LMFDB - Embedded newform 270.3.q.a.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(7,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([32, 9]))

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

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

chi := DirichletCharacter("270.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.q (of order $36$, degree $12$, 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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	270.103
Dual form			270.3.q.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.123257 - 1.40883i) q^{2} +(-2.55916 - 1.56548i) q^{3} +(-1.96962 - 0.347296i) q^{4} +(-4.02280 + 2.96936i) q^{5} +(-2.52093 + 3.41247i) q^{6} +(2.35838 + 1.65135i) q^{7} +(-0.732051 + 2.73205i) q^{8} +(4.09857 + 8.01260i) q^{9} +(3.68749 + 6.03344i) q^{10} +(5.11381 + 1.86128i) q^{11} +(4.49687 + 3.97217i) q^{12} +(-1.40437 - 16.0520i) q^{13} +(2.61716 - 3.11901i) q^{14} +(14.9434 - 1.30146i) q^{15} +(3.75877 + 1.36808i) q^{16} +(7.49195 + 27.9603i) q^{17} +(11.7936 - 4.78659i) q^{18} +(0.970790 - 0.560486i) q^{19} +(8.95462 - 4.45139i) q^{20} +(-3.45030 - 7.91805i) q^{21} +(3.25254 - 6.97509i) q^{22} +(34.3534 - 24.0545i) q^{23} +(6.15039 - 5.84574i) q^{24} +(7.36583 - 23.8903i) q^{25} -22.7876 q^{26} +(2.05464 - 26.9217i) q^{27} +(-4.07158 - 4.07158i) q^{28} +(3.65957 + 4.36130i) q^{29} +(0.00834613 - 21.2132i) q^{30} +(-8.44013 + 47.8664i) q^{31} +(2.39069 - 5.12685i) q^{32} +(-10.1733 - 12.7689i) q^{33} +(40.3149 - 7.10860i) q^{34} +(-14.3907 + 0.359800i) q^{35} +(-5.28986 - 17.2052i) q^{36} +(-2.23659 - 8.34706i) q^{37} +(-0.669974 - 1.43676i) q^{38} +(-21.5350 + 43.2780i) q^{39} +(-5.16754 - 13.1642i) q^{40} +(50.5697 + 42.4330i) q^{41} +(-11.5805 + 3.88494i) q^{42} +(10.5200 + 22.5603i) q^{43} +(-9.42583 - 5.44201i) q^{44} +(-40.2800 - 20.0629i) q^{45} +(-29.6544 - 51.3630i) q^{46} +(50.5606 + 35.4029i) q^{47} +(-7.47759 - 9.38540i) q^{48} +(-13.9240 - 38.2559i) q^{49} +(-32.7495 - 13.3219i) q^{50} +(24.5982 - 83.2834i) q^{51} +(-2.80873 + 32.1039i) q^{52} +(-20.4015 - 20.4015i) q^{53} +(-37.6749 - 6.21292i) q^{54} +(-26.0986 + 7.69720i) q^{55} +(-6.23803 + 5.23433i) q^{56} +(-3.36183 - 0.0853767i) q^{57} +(6.59541 - 4.61815i) q^{58} +(32.9877 + 90.6329i) q^{59} +(-29.8848 - 2.62643i) q^{60} +(7.17732 + 40.7046i) q^{61} +(66.3954 + 17.7906i) q^{62} +(-3.56565 + 25.6649i) q^{63} +(-6.92820 - 4.00000i) q^{64} +(53.3135 + 60.4038i) q^{65} +(-19.2431 + 12.7586i) q^{66} +(83.9811 - 7.34739i) q^{67} +(-5.04574 - 57.6731i) q^{68} +(-125.572 + 7.77985i) q^{69} +(-1.26686 + 20.3185i) q^{70} +(-41.0311 + 71.0679i) q^{71} +(-24.8912 + 5.33188i) q^{72} +(4.21248 - 15.7212i) q^{73} +(-12.0353 + 2.12215i) q^{74} +(-56.2500 + 49.6079i) q^{75} +(-2.10674 + 0.766789i) q^{76} +(8.98667 + 12.8343i) q^{77} +(58.3171 + 35.6735i) q^{78} +(-33.9874 - 40.5046i) q^{79} +(-19.1831 + 5.65762i) q^{80} +(-47.4034 + 65.6804i) q^{81} +(66.0140 - 66.0140i) q^{82} +(7.66773 + 0.670839i) q^{83} +(4.04586 + 16.7938i) q^{84} +(-113.163 - 90.2326i) q^{85} +(33.0803 - 12.0402i) q^{86} +(-2.53789 - 16.8902i) q^{87} +(-8.82867 + 12.6087i) q^{88} +(-67.5355 + 38.9917i) q^{89} +(-33.2301 + 54.2749i) q^{90} +(23.1954 - 40.1757i) q^{91} +(-76.0169 + 35.4473i) q^{92} +(96.5332 - 109.285i) q^{93} +(56.1087 - 66.8678i) q^{94} +(-2.24101 + 5.13734i) q^{95} +(-14.1441 + 9.37785i) q^{96} +(86.1483 - 40.1716i) q^{97} +(-55.6124 + 14.9013i) q^{98} +(6.04568 + 48.6035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 36 q^{6} + 18 q^{7} + 216 q^{8} + 36 q^{11} - 18 q^{15} + 72 q^{20} + 288 q^{21} + 36 q^{22} + 108 q^{23} + 54 q^{25} - 162 q^{27} - 120 q^{30} - 432 q^{31} + 114 q^{33} - 162 q^{35} + 48 q^{36}+ \cdots + 756 q^{98}+O(q^{100}) $ 216 * q - 36 * q^6 + 18 * q^7 + 216 * q^8 + 36 * q^11 - 18 * q^15 + 72 * q^20 + 288 * q^21 + 36 * q^22 + 108 * q^23 + 54 * q^25 - 162 * q^27 - 120 * q^30 - 432 * q^31 + 114 * q^33 - 162 * q^35 + 48 * q^36 + 108 * q^38 - 36 * q^40 + 216 * q^41 - 48 * q^42 - 216 * q^43 + 18 * q^45 + 108 * q^46 - 144 * q^47 - 72 * q^48 - 162 * q^50 + 60 * q^51 - 540 * q^53 + 324 * q^55 - 72 * q^56 - 234 * q^57 + 72 * q^58 - 96 * q^60 + 504 * q^61 - 24 * q^63 - 144 * q^66 + 72 * q^67 + 108 * q^68 + 72 * q^70 + 240 * q^72 - 216 * q^73 - 84 * q^75 + 216 * q^76 + 576 * q^77 + 168 * q^78 - 1068 * q^81 + 576 * q^83 + 576 * q^85 - 432 * q^86 - 324 * q^87 - 72 * q^88 - 606 * q^90 + 756 * q^91 - 324 * q^92 + 168 * q^93 - 468 * q^95 - 1332 * q^97 + 756 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.123257	−	1.40883i	0.0616284	−	0.704416i
$2$	0.123257	−	1.40883i	0.0616284	−	0.704416i
$3$	−2.55916	−	1.56548i	−0.853052	−	0.521825i
$3$	−2.55916	−	1.56548i	−0.853052	−	0.521825i
$4$	−1.96962	−	0.347296i	−0.492404	−	0.0868241i
$5$	−4.02280	+	2.96936i	−0.804560	+	0.593871i
$5$	−4.02280	+	2.96936i	−0.804560	+	0.593871i
$6$	−2.52093	+	3.41247i	−0.420154	+	0.568745i
$7$	2.35838	+	1.65135i	0.336911	+	0.235907i	0.729772	−	0.683690i	$-0.239626\pi$
$7$	2.35838	+	1.65135i	0.336911	+	0.235907i	−0.392862	+	0.919598i	$0.628515\pi$
$8$	−0.732051	+	2.73205i	−0.0915064	+	0.341506i
$9$	4.09857	+	8.01260i	0.455397	+	0.890289i
$10$	3.68749	+	6.03344i	0.368749	+	0.603344i
$11$	5.11381	+	1.86128i	0.464892	+	0.169207i	0.563837	−	0.825886i	$-0.309325\pi$
$11$	5.11381	+	1.86128i	0.464892	+	0.169207i	−0.0989449	+	0.995093i	$0.531547\pi$
$12$	4.49687	+	3.97217i	0.374739	+	0.331014i
$13$	−1.40437	−	16.0520i	−0.108028	−	1.23477i	−0.835833	−	0.548983i	$-0.815015\pi$
$13$	−1.40437	−	16.0520i	−0.108028	−	1.23477i	0.727805	−	0.685784i	$-0.240540\pi$
$14$	2.61716	−	3.11901i	0.186940	−	0.222787i
$15$	14.9434	−	1.30146i	0.996229	−	0.0867638i
$16$	3.75877	+	1.36808i	0.234923	+	0.0855050i
$17$	7.49195	+	27.9603i	0.440703	+	1.64473i	0.727039	+	0.686597i	$0.240896\pi$
$17$	7.49195	+	27.9603i	0.440703	+	1.64473i	−0.286336	+	0.958129i	$0.592437\pi$
$18$	11.7936	−	4.78659i	0.655199	−	0.265922i
$19$	0.970790	−	0.560486i	0.0510942	−	0.0294992i	−0.474235	−	0.880398i	$-0.657275\pi$
$19$	0.970790	−	0.560486i	0.0510942	−	0.0294992i	0.525329	+	0.850899i	$0.323942\pi$
$20$	8.95462	−	4.45139i	0.447731	−	0.222569i
$21$	−3.45030	−	7.91805i	−0.164300	−	0.377050i
$22$	3.25254	−	6.97509i	0.147843	−	0.317050i
$23$	34.3534	−	24.0545i	1.49362	−	1.04585i	0.511141	−	0.859497i	$-0.329223\pi$
$23$	34.3534	−	24.0545i	1.49362	−	1.04585i	0.982483	−	0.186350i	$-0.0596659\pi$
$24$	6.15039	−	5.84574i	0.256266	−	0.243572i
$25$	7.36583	−	23.8903i	0.294633	−	0.955610i
$26$	−22.7876			−0.876447
$27$	2.05464	−	26.9217i	0.0760977	−	0.997100i
$28$	−4.07158	−	4.07158i	−0.145414	−	0.145414i
$29$	3.65957	+	4.36130i	0.126192	+	0.150390i	0.825441	−	0.564489i	$-0.190927\pi$
$29$	3.65957	+	4.36130i	0.126192	+	0.150390i	−0.699249	+	0.714878i	$0.746482\pi$
$30$	0.00834613	−	21.2132i	0.000278204	−	0.707107i
$31$	−8.44013	+	47.8664i	−0.272262	+	1.54408i	0.475264	+	0.879843i	$0.342353\pi$
$31$	−8.44013	+	47.8664i	−0.272262	+	1.54408i	−0.747526	+	0.664233i	$0.768758\pi$
$32$	2.39069	−	5.12685i	0.0747091	−	0.160214i
$33$	−10.1733	−	12.7689i	−0.308281	−	0.386935i
$34$	40.3149	−	7.10860i	1.18573	−	0.209076i
$35$	−14.3907	+	0.359800i	−0.411164	+	0.0102800i
$36$	−5.28986	−	17.2052i	−0.146941	−	0.477921i
$37$	−2.23659	−	8.34706i	−0.0604484	−	0.225596i	0.929093	−	0.369846i	$-0.120590\pi$
$37$	−2.23659	−	8.34706i	−0.0604484	−	0.225596i	−0.989541	+	0.144250i	$0.953923\pi$
$38$	−0.669974	−	1.43676i	−0.0176309	−	0.0378096i
$39$	−21.5350	+	43.2780i	−0.552179	+	1.10969i
$40$	−5.16754	−	13.1642i	−0.129189	−	0.329105i
$41$	50.5697	+	42.4330i	1.23341	+	1.03495i	0.998010	+	0.0630520i	$0.0200834\pi$
$41$	50.5697	+	42.4330i	1.23341	+	1.03495i	0.235397	+	0.971899i	$0.424361\pi$
$42$	−11.5805	+	3.88494i	−0.275726	+	0.0924986i
$43$	10.5200	+	22.5603i	0.244652	+	0.524657i	0.989838	−	0.142199i	$-0.0454173\pi$
$43$	10.5200	+	22.5603i	0.244652	+	0.524657i	−0.745186	+	0.666856i	$0.767640\pi$
$44$	−9.42583	−	5.44201i	−0.214224	−	0.123682i
$45$	−40.2800	−	20.0629i	−0.895111	−	0.445843i
$46$	−29.6544	−	51.3630i	−0.644662	−	1.11659i
$47$	50.5606	+	35.4029i	1.07576	+	0.753254i	0.970478	−	0.241189i	$-0.0775373\pi$
$47$	50.5606	+	35.4029i	1.07576	+	0.753254i	0.105280	+	0.994443i	$0.466426\pi$
$48$	−7.47759	−	9.38540i	−0.155783	−	0.195529i
$49$	−13.9240	−	38.2559i	−0.284164	−	0.780733i
$50$	−32.7495	−	13.3219i	−0.654989	−	0.266437i
$51$	24.5982	−	83.2834i	0.482317	−	1.63301i
$52$	−2.80873	+	32.1039i	−0.0540141	+	0.617383i
$53$	−20.4015	−	20.4015i	−0.384934	−	0.384934i	0.487942	−	0.872876i	$-0.337748\pi$
$53$	−20.4015	−	20.4015i	−0.384934	−	0.384934i	−0.872876	+	0.487942i	$0.837748\pi$
$54$	−37.6749	−	6.21292i	−0.697684	−	0.115054i
$55$	−26.0986	+	7.69720i	−0.474521	+	0.139949i
$56$	−6.23803	+	5.23433i	−0.111393	+	0.0934701i
$57$	−3.36183	−	0.0853767i	−0.0589795	−	0.00149784i
$58$	6.59541	−	4.61815i	0.113714	−	0.0796233i
$59$	32.9877	+	90.6329i	0.559113	+	1.53615i	0.820928	+	0.571032i	$0.193457\pi$
$59$	32.9877	+	90.6329i	0.559113	+	1.53615i	−0.261815	+	0.965118i	$0.584321\pi$
$60$	−29.8848	−	2.62643i	−0.498080	−	0.0437738i
$61$	7.17732	+	40.7046i	0.117661	+	0.667288i	0.985398	+	0.170265i	$0.0544624\pi$
$61$	7.17732	+	40.7046i	0.117661	+	0.667288i	−0.867737	+	0.497023i	$0.834426\pi$
$62$	66.3954	+	17.7906i	1.07089	+	0.286945i
$63$	−3.56565	+	25.6649i	−0.0565976	+	0.407379i
$64$	−6.92820	−	4.00000i	−0.108253	−	0.0625000i
$65$	53.3135	+	60.4038i	0.820208	+	0.929289i
$66$	−19.2431	+	12.7586i	−0.291562	+	0.193312i
$67$	83.9811	−	7.34739i	1.25345	−	0.109663i	0.558978	−	0.829183i	$-0.311194\pi$
$67$	83.9811	−	7.34739i	1.25345	−	0.109663i	0.694472	+	0.719520i	$0.255638\pi$
$68$	−5.04574	−	57.6731i	−0.0742020	−	0.848133i
$69$	−125.572	+	7.77985i	−1.81989	+	0.112751i
$70$	−1.26686	+	20.3185i	−0.0180980	+	0.290264i
$71$	−41.0311	+	71.0679i	−0.577902	+	1.00096i	0.417817	+	0.908531i	$0.362795\pi$
$71$	−41.0311	+	71.0679i	−0.577902	+	1.00096i	−0.995720	+	0.0924252i	$0.970538\pi$
$72$	−24.8912	+	5.33188i	−0.345711	+	0.0740539i
$73$	4.21248	−	15.7212i	0.0577052	−	0.215359i	−0.931053	−	0.364885i	$-0.881108\pi$
$73$	4.21248	−	15.7212i	0.0577052	−	0.215359i	0.988758	+	0.149526i	$0.0477749\pi$
$74$	−12.0353	+	2.12215i	−0.162639	+	0.0286776i
$75$	−56.2500	+	49.6079i	−0.749999	+	0.661439i
$76$	−2.10674	+	0.766789i	−0.0277202	+	0.0100893i
$77$	8.98667	+	12.8343i	0.116710	+	0.166679i
$78$	58.3171	+	35.6735i	0.747655	+	0.457352i
$79$	−33.9874	−	40.5046i	−0.430220	−	0.512716i	0.506766	−	0.862084i	$-0.330841\pi$
$79$	−33.9874	−	40.5046i	−0.430220	−	0.512716i	−0.936986	+	0.349368i	$0.886396\pi$
$80$	−19.1831	+	5.65762i	−0.239789	+	0.0707202i
$81$	−47.4034	+	65.6804i	−0.585227	+	0.810869i
$82$	66.0140	−	66.0140i	0.805049	−	0.805049i
$83$	7.66773	+	0.670839i	0.0923823	+	0.00808240i	0.133253	−	0.991082i	$-0.457458\pi$
$83$	7.66773	+	0.670839i	0.0923823	+	0.00808240i	−0.0408709	+	0.999164i	$0.513013\pi$
$84$	4.04586	+	16.7938i	0.0481650	+	0.199926i
$85$	−113.163	−	90.2326i	−1.33133	−	1.06156i
$86$	33.0803	−	12.0402i	0.384654	−	0.140003i
$87$	−2.53789	−	16.8902i	−0.0291712	−	0.194140i
$88$	−8.82867	+	12.6087i	−0.100326	+	0.143280i
$89$	−67.5355	+	38.9917i	−0.758826	+	0.438109i	−0.828874	−	0.559435i	$-0.811018\pi$
$89$	−67.5355	+	38.9917i	−0.758826	+	0.438109i	0.0700479	+	0.997544i	$0.477685\pi$
$90$	−33.2301	+	54.2749i	−0.369223	+	0.603054i
$91$	23.1954	−	40.1757i	0.254895	−	0.441491i
$92$	−76.0169	+	35.4473i	−0.826271	+	0.385297i
$93$	96.5332	−	109.285i	1.03799	−	1.17510i
$94$	56.1087	−	66.8678i	0.596901	−	0.711359i
$95$	−2.24101	+	5.13734i	−0.0235896	+	0.0540773i
$96$	−14.1441	+	9.37785i	−0.147335	+	0.0976859i
$97$	86.1483	−	40.1716i	0.888127	−	0.414140i	0.0756503	−	0.997134i	$-0.475897\pi$
$97$	86.1483	−	40.1716i	0.888127	−	0.414140i	0.812476	+	0.582994i	$0.198119\pi$
$98$	−55.6124	+	14.9013i	−0.567473	+	0.152054i
$99$	6.04568	+	48.6035i	0.0610675	+	0.490945i
$100$	−22.8049	+	44.4965i	−0.228049	+	0.444965i
$101$	−26.4481	−	149.995i	−0.261863	−	1.48510i	−0.777823	−	0.628484i	$-0.783676\pi$
$101$	−26.4481	−	149.995i	−0.261863	−	1.48510i	0.515960	−	0.856613i	$-0.327435\pi$
$102$	−114.300	−	44.9199i	−1.12059	−	0.440391i
$103$	89.9084	+	41.9250i	0.872897	+	0.407039i	0.806835	−	0.590777i	$-0.201179\pi$
$103$	89.9084	+	41.9250i	0.872897	+	0.407039i	0.0660622	+	0.997816i	$0.478956\pi$
$104$	44.8829	+	7.91406i	0.431566	+	0.0760967i
$105$	37.3914	+	21.6075i	0.356108	+	0.205786i
$106$	−31.2569	+	26.2276i	−0.294876	+	0.247431i
$107$	−127.669	+	127.669i	−1.19317	+	1.19317i	−0.217001	+	0.976171i	$0.569628\pi$
$107$	−127.669	+	127.669i	−1.19317	+	1.19317i	−0.976171	+	0.217001i	$0.930372\pi$
$108$	−13.3967	+	52.3118i	−0.124043	+	0.484369i
$109$			34.5808i			0.317255i	0.987339	+	0.158627i	$0.0507069\pi$
$109$			34.5808i			0.317255i	−0.987339	+	0.158627i	$0.949293\pi$
$110$	7.62723	+	37.7173i	0.0693384	+	0.342885i
$111$	−7.34334	+	24.8628i	−0.0661562	+	0.223989i
$112$	6.60541	+	9.43350i	0.0589769	+	0.0842277i
$113$	−45.8194	−	21.3659i	−0.405482	−	0.189079i	0.209167	−	0.977880i	$-0.432925\pi$
$113$	−45.8194	−	21.3659i	−0.405482	−	0.189079i	−0.614649	+	0.788801i	$0.710702\pi$
$114$	−0.534650	+	4.72573i	−0.00468991	+	0.0414538i
$115$	−66.7703	+	198.774i	−0.580612	+	1.72847i
$116$	−5.69327	−	9.86104i	−0.0490799	−	0.0850090i
$117$	122.862	−	77.0428i	1.05010	−	0.658485i
$118$	131.752	−	35.3030i	1.11655	−	0.299178i
$119$	−28.5035	+	78.3128i	−0.239526	+	0.658091i
$120$	−7.38371	+	41.7790i	−0.0615309	+	0.348158i
$121$	−70.0046	−	58.7409i	−0.578551	−	0.485462i
$122$	58.2306	−	5.09451i	0.477300	−	0.0417583i
$123$	−62.9879	−	187.758i	−0.512097	−	1.52649i
$124$	33.2476	−	91.3471i	0.268126	−	0.736670i
$125$	41.3074	+	117.978i	0.330459	+	0.943820i
$126$	35.7180	+	8.18677i	0.283476	+	0.0649744i
$127$	−68.1153	−	18.2514i	−0.536341	−	0.143712i	−0.0195263	−	0.999809i	$-0.506216\pi$
$127$	−68.1153	−	18.2514i	−0.536341	−	0.143712i	−0.516815	+	0.856097i	$0.672882\pi$
$128$	−6.48928	+	9.26765i	−0.0506975	+	0.0724035i
$129$	8.39515	−	74.2041i	0.0650786	−	0.575225i
$130$	91.6701	−	67.6646i	0.705154	−	0.520497i
$131$	13.0516	−	74.0191i	0.0996302	−	0.565031i	−0.893600	−	0.448865i	$-0.851828\pi$
$131$	13.0516	−	74.0191i	0.0996302	−	0.565031i	0.993230	−	0.116166i	$-0.0370605\pi$
$132$	15.6029	+	28.6829i	0.118203	+	0.217294i
$133$	3.21505	+	0.281280i	0.0241733	+	0.00211489i
$134$		−	119.221i		−	0.889708i
$135$	71.6748	+	114.402i	0.530924	+	0.847419i
$136$	−81.8736			−0.602012
$137$	5.37103	−	61.3912i	0.0392046	−	0.448111i	−0.951069	−	0.308978i	$-0.900013\pi$
$137$	5.37103	−	61.3912i	0.0392046	−	0.448111i	0.990274	−	0.139133i	$-0.0444315\pi$
$138$	−4.51715	+	177.869i	−0.0327330	+	1.28891i
$139$	−16.6321	−	2.93269i	−0.119655	−	0.0210985i	0.113500	−	0.993538i	$-0.463794\pi$
$139$	−16.6321	−	2.93269i	−0.119655	−	0.0210985i	−0.233155	+	0.972440i	$0.574905\pi$
$140$	28.4692	+	4.28918i	0.203351	+	0.0306370i
$141$	−73.9702	−	169.753i	−0.524611	−	1.20392i
$142$	95.0654	+	66.5655i	0.669474	+	0.468771i
$143$	22.6955	−	84.7007i	0.158710	−	0.592313i
$144$	4.44371	+	35.7247i	0.0308591	+	0.248088i
$145$	−27.6720	−	6.67808i	−0.190841	−	0.0460557i
$146$	−21.6293	−	7.87242i	−0.148146	−	0.0539207i
$147$	−24.2550	+	119.701i	−0.165000	+	0.814290i
$148$	1.50632	+	17.2173i	0.0101778	+	0.116333i
$149$	74.1761	−	88.3997i	0.497826	−	0.593286i	−0.457364	−	0.889280i	$-0.651206\pi$
$149$	74.1761	−	88.3997i	0.497826	−	0.593286i	0.955190	+	0.295993i	$0.0956506\pi$
$150$	62.9560	+	85.3612i	0.419707	+	0.569075i
$151$	57.2573	+	20.8399i	0.379187	+	0.138013i	0.524580	−	0.851361i	$-0.324222\pi$
$151$	57.2573	+	20.8399i	0.379187	+	0.138013i	−0.145393	+	0.989374i	$0.546445\pi$
$152$	0.820608	+	3.06255i	0.00539874	+	0.0201484i
$153$	−193.329	+	174.627i	−1.26359	+	1.14136i
$154$	19.1890	−	11.0788i	0.124604	−	0.0719402i
$155$	−108.179	−	217.619i	−0.697931	−	1.40399i
$156$	57.4459	−	77.7620i	0.368243	−	0.498475i
$157$	70.0721	−	150.270i	0.446319	−	0.957135i	−0.546494	−	0.837463i	$-0.684038\pi$
$157$	70.0721	−	150.270i	0.446319	−	0.957135i	0.992813	−	0.119672i	$-0.0381843\pi$
$158$	−61.2533	+	42.8900i	−0.387679	+	0.271456i
$159$	20.2726	+	84.1486i	0.127500	+	0.529237i
$160$	5.60619	+	27.7231i	0.0350387	+	0.173269i
$161$	120.741			0.749941
$162$	86.6899	+	74.8790i	0.535123	+	0.462216i
$163$	−106.195	−	106.195i	−0.651504	−	0.651504i	0.301851	−	0.953355i	$-0.402395\pi$
$163$	−106.195	−	106.195i	−0.651504	−	0.651504i	−0.953355	+	0.301851i	$0.902395\pi$
$164$	−84.8660	−	101.139i	−0.517476	−	0.616704i
$165$	78.8403	+	21.1585i	0.477820	+	0.128233i
$166$	1.89020	−	10.7199i	0.0113867	−	0.0645774i
$167$	−6.92219	+	14.8447i	−0.0414502	+	0.0888903i	−0.925942	−	0.377665i	$-0.876727\pi$
$167$	−6.92219	+	14.8447i	−0.0414502	+	0.0888903i	0.884492	+	0.466555i	$0.154505\pi$
$168$	24.1583	−	3.62998i	0.143799	−	0.0216071i
$169$	−89.2610	+	15.7391i	−0.528172	+	0.0931309i
$170$	−141.071	+	148.306i	−0.829827	+	0.872386i
$171$	8.46980	+	5.48135i	0.0495310	+	0.0320547i
$172$	−12.8853	−	48.0886i	−0.0749145	−	0.279585i
$173$	−46.8337	−	100.435i	−0.270715	−	0.580550i	0.723208	−	0.690631i	$-0.242667\pi$
$173$	−46.8337	−	100.435i	−0.270715	−	0.580550i	−0.993923	+	0.110080i	$0.964889\pi$
$174$	−24.1083	+	1.49363i	−0.138553	+	0.00858409i
$175$	56.8226	−	44.1786i	0.324701	−	0.252449i
$176$	16.6753	+	13.9922i	0.0947459	+	0.0795013i
$177$	57.4629	−	283.585i	0.324649	−	1.60218i
$178$	46.6085	+	99.9522i	0.261845	+	0.561529i
$179$	201.293	+	116.217i	1.12454	+	0.649256i	0.942557	−	0.334045i	$-0.108414\pi$
$179$	201.293	+	116.217i	1.12454	+	0.649256i	0.181987	+	0.983301i	$0.441747\pi$
$180$	72.3683	+	53.5054i	0.402046	+	0.297252i
$181$	−15.0722	−	26.1057i	−0.0832716	−	0.144231i	0.821382	−	0.570379i	$-0.193204\pi$
$181$	−15.0722	−	26.1057i	−0.0832716	−	0.144231i	−0.904653	+	0.426148i	$0.859870\pi$
$182$	−53.7418	−	37.6304i	−0.295284	−	0.206760i
$183$	45.3541	−	115.405i	0.247837	−	0.630630i
$184$	40.5697	+	111.464i	0.220487	+	0.605784i
$185$	33.7828	+	26.9373i	0.182610	+	0.145607i
$186$	−142.065	−	149.469i	−0.763793	−	0.803598i
$187$	−13.7295	+	156.929i	−0.0734196	+	0.839190i
$188$	−87.2897	−	87.2897i	−0.464307	−	0.464307i
$189$	49.3028	−	60.0986i	0.260862	−	0.317982i
$190$	6.96143	+	3.79042i	0.0366391	+	0.0199496i
$191$	5.78873	−	4.85732i	0.0303075	−	0.0254310i	−0.627508	−	0.778610i	$-0.715925\pi$
$191$	5.78873	−	4.85732i	0.0303075	−	0.0254310i	0.657816	+	0.753179i	$0.271481\pi$
$192$	11.4685	+	21.0826i	0.0597316	+	0.109805i
$193$	36.2836	−	25.4061i	0.187998	−	0.131638i	−0.475788	−	0.879560i	$-0.657837\pi$
$193$	36.2836	−	25.4061i	0.187998	−	0.131638i	0.663787	+	0.747922i	$0.268948\pi$
$194$	−45.9767	−	126.320i	−0.236993	−	0.651133i
$195$	−41.8770	−	238.044i	−0.214754	−	1.22074i
$196$	14.1388	+	80.1852i	0.0721368	+	0.409108i
$197$	317.504	+	85.0749i	1.61170	+	0.431852i	0.948547	−	0.316636i	$-0.102553\pi$
$197$	317.504	+	85.0749i	1.61170	+	0.431852i	0.663148	+	0.748488i	$0.269220\pi$
$198$	69.2194	−	2.52663i	0.349593	−	0.0127608i
$199$	249.260	+	143.911i	1.25256	+	0.723169i	0.971618	−	0.236555i	$-0.0760182\pi$
$199$	249.260	+	143.911i	1.25256	+	0.723169i	0.280947	+	0.959723i	$0.409352\pi$
$200$	59.8772	+	37.6127i	0.299386	+	0.188064i
$201$	−226.423	−	112.667i	−1.12648	−	0.560534i
$202$	−214.577	+	18.7731i	−1.06226	+	0.0929360i
$203$	1.42859	+	16.3288i	0.00703737	+	0.0804375i
$204$	−77.3729	+	155.493i	−0.379279	+	0.762222i
$205$	−329.430	−	20.5400i	−1.60698	−	0.100195i
$206$	70.1471	−	121.498i	0.340520	−	0.589798i
$207$	333.539	+	176.671i	1.61130	+	0.853481i
$208$	16.6817	−	62.2570i	0.0802005	−	0.299312i
$209$	6.00766	−	1.05931i	0.0287448	−	0.00506848i
$210$	35.0501	−	50.0149i	0.166905	−	0.238166i
$211$	93.2178	−	33.9285i	0.441790	−	0.160799i	−0.111541	−	0.993760i	$-0.535579\pi$
$211$	93.2178	−	33.9285i	0.441790	−	0.160799i	0.553331	+	0.832961i	$0.313356\pi$
$212$	33.0977	+	47.2684i	0.156121	+	0.222964i
$213$	216.260	−	117.641i	1.01531	−	0.552304i
$214$	164.129	+	195.601i	0.766957	+	0.914023i
$215$	−109.309	−	59.5177i	−0.508416	−	0.276826i
$216$	72.0474	+	25.3214i	0.333553	+	0.117229i
$217$	−98.9492	+	98.9492i	−0.455987	+	0.455987i
$218$	48.7185	+	4.26232i	0.223479	+	0.0195519i
$219$	−35.3915	+	33.6385i	−0.161605	+	0.153600i
$220$	54.0775	−	6.09656i	0.245807	−	0.0277116i
$221$	438.297	−	159.527i	1.98325	−	0.721842i
$222$	34.1224	+	13.4100i	0.153704	+	0.0604056i
$223$	−5.62289	+	8.03032i	−0.0252148	+	0.0360104i	−0.831562	−	0.555433i	$-0.812553\pi$
$223$	−5.62289	+	8.03032i	−0.0252148	+	0.0360104i	0.806347	+	0.591443i	$0.201442\pi$
$224$	14.1044	−	8.14317i	0.0629660	−	0.0363534i
$225$	221.612	−	38.8965i	0.984944	−	0.172873i
$226$	−35.7486	+	61.9184i	−0.158180	+	0.273975i
$227$	46.6192	−	21.7389i	0.205371	−	0.0957660i	−0.317212	−	0.948355i	$-0.602747\pi$
$227$	46.6192	−	21.7389i	0.205371	−	0.0957660i	0.522582	+	0.852589i	$0.324969\pi$
$228$	6.59186	+	1.33571i	0.0289117	+	0.00585838i
$229$	88.5611	−	105.543i	0.386730	−	0.460887i	−0.537196	−	0.843457i	$-0.680517\pi$
$229$	88.5611	−	105.543i	0.386730	−	0.460887i	0.923926	+	0.382570i	$0.124961\pi$
$230$	271.809	+	118.568i	1.18178	+	0.515515i
$231$	−2.90653	−	46.9134i	−0.0125824	−	0.203088i
$232$	−14.5943	+	6.80543i	−0.0629064	+	0.0293337i
$233$	−410.447	+	109.979i	−1.76158	+	0.472013i	−0.987034	−	0.160509i	$-0.948686\pi$
$233$	−410.447	+	109.979i	−1.76158	+	0.472013i	−0.774542	+	0.632522i	$0.782020\pi$
$234$	−93.3967	−	182.588i	−0.399131	−	0.780291i
$235$	−308.519	+	7.71366i	−1.31285	+	0.0328241i
$236$	−33.4966	−	189.968i	−0.141935	−	0.804951i
$237$	23.5701	+	156.864i	0.0994519	+	0.661873i
$238$	106.816	+	49.8093i	0.448808	+	0.209283i
$239$	−236.039	−	41.6201i	−0.987612	−	0.174143i	−0.343566	−	0.939129i	$-0.611635\pi$
$239$	−236.039	−	41.6201i	−0.987612	−	0.174143i	−0.644047	+	0.764986i	$0.722746\pi$
$240$	57.9494	+	15.5519i	0.241456	+	0.0647998i
$241$	−205.585	+	172.507i	−0.853051	+	0.715795i	−0.960459	−	0.278420i	$-0.910189\pi$
$241$	−205.585	+	172.507i	−0.853051	+	0.715795i	0.107408	+	0.994215i	$0.465745\pi$
$242$	−91.3845	+	91.3845i	−0.377622	+	0.377622i
$243$	224.134	−	93.8776i	0.922362	−	0.386327i
$244$		−	82.6650i		−	0.338791i
$245$	169.609	+	112.551i	0.692282	+	0.459390i
$246$	−272.284	+	65.5969i	−1.10684	+	0.266654i
$247$	−10.3602	−	14.7960i	−0.0419443	−	0.0599027i
$248$	−124.595	−	58.0995i	−0.502398	−	0.234272i
$249$	−18.5727	−	13.7204i	−0.0745893	−	0.0551021i
$250$	171.302	−	43.6537i	0.685208	−	0.174615i
$251$	−71.5298	−	123.893i	−0.284979	−	0.493598i	0.687625	−	0.726066i	$-0.258653\pi$
$251$	−71.5298	−	123.893i	−0.284979	−	0.493598i	−0.972604	+	0.232468i	$0.925320\pi$
$252$	15.9363	−	49.3116i	0.0632392	−	0.195681i
$253$	220.449	−	59.0691i	0.871339	−	0.233475i
$254$	−34.1089	+	93.7135i	−0.134287	+	0.368951i
$255$	148.345	+	408.073i	0.581744	+	1.60029i
$256$	12.2567	+	10.2846i	0.0478778	+	0.0401742i
$257$	−226.750	+	19.8380i	−0.882294	+	0.0771907i	−0.519291	−	0.854597i	$-0.673804\pi$
$257$	−226.750	+	19.8380i	−0.882294	+	0.0771907i	−0.363003	+	0.931788i	$0.618248\pi$
$258$	−103.506	−	20.9735i	−0.401187	−	0.0812927i
$259$	8.50923	−	23.3789i	0.0328542	−	0.0902661i
$260$	−84.0291	−	137.488i	−0.323189	−	0.528799i
$261$	−19.9464	+	47.1977i	−0.0764228	+	0.180834i
$262$	−102.672	−	27.5108i	−0.391877	−	0.105003i
$263$	138.480	−	197.770i	0.526540	−	0.751977i	−0.464496	−	0.885575i	$-0.653764\pi$
$263$	138.480	−	197.770i	0.526540	−	0.751977i	0.991036	+	0.133599i	$0.0426533\pi$
$264$	42.3325	−	18.4465i	0.160350	−	0.0698729i
$265$	142.650	+	21.4918i	0.538303	+	0.0811011i
$266$	0.792553	−	4.49479i	0.00297952	−	0.0168977i
$267$	233.875	+	5.93945i	0.875935	+	0.0222451i
$268$	−167.962	−	14.6948i	−0.626725	−	0.0548313i
$269$			185.622i			0.690043i	0.938595	+	0.345021i	$0.112128\pi$
$269$			185.622i			0.690043i	−0.938595	+	0.345021i	$0.887872\pi$
$270$	170.007	−	86.8770i	0.629656	−	0.321766i
$271$	−251.487			−0.927995			−0.463998	−	0.885836i	$-0.653585\pi$
$271$	−251.487			−0.927995			−0.463998	+	0.885836i	$0.653585\pi$
$272$	−10.0915	+	115.346i	−0.0371010	+	0.424067i
$273$	−122.255	+	66.5040i	−0.447820	+	0.243604i
$274$	−85.8279	−	15.1338i	−0.313240	−	0.0552327i
$275$	82.1339	−	108.461i	0.298669	−	0.394402i
$276$	250.031	+	28.2875i	0.905910	+	0.102491i
$277$	11.5428	+	8.08234i	0.0416707	+	0.0291781i	0.594226	−	0.804298i	$-0.297458\pi$
$277$	11.5428	+	8.08234i	0.0416707	+	0.0291781i	−0.552556	+	0.833476i	$0.686347\pi$
$278$	−6.18169	+	23.0704i	−0.0222363	+	0.0829869i
$279$	−418.126	+	128.556i	−1.49866	+	0.460775i
$280$	9.55175	−	39.5796i	0.0341134	−	0.141356i
$281$	460.977	+	167.782i	1.64049	+	0.597089i	0.987124	−	0.159955i	$-0.0511350\pi$
$281$	460.977	+	167.782i	1.64049	+	0.597089i	0.653364	+	0.757044i	$0.273357\pi$
$282$	−248.271	+	83.2883i	−0.880394	+	0.295349i
$283$	24.0212	+	274.563i	0.0848804	+	0.970187i	0.912548	+	0.408969i	$0.134112\pi$
$283$	24.0212	+	274.563i	0.0848804	+	0.970187i	−0.827668	+	0.561218i	$0.810333\pi$
$284$	105.497	−	125.726i	0.371468	−	0.442699i
$285$	13.7775	−	9.63902i	0.0483420	−	0.0338211i
$286$	−116.532	−	42.4141i	−0.407454	−	0.148301i
$287$	49.1905	+	183.581i	0.171395	+	0.639656i
$288$	50.8778	−	1.85713i	0.176659	−	0.00644837i
$289$	−475.370	+	274.455i	−1.64488	+	0.949671i
$290$	−12.8191	+	38.1620i	−0.0442036	+	0.131593i
$291$	−283.355	−	32.0576i	−0.973727	−	0.110164i
$292$	−13.7569	+	29.5017i	−0.0471126	+	0.101033i
$293$	−244.340	+	171.089i	−0.833926	+	0.583922i	−0.910672	−	0.413129i	$-0.864436\pi$
$293$	−244.340	+	171.089i	−0.833926	+	0.583922i	0.0767460	+	0.997051i	$0.475547\pi$
$294$	165.648	+	48.9251i	0.563430	+	0.166412i
$295$	−401.824	−	266.646i	−1.36212	−	0.903884i
$296$	24.4419			0.0825740
$297$	60.6158	−	133.848i	0.204094	−	0.450668i
$298$	−115.398	−	115.398i	−0.387240	−	0.387240i
$299$	−434.366	−	517.658i	−1.45273	−	1.73130i
$300$	128.019	−	78.1731i	0.426731	−	0.260577i
$301$	−12.4448	+	70.5778i	−0.0413447	+	0.234478i
$302$	36.4173	−	78.0972i	0.120587	−	0.258600i
$303$	−167.128	+	425.264i	−0.551578	+	1.40351i
$304$	4.41576	−	0.778618i	0.0145255	−	0.00256124i
$305$	−149.739	−	142.434i	−0.490949	−	0.466998i
$306$	222.192	+	293.892i	0.726117	+	0.960430i
$307$	34.5050	+	128.775i	0.112394	+	0.419461i	0.999079	−	0.0429139i	$-0.0136641\pi$
$307$	34.5050	+	128.775i	0.112394	+	0.419461i	−0.886685	+	0.462375i	$0.846997\pi$
$308$	−13.2430	−	28.3997i	−0.0429967	−	0.0922067i
$309$	−164.457	−	248.042i	−0.532224	−	0.802725i
$310$	−319.922	+	125.584i	−1.03201	+	0.405108i
$311$	383.170	+	321.518i	1.23206	+	1.03382i	0.998103	+	0.0615735i	$0.0196119\pi$
$311$	383.170	+	321.518i	1.23206	+	1.03382i	0.233957	+	0.972247i	$0.424833\pi$
$312$	−102.473	−	90.5164i	−0.328439	−	0.290117i
$313$	214.828	+	460.699i	0.686350	+	1.47188i	0.872122	+	0.489289i	$0.162744\pi$
$313$	214.828	+	460.699i	0.686350	+	1.47188i	−0.185772	+	0.982593i	$0.559478\pi$
$314$	−203.069	−	117.242i	−0.646715	−	0.373381i
$315$	−61.8644	−	113.832i	−0.196395	−	0.361373i
$316$	52.8750	+	91.5821i	0.167326	+	0.289817i
$317$	−476.245	−	333.470i	−1.50235	−	1.05196i	−0.979947	−	0.199259i	$-0.936146\pi$
$317$	−476.245	−	333.470i	−1.50235	−	1.05196i	−0.522404	−	0.852698i	$-0.674965\pi$
$318$	121.050	−	18.1888i	0.380660	−	0.0571974i
$319$	10.5968	+	29.1143i	0.0332187	+	0.0912675i
$320$	39.7482	−	4.48111i	0.124213	−	0.0140035i
$321$	526.590	−	126.863i	1.64047	−	0.395211i
$322$	14.8821	−	170.103i	0.0462177	−	0.528271i
$323$	22.9445	+	22.9445i	0.0710355	+	0.0710355i
$324$	116.177	−	112.902i	0.358571	−	0.348463i
$325$	−393.830	−	84.6855i	−1.21178	−	0.260571i
$326$	−162.700	+	136.522i	−0.499081	+	0.418779i
$327$	54.1354	−	88.4977i	0.165552	−	0.270635i
$328$	−152.949	+	107.096i	−0.466307	+	0.326512i
$329$	60.7782	+	166.987i	0.184736	+	0.507559i
$330$	39.5263	−	108.465i	0.119777	−	0.328681i
$331$	−10.8947	−	61.7871i	−0.0329146	−	0.186668i	0.963918	−	0.266201i	$-0.0857684\pi$
$331$	−10.8947	−	61.7871i	−0.0329146	−	0.186668i	−0.996832	+	0.0795325i	$0.974657\pi$
$332$	−14.8695	−	3.98427i	−0.0447876	−	0.0120008i
$333$	57.7148	−	52.1319i	0.173318	−	0.156552i
$334$	20.0604	+	11.5819i	0.0600612	+	0.0346764i
$335$	−316.022	+	278.927i	−0.943350	+	0.832618i
$336$	−2.13636	−	34.4824i	−0.00635822	−	0.102626i
$337$	153.736	−	13.4501i	0.456189	−	0.0399114i	0.143254	−	0.989686i	$-0.454243\pi$
$337$	153.736	−	13.4501i	0.456189	−	0.0399114i	0.312935	+	0.949775i	$0.398688\pi$
$338$	11.1718	+	127.694i	0.0330525	+	0.377792i
$339$	83.8112	+	126.408i	0.247231	+	0.372885i
$340$	191.550	+	217.025i	0.563382	+	0.638307i
$341$	−132.254	+	229.070i	−0.387841	+	0.671760i
$342$	8.76627	−	11.2569i	0.0256324	−	0.0329149i
$343$	66.8484	−	249.482i	0.194893	−	0.727351i
$344$	−69.3369	+	12.2260i	−0.201561	+	0.0355406i
$345$	482.051	−	404.166i	1.39725	−	1.17150i
$346$	−147.269	+	53.6015i	−0.425633	+	0.154918i
$347$	−240.071	−	342.857i	−0.691848	−	0.988061i	−0.999333	−	0.0365086i	$-0.988376\pi$
$347$	−240.071	−	342.857i	−0.691848	−	0.988061i	0.307485	−	0.951553i	$-0.400513\pi$
$348$	−0.867235	+	34.1486i	−0.00249205	+	0.0981283i
$349$	142.955	+	170.367i	0.409613	+	0.488158i	0.930926	−	0.365207i	$-0.119002\pi$
$349$	142.955	+	170.367i	0.409613	+	0.488158i	−0.521313	+	0.853366i	$0.674557\pi$
$350$	−55.2365	−	85.4989i	−0.157818	−	0.244282i
$351$	−435.032	+	4.82695i	−1.23941	+	0.0137520i
$352$	21.7680	−	21.7680i	0.0618410	−	0.0618410i
$353$	−473.052	−	41.3867i	−1.34009	−	0.117243i	−0.605550	−	0.795807i	$-0.707047\pi$
$353$	−473.052	−	41.3867i	−1.34009	−	0.117243i	−0.734541	+	0.678564i	$0.762603\pi$
$354$	−392.441	−	115.909i	−1.10859	−	0.327428i
$355$	−45.9662	−	407.728i	−0.129482	−	1.14853i
$356$	146.561	−	53.3437i	0.411687	−	0.149842i
$357$	195.542	−	155.793i	0.547736	−	0.436396i
$358$	188.541	−	269.264i	0.526650	−	0.752134i
$359$	231.262	−	133.519i	0.644184	−	0.371920i	−0.142040	−	0.989861i	$-0.545366\pi$
$359$	231.262	−	133.519i	0.644184	−	0.371920i	0.786225	+	0.617941i	$0.212033\pi$
$360$	84.3000	−	95.3599i	0.234167	−	0.264889i
$361$	−179.872	+	311.547i	−0.498260	+	0.863011i
$362$	−38.6364	+	18.0164i	−0.106730	+	0.0497691i
$363$	87.1955	+	259.918i	0.240208	+	0.716027i
$364$	−59.6390	+	71.0749i	−0.163843	+	0.195261i
$365$	29.7359	+	75.7516i	0.0814681	+	0.207539i
$366$	−156.997	−	78.1209i	−0.428952	−	0.213445i
$367$	95.8708	−	44.7053i	0.261228	−	0.121813i	−0.287592	−	0.957753i	$-0.592855\pi$
$367$	95.8708	−	44.7053i	0.261228	−	0.121813i	0.548821	+	0.835940i	$0.315077\pi$
$368$	162.035	−	43.4171i	0.440312	−	0.117981i
$369$	−132.735	+	579.109i	−0.359716	+	1.56940i
$370$	42.1141	−	44.2740i	0.113822	−	0.119660i
$371$	−14.4243	−	81.8044i	−0.0388796	−	0.220497i
$372$	−228.088	+	181.723i	−0.613139	+	0.488503i
$373$	−279.177	−	130.182i	−0.748463	−	0.349014i	0.0106754	−	0.999943i	$-0.496602\pi$
$373$	−279.177	−	130.182i	−0.748463	−	0.349014i	−0.759139	+	0.650929i	$0.774380\pi$
$374$	219.394	+	38.6850i	0.586614	+	0.103436i
$375$	78.9787	−	366.589i	0.210610	−	0.977570i
$376$	−133.736	+	112.217i	−0.355680	+	0.298451i
$377$	64.8681	−	64.8681i	0.172064	−	0.172064i
$378$	−78.5919	−	76.8670i	−0.207915	−	0.203352i
$379$			370.662i			0.978000i	0.872284	+	0.489000i	$0.162638\pi$
$379$			370.662i			0.978000i	−0.872284	+	0.489000i	$0.837362\pi$
$380$	6.19811	−	9.34029i	0.0163108	−	0.0245797i
$381$	145.746	+	153.341i	0.382535	+	0.402470i
$382$	−6.12965	−	8.75405i	−0.0160462	−	0.0229164i
$383$	−304.152	−	141.829i	−0.794131	−	0.370309i	−0.0171657	−	0.999853i	$-0.505464\pi$
$383$	−304.152	−	141.829i	−0.794131	−	0.370309i	−0.776965	+	0.629543i	$0.783242\pi$
$384$	31.1154	−	13.5586i	0.0810296	−	0.0353088i
$385$	−74.2612	−	24.9452i	−0.192886	−	0.0647926i
$386$	−31.3207	−	54.2490i	−0.0811417	−	0.140541i
$387$	−137.649	+	176.757i	−0.355683	+	0.456738i
$388$	−183.630	+	49.2036i	−0.473274	+	0.126813i
$389$	255.936	−	703.179i	0.657934	−	1.80766i	0.0718390	−	0.997416i	$-0.477113\pi$
$389$	255.936	−	703.179i	0.657934	−	1.80766i	0.586095	−	0.810242i	$-0.300665\pi$
$390$	−340.525	+	29.6571i	−0.873142	+	0.0760439i
$391$	929.945	+	780.317i	2.37838	+	1.99569i
$392$	114.710	−	10.0358i	0.292628	−	0.0256016i
$393$	−149.276	+	168.995i	−0.379837	+	0.430012i
$394$	158.991	−	436.824i	0.403530	−	1.10869i
$395$	256.997	+	62.0211i	0.650625	+	0.157016i
$396$	4.97216	−	97.8299i	0.0125560	−	0.247045i
$397$	−486.769	−	130.429i	−1.22612	−	0.328538i	−0.413052	−	0.910707i	$-0.635537\pi$
$397$	−486.769	−	130.429i	−1.22612	−	0.328538i	−0.813067	+	0.582170i	$0.802204\pi$
$398$	233.469	−	333.428i	0.586605	−	0.837759i
$399$	−7.78747	−	5.75291i	−0.0195175	−	0.0144183i
$400$	60.3703	−	79.7209i	0.150926	−	0.199302i
$401$	45.4298	−	257.645i	0.113291	−	0.642507i	−0.874291	−	0.485403i	$-0.838673\pi$
$401$	45.4298	−	257.645i	0.113291	−	0.642507i	0.987582	−	0.157104i	$-0.0502159\pi$
$402$	−186.637	+	305.105i	−0.464272	+	0.758968i
$403$	780.202	+	68.2589i	1.93599	+	0.169377i
$404$			304.617i			0.754003i
$405$	−4.33412	−	404.977i	−0.0107015	−	0.999943i
$406$	23.1806			0.0570952
$407$	4.09869	−	46.8483i	0.0100705	−	0.115106i
$408$	209.527	+	128.171i	0.513547	+	0.314145i
$409$	267.870	+	47.2327i	0.654939	+	0.115483i	0.491237	−	0.871026i	$-0.336545\pi$
$409$	267.870	+	47.2327i	0.654939	+	0.115483i	0.163703	+	0.986510i	$0.447656\pi$
$410$	−69.5420	+	461.581i	−0.169615	+	1.12581i
$411$	−109.852	+	148.701i	−0.267279	+	0.361804i
$412$	−162.525	−	113.801i	−0.394477	−	0.276216i
$413$	−71.8695	+	268.221i	−0.174018	+	0.649445i
$414$	290.010	−	448.124i	0.700508	−	1.08243i
$415$	−32.8377	+	20.0696i	−0.0791270	+	0.0483604i
$416$	−85.6535	−	31.1753i	−0.205898	−	0.0749407i
$417$	37.9731	+	33.5424i	0.0910626	+	0.0804373i
$418$	−0.751908	−	8.59435i	−0.00179882	−	0.0205606i
$419$	30.2551	−	36.0567i	0.0722080	−	0.0860541i	−0.728731	−	0.684800i	$-0.759890\pi$
$419$	30.2551	−	36.0567i	0.0722080	−	0.0860541i	0.800939	+	0.598746i	$0.204334\pi$
$420$	−66.1424	−	55.5445i	−0.157482	−	0.132249i
$421$	−435.291	−	158.433i	−1.03395	−	0.376325i	−0.231364	−	0.972867i	$-0.574319\pi$
$421$	−435.291	−	158.433i	−1.03395	−	0.376325i	−0.802582	+	0.596542i	$0.796541\pi$
$422$	−36.3098	−	135.510i	−0.0860422	−	0.321114i
$423$	−76.4431	+	550.223i	−0.180717	+	1.30076i
$424$	70.6728	−	40.8030i	0.166681	−	0.0962334i
$425$	723.164	+	26.9666i	1.70156	+	0.0634509i
$426$	−139.081	−	319.174i	−0.326480	−	0.749235i
$427$	−50.2908	+	107.849i	−0.117777	+	0.252574i
$428$	295.799	−	207.121i	0.691119	−	0.483927i
$429$	−190.678	+	181.233i	−0.444471	+	0.422455i
$430$	−97.3235	+	146.663i	−0.226334	+	0.341076i
$431$	408.606			0.948041			0.474020	−	0.880514i	$-0.342802\pi$
$431$	408.606			0.948041			0.474020	+	0.880514i	$0.342802\pi$
$432$	44.5540	−	98.3816i	0.103134	−	0.227735i
$433$	−263.913	−	263.913i	−0.609499	−	0.609499i	0.333316	−	0.942815i	$-0.391832\pi$
$433$	−263.913	−	263.913i	−0.609499	−	0.609499i	−0.942815	+	0.333316i	$0.891832\pi$
$434$	127.207	+	151.599i	0.293103	+	0.349306i
$435$	60.3625	+	60.4100i	0.138764	+	0.138874i
$436$	12.0098	−	68.1108i	0.0275454	−	0.156218i
$437$	19.8677	−	42.6064i	0.0454638	−	0.0974975i
$438$	43.0287	+	54.0069i	0.0982390	+	0.123303i
$439$	470.665	−	82.9910i	1.07213	−	0.189045i	0.390397	−	0.920647i	$-0.372338\pi$
$439$	470.665	−	82.9910i	1.07213	−	0.189045i	0.681733	+	0.731601i	$0.261227\pi$
$440$	−1.92361	−	76.9376i	−0.00437184	−	0.174858i
$441$	249.461	−	268.362i	0.565671	−	0.608531i
$442$	−170.724	−	637.150i	−0.386253	−	1.44152i
$443$	226.673	+	486.102i	0.511678	+	1.09730i	0.977212	+	0.212267i	$0.0680845\pi$
$443$	226.673	+	486.102i	0.511678	+	1.09730i	−0.465534	+	0.885030i	$0.654138\pi$
$444$	23.0983	−	46.4198i	0.0520232	−	0.104549i
$445$	155.902	−	357.393i	0.350341	−	0.803130i
$446$	10.6203	+	8.91150i	0.0238124	+	0.0199809i
$447$	−328.216	+	110.108i	−0.734264	+	0.246326i
$448$	−9.73389	−	20.8744i	−0.0217274	−	0.0465947i
$449$	−156.641	−	90.4366i	−0.348866	−	0.201418i	0.315320	−	0.948985i	$-0.397888\pi$
$449$	−156.641	−	90.4366i	−0.348866	−	0.201418i	−0.664186	+	0.747568i	$0.731222\pi$
$450$	−27.4833	−	317.009i	−0.0610741	−	0.704464i
$451$	179.624	+	311.119i	0.398280	+	0.689842i
$452$	82.8263	+	57.9956i	0.183244	+	0.128309i
$453$	−113.906	−	142.968i	−0.251448	−	0.315602i
$454$	−24.8803	−	68.3580i	−0.0548024	−	0.150568i
$455$	25.9853	+	230.494i	0.0571106	+	0.506581i
$456$	2.69428	−	9.12219i	0.00590852	−	0.0200048i
$457$	24.6212	−	281.422i	0.0538757	−	0.615802i	−0.920480	−	0.390789i	$-0.872202\pi$
$457$	24.6212	−	281.422i	0.0538757	−	0.615802i	0.974356	−	0.225013i	$-0.0722424\pi$
$458$	−137.777	−	137.777i	−0.300822	−	0.300822i
$459$	768.133	−	144.248i	1.67349	−	0.314265i
$460$	200.545	−	368.319i	0.435968	−	0.800693i
$461$	−432.193	+	362.653i	−0.937512	+	0.786666i	−0.977151	−	0.212548i	$-0.931824\pi$
$461$	−432.193	+	362.653i	−0.937512	+	0.786666i	0.0396388	+	0.999214i	$0.487379\pi$
$462$	−66.4514	−	1.68759i	−0.143834	−	0.00365280i
$463$	657.925	−	460.684i	1.42100	−	0.994997i	0.425046	−	0.905172i	$-0.360258\pi$
$463$	657.925	−	460.684i	1.42100	−	0.994997i	0.995958	−	0.0898257i	$-0.0286310\pi$
$464$	7.78886	+	21.3997i	0.0167863	+	0.0461201i
$465$	−63.8285	+	726.272i	−0.137266	+	1.56188i
$466$	104.352	+	591.807i	0.223930	+	1.26997i
$467$	−105.062	−	28.1512i	−0.224972	−	0.0602810i	0.144572	−	0.989494i	$-0.453819\pi$
$467$	−105.062	−	28.1512i	−0.224972	−	0.0602810i	−0.369544	+	0.929213i	$0.620486\pi$
$468$	−268.748	+	109.075i	−0.574247	+	0.233066i
$469$	210.192	+	121.354i	0.448171	+	0.258752i
$470$	−27.1599	+	435.603i	−0.0577869	+	0.926814i
$471$	−414.570	+	274.869i	−0.880191	+	0.583586i
$472$	−271.762	+	23.7761i	−0.575768	+	0.0503731i
$473$	11.8066	+	134.950i	0.0249610	+	0.285306i
$474$	223.900	−	13.8718i	0.472363	−	0.0292653i
$475$	−6.23947	−	27.3209i	−0.0131357	−	0.0575176i
$476$	83.3388	−	144.347i	0.175081	−	0.303250i
$477$	79.8519	−	247.086i	0.167404	−	0.518000i
$478$	−87.7292	+	327.410i	−0.183534	+	0.684958i
$479$	349.095	−	61.5548i	0.728799	−	0.128507i	0.203076	−	0.979163i	$-0.434906\pi$
$479$	349.095	−	61.5548i	0.728799	−	0.128507i	0.525723	+	0.850656i	$0.323795\pi$
$480$	29.0527	−	79.7241i	0.0605265	−	0.166092i
$481$	−130.846	+	47.6240i	−0.272029	+	0.0990104i
$482$	217.693	+	310.898i	0.451645	+	0.645016i
$483$	−308.994	−	189.016i	−0.639739	−	0.391338i
$484$	117.482	+	140.009i	0.242731	+	0.289275i
$485$	−227.273	+	417.407i	−0.468605	+	0.860634i
$486$	−104.632	−	327.338i	−0.215292	−	0.673535i
$487$	462.491	−	462.491i	0.949673	−	0.949673i	−0.0491203	−	0.998793i	$-0.515642\pi$
$487$	462.491	−	462.491i	0.949673	−	0.949673i	0.998793	+	0.0491203i	$0.0156418\pi$
$488$	−116.461	−	10.1890i	−0.238650	−	0.0208792i
$489$	105.524	+	438.016i	0.215796	+	0.895738i
$490$	179.470	−	225.078i	0.366266	−	0.459343i
$491$	−351.646	+	127.989i	−0.716184	+	0.260670i	−0.674305	−	0.738453i	$-0.735557\pi$
$491$	−351.646	+	127.989i	−0.716184	+	0.260670i	−0.0418790	+	0.999123i	$0.513334\pi$
$492$	58.8542	+	391.687i	0.119622	+	0.796112i
$493$	−94.5262	+	134.997i	−0.191737	+	0.273828i
$494$	−22.1220	+	12.7721i	−0.0447814	+	0.0258545i
$495$	−168.642	−	177.570i	−0.340690	−	0.358728i
$496$	−97.2095	+	168.372i	−0.195987	+	0.339459i
$497$	−214.125	+	99.8480i	−0.430835	+	0.200901i
$498$	−21.6190	+	24.4747i	−0.0434116	+	0.0491460i
$499$	48.8428	−	58.2086i	0.0978813	−	0.116650i	−0.714880	−	0.699247i	$-0.753519\pi$
$499$	48.8428	−	58.2086i	0.0978813	−	0.116650i	0.812761	+	0.582597i	$0.197963\pi$
$500$	−40.3866	−	246.716i	−0.0807732	−	0.493433i
$501$	40.9539	−	27.1533i	0.0817444	−	0.0541983i
$502$	−183.361	+	85.5027i	−0.365261	+	0.170324i
$503$	432.568	−	115.906i	0.859975	−	0.230430i	0.198227	−	0.980156i	$-0.436482\pi$
$503$	432.568	−	115.906i	0.859975	−	0.230430i	0.661748	+	0.749726i	$0.269815\pi$
$504$	−67.5076	−	28.5295i	−0.133944	−	0.0566062i
$505$	551.783	+	524.865i	1.09264	+	1.03934i
$506$	−56.0466	−	317.856i	−0.110764	−	0.628174i
$507$	253.072	+	99.4570i	0.499156	+	0.196168i
$508$	127.822	+	59.6045i	0.251619	+	0.117332i
$509$	349.463	+	61.6198i	0.686569	+	0.121061i	0.506041	−	0.862509i	$-0.331108\pi$
$509$	349.463	+	61.6198i	0.686569	+	0.121061i	0.180527	+	0.983570i	$0.442220\pi$
$510$	593.191	−	158.695i	1.16312	−	0.311166i
$511$	35.8958	−	30.1202i	0.0702462	−	0.0589436i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−13.0946	−	27.2869i	−0.0255256	−	0.0531909i
$514$			321.897i			0.626259i
$515$	−486.174	+	98.3144i	−0.944027	+	0.190902i
$516$	−42.3060	+	143.238i	−0.0819884	+	0.277593i
$517$	192.663	+	275.151i	0.372656	+	0.532208i
$518$	−31.8881	−	14.8697i	−0.0615601	−	0.0287059i
$519$	−37.3740	+	330.346i	−0.0720116	+	0.636506i
$520$	−204.054	+	101.437i	−0.392412	+	0.195070i
$521$	302.699	+	524.290i	0.580996	+	1.00631i	0.995362	+	0.0962041i	$0.0306702\pi$
$521$	302.699	+	524.290i	0.580996	+	1.00631i	−0.414366	+	0.910111i	$0.635997\pi$
$522$	64.0351	+	33.9185i	0.122673	+	0.0649780i
$523$	384.148	−	102.932i	0.734508	−	0.196811i	0.127872	−	0.991791i	$-0.459185\pi$
$523$	384.148	−	102.932i	0.734508	−	0.196811i	0.606636	+	0.794980i	$0.292519\pi$
$524$	−51.4131	+	141.256i	−0.0981166	+	0.269573i
$525$	−214.579	+	24.1056i	−0.408721	+	0.0459153i
$526$	−261.556	−	219.471i	−0.497255	−	0.417246i
$527$	−1401.59	+	122.623i	−2.65957	+	0.232682i
$528$	−20.7702	−	61.9130i	−0.0393375	−	0.117260i
$529$	420.607	−	1155.61i	0.795098	−	2.18451i
$530$	47.8609	−	198.321i	0.0903037	−	0.374191i
$531$	−591.002	+	635.782i	−1.11300	+	1.19733i
$532$	−6.23472	−	1.67059i	−0.0117194	−	0.00314020i
$533$	610.115	−	871.335i	1.14468	−	1.63477i
$534$	37.1943	−	328.758i	0.0696523	−	0.615652i
$535$	134.492	−	892.685i	0.251388	−	1.66857i
$536$	−41.4050	+	234.819i	−0.0772481	+	0.438096i
$537$	−333.207	−	612.537i	−0.620497	−	1.14066i
$538$	261.510	+	22.8791i	0.486077	+	0.0425262i
$539$		−	221.550i		−	0.411039i
$540$	−101.441	−	250.220i	−0.187853	−	0.463370i
$541$	937.706			1.73328			0.866641	−	0.498932i	$-0.166274\pi$
$541$	937.706			1.73328			0.866641	+	0.498932i	$0.166274\pi$
$542$	−30.9975	+	354.303i	−0.0571909	+	0.653695i
$543$	−2.29589	+	90.4038i	−0.00422815	+	0.166490i
$544$	161.259	+	28.4344i	0.296433	+	0.0522691i
$545$	−102.683	−	139.112i	−0.188409	−	0.255251i
$546$	78.6242	+	180.434i	0.144000	+	0.330464i
$547$	−680.332	−	476.374i	−1.24375	−	0.870885i	−0.248540	−	0.968622i	$-0.579951\pi$
$547$	−680.332	−	476.374i	−1.24375	−	0.870885i	−0.995212	+	0.0977371i	$0.968840\pi$
$548$	−31.8998	+	119.052i	−0.0582113	+	0.217248i
$549$	−296.733	+	224.340i	−0.540497	+	0.408633i
$550$	−142.679	−	129.081i	−0.259417	−	0.234693i
$551$	5.99711	+	2.18277i	0.0108841	+	0.00396147i
$552$	70.6704	−	348.765i	0.128026	−	0.631821i
$553$	−13.2677	−	151.650i	−0.0239922	−	0.274232i
$554$	12.8094	−	15.2656i	0.0231216	−	0.0275553i
$555$	−44.2857	−	121.823i	−0.0797940	−	0.219501i
$556$	31.7403	+	11.5525i	0.0570869	+	0.0207779i
$557$	189.603	+	707.608i	0.340400	+	1.27039i	0.897895	+	0.440210i	$0.145096\pi$
$557$	189.603	+	707.608i	0.340400	+	1.27039i	−0.557495	+	0.830181i	$0.688237\pi$
$558$	129.577	+	604.915i	0.232217	+	1.08408i
$559$	347.363	−	200.550i	0.621400	−	0.358765i
$560$	−54.5837	−	18.3353i	−0.0974708	−	0.0327415i
$561$	280.804	−	380.112i	0.500542	−	0.677561i
$562$	293.195	−	628.759i	0.521700	−	1.11879i
$563$	−242.785	+	170.000i	−0.431235	+	0.301954i	−0.768967	−	0.639288i	$-0.779229\pi$
$563$	−242.785	+	170.000i	−0.431235	+	0.301954i	0.337732	+	0.941242i	$0.390340\pi$
$564$	86.7382	+	360.038i	0.153791	+	0.638365i
$565$	247.766	−	50.1033i	0.438523	−	0.0886784i
$566$	389.774			0.688647
$567$	−220.257	+	76.6193i	−0.388460	+	0.135131i
$568$	−164.124	−	164.124i	−0.288951	−	0.288951i
$569$	−248.598	−	296.267i	−0.436903	−	0.520680i	0.501998	−	0.864869i	$-0.332598\pi$
$569$	−248.598	−	296.267i	−0.436903	−	0.520680i	−0.938901	+	0.344189i	$0.888154\pi$
$570$	−11.8816	−	20.5982i	−0.0208449	−	0.0361372i
$571$	−10.8180	+	61.3520i	−0.0189457	+	0.107447i	−0.992814	−	0.119666i	$-0.961818\pi$
$571$	−10.8180	+	61.3520i	−0.0189457	+	0.107447i	0.973868	+	0.227113i	$0.0729286\pi$
$572$	−74.1176	+	158.946i	−0.129576	+	0.277877i
$573$	−22.4183	+	3.36853i	−0.0391244	+	0.00587877i
$574$	264.698	−	46.6735i	0.461147	−	0.0813126i
$575$	−321.627	−	997.892i	−0.559351	−	1.73546i
$576$	3.65465	−	71.9072i	0.00634488	−	0.124839i
$577$	190.382	+	710.514i	0.329951	+	1.23139i	0.909240	+	0.416271i	$0.136663\pi$
$577$	190.382	+	710.514i	0.329951	+	1.23139i	−0.579290	+	0.815122i	$0.696670\pi$
$578$	328.068	+	703.545i	0.567592	+	1.21721i
$579$	−132.628	+	8.21699i	−0.229064	+	0.0141917i
$580$	52.1838	+	22.7636i	0.0899722	+	0.0392476i
$581$	16.9756	+	14.2442i	0.0292179	+	0.0245167i
$582$	−80.0892	+	395.248i	−0.137610	+	0.679120i
$583$	−66.3566	−	142.302i	−0.113819	−	0.244086i
$584$	39.8673	+	23.0174i	0.0682660	+	0.0394134i
$585$	−265.482	+	674.749i	−0.453815	+	1.15342i
$586$	210.919	+	365.323i	0.359930	+	0.623417i
$587$	−345.328	−	241.801i	−0.588293	−	0.411927i	0.241175	−	0.970482i	$-0.422467\pi$
$587$	−345.328	−	241.801i	−0.588293	−	0.411927i	−0.829468	+	0.558555i	$0.811356\pi$
$588$	89.3446	−	227.341i	0.151947	−	0.386634i
$589$	18.6348	+	51.1987i	0.0316381	+	0.0869248i
$590$	−425.187	+	533.237i	−0.720655	+	0.903791i
$591$	−679.360	−	714.765i	−1.14951	−	1.20942i
$592$	3.01263	−	34.4345i	0.00508890	−	0.0581664i
$593$	−276.922	−	276.922i	−0.466986	−	0.466986i	0.433951	−	0.900937i	$-0.357119\pi$
$593$	−276.922	−	276.922i	−0.466986	−	0.466986i	−0.900937	+	0.433951i	$0.857119\pi$
$594$	−181.099	−	101.895i	−0.304880	−	0.171541i
$595$	−117.875	−	399.674i	−0.198109	−	0.671721i
$596$	−176.799	+	148.352i	−0.296643	+	0.248913i
$597$	−412.608	−	758.501i	−0.691136	−	1.27052i
$598$	−782.832	+	548.145i	−1.30908	+	0.916630i
$599$	205.383	+	564.285i	0.342876	+	0.942045i	0.984556	+	0.175072i	$0.0560159\pi$
$599$	205.383	+	564.285i	0.342876	+	0.942045i	−0.641679	+	0.766973i	$0.721762\pi$
$600$	−94.3535	−	189.993i	−0.157256	−	0.316655i
$601$	−161.204	−	914.236i	−0.268227	−	1.52119i	−0.759686	−	0.650290i	$-0.774647\pi$
$601$	−161.204	−	914.236i	−0.268227	−	1.52119i	0.491459	−	0.870901i	$-0.336464\pi$
$602$	97.8984	+	26.2318i	0.162622	+	0.0435744i
$603$	403.074	+	642.793i	0.668448	+	1.06599i
$604$	−105.537	−	60.9319i	−0.174730	−	0.100881i
$605$	456.037	+	28.4340i	0.753780	+	0.0469983i
$606$	578.526	+	287.872i	0.954663	+	0.475037i
$607$	15.2056	−	1.33031i	0.0250503	−	0.00219162i	−0.0746237	−	0.997212i	$-0.523776\pi$
$607$	15.2056	−	1.33031i	0.0250503	−	0.00219162i	0.0996740	+	0.995020i	$0.468220\pi$
$608$	−0.552669	−	6.31704i	−0.000908996	−	0.0103899i
$609$	21.9064	−	44.0244i	0.0359711	−	0.0722897i
$610$	−219.122	+	193.402i	−0.359217	+	0.317052i
$611$	497.281	−	861.316i	0.813881	−	1.40968i
$612$	441.431	−	276.807i	0.721292	−	0.452298i
$613$	109.211	−	407.581i	0.178158	−	0.664896i	−0.817834	−	0.575455i	$-0.804825\pi$
$613$	109.211	−	407.581i	0.178158	−	0.664896i	0.995992	−	0.0894415i	$-0.0285082\pi$
$614$	185.675	−	32.7394i	0.302402	−	0.0533216i
$615$	810.910	+	568.281i	1.31855	+	0.924033i
$616$	−41.6427	+	15.1567i	−0.0676017	+	0.0246050i
$617$	353.557	+	504.932i	0.573026	+	0.818366i	0.996146	−	0.0877077i	$-0.0279541\pi$
$617$	353.557	+	504.932i	0.573026	+	0.818366i	−0.423120	+	0.906073i	$0.639065\pi$
$618$	−369.720	+	201.120i	−0.598253	+	0.325436i
$619$	−688.538	−	820.568i	−1.11234	−	1.32563i	−0.940223	−	0.340558i	$-0.889384\pi$
$619$	−688.538	−	820.568i	−1.11234	−	1.32563i	−0.172116	−	0.985077i	$-0.555060\pi$
$620$	137.494	+	466.195i	0.221764	+	0.751928i
$621$	−577.004	−	974.274i	−0.929153	−	1.56888i
$622$	500.193	−	500.193i	0.804170	−	0.804170i
$623$	−223.663	−	19.5680i	−0.359010	−	0.0314093i
$624$	−140.153	+	133.211i	−0.224604	+	0.213478i
$625$	−516.489	−	351.943i	−0.826382	−	0.563109i
$626$	675.527	−	245.872i	1.07912	−	0.392766i
$627$	−17.0329	−	6.69389i	−0.0271657	−	0.0106761i
$628$	−190.203	+	271.639i	−0.302872	+	0.432546i
$629$	216.630	−	125.072i	0.344404	−	0.198842i
$630$	−167.996	+	73.1259i	−0.266660	+	0.116073i
$631$	71.0481	−	123.059i	0.112596	−	0.195022i	−0.804220	−	0.594331i	$-0.797417\pi$
$631$	71.0481	−	123.059i	0.112596	−	0.195022i	0.916816	+	0.399309i	$0.130750\pi$
$632$	135.541	−	63.2038i	0.214464	−	0.100006i
$633$	−291.673	−	59.1018i	−0.460779	−	0.0933678i
$634$	−528.504	+	629.847i	−0.833603	+	0.993449i
$635$	328.209	−	128.837i	0.516865	−	0.202893i
$636$	−10.7047	−	172.781i	−0.0168312	−	0.271668i
$637$	−594.529	+	277.233i	−0.933326	+	0.435217i
$638$	42.3233	−	11.3405i	0.0663375	−	0.0177751i
$639$	−737.607	−	37.4886i	−1.15431	−	0.0586675i
$640$	−1.41390	−	56.5509i	−0.00220921	−	0.0883607i
$641$	126.448	+	717.120i	0.197266	+	1.11875i	0.909154	+	0.416459i	$0.136729\pi$
$641$	126.448	+	717.120i	0.197266	+	1.11875i	−0.711888	+	0.702293i	$0.752160\pi$
$642$	−113.823	−	757.513i	−0.177294	−	1.17993i
$643$	−567.617	−	264.684i	−0.882763	−	0.411639i	−0.0722685	−	0.997385i	$-0.523024\pi$
$643$	−567.617	−	264.684i	−0.882763	−	0.411639i	−0.810495	+	0.585746i	$0.800802\pi$
$644$	−237.812	−	41.9327i	−0.369274	−	0.0651130i
$645$	186.566	+	323.436i	0.289250	+	0.501452i
$646$	35.1530	−	29.4969i	0.0544164	−	0.0456608i
$647$	225.191	−	225.191i	0.348054	−	0.348054i	−0.511330	−	0.859384i	$-0.670847\pi$
$647$	225.191	−	225.191i	0.348054	−	0.348054i	0.859384	+	0.511330i	$0.170847\pi$
$648$	−144.740	−	177.590i	−0.223365	−	0.274059i
$649$			524.879i			0.808750i
$650$	−167.850	+	544.402i	−0.258231	+	0.837542i
$651$	408.129	−	98.3240i	0.626927	−	0.151035i
$652$	172.282	+	246.045i	0.264237	+	0.377369i
$653$	−744.038	−	346.950i	−1.13941	−	0.531318i	−0.241026	−	0.970519i	$-0.577484\pi$
$653$	−744.038	−	346.950i	−1.13941	−	0.531318i	−0.898389	+	0.439201i	$0.855262\pi$
$654$	−118.006	−	87.1756i	−0.180437	−	0.133296i
$655$	167.285	+	336.519i	0.255397	+	0.513769i
$656$	132.028	+	228.679i	0.201262	+	0.348597i
$657$	143.233	−	30.6815i	0.218010	−	0.0466994i
$658$	242.748	−	65.0441i	0.368918	−	0.0988512i
$659$	106.201	−	291.785i	0.161155	−	0.442770i	−0.832664	−	0.553778i	$-0.813186\pi$
$659$	106.201	−	291.785i	0.161155	−	0.442770i	0.993820	+	0.111008i	$0.0354079\pi$
$660$	−147.937	−	69.0550i	−0.224147	−	0.104629i
$661$	−493.250	−	413.886i	−0.746218	−	0.626151i	0.188282	−	0.982115i	$-0.439708\pi$
$661$	−493.250	−	413.886i	−0.746218	−	0.626151i	−0.934500	+	0.355964i	$0.884153\pi$
$662$	−88.3905	+	7.73317i	−0.133520	+	0.0116815i
$663$	−1371.41	−	277.889i	−2.06849	−	0.419138i
$664$	−7.44593	+	20.4575i	−0.0112138	+	0.0308095i
$665$	−13.7687	+	8.41508i	−0.0207048	+	0.0126543i
$666$	−66.3314	−	87.7361i	−0.0995967	−	0.131736i
$667$	230.627	+	61.7964i	0.345768	+	0.0926482i
$668$	18.7895	−	26.8343i	0.0281281	−	0.0401710i
$669$	26.9611	−	11.7484i	0.0403006	−	0.0175611i
$670$	354.009	+	479.602i	0.528372	+	0.715824i
$671$	−39.0590	+	221.515i	−0.0582101	+	0.330126i
$672$	−48.8433	−	1.24042i	−0.0726834	−	0.00184586i
$673$	−343.113	−	30.0185i	−0.509827	−	0.0446040i	−0.170659	−	0.985330i	$-0.554590\pi$
$673$	−343.113	−	30.0185i	−0.509827	−	0.0446040i	−0.339167	+	0.940726i	$0.610145\pi$
$674$		−	218.246i		−	0.323807i
$675$	−628.033	−	247.387i	−0.930419	−	0.366499i
$676$	181.276			0.268160
$677$	20.4310	−	233.527i	0.0301787	−	0.344944i	−0.966062	−	0.258311i	$-0.916834\pi$
$677$	20.4310	−	233.527i	0.0301787	−	0.344944i	0.996240	−	0.0866323i	$-0.0276105\pi$
$678$	188.418	−	102.495i	0.277903	−	0.151173i
$679$	269.507	+	47.5214i	0.396918	+	0.0699874i
$680$	329.361	−	243.112i	0.484354	−	0.357517i
$681$	−153.337	−	17.3480i	−0.225165	−	0.0254743i
$682$	306.420	+	214.558i	0.449297	+	0.314601i
$683$	−169.968	+	634.328i	−0.248855	+	0.928738i	0.722552	+	0.691317i	$0.242969\pi$
$683$	−169.968	+	634.328i	−0.248855	+	0.928738i	−0.971407	+	0.237422i	$0.923698\pi$
$684$	−14.7786	−	13.7377i	−0.0216061	−	0.0200843i
$685$	160.686	+	262.913i	0.234578	+	0.383815i
$686$	−343.238	−	124.928i	−0.500347	−	0.182111i
$687$	−391.867	+	131.461i	−0.570403	+	0.191355i
$688$	8.67809	+	99.1910i	0.0126135	+	0.144173i
$689$	−298.833	+	356.135i	−0.433720	+	0.516887i
$690$	−509.986	−	728.946i	−0.739110	−	1.05644i
$691$	820.059	+	298.477i	1.18677	+	0.431950i	0.858589	−	0.512665i	$-0.171342\pi$
$691$	820.059	+	298.477i	1.18677	+	0.431950i	0.328183	+	0.944614i	$0.393564\pi$
$692$	57.3636	+	214.084i	0.0828954	+	0.309370i
$693$	−66.0035	+	124.609i	−0.0952432	+	0.179811i
$694$	−512.619	+	295.961i	−0.738644	+	0.426456i
$695$	75.6158	−	37.5890i	0.108800	−	0.0540849i
$696$	48.0028	+	5.43084i	0.0689695	+	0.00780293i
$697$	−807.576	+	1731.85i	−1.15865	+	2.48472i
$698$	257.639	−	180.401i	0.369110	−	0.258454i
$699$	1222.57	+	361.092i	1.74903	+	0.516583i
$700$	−127.262	+	67.2806i	−0.181803	+	0.0961151i
$701$	−53.2733			−0.0759961			−0.0379981	−	0.999278i	$-0.512098\pi$
$701$	−53.2733			−0.0759961			−0.0379981	+	0.999278i	$0.512098\pi$
$702$	−46.8203	+	613.482i	−0.0666956	+	0.873906i
$703$	−6.84967	−	6.84967i	−0.00974348	−	0.00974348i
$704$	−27.9844	−	33.3506i	−0.0397506	−	0.0473730i
$705$	801.625	+	463.239i	1.13706	+	0.657077i
$706$	−116.614	+	661.350i	−0.165175	+	0.936756i
$707$	185.320	−	397.419i	0.262121	−	0.562120i
$708$	−211.668	+	538.597i	−0.298966	+	0.760730i
$709$	−46.2646	+	8.15770i	−0.0652533	+	0.0115059i	−0.206180	−	0.978514i	$-0.566103\pi$
$709$	−46.2646	+	8.15770i	−0.0652533	+	0.0115059i	0.140926	+	0.990020i	$0.454992\pi$
$710$	−580.086	+	14.5034i	−0.817022	+	0.0204273i
$711$	185.247	−	438.338i	0.260544	−	0.616509i
$712$	−57.0878	−	213.054i	−0.0801794	−	0.299234i
$713$	861.454	+	1847.39i	1.20821	+	2.59101i
$714$	−195.385	−	294.688i	−0.273648	−	0.412729i
$715$	160.207	+	408.125i	0.224066	+	0.570804i
$716$	−356.109	−	298.811i	−0.497359	−	0.417334i
$717$	538.907	+	476.026i	0.751613	+	0.663914i
$718$	−159.602	−	342.267i	−0.222286	−	0.476695i
$719$	−215.560	−	124.453i	−0.299805	−	0.173092i	0.342550	−	0.939499i	$-0.388709\pi$
$719$	−215.560	−	124.453i	−0.299805	−	0.173092i	−0.642355	+	0.766407i	$0.722043\pi$
$720$	−123.956	−	130.518i	−0.172160	−	0.181275i
$721$	142.805	+	247.345i	0.198065	+	0.343059i
$722$	416.747	+	291.809i	0.577212	+	0.404168i
$723$	796.180	−	119.633i	1.10122	−	0.165467i
$724$	20.6199	+	56.6528i	0.0284806	+	0.0782497i
$725$	131.148	−	55.3034i	0.180894	−	0.0762805i
$726$	376.928	−	90.8071i	0.519184	−	0.125079i
$727$	65.6856	−	750.790i	0.0903516	−	1.03272i	−0.806748	−	0.590895i	$-0.798775\pi$
$727$	65.6856	−	750.790i	0.0903516	−	1.03272i	0.897100	−	0.441828i	$-0.145670\pi$
$728$	92.7817	+	92.7817i	0.127447	+	0.127447i
$729$	−720.557	−	110.629i	−0.988418	−	0.151754i
$730$	110.386	−	32.5559i	0.151214	−	0.0445972i
$731$	−551.977	+	463.164i	−0.755098	+	0.633603i
$732$	−129.410	+	211.553i	−0.176790	+	0.289007i
$733$	167.603	−	117.357i	0.228654	−	0.160105i	−0.453636	−	0.891187i	$-0.649873\pi$
$733$	167.603	−	117.357i	0.228654	−	0.160105i	0.682289	+	0.731082i	$0.260984\pi$
$734$	−51.1655	−	140.576i	−0.0697078	−	0.191521i
$735$	−257.861	−	553.553i	−0.350831	−	0.753134i
$736$	−41.1955	−	233.631i	−0.0559722	−	0.317434i
$737$	443.139	+	118.739i	0.601275	+	0.161111i
$738$	799.507	+	258.381i	1.08334	+	0.350109i
$739$	−911.927	−	526.501i	−1.23400	−	0.712451i	−0.266139	−	0.963935i	$-0.585748\pi$
$739$	−911.927	−	526.501i	−1.23400	−	0.712451i	−0.967862	+	0.251484i	$0.919081\pi$
$740$	−57.1838	−	64.7888i	−0.0772754	−	0.0875525i
$741$	3.35077	+	54.0839i	0.00452196	+	0.0729877i
$742$	−117.027	+	10.2385i	−0.157718	+	0.0137985i
$743$	−111.678	−	1276.48i	−0.150307	−	1.71801i	−0.579646	−	0.814869i	$-0.696809\pi$
$743$	−111.678	−	1276.48i	−0.150307	−	1.71801i	0.429339	−	0.903143i	$-0.358747\pi$
$744$	227.904	+	343.736i	0.306323	+	0.462010i
$745$	−35.9055	+	575.870i	−0.0481953	+	0.772979i
$746$	−217.815	+	377.267i	−0.291978	+	0.505720i
$747$	26.0516	+	64.1879i	0.0348749	+	0.0859276i
$748$	81.5425	−	304.321i	0.109014	−	0.406846i
$749$	−511.920	+	90.2653i	−0.683471	+	0.120514i
$750$	−506.727	−	156.452i	−0.675637	−	0.208603i
$751$	−1098.89	+	399.964i	−1.46324	+	0.532576i	−0.946256	−	0.323420i	$-0.895167\pi$
$751$	−1098.89	+	399.964i	−1.46324	+	0.532576i	−0.516984	+	0.855995i	$0.672945\pi$
$752$	141.612	+	202.243i	0.188313	+	0.268940i
$753$	−10.8959	+	429.040i	−0.0144699	+	0.569775i
$754$	−83.3928	−	99.3837i	−0.110601	−	0.131809i
$755$	−292.216	+	86.1824i	−0.387041	+	0.114149i
$756$	−117.980	+	101.248i	−0.156058	+	0.133926i
$757$	−595.606	+	595.606i	−0.786798	+	0.786798i	−0.980968	−	0.194170i	$-0.937799\pi$
$757$	−595.606	+	595.606i	−0.786798	+	0.786798i	0.194170	+	0.980968i	$0.437799\pi$
$758$	522.200	+	45.6866i	0.688919	+	0.0602726i
$759$	−656.634	−	193.940i	−0.865131	−	0.255521i
$760$	−12.3949	−	9.88335i	−0.0163091	−	0.0130044i
$761$	−1341.75	+	488.358i	−1.76314	+	0.641732i	−0.999990	−	0.00448511i	$-0.998572\pi$
$761$	−1341.75	+	488.358i	−1.76314	+	0.641732i	−0.763154	+	0.646217i	$0.776350\pi$
$762$	233.996	−	186.431i	0.307082	−	0.244660i
$763$	−57.1051	+	81.5545i	−0.0748428	+	0.106887i
$764$	−13.0885	+	7.55665i	−0.0171316	+	0.00989091i
$765$	259.191	−	1276.55i	0.338812	−	1.66870i
$766$	−237.301	+	411.018i	−0.309793	+	0.536577i
$767$	1408.51	−	656.799i	1.83639	−	0.856322i
$768$	−15.2666	−	45.5075i	−0.0198783	−	0.0592546i
$769$	364.202	−	434.039i	0.473604	−	0.564419i	−0.475365	−	0.879789i	$-0.657684\pi$
$769$	364.202	−	434.039i	0.473604	−	0.564419i	0.948969	+	0.315369i	$0.102128\pi$
$770$	−44.2968	+	101.547i	−0.0575283	+	0.131879i
$771$	611.344	+	304.202i	0.792923	+	0.394556i
$772$	−80.2882	+	37.4390i	−0.104000	+	0.0484961i
$773$	−765.077	+	205.002i	−0.989751	+	0.265203i	−0.717146	−	0.696923i	$-0.754552\pi$
$773$	−765.077	+	205.002i	−0.989751	+	0.265203i	−0.272605	+	0.962126i	$0.587885\pi$
$774$	232.055	+	215.711i	0.299813	+	0.278697i
$775$	1081.37	+	554.213i	1.39532	+	0.715113i
$776$	46.6859	+	264.769i	0.0601623	+	0.341197i
$777$	−58.3756	+	46.5093i	−0.0751294	+	0.0598575i
$778$	−959.116	−	447.243i	−1.23280	−	0.574862i
$779$	72.8756	+	12.8499i	0.0935502	+	0.0164954i
$780$	−0.190188	+	483.399i	−0.000243831	+	0.619742i
$781$	−342.102	+	287.058i	−0.438031	+	0.367552i
$782$	1213.96	−	1213.96i	1.55238	−	1.55238i
$783$	124.933	−	89.5609i	0.159557	−	0.114382i
$784$		−	162.844i		−	0.207710i
$785$	164.320	+	812.576i	0.209324	+	1.03513i
$786$	219.686	+	231.135i	0.279498	+	0.294064i
$787$	466.649	+	666.444i	0.592947	+	0.846816i	0.997712	−	0.0676048i	$-0.0215357\pi$
$787$	466.649	+	666.444i	0.592947	+	0.846816i	−0.404765	+	0.914421i	$0.632647\pi$
$788$	−595.814	−	277.833i	−0.756110	−	0.352580i
$789$	−663.996	+	289.337i	−0.841566	+	0.366714i
$790$	119.054	−	354.421i	0.150701	−	0.448634i
$791$	−72.7767	−	126.053i	−0.0920059	−	0.159359i
$792$	−137.213	−	19.0631i	−0.173249	−	0.0240696i
$793$	643.309	−	172.374i	0.811235	−	0.217370i
$794$	−243.751	+	669.700i	−0.306991	+	0.843451i
$795$	−331.420	−	278.317i	−0.416880	−	0.350084i
$796$	−440.968	−	370.016i	−0.553979	−	0.464844i
$797$	−1187.03	+	103.852i	−1.48937	+	0.130303i	−0.802577	−	0.596549i	$-0.796538\pi$
$797$	−1187.03	+	103.852i	−1.48937	+	0.130303i	−0.686794	+	0.726852i	$0.740983\pi$
$798$	−9.06475	+	10.2621i	−0.0113593	+	0.0128598i
$799$	−611.080	+	1678.93i	−0.764807	+	2.10129i
$800$	−104.872	−	94.8777i	−0.131090	−	0.118597i
$801$	−589.224	−	381.325i	−0.735610	−	0.476061i
$802$	−357.379	−	95.7595i	−0.445610	−	0.119401i
$803$	50.8033	−	72.5547i	0.0632669	−	0.0903545i
$804$	406.837	+	300.547i	0.506017	+	0.373815i
$805$	−485.715	+	358.522i	−0.603373	+	0.445369i
$806$	192.331	−	1090.76i	0.238624	−	1.35330i
$807$	290.586	−	475.035i	0.360082	−	0.588643i
$808$	429.155	+	37.5462i	0.531132	+	0.0464680i
$809$		−	31.6682i		−	0.0391449i	−0.999808	−	0.0195724i	$-0.993769\pi$
$809$		−	31.6682i		−	0.0391449i	0.999808	−	0.0195724i	$-0.00623050\pi$
$810$	−571.079	−	43.8101i	−0.705035	−	0.0540866i
$811$	114.317			0.140958			0.0704790	−	0.997513i	$-0.477547\pi$
$811$	114.317			0.140958			0.0704790	+	0.997513i	$0.477547\pi$
$812$	2.85717	−	32.6576i	0.00351869	−	0.0402188i
$813$	643.594	+	393.696i	0.791629	+	0.484251i
$814$	−65.4961	−	11.5487i	−0.0804621	−	0.0141876i
$815$	742.533	+	111.871i	0.911084	+	0.137264i
$816$	206.397	−	279.391i	0.252938	−	0.342391i
$817$	22.8574	+	16.0049i	0.0279773	+	0.0195899i
$818$	99.5598	−	371.562i	0.121711	−	0.454233i
$819$	416.980	+	21.1928i	0.509133	+	0.0258764i
$820$	641.718	+	154.866i	0.782583	+	0.188861i
$821$	1499.49	+	545.771i	1.82642	+	0.664764i	0.993835	+	0.110872i	$0.0353645\pi$
$821$	1499.49	+	545.771i	1.82642	+	0.664764i	0.832589	+	0.553891i	$0.186858\pi$
$822$	195.955	+	173.091i	0.238389	+	0.210573i
$823$	3.06692	+	35.0551i	0.00372652	+	0.0425943i	0.997830	−	0.0658387i	$-0.0209723\pi$
$823$	3.06692	+	35.0551i	0.00372652	+	0.0425943i	−0.994104	+	0.108433i	$0.965417\pi$
$824$	−180.359	+	214.943i	−0.218882	+	0.260853i
$825$	−379.986	+	148.989i	−0.460589	+	0.180593i
$826$	369.019	+	134.312i	0.446755	+	0.162605i
$827$	−252.843	−	943.622i	−0.305735	−	1.14102i	−0.932311	−	0.361658i	$-0.882211\pi$
$827$	−252.843	−	943.622i	−0.305735	−	1.14102i	0.626576	−	0.779360i	$-0.284456\pi$
$828$	−595.586	−	463.810i	−0.719306	−	0.560157i
$829$	−417.564	+	241.081i	−0.503696	+	0.290809i	−0.730238	−	0.683192i	$-0.760591\pi$
$829$	−417.564	+	241.081i	−0.503696	+	0.290809i	0.226543	+	0.974001i	$0.427258\pi$
$830$	24.2272	+	48.7365i	0.0291894	+	0.0587187i
$831$	−16.8871	−	38.7539i	−0.0203214	−	0.0466353i
$832$	−54.4782	+	116.829i	−0.0654785	+	0.140419i
$833$	965.331	−	675.932i	1.15886	−	0.811443i
$834$	51.9360	−	49.3634i	0.0622734	−	0.0591887i
$835$	−16.2326	−	80.2716i	−0.0194402	−	0.0961336i
$836$	−12.2007			−0.0145941
$837$	1271.30	+	325.571i	1.51888	+	0.388973i
$838$	−47.0686	−	47.0686i	−0.0561678	−	0.0561678i
$839$	−1027.28	−	1224.27i	−1.22441	−	1.45920i	−0.845677	−	0.533695i	$-0.820803\pi$
$839$	−1027.28	−	1224.27i	−1.22441	−	1.45920i	−0.378737	−	0.925504i	$-0.623642\pi$
$840$	−86.4053	+	86.3374i	−0.102863	+	0.102783i
$841$	140.410	−	796.302i	0.166956	−	0.946852i
$842$	−276.858	+	593.724i	−0.328810	+	0.705135i
$843$	−917.054	−	1151.03i	−1.08785	−	1.36540i
$844$	−195.386	+	34.4519i	−0.231500	+	0.0408198i
$845$	312.344	−	328.363i	0.369638	−	0.388595i
$846$	765.750	+	175.514i	0.905142	+	0.207464i
$847$	−68.0953	−	254.135i	−0.0803959	−	0.300042i
$848$	−48.7736	−	104.595i	−0.0575161	−	0.123344i
$849$	368.348	−	740.255i	0.433861	−	0.871913i
$850$	127.126	−	1015.49i	0.149560	−	1.19470i
$851$	−277.619	−	232.950i	−0.326226	−	0.273736i
$852$	−466.805	+	156.601i	−0.547894	+	0.183804i
$853$	−10.8989	−	23.3727i	−0.0127771	−	0.0274006i	0.899816	−	0.436270i	$-0.143701\pi$
$853$	−10.8989	−	23.3727i	−0.0127771	−	0.0274006i	−0.912593	+	0.408870i	$0.865923\pi$
$854$	145.742	+	84.1444i	0.170659	+	0.0985297i
$855$	−50.3484	+	3.09946i	−0.0588870	+	0.00362509i
$856$	−255.339	−	442.260i	−0.298293	−	0.516659i
$857$	770.919	+	539.803i	0.899556	+	0.629876i	0.929157	−	0.369686i	$-0.120535\pi$
$857$	770.919	+	539.803i	0.899556	+	0.629876i	−0.0296010	+	0.999562i	$0.509424\pi$
$858$	231.825	+	290.972i	0.270192	+	0.339128i
$859$	208.312	+	572.334i	0.242506	+	0.666279i	0.999911	+	0.0133342i	$0.00424453\pi$
$859$	208.312	+	572.334i	0.242506	+	0.666279i	−0.757405	+	0.652945i	$0.773533\pi$
$860$	194.627	+	155.190i	0.226311	+	0.180453i
$861$	161.506	−	546.820i	0.187580	−	0.635099i
$862$	50.3634	−	575.657i	0.0584263	−	0.667815i
$863$	391.183	+	391.183i	0.453283	+	0.453283i	0.896443	−	0.443160i	$-0.146143\pi$
$863$	391.183	+	391.183i	0.453283	+	0.453283i	−0.443160	+	0.896443i	$0.646143\pi$
$864$	−133.112	−	74.8953i	−0.154064	−	0.0866843i
$865$	486.630	+	264.965i	0.562579	+	0.306317i
$866$	−404.338	+	339.280i	−0.466903	+	0.391778i
$867$	1646.20	+	41.8067i	1.89873	+	0.0482200i
$868$	229.257	−	160.527i	0.264120	−	0.184939i
$869$	−98.4149	−	270.393i	−0.113251	−	0.311154i
$870$	92.5477	−	77.5947i	0.106377	−	0.0891893i
$871$	−235.880	−	1337.74i	−0.270816	−	1.53587i
$872$	−94.4765	−	25.3149i	−0.108345	−	0.0290308i
$873$	674.964	+	525.625i	0.773154	+	0.602091i
$874$	−57.5764	−	33.2418i	−0.0658769	−	0.0380341i
$875$	−97.4040	+	346.448i	−0.111319	+	0.395941i
$876$	81.3902	−	53.9635i	0.0929112	−	0.0616022i
$877$	544.177	−	47.6093i	0.620499	−	0.0542866i	0.227428	−	0.973795i	$-0.426968\pi$
$877$	544.177	−	47.6093i	0.620499	−	0.0542866i	0.393071	+	0.919508i	$0.371413\pi$
$878$	−58.9076	−	673.317i	−0.0670930	−	0.766876i
$879$	893.141	−	55.3347i	1.01609	−	0.0629518i
$880$	−108.629	−	6.77304i	−0.123442	−	0.00769664i
$881$	607.609	−	1052.41i	0.689681	−	1.19456i	−0.282260	−	0.959338i	$-0.591084\pi$
$881$	607.609	−	1052.41i	0.689681	−	1.19456i	0.971941	−	0.235224i	$-0.0755824\pi$
$882$	−347.329	−	384.526i	−0.393798	−	0.435970i
$883$	259.520	−	968.540i	0.293907	−	1.09687i	−0.648175	−	0.761491i	$-0.724468\pi$
$883$	259.520	−	968.540i	0.293907	−	1.09687i	0.942082	−	0.335383i	$-0.108866\pi$
$884$	−918.680	+	161.988i	−1.03923	+	0.183244i
$885$	610.904	+	1311.43i	0.690287	+	1.48185i
$886$	712.776	−	259.429i	0.804487	−	0.292809i
$887$	−888.008	−	1268.21i	−1.00114	−	1.42977i	−0.900504	−	0.434848i	$-0.856802\pi$
$887$	−888.008	−	1268.21i	−1.00114	−	1.42977i	−0.100633	−	0.994924i	$-0.532087\pi$
$888$	−62.5507	−	38.2632i	−0.0704399	−	0.0430892i
$889$	−130.502	−	155.526i	−0.146796	−	0.174945i
$890$	−484.290	−	263.691i	−0.544147	−	0.296281i
$891$	−364.662	+	247.647i	−0.409272	+	0.277942i
$892$	13.8638	−	13.8638i	0.0155424	−	0.0155424i
$893$	68.9266	+	6.03029i	0.0771854	+	0.00675285i
$894$	114.668	+	475.973i	0.128264	+	0.532408i
$895$	−1154.85	+	130.195i	−1.29034	+	0.145469i
$896$	−30.6083	+	11.1405i	−0.0341610	+	0.0124336i
$897$	301.231	+	2004.76i	0.335821	+	2.23496i
$898$	−146.717	+	209.534i	−0.163382	+	0.233334i
$899$	−239.647	+	138.360i	−0.266570	+	0.153904i
$900$	−450.000	−	0.354096i	−0.500000	−	0.000393440i
$901$	417.585	−	723.279i	0.463469	−	0.802752i
$902$	460.454	−	214.713i	0.510481	−	0.238041i
$903$	142.336	−	161.138i	0.157626	−	0.178447i
$904$	91.9150	−	109.540i	0.101676	−	0.121173i
$905$	138.150	+	60.2636i	0.152651	+	0.0665896i
$906$	−215.457	+	142.853i	−0.237811	+	0.157674i
$907$	1075.92	−	501.710i	1.18624	−	0.553153i	0.273571	−	0.961852i	$-0.411795\pi$
$907$	1075.92	−	501.710i	1.18624	−	0.553153i	0.912669	+	0.408699i	$0.134017\pi$
$908$	−99.3717	+	26.6266i	−0.109440	+	0.0293244i
$909$	1093.45	−	826.682i	1.20291	−	0.909441i
$910$	327.931	−	8.19898i	0.360363	−	0.00900987i
$911$	−85.9424	−	487.404i	−0.0943385	−	0.535020i	−0.994948	−	0.100391i	$-0.967991\pi$
$911$	−85.9424	−	487.404i	−0.0943385	−	0.535020i	0.900610	−	0.434629i	$-0.143121\pi$
$912$	−12.5195	−	4.92017i	−0.0137276	−	0.00539492i
$913$	37.9627	+	17.7023i	0.0415802	+	0.0193892i
$914$	−393.441	−	69.3743i	−0.430461	−	0.0759018i
$915$	160.229	+	598.925i	0.175114	+	0.654563i
$916$	−211.086	+	177.122i	−0.230443	+	0.193365i
$917$	153.012	−	153.012i	0.166862	−	0.166862i
$918$	−108.543	−	1099.95i	−0.118239	−	1.19820i
$919$			375.834i			0.408960i	0.978871	+	0.204480i	$0.0655503\pi$
$919$			375.834i			0.408960i	−0.978871	+	0.204480i	$0.934450\pi$
$920$	−494.181	−	327.932i	−0.537153	−	0.356448i
$921$	113.290	−	383.571i	0.123007	−	0.416472i
$922$	457.646	+	653.587i	0.496363	+	0.708879i
$923$	1198.40	+	558.824i	1.29838	+	0.605443i
$924$	−10.5681	+	93.4108i	−0.0114374	+	0.101094i
$925$	−215.888	−	8.05040i	−0.233392	−	0.00870314i
$926$	−567.932	−	983.688i	−0.613318	−	1.06230i
$927$	32.5681	+	892.232i	0.0351328	+	0.962494i
$928$	31.1086	−	8.33553i	0.0335222	−	0.00898225i
$929$	−29.5642	+	81.2270i	−0.0318237	+	0.0874348i	−0.954587	−	0.297932i	$-0.903703\pi$
$929$	−29.5642	+	81.2270i	−0.0318237	+	0.0874348i	0.922763	+	0.385367i	$0.125925\pi$
$930$	1015.33	+	179.442i	1.09175	+	0.192948i
$931$	−34.9592	−	29.3342i	−0.0375501	−	0.0315083i
$932$	846.619	−	74.0696i	0.908389	−	0.0794738i
$933$	−477.265	−	1422.66i	−0.511538	−	1.52482i
$934$	−52.6099	+	144.545i	−0.0563275	+	0.154759i
$935$	−410.746	−	672.060i	−0.439301	−	0.718781i
$936$	120.543	+	392.065i	0.128786	+	0.418872i
$937$	147.763	+	39.5929i	0.157698	+	0.0422549i	0.336804	−	0.941575i	$-0.390654\pi$
$937$	147.763	+	39.5929i	0.157698	+	0.0422549i	−0.179107	+	0.983830i	$0.557321\pi$
$938$	196.876	−	281.168i	0.209889	−	0.299752i
$939$	171.436	−	1515.31i	0.182573	−	1.61375i
$940$	610.343	+	91.9547i	0.649301	+	0.0978241i
$941$	116.723	−	661.971i	0.124042	−	0.703476i	−0.857831	−	0.513933i	$-0.828188\pi$
$941$	116.723	−	661.971i	0.124042	−	0.703476i	0.981872	−	0.189543i	$-0.0607008\pi$
$942$	336.145	+	617.939i	0.356842	+	0.655986i
$943$	2757.94	+	241.289i	2.92465	+	0.255874i
$944$			385.798i			0.408684i
$945$	−19.8813	+	388.162i	−0.0210384	+	0.410754i
$946$	191.577			0.202512
$947$	−126.124	+	1441.60i	−0.133183	+	1.52228i	0.576112	+	0.817371i	$0.304569\pi$
$947$	−126.124	+	1441.60i	−0.133183	+	1.52228i	−0.709294	+	0.704912i	$0.750986\pi$
$948$	8.05424	−	317.148i	0.00849604	−	0.334544i
$949$	−258.272	−	45.5403i	−0.272152	−	0.0479877i
$950$	−39.2596	+	5.42288i	−0.0413258	+	0.00570830i
$951$	696.746	+	1598.95i	0.732646	+	1.68134i
$952$	−193.089	−	135.202i	−0.202824	−	0.142019i
$953$	−442.611	+	1651.85i	−0.464439	+	1.73331i	0.194302	+	0.980942i	$0.437756\pi$
$953$	−442.611	+	1651.85i	−0.464439	+	1.73331i	−0.658742	+	0.752369i	$0.728911\pi$
$954$	−338.260	−	142.953i	−0.354570	−	0.149846i
$955$	−8.86378	+	36.7289i	−0.00928145	+	0.0384595i
$956$	450.452	+	163.951i	0.471184	+	0.171497i
$957$	18.4590	−	91.0972i	0.0192884	−	0.0951903i
$958$	−43.6921	−	499.403i	−0.0456076	−	0.521298i
$959$	114.045	−	135.914i	0.118921	−	0.141725i
$960$	−108.737	−	50.7570i	−0.113268	−	0.0528719i
$961$	−1316.91	−	479.315i	−1.37035	−	0.498767i
$962$	50.9666	+	190.210i	0.0529798	+	0.197723i
$963$	−1546.23	−	499.702i	−1.60564	−	0.518901i
$964$	464.835	−	268.373i	0.482194	−	0.278395i
$965$	−70.5221	+	209.943i	−0.0730799	+	0.217557i
$966$	−304.378	+	412.023i	−0.315091	+	0.426525i
$967$	−365.933	+	784.746i	−0.378421	+	0.811527i	0.621190	+	0.783660i	$0.286649\pi$
$967$	−365.933	+	784.746i	−0.378421	+	0.811527i	−0.999612	+	0.0278672i	$0.991128\pi$
$968$	211.730	−	148.255i	0.218729	−	0.153156i
$969$	−22.7995	−	94.6375i	−0.0235289	−	0.0976652i
$970$	560.044	+	371.638i	0.577365	+	0.383132i
$971$	−1827.38			−1.88196			−0.940980	−	0.338461i	$-0.890094\pi$
$971$	−1827.38			−1.88196			−0.940980	+	0.338461i	$0.890094\pi$
$972$	−474.061	+	107.062i	−0.487717	+	0.110146i
$973$	−34.3818	−	34.3818i	−0.0353359	−	0.0353359i
$974$	−594.566	−	708.577i	−0.610438	−	0.727491i
$975$	875.300	+	833.255i	0.897744	+	0.854620i
$976$	−28.7093	+	162.818i	−0.0294152	+	0.166822i
$977$	71.0344	−	152.334i	0.0727067	−	0.155920i	−0.866595	−	0.499012i	$-0.833696\pi$
$977$	71.0344	−	152.334i	0.0727067	−	0.155920i	0.939302	+	0.343092i	$0.111474\pi$
$978$	630.098	−	94.6774i	0.644272	−	0.0968071i
$979$	−417.939	+	73.6938i	−0.426903	+	0.0752746i
$980$	−294.976	−	280.586i	−0.300996	−	0.286312i
$981$	−277.082	+	141.732i	−0.282448	+	0.144477i
$982$	136.972	+	511.186i	0.139483	+	0.520556i
$983$	−208.155	−	446.390i	−0.211755	−	0.454110i	0.771528	−	0.636196i	$-0.219493\pi$
$983$	−208.155	−	446.390i	−0.211755	−	0.454110i	−0.983283	+	0.182086i	$0.941715\pi$
$984$	559.076	−	34.6376i	0.568166	−	0.0352008i
$985$	−1529.87	+	600.543i	−1.55317	+	0.609689i
$986$	178.538	+	149.811i	0.181073	+	0.151938i
$987$	105.873	−	522.492i	0.107267	−	0.529374i
$988$	15.2671	+	32.7404i	0.0154525	+	0.0331381i
$989$	904.073	+	521.967i	0.914129	+	0.527772i
$990$	−270.953	+	215.701i	−0.273690	+	0.217880i
$991$	169.142	+	292.963i	0.170678	+	0.295623i	0.938657	−	0.344852i	$-0.112071\pi$
$991$	169.142	+	292.963i	0.170678	+	0.295623i	−0.767979	+	0.640475i	$0.778737\pi$
$992$	225.226	+	157.705i	0.227042	+	0.158977i
$993$	−68.8449	+	175.178i	−0.0693302	+	0.176413i
$994$	114.277	+	313.973i	0.114967	+	0.315868i
$995$	−1430.05	+	161.220i	−1.43723	+	0.162030i
$996$	31.8161	+	33.4742i	0.0319439	+	0.0336086i
$997$	21.4522	−	245.199i	0.0215167	−	0.245937i	−0.977818	−	0.209458i	$-0.932830\pi$
$997$	21.4522	−	245.199i	0.0215167	−	0.245937i	0.999334	−	0.0364794i	$-0.0116143\pi$
$998$	−75.9859	−	75.9859i	−0.0761382	−	0.0761382i
$999$	−229.313	+	43.0626i	−0.229542	+	0.0431057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.q.a.103.3	yes	216
5.2	odd	4	inner	270.3.q.a.157.7	yes	216
27.16	even	9	inner	270.3.q.a.43.7	✓	216
135.97	odd	36	inner	270.3.q.a.97.3	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.q.a.43.7	✓	216	27.16	even	9	inner
270.3.q.a.97.3	yes	216	135.97	odd	36	inner
270.3.q.a.103.3	yes	216	1.1	even	1	trivial
270.3.q.a.157.7	yes	216	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.123257 - 1.40883i) q^{2} +(-2.55916 - 1.56548i) q^{3} +(-1.96962 - 0.347296i) q^{4} +(-4.02280 + 2.96936i) q^{5} +(-2.52093 + 3.41247i) q^{6} +(2.35838 + 1.65135i) q^{7} +(-0.732051 + 2.73205i) q^{8} +(4.09857 + 8.01260i) q^{9} +(3.68749 + 6.03344i) q^{10} +(5.11381 + 1.86128i) q^{11} +(4.49687 + 3.97217i) q^{12} +(-1.40437 - 16.0520i) q^{13} +(2.61716 - 3.11901i) q^{14} +(14.9434 - 1.30146i) q^{15} +(3.75877 + 1.36808i) q^{16} +(7.49195 + 27.9603i) q^{17} +(11.7936 - 4.78659i) q^{18} +(0.970790 - 0.560486i) q^{19} +(8.95462 - 4.45139i) q^{20} +(-3.45030 - 7.91805i) q^{21} +(3.25254 - 6.97509i) q^{22} +(34.3534 - 24.0545i) q^{23} +(6.15039 - 5.84574i) q^{24} +(7.36583 - 23.8903i) q^{25} -22.7876 q^{26} +(2.05464 - 26.9217i) q^{27} +(-4.07158 - 4.07158i) q^{28} +(3.65957 + 4.36130i) q^{29} +(0.00834613 - 21.2132i) q^{30} +(-8.44013 + 47.8664i) q^{31} +(2.39069 - 5.12685i) q^{32} +(-10.1733 - 12.7689i) q^{33} +(40.3149 - 7.10860i) q^{34} +(-14.3907 + 0.359800i) q^{35} +(-5.28986 - 17.2052i) q^{36} +(-2.23659 - 8.34706i) q^{37} +(-0.669974 - 1.43676i) q^{38} +(-21.5350 + 43.2780i) q^{39} +(-5.16754 - 13.1642i) q^{40} +(50.5697 + 42.4330i) q^{41} +(-11.5805 + 3.88494i) q^{42} +(10.5200 + 22.5603i) q^{43} +(-9.42583 - 5.44201i) q^{44} +(-40.2800 - 20.0629i) q^{45} +(-29.6544 - 51.3630i) q^{46} +(50.5606 + 35.4029i) q^{47} +(-7.47759 - 9.38540i) q^{48} +(-13.9240 - 38.2559i) q^{49} +(-32.7495 - 13.3219i) q^{50} +(24.5982 - 83.2834i) q^{51} +(-2.80873 + 32.1039i) q^{52} +(-20.4015 - 20.4015i) q^{53} +(-37.6749 - 6.21292i) q^{54} +(-26.0986 + 7.69720i) q^{55} +(-6.23803 + 5.23433i) q^{56} +(-3.36183 - 0.0853767i) q^{57} +(6.59541 - 4.61815i) q^{58} +(32.9877 + 90.6329i) q^{59} +(-29.8848 - 2.62643i) q^{60} +(7.17732 + 40.7046i) q^{61} +(66.3954 + 17.7906i) q^{62} +(-3.56565 + 25.6649i) q^{63} +(-6.92820 - 4.00000i) q^{64} +(53.3135 + 60.4038i) q^{65} +(-19.2431 + 12.7586i) q^{66} +(83.9811 - 7.34739i) q^{67} +(-5.04574 - 57.6731i) q^{68} +(-125.572 + 7.77985i) q^{69} +(-1.26686 + 20.3185i) q^{70} +(-41.0311 + 71.0679i) q^{71} +(-24.8912 + 5.33188i) q^{72} +(4.21248 - 15.7212i) q^{73} +(-12.0353 + 2.12215i) q^{74} +(-56.2500 + 49.6079i) q^{75} +(-2.10674 + 0.766789i) q^{76} +(8.98667 + 12.8343i) q^{77} +(58.3171 + 35.6735i) q^{78} +(-33.9874 - 40.5046i) q^{79} +(-19.1831 + 5.65762i) q^{80} +(-47.4034 + 65.6804i) q^{81} +(66.0140 - 66.0140i) q^{82} +(7.66773 + 0.670839i) q^{83} +(4.04586 + 16.7938i) q^{84} +(-113.163 - 90.2326i) q^{85} +(33.0803 - 12.0402i) q^{86} +(-2.53789 - 16.8902i) q^{87} +(-8.82867 + 12.6087i) q^{88} +(-67.5355 + 38.9917i) q^{89} +(-33.2301 + 54.2749i) q^{90} +(23.1954 - 40.1757i) q^{91} +(-76.0169 + 35.4473i) q^{92} +(96.5332 - 109.285i) q^{93} +(56.1087 - 66.8678i) q^{94} +(-2.24101 + 5.13734i) q^{95} +(-14.1441 + 9.37785i) q^{96} +(86.1483 - 40.1716i) q^{97} +(-55.6124 + 14.9013i) q^{98} +(6.04568 + 48.6035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 36 q^{6} + 18 q^{7} + 216 q^{8} + 36 q^{11} - 18 q^{15} + 72 q^{20} + 288 q^{21} + 36 q^{22} + 108 q^{23} + 54 q^{25} - 162 q^{27} - 120 q^{30} - 432 q^{31} + 114 q^{33} - 162 q^{35} + 48 q^{36}+ \cdots + 756 q^{98}+O(q^{100}) \) 216 * q - 36 * q^6 + 18 * q^7 + 216 * q^8 + 36 * q^11 - 18 * q^15 + 72 * q^20 + 288 * q^21 + 36 * q^22 + 108 * q^23 + 54 * q^25 - 162 * q^27 - 120 * q^30 - 432 * q^31 + 114 * q^33 - 162 * q^35 + 48 * q^36 + 108 * q^38 - 36 * q^40 + 216 * q^41 - 48 * q^42 - 216 * q^43 + 18 * q^45 + 108 * q^46 - 144 * q^47 - 72 * q^48 - 162 * q^50 + 60 * q^51 - 540 * q^53 + 324 * q^55 - 72 * q^56 - 234 * q^57 + 72 * q^58 - 96 * q^60 + 504 * q^61 - 24 * q^63 - 144 * q^66 + 72 * q^67 + 108 * q^68 + 72 * q^70 + 240 * q^72 - 216 * q^73 - 84 * q^75 + 216 * q^76 + 576 * q^77 + 168 * q^78 - 1068 * q^81 + 576 * q^83 + 576 * q^85 - 432 * q^86 - 324 * q^87 - 72 * q^88 - 606 * q^90 + 756 * q^91 - 324 * q^92 + 168 * q^93 - 468 * q^95 - 1332 * q^97 + 756 * q^98

Introduction

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