LMFDB - Embedded newform 60.3.l.a.23.6

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			23.6
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07935 + 1.68375i) q^{2} +(0.130491 + 2.99716i) q^{3} +(-1.67002 - 3.63470i) q^{4} +(-1.65103 + 4.71955i) q^{5} +(-5.18731 - 3.01526i) q^{6} +(-1.91561 - 1.91561i) q^{7} +(7.92245 + 1.11122i) q^{8} +(-8.96594 + 0.782204i) q^{9} +O(q^{10})$	\(q+(-1.07935 + 1.68375i) q^{2} +(0.130491 + 2.99716i) 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} +(7.92245 + 1.11122i) q^{8} +(-8.96594 + 0.782204i) q^{9} +(-6.16449 - 7.87394i) q^{10} -6.87236 q^{11} +(10.6759 - 5.47960i) q^{12} +(12.2746 + 12.2746i) q^{13} +(5.29303 - 1.15780i) q^{14} +(-14.3607 - 4.33254i) q^{15} +(-10.4221 + 12.1400i) q^{16} +(9.47120 + 9.47120i) q^{17} +(8.36034 - 15.9407i) 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} +(-2.29669 + 23.8899i) q^{24} +(-19.5482 - 15.5842i) q^{25} +(-33.9159 + 7.41877i) q^{26} +(-3.51436 - 26.7703i) q^{27} +(-3.76357 + 10.1618i) q^{28} +2.29155 q^{29} +(22.7951 - 19.5035i) q^{30} +12.1558i q^{31} +(-9.19168 - 30.6515i) q^{32} +(-0.896780 - 20.5976i) 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} +(-35.8909 + 55.9886i) q^{38} +(-35.1872 + 38.3906i) q^{39} +(-18.3246 + 35.5557i) q^{40} -50.9173i q^{41} +(4.16080 + 15.7130i) q^{42} +(15.1975 - 15.1975i) q^{43} +(11.4770 + 24.9790i) q^{44} +(11.1114 - 43.6066i) q^{45} +(-19.9218 + 4.35769i) q^{46} +(-26.7793 + 26.7793i) q^{47} +(-37.7456 - 29.6525i) 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} +(48.8677 + 22.9772i) q^{54} +(11.3465 - 32.4344i) q^{55} +(-13.0477 - 17.3050i) q^{56} +(4.33913 + 99.6627i) q^{57} +(-2.47338 + 3.85839i) q^{58} -63.0946i q^{59} +(8.23511 + 59.4322i) q^{60} +28.4752 q^{61} +(-20.4672 - 13.1203i) q^{62} +(18.6737 + 15.6769i) 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} +(18.6079 - 50.2420i) q^{68} +(-20.6685 + 22.5502i) q^{69} +(-3.27465 + 26.8922i) q^{70} +88.8377 q^{71} +(-71.9014 - 3.76614i) q^{72} +(71.1740 + 71.1740i) q^{73} +(-12.5286 - 57.2763i) q^{74} +(44.1575 - 60.6227i) q^{75} +(-55.5320 - 120.862i) q^{76} +(13.1648 + 13.1648i) q^{77} +(-26.6609 - 100.683i) 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} +(-30.9476 - 9.95402i) q^{84} +(-60.3369 + 29.0625i) q^{85} +(9.18537 + 41.9921i) q^{86} +(0.299026 + 6.86815i) q^{87} +(-54.4459 - 7.63668i) q^{88} -41.1063 q^{89} +(61.4295 + 65.7755i) q^{90} -47.0267i q^{91} +(14.1653 - 38.2467i) q^{92} +(-36.4327 + 1.58621i) 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} +(70.1464 + 44.9665i) 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 $

$2$	−1.07935	+	1.68375i	−0.539674	+	0.841874i
$2$	−1.07935	+	1.68375i	−0.539674	+	0.841874i
$3$	0.130491	+	2.99716i	0.0434969	+	0.999054i
$3$	0.130491	+	2.99716i	0.0434969	+	0.999054i
$4$	−1.67002	−	3.63470i	−0.417504	−	0.908675i
$5$	−1.65103	+	4.71955i	−0.330205	+	0.943909i
$5$	−1.65103	+	4.71955i	−0.330205	+	0.943909i
$6$	−5.18731	−	3.01526i	−0.864552	−	0.502544i
$7$	−1.91561	−	1.91561i	−0.273659	−	0.273659i	0.556912	−	0.830571i	$-0.311986\pi$
$7$	−1.91561	−	1.91561i	−0.273659	−	0.273659i	−0.830571	+	0.556912i	$0.811986\pi$
$8$	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	$-0.601126\pi$
$11$	−6.87236			−0.624760			−0.312380	+	0.949957i	$0.601126\pi$
$12$	10.6759	−	5.47960i	0.889655	−	0.456634i
$13$	12.2746	+	12.2746i	0.944199	+	0.944199i	0.998523	−	0.0543246i	$-0.0173006\pi$
$13$	12.2746	+	12.2746i	0.944199	+	0.944199i	−0.0543246	+	0.998523i	$0.517301\pi$
$14$	5.29303	−	1.15780i	0.378073	−	0.0826999i
$15$	−14.3607	−	4.33254i	−0.957379	−	0.288836i
$16$	−10.4221	+	12.1400i	−0.651380	+	0.758751i
$17$	9.47120	+	9.47120i	0.557129	+	0.557129i	0.928489	−	0.371360i	$-0.121108\pi$
$17$	9.47120	+	9.47120i	0.557129	+	0.557129i	−0.371360	+	0.928489i	$0.621108\pi$
$18$	8.36034	−	15.9407i	0.464463	−	0.885592i
$19$	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	$-0.178852\pi$
$23$	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
$27$	−3.51436	−	26.7703i	−0.130162	−	0.991493i
$28$	−3.76357	+	10.1618i	−0.134413	+	0.362921i
$29$	2.29155			0.0790190			0.0395095	−	0.999219i	$-0.487420\pi$
$29$	2.29155			0.0790190			0.0395095	+	0.999219i	$0.487420\pi$
$30$	22.7951	−	19.5035i	0.759836	−	0.650115i
$31$			12.1558i			0.392121i	0.980592	+	0.196061i	$0.0628149\pi$
$31$			12.1558i			0.392121i	−0.980592	+	0.196061i	$0.937185\pi$
$32$	−9.19168	−	30.6515i	−0.287240	−	0.957859i
$33$	−0.896780	−	20.5976i	−0.0271752	−	0.624169i
$34$	−26.1698	+	5.72440i	−0.769701	+	0.168365i
$35$	12.2036	−	5.87810i	0.348673	−	0.167946i
$36$	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	$0.379655\pi$
$38$	−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	$-0.213250\pi$
$42$	4.16080	+	15.7130i	0.0990666	+	0.374118i
$43$	15.1975	−	15.1975i	0.353430	−	0.353430i	−0.507954	−	0.861384i	$-0.669598\pi$
$43$	15.1975	−	15.1975i	0.353430	−	0.353430i	0.861384	+	0.507954i	$0.169598\pi$
$44$	11.4770	+	24.9790i	0.260840	+	0.567704i
$45$	11.1114	−	43.6066i	0.246919	−	0.969036i
$46$	−19.9218	+	4.35769i	−0.433082	+	0.0947325i
$47$	−26.7793	+	26.7793i	−0.569772	+	0.569772i	−0.932064	−	0.362293i	$-0.881994\pi$
$47$	−26.7793	+	26.7793i	−0.569772	+	0.569772i	0.362293	+	0.932064i	$0.381994\pi$
$48$	−37.7456	−	29.6525i	−0.786366	−	0.617761i
$49$		−	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	$-0.683617\pi$
$53$	15.5183	−	15.5183i	0.292799	−	0.292799i	0.838185	+	0.545386i	$0.183617\pi$
$54$	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
$57$	4.33913	+	99.6627i	0.0761251	+	1.74847i
$58$	−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	$-0.179575\pi$
$60$	8.23511	+	59.4322i	0.137252	+	0.990536i
$61$	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
$63$	18.6737	+	15.6769i	0.296408	+	0.248839i
$64$	61.5304	+	17.6071i	0.961412	+	0.275111i
$65$	−78.1961	+	37.6648i	−1.20302	+	0.579458i
$66$	35.6491	+	20.7220i	0.540137	+	0.313970i
$67$	32.4542	+	32.4542i	0.484392	+	0.484392i	0.906531	−	0.422139i	$-0.138721\pi$
$67$	32.4542	+	32.4542i	0.484392	+	0.484392i	−0.422139	+	0.906531i	$0.638721\pi$
$68$	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	$-0.284847\pi$
$71$	88.8377			1.25124			0.625618	+	0.780130i	$0.284847\pi$
$72$	−71.9014	−	3.76614i	−0.998631	−	0.0523075i
$73$	71.1740	+	71.1740i	0.974987	+	0.974987i	0.999695	−	0.0247079i	$-0.00786556\pi$
$73$	71.1740	+	71.1740i	0.974987	+	0.974987i	−0.0247079	+	0.999695i	$0.507866\pi$
$74$	−12.5286	−	57.2763i	−0.169306	−	0.774004i
$75$	44.1575	−	60.6227i	0.588766	−	0.808303i
$76$	−55.5320	−	120.862i	−0.730685	−	1.59029i
$77$	13.1648	+	13.1648i	0.170971	+	0.170971i
$78$	−26.6609	−	100.683i	−0.341807	−	1.29081i
$79$	−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	$-0.416555\pi$
$83$	−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
$87$	0.299026	+	6.86815i	0.00343708	+	0.0789442i
$88$	−54.4459	−	7.63668i	−0.618704	−	0.0867805i
$89$	−41.1063			−0.461868			−0.230934	−	0.972969i	$-0.574178\pi$
$89$	−41.1063			−0.461868			−0.230934	+	0.972969i	$0.574178\pi$
$90$	61.4295	+	65.7755i	0.682551	+	0.730838i
$91$		−	47.0267i		−	0.516777i
$92$	14.1653	−	38.2467i	0.153970	−	0.415725i
$93$	−36.4327	+	1.58621i	−0.391750	+	0.0170561i
$94$	−16.1854	−	73.9937i	−0.172185	−	0.787167i
$95$	−54.9006	+	156.936i	−0.577901	+	1.65196i
$96$	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	$0.178992\pi$
$98$	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	$0.789022\pi$
$102$	−20.5719	−	77.6882i	−0.201685	−	0.761649i
$103$	−131.168	+	131.168i	−1.27348	+	1.27348i	−0.329223	+	0.944252i	$0.606787\pi$
$103$	−131.168	+	131.168i	−1.27348	+	1.27348i	−0.944252	+	0.329223i	$0.893213\pi$
$104$	83.6050	+	110.884i	0.803895	+	1.06620i
$105$	19.2101	+	35.8090i	0.182953	+	0.341038i
$106$	9.37929	+	42.8786i	0.0884839	+	0.404516i
$107$	−11.4672	+	11.4672i	−0.107170	+	0.107170i	−0.758659	−	0.651488i	$-0.774145\pi$
$107$	−11.4672	+	11.4672i	−0.107170	+	0.107170i	0.651488	+	0.758659i	$0.274145\pi$
$108$	−91.4330	+	57.4805i	−0.846602	+	0.532227i
$109$		−	80.0130i		−	0.734065i	−0.930208	−	0.367032i	$-0.880374\pi$
$109$		−	80.0130i		−	0.734065i	0.930208	−	0.367032i	$-0.119626\pi$
$110$	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	$-0.616979\pi$
$113$	64.8556	−	64.8556i	0.573943	−	0.573943i	0.933228	+	0.359285i	$0.116979\pi$
$114$	−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
$117$	−119.654	−	100.452i	−1.02269	−	0.858564i
$118$	106.235	+	68.1010i	0.900301	+	0.577127i
$119$		−	36.2863i		−	0.304927i
$120$	−108.957	−	50.2821i	−0.907978	−	0.419018i
$121$	−73.7706			−0.609675
$122$	−30.7346	+	47.9450i	−0.251923	+	0.392992i
$123$	152.607	−	6.64423i	1.24071	−	0.0540182i
$124$	44.1825	−	20.3003i	0.356311	−	0.163712i
$125$	105.825	−	66.5288i	0.846600	−	0.532230i
$126$	−46.5513	+	14.5210i	−0.369455	+	0.115246i
$127$	−63.5895	−	63.5895i	−0.500705	−	0.500705i	0.410952	−	0.911657i	$-0.365196\pi$
$127$	−63.5895	−	63.5895i	−0.500705	−	0.500705i	−0.911657	+	0.410952i	$0.865196\pi$
$128$	−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	$-0.314729\pi$
$131$	144.030			1.09947			0.549734	+	0.835340i	$0.314729\pi$
$132$	−73.3684	+	37.6578i	−0.555821	+	0.285287i
$133$	−63.6987	−	63.6987i	−0.478938	−	0.478938i
$134$	−89.6742	+	19.6154i	−0.669210	+	0.146383i
$135$	132.146	+	27.6123i	0.978859	+	0.204536i
$136$	64.5105	+	85.5596i	0.474342	+	0.629115i
$137$	−13.6200	−	13.6200i	−0.0994161	−	0.0994161i	0.655649	−	0.755065i	$-0.272395\pi$
$137$	−13.6200	−	13.6200i	−0.0994161	−	0.0994161i	−0.755065	+	0.655649i	$0.772395\pi$
$138$	−15.6603	−	59.1401i	−0.113481	−	0.428551i
$139$	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
$144$	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
$147$	124.864	−	5.43636i	0.849417	−	0.0369820i
$148$	109.962	+	40.7259i	0.742983	+	0.275175i
$149$	167.292			1.12277			0.561383	−	0.827556i	$-0.310270\pi$
$149$	167.292			1.12277			0.561383	+	0.827556i	$0.310270\pi$
$150$	54.4122	+	139.783i	0.362748	+	0.931887i
$151$		−	75.2596i		−	0.498408i	−0.968451	−	0.249204i	$-0.919831\pi$
$151$		−	75.2596i		−	0.498408i	0.968451	−	0.249204i	$-0.0801690\pi$
$152$	263.440	+	36.9506i	1.73316	+	0.243096i
$153$	−92.3266	−	77.5098i	−0.603442	−	0.506600i
$154$	−36.3756	+	7.95681i	−0.236205	+	0.0516676i
$155$	−57.3696	−	20.0695i	−0.370127	−	0.129480i
$156$	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	$0.145356\pi$
$158$	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
$162$	−62.4895	+	149.463i	−0.385737	+	0.922609i
$163$	61.4502	−	61.4502i	0.376995	−	0.376995i	−0.493022	−	0.870017i	$-0.664108\pi$
$163$	61.4502	−	61.4502i	0.376995	−	0.376995i	0.870017	+	0.493022i	$0.164108\pi$
$164$	−185.069	+	85.0327i	−1.12847	+	0.518492i
$165$	98.6918	+	29.7748i	0.598132	+	0.180453i
$166$	162.067	−	35.4507i	0.976309	−	0.213558i
$167$	−36.7847	+	36.7847i	−0.220268	+	0.220268i	−0.808611	−	0.588344i	$-0.799780\pi$
$167$	−36.7847	+	36.7847i	−0.220268	+	0.220268i	0.588344	+	0.808611i	$0.299780\pi$
$168$	50.1633	−	41.3642i	0.298591	−	0.246215i
$169$			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	$-0.940595\pi$
$173$	−137.897	+	137.897i	−0.797091	+	0.797091i	0.185545	+	0.982636i	$0.440595\pi$
$174$	−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
$177$	189.105	−	8.23327i	1.06839	−	0.0465156i
$178$	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	$0.903413\pi$
$180$	−177.053	+	32.4373i	−0.983629	+	0.180207i
$181$	−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
$183$	3.71575	+	85.3446i	0.0203046	+	0.466364i
$184$	49.1086	+	65.1322i	0.266895	+	0.353979i
$185$	−63.6074	−	132.056i	−0.343824	−	0.713815i
$186$	36.6528	−	63.0556i	0.197058	−	0.339009i
$187$	−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	$-0.384200\pi$
$191$	135.925			0.711648			0.355824	+	0.934553i	$0.384200\pi$
$192$	−44.7422	+	186.714i	−0.233032	+	0.972469i
$193$	−62.7362	−	62.7362i	−0.325058	−	0.325058i	0.525646	−	0.850704i	$-0.323824\pi$
$193$	−62.7362	−	62.7362i	−0.325058	−	0.325058i	−0.850704	+	0.525646i	$0.823824\pi$
$194$	18.3426	+	83.8556i	0.0945494	+	0.432245i
$195$	−123.091	−	229.451i	−0.631237	−	1.17667i
$196$	−151.425	+	69.5743i	−0.772575	+	0.354971i
$197$	−96.9852	−	96.9852i	−0.492311	−	0.492311i	0.416723	−	0.909034i	$-0.363179\pi$
$197$	−96.9852	−	96.9852i	−0.492311	−	0.492311i	−0.909034	+	0.416723i	$0.863179\pi$
$198$	−57.4553	+	109.550i	−0.290178	+	0.553283i
$199$	−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
$204$	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
$207$	−70.2836	−	59.0043i	−0.339534	−	0.285045i
$208$	−276.940	+	21.0869i	−1.33144	+	0.101379i
$209$	−228.522			−1.09341
$210$	−81.0276	−	6.30545i	−0.385846	−	0.0300260i
$211$			376.951i			1.78650i	0.449561	+	0.893250i	$0.351580\pi$
$211$			376.951i			1.78650i	−0.449561	+	0.893250i	$0.648420\pi$
$212$	−82.3204	−	30.4886i	−0.388304	−	0.143814i
$213$	11.5925	+	266.261i	0.0544249	+	1.25005i
$214$	−6.93079	−	31.6850i	−0.0323869	−	0.148061i
$215$	46.6338	+	96.8167i	0.216901	+	0.450310i
$216$	1.90525	−	215.992i	0.00882060	−	0.999961i
$217$	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
$222$	170.031	−	45.0243i	0.765907	−	0.202812i
$223$	255.505	−	255.505i	1.14576	−	1.14576i	0.158385	−	0.987377i	$-0.449371\pi$
$223$	255.505	−	255.505i	1.14576	−	1.14576i	0.987377	−	0.158385i	$-0.0506288\pi$
$224$	−41.1087	+	76.3241i	−0.183521	+	0.340733i
$225$	187.458	+	124.436i	0.833148	+	0.553050i
$226$	39.1988	+	179.202i	0.173446	+	0.792930i
$227$	109.045	−	109.045i	0.480375	−	0.480375i	−0.424876	−	0.905251i	$-0.639682\pi$
$227$	109.045	−	109.045i	0.480375	−	0.480375i	0.905251	+	0.424876i	$0.139682\pi$
$228$	354.998	−	182.210i	1.55701	−	0.799166i
$229$			223.738i			0.977023i	0.872557	+	0.488512i	$0.162460\pi$
$229$			223.738i			0.977023i	−0.872557	+	0.488512i	$0.837540\pi$
$230$	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	$-0.810669\pi$
$233$	−62.4244	+	62.4244i	−0.267916	+	0.267916i	0.560344	+	0.828260i	$0.310669\pi$
$234$	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
$237$	−9.80522	−	225.210i	−0.0413722	−	0.950252i
$238$	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	$-0.224808\pi$
$240$	202.265	−	129.185i	0.842772	−	0.538270i
$241$	−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
$243$	52.4494	+	237.272i	0.215841	+	0.976428i
$244$	−47.5540	−	103.499i	−0.194893	−	0.424175i
$245$	196.620	+	68.7832i	0.802532	+	0.280748i
$246$	−153.529	+	264.124i	−0.624102	+	1.07367i
$247$	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	$-0.733631\pi$
$251$	−336.252			−1.33965			−0.669825	+	0.742519i	$0.733631\pi$
$252$	25.7954	−	94.0539i	0.102363	−	0.373230i
$253$	−49.5493	−	49.5493i	−0.195847	−	0.195847i
$254$	175.704	−	38.4336i	0.691748	−	0.151313i
$255$	−94.9785	−	177.047i	−0.372465	−	0.694302i
$256$	−38.7602	−	253.049i	−0.151407	−	0.988472i
$257$	−199.642	−	199.642i	−0.776816	−	0.776816i	0.202472	−	0.979288i	$-0.435102\pi$
$257$	−199.642	−	199.642i	−0.776816	−	0.776816i	−0.979288	+	0.202472i	$0.935102\pi$
$258$	−124.659	+	33.0096i	−0.483173	+	0.127944i
$259$	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	$-0.343713\pi$
$263$	−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
$267$	−5.36399	−	123.202i	−0.0200899	−	0.461431i
$268$	63.7623	−	172.161i	0.237919	−	0.642390i
$269$	279.355			1.03850			0.519248	−	0.854624i	$-0.326212\pi$
$269$	279.355			1.03850			0.519248	+	0.854624i	$0.326212\pi$
$270$	−189.124	+	192.697i	−0.700458	+	0.713694i
$271$		−	353.019i		−	1.30265i	−0.758797	−	0.651327i	$-0.774213\pi$
$271$		−	353.019i		−	1.30265i	0.758797	−	0.651327i	$-0.225787\pi$
$272$	−213.690	+	16.2709i	−0.785626	+	0.0598194i
$273$	140.947	−	6.13656i	0.516288	−	0.0224782i
$274$	37.6334	−	8.23194i	0.137348	−	0.0300436i
$275$	134.342	+	107.100i	0.488518	+	0.389455i
$276$	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	$0.242634\pi$
$278$	−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	$-0.118549\pi$
$282$	219.659	−	58.1658i	0.778933	−	0.206262i
$283$	4.95961	−	4.95961i	0.0175251	−	0.0175251i	−0.698290	−	0.715815i	$-0.746055\pi$
$283$	4.95961	−	4.95961i	0.0175251	−	0.0175251i	0.715815	+	0.698290i	$0.246055\pi$
$284$	−148.360	−	322.898i	−0.522396	−	1.13697i
$285$	−477.527	−	144.067i	−1.67553	−	0.505499i
$286$	233.082	−	50.9844i	0.814972	−	0.178267i
$287$	−97.5378	+	97.5378i	−0.339853	+	0.339853i
$288$	106.388	+	267.630i	0.369402	+	0.929270i
$289$		−	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	$-0.593484\pi$
$293$	195.635	−	195.635i	0.667697	−	0.667697i	0.957182	+	0.289485i	$0.0934842\pi$
$294$	−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
$297$	24.1520	+	183.975i	0.0813198	+	0.619445i
$298$	−180.566	+	281.678i	−0.605927	+	0.945227i
$299$			176.998i			0.591967i
$300$	−294.089	−	59.2581i	−0.980297	−	0.197527i
$301$	−58.2251			−0.193439
$302$	126.718	+	81.2313i	0.419597	+	0.268978i
$303$	−372.539	+	16.2196i	−1.22950	+	0.0535302i
$304$	−346.559	+	403.685i	−1.14000	+	1.32791i
$305$	−47.0133	+	134.390i	−0.154142	+	0.440622i
$306$	230.160	−	71.7948i	0.752155	−	0.234623i
$307$	−323.877	−	323.877i	−1.05497	−	1.05497i	−0.998398	−	0.0565751i	$-0.981982\pi$
$307$	−323.877	−	323.877i	−1.05497	−	1.05497i	−0.0565751	−	0.998398i	$-0.518018\pi$
$308$	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	$-0.257760\pi$
$311$	428.968			1.37932			0.689660	+	0.724133i	$0.257760\pi$
$312$	−321.429	+	265.047i	−1.03022	+	0.849510i
$313$	−144.149	−	144.149i	−0.460541	−	0.460541i	0.438292	−	0.898833i	$-0.355584\pi$
$313$	−144.149	−	144.149i	−0.460541	−	0.460541i	−0.898833	+	0.438292i	$0.855584\pi$
$314$	43.3266	+	198.073i	0.137983	+	0.630806i
$315$	−104.819	+	62.2484i	−0.332757	+	0.197614i
$316$	125.487	+	273.115i	0.397110	+	0.864288i
$317$	299.797	+	299.797i	0.945733	+	0.945733i	0.998601	−	0.0528685i	$-0.0168364\pi$
$317$	299.797	+	299.797i	0.945733	+	0.945733i	−0.0528685	+	0.998601i	$0.516836\pi$
$318$	−127.290	+	33.7065i	−0.400284	+	0.105995i
$319$	−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
$324$	−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
$327$	239.812	−	10.4410i	0.733370	−	0.0319296i
$328$	56.5801	−	403.389i	0.172500	−	1.22985i
$329$	102.598			0.311847
$330$	−156.656	+	134.035i	−0.474715	+	0.406166i
$331$		−	89.1276i		−	0.269268i	−0.990895	−	0.134634i	$-0.957014\pi$
$331$		−	89.1276i		−	0.269268i	0.990895	−	0.134634i	$-0.0429858\pi$
$332$	−115.237	+	311.144i	−0.347100	+	0.937181i
$333$	169.641	−	202.070i	0.509432	−	0.606815i
$334$	−22.2327	−	101.640i	−0.0665649	−	0.304310i
$335$	−206.752	+	99.5864i	−0.617170	+	0.297273i
$336$	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	$0.371098\pi$
$338$	−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
$342$	278.001	−	530.065i	0.812869	−	1.54990i
$343$	−173.671	+	173.671i	−0.506330	+	0.506330i
$344$	137.289	−	103.514i	0.399096	−	0.300912i
$345$	−72.3024	−	134.777i	−0.209572	−	0.390658i
$346$	−83.3448	−	381.022i	−0.240881	−	1.10122i
$347$	−341.548	+	341.548i	−0.984288	+	0.984288i	−0.999878	−	0.0155906i	$-0.995037\pi$
$347$	−341.548	+	341.548i	−0.984288	+	0.984288i	0.0155906	+	0.999878i	$0.495037\pi$
$348$	24.4643	−	12.5568i	0.0702996	−	0.0360827i
$349$			190.129i			0.544782i	0.962187	+	0.272391i	$0.0878144\pi$
$349$			190.129i			0.544782i	−0.962187	+	0.272391i	$0.912186\pi$
$350$	−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	$-0.707534\pi$
$353$	66.4041	−	66.4041i	0.188114	−	0.188114i	0.794880	+	0.606767i	$0.207534\pi$
$354$	−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
$357$	108.756	−	4.73503i	0.304638	−	0.0132634i
$358$	−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	$-0.189158\pi$
$360$	136.486	−	333.124i	0.379127	−	0.925345i
$361$	744.721			2.06294
$362$	12.5266	−	19.5411i	0.0346038	−	0.0539809i
$363$	−9.62639	−	221.102i	−0.0265190	−	0.609098i
$364$	−170.928	+	78.5354i	−0.469582	+	0.215757i
$365$	−453.419	+	218.399i	−1.24224	+	0.598353i
$366$	−147.709	−	85.8602i	−0.403578	−	0.234591i
$367$	−183.244	−	183.244i	−0.499301	−	0.499301i	0.411919	−	0.911220i	$-0.364859\pi$
$367$	−183.244	−	183.244i	−0.499301	−	0.499301i	−0.911220	+	0.411919i	$0.864859\pi$
$368$	−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
$372$	66.6087	+	129.773i	0.179056	+	0.348852i
$373$	−78.2141	−	78.2141i	−0.209689	−	0.209689i	0.594446	−	0.804135i	$-0.297371\pi$
$373$	−78.2141	−	78.2141i	−0.209689	−	0.209689i	−0.804135	+	0.594446i	$0.797371\pi$
$374$	179.848	−	39.3401i	0.480878	−	0.105187i
$375$	213.207	+	308.493i	0.568551	+	0.822648i
$376$	−241.915	+	182.400i	−0.643391	+	0.485106i
$377$	28.1278	+	28.1278i	0.0746096	+	0.0746096i
$378$	−49.5962	−	137.627i	−0.131207	−	0.364093i
$379$	−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	−0.986904	−	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
$387$	−124.372	+	148.147i	−0.321376	+	0.382810i
$388$	−160.990	−	59.6250i	−0.414922	−	0.153673i
$389$	−120.985			−0.311017			−0.155508	−	0.987835i	$-0.549702\pi$
$389$	−120.985			−0.311017			−0.155508	+	0.987835i	$0.549702\pi$
$390$	519.197	+	40.4031i	1.33127	+	0.103598i
$391$			136.574i			0.349293i
$392$	46.2942	−	330.056i	0.118098	−	0.841979i
$393$	18.7946	+	431.682i	0.0478235	+	1.09843i
$394$	267.980	−	58.6179i	0.680151	−	0.148776i
$395$	124.060	−	354.632i	0.314076	−	0.897802i
$396$	−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	$0.816411\pi$
$398$	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	$0.928924\pi$
$402$	−70.4920	−	266.208i	−0.175353	−	0.662210i
$403$	−149.207	+	149.207i	−0.370240	+	0.370240i
$404$	451.783	−	207.578i	1.11827	−	0.513808i
$405$	−65.5147	+	399.666i	−0.161765	+	0.986829i
$406$	12.1292	−	2.65315i	0.0298750	−	0.00653486i
$407$	142.457	−	142.457i	0.350018	−	0.350018i
$408$	−248.018	+	204.513i	−0.607887	+	0.501258i
$409$		−	348.822i		−	0.852865i	−0.904519	−	0.426433i	$-0.859770\pi$
$409$		−	348.822i		−	0.852865i	0.904519	−	0.426433i	$-0.140230\pi$
$410$	−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
$414$	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
$417$	8.18518	+	188.000i	0.0196287	+	0.450840i
$418$	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	$0.960152\pi$
$420$	98.0738	−	129.624i	0.233509	−	0.308629i
$421$	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
$423$	219.155	−	261.048i	0.518096	−	0.617136i
$424$	140.187	−	105.699i	0.330631	−	0.249290i
$425$	−37.5441	−	332.746i	−0.0883390	−	0.782932i
$426$	−460.829	−	267.869i	−1.08176	−	0.628801i
$427$	−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	$-0.550419\pi$
$431$	−135.966			−0.315467			−0.157734	+	0.987482i	$0.550419\pi$
$432$	361.619	+	236.338i	0.837081	+	0.547079i
$433$	426.207	+	426.207i	0.984312	+	0.984312i	0.999879	−	0.0155664i	$-0.00495515\pi$
$433$	426.207	+	426.207i	0.984312	+	0.984312i	−0.0155664	+	0.999879i	$0.504955\pi$
$434$	14.0739	+	64.3407i	0.0324284	+	0.148250i
$435$	−32.9082	−	9.92823i	−0.0756511	−	0.0228235i
$436$	−290.823	+	133.623i	−0.667026	+	0.306475i
$437$	239.748	+	239.748i	0.548622	+	0.548622i
$438$	−154.593	−	583.810i	−0.352952	−	1.33290i
$439$	−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	$-0.0585604\pi$
$443$	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
$447$	21.8301	+	501.401i	0.0488368	+	1.12170i
$448$	−84.1400	−	151.597i	−0.187813	−	0.338386i
$449$	−452.663			−1.00816			−0.504079	−	0.863657i	$-0.668168\pi$
$449$	−452.663			−1.00816			−0.504079	+	0.863657i	$0.668168\pi$
$450$	−411.852	+	181.322i	−0.915227	+	0.402939i
$451$			349.922i			0.775880i
$452$	−344.041	−	127.421i	−0.761152	−	0.281904i
$453$	225.565	−	9.82069i	0.497936	−	0.0216792i
$454$	65.9070	+	301.302i	0.145170	+	0.663661i
$455$	221.945	+	77.6424i	0.487791	+	0.170643i
$456$	−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	$0.112548\pi$
$458$	−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	$-0.217661\pi$
$462$	−28.5945	−	107.985i	−0.0618929	−	0.233734i
$463$	−318.146	+	318.146i	−0.687140	+	0.687140i	−0.961599	−	0.274459i	$-0.911501\pi$
$463$	−318.146	+	318.146i	−0.687140	+	0.687140i	0.274459	+	0.961599i	$0.411501\pi$
$464$	−23.8827	+	27.8195i	−0.0514714	+	0.0599558i
$465$	52.6652	−	174.565i	0.113259	−	0.375408i
$466$	−37.7293	−	172.485i	−0.0809642	−	0.370139i
$467$	554.211	−	554.211i	1.18675	−	1.18675i	0.208786	−	0.977961i	$-0.433049\pi$
$467$	554.211	−	554.211i	1.18675	−	1.18675i	0.977961	−	0.208786i	$-0.0669514\pi$
$468$	−165.288	+	602.665i	−0.353179	+	1.28774i
$469$		−	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
$474$	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
$477$	−126.998	+	151.275i	−0.266243	+	0.317138i
$478$	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	$0.647375\pi$
$480$	−0.799796	+	479.999i	−0.00166624	+	0.999999i
$481$	−508.880			−1.05796
$482$	129.419	−	201.889i	0.268504	−	0.418857i
$483$	82.7904	−	3.60454i	0.171409	−	0.00746281i
$484$	123.198	+	268.134i	0.254542	+	0.553996i
$485$	93.1246	+	193.337i	0.192010	+	0.398632i
$486$	−456.118	−	167.787i	−0.938514	−	0.345242i
$487$	−97.7824	−	97.7824i	−0.200785	−	0.200785i	0.599551	−	0.800336i	$-0.295346\pi$
$487$	−97.7824	−	97.7824i	−0.200785	−	0.200785i	−0.800336	+	0.599551i	$0.795346\pi$
$488$	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	$-0.786994\pi$
$491$	−770.213			−1.56866			−0.784331	+	0.620342i	$0.786994\pi$
$492$	−279.006	−	543.585i	−0.567086	−	1.10485i
$493$	21.7037	+	21.7037i	0.0440238	+	0.0440238i
$494$	−1127.78	+	246.692i	−2.28296	+	0.499376i
$495$	−76.3613	+	299.680i	−0.154265	+	0.605415i
$496$	−147.571	−	126.688i	−0.297522	−	0.255420i
$497$	−170.179	−	170.179i	−0.342412	−	0.342412i
$498$	127.400	+	481.116i	0.255823	+	0.966096i
$499$	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	$-0.0866564\pi$
$503$	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
$507$	−396.617	+	17.2680i	−0.782281	+	0.0340591i
$508$	−124.933	+	337.325i	−0.245932	+	0.664025i
$509$	−447.822			−0.879807			−0.439904	−	0.898045i	$-0.644987\pi$
$509$	−447.822			−0.879807			−0.439904	+	0.898045i	$0.644987\pi$
$510$	400.618	+	31.1755i	0.785525	+	0.0611284i
$511$		−	272.684i		−	0.533628i
$512$	467.906	+	207.865i	0.913879	+	0.405987i
$513$	−116.861	−	890.176i	−0.227799	−	1.73524i
$514$	551.629	−	120.664i	1.07321	−	0.234754i
$515$	−402.491	−	835.615i	−0.781536	−	1.62255i
$516$	78.9700	−	245.523i	0.153043	−	0.475819i
$517$	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	$-0.116560\pi$
$522$	19.1581	−	36.5288i	0.0367014	−	0.0699786i
$523$	593.137	−	593.137i	1.13411	−	1.13411i	0.144618	−	0.989488i	$-0.453805\pi$
$523$	593.137	−	593.137i	1.13411	−	1.13411i	0.989488	−	0.144618i	$-0.0461953\pi$
$524$	−240.533	−	523.507i	−0.459032	−	0.999058i
$525$	−200.718	+	31.5411i	−0.382321	+	0.0600783i
$526$	298.212	−	65.2311i	0.566943	−	0.124013i
$527$	−115.130	+	115.130i	−0.218462	+	0.218462i
$528$	259.401	+	203.783i	0.491290	+	0.385952i
$529$		−	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
$534$	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
$537$	−320.609	+	13.9587i	−0.597036	+	0.0259939i
$538$	−301.522	+	470.364i	−0.560449	+	0.874283i
$539$			286.308i			0.531184i
$540$	−120.324	−	526.424i	−0.222822	−	0.974859i
$541$	−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
$543$	−1.51444	−	34.7842i	−0.00278902	−	0.0640592i
$544$	203.250	−	377.362i	0.373621	−	0.693681i
$545$	377.625	+	132.104i	0.692890	+	0.242392i
$546$	−141.798	+	243.942i	−0.259703	+	0.446781i
$547$	586.492	+	586.492i	1.07220	+	1.07220i	0.997182	+	0.0750146i	$0.0239004\pi$
$547$	586.492	+	586.492i	1.07220	+	1.07220i	0.0750146	+	0.997182i	$0.476100\pi$
$548$	−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
$552$	−188.804	+	155.686i	−0.342035	+	0.282039i
$553$	143.941	+	143.941i	0.260292	+	0.260292i
$554$	5.47855	+	25.0459i	0.00988908	+	0.0452092i
$555$	387.492	−	207.874i	0.698184	−	0.374547i
$556$	−104.754	−	227.991i	−0.188406	−	0.410055i
$557$	413.911	+	413.911i	0.743108	+	0.743108i	0.973175	−	0.230067i	$-0.0738945\pi$
$557$	413.911	+	413.911i	0.743108	+	0.743108i	−0.230067	+	0.973175i	$0.573894\pi$
$558$	193.771	+	101.626i	0.347259	+	0.182126i
$559$	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	$-0.174964\pi$
$563$	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
$567$	−179.690	−	125.951i	−0.316913	−	0.222137i
$568$	703.812	+	98.7180i	1.23911	+	0.173799i
$569$	745.467			1.31014			0.655068	−	0.755570i	$-0.272640\pi$
$569$	745.467			1.31014			0.655068	+	0.755570i	$0.272640\pi$
$570$	757.990	−	648.536i	1.32981	−	1.13778i
$571$			406.663i			0.712195i	0.934449	+	0.356097i	$0.115893\pi$
$571$			406.663i			0.712195i	−0.934449	+	0.356097i	$0.884107\pi$
$572$	−165.732	+	447.481i	−0.289741	+	0.782310i
$573$	17.7369	+	407.388i	0.0309545	+	0.710975i
$574$	−58.9519	−	269.506i	−0.102704	−	0.469523i
$575$	−28.5804	−	253.303i	−0.0497050	−	0.440526i
$576$	−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	$0.221106\pi$
$578$	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
$582$	−248.935	+	65.9181i	−0.427723	+	0.113261i
$583$	−106.648	+	106.648i	−0.182929	+	0.182929i
$584$	484.783	+	642.962i	0.830108	+	1.10096i
$585$	671.641	−	398.866i	1.14810	−	0.681822i
$586$	118.242	+	540.559i	0.201778	+	0.922456i
$587$	422.201	−	422.201i	0.719251	−	0.719251i	−0.249200	−	0.968452i	$-0.580168\pi$
$587$	422.201	−	422.201i	0.719251	−	0.719251i	0.968452	+	0.249200i	$0.0801678\pi$
$588$	−228.285	−	444.765i	−0.388240	−	0.756404i
$589$			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	$-0.911238\pi$
$593$	−406.869	+	406.869i	−0.686119	+	0.686119i	0.275253	+	0.961372i	$0.411238\pi$
$594$	−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
$597$	−3.78796	−	87.0033i	−0.00634500	−	0.145734i
$598$	−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	$-0.0787100\pi$
$600$	417.200	−	431.212i	0.695334	−	0.718687i
$601$	−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
$603$	−316.369	−	265.597i	−0.524658	−	0.440459i
$604$	−273.546	+	125.685i	−0.452891	+	0.208087i
$605$	121.797	−	348.164i	0.201318	−	0.575478i
$606$	374.789	−	644.768i	0.618464	−	1.06397i
$607$	−74.9651	−	74.9651i	−0.123501	−	0.123501i	0.642655	−	0.766156i	$-0.277833\pi$
$607$	−74.9651	−	74.9651i	−0.123501	−	0.123501i	−0.766156	+	0.642655i	$0.777833\pi$
$608$	−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
$612$	−127.538	+	465.022i	−0.208395	+	0.759840i
$613$	22.9005	+	22.9005i	0.0373581	+	0.0373581i	0.725539	−	0.688181i	$-0.241590\pi$
$613$	22.9005	+	22.9005i	0.0373581	+	0.0373581i	−0.688181	+	0.725539i	$0.741590\pi$
$614$	894.903	−	195.751i	1.45750	−	0.318813i
$615$	−220.601	+	731.206i	−0.358701	+	1.18895i
$616$	89.6684	+	118.926i	0.145566	+	0.193062i
$617$	−115.002	−	115.002i	−0.186389	−	0.186389i	0.607744	−	0.794133i	$-0.292075\pi$
$617$	−115.002	−	115.002i	−0.186389	−	0.186389i	−0.794133	+	0.607744i	$0.792075\pi$
$618$	1075.91	−	284.903i	1.74096	−	0.461007i
$619$	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
$624$	−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
$627$	−29.8201	−	684.918i	−0.0475599	−	1.09237i
$628$	−380.270	−	140.839i	−0.605525	−	0.224265i
$629$	−392.657			−0.624256
$630$	8.32509	−	243.676i	0.0132144	−	0.386787i
$631$		−	209.771i		−	0.332443i	−0.986088	−	0.166221i	$-0.946843\pi$
$631$		−	209.771i		−	0.332443i	0.986088	−	0.166221i	$-0.0531566\pi$
$632$	−595.301	−	83.4980i	−0.941932	−	0.132117i
$633$	−1129.78	+	49.1887i	−1.78481	+	0.0777072i
$634$	−828.369	+	181.198i	−1.30658	+	0.285801i
$635$	405.102	−	195.126i	0.637956	−	0.307285i
$636$	80.6372	−	250.706i	0.126788	−	0.394192i
$637$	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	$0.619007\pi$
$642$	94.0607	−	24.9073i	0.146512	−	0.0387964i
$643$	424.387	−	424.387i	0.660012	−	0.660012i	−0.295371	−	0.955383i	$-0.595443\pi$
$643$	424.387	−	424.387i	0.660012	−	0.660012i	0.955383	+	0.295371i	$0.0954433\pi$
$644$	−100.401	+	46.1308i	−0.155902	+	0.0716316i
$645$	−284.090	+	152.403i	−0.440450	+	0.236283i
$646$	−870.209	+	190.350i	−1.34707	+	0.294659i
$647$	−556.306	+	556.306i	−0.859824	+	0.859824i	−0.991317	−	0.131493i	$-0.958023\pi$
$647$	−556.306	+	556.306i	−0.859824	+	0.859824i	0.131493	+	0.991317i	$0.458023\pi$
$648$	647.610	−	22.4746i	0.999398	−	0.0346830i
$649$			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	−0.126340	+	0.991987i	$0.540323\pi$
$653$	−730.267	+	730.267i	−1.11833	+	1.11833i	−0.991987	+	0.126340i	$0.959677\pi$
$654$	−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
$657$	−693.815	−	582.470i	−1.05604	−	0.886560i
$658$	−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	$0.750835\pi$
$660$	−56.5947	−	408.439i	−0.0857495	−	0.618848i
$661$	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
$663$	−696.870	+	30.3404i	−1.05109	+	0.0457623i
$664$	−399.508	−	529.863i	−0.601668	−	0.797986i
$665$	405.797	−	195.461i	0.610221	−	0.293926i
$666$	157.133	+	503.736i	0.235935	+	0.756360i
$667$	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
$672$	−234.120	−	113.250i	−0.348393	−	0.168526i
$673$	301.487	+	301.487i	0.447975	+	0.447975i	0.894681	−	0.446706i	$-0.147403\pi$
$673$	301.487	+	301.487i	0.447975	+	0.447975i	−0.446706	+	0.894681i	$0.647403\pi$
$674$	−106.962	−	488.992i	−0.158698	−	0.725508i
$675$	−348.494	+	578.080i	−0.516288	+	0.856415i
$676$	480.983	−	220.995i	0.711513	−	0.326915i
$677$	−530.496	−	530.496i	−0.783598	−	0.783598i	0.196838	−	0.980436i	$-0.436933\pi$
$677$	−530.496	−	530.496i	−0.783598	−	0.783598i	−0.980436	+	0.196838i	$0.936933\pi$
$678$	−531.983	+	140.869i	−0.784635	+	0.207772i
$679$	−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	$-0.378133\pi$
$683$	−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
$687$	−670.580	+	29.1958i	−0.976099	+	0.0424975i
$688$	26.1083	+	342.887i	0.0379481	+	0.498383i
$689$	380.962			0.552920
$690$	304.970	+	23.7323i	0.441986	+	0.0343947i
$691$		−	690.583i		−	0.999396i	−0.866200	−	0.499698i	$-0.833444\pi$
$691$		−	690.583i		−	0.999396i	0.866200	−	0.499698i	$-0.166556\pi$
$692$	731.503	+	270.923i	1.05708	+	0.391508i
$693$	−128.332	−	107.737i	−0.185184	−	0.155465i
$694$	−206.432	−	943.730i	−0.297452	−	1.35984i
$695$	−103.563	+	296.039i	−0.149011	+	0.425955i
$696$	−5.26298	+	54.7448i	−0.00756175	+	0.0786563i
$697$	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	$0.970535\pi$
$702$	317.795	+	881.865i	0.452700	+	1.25622i
$703$	−689.289	+	689.289i	−0.980496	+	0.980496i
$704$	−422.859	−	121.002i	−0.600652	−	0.171879i
$705$	500.591	−	268.546i	0.710058	−	0.380917i
$706$	40.1347	+	183.481i	0.0568480	+	0.259888i
$707$	238.105	−	238.105i	0.336783	−	0.336783i
$708$	−345.734	−	673.589i	−0.488324	−	0.951397i
$709$		−	86.8545i		−	0.122503i	−0.998122	−	0.0612514i	$-0.980491\pi$
$709$		−	86.8545i		−	0.122503i	0.998122	−	0.0612514i	$-0.0195091\pi$
$710$	−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
$714$	−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
$717$	929.769	−	40.4804i	1.29675	−	0.0564581i
$718$	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	$0.976937\pi$
$720$	413.582	+	589.364i	0.574419	+	0.818561i
$721$	502.534			0.696996
$722$	−803.812	+	1253.92i	−1.11331	+	1.73673i
$723$	−15.6464	−	359.373i	−0.0216410	−	0.497059i
$724$	19.3817	+	42.1833i	0.0267703	+	0.0582642i
$725$	−44.7957	−	35.7120i	−0.0617872	−	0.0492579i
$726$	382.671	+	222.438i	0.527095	+	0.306388i
$727$	252.054	+	252.054i	0.346704	+	0.346704i	0.858880	−	0.512176i	$-0.171161\pi$
$727$	252.054	+	252.054i	0.346704	+	0.346704i	−0.512176	+	0.858880i	$0.671161\pi$
$728$	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
$732$	303.997	−	156.033i	0.415296	−	0.213159i
$733$	−795.114	−	795.114i	−1.08474	−	1.08474i	−0.996060	−	0.0886791i	$-0.971735\pi$
$733$	−795.114	−	795.114i	−1.08474	−	1.08474i	−0.0886791	−	0.996060i	$-0.528265\pi$
$734$	506.320	−	110.753i	0.689809	−	0.150889i
$735$	−180.497	+	598.278i	−0.245574	+	0.813984i
$736$	154.724	−	287.267i	0.210223	−	0.390308i
$737$	−223.037	−	223.037i	−0.302629	−	0.302629i
$738$	−811.655	−	425.685i	−1.09980	−	0.576810i
$739$	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	$-0.0963914\pi$
$743$	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
$747$	571.770	+	480.011i	0.765422	+	0.642585i
$748$	−127.880	+	345.281i	−0.170963	+	0.461606i
$749$	43.9335			0.0586562
$750$	−749.549	+	26.0151i	−0.999398	+	0.0346868i
$751$		−	1089.00i		−	1.45007i	−0.688711	−	0.725036i	$-0.741823\pi$
$751$		−	1089.00i		−	1.45007i	0.688711	−	0.725036i	$-0.258177\pi$
$752$	−46.0050	−	604.197i	−0.0611769	−	0.803454i
$753$	−43.8778	−	1007.80i	−0.0582706	−	1.33838i
$754$	−77.7199	+	17.0005i	−0.103077	+	0.0225470i
$755$	355.191	+	124.256i	0.470452	+	0.164577i
$756$	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	$0.449590\pi$
$758$	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	$-0.157625\pi$
$762$	138.119	+	521.598i	0.181259	+	0.684512i
$763$	−153.274	+	153.274i	−0.200883	+	0.200883i
$764$	−226.997	−	494.046i	−0.297116	−	0.646657i
$765$	518.245	−	307.769i	0.677444	−	0.402312i
$766$	1215.11	−	265.794i	1.58631	−	0.346990i
$767$	774.460	−	774.460i	1.00973	−	1.00973i
$768$	753.370	−	149.191i	0.980950	−	0.194259i
$769$		−	180.270i		−	0.234421i	−0.993107	−	0.117210i	$-0.962605\pi$
$769$		−	180.270i		−	0.234421i	0.993107	−	0.117210i	$-0.0373952\pi$
$770$	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	$-0.604620\pi$
$773$	482.107	−	482.107i	0.623683	−	0.623683i	0.946471	+	0.322788i	$0.104620\pi$
$774$	−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
$777$	10.3633	+	238.027i	0.0133375	+	0.306341i
$778$	130.585	−	203.709i	0.167848	−	0.261837i
$779$		−	1693.12i		−	2.17345i
$780$	−628.423	+	830.588i	−0.805670	+	1.06486i
$781$	−610.525			−0.781722
$782$	−229.956	−	147.410i	−0.294061	−	0.188504i
$783$	−8.05334	−	61.3455i	−0.0102852	−	0.0783468i
$784$	505.764	+	434.193i	0.645107	+	0.553818i
$785$	219.967	+	456.676i	0.280213	+	0.581752i
$786$	−747.129	−	434.289i	−0.950546	−	0.552531i
$787$	−279.225	−	279.225i	−0.354797	−	0.354797i	0.507094	−	0.861891i	$-0.330720\pi$
$787$	−279.225	−	279.225i	−0.354797	−	0.354797i	−0.861891	+	0.507094i	$0.830720\pi$
$788$	−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
$792$	494.133	+	25.8823i	0.623905	+	0.0326796i
$793$	349.521	+	349.521i	0.440758	+	0.440758i
$794$	−331.978	−	1517.68i	−0.418108	−	1.91143i
$795$	−290.088	+	155.620i	−0.364890	+	0.195749i
$796$	48.4782	+	105.510i	0.0609023	+	0.132550i
$797$	−861.626	−	861.626i	−1.08109	−	1.08109i	−0.996408	−	0.0846783i	$-0.973014\pi$
$797$	−861.626	−	861.626i	−1.08109	−	1.08109i	−0.0846783	−	0.996408i	$-0.526986\pi$
$798$	138.356	+	522.493i	0.173379	+	0.654754i
$799$	−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
$804$	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
$807$	36.4533	+	837.273i	0.0451714	+	1.03751i
$808$	−138.121	+	984.738i	−0.170942	+	1.21874i
$809$	430.022			0.531548			0.265774	−	0.964035i	$-0.414373\pi$
$809$	430.022			0.531548			0.265774	+	0.964035i	$0.414373\pi$
$810$	−602.224	−	541.689i	−0.743486	−	0.668751i
$811$			1351.37i			1.66630i	0.553047	+	0.833150i	$0.313465\pi$
$811$			1351.37i			1.66630i	−0.553047	+	0.833150i	$0.686535\pi$
$812$	−8.62442	+	23.2863i	−0.0106212	+	0.0286777i
$813$	1058.06	−	46.0658i	1.30142	−	0.0566614i
$814$	86.1013	+	393.623i	0.105776	+	0.483567i
$815$	188.561	+	391.473i	0.231363	+	0.480335i
$816$	−76.6511	−	638.341i	−0.0939351	−	0.782280i
$817$	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	$-0.185100\pi$
$822$	29.5833	+	111.719i	0.0359894	+	0.135911i
$823$	512.252	−	512.252i	0.622421	−	0.622421i	−0.323729	−	0.946150i	$-0.604937\pi$
$823$	512.252	−	512.252i	0.622421	−	0.622421i	0.946150	+	0.323729i	$0.104937\pi$
$824$	−1184.93	+	893.415i	−1.43802	+	1.08424i
$825$	−303.466	+	416.621i	−0.367838	+	0.504996i
$826$	−73.0508	−	333.961i	−0.0884393	−	0.404312i
$827$	−683.717	+	683.717i	−0.826744	+	0.826744i	−0.987065	−	0.160321i	$-0.948747\pi$
$827$	−683.717	+	683.717i	−0.826744	+	0.826744i	0.160321	+	0.987065i	$0.448747\pi$
$828$	−97.0882	+	353.998i	−0.117256	+	0.427534i
$829$		−	1001.78i		−	1.20842i	−0.796827	−	0.604208i	$-0.793490\pi$
$829$		−	1001.78i		−	1.20842i	0.796827	−	0.604208i	$-0.206510\pi$
$830$	−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
$834$	−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
$837$	325.413	−	42.7197i	0.388785	−	0.0510391i
$838$	−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	$0.964035\pi$
$840$	112.399	+	305.041i	0.133808	+	0.363145i
$841$	−835.749			−0.993756
$842$	−224.120	+	349.621i	−0.266176	+	0.415227i
$843$	612.923	−	26.6855i	0.727073	−	0.0316554i
$844$	1370.10	−	629.515i	1.62335	−	0.745871i
$845$	−624.541	−	218.482i	−0.739102	−	0.258558i
$846$	202.996	+	650.763i	0.239948	+	0.769224i
$847$	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
$852$	948.419	−	486.795i	1.11317	−	0.571356i
$853$	−430.775	−	430.775i	−0.505011	−	0.505011i	0.407980	−	0.912991i	$-0.366233\pi$
$853$	−430.775	−	430.775i	−0.505011	−	0.505011i	−0.912991	+	0.407980i	$0.866233\pi$
$854$	150.720	−	32.9685i	0.176487	−	0.0386048i
$855$	369.479	−	1450.02i	0.432140	−	1.69593i
$856$	−103.591	+	78.1059i	−0.121018	+	0.0912452i
$857$	684.012	+	684.012i	0.798147	+	0.798147i	0.982803	−	0.184656i	$-0.0591172\pi$
$857$	684.012	+	684.012i	0.798147	+	0.798147i	−0.184656	+	0.982803i	$0.559117\pi$
$858$	183.224	+	691.931i	0.213547	+	0.806447i
$859$	−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	$-0.226454\pi$
$863$	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
$867$	328.468	−	14.3009i	0.378855	−	0.0164947i
$868$	−123.524	−	45.7491i	−0.142309	−	0.0527063i
$869$	516.396			0.594242
$870$	52.2360	−	44.6932i	0.0600414	−	0.0513714i
$871$			796.724i			0.914724i
$872$	88.9118	−	633.899i	0.101963	−	0.726949i
$873$	−248.363	+	295.841i	−0.284494	+	0.338878i
$874$	−662.446	+	144.904i	−0.757948	+	0.165794i
$875$	−330.163	−	75.2763i	−0.377329	−	0.0860300i
$876$	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	$0.245039\pi$
$878$	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	$0.865751\pi$
$882$	−664.102	−	348.299i	−0.752950	−	0.394897i
$883$	−941.983	+	941.983i	−1.06680	+	1.06680i	−0.0691949	+	0.997603i	$0.522043\pi$
$883$	−941.983	+	941.983i	−1.06680	+	1.06680i	−0.997603	+	0.0691949i	$0.977957\pi$
$884$	845.104	−	388.296i	0.956000	−	0.439248i
$885$	−273.360	+	906.082i	−0.308881	+	1.02382i
$886$	−979.471	+	214.250i	−1.10550	+	0.241817i
$887$	−489.902	+	489.902i	−0.552313	+	0.552313i	−0.927108	−	0.374795i	$-0.877713\pi$
$887$	−489.902	+	489.902i	−0.552313	+	0.552313i	0.374795	+	0.927108i	$0.377713\pi$
$888$	−447.605	−	542.821i	−0.504060	−	0.611285i
$889$			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
$894$	−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
$897$	−530.492	+	23.0966i	−0.591407	+	0.0257487i
$898$	488.581	−	762.171i	0.544077	−	0.848743i
$899$			27.8555i			0.0309850i
$900$	139.230	−	889.165i	0.154700	−	0.987961i
$901$	293.954			0.326253
$902$	−589.180	−	377.687i	−0.653193	−	0.418722i
$903$	−7.59784	−	174.510i	−0.00841399	−	0.193256i
$904$	585.884	−	441.746i	0.648101	−	0.488658i
$905$	19.1613	−	54.7736i	0.0211727	−	0.0605234i
$906$	−226.928	+	390.395i	−0.250472	+	0.430899i
$907$	193.827	+	193.827i	0.213701	+	0.213701i	0.805838	−	0.592137i	$-0.201715\pi$
$907$	193.827	+	193.827i	0.213701	+	0.213701i	−0.592137	+	0.805838i	$0.701715\pi$
$908$	−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	$-0.349385\pi$
$911$	830.304			0.911421			0.455710	+	0.890128i	$0.349385\pi$
$912$	−1255.13	−	986.016i	−1.37624	−	1.08116i
$913$	403.093	+	403.093i	0.441504	+	0.441504i
$914$	163.484	+	747.386i	0.178866	+	0.817709i
$915$	−408.923	−	123.370i	−0.446910	−	0.134830i
$916$	813.222	−	373.647i	0.887797	−	0.407911i
$917$	−275.906	−	275.906i	−0.300879	−	0.300879i
$918$	245.214	+	680.457i	0.267118	+	0.741238i
$919$	−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
$924$	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
$927$	1073.44	−	1278.64i	1.15798	−	1.37934i
$928$	−21.0632	−	70.2394i	−0.0226974	−	0.0756890i
$929$	−1289.64			−1.38821			−0.694103	−	0.719876i	$-0.744199\pi$
$929$	−1289.64			−1.38821			−0.694103	+	0.719876i	$0.744199\pi$
$930$	237.079	+	277.091i	0.254924	+	0.297948i
$931$		−	1385.32i		−	1.48799i
$932$	331.144	+	122.644i	0.355304	+	0.131592i
$933$	55.9764	+	1285.69i	0.0599962	+	1.37801i
$934$	334.966	+	1531.34i	0.358636	+	1.63955i
$935$	414.657	−	199.728i	0.443484	−	0.213613i
$936$	−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	$0.374974\pi$
$938$	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	$0.877288\pi$
$942$	−588.003	+	155.703i	−0.624207	+	0.165290i
$943$	367.111	−	367.111i	0.389301	−	0.389301i
$944$	765.970	+	657.578i	0.811409	+	0.696586i
$945$	−200.246	−	306.035i	−0.211901	−	0.323847i
$946$	−63.1252	−	288.585i	−0.0667286	−	0.305058i
$947$	−233.033	+	233.033i	−0.246075	+	0.246075i	−0.819358	−	0.573283i	$-0.805670\pi$
$947$	−233.033	+	233.033i	−0.246075	+	0.246075i	0.573283	+	0.819358i	$0.305670\pi$
$948$	−802.195	+	411.743i	−0.846197	+	0.434328i
$949$			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	$-0.650607\pi$
$953$	414.033	−	414.033i	0.434452	−	0.434452i	0.890140	+	0.455688i	$0.150607\pi$
$954$	−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
$957$	−2.05502	−	47.2004i	−0.00214735	−	0.0493212i
$958$	−1443.21	−	925.153i	−1.50648	−	0.965713i
$959$			52.1813i			0.0544122i
$960$	−807.335	−	519.433i	−0.840974	−	0.541076i
$961$	813.238			0.846241
$962$	549.259	−	856.826i	0.570955	−	0.890671i
$963$	93.8447	−	111.784i	0.0974504	−	0.116079i
$964$	200.243	+	435.817i	0.207721	+	0.452093i
$965$	399.665	−	192.507i	0.414161	−	0.199489i
$966$	−83.2905	+	143.289i	−0.0862220	+	0.148332i
$967$	−534.588	−	534.588i	−0.552831	−	0.552831i	0.374426	−	0.927257i	$-0.377840\pi$
$967$	−534.588	−	534.588i	−0.552831	−	0.552831i	−0.927257	+	0.374426i	$0.877840\pi$
$968$	−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	$-0.427518\pi$
$971$	438.396			0.451490			0.225745	+	0.974186i	$0.427518\pi$
$972$	774.822	−	586.886i	0.797141	−	0.603793i
$973$	−120.159	−	120.159i	−0.123493	−	0.123493i
$974$	270.182	−	59.0997i	0.277394	−	0.0606773i
$975$	1286.13	−	202.104i	1.31911	−	0.207287i
$976$	−296.771	+	345.689i	−0.304068	+	0.354190i
$977$	1230.19	+	1230.19i	1.25915	+	1.25915i	0.951501	+	0.307644i	$0.0995406\pi$
$977$	1230.19	+	1230.19i	1.25915	+	1.25915i	0.307644	+	0.951501i	$0.400459\pi$
$978$	−504.050	+	133.472i	−0.515388	+	0.136475i
$979$	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	−0.947867	−	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
$987$	13.3880	+	307.501i	0.0135644	+	0.311551i
$988$	801.903	−	2165.17i	0.811643	−	2.19147i
$989$	219.146			0.221584
$990$	−422.166	−	452.033i	−0.426430	−	0.456599i
$991$			1328.35i			1.34041i	0.742176	+	0.670205i	$0.233794\pi$
$991$			1328.35i			1.34041i	−0.742176	+	0.670205i	$0.766206\pi$
$992$	372.592	−	111.732i	0.375597	−	0.112633i
$993$	267.130	−	11.6303i	0.269013	−	0.0117123i
$994$	470.220	−	102.856i	0.473059	−	0.103477i
$995$	47.9270	−	137.002i	0.0481678	−	0.137690i
$996$	−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	$0.378374\pi$
$998$	−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.23.6	yes	40
3.2	odd	2	inner	60.3.l.a.23.15	yes	40
4.3	odd	2	inner	60.3.l.a.23.16	yes	40
5.2	odd	4	inner	60.3.l.a.47.5	yes	40
5.3	odd	4		300.3.l.g.107.16		40
5.4	even	2		300.3.l.g.143.15		40
12.11	even	2	inner	60.3.l.a.23.5	✓	40
15.2	even	4	inner	60.3.l.a.47.16	yes	40
15.8	even	4		300.3.l.g.107.5		40
15.14	odd	2		300.3.l.g.143.6		40
20.3	even	4		300.3.l.g.107.6		40
20.7	even	4	inner	60.3.l.a.47.15	yes	40
20.19	odd	2		300.3.l.g.143.5		40
60.23	odd	4		300.3.l.g.107.15		40
60.47	odd	4	inner	60.3.l.a.47.6	yes	40
60.59	even	2		300.3.l.g.143.16		40

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

\(f(q)\)	\(=\)	\(q+(-1.07935 + 1.68375i) q^{2} +(0.130491 + 2.99716i) q^{3} +(-1.67002 - 3.63470i) q^{4} +(-1.65103 + 4.71955i) q^{5} +(-5.18731 - 3.01526i) q^{6} +(-1.91561 - 1.91561i) q^{7} +(7.92245 + 1.11122i) q^{8} +(-8.96594 + 0.782204i) q^{9} +O(q^{10})\)	\(q+(-1.07935 + 1.68375i) q^{2} +(0.130491 + 2.99716i) 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} +(7.92245 + 1.11122i) q^{8} +(-8.96594 + 0.782204i) q^{9} +(-6.16449 - 7.87394i) q^{10} -6.87236 q^{11} +(10.6759 - 5.47960i) q^{12} +(12.2746 + 12.2746i) q^{13} +(5.29303 - 1.15780i) q^{14} +(-14.3607 - 4.33254i) q^{15} +(-10.4221 + 12.1400i) q^{16} +(9.47120 + 9.47120i) q^{17} +(8.36034 - 15.9407i) 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} +(-2.29669 + 23.8899i) q^{24} +(-19.5482 - 15.5842i) q^{25} +(-33.9159 + 7.41877i) q^{26} +(-3.51436 - 26.7703i) q^{27} +(-3.76357 + 10.1618i) q^{28} +2.29155 q^{29} +(22.7951 - 19.5035i) q^{30} +12.1558i q^{31} +(-9.19168 - 30.6515i) q^{32} +(-0.896780 - 20.5976i) 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} +(-35.8909 + 55.9886i) q^{38} +(-35.1872 + 38.3906i) q^{39} +(-18.3246 + 35.5557i) q^{40} -50.9173i q^{41} +(4.16080 + 15.7130i) q^{42} +(15.1975 - 15.1975i) q^{43} +(11.4770 + 24.9790i) q^{44} +(11.1114 - 43.6066i) q^{45} +(-19.9218 + 4.35769i) q^{46} +(-26.7793 + 26.7793i) q^{47} +(-37.7456 - 29.6525i) 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} +(48.8677 + 22.9772i) q^{54} +(11.3465 - 32.4344i) q^{55} +(-13.0477 - 17.3050i) q^{56} +(4.33913 + 99.6627i) q^{57} +(-2.47338 + 3.85839i) q^{58} -63.0946i q^{59} +(8.23511 + 59.4322i) q^{60} +28.4752 q^{61} +(-20.4672 - 13.1203i) q^{62} +(18.6737 + 15.6769i) 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} +(18.6079 - 50.2420i) q^{68} +(-20.6685 + 22.5502i) q^{69} +(-3.27465 + 26.8922i) q^{70} +88.8377 q^{71} +(-71.9014 - 3.76614i) q^{72} +(71.1740 + 71.1740i) q^{73} +(-12.5286 - 57.2763i) q^{74} +(44.1575 - 60.6227i) q^{75} +(-55.5320 - 120.862i) q^{76} +(13.1648 + 13.1648i) q^{77} +(-26.6609 - 100.683i) 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} +(-30.9476 - 9.95402i) q^{84} +(-60.3369 + 29.0625i) q^{85} +(9.18537 + 41.9921i) q^{86} +(0.299026 + 6.86815i) q^{87} +(-54.4459 - 7.63668i) q^{88} -41.1063 q^{89} +(61.4295 + 65.7755i) q^{90} -47.0267i q^{91} +(14.1653 - 38.2467i) q^{92} +(-36.4327 + 1.58621i) 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} +(70.1464 + 44.9665i) 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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