LMFDB - Embedded newform 60.3.l.a.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68375 + 1.07935i) q^{2} +(2.99716 + 0.130491i) q^{3} +(1.67002 - 3.63470i) q^{4} +(1.65103 - 4.71955i) q^{5} +(-5.18731 + 3.01526i) q^{6} +(1.91561 + 1.91561i) q^{7} +(1.11122 + 7.92245i) q^{8} +(8.96594 + 0.782204i) q^{9} +O(q^{10})$	\(q+(-1.68375 + 1.07935i) q^{2} +(2.99716 + 0.130491i) q^{3} +(1.67002 - 3.63470i) q^{4} +(1.65103 - 4.71955i) q^{5} +(-5.18731 + 3.01526i) 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} +(5.47960 - 10.6759i) 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} +(-15.9407 + 8.36034i) 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} +(2.29669 + 23.8899i) q^{24} +(-19.5482 - 15.5842i) q^{25} +(-33.9159 - 7.41877i) q^{26} +(26.7703 + 3.51436i) q^{27} +(10.1618 - 3.76357i) q^{28} -2.29155 q^{29} +(5.66629 + 29.4600i) q^{30} -12.1558i q^{31} +(30.6515 + 9.19168i) q^{32} +(-20.5976 - 0.896780i) q^{33} +(26.1698 + 5.72440i) q^{34} +(12.2036 - 5.87810i) q^{35} +(17.8164 - 31.2822i) 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} +(-15.7130 - 4.16080i) 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} +(-29.6525 - 37.7456i) 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} +(-48.8677 + 22.9772i) q^{54} +(-11.3465 + 32.4344i) q^{55} +(-13.0477 + 17.3050i) q^{56} +(-99.6627 - 4.33913i) q^{57} +(3.85839 - 2.47338i) q^{58} -63.0946i q^{59} +(-41.3382 - 43.4874i) q^{60} +28.4752 q^{61} +(13.1203 + 20.4672i) q^{62} +(15.6769 + 18.6737i) q^{63} +(-61.5304 + 17.6071i) q^{64} +(78.1961 - 37.6648i) q^{65} +(35.6491 - 20.7220i) 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} +(3.76614 + 71.9014i) 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} +(-100.683 - 26.6609i) 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} +(30.9476 - 9.95402i) q^{84} +(-60.3369 + 29.0625i) q^{85} +(9.18537 - 41.9921i) q^{86} +(-6.86815 - 0.299026i) q^{87} +(-7.63668 - 54.4459i) q^{88} +41.1063 q^{89} +(13.1385 + 89.0358i) q^{90} +47.0267i q^{91} +(38.2467 - 14.1653i) q^{92} +(1.58621 - 36.4327i) q^{93} +(16.1854 - 73.9937i) q^{94} +(-54.9006 + 156.936i) q^{95} +(90.6680 + 31.5487i) q^{96} +(30.3484 - 30.3484i) q^{97} +(44.9665 + 70.1464i) q^{98} +(-61.6172 - 5.37559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.68375	+	1.07935i	−0.841874	+	0.539674i
$2$	−1.68375	+	1.07935i	−0.841874	+	0.539674i
$3$	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
$6$	−5.18731	+	3.01526i	−0.864552	+	0.502544i
$7$	1.91561	+	1.91561i	0.273659	+	0.273659i	0.830571	−	0.556912i	$-0.188014\pi$
$7$	1.91561	+	1.91561i	0.273659	+	0.273659i	−0.556912	+	0.830571i	$0.688014\pi$
$8$	1.11122	+	7.92245i	0.138902	+	0.990306i
$9$	8.96594	+	0.782204i	0.996216	+	0.0869115i
$10$	2.31412	+	9.72856i	0.231412	+	0.972856i
$11$	−6.87236			−0.624760			−0.312380	−	0.949957i	$-0.601126\pi$
$11$	−6.87236			−0.624760			−0.312380	+	0.949957i	$0.601126\pi$
$12$	5.47960	−	10.6759i	0.456634	−	0.889655i
$13$	12.2746	+	12.2746i	0.944199	+	0.944199i	0.998523	−	0.0543246i	$-0.0173006\pi$
$13$	12.2746	+	12.2746i	0.944199	+	0.944199i	−0.0543246	+	0.998523i	$0.517301\pi$
$14$	−5.29303	−	1.15780i	−0.378073	−	0.0826999i
$15$	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	0.371360	−	0.928489i	$-0.378892\pi$
$17$	−9.47120	−	9.47120i	−0.557129	−	0.557129i	−0.928489	+	0.371360i	$0.878892\pi$
$18$	−15.9407	+	8.36034i	−0.885592	+	0.464463i
$19$	−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	$-0.178852\pi$
$23$	7.20994	+	7.20994i	0.313476	+	0.313476i	−0.532779	+	0.846255i	$0.678852\pi$
$24$	2.29669	+	23.8899i	0.0956954	+	0.995411i
$25$	−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
$28$	10.1618	−	3.76357i	0.362921	−	0.134413i
$29$	−2.29155			−0.0790190			−0.0395095	−	0.999219i	$-0.512580\pi$
$29$	−2.29155			−0.0790190			−0.0395095	+	0.999219i	$0.512580\pi$
$30$	5.66629	+	29.4600i	0.188876	+	0.982001i
$31$		−	12.1558i		−	0.392121i	−0.980592	−	0.196061i	$-0.937185\pi$
$31$		−	12.1558i		−	0.392121i	0.980592	−	0.196061i	$-0.0628149\pi$
$32$	30.6515	+	9.19168i	0.957859	+	0.287240i
$33$	−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
$36$	17.8164	−	31.2822i	0.494899	−	0.868951i
$37$	−20.7290	+	20.7290i	−0.560244	+	0.560244i	−0.929377	−	0.369133i	$-0.879655\pi$
$37$	−20.7290	+	20.7290i	−0.560244	+	0.560244i	0.369133	+	0.929377i	$0.379655\pi$
$38$	55.9886	−	35.8909i	1.47339	−	0.944497i
$39$	35.1872	+	38.3906i	0.902235	+	0.984375i
$40$	39.2250	+	7.83574i	0.980625	+	0.195893i
$41$			50.9173i			1.24188i	0.783856	+	0.620942i	$0.213250\pi$
$41$			50.9173i			1.24188i	−0.783856	+	0.620942i	$0.786750\pi$
$42$	−15.7130	−	4.16080i	−0.374118	−	0.0990666i
$43$	−15.1975	+	15.1975i	−0.353430	+	0.353430i	−0.861384	−	0.507954i	$-0.830402\pi$
$43$	−15.1975	+	15.1975i	−0.353430	+	0.353430i	0.507954	+	0.861384i	$0.330402\pi$
$44$	−11.4770	+	24.9790i	−0.260840	+	0.567704i
$45$	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	$-0.881994\pi$
$47$	−26.7793	+	26.7793i	−0.569772	+	0.569772i	0.362293	+	0.932064i	$0.381994\pi$
$48$	−29.6525	−	37.7456i	−0.617761	−	0.786366i
$49$		−	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	$-0.816383\pi$
$53$	−15.5183	+	15.5183i	−0.292799	+	0.292799i	0.545386	+	0.838185i	$0.316383\pi$
$54$	−48.8677	+	22.9772i	−0.904957	+	0.425503i
$55$	−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
$58$	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	$-0.179575\pi$
$60$	−41.3382	−	43.4874i	−0.688970	−	0.724789i
$61$	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
$63$	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
$66$	35.6491	−	20.7220i	0.540137	−	0.313970i
$67$	−32.4542	−	32.4542i	−0.484392	−	0.484392i	0.422139	−	0.906531i	$-0.361279\pi$
$67$	−32.4542	−	32.4542i	−0.484392	−	0.484392i	−0.906531	+	0.422139i	$0.861279\pi$
$68$	−50.2420	+	18.6079i	−0.738853	+	0.273646i
$69$	20.6685	+	22.5502i	0.299544	+	0.326814i
$70$	−14.2032	+	23.0691i	−0.202903	+	0.329559i
$71$	88.8377			1.25124			0.625618	−	0.780130i	$-0.284847\pi$
$71$	88.8377			1.25124			0.625618	+	0.780130i	$0.284847\pi$
$72$	3.76614	+	71.9014i	0.0523075	+	0.998631i
$73$	71.1740	+	71.1740i	0.974987	+	0.974987i	0.999695	−	0.0247079i	$-0.00786556\pi$
$73$	71.1740	+	71.1740i	0.974987	+	0.974987i	−0.0247079	+	0.999695i	$0.507866\pi$
$74$	12.5286	−	57.2763i	0.169306	−	0.774004i
$75$	−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
$78$	−100.683	−	26.6609i	−1.29081	−	0.341807i
$79$	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	$-0.416555\pi$
$83$	−58.6543	−	58.6543i	−0.706678	−	0.706678i	−0.965835	+	0.259157i	$0.916555\pi$
$84$	30.9476	−	9.95402i	0.368424	−	0.118500i
$85$	−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
$88$	−7.63668	−	54.4459i	−0.0867805	−	0.618704i
$89$	41.1063			0.461868			0.230934	−	0.972969i	$-0.425822\pi$
$89$	41.1063			0.461868			0.230934	+	0.972969i	$0.425822\pi$
$90$	13.1385	+	89.0358i	0.145984	+	0.989287i
$91$			47.0267i			0.516777i
$92$	38.2467	−	14.1653i	0.415725	−	0.153970i
$93$	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
$96$	90.6680	+	31.5487i	0.944458	+	0.328632i
$97$	30.3484	−	30.3484i	0.312870	−	0.312870i	−0.533150	−	0.846020i	$-0.678992\pi$
$97$	30.3484	−	30.3484i	0.312870	−	0.312870i	0.846020	+	0.533150i	$0.178992\pi$
$98$	44.9665	+	70.1464i	0.458842	+	0.715779i
$99$	−61.6172	−	5.37559i	−0.622396	−	0.0542989i
$100$	−89.2897	+	45.0260i	−0.892897	+	0.450260i
$101$		−	124.297i		−	1.23067i	−0.788267	−	0.615333i	$-0.789022\pi$
$101$		−	124.297i		−	1.23067i	0.788267	−	0.615333i	$-0.210978\pi$
$102$	77.6882	+	20.5719i	0.761649	+	0.201685i
$103$	131.168	−	131.168i	1.27348	−	1.27348i	0.329223	−	0.944252i	$-0.393213\pi$
$103$	131.168	−	131.168i	1.27348	−	1.27348i	0.944252	−	0.329223i	$-0.106787\pi$
$104$	−83.6050	+	110.884i	−0.803895	+	1.06620i
$105$	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	$-0.774145\pi$
$107$	−11.4672	+	11.4672i	−0.107170	+	0.107170i	0.651488	+	0.758659i	$0.274145\pi$
$108$	57.4805	−	91.4330i	0.532227	−	0.846602i
$109$		−	80.0130i		−	0.734065i	−0.930208	−	0.367032i	$-0.880374\pi$
$109$		−	80.0130i		−	0.734065i	0.930208	−	0.367032i	$-0.119626\pi$
$110$	−15.9034	−	66.8582i	−0.144577	−	0.607802i
$111$	−64.8331	+	59.4232i	−0.584082	+	0.535345i
$112$	3.29090	−	43.2203i	0.0293830	−	0.385895i
$113$	−64.8556	+	64.8556i	−0.573943	+	0.573943i	−0.933228	−	0.359285i	$-0.883021\pi$
$113$	−64.8556	+	64.8556i	−0.573943	+	0.573943i	0.359285	+	0.933228i	$0.383021\pi$
$114$	172.490	−	100.265i	1.51307	−	0.879515i
$115$	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
$118$	68.1010	+	106.235i	0.577127	+	0.900301i
$119$		−	36.2863i		−	0.304927i
$120$	116.541	+	28.6035i	0.971176	+	0.238362i
$121$	−73.7706			−0.609675
$122$	−47.9450	+	30.7346i	−0.392992	+	0.251923i
$123$	−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
$126$	−46.5513	−	14.5210i	−0.369455	−	0.115246i
$127$	63.5895	+	63.5895i	0.500705	+	0.500705i	0.911657	−	0.410952i	$-0.134804\pi$
$127$	63.5895	+	63.5895i	0.500705	+	0.500705i	−0.410952	+	0.911657i	$0.634804\pi$
$128$	84.5975	−	96.0586i	0.660918	−	0.750458i
$129$	−47.5325	+	43.5662i	−0.368469	+	0.337722i
$130$	−91.0092	+	147.819i	−0.700071	+	1.13707i
$131$	144.030			1.09947			0.549734	−	0.835340i	$-0.314729\pi$
$131$	144.030			1.09947			0.549734	+	0.835340i	$0.314729\pi$
$132$	−37.6578	+	73.3684i	−0.285287	+	0.555821i
$133$	−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	0.755065	−	0.655649i	$-0.227605\pi$
$137$	13.6200	+	13.6200i	0.0994161	+	0.0994161i	−0.655649	+	0.755065i	$0.727605\pi$
$138$	−59.1401	−	15.6603i	−0.428551	−	0.113481i
$139$	−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
$144$	−83.9479	−	116.999i	−0.582971	−	0.812493i
$145$	−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
$148$	40.7259	+	109.962i	0.275175	+	0.742983i
$149$	−167.292			−1.12277			−0.561383	−	0.827556i	$-0.689730\pi$
$149$	−167.292			−1.12277			−0.561383	+	0.827556i	$0.689730\pi$
$150$	148.393	+	21.8970i	0.989288	+	0.145980i
$151$			75.2596i			0.498408i	0.968451	+	0.249204i	$0.0801690\pi$
$151$			75.2596i			0.498408i	−0.968451	+	0.249204i	$0.919831\pi$
$152$	−36.9506	−	263.440i	−0.243096	−	1.73316i
$153$	−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
$156$	198.302	−	63.7819i	1.27116	−	0.408858i
$157$	71.6852	−	71.6852i	0.456593	−	0.456593i	−0.440942	−	0.897536i	$-0.645356\pi$
$157$	71.6852	−	71.6852i	0.456593	−	0.456593i	0.897536	+	0.440942i	$0.145356\pi$
$158$	−126.519	+	81.1033i	−0.800751	+	0.513312i
$159$	−48.5359	+	44.4859i	−0.305258	+	0.279786i
$160$	93.9870	−	129.485i	0.587419	−	0.809283i
$161$			27.6229i			0.171571i
$162$	−149.463	+	62.4895i	−0.922609	+	0.385737i
$163$	−61.4502	+	61.4502i	−0.376995	+	0.376995i	−0.870017	−	0.493022i	$-0.835892\pi$
$163$	−61.4502	+	61.4502i	−0.376995	+	0.376995i	0.493022	+	0.870017i	$0.335892\pi$
$164$	185.069	+	85.0327i	1.12847	+	0.518492i
$165$	−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	$-0.799780\pi$
$167$	−36.7847	+	36.7847i	−0.220268	+	0.220268i	0.588344	+	0.808611i	$0.299780\pi$
$168$	−41.3642	+	50.1633i	−0.246215	+	0.298591i
$169$			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	$-0.559405\pi$
$173$	137.897	−	137.897i	0.797091	−	0.797091i	0.982636	+	0.185545i	$0.0594051\pi$
$174$	11.8870	−	6.90963i	0.0683160	−	0.0397105i
$175$	−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
$178$	−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	$0.903413\pi$
$180$	−118.223	−	135.733i	−0.656792	−	0.754072i
$181$	−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
$183$	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
$186$	36.6528	+	63.0556i	0.197058	+	0.339009i
$187$	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	$-0.384200\pi$
$191$	135.925			0.711648			0.355824	+	0.934553i	$0.384200\pi$
$192$	−186.714	+	44.7422i	−0.972469	+	0.233032i
$193$	−62.7362	−	62.7362i	−0.325058	−	0.325058i	0.525646	−	0.850704i	$-0.323824\pi$
$193$	−62.7362	−	62.7362i	−0.325058	−	0.325058i	−0.850704	+	0.525646i	$0.823824\pi$
$194$	−18.3426	+	83.8556i	−0.0945494	+	0.432245i
$195$	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	0.909034	−	0.416723i	$-0.136821\pi$
$197$	96.9852	+	96.9852i	0.492311	+	0.492311i	−0.416723	+	0.909034i	$0.636821\pi$
$198$	109.550	−	57.4553i	0.553283	−	0.290178i
$199$	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
$204$	−153.012	+	49.2147i	−0.750057	+	0.241249i
$205$	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
$208$	21.0869	−	276.940i	0.101379	−	1.33144i
$209$	228.522			1.09341
$210$	−45.5796	+	67.2885i	−0.217046	+	0.320421i
$211$		−	376.951i		−	1.78650i	−0.449561	−	0.893250i	$-0.648420\pi$
$211$		−	376.951i		−	1.78650i	0.449561	−	0.893250i	$-0.351580\pi$
$212$	30.4886	+	82.3204i	0.143814	+	0.388304i
$213$	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
$216$	1.90525	+	215.992i	0.00882060	+	0.999961i
$217$	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
$222$	45.0243	−	170.031i	0.202812	−	0.765907i
$223$	−255.505	+	255.505i	−1.14576	+	1.14576i	−0.158385	+	0.987377i	$0.550629\pi$
$223$	−255.505	+	255.505i	−1.14576	+	1.14576i	−0.987377	+	0.158385i	$0.949371\pi$
$224$	41.1087	+	76.3241i	0.183521	+	0.340733i
$225$	−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	$-0.639682\pi$
$227$	109.045	−	109.045i	0.480375	−	0.480375i	0.905251	+	0.424876i	$0.139682\pi$
$228$	−182.210	+	354.998i	−0.799166	+	1.55701i
$229$			223.738i			0.977023i	0.872557	+	0.488512i	$0.162460\pi$
$229$			223.738i			0.977023i	−0.872557	+	0.488512i	$0.837540\pi$
$230$	−53.4577	+	86.8270i	−0.232425	+	0.377509i
$231$	−37.7391	−	41.1749i	−0.163373	−	0.178246i
$232$	−2.54641	−	18.1547i	−0.0109759	−	0.0782530i
$233$	62.4244	−	62.4244i	0.267916	−	0.267916i	−0.560344	−	0.828260i	$-0.689331\pi$
$233$	62.4244	−	62.4244i	0.267916	−	0.267916i	0.828260	+	0.560344i	$0.189331\pi$
$234$	−298.285	−	93.0453i	−1.27472	−	0.397630i
$235$	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
$238$	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	$-0.224808\pi$
$240$	−227.099	+	77.6274i	−0.946246	+	0.323447i
$241$	−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
$243$	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
$246$	−153.529	−	264.124i	−0.624102	−	1.07367i
$247$	−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	$-0.733631\pi$
$251$	−336.252			−1.33965			−0.669825	+	0.742519i	$0.733631\pi$
$252$	94.0539	−	25.7954i	0.373230	−	0.102363i
$253$	−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	0.979288	−	0.202472i	$-0.0648975\pi$
$257$	199.642	+	199.642i	0.776816	+	0.776816i	−0.202472	+	0.979288i	$0.564898\pi$
$258$	33.0096	−	124.659i	0.127944	−	0.483173i
$259$	−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	$-0.343713\pi$
$263$	−107.927	−	107.927i	−0.410368	−	0.410368i	−0.881867	+	0.471499i	$0.843713\pi$
$264$	−15.7837	−	164.180i	−0.0597867	−	0.621893i
$265$	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
$268$	−172.161	+	63.7623i	−0.642390	+	0.237919i
$269$	−279.355			−1.03850			−0.519248	−	0.854624i	$-0.673788\pi$
$269$	−279.355			−1.03850			−0.519248	+	0.854624i	$0.673788\pi$
$270$	27.7599	+	268.569i	0.102815	+	0.994701i
$271$			353.019i			1.30265i	0.758797	+	0.651327i	$0.225787\pi$
$271$			353.019i			1.30265i	−0.758797	+	0.651327i	$0.774213\pi$
$272$	−16.2709	+	213.690i	−0.0598194	+	0.785626i
$273$	−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
$276$	116.480	−	37.4647i	0.422029	−	0.135742i
$277$	9.06443	−	9.06443i	0.0327236	−	0.0327236i	−0.690556	−	0.723279i	$-0.742634\pi$
$277$	9.06443	−	9.06443i	0.0327236	−	0.0327236i	0.723279	+	0.690556i	$0.242634\pi$
$278$	105.615	−	67.7033i	0.379910	−	0.243537i
$279$	9.50828	−	108.988i	0.0340798	−	0.390637i
$280$	60.1297	+	90.1502i	0.214749	+	0.321965i
$281$			204.501i			0.727762i	0.931445	+	0.363881i	$0.118549\pi$
$281$			204.501i			0.727762i	−0.931445	+	0.363881i	$0.881451\pi$
$282$	58.1658	−	219.659i	0.206262	−	0.778933i
$283$	−4.95961	+	4.95961i	−0.0175251	+	0.0175251i	−0.715815	−	0.698290i	$-0.753945\pi$
$283$	−4.95961	+	4.95961i	−0.0175251	+	0.0175251i	0.698290	+	0.715815i	$0.253945\pi$
$284$	148.360	−	322.898i	0.522396	−	1.13697i
$285$	−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
$288$	267.630	+	106.388i	0.929270	+	0.369402i
$289$		−	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	$-0.906516\pi$
$293$	−195.635	+	195.635i	−0.667697	+	0.667697i	0.289485	+	0.957182i	$0.406516\pi$
$294$	125.618	+	216.108i	0.427274	+	0.735060i
$295$	−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
$298$	281.678	−	180.566i	0.945227	−	0.605927i
$299$			176.998i			0.591967i
$300$	−273.491	+	123.299i	−0.911637	+	0.410996i
$301$	−58.2251			−0.193439
$302$	−81.2313	−	126.718i	−0.268978	−	0.419597i
$303$	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
$306$	230.160	+	71.7948i	0.752155	+	0.234623i
$307$	323.877	+	323.877i	1.05497	+	1.05497i	0.998398	+	0.0565751i	$0.0180180\pi$
$307$	323.877	+	323.877i	1.05497	+	1.05497i	0.0565751	+	0.998398i	$0.481982\pi$
$308$	−69.8355	+	25.8646i	−0.226739	+	0.0839761i
$309$	410.248	−	376.015i	1.32766	−	1.21688i
$310$	118.258	−	28.1298i	0.381477	−	0.0907414i
$311$	428.968			1.37932			0.689660	−	0.724133i	$-0.257760\pi$
$311$	428.968			1.37932			0.689660	+	0.724133i	$0.257760\pi$
$312$	−265.047	+	321.429i	−0.849510	+	1.03022i
$313$	−144.149	−	144.149i	−0.460541	−	0.460541i	0.438292	−	0.898833i	$-0.355584\pi$
$313$	−144.149	−	144.149i	−0.460541	−	0.460541i	−0.898833	+	0.438292i	$0.855584\pi$
$314$	−43.3266	+	198.073i	−0.137983	+	0.630806i
$315$	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	0.0528685	−	0.998601i	$-0.483164\pi$
$317$	−299.797	−	299.797i	−0.945733	−	0.945733i	−0.998601	+	0.0528685i	$0.983164\pi$
$318$	33.7065	−	127.290i	0.105995	−	0.400284i
$319$	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
$324$	184.210	−	266.539i	0.568548	−	0.822650i
$325$	−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
$328$	−403.389	+	56.5801i	−1.22985	+	0.172500i
$329$	−102.598			−0.311847
$330$	−38.9408	−	202.460i	−0.118002	−	0.613515i
$331$			89.1276i			0.269268i	0.990895	+	0.134634i	$0.0429858\pi$
$331$			89.1276i			0.269268i	−0.990895	+	0.134634i	$0.957014\pi$
$332$	−311.144	+	115.237i	−0.937181	+	0.347100i
$333$	−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
$336$	15.5032	−	129.109i	0.0461405	−	0.384252i
$337$	−176.973	+	176.973i	−0.525141	+	0.525141i	−0.919120	−	0.393978i	$-0.871098\pi$
$337$	−176.973	+	176.973i	−0.525141	+	0.525141i	0.393978	+	0.919120i	$0.371098\pi$
$338$	−142.831	−	222.812i	−0.422577	−	0.659206i
$339$	−202.846	+	185.920i	−0.598365	+	0.548435i
$340$	4.86990	+	267.842i	0.0143232	+	0.787769i
$341$			83.5387i			0.244982i
$342$	530.065	−	278.001i	1.54990	−	0.812869i
$343$	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	$-0.995037\pi$
$347$	−341.548	+	341.548i	−0.984288	+	0.984288i	0.0155906	+	0.999878i	$0.495037\pi$
$348$	−12.5568	+	24.4643i	−0.0360827	+	0.0702996i
$349$			190.129i			0.544782i	0.962187	+	0.272391i	$0.0878144\pi$
$349$			190.129i			0.544782i	−0.962187	+	0.272391i	$0.912186\pi$
$350$	85.4259	+	105.120i	0.244074	+	0.300344i
$351$	285.457	+	371.732i	0.813268	+	1.05906i
$352$	−210.648	−	63.1686i	−0.598432	−	0.179456i
$353$	−66.4041	+	66.4041i	−0.188114	+	0.188114i	−0.794880	−	0.606767i	$-0.792466\pi$
$353$	−66.4041	+	66.4041i	−0.188114	+	0.188114i	0.606767	+	0.794880i	$0.292466\pi$
$354$	190.247	+	327.291i	0.537421	+	0.924552i
$355$	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
$358$	−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	$-0.189158\pi$
$360$	345.560	+	100.937i	0.959889	+	0.280380i
$361$	744.721			2.06294
$362$	19.5411	−	12.5266i	0.0539809	−	0.0346038i
$363$	−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
$366$	−147.709	+	85.8602i	−0.403578	+	0.234591i
$367$	183.244	+	183.244i	0.499301	+	0.499301i	0.911220	−	0.411919i	$-0.135141\pi$
$367$	183.244	+	183.244i	0.499301	+	0.499301i	−0.411919	+	0.911220i	$0.635141\pi$
$368$	12.3862	−	162.672i	0.0336582	−	0.442042i
$369$	−39.8277	+	456.521i	−0.107934	+	1.23719i
$370$	−249.633	−	153.694i	−0.674683	−	0.415389i
$371$	−59.4543			−0.160254
$372$	−129.773	−	66.6087i	−0.348852	−	0.179056i
$373$	−78.2141	−	78.2141i	−0.209689	−	0.209689i	0.594446	−	0.804135i	$-0.297371\pi$
$373$	−78.2141	−	78.2141i	−0.209689	−	0.209689i	−0.804135	+	0.594446i	$0.797371\pi$
$374$	−179.848	−	39.3401i	−0.480878	−	0.105187i
$375$	−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
$378$	−137.627	−	49.5962i	−0.364093	−	0.131207i
$379$	116.155			0.306478			0.153239	−	0.988189i	$-0.451030\pi$
$379$	116.155			0.306478			0.153239	+	0.988189i	$0.451030\pi$
$380$	478.731	+	461.633i	1.25982	+	1.21482i
$381$	182.290	+	198.886i	0.478452	+	0.522010i
$382$	−228.863	+	146.710i	−0.599118	+	0.384058i
$383$	−439.765	−	439.765i	−1.14821	−	1.14821i	−0.986904	−	0.161308i	$-0.948429\pi$
$383$	−439.765	−	439.765i	−1.14821	−	1.14821i	−0.161308	−	0.986904i	$-0.551571\pi$
$384$	266.087	−	276.864i	0.692935	−	0.721000i
$385$	−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
$388$	−59.6250	−	160.990i	−0.153673	−	0.414922i
$389$	120.985			0.311017			0.155508	−	0.987835i	$-0.450298\pi$
$389$	120.985			0.311017			0.155508	+	0.987835i	$0.450298\pi$
$390$	−292.058	+	431.161i	−0.748867	+	1.10554i
$391$		−	136.574i		−	0.349293i
$392$	330.056	−	46.2942i	0.841979	−	0.118098i
$393$	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
$396$	−122.440	+	214.983i	−0.309193	+	0.542886i
$397$	−549.267	+	549.267i	−1.38355	+	1.38355i	−0.545313	+	0.838233i	$0.683589\pi$
$397$	−549.267	+	549.267i	−1.38355	+	1.38355i	−0.838233	+	0.545313i	$0.816411\pi$
$398$	−48.8768	+	31.3319i	−0.122806	+	0.0787234i
$399$	−182.603	−	199.227i	−0.457652	−	0.499317i
$400$	14.5408	+	399.736i	0.0363520	+	0.999339i
$401$		−	177.597i		−	0.442885i	−0.975173	−	0.221442i	$-0.928924\pi$
$401$		−	177.597i		−	0.442885i	0.975173	−	0.221442i	$-0.0710765\pi$
$402$	266.208	+	70.4920i	0.662210	+	0.175353i
$403$	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
$408$	204.513	−	248.018i	0.501258	−	0.607887i
$409$		−	348.822i		−	0.852865i	−0.904519	−	0.426433i	$-0.859770\pi$
$409$		−	348.822i		−	0.852865i	0.904519	−	0.426433i	$-0.140230\pi$
$410$	−495.352	+	117.828i	−1.20817	+	0.287387i
$411$	39.0441	+	42.5986i	0.0949977	+	0.103646i
$412$	−257.703	−	695.809i	−0.625494	−	1.68886i
$413$	120.865	−	120.865i	0.292651	−	0.292651i
$414$	−175.209	−	54.6537i	−0.423210	−	0.132014i
$415$	−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
$418$	−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	$0.960152\pi$
$420$	4.11694	−	162.493i	0.00980223	−	0.386888i
$421$	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
$423$	−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
$426$	−460.829	+	267.869i	−1.08176	+	0.628801i
$427$	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	$-0.550419\pi$
$431$	−135.966			−0.315467			−0.157734	+	0.987482i	$0.550419\pi$
$432$	−236.338	−	361.619i	−0.547079	−	0.837081i
$433$	426.207	+	426.207i	0.984312	+	0.984312i	0.999879	−	0.0155664i	$-0.00495515\pi$
$433$	426.207	+	426.207i	0.984312	+	0.984312i	−0.0155664	+	0.999879i	$0.504955\pi$
$434$	−14.0739	+	64.3407i	−0.0324284	+	0.148250i
$435$	−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
$438$	−583.810	−	154.593i	−1.33290	−	0.352952i
$439$	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	$-0.0585604\pi$
$443$	354.483	+	354.483i	0.800188	+	0.800188i	−0.182937	+	0.983125i	$0.558560\pi$
$444$	107.713	+	334.887i	0.242597	+	0.754250i
$445$	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
$448$	−151.597	−	84.1400i	−0.338386	−	0.187813i
$449$	452.663			1.00816			0.504079	−	0.863657i	$-0.331832\pi$
$449$	452.663			1.00816			0.504079	+	0.863657i	$0.331832\pi$
$450$	441.901	+	84.9927i	0.982002	+	0.188873i
$451$		−	349.922i		−	0.775880i
$452$	127.421	+	344.041i	0.281904	+	0.761152i
$453$	−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
$456$	−76.3704	−	794.394i	−0.167479	−	1.74209i
$457$	270.489	−	270.489i	0.591879	−	0.591879i	−0.346260	−	0.938139i	$-0.612548\pi$
$457$	270.489	−	270.489i	0.591879	−	0.591879i	0.938139	+	0.346260i	$0.112548\pi$
$458$	−241.491	−	376.719i	−0.527274	−	0.822531i
$459$	−220.262	−	286.832i	−0.479873	−	0.624906i
$460$	−3.70721	−	203.894i	−0.00805915	−	0.443249i
$461$			582.469i			1.26349i	0.775176	+	0.631745i	$0.217661\pi$
$461$			582.469i			1.26349i	−0.775176	+	0.631745i	$0.782339\pi$
$462$	107.985	+	28.5945i	0.233734	+	0.0618929i
$463$	318.146	−	318.146i	0.687140	−	0.687140i	−0.274459	−	0.961599i	$-0.588499\pi$
$463$	318.146	−	318.146i	0.687140	−	0.687140i	0.961599	+	0.274459i	$0.0884986\pi$
$464$	23.8827	+	27.8195i	0.0514714	+	0.0599558i
$465$	−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	0.208786	−	0.977961i	$-0.433049\pi$
$467$	554.211	−	554.211i	1.18675	−	1.18675i	0.977961	−	0.208786i	$-0.0669514\pi$
$468$	602.665	−	165.288i	1.28774	−	0.353179i
$469$		−	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
$474$	−389.780	+	226.570i	−0.822320	+	0.477996i
$475$	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
$478$	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	$0.647375\pi$
$480$	298.591	−	375.824i	0.622064	−	0.782966i
$481$	−508.880			−1.05796
$482$	201.889	−	129.419i	0.418857	−	0.268504i
$483$	−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
$486$	−456.118	+	167.787i	−0.938514	+	0.345242i
$487$	97.7824	+	97.7824i	0.200785	+	0.200785i	0.800336	−	0.599551i	$-0.204654\pi$
$487$	97.7824	+	97.7824i	0.200785	+	0.200785i	−0.599551	+	0.800336i	$0.704654\pi$
$488$	31.6421	+	225.593i	0.0648403	+	0.462281i
$489$	−192.195	+	176.157i	−0.393036	+	0.360240i
$490$	405.300	−	96.4081i	0.827143	−	0.196751i
$491$	−770.213			−1.56866			−0.784331	−	0.620342i	$-0.786994\pi$
$491$	−770.213			−1.56866			−0.784331	+	0.620342i	$0.786994\pi$
$492$	543.585	+	279.006i	1.10485	+	0.567086i
$493$	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
$498$	481.116	+	127.400i	0.966096	+	0.255823i
$499$	−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	$-0.0866564\pi$
$503$	349.224	+	349.224i	0.694282	+	0.694282i	−0.268889	+	0.963171i	$0.586656\pi$
$504$	−130.521	+	144.950i	−0.258970	+	0.287599i
$505$	−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
$508$	337.325	−	124.933i	0.664025	−	0.245932i
$509$	447.822			0.879807			0.439904	−	0.898045i	$-0.355013\pi$
$509$	447.822			0.879807			0.439904	+	0.898045i	$0.355013\pi$
$510$	225.355	−	332.688i	0.441873	−	0.652330i
$511$			272.684i			0.533628i
$512$	−207.865	−	467.906i	−0.405987	−	0.913879i
$513$	−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
$516$	78.9700	+	245.523i	0.153043	+	0.475819i
$517$	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	$0.883440\pi$
$522$	36.5288	−	19.1581i	0.0699786	−	0.0367014i
$523$	−593.137	+	593.137i	−1.13411	+	1.13411i	−0.144618	+	0.989488i	$0.546195\pi$
$523$	−593.137	+	593.137i	−1.13411	+	1.13411i	−0.989488	+	0.144618i	$0.953805\pi$
$524$	240.533	−	523.507i	0.459032	−	0.999058i
$525$	−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
$528$	203.783	+	259.401i	0.385952	+	0.491290i
$529$		−	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
$534$	−213.231	+	123.946i	−0.399309	+	0.232109i
$535$	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
$538$	470.364	−	301.522i	0.874283	−	0.560449i
$539$			286.308i			0.531184i
$540$	−336.620	−	422.240i	−0.623371	−	0.781926i
$541$	−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
$543$	−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
$546$	−141.798	−	243.942i	−0.259703	−	0.446781i
$547$	−586.492	−	586.492i	−1.07220	−	1.07220i	−0.997182	−	0.0750146i	$-0.976100\pi$
$547$	−586.492	−	586.492i	−1.07220	−	1.07220i	−0.0750146	−	0.997182i	$-0.523900\pi$
$548$	72.2503	−	26.7590i	0.131844	−	0.0488303i
$549$	255.307	+	22.2734i	0.465040	+	0.0405708i
$550$	−341.797	−	35.3276i	−0.621450	−	0.0642320i
$551$	76.1995			0.138293
$552$	−155.686	+	188.804i	−0.282039	+	0.342035i
$553$	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	0.230067	−	0.973175i	$-0.426106\pi$
$557$	−413.911	−	413.911i	−0.743108	−	0.743108i	−0.973175	+	0.230067i	$0.926106\pi$
$558$	101.626	+	193.771i	0.182126	+	0.347259i
$559$	−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	$-0.174964\pi$
$563$	185.957	+	185.957i	0.330296	+	0.330296i	−0.522403	+	0.852699i	$0.674964\pi$
$564$	139.152	+	432.632i	0.246723	+	0.767077i
$565$	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
$568$	98.7180	+	703.812i	0.173799	+	1.23911i
$569$	−745.467			−1.31014			−0.655068	−	0.755570i	$-0.727360\pi$
$569$	−745.467			−1.31014			−0.655068	+	0.755570i	$0.727360\pi$
$570$	−188.418	−	979.616i	−0.330557	−	1.71862i
$571$		−	406.663i		−	0.712195i	−0.934449	−	0.356097i	$-0.884107\pi$
$571$		−	406.663i		−	0.712195i	0.934449	−	0.356097i	$-0.115893\pi$
$572$	−447.481	+	165.732i	−0.782310	+	0.289741i
$573$	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
$576$	−565.450	+	109.735i	−0.981685	+	0.190512i
$577$	73.9694	−	73.9694i	0.128197	−	0.128197i	−0.640097	−	0.768294i	$-0.721106\pi$
$577$	73.9694	−	73.9694i	0.128197	−	0.128197i	0.768294	+	0.640097i	$0.221106\pi$
$578$	118.289	+	184.527i	0.204652	+	0.319251i
$579$	−179.844	−	196.217i	−0.310611	−	0.338889i
$580$	32.9912	+	31.8129i	0.0568814	+	0.0548499i
$581$		−	224.718i		−	0.386778i
$582$	−65.9181	+	248.935i	−0.113261	+	0.427723i
$583$	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	$-0.580168\pi$
$587$	422.201	−	422.201i	0.719251	−	0.719251i	0.968452	+	0.249200i	$0.0801678\pi$
$588$	−444.765	−	228.285i	−0.756404	−	0.388240i
$589$			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	$-0.588762\pi$
$593$	406.869	−	406.869i	0.686119	−	0.686119i	0.961372	+	0.275253i	$0.0887616\pi$
$594$	335.836	−	157.907i	0.565381	−	0.265837i
$595$	−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
$598$	−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	$-0.0787100\pi$
$600$	327.408	−	502.796i	0.545680	−	0.837994i
$601$	−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
$603$	−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
$606$	374.789	+	644.768i	0.618464	+	1.06397i
$607$	74.9651	+	74.9651i	0.123501	+	0.123501i	0.766156	−	0.642655i	$-0.222167\pi$
$607$	74.9651	+	74.9651i	0.123501	+	0.123501i	−0.642655	+	0.766156i	$0.722167\pi$
$608$	−1019.23	−	305.645i	−1.67637	−	0.502706i
$609$	−12.5839	−	13.7295i	−0.0206632	−	0.0225444i
$610$	65.8949	+	277.022i	0.108024	+	0.454135i
$611$	−657.409			−1.07596
$612$	−465.022	+	127.538i	−0.759840	+	0.208395i
$613$	22.9005	+	22.9005i	0.0373581	+	0.0373581i	0.725539	−	0.688181i	$-0.241590\pi$
$613$	22.9005	+	22.9005i	0.0373581	+	0.0373581i	−0.688181	+	0.725539i	$0.741590\pi$
$614$	−894.903	−	195.751i	−1.45750	−	0.318813i
$615$	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	0.794133	−	0.607744i	$-0.207925\pi$
$617$	115.002	+	115.002i	0.186389	+	0.186389i	−0.607744	+	0.794133i	$0.707925\pi$
$618$	−284.903	+	1075.91i	−0.461007	+	1.74096i
$619$	−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
$624$	99.3391	−	827.283i	0.159197	−	1.32577i
$625$	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
$628$	−140.839	−	380.270i	−0.224265	−	0.605525i
$629$	392.657			0.624256
$630$	−145.390	+	195.727i	−0.230778	+	0.310677i
$631$			209.771i			0.332443i	0.986088	+	0.166221i	$0.0531566\pi$
$631$			209.771i			0.332443i	−0.986088	+	0.166221i	$0.946843\pi$
$632$	83.4980	+	595.301i	0.132117	+	0.941932i
$633$	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
$636$	80.6372	+	250.706i	0.126788	+	0.394192i
$637$	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	$-0.380993\pi$
$642$	24.9073	−	94.0607i	0.0387964	−	0.146512i
$643$	−424.387	+	424.387i	−0.660012	+	0.660012i	−0.955383	−	0.295371i	$-0.904557\pi$
$643$	−424.387	+	424.387i	−0.660012	+	0.660012i	0.295371	+	0.955383i	$0.404557\pi$
$644$	100.401	+	46.1308i	0.155902	+	0.0716316i
$645$	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	$-0.958023\pi$
$647$	−556.306	+	556.306i	−0.859824	+	0.859824i	0.131493	+	0.991317i	$0.458023\pi$
$648$	−22.4746	+	647.610i	−0.0346830	+	0.999398i
$649$			433.609i			0.668119i
$650$	547.379	+	673.575i	0.842122	+	1.03627i
$651$	72.8296	−	66.7525i	0.111873	−	0.102538i
$652$	120.730	+	325.976i	0.185169	+	0.499963i
$653$	730.267	−	730.267i	1.11833	−	1.11833i	0.126340	−	0.991987i	$-0.459677\pi$
$653$	730.267	−	730.267i	1.11833	−	1.11833i	0.991987	−	0.126340i	$-0.0403230\pi$
$654$	241.261	+	415.052i	0.368900	+	0.634637i
$655$	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
$658$	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	$0.750835\pi$
$660$	284.091	+	298.861i	0.430441	+	0.452820i
$661$	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
$663$	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
$666$	157.133	−	503.736i	0.235935	−	0.756360i
$667$	−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
$672$	113.250	+	234.120i	0.168526	+	0.348393i
$673$	301.487	+	301.487i	0.447975	+	0.447975i	0.894681	−	0.446706i	$-0.147403\pi$
$673$	301.487	+	301.487i	0.447975	+	0.447975i	−0.446706	+	0.894681i	$0.647403\pi$
$674$	106.962	−	488.992i	0.158698	−	0.725508i
$675$	−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	0.980436	−	0.196838i	$-0.0630672\pi$
$677$	530.496	+	530.496i	0.783598	+	0.783598i	−0.196838	+	0.980436i	$0.563067\pi$
$678$	140.869	−	531.983i	0.207772	−	0.784635i
$679$	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	$-0.378133\pi$
$683$	−378.401	−	378.401i	−0.554028	−	0.554028i	−0.927601	+	0.373573i	$0.878133\pi$
$684$	−592.436	+	1040.21i	−0.866135	+	1.52077i
$685$	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
$688$	342.887	+	26.1083i	0.498383	+	0.0379481i
$689$	−380.962			−0.552920
$690$	−171.551	+	253.259i	−0.248625	+	0.367042i
$691$			690.583i			0.999396i	0.866200	+	0.499698i	$0.166556\pi$
$691$			690.583i			0.999396i	−0.866200	+	0.499698i	$0.833444\pi$
$692$	−270.923	−	731.503i	−0.391508	−	1.05708i
$693$	−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
$696$	−5.26298	−	54.7448i	−0.00756175	−	0.0786563i
$697$	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	$-0.0294648\pi$
$702$	−881.865	−	317.795i	−1.25622	−	0.452700i
$703$	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
$708$	−673.589	−	345.734i	−0.951397	−	0.488324i
$709$		−	86.8545i		−	0.122503i	−0.998122	−	0.0612514i	$-0.980491\pi$
$709$		−	86.8545i		−	0.122503i	0.998122	−	0.0612514i	$-0.0195091\pi$
$710$	205.581	+	864.263i	0.289550	+	1.21727i
$711$	673.710	+	58.7756i	0.947553	+	0.0826661i
$712$	45.6780	+	325.662i	0.0641545	+	0.457391i
$713$	87.6423	−	87.6423i	0.122920	−	0.122920i
$714$	109.413	+	188.228i	0.153239	+	0.263625i
$715$	−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
$718$	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	$0.976937\pi$
$720$	−690.782	+	203.027i	−0.959420	+	0.281983i
$721$	502.534			0.696996
$722$	−1253.92	+	803.812i	−1.73673	+	1.11331i
$723$	−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
$726$	382.671	−	222.438i	0.527095	−	0.306388i
$727$	−252.054	−	252.054i	−0.346704	−	0.346704i	0.512176	−	0.858880i	$-0.328839\pi$
$727$	−252.054	−	252.054i	−0.346704	−	0.346704i	−0.858880	+	0.512176i	$0.828839\pi$
$728$	−372.567	+	52.2569i	−0.511768	+	0.0717814i
$729$	704.298	+	188.161i	0.966116	+	0.258109i
$730$	−527.716	+	857.126i	−0.722898	+	1.17415i
$731$	287.877			0.393812
$732$	156.033	−	303.997i	0.213159	−	0.415296i
$733$	−795.114	−	795.114i	−1.08474	−	1.08474i	−0.996060	−	0.0886791i	$-0.971735\pi$
$733$	−795.114	−	795.114i	−1.08474	−	1.08474i	−0.0886791	−	0.996060i	$-0.528265\pi$
$734$	−506.320	−	110.753i	−0.689809	−	0.150889i
$735$	−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
$738$	−425.685	−	811.655i	−0.576810	−	1.09980i
$739$	−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	$-0.0963914\pi$
$743$	487.618	+	487.618i	0.656283	+	0.656283i	−0.298216	+	0.954499i	$0.596391\pi$
$744$	290.399	−	27.9180i	0.390321	−	0.0375242i
$745$	−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
$748$	345.281	−	127.880i	0.461606	−	0.170963i
$749$	−43.9335			−0.0586562
$750$	348.345	−	664.196i	0.464460	−	0.885594i
$751$			1089.00i			1.45007i	0.688711	+	0.725036i	$0.258177\pi$
$751$			1089.00i			1.45007i	−0.688711	+	0.725036i	$0.741823\pi$
$752$	604.197	+	46.0050i	0.803454	+	0.0611769i
$753$	−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
$756$	285.261	−	65.0398i	0.377329	−	0.0860315i
$757$	−628.144	+	628.144i	−0.829781	+	0.829781i	−0.987486	−	0.157705i	$-0.949590\pi$
$757$	−628.144	+	628.144i	−0.829781	+	0.829781i	0.157705	+	0.987486i	$0.449590\pi$
$758$	−195.576	+	125.372i	−0.258016	+	0.165398i
$759$	−142.042	−	154.973i	−0.187143	−	0.204181i
$760$	−1304.32	−	260.557i	−1.71622	−	0.342838i
$761$			723.259i			0.950407i	0.879876	+	0.475203i	$0.157625\pi$
$761$			723.259i			0.950407i	−0.879876	+	0.475203i	$0.842375\pi$
$762$	−521.598	−	138.119i	−0.684512	−	0.181259i
$763$	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
$768$	−149.191	+	753.370i	−0.194259	+	0.980950i
$769$		−	180.270i		−	0.234421i	−0.993107	−	0.117210i	$-0.962605\pi$
$769$		−	180.270i		−	0.234421i	0.993107	−	0.117210i	$-0.0373952\pi$
$770$	97.6096	−	158.539i	0.126766	−	0.205895i
$771$	572.307	+	624.410i	0.742292	+	0.809870i
$772$	−332.798	+	123.257i	−0.431085	+	0.159659i
$773$	−482.107	+	482.107i	−0.623683	+	0.623683i	−0.946471	−	0.322788i	$-0.895380\pi$
$773$	−482.107	+	482.107i	−0.623683	+	0.623683i	0.322788	+	0.946471i	$0.395380\pi$
$774$	115.202	−	369.314i	0.148840	−	0.477150i
$775$	−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
$778$	−203.709	+	130.585i	−0.261837	+	0.167848i
$779$		−	1693.12i		−	2.17345i
$780$	26.3799	−	1041.20i	0.0338204	−	1.33487i
$781$	−610.525			−0.781722
$782$	147.410	+	229.956i	0.188504	+	0.294061i
$783$	−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
$786$	−747.129	+	434.289i	−0.950546	+	0.552531i
$787$	279.225	+	279.225i	0.354797	+	0.354797i	0.861891	−	0.507094i	$-0.169280\pi$
$787$	279.225	+	279.225i	0.354797	+	0.354797i	−0.507094	+	0.861891i	$0.669280\pi$
$788$	514.479	−	190.545i	0.652892	−	0.241809i
$789$	−309.391	−	337.558i	−0.392130	−	0.427830i
$790$	173.885	+	731.014i	0.220108	+	0.925334i
$791$	−248.477			−0.314130
$792$	−25.8823	−	494.133i	−0.0326796	−	0.623905i
$793$	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	0.996408	+	0.0846783i	$0.0269863\pi$
$797$	861.626	+	861.626i	1.08109	+	1.08109i	0.0846783	+	0.996408i	$0.473014\pi$
$798$	522.493	+	138.356i	0.654754	+	0.173379i
$799$	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
$804$	−524.313	+	168.640i	−0.652131	+	0.209752i
$805$	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
$808$	984.738	−	138.121i	1.21874	−	0.170942i
$809$	−430.022			−0.531548			−0.265774	−	0.964035i	$-0.585627\pi$
$809$	−430.022			−0.531548			−0.265774	+	0.964035i	$0.585627\pi$
$810$	48.1551	+	808.567i	0.0594508	+	0.998231i
$811$		−	1351.37i		−	1.66630i	−0.553047	−	0.833150i	$-0.686535\pi$
$811$		−	1351.37i		−	1.66630i	0.553047	−	0.833150i	$-0.313465\pi$
$812$	−23.2863	+	8.62442i	−0.0286777	+	0.0106212i
$813$	−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
$816$	−76.6511	+	638.341i	−0.0939351	+	0.782280i
$817$	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	$0.814900\pi$
$822$	−111.719	−	29.5833i	−0.135911	−	0.0359894i
$823$	−512.252	+	512.252i	−0.622421	+	0.622421i	−0.946150	−	0.323729i	$-0.895063\pi$
$823$	−512.252	+	512.252i	−0.622421	+	0.622421i	0.323729	+	0.946150i	$0.395063\pi$
$824$	1184.93	+	893.415i	1.43802	+	1.08424i
$825$	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	$-0.948747\pi$
$827$	−683.717	+	683.717i	−0.826744	+	0.826744i	0.160321	+	0.987065i	$0.448747\pi$
$828$	353.998	−	97.0882i	0.427534	−	0.117256i
$829$		−	1001.78i		−	1.20842i	−0.796827	−	0.604208i	$-0.793490\pi$
$829$		−	1001.78i		−	1.20842i	0.796827	−	0.604208i	$-0.206510\pi$
$830$	434.889	−	706.354i	0.523962	−	0.851029i
$831$	28.3504	−	25.9847i	0.0341160	−	0.0312692i
$832$	−971.380	−	539.140i	−1.16752	−	0.648005i
$833$	−394.578	+	394.578i	−0.473683	+	0.473683i
$834$	325.380	−	189.136i	0.390144	−	0.226782i
$835$	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
$838$	−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	$0.964035\pi$
$840$	168.455	+	278.041i	0.200541	+	0.331001i
$841$	−835.749			−0.993756
$842$	−349.621	+	224.120i	−0.415227	+	0.266176i
$843$	−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
$846$	202.996	−	650.763i	0.239948	−	0.769224i
$847$	−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
$852$	486.795	−	948.419i	0.571356	−	1.11317i
$853$	−430.775	−	430.775i	−0.505011	−	0.505011i	0.407980	−	0.912991i	$-0.366233\pi$
$853$	−430.775	−	430.775i	−0.505011	−	0.505011i	−0.912991	+	0.407980i	$0.866233\pi$
$854$	−150.720	−	32.9685i	−0.176487	−	0.0386048i
$855$	−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	0.184656	−	0.982803i	$-0.440883\pi$
$857$	−684.012	−	684.012i	−0.798147	−	0.798147i	−0.982803	+	0.184656i	$0.940883\pi$
$858$	691.931	+	183.224i	0.806447	+	0.213547i
$859$	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	$-0.226454\pi$
$863$	90.1987	+	90.1987i	0.104518	+	0.104518i	−0.652914	+	0.757432i	$0.726454\pi$
$864$	788.246	+	353.785i	0.912322	+	0.409473i
$865$	−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
$868$	−45.7491	−	123.524i	−0.0527063	−	0.142309i
$869$	−516.396			−0.594242
$870$	−12.9846	−	67.5091i	−0.0149248	−	0.0775967i
$871$		−	796.724i		−	0.914724i
$872$	633.899	−	88.9118i	0.726949	−	0.101963i
$873$	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
$876$	1149.85	−	369.838i	1.31261	−	0.422190i
$877$	19.3296	−	19.3296i	0.0220406	−	0.0220406i	−0.696001	−	0.718041i	$-0.745039\pi$
$877$	19.3296	−	19.3296i	0.0220406	−	0.0220406i	0.718041	+	0.696001i	$0.245039\pi$
$878$	−687.483	+	440.703i	−0.783010	+	0.501940i
$879$	−611.879	+	560.822i	−0.696108	+	0.638022i
$880$	512.008	−	200.288i	0.581828	−	0.227600i
$881$		−	721.297i		−	0.818725i	−0.912372	−	0.409363i	$-0.865751\pi$
$881$		−	721.297i		−	0.818725i	0.912372	−	0.409363i	$-0.134249\pi$
$882$	348.299	+	664.102i	0.394897	+	0.752950i
$883$	941.983	−	941.983i	1.06680	−	1.06680i	0.0691949	−	0.997603i	$-0.477957\pi$
$883$	941.983	−	941.983i	1.06680	−	1.06680i	0.997603	−	0.0691949i	$-0.0220430\pi$
$884$	−845.104	−	388.296i	−0.956000	−	0.439248i
$885$	−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	$-0.877713\pi$
$887$	−489.902	+	489.902i	−0.552313	+	0.552313i	0.374795	+	0.927108i	$0.377713\pi$
$888$	−542.821	−	447.605i	−0.611285	−	0.504060i
$889$			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
$894$	867.795	−	504.430i	0.970688	−	0.564239i
$895$	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
$898$	−762.171	+	488.581i	−0.848743	+	0.544077i
$899$			27.8555i			0.0309850i
$900$	−835.786	+	333.858i	−0.928651	+	0.370954i
$901$	293.954			0.326253
$902$	377.687	+	589.180i	0.418722	+	0.653193i
$903$	−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
$906$	−226.928	−	390.395i	−0.250472	−	0.430899i
$907$	−193.827	−	193.827i	−0.213701	−	0.213701i	0.592137	−	0.805838i	$-0.298285\pi$
$907$	−193.827	−	193.827i	−0.213701	−	0.213701i	−0.805838	+	0.592137i	$0.798285\pi$
$908$	−214.239	−	578.454i	−0.235946	−	0.637064i
$909$	97.2258	−	1114.44i	0.106959	−	1.22601i
$910$	−457.502	+	108.825i	−0.502750	+	0.119588i
$911$	830.304			0.911421			0.455710	−	0.890128i	$-0.349385\pi$
$911$	830.304			0.911421			0.455710	+	0.890128i	$0.349385\pi$
$912$	986.016	+	1255.13i	1.08116	+	1.37624i
$913$	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
$918$	680.457	+	245.214i	0.741238	+	0.267118i
$919$	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
$924$	−212.683	+	68.4076i	−0.230177	+	0.0740342i
$925$	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
$928$	−70.2394	−	21.0632i	−0.0756890	−	0.0226974i
$929$	1289.64			1.38821			0.694103	−	0.719876i	$-0.255801\pi$
$929$	1289.64			1.38821			0.694103	+	0.719876i	$0.255801\pi$
$930$	358.109	−	68.8780i	0.385063	−	0.0740624i
$931$			1385.32i			1.48799i
$932$	−122.644	−	331.144i	−0.131592	−	0.355304i
$933$	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
$936$	−836.332	+	928.788i	−0.893517	+	0.992295i
$937$	−507.002	+	507.002i	−0.541091	+	0.541091i	−0.923849	−	0.382758i	$-0.874974\pi$
$937$	−507.002	+	507.002i	−0.541091	+	0.541091i	0.382758	+	0.923849i	$0.374974\pi$
$938$	134.206	+	209.357i	0.143076	+	0.223195i
$939$	−413.229	−	450.849i	−0.440073	−	0.480138i
$940$	757.307	−	13.7694i	0.805646	−	0.0146483i
$941$		−	707.695i		−	0.752067i	−0.926606	−	0.376033i	$-0.877288\pi$
$941$		−	707.695i		−	0.752067i	0.926606	−	0.376033i	$-0.122712\pi$
$942$	−155.703	+	588.003i	−0.165290	+	0.624207i
$943$	−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	$-0.805670\pi$
$947$	−233.033	+	233.033i	−0.246075	+	0.246075i	0.573283	+	0.819358i	$0.305670\pi$
$948$	411.743	−	802.195i	0.434328	−	0.846197i
$949$			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	$-0.849393\pi$
$953$	−414.033	+	414.033i	−0.434452	+	0.434452i	0.455688	+	0.890140i	$0.349393\pi$
$954$	117.634	−	377.111i	0.123306	−	0.395295i
$955$	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
$958$	−925.153	−	1443.21i	−0.965713	−	1.50648i
$959$			52.1813i			0.0544122i
$960$	−97.1070	+	955.076i	−0.101153	+	0.994871i
$961$	813.238			0.846241
$962$	856.826	−	549.259i	0.890671	−	0.570955i
$963$	−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
$966$	−83.2905	−	143.289i	−0.0862220	−	0.148332i
$967$	534.588	+	534.588i	0.552831	+	0.552831i	0.927257	−	0.374426i	$-0.122160\pi$
$967$	534.588	+	534.588i	0.552831	+	0.552831i	−0.374426	+	0.927257i	$0.622160\pi$
$968$	−81.9752	−	584.444i	−0.0846851	−	0.603765i
$969$	902.828	+	985.022i	0.931711	+	1.01653i
$970$	365.476	+	225.016i	0.376779	+	0.231976i
$971$	438.396			0.451490			0.225745	−	0.974186i	$-0.427518\pi$
$971$	438.396			0.451490			0.225745	+	0.974186i	$0.427518\pi$
$972$	586.886	−	774.822i	0.603793	−	0.797141i
$973$	−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	−0.951501	−	0.307644i	$-0.900459\pi$
$977$	−1230.19	−	1230.19i	−1.25915	−	1.25915i	−0.307644	−	0.951501i	$-0.599541\pi$
$978$	133.472	−	504.050i	0.136475	−	0.515388i
$979$	−282.497			−0.288557
$980$	−578.365	+	599.787i	−0.590169	+	0.612027i
$981$	62.5865	−	717.392i	0.0637987	−	0.731287i
$982$	1296.85	−	831.328i	1.32062	−	0.846566i
$983$	−1245.00	−	1245.00i	−1.26653	−	1.26653i	−0.947867	−	0.318665i	$-0.896765\pi$
$983$	−1245.00	−	1245.00i	−1.26653	−	1.26653i	−0.318665	−	0.947867i	$-0.603235\pi$
$984$	−1216.41	+	116.941i	−1.23618	+	0.118843i
$985$	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
$988$	−2165.17	+	801.903i	−2.19147	+	0.811643i
$989$	−219.146			−0.221584
$990$	−90.2927	−	611.886i	−0.0912048	−	0.618067i
$991$		−	1328.35i		−	1.34041i	−0.742176	−	0.670205i	$-0.766206\pi$
$991$		−	1328.35i		−	1.34041i	0.742176	−	0.670205i	$-0.233794\pi$
$992$	111.732	−	372.592i	0.112633	−	0.375597i
$993$	−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
$996$	−947.587	+	304.782i	−0.951392	+	0.306006i
$997$	−553.349	+	553.349i	−0.555014	+	0.555014i	−0.927884	−	0.372870i	$-0.878374\pi$
$997$	−553.349	+	553.349i	−0.555014	+	0.555014i	0.372870	+	0.927884i	$0.378374\pi$
$998$	111.773	−	71.6510i	0.111997	−	0.0717945i
$999$	−627.771	+	482.073i	−0.628400	+	0.482555i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.68375 + 1.07935i) q^{2} +(2.99716 + 0.130491i) q^{3} +(1.67002 - 3.63470i) q^{4} +(1.65103 - 4.71955i) q^{5} +(-5.18731 + 3.01526i) q^{6} +(1.91561 + 1.91561i) q^{7} +(1.11122 + 7.92245i) q^{8} +(8.96594 + 0.782204i) q^{9} +O(q^{10})\)	\(q+(-1.68375 + 1.07935i) q^{2} +(2.99716 + 0.130491i) q^{3} +(1.67002 - 3.63470i) q^{4} +(1.65103 - 4.71955i) q^{5} +(-5.18731 + 3.01526i) 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} +(5.47960 - 10.6759i) 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} +(-15.9407 + 8.36034i) 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} +(2.29669 + 23.8899i) q^{24} +(-19.5482 - 15.5842i) q^{25} +(-33.9159 - 7.41877i) q^{26} +(26.7703 + 3.51436i) q^{27} +(10.1618 - 3.76357i) q^{28} -2.29155 q^{29} +(5.66629 + 29.4600i) q^{30} -12.1558i q^{31} +(30.6515 + 9.19168i) q^{32} +(-20.5976 - 0.896780i) q^{33} +(26.1698 + 5.72440i) q^{34} +(12.2036 - 5.87810i) q^{35} +(17.8164 - 31.2822i) 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} +(-15.7130 - 4.16080i) 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} +(-29.6525 - 37.7456i) 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} +(-48.8677 + 22.9772i) q^{54} +(-11.3465 + 32.4344i) q^{55} +(-13.0477 + 17.3050i) q^{56} +(-99.6627 - 4.33913i) q^{57} +(3.85839 - 2.47338i) q^{58} -63.0946i q^{59} +(-41.3382 - 43.4874i) q^{60} +28.4752 q^{61} +(13.1203 + 20.4672i) q^{62} +(15.6769 + 18.6737i) q^{63} +(-61.5304 + 17.6071i) q^{64} +(78.1961 - 37.6648i) q^{65} +(35.6491 - 20.7220i) 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} +(3.76614 + 71.9014i) 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} +(-100.683 - 26.6609i) 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} +(30.9476 - 9.95402i) q^{84} +(-60.3369 + 29.0625i) q^{85} +(9.18537 - 41.9921i) q^{86} +(-6.86815 - 0.299026i) q^{87} +(-7.63668 - 54.4459i) q^{88} +41.1063 q^{89} +(13.1385 + 89.0358i) q^{90} +47.0267i q^{91} +(38.2467 - 14.1653i) q^{92} +(1.58621 - 36.4327i) q^{93} +(16.1854 - 73.9937i) q^{94} +(-54.9006 + 156.936i) q^{95} +(90.6680 + 31.5487i) 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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