LMFDB - Embedded newform 220.3.i.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, degree $2$, 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:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33338 + 1.49067i) q^{2} +(3.87627 - 3.87627i) q^{3} +(-0.444207 - 3.97526i) q^{4} +(3.64792 + 3.41945i) q^{5} +(0.609714 + 10.9468i) q^{6} +(5.44609 - 5.44609i) q^{7} +(6.51810 + 4.63836i) q^{8} -21.0509i q^{9} +(-9.96134 + 0.878432i) q^{10} +(7.73363 + 7.82247i) q^{11} +(-17.1310 - 13.6873i) q^{12} +(-14.7946 + 14.7946i) q^{13} +(0.856637 + 15.3800i) q^{14} +(27.3951 - 0.885606i) q^{15} +(-15.6054 + 3.53167i) q^{16} +(-5.69580 - 5.69580i) q^{17} +(31.3800 + 28.0688i) q^{18} -21.1920i q^{19} +(11.9728 - 16.0204i) q^{20} -42.2210i q^{21} +(-21.9726 + 1.09800i) q^{22} +(7.64133 - 7.64133i) q^{23} +(43.2454 - 7.28640i) q^{24} +(1.61467 + 24.9478i) q^{25} +(-2.32710 - 41.7806i) q^{26} +(-46.7126 - 46.7126i) q^{27} +(-24.0688 - 19.2304i) q^{28} +2.11660 q^{29} +(-35.2078 + 42.0179i) q^{30} +23.3398i q^{31} +(15.5433 - 27.9715i) q^{32} +(60.2996 + 0.344346i) q^{33} +(16.0852 - 0.895915i) q^{34} +(38.4895 - 1.24426i) q^{35} +(-83.6829 + 9.35096i) q^{36} +(7.12170 - 7.12170i) q^{37} +(31.5904 + 28.2570i) q^{38} +114.695i q^{39} +(7.91689 + 39.2087i) q^{40} +13.4770i q^{41} +(62.9377 + 56.2965i) q^{42} +(-18.4300 - 18.4300i) q^{43} +(27.6610 - 34.2180i) q^{44} +(71.9827 - 76.7922i) q^{45} +(1.20194 + 21.5795i) q^{46} +(25.7009 + 25.7009i) q^{47} +(-46.8009 + 74.1803i) q^{48} -10.3197i q^{49} +(-39.3420 - 30.8579i) q^{50} -44.1569 q^{51} +(65.3840 + 52.2403i) q^{52} +(-10.8004 - 10.8004i) q^{53} +(131.919 - 7.34763i) q^{54} +(1.46313 + 54.9805i) q^{55} +(60.7590 - 10.2373i) q^{56} +(-82.1460 - 82.1460i) q^{57} +(-2.82223 + 3.15516i) q^{58} -84.0088 q^{59} +(-15.6896 - 108.509i) q^{60} +87.3519i q^{61} +(-34.7919 - 31.1207i) q^{62} +(-114.645 - 114.645i) q^{63} +(20.9713 + 60.4666i) q^{64} +(-104.559 + 3.38009i) q^{65} +(-80.9155 + 89.4278i) q^{66} +(-55.9563 - 55.9563i) q^{67} +(-20.1122 + 25.1724i) q^{68} -59.2397i q^{69} +(-49.4663 + 59.0344i) q^{70} -24.0536i q^{71} +(97.6417 - 137.212i) q^{72} +(69.0302 - 69.0302i) q^{73} +(1.12020 + 20.1120i) q^{74} +(102.963 + 90.4455i) q^{75} +(-84.2438 + 9.41364i) q^{76} +(84.7198 + 0.483800i) q^{77} +(-170.973 - 152.932i) q^{78} +47.8344i q^{79} +(-69.0035 - 40.4785i) q^{80} -172.683 q^{81} +(-20.0898 - 17.9699i) q^{82} +(11.0631 + 11.0631i) q^{83} +(-167.839 + 18.7548i) q^{84} +(-1.30131 - 40.2543i) q^{85} +(52.0472 - 2.89893i) q^{86} +(8.20451 - 8.20451i) q^{87} +(14.1252 + 86.8590i) q^{88} +90.4306i q^{89} +(18.4918 + 209.696i) q^{90} +161.145i q^{91} +(-33.7706 - 26.9819i) q^{92} +(90.4712 + 90.4712i) q^{93} +(-72.5807 + 4.04261i) q^{94} +(72.4652 - 77.3069i) q^{95} +(-48.1752 - 168.675i) q^{96} +(-88.2136 + 88.2136i) q^{97} +(15.3833 + 13.7601i) q^{98} +(164.670 - 162.800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.33338	+	1.49067i	−0.666689	+	0.745336i
$2$	−1.33338	+	1.49067i	−0.666689	+	0.745336i
$3$	3.87627	−	3.87627i	1.29209	−	1.29209i	0.358598	−	0.933492i	$-0.383255\pi$
$3$	3.87627	−	3.87627i	1.29209	−	1.29209i	0.933492	−	0.358598i	$-0.116745\pi$
$4$	−0.444207	−	3.97526i	−0.111052	−	0.993815i
$5$	3.64792	+	3.41945i	0.729584	+	0.683891i
$5$	3.64792	+	3.41945i	0.729584	+	0.683891i
$6$	0.609714	+	10.9468i	0.101619	+	1.82446i
$7$	5.44609	−	5.44609i	0.778012	−	0.778012i	−0.201480	−	0.979493i	$-0.564575\pi$
$7$	5.44609	−	5.44609i	0.778012	−	0.778012i	0.979493	+	0.201480i	$0.0645752\pi$
$8$	6.51810	+	4.63836i	0.814763	+	0.579794i
$9$		−	21.0509i		−	2.33899i
$10$	−9.96134	+	0.878432i	−0.996134	+	0.0878432i
$11$	7.73363	+	7.82247i	0.703057	+	0.711133i
$11$	7.73363	+	7.82247i	0.703057	+	0.711133i
$12$	−17.1310	−	13.6873i	−1.42759	−	1.14061i
$13$	−14.7946	+	14.7946i	−1.13804	+	1.13804i	−0.149242	+	0.988801i	$0.547683\pi$
$13$	−14.7946	+	14.7946i	−1.13804	+	1.13804i	−0.988801	+	0.149242i	$0.952317\pi$
$14$	0.856637	+	15.3800i	0.0611884	+	1.09857i
$15$	27.3951	−	0.885606i	1.82634	−	0.0590404i
$16$	−15.6054	+	3.53167i	−0.975335	+	0.220729i
$17$	−5.69580	−	5.69580i	−0.335047	−	0.335047i	0.519452	−	0.854499i	$-0.326136\pi$
$17$	−5.69580	−	5.69580i	−0.335047	−	0.335047i	−0.854499	+	0.519452i	$0.826136\pi$
$18$	31.3800	+	28.0688i	1.74334	+	1.55938i
$19$		−	21.1920i		−	1.11537i	−0.830053	−	0.557685i	$-0.811690\pi$
$19$		−	21.1920i		−	1.11537i	0.830053	−	0.557685i	$-0.188310\pi$
$20$	11.9728	−	16.0204i	0.598639	−	0.801019i
$21$		−	42.2210i		−	2.01052i
$22$	−21.9726	+	1.09800i	−0.998754	+	0.0499093i
$23$	7.64133	−	7.64133i	0.332232	−	0.332232i	−0.521202	−	0.853434i	$-0.674516\pi$
$23$	7.64133	−	7.64133i	0.332232	−	0.332232i	0.853434	+	0.521202i	$0.174516\pi$
$24$	43.2454	−	7.28640i	1.80189	−	0.303600i
$25$	1.61467	+	24.9478i	0.0645869	+	0.997912i
$26$	−2.32710	−	41.7806i	−0.0895037	−	1.60694i
$27$	−46.7126	−	46.7126i	−1.73010	−	1.73010i
$28$	−24.0688	−	19.2304i	−0.859600	−	0.686801i
$29$	2.11660			0.0729862			0.0364931	−	0.999334i	$-0.488381\pi$
$29$	2.11660			0.0729862			0.0364931	+	0.999334i	$0.488381\pi$
$30$	−35.2078	+	42.0179i	−1.17359	+	1.40060i
$31$			23.3398i			0.752896i	0.926438	+	0.376448i	$0.122855\pi$
$31$			23.3398i			0.752896i	−0.926438	+	0.376448i	$0.877145\pi$
$32$	15.5433	−	27.9715i	0.485728	−	0.874110i
$33$	60.2996	+	0.344346i	1.82726	+	0.0104347i
$34$	16.0852	−	0.895915i	0.473095	−	0.0263505i
$35$	38.4895	−	1.24426i	1.09970	−	0.0355503i
$36$	−83.6829	+	9.35096i	−2.32452	+	0.259749i
$37$	7.12170	−	7.12170i	0.192478	−	0.192478i	−0.604288	−	0.796766i	$-0.706542\pi$
$37$	7.12170	−	7.12170i	0.192478	−	0.192478i	0.796766	+	0.604288i	$0.206542\pi$
$38$	31.5904	+	28.2570i	0.831326	+	0.743605i
$39$			114.695i			2.94091i
$40$	7.91689	+	39.2087i	0.197922	+	0.980218i
$41$			13.4770i			0.328707i	0.986401	+	0.164354i	$0.0525538\pi$
$41$			13.4770i			0.328707i	−0.986401	+	0.164354i	$0.947446\pi$
$42$	62.9377	+	56.2965i	1.49852	+	1.34039i
$43$	−18.4300	−	18.4300i	−0.428604	−	0.428604i	0.459548	−	0.888153i	$-0.348011\pi$
$43$	−18.4300	−	18.4300i	−0.428604	−	0.428604i	−0.888153	+	0.459548i	$0.848011\pi$
$44$	27.6610	−	34.2180i	0.628659	−	0.777681i
$45$	71.9827	−	76.7922i	1.59962	−	1.70649i
$46$	1.20194	+	21.5795i	0.0261291	+	0.469120i
$47$	25.7009	+	25.7009i	0.546829	+	0.546829i	0.925522	−	0.378694i	$-0.123627\pi$
$47$	25.7009	+	25.7009i	0.546829	+	0.546829i	−0.378694	+	0.925522i	$0.623627\pi$
$48$	−46.8009	+	74.1803i	−0.975018	+	1.54542i
$49$		−	10.3197i		−	0.210606i
$50$	−39.3420	−	30.8579i	−0.786839	−	0.617158i
$51$	−44.1569			−0.865821
$52$	65.3840	+	52.2403i	1.25739	+	1.00462i
$53$	−10.8004	−	10.8004i	−0.203782	−	0.203782i	0.597836	−	0.801618i	$-0.296027\pi$
$53$	−10.8004	−	10.8004i	−0.203782	−	0.203782i	−0.801618	+	0.597836i	$0.796027\pi$
$54$	131.919	−	7.34763i	2.44294	−	0.136067i
$55$	1.46313	+	54.9805i	0.0266023	+	0.999646i
$56$	60.7590	−	10.2373i	1.08498	−	0.182808i
$57$	−82.1460	−	82.1460i	−1.44116	−	1.44116i
$58$	−2.82223	+	3.15516i	−0.0486591	+	0.0543992i
$59$	−84.0088			−1.42388			−0.711939	−	0.702242i	$-0.752183\pi$
$59$	−84.0088			−1.42388			−0.711939	+	0.702242i	$0.752183\pi$
$60$	−15.6896	−	108.509i	−0.261493	−	1.80848i
$61$			87.3519i			1.43200i	0.698101	+	0.715999i	$0.254029\pi$
$61$			87.3519i			1.43200i	−0.698101	+	0.715999i	$0.745971\pi$
$62$	−34.7919	−	31.1207i	−0.561160	−	0.501947i
$63$	−114.645	−	114.645i	−1.81976	−	1.81976i
$64$	20.9713	+	60.4666i	0.327677	+	0.944790i
$65$	−104.559	+	3.38009i	−1.60860	+	0.0520014i
$66$	−80.9155	+	89.4278i	−1.22599	+	1.35497i
$67$	−55.9563	−	55.9563i	−0.835169	−	0.835169i	0.153050	−	0.988218i	$-0.451091\pi$
$67$	−55.9563	−	55.9563i	−0.835169	−	0.835169i	−0.988218	+	0.153050i	$0.951091\pi$
$68$	−20.1122	+	25.1724i	−0.295767	+	0.370182i
$69$		−	59.2397i		−	0.858547i
$70$	−49.4663	+	59.0344i	−0.706662	+	0.843348i
$71$		−	24.0536i		−	0.338784i	−0.985549	−	0.169392i	$-0.945820\pi$
$71$		−	24.0536i		−	0.338784i	0.985549	−	0.169392i	$-0.0541804\pi$
$72$	97.6417	−	137.212i	1.35613	−	1.90572i
$73$	69.0302	−	69.0302i	0.945619	−	0.945619i	−0.0529764	−	0.998596i	$-0.516871\pi$
$73$	69.0302	−	69.0302i	0.945619	−	0.945619i	0.998596	+	0.0529764i	$0.0168708\pi$
$74$	1.12020	+	20.1120i	0.0151379	+	0.271784i
$75$	102.963	+	90.4455i	1.37284	+	1.20594i
$76$	−84.2438	+	9.41364i	−1.10847	+	0.123864i
$77$	84.7198	+	0.483800i	1.10026	+	0.00628312i
$78$	−170.973	−	152.932i	−2.19196	−	1.96067i
$79$			47.8344i			0.605499i	0.953070	+	0.302749i	$0.0979045\pi$
$79$			47.8344i			0.605499i	−0.953070	+	0.302749i	$0.902095\pi$
$80$	−69.0035	−	40.4785i	−0.862544	−	0.505982i
$81$	−172.683			−2.13189
$82$	−20.0898	−	17.9699i	−0.244997	−	0.219145i
$83$	11.0631	+	11.0631i	0.133290	+	0.133290i	0.770604	−	0.637314i	$-0.219955\pi$
$83$	11.0631	+	11.0631i	0.133290	+	0.133290i	−0.637314	+	0.770604i	$0.719955\pi$
$84$	−167.839	+	18.7548i	−1.99809	+	0.223272i
$85$	−1.30131	−	40.2543i	−0.0153095	−	0.473580i
$86$	52.0472	−	2.89893i	0.605200	−	0.0337085i
$87$	8.20451	−	8.20451i	0.0943047	−	0.0943047i
$88$	14.1252	+	86.8590i	0.160514	+	0.987034i
$89$			90.4306i			1.01607i	0.861335	+	0.508037i	$0.169629\pi$
$89$			90.4306i			1.01607i	−0.861335	+	0.508037i	$0.830371\pi$
$90$	18.4918	+	209.696i	0.205465	+	2.32995i
$91$			161.145i			1.77082i
$92$	−33.7706	−	26.9819i	−0.367072	−	0.293282i
$93$	90.4712	+	90.4712i	0.972809	+	0.972809i
$94$	−72.5807	+	4.04261i	−0.772136	+	0.0430065i
$95$	72.4652	−	77.3069i	0.762791	−	0.813757i
$96$	−48.1752	−	168.675i	−0.501825	−	1.75703i
$97$	−88.2136	+	88.2136i	−0.909418	+	0.909418i	−0.996225	−	0.0868070i	$-0.972334\pi$
$97$	−88.2136	+	88.2136i	−0.909418	+	0.909418i	0.0868070	+	0.996225i	$0.472334\pi$
$98$	15.3833	+	13.7601i	0.156973	+	0.140409i
$99$	164.670	−	162.800i	1.66333	−	1.64445i
$100$	98.4567	−	17.5007i	0.984567	−	0.175007i
$101$			52.6106i			0.520897i	0.965488	+	0.260449i	$0.0838704\pi$
$101$			52.6106i			0.520897i	−0.965488	+	0.260449i	$0.916130\pi$
$102$	58.8778	−	65.8234i	0.577234	−	0.645328i
$103$	53.2977	−	53.2977i	0.517453	−	0.517453i	−0.399347	−	0.916800i	$-0.630763\pi$
$103$	53.2977	−	53.2977i	0.517453	−	0.517453i	0.916800	+	0.399347i	$0.130763\pi$
$104$	−165.055	+	27.8100i	−1.58707	+	0.267404i
$105$	144.373	−	154.019i	1.37498	−	1.46685i
$106$	30.5010	−	1.69885i	0.287745	−	0.0160269i
$107$	−47.1165	+	47.1165i	−0.440341	+	0.440341i	−0.892127	−	0.451786i	$-0.850787\pi$
$107$	−47.1165	+	47.1165i	−0.440341	+	0.440341i	0.451786	+	0.892127i	$0.350787\pi$
$108$	−164.945	+	206.445i	−1.52727	+	1.91153i
$109$	−178.673			−1.63920			−0.819599	−	0.572938i	$-0.805804\pi$
$109$	−178.673			−1.63920			−0.819599	+	0.572938i	$0.805804\pi$
$110$	−83.9088	−	71.1288i	−0.762808	−	0.646625i
$111$		−	55.2113i		−	0.497399i
$112$	−65.7544	+	104.222i	−0.587092	+	0.930553i
$113$	−22.6903	−	22.6903i	−0.200799	−	0.200799i	0.599543	−	0.800342i	$-0.295349\pi$
$113$	−22.6903	−	22.6903i	−0.200799	−	0.200799i	−0.800342	+	0.599543i	$0.795349\pi$
$114$	231.985	−	12.9211i	2.03495	−	0.113343i
$115$	54.0042	−	1.74580i	0.469601	−	0.0151809i
$116$	−0.940207	−	8.41403i	−0.00810524	−	0.0725347i
$117$	311.439	+	311.439i	2.66187	+	2.66187i
$118$	112.015	−	125.230i	0.949283	−	1.06127i
$119$	−62.0396			−0.521341
$120$	182.672	+	121.296i	1.52226	+	1.01080i
$121$	−1.38192	+	120.992i	−0.0114208	+	0.999935i
$122$	−130.213	−	116.473i	−1.06732	−	0.954698i
$123$	52.2405	+	52.2405i	0.424719	+	0.424719i
$124$	92.7816	−	10.3677i	0.748239	−	0.0836103i
$125$	−79.4176	+	96.5289i	−0.635341	+	0.772232i
$126$	323.764	−	18.0330i	2.56955	−	0.143119i
$127$	0.187577	−	0.187577i	0.00147699	−	0.00147699i	−0.706368	−	0.707845i	$-0.749668\pi$
$127$	0.187577	−	0.187577i	0.00147699	−	0.00147699i	0.707845	+	0.706368i	$0.249668\pi$
$128$	−118.098	−	49.3634i	−0.922644	−	0.385652i
$129$	−142.879			−1.10759
$130$	134.378	−	160.370i	1.03367	−	1.23361i
$131$	106.461			0.812681			0.406340	−	0.913722i	$-0.366805\pi$
$131$	106.461			0.812681			0.406340	+	0.913722i	$0.366805\pi$
$132$	−25.4166	−	239.860i	−0.192550	−	1.81712i
$133$	−115.414	−	115.414i	−0.867772	−	0.867772i
$134$	158.023	−	8.80160i	1.17928	−	0.0656836i
$135$	−10.6724	−	330.136i	−0.0790546	−	2.44545i
$136$	−10.7067	−	63.5449i	−0.0787254	−	0.467242i
$137$	63.3415	−	63.3415i	0.462347	−	0.462347i	−0.437077	−	0.899424i	$-0.643986\pi$
$137$	63.3415	−	63.3415i	0.462347	−	0.462347i	0.899424	+	0.437077i	$0.143986\pi$
$138$	88.3070	+	78.9889i	0.639906	+	0.572384i
$139$			224.103i			1.61225i	0.591746	+	0.806124i	$0.298439\pi$
$139$			224.103i			1.61225i	−0.591746	+	0.806124i	$0.701561\pi$
$140$	−22.0436	−	152.453i	−0.157454	−	1.08895i
$141$	199.248			1.41310
$142$	35.8561	+	32.0726i	0.252508	+	0.225863i
$143$	−230.146	−	1.31427i	−1.60941	−	0.00919067i
$144$	74.3450	+	328.507i	0.516284	+	2.28130i
$145$	7.72119	+	7.23761i	0.0532496	+	0.0499146i
$146$	10.8580	+	194.945i	0.0743702	+	1.33524i
$147$	−40.0020	−	40.0020i	−0.272122	−	0.272122i
$148$	−31.4741	−	25.1471i	−0.212663	−	0.169913i
$149$	160.633			1.07807			0.539037	−	0.842282i	$-0.318788\pi$
$149$	160.633			1.07807			0.539037	+	0.842282i	$0.318788\pi$
$150$	−272.114	+	32.8865i	−1.81409	+	0.219243i
$151$	190.101			1.25895			0.629474	−	0.777022i	$-0.283271\pi$
$151$	190.101			1.25895			0.629474	+	0.777022i	$0.283271\pi$
$152$	98.2962	−	138.132i	0.646686	−	0.908762i
$153$	−119.902	+	119.902i	−0.783672	+	0.783672i
$154$	−113.685	+	125.644i	−0.738213	+	0.815873i
$155$	−79.8093	+	85.1417i	−0.514898	+	0.549301i
$156$	455.944	−	50.9484i	2.92272	−	0.326592i
$157$	−60.5266	+	60.5266i	−0.385520	+	0.385520i	−0.873086	−	0.487566i	$-0.837885\pi$
$157$	−60.5266	+	60.5266i	−0.385520	+	0.385520i	0.487566	+	0.873086i	$0.337885\pi$
$158$	−71.3054	−	63.7813i	−0.451300	−	0.403679i
$159$	−83.7309			−0.526609
$160$	152.348	−	48.8884i	0.952175	−	0.305553i
$161$		−	83.2307i		−	0.516961i
$162$	230.252	−	257.414i	1.42131	−	1.58898i
$163$	40.7392	−	40.7392i	0.249934	−	0.249934i	−0.571010	−	0.820943i	$-0.693448\pi$
$163$	40.7392	−	40.7392i	0.249934	−	0.249934i	0.820943	+	0.571010i	$0.193448\pi$
$164$	53.5745	−	5.98657i	0.326674	−	0.0365035i
$165$	218.791	+	207.448i	1.32601	+	1.25726i
$166$	−31.2428	+	1.74016i	−0.188209	+	0.0104829i
$167$	100.104	−	100.104i	0.599423	−	0.599423i	−0.340736	−	0.940159i	$-0.610676\pi$
$167$	100.104	−	100.104i	0.599423	−	0.599423i	0.940159	+	0.340736i	$0.110676\pi$
$168$	195.836	−	275.201i	1.16569	−	1.63810i
$169$		−	268.758i		−	1.59028i
$170$	61.7412	+	51.7344i	0.363183	+	0.304320i
$171$	−446.112			−2.60884
$172$	−65.0772	+	81.4507i	−0.378356	+	0.473551i
$173$	139.979	−	139.979i	0.809126	−	0.809126i	−0.175376	−	0.984502i	$-0.556114\pi$
$173$	139.979	−	139.979i	0.809126	−	0.809126i	0.984502	+	0.175376i	$0.0561141\pi$
$174$	1.29052	+	23.1699i	0.00741679	+	0.133161i
$175$	144.662	+	127.074i	0.826637	+	0.726138i
$176$	−148.312	−	94.7597i	−0.842685	−	0.538408i
$177$	−325.641	+	325.641i	−1.83978	+	1.83978i
$178$	−134.802	−	120.578i	−0.757316	−	0.677405i
$179$	−106.678			−0.595964			−0.297982	−	0.954571i	$-0.596314\pi$
$179$	−106.678			−0.595964			−0.297982	+	0.954571i	$0.596314\pi$
$180$	−337.244	−	252.038i	−1.87358	−	1.40021i
$181$	12.7141			0.0702438			0.0351219	−	0.999383i	$-0.488818\pi$
$181$	12.7141			0.0702438			0.0351219	+	0.999383i	$0.488818\pi$
$182$	−240.214	−	214.867i	−1.31986	−	1.18059i
$183$	338.600	+	338.600i	1.85027	+	1.85027i
$184$	85.2502	−	14.3638i	0.463316	−	0.0780639i
$185$	50.3318	−	1.62709i	0.272064	−	0.00879506i
$186$	−255.495	+	14.2306i	−1.37363	+	0.0765086i
$187$	0.505983	−	88.6044i	0.00270579	−	0.473820i
$188$	90.7514	−	113.584i	0.482720	−	0.604172i
$189$	−508.802			−2.69208
$190$	18.6158	+	211.101i	0.0979777	+	1.11106i
$191$			4.38351i			0.0229503i	0.999934	+	0.0114751i	$0.00365273\pi$
$191$			4.38351i			0.0229503i	−0.999934	+	0.0114751i	$0.996347\pi$
$192$	315.675	+	153.094i	1.64414	+	0.797366i
$193$	−194.296	+	194.296i	−1.00672	+	1.00672i	−0.00673955	+	0.999977i	$0.502145\pi$
$193$	−194.296	+	194.296i	−1.00672	+	1.00672i	−0.999977	+	0.00673955i	$0.997855\pi$
$194$	−13.8755	−	249.119i	−0.0715231	−	1.28412i
$195$	−392.195	+	418.400i	−2.01126	+	2.14564i
$196$	−41.0235	+	4.58408i	−0.209304	+	0.0233882i
$197$	−119.247	−	119.247i	−0.605314	−	0.605314i	0.336404	−	0.941718i	$-0.390789\pi$
$197$	−119.247	−	119.247i	−0.605314	−	0.605314i	−0.941718	+	0.336404i	$0.890789\pi$
$198$	23.1140	+	462.543i	0.116737	+	2.33608i
$199$	351.199			1.76482			0.882410	−	0.470482i	$-0.155920\pi$
$199$	351.199			1.76482			0.882410	+	0.470482i	$0.155920\pi$
$200$	−105.192	+	170.102i	−0.525961	+	0.850509i
$201$	−433.803			−2.15823
$202$	−78.4252	−	70.1498i	−0.388243	−	0.347276i
$203$	11.5272	−	11.5272i	0.0567842	−	0.0567842i
$204$	19.6148	+	175.535i	0.0961509	+	0.860466i
$205$	−46.0840	+	49.1630i	−0.224800	+	0.239820i
$206$	8.38341	+	150.515i	0.0406962	+	0.730657i
$207$	−160.857	−	160.857i	−0.777088	−	0.777088i
$208$	178.625	−	283.124i	0.858773	−	1.36117i
$209$	165.774	−	163.891i	0.793177	−	0.784169i
$210$	37.0883	+	420.578i	0.176611	+	2.00275i
$211$	−253.350			−1.20071			−0.600355	−	0.799734i	$-0.704974\pi$
$211$	−253.350			−1.20071			−0.600355	+	0.799734i	$0.704974\pi$
$212$	−38.1369	+	47.7322i	−0.179891	+	0.225152i
$213$	−93.2384	−	93.2384i	−0.437739	−	0.437739i
$214$	−7.41114	−	133.059i	−0.0346315	−	0.621772i
$215$	−4.21067	−	130.252i	−0.0195845	−	0.605822i
$216$	−87.8079	−	521.148i	−0.406518	−	2.41272i
$217$	127.110	+	127.110i	0.585762	+	0.585762i
$218$	238.238	−	266.342i	1.09283	−	1.22175i
$219$		−	535.159i		−	2.44365i
$220$	217.912	−	30.2390i	0.990509	−	0.137450i
$221$	168.534			0.762595
$222$	82.3019	+	73.6175i	0.370729	+	0.331610i
$223$	−77.2143	+	77.2143i	−0.346252	+	0.346252i	−0.858712	−	0.512459i	$-0.828735\pi$
$223$	−77.2143	+	77.2143i	−0.346252	+	0.346252i	0.512459	+	0.858712i	$0.328735\pi$
$224$	−67.6853	−	236.985i	−0.302167	−	1.05797i
$225$	525.174	−	33.9904i	2.33411	−	0.151068i
$226$	64.0785	−	3.56905i	0.283533	−	0.0157922i
$227$	219.293	−	219.293i	0.966048	−	0.966048i	−0.0333944	−	0.999442i	$-0.510632\pi$
$227$	219.293	−	219.293i	0.966048	−	0.966048i	0.999442	+	0.0333944i	$0.0106317\pi$
$228$	−290.062	+	363.042i	−1.27220	+	1.59229i
$229$		−	257.724i		−	1.12543i	−0.826650	−	0.562717i	$-0.809756\pi$
$229$		−	257.724i		−	1.12543i	0.826650	−	0.562717i	$-0.190244\pi$
$230$	−69.4055	+	82.8303i	−0.301763	+	0.360132i
$231$	330.272	−	326.522i	1.42975	−	1.41351i
$232$	13.7962	+	9.81754i	0.0594664	+	0.0423170i
$233$	153.796	−	153.796i	0.660067	−	0.660067i	−0.295328	−	0.955396i	$-0.595429\pi$
$233$	153.796	−	153.796i	0.660067	−	0.660067i	0.955396	+	0.295328i	$0.0954291\pi$
$234$	−879.520	+	48.9876i	−3.75863	+	0.209349i
$235$	5.87186	+	181.638i	0.0249866	+	0.772929i
$236$	37.3172	+	333.957i	0.158124	+	1.41507i
$237$	185.419	+	185.419i	0.782359	+	0.782359i
$238$	82.7222	−	92.4807i	0.347572	−	0.388574i
$239$		−	38.8269i		−	0.162456i	−0.996696	−	0.0812279i	$-0.974116\pi$
$239$		−	38.8269i		−	0.162456i	0.996696	−	0.0812279i	$-0.0258842\pi$
$240$	−424.382	+	110.571i	−1.76826	+	0.460711i
$241$			0.772619i			0.00320589i	0.999999	+	0.00160294i	$0.000510233\pi$
$241$			0.772619i			0.00320589i	−0.999999	+	0.00160294i	$0.999490\pi$
$242$	−178.517	−	163.388i	−0.737673	−	0.675158i
$243$	−248.953	+	248.953i	−1.02450	+	1.02450i
$244$	347.246	−	38.8023i	1.42314	−	0.159026i
$245$	35.2878	−	37.6455i	0.144032	−	0.153655i
$246$	−147.530	+	8.21712i	−0.599714	+	0.0334029i
$247$	313.527	+	313.527i	1.26934	+	1.26934i
$248$	−108.258	+	152.131i	−0.436525	+	0.613431i
$249$	85.7672			0.344446
$250$	−37.9993	−	247.095i	−0.151997	−	0.988381i
$251$			14.8441i			0.0591399i	0.999563	+	0.0295699i	$0.00941378\pi$
$251$			14.8441i			0.0591399i	−0.999563	+	0.0295699i	$0.990586\pi$
$252$	−404.818	+	506.670i	−1.60642	+	2.01060i
$253$	118.869	+	0.678814i	0.469839	+	0.00268306i
$254$	0.0295048	+	0.529727i	0.000116161	+	0.00208554i
$255$	−161.081	−	150.992i	−0.631690	−	0.592127i
$256$	231.055	−	110.226i	0.902557	−	0.430570i
$257$	−64.3743	+	64.3743i	−0.250484	+	0.250484i	−0.821169	−	0.570685i	$-0.806678\pi$
$257$	−64.3743	+	64.3743i	−0.250484	+	0.250484i	0.570685	+	0.821169i	$0.306678\pi$
$258$	190.512	−	212.986i	0.738418	−	0.825527i
$259$		−	77.5708i		−	0.299501i
$260$	59.8824	+	414.146i	0.230317	+	1.59287i
$261$		−	44.5564i		−	0.170714i
$262$	−141.953	+	158.699i	−0.541805	+	0.605720i
$263$	−67.4719	−	67.4719i	−0.256547	−	0.256547i	0.567101	−	0.823648i	$-0.308065\pi$
$263$	−67.4719	−	67.4719i	−0.256547	−	0.256547i	−0.823648	+	0.567101i	$0.808065\pi$
$264$	391.442	+	281.936i	1.48273	+	1.06794i
$265$	−2.46756	−	76.3308i	−0.00931156	−	0.288041i
$266$	325.934	−	18.1539i	1.22532	−	0.0682477i
$267$	350.533	+	350.533i	1.31286	+	1.31286i
$268$	−197.585	+	247.297i	−0.737256	+	0.922750i
$269$			261.542i			0.972275i	0.873882	+	0.486137i	$0.161595\pi$
$269$			261.542i			0.972275i	−0.873882	+	0.486137i	$0.838405\pi$
$270$	506.355	+	424.287i	1.87539	+	1.57143i
$271$	−383.025			−1.41338			−0.706689	−	0.707525i	$-0.749812\pi$
$271$	−383.025			−1.41338			−0.706689	+	0.707525i	$0.749812\pi$
$272$	109.001	+	68.7693i	0.400738	+	0.252828i
$273$	624.641	+	624.641i	2.28806	+	2.28806i
$274$	9.96325	+	178.880i	0.0363622	+	0.652845i
$275$	−182.666	+	205.568i	−0.664240	+	0.747519i
$276$	−235.493	+	26.3147i	−0.853236	+	0.0953430i
$277$	−105.551	−	105.551i	−0.381051	−	0.381051i	0.490430	−	0.871481i	$-0.336840\pi$
$277$	−105.551	−	105.551i	−0.381051	−	0.381051i	−0.871481	+	0.490430i	$0.836840\pi$
$278$	−334.063	−	298.813i	−1.20167	−	1.07487i
$279$	491.324			1.76102
$280$	256.650	+	170.418i	0.916607	+	0.608636i
$281$		−	198.947i		−	0.707998i	−0.935246	−	0.353999i	$-0.884822\pi$
$281$		−	198.947i		−	0.707998i	0.935246	−	0.353999i	$-0.115178\pi$
$282$	−265.672	+	297.013i	−0.942100	+	1.05324i
$283$	−169.428	−	169.428i	−0.598687	−	0.598687i	0.341276	−	0.939963i	$-0.389141\pi$
$283$	−169.428	−	169.428i	−0.598687	−	0.598687i	−0.939963	+	0.341276i	$0.889141\pi$
$284$	−95.6195	+	10.6848i	−0.336688	+	0.0376225i
$285$	−18.7678	−	580.557i	−0.0658519	−	2.03704i
$286$	308.830	−	341.319i	1.07983	−	1.19342i
$287$	73.3969	+	73.3969i	0.255738	+	0.255738i
$288$	−588.827	−	327.200i	−2.04454	−	1.13611i
$289$		−	224.116i		−	0.775487i
$290$	−21.0842	+	1.85929i	−0.0727041	+	0.00641134i
$291$			683.879i			2.35010i
$292$	−305.077	−	243.749i	−1.04478	−	0.834758i
$293$	118.377	−	118.377i	0.404016	−	0.404016i	−0.475629	−	0.879646i	$-0.657780\pi$
$293$	118.377	−	118.377i	0.404016	−	0.404016i	0.879646	+	0.475629i	$0.157780\pi$
$294$	112.968	−	6.29208i	0.384244	−	0.0214016i
$295$	−306.457	−	287.264i	−1.03884	−	0.973777i
$296$	79.4530	−	13.3870i	0.268422	−	0.0452263i
$297$	4.14969	−	726.666i	0.0139720	−	2.44669i
$298$	−214.185	+	239.451i	−0.718740	+	0.803528i
$299$			226.100i			0.756188i
$300$	313.807	−	449.482i	1.04602	−	1.49827i
$301$	−200.743			−0.666919
$302$	−253.477	+	283.378i	−0.839326	+	0.938339i
$303$	203.933	+	203.933i	0.673046	+	0.673046i
$304$	74.8433	+	330.709i	0.246195	+	1.08786i
$305$	−298.696	+	318.653i	−0.979331	+	1.04476i
$306$	−18.8599	−	338.609i	−0.0616335	−	1.10656i
$307$	195.242	−	195.242i	0.635966	−	0.635966i	−0.313592	−	0.949558i	$-0.601532\pi$
$307$	195.242	−	195.242i	0.635966	−	0.635966i	0.949558	+	0.313592i	$0.101532\pi$
$308$	−35.7099	−	336.998i	−0.115941	−	1.09415i
$309$		−	413.192i		−	1.33719i
$310$	−20.5024	−	232.495i	−0.0661368	−	0.749985i
$311$		−	522.926i		−	1.68144i	−0.541474	−	0.840718i	$-0.682133\pi$
$311$		−	522.926i		−	1.68144i	0.541474	−	0.840718i	$-0.317867\pi$
$312$	−531.998	+	747.596i	−1.70512	+	2.39614i
$313$	−242.759	−	242.759i	−0.775587	−	0.775587i	0.203490	−	0.979077i	$-0.434772\pi$
$313$	−242.759	−	242.759i	−0.775587	−	0.775587i	−0.979077	+	0.203490i	$0.934772\pi$
$314$	−9.52047	−	170.930i	−0.0303200	−	0.544363i
$315$	−26.1928	−	810.241i	−0.0831518	−	2.57219i
$316$	190.154	−	21.2484i	0.601753	−	0.0672416i
$317$	−33.9249	+	33.9249i	−0.107019	+	0.107019i	−0.758589	−	0.651570i	$-0.774111\pi$
$317$	−33.9249	+	33.9249i	−0.107019	+	0.107019i	0.651570	+	0.758589i	$0.274111\pi$
$318$	111.645	−	124.815i	0.351085	−	0.392501i
$319$	16.3690	+	16.5570i	0.0513135	+	0.0519029i
$320$	−130.261	+	292.288i	−0.407065	+	0.913399i
$321$			365.272i			1.13792i
$322$	124.070	+	110.978i	0.385310	+	0.344652i
$323$	−120.706	+	120.706i	−0.373701	+	0.373701i
$324$	76.7070	+	686.461i	0.236750	+	2.11871i
$325$	−392.980	−	345.203i	−1.20917	−	1.06216i
$326$	6.40803	+	115.049i	0.0196565	+	0.352912i
$327$	−692.583	+	692.583i	−2.11799	+	2.11799i
$328$	−62.5111	+	87.8444i	−0.190583	+	0.267818i
$329$	279.939			0.850879
$330$	−600.968	+	49.5389i	−1.82111	+	0.150118i
$331$		−	423.596i		−	1.27975i	−0.768480	−	0.639873i	$-0.778987\pi$
$331$		−	423.596i		−	1.27975i	0.768480	−	0.639873i	$-0.221013\pi$
$332$	39.0644	−	48.8930i	0.117664	−	0.147268i
$333$	−149.918	−	149.918i	−0.450206	−	0.450206i
$334$	15.7457	+	282.698i	0.0471429	+	0.846400i
$335$	−12.7843	−	395.464i	−0.0381620	−	1.18049i
$336$	149.111	+	658.874i	0.443782	+	1.96093i
$337$	−295.524	−	295.524i	−0.876926	−	0.876926i	0.116290	−	0.993215i	$-0.462900\pi$
$337$	−295.524	−	295.524i	−0.876926	−	0.876926i	−0.993215	+	0.116290i	$0.962900\pi$
$338$	400.630	+	358.356i	1.18529	+	1.06022i
$339$	−175.907			−0.518900
$340$	−159.443	+	23.0543i	−0.468951	+	0.0678067i
$341$	−182.575	+	180.501i	−0.535409	+	0.529329i
$342$	594.836	−	665.007i	1.73929	−	1.94446i
$343$	210.656	+	210.656i	0.614158	+	0.614158i
$344$	−34.6437	−	205.613i	−0.100708	−	0.597713i
$345$	202.567	−	216.102i	0.587152	−	0.626382i
$346$	22.0178	+	395.307i	0.0636354	+	1.14251i
$347$	−235.404	+	235.404i	−0.678398	+	0.678398i	−0.959638	−	0.281239i	$-0.909255\pi$
$347$	−235.404	+	235.404i	−0.678398	+	0.678398i	0.281239	+	0.959638i	$0.409255\pi$
$348$	−36.2595	−	28.9706i	−0.104194	−	0.0832487i
$349$	−487.495			−1.39683			−0.698416	−	0.715692i	$-0.746112\pi$
$349$	−487.495			−1.39683			−0.698416	+	0.715692i	$0.746112\pi$
$350$	−382.315	+	46.2049i	−1.09233	+	0.132014i
$351$	1382.19			3.93785
$352$	339.012	−	94.7347i	0.963103	−	0.269133i
$353$	292.174	+	292.174i	0.827689	+	0.827689i	0.987197	−	0.159508i	$-0.0509907\pi$
$353$	292.174	+	292.174i	0.827689	+	0.827689i	−0.159508	+	0.987197i	$0.550991\pi$
$354$	−51.2214	−	919.625i	−0.144693	−	2.59781i
$355$	82.2503	−	87.7458i	0.231691	−	0.247171i
$356$	359.485	−	40.1698i	1.00979	−	0.112837i
$357$	−240.482	+	240.482i	−0.673620	+	0.673620i
$358$	142.242	−	159.021i	0.397323	−	0.444194i
$359$		−	183.518i		−	0.511193i	−0.966784	−	0.255596i	$-0.917728\pi$
$359$		−	183.518i		−	0.511193i	0.966784	−	0.255596i	$-0.0822718\pi$
$360$	825.380	−	166.658i	2.29272	−	0.462938i
$361$	−88.1024			−0.244051
$362$	−16.9527	+	18.9526i	−0.0468308	+	0.0523553i
$363$	463.641	+	474.355i	1.27725	+	1.30676i
$364$	640.592	−	71.5816i	1.75987	−	0.196653i
$365$	487.862	−	15.7712i	1.33661	−	0.0432089i
$366$	−956.222	+	53.2597i	−2.61263	+	0.145518i
$367$	−309.683	−	309.683i	−0.843822	−	0.843822i	0.145532	−	0.989354i	$-0.453511\pi$
$367$	−309.683	−	309.683i	−0.843822	−	0.843822i	−0.989354	+	0.145532i	$0.953511\pi$
$368$	−92.2591	+	146.232i	−0.250704	+	0.397371i
$369$	283.703			0.768843
$370$	−64.6858	+	77.1977i	−0.174827	+	0.208642i
$371$	−117.640			−0.317090
$372$	319.459	−	399.834i	0.858760	−	1.07482i
$373$	−195.281	+	195.281i	−0.523542	+	0.523542i	−0.918639	−	0.395097i	$-0.870711\pi$
$373$	−195.281	+	195.281i	−0.523542	+	0.523542i	0.395097	+	0.918639i	$0.370711\pi$
$374$	131.405	+	118.897i	0.351351	+	0.317907i
$375$	66.3280	+	682.016i	0.176875	+	1.81871i
$376$	48.3112	+	286.731i	0.128487	+	0.762584i
$377$	−31.3142	+	31.3142i	−0.0830614	+	0.0830614i
$378$	678.426	−	758.457i	1.79478	−	2.00650i
$379$	−683.030			−1.80219			−0.901095	−	0.433621i	$-0.857236\pi$
$379$	−683.030			−1.80219			−0.901095	+	0.433621i	$0.857236\pi$
$380$	−339.504	−	253.728i	−0.893433	−	0.667704i
$381$		−	1.45420i		−	0.00381680i
$382$	−6.53437	−	5.84487i	−0.0171057	−	0.0153007i
$383$	283.380	−	283.380i	0.739895	−	0.739895i	−0.232663	−	0.972557i	$-0.574744\pi$
$383$	283.380	−	283.380i	0.739895	−	0.739895i	0.972557	+	0.232663i	$0.0747438\pi$
$384$	−649.127	+	266.436i	−1.69044	+	0.693843i
$385$	307.397	+	291.460i	0.798434	+	0.757040i
$386$	−30.5617	−	548.703i	−0.0791753	−	1.42151i
$387$	−387.968	+	387.968i	−1.00250	+	1.00250i
$388$	389.857	+	311.487i	1.00479	+	0.802801i
$389$			699.754i			1.79885i	0.437072	+	0.899427i	$0.356016\pi$
$389$			699.754i			1.79885i	−0.437072	+	0.899427i	$0.643984\pi$
$390$	−100.752	−	1142.52i	−0.258339	−	2.92954i
$391$	−87.0469			−0.222626
$392$	47.8665	−	67.2650i	0.122108	−	0.171594i
$393$	412.672	−	412.672i	1.05006	−	1.05006i
$394$	336.759	−	18.7568i	0.854718	−	0.0476062i
$395$	−163.568	+	174.496i	−0.414095	+	0.441762i
$396$	−720.320	−	582.290i	−1.81899	−	1.47043i
$397$	482.013	−	482.013i	1.21414	−	1.21414i	0.244487	−	0.969653i	$-0.421380\pi$
$397$	482.013	−	482.013i	1.21414	−	1.21414i	0.969653	−	0.244487i	$-0.0786195\pi$
$398$	−468.281	+	523.523i	−1.17659	+	1.31538i
$399$	−894.749			−2.24248
$400$	−113.305	−	383.617i	−0.283263	−	0.959042i
$401$	615.908			1.53593			0.767965	−	0.640492i	$-0.221270\pi$
$401$	615.908			1.53593			0.767965	+	0.640492i	$0.221270\pi$
$402$	578.424	−	646.659i	1.43887	−	1.60860i
$403$	−345.301	−	345.301i	−0.856828	−	0.856828i
$404$	209.141	−	23.3700i	0.517675	−	0.0578465i
$405$	−629.935	−	590.482i	−1.55540	−	1.45798i
$406$	1.81316	+	32.5533i	0.00446591	+	0.0801807i
$407$	110.786	+	0.632653i	0.272201	+	0.00155443i
$408$	−287.819	−	204.815i	−0.705439	−	0.501998i
$409$	330.071			0.807019			0.403509	−	0.914976i	$-0.367790\pi$
$409$	330.071			0.807019			0.403509	+	0.914976i	$0.367790\pi$
$410$	−11.8386	−	134.249i	−0.0288747	−	0.327436i
$411$		−	491.058i		−	1.19479i
$412$	−235.547	−	188.197i	−0.571717	−	0.456789i
$413$	−457.519	+	457.519i	−1.10779	+	1.10779i
$414$	454.269	−	25.3019i	1.09727	−	0.0611157i
$415$	2.52757	+	78.1871i	0.00609054	+	0.188403i
$416$	183.870	+	643.782i	0.441996	+	1.54755i
$417$	868.682	+	868.682i	2.08317	+	2.08317i
$418$	23.2690	+	465.644i	0.0556674	+	1.11398i
$419$	429.690			1.02551			0.512757	−	0.858534i	$-0.328624\pi$
$419$	429.690			1.02551			0.512757	+	0.858534i	$0.328624\pi$
$420$	−676.396	−	505.503i	−1.61047	−	1.20358i
$421$	261.974			0.622267			0.311134	−	0.950366i	$-0.399291\pi$
$421$	261.974			0.622267			0.311134	+	0.950366i	$0.399291\pi$
$422$	337.811	−	377.661i	0.800500	−	0.894932i
$423$	541.029	−	541.029i	1.27903	−	1.27903i
$424$	−20.3021	−	120.495i	−0.0478823	−	0.284186i
$425$	132.901	−	151.294i	0.312708	−	0.355987i
$426$	263.310	−	14.6659i	0.618098	−	0.0344269i
$427$	475.726	+	475.726i	1.11411	+	1.11411i
$428$	208.230	+	166.371i	0.486518	+	0.388717i
$429$	−897.201	+	887.012i	−2.09138	+	2.06763i
$430$	199.777	+	167.398i	0.464597	+	0.389298i
$431$	−425.806			−0.987949			−0.493974	−	0.869476i	$-0.664456\pi$
$431$	−425.806			−0.987949			−0.493974	+	0.869476i	$0.664456\pi$
$432$	893.941	+	563.994i	2.06931	+	1.30554i
$433$	−441.920	−	441.920i	−1.02060	−	1.02060i	−0.999783	−	0.0208168i	$-0.993373\pi$
$433$	−441.920	−	441.920i	−1.02060	−	1.02060i	−0.0208168	−	0.999783i	$-0.506627\pi$
$434$	−358.966	+	19.9937i	−0.827111	+	0.0460685i
$435$	57.9844	−	1.87447i	0.133297	−	0.00430913i
$436$	79.3675	+	710.270i	0.182036	+	1.62906i
$437$	−161.935	−	161.935i	−0.370561	−	0.370561i
$438$	797.747	+	713.570i	1.82134	+	1.62915i
$439$		−	39.1211i		−	0.0891140i	−0.999007	−	0.0445570i	$-0.985812\pi$
$439$		−	39.1211i		−	0.0891140i	0.999007	−	0.0445570i	$-0.0141876\pi$
$440$	−245.482	+	365.155i	−0.557915	+	0.829898i
$441$	−217.240			−0.492607
$442$	−224.719	+	251.228i	−0.508414	+	0.568390i
$443$	441.330	−	441.330i	0.996231	−	0.996231i	−0.00376227	−	0.999993i	$-0.501198\pi$
$443$	441.330	−	441.330i	0.996231	−	0.996231i	0.999993	+	0.00376227i	$0.00119757\pi$
$444$	−219.479	+	24.5252i	−0.494322	+	0.0552370i
$445$	−309.223	+	329.884i	−0.694883	+	0.741312i
$446$	−12.1454	−	218.057i	−0.0272317	−	0.488917i
$447$	622.657	−	622.657i	1.39297	−	1.39297i
$448$	443.518	+	215.095i	0.989995	+	0.480122i
$449$		−	553.397i		−	1.23251i	−0.787547	−	0.616254i	$-0.788649\pi$
$449$		−	553.397i		−	1.23251i	0.787547	−	0.616254i	$-0.211351\pi$
$450$	−649.587	+	828.185i	−1.44353	+	1.84041i
$451$	−105.423	+	104.226i	−0.233755	+	0.231100i
$452$	−80.1205	+	100.279i	−0.177258	+	0.221856i
$453$	736.883	−	736.883i	1.62667	−	1.62667i
$454$	34.4935	+	619.294i	0.0759768	+	1.36408i
$455$	−551.027	+	587.844i	−1.21105	+	1.29196i
$456$	−154.414	−	916.459i	−0.338627	−	2.00978i
$457$	154.432	+	154.432i	0.337925	+	0.337925i	0.855586	−	0.517661i	$-0.173197\pi$
$457$	154.432	+	154.432i	0.337925	+	0.337925i	−0.517661	+	0.855586i	$0.673197\pi$
$458$	384.182	+	343.644i	0.838826	+	0.750314i
$459$			532.132i			1.15933i
$460$	−30.9290	−	213.905i	−0.0672370	−	0.465011i
$461$			471.965i			1.02379i	0.859049	+	0.511893i	$0.171056\pi$
$461$			471.965i			1.02379i	−0.859049	+	0.511893i	$0.828944\pi$
$462$	46.3589	+	927.704i	0.100344	+	2.00802i
$463$	100.365	−	100.365i	0.216771	−	0.216771i	−0.590365	−	0.807136i	$-0.701016\pi$
$463$	100.365	−	100.365i	0.216771	−	0.216771i	0.807136	+	0.590365i	$0.201016\pi$
$464$	−33.0303	+	7.47513i	−0.0711860	+	0.0161102i
$465$	20.6698	+	639.394i	0.0444513	+	1.37504i
$466$	24.1912	+	434.327i	0.0519124	+	0.932032i
$467$	239.686	+	239.686i	0.513247	+	0.513247i	0.915520	−	0.402273i	$-0.131780\pi$
$467$	239.686	+	239.686i	0.513247	+	0.513247i	−0.402273	+	0.915520i	$0.631780\pi$
$468$	1099.71	−	1376.39i	2.34980	−	2.94101i
$469$	−609.486			−1.29954
$470$	−278.592	−	233.439i	−0.592750	−	0.496680i
$471$			469.235i			0.996252i
$472$	−547.578	−	389.663i	−1.16012	−	0.825556i
$473$	1.63722	−	286.699i	0.00346135	−	0.606128i
$474$	−523.633	+	29.1653i	−1.10471	+	0.0615302i
$475$	528.695	−	34.2182i	1.11304	−	0.0720384i
$476$	27.5584	+	246.623i	0.0578958	+	0.518117i
$477$	−227.359	+	227.359i	−0.476645	+	0.476645i
$478$	57.8782	+	51.7710i	0.121084	+	0.108307i
$479$			400.843i			0.836833i	0.908255	+	0.418417i	$0.137415\pi$
$479$			400.843i			0.836833i	−0.908255	+	0.418417i	$0.862585\pi$
$480$	401.037	−	780.047i	0.835494	−	1.62510i
$481$			210.725i			0.438098i
$482$	−1.15172	−	1.03019i	−0.00238946	−	0.00213733i
$483$	−322.625	−	322.625i	−0.667960	−	0.667960i
$484$	481.589	−	48.2520i	0.995018	−	0.0996942i
$485$	−623.438	+	20.1540i	−1.28544	+	0.0415547i
$486$	−39.1588	−	703.056i	−0.0805738	−	1.44662i
$487$	−24.4248	−	24.4248i	−0.0501536	−	0.0501536i	0.681585	−	0.731739i	$-0.261291\pi$
$487$	−24.4248	−	24.4248i	−0.0501536	−	0.0501536i	−0.731739	+	0.681585i	$0.761291\pi$
$488$	−405.169	+	569.369i	−0.830265	+	1.16674i
$489$		−	315.832i		−	0.645873i
$490$	9.06517	+	102.798i	0.0185003	+	0.209792i
$491$	311.219			0.633846			0.316923	−	0.948451i	$-0.397350\pi$
$491$	311.219			0.633846			0.316923	+	0.948451i	$0.397350\pi$
$492$	184.464	−	230.875i	0.374926	−	0.469258i
$493$	−12.0557	−	12.0557i	−0.0244538	−	0.0244538i
$494$	−885.415	+	49.3159i	−1.79234	+	0.0998298i
$495$	1157.39	−	30.8002i	2.33816	−	0.0622226i
$496$	−82.4284	−	364.226i	−0.166186	−	0.734326i
$497$	−130.998	−	130.998i	−0.263578	−	0.263578i
$498$	−114.360	+	127.851i	−0.229639	+	0.256728i
$499$	108.280			0.216994			0.108497	−	0.994097i	$-0.465396\pi$
$499$	108.280			0.216994			0.108497	+	0.994097i	$0.465396\pi$
$500$	419.005	+	272.827i	0.838011	+	0.545654i
$501$		−	776.057i		−	1.54902i
$502$	−22.1277	−	19.7928i	−0.0440791	−	0.0394279i
$503$	22.0758	+	22.0758i	0.0438882	+	0.0438882i	0.728710	−	0.684822i	$-0.240120\pi$
$503$	22.0758	+	22.0758i	0.0438882	+	0.0438882i	−0.684822	+	0.728710i	$0.740120\pi$
$504$	−215.504	−	1279.03i	−0.427587	−	2.53777i
$505$	−179.900	+	191.919i	−0.356237	+	0.380038i
$506$	−159.510	+	176.290i	−0.315236	+	0.348399i
$507$	−1041.78	−	1041.78i	−2.05479	−	2.05479i
$508$	−0.828991	−	0.662345i	−0.00163187	−	0.00130383i
$509$			417.953i			0.821125i	0.911832	+	0.410562i	$0.134668\pi$
$509$			417.953i			0.821125i	−0.911832	+	0.410562i	$0.865332\pi$
$510$	439.862	−	38.7888i	0.862474	−	0.0760565i
$511$		−	751.889i		−	1.47141i
$512$	−143.772	+	491.400i	−0.280805	+	0.959765i
$513$	−989.936	+	989.936i	−1.92970	+	1.92970i
$514$	−10.1257	−	181.796i	−0.0196998	−	0.353689i
$515$	376.675	−	12.1768i	0.731407	−	0.0236444i
$516$	63.4679	+	567.982i	0.123000	+	1.10074i
$517$	−2.28313	+	399.806i	−0.00441611	+	0.773320i
$518$	115.633	+	103.431i	0.223229	+	0.199674i
$519$		−	1085.19i		−	2.09093i
$520$	−697.202	−	462.949i	−1.34077	−	0.890286i
$521$	253.019			0.485640			0.242820	−	0.970071i	$-0.421927\pi$
$521$	253.019			0.485640			0.242820	+	0.970071i	$0.421927\pi$
$522$	66.4190	+	59.4105i	0.127239	+	0.113813i
$523$	−605.834	−	605.834i	−1.15838	−	1.15838i	−0.984823	−	0.173559i	$-0.944473\pi$
$523$	−605.834	−	605.834i	−1.15838	−	1.15838i	−0.173559	−	0.984823i	$-0.555527\pi$
$524$	−47.2907	−	423.211i	−0.0902495	−	0.807654i
$525$	1053.32	−	68.1731i	2.00633	−	0.129854i
$526$	190.544	−	10.6129i	0.362251	−	0.0201767i
$527$	132.939	−	132.939i	0.252255	−	0.252255i
$528$	−942.213	+	207.585i	−1.78450	+	0.393153i
$529$			412.220i			0.779244i
$530$	117.074	+	98.0995i	0.220895	+	0.185093i
$531$			1768.46i			3.33044i
$532$	−407.532	+	510.067i	−0.766037	+	0.958772i
$533$	−199.386	−	199.386i	−0.374083	−	0.374083i
$534$	−989.923	+	55.1368i	−1.85379	+	0.103252i
$535$	−332.990	+	10.7646i	−0.622411	+	0.0201208i
$536$	−105.184	−	624.274i	−0.196238	−	1.16469i
$537$	−413.511	+	413.511i	−0.770040	+	0.770040i
$538$	−389.873	−	348.734i	−0.724671	−	0.648205i
$539$	80.7256	−	79.8089i	0.149769	−	0.148068i
$540$	−1307.63	+	189.074i	−2.42155	+	0.350137i
$541$			391.623i			0.723887i	0.932200	+	0.361944i	$0.117887\pi$
$541$			391.623i			0.723887i	−0.932200	+	0.361944i	$0.882113\pi$
$542$	510.718	−	570.965i	0.942283	−	1.05344i
$543$	49.2834	−	49.2834i	0.0907613	−	0.0907613i
$544$	−247.852	+	70.7888i	−0.455609	+	0.130126i
$545$	−651.784	−	610.962i	−1.19593	−	1.12103i
$546$	−1764.02	+	98.2524i	−3.23080	+	0.179949i
$547$	−166.752	+	166.752i	−0.304847	+	0.304847i	−0.842907	−	0.538059i	$-0.819158\pi$
$547$	−166.752	+	166.752i	−0.304847	+	0.304847i	0.538059	+	0.842907i	$0.319158\pi$
$548$	−279.936	−	223.662i	−0.510832	−	0.408143i
$549$	1838.84			3.34943
$550$	−62.8714	−	546.395i	−0.114312	−	0.993445i
$551$		−	44.8551i		−	0.0814066i
$552$	274.775	−	386.131i	0.497781	−	0.699512i
$553$	260.510	+	260.510i	0.471085	+	0.471085i
$554$	298.082	−	16.6026i	0.538053	−	0.0299685i
$555$	188.792	−	201.406i	0.340167	−	0.362895i
$556$	890.866	−	99.5478i	1.60228	−	0.179043i
$557$	−355.499	−	355.499i	−0.638238	−	0.638238i	0.311883	−	0.950121i	$-0.399040\pi$
$557$	−355.499	−	355.499i	−0.638238	−	0.638238i	−0.950121	+	0.311883i	$0.899040\pi$
$558$	−655.120	+	732.403i	−1.17405	+	1.31255i
$559$	545.327			0.975540
$560$	−596.249	+	155.350i	−1.06473	+	0.277410i
$561$	−341.493	−	345.416i	−0.608722	−	0.615714i
$562$	296.565	+	265.272i	0.527696	+	0.472014i
$563$	−608.314	−	608.314i	−1.08049	−	1.08049i	−0.996464	−	0.0840234i	$-0.973223\pi$
$563$	−608.314	−	608.314i	−1.08049	−	1.08049i	−0.0840234	−	0.996464i	$-0.526777\pi$
$564$	−88.5071	−	792.060i	−0.156927	−	1.40436i
$565$	−5.18401	−	160.361i	−0.00917525	−	0.283824i
$566$	478.474	−	26.6501i	0.845361	−	0.0470850i
$567$	−940.448	+	940.448i	−1.65864	+	1.65864i
$568$	111.569	−	156.784i	0.196425	−	0.276028i
$569$	937.364			1.64739			0.823694	−	0.567035i	$-0.191909\pi$
$569$	937.364			1.64739			0.823694	+	0.567035i	$0.191909\pi$
$570$	890.445	+	746.125i	1.56218	+	1.30899i
$571$	703.275			1.23166			0.615828	−	0.787881i	$-0.288822\pi$
$571$	703.275			1.23166			0.615828	+	0.787881i	$0.288822\pi$
$572$	97.0076	+	915.472i	0.169594	+	1.60048i
$573$	16.9917	+	16.9917i	0.0296538	+	0.0296538i
$574$	−207.276	+	11.5449i	−0.361109	+	0.0201131i
$575$	202.973	+	178.296i	0.352996	+	0.310080i
$576$	1272.88	−	441.466i	2.20986	−	0.766433i
$577$	−123.821	+	123.821i	−0.214594	+	0.214594i	−0.806216	−	0.591621i	$-0.798488\pi$
$577$	−123.821	+	123.821i	−0.214594	+	0.214594i	0.591621	+	0.806216i	$0.298488\pi$
$578$	334.083	+	298.831i	0.577999	+	0.517009i
$579$			1506.29i			2.60154i
$580$	25.3416	−	33.9087i	0.0436924	−	0.0584633i
$581$	120.501			0.207403
$582$	−1019.44	−	911.869i	−1.75161	−	1.56679i
$583$	0.959452	−	168.013i	0.00164572	−	0.288187i
$584$	770.133	−	129.759i	1.31872	−	0.222191i
$585$	71.1541	+	2201.06i	0.121631	+	3.76249i
$586$	18.6200	+	334.302i	0.0317747	+	0.570481i
$587$	37.1908	+	37.1908i	0.0633573	+	0.0633573i	0.738075	−	0.674718i	$-0.235735\pi$
$587$	37.1908	+	37.1908i	0.0633573	+	0.0633573i	−0.674718	+	0.738075i	$0.735735\pi$
$588$	−141.249	+	176.787i	−0.240220	+	0.300659i
$589$	494.617			0.839758
$590$	836.840	−	73.7960i	1.41837	−	0.125078i
$591$	−924.465			−1.56424
$592$	−85.9852	+	136.288i	−0.145245	+	0.230217i
$593$	113.671	−	113.671i	0.191688	−	0.191688i	−0.604737	−	0.796425i	$-0.706722\pi$
$593$	113.671	−	113.671i	0.191688	−	0.191688i	0.796425	+	0.604737i	$0.206722\pi$
$594$	1077.69	+	975.107i	1.81429	+	1.64159i
$595$	−226.316	−	212.142i	−0.380362	−	0.356540i
$596$	−71.3543	−	638.558i	−0.119722	−	1.07141i
$597$	1361.34	−	1361.34i	2.28031	−	2.28031i
$598$	−337.041	−	301.477i	−0.563614	−	0.504142i
$599$	−811.770			−1.35521			−0.677605	−	0.735426i	$-0.736982\pi$
$599$	−811.770			−1.35521			−0.677605	+	0.735426i	$0.736982\pi$
$600$	251.607	+	1067.11i	0.419345	+	1.77852i
$601$		−	210.411i		−	0.350102i	−0.984559	−	0.175051i	$-0.943991\pi$
$601$		−	210.411i		−	0.350102i	0.984559	−	0.175051i	$-0.0560091\pi$
$602$	267.666	−	299.241i	0.444628	−	0.497079i
$603$	−1177.93	+	1177.93i	−1.95345	+	1.95345i
$604$	−84.4441	−	755.701i	−0.139808	−	1.25116i
$605$	−418.768	+	436.644i	−0.692179	+	0.721726i
$606$	−575.917	+	32.0774i	−0.950358	+	0.0529331i
$607$	14.5520	−	14.5520i	0.0239736	−	0.0239736i	−0.695018	−	0.718992i	$-0.744604\pi$
$607$	14.5520	−	14.5520i	0.0239736	−	0.0239736i	0.718992	+	0.695018i	$0.244604\pi$
$608$	−592.774	−	329.394i	−0.974957	−	0.541766i
$609$		−	89.3649i		−	0.146740i
$610$	−76.7327	−	870.142i	−0.125791	−	1.42646i
$611$	−760.468			−1.24463
$612$	529.902	+	423.380i	0.865853	+	0.691797i
$613$	−511.327	+	511.327i	−0.834139	+	0.834139i	−0.988080	−	0.153941i	$-0.950803\pi$
$613$	−511.327	+	511.327i	−0.834139	+	0.834139i	0.153941	+	0.988080i	$0.450803\pi$
$614$	30.7104	+	551.372i	0.0500169	+	0.898000i
$615$	11.9353	+	369.203i	0.0194070	+	0.600330i
$616$	549.969	+	396.114i	0.892806	+	0.643043i
$617$	−307.862	+	307.862i	−0.498965	+	0.498965i	−0.911116	−	0.412151i	$-0.864778\pi$
$617$	−307.862	+	307.862i	−0.498965	+	0.498965i	0.412151	+	0.911116i	$0.364778\pi$
$618$	615.934	+	550.942i	0.996657	+	0.891491i
$619$	149.498			0.241515			0.120758	−	0.992682i	$-0.461468\pi$
$619$	149.498			0.241515			0.120758	+	0.992682i	$0.461468\pi$
$620$	373.912	+	279.442i	0.603084	+	0.450713i
$621$	−713.894			−1.14959
$622$	779.512	+	697.259i	1.25323	+	1.12099i
$623$	492.493	+	492.493i	0.790518	+	0.790518i
$624$	−405.066	−	1789.86i	−0.649145	−	2.86837i
$625$	−619.786	+	80.5651i	−0.991657	+	0.128904i
$626$	685.563	−	38.1845i	1.09515	−	0.0609976i
$627$	7.29740	−	1277.87i	0.0116386	−	2.03807i
$628$	267.495	+	213.722i	0.425948	+	0.340322i
$629$	−81.1276			−0.128979
$630$	1242.73	+	1041.31i	1.97258	+	1.65288i
$631$			367.025i			0.581655i	0.956775	+	0.290828i	$0.0939306\pi$
$631$			367.025i			0.581655i	−0.956775	+	0.290828i	$0.906069\pi$
$632$	−221.873	+	311.789i	−0.351065	+	0.493338i
$633$	−982.052	+	982.052i	−1.55142	+	1.55142i
$634$	−5.33619	−	95.8057i	−0.00841671	−	0.151113i
$635$	1.32568	−	0.0428555i	0.00208768	−	6.74890e-5i
$636$	37.1938	+	332.852i	0.0584808	+	0.523352i
$637$	152.676	+	152.676i	0.239679	+	0.239679i
$638$	−46.5072	+	2.32404i	−0.0728952	+	0.00364269i
$639$	−506.352			−0.792413
$640$	−262.018	−	583.906i	−0.409403	−	0.912353i
$641$	−768.223			−1.19848			−0.599238	−	0.800571i	$-0.704530\pi$
$641$	−768.223			−1.19848			−0.599238	+	0.800571i	$0.704530\pi$
$642$	−544.501	−	487.046i	−0.848133	−	0.758639i
$643$	−440.590	+	440.590i	−0.685210	+	0.685210i	−0.961169	−	0.275959i	$-0.911004\pi$
$643$	−440.590	+	440.590i	−0.685210	+	0.685210i	0.275959	+	0.961169i	$0.411004\pi$
$644$	−330.864	+	36.9716i	−0.513763	+	0.0574093i
$645$	−521.212	−	488.569i	−0.808081	−	0.757471i
$646$	−18.9863	−	340.878i	−0.0293905	−	0.527676i
$647$	93.8740	+	93.8740i	0.145091	+	0.145091i	0.775921	−	0.630830i	$-0.217285\pi$
$647$	93.8740	+	93.8740i	0.145091	+	0.145091i	−0.630830	+	0.775921i	$0.717285\pi$
$648$	−1125.57	−	800.966i	−1.73699	−	1.23606i
$649$	−649.693	−	657.156i	−1.00107	−	1.01257i
$650$	1038.58	−	125.518i	1.59781	−	0.193105i
$651$	985.428			1.51371
$652$	−180.045	−	143.852i	−0.276143	−	0.220632i
$653$	539.451	+	539.451i	0.826112	+	0.826112i	0.986977	−	0.160864i	$-0.0514281\pi$
$653$	539.451	+	539.451i	0.826112	+	0.826112i	−0.160864	+	0.986977i	$0.551428\pi$
$654$	−108.939	−	1955.89i	−0.166574	−	2.99066i
$655$	388.362	+	364.039i	0.592919	+	0.555785i
$656$	−47.5963	−	210.313i	−0.0725554	−	0.320600i
$657$	−1453.15	−	1453.15i	−2.21180	−	2.21180i
$658$	−373.265	+	417.297i	−0.567271	+	0.634191i
$659$			232.233i			0.352402i	0.984354	+	0.176201i	$0.0563809\pi$
$659$			232.233i			0.352402i	−0.984354	+	0.176201i	$0.943619\pi$
$660$	727.471	−	961.900i	1.10223	−	1.45742i
$661$	579.441			0.876613			0.438306	−	0.898826i	$-0.355578\pi$
$661$	579.441			0.876613			0.438306	+	0.898826i	$0.355578\pi$
$662$	631.443	+	564.814i	0.953841	+	0.853193i
$663$	653.282	−	653.282i	0.985342	−	0.985342i
$664$	20.7958	+	123.425i	0.0313190	+	0.185881i
$665$	−26.3684	−	815.672i	−0.0396517	−	1.22657i
$666$	423.377	−	23.5813i	0.635702	−	0.0354074i
$667$	16.1736	−	16.1736i	0.0242483	−	0.0242483i
$668$	−442.405	−	353.471i	−0.662282	−	0.529148i
$669$			598.607i			0.894778i
$670$	606.554	+	508.246i	0.905304	+	0.758576i
$671$	−683.307	+	675.547i	−1.01834	+	1.00678i
$672$	−1180.99	−	656.253i	−1.75742	−	0.976567i
$673$	727.635	−	727.635i	1.08118	−	1.08118i	0.0847817	−	0.996400i	$-0.472981\pi$
$673$	727.635	−	727.635i	1.08118	−	1.08118i	0.996400	−	0.0847817i	$-0.0270193\pi$
$674$	834.574	−	46.4842i	1.23824	−	0.0689676i
$675$	1089.95	−	1240.80i	1.61474	−	1.83823i
$676$	−1068.38	+	119.384i	−1.58045	+	0.176603i
$677$	464.202	+	464.202i	0.685675	+	0.685675i	0.961273	−	0.275598i	$-0.0888757\pi$
$677$	464.202	+	464.202i	0.685675	+	0.685675i	−0.275598	+	0.961273i	$0.588876\pi$
$678$	234.551	−	262.220i	0.345945	−	0.386755i
$679$			960.837i			1.41508i
$680$	178.232	−	268.418i	0.262106	−	0.394732i
$681$		−	1700.08i		−	2.49644i
$682$	−25.6272	−	512.835i	−0.0375765	−	0.751957i
$683$	419.389	−	419.389i	0.614040	−	0.614040i	−0.329956	−	0.943996i	$-0.607034\pi$
$683$	419.389	−	419.389i	0.614040	−	0.614040i	0.943996	+	0.329956i	$0.107034\pi$
$684$	198.166	+	1773.41i	0.289716	+	2.59271i
$685$	447.658	−	14.4716i	0.653516	−	0.0211264i
$686$	−594.904	+	33.1350i	−0.867206	+	0.0483017i
$687$	−999.009	−	999.009i	−1.45416	−	1.45416i
$688$	352.695	+	222.518i	0.512638	+	0.323427i
$689$	319.576			0.463825
$690$	52.0380	+	590.107i	0.0754175	+	0.855228i
$691$		−	1091.80i		−	1.58003i	−0.613085	−	0.790017i	$-0.710072\pi$
$691$		−	1091.80i		−	1.58003i	0.613085	−	0.790017i	$-0.289928\pi$
$692$	−618.631	−	494.272i	−0.893976	−	0.714266i
$693$	10.1844	−	1783.43i	0.0146962	−	2.57349i
$694$	−37.0277	−	664.793i	−0.0533541	−	0.957916i
$695$	−766.308	+	817.509i	−1.10260	+	1.17627i
$696$	91.5333	−	15.4224i	0.131513	−	0.0221586i
$697$	76.7622	−	76.7622i	0.110132	−	0.110132i
$698$	650.015	−	726.695i	0.931253	−	1.04111i
$699$		−	1192.31i		−	1.70573i
$700$	440.893	−	631.514i	0.629848	−	0.902163i
$701$			1231.26i			1.75643i	0.478262	+	0.878217i	$0.341267\pi$
$701$			1231.26i			1.75643i	−0.478262	+	0.878217i	$0.658733\pi$
$702$	−1842.98	+	2060.39i	−2.62532	+	2.93502i
$703$	−150.923	−	150.923i	−0.214685	−	0.214685i
$704$	−310.813	+	631.673i	−0.441496	+	0.897263i
$705$	726.840	+	681.318i	1.03098	+	0.966408i
$706$	−825.115	+	45.9573i	−1.16872	+	0.0650953i
$707$	286.522	+	286.522i	0.405264	+	0.405264i
$708$	1439.16	+	1149.85i	2.03271	+	1.62409i
$709$			172.519i			0.243327i	0.992571	+	0.121664i	$0.0388229\pi$
$709$			172.519i			0.243327i	−0.992571	+	0.121664i	$0.961177\pi$
$710$	21.1295	+	239.607i	0.0297598	+	0.337474i
$711$	1006.96			1.41626
$712$	−419.449	+	589.436i	−0.589114	+	0.827859i
$713$	178.347	+	178.347i	0.250136	+	0.250136i
$714$	−37.8264	−	679.134i	−0.0529782	−	0.951168i
$715$	−835.059	−	791.766i	−1.16791	−	1.10737i
$716$	47.3869	+	424.071i	0.0661828	+	0.592278i
$717$	−150.504	−	150.504i	−0.209907	−	0.209907i
$718$	273.566	+	244.699i	0.381011	+	0.340807i
$719$	157.766			0.219424			0.109712	−	0.993963i	$-0.465007\pi$
$719$	157.766			0.219424			0.109712	+	0.993963i	$0.465007\pi$
$720$	−852.111	+	1452.59i	−1.18349	+	2.01748i
$721$		−	580.528i		−	0.805170i
$722$	117.474	−	131.332i	0.162706	−	0.181900i
$723$	2.99488	+	2.99488i	0.00414229	+	0.00414229i
$724$	−5.64770	−	50.5420i	−0.00780069	−	0.0698093i
$725$	3.41762	+	52.8045i	0.00471396	+	0.0728338i
$726$	−1325.32	+	58.6431i	−1.82550	+	0.0807756i
$727$	883.116	+	883.116i	1.21474	+	1.21474i	0.969450	+	0.245290i	$0.0788833\pi$
$727$	883.116	+	883.116i	1.21474	+	1.21474i	0.245290	+	0.969450i	$0.421117\pi$
$728$	−747.447	+	1050.36i	−1.02671	+	1.44280i
$729$			375.868i			0.515595i
$730$	−626.995	+	748.272i	−0.858898	+	1.02503i
$731$			209.947i			0.287205i
$732$	1195.61	−	1496.43i	1.63335	−	2.04430i
$733$	125.612	−	125.612i	0.171366	−	0.171366i	−0.616213	−	0.787580i	$-0.711334\pi$
$733$	125.612	−	125.612i	0.171366	−	0.171366i	0.787580	+	0.616213i	$0.211334\pi$
$734$	874.559	−	48.7112i	1.19150	−	0.0663641i
$735$	−9.13920	−	282.709i	−0.0124343	−	0.384638i
$736$	−94.9684	−	332.511i	−0.129033	−	0.451781i
$737$	4.97085	−	870.462i	0.00674471	−	1.18109i
$738$	−378.284	+	422.909i	−0.512579	+	0.573047i
$739$			47.4462i			0.0642033i	0.999485	+	0.0321016i	$0.0102200\pi$
$739$			47.4462i			0.0642033i	−0.999485	+	0.0321016i	$0.989780\pi$
$740$	−28.8258	−	199.359i	−0.0389538	−	0.269404i
$741$	2430.63			3.28020
$742$	156.859	−	175.363i	0.211400	−	0.236339i
$743$	735.075	+	735.075i	0.989334	+	0.989334i	0.999944	−	0.0106101i	$-0.00337736\pi$
$743$	735.075	+	735.075i	0.989334	+	0.989334i	−0.0106101	+	0.999944i	$0.503377\pi$
$744$	170.063	+	1009.34i	0.228579	+	1.35664i
$745$	585.977	+	549.277i	0.786546	+	0.737285i
$746$	−30.7166	−	551.484i	−0.0411751	−	0.739255i
$747$	232.889	−	232.889i	0.311765	−	0.311765i
$748$	−352.450	+	37.3472i	−0.471190	+	0.0499294i
$749$			513.201i			0.685181i
$750$	−1105.10	−	810.512i	−1.47347	−	1.08068i
$751$		−	1011.71i		−	1.34715i	−0.739120	−	0.673573i	$-0.764759\pi$
$751$		−	1011.71i		−	1.34715i	0.739120	−	0.673573i	$-0.235241\pi$
$752$	−491.840	−	310.305i	−0.654042	−	0.412640i
$753$	57.5398	+	57.5398i	0.0764140	+	0.0764140i
$754$	−4.92553	−	88.4327i	−0.00653254	−	0.117285i
$755$	693.474	+	650.042i	0.918509	+	0.860983i
$756$	226.013	+	2022.62i	0.298959	+	2.67542i
$757$	−788.218	+	788.218i	−1.04124	+	1.04124i	−0.0421273	+	0.999112i	$0.513414\pi$
$757$	−788.218	+	788.218i	−1.04124	+	1.04124i	−0.999112	+	0.0421273i	$0.986586\pi$
$758$	910.737	−	1018.17i	1.20150	−	1.34324i
$759$	463.401	−	458.138i	0.610541	−	0.603607i
$760$	830.912	−	167.775i	1.09331	−	0.220757i
$761$		−	1401.09i		−	1.84111i	−0.390609	−	0.920557i	$-0.627735\pi$
$761$		−	1401.09i		−	1.84111i	0.390609	−	0.920557i	$-0.372265\pi$
$762$	2.16774	+	1.93900i	0.00284480	+	0.00254462i
$763$	−973.066	+	973.066i	−1.27532	+	1.27532i
$764$	17.4256	−	1.94718i	0.0228083	−	0.00254867i
$765$	−847.391	+	27.3938i	−1.10770	+	0.0358089i
$766$	44.5740	+	800.279i	0.0581906	+	1.04475i
$767$	1242.87	−	1242.87i	1.62043	−	1.62043i
$768$	468.364	−	1322.90i	0.609849	−	1.72252i
$769$	392.963			0.511005			0.255502	−	0.966808i	$-0.417759\pi$
$769$	392.963			0.511005			0.255502	+	0.966808i	$0.417759\pi$
$770$	−844.348	+	69.6013i	−1.09656	+	0.0903913i
$771$			499.064i			0.647295i
$772$	858.686	+	686.071i	1.11229	+	0.888692i

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.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33338 + 1.49067i) q^{2} +(3.87627 - 3.87627i) q^{3} +(-0.444207 - 3.97526i) q^{4} +(3.64792 + 3.41945i) q^{5} +(0.609714 + 10.9468i) q^{6} +(5.44609 - 5.44609i) q^{7} +(6.51810 + 4.63836i) q^{8} -21.0509i q^{9} +(-9.96134 + 0.878432i) q^{10} +(7.73363 + 7.82247i) q^{11} +(-17.1310 - 13.6873i) q^{12} +(-14.7946 + 14.7946i) q^{13} +(0.856637 + 15.3800i) q^{14} +(27.3951 - 0.885606i) q^{15} +(-15.6054 + 3.53167i) q^{16} +(-5.69580 - 5.69580i) q^{17} +(31.3800 + 28.0688i) q^{18} -21.1920i q^{19} +(11.9728 - 16.0204i) q^{20} -42.2210i q^{21} +(-21.9726 + 1.09800i) q^{22} +(7.64133 - 7.64133i) q^{23} +(43.2454 - 7.28640i) q^{24} +(1.61467 + 24.9478i) q^{25} +(-2.32710 - 41.7806i) q^{26} +(-46.7126 - 46.7126i) q^{27} +(-24.0688 - 19.2304i) q^{28} +2.11660 q^{29} +(-35.2078 + 42.0179i) q^{30} +23.3398i q^{31} +(15.5433 - 27.9715i) q^{32} +(60.2996 + 0.344346i) q^{33} +(16.0852 - 0.895915i) q^{34} +(38.4895 - 1.24426i) q^{35} +(-83.6829 + 9.35096i) q^{36} +(7.12170 - 7.12170i) q^{37} +(31.5904 + 28.2570i) q^{38} +114.695i q^{39} +(7.91689 + 39.2087i) q^{40} +13.4770i q^{41} +(62.9377 + 56.2965i) q^{42} +(-18.4300 - 18.4300i) q^{43} +(27.6610 - 34.2180i) q^{44} +(71.9827 - 76.7922i) q^{45} +(1.20194 + 21.5795i) q^{46} +(25.7009 + 25.7009i) q^{47} +(-46.8009 + 74.1803i) q^{48} -10.3197i q^{49} +(-39.3420 - 30.8579i) q^{50} -44.1569 q^{51} +(65.3840 + 52.2403i) q^{52} +(-10.8004 - 10.8004i) q^{53} +(131.919 - 7.34763i) q^{54} +(1.46313 + 54.9805i) q^{55} +(60.7590 - 10.2373i) q^{56} +(-82.1460 - 82.1460i) q^{57} +(-2.82223 + 3.15516i) q^{58} -84.0088 q^{59} +(-15.6896 - 108.509i) q^{60} +87.3519i q^{61} +(-34.7919 - 31.1207i) q^{62} +(-114.645 - 114.645i) q^{63} +(20.9713 + 60.4666i) q^{64} +(-104.559 + 3.38009i) q^{65} +(-80.9155 + 89.4278i) q^{66} +(-55.9563 - 55.9563i) q^{67} +(-20.1122 + 25.1724i) q^{68} -59.2397i q^{69} +(-49.4663 + 59.0344i) q^{70} -24.0536i q^{71} +(97.6417 - 137.212i) q^{72} +(69.0302 - 69.0302i) q^{73} +(1.12020 + 20.1120i) q^{74} +(102.963 + 90.4455i) q^{75} +(-84.2438 + 9.41364i) q^{76} +(84.7198 + 0.483800i) q^{77} +(-170.973 - 152.932i) q^{78} +47.8344i q^{79} +(-69.0035 - 40.4785i) q^{80} -172.683 q^{81} +(-20.0898 - 17.9699i) q^{82} +(11.0631 + 11.0631i) q^{83} +(-167.839 + 18.7548i) q^{84} +(-1.30131 - 40.2543i) q^{85} +(52.0472 - 2.89893i) q^{86} +(8.20451 - 8.20451i) q^{87} +(14.1252 + 86.8590i) q^{88} +90.4306i q^{89} +(18.4918 + 209.696i) q^{90} +161.145i q^{91} +(-33.7706 - 26.9819i) q^{92} +(90.4712 + 90.4712i) q^{93} +(-72.5807 + 4.04261i) q^{94} +(72.4652 - 77.3069i) q^{95} +(-48.1752 - 168.675i) q^{96} +(-88.2136 + 88.2136i) q^{97} +(15.3833 + 13.7601i) q^{98} +(164.670 - 162.800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more