LMFDB - Embedded newform 60.3.l.a.47.16

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			47.16
Character	$\chi$	$=$	60.47
Dual form			60.3.l.a.23.16

$q$-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 $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

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

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	−0.556912	−	0.830571i	$-0.688014\pi$
$7$	1.91561	−	1.91561i	0.273659	−	0.273659i	0.830571	+	0.556912i	$0.188014\pi$
$8$	−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	−0.0543246	−	0.998523i	$-0.517301\pi$
$13$	12.2746	−	12.2746i	0.944199	−	0.944199i	0.998523	+	0.0543246i	$0.0173006\pi$
$14$	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	−0.371360	−	0.928489i	$-0.621108\pi$
$17$	9.47120	−	9.47120i	0.557129	−	0.557129i	0.928489	+	0.371360i	$0.121108\pi$
$18$	−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	−0.846255	−	0.532779i	$-0.821148\pi$
$23$	−7.20994	+	7.20994i	−0.313476	+	0.313476i	0.532779	+	0.846255i	$0.321148\pi$
$24$	−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	$0.0628149\pi$
$31$			12.1558i			0.392121i	−0.980592	+	0.196061i	$0.937185\pi$
$32$	−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	0.369133	−	0.929377i	$-0.379655\pi$
$37$	−20.7290	−	20.7290i	−0.560244	−	0.560244i	−0.929377	+	0.369133i	$0.879655\pi$
$38$	−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	$0.213250\pi$
$41$			50.9173i			1.24188i	−0.783856	+	0.620942i	$0.786750\pi$
$42$	2.77942	+	16.0151i	0.0661766	+	0.381313i
$43$	−15.1975	−	15.1975i	−0.353430	−	0.353430i	0.507954	−	0.861384i	$-0.330402\pi$
$43$	−15.1975	−	15.1975i	−0.353430	−	0.353430i	−0.861384	+	0.507954i	$0.830402\pi$
$44$	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	0.932064	−	0.362293i	$-0.118006\pi$
$47$	26.7793	+	26.7793i	0.569772	+	0.569772i	−0.362293	+	0.932064i	$0.618006\pi$
$48$	−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	0.838185	−	0.545386i	$-0.183617\pi$
$53$	15.5183	+	15.5183i	0.292799	+	0.292799i	−0.545386	+	0.838185i	$0.683617\pi$
$54$	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	$-0.820425\pi$
$59$		−	63.0946i		−	1.06940i	0.845042	−	0.534700i	$-0.179575\pi$
$60$	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	−0.906531	−	0.422139i	$-0.861279\pi$
$67$	−32.4542	+	32.4542i	−0.484392	+	0.484392i	0.422139	+	0.906531i	$0.361279\pi$
$68$	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	−0.0247079	−	0.999695i	$-0.507866\pi$
$73$	71.1740	−	71.1740i	0.974987	−	0.974987i	0.999695	+	0.0247079i	$0.00786556\pi$
$74$	−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	−0.259157	−	0.965835i	$-0.583445\pi$
$83$	58.6543	−	58.6543i	0.706678	−	0.706678i	0.965835	+	0.259157i	$0.0834448\pi$
$84$	−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	0.846020	−	0.533150i	$-0.178992\pi$
$97$	30.3484	+	30.3484i	0.312870	+	0.312870i	−0.533150	+	0.846020i	$0.678992\pi$
$98$	−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	$-0.789022\pi$
$101$		−	124.297i		−	1.23067i	0.788267	−	0.615333i	$-0.210978\pi$
$102$	13.7420	+	79.1822i	0.134726	+	0.776296i
$103$	131.168	+	131.168i	1.27348	+	1.27348i	0.944252	+	0.329223i	$0.106787\pi$
$103$	131.168	+	131.168i	1.27348	+	1.27348i	0.329223	+	0.944252i	$0.393213\pi$
$104$	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	0.758659	−	0.651488i	$-0.225855\pi$
$107$	11.4672	+	11.4672i	0.107170	+	0.107170i	−0.651488	+	0.758659i	$0.725855\pi$
$108$	103.171	−	31.9332i	0.955288	−	0.295678i
$109$			80.0130i			0.734065i	0.930208	+	0.367032i	$0.119626\pi$
$109$			80.0130i			0.734065i	−0.930208	+	0.367032i	$0.880374\pi$
$110$	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	0.933228	−	0.359285i	$-0.116979\pi$
$113$	64.8556	+	64.8556i	0.573943	+	0.573943i	−0.359285	+	0.933228i	$0.616979\pi$
$114$	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	−0.410952	−	0.911657i	$-0.634804\pi$
$127$	63.5895	−	63.5895i	0.500705	−	0.500705i	0.911657	+	0.410952i	$0.134804\pi$
$128$	−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	−0.755065	−	0.655649i	$-0.772395\pi$
$137$	−13.6200	+	13.6200i	−0.0994161	+	0.0994161i	0.655649	+	0.755065i	$0.272395\pi$
$138$	−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	$-0.919831\pi$
$151$		−	75.2596i		−	0.498408i	0.968451	−	0.249204i	$-0.0801690\pi$
$152$	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	0.897536	−	0.440942i	$-0.145356\pi$
$157$	71.6852	+	71.6852i	0.456593	+	0.456593i	−0.440942	+	0.897536i	$0.645356\pi$
$158$	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	0.493022	−	0.870017i	$-0.335892\pi$
$163$	−61.4502	−	61.4502i	−0.376995	−	0.376995i	−0.870017	+	0.493022i	$0.835892\pi$
$164$	−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	0.808611	−	0.588344i	$-0.200220\pi$
$167$	36.7847	+	36.7847i	0.220268	+	0.220268i	−0.588344	+	0.808611i	$0.700220\pi$
$168$	−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	0.185545	−	0.982636i	$-0.440595\pi$
$173$	−137.897	−	137.897i	−0.797091	−	0.797091i	−0.982636	+	0.185545i	$0.940595\pi$
$174$	−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	$0.0965867\pi$
$179$			106.971i			0.597602i	−0.954315	+	0.298801i	$0.903413\pi$
$180$	−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	−0.850704	−	0.525646i	$-0.823824\pi$
$193$	−62.7362	+	62.7362i	−0.325058	+	0.325058i	0.525646	+	0.850704i	$0.323824\pi$
$194$	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	−0.909034	−	0.416723i	$-0.863179\pi$
$197$	−96.9852	+	96.9852i	−0.492311	+	0.492311i	0.416723	+	0.909034i	$0.363179\pi$
$198$	−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	$0.351580\pi$
$211$			376.951i			1.78650i	−0.449561	+	0.893250i	$0.648420\pi$
$212$	−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	−0.987377	−	0.158385i	$-0.949371\pi$
$223$	−255.505	−	255.505i	−1.14576	−	1.14576i	−0.158385	−	0.987377i	$-0.550629\pi$
$224$	−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	0.424876	−	0.905251i	$-0.360318\pi$
$227$	−109.045	−	109.045i	−0.480375	−	0.480375i	−0.905251	+	0.424876i	$0.860318\pi$
$228$	369.490	−	150.667i	1.62057	−	0.660820i
$229$		−	223.738i		−	0.977023i	−0.872557	−	0.488512i	$-0.837540\pi$
$229$		−	223.738i		−	0.977023i	0.872557	−	0.488512i	$-0.162460\pi$
$230$	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	0.560344	−	0.828260i	$-0.310669\pi$
$233$	−62.4244	−	62.4244i	−0.267916	−	0.267916i	−0.828260	+	0.560344i	$0.810669\pi$
$234$	−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	$-0.775192\pi$
$239$		−	310.217i		−	1.29798i	0.760798	−	0.648989i	$-0.224808\pi$
$240$	−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	−0.979288	−	0.202472i	$-0.935102\pi$
$257$	−199.642	+	199.642i	−0.776816	+	0.776816i	0.202472	+	0.979288i	$0.435102\pi$
$258$	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	−0.471499	−	0.881867i	$-0.656287\pi$
$263$	107.927	−	107.927i	0.410368	−	0.410368i	0.881867	+	0.471499i	$0.156287\pi$
$264$	−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	$-0.774213\pi$
$271$		−	353.019i		−	1.30265i	0.758797	−	0.651327i	$-0.225787\pi$
$272$	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	0.723279	−	0.690556i	$-0.242634\pi$
$277$	9.06443	+	9.06443i	0.0327236	+	0.0327236i	−0.690556	+	0.723279i	$0.742634\pi$
$278$	−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	$0.118549\pi$
$281$			204.501i			0.727762i	−0.931445	+	0.363881i	$0.881451\pi$
$282$	−223.883	+	38.8548i	−0.793912	+	0.137783i
$283$	−4.95961	−	4.95961i	−0.0175251	−	0.0175251i	0.698290	−	0.715815i	$-0.253945\pi$
$283$	−4.95961	−	4.95961i	−0.0175251	−	0.0175251i	−0.715815	+	0.698290i	$0.753945\pi$
$284$	−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	0.957182	−	0.289485i	$-0.0934842\pi$
$293$	195.635	+	195.635i	0.667697	+	0.667697i	−0.289485	+	0.957182i	$0.593484\pi$
$294$	−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	0.0565751	−	0.998398i	$-0.481982\pi$
$307$	323.877	−	323.877i	1.05497	−	1.05497i	0.998398	−	0.0565751i	$-0.0180180\pi$
$308$	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	−0.898833	−	0.438292i	$-0.855584\pi$
$313$	−144.149	+	144.149i	−0.460541	+	0.460541i	0.438292	+	0.898833i	$0.355584\pi$
$314$	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	−0.0528685	−	0.998601i	$-0.516836\pi$
$317$	299.797	−	299.797i	0.945733	−	0.945733i	0.998601	+	0.0528685i	$0.0168364\pi$
$318$	−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	$-0.957014\pi$
$331$		−	89.1276i		−	0.269268i	0.990895	−	0.134634i	$-0.0429858\pi$
$332$	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	0.393978	−	0.919120i	$-0.371098\pi$
$337$	−176.973	−	176.973i	−0.525141	−	0.525141i	−0.919120	+	0.393978i	$0.871098\pi$
$338$	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	0.999878	−	0.0155906i	$-0.00496283\pi$
$347$	341.548	+	341.548i	0.984288	+	0.984288i	−0.0155906	+	0.999878i	$0.504963\pi$
$348$	−25.4630	+	10.3830i	−0.0731696	+	0.0298363i
$349$		−	190.129i		−	0.544782i	−0.962187	−	0.272391i	$-0.912186\pi$
$349$		−	190.129i		−	0.544782i	0.962187	−	0.272391i	$-0.0878144\pi$
$350$	−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	0.794880	−	0.606767i	$-0.207534\pi$
$353$	66.4041	+	66.4041i	0.188114	+	0.188114i	−0.606767	+	0.794880i	$0.707534\pi$
$354$	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	$-0.810842\pi$
$359$		−	402.003i		−	1.11979i	0.828565	−	0.559893i	$-0.189158\pi$
$360$	−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	−0.411919	−	0.911220i	$-0.635141\pi$
$367$	183.244	−	183.244i	0.499301	−	0.499301i	0.911220	+	0.411919i	$0.135141\pi$
$368$	−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	−0.804135	−	0.594446i	$-0.797371\pi$
$373$	−78.2141	+	78.2141i	−0.209689	+	0.209689i	0.594446	+	0.804135i	$0.297371\pi$
$374$	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	0.161308	−	0.986904i	$-0.448429\pi$
$383$	439.765	−	439.765i	1.14821	−	1.14821i	0.986904	−	0.161308i	$-0.0515712\pi$
$384$	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	−0.838233	−	0.545313i	$-0.816411\pi$
$397$	−549.267	−	549.267i	−1.38355	−	1.38355i	−0.545313	−	0.838233i	$-0.683589\pi$
$398$	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	$-0.928924\pi$
$401$		−	177.597i		−	0.442885i	0.975173	−	0.221442i	$-0.0710765\pi$
$402$	−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	$0.140230\pi$
$409$			348.822i			0.852865i	−0.904519	+	0.426433i	$0.859770\pi$
$410$	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	$0.0398476\pi$
$419$			104.631i			0.249716i	−0.992175	+	0.124858i	$0.960152\pi$
$420$	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	−0.0155664	−	0.999879i	$-0.504955\pi$
$433$	426.207	−	426.207i	0.984312	−	0.984312i	0.999879	+	0.0155664i	$0.00495515\pi$
$434$	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	−0.983125	−	0.182937i	$-0.941440\pi$
$443$	−354.483	+	354.483i	−0.800188	+	0.800188i	0.182937	+	0.983125i	$0.441440\pi$
$444$	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	0.938139	−	0.346260i	$-0.112548\pi$
$457$	270.489	+	270.489i	0.591879	+	0.591879i	−0.346260	+	0.938139i	$0.612548\pi$
$458$	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	$0.217661\pi$
$461$			582.469i			1.26349i	−0.775176	+	0.631745i	$0.782339\pi$
$462$	19.1012	+	110.062i	0.0413445	+	0.238229i
$463$	318.146	+	318.146i	0.687140	+	0.687140i	0.961599	−	0.274459i	$-0.0884986\pi$
$463$	318.146	+	318.146i	0.687140	+	0.687140i	−0.274459	+	0.961599i	$0.588499\pi$
$464$	−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	−0.977961	−	0.208786i	$-0.933049\pi$
$467$	−554.211	−	554.211i	−1.18675	−	1.18675i	−0.208786	−	0.977961i	$-0.566951\pi$
$468$	−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	$0.352625\pi$
$479$			857.141i			1.78944i	−0.446629	+	0.894719i	$0.647375\pi$
$480$	−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	−0.599551	−	0.800336i	$-0.704654\pi$
$487$	97.7824	−	97.7824i	0.200785	−	0.200785i	0.800336	+	0.599551i	$0.204654\pi$
$488$	−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	−0.963171	−	0.268889i	$-0.913344\pi$
$503$	−349.224	+	349.224i	−0.694282	+	0.694282i	0.268889	+	0.963171i	$0.413344\pi$
$504$	−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	$0.116560\pi$
$521$			373.093i			0.716109i	−0.933701	+	0.358054i	$0.883440\pi$
$522$	−32.6595	−	25.1942i	−0.0625660	−	0.0482648i
$523$	−593.137	−	593.137i	−1.13411	−	1.13411i	−0.989488	−	0.144618i	$-0.953805\pi$
$523$	−593.137	−	593.137i	−1.13411	−	1.13411i	−0.144618	−	0.989488i	$-0.546195\pi$
$524$	−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	−0.0750146	+	0.997182i	$0.523900\pi$
$547$	−586.492	+	586.492i	−1.07220	+	1.07220i	−0.997182	+	0.0750146i	$0.976100\pi$
$548$	−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	−0.230067	−	0.973175i	$-0.573894\pi$
$557$	413.911	−	413.911i	0.743108	−	0.743108i	0.973175	+	0.230067i	$0.0738945\pi$
$558$	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	−0.852699	−	0.522403i	$-0.825036\pi$
$563$	−185.957	+	185.957i	−0.330296	+	0.330296i	0.522403	+	0.852699i	$0.325036\pi$
$564$	−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	$0.115893\pi$
$571$			406.663i			0.712195i	−0.934449	+	0.356097i	$0.884107\pi$
$572$	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	0.768294	−	0.640097i	$-0.221106\pi$
$577$	73.9694	+	73.9694i	0.128197	+	0.128197i	−0.640097	+	0.768294i	$0.721106\pi$
$578$	−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	0.249200	−	0.968452i	$-0.419832\pi$
$587$	−422.201	−	422.201i	−0.719251	−	0.719251i	−0.968452	+	0.249200i	$0.919832\pi$
$588$	−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	0.275253	−	0.961372i	$-0.411238\pi$
$593$	−406.869	−	406.869i	−0.686119	−	0.686119i	−0.961372	+	0.275253i	$0.911238\pi$
$594$	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	$-0.921290\pi$
$599$		−	293.225i		−	0.489525i	0.969583	−	0.244762i	$-0.0787100\pi$
$600$	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	−0.642655	−	0.766156i	$-0.722167\pi$
$607$	74.9651	−	74.9651i	0.123501	−	0.123501i	0.766156	+	0.642655i	$0.222167\pi$
$608$	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	−0.688181	−	0.725539i	$-0.741590\pi$
$613$	22.9005	−	22.9005i	0.0373581	−	0.0373581i	0.725539	+	0.688181i	$0.241590\pi$
$614$	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	−0.794133	−	0.607744i	$-0.792075\pi$
$617$	−115.002	+	115.002i	−0.186389	+	0.186389i	0.607744	+	0.794133i	$0.292075\pi$
$618$	−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	$-0.946843\pi$
$631$		−	209.771i		−	0.332443i	0.986088	−	0.166221i	$-0.0531566\pi$
$632$	−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	$-0.619007\pi$
$641$		−	1193.44i		−	1.86184i	0.365221	−	0.930921i	$-0.380993\pi$
$642$	−95.8695	+	16.6381i	−0.149329	+	0.0259160i
$643$	−424.387	−	424.387i	−0.660012	−	0.660012i	0.295371	−	0.955383i	$-0.404557\pi$
$643$	−424.387	−	424.387i	−0.660012	−	0.660012i	−0.955383	+	0.295371i	$0.904557\pi$
$644$	−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	0.991317	−	0.131493i	$-0.0419772\pi$
$647$	556.306	+	556.306i	0.859824	+	0.859824i	−0.131493	+	0.991317i	$0.541977\pi$
$648$	−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	−0.991987	−	0.126340i	$-0.959677\pi$
$653$	−730.267	−	730.267i	−1.11833	−	1.11833i	−0.126340	−	0.991987i	$-0.540323\pi$
$654$	−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	$0.249165\pi$
$659$			929.519i			1.41050i	−0.708959	+	0.705250i	$0.750835\pi$
$660$	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	−0.446706	−	0.894681i	$-0.647403\pi$
$673$	301.487	−	301.487i	0.447975	−	0.447975i	0.894681	+	0.446706i	$0.147403\pi$
$674$	−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	−0.980436	−	0.196838i	$-0.936933\pi$
$677$	−530.496	+	530.496i	−0.783598	+	0.783598i	0.196838	+	0.980436i	$0.436933\pi$
$678$	−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	−0.373573	−	0.927601i	$-0.621867\pi$
$683$	378.401	−	378.401i	0.554028	−	0.554028i	0.927601	+	0.373573i	$0.121867\pi$
$684$	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	$-0.833444\pi$
$691$		−	690.583i		−	0.999396i	0.866200	−	0.499698i	$-0.166556\pi$
$692$	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	$-0.970535\pi$
$701$		−	129.593i		−	0.184869i	0.995719	−	0.0924343i	$-0.0294648\pi$
$702$	−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	$0.0195091\pi$
$709$			86.8545i			0.122503i	−0.998122	+	0.0612514i	$0.980491\pi$
$710$	−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	$0.0230630\pi$
$719$			104.099i			0.144782i	−0.997376	+	0.0723912i	$0.976937\pi$
$720$	−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	−0.858880	−	0.512176i	$-0.828839\pi$
$727$	−252.054	+	252.054i	−0.346704	+	0.346704i	0.512176	+	0.858880i	$0.328839\pi$
$728$	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	−0.0886791	+	0.996060i	$0.528265\pi$
$733$	−795.114	+	795.114i	−1.08474	+	1.08474i	−0.996060	+	0.0886791i	$0.971735\pi$
$734$	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	−0.954499	−	0.298216i	$-0.903609\pi$
$743$	−487.618	+	487.618i	−0.656283	+	0.656283i	0.298216	+	0.954499i	$0.403609\pi$
$744$	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	$-0.741823\pi$
$751$		−	1089.00i		−	1.45007i	0.688711	−	0.725036i	$-0.258177\pi$
$752$	−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	0.157705	−	0.987486i	$-0.449590\pi$
$757$	−628.144	−	628.144i	−0.829781	−	0.829781i	−0.987486	+	0.157705i	$0.949590\pi$
$758$	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	$0.157625\pi$
$761$			723.259i			0.950407i	−0.879876	+	0.475203i	$0.842375\pi$
$762$	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	$0.0373952\pi$
$769$			180.270i			0.234421i	−0.993107	+	0.117210i	$0.962605\pi$
$770$	−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	0.946471	−	0.322788i	$-0.104620\pi$
$773$	482.107	+	482.107i	0.623683	+	0.623683i	−0.322788	+	0.946471i	$0.604620\pi$
$774$	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	−0.507094	−	0.861891i	$-0.669280\pi$
$787$	279.225	−	279.225i	0.354797	−	0.354797i	0.861891	+	0.507094i	$0.169280\pi$
$788$	−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	−0.0846783	+	0.996408i	$0.526986\pi$
$797$	−861.626	+	861.626i	−1.08109	+	1.08109i	−0.996408	+	0.0846783i	$0.973014\pi$
$798$	−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	$0.313465\pi$
$811$			1351.37i			1.66630i	−0.553047	+	0.833150i	$0.686535\pi$
$812$	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	$0.185100\pi$
$821$			901.925i			1.09857i	−0.835636	+	0.549284i	$0.814900\pi$
$822$	−19.7616	−	113.867i	−0.0240409	−	0.138525i
$823$	−512.252	−	512.252i	−0.622421	−	0.622421i	0.323729	−	0.946150i	$-0.395063\pi$
$823$	−512.252	−	512.252i	−0.622421	−	0.622421i	−0.946150	+	0.323729i	$0.895063\pi$
$824$	−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	0.987065	−	0.160321i	$-0.0512530\pi$
$827$	683.717	+	683.717i	0.826744	+	0.826744i	−0.160321	+	0.987065i	$0.551253\pi$
$828$	331.838	+	156.922i	0.400770	+	0.189519i
$829$			1001.78i			1.20842i	0.796827	+	0.604208i	$0.206510\pi$
$829$			1001.78i			1.20842i	−0.796827	+	0.604208i	$0.793490\pi$
$830$	−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	$0.0359654\pi$
$839$			189.192i			0.225497i	−0.993624	+	0.112749i	$0.964035\pi$
$840$	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	−0.912991	−	0.407980i	$-0.866233\pi$
$853$	−430.775	+	430.775i	−0.505011	+	0.505011i	0.407980	+	0.912991i	$0.366233\pi$
$854$	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	−0.184656	−	0.982803i	$-0.559117\pi$
$857$	684.012	−	684.012i	0.798147	−	0.798147i	0.982803	+	0.184656i	$0.0591172\pi$
$858$	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	−0.757432	−	0.652914i	$-0.773546\pi$
$863$	−90.1987	+	90.1987i	−0.104518	+	0.104518i	0.652914	+	0.757432i	$0.273546\pi$
$864$	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	0.718041	−	0.696001i	$-0.245039\pi$
$877$	19.3296	+	19.3296i	0.0220406	+	0.0220406i	−0.696001	+	0.718041i	$0.745039\pi$
$878$	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	$-0.865751\pi$
$881$		−	721.297i		−	0.818725i	0.912372	−	0.409363i	$-0.134249\pi$
$882$	458.036	−	593.756i	0.519315	−	0.673192i
$883$	941.983	+	941.983i	1.06680	+	1.06680i	0.997603	+	0.0691949i	$0.0220430\pi$
$883$	941.983	+	941.983i	1.06680	+	1.06680i	0.0691949	+	0.997603i	$0.477957\pi$
$884$	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	0.927108	−	0.374795i	$-0.122287\pi$
$887$	489.902	+	489.902i	0.552313	+	0.552313i	−0.374795	+	0.927108i	$0.622287\pi$
$888$	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	−0.805838	−	0.592137i	$-0.798285\pi$
$907$	−193.827	+	193.827i	−0.213701	+	0.213701i	0.592137	+	0.805838i	$0.298285\pi$
$908$	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	0.382758	−	0.923849i	$-0.374974\pi$
$937$	−507.002	−	507.002i	−0.541091	−	0.541091i	−0.923849	+	0.382758i	$0.874974\pi$
$938$	−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	$-0.877288\pi$
$941$		−	707.695i		−	0.752067i	0.926606	−	0.376033i	$-0.122712\pi$
$942$	−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	0.819358	−	0.573283i	$-0.194330\pi$
$947$	233.033	+	233.033i	0.246075	+	0.246075i	−0.573283	+	0.819358i	$0.694330\pi$
$948$	−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	0.890140	−	0.455688i	$-0.150607\pi$
$953$	414.033	+	414.033i	0.434452	+	0.434452i	−0.455688	+	0.890140i	$0.650607\pi$
$954$	−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	−0.374426	−	0.927257i	$-0.622160\pi$
$967$	534.588	−	534.588i	0.552831	−	0.552831i	0.927257	+	0.374426i	$0.122160\pi$
$968$	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	0.307644	−	0.951501i	$-0.400459\pi$
$977$	1230.19	−	1230.19i	1.25915	−	1.25915i	0.951501	−	0.307644i	$-0.0995406\pi$
$978$	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	0.318665	−	0.947867i	$-0.396765\pi$
$983$	1245.00	−	1245.00i	1.26653	−	1.26653i	0.947867	−	0.318665i	$-0.103235\pi$
$984$	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	$0.233794\pi$
$991$			1328.35i			1.34041i	−0.742176	+	0.670205i	$0.766206\pi$
$992$	−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	0.372870	−	0.927884i	$-0.378374\pi$
$997$	−553.349	−	553.349i	−0.555014	−	0.555014i	−0.927884	+	0.372870i	$0.878374\pi$
$998$	−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.47.16	yes	40
3.2	odd	2	inner	60.3.l.a.47.5	yes	40
4.3	odd	2	inner	60.3.l.a.47.6	yes	40
5.2	odd	4		300.3.l.g.143.6		40
5.3	odd	4	inner	60.3.l.a.23.15	yes	40
5.4	even	2		300.3.l.g.107.5		40
12.11	even	2	inner	60.3.l.a.47.15	yes	40
15.2	even	4		300.3.l.g.143.15		40
15.8	even	4	inner	60.3.l.a.23.6	yes	40
15.14	odd	2		300.3.l.g.107.16		40
20.3	even	4	inner	60.3.l.a.23.5	✓	40
20.7	even	4		300.3.l.g.143.16		40
20.19	odd	2		300.3.l.g.107.15		40
60.23	odd	4	inner	60.3.l.a.23.16	yes	40
60.47	odd	4		300.3.l.g.143.5		40
60.59	even	2		300.3.l.g.107.6		40

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

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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