LMFDB - Embedded newform 60.3.l.a.47.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [60,3,Mod(23,60)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("60.23"); S:= CuspForms(chi, 3); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.63488158616$
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			47.15
Character	$\chi$	$=$	60.47
Dual form			60.3.l.a.23.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07935 + 1.68375i) q^{2} +(-2.99716 + 0.130491i) 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} +(-7.92245 + 1.11122i) q^{8} +(8.96594 - 0.782204i) q^{9} +(-6.16449 + 7.87394i) q^{10} +6.87236 q^{11} +(4.53101 - 11.1117i) q^{12} +(12.2746 - 12.2746i) q^{13} +(-5.29303 - 1.15780i) q^{14} +(-5.56425 - 13.9298i) q^{15} +(-10.4221 - 12.1400i) q^{16} +(-9.47120 + 9.47120i) q^{17} +(10.9944 + 14.2521i) q^{18} +33.2524 q^{19} +(-19.9114 - 1.88073i) q^{20} +(5.49143 - 5.99137i) q^{21} +(7.41767 + 11.5713i) 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} +(-26.7703 + 3.51436i) q^{27} +(-3.76357 - 10.1618i) q^{28} -2.29155 q^{29} +(17.4485 - 24.4039i) q^{30} -12.1558i q^{31} +(9.19168 - 30.6515i) q^{32} +(-20.5976 + 0.896780i) 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} +(35.8909 + 55.9886i) q^{38} +(-35.1872 + 38.3906i) q^{39} +(-18.3246 - 35.5557i) q^{40} -50.9173i q^{41} +(16.0151 + 2.77942i) q^{42} +(15.1975 + 15.1975i) q^{43} +(-11.4770 + 24.9790i) q^{44} +(18.4947 + 41.0237i) q^{45} +(-19.9218 - 4.35769i) q^{46} +(26.7793 + 26.7793i) q^{47} +(32.8208 + 35.0256i) q^{48} +41.6608i q^{49} +(-47.3392 - 16.0935i) q^{50} +(27.1508 - 29.6226i) q^{51} +(24.1157 + 65.1132i) 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} +(-99.6627 + 4.33913i) q^{57} +(-2.47338 - 3.85839i) q^{58} -63.0946i q^{59} +(59.9230 + 3.03861i) q^{60} +28.4752 q^{61} +(20.4672 - 13.1203i) q^{62} +(-15.6769 + 18.6737i) 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} +(-18.6079 - 50.2420i) q^{68} +(20.6685 - 22.5502i) q^{69} +(-3.27465 - 26.8922i) q^{70} -88.8377 q^{71} +(-70.1630 + 16.1601i) q^{72} +(71.1740 - 71.1740i) q^{73} +(12.5286 - 57.2763i) q^{74} +(56.5556 - 49.2592i) q^{75} +(-55.5320 + 120.862i) q^{76} +(-13.1648 + 13.1648i) q^{77} +(-102.619 - 17.8095i) q^{78} -75.1410 q^{79} +(40.0882 - 69.2310i) q^{80} +(79.7763 - 14.0264i) q^{81} +(85.7318 - 54.9574i) 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} +(6.86815 - 0.299026i) q^{87} +(-54.4459 + 7.63668i) q^{88} +41.1063 q^{89} +(-49.1115 + 75.4192i) q^{90} +47.0267i q^{91} +(-14.1653 - 38.2467i) q^{92} +(1.58621 + 36.4327i) 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} +(-70.1464 + 44.9665i) q^{98} +(61.6172 - 5.37559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	1.07935	+	1.68375i	0.539674	+	0.841874i
$2$	1.07935	+	1.68375i	0.539674	+	0.841874i
$3$	−2.99716	+	0.130491i	−0.999054	+	0.0434969i
$3$	−2.99716	+	0.130491i	−0.999054	+	0.0434969i
$4$	−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	$-0.811986\pi$
$7$	−1.91561	+	1.91561i	−0.273659	+	0.273659i	0.556912	+	0.830571i	$0.311986\pi$
$8$	−7.92245	+	1.11122i	−0.990306	+	0.138902i
$9$	8.96594	−	0.782204i	0.996216	−	0.0869115i
$10$	−6.16449	+	7.87394i	−0.616449	+	0.787394i
$11$	6.87236			0.624760			0.312380	−	0.949957i	$-0.398874\pi$
$11$	6.87236			0.624760			0.312380	+	0.949957i	$0.398874\pi$
$12$	4.53101	−	11.1117i	0.377585	−	0.925975i
$13$	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
$15$	−5.56425	−	13.9298i	−0.370950	−	0.928653i
$16$	−10.4221	−	12.1400i	−0.651380	−	0.758751i
$17$	−9.47120	+	9.47120i	−0.557129	+	0.557129i	−0.928489	−	0.371360i	$-0.878892\pi$
$17$	−9.47120	+	9.47120i	−0.557129	+	0.557129i	0.371360	+	0.928489i	$0.378892\pi$
$18$	10.9944	+	14.2521i	0.610800	+	0.791785i
$19$	33.2524			1.75013			0.875063	−	0.484010i	$-0.160820\pi$
$19$	33.2524			1.75013			0.875063	+	0.484010i	$0.160820\pi$
$20$	−19.9114	−	1.88073i	−0.995569	−	0.0940367i
$21$	5.49143	−	5.99137i	0.261497	−	0.285303i
$22$	7.41767	+	11.5713i	0.337167	+	0.525969i
$23$	−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
$27$	−26.7703	+	3.51436i	−0.991493	+	0.130162i
$28$	−3.76357	−	10.1618i	−0.134413	−	0.362921i
$29$	−2.29155			−0.0790190			−0.0395095	−	0.999219i	$-0.512580\pi$
$29$	−2.29155			−0.0790190			−0.0395095	+	0.999219i	$0.512580\pi$
$30$	17.4485	−	24.4039i	0.581617	−	0.813463i
$31$		−	12.1558i		−	0.392121i	−0.980592	−	0.196061i	$-0.937185\pi$
$31$		−	12.1558i		−	0.392121i	0.980592	−	0.196061i	$-0.0628149\pi$
$32$	9.19168	−	30.6515i	0.287240	−	0.957859i
$33$	−20.5976	+	0.896780i	−0.624169	+	0.0271752i
$34$	−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	$0.879655\pi$
$38$	35.8909	+	55.9886i	0.944497	+	1.47339i
$39$	−35.1872	+	38.3906i	−0.902235	+	0.984375i
$40$	−18.3246	−	35.5557i	−0.458115	−	0.888893i
$41$		−	50.9173i		−	1.24188i	−0.783856	−	0.620942i	$-0.786750\pi$
$41$		−	50.9173i		−	1.24188i	0.783856	−	0.620942i	$-0.213250\pi$
$42$	16.0151	+	2.77942i	0.381313	+	0.0661766i
$43$	15.1975	+	15.1975i	0.353430	+	0.353430i	0.861384	−	0.507954i	$-0.169598\pi$
$43$	15.1975	+	15.1975i	0.353430	+	0.353430i	−0.507954	+	0.861384i	$0.669598\pi$
$44$	−11.4770	+	24.9790i	−0.260840	+	0.567704i
$45$	18.4947	+	41.0237i	0.410993	+	0.911639i
$46$	−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	$0.618006\pi$
$48$	32.8208	+	35.0256i	0.683767	+	0.729700i
$49$			41.6608i			0.850221i
$50$	−47.3392	−	16.0935i	−0.946784	−	0.321870i
$51$	27.1508	−	29.6226i	0.532368	−	0.580835i
$52$	24.1157	+	65.1132i	0.463763	+	1.25218i
$53$	−15.5183	−	15.5183i	−0.292799	−	0.292799i	0.545386	−	0.838185i	$-0.316383\pi$
$53$	−15.5183	−	15.5183i	−0.292799	−	0.292799i	−0.838185	+	0.545386i	$0.816383\pi$
$54$	−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
$57$	−99.6627	+	4.33913i	−1.74847	+	0.0761251i
$58$	−2.47338	−	3.85839i	−0.0426445	−	0.0665240i
$59$		−	63.0946i		−	1.06940i	−0.845042	−	0.534700i	$-0.820425\pi$
$59$		−	63.0946i		−	1.06940i	0.845042	−	0.534700i	$-0.179575\pi$
$60$	59.9230	+	3.03861i	0.998717	+	0.0506435i
$61$	28.4752			0.466806			0.233403	−	0.972380i	$-0.425014\pi$
$61$	28.4752			0.466806			0.233403	+	0.972380i	$0.425014\pi$
$62$	20.4672	−	13.1203i	0.330117	−	0.211617i
$63$	−15.6769	+	18.6737i	−0.248839	+	0.296408i
$64$	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	$-0.638721\pi$
$67$	32.4542	−	32.4542i	0.484392	−	0.484392i	0.906531	+	0.422139i	$0.138721\pi$
$68$	−18.6079	−	50.2420i	−0.273646	−	0.738853i
$69$	20.6685	−	22.5502i	0.299544	−	0.326814i
$70$	−3.27465	−	26.8922i	−0.0467807	−	0.384175i
$71$	−88.8377			−1.25124			−0.625618	−	0.780130i	$-0.715153\pi$
$71$	−88.8377			−1.25124			−0.625618	+	0.780130i	$0.715153\pi$
$72$	−70.1630	+	16.1601i	−0.974487	+	0.224446i
$73$	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
$75$	56.5556	−	49.2592i	0.754074	−	0.656789i
$76$	−55.5320	+	120.862i	−0.730685	+	1.59029i
$77$	−13.1648	+	13.1648i	−0.170971	+	0.170971i
$78$	−102.619	−	17.8095i	−1.31563	−	0.228327i
$79$	−75.1410			−0.951153			−0.475576	−	0.879675i	$-0.657760\pi$
$79$	−75.1410			−0.951153			−0.475576	+	0.879675i	$0.657760\pi$
$80$	40.0882	−	69.2310i	0.501103	−	0.865388i
$81$	79.7763	−	14.0264i	0.984893	−	0.173165i
$82$	85.7318	−	54.9574i	1.04551	−	0.670213i
$83$	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
$87$	6.86815	−	0.299026i	0.0789442	−	0.00343708i
$88$	−54.4459	+	7.63668i	−0.618704	+	0.0867805i
$89$	41.1063			0.461868			0.230934	−	0.972969i	$-0.425822\pi$
$89$	41.1063			0.461868			0.230934	+	0.972969i	$0.425822\pi$
$90$	−49.1115	+	75.4192i	−0.545683	+	0.837992i
$91$			47.0267i			0.516777i
$92$	−14.1653	−	38.2467i	−0.153970	−	0.415725i
$93$	1.58621	+	36.4327i	0.0170561	+	0.391750i
$94$	−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	$0.678992\pi$
$98$	−70.1464	+	44.9665i	−0.715779	+	0.458842i
$99$	61.6172	−	5.37559i	0.622396	−	0.0542989i
$100$	−23.9980	−	97.0778i	−0.239980	−	0.970778i
$101$			124.297i			1.23067i	0.788267	+	0.615333i	$0.210978\pi$
$101$			124.297i			1.23067i	−0.788267	+	0.615333i	$0.789022\pi$
$102$	79.1822	+	13.7420i	0.776296	+	0.134726i
$103$	−131.168	−	131.168i	−1.27348	−	1.27348i	−0.944252	−	0.329223i	$-0.893213\pi$
$103$	−131.168	−	131.168i	−1.27348	−	1.27348i	−0.329223	−	0.944252i	$-0.606787\pi$
$104$	−83.6050	+	110.884i	−0.803895	+	1.06620i
$105$	37.3431	+	16.0251i	0.355648	+	0.152620i
$106$	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	$0.725855\pi$
$108$	31.9332	−	103.171i	0.295678	−	0.955288i
$109$			80.0130i			0.734065i	0.930208	+	0.367032i	$0.119626\pi$
$109$			80.0130i			0.734065i	−0.930208	+	0.367032i	$0.880374\pi$
$110$	−42.3646	+	54.1126i	−0.385133	+	0.491933i
$111$	64.8331	+	59.4232i	0.584082	+	0.535345i
$112$	43.2203	+	3.29090i	0.385895	+	0.0293830i
$113$	−64.8556	−	64.8556i	−0.573943	−	0.573943i	0.359285	−	0.933228i	$-0.383021\pi$
$113$	−64.8556	−	64.8556i	−0.573943	−	0.573943i	−0.933228	+	0.359285i	$0.883021\pi$
$114$	−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
$117$	100.452	−	119.654i	0.858564	−	1.02269i
$118$	106.235	−	68.1010i	0.900301	−	0.577127i
$119$		−	36.2863i		−	0.304927i
$120$	59.5615	+	104.175i	0.496346	+	0.868125i
$121$	−73.7706			−0.609675
$122$	30.7346	+	47.9450i	0.251923	+	0.392992i
$123$	6.64423	+	152.607i	0.0540182	+	1.24071i
$124$	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	$-0.865196\pi$
$127$	−63.5895	+	63.5895i	−0.500705	+	0.500705i	0.410952	+	0.911657i	$0.365196\pi$
$128$	96.0586	+	84.5975i	0.750458	+	0.660918i
$129$	−47.5325	−	43.5662i	−0.368469	−	0.337722i
$130$	20.9828	+	172.316i	0.161406	+	1.32551i
$131$	−144.030			−1.09947			−0.549734	−	0.835340i	$-0.685271\pi$
$131$	−144.030			−1.09947			−0.549734	+	0.835340i	$0.685271\pi$
$132$	31.1388	−	76.3636i	0.235900	−	0.578512i
$133$	−63.6987	+	63.6987i	−0.478938	+	0.478938i
$134$	89.6742	+	19.6154i	0.669210	+	0.146383i
$135$	−60.7847	−	120.541i	−0.450257	−	0.892899i
$136$	64.5105	−	85.5596i	0.474342	−	0.629115i
$137$	13.6200	−	13.6200i	0.0994161	−	0.0994161i	−0.655649	−	0.755065i	$-0.727605\pi$
$137$	13.6200	−	13.6200i	0.0994161	−	0.0994161i	0.755065	+	0.655649i	$0.227605\pi$
$138$	60.2774	+	10.4611i	0.436793	+	0.0758051i
$139$	62.7261			0.451267			0.225634	−	0.974212i	$-0.427555\pi$
$139$	62.7261			0.451267			0.225634	+	0.974212i	$0.427555\pi$
$140$	41.7453	−	34.5397i	0.298180	−	0.246712i
$141$	−83.7563	−	76.7674i	−0.594016	−	0.544449i
$142$	−95.8868	−	149.580i	−0.675259	−	1.05338i
$143$	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
$147$	−5.43636	−	124.864i	−0.0369820	−	0.849417i
$148$	109.962	−	40.7259i	0.742983	−	0.275175i
$149$	−167.292			−1.12277			−0.561383	−	0.827556i	$-0.689730\pi$
$149$	−167.292			−1.12277			−0.561383	+	0.827556i	$0.689730\pi$
$150$	143.983	+	42.0575i	0.959888	+	0.280384i
$151$			75.2596i			0.498408i	0.968451	+	0.249204i	$0.0801690\pi$
$151$			75.2596i			0.498408i	−0.968451	+	0.249204i	$0.919831\pi$
$152$	−263.440	+	36.9506i	−1.73316	+	0.243096i
$153$	−77.5098	+	92.3266i	−0.506600	+	0.603442i
$154$	−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	$0.645356\pi$
$158$	−81.1033	−	126.519i	−0.513312	−	0.800751i
$159$	48.5359	+	44.4859i	0.305258	+	0.279786i
$160$	159.837	−	7.22585i	0.998980	−	0.0451615i
$161$		−	27.6229i		−	0.171571i
$162$	109.723	+	119.184i	0.677304	+	0.735703i
$163$	61.4502	+	61.4502i	0.376995	+	0.376995i	0.870017	−	0.493022i	$-0.164108\pi$
$163$	61.4502	+	61.4502i	0.376995	+	0.376995i	−0.493022	+	0.870017i	$0.664108\pi$
$164$	185.069	+	85.0327i	1.12847	+	0.518492i
$165$	−38.2395	−	95.7306i	−0.231755	−	0.580185i
$166$	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	$0.700220\pi$
$168$	−36.8479	+	53.5685i	−0.219333	+	0.318860i
$169$		−	132.331i		−	0.783022i
$170$	−16.1905	−	132.961i	−0.0952385	−	0.782122i
$171$	298.139	−	26.0101i	1.74350	−	0.152106i
$172$	−80.6184	+	29.8583i	−0.468712	+	0.173595i
$173$	137.897	+	137.897i	0.797091	+	0.797091i	0.982636	−	0.185545i	$-0.0594051\pi$
$173$	137.897	+	137.897i	0.797091	+	0.797091i	−0.185545	+	0.982636i	$0.559405\pi$
$174$	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
$177$	8.23327	+	189.105i	0.0465156	+	1.06839i
$178$	44.3680	+	69.2126i	0.249258	+	0.388835i
$179$			106.971i			0.597602i	0.954315	+	0.298801i	$0.0965867\pi$
$179$			106.971i			0.597602i	−0.954315	+	0.298801i	$0.903413\pi$
$180$	−179.995	−	1.28779i	−0.999974	−	0.00715441i
$181$	−11.6057			−0.0641199			−0.0320600	−	0.999486i	$-0.510207\pi$
$181$	−11.6057			−0.0641199			−0.0320600	+	0.999486i	$0.510207\pi$
$182$	−79.1812	+	50.7582i	−0.435061	+	0.278891i
$183$	−85.3446	+	3.71575i	−0.466364	+	0.0203046i
$184$	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
$188$	−142.057	+	52.6128i	−0.755620	+	0.279855i
$189$	44.5494	−	58.0137i	0.235711	−	0.306951i
$190$	−204.984	+	261.827i	−1.07886	+	1.37804i
$191$	−135.925			−0.711648			−0.355824	−	0.934553i	$-0.615800\pi$
$191$	−135.925			−0.711648			−0.355824	+	0.934553i	$0.615800\pi$
$192$	−182.119	+	60.8005i	−0.948536	+	0.316669i
$193$	−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
$195$	−239.281	−	102.684i	−1.22708	−	0.526582i
$196$	−151.425	−	69.5743i	−0.772575	−	0.354971i
$197$	96.9852	−	96.9852i	0.492311	−	0.492311i	−0.416723	−	0.909034i	$-0.636821\pi$
$197$	96.9852	−	96.9852i	0.492311	−	0.492311i	0.909034	+	0.416723i	$0.136821\pi$
$198$	75.5575	+	97.9457i	0.381604	+	0.494675i
$199$	−29.0286			−0.145872			−0.0729361	−	0.997337i	$-0.523237\pi$
$199$	−29.0286			−0.145872			−0.0729361	+	0.997337i	$0.523237\pi$
$200$	137.552	−	145.187i	0.687762	−	0.725936i
$201$	−93.0356	+	101.506i	−0.462864	+	0.505003i
$202$	−209.285	+	134.160i	−1.03607	+	0.664158i
$203$	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
$207$	−59.0043	+	70.2836i	−0.285045	+	0.339534i
$208$	−276.940	−	21.0869i	−1.33144	−	0.101379i
$209$	228.522			1.09341
$210$	13.3238	+	80.1730i	0.0634468	+	0.381776i
$211$		−	376.951i		−	1.78650i	−0.449561	−	0.893250i	$-0.648420\pi$
$211$		−	376.951i		−	1.78650i	0.449561	−	0.893250i	$-0.351580\pi$
$212$	82.3204	−	30.4886i	0.388304	−	0.143814i
$213$	266.261	−	11.5925i	1.25005	−	0.0544249i
$214$	−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
$218$	−134.722	+	86.3619i	−0.617990	+	0.396155i
$219$	−204.032	+	222.608i	−0.931655	+	1.01647i
$220$	−136.838	−	12.9251i	−0.621992	−	0.0587504i
$221$			232.510i			1.05208i
$222$	−30.0763	+	173.301i	−0.135479	+	0.780635i
$223$	255.505	+	255.505i	1.14576	+	1.14576i	0.987377	+	0.158385i	$0.0506288\pi$
$223$	255.505	+	255.505i	1.14576	+	1.14576i	0.158385	+	0.987377i	$0.449371\pi$
$224$	41.1087	+	76.3241i	0.183521	+	0.340733i
$225$	−163.078	+	155.018i	−0.724792	+	0.688968i
$226$	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	$0.860318\pi$
$228$	150.667	−	369.490i	0.660820	−	1.62057i
$229$		−	223.738i		−	0.977023i	−0.872557	−	0.488512i	$-0.837540\pi$
$229$		−	223.738i		−	0.977023i	0.872557	−	0.488512i	$-0.162460\pi$
$230$	−12.3250	−	101.216i	−0.0535871	−	0.440071i
$231$	37.7391	−	41.1749i	0.163373	−	0.178246i
$232$	18.1547	−	2.54641i	0.0782530	−	0.0109759i
$233$	62.4244	+	62.4244i	0.267916	+	0.267916i	0.828260	−	0.560344i	$-0.189331\pi$
$233$	62.4244	+	62.4244i	0.267916	+	0.267916i	−0.560344	+	0.828260i	$0.689331\pi$
$234$	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
$237$	225.210	−	9.80522i	0.950252	−	0.0413722i
$238$	61.0970	−	39.1655i	0.256710	−	0.164561i
$239$		−	310.217i		−	1.29798i	−0.760798	−	0.648989i	$-0.775192\pi$
$239$		−	310.217i		−	1.29798i	0.760798	−	0.648989i	$-0.224808\pi$
$240$	−111.117	+	212.728i	−0.462987	+	0.886365i
$241$	−119.905			−0.497529			−0.248765	−	0.968564i	$-0.580025\pi$
$241$	−119.905			−0.497529			−0.248765	+	0.968564i	$0.580025\pi$
$242$	−79.6242	−	124.211i	−0.329026	−	0.513269i
$243$	−237.272	+	52.4494i	−0.976428	+	0.215841i
$244$	−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
$248$	13.5077	+	96.3033i	0.0544664	+	0.388320i
$249$	−168.142	+	183.450i	−0.675271	+	0.736747i
$250$	−2.20419	−	249.990i	−0.00881676	−	0.999961i
$251$	336.252			1.33965			0.669825	−	0.742519i	$-0.266369\pi$
$251$	336.252			1.33965			0.669825	+	0.742519i	$0.266369\pi$
$252$	−41.6926	−	88.1662i	−0.165447	−	0.349866i
$253$	−49.5493	+	49.5493i	−0.195847	+	0.195847i
$254$	−175.704	−	38.4336i	−0.691748	−	0.151313i
$255$	184.632	+	79.2317i	0.724047	+	0.310712i
$256$	−38.7602	+	253.049i	−0.151407	+	0.988472i
$257$	199.642	−	199.642i	0.776816	−	0.776816i	−0.202472	−	0.979288i	$-0.564898\pi$
$257$	199.642	−	199.642i	0.776816	−	0.776816i	0.979288	+	0.202472i	$0.0648975\pi$
$258$	22.0505	−	127.056i	0.0854669	−	0.492464i
$259$	79.4176			0.306632
$260$	−267.489	+	221.319i	−1.02880	+	0.851225i
$261$	−20.5459	+	1.79246i	−0.0787200	+	0.00686766i
$262$	−155.459	−	242.511i	−0.593354	−	0.925613i
$263$	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
$267$	−123.202	+	5.36399i	−0.461431	+	0.0200899i
$268$	63.7623	+	172.161i	0.237919	+	0.642390i
$269$	−279.355			−1.03850			−0.519248	−	0.854624i	$-0.673788\pi$
$269$	−279.355			−1.03850			−0.519248	+	0.854624i	$0.673788\pi$
$270$	137.353	−	232.452i	0.508717	−	0.860934i
$271$			353.019i			1.30265i	0.758797	+	0.651327i	$0.225787\pi$
$271$			353.019i			1.30265i	−0.758797	+	0.651327i	$0.774213\pi$
$272$	213.690	+	16.2709i	0.785626	+	0.0598194i
$273$	−6.13656	−	140.947i	−0.0224782	−	0.516288i
$274$	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	$0.742634\pi$
$278$	67.7033	+	105.615i	0.243537	+	0.379910i
$279$	−9.50828	−	108.988i	−0.0340798	−	0.390637i
$280$	103.214	+	33.0081i	0.368621	+	0.117886i
$281$		−	204.501i		−	0.727762i	−0.931445	−	0.363881i	$-0.881451\pi$
$281$		−	204.501i		−	0.727762i	0.931445	−	0.363881i	$-0.118549\pi$
$282$	38.8548	−	223.883i	0.137783	−	0.793912i
$283$	4.95961	+	4.95961i	0.0175251	+	0.0175251i	0.715815	−	0.698290i	$-0.246055\pi$
$283$	4.95961	+	4.95961i	0.0175251	+	0.0175251i	−0.698290	+	0.715815i	$0.746055\pi$
$284$	148.360	−	322.898i	0.522396	−	1.13697i
$285$	−185.025	−	463.199i	−0.649209	−	1.62526i
$286$	233.082	+	50.9844i	0.814972	+	0.178267i
$287$	97.5378	+	97.5378i	0.339853	+	0.339853i
$288$	58.4364	−	282.009i	0.202904	−	0.979199i
$289$			109.593i			0.379214i
$290$	14.1263	−	18.0435i	0.0487112	−	0.0622191i
$291$	−94.9192	−	86.9988i	−0.326183	−	0.298965i
$292$	139.834	+	377.558i	0.478885	+	1.29301i
$293$	−195.635	−	195.635i	−0.667697	−	0.667697i	0.289485	−	0.957182i	$-0.406516\pi$
$293$	−195.635	−	195.635i	−0.667697	−	0.667697i	−0.957182	+	0.289485i	$0.906516\pi$
$294$	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
$297$	−183.975	+	24.1520i	−0.619445	+	0.0813198i
$298$	−180.566	−	281.678i	−0.605927	−	0.945227i
$299$			176.998i			0.591967i
$300$	84.5937	+	287.826i	0.281979	+	0.959421i
$301$	−58.2251			−0.193439
$302$	−126.718	+	81.2313i	−0.419597	+	0.268978i
$303$	−16.2196	−	372.539i	−0.0535302	−	1.22950i
$304$	−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	$0.518018\pi$
$307$	−323.877	+	323.877i	−1.05497	+	1.05497i	−0.998398	+	0.0565751i	$0.981982\pi$
$308$	−25.8646	−	69.8355i	−0.0839761	−	0.226739i
$309$	410.248	+	376.015i	1.32766	+	1.21688i
$310$	95.7137	+	74.9341i	0.308754	+	0.241723i
$311$	−428.968			−1.37932			−0.689660	−	0.724133i	$-0.742240\pi$
$311$	−428.968			−1.37932			−0.689660	+	0.724133i	$0.742240\pi$
$312$	236.108	−	343.248i	0.756757	−	1.10015i
$313$	−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
$315$	−114.014	−	43.1570i	−0.361950	−	0.137006i
$316$	125.487	−	273.115i	0.397110	−	0.864288i
$317$	−299.797	+	299.797i	−0.945733	+	0.945733i	−0.998601	−	0.0528685i	$-0.983164\pi$
$317$	−299.797	+	299.797i	−0.945733	+	0.945733i	0.0528685	+	0.998601i	$0.483164\pi$
$318$	−22.5160	+	129.738i	−0.0708049	+	0.407981i
$319$	−15.7484			−0.0493679
$320$	184.686	+	261.326i	0.577144	+	0.816643i
$321$	−35.8655	−	32.8727i	−0.111730	−	0.102407i
$322$	46.5101	−	29.8148i	0.144441	−	0.0925924i
$323$	−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
$327$	−10.4410	−	239.812i	−0.0319296	−	0.733370i
$328$	56.5801	+	403.389i	0.172500	+	1.22985i
$329$	−102.598			−0.311847
$330$	119.912	−	167.712i	0.363371	−	0.508219i
$331$			89.1276i			0.269268i	0.990895	+	0.134634i	$0.0429858\pi$
$331$			89.1276i			0.269268i	−0.990895	+	0.134634i	$0.957014\pi$
$332$	115.237	+	311.144i	0.347100	+	0.937181i
$333$	−202.070	−	169.641i	−0.606815	−	0.509432i
$334$	−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	$0.871098\pi$
$338$	222.812	−	142.831i	0.659206	−	0.422577i
$339$	202.846	+	185.920i	0.598365	+	0.548435i
$340$	206.397	−	170.772i	0.607051	−	0.502270i
$341$		−	83.5387i		−	0.244982i
$342$	365.590	+	473.917i	1.06898	+	1.38572i
$343$	−173.671	−	173.671i	−0.506330	−	0.506330i
$344$	−137.289	−	103.514i	−0.399096	−	0.300912i
$345$	140.551	+	60.3151i	0.407394	+	0.174826i
$346$	−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	$0.504963\pi$
$348$	−10.3830	+	25.4630i	−0.0298363	+	0.0731696i
$349$		−	190.129i		−	0.544782i	−0.962187	−	0.272391i	$-0.912186\pi$
$349$		−	190.129i		−	0.544782i	0.962187	−	0.272391i	$-0.0878144\pi$
$350$	121.513	−	59.8546i	0.347179	−	0.171013i
$351$	−285.457	+	371.732i	−0.813268	+	1.05906i
$352$	63.1686	−	210.648i	0.179456	−	0.598432i
$353$	−66.4041	−	66.4041i	−0.188114	−	0.188114i	0.606767	−	0.794880i	$-0.292466\pi$
$353$	−66.4041	−	66.4041i	−0.188114	−	0.188114i	−0.794880	+	0.606767i	$0.792466\pi$
$354$	−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
$357$	4.73503	+	108.756i	0.0132634	+	0.304638i
$358$	−180.112	+	115.459i	−0.503106	+	0.322510i
$359$		−	402.003i		−	1.11979i	−0.828565	−	0.559893i	$-0.810842\pi$
$359$		−	402.003i		−	1.11979i	0.828565	−	0.559893i	$-0.189158\pi$
$360$	−192.109	−	304.457i	−0.533637	−	0.845714i
$361$	744.721			2.06294
$362$	−12.5266	−	19.5411i	−0.0346038	−	0.0539809i
$363$	221.102	−	9.62639i	0.609098	−	0.0265190i
$364$	−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	$-0.864859\pi$
$367$	−183.244	+	183.244i	−0.499301	+	0.499301i	0.411919	+	0.911220i	$0.364859\pi$
$368$	162.672	+	12.3862i	0.442042	+	0.0336582i
$369$	−39.8277	−	456.521i	−0.107934	−	1.23719i
$370$	291.003	−	35.4352i	0.786495	−	0.0957709i
$371$	59.4543			0.160254
$372$	−135.071	−	55.0779i	−0.363094	−	0.148059i
$373$	−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
$375$	325.856	+	185.588i	0.868949	+	0.494902i
$376$	−241.915	−	182.400i	−0.643391	−	0.485106i
$377$	−28.1278	+	28.1278i	−0.0746096	+	0.0746096i
$378$	145.765	+	12.3930i	0.385621	+	0.0327857i
$379$	−116.155			−0.306478			−0.153239	−	0.988189i	$-0.548970\pi$
$379$	−116.155			−0.306478			−0.153239	+	0.988189i	$0.548970\pi$
$380$	−662.101	−	62.5388i	−1.74237	−	0.164576i
$381$	182.290	−	198.886i	0.478452	−	0.522010i
$382$	−146.710	−	228.863i	−0.384058	−	0.599118i
$383$	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
$387$	148.147	+	124.372i	0.382810	+	0.321376i
$388$	−160.990	+	59.6250i	−0.414922	+	0.153673i
$389$	120.985			0.311017			0.155508	−	0.987835i	$-0.450298\pi$
$389$	120.985			0.311017			0.155508	+	0.987835i	$0.450298\pi$
$390$	−85.3744	−	513.721i	−0.218909	−	1.31723i
$391$		−	136.574i		−	0.349293i
$392$	−46.2942	−	330.056i	−0.118098	−	0.841979i
$393$	431.682	−	18.7946i	1.09843	−	0.0478235i
$394$	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	$-0.683589\pi$
$398$	−31.3319	−	48.8768i	−0.0787234	−	0.122806i
$399$	182.603	−	199.227i	0.457652	−	0.499317i
$400$	392.926	+	74.8960i	0.982314	+	0.187240i
$401$			177.597i			0.442885i	0.975173	+	0.221442i	$0.0710765\pi$
$401$			177.597i			0.442885i	−0.975173	+	0.221442i	$0.928924\pi$
$402$	−271.328	−	47.0887i	−0.674944	−	0.117136i
$403$	−149.207	−	149.207i	−0.370240	−	0.370240i
$404$	−451.783	−	207.578i	−1.11827	−	0.513808i
$405$	197.911	+	353.350i	0.488669	+	0.872469i
$406$	12.1292	+	2.65315i	0.0298750	+	0.00653486i
$407$	−142.457	−	142.457i	−0.350018	−	0.350018i
$408$	−182.184	+	264.854i	−0.446529	+	0.649152i
$409$			348.822i			0.852865i	0.904519	+	0.426433i	$0.140230\pi$
$409$			348.822i			0.852865i	−0.904519	+	0.426433i	$0.859770\pi$
$410$	400.920	+	313.879i	0.977853	+	0.765559i
$411$	−39.0441	+	42.5986i	−0.0949977	+	0.103646i
$412$	695.809	−	257.703i	1.68886	−	0.625494i
$413$	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
$417$	−188.000	+	8.18518i	−0.450840	+	0.0196287i
$418$	246.655	+	384.774i	0.590084	+	0.920512i
$419$			104.631i			0.249716i	0.992175	+	0.124858i	$0.0398476\pi$
$419$			104.631i			0.249716i	−0.992175	+	0.124858i	$0.960152\pi$
$420$	−120.610	+	108.969i	−0.287167	+	0.259449i
$421$	207.644			0.493217			0.246609	−	0.969115i	$-0.420684\pi$
$421$	207.644			0.493217			0.246609	+	0.969115i	$0.420684\pi$
$422$	634.691	−	406.862i	1.50401	−	0.964127i
$423$	261.048	+	219.155i	0.617136	+	0.518096i
$424$	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
$428$	−60.8303	+	22.5294i	−0.142127	+	0.0526389i
$429$	−241.819	+	263.834i	−0.563681	+	0.614998i
$430$	−213.349	+	25.9794i	−0.496161	+	0.0604171i
$431$	135.966			0.315467			0.157734	−	0.987482i	$-0.449581\pi$
$431$	135.966			0.315467			0.157734	+	0.987482i	$0.449581\pi$
$432$	321.667	+	288.365i	0.744599	+	0.667512i
$433$	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
$435$	12.7508	+	31.9208i	0.0293121	+	0.0733812i
$436$	−290.823	−	133.623i	−0.667026	−	0.306475i
$437$	−239.748	+	239.748i	−0.548622	+	0.548622i
$438$	−595.037	−	103.268i	−1.35853	−	0.235772i
$439$	−408.305			−0.930080			−0.465040	−	0.885290i	$-0.653960\pi$
$439$	−408.305			−0.930080			−0.465040	+	0.885290i	$0.653960\pi$
$440$	−125.933	−	244.352i	−0.286212	−	0.555345i
$441$	32.5873	+	373.529i	0.0738940	+	0.847004i
$442$	−391.488	+	250.959i	−0.885720	+	0.567781i
$443$	−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
$447$	501.401	−	21.8301i	1.12170	−	0.0488368i
$448$	−84.1400	+	151.597i	−0.187813	+	0.338386i
$449$	452.663			1.00816			0.504079	−	0.863657i	$-0.331832\pi$
$449$	452.663			1.00816			0.504079	+	0.863657i	$0.331832\pi$
$450$	−437.029	−	107.265i	−0.971175	−	0.238366i
$451$		−	349.922i		−	0.775880i
$452$	344.041	−	127.421i	0.761152	−	0.281904i
$453$	−9.82069	−	225.565i	−0.0216792	−	0.497936i
$454$	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	$0.612548\pi$
$458$	376.719	−	241.491i	0.822531	−	0.527274i
$459$	220.262	−	286.832i	0.479873	−	0.624906i
$460$	157.120	−	130.000i	0.341565	−	0.282609i
$461$		−	582.469i		−	1.26349i	−0.775176	−	0.631745i	$-0.782339\pi$
$461$		−	582.469i		−	1.26349i	0.775176	−	0.631745i	$-0.217661\pi$
$462$	110.062	+	19.1012i	0.238229	+	0.0413445i
$463$	−318.146	−	318.146i	−0.687140	−	0.687140i	0.274459	−	0.961599i	$-0.411501\pi$
$463$	−318.146	−	318.146i	−0.687140	−	0.687140i	−0.961599	+	0.274459i	$0.911501\pi$
$464$	23.8827	+	27.8195i	0.0514714	+	0.0599558i
$465$	−169.327	+	67.6376i	−0.364144	+	0.145457i
$466$	−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	$-0.566951\pi$
$468$	267.151	+	564.938i	0.570837	+	1.20713i
$469$			124.340i			0.265116i
$470$	−375.939	+	45.7778i	−0.799871	+	0.0973997i
$471$	−224.206	−	205.498i	−0.476022	−	0.436301i
$472$	70.1118	+	499.864i	0.148542	+	1.05903i
$473$	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
$477$	−151.275	−	126.998i	−0.317138	−	0.266243i
$478$	522.327	−	334.832i	1.09273	−	0.700485i
$479$			857.141i			1.78944i	0.446629	+	0.894719i	$0.352625\pi$
$479$			857.141i			1.78944i	−0.446629	+	0.894719i	$0.647375\pi$
$480$	−478.114	+	42.5142i	−0.996070	+	0.0885714i
$481$	−508.880			−1.05796
$482$	−129.419	−	201.889i	−0.268504	−	0.418857i
$483$	3.60454	+	82.7904i	0.00746281	+	0.171409i
$484$	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	$-0.795346\pi$
$487$	−97.7824	+	97.7824i	−0.200785	+	0.200785i	0.599551	+	0.800336i	$0.295346\pi$
$488$	−225.593	+	31.6421i	−0.462281	+	0.0648403i
$489$	−192.195	−	176.157i	−0.393036	−	0.360240i
$490$	−328.035	−	256.818i	−0.669460	−	0.524119i
$491$	770.213			1.56866			0.784331	−	0.620342i	$-0.213006\pi$
$491$	770.213			1.56866			0.784331	+	0.620342i	$0.213006\pi$
$492$	−565.777	−	230.707i	−1.14995	−	0.468916i
$493$	21.7037	−	21.7037i	0.0440238	−	0.0440238i
$494$	1127.78	+	246.692i	2.28296	+	0.499376i
$495$	127.102	+	281.930i	0.256772	+	0.569556i
$496$	−147.571	+	126.688i	−0.297522	+	0.255420i
$497$	170.179	−	170.179i	0.342412	−	0.342412i
$498$	−490.368	−	85.1031i	−0.984675	−	0.170890i
$499$	66.3836			0.133033			0.0665166	−	0.997785i	$-0.478811\pi$
$499$	66.3836			0.133033			0.0665166	+	0.997785i	$0.478811\pi$
$500$	418.542	−	273.538i	0.837083	−	0.547075i
$501$	−115.050	−	105.450i	−0.229640	−	0.210478i
$502$	362.933	+	566.164i	0.722974	+	1.12782i
$503$	−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
$507$	17.2680	+	396.617i	0.0340591	+	0.782281i
$508$	−124.933	−	337.325i	−0.245932	−	0.664025i
$509$	447.822			0.879807			0.439904	−	0.898045i	$-0.355013\pi$
$509$	447.822			0.879807			0.439904	+	0.898045i	$0.355013\pi$
$510$	65.8758	+	396.392i	0.129168	+	0.777240i
$511$			272.684i			0.533628i
$512$	−467.906	+	207.865i	−0.913879	+	0.405987i
$513$	−890.176	+	116.861i	−1.73524	+	0.227799i
$514$	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
$518$	85.7192	+	133.719i	0.165481	+	0.258145i
$519$	−431.293	−	395.304i	−0.831007	−	0.761665i
$520$	−661.359	−	211.504i	−1.27184	−	0.406739i
$521$		−	373.093i		−	0.716109i	−0.933701	−	0.358054i	$-0.883440\pi$
$521$		−	373.093i		−	0.716109i	0.933701	−	0.358054i	$-0.116560\pi$
$522$	−25.1942	−	32.6595i	−0.0482648	−	0.0625660i
$523$	593.137	+	593.137i	1.13411	+	1.13411i	0.989488	+	0.144618i	$0.0461953\pi$
$523$	593.137	+	593.137i	1.13411	+	1.13411i	0.144618	+	0.989488i	$0.453805\pi$
$524$	240.533	−	523.507i	0.459032	−	0.999058i
$525$	−13.9770	+	202.700i	−0.0266229	+	0.386096i
$526$	298.212	+	65.2311i	0.566943	+	0.124013i
$527$	115.130	+	115.130i	0.218462	+	0.218462i
$528$	225.557	+	240.709i	0.427191	+	0.455888i
$529$			425.033i			0.803466i
$530$	217.853	−	26.5278i	0.411044	−	0.0500525i
$531$	−49.3529	−	565.703i	−0.0929432	−	1.06535i
$532$	−125.148	−	337.904i	−0.235240	−	0.635157i
$533$	−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
$537$	−13.9587	−	320.609i	−0.0259939	−	0.597036i
$538$	−301.522	−	470.364i	−0.560449	−	0.874283i
$539$			286.308i			0.531184i
$540$	539.643	−	19.6280i	0.999339	−	0.0363482i
$541$	−46.0398			−0.0851012			−0.0425506	−	0.999094i	$-0.513548\pi$
$541$	−46.0398			−0.0851012			−0.0425506	+	0.999094i	$0.513548\pi$
$542$	−594.395	+	381.030i	−1.09667	+	0.703008i
$543$	34.7842	−	1.51444i	0.0640592	−	0.00278902i
$544$	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	$-0.476100\pi$
$547$	586.492	−	586.492i	1.07220	−	1.07220i	0.997182	−	0.0750146i	$-0.0239004\pi$
$548$	26.7590	+	72.2503i	0.0488303	+	0.131844i
$549$	255.307	−	22.2734i	0.465040	−	0.0405708i
$550$	−325.332	−	110.600i	−0.591513	−	0.201092i
$551$	−76.1995			−0.138293
$552$	−138.687	+	201.620i	−0.251245	+	0.365254i
$553$	143.941	−	143.941i	0.260292	−	0.260292i
$554$	−5.47855	+	25.0459i	−0.00988908	+	0.0452092i
$555$	−173.409	+	404.092i	−0.312449	+	0.728094i
$556$	−104.754	+	227.991i	−0.188406	+	0.410055i
$557$	−413.911	+	413.911i	−0.743108	+	0.743108i	−0.973175	−	0.230067i	$-0.926106\pi$
$557$	−413.911	+	413.911i	−0.743108	+	0.743108i	0.230067	+	0.973175i	$0.426106\pi$
$558$	173.245	−	133.645i	0.310475	−	0.239508i
$559$	373.086			0.667416
$560$	55.8263	+	209.413i	0.0996899	+	0.373953i
$561$	186.590	−	203.577i	0.332603	−	0.362883i
$562$	344.328	−	220.728i	0.612684	−	0.392754i
$563$	−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
$567$	−125.951	+	179.690i	−0.222137	+	0.316913i
$568$	703.812	−	98.7180i	1.23911	−	0.173799i
$569$	−745.467			−1.31014			−0.655068	−	0.755570i	$-0.727360\pi$
$569$	−745.467			−1.31014			−0.655068	+	0.755570i	$0.727360\pi$
$570$	580.204	−	811.487i	1.01790	−	1.42366i
$571$		−	406.663i		−	0.712195i	−0.934449	−	0.356097i	$-0.884107\pi$
$571$		−	406.663i		−	0.712195i	0.934449	−	0.356097i	$-0.115893\pi$
$572$	165.732	+	447.481i	0.289741	+	0.782310i
$573$	407.388	−	17.7369i	0.710975	−	0.0309545i
$574$	−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	$0.721106\pi$
$578$	−184.527	+	118.289i	−0.319251	+	0.204652i
$579$	179.844	−	196.217i	0.310611	−	0.338889i
$580$	45.6279	+	4.30979i	0.0786688	+	0.00743068i
$581$			224.718i			0.386778i
$582$	44.0333	−	253.722i	0.0756586	−	0.435949i
$583$	−106.648	−	106.648i	−0.182929	−	0.182929i
$584$	−484.783	+	642.962i	−0.830108	+	1.10096i
$585$	730.564	+	276.535i	1.24883	+	0.472710i
$586$	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	$0.919832\pi$
$588$	462.923	+	188.766i	0.787284	+	0.321030i
$589$		−	404.208i		−	0.686261i
$590$	496.804	+	388.946i	0.842040	+	0.659231i
$591$	−278.025	+	303.336i	−0.470431	+	0.513259i
$592$	−35.6111	+	467.690i	−0.0601538	+	0.790017i
$593$	406.869	+	406.869i	0.686119	+	0.686119i	0.961372	−	0.275253i	$-0.0887616\pi$
$593$	406.869	+	406.869i	0.686119	+	0.686119i	−0.275253	+	0.961372i	$0.588762\pi$
$594$	−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
$597$	87.0033	−	3.78796i	0.145734	−	0.00634500i
$598$	−298.020	+	191.043i	−0.498362	+	0.319469i
$599$		−	293.225i		−	0.489525i	−0.969583	−	0.244762i	$-0.921290\pi$
$599$		−	293.225i		−	0.489525i	0.969583	−	0.244762i	$-0.0787100\pi$
$600$	−393.321	+	453.099i	−0.655535	+	0.755165i
$601$	−1087.24			−1.80905			−0.904523	−	0.426424i	$-0.859773\pi$
$601$	−1087.24			−1.80905			−0.904523	+	0.426424i	$0.859773\pi$
$602$	−62.8451	−	98.0363i	−0.104394	−	0.162851i
$603$	265.597	−	316.369i	0.440459	−	0.524658i
$604$	−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	$-0.777833\pi$
$607$	−74.9651	+	74.9651i	−0.123501	+	0.123501i	0.642655	+	0.766156i	$0.277833\pi$
$608$	305.645	−	1019.23i	0.502706	−	1.67637i
$609$	−12.5839	+	13.7295i	−0.0206632	+	0.0225444i
$610$	−175.535	+	224.212i	−0.287762	+	0.367560i
$611$	657.409			1.07596
$612$	−206.137	−	435.912i	−0.336825	−	0.712274i
$613$	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
$615$	−709.267	+	283.316i	−1.15328	+	0.460677i
$616$	89.6684	−	118.926i	0.145566	−	0.193062i
$617$	115.002	−	115.002i	0.186389	−	0.186389i	−0.607744	−	0.794133i	$-0.707925\pi$
$617$	115.002	−	115.002i	0.186389	−	0.186389i	0.794133	+	0.607744i	$0.207925\pi$
$618$	−190.315	+	1096.60i	−0.307953	+	1.77444i
$619$	710.704			1.14815			0.574074	−	0.818803i	$-0.305362\pi$
$619$	710.704			1.14815			0.574074	+	0.818803i	$0.305362\pi$
$620$	−22.8617	+	242.038i	−0.0368737	+	0.390383i
$621$	167.674	−	218.351i	0.270006	−	0.351612i
$622$	−463.006	−	722.275i	−0.744383	−	1.16121i
$623$	−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
$627$	−684.918	+	29.8201i	−1.09237	+	0.0475599i
$628$	−380.270	+	140.839i	−0.605525	+	0.224265i
$629$	392.657			0.624256
$630$	−50.3955	−	238.553i	−0.0799929	−	0.378655i
$631$			209.771i			0.332443i	0.986088	+	0.166221i	$0.0531566\pi$
$631$			209.771i			0.332443i	−0.986088	+	0.166221i	$0.946843\pi$
$632$	595.301	−	83.4980i	0.941932	−	0.132117i
$633$	49.1887	+	1129.78i	0.0777072	+	1.78481i
$634$	−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
$638$	−16.9980	−	26.5163i	−0.0266426	−	0.0415616i
$639$	−796.514	+	69.4892i	−1.24650	+	0.108747i
$640$	−240.666	+	593.026i	−0.376041	+	0.926603i
$641$			1193.44i			1.86184i	0.365221	+	0.930921i	$0.380993\pi$
$641$			1193.44i			1.86184i	−0.365221	+	0.930921i	$0.619007\pi$
$642$	16.6381	−	95.8695i	0.0259160	−	0.149329i
$643$	424.387	+	424.387i	0.660012	+	0.660012i	0.955383	−	0.295371i	$-0.0954433\pi$
$643$	424.387	+	424.387i	0.660012	+	0.660012i	−0.295371	+	0.955383i	$0.595443\pi$
$644$	100.401	+	46.1308i	0.155902	+	0.0716316i
$645$	127.135	−	296.261i	0.197109	−	0.459319i
$646$	−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	$0.541977\pi$
$648$	−616.437	+	199.772i	−0.951292	+	0.308290i
$649$		−	433.609i		−	0.668119i
$650$	−778.610	+	383.528i	−1.19786	+	0.590042i
$651$	−72.8296	−	66.7525i	−0.111873	−	0.102538i
$652$	−325.976	+	120.730i	−0.499963	+	0.185169i
$653$	730.267	+	730.267i	1.11833	+	1.11833i	0.991987	+	0.126340i	$0.0403230\pi$
$653$	730.267	+	730.267i	1.11833	+	1.11833i	0.126340	+	0.991987i	$0.459677\pi$
$654$	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
$657$	582.470	−	693.815i	0.886560	−	1.05604i
$658$	−110.738	−	172.748i	−0.168295	−	0.262536i
$659$			929.519i			1.41050i	0.708959	+	0.705250i	$0.249165\pi$
$659$			929.519i			1.41050i	−0.708959	+	0.705250i	$0.750835\pi$
$660$	411.813	+	20.8824i	0.623958	+	0.0316400i
$661$	564.895			0.854607			0.427303	−	0.904108i	$-0.359464\pi$
$661$	564.895			0.854607			0.427303	+	0.904108i	$0.359464\pi$
$662$	−150.068	+	96.1997i	−0.226690	+	0.145317i
$663$	−30.3404	−	696.870i	−0.0457623	−	1.05109i
$664$	−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
$668$	−195.132	+	72.2703i	−0.292114	+	0.108189i
$669$	−799.131	−	732.449i	−1.19452	−	1.09484i
$670$	55.4789	+	455.607i	0.0828043	+	0.680010i
$671$	195.692			0.291642
$672$	−133.169	−	223.391i	−0.198168	−	0.332428i
$673$	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
$675$	468.543	−	485.893i	0.694138	−	0.719842i
$676$	480.983	+	220.995i	0.711513	+	0.326915i
$677$	530.496	−	530.496i	0.783598	−	0.783598i	−0.196838	−	0.980436i	$-0.563067\pi$
$677$	530.496	−	530.496i	0.783598	−	0.783598i	0.980436	+	0.196838i	$0.0630672\pi$
$678$	−94.1007	+	542.213i	−0.138792	+	0.799724i
$679$	−116.272			−0.171240
$680$	510.311	+	163.199i	0.750458	+	0.239999i
$681$	341.055	+	312.596i	0.500815	+	0.459026i
$682$	140.658	−	90.1673i	0.206244	−	0.132210i
$683$	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
$687$	29.1958	+	670.580i	0.0424975	+	0.976099i
$688$	26.1083	−	342.887i	0.0379481	−	0.498383i
$689$	−380.962			−0.552920
$690$	50.1479	+	301.753i	0.0726782	+	0.437324i
$691$			690.583i			0.999396i	0.866200	+	0.499698i	$0.166556\pi$
$691$			690.583i			0.999396i	−0.866200	+	0.499698i	$0.833444\pi$
$692$	−731.503	+	270.923i	−1.05708	+	0.391508i
$693$	−107.737	+	128.332i	−0.155465	+	0.185184i
$694$	−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
$698$	320.129	−	205.215i	0.458638	−	0.294004i
$699$	−195.242	−	178.950i	−0.279316	−	0.256009i
$700$	231.934	+	139.993i	0.331335	+	0.199989i
$701$			129.593i			0.184869i	0.995719	+	0.0924343i	$0.0294648\pi$
$701$			129.593i			0.184869i	−0.995719	+	0.0924343i	$0.970535\pi$
$702$	−934.010	−	79.4100i	−1.33050	−	0.113120i
$703$	−689.289	−	689.289i	−0.980496	−	0.980496i
$704$	422.859	−	121.002i	0.600652	−	0.171879i
$705$	224.023	−	522.036i	0.317763	−	0.740477i
$706$	40.1347	−	183.481i	0.0568480	−	0.259888i
$707$	−238.105	−	238.105i	−0.336783	−	0.336783i
$708$	−701.089	−	285.883i	−0.990238	−	0.403789i
$709$			86.8545i			0.122503i	0.998122	+	0.0612514i	$0.0195091\pi$
$709$			86.8545i			0.122503i	−0.998122	+	0.0612514i	$0.980491\pi$
$710$	547.640	−	699.503i	0.771323	−	0.985216i
$711$	−673.710	+	58.7756i	−0.947553	+	0.0826661i
$712$	−325.662	+	45.6780i	−0.457391	+	0.0641545i
$713$	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
$717$	40.4804	+	929.769i	0.0564581	+	1.29675i
$718$	676.872	−	433.901i	0.942719	−	0.604319i
$719$			104.099i			0.144782i	0.997376	+	0.0723912i	$0.0230630\pi$
$719$			104.099i			0.144782i	−0.997376	+	0.0723912i	$0.976937\pi$
$720$	305.276	−	652.079i	0.423995	−	0.905665i
$721$	502.534			0.696996
$722$	803.812	+	1253.92i	1.11331	+	1.73673i
$723$	359.373	−	15.6464i	0.497059	−	0.0216410i
$724$	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	$-0.671161\pi$
$727$	252.054	−	252.054i	0.346704	−	0.346704i	0.858880	+	0.512176i	$0.171161\pi$
$728$	−52.2569	−	372.567i	−0.0717814	−	0.511768i
$729$	704.298	−	188.161i	0.966116	−	0.258109i
$730$	121.668	+	999.172i	0.166669	+	1.36873i
$731$	−287.877			−0.393812
$732$	129.021	−	316.408i	0.176259	−	0.432251i
$733$	−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
$735$	580.327	−	231.811i	0.789560	−	0.315390i
$736$	154.724	+	287.267i	0.210223	+	0.390308i
$737$	223.037	−	223.037i	0.302629	−	0.302629i
$738$	725.679	−	559.805i	0.983305	−	0.758543i
$739$	622.137			0.841863			0.420931	−	0.907092i	$-0.361703\pi$
$739$	622.137			0.841863			0.420931	+	0.907092i	$0.361703\pi$
$740$	373.757	+	451.729i	0.505078	+	0.610445i
$741$	−1170.06	+	1276.58i	−1.57902	+	1.72278i
$742$	64.1718	+	100.106i	0.0864850	+	0.134914i
$743$	−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
$747$	480.011	−	571.770i	0.642585	−	0.765422i
$748$	−127.880	−	345.281i	−0.170963	−	0.461606i
$749$	−43.9335			−0.0586562
$750$	39.2277	+	748.973i	0.0523037	+	0.998631i
$751$			1089.00i			1.45007i	0.688711	+	0.725036i	$0.258177\pi$
$751$			1089.00i			1.45007i	−0.688711	+	0.725036i	$0.741823\pi$
$752$	46.0050	−	604.197i	0.0611769	−	0.803454i
$753$	−1007.80	+	43.8778i	−1.33838	+	0.0582706i
$754$	−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	$0.949590\pi$
$758$	−125.372	−	195.576i	−0.165398	−	0.258016i
$759$	142.042	−	154.973i	0.187143	−	0.204181i
$760$	−609.337	−	1182.31i	−0.801759	−	1.55567i
$761$		−	723.259i		−	0.950407i	−0.879876	−	0.475203i	$-0.842375\pi$
$761$		−	723.259i		−	0.950407i	0.879876	−	0.475203i	$-0.157625\pi$
$762$	531.628	+	92.2638i	0.697675	+	0.121081i
$763$	−153.274	−	153.274i	−0.200883	−	0.200883i
$764$	226.997	−	494.046i	0.297116	−	0.646657i
$765$	−563.710	−	213.377i	−0.736876	−	0.278925i
$766$	1215.11	+	265.794i	1.58631	+	0.346990i
$767$	−774.460	−	774.460i	−1.00973	−	1.00973i
$768$	83.1500	−	763.485i	0.108268	−	0.994122i
$769$			180.270i			0.234421i	0.993107	+	0.117210i	$0.0373952\pi$
$769$			180.270i			0.234421i	−0.993107	+	0.117210i	$0.962605\pi$
$770$	−22.5046	−	184.813i	−0.0292267	−	0.240017i
$771$	−572.307	+	624.410i	−0.742292	+	0.809870i
$772$	−123.257	−	332.798i	−0.159659	−	0.431085i
$773$	−482.107	−	482.107i	−0.623683	−	0.623683i	0.322788	−	0.946471i	$-0.395380\pi$
$773$	−482.107	−	482.107i	−0.623683	−	0.623683i	−0.946471	+	0.322788i	$0.895380\pi$
$774$	−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
$777$	−238.027	+	10.3633i	−0.306341	+	0.0133375i
$778$	130.585	+	203.709i	0.167848	+	0.261837i
$779$		−	1693.12i		−	2.17345i
$780$	772.828	−	698.232i	0.990805	−	0.895170i
$781$	−610.525			−0.781722
$782$	229.956	−	147.410i	0.294061	−	0.188504i
$783$	61.3455	−	8.05334i	0.0783468	−	0.0102852i
$784$	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	$-0.830720\pi$
$787$	−279.225	+	279.225i	−0.354797	+	0.354797i	0.507094	+	0.861891i	$0.330720\pi$
$788$	190.545	+	514.479i	0.241809	+	0.652892i
$789$	−309.391	+	337.558i	−0.392130	+	0.427830i
$790$	463.207	−	591.656i	0.586337	−	0.748932i
$791$	248.477			0.314130
$792$	−482.186	+	111.058i	−0.608820	+	0.140225i
$793$	349.521	−	349.521i	0.440758	−	0.440758i
$794$	331.978	−	1517.68i	0.418108	−	1.91143i
$795$	−129.819	+	302.515i	−0.163295	+	0.380522i
$796$	48.4782	−	105.510i	0.0609023	−	0.132550i
$797$	861.626	−	861.626i	1.08109	−	1.08109i	0.0846783	−	0.996408i	$-0.473014\pi$
$797$	861.626	−	861.626i	1.08109	−	1.08109i	0.996408	−	0.0846783i	$-0.0269863\pi$
$798$	532.541	+	92.4222i	0.667345	+	0.115817i
$799$	−507.264			−0.634873
$800$	297.998	+	742.427i	0.372497	+	0.928033i
$801$	368.557	−	32.1535i	0.460121	−	0.0401417i
$802$	−299.028	+	191.689i	−0.372853	+	0.239013i
$803$	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
$807$	837.273	−	36.4533i	1.03751	−	0.0451714i
$808$	−138.121	−	984.738i	−0.170942	−	1.21874i
$809$	−430.022			−0.531548			−0.265774	−	0.964035i	$-0.585627\pi$
$809$	−430.022			−0.531548			−0.265774	+	0.964035i	$0.585627\pi$
$810$	−381.338	+	714.620i	−0.470787	+	0.882247i
$811$		−	1351.37i		−	1.66630i	−0.553047	−	0.833150i	$-0.686535\pi$
$811$		−	1351.37i		−	1.66630i	0.553047	−	0.833150i	$-0.313465\pi$
$812$	8.62442	+	23.2863i	0.0106212	+	0.0286777i
$813$	−46.0658	−	1058.06i	−0.0566614	−	1.30142i
$814$	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
$818$	−587.328	+	376.500i	−0.718005	+	0.460269i
$819$	36.7845	+	421.639i	0.0449139	+	0.514822i
$820$	−95.7618	+	1013.83i	−0.116783	+	1.23638i
$821$		−	901.925i		−	1.09857i	−0.835636	−	0.549284i	$-0.814900\pi$
$821$		−	901.925i		−	1.09857i	0.835636	−	0.549284i	$-0.185100\pi$
$822$	−113.867	−	19.7616i	−0.138525	−	0.0240409i
$823$	512.252	+	512.252i	0.622421	+	0.622421i	0.946150	−	0.323729i	$-0.104937\pi$
$823$	512.252	+	512.252i	0.622421	+	0.622421i	−0.323729	+	0.946150i	$0.604937\pi$
$824$	1184.93	+	893.415i	1.43802	+	1.08424i
$825$	388.670	−	338.527i	0.471115	−	0.410336i
$826$	−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	$0.551253\pi$
$828$	−156.922	−	331.838i	−0.189519	−	0.400770i
$829$			1001.78i			1.20842i	0.796827	+	0.604208i	$0.206510\pi$
$829$			1001.78i			1.20842i	−0.796827	+	0.604208i	$0.793490\pi$
$830$	100.267	+	823.414i	0.120803	+	0.992065i
$831$	−28.3504	−	25.9847i	−0.0341160	−	0.0312692i
$832$	539.140	−	971.380i	0.648005	−	1.16752i
$833$	−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
$837$	42.7197	+	325.413i	0.0510391	+	0.388785i
$838$	−176.173	+	112.933i	−0.210230	+	0.134765i
$839$			189.192i			0.225497i	0.993624	+	0.112749i	$0.0359654\pi$
$839$			189.192i			0.225497i	−0.993624	+	0.112749i	$0.964035\pi$
$840$	−313.656	−	85.4622i	−0.373400	−	0.101741i
$841$	−835.749			−0.993756
$842$	224.120	+	349.621i	0.266176	+	0.415227i
$843$	26.6855	+	612.923i	0.0316554	+	0.727073i
$844$	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
$848$	−26.6595	+	350.126i	−0.0314381	+	0.412885i
$849$	−15.5119	−	14.2176i	−0.0182708	−	0.0167462i
$850$	600.784	−	295.934i	0.706804	−	0.348157i
$851$	298.910			0.351246
$852$	−402.525	+	987.138i	−0.472447	+	1.15861i
$853$	−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
$855$	614.991	+	1364.14i	0.719288	+	1.59548i
$856$	−103.591	−	78.1059i	−0.121018	−	0.0912452i
$857$	−684.012	+	684.012i	−0.798147	+	0.798147i	−0.982803	−	0.184656i	$-0.940883\pi$
$857$	−684.012	+	684.012i	−0.798147	+	0.798147i	0.184656	+	0.982803i	$0.440883\pi$
$858$	−705.237	−	122.393i	−0.821955	−	0.142650i
$859$	−1397.70			−1.62712			−0.813560	−	0.581481i	$-0.802473\pi$
$859$	−1397.70			−1.62712			−0.813560	+	0.581481i	$0.802473\pi$
$860$	−274.021	−	331.185i	−0.318629	−	0.385099i
$861$	−305.064	−	279.609i	−0.354314	−	0.324749i
$862$	146.755	+	228.933i	0.170249	+	0.265584i
$863$	−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
$867$	−14.3009	−	328.468i	−0.0164947	−	0.378855i
$868$	−123.524	+	45.7491i	−0.142309	+	0.0527063i
$869$	−516.396			−0.594242
$870$	−39.9841	+	55.9227i	−0.0459588	+	0.0642790i
$871$		−	796.724i		−	0.914724i
$872$	−88.9118	−	633.899i	−0.101963	−	0.726949i
$873$	295.841	+	248.363i	0.338878	+	0.284494i
$874$	−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	$0.745039\pi$
$878$	−440.703	−	687.483i	−0.501940	−	0.783010i
$879$	611.879	+	560.822i	0.696108	+	0.638022i
$880$	275.501	−	475.781i	0.313069	−	0.540660i
$881$			721.297i			0.818725i	0.912372	+	0.409363i	$0.134249\pi$
$881$			721.297i			0.818725i	−0.912372	+	0.409363i	$0.865751\pi$
$882$	−593.756	+	458.036i	−0.673192	+	0.519315i
$883$	−941.983	−	941.983i	−1.06680	−	1.06680i	−0.997603	−	0.0691949i	$-0.977957\pi$
$883$	−941.983	−	941.983i	−1.06680	−	1.06680i	−0.0691949	−	0.997603i	$-0.522043\pi$
$884$	−845.104	−	388.296i	−0.956000	−	0.439248i
$885$	−878.895	+	351.074i	−0.993102	+	0.396694i
$886$	−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	$0.622287\pi$
$888$	−579.669	−	398.734i	−0.652781	−	0.449025i
$889$		−	243.626i		−	0.274045i
$890$	−253.399	+	323.669i	−0.284718	+	0.363673i
$891$	548.252	−	96.3944i	0.615322	−	0.108187i
$892$	−1355.38	+	501.986i	−1.51949	+	0.562765i
$893$	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
$897$	−23.0966	−	530.492i	−0.0257487	−	0.591407i
$898$	488.581	+	762.171i	0.544077	+	0.848743i
$899$			27.8555i			0.0309850i
$900$	−291.099	−	851.623i	−0.323444	−	0.946247i
$901$	293.954			0.326253
$902$	589.180	−	377.687i	0.653193	−	0.418722i
$903$	174.510	−	7.59784i	0.193256	−	0.00841399i
$904$	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	$-0.701715\pi$
$907$	193.827	−	193.827i	0.213701	−	0.213701i	0.805838	+	0.592137i	$0.201715\pi$
$908$	578.454	−	214.239i	0.637064	−	0.235946i
$909$	97.2258	+	1114.44i	0.106959	+	1.22601i
$910$	−370.286	−	289.896i	−0.406908	−	0.318567i
$911$	−830.304			−0.911421			−0.455710	−	0.890128i	$-0.650615\pi$
$911$	−830.304			−0.911421			−0.455710	+	0.890128i	$0.650615\pi$
$912$	1091.37	+	1164.68i	1.19668	+	1.27707i
$913$	403.093	−	403.093i	0.441504	−	0.441504i
$914$	−163.484	+	747.386i	−0.178866	+	0.817709i
$915$	−158.443	−	396.653i	−0.173162	−	0.433501i
$916$	813.222	+	373.647i	0.887797	+	0.407911i
$917$	275.906	−	275.906i	0.300879	−	0.300879i
$918$	720.692	+	61.2736i	0.785067	+	0.0667468i
$919$	−1072.00			−1.16649			−0.583245	−	0.812296i	$-0.698217\pi$
$919$	−1072.00			−1.16649			−0.583245	+	0.812296i	$0.698217\pi$
$920$	388.474	+	124.235i	0.422254	+	0.135038i
$921$	928.448	−	1012.97i	1.00809	−	1.09986i
$922$	980.731	−	628.687i	1.06370	−	0.681873i
$923$	−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
$927$	−1278.64	−	1073.44i	−1.37934	−	1.15798i
$928$	−21.0632	+	70.2394i	−0.0226974	+	0.0756890i
$929$	1289.64			1.38821			0.694103	−	0.719876i	$-0.255801\pi$
$929$	1289.64			1.38821			0.694103	+	0.719876i	$0.255801\pi$
$930$	−296.648	−	212.100i	−0.318976	−	0.228064i
$931$			1385.32i			1.48799i
$932$	−331.144	+	122.644i	−0.355304	+	0.131592i
$933$	1285.69	−	55.9764i	1.37801	−	0.0599962i
$934$	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	$0.874974\pi$
$938$	−209.357	+	134.206i	−0.223195	+	0.143076i
$939$	413.229	−	450.849i	0.440073	−	0.480138i
$940$	−482.848	−	583.577i	−0.513668	−	0.620827i
$941$			707.695i			0.752067i	0.926606	+	0.376033i	$0.122712\pi$
$941$			707.695i			0.752067i	−0.926606	+	0.376033i	$0.877288\pi$
$942$	104.010	−	599.310i	0.110414	−	0.636211i
$943$	367.111	+	367.111i	0.389301	+	0.389301i
$944$	−765.970	+	657.578i	−0.811409	+	0.696586i
$945$	347.351	+	114.471i	0.367567	+	0.121133i
$946$	−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	$0.694330\pi$
$948$	−340.465	+	834.945i	−0.359140	+	0.880744i
$949$		−	1747.26i		−	1.84116i
$950$	−1574.14	−	535.148i	−1.65699	−	0.563313i
$951$	859.420	−	937.662i	0.903701	−	0.985974i
$952$	40.3220	+	287.476i	0.0423550	+	0.301971i
$953$	−414.033	−	414.033i	−0.434452	−	0.434452i	0.455688	−	0.890140i	$-0.349393\pi$
$953$	−414.033	−	414.033i	−0.434452	−	0.434452i	−0.890140	+	0.455688i	$0.849393\pi$
$954$	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
$957$	47.2004	−	2.05502i	0.0493212	−	0.00214735i
$958$	−1443.21	+	925.153i	−1.50648	+	0.965713i
$959$			52.1813i			0.0544122i
$960$	−587.634	−	759.135i	−0.612119	−	0.790766i
$961$	813.238			0.846241
$962$	−549.259	−	856.826i	−0.570955	−	0.890671i
$963$	111.784	+	93.8447i	0.116079	+	0.0974504i
$964$	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	$-0.877840\pi$
$967$	−534.588	+	534.588i	−0.552831	+	0.552831i	0.374426	+	0.927257i	$0.377840\pi$
$968$	584.444	−	81.9752i	0.603765	−	0.0846851i
$969$	902.828	−	985.022i	0.931711	−	1.01653i
$970$	−426.044	+	51.8791i	−0.439221	+	0.0534836i
$971$	−438.396			−0.451490			−0.225745	−	0.974186i	$-0.572482\pi$
$971$	−438.396			−0.451490			−0.225745	+	0.974186i	$0.572482\pi$
$972$	205.611	−	950.004i	0.211533	−	0.977371i
$973$	−120.159	+	120.159i	−0.123493	+	0.123493i
$974$	−270.182	−	59.0997i	−0.277394	−	0.0606773i
$975$	89.5598	−	1298.83i	0.0918562	−	1.33214i
$976$	−296.771	−	345.689i	−0.304068	−	0.354190i
$977$	−1230.19	+	1230.19i	−1.25915	+	1.25915i	−0.307644	+	0.951501i	$0.599541\pi$
$977$	−1230.19	+	1230.19i	−1.25915	+	1.25915i	−0.951501	+	0.307644i	$0.900459\pi$
$978$	89.1597	−	513.743i	0.0911654	−	0.525299i
$979$	282.497			0.288557
$980$	78.3529	−	829.525i	0.0799520	−	0.846454i
$981$	62.5865	+	717.392i	0.0637987	+	0.731287i
$982$	831.328	+	1296.85i	0.846566	+	1.32062i
$983$	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
$987$	307.501	−	13.3880i	0.311551	−	0.0135644i
$988$	801.903	+	2165.17i	0.811643	+	2.19147i
$989$	−219.146			−0.221584
$990$	−337.512	+	518.308i	−0.340921	+	0.523544i
$991$		−	1328.35i		−	1.34041i	−0.742176	−	0.670205i	$-0.766206\pi$
$991$		−	1328.35i		−	1.34041i	0.742176	−	0.670205i	$-0.233794\pi$
$992$	−372.592	−	111.732i	−0.375597	−	0.112633i
$993$	−11.6303	−	267.130i	−0.0117123	−	0.269013i
$994$	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	$0.878374\pi$
$998$	71.6510	+	111.773i	0.0717945	+	0.111997i
$999$	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.47.15	yes	40
3.2	odd	2	inner	60.3.l.a.47.6	yes	40
4.3	odd	2	inner	60.3.l.a.47.5	yes	40
5.2	odd	4		300.3.l.g.143.5		40
5.3	odd	4	inner	60.3.l.a.23.16	yes	40
5.4	even	2		300.3.l.g.107.6		40
12.11	even	2	inner	60.3.l.a.47.16	yes	40
15.2	even	4		300.3.l.g.143.16		40
15.8	even	4	inner	60.3.l.a.23.5	✓	40
15.14	odd	2		300.3.l.g.107.15		40
20.3	even	4	inner	60.3.l.a.23.6	yes	40
20.7	even	4		300.3.l.g.143.15		40
20.19	odd	2		300.3.l.g.107.16		40
60.23	odd	4	inner	60.3.l.a.23.15	yes	40
60.47	odd	4		300.3.l.g.143.6		40
60.59	even	2		300.3.l.g.107.5		40

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

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+(1.07935 + 1.68375i) q^{2} +(-2.99716 + 0.130491i) 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} +(-7.92245 + 1.11122i) q^{8} +(8.96594 - 0.782204i) q^{9} +(-6.16449 + 7.87394i) q^{10} +6.87236 q^{11} +(4.53101 - 11.1117i) q^{12} +(12.2746 - 12.2746i) q^{13} +(-5.29303 - 1.15780i) q^{14} +(-5.56425 - 13.9298i) q^{15} +(-10.4221 - 12.1400i) q^{16} +(-9.47120 + 9.47120i) q^{17} +(10.9944 + 14.2521i) q^{18} +33.2524 q^{19} +(-19.9114 - 1.88073i) q^{20} +(5.49143 - 5.99137i) q^{21} +(7.41767 + 11.5713i) 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} +(-26.7703 + 3.51436i) q^{27} +(-3.76357 - 10.1618i) q^{28} -2.29155 q^{29} +(17.4485 - 24.4039i) q^{30} -12.1558i q^{31} +(9.19168 - 30.6515i) q^{32} +(-20.5976 + 0.896780i) 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} +(35.8909 + 55.9886i) q^{38} +(-35.1872 + 38.3906i) q^{39} +(-18.3246 - 35.5557i) q^{40} -50.9173i q^{41} +(16.0151 + 2.77942i) q^{42} +(15.1975 + 15.1975i) q^{43} +(-11.4770 + 24.9790i) q^{44} +(18.4947 + 41.0237i) q^{45} +(-19.9218 - 4.35769i) q^{46} +(26.7793 + 26.7793i) q^{47} +(32.8208 + 35.0256i) q^{48} +41.6608i q^{49} +(-47.3392 - 16.0935i) q^{50} +(27.1508 - 29.6226i) q^{51} +(24.1157 + 65.1132i) 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} +(-99.6627 + 4.33913i) q^{57} +(-2.47338 - 3.85839i) q^{58} -63.0946i q^{59} +(59.9230 + 3.03861i) q^{60} +28.4752 q^{61} +(20.4672 - 13.1203i) q^{62} +(-15.6769 + 18.6737i) 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} +(-18.6079 - 50.2420i) q^{68} +(20.6685 - 22.5502i) q^{69} +(-3.27465 - 26.8922i) q^{70} -88.8377 q^{71} +(-70.1630 + 16.1601i) q^{72} +(71.1740 - 71.1740i) q^{73} +(12.5286 - 57.2763i) q^{74} +(56.5556 - 49.2592i) q^{75} +(-55.5320 + 120.862i) q^{76} +(-13.1648 + 13.1648i) q^{77} +(-102.619 - 17.8095i) q^{78} -75.1410 q^{79} +(40.0882 - 69.2310i) q^{80} +(79.7763 - 14.0264i) q^{81} +(85.7318 - 54.9574i) 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} +(6.86815 - 0.299026i) q^{87} +(-54.4459 + 7.63668i) q^{88} +41.1063 q^{89} +(-49.1115 + 75.4192i) q^{90} +47.0267i q^{91} +(-14.1653 - 38.2467i) q^{92} +(1.58621 + 36.4327i) 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} +(-70.1464 + 44.9665i) q^{98} +(61.6172 - 5.37559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45}+ \cdots + 72 q^{97}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more