	−1.32952	+	0.708643i
$709$	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	$0.656861\pi$
$710$	1000.08	+	89.4491i	1.40857	+	0.125985i
$711$	−340.938	−	1049.30i	−0.479519	−	1.47581i
$712$	−552.565	+	196.616i	−0.776075	+	0.276146i
$713$	−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
$718$	−189.052	+	265.325i	−0.263304	+	0.369533i
$719$	−36.2624	−	111.604i	−0.0504345	−	0.155221i	0.922667	−	0.385597i	$-0.126004\pi$
$719$	−36.2624	−	111.604i	−0.0504345	−	0.155221i	−0.973102	+	0.230376i	$0.926004\pi$
$720$	−1031.66	+	656.628i	−1.43287	+	0.911983i
$721$	84.7872	+	116.700i	0.117597	+	0.161858i
$722$	−362.959	+	3.35069i	−0.502713	+	0.00464084i
$723$	−1051.20	−	2063.09i	−1.45394	−	2.85351i
$724$	338.819	+	980.785i	0.467982	+	1.35467i
$725$	437.149	+	473.400i	0.602964	+	0.652966i
$726$	52.4439	−	1191.45i	0.0722368	−	1.64111i
$727$	626.526	−	626.526i	0.861797	−	0.861797i	−0.129750	−	0.991547i	$-0.541418\pi$
$727$	626.526	−	626.526i	0.861797	−	0.861797i	0.991547	+	0.129750i	$0.0414175\pi$
$728$	1.68107	+	60.6862i	0.00230916	+	0.0833601i
$729$	1087.35	+	353.301i	1.49156	+	0.484637i
$730$	−357.058	−	888.704i	−0.489121	−	1.21740i
$731$	0.658534	+	0.906395i	0.000900868	+	0.00123994i
$732$	−1496.74	+	1553.05i	−2.04472	+	2.12165i
$733$	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	$0.0815109\pi$
$734$	621.205	−	104.276i	0.846328	−	0.142066i
$735$	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
$738$	−94.0890	+	298.938i	−0.127492	+	0.405065i
$739$	−806.430	+	1109.96i	−1.09124	+	1.50197i	−0.244740	+	0.969589i	$0.578703\pi$
$739$	−806.430	+	1109.96i	−1.09124	+	1.50197i	−0.846505	+	0.532381i	$0.821297\pi$
$740$	1204.87	+	740.721i	1.62820	+	1.00097i
$741$	−94.7040	−	291.469i	−0.127806	−	0.393345i
$742$	126.984	+	378.881i	0.171138	+	0.510621i
$743$	−46.2152	+	291.791i	−0.0622008	+	0.392721i	0.936872	+	0.349672i	$0.113707\pi$
$743$	−46.2152	+	291.791i	−0.0622008	+	0.392721i	−0.999073	+	0.0430485i	$0.986293\pi$
$744$	986.327	−	184.350i	1.32571	−	0.247782i
$745$	−389.669	+	438.279i	−0.523046	+	0.588294i
$746$	−1263.41	−	188.167i	−1.69358	−	0.252234i
$747$	1569.86	+	1569.86i	2.10156	+	2.10156i
$748$	4.80313	−	19.3120i	0.00642130	−	0.0258181i
$749$			61.9180i			0.0826675i
$750$	226.825	+	1210.97i	0.302434	+	1.61462i
$751$	−111.707	−	36.2957i	−0.148744	−	0.0483298i	0.233699	−	0.972309i	$-0.424917\pi$
$751$	−111.707	−	36.2957i	−0.148744	−	0.0483298i	−0.382443	+	0.923979i	$0.624917\pi$
$752$	−11.4524	+	94.8551i	−0.0152293	+	0.126137i
$753$	102.204	−	645.290i	0.135729	−	0.856959i
$754$	61.3509	−	123.206i	0.0813672	−	0.163404i
$755$	−68.0869	+	689.454i	−0.0901813	+	0.913184i
$756$	−281.065	+	212.243i	−0.371780	+	0.280745i
$757$	−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	$-0.119981\pi$
$758$	−285.956	+	908.534i	−0.377250	+	1.19859i
$759$	135.119	−	1280.27i	0.178022	−	1.68679i
$760$	−224.548	−	904.189i	−0.295458	−	1.18972i
$761$	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	$0.158327\pi$
$762$	807.163	−	1132.81i	1.05927	−	1.48663i
$763$	35.6608	−	69.9882i	0.0467376	−	0.0917276i
$764$	−16.8934	−	914.902i	−0.0221118	−	1.19752i
$765$	−29.1092	−	18.6447i	−0.0380513	−	0.0243722i
$766$	−405.258	−	397.845i	−0.529058	−	0.519379i
$767$	128.730	−	65.5911i	0.167835	−	0.0855164i
$768$	955.473	+	823.831i	1.24411	+	1.07270i
$769$	331.548			0.431142			0.215571	−	0.976488i	$-0.430839\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60711 + 1.19046i) q^{2} +(4.39098 - 2.23732i) q^{3} +(1.16563 - 3.82640i) q^{4} +(4.88411 - 1.07027i) q^{5} +(-4.39337 + 8.82289i) q^{6} +(1.29034 - 2.53243i) q^{7} +(2.68187 + 7.53708i) q^{8} +(8.98505 - 12.3669i) q^{9} +(-6.57520 + 7.53437i) q^{10} +(2.28240 + 10.7606i) q^{11} +(-3.44262 - 19.4095i) q^{12} +(0.417679 + 2.63712i) q^{13} +(0.941028 + 5.60598i) q^{14} +(19.0515 - 15.6268i) q^{15} +(-13.2826 - 8.92029i) q^{16} +(0.0707521 - 0.446711i) q^{17} +(0.282221 + 30.5712i) q^{18} +(-22.1514 - 7.19742i) q^{19} +(1.59775 - 19.9361i) q^{20} -14.0067i q^{21} +(-16.4781 - 14.5764i) q^{22} +(-16.7927 - 16.7927i) q^{23} +(28.6389 + 27.0950i) q^{24} +(22.7090 - 10.4547i) q^{25} +(-3.81064 - 3.74093i) q^{26} +(4.84625 - 30.5980i) q^{27} +(-8.18602 - 7.88919i) q^{28} +(7.96480 + 24.5131i) q^{29} +(-12.0148 + 47.7941i) q^{30} +(14.9598 - 20.5904i) q^{31} +(31.9659 - 1.47649i) q^{32} +(34.0968 + 42.1431i) q^{33} +(0.418084 + 0.802143i) q^{34} +(3.59175 - 13.7496i) q^{35} +(-36.8473 - 48.7955i) q^{36} +(-32.1050 + 63.0096i) q^{37} +(44.1680 - 14.8032i) q^{38} +(7.73410 + 10.6451i) q^{39} +(21.1653 + 33.9416i) q^{40} +(9.74917 + 3.16770i) q^{41} +(16.6744 + 22.5104i) q^{42} +(-1.75161 + 1.75161i) q^{43} +(43.8348 + 3.80946i) q^{44} +(30.6480 - 70.0175i) q^{45} +(46.9786 + 6.99677i) q^{46} +(-2.71100 - 5.32065i) q^{47} +(-78.2813 - 9.45136i) q^{48} +(24.0533 + 33.1065i) q^{49} +(-24.0502 + 43.8359i) q^{50} +(-0.688763 - 2.11980i) q^{51} +(10.5775 + 1.47569i) 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} +(-41.9822 - 29.9136i) q^{58} +(-16.7213 - 51.4628i) q^{59} +(-37.5876 - 91.1136i) q^{60} +(-64.3142 - 88.5209i) q^{61} +(0.469889 + 50.9001i) q^{62} +(-19.7244 - 38.7113i) q^{63} +(-49.6152 + 40.4269i) q^{64} +(4.86243 + 12.4330i) q^{65} +(-104.967 - 27.1380i) q^{66} +(-70.1944 + 70.1944i) q^{67} +(-1.62683 - 0.791424i) q^{68} +(-111.307 - 36.1657i) q^{69} +(10.5960 + 26.3731i) q^{70} +(-59.0181 - 81.2315i) q^{71} +(117.307 + 34.5547i) q^{72} +(-43.4809 + 85.3361i) q^{73} +(-23.4138 - 139.483i) q^{74} +(76.3245 - 96.7134i) q^{75} +(-53.3604 + 76.3705i) q^{76} +(30.1955 + 8.10477i) q^{77} +(-25.1021 - 7.90073i) q^{78} +(42.4238 - 58.3914i) q^{79} +(-74.4210 - 29.3516i) q^{80} +(-4.66421 - 14.3550i) q^{81} +(-19.4390 + 6.51511i) q^{82} +(-22.7200 + 143.448i) q^{83} +(-53.5952 - 16.3266i) q^{84} +(-0.132542 - 2.25751i) q^{85} +(0.729820 - 4.90025i) q^{86} +(89.8169 + 89.8169i) q^{87} +(-74.9824 + 46.0612i) q^{88} +73.3129i q^{89} +(34.0980 + 149.011i) q^{90} +(7.21727 + 2.34503i) q^{91} +(-83.8293 + 44.6814i) q^{92} +(19.6209 - 123.882i) q^{93} +(10.6909 + 5.32355i) q^{94} +(-115.893 - 11.4450i) q^{95} +(137.058 - 78.0011i) q^{96} +(8.07153 + 50.9617i) q^{97} +(-78.0682 - 24.5715i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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