LMFDB - Embedded newform 60.3.l.a.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.l (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:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68375 - 1.07935i) q^{2} +(-0.130491 - 2.99716i) q^{3} +(1.67002 - 3.63470i) q^{4} +(-1.65103 + 4.71955i) q^{5} +(-3.45469 - 4.90562i) q^{6} +(1.91561 + 1.91561i) q^{7} +(-1.11122 - 7.92245i) q^{8} +(-8.96594 + 0.782204i) q^{9} +O(q^{10})$	\(q+(1.68375 - 1.07935i) q^{2} +(-0.130491 - 2.99716i) q^{3} +(1.67002 - 3.63470i) q^{4} +(-1.65103 + 4.71955i) q^{5} +(-3.45469 - 4.90562i) q^{6} +(1.91561 + 1.91561i) q^{7} +(-1.11122 - 7.92245i) q^{8} +(-8.96594 + 0.782204i) q^{9} +(2.31412 + 9.72856i) q^{10} +6.87236 q^{11} +(-11.1117 - 4.53101i) q^{12} +(12.2746 + 12.2746i) q^{13} +(5.29303 + 1.15780i) q^{14} +(14.3607 + 4.33254i) q^{15} +(-10.4221 - 12.1400i) q^{16} +(9.47120 + 9.47120i) q^{17} +(-14.2521 + 10.9944i) q^{18} -33.2524 q^{19} +(14.3969 + 13.8827i) q^{20} +(5.49143 - 5.99137i) q^{21} +(11.5713 - 7.41767i) q^{22} +(-7.20994 - 7.20994i) q^{23} +(-23.5998 + 4.36430i) q^{24} +(-19.5482 - 15.5842i) q^{25} +(33.9159 + 7.41877i) q^{26} +(3.51436 + 26.7703i) q^{27} +(10.1618 - 3.76357i) q^{28} +2.29155 q^{29} +(28.8561 - 8.20527i) q^{30} -12.1558i q^{31} +(-30.6515 - 9.19168i) q^{32} +(-0.896780 - 20.5976i) q^{33} +(26.1698 + 5.72440i) q^{34} +(-12.2036 + 5.87810i) q^{35} +(-12.1302 + 33.8948i) q^{36} +(-20.7290 + 20.7290i) q^{37} +(-55.9886 + 35.8909i) q^{38} +(35.1872 - 38.3906i) q^{39} +(39.2250 + 7.83574i) q^{40} -50.9173i q^{41} +(2.77942 - 16.0151i) q^{42} +(-15.1975 + 15.1975i) q^{43} +(11.4770 - 24.9790i) q^{44} +(11.1114 - 43.6066i) q^{45} +(-19.9218 - 4.35769i) q^{46} +(26.7793 - 26.7793i) q^{47} +(-35.0256 + 32.8208i) q^{48} -41.6608i q^{49} +(-49.7350 - 5.14053i) q^{50} +(27.1508 - 29.6226i) q^{51} +(65.1132 - 24.1157i) q^{52} +(15.5183 - 15.5183i) q^{53} +(34.8118 + 41.2812i) q^{54} +(-11.3465 + 32.4344i) q^{55} +(13.0477 - 17.3050i) q^{56} +(4.33913 + 99.6627i) q^{57} +(3.85839 - 2.47338i) q^{58} +63.0946i q^{59} +(39.7300 - 44.9614i) q^{60} +28.4752 q^{61} +(-13.1203 - 20.4672i) q^{62} +(-18.6737 - 15.6769i) q^{63} +(-61.5304 + 17.6071i) q^{64} +(-78.1961 + 37.6648i) q^{65} +(-23.7419 - 33.7132i) q^{66} +(-32.4542 - 32.4542i) q^{67} +(50.2420 - 18.6079i) q^{68} +(-20.6685 + 22.5502i) q^{69} +(-14.2032 + 23.0691i) q^{70} -88.8377 q^{71} +(16.1601 + 70.1630i) q^{72} +(71.1740 + 71.1740i) q^{73} +(-12.5286 + 57.2763i) q^{74} +(-44.1575 + 60.6227i) q^{75} +(-55.5320 + 120.862i) q^{76} +(13.1648 + 13.1648i) q^{77} +(17.8095 - 102.619i) q^{78} +75.1410 q^{79} +(74.5025 - 29.1440i) q^{80} +(79.7763 - 14.0264i) q^{81} +(-54.9574 - 85.7318i) q^{82} +(58.6543 + 58.6543i) q^{83} +(-12.6061 - 29.9654i) q^{84} +(-60.3369 + 29.0625i) q^{85} +(-9.18537 + 41.9921i) q^{86} +(-0.299026 - 6.86815i) q^{87} +(-7.63668 - 54.4459i) q^{88} -41.1063 q^{89} +(-28.3580 - 85.4156i) q^{90} +47.0267i q^{91} +(-38.2467 + 14.1653i) q^{92} +(-36.4327 + 1.58621i) q^{93} +(16.1854 - 73.9937i) q^{94} +(54.9006 - 156.936i) q^{95} +(-23.5492 + 93.0668i) q^{96} +(30.3484 - 30.3484i) q^{97} +(-44.9665 - 70.1464i) q^{98} +(-61.6172 + 5.37559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.68375	−	1.07935i	0.841874	−	0.539674i
$2$	1.68375	−	1.07935i	0.841874	−	0.539674i
$3$	−0.130491	−	2.99716i	−0.0434969	−	0.999054i
$3$	−0.130491	−	2.99716i	−0.0434969	−	0.999054i
$4$	1.67002	−	3.63470i	0.417504	−	0.908675i
$5$	−1.65103	+	4.71955i	−0.330205	+	0.943909i
$5$	−1.65103	+	4.71955i	−0.330205	+	0.943909i
$6$	−3.45469	−	4.90562i	−0.575782	−	0.817603i
$7$	1.91561	+	1.91561i	0.273659	+	0.273659i	0.830571	−	0.556912i	$-0.188014\pi$
$7$	1.91561	+	1.91561i	0.273659	+	0.273659i	−0.556912	+	0.830571i	$0.688014\pi$
$8$	−1.11122	−	7.92245i	−0.138902	−	0.990306i
$9$	−8.96594	+	0.782204i	−0.996216	+	0.0869115i
$10$	2.31412	+	9.72856i	0.231412	+	0.972856i
$11$	6.87236			0.624760			0.312380	−	0.949957i	$-0.398874\pi$
$11$	6.87236			0.624760			0.312380	+	0.949957i	$0.398874\pi$
$12$	−11.1117	−	4.53101i	−0.925975	−	0.377585i
$13$	12.2746	+	12.2746i	0.944199	+	0.944199i	0.998523	−	0.0543246i	$-0.0173006\pi$
$13$	12.2746	+	12.2746i	0.944199	+	0.944199i	−0.0543246	+	0.998523i	$0.517301\pi$
$14$	5.29303	+	1.15780i	0.378073	+	0.0826999i
$15$	14.3607	+	4.33254i	0.957379	+	0.288836i
$16$	−10.4221	−	12.1400i	−0.651380	−	0.758751i
$17$	9.47120	+	9.47120i	0.557129	+	0.557129i	0.928489	−	0.371360i	$-0.121108\pi$
$17$	9.47120	+	9.47120i	0.557129	+	0.557129i	−0.371360	+	0.928489i	$0.621108\pi$
$18$	−14.2521	+	10.9944i	−0.791785	+	0.610800i
$19$	−33.2524			−1.75013			−0.875063	−	0.484010i	$-0.839180\pi$
$19$	−33.2524			−1.75013			−0.875063	+	0.484010i	$0.839180\pi$
$20$	14.3969	+	13.8827i	0.719844	+	0.694135i
$21$	5.49143	−	5.99137i	0.261497	−	0.285303i
$22$	11.5713	−	7.41767i	0.525969	−	0.337167i
$23$	−7.20994	−	7.20994i	−0.313476	−	0.313476i	0.532779	−	0.846255i	$-0.321148\pi$
$23$	−7.20994	−	7.20994i	−0.313476	−	0.313476i	−0.846255	+	0.532779i	$0.821148\pi$
$24$	−23.5998	+	4.36430i	−0.983327	+	0.181846i
$25$	−19.5482	−	15.5842i	−0.781929	−	0.623368i
$26$	33.9159	+	7.41877i	1.30446	+	0.285337i
$27$	3.51436	+	26.7703i	0.130162	+	0.991493i
$28$	10.1618	−	3.76357i	0.362921	−	0.134413i
$29$	2.29155			0.0790190			0.0395095	−	0.999219i	$-0.487420\pi$
$29$	2.29155			0.0790190			0.0395095	+	0.999219i	$0.487420\pi$
$30$	28.8561	−	8.20527i	0.961869	−	0.273509i
$31$		−	12.1558i		−	0.392121i	−0.980592	−	0.196061i	$-0.937185\pi$
$31$		−	12.1558i		−	0.392121i	0.980592	−	0.196061i	$-0.0628149\pi$
$32$	−30.6515	−	9.19168i	−0.957859	−	0.287240i
$33$	−0.896780	−	20.5976i	−0.0271752	−	0.624169i
$34$	26.1698	+	5.72440i	0.769701	+	0.168365i
$35$	−12.2036	+	5.87810i	−0.348673	+	0.167946i
$36$	−12.1302	+	33.8948i	−0.336950	+	0.941523i
$37$	−20.7290	+	20.7290i	−0.560244	+	0.560244i	−0.929377	−	0.369133i	$-0.879655\pi$
$37$	−20.7290	+	20.7290i	−0.560244	+	0.560244i	0.369133	+	0.929377i	$0.379655\pi$
$38$	−55.9886	+	35.8909i	−1.47339	+	0.944497i
$39$	35.1872	−	38.3906i	0.902235	−	0.984375i
$40$	39.2250	+	7.83574i	0.980625	+	0.195893i
$41$		−	50.9173i		−	1.24188i	−0.783856	−	0.620942i	$-0.786750\pi$
$41$		−	50.9173i		−	1.24188i	0.783856	−	0.620942i	$-0.213250\pi$
$42$	2.77942	−	16.0151i	0.0661766	−	0.381313i
$43$	−15.1975	+	15.1975i	−0.353430	+	0.353430i	−0.861384	−	0.507954i	$-0.830402\pi$
$43$	−15.1975	+	15.1975i	−0.353430	+	0.353430i	0.507954	+	0.861384i	$0.330402\pi$
$44$	11.4770	−	24.9790i	0.260840	−	0.567704i
$45$	11.1114	−	43.6066i	0.246919	−	0.969036i
$46$	−19.9218	−	4.35769i	−0.433082	−	0.0947325i
$47$	26.7793	−	26.7793i	0.569772	−	0.569772i	−0.362293	−	0.932064i	$-0.618006\pi$
$47$	26.7793	−	26.7793i	0.569772	−	0.569772i	0.932064	+	0.362293i	$0.118006\pi$
$48$	−35.0256	+	32.8208i	−0.729700	+	0.683767i
$49$		−	41.6608i		−	0.850221i
$50$	−49.7350	−	5.14053i	−0.994701	−	0.102811i
$51$	27.1508	−	29.6226i	0.532368	−	0.580835i
$52$	65.1132	−	24.1157i	1.25218	−	0.463763i
$53$	15.5183	−	15.5183i	0.292799	−	0.292799i	−0.545386	−	0.838185i	$-0.683617\pi$
$53$	15.5183	−	15.5183i	0.292799	−	0.292799i	0.838185	+	0.545386i	$0.183617\pi$
$54$	34.8118	+	41.2812i	0.644662	+	0.764467i
$55$	−11.3465	+	32.4344i	−0.206299	+	0.589717i
$56$	13.0477	−	17.3050i	0.232994	−	0.309018i
$57$	4.33913	+	99.6627i	0.0761251	+	1.74847i
$58$	3.85839	−	2.47338i	0.0665240	−	0.0426445i
$59$			63.0946i			1.06940i	0.845042	+	0.534700i	$0.179575\pi$
$59$			63.0946i			1.06940i	−0.845042	+	0.534700i	$0.820425\pi$
$60$	39.7300	−	44.9614i	0.662167	−	0.749356i
$61$	28.4752			0.466806			0.233403	−	0.972380i	$-0.425014\pi$
$61$	28.4752			0.466806			0.233403	+	0.972380i	$0.425014\pi$
$62$	−13.1203	−	20.4672i	−0.211617	−	0.330117i
$63$	−18.6737	−	15.6769i	−0.296408	−	0.248839i
$64$	−61.5304	+	17.6071i	−0.961412	+	0.275111i
$65$	−78.1961	+	37.6648i	−1.20302	+	0.579458i
$66$	−23.7419	−	33.7132i	−0.359726	−	0.510806i
$67$	−32.4542	−	32.4542i	−0.484392	−	0.484392i	0.422139	−	0.906531i	$-0.361279\pi$
$67$	−32.4542	−	32.4542i	−0.484392	−	0.484392i	−0.906531	+	0.422139i	$0.861279\pi$
$68$	50.2420	−	18.6079i	0.738853	−	0.273646i
$69$	−20.6685	+	22.5502i	−0.299544	+	0.326814i
$70$	−14.2032	+	23.0691i	−0.202903	+	0.329559i
$71$	−88.8377			−1.25124			−0.625618	−	0.780130i	$-0.715153\pi$
$71$	−88.8377			−1.25124			−0.625618	+	0.780130i	$0.715153\pi$
$72$	16.1601	+	70.1630i	0.224446	+	0.974487i
$73$	71.1740	+	71.1740i	0.974987	+	0.974987i	0.999695	−	0.0247079i	$-0.00786556\pi$
$73$	71.1740	+	71.1740i	0.974987	+	0.974987i	−0.0247079	+	0.999695i	$0.507866\pi$
$74$	−12.5286	+	57.2763i	−0.169306	+	0.774004i
$75$	−44.1575	+	60.6227i	−0.588766	+	0.808303i
$76$	−55.5320	+	120.862i	−0.730685	+	1.59029i
$77$	13.1648	+	13.1648i	0.170971	+	0.170971i
$78$	17.8095	−	102.619i	0.228327	−	1.31563i
$79$	75.1410			0.951153			0.475576	−	0.879675i	$-0.342240\pi$
$79$	75.1410			0.951153			0.475576	+	0.879675i	$0.342240\pi$
$80$	74.5025	−	29.1440i	0.931282	−	0.364300i
$81$	79.7763	−	14.0264i	0.984893	−	0.173165i
$82$	−54.9574	−	85.7318i	−0.670213	−	1.04551i
$83$	58.6543	+	58.6543i	0.706678	+	0.706678i	0.965835	−	0.259157i	$-0.0834448\pi$
$83$	58.6543	+	58.6543i	0.706678	+	0.706678i	−0.259157	+	0.965835i	$0.583445\pi$
$84$	−12.6061	−	29.9654i	−0.150072	−	0.356731i
$85$	−60.3369	+	29.0625i	−0.709846	+	0.341912i
$86$	−9.18537	+	41.9921i	−0.106807	+	0.488281i
$87$	−0.299026	−	6.86815i	−0.00343708	−	0.0789442i
$88$	−7.63668	−	54.4459i	−0.0867805	−	0.618704i
$89$	−41.1063			−0.461868			−0.230934	−	0.972969i	$-0.574178\pi$
$89$	−41.1063			−0.461868			−0.230934	+	0.972969i	$0.574178\pi$
$90$	−28.3580	−	85.4156i	−0.315088	−	0.949062i
$91$			47.0267i			0.516777i
$92$	−38.2467	+	14.1653i	−0.415725	+	0.153970i
$93$	−36.4327	+	1.58621i	−0.391750	+	0.0170561i
$94$	16.1854	−	73.9937i	0.172185	−	0.787167i
$95$	54.9006	−	156.936i	0.577901	−	1.65196i
$96$	−23.5492	+	93.0668i	−0.245304	+	0.969446i
$97$	30.3484	−	30.3484i	0.312870	−	0.312870i	−0.533150	−	0.846020i	$-0.678992\pi$
$97$	30.3484	−	30.3484i	0.312870	−	0.312870i	0.846020	+	0.533150i	$0.178992\pi$
$98$	−44.9665	−	70.1464i	−0.458842	−	0.715779i
$99$	−61.6172	+	5.37559i	−0.622396	+	0.0542989i
$100$	−89.2897	+	45.0260i	−0.892897	+	0.450260i
$101$			124.297i			1.23067i	0.788267	+	0.615333i	$0.210978\pi$
$101$			124.297i			1.23067i	−0.788267	+	0.615333i	$0.789022\pi$
$102$	13.7420	−	79.1822i	0.134726	−	0.776296i
$103$	131.168	−	131.168i	1.27348	−	1.27348i	0.329223	−	0.944252i	$-0.393213\pi$
$103$	131.168	−	131.168i	1.27348	−	1.27348i	0.944252	−	0.329223i	$-0.106787\pi$
$104$	83.6050	−	110.884i	0.803895	−	1.06620i
$105$	19.2101	+	35.8090i	0.182953	+	0.341038i
$106$	9.37929	−	42.8786i	0.0884839	−	0.404516i
$107$	11.4672	−	11.4672i	0.107170	−	0.107170i	−0.651488	−	0.758659i	$-0.725855\pi$
$107$	11.4672	−	11.4672i	0.107170	−	0.107170i	0.758659	+	0.651488i	$0.225855\pi$
$108$	103.171	+	31.9332i	0.955288	+	0.295678i
$109$		−	80.0130i		−	0.734065i	−0.930208	−	0.367032i	$-0.880374\pi$
$109$		−	80.0130i		−	0.734065i	0.930208	−	0.367032i	$-0.119626\pi$
$110$	15.9034	+	66.8582i	0.144577	+	0.607802i
$111$	64.8331	+	59.4232i	0.584082	+	0.535345i
$112$	3.29090	−	43.2203i	0.0293830	−	0.385895i
$113$	64.8556	−	64.8556i	0.573943	−	0.573943i	−0.359285	−	0.933228i	$-0.616979\pi$
$113$	64.8556	−	64.8556i	0.573943	−	0.573943i	0.933228	+	0.359285i	$0.116979\pi$
$114$	114.877	+	163.124i	1.00769	+	1.43091i
$115$	45.9315	−	22.1238i	0.399404	−	0.192381i
$116$	3.82693	−	8.32910i	0.0329908	−	0.0718026i
$117$	−119.654	−	100.452i	−1.02269	−	0.858564i
$118$	68.1010	+	106.235i	0.577127	+	0.900301i
$119$			36.2863i			0.304927i
$120$	18.3665	−	118.586i	0.153054	−	0.988218i
$121$	−73.7706			−0.609675
$122$	47.9450	−	30.7346i	0.392992	−	0.251923i
$123$	−152.607	+	6.64423i	−1.24071	+	0.0540182i
$124$	−44.1825	−	20.3003i	−0.356311	−	0.163712i
$125$	105.825	−	66.5288i	0.846600	−	0.532230i
$126$	−48.3626	−	6.24053i	−0.383830	−	0.0495280i
$127$	63.5895	+	63.5895i	0.500705	+	0.500705i	0.911657	−	0.410952i	$-0.134804\pi$
$127$	63.5895	+	63.5895i	0.500705	+	0.500705i	−0.410952	+	0.911657i	$0.634804\pi$
$128$	−84.5975	+	96.0586i	−0.660918	+	0.750458i
$129$	47.5325	+	43.5662i	0.368469	+	0.337722i
$130$	−91.0092	+	147.819i	−0.700071	+	1.13707i
$131$	−144.030			−1.09947			−0.549734	−	0.835340i	$-0.685271\pi$
$131$	−144.030			−1.09947			−0.549734	+	0.835340i	$0.685271\pi$
$132$	−76.3636	−	31.1388i	−0.578512	−	0.235900i
$133$	−63.6987	−	63.6987i	−0.478938	−	0.478938i
$134$	−89.6742	−	19.6154i	−0.669210	−	0.146383i
$135$	−132.146	−	27.6123i	−0.978859	−	0.204536i
$136$	64.5105	−	85.5596i	0.474342	−	0.629115i
$137$	−13.6200	−	13.6200i	−0.0994161	−	0.0994161i	0.655649	−	0.755065i	$-0.272395\pi$
$137$	−13.6200	−	13.6200i	−0.0994161	−	0.0994161i	−0.755065	+	0.655649i	$0.772395\pi$
$138$	−10.4611	+	60.2774i	−0.0758051	+	0.436793i
$139$	−62.7261			−0.451267			−0.225634	−	0.974212i	$-0.572445\pi$
$139$	−62.7261			−0.451267			−0.225634	+	0.974212i	$0.572445\pi$
$140$	0.984971	+	54.1728i	0.00703550	+	0.386948i
$141$	−83.7563	−	76.7674i	−0.594016	−	0.544449i
$142$	−149.580	+	95.8868i	−1.05338	+	0.675259i
$143$	84.3554	+	84.3554i	0.589898	+	0.589898i
$144$	102.940	+	100.695i	0.714860	+	0.699268i
$145$	−3.78341	+	10.8151i	−0.0260925	+	0.0745867i
$146$	196.661	+	43.0176i	1.34699	+	0.294641i
$147$	−124.864	+	5.43636i	−0.849417	+	0.0369820i
$148$	40.7259	+	109.962i	0.275175	+	0.742983i
$149$	167.292			1.12277			0.561383	−	0.827556i	$-0.310270\pi$
$149$	167.292			1.12277			0.561383	+	0.827556i	$0.310270\pi$
$150$	−8.91704	+	149.735i	−0.0594469	+	0.998231i
$151$			75.2596i			0.498408i	0.968451	+	0.249204i	$0.0801690\pi$
$151$			75.2596i			0.498408i	−0.968451	+	0.249204i	$0.919831\pi$
$152$	36.9506	+	263.440i	0.243096	+	1.73316i
$153$	−92.3266	−	77.5098i	−0.603442	−	0.506600i
$154$	36.3756	+	7.95681i	0.236205	+	0.0516676i
$155$	57.3696	+	20.0695i	0.370127	+	0.129480i
$156$	−80.7752	−	192.008i	−0.517790	−	1.23082i
$157$	71.6852	−	71.6852i	0.456593	−	0.456593i	−0.440942	−	0.897536i	$-0.645356\pi$
$157$	71.6852	−	71.6852i	0.456593	−	0.456593i	0.897536	+	0.440942i	$0.145356\pi$
$158$	126.519	−	81.1033i	0.800751	−	0.513312i
$159$	−48.5359	−	44.4859i	−0.305258	−	0.279786i
$160$	93.9870	−	129.485i	0.587419	−	0.809283i
$161$		−	27.6229i		−	0.171571i
$162$	119.184	−	109.723i	0.735703	−	0.677304i
$163$	−61.4502	+	61.4502i	−0.376995	+	0.376995i	−0.870017	−	0.493022i	$-0.835892\pi$
$163$	−61.4502	+	61.4502i	−0.376995	+	0.376995i	0.493022	+	0.870017i	$0.335892\pi$
$164$	−185.069	−	85.0327i	−1.12847	−	0.518492i
$165$	98.6918	+	29.7748i	0.598132	+	0.180453i
$166$	162.067	+	35.4507i	0.976309	+	0.213558i
$167$	36.7847	−	36.7847i	0.220268	−	0.220268i	−0.588344	−	0.808611i	$-0.700220\pi$
$167$	36.7847	−	36.7847i	0.220268	−	0.220268i	0.808611	+	0.588344i	$0.200220\pi$
$168$	−53.5685	−	36.8479i	−0.318860	−	0.219333i
$169$			132.331i			0.783022i
$170$	−70.2236	+	114.059i	−0.413080	+	0.670933i
$171$	298.139	−	26.0101i	1.74350	−	0.152106i
$172$	29.8583	+	80.6184i	0.173595	+	0.468712i
$173$	−137.897	+	137.897i	−0.797091	+	0.797091i	−0.982636	−	0.185545i	$-0.940595\pi$
$173$	−137.897	+	137.897i	−0.797091	+	0.797091i	0.185545	+	0.982636i	$0.440595\pi$
$174$	−7.91660	−	11.2415i	−0.0454977	−	0.0646062i
$175$	−7.59354	−	67.3001i	−0.0433917	−	0.384572i
$176$	−71.6244	−	83.4306i	−0.406957	−	0.474038i
$177$	189.105	−	8.23327i	1.06839	−	0.0465156i
$178$	−69.2126	+	44.3680i	−0.388835	+	0.249258i
$179$		−	106.971i		−	0.597602i	−0.954315	−	0.298801i	$-0.903413\pi$
$179$		−	106.971i		−	0.597602i	0.954315	−	0.298801i	$-0.0965867\pi$
$180$	−139.941	−	113.210i	−0.777449	−	0.628946i
$181$	−11.6057			−0.0641199			−0.0320600	−	0.999486i	$-0.510207\pi$
$181$	−11.6057			−0.0641199			−0.0320600	+	0.999486i	$0.510207\pi$
$182$	50.7582	+	79.1812i	0.278891	+	0.435061i
$183$	−3.71575	−	85.3446i	−0.0203046	−	0.466364i
$184$	−49.1086	+	65.1322i	−0.266895	+	0.353979i
$185$	−63.6074	−	132.056i	−0.343824	−	0.713815i
$186$	−59.6315	+	41.9944i	−0.320599	+	0.225776i
$187$	65.0895	+	65.0895i	0.348072	+	0.348072i
$188$	−52.6128	−	142.057i	−0.279855	−	0.755620i
$189$	−44.5494	+	58.0137i	−0.235711	+	0.306951i
$190$	−76.9499	−	323.498i	−0.404999	−	1.70262i
$191$	−135.925			−0.711648			−0.355824	−	0.934553i	$-0.615800\pi$
$191$	−135.925			−0.711648			−0.355824	+	0.934553i	$0.615800\pi$
$192$	60.8005	+	182.119i	0.316669	+	0.948536i
$193$	−62.7362	−	62.7362i	−0.325058	−	0.325058i	0.525646	−	0.850704i	$-0.323824\pi$
$193$	−62.7362	−	62.7362i	−0.325058	−	0.325058i	−0.850704	+	0.525646i	$0.823824\pi$
$194$	18.3426	−	83.8556i	0.0945494	−	0.432245i
$195$	123.091	+	229.451i	0.631237	+	1.17667i
$196$	−151.425	−	69.5743i	−0.772575	−	0.354971i
$197$	−96.9852	−	96.9852i	−0.492311	−	0.492311i	0.416723	−	0.909034i	$-0.363179\pi$
$197$	−96.9852	−	96.9852i	−0.492311	−	0.492311i	−0.909034	+	0.416723i	$0.863179\pi$
$198$	−97.9457	+	75.5575i	−0.494675	+	0.381604i
$199$	29.0286			0.145872			0.0729361	−	0.997337i	$-0.476763\pi$
$199$	29.0286			0.145872			0.0729361	+	0.997337i	$0.476763\pi$
$200$	−101.743	+	172.187i	−0.508713	+	0.860936i
$201$	−93.0356	+	101.506i	−0.462864	+	0.505003i
$202$	134.160	+	209.285i	0.664158	+	1.03607i
$203$	4.38973	+	4.38973i	0.0216243	+	0.0216243i
$204$	−62.3270	−	148.155i	−0.305524	−	0.726251i
$205$	240.306	+	84.0658i	1.17223	+	0.410077i
$206$	79.2780	−	362.430i	0.384845	−	1.75937i
$207$	70.2836	+	59.0043i	0.339534	+	0.285045i
$208$	21.0869	−	276.940i	0.101379	−	1.33144i
$209$	−228.522			−1.09341
$210$	70.9952	+	39.5590i	0.338073	+	0.188376i
$211$		−	376.951i		−	1.78650i	−0.449561	−	0.893250i	$-0.648420\pi$
$211$		−	376.951i		−	1.78650i	0.449561	−	0.893250i	$-0.351580\pi$
$212$	−30.4886	−	82.3204i	−0.143814	−	0.388304i
$213$	11.5925	+	266.261i	0.0544249	+	1.25005i
$214$	6.93079	−	31.6850i	0.0323869	−	0.148061i
$215$	−46.6338	−	96.8167i	−0.216901	−	0.450310i
$216$	208.181	−	57.5900i	0.963802	−	0.266620i
$217$	23.2857	−	23.2857i	0.107307	−	0.107307i
$218$	−86.3619	−	134.722i	−0.396155	−	0.617990i
$219$	204.032	−	222.608i	0.931655	−	1.01647i
$220$	98.9406	+	95.4070i	0.449730	+	0.433668i
$221$			232.510i			1.05208i
$222$	173.301	+	30.0763i	0.780635	+	0.135479i
$223$	−255.505	+	255.505i	−1.14576	+	1.14576i	−0.158385	+	0.987377i	$0.550629\pi$
$223$	−255.505	+	255.505i	−1.14576	+	1.14576i	−0.987377	+	0.158385i	$0.949371\pi$
$224$	−41.1087	−	76.3241i	−0.183521	−	0.340733i
$225$	187.458	+	124.436i	0.833148	+	0.553050i
$226$	39.1988	−	179.202i	0.173446	−	0.792930i
$227$	−109.045	+	109.045i	−0.480375	+	0.480375i	−0.905251	−	0.424876i	$-0.860318\pi$
$227$	−109.045	+	109.045i	−0.480375	+	0.480375i	0.424876	+	0.905251i	$0.360318\pi$
$228$	369.490	+	150.667i	1.62057	+	0.660820i
$229$			223.738i			0.977023i	0.872557	+	0.488512i	$0.162460\pi$
$229$			223.738i			0.977023i	−0.872557	+	0.488512i	$0.837540\pi$
$230$	53.4577	−	86.8270i	0.232425	−	0.377509i
$231$	37.7391	−	41.1749i	0.163373	−	0.178246i
$232$	−2.54641	−	18.1547i	−0.0109759	−	0.0782530i
$233$	−62.4244	+	62.4244i	−0.267916	+	0.267916i	−0.828260	−	0.560344i	$-0.810669\pi$
$233$	−62.4244	+	62.4244i	−0.267916	+	0.267916i	0.560344	+	0.828260i	$0.310669\pi$
$234$	−309.891	−	39.9871i	−1.32432	−	0.170885i
$235$	82.1727	+	170.599i	0.349671	+	0.725955i
$236$	229.330	+	105.369i	0.971737	+	0.446479i
$237$	−9.80522	−	225.210i	−0.0413722	−	0.950252i
$238$	39.1655	+	61.0970i	0.164561	+	0.256710i
$239$			310.217i			1.29798i	0.760798	+	0.648989i	$0.224808\pi$
$239$			310.217i			1.29798i	−0.760798	+	0.648989i	$0.775192\pi$
$240$	−97.0712	−	219.493i	−0.404463	−	0.914554i
$241$	−119.905			−0.497529			−0.248765	−	0.968564i	$-0.580025\pi$
$241$	−119.905			−0.497529			−0.248765	+	0.968564i	$0.580025\pi$
$242$	−124.211	+	79.6242i	−0.513269	+	0.329026i
$243$	−52.4494	−	237.272i	−0.215841	−	0.976428i
$244$	47.5540	−	103.499i	0.194893	−	0.424175i
$245$	196.620	+	68.7832i	0.802532	+	0.280748i
$246$	−249.781	+	175.903i	−1.01537	+	0.715055i
$247$	−408.159	−	408.159i	−1.65247	−	1.65247i
$248$	−96.3033	+	13.5077i	−0.388320	+	0.0544664i
$249$	168.142	−	183.450i	0.675271	−	0.736747i
$250$	106.375	−	226.240i	0.425500	−	0.904959i
$251$	336.252			1.33965			0.669825	−	0.742519i	$-0.266369\pi$
$251$	336.252			1.33965			0.669825	+	0.742519i	$0.266369\pi$
$252$	−88.1662	+	41.6926i	−0.349866	+	0.165447i
$253$	−49.5493	−	49.5493i	−0.195847	−	0.195847i
$254$	175.704	+	38.4336i	0.691748	+	0.151313i
$255$	94.9785	+	177.047i	0.372465	+	0.694302i
$256$	−38.7602	+	253.049i	−0.151407	+	0.988472i
$257$	−199.642	−	199.642i	−0.776816	−	0.776816i	0.202472	−	0.979288i	$-0.435102\pi$
$257$	−199.642	−	199.642i	−0.776816	−	0.776816i	−0.979288	+	0.202472i	$0.935102\pi$
$258$	127.056	+	22.0505i	0.492464	+	0.0854669i
$259$	−79.4176			−0.306632
$260$	6.31135	+	347.120i	0.0242744	+	1.33508i
$261$	−20.5459	+	1.79246i	−0.0787200	+	0.00686766i
$262$	−242.511	+	155.459i	−0.925613	+	0.593354i
$263$	107.927	+	107.927i	0.410368	+	0.410368i	0.881867	−	0.471499i	$-0.156287\pi$
$263$	107.927	+	107.927i	0.410368	+	0.410368i	−0.471499	+	0.881867i	$0.656287\pi$
$264$	−162.187	+	29.9931i	−0.614344	+	0.113610i
$265$	47.6183	+	98.8607i	0.179692	+	0.373059i
$266$	−176.006	−	38.4995i	−0.661675	−	0.144735i
$267$	5.36399	+	123.202i	0.0200899	+	0.461431i
$268$	−172.161	+	63.7623i	−0.642390	+	0.237919i
$269$	279.355			1.03850			0.519248	−	0.854624i	$-0.326212\pi$
$269$	279.355			1.03850			0.519248	+	0.854624i	$0.326212\pi$
$270$	−252.304	+	96.1393i	−0.934459	+	0.356072i
$271$			353.019i			1.30265i	0.758797	+	0.651327i	$0.225787\pi$
$271$			353.019i			1.30265i	−0.758797	+	0.651327i	$0.774213\pi$
$272$	16.2709	−	213.690i	0.0598194	−	0.785626i
$273$	140.947	−	6.13656i	0.516288	−	0.0224782i
$274$	−37.6334	−	8.23194i	−0.137348	−	0.0300436i
$275$	−134.342	−	107.100i	−0.488518	−	0.389455i
$276$	47.4464	+	112.783i	0.171907	+	0.408634i
$277$	9.06443	−	9.06443i	0.0327236	−	0.0327236i	−0.690556	−	0.723279i	$-0.742634\pi$
$277$	9.06443	−	9.06443i	0.0327236	−	0.0327236i	0.723279	+	0.690556i	$0.242634\pi$
$278$	−105.615	+	67.7033i	−0.379910	+	0.243537i
$279$	9.50828	+	108.988i	0.0340798	+	0.390637i
$280$	60.1297	+	90.1502i	0.214749	+	0.321965i
$281$		−	204.501i		−	0.727762i	−0.931445	−	0.363881i	$-0.881451\pi$
$281$		−	204.501i		−	0.727762i	0.931445	−	0.363881i	$-0.118549\pi$
$282$	−223.883	−	38.8548i	−0.793912	−	0.137783i
$283$	−4.95961	+	4.95961i	−0.0175251	+	0.0175251i	−0.715815	−	0.698290i	$-0.753945\pi$
$283$	−4.95961	+	4.95961i	−0.0175251	+	0.0175251i	0.698290	+	0.715815i	$0.253945\pi$
$284$	−148.360	+	322.898i	−0.522396	+	1.13697i
$285$	−477.527	−	144.067i	−1.67553	−	0.505499i
$286$	233.082	+	50.9844i	0.814972	+	0.178267i
$287$	97.5378	−	97.5378i	0.339853	−	0.339853i
$288$	282.009	+	58.4364i	0.979199	+	0.202904i
$289$		−	109.593i		−	0.379214i
$290$	5.30292	+	22.2935i	0.0182859	+	0.0768741i
$291$	−94.9192	−	86.9988i	−0.326183	−	0.298965i
$292$	377.558	−	139.834i	1.29301	−	0.478885i
$293$	195.635	−	195.635i	0.667697	−	0.667697i	−0.289485	−	0.957182i	$-0.593484\pi$
$293$	195.635	−	195.635i	0.667697	−	0.667697i	0.957182	+	0.289485i	$0.0934842\pi$
$294$	−204.372	+	143.925i	−0.695144	+	0.489542i
$295$	−297.778	−	104.171i	−1.00942	−	0.353122i
$296$	187.259	+	141.190i	0.632632	+	0.476994i
$297$	24.1520	+	183.975i	0.0813198	+	0.619445i
$298$	281.678	−	180.566i	0.945227	−	0.605927i
$299$		−	176.998i		−	0.591967i
$300$	146.602	+	261.740i	0.488673	+	0.872467i
$301$	−58.2251			−0.193439
$302$	81.2313	+	126.718i	0.268978	+	0.419597i
$303$	372.539	−	16.2196i	1.22950	−	0.0535302i
$304$	346.559	+	403.685i	1.14000	+	1.32791i
$305$	−47.0133	+	134.390i	−0.154142	+	0.440622i
$306$	−239.115	−	30.8545i	−0.781421	−	0.100832i
$307$	323.877	+	323.877i	1.05497	+	1.05497i	0.998398	+	0.0565751i	$0.0180180\pi$
$307$	323.877	+	323.877i	1.05497	+	1.05497i	0.0565751	+	0.998398i	$0.481982\pi$
$308$	69.8355	−	25.8646i	0.226739	−	0.0839761i
$309$	−410.248	−	376.015i	−1.32766	−	1.21688i
$310$	118.258	−	28.1298i	0.381477	−	0.0907414i
$311$	−428.968			−1.37932			−0.689660	−	0.724133i	$-0.742240\pi$
$311$	−428.968			−1.37932			−0.689660	+	0.724133i	$0.742240\pi$
$312$	−343.248	−	236.108i	−1.10015	−	0.756757i
$313$	−144.149	−	144.149i	−0.460541	−	0.460541i	0.438292	−	0.898833i	$-0.355584\pi$
$313$	−144.149	−	144.149i	−0.460541	−	0.460541i	−0.898833	+	0.438292i	$0.855584\pi$
$314$	43.3266	−	198.073i	0.137983	−	0.630806i
$315$	104.819	−	62.2484i	0.332757	−	0.197614i
$316$	125.487	−	273.115i	0.397110	−	0.864288i
$317$	299.797	+	299.797i	0.945733	+	0.945733i	0.998601	−	0.0528685i	$-0.0168364\pi$
$317$	299.797	+	299.797i	0.945733	+	0.945733i	−0.0528685	+	0.998601i	$0.516836\pi$
$318$	−129.738	−	22.5160i	−0.407981	−	0.0708049i
$319$	15.7484			0.0493679
$320$	18.4907	−	319.465i	0.0577836	−	0.998329i
$321$	−35.8655	−	32.8727i	−0.111730	−	0.102407i
$322$	−29.8148	−	46.5101i	−0.0925924	−	0.144441i
$323$	−314.940	−	314.940i	−0.975046	−	0.975046i
$324$	82.2461	−	313.387i	0.253846	−	0.967245i
$325$	−48.6568	−	431.236i	−0.149713	−	1.32688i
$326$	−37.1405	+	169.793i	−0.113928	+	0.520837i
$327$	−239.812	+	10.4410i	−0.733370	+	0.0319296i
$328$	−403.389	+	56.5801i	−1.22985	+	0.172500i
$329$	102.598			0.311847
$330$	198.309	−	56.3896i	0.600938	−	0.170877i
$331$			89.1276i			0.269268i	0.990895	+	0.134634i	$0.0429858\pi$
$331$			89.1276i			0.269268i	−0.990895	+	0.134634i	$0.957014\pi$
$332$	311.144	−	115.237i	0.937181	−	0.347100i
$333$	169.641	−	202.070i	0.509432	−	0.606815i
$334$	22.2327	−	101.640i	0.0665649	−	0.304310i
$335$	206.752	−	99.5864i	0.617170	−	0.297273i
$336$	−129.968	−	4.22350i	−0.386808	−	0.0125699i
$337$	−176.973	+	176.973i	−0.525141	+	0.525141i	−0.919120	−	0.393978i	$-0.871098\pi$
$337$	−176.973	+	176.973i	−0.525141	+	0.525141i	0.393978	+	0.919120i	$0.371098\pi$
$338$	142.831	+	222.812i	0.422577	+	0.659206i
$339$	−202.846	−	185.920i	−0.598365	−	0.548435i
$340$	4.86990	+	267.842i	0.0143232	+	0.787769i
$341$		−	83.5387i		−	0.244982i
$342$	473.917	−	365.590i	1.38572	−	1.06898i
$343$	173.671	−	173.671i	0.506330	−	0.506330i
$344$	137.289	+	103.514i	0.399096	+	0.300912i
$345$	−72.3024	−	134.777i	−0.209572	−	0.390658i
$346$	−83.3448	+	381.022i	−0.240881	+	1.10122i
$347$	341.548	−	341.548i	0.984288	−	0.984288i	−0.0155906	−	0.999878i	$-0.504963\pi$
$347$	341.548	−	341.548i	0.984288	−	0.984288i	0.999878	+	0.0155906i	$0.00496283\pi$
$348$	−25.4630	−	10.3830i	−0.0731696	−	0.0298363i
$349$			190.129i			0.544782i	0.962187	+	0.272391i	$0.0878144\pi$
$349$			190.129i			0.544782i	−0.962187	+	0.272391i	$0.912186\pi$
$350$	−85.4259	−	105.120i	−0.244074	−	0.300344i
$351$	−285.457	+	371.732i	−0.813268	+	1.05906i
$352$	−210.648	−	63.1686i	−0.598432	−	0.179456i
$353$	66.4041	−	66.4041i	0.188114	−	0.188114i	−0.606767	−	0.794880i	$-0.707534\pi$
$353$	66.4041	−	66.4041i	0.188114	−	0.188114i	0.794880	+	0.606767i	$0.207534\pi$
$354$	309.518	−	217.972i	0.874345	−	0.615742i
$355$	146.673	−	419.274i	0.413165	−	1.18105i
$356$	−68.6482	+	149.409i	−0.192832	+	0.419688i
$357$	108.756	−	4.73503i	0.304638	−	0.0132634i
$358$	−115.459	−	180.112i	−0.322510	−	0.503106i
$359$			402.003i			1.11979i	0.828565	+	0.559893i	$0.189158\pi$
$359$			402.003i			1.11979i	−0.828565	+	0.559893i	$0.810842\pi$
$360$	−357.818	−	39.5728i	−0.993940	−	0.109925i
$361$	744.721			2.06294
$362$	−19.5411	+	12.5266i	−0.0539809	+	0.0346038i
$363$	9.62639	+	221.102i	0.0265190	+	0.609098i
$364$	170.928	+	78.5354i	0.469582	+	0.215757i
$365$	−453.419	+	218.399i	−1.24224	+	0.598353i
$366$	−98.3729	−	139.688i	−0.268779	−	0.381662i
$367$	183.244	+	183.244i	0.499301	+	0.499301i	0.911220	−	0.411919i	$-0.135141\pi$
$367$	183.244	+	183.244i	0.499301	+	0.499301i	−0.411919	+	0.911220i	$0.635141\pi$
$368$	−12.3862	+	162.672i	−0.0336582	+	0.442042i
$369$	39.8277	+	456.521i	0.107934	+	1.23719i
$370$	−249.633	−	153.694i	−0.674683	−	0.415389i
$371$	59.4543			0.160254
$372$	−55.0779	+	135.071i	−0.148059	+	0.363094i
$373$	−78.2141	−	78.2141i	−0.209689	−	0.209689i	0.594446	−	0.804135i	$-0.297371\pi$
$373$	−78.2141	−	78.2141i	−0.209689	−	0.209689i	−0.804135	+	0.594446i	$0.797371\pi$
$374$	179.848	+	39.3401i	0.480878	+	0.105187i
$375$	−213.207	−	308.493i	−0.568551	−	0.822648i
$376$	−241.915	−	182.400i	−0.643391	−	0.485106i
$377$	28.1278	+	28.1278i	0.0746096	+	0.0746096i
$378$	−12.3930	+	145.765i	−0.0327857	+	0.385621i
$379$	116.155			0.306478			0.153239	−	0.988189i	$-0.451030\pi$
$379$	116.155			0.306478			0.153239	+	0.988189i	$0.451030\pi$
$380$	−478.731	−	461.633i	−1.25982	−	1.21482i
$381$	182.290	−	198.886i	0.478452	−	0.522010i
$382$	−228.863	+	146.710i	−0.599118	+	0.384058i
$383$	439.765	+	439.765i	1.14821	+	1.14821i	0.986904	+	0.161308i	$0.0515712\pi$
$383$	439.765	+	439.765i	1.14821	+	1.14821i	0.161308	+	0.986904i	$0.448429\pi$
$384$	298.942	+	241.018i	0.778496	+	0.627650i
$385$	−83.8673	+	40.3964i	−0.217837	+	0.104926i
$386$	−173.346	−	37.9178i	−0.449083	−	0.0982326i
$387$	124.372	−	148.147i	0.321376	−	0.382810i
$388$	−59.6250	−	160.990i	−0.153673	−	0.414922i
$389$	−120.985			−0.311017			−0.155508	−	0.987835i	$-0.549702\pi$
$389$	−120.985			−0.311017			−0.155508	+	0.987835i	$0.549702\pi$
$390$	454.913	+	253.480i	1.16644	+	0.649949i
$391$		−	136.574i		−	0.349293i
$392$	−330.056	+	46.2942i	−0.841979	+	0.118098i
$393$	18.7946	+	431.682i	0.0478235	+	1.09843i
$394$	−267.980	−	58.6179i	−0.680151	−	0.148776i
$395$	−124.060	+	354.632i	−0.314076	+	0.897802i
$396$	−83.3631	+	232.937i	−0.210513	+	0.588226i
$397$	−549.267	+	549.267i	−1.38355	+	1.38355i	−0.545313	+	0.838233i	$0.683589\pi$
$397$	−549.267	+	549.267i	−1.38355	+	1.38355i	−0.838233	+	0.545313i	$0.816411\pi$
$398$	48.8768	−	31.3319i	0.122806	−	0.0787234i
$399$	−182.603	+	199.227i	−0.457652	+	0.499317i
$400$	14.5408	+	399.736i	0.0363520	+	0.999339i
$401$			177.597i			0.442885i	0.975173	+	0.221442i	$0.0710765\pi$
$401$			177.597i			0.442885i	−0.975173	+	0.221442i	$0.928924\pi$
$402$	−47.0887	+	271.328i	−0.117136	+	0.674944i
$403$	149.207	−	149.207i	0.370240	−	0.370240i
$404$	451.783	+	207.578i	1.11827	+	0.513808i
$405$	−65.5147	+	399.666i	−0.161765	+	0.986829i
$406$	12.1292	+	2.65315i	0.0298750	+	0.00653486i
$407$	−142.457	+	142.457i	−0.350018	+	0.350018i
$408$	−264.854	−	182.184i	−0.649152	−	0.446529i
$409$		−	348.822i		−	0.852865i	−0.904519	−	0.426433i	$-0.859770\pi$
$409$		−	348.822i		−	0.852865i	0.904519	−	0.426433i	$-0.140230\pi$
$410$	495.352	−	117.828i	1.20817	−	0.287387i
$411$	−39.0441	+	42.5986i	−0.0949977	+	0.103646i
$412$	−257.703	−	695.809i	−0.625494	−	1.68886i
$413$	−120.865	+	120.865i	−0.292651	+	0.292651i
$414$	182.026	+	23.4880i	0.439676	+	0.0567342i
$415$	−373.661	+	179.982i	−0.900389	+	0.433691i
$416$	−263.410	−	489.058i	−0.633197	−	1.17562i
$417$	8.18518	+	188.000i	0.0196287	+	0.450840i
$418$	−384.774	+	246.655i	−0.920512	+	0.590084i
$419$		−	104.631i		−	0.249716i	−0.992175	−	0.124858i	$-0.960152\pi$
$419$		−	104.631i		−	0.249716i	0.992175	−	0.124858i	$-0.0398476\pi$
$420$	162.236	−	10.0212i	0.386276	−	0.0238599i
$421$	207.644			0.493217			0.246609	−	0.969115i	$-0.420684\pi$
$421$	207.644			0.493217			0.246609	+	0.969115i	$0.420684\pi$
$422$	−406.862	−	634.691i	−0.964127	−	1.50401i
$423$	−219.155	+	261.048i	−0.518096	+	0.617136i
$424$	−140.187	−	105.699i	−0.330631	−	0.249290i
$425$	−37.5441	−	332.746i	−0.0883390	−	0.782932i
$426$	306.907	+	435.804i	0.720439	+	1.02301i
$427$	54.5474	+	54.5474i	0.127746	+	0.127746i
$428$	−22.5294	−	60.8303i	−0.0526389	−	0.142127i
$429$	241.819	−	263.834i	0.563681	−	0.614998i
$430$	−183.018	−	112.681i	−0.425624	−	0.262049i
$431$	135.966			0.315467			0.157734	−	0.987482i	$-0.449581\pi$
$431$	135.966			0.315467			0.157734	+	0.987482i	$0.449581\pi$
$432$	288.365	−	321.667i	0.667512	−	0.744599i
$433$	426.207	+	426.207i	0.984312	+	0.984312i	0.999879	−	0.0155664i	$-0.00495515\pi$
$433$	426.207	+	426.207i	0.984312	+	0.984312i	−0.0155664	+	0.999879i	$0.504955\pi$
$434$	14.0739	−	64.3407i	0.0324284	−	0.148250i
$435$	32.9082	+	9.92823i	0.0756511	+	0.0228235i
$436$	−290.823	−	133.623i	−0.667026	−	0.306475i
$437$	239.748	+	239.748i	0.548622	+	0.548622i
$438$	103.268	−	595.037i	0.235772	−	1.35853i
$439$	408.305			0.930080			0.465040	−	0.885290i	$-0.346040\pi$
$439$	408.305			0.930080			0.465040	+	0.885290i	$0.346040\pi$
$440$	269.568	+	53.8500i	0.612656	+	0.122386i
$441$	32.5873	+	373.529i	0.0738940	+	0.847004i
$442$	250.959	+	391.488i	0.567781	+	0.885720i
$443$	−354.483	−	354.483i	−0.800188	−	0.800188i	0.182937	−	0.983125i	$-0.441440\pi$
$443$	−354.483	−	354.483i	−0.800188	−	0.800188i	−0.983125	+	0.182937i	$0.941440\pi$
$444$	324.258	−	136.411i	0.730311	−	0.307232i
$445$	67.8676	−	194.003i	0.152511	−	0.435962i
$446$	−154.427	+	705.985i	−0.346250	+	1.58293i
$447$	−21.8301	−	501.401i	−0.0488368	−	1.12170i
$448$	−151.597	−	84.1400i	−0.338386	−	0.187813i
$449$	−452.663			−1.00816			−0.504079	−	0.863657i	$-0.668168\pi$
$449$	−452.663			−1.00816			−0.504079	+	0.863657i	$0.668168\pi$
$450$	449.943	+	7.18680i	0.999872	+	0.0159707i
$451$		−	349.922i		−	0.775880i
$452$	−127.421	−	344.041i	−0.281904	−	0.761152i
$453$	225.565	−	9.82069i	0.497936	−	0.0216792i
$454$	−65.9070	+	301.302i	−0.145170	+	0.663661i
$455$	−221.945	−	77.6424i	−0.487791	−	0.170643i
$456$	784.751	−	145.123i	1.72095	−	0.318253i
$457$	270.489	−	270.489i	0.591879	−	0.591879i	−0.346260	−	0.938139i	$-0.612548\pi$
$457$	270.489	−	270.489i	0.591879	−	0.591879i	0.938139	+	0.346260i	$0.112548\pi$
$458$	241.491	+	376.719i	0.527274	+	0.822531i
$459$	−220.262	+	286.832i	−0.479873	+	0.624906i
$460$	−3.70721	−	203.894i	−0.00805915	−	0.443249i
$461$		−	582.469i		−	1.26349i	−0.775176	−	0.631745i	$-0.782339\pi$
$461$		−	582.469i		−	1.26349i	0.775176	−	0.631745i	$-0.217661\pi$
$462$	19.1012	−	110.062i	0.0413445	−	0.238229i
$463$	318.146	−	318.146i	0.687140	−	0.687140i	−0.274459	−	0.961599i	$-0.588499\pi$
$463$	318.146	−	318.146i	0.687140	−	0.687140i	0.961599	+	0.274459i	$0.0884986\pi$
$464$	−23.8827	−	27.8195i	−0.0514714	−	0.0599558i
$465$	52.6652	−	174.565i	0.113259	−	0.375408i
$466$	−37.7293	+	172.485i	−0.0809642	+	0.370139i
$467$	−554.211	+	554.211i	−1.18675	+	1.18675i	−0.208786	+	0.977961i	$0.566951\pi$
$467$	−554.211	+	554.211i	−1.18675	+	1.18675i	−0.977961	+	0.208786i	$0.933049\pi$
$468$	−564.938	+	267.151i	−1.20713	+	0.570837i
$469$		−	124.340i		−	0.265116i
$470$	322.494	+	198.553i	0.686158	+	0.422454i
$471$	−224.206	−	205.498i	−0.476022	−	0.436301i
$472$	499.864	−	70.1118i	1.05903	−	0.148542i
$473$	−104.443	+	104.443i	−0.220809	+	0.220809i
$474$	−259.589	−	368.613i	−0.547657	−	0.777665i
$475$	650.025	+	518.212i	1.36847	+	1.09097i
$476$	131.890	+	60.5987i	0.277080	+	0.127308i
$477$	−126.998	+	151.275i	−0.266243	+	0.317138i
$478$	334.832	+	522.327i	0.700485	+	1.09273i
$479$		−	857.141i		−	1.78944i	−0.446629	−	0.894719i	$-0.647375\pi$
$479$		−	857.141i		−	1.78944i	0.446629	−	0.894719i	$-0.352625\pi$
$480$	−400.353	−	264.797i	−0.834068	−	0.551661i
$481$	−508.880			−1.05796
$482$	−201.889	+	129.419i	−0.418857	+	0.268504i
$483$	−82.7904	+	3.60454i	−0.171409	+	0.00746281i
$484$	−123.198	+	268.134i	−0.254542	+	0.553996i
$485$	93.1246	+	193.337i	0.192010	+	0.398632i
$486$	−344.411	−	342.895i	−0.708664	−	0.705546i
$487$	97.7824	+	97.7824i	0.200785	+	0.200785i	0.800336	−	0.599551i	$-0.204654\pi$
$487$	97.7824	+	97.7824i	0.200785	+	0.200785i	−0.599551	+	0.800336i	$0.704654\pi$
$488$	−31.6421	−	225.593i	−0.0648403	−	0.462281i
$489$	192.195	+	176.157i	0.393036	+	0.360240i
$490$	405.300	−	96.4081i	0.827143	−	0.196751i
$491$	770.213			1.56866			0.784331	−	0.620342i	$-0.213006\pi$
$491$	770.213			1.56866			0.784331	+	0.620342i	$0.213006\pi$
$492$	−230.707	+	565.777i	−0.468916	+	1.14995i
$493$	21.7037	+	21.7037i	0.0440238	+	0.0440238i
$494$	−1127.78	−	246.692i	−2.28296	−	0.499376i
$495$	76.3613	−	299.680i	0.154265	−	0.605415i
$496$	−147.571	+	126.688i	−0.297522	+	0.255420i
$497$	−170.179	−	170.179i	−0.342412	−	0.342412i
$498$	85.1031	−	490.368i	0.170890	−	0.984675i
$499$	−66.3836			−0.133033			−0.0665166	−	0.997785i	$-0.521189\pi$
$499$	−66.3836			−0.133033			−0.0665166	+	0.997785i	$0.521189\pi$
$500$	−65.0827	−	495.746i	−0.130165	−	0.991492i
$501$	−115.050	−	105.450i	−0.229640	−	0.210478i
$502$	566.164	−	362.933i	1.12782	−	0.722974i
$503$	−349.224	−	349.224i	−0.694282	−	0.694282i	0.268889	−	0.963171i	$-0.413344\pi$
$503$	−349.224	−	349.224i	−0.694282	−	0.694282i	−0.963171	+	0.268889i	$0.913344\pi$
$504$	−103.449	+	165.362i	−0.205256	+	0.328099i
$505$	−586.626	−	205.218i	−1.16164	−	0.406372i
$506$	−136.910	−	29.9477i	−0.270572	−	0.0591851i
$507$	396.617	−	17.2680i	0.782281	−	0.0340591i
$508$	337.325	−	124.933i	0.664025	−	0.245932i
$509$	−447.822			−0.879807			−0.439904	−	0.898045i	$-0.644987\pi$
$509$	−447.822			−0.879807			−0.439904	+	0.898045i	$0.644987\pi$
$510$	351.015	+	195.588i	0.688265	+	0.383506i
$511$			272.684i			0.533628i
$512$	207.865	+	467.906i	0.405987	+	0.913879i
$513$	−116.861	−	890.176i	−0.227799	−	1.73524i
$514$	−551.629	−	120.664i	−1.07321	−	0.234754i
$515$	402.491	+	835.615i	0.781536	+	1.62255i
$516$	237.730	−	100.010i	0.460717	−	0.193818i
$517$	184.037	−	184.037i	0.355971	−	0.355971i
$518$	−133.719	+	85.7192i	−0.258145	+	0.165481i
$519$	431.293	+	395.304i	0.831007	+	0.761665i
$520$	385.290	+	577.651i	0.740943	+	1.11087i
$521$		−	373.093i		−	0.716109i	−0.933701	−	0.358054i	$-0.883440\pi$
$521$		−	373.093i		−	0.716109i	0.933701	−	0.358054i	$-0.116560\pi$
$522$	−32.6595	+	25.1942i	−0.0625660	+	0.0482648i
$523$	−593.137	+	593.137i	−1.13411	+	1.13411i	−0.144618	+	0.989488i	$0.546195\pi$
$523$	−593.137	+	593.137i	−1.13411	+	1.13411i	−0.989488	+	0.144618i	$0.953805\pi$
$524$	−240.533	+	523.507i	−0.459032	+	0.999058i
$525$	−200.718	+	31.5411i	−0.382321	+	0.0600783i
$526$	298.212	+	65.2311i	0.566943	+	0.124013i
$527$	115.130	−	115.130i	0.218462	−	0.218462i
$528$	−240.709	+	225.557i	−0.455888	+	0.427191i
$529$		−	425.033i		−	0.803466i
$530$	186.882	+	115.060i	0.352608	+	0.217094i
$531$	−49.3529	−	565.703i	−0.0929432	−	1.06535i
$532$	−337.904	+	125.148i	−0.635157	+	0.235240i
$533$	624.988	−	624.988i	1.17259	−	1.17259i
$534$	142.010	+	201.652i	0.265935	+	0.377625i
$535$	35.1874	+	73.0527i	0.0657708	+	0.136547i
$536$	−221.053	+	293.181i	−0.412413	+	0.546979i
$537$	−320.609	+	13.9587i	−0.597036	+	0.0259939i
$538$	470.364	−	301.522i	0.874283	−	0.560449i
$539$		−	286.308i		−	0.531184i
$540$	−321.048	+	434.198i	−0.594534	+	0.804070i
$541$	−46.0398			−0.0851012			−0.0425506	−	0.999094i	$-0.513548\pi$
$541$	−46.0398			−0.0851012			−0.0425506	+	0.999094i	$0.513548\pi$
$542$	381.030	+	594.395i	0.703008	+	1.09667i
$543$	1.51444	+	34.7842i	0.00278902	+	0.0640592i
$544$	−203.250	−	377.362i	−0.373621	−	0.693681i
$545$	377.625	+	132.104i	0.692890	+	0.242392i
$546$	230.695	−	162.463i	0.422519	−	0.297551i
$547$	−586.492	−	586.492i	−1.07220	−	1.07220i	−0.997182	−	0.0750146i	$-0.976100\pi$
$547$	−586.492	−	586.492i	−1.07220	−	1.07220i	−0.0750146	−	0.997182i	$-0.523900\pi$
$548$	−72.2503	+	26.7590i	−0.131844	+	0.0488303i
$549$	−255.307	+	22.2734i	−0.465040	+	0.0405708i
$550$	−341.797	−	35.3276i	−0.621450	−	0.0642320i
$551$	−76.1995			−0.138293
$552$	201.620	+	138.687i	0.365254	+	0.251245i
$553$	143.941	+	143.941i	0.260292	+	0.260292i
$554$	5.47855	−	25.0459i	0.00988908	−	0.0452092i
$555$	−387.492	+	207.874i	−0.698184	+	0.374547i
$556$	−104.754	+	227.991i	−0.188406	+	0.410055i
$557$	413.911	+	413.911i	0.743108	+	0.743108i	0.973175	−	0.230067i	$-0.0738945\pi$
$557$	413.911	+	413.911i	0.743108	+	0.743108i	−0.230067	+	0.973175i	$0.573894\pi$
$558$	133.645	+	173.245i	0.239508	+	0.310475i
$559$	−373.086			−0.667416
$560$	198.547	+	86.8894i	0.354548	+	0.155160i
$561$	186.590	−	203.577i	0.332603	−	0.362883i
$562$	−220.728	−	344.328i	−0.392754	−	0.612684i
$563$	−185.957	−	185.957i	−0.330296	−	0.330296i	0.522403	−	0.852699i	$-0.325036\pi$
$563$	−185.957	−	185.957i	−0.330296	−	0.330296i	−0.852699	+	0.522403i	$0.825036\pi$
$564$	−418.901	+	176.226i	−0.742732	+	0.312458i
$565$	199.011	+	413.167i	0.352231	+	0.731269i
$566$	−2.99759	+	13.7039i	−0.00529610	+	0.0242118i
$567$	179.690	+	125.951i	0.316913	+	0.222137i
$568$	98.7180	+	703.812i	0.173799	+	1.23911i
$569$	745.467			1.31014			0.655068	−	0.755570i	$-0.272640\pi$
$569$	745.467			1.31014			0.655068	+	0.755570i	$0.272640\pi$
$570$	−959.533	+	272.845i	−1.68339	+	0.478675i
$571$		−	406.663i		−	0.712195i	−0.934449	−	0.356097i	$-0.884107\pi$
$571$		−	406.663i		−	0.712195i	0.934449	−	0.356097i	$-0.115893\pi$
$572$	447.481	−	165.732i	0.782310	−	0.289741i
$573$	17.7369	+	407.388i	0.0309545	+	0.710975i
$574$	58.9519	−	269.506i	0.102704	−	0.469523i
$575$	28.5804	+	253.303i	0.0497050	+	0.440526i
$576$	537.906	−	205.994i	0.933864	−	0.357628i
$577$	73.9694	−	73.9694i	0.128197	−	0.128197i	−0.640097	−	0.768294i	$-0.721106\pi$
$577$	73.9694	−	73.9694i	0.128197	−	0.128197i	0.768294	+	0.640097i	$0.221106\pi$
$578$	−118.289	−	184.527i	−0.204652	−	0.319251i
$579$	−179.844	+	196.217i	−0.310611	+	0.338889i
$580$	32.9912	+	31.8129i	0.0568814	+	0.0548499i
$581$			224.718i			0.386778i
$582$	−253.722	−	44.0333i	−0.435949	−	0.0756586i
$583$	106.648	−	106.648i	0.182929	−	0.182929i
$584$	484.783	−	642.962i	0.830108	−	1.10096i
$585$	671.641	−	398.866i	1.14810	−	0.681822i
$586$	118.242	−	540.559i	0.201778	−	0.922456i
$587$	−422.201	+	422.201i	−0.719251	+	0.719251i	−0.968452	−	0.249200i	$-0.919832\pi$
$587$	−422.201	+	422.201i	−0.719251	+	0.719251i	0.249200	+	0.968452i	$0.419832\pi$
$588$	−188.766	+	462.923i	−0.321030	+	0.787284i
$589$			404.208i			0.686261i
$590$	−613.820	+	146.008i	−1.04037	+	0.247472i
$591$	−278.025	+	303.336i	−0.470431	+	0.513259i
$592$	467.690	+	35.6111i	0.790017	+	0.0601538i
$593$	−406.869	+	406.869i	−0.686119	+	0.686119i	−0.961372	−	0.275253i	$-0.911238\pi$
$593$	−406.869	+	406.869i	−0.686119	+	0.686119i	0.275253	+	0.961372i	$0.411238\pi$
$594$	239.239	+	283.700i	0.402759	+	0.477609i
$595$	−171.255	−	59.9097i	−0.287823	−	0.100689i
$596$	279.381	−	608.056i	0.468759	−	1.02023i
$597$	−3.78796	−	87.0033i	−0.00634500	−	0.145734i
$598$	−191.043	−	298.020i	−0.319469	−	0.498362i
$599$			293.225i			0.489525i	0.969583	+	0.244762i	$0.0787100\pi$
$599$			293.225i			0.489525i	−0.969583	+	0.244762i	$0.921290\pi$
$600$	529.349	+	282.470i	0.882249	+	0.470784i
$601$	−1087.24			−1.80905			−0.904523	−	0.426424i	$-0.859773\pi$
$601$	−1087.24			−1.80905			−0.904523	+	0.426424i	$0.859773\pi$
$602$	−98.0363	+	62.8451i	−0.162851	+	0.104394i
$603$	316.369	+	265.597i	0.524658	+	0.440459i
$604$	273.546	+	125.685i	0.452891	+	0.208087i
$605$	121.797	−	348.164i	0.201318	−	0.575478i
$606$	609.755	−	429.409i	1.00620	−	0.708595i
$607$	74.9651	+	74.9651i	0.123501	+	0.123501i	0.766156	−	0.642655i	$-0.222167\pi$
$607$	74.9651	+	74.9651i	0.123501	+	0.123501i	−0.642655	+	0.766156i	$0.722167\pi$
$608$	1019.23	+	305.645i	1.67637	+	0.502706i
$609$	12.5839	−	13.7295i	0.0206632	−	0.0225444i
$610$	65.8949	+	277.022i	0.108024	+	0.454135i
$611$	657.409			1.07596
$612$	−435.912	+	206.137i	−0.712274	+	0.336825i
$613$	22.9005	+	22.9005i	0.0373581	+	0.0373581i	0.725539	−	0.688181i	$-0.241590\pi$
$613$	22.9005	+	22.9005i	0.0373581	+	0.0373581i	−0.688181	+	0.725539i	$0.741590\pi$
$614$	894.903	+	195.751i	1.45750	+	0.318813i
$615$	220.601	−	731.206i	0.358701	−	1.18895i
$616$	89.6684	−	118.926i	0.145566	−	0.193062i
$617$	−115.002	−	115.002i	−0.186389	−	0.186389i	0.607744	−	0.794133i	$-0.292075\pi$
$617$	−115.002	−	115.002i	−0.186389	−	0.186389i	−0.794133	+	0.607744i	$0.792075\pi$
$618$	−1096.60	−	190.315i	−1.77444	−	0.307953i
$619$	−710.704			−1.14815			−0.574074	−	0.818803i	$-0.694638\pi$
$619$	−710.704			−1.14815			−0.574074	+	0.818803i	$0.694638\pi$
$620$	168.755	−	175.005i	0.272185	−	0.282266i
$621$	167.674	−	218.351i	0.270006	−	0.351612i
$622$	−722.275	+	463.006i	−1.16121	+	0.744383i
$623$	−78.7438	−	78.7438i	−0.126394	−	0.126394i
$624$	−832.787	−	27.0627i	−1.33459	−	0.0433697i
$625$	139.266	+	609.287i	0.222825	+	0.974858i
$626$	−398.299	−	87.1240i	−0.636260	−	0.139176i
$627$	29.8201	+	684.918i	0.0475599	+	1.09237i
$628$	−140.839	−	380.270i	−0.224265	−	0.605525i
$629$	−392.657			−0.624256
$630$	109.300	−	217.946i	0.173493	−	0.345946i
$631$			209.771i			0.332443i	0.986088	+	0.166221i	$0.0531566\pi$
$631$			209.771i			0.332443i	−0.986088	+	0.166221i	$0.946843\pi$
$632$	−83.4980	−	595.301i	−0.132117	−	0.941932i
$633$	−1129.78	+	49.1887i	−1.78481	+	0.0777072i
$634$	828.369	+	181.198i	1.30658	+	0.285801i
$635$	−405.102	+	195.126i	−0.637956	+	0.307285i
$636$	−242.749	+	102.121i	−0.381681	+	0.160568i
$637$	511.370	−	511.370i	0.802778	−	0.802778i
$638$	26.5163	−	16.9980i	0.0415616	−	0.0266426i
$639$	796.514	−	69.4892i	1.24650	−	0.108747i
$640$	−313.680	−	557.857i	−0.490126	−	0.871652i
$641$			1193.44i			1.86184i	0.365221	+	0.930921i	$0.380993\pi$
$641$			1193.44i			1.86184i	−0.365221	+	0.930921i	$0.619007\pi$
$642$	−95.8695	−	16.6381i	−0.149329	−	0.0259160i
$643$	−424.387	+	424.387i	−0.660012	+	0.660012i	−0.955383	−	0.295371i	$-0.904557\pi$
$643$	−424.387	+	424.387i	−0.660012	+	0.660012i	0.295371	+	0.955383i	$0.404557\pi$
$644$	−100.401	−	46.1308i	−0.155902	−	0.0716316i
$645$	−284.090	+	152.403i	−0.440450	+	0.236283i
$646$	−870.209	−	190.350i	−1.34707	−	0.294659i
$647$	556.306	−	556.306i	0.859824	−	0.859824i	−0.131493	−	0.991317i	$-0.541977\pi$
$647$	556.306	−	556.306i	0.859824	−	0.859824i	0.991317	+	0.131493i	$0.0419772\pi$
$648$	−199.772	−	616.437i	−0.308290	−	0.951292i
$649$			433.609i			0.668119i
$650$	−547.379	−	673.575i	−0.842122	−	1.03627i
$651$	−72.8296	−	66.7525i	−0.111873	−	0.102538i
$652$	120.730	+	325.976i	0.185169	+	0.499963i
$653$	−730.267	+	730.267i	−1.11833	+	1.11833i	−0.126340	+	0.991987i	$0.540323\pi$
$653$	−730.267	+	730.267i	−1.11833	+	1.11833i	−0.991987	+	0.126340i	$0.959677\pi$
$654$	−392.513	+	276.420i	−0.600174	+	0.422661i
$655$	237.798	−	679.757i	0.363050	−	1.03780i
$656$	−618.137	+	530.664i	−0.942281	+	0.808939i
$657$	−693.815	−	582.470i	−1.05604	−	0.886560i
$658$	172.748	−	110.738i	0.262536	−	0.168295i
$659$		−	929.519i		−	1.41050i	−0.708959	−	0.705250i	$-0.750835\pi$
$659$		−	929.519i		−	1.41050i	0.708959	−	0.705250i	$-0.249165\pi$
$660$	273.039	−	308.991i	0.413696	−	0.468168i
$661$	564.895			0.854607			0.427303	−	0.904108i	$-0.359464\pi$
$661$	564.895			0.854607			0.427303	+	0.904108i	$0.359464\pi$
$662$	96.1997	+	150.068i	0.145317	+	0.226690i
$663$	696.870	−	30.3404i	1.05109	−	0.0457623i
$664$	399.508	−	529.863i	0.601668	−	0.797986i
$665$	405.797	−	195.461i	0.610221	−	0.293926i
$666$	67.5293	−	523.336i	0.101395	−	0.785789i
$667$	−16.5220	−	16.5220i	−0.0247705	−	0.0247705i
$668$	−72.2703	−	195.132i	−0.108189	−	0.292114i
$669$	799.131	+	732.449i	1.19452	+	1.09484i
$670$	240.630	−	390.836i	0.359149	−	0.583337i
$671$	195.692			0.291642
$672$	−223.391	+	133.169i	−0.332428	+	0.198168i
$673$	301.487	+	301.487i	0.447975	+	0.447975i	0.894681	−	0.446706i	$-0.147403\pi$
$673$	301.487	+	301.487i	0.447975	+	0.447975i	−0.446706	+	0.894681i	$0.647403\pi$
$674$	−106.962	+	488.992i	−0.158698	+	0.725508i
$675$	348.494	−	578.080i	0.516288	−	0.856415i
$676$	480.983	+	220.995i	0.711513	+	0.326915i
$677$	−530.496	−	530.496i	−0.783598	−	0.783598i	0.196838	−	0.980436i	$-0.436933\pi$
$677$	−530.496	−	530.496i	−0.783598	−	0.783598i	−0.980436	+	0.196838i	$0.936933\pi$
$678$	−542.213	−	94.1007i	−0.799724	−	0.138792i
$679$	116.272			0.171240
$680$	297.294	+	445.722i	0.437197	+	0.655473i
$681$	341.055	+	312.596i	0.500815	+	0.459026i
$682$	−90.1673	−	140.658i	−0.132210	−	0.206244i
$683$	378.401	+	378.401i	0.554028	+	0.554028i	0.927601	−	0.373573i	$-0.121867\pi$
$683$	378.401	+	378.401i	0.554028	+	0.554028i	−0.373573	+	0.927601i	$0.621867\pi$
$684$	403.358	−	1127.08i	0.589705	−	1.64778i
$685$	86.7672	−	41.7932i	0.126667	−	0.0610120i
$686$	104.967	−	479.870i	0.153013	−	0.699519i
$687$	670.580	−	29.1958i	0.976099	−	0.0424975i
$688$	342.887	+	26.1083i	0.498383	+	0.0379481i
$689$	380.962			0.552920
$690$	−267.210	−	148.891i	−0.387261	−	0.215784i
$691$			690.583i			0.999396i	0.866200	+	0.499698i	$0.166556\pi$
$691$			690.583i			0.999396i	−0.866200	+	0.499698i	$0.833444\pi$
$692$	270.923	+	731.503i	0.391508	+	1.05708i
$693$	−128.332	−	107.737i	−0.185184	−	0.155465i
$694$	206.432	−	943.730i	0.297452	−	1.35984i
$695$	103.563	−	296.039i	0.149011	−	0.425955i
$696$	−54.0802	+	10.0010i	−0.0777015	+	0.0143693i
$697$	482.247	−	482.247i	0.691890	−	0.691890i
$698$	205.215	+	320.129i	0.294004	+	0.458638i
$699$	195.242	+	178.950i	0.279316	+	0.256009i
$700$	−257.297	−	84.7921i	−0.367567	−	0.121132i
$701$			129.593i			0.184869i	0.995719	+	0.0924343i	$0.0294648\pi$
$701$			129.593i			0.184869i	−0.995719	+	0.0924343i	$0.970535\pi$
$702$	−79.4100	+	934.010i	−0.113120	+	1.33050i
$703$	689.289	−	689.289i	0.980496	−	0.980496i
$704$	−422.859	+	121.002i	−0.600652	+	0.171879i
$705$	500.591	−	268.546i	0.710058	−	0.380917i
$706$	40.1347	−	183.481i	0.0568480	−	0.259888i
$707$	−238.105	+	238.105i	−0.336783	+	0.336783i
$708$	285.883	−	701.089i	0.403789	−	0.990238i
$709$		−	86.8545i		−	0.122503i	−0.998122	−	0.0612514i	$-0.980491\pi$
$709$		−	86.8545i		−	0.122503i	0.998122	−	0.0612514i	$-0.0195091\pi$
$710$	−205.581	−	864.263i	−0.289550	−	1.21727i
$711$	−673.710	+	58.7756i	−0.947553	+	0.0826661i
$712$	45.6780	+	325.662i	0.0641545	+	0.457391i
$713$	−87.6423	+	87.6423i	−0.122920	+	0.122920i
$714$	178.007	−	125.358i	0.249309	−	0.175571i
$715$	−537.392	+	258.846i	−0.751597	+	0.362022i
$716$	−388.807	−	178.643i	−0.543026	−	0.249501i
$717$	929.769	−	40.4804i	1.29675	−	0.0564581i
$718$	433.901	+	676.872i	0.604319	+	0.942719i
$719$		−	104.099i		−	0.144782i	−0.997376	−	0.0723912i	$-0.976937\pi$
$719$		−	104.099i		−	0.144782i	0.997376	−	0.0723912i	$-0.0230630\pi$
$720$	−645.189	+	319.580i	−0.896096	+	0.443861i
$721$	502.534			0.696996
$722$	1253.92	−	803.812i	1.73673	−	1.11331i
$723$	15.6464	+	359.373i	0.0216410	+	0.497059i
$724$	−19.3817	+	42.1833i	−0.0267703	+	0.0582642i
$725$	−44.7957	−	35.7120i	−0.0617872	−	0.0492579i
$726$	254.855	+	361.891i	0.351040	+	0.498472i
$727$	−252.054	−	252.054i	−0.346704	−	0.346704i	0.512176	−	0.858880i	$-0.328839\pi$
$727$	−252.054	−	252.054i	−0.346704	−	0.346704i	−0.858880	+	0.512176i	$0.828839\pi$
$728$	372.567	−	52.2569i	0.511768	−	0.0717814i
$729$	−704.298	+	188.161i	−0.966116	+	0.258109i
$730$	−527.716	+	857.126i	−0.722898	+	1.17415i
$731$	−287.877			−0.393812
$732$	−316.408	−	129.021i	−0.432251	−	0.176259i
$733$	−795.114	−	795.114i	−1.08474	−	1.08474i	−0.996060	−	0.0886791i	$-0.971735\pi$
$733$	−795.114	−	795.114i	−1.08474	−	1.08474i	−0.0886791	−	0.996060i	$-0.528265\pi$
$734$	506.320	+	110.753i	0.689809	+	0.150889i
$735$	180.497	−	598.278i	0.245574	−	0.813984i
$736$	154.724	+	287.267i	0.210223	+	0.390308i
$737$	−223.037	−	223.037i	−0.302629	−	0.302629i
$738$	559.805	+	725.679i	0.758543	+	0.983305i
$739$	−622.137			−0.841863			−0.420931	−	0.907092i	$-0.638297\pi$
$739$	−622.137			−0.841863			−0.420931	+	0.907092i	$0.638297\pi$
$740$	−586.208	+	10.6584i	−0.792173	+	0.0144033i
$741$	−1170.06	+	1276.58i	−1.57902	+	1.72278i
$742$	100.106	−	64.1718i	0.134914	−	0.0864850i
$743$	−487.618	−	487.618i	−0.656283	−	0.656283i	0.298216	−	0.954499i	$-0.403609\pi$
$743$	−487.618	−	487.618i	−0.656283	−	0.656283i	−0.954499	+	0.298216i	$0.903609\pi$
$744$	53.0514	+	286.874i	0.0713056	+	0.385583i
$745$	−276.204	+	789.542i	−0.370743	+	1.05979i
$746$	−216.113	−	47.2726i	−0.289696	−	0.0633681i
$747$	−571.770	−	480.011i	−0.765422	−	0.642585i
$748$	345.281	−	127.880i	0.461606	−	0.170963i
$749$	43.9335			0.0586562
$750$	−691.958	−	289.300i	−0.922610	−	0.385734i
$751$			1089.00i			1.45007i	0.688711	+	0.725036i	$0.258177\pi$
$751$			1089.00i			1.45007i	−0.688711	+	0.725036i	$0.741823\pi$
$752$	−604.197	−	46.0050i	−0.803454	−	0.0611769i
$753$	−43.8778	−	1007.80i	−0.0582706	−	1.33838i
$754$	77.7199	+	17.0005i	0.103077	+	0.0225470i
$755$	−355.191	−	124.256i	−0.470452	−	0.164577i
$756$	136.464	+	258.808i	0.180508	+	0.342338i
$757$	−628.144	+	628.144i	−0.829781	+	0.829781i	−0.987486	−	0.157705i	$-0.949590\pi$
$757$	−628.144	+	628.144i	−0.829781	+	0.829781i	0.157705	+	0.987486i	$0.449590\pi$
$758$	195.576	−	125.372i	0.258016	−	0.165398i
$759$	−142.042	+	154.973i	−0.187143	+	0.204181i
$760$	−1304.32	−	260.557i	−1.71622	−	0.342838i
$761$		−	723.259i		−	0.950407i	−0.879876	−	0.475203i	$-0.842375\pi$
$761$		−	723.259i		−	0.950407i	0.879876	−	0.475203i	$-0.157625\pi$
$762$	92.2638	−	531.628i	0.121081	−	0.697675i
$763$	153.274	−	153.274i	0.200883	−	0.200883i
$764$	−226.997	+	494.046i	−0.297116	+	0.646657i
$765$	518.245	−	307.769i	0.677444	−	0.402312i
$766$	1215.11	+	265.794i	1.58631	+	0.346990i
$767$	−774.460	+	774.460i	−1.00973	+	1.00973i
$768$	763.485	+	83.1500i	0.994122	+	0.108268i
$769$		−	180.270i		−	0.234421i	−0.993107	−	0.117210i	$-0.962605\pi$
$769$		−	180.270i		−	0.234421i	0.993107	−	0.117210i	$-0.0373952\pi$
$770$	−97.6096	+	158.539i	−0.126766	+	0.205895i
$771$	−572.307	+	624.410i	−0.742292	+	0.809870i
$772$	−332.798	+	123.257i	−0.431085	+	0.159659i
$773$	482.107	−	482.107i	0.623683	−	0.623683i	−0.322788	−	0.946471i	$-0.604620\pi$
$773$	482.107	−	482.107i	0.623683	−	0.623683i	0.946471	+	0.322788i	$0.104620\pi$
$774$	49.5091	−	383.684i	0.0639653	−	0.495716i
$775$	−189.438	+	237.623i	−0.244436	+	0.306611i
$776$	−274.157	−	206.710i	−0.353296	−	0.266379i
$777$	10.3633	+	238.027i	0.0133375	+	0.306341i
$778$	−203.709	+	130.585i	−0.261837	+	0.167848i
$779$			1693.12i			2.17345i
$780$	1039.55	−	64.2121i	1.33276	−	0.0823232i
$781$	−610.525			−0.781722
$782$	−147.410	−	229.956i	−0.188504	−	0.294061i
$783$	8.05334	+	61.3455i	0.0102852	+	0.0783468i
$784$	−505.764	+	434.193i	−0.645107	+	0.553818i
$785$	219.967	+	456.676i	0.280213	+	0.581752i
$786$	497.580	+	706.557i	0.633053	+	0.898928i
$787$	279.225	+	279.225i	0.354797	+	0.354797i	0.861891	−	0.507094i	$-0.169280\pi$
$787$	279.225	+	279.225i	0.354797	+	0.354797i	−0.507094	+	0.861891i	$0.669280\pi$
$788$	−514.479	+	190.545i	−0.652892	+	0.241809i
$789$	309.391	−	337.558i	0.392130	−	0.427830i
$790$	173.885	+	731.014i	0.220108	+	0.925334i
$791$	248.477			0.314130
$792$	111.058	+	482.186i	0.140225	+	0.608820i
$793$	349.521	+	349.521i	0.440758	+	0.440758i
$794$	−331.978	+	1517.68i	−0.418108	+	1.91143i
$795$	290.088	−	155.620i	0.364890	−	0.195749i
$796$	48.4782	−	105.510i	0.0609023	−	0.132550i
$797$	−861.626	−	861.626i	−1.08109	−	1.08109i	−0.996408	−	0.0846783i	$-0.973014\pi$
$797$	−861.626	−	861.626i	−1.08109	−	1.08109i	−0.0846783	−	0.996408i	$-0.526986\pi$
$798$	−92.4222	+	532.541i	−0.115817	+	0.667345i
$799$	507.264			0.634873
$800$	455.937	+	657.360i	0.569921	+	0.821699i
$801$	368.557	−	32.1535i	0.460121	−	0.0401417i
$802$	191.689	+	299.028i	0.239013	+	0.372853i
$803$	489.134	+	489.134i	0.609133	+	0.609133i
$804$	213.571	+	507.672i	0.265636	+	0.631433i
$805$	130.368	+	45.6062i	0.161947	+	0.0566537i
$806$	90.1807	−	412.273i	0.111887	−	0.511505i
$807$	−36.4533	−	837.273i	−0.0451714	−	1.03751i
$808$	984.738	−	138.121i	1.21874	−	0.170942i
$809$	430.022			0.531548			0.265774	−	0.964035i	$-0.414373\pi$
$809$	430.022			0.531548			0.265774	+	0.964035i	$0.414373\pi$
$810$	321.068	+	743.650i	0.396381	+	0.918086i
$811$		−	1351.37i		−	1.66630i	−0.553047	−	0.833150i	$-0.686535\pi$
$811$		−	1351.37i		−	1.66630i	0.553047	−	0.833150i	$-0.313465\pi$
$812$	23.2863	−	8.62442i	0.0286777	−	0.0106212i
$813$	1058.06	−	46.0658i	1.30142	−	0.0566614i
$814$	−86.1013	+	393.623i	−0.105776	+	0.483567i
$815$	−188.561	−	391.473i	−0.231363	−	0.480335i
$816$	−642.587	−	20.8819i	−0.787484	−	0.0255905i
$817$	505.353	−	505.353i	0.618547	−	0.618547i
$818$	−376.500	−	587.328i	−0.460269	−	0.718005i
$819$	−36.7845	−	421.639i	−0.0449139	−	0.514822i
$820$	706.869	−	733.050i	0.862036	−	0.893964i
$821$		−	901.925i		−	1.09857i	−0.835636	−	0.549284i	$-0.814900\pi$
$821$		−	901.925i		−	1.09857i	0.835636	−	0.549284i	$-0.185100\pi$
$822$	−19.7616	+	113.867i	−0.0240409	+	0.138525i
$823$	−512.252	+	512.252i	−0.622421	+	0.622421i	−0.946150	−	0.323729i	$-0.895063\pi$
$823$	−512.252	+	512.252i	−0.622421	+	0.622421i	0.323729	+	0.946150i	$0.395063\pi$
$824$	−1184.93	−	893.415i	−1.43802	−	1.08424i
$825$	−303.466	+	416.621i	−0.367838	+	0.504996i
$826$	−73.0508	+	333.961i	−0.0884393	+	0.404312i
$827$	683.717	−	683.717i	0.826744	−	0.826744i	−0.160321	−	0.987065i	$-0.551253\pi$
$827$	683.717	−	683.717i	0.826744	−	0.826744i	0.987065	+	0.160321i	$0.0512530\pi$
$828$	331.838	−	156.922i	0.400770	−	0.189519i
$829$		−	1001.78i		−	1.20842i	−0.796827	−	0.604208i	$-0.793490\pi$
$829$		−	1001.78i		−	1.20842i	0.796827	−	0.604208i	$-0.206510\pi$
$830$	−434.889	+	706.354i	−0.523962	+	0.851029i
$831$	−28.3504	−	25.9847i	−0.0341160	−	0.0312692i
$832$	−971.380	−	539.140i	−1.16752	−	0.648005i
$833$	394.578	−	394.578i	0.473683	−	0.473683i
$834$	216.699	+	307.711i	0.259832	+	0.368957i
$835$	112.874	+	234.340i	0.135179	+	0.280646i
$836$	−381.636	+	830.610i	−0.456503	+	0.993553i
$837$	325.413	−	42.7197i	0.388785	−	0.0510391i
$838$	−112.933	−	176.173i	−0.134765	−	0.210230i
$839$		−	189.192i		−	0.225497i	−0.993624	−	0.112749i	$-0.964035\pi$
$839$		−	189.192i		−	0.225497i	0.993624	−	0.112749i	$-0.0359654\pi$
$840$	262.348	−	191.982i	0.312319	−	0.228550i
$841$	−835.749			−0.993756
$842$	349.621	−	224.120i	0.415227	−	0.266176i
$843$	−612.923	+	26.6855i	−0.727073	+	0.0316554i
$844$	−1370.10	−	629.515i	−1.62335	−	0.745871i
$845$	−624.541	−	218.482i	−0.739102	−	0.258558i
$846$	−87.2393	+	676.084i	−0.103120	+	0.799154i
$847$	−141.316	−	141.316i	−0.166843	−	0.166843i
$848$	−350.126	−	26.6595i	−0.412885	−	0.0314381i
$849$	15.5119	+	14.2176i	0.0182708	+	0.0167462i
$850$	−422.363	−	519.737i	−0.496898	−	0.611456i
$851$	298.910			0.351246
$852$	987.138	+	402.525i	1.15861	+	0.472447i
$853$	−430.775	−	430.775i	−0.505011	−	0.505011i	0.407980	−	0.912991i	$-0.366233\pi$
$853$	−430.775	−	430.775i	−0.505011	−	0.505011i	−0.912991	+	0.407980i	$0.866233\pi$
$854$	150.720	+	32.9685i	0.176487	+	0.0386048i
$855$	−369.479	+	1450.02i	−0.432140	+	1.69593i
$856$	−103.591	−	78.1059i	−0.121018	−	0.0912452i
$857$	684.012	+	684.012i	0.798147	+	0.798147i	0.982803	−	0.184656i	$-0.0591172\pi$
$857$	684.012	+	684.012i	0.798147	+	0.798147i	−0.184656	+	0.982803i	$0.559117\pi$
$858$	122.393	−	705.237i	0.142650	−	0.821955i
$859$	1397.70			1.62712			0.813560	−	0.581481i	$-0.197527\pi$
$859$	1397.70			1.62712			0.813560	+	0.581481i	$0.197527\pi$
$860$	−429.779	+	7.81425i	−0.499743	+	0.00908634i
$861$	−305.064	−	279.609i	−0.354314	−	0.324749i
$862$	228.933	−	146.755i	0.265584	−	0.170249i
$863$	−90.1987	−	90.1987i	−0.104518	−	0.104518i	0.652914	−	0.757432i	$-0.273546\pi$
$863$	−90.1987	−	90.1987i	−0.104518	−	0.104518i	−0.757432	+	0.652914i	$0.773546\pi$
$864$	138.344	−	852.852i	0.160120	−	0.987098i
$865$	−423.138	−	878.481i	−0.489177	−	1.01558i
$866$	1177.65	+	257.600i	1.35987	+	0.297459i
$867$	−328.468	+	14.3009i	−0.378855	+	0.0164947i
$868$	−45.7491	−	123.524i	−0.0527063	−	0.142309i
$869$	516.396			0.594242
$870$	66.1252	−	18.8028i	0.0760059	−	0.0216124i
$871$		−	796.724i		−	0.914724i
$872$	−633.899	+	88.9118i	−0.726949	+	0.101963i
$873$	−248.363	+	295.841i	−0.284494	+	0.338878i
$874$	662.446	+	144.904i	0.757948	+	0.165794i
$875$	330.163	+	75.2763i	0.377329	+	0.0860300i
$876$	−468.374	−	1113.36i	−0.534674	−	1.27095i
$877$	19.3296	−	19.3296i	0.0220406	−	0.0220406i	−0.696001	−	0.718041i	$-0.745039\pi$
$877$	19.3296	−	19.3296i	0.0220406	−	0.0220406i	0.718041	+	0.696001i	$0.245039\pi$
$878$	687.483	−	440.703i	0.783010	−	0.501940i
$879$	−611.879	−	560.822i	−0.696108	−	0.638022i
$880$	512.008	−	200.288i	0.581828	−	0.227600i
$881$			721.297i			0.818725i	0.912372	+	0.409363i	$0.134249\pi$
$881$			721.297i			0.818725i	−0.912372	+	0.409363i	$0.865751\pi$
$882$	458.036	+	593.756i	0.519315	+	0.673192i
$883$	941.983	−	941.983i	1.06680	−	1.06680i	0.0691949	−	0.997603i	$-0.477957\pi$
$883$	941.983	−	941.983i	1.06680	−	1.06680i	0.997603	−	0.0691949i	$-0.0220430\pi$
$884$	845.104	+	388.296i	0.956000	+	0.439248i
$885$	−273.360	+	906.082i	−0.308881	+	1.02382i
$886$	−979.471	−	214.250i	−1.10550	−	0.241817i
$887$	489.902	−	489.902i	0.552313	−	0.552313i	−0.374795	−	0.927108i	$-0.622287\pi$
$887$	489.902	−	489.902i	0.552313	−	0.552313i	0.927108	+	0.374795i	$0.122287\pi$
$888$	398.734	−	579.669i	0.449025	−	0.652781i
$889$			243.626i			0.274045i
$890$	−95.1247	−	399.905i	−0.106882	−	0.449331i
$891$	548.252	−	96.3944i	0.615322	−	0.108187i
$892$	501.986	+	1355.38i	0.562765	+	1.51949i
$893$	−890.475	+	890.475i	−0.997172	+	0.997172i
$894$	−577.942	−	820.671i	−0.646468	−	0.917976i
$895$	504.853	+	176.612i	0.564082	+	0.197331i
$896$	−346.067	+	21.9551i	−0.386236	+	0.0245035i
$897$	−530.492	+	23.0966i	−0.591407	+	0.0257487i
$898$	−762.171	+	488.581i	−0.848743	+	0.544077i
$899$		−	27.8555i		−	0.0309850i
$900$	765.347	−	473.544i	0.850386	−	0.526160i
$901$	293.954			0.326253
$902$	−377.687	−	589.180i	−0.418722	−	0.653193i
$903$	7.59784	+	174.510i	0.00841399	+	0.193256i
$904$	−585.884	−	441.746i	−0.648101	−	0.488658i
$905$	19.1613	−	54.7736i	0.0211727	−	0.0605234i
$906$	369.195	−	259.999i	0.407500	−	0.286974i
$907$	−193.827	−	193.827i	−0.213701	−	0.213701i	0.592137	−	0.805838i	$-0.298285\pi$
$907$	−193.827	−	193.827i	−0.213701	−	0.213701i	−0.805838	+	0.592137i	$0.798285\pi$
$908$	214.239	+	578.454i	0.235946	+	0.637064i
$909$	−97.2258	−	1114.44i	−0.106959	−	1.22601i
$910$	−457.502	+	108.825i	−0.502750	+	0.119588i
$911$	−830.304			−0.911421			−0.455710	−	0.890128i	$-0.650615\pi$
$911$	−830.304			−0.911421			−0.455710	+	0.890128i	$0.650615\pi$
$912$	1164.68	−	1091.37i	1.27707	−	1.19668i
$913$	403.093	+	403.093i	0.441504	+	0.441504i
$914$	163.484	−	747.386i	0.178866	−	0.817709i
$915$	408.923	+	123.370i	0.446910	+	0.134830i
$916$	813.222	+	373.647i	0.887797	+	0.407911i
$917$	−275.906	−	275.906i	−0.300879	−	0.300879i
$918$	−61.2736	+	720.692i	−0.0667468	+	0.785067i
$919$	1072.00			1.16649			0.583245	−	0.812296i	$-0.301783\pi$
$919$	1072.00			1.16649			0.583245	+	0.812296i	$0.301783\pi$
$920$	−226.315	−	339.305i	−0.245994	−	0.368810i
$921$	928.448	−	1012.97i	1.00809	−	1.09986i
$922$	−628.687	−	980.731i	−0.681873	−	1.06370i
$923$	−1090.45	−	1090.45i	−1.18141	−	1.18141i
$924$	−86.6334	−	205.933i	−0.0937591	−	0.222871i
$925$	728.260	−	82.1703i	0.787308	−	0.0888328i
$926$	192.288	−	879.068i	0.207654	−	0.949317i
$927$	−1073.44	+	1278.64i	−1.15798	+	1.37934i
$928$	−70.2394	−	21.0632i	−0.0756890	−	0.0226974i
$929$	−1289.64			−1.38821			−0.694103	−	0.719876i	$-0.744199\pi$
$929$	−1289.64			−1.38821			−0.694103	+	0.719876i	$0.744199\pi$
$930$	−99.7412	−	350.767i	−0.107249	−	0.377169i
$931$			1385.32i			1.48799i
$932$	122.644	+	331.144i	0.131592	+	0.355304i
$933$	55.9764	+	1285.69i	0.0599962	+	1.37801i
$934$	−334.966	+	1531.34i	−0.358636	+	1.63955i
$935$	−414.657	+	199.728i	−0.443484	+	0.213613i
$936$	−662.864	+	1059.58i	−0.708188	+	1.13203i
$937$	−507.002	+	507.002i	−0.541091	+	0.541091i	−0.923849	−	0.382758i	$-0.874974\pi$
$937$	−507.002	+	507.002i	−0.541091	+	0.541091i	0.382758	+	0.923849i	$0.374974\pi$
$938$	−134.206	−	209.357i	−0.143076	−	0.223195i
$939$	−413.229	+	450.849i	−0.440073	+	0.480138i
$940$	757.307	−	13.7694i	0.805646	−	0.0146483i
$941$			707.695i			0.752067i	0.926606	+	0.376033i	$0.122712\pi$
$941$			707.695i			0.752067i	−0.926606	+	0.376033i	$0.877288\pi$
$942$	−599.310	−	104.010i	−0.636211	−	0.110414i
$943$	−367.111	+	367.111i	−0.389301	+	0.389301i
$944$	765.970	−	657.578i	0.811409	−	0.696586i
$945$	−200.246	−	306.035i	−0.211901	−	0.323847i
$946$	−63.1252	+	288.585i	−0.0667286	+	0.305058i
$947$	233.033	−	233.033i	0.246075	−	0.246075i	−0.573283	−	0.819358i	$-0.694330\pi$
$947$	233.033	−	233.033i	0.246075	−	0.246075i	0.819358	+	0.573283i	$0.194330\pi$
$948$	−834.945	−	340.465i	−0.880744	−	0.359140i
$949$			1747.26i			1.84116i
$950$	1653.81	+	170.935i	1.74085	+	0.179932i
$951$	859.420	−	937.662i	0.903701	−	0.985974i
$952$	287.476	−	40.3220i	0.301971	−	0.0423550i
$953$	414.033	−	414.033i	0.434452	−	0.434452i	−0.455688	−	0.890140i	$-0.650607\pi$
$953$	414.033	−	414.033i	0.434452	−	0.434452i	0.890140	+	0.455688i	$0.150607\pi$
$954$	−50.5544	+	391.784i	−0.0529920	+	0.410675i
$955$	224.416	−	641.503i	0.234990	−	0.671731i
$956$	1127.54	+	518.067i	1.17944	+	0.541911i
$957$	−2.05502	−	47.2004i	−0.00214735	−	0.0493212i
$958$	−925.153	−	1443.21i	−0.965713	−	1.50648i
$959$		−	52.1813i		−	0.0544122i
$960$	−959.902	−	13.7324i	−0.999898	−	0.0143046i
$961$	813.238			0.846241
$962$	−856.826	+	549.259i	−0.890671	+	0.570955i
$963$	−93.8447	+	111.784i	−0.0974504	+	0.116079i
$964$	−200.243	+	435.817i	−0.207721	+	0.452093i
$965$	399.665	−	192.507i	0.414161	−	0.199489i
$966$	−135.508	+	95.4288i	−0.140277	+	0.0987875i
$967$	534.588	+	534.588i	0.552831	+	0.552831i	0.927257	−	0.374426i	$-0.122160\pi$
$967$	534.588	+	534.588i	0.552831	+	0.552831i	−0.374426	+	0.927257i	$0.622160\pi$
$968$	81.9752	+	584.444i	0.0846851	+	0.603765i
$969$	−902.828	+	985.022i	−0.931711	+	1.01653i
$970$	365.476	+	225.016i	0.376779	+	0.231976i
$971$	−438.396			−0.451490			−0.225745	−	0.974186i	$-0.572482\pi$
$971$	−438.396			−0.451490			−0.225745	+	0.974186i	$0.572482\pi$
$972$	−950.004	−	205.611i	−0.977371	−	0.211533i
$973$	−120.159	−	120.159i	−0.123493	−	0.123493i
$974$	270.182	+	59.0997i	0.277394	+	0.0606773i
$975$	−1286.13	+	202.104i	−1.31911	+	0.207287i
$976$	−296.771	−	345.689i	−0.304068	−	0.354190i
$977$	1230.19	+	1230.19i	1.25915	+	1.25915i	0.951501	+	0.307644i	$0.0995406\pi$
$977$	1230.19	+	1230.19i	1.25915	+	1.25915i	0.307644	+	0.951501i	$0.400459\pi$
$978$	513.743	+	89.1597i	0.525299	+	0.0911654i
$979$	−282.497			−0.288557
$980$	578.365	−	599.787i	0.590169	−	0.612027i
$981$	62.5865	+	717.392i	0.0637987	+	0.731287i
$982$	1296.85	−	831.328i	1.32062	−	0.846566i
$983$	1245.00	+	1245.00i	1.26653	+	1.26653i	0.947867	+	0.318665i	$0.103235\pi$
$983$	1245.00	+	1245.00i	1.26653	+	1.26653i	0.318665	+	0.947867i	$0.396765\pi$
$984$	222.218	+	1201.64i	0.225832	+	1.22118i
$985$	617.852	−	297.601i	0.627260	−	0.302133i
$986$	59.9695	+	13.1177i	0.0608210	+	0.0133040i
$987$	−13.3880	−	307.501i	−0.0135644	−	0.311551i
$988$	−2165.17	+	801.903i	−2.19147	+	0.811643i
$989$	219.146			0.221584
$990$	−194.886	−	587.007i	−0.196855	−	0.592936i
$991$		−	1328.35i		−	1.34041i	−0.742176	−	0.670205i	$-0.766206\pi$
$991$		−	1328.35i		−	1.34041i	0.742176	−	0.670205i	$-0.233794\pi$
$992$	−111.732	+	372.592i	−0.112633	+	0.375597i
$993$	267.130	−	11.6303i	0.269013	−	0.0117123i
$994$	−470.220	−	102.856i	−0.473059	−	0.103477i
$995$	−47.9270	+	137.002i	−0.0481678	+	0.137690i
$996$	−385.985	−	917.512i	−0.387536	−	0.921197i
$997$	−553.349	+	553.349i	−0.555014	+	0.555014i	−0.927884	−	0.372870i	$-0.878374\pi$
$997$	−553.349	+	553.349i	−0.555014	+	0.555014i	0.372870	+	0.927884i	$0.378374\pi$
$998$	−111.773	+	71.6510i	−0.111997	+	0.0717945i
$999$	−627.771	−	482.073i	−0.628400	−	0.482555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.l.a.23.16	yes	40
3.2	odd	2	inner	60.3.l.a.23.5	✓	40
4.3	odd	2	inner	60.3.l.a.23.6	yes	40
5.2	odd	4	inner	60.3.l.a.47.15	yes	40
5.3	odd	4		300.3.l.g.107.6		40
5.4	even	2		300.3.l.g.143.5		40
12.11	even	2	inner	60.3.l.a.23.15	yes	40
15.2	even	4	inner	60.3.l.a.47.6	yes	40
15.8	even	4		300.3.l.g.107.15		40
15.14	odd	2		300.3.l.g.143.16		40
20.3	even	4		300.3.l.g.107.16		40
20.7	even	4	inner	60.3.l.a.47.5	yes	40
20.19	odd	2		300.3.l.g.143.15		40
60.23	odd	4		300.3.l.g.107.5		40
60.47	odd	4	inner	60.3.l.a.47.16	yes	40
60.59	even	2		300.3.l.g.143.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.5	✓	40	3.2	odd	2	inner
60.3.l.a.23.6	yes	40	4.3	odd	2	inner
60.3.l.a.23.15	yes	40	12.11	even	2	inner
60.3.l.a.23.16	yes	40	1.1	even	1	trivial
60.3.l.a.47.5	yes	40	20.7	even	4	inner
60.3.l.a.47.6	yes	40	15.2	even	4	inner
60.3.l.a.47.15	yes	40	5.2	odd	4	inner
60.3.l.a.47.16	yes	40	60.47	odd	4	inner
300.3.l.g.107.5		40	60.23	odd	4
300.3.l.g.107.6		40	5.3	odd	4
300.3.l.g.107.15		40	15.8	even	4
300.3.l.g.107.16		40	20.3	even	4
300.3.l.g.143.5		40	5.4	even	2
300.3.l.g.143.6		40	60.59	even	2
300.3.l.g.143.15		40	20.19	odd	2
300.3.l.g.143.16		40	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68375 - 1.07935i) q^{2} +(-0.130491 - 2.99716i) q^{3} +(1.67002 - 3.63470i) q^{4} +(-1.65103 + 4.71955i) q^{5} +(-3.45469 - 4.90562i) q^{6} +(1.91561 + 1.91561i) q^{7} +(-1.11122 - 7.92245i) q^{8} +(-8.96594 + 0.782204i) q^{9} +O(q^{10})\)	\(q+(1.68375 - 1.07935i) q^{2} +(-0.130491 - 2.99716i) q^{3} +(1.67002 - 3.63470i) q^{4} +(-1.65103 + 4.71955i) q^{5} +(-3.45469 - 4.90562i) q^{6} +(1.91561 + 1.91561i) q^{7} +(-1.11122 - 7.92245i) q^{8} +(-8.96594 + 0.782204i) q^{9} +(2.31412 + 9.72856i) q^{10} +6.87236 q^{11} +(-11.1117 - 4.53101i) q^{12} +(12.2746 + 12.2746i) q^{13} +(5.29303 + 1.15780i) q^{14} +(14.3607 + 4.33254i) q^{15} +(-10.4221 - 12.1400i) q^{16} +(9.47120 + 9.47120i) q^{17} +(-14.2521 + 10.9944i) q^{18} -33.2524 q^{19} +(14.3969 + 13.8827i) q^{20} +(5.49143 - 5.99137i) q^{21} +(11.5713 - 7.41767i) q^{22} +(-7.20994 - 7.20994i) q^{23} +(-23.5998 + 4.36430i) q^{24} +(-19.5482 - 15.5842i) q^{25} +(33.9159 + 7.41877i) q^{26} +(3.51436 + 26.7703i) q^{27} +(10.1618 - 3.76357i) q^{28} +2.29155 q^{29} +(28.8561 - 8.20527i) q^{30} -12.1558i q^{31} +(-30.6515 - 9.19168i) q^{32} +(-0.896780 - 20.5976i) q^{33} +(26.1698 + 5.72440i) q^{34} +(-12.2036 + 5.87810i) q^{35} +(-12.1302 + 33.8948i) q^{36} +(-20.7290 + 20.7290i) q^{37} +(-55.9886 + 35.8909i) q^{38} +(35.1872 - 38.3906i) q^{39} +(39.2250 + 7.83574i) q^{40} -50.9173i q^{41} +(2.77942 - 16.0151i) q^{42} +(-15.1975 + 15.1975i) q^{43} +(11.4770 - 24.9790i) q^{44} +(11.1114 - 43.6066i) q^{45} +(-19.9218 - 4.35769i) q^{46} +(26.7793 - 26.7793i) q^{47} +(-35.0256 + 32.8208i) q^{48} -41.6608i q^{49} +(-49.7350 - 5.14053i) q^{50} +(27.1508 - 29.6226i) q^{51} +(65.1132 - 24.1157i) q^{52} +(15.5183 - 15.5183i) q^{53} +(34.8118 + 41.2812i) q^{54} +(-11.3465 + 32.4344i) q^{55} +(13.0477 - 17.3050i) q^{56} +(4.33913 + 99.6627i) q^{57} +(3.85839 - 2.47338i) q^{58} +63.0946i q^{59} +(39.7300 - 44.9614i) q^{60} +28.4752 q^{61} +(-13.1203 - 20.4672i) q^{62} +(-18.6737 - 15.6769i) q^{63} +(-61.5304 + 17.6071i) q^{64} +(-78.1961 + 37.6648i) q^{65} +(-23.7419 - 33.7132i) q^{66} +(-32.4542 - 32.4542i) q^{67} +(50.2420 - 18.6079i) q^{68} +(-20.6685 + 22.5502i) q^{69} +(-14.2032 + 23.0691i) q^{70} -88.8377 q^{71} +(16.1601 + 70.1630i) q^{72} +(71.1740 + 71.1740i) q^{73} +(-12.5286 + 57.2763i) q^{74} +(-44.1575 + 60.6227i) q^{75} +(-55.5320 + 120.862i) q^{76} +(13.1648 + 13.1648i) q^{77} +(17.8095 - 102.619i) q^{78} +75.1410 q^{79} +(74.5025 - 29.1440i) q^{80} +(79.7763 - 14.0264i) q^{81} +(-54.9574 - 85.7318i) q^{82} +(58.6543 + 58.6543i) q^{83} +(-12.6061 - 29.9654i) q^{84} +(-60.3369 + 29.0625i) q^{85} +(-9.18537 + 41.9921i) q^{86} +(-0.299026 - 6.86815i) q^{87} +(-7.63668 - 54.4459i) q^{88} -41.1063 q^{89} +(-28.3580 - 85.4156i) q^{90} +47.0267i q^{91} +(-38.2467 + 14.1653i) q^{92} +(-36.4327 + 1.58621i) q^{93} +(16.1854 - 73.9937i) q^{94} +(54.9006 - 156.936i) q^{95} +(-23.5492 + 93.0668i) q^{96} +(30.3484 - 30.3484i) q^{97} +(-44.9665 - 70.1464i) q^{98} +(-61.6172 + 5.37559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Introduction

L-functions

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